Innovations in Macroeconomics, 3rd Edition

Innovations in Macroeconomics

Paul J.J. Welfens

Innovations in Macroeconomics Third Edition

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Prof. Dr. Paul J.J. Welfens EIIW – European Institute for International Economic Relations at the University of Wuppertal Rainer-Gruenter-Str. 21 42119 Wuppertal Germany and Sciences Po, Paris 27, Rue St. Guillaume [email protected]

ISBN 978-3-642-11907-1 e-ISBN 978-3-642-11909-5 DOI 10.1007/978-3-642-11909-5 Springer Heidelberg New York Dordrecht London Library of Congress Control Number: 2011934030 © Springer-Verlag Berlin Heidelberg 2006, 2008, 2011 This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilm or in any other way, and storage in data banks. Duplication of this publication or parts thereof is permitted only under the provisions of the German Copyright Law of September 9, 1965, in its current version, and permission for use must always be obtained from Springer. Violations are liable to prosecution under the German Copyright Law. The use of general descriptive names, registered names, trademarks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. Cover design: estudio calamar, Berlin/Figueres Springer is part of Springer Science+Business Media (www.springer.com)

Preface to the Third Edition

It is certainly unusual to have a book in its third edition within four years—I hope that this testifies to the growing interest in innovation dynamics on the one hand and on the other hand in finding better ways for macroeconomic modeling. I have benefited from encouragement from David Audretsch and several other colleagues; this particularly refers to the cooperation in a Jean Monnet Project where I have enjoyed fruitful discussions with Cillian Ryan and Andrew Mullineux, University of Birmingham. As regards the new chapter on the Transatlantic Financial Market Crisis I am also indebted to discussions with Werner Roeger and Jürgen Kröger, European Commission, Caroline Fohlin, Johns Hopkins University, Baltimore and Walter Eubanks, Congressional Research Service, Washington DC; the author also appreciates the debate at the Global Jean Monnet Conference/ECSA-World Conference 2008 “A Europe of Achievements in a Changing World”; Brussels, November 24-25, 2008. I am also grateful for technical support by Michael Agner, University of Odense and Mevlud Islami as well as Jens Perret, EIIW/Schumpeter School of Business and Economics at the University of Wuppertal. The new medium-term hybrid macro model presented in the first edition seems to be particularly useful in understanding the effects of the international banking crisis: Output is determined—via a modified version of Friedman’s permanent income consumption hypothesis—by both short-term aggregate demand and by the anticipated long-run (steady state) income as derived from the neoclassical growth model. I have also included a chapter on financial innovations in this enlarged edition. The readers interested in a broader analysis of the international banking crisis are invited to take a closer look at the book Transatlantic Banking Crisis and Sovereign Debt Dynamics. Explaining a Modern Disaster of the West is suggested, but the offered reflections only give a new starting point in this field. The institutional innovations suggested here and presented at the Congressional Research Service, the European Commission, the University of Economics and Finance, St. Petersburg, and the Johns Hopkins University, Baltimore, in 2009 are part and parcel of innovative institutional reforms that seem to be necessary in a world economy with potentially unstable globalization dynamics. Last but not least, I am also grateful to the institutional network at the Schumpeter School of Business and Economics at the University of Wuppertal.

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One of the final chapters look into a reformulation of the Marshall-Lerner condition for a world with foreign direct investment and comes up—compared to the standard approach—with rather different results for some parameter constellations. As foreign direct investment continues to grow relative to GDP in many countries, one should carefully consider the implications, namely that real depreciations of currencies will often only contribute to a change in the current account position to a limited extent; this is a point that has been emphasized time and again by Ronald McKinnon (the specific points which I suggest are, however, somewhat different to the well-known arguments of McKinnon). Moreover, new approaches to optimum growth and for the link between trade, FDI and output are developed. Finally, the role of a hybrid macroeconomic model for the understanding of banking crisis is emphasized—and new insights into modified neoclassical growth models of closed and open economies are considered (with due emphasis on innovation dynamics and R&D employment as well as aspects of the CES-function). Those who consider market economy and democracy as two crucial elements for a decent life cannot avoid to frankly discuss the strange developments of financial globalization and to push for consistent reforms. The responsibility for the analysis is all mine. December 2010 Wuppertal and Paris

Prof. Dr. Paul J.J. Welfens

Preface to the Second Edition

Within one year, this book has already been published in a second edition, testifying to the broad interest in the important subjects covered. I have made some clarifications and also some corrections, while also adding a new chapter on Innovations and the Economics of Exhaustible Resources, an important field with respect to the link between modern Schumpeterian innovation analysis and macroeconomics. In Chap. G, there are additional reflections on the ambiguity of the traditional approach of optimum growth theory as well with key insights drawing on my Kondratieff Prize Lecture in Moscow in 2007. I have also added some new ideas on the Macroeconomics of Microeconomics which basically argues that there should be a double consistency in Economics. The basic perspective of this book is to emphasize the need to consider the innovation phenomenon in a broader perspective; it is not only relevant for certain cyclical dynamics but also—in a more traditional vein—for long term growth analysis as well as sustainable economic development. I have particularly benefited from my visiting Alfred Grosser professorship 2007/2008 at Sciences Po, Paris, and the interesting discussions with Antoine Leblois, Paris, and the suggestions of Gerhard Huhn, Mevlud Islami and Jens Perret, EIIW Wuppertal. Finally, I am grateful to discussions with my colleagues in the Jean Monnet Project Financial Market Integration, Structural Change, Foreign Direct Investment and Economic Growth in EU25. I am particularly grateful to Julius Horvath at the Central European University, Budapest. My greatest gratitude goes to my wonderful family who has supported my research with so much patience over so many years. December 2008 Wuppertal and Paris

Prof. Dr. Paul J.J. Welfens

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Preface to the First Edition

This book deals with the role of innovations in macroeconomics, and it presents innovations in macroeconomic theory. Growth and structural change are key issues here, but we also touch upon links between exchange rate dynamics and innovations. The approaches and ideas presented are not integrated into a large comprehensive model. Rather, we present analytical building blocks in selected fields of Schumpeterian Macroeconomics, including new insights about trade, growth, exchange rate dynamics, innovations and policy options. An important starting point in Chap. A is a generalization of the Solow growth model and a long term analysis of the link between process innovations and the price level as well as the exchange rate, which is shown to critically depend on the income elasticity of the demand for money. Moreover, we discuss the long term Phillips curve in the context of a growth model and can thereby gain some new insights. The theoretical reflections presented suggest the need for new empirical work. We also consider the role of foreign direct investment flows. Chapter B is an attempt to bridge the medium term analysis with the long run growth analysis. It is argued that individuals will partly base consumption—and thus savings—on current income and expected steady state income. While this approach is closely related to the permanent income hypothesis, its specific implications are quite interesting. Chapter C takes a closer look at some integration issues. Chapter D puts the focus on both growth in open economies and the real exchange rate. The analysis in Chap. E is again devoted to open economy topics, where we present a Mundell-FlemingSchumpeter model with product innovations. Chap. F focuses on the link between stock market dynamics and the exchange rate, and the framework presented is new and works rather satisfactorily from an empirical perspective. Chapter G starts with the traditional optimum growth framework and then proceeds by looking at the topic of endogenous growth (or quasi-endogenous growth). Chapter H involves trade, structural change and growth in open economies, while Chap. I looks at the role of innovations in a digital market economy. Chapter J puts the focus on EU innovation policy and raises some critical questions about the EU economic policy. Finally, Chap. K considers some aspects of monetary integration and growth including basic policy implications. In a rather simple approach, we explain why the integration of global financial markets has brought about a global fall of the interest rate along with ix

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a higher stock market price index. Essentially, there is an interplay between Asian capital inflows into the US and an increasing international bonds substitutability concerning Dollar-denominated and Euro-denominated assets (the start of the Euro has created a European bonds market which effectively offers better substitutes to the Dollar bonds than was the case for the previous DM-$ comparison). We also look at some other monetary issues. As regards the link between economic policy measures and economic development, one should emphasize that policy makers rarely make the crucial distinction between changes in the level of the growth path and the growth rate itself. This distinction is quite important in the context of the basic and modified neoclassical growth model. Possibly the most important shift of analytical emphasis is the idea that one should take a look at various modeling approaches whereby the choice of model depends on the time horizon and the specific initial situation. From a policy perspective medium term models could be quite useful, however there is no adequate model which bridges the short run and the long run. One of the new ideas presented here is to link the short term and long run aspects in a new medium term Keynes-Solow model. In this approach, it is emphasized that both aggregate demand and aggregate supply determine the dynamics of actual income. In a medium term perspective, this approach can also be applied to hybrid growth modeling; in reality there is rarely a case for which only the demand side or only the supply side is valid. Some of the analytical elements presented are refinements or extensions of existing approaches; other contributions aim at clarifying apparent inconsistencies in the literature. An important aspect here is the inconsistency, implying for instance that Poland or China export mainly capital goods to the USA and EU15, while reality is characterized by trade flows of machinery and equipment in the opposite direction between neoclassical growth theory and neoclassical (Heckscher-Ohlin-Samuelson) trade theory. Economics is a scientific field in which competition among researchers stimulates the specialization of scientists as well as the exploration of narrow islands. Little research is devoted to building intellectual bridges between islands in order to analyze the combined insights or to combine possible variants of models developed on each island. A few bridges are presented here. In market economies, innovation dynamics have played a crucial role since the Industrial Revolution. Schumpeterian Economics has analyzed some of these developments on the basis of an evolutionary approach which is useful in many fields. At the other end of the spectrum, there are innovation researchers who persue a rather narrow focus on invention and novel products or on new process technologies in certain sectors. This is unsatisfactory in the sense that innovation dynamics should be combined with macroeconomic analysis, including growth analysis and models of stabilization policy. The new growth theory has delivered some interesting results including aspects related to product differentiation and spillover effects. In a different context, real business cycle models have shown that technological changes are able to generate economic cycles in a quasi-Walrasian world with no frictions in markets. However, the latter is a contradiction in itself since every innovation automatically creates information asymmetries which, in turn, take us away from competitive market clearing.

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From an input perspective, one can measure innovation dynamics to some extent using the ratio of expenditures on research and development (R&D) to Gross Domestic Product or R&D expenditures per capita, from an output perspective through the number of (international) patents or patent applications per capita. In the second half of the twentieth century, the R&D-GDP ratio increased continuously in OECD countries as did the number of patent applications per capita. At the start of the twenty-first century the R&D-GDP ratio in the leading OECD country, Sweden, reached 4%, in Japan 3%, and in the US and the EU15 it was close to 2.5%, up from about 1% in the early 1960s. It is not only impressive to observe how strongly R&D expenditures have increased, but one must also consider the R&D-GDP ratio in comparison with the investment-GDP ratio, which is around 20% in leading OECD countries. As much as investment in machinery and equipment is the basis for the accumulation of a physical capital stock, the stream of R&D expenditures amounts to the accumulation of an R&D stock, which obviously contributes to the output of individual firms and the overall economy. Patent applications also increased in OECD countries in the 1980s and 1990s. However, many innovations cannot easily be patented; software is a difficult field in this respect. Patenting behavior can also change considerably as market structures change. With respect to this, the case of liberalization in European fixed-line telecommunications is interesting. Apparently, privatized former state-owned monopolies have intensified patenting which is natural in an environment that has become more competitive and more internationalized. (At the same time it seems that innovation activities have shifted away from network operators to the equipment industry.) Changes in patenting behavior make interpretation of growth in patent applications rather difficult. The results of innovation efforts are not simply patents, but what matters most are two types of innovations: • Process innovations which imply cutting costs and thus bringing about a higher equilibrium output in markets; even modeling the simple case of endogenous technological progress in the context of a macroeconomic production function is not easy. Special problems occur if the industry has static or dynamic scale economies, a field not analyzed much in this book. • Product innovations increase the willingness to pay on the demand side. This is a field of particular interest here, specifically in the case of open economies. Schumpeterian competition—based on product innovations—in a two-country model no longer allows for the assumption that the law of one price will hold. As discussed in Industrial Economics literature, existing innovation-related literature in economics is divided on the one hand into innovation analysis. On the other hand, there is a niche in macroeconomic analysis, with some strands in the new growth literature looking into process innovations including technology spillovers. This is done, for example, in models by ROMER and LUCAS. GROSSMAN/HELPMAN have emphasized the role of product differentiation and hence product innovation broadly defined. However, those are rare efforts which indeed concern only part of macroeconomic analysis. This book seeks to add some building blocks to the existing

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literature, offering a particular focus on open economies in which the role of foreign direct investment and network effects in telecommunications is emphasized. Moreover, we are interested in integrating innovations into short-term financial market analysis and medium-term models of the Mundell Fleming type. By doing so, we wish to link product innovations with modified long-term growth modeling. It must be emphasized, however, that we will not present comprehensive macroeconomic foundations for the innovations in our analysis. We present new ideas and building blocks for more realistic macroeconomic modeling on issues such as real exchange rate dynamics, fiscal and monetary policies in economies with foreign direct investment, and issues related to the use of telecommunications and the internet. At the bottom line, it certainly is desirable to combine the analytical blocks developed here to a more comprehensive two-sector growth model for an open economy, but this ambitious goal is beyond the scope of this book. Our more modest aim is to suggest consistent improvement in Macroeconomics including approaches valid for a situation with unemployment. (In this context, a theoretical basis for OKUN’s Law is presented.) A key element in the approach presented is that the law of one price is not assumed to hold strictly. This, however, is not really surprising for a world economy in which many innovative firms in many countries contribute to imperfect competition in global markets. Moreover, in part of the analysis presented here we look into convergence dynamics and product upgrading. At the same time, we integrate unemployment into some of the models. It would be a true surprise if this book is liked by very many, as the approaches presented are to some degree unorthodox and also bridge Real Economics and Monetary Economics, which in the standard literature are rather distinct fields. This book should, however, have a lasting impact by encouraging economists and policymakers to take a fresh look at important macroeconomic topics and issues. I am quite grateful to have had the opportunity to present some of my ideas to seminars at the IMF and the AICGS/the Johns Hopkins University in 2004 as well as at the Research Committee on International Economics and Economic Policy (Ausschuss für Außenwirtschaftstheorie und -politik) of the Verein für Socialpolitik at the 2004 Paderborn meeting. Moreover, I would like to express my gratitude for the excellent research support of Dora Borbély, Jens Perret and Andre Jungmittag (EIIW at the University of Wuppertal) as well as Albrecht Kauffmann (EIIW Center at the University of Potsdam). I am also grateful for discussions with many colleagues during a conference at Chulalongkorn University in Bangkok in 2001 as well as within the scope of the 2005 workshop “The EU and Asean Facing Economic Globalization”, jointly organized by Jean Monnet Chairs at the University of Wuppertal and the University of Birmingham as well as the Center for European Studies, Bangkok. With respect to stimulus of research, I would also like to mention the intellectual support of my colleagues in the EU 5th framework project: “Changes in Industrial Competitiveness as a Factor of Integration: Identifying Challenges of the Enlarged Single European Market” (Contract No. HPSE-CT-2002-00148), with special gratitude going to Anna Wziiatek-Kubiak (CASE, Warsaw) who offered valuable criticism during the project meetings at CEPS, Brussels in November 2004 and November 2005. Finally, I am grateful to Jackson Janes from AICGS/The John

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Hopkins University who organized a seminar in Washington with SAIS in January 2006. My basic policy perception for continental Europa is that weak growth in the Euro zone and in Germany in particular has reasons which can easily be identified. The usual caveat holds here: I am solely responsible for the analysis. The editorial support by Michael Agner, Stephanie Kullmann, and Christian Schröder is deeply appreciated. August 2006 Wuppertal and Washington

Prof. Dr. Paul J.J. Welfens

Contents

A.

Globalization, Specialization and Innovation Dynamics . . . . . . . . . . . A.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . A.2 Approaches in Modern Macroeconomics . . . . . . . . . . . . . . . . . . . . . A.3 Human Capital, Physical Capital and Innovations in Open Economies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . A.4 A Critique of the Heckscher–Ohlin–Samuelson Approach . . . . . . . A.5 Solving the Leontief Paradox? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . A.6 Variations on the Solow Model: Some New Insights for a Monetary Economy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . A.6.1 A Generalization of the Solow Growth Model . . . . . . . . . . A.6.2 Aspects of Empirical Analysis of Economic Development . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . A.7 Technological Progress and the Long-run Price Level . . . . . . . . . . . A.7.1 Process Innovations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . A.7.2 The Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . A.7.3 Conclusions for Analysis of Process Innovations in a Monetary Economy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . A.7.4 Solow Model and Role of Money for Growth . . . . . . . . . . . A.7.5 Monetary Growth Model and Tobin Paradox . . . . . . . . . . . A.7.6 Technological Progress Cycles . . . . . . . . . . . . . . . . . . . . . . . A.7.7 Equilibrium and Terms of Trade Aspects in a Simple Open-economy Growth Model . . . . . . . . . . . . . . . . . . . . . . . A.7.8 International Macroeconomics, FDI and Fiscal and Monetary Policy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . A.7.9 Long-run Phillips Curve in a Growing Economy . . . . . . . . A.7.10 Variable Output Elasticity of Capital . . . . . . . . . . . . . . . . . . A.8 Foreign Direct Investment and Innovation . . . . . . . . . . . . . . . . . . . . . A.8.1 Innovation Dynamics and Multinational Companies . . . . . A.8.2 Modified Multiplier in Macro Model with FDI Outflows . A.9 Output Dynamics: Interaction of the Demand Side and the Supply Side . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

1 1 3 7 11 14 20 20 28 35 35 36 43 43 53 56 58 59 63 65 66 66 78 82

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A.10 Growth Accounting Under Unemployment and Okun’s Law . . . . . 84 A.11 Innovation, Trade and Foreign Investment . . . . . . . . . . . . . . . . . . . . 86 A.12 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92 Appendix A.1: Aggregation in a Two-Sector Growth Model: A Modified Solow Approach with Cobb–Douglas Production Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94 Appendix A.2: Two-Sector Model (KHAN/BILGINSOY 1994) . . . . . . . 98 Appendix A.3: Labor Markets with Tradables and Nontradables . . . . . . . 100 Appendix A.4: Product Innovations with Schumpeterian Intermediate Products: A Simple Formula . . . . . . . . . . . . 102 Appendix A.5: Medium-term Output and Wage Policies in an Open Economy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103 B.

C.

D.

Savings, Investment and Growth: New Approaches for Macroeconomic Modeling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . B.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . B.2 A Medium-term Keynes–Solow Model . . . . . . . . . . . . . . . . . . . . . . . B.2.1 Capital Accumulation Dynamics and Profit Maximization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . B.2.2 Choosing a Consistent Investment Function and a New Consumption Function . . . . . . . . . . . . . . . . . . . . . . . . . . . . . B.2.3 Multiplier Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . B.3 Conclusions and Possible Extensions . . . . . . . . . . . . . . . . . . . . . . . . Economic Integration, Technological Progress and Growth . . . . . . . . C.1 Rich Countries vs. Poor Countries and Economic Integration . . . . C.2 Setup of the Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . C.2.1 Convergence in a Hybrid Growth Model with Trade and R&D . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . C.2.2 Profit Maximization in the Hybrid Growth Model . . . . . . . C.3 Asymmetric Foreign Direct Investment in a Two-Country Growth Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . C.4 Policy Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Appendix C.1: Basic Neoclassical Model . . . . . . . . . . . . . . . . . . . . . . . . . . Appendix C.2: General Approach and Simulations . . . . . . . . . . . . . . . . . . Impact of the Real Exchange Rate on Trade, Structural Change and Growth . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . D.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . D.2 Reputation, Market Size and Relative Price Effects: A Quasi–Balassa–Samuelson Effect . . . . . . . . . . . . . . . . . . . . . . . . . . D.3 Real Exchange Rate Dynamics and Economic Effects . . . . . . . . . . . D.3.1 Real Exchange Rate and Trade . . . . . . . . . . . . . . . . . . . . . . . D.3.2 Real Exchange Rate and Structural Change . . . . . . . . . . . . D.3.3 Real Exchange Rate and Growth . . . . . . . . . . . . . . . . . . . . .

109 109 111 112 115 117 125 129 129 132 134 137 138 141 141 142

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D.4 Real Effective Exchange Rate (p/ep∗ ) Dynamics in Selected EU Countries . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . D.5 Wages, Prices and the Real Exchange Rate . . . . . . . . . . . . . . . . . . . . D.6 Towards an Integrated Macroeconomic Approach . . . . . . . . . . . . . . D.7 Medium-Term Approach to Product Innovations, Output and the Exchange Rate . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . D.8 Economic Catching-up and Long-Term Real Exchange Rate Dynamics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . D.9 Policy Implications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . E.

F.

Macroeconomic Aspects of Opening up, Unemployment, Growth and Transition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . E.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . E.2 Growth, Trade and Innovation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . E.2.1 New Production Function for Open Economies . . . . . . . . . E.2.2 Foreign Direct Investment . . . . . . . . . . . . . . . . . . . . . . . . . . . E.3 Growth, Resource Dynamics, Balassa–Samuelson Effects and Unemployment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . E.3.1 Growth, Natural Resources and EconomicWelfare . . . . . . E.3.2 The Balassa-–Samuelson Effect, Unemployment and Exports . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . E.3.3 Wage Bargaining as Inherent Source of Unemployment? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . E.4 Product Innovation and Macroeconomic Developments: Schumpeter and the Mundell–Fleming Model . . . . . . . . . . . . . . . . . E.4.1 The Role of Risk and Innovation . . . . . . . . . . . . . . . . . . . . . E.4.2 Endogenous Product Innovations in Countries with Similar Development Levels . . . . . . . . . . . . . . . . . . . . E.5 Conclusions and Policy Implications . . . . . . . . . . . . . . . . . Appendix E.1: Maximization of Total Quasi-Income of Workers through Trade Unions (labor supply L0 is exogenous, parameter 0 ≤ α ≤ 1) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Appendix E.2: Mathematical Appendix . . . . . . . . . . . . . . . . . . . . . . . . . . . . Appendix E.3: Reflections on EU Eastern Enlargement . . . . . . . . . . . . . . Appendix E.4: Fiscal Multiplier in a Hybrid Approach . . . . . . . . . . . . . . . Appendix E.5: Reconsidering Aggregate Output in a Two-Sector Approach . . . . . . . . . . . . . . . . . . . . . . . . . .

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157 157 158 164 169 174 177 177 180 180 183 188 188 190 193 198 198 199 200

201 204 206 212 213

Productivity Shocks, Innovations, Stock Market Dynamics and Growth . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 215 F.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 215 F.2 Traditional and New Approaches to the Exchange Rate and Stock Market Dynamics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 221

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F.2.1

Stylized Facts of Exchange Rates and Stock Market Prices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . F.2.1 Short-Term Analysis of Financial Market Dynamics and Technology Shocks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . F.3 Hybrid Model: Combining Interest Parity and Augmented Money Market Equilibrium . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . F.4 Capital Asset Pricing Model and Product Innovations . . . . . . . . . . . F.5 Consumption, Volatility and Growth . . . . . . . . . . . . . . . . . . . . . . . . . F.6 Policy Issues and Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Appendix F.1: Slope of Equilibrium Lines . . . . . . . . . . . . . . . . . . . . . . . . . Appendix F.2: International Bonds Market Integration, Interest Rates and Stock Market Volatility . . . . . . . . . . . . . . . . . . . G.

H.

Innovation Dynamics and Optimum Growth . . . . . . . . . . . . . . . . . . . . . G.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . G.2 Endogenous Growth, Innovation and Maximum Consumption per Capita . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . G.2.1 Optimum Endogenous Growth . . . . . . . . . . . . . . . . . . . . . . . G.2.2 Optimum Growth and Endogenous Growth Modeling in Open and Closed Economies . . . . . . . . . . . . . . . . . . . . . . G.2.3 Biased Technological Progress and Optimum Growth . . . . G.2.4 Efficient vs. Optimal International Specialization . . . . . . . G.3 Policy Implications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Appendix G.1: Optimum Quantity of Money . . . . . . . . . . . . . . . . . . . . . . . Appendix G.2: Specialization, Technological Progress and Factor Price Ratios . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Appendix G.3: Endogenous Progress in the Capital Goods Sector . . . . . . Appendix G.4: Simple Differential Equation and Bernoulli Differential Equation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Appendix G.5: The Macroeconomic Foundation of Microeconomics . . . Trade, Structural Change and Growth in an Open Monetary Economy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . H.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . H.2 Exchange Rate Dynamics, Relative Prices, Employment and Growth . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . H.2.1 Nominal Exchange Rate, Real Exchange Rate and True Long-Run Money Market Equilibrium . . . . . . . . H.2.2 Real Exchange Rate, Growth Path and Steady State . . . . . H.2.3 Investment, Real Exchange Rate and Employment . . . . . . H.2.4 Technology, Exchange Rate Changes and the Relative Tradable Price . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . H.3 Real Exchange Rate Dynamics and Economic Effects . . . . . . . . . . . Appendix H.1: Statistical Measures of Structural Change . . . . . . . . . . . . . Appendix H.2: Indicators Measuring Structural Change . . . . . . . . . . . . . .

221 228 232 234 238 240 242 243 247 247 250 250 256 261 262 264 266 267 268 270 271 273 273 275 275 280 284 286 290 292 294

Contents

I.

J.

K.

Innovations in the Digital Economy: Promotion of R&D and Growth in Open Economies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . I.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . I.2 Innovations and New Economic Structures in the Digital Economy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . I.2.1 Selected Innovation Traits in OECD Countries . . . . . . . . . I.2.2 Innovation System and Innovation Record . . . . . . . . . . . . . I.2.3 High Technology, ICT Growth and Modernization of the Economic System . . . . . . . . . . . . . . . . . . . . . . . . . . . . I.3 Theory of Innovation Policy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . I.3.1 The Standard Case . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . I.4 Policy Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . I.4.1 General Policy Conclusions for Innovation Policy in Open Economies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . I.4.2 Specific Policy Conclusions for Germany . . . . . . . . . . . . . . Appendix I.1: Optimum Product Innovation under Uncertainty . . . . . . . . Appendix I.2: Product Innovations and Network Effects in a Simple Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Appendix I.3: NACE (EU classification) rev. 1.1 Classification at the 2-Digit Level (in Parts) . . . . . . . . . . . . . . . . . . . . . . . . . . . . Appendix I.4: Market Entry of Digital Good Producers in a General Equilibrium Model . . . . . . . . . . . . . . . . . . . . . EU Innovation Policy: Analysis and Critique . . . . . . . . . . . . . . . . . . . . . J.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . J.2 Innovation Policy in the EU . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . J.3 Innovation Dynamics in OECD Countries . . . . . . . . . . . . . . . . . . . . . J.3.1 Innovation, Specialization and Growth: Empirical Analysis for EU-15 and USA . . . . . . . . . . . . . . . J.3.2 Comparative Innovation Dynamics . . . . . . . . . . . . . . . . . . . J.3.3 Acceleration of Innovation Dynamics . . . . . . . . . . . . . . . . . J.3.4 Specialization in Innovation and ICT Network Perspectives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . J.4 Recommendations for Future EU Innovation Policy . . . . . . . . . . . . Financial Market Integration, Interest Rates and Economic Development . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . K.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . K.2 Financial Market Integration in the EU . . . . . . . . . . . . . . . . . . . . . . . K.2.1 From Basic Theory to Endogenous Growth Approaches . . K.2.2 Current Account Dynamics: A New Approach . . . . . . . . . . K.2.3 Monetary Integration, Financial Market Integration and Welfare Effects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . K.3 Integration of Financial Markets in the Euro Zone and Global Dynamics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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295 295 298 298 302 311 320 320 329 329 330 334 336 339 340 347 347 349 350 350 350 355 358 363

367 367 373 373 377 380 384

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K.4 Policy Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . K.5 FDI and Information and Communication Technology in the Dornbusch Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . K.5.1 Basics of the Dornbusch Model . . . . . . . . . . . . . . . . . . . . . . K.5.2 The Modified Dornbusch Model . . . . . . . . . . . . . . . . . . . . . K.5.3 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Appendix K.1: Aspects of Transition and Trend Growth in a Setup with Technology Shifts . . . . . . . . . . . . . . . . . . . Appendix K.2: Uncertainty, Savings and Product Innovations . . . . . . . . . Appendix K.3: A Macro-Model with Unemployment and Endogenous Taxation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . L.

386 388 388 389 398 400 400 402

Natural Resources, Oil Prices and Innovation Dynamics . . . . . . . . . . L.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . L.2 Theory of Natural Resource Pricing . . . . . . . . . . . . . . . . . . . . . . . . . . L.2.1 Technological Progress in the Oil Industry . . . . . . . . . . . . . L.2.2 Non-Stationarity of Oil Prices? . . . . . . . . . . . . . . . . . . . . . . L.2.3 Which Interest Rate Is Relevant? . . . . . . . . . . . . . . . . . . . . . L.2.4 Long-term Macroeconomic Aspects of Oil Price Dynamics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . L.3 Oil Price Regression Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . L.4 Policy Implications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . L.5 Sustainability Issues . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Appendix L.1: Data Sources . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

405 405 409 410 413 415 417 419 423 425 430

M.

Portfolio Modeling and Growth in Open Economies . . . . . . . . . . . . . . M.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . M.2 Combining the Portfolio Model and Growth Analysis . . . . . . . . . . . M.3 Oil Price Dynamics in a Double Perspective . . . . . . . . . . . . . . . . . . . M.4 Stock Market Analysis and Hybrid Portfolio Growth Model . . . . . . M.5 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

431 431 433 436 439 445

N.

Transatlantic Banking Crisis: Analysis, Rating, Policy Issues . . . . . . N.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . N.2 The Dynamics of the Banking Crisis . . . . . . . . . . . . . . . . . . . . . . . . . N.3 Banking Crisis and Critical Reform Proposals . . . . . . . . . . . . . . . . . N.4 Theoretical Aspects of Sustainable Financial Market Globalization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . N.5 Macroeconomic Modeling Aspects . . . . . . . . . . . . . . . . . . . . . . . . . . N.5.1 A Macro Model with Foreign Direct Investment and Rating . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . N.5.2 Multiplier Analysis and Key Conclusions on Ratings . . . . N.6 The Effects of a Banking Crisis in a Hybrid Macroeconomic Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . N.7 Policy Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

447 447 452 459 467 474 475 478 481 491

Contents

O.

P.

Q.

R.

International Banking Crisis and Innovation . . . . . . . . . . . . . . . . . . . . O.1 The Effects of a Banking Crisis in a Hybrid Macroeconomic Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . O.2 Financial Innovations, Banking Crises, and Schumpeterian Growth Dynamics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . O.2.1 Introduction: Financial Innovations Dynamics versus Industrial Innovations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . O.2.2 Financial Innovations and Growth . . . . . . . . . . . . . . . . . . . . O.2.3 Policy Issues: Financial Innovations and Government R&D Support? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . New MARSHALL–LERNER Condition and Economic Globalization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . P.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . P.2 FDI, the External Balance and the Real Exchange Rate . . . . . . . . . P.3 Policy Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Appendix P.1: Macro Model with FDI . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Trade, Innovation and Output Dynamics . . . . . . . . . . . . . . . . . . . . . . . . Q.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Q.2 Trade and the Production Function: Growth in Open Economies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Q.2.1 Alternative Asymmetric Model for Trade and Growth . . . . Q.2.2 Quasi Economies of Scale in a Simple Two-Country Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Q.2.3 Open Economies Growth Model: The Role of Technological Progress . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Q.2.4 Growth Modeling of Open Economies: Technology Spillovers and the Role of Trade . . . . . . . . . . . . . . . . . . . . . Q.3 The Gravity Equation in a Long-Term Analytical Perspective . . . . Q.3.1 Towards a Consistent Long-Run Gravity Trade Model . . . Q.3.2 Combining the Gravity Equation and Growth Modeling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Q.3.3 Implications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Q.4 Growth, Optimum Taxation, and Innovation Policy . . . . . . . . . . . . . Q.4.1 A New Optimum Taxation Approach . . . . . . . . . . . . . . . . . . Q.4.2 Optimum FDI Policy in an Open Economy with Subsidiaries from Abroad . . . . . . . . . . . . . . . . . . . . . . . . . . . Q.5 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . New Open Economy Policy Perspectives: Modified Golden Rule and Hybrid Welfare . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . R.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . R.2 From the Traditional Model Toward a New Approach . . . . . . . . . . . R.3 Endogenous Population Growth . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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515 515 518 523 525 531 531 535 543 546 547 549 552 554 555 559 560 560 562 563

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R.4 Economic Welfare, Golden Rule and CO2 Emissions in the Context of a Modified Growth Model . . . . . . . . . . . . . . . . . . . 573 R.5 Open Economy and Economic Growth . . . . . . . . . . . . . . . . . . . . . . . 577 R.6 A Broader View on the Golden Rule and Innovation in Open Economies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 582 S.

T.

Employment in the R&D Sector, Economic Policy and the Golden Rule . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . S.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . S.2 Towards a New Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . S.3 Policy Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Some Remarks on Growth Analysis on the Basis of CES . . . . . . . . . . T.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T.2 Neoclassical Growth Model with CES: Ambiguous Role of the Savings Rate . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T.3 Two-country Macro Model with CES Functions . . . . . . . . . . . . . . . T.4 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Appendix T.1: Further Considerations on CES . . . . . . . . . . . . . . . . . . . . . . Appendix T.2: The Role of Domestic and Foreign Sovereign Debt in a Simple Medium-term Macro Model with Flexible Exchange Rates . . . . . . . . . . . . . . . . . . . . . . .

587 587 589 595 607 607 607 611 614 615

615

References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 619

A. Globalization, Specialization and Innovation Dynamics

A.1 Introduction Economic globalization means the combined growth of trade and foreign direct investment (FDI) on a worldwide scale. FDI grew particularly in the 1980s and 1990s, when the role of multinational companies (MNCs) started to grow strongly for various reasons: • Privatization in many countries around the globe has created a larger menu for international mergers and acquisitions. For example, the infrastructure sector in Europe, Asia, Latin America and Africa has become strongly shaped by MNCs. • Regional integration in North America (NAFTA), Latin America (MERCOSUR), Europe (EU, most notably the full establishment of the EU single market in 1992) and Asia (ASEAN) created larger regional markets which in turn, raised the optimum firm size—this in turn implied strong motives for mergers and acquisitions, including international M&As. • Opening up and systemic transformation in China in the 1980s and in Eastern Europe as well as the former Soviet Union have enlarged both the opportunities for trade and foreign direct investment. About 1/3 of OECD countries’ trade is intra-company trade, that is, trade within MNCs, so that FDI is crucial for three reasons: • International trade—which includes trade in intermediate products; and growing intra-industrial trade whose expansion is linked to the rise of per capita income (the demand for differentiated products is a positive function of per capita income, y; and y can be raised by FDI inflows). Trade, in turn, can be reinforced by regional and global trade liberalization; • Capital formation in the host country; • International technology transfer: as markets for both patents and technologies are quite imperfect, the bulk of technology transfer is either intra-MNC technology transfer or—similar to the exchange of hostages—cross-licensing among MNCs. P. J. J. Welfens, Innovations in Macroeconomics, DOI 10.1007/978-3-642-11909-5_1, © Springer-Verlag Berlin Heidelberg 2011

1

2

Innovations in Macroeconomics

There are various types of trade. International differences in preferences, differences in productivity, economies of scale and geographical proximity can all explain international trade. Regional integration schemes also stimulate trade which in turn could raise economic growth through higher investment-GDP ratios or through efficiency gains. LEVINE/RENELT (1992) found that a higher degree of economic openness raises the availability of physical capital but leaves efficiency unchanged. KORMENDI/MEGUIRE (1985) found weak empirical evidence that a higher trade share raises growth through increased efficiency. SHEEHEY (1995) finds that a higher degree of openness—as proxied by the export share—stimulates economic growth and contributes to improved efficiency. This, however, leaves open the question which sectors particularly benefit from economic opening up and trade. As regards FDI inflows such investments could go to the tradables sector—giving a long-term stimulus to exports—or the nontradables sector. In both cases, imports of machinery and equipment could increase if the host country is poorly endowed with capital. Foreign investors (e.g., from the US or Germany) often have a tendency to indeed import machinery and equipment from the country where the headquarters is located or use the same supplier from a third country which has successfully specialized as a producer and exporter of machinery and equipment. Convergence issues and technology dynamics have been found to be interdependent in recent empirical analysis. JUNGMITTAG (2004) shows for the EU15 countries that technological specialization contributes to economic growth. Indeed, there are technological differences among OECD countries so that the assumption of identical production functions across countries—a basic ingredient of the Heckscher–Ohlin approach—cannot easily be defended unless there is technological convergence across countries. Empirical analysis has also shown that OECD countries absolutely abundant in skilled labor are net exporters in R&D-intensive industries and—with relatively weak evidence—that countries with a large domestic market will be net exporters of scale intensive goods (TORSTENSSON 1998). Economic opening up of eastern Europe has, however, revealed that some of the small transition countries (Hungary and Czech Republic in 2001) have a positive revealed comparative advantage (RCA) in scale intensive goods (BORBÉLY 2004). As regards international economic convergence it is clear that there can be no full convergence in a simple neoclassical framework unless capital intensities have converged in open economies with free trade. According to neoclassical theory, changes in capital intensity are associated with changes in the structure of output and trade. Is it possible to easily classify the structure of output and trade? Furthermore, can standard models of trade explain international trade dynamics? This trade is characterized by trade growing faster than national output and by intra-industrial trade gaining in relative importance in the long run. Moreover, trade with intermediate products seems to be growing relatively fast, namely in the context of growing vertical foreign direct investment. Free trade brings equalization of relative goods prices and this in turn will bring about equalization of relative factor prices. This is the basic message of the Heckscher–Ohlin–Samuelson (HOS) model which assumes competition in goods markets and factor markets—so that capital K and labor L are rewarded in accor-

A.2 Approaches in Modern Macroeconomics

3

dance with their respective marginal product—and considers two goods produced in both countries with identical technologies under autarky. There is factor mobility within each country, but there is no international factor mobility; opening this up leads only to trade. After economic opening up there will be structural change in accordance with changes in the relative price. This is the standard model in economics which is useful for analyzing some of the effects of economic opening up as well as trade liberalization. It is also useful to some extent, for understanding the effects of regional integration—see for example, the case of the EU where considerable economic catching-up has occurred without much migration. This holds at least for the case of southern EU enlargement in the 1980s when Greece (1981) and later Spain and Portugal (1986) joined the Community. However, the HOS approach has certain deficiencies as we will see. Taking a broader look at global trade liberalization is quite useful in this context. The economic opening up of China has increased the global supply of unskilled workers, and this process will continue as long as there is excess supply in China’s agriculture (so well into the middle of the twenty-first century). China’s opening up will thus lead to a fall in wages, at least of the wages of unskilled workers worldwide. The relative fall of unskilled workers’wages in the 1980s and 1990s in the US, the UK and a few other countries has been interpreted in this sense, or it has been attributed to biased technological progress. That is, in model with unskilled labor, skilled labor (“human capital”) and capital, the progress rate for unskilled labor is relatively high, and this then reduces the relative wage of unskilled workers worldwide. It is not really clear to which extent biased technological progress or the economic opening up of China has brought about the relative fall of unskilled labor (e.g., WOOD 1999). To some extent one also could argue that the economic opening up of Eastern Europe and the former Soviet Union has increased the global supply of unskilled labor. (There is a caveat since one may argue that Eastern Europe and the former Soviet Union represent a well-educated labor force.)

A.2 Approaches in Modern Macroeconomics Modern macroeconomics to a large extent has switched toward approaches which rely on explicit micro foundation and intertemporal optimization analysis. Such work is useful for many issues as it allows the understanding of the models mechanics to some extent. In a survey of modern open economy macroeconomics LANE (2001) points out the important role of the Obstfeld–Rogoff Redux model (OBSTFELD/ROGOFF 1996) and concludes (p. 48): “Although the impact effects of shocks on real variables in many cases are largely similar to those predicted by traditional reduced-form models, the intertemporal nature of the recent models also allows the tracking of dynamic effects. More importantly, the solid micro foundations embedded in these models permits welfare analysis, which can generate some surprising results. In turn, welfare analysis opens the door to rigorous policy evaluation, providing new foundations for the analysis of international policy interdependence. In related fashion, the stochastic

4

Innovations in Macroeconomics

versions of these new models are well-designed for making meaningful comparisons across different policy regimes. As is readily apparent . . . many welfare results are highly sensitive to the precise denomination of price stickiness, the specification of preferences and financial structure. For this reason, any policy recommendations emanating from this literature must be highly qualified.” There is, however, no doubt that models with explicit optimization behavior often are quite useful. Even if the real world is not characterized by fully flexible prices, a dynamic general equilibrium model with optimizing agents and full price flexibility—for example BAXTER/KING (1993)—can be quite useful. This is because it gives a better understanding of fiscal policy transmission effects in a setting with very high price flexibility. So if the expansion of information and communication technology should bring about generally greater price flexibility one can thus get a better idea about the potential relevance of fiscal policy in the age of the digital economy. In the BAXTER/KING model, fiscal policy has a negative wealth effect implied by tax financed, rising government expenditure which brings about a reduction of private consumption along with an increase in labor supply, so that output and employment increase while the wage rate falls—this is a potentially crucial “wealth effect”. This view is in sharp contrast to the Keynesian model which implies that expansionary fiscal policy will raise output, consumption and employment. One should note, however, that the BAXTER/KING results rely on the assumption that government’s fiscal policy means a rise of government consumption. The alternative, that fiscal policy is exclusively or partly a rise of R&D subsidies and hence a double impulse—namely a rise of aggregate demand (as new R&D equipment is purchased) and a rise of the level of technology (assuming that higher R&D capital stocks translates into a higher level of labor-saving technology or product innovations), is not discussed. In a world economy which is more and more characterized by Schumpeterian competition and where government plays a crucial role with respect to R&D expenditures and human capital formation—complementary to R&D—one should indeed consider the implications of such a supply-side fiscal policy. As we will show some key aspects can be easily highlighted in the context of a neoclassical model; a modified Solow model makes clear that long-term expectations with respect to long-run equilibrium output must take into account implications of modern growth models. With respect to monetary policy—analyzed in a new neoclassical synthesis approach by LINNEMANN/SCHABERT (2003)—there are also interesting aspects in this context. From the perspective adopted here the most interesting policy perspectives concern a KEYNES–SOLOW model with money as the production function. An adequately specified growth model helps to avoid the TOBIN paradox according to which the introduction of money in a growth model implies a lower steadystate capital intensity and hence a lower per captia income than the non-monetary SOLOW-growth model (the KEYNES–SOLOW model developed here allows, in principle, the linking of the long-run equilibrium solution of various growth models into a consistent medium-term modeling). To some extent there is a trade-off between analytical rigor and relevance. Ideally one would look for an intertemporal optimization framework with differentiated goods and price adjustment costs as well as process innovations. However, it does

A.2 Approaches in Modern Macroeconomics

5

not really make sense to use very complex models when simple macro modeling gives complex analytical results. The microeconomic underpinning is, however, quite useful in the field of welfare analysis. KING (1993) has voiced harsh criticism about the viability of the traditional Keynesian IS–LM model since it neglects the role of expectations; in his view rational expectations are a key ingredient of modern macroeconomics. PALACIO-VERA (2005) has argued that recent approaches that drop the LM curve and replace it through an interest rate reaction function—as suggested by ROMER (2000)—are not really consistent with reality and do not consistently cover the interdependence of supply and demand. With respect to the real world one may point out that adjustment cost functions for investors are important and that nominal price stickiness in the form of CALVO (1983) and YUN (1996) is useful for analyzing certain issues; the approach of YUN (1996) implies that profit-maximization of symmetrical firms leads to a condition which states that the deviation of current inflation πt from the steady-state inflation π#—we dub this excess inflation—is a positive function of the deviation of real money balances from its steady-state value m# (weighted with the level of consumption C); moreover, the expected inflation rate for t + 1 positively affects “excess inflation”. A useful new neoclassical synthesis is the GOODFRIEND/KING (1997) approach and a rather simple hybrid model is the analysis of GOODFRIEND (2004). Basically, the model of GOODFRIEND (2004) refers to a closed economy and puts the focus on intertemporal optimization. Households maximize utility which refers to present consumption C1 and future consumption C2 , at the same time households consider the work-leisure trade-off (with leisure time F and working time L adding up to unity) which leads to a labor supply function Ls which positively depends on the real wage rate w =: W/P (W is nominal wage, P the price level of consumption goods) and negatively on consumption. Firms use a mark-up μ and are active in a regime with monopolistic competition. The household’s utility function is given by U(C1 , C2 ) where utility refers to consumption in period 1 and period 2. Assuming given expected real income Y1 and Y2 the budget constraint for households—able to save or borrow at interest rate r— can be stated as C1 + C2 /(1 + r) =Y1 +Y2 /(1 + r) which implies with a logarithmic utility function U(C1 , C2 ) = ln C1 + [1/(1 + ρ)]ln C2 . Here ρ is the time preference rate. The well-known result is C2 /C1 = [1 + r]/[1 + ρ]. Hence, consumption will rise over time if the real interest rate exceeds the time preference rate. Labor supply— based on a logarithmic utility function (and taking into account the constraint that leisure time plus working time adds up to unity) is given by Ls = 1 − [C/w] where w is the real wage rate W/P (with W denoting the nominal wage rate and P the price of consumer goods). Labor productivity is denoted as α and a constant mark-up μ = P/k is assumed; note that marginal costs k  = W/α and hence μ = α/[W/P] = α/w. The equilibrium wage then is w# = α/μ# and the equilibrium labor supply is equal to Ls = 1 − [αL/(α/μ)] = 1/[1 + μ#]. Equilibrium consumption is C# = α/[1 + μ]. The role of the interest rate becomes clear from the equilibrium expression (1 + r#) = (1 + ρ)(α2 /α1 ) so that a rise of labor productivity over time will raise the long-run real interest rate. Inflation π is determined by the expected trend inflation rate E(π) plus a term reflecting the impact of actual and future mark-up rates π = f(μ1 , Eμ2 )

6

Innovations in Macroeconomics

+ E(π). This model is indeed useful as a primer for analyzing inflation problems and monetary policy effectiveness in a closed economy. However, in the following analysis we rarely will deal with inflation and we often adopt a more conventional approach which we modify in various ways. With respect to the GOODFRIEND approach one should note one simple interesting modification with respect to the role of productivity growth: If we assume that consumers anticipate that real-consumption expenditures will raise aggregate output and hence individual income (as the rational central planner would do), we will use a modified condition for utility maximization: C2 /C1 = [1 + r]/[1 + ρ]{(1 − ∂Y/∂C1 )/(1 − ∂Y/∂C2 )}

(1)

The additional term is {. . . } which is positive as 0 < ∂Y/∂Ci < 1 is positive (for i = 1, 2); basically, there are two possible interpretations as one may consider an economy with consumption plus investment and look at first at a situation with initial unemployment and full employment in period 2; or at full employment in both periods. In a model with initial unemployment, ∂Y/∂C1 indicates by how much quasi-equilibrium output—as defined by the goods market equilibrium condition—is raised through a rise of C and a fall of L. In a permanent full employment economy ∂Y/∂C2 is the marginal product of labor in the overall economy occurring as a consequence of higher consumption and hence lower labor input. Taking logs (and using ln[1 + x] ≈ x) in the modified equilibrium condition for households gives: ln (C2 /C1 ) = (r − ρ) + [∂Y/∂C2 − ∂Y/∂C1 ]

(2)

Interpreting ∂Y/∂Ci as the marginal product of the consumption goods sector we can argue that the ratio C2 /C1 will rise over time if productivity—see the term [. . . ] on the RHS of the equation—is increasing over time. One should note that complex dynamic optimization analysis does not always give crucial additional insights and certainly model-building will consider the relative analytical benefit from increased complexity; for example the message from the simple (GOODFRIEND) household optimization approach does not differ much from the continuous optimization analysis (see e.g. DIXIT 1990a, Chap. 10) when households maximize discounted utility U—depending on consumption C—over  an infinite time span (from t = 0 to ∞): The representative household maximizes U(c) e−ρt dt subject to the constraint dK/dt = F(K) − δK − C; here C is consumption at point t, δ the depreciation rate of capital K and F(K) is a simple production function with standard properties. The Hamiltonian is H = U(C) e−ρt + π [F(K) − δK − C] and the conditions dH/dC = 0 and dπ /dt = −∂H/∂K lead to the optimum consumption plan described by dlnC/dt = [F (K) − (ρ + δ)]/ε. Note that we have assumed (with ε > 0) a convenient utility function U(C) = C1−ε /(1 − ε) so that the parameter ε = −CU /U . As long as the marginal product of capital exceeds ρ + δ consumption will increase over time. Since one can show that the capital stock K will finally reach a steady state K# it is clear that consumption then will be stationary

A.3 Human Capital, Physical Capital and Innovations in Open Economies

7

and hence dlnC/dt = 0 if F (K) = ρ + δ; the latter indeed is the condition for profitmaximization if we replace the time preference rate by the real interest rate. Certainly, the GOODFRIEND setup is an interesting approach. However, there are alternative models which refer both to the closed and the open economy. An important aspect emphasized in the following analysis is the focus on medium-term and longrun policy perspectives. In ageing societies—with longevity increasing—long-term decision-making might indeed become more important. Modern information and communication technology also could reinforce the emphasis on long-run planning (WELFENS 2005). As long as the basic behavioral functions are in line with well established empirical findings one should not worry too much about explicit microeconomic foundations since taking into account the broad range of alternative utility functions used in modern Economics allows various aggregate functions to be derived rather easily. From an evolutionary perspective one also should emphasize that behavioral patterns rarely are characterized by strict profit-maximization. Often managers in firms will simply want to achieve certain benchmarks, for example realize the same benchmark as the industry leader. Whether or not the industry leader itself is a profit-maximizing company remains to be seen. Finally, what looks like alternative approaches at first sight could in effect be complementary modeling efforts; for example in a period of turbulence many individuals will place less emphasis on long-run equilibrium perspectives but rather on short-term adjustment. As economic developments converge to normal dynamics in the medium term a more long-term orientation might become more common again.

A.3 Human Capital, Physical Capital and Innovations in Open Economies An important element of growth dynamics is human capital formation. This has been emphasized by various authors, including LUCAS (1988) and GOULD/RUFFIN (1995). The mechanics of integrating human capital are rather simple if we follow MANKIW et al. (1992) as well as GOULD/RUFFIN. Output can be consumed, invested in physical capital formation or invested in the formation of human capital so that the equilibrium condition for the goods market reads (δ denotes the depreciation rate; s and s are positive parameters): dK/dt + δK + dH/dt + δH = [s + s ]Y

(A.I)

The share of output devoted to gross physical capital formation is s and the share devoted to human capital formation is s . The aggregate production function is given by y(t) = A(t) f(k(t), h(t)) where L is labor, y := Y/L, k := K/L, H := H/L and A is the level of technology, so that the dynamic equations for dk/dt and for dh/dt are—with s := s + s , n := dlnL/dt, a := dlnA/dt—given by dk/dt = (s − s ) f(k, h) − [n + a + δ]k

(A.II)

8

Innovations in Macroeconomics

dh/dt = s f(k, h) − [n + a + δ]h

(A.III)

Equilibrium requires—this is an important modification compared to MANKIW et al.—that the marginal product of H(fh ) is equal to the marginal product of K(fk ); hence fk = fh

(A.IV)

Indeed WIILLIS (1986) and McMAHON (1991) have provided some evidence that the rate of return to physical capital is similar to the rate of return to schooling (on human capital and growth see also ROMER 1990a and STOKEY N. L. 1991). If we assume that the common rate of return is equal to the real interest rate r the slope of the schedule for dk/dt = 0—implying a steady-state value k#—is given by dk/dh = [s /r]/[n + a + δ − s r]

(A.V)

The slope for the dh/dt = 0 schedule is given by dk/dh = [s /r]/[n + a + δ − s r]

(A.VI)

Due to stability requirements, one may assume that the curve indicating dk/dt = 0 is steeper than that for dk/dt = 0. If the savings rate s is chosen in such a way that dk/dt = 0 curve and the dh/dt = 0 curve intersect on the fk = fh curve, we get a combination of k and h representating a steady state. GOULD and RUFFIN implement the model on the basis of a Cobb–Douglas function in which A is Harrod-neutral progress with respect to L. 



Y = Kß Hß (AL)1−ß−ß

(A.VII)

The steady-state values are given by k# = s

1−ß  ß

h# = s

s



/[n + a + δ]1/(1−ß−ß ) 

1−ß  ß

s /[n + a + δ]1/(1−ß−ß )

(A.VIII) (A.IX)

If the rate of return on physical capital is equal to the rate of return on human capital, the implication is that ß k# = ßh#

(A.X)

and taking into account the steady-state solutions gives: 

(s /s )ß−ß = ß /ß

(A.XI)

Moreover, since s = s + s , one obtains: s = sß/(ß + ß )

(A.XII)

A.3 Human Capital, Physical Capital and Innovations in Open Economies

s = sß /(ß + ß )

9

(A.XIII)

Note that in the steady state, we have ln(y(t)) = lnA0 + at + [(ß + ß )(1 − ß − ß )ln[s/(n + a + δ)]]

(A.XIV)

Considering the economy in the vicinity of the steady state, we have in the vicinity of the steady state: dln(y(t))/dt = λ[ln(y#) − ln(y0 )]

(A.XV)

The adjustment speed λ = (n + a + δ)(1 − ß − ß ). The solution of the differential equation is (with e denoting the Euler number): ln(y#) − ln(y0 ) = (1 − e

−λt

)ln(y#) − (1 − e

−λt

)ln(y0 )

(A.XVI)

Next we substitute ln(y(t)) = ln A0 + at + [(ß + ß )(1 – ß – ß )ln[s/(n + a + δ)]] in this equation and obtain: ln[y(t)/y(0)] = C + (1 − e − (1 − e

−λt

−λt

)[(ß + ß’)(1 − ß − ß’)ln[s/(n + a + δ)]]

)ln(y0 )

(A.XVII)

Note that C is defined as C = (1 − e−λt ) (lnA0 + at). GOULD/RUFFIN use the MANKIW et al. equation for ln[y(t)/y(0)] in a modified form, adding a term ηlnH0 to capture additional effects of human capital. They find a significant positive effect for H0 . GOULD/RUFFIN discuss how economic openness affects growth, and they argue that in an open-economy model both countries can benefit from the human capital stock in both countries. The authors rightly emphasize that endogenous two-sector growth models in open economies could be characterized by higher growth due to adjustment pressure from free trade leading to a shift of resources to the dynamic sector. One also should note that in the model of GROSSMAN/HELPMAN (1991)—with two factors, three sectors, including an R&D sector—the innovation sector reinforces the profitability of high technology goods and effectively stimulates human capital formation which in turn implies reduced costs of R&D and hence higher innovation dynamics (on some two-sector aspects, see the appendix). Free trade/trade liberalization in a country which has a comparative advantage in R&D will contribute in this endogenous growth setting to higher growth while the country with a comparative disadvantage will experience a lower growth rate as resources move out of the innovation sector. In their empirical analysis, GOULD/RUFFIN find that the human capital variable has a higher effect on growth than in a closed economy. There is, however, not a simple explanation for this. Here one might consider a new explanation for a link between human capital accumulation and growth in open economies: • A higher stock of human capital implies a higher demand for differentiated products, as we assume that people’s love for variety is a positive function of the level

10

Innovations in Macroeconomics

of education; thus, there is a human capital-based positive STIGLITZ effect (by implication one should consider a STIGLITZ utility function with a finite number of goods n ; human capital accumulation will raise the number of varieties produced which means that the number of additional new varieties will exceed the number of basic varieties dropped from the production assortment). • Given rising demand for product varieties, firms will indeed reinforce innovations and launch new product innovations. Those will fetch higher prices than standard products, but it is also true that the price of existing varieties will fall as new and superior alternatives emerge. We assume that at least part of the old varieties will survive—at reduced market-clearing prices—namely due to “second-tier economies of scale” which indeed must be exploited by producers facing declining prices for older product varieties. Second-tier economies of scale refer to the fact that all sophisticated products can be decomposed into basic intermediate products which may can be produced under static or dynamic economies of scale (tier-one economies of scale would refer to economies of scale in the production of final goods). If product innovations essentially imply that the overall number of product varieties which exist in the market is rising, there will be increasing opportunities for exploiting scale economies in the production of intermediate products, provided that all existing varieties require at least one unit of the respective component (e.g., a computer chip). As all standardized economies of scale products are quite price sensitive, those intermediate products are naturally product-cycle trade goods. The more intensive price competition is, the more important international outsourcing and offshoring (the latter involving FDI—typically for the production of technology-intensive components) is. The implication here is that human capital formation can generate “SCHUMPETER–STIGLITZ effects” in combination with economies of scale and growing international trade in intermediate products. The hypothesis stated here implies that increasing human capital formation in OECD countries and Newly Industrializing Countries indeed stimulates international trade and FDI—including technology transfer—so that human capital formation in open economies should bring a higher growth effect than in closed economies. As regards advantages in the production of scale intensive products, one may assume that large economies such as the US or Germany have favorable production conditions in scale-intensive sectors. While the US is richly endowed with capital, it is not clear that the country has a special advantage in producing machinery & equipment since machinery & equipment are not scale-intensive. Rather, it is knowledge-intensive so that relatively small economies with a relative abundance of skilled labor should be particularly competitive in the production of innovative machinery & equipment (this sector represents highly customized Schumpeterian products). This points to the particular importance of education policy in small open economies. From this perspective, small open economies specialized in knowledgeintensive production—and active in innovations in the tradables goods sector—could benefit from specialization patterns which emphasize both human capital formation and skilled labor. The endogenous growth effects associated with such specialization could explain why many small open economies have achieved relatively high

A.4 A Critique of the Heckscher–Ohlin–Samuelson Approach

11

per capita incomes so that there is no large gap between the per capita income of the US and that of many leading small OECD countries. Taking into account trade in scale-intensive products—with some of them also being knowledge-intensive (e.g., aircraft, software)—and assuming that the largest economy, the US, has sufficient economic leverage (i.e., a large home market) and political leverage to specialize in the Schumpeterian scale-intensive products, it would be natural to expect that the US has a clear leadership in per capita income among OECD countries. Markets, which are characterized both by scale economies and high R&D intensity, will be characterized by monopolistic competition and high Schumpeterian rents which effectively imply a rather high US per capita income. Taking these considerations into account one also should not be surprised to find that the US is not generally specialized in capital-intensive goods—this is potentially important in understanding the Leontief paradox. Even more important could be the fact that the high capital intensity of the US partly reflects high capital intensity in infrastructure sectors which largely represent the nontradables sector. One should, however, consider the generally trade-promoting effect of infrastructure investment; lower transportation costs typically also imply lower transportation costs to the next international airport or sea port. The issues explored subsequently are rather simple as we often will rely on the onesector neoclassical growth model and augmented versions of the Mundell–Flemming model (while incorporating product innovations). The notion of competitiveness used subsequently is not simply the ability to sell but the ability to generate longterm revenues: Thus we are interested not only in quantity of product X sold in the market but in the long-term evolution of export unit values as well. Countries may be specialized in various product groups—for example capital intensive, knowledgeintensive etc. If a country is specialized in product groups where a stable comparative advantage can be combined with improved export unit values we consider this as a clear indication of international competitiveness. Improving export unit values in the long-run is linked to innovativeness. Explaining dynamic specialization patterns in a Schumpeterian world with FDI is a crucial challenge in Economics. Later we will present many statistics on (modified) RCA and export unit values in selected OECD countries.

A.4 A Critique of the Heckscher–Ohlin–Samuelson Approach The workhorse of International Economics is the HOS approach which helps to understand the dynamics of trade and structural change in countries which differ in terms of relative factor endowments. Following the HOS approach (simple two-country model with factors labor and capital) the country richly endowed with unskilled labor—country I which is assumed to have a relatively low per capita income—will specialize in labor intensive products. The export of labor-intensive products will start and expand which effectively implies a gradual rise in the wage-real interest ratio. As a result, the supply of unskilled labor in country II which imports the labor

12

Innovations in Macroeconomics

intensively produced good will increase. Country II in turn, will specialize in the production and export of goods which use capital intensively; the relatively poor country I, will import capita intensive goods which will effectively reduce the supply price of capital—the factor price ratio, namely the ratio of the real interest rate to the real wage rate will fall. Factor Price Equalization will occur in the long run. The HOS approach has its problems since it assumes that the capital intensity in country I and II are given, while the Factor Price Ratio is changing. This is, of course, inconsistent since profit-maximization implies that the capital intensity k := K/L (K is capital, L is labor) is a positive function of the wage-real interest rate ratio. Thus, the equalization of factor prices should cause an equalization of capital intensities across countries. As capital intensities have differed initially, there must be some accumulation of capital in the medium term. In particular the poor country must raise the capital intensity faster than the rich country. This holds since per capita income y := f(k), and technologies in both countries are assumed to be identical in the HOS model. With a linear homogenous production function and competition in goods and factor markets we have y = w + rk where w is the real wage rate and r the real interest rate so that w/r = w∗ /r∗ implies—with ∗ denoting foreign variables—f(k(w/r)) = f∗ (k∗ (w∗ /r∗ )) and hence y = y∗ . This is difficult to reconcile with the neoclassical growth theory which suggests in a context of a model—with s, n and δ denoting the exogenous savings rate, the growth rate of the population and the capital depreciation rate, respectively—with a simple Cobb–Douglas function y = bkß and y∗ = bk∗ß that in long-term equilibrium per capita income is given in the home country I by y = b{s/[n + δ]}ß/(1−ß)

(A.1)

For the foreign country II we have y∗ = b{s∗ /[n∗ + δ∗ ]}ß/(1−ß)

(A.2)

As technologies are assumed to be identical in both countries, ß∗ = ß, δ∗ = δ and b∗ = b. The problem is that there is no mechanism which suggests an endogenous convergence of s/n = s∗ /n∗ ; unless one assumes that both the savings rate and the growth rate of the population depend on per capita income or capital intensity. Taking a look at the EU and China or at the US and China: Should one expect that relatively poor Poland or China will mainly export investment goods to the EU15 (or the US) while the EU (or the US) will mainly export consumer goods? This is exactly what the HOS approach in combination with standard neoclassical growth theory suggests: In a dynamic perspective—with capital accumulation and growth—the HOS approach indeed raises a serious problem, namely that the neoclassical growth model is stable only if one assumes that the capital intensity of investment goods are higher than that of consumption goods. By implication, the rich country—with a high capital intensity—will mainly or exclusively export consumption goods. The poor country—with a low capital intensity—will mainly or exclusively export investment goods. This is obviously, totally unrealistic.

A.4 A Critique of the Heckscher–Ohlin–Samuelson Approach

13

How can one reconcile neoclassical trade theory and neoclassical growth theory? The obvious and realistic way is as follows. Start with the observation that a country is likely to specialize in production and export of machinery and equipment if the domestic market for capital goods is relatively large and competitive. The first requirement implies that there is a high overall capital intensity which implies that workers and managers in this economy have much experience and expertise with modern machinery and equipments. Note that we do not say anything about the relative capital intensity of the production of sector 1 (investment good) or of sector 2 (consumption good). However, there are two constraints, namely that overall capital stock K = K  + K where K is the capital stock in sector 1 and K the capital stock employed in sector 2 and we have a similar restriction for labor, namely L = L + L . Assume that the production of investment goods can be written in country I, richly endowed with capital, as ß

Y = b K  L

1−ß

(A.3)

and output in the consumption goods industry is ß

Y = b K  L

1−ß

(A.4)

We assume 0 < ß < 1 and 0 < ß < 1 and that capital intensity in the consumption goods sector is higher than in the investment goods sector (country I which is capital rich and has a higher per capita income than country II will then increase output of consumption goods and export in particular consumption goods while country II— the poor country—would specialize in the production of investment goods). Now, let us assume that there are cross-sectoral spillovers in the sense that using capital goods in the consumption goods sector—or cumulated past investment experiencegenerates useful knowledge for sector 1 where optimal combination of K and L can indeed be achieved only by using all experiences in the sector using investment goods intensively: the consumption goods sector. That is, there are positive crosssector productivity spillover effects. We may thus replace the parameter b in Eq. (A.3) by the term bKσ where Kσ reflect the cross-sector spillover effect. Hence, the effective production function for the investment goods sector reads: σ

ß

Y = bK K  L

1−ß

(A.5a)

Effectively the overall capital stock K(K = K + K  so that we writeY = b[K − K ]σ   Kß L1 − ß ) affects the production of investment goods which at a sectoral level is reflecting the concept of learning by doing (ARROW 1962) and is also similar to the approach of ROMER (1986) which, however, has its focus on the aggregate production function. The emphasis here on the sectoral spillover effect is indeed, crucial as we will also show in our subsequent discussion of the Leontief paradox which can be solved by the mechanism presented here. As regards the positive cross-sectoral productivity effect in the investment goods sector one will have to carefully study empirically, whether the spillover is mainly related to the use of capital equipment or

14

Innovations in Macroeconomics

both to the use of equipment in sector 2 and to the past cumulated production in sector 1 (suggesting a virtuous circle of producing investment goods where the benefits could obviously be related to the size of the economy). This question has also been important in the debate about the New Economy where the evidence suggests that technological progress and learning by doing effects are very fast in the production of information and communication technology (ICT) while the use of ICT is less dynamic in terms of productivity growth. Note also that the productivity spillovers could be enhanced through the presence of human capital. For simplicity we assume the special case that K  = K  (and we assume that  L > L so that apparent capital intensity in sector 1 is lower than in the consumption sector) so that we can rewrite the above equation Y = b K 

σ+ß  1−ß

L

(A.5b)

The approach presented is plausible and can solve the above-mentioned inconsistency. The apparent capital intensity in the investment goods sector is lower than in the consumption goods sector, but the effective capital goods intensity in the investment goods sector is higher than in the consumption goods sector. Factor proportion theory now suggests that the capital-rich country will specialize toward production and export of investment goods (so the US or EU15 will export investment goods to Poland or China).

A.5 Solving the Leontief Paradox? Our simple approach could also shed light on the Leontief paradox dealing with application of the HOS approach to the US: The empirical analysis of LEONTIEF (1953, 1956) found that the US—a country which is obviously relatively capital abundant—has a comparative advantage in labor intensive products: Labor intensive products, including machinery and equipment, are exported while capital intensive goods (from the UK and other countries) are imported. As is well known, LEONTIEF did not really analyze figures for the factor intensity of other countries exporting to the US, rather he looked at import-competing industries and their relative factor contents as a means to indirectly detect the factor intensity of imported products. The assumption was, of course, that production technology in the US and abroad was the same. However, correct analysis of effective factor content might well reveal that certain goods were misspecified in terms of effective factor intensities. Indeed, taking import competing firms and sectors, respectively, as a substitute for analyzing exports of foreign countries can be quite misleading. As capital intensities differ across countries cross-sectoral national spillover effects will differ. The US, having the highest absolute capital stock among all industrialized countries, might be shaped by the following spillover mechanism: A high capital intensity in the US consumption goods sector generates relatively high learning-by-doing effects for the US investment goods industry whose effective capital intensity thus is higher than the

A.5 Solving the Leontief Paradox?

15

statistically-measured capital intensity. Taking into account such spillover effects, the US investment goods sector is capital intensive and not labor intensive. (We disregard the influence of human capital which already has been discussed in the literature as a mechanism to explain the Leontief Paradox.) Moreover, the spillover effects relevant for the US import-competing industries are different from the spillovers relevant for the UK export industry. If we consider the sector machinery and equipment in the UK, the relatively small capital stock of the UK will generate positive spillover effects while the productivity of machinery and equipment in the US benefits from the overall US capital stock—that is there is the direct effect of the capital stock of the sector employed in machinery and equipment plus the spillover effect from the capital stock in the consumption goods industry of the US in which the investment goods sector will differ across countries. Thus importing competing sectors’ factor contents can be quite misleading when the task is to assess the effective relative factor proportions and the effective factor content of exports of supplier countries, respectively.

RCAs in Machinery and Equipment Taking a closer look at the RCA—based here on the EU15 market—in the field of machinery and equipment (M&E) we can clearly see that Germany and some other EU15 countries, have a positive RCA in machinery and equipment while China and east European accession countries have a negative RCA in this field. Assuming that sectoral patents (PATM&E) also affect competitiveness we can run a cross-country regression: ∗

∗

RCAM&E = a0 + a1 PATM&E + a2 K  /K  + a3 L /L + a4 K + ε

(A.6)

We expect a positive sign for a4 ; however, K also is an implicit indicator for the size of the home market and hence for opportunities to exploit economies of scale so that production of scale-intensive goods is favored by a high GDP. A more refined specification thus is to consider a4 K + a5 K2 where a5 is expected to be negative which implies a critical size Kc beyond which K contributes to an unfavorable RCA in M&E. Regarding further options to come up with a refined and more realistic HOS model, it is clear that an obvious assumption which should be relaxed is that technologies are the same in both countries. If country II has a high capital intensity—and if machinery and equipment is not falling like manna from heaven—one may assume that country II has a technological advantage in the production of capital goods, and as international technology transfer is costly and since patents exist—those provide necessary incentives for innovations—one should not assume that the technology in both countries is identical. Even more important, the types of goods that can be produced are not the same in country I and II. This assumption has dramatic implications as the price index P = pα1 p1−α and in country II—producing by assumption a third high 2 ∗ −α∗ ∗ ∗ . If the high-technology technology good—the price index is P∗ = pα1∗ pα2∗  p1−α 3

16

Innovations in Macroeconomics

1.0

0.5

0.0

–0.5

1999

2000

2001

2002

2003

2004

2005

2006

2007

2008

–1.0 UK

Germany

France

Italy

China

USA

Fig. 1 RCAs for machinery and equipment in selected countries, 1992–2003. (Source: COMEXT database and own calculations)

good is a tradable good, we still could have a uniform international relative price, namely P = p1 /p2 = p1∗ /p2∗ . However, it is clear that in a comprehensive way, namely taking into account not only goods 1 and 2 but also the high-tech good 3—there is no common relative price. Hence, there can be no factor prize equalization. If good 3 is capital intensive the fact that it is employed in a high-technology sector naturally means that the rate of return on capital in this sector is above the average rate of return. The marginal product of capital expressed in units of the consumption good—say good 1—must be relatively high either because the relative price of the high-technology good will reflect a Schumpeterian monopoly element or because investors in risky innovative sectors demand and get a risk premium R so that the marginal product of capital in the high-technology sector is not equal to r∗ but to r ∗ + R. It is also clear that there cannot be such a thing as the law of one price in the simplistic form P = eP∗ . Innovation is not really considered in the HOS model. As regards innovation we distinguish between product innovations—that is novel products—and process innovations which bring about a reduction of costs. A product innovation means that the demand curve is rotating to the right in p–q-space. If the marginal costs curve is upward-sloping, the effect is a rise of the equilibrium price and of the equilibrium output. If product innovations were costly profit-maximizing firms would undertake any possible product innovation as such innovations raise (residual) profits. Compare the triangle p1 E1 H and the initial triangle p0 E0 H in the following graph. Product innovations are however not costly, rather it is necessary to incur some additional costs which could be purely fixed costs (the case of pharmaceuticals) or which might raise marginal costs as more complex

A.5 Solving the Leontief Paradox? p

17 p

A′

A′ k′1

A

A k′0 E1

p1

E2

k′0

p2

p0

E1

p0 E0

E0 DD1

H a 0

DD0 q0

q1

DD1 H

Z q b 0

DD0 q0 q2

Z q

Fig. 2 Product innovations and changes of costs

production technologies become necessary—see the diagram in part b) which shows both an upward rotation of the demand curve and an upward shift of the marginal costs curve. Thus, there is a problem of optimal product innovations. In reality, product innovations often go along with process innovations as new products can often be built only on new machinery and equipment which embody new technologies. Firms in technology intensive sectors will normally further consider an optimization problem, namely that expenditures on research and development (R&D) have to be split between projects with a focus on product innovations and projects with a focus on process innovations. Innovations are a key feature of the modern economy. At the same time it is true that—according to DUNNING (1977)—MNCs are characterized by owner-specific advantages which typically are technological advantages. As MNCs have become increasingly important in the Twentieth century and since FDI inflows and FDI outflows globally are very asymmetrically distributed, it must be true that technologies differ across countries. Taking a look at the EU15 or the EU25 also reveals considerable differences in FDI per capita or FDI relative to GDP. Given the growing role of FDI it would seem natural to incorporate FDI in a refined HOS model and to also consider differences in technologies across countries and their effects on income, inflation and employment—or one might want to study technological catching-up dynamics. This, however, is not so easy. The modeling challenge is compounded further by the existence of nontradable goods. One might even study a model without trade but with FDI flowing from country I to II (or from II to I) where all FDI accrues only to the nontradables sector. If FDI inflows are greenfield investments, one may anticipate both a boost to capital accumulation and technology transfer. If FDI inflows are merely international mergers and acquisitions, there might only be a modest technology transfer. As FDI

18

Innovations in Macroeconomics

inflows raise capital intensity of the overall economy, this will affect the relative factor prices. Now, suppose that FDI inflows occur in an economy which has also opened up to trade. Then FDI inflows in the nontradables sector will raise the wagereal interest ratio which undermines the international competitiveness in a country which initially is characterized as richly endowed with labor. However, if capital accumulation in country II is faster than in country I, one still has to anticipate that labor-intensive exports of country I will increase—in international economics it is the relative factor endowment which matters. Problems become more complex if investment is associated with a certain bias in technological progress, a topic which we will largely ignore in the analysis. To put it differently, we will concentrate on Harrod-neutral, that is, labor-augmenting technological progress. A final element which makes the analysis of structural change and growth difficult is the role of intermediate products. In the New Growth Theory intermediate products are considered to be a source of growth. International trade with intermediate products facilitates exploitation of economies of scale and allows at the same time, to build more product varieties which in some models itself, is conductive to growth. The problem which really occurs in a simple two-country model with two intermediate goods and two final goods—with country I and country II each exporting one intermediate product and one final product—is that it is very difficult to define in certain cases which country is specialized in exports in which way. Take as a starting point the case that country I is producing and exporting automobiles (A sector) while country II is producing computers (C -sector) and exporting both computers and engines for automobiles (intermediate product sector a ) to be produced in I. Country I is also producing and exporting computer chips (c-sector) which are used in the production of computers in country II. Assume that the initial valued-added in the A-industry and the C-industry and in the a-industry and the c-industry are as follows where the share in value-added of the final product is in brackets. Table 1 Dynamics of specialization in the case of trade in intermediate products (1/2 of final product is assumed to be exported) COUNTRY I

COUNTRY II

SITUATION in to A-industry C-industry

Automobiles (A = 70%) Chips (c = 20%)

Engines (a = 30%) Computers (C = 80%)

SITUATION in tn A-industry C-industry

Automobiles (A = 40%) Chips (c = 70%)

Engines (a = 60%) Computers (C = 30%)

One may characterize both countries by saying that country I is strongly specialized in the export of automobiles while country II is strongly specialized in the export of computers. Now assume that some years later we observe the following picture: Based on sales, one would argue that specialization has not changed, but based on value-added, one could indeed argue that country I is strongly specialized in the export of computers while country II is strongly specialized in the export of automobiles. Specialization in production and specialization of exports could diverge,

A.5 Solving the Leontief Paradox?

19

namely to the extent that the growth rate of the number of computers is relatively high in country II in tn : The share of value-added in the global computer sector has fallen, but the share of computer exports in country II’s overall exports could rise. This will happen if the number of computers exported rises strongly while the number of engines exported falls. The situation indeed would be even more paradoxical if the supply of intermediate products came from subsidiaries (abroad) of the firm producing the respective final product. In the case of Germany, statistics for the 1990s show that a high share of imports is indeed built into export products. The share of imported intermediate products increased from 27% in 1991 to 38% in 2002, in the case of the automotive industry where international outsourcing through vertical FDI is often observed. In the case of the computer industry the share of imported intermediate products even rose from about 45% in the mid-1980s to 57% in 1991, and to 80% in 2002. If in the period 1980–2002 Germany’s exports of computers increased relative to overall exports should one argue that Germany’s export specialization with respect to computers was reinforced? Probably not. Obviously, one can classify trade specialization only if one takes into account the global input–output table. Here one finds a challenge for all statistical offices of the world, and probably one for the World Bank as well. How would the international income distribution be if intermediate products traded would represent close to 50% of the respective value-added in both sectors? The answer is that it depends which sector is characterized by the higher Schumpeterian mark-up factor in final production. It is well-known that the firm producing the final product—say in the automotive industry—normally has a higher profit rate than the supplier firms, a fact which might partly be related to the size of the firm at different stages of the overall production process. If the Schumpeterian mark-up factor is positively related to technology intensity (one good is medium technology, the other high tech), the country with the final production of the high-technology good has bright prospects to have a lead in international per capita income comparison provided value-added of the high-tech sector is relatively large. One might think of the computer sector as being a high-tech sector. However, a caveat is necessary to the extent that the intermediate product is the real high-technology element of the computer. In this case, Schumpeterian rents will accrue to the chip makers while firms assembling the final product will not get much of a Schumpeterian rent. Thus it is not surprising that computers produced in Poland, Malaysia or Thailand are not generating very high incomes for those working in that industry. This could, however, change in the long run if firms which assemble computers today should be able to upgrade technological and entrepreneurial skills adequately. This statement holds in a broader sense as the example of Toyota tells us. Toyota started as producers of textiles, then became a producer of textile machinery and finally became the world’s leading and most profitable car producer. Assume a poor country with low capital intensity k wants to catch up with country II which is rich and has a high capital intensity k∗ . To which extent does it make a difference whether catching-up is through the import of capital goods or FDI inflows? Capital accumulation can accelerate through the import of capital goods; in the extreme case that the country is producing only consumer goods and all imported

20

Innovations in Macroeconomics

goods are capital accumulation is governed by (with J denoting imports): dK/dt + δK = J

(A.7)

Assume that J = j(q∗ )Y where q∗ is defined as eP∗ /P which in effect is the international relative price of capital goods. We assume that output is produced according to a Cobb–Douglas function so that Y = Kß L1−ß

(A.8)

y = kß

(A.9)

or

Then—assuming that population growth at a constant rate n—we have a simple modified neoclassical growth model whose steady state is: k# = {j(q∗ )/[n + δ]}1/(1−ß)

(A.10)

Per capita GDP is y = f(k) which is equal to gross national product. With no government expenditures exports X will be equal to (1 – c)Y where c is the consumption–expenditure ratio. The balance of payments constraints reads: P(1 – c)Y = eP∗ jY. Therefore the real exchange rate P/eP∗ is given by j/s. If both goods are identical so that one cannot distinguish between capital goods and consumption goods it must hold under free trade that P = eP∗ and hence j = s. Next, assume that the same amount of capital goods comes through FDI inflows. Then all machines and firms, respectively, are owned by foreigners who decide about the structure of production. In the steady-state national output per capita will be equal to y = {j(q∗ )/[n + δ]}ß/(1−ß) , but national income obviously is equal to y = (1 − ß)y. From this perspective, it seems natural that countries prefer trade with incentives for both investment and savings rather than free FDI inflows. This however, holds only under the assumption that the technology is the same both in the case of free trade (and not FDI) and in a system where capital accumulation is dominated by FDI inflows. Assume that in a regime with trade y = f(k) while in a system with FDI inflows we have per capita output according to y = F(K∗∗ /K)f(k) where the technology transfer factor F is larger than unity; K∗∗ is that of the overall capital stock K in country I which is owned by foreigners. A simple specification could be y = [1 + K∗∗ /K]f(k); if the technology transfer effect is larger than ß it would make sense for society to fully rely on foreign investors.

A.6 Variations on the Solow Model: Some New Insights for a Monetary Economy A.6.1 A Generalization of the Solow Growth Model Sustained economic growth is crucial for the well-being of individuals but also for the power of nations. As regards these two aspects of growth, it is clear that these are

A.6 Variations on the Solow Model

21

two distinct categories. A government which wants to impress its trading partners (or potentially adverse countries) will point to the size of the overall gross national income as well as its growth rate. Individual well-being is, however, related to per capita income and the growth rate of per capita income. Strictly speaking, we should use purchasing power figures in international comparisons, and we ultimately are interested in per capita consumption which leads to the issue of optimum growth. Growth analysis is of key importance for both countries eager at catching-up with rich countries and for the leading economies which want to stay ahead of “follower countries”. Moreover, as short-term cyclical dynamics are superseded by long-run growth dynamics, one should be interested in long-run growth issues even if one adopts the policy perspective of politicians with a medium-term time horizon. This holds not in the least since the steady-state solutions implied by growth models will certainly affect expectations of individual investors and consumers. Growth models have a long-term perspective while traditional macro models typically adopt a medium-term perspective. It is not easy to reconcile the different approaches. Standard macro models are useful for business cycle analysis and for gaining an understanding into policy impacts in the short run and medium run. The enormous speed of financial markets and the considerable role of asset markets to some extent suggest putting more emphasis on short-term approaches and mediumterm models. At the same time, it is true that financial markets also represent a relatively large volume of medium-and long-term transactions as can be seen from the average maturity in bonds markets in countries with low inflation rates and stable governments. It is thus true that under high inflation, maturity will strongly decline. Are there arguments why one should consider the implications of growth models? A classical argument is that the production potential and hence the production function will be a limiting factor of economic development in the long run. From this perspective, the accumulation of capital and knowledge is quite crucial. The latter in turn is linked to innovations. Another important argument for considering growth models is the phenomenon of ageing societies which is a global challenge, as ageing will characterize the majority of countries and people in the world economy in the tweny-first century. Rising longevity could imply that people—households, investors and politicians—will become more interested in long-run economic perspectives. Thus growth theory could be quite useful. Moreover, there has been considerable analytical progress in recent years, and this includes endogenous growth models which go well beyond the standard SOLOW growth model. There are also typical caveats to neoclassical growth models, however, they are not really justified. The basic SOLOW model assumes a linear-homogenous production functionY(K, L) where K and L represent capital and labor, respectively, and then explores the implication of goods market equilibrium in the sense of sY = dK/dt—savings S = sY where s is the savings rate. The basic finding is that there is a unique long-run steady-state solution for capital intensity k := K/L which is associated with a steady-state equilibrium per capita income y := Y/L. The higher the savings rate, the higher the steady-state value for both k and y. The model can be easily extended to include technological progress which often is assumed to be Harrod-neutral, as it is labor saving. The steady-state variable determined in the model with an exogenous growth rate of the

22

Innovations in Macroeconomics

level of technology (A) then is k := K/(AL) where AL is dubbed labor in efficiency units. If one uses a Cobb–Douglas production function Y = Kß (AL) 1−ß —where ß is the output elasticity of capital and y := Y/(AL)—we can write y = kß and with k # denoting the steady-state value of k we get y # = k #ß . The steady-state value in a setting with an exogenous growth rate of the population n and an exogenous progress rate dln A/dt = a is simply given by k # = [s/(n + a)]1/(1−ß) . This implies Y/L = [s/(n + a)]β/(1−ß) A0 e at (e is the Euler number, A0 the initial level of A). Hence, the level of the growth path positively depends on s and negatively on the sum of n and a, while the long-run growth rate is given by a. It is clear that a rise in the progress rate a thus reduces the growth path, but the growth rate will increase which will be the dominant effect on per capita income in the long run. This in a nutshell is what the SOLOW model says. (Note that we have disregarded capital depreciation which, however, is not difficult to include in the analysis.) The SOLOW model is a non-monetary growth model.

The SOLOW Model as an Analytical Starting Point The neoclassical SOLOW growth model is elegant on the one hand, but it also is rather simple on the other hand. The latter does not, however, rule out our considering interesting modifications. While it is often claimed that the SOLOW model does not consider institutional aspects, it is quite easy to integrate at least two basic aspects. Write the production function—based on a Cobb–Douglas function with capital K, labor input L and the level of labor-saving technology A—as Y = Z K ß (λ AL)1−ß

(A.I)

Therefore per capita income Y/L =: y is given by y = Z k ß (λ A)1−ß

(A.II)

Here Z represents the quality of the basic political and economic institutional network which facilitates coordination in markets and within firms. Hence transaction costs aspects in markets and in firms are relevant here. The variable λ indicates the effort of the average worker. It is obvious that this effort is not only influenced by wages—here we have a bridge to the efficiency wage theory—but by the social security system as well; if there are generous benefits which can be obtained by those who are unemployed, the effort parameter will be low. The growth rate of per capita output therefore (with g denoting growth rates and a signifying gA ) is given by gy = gZ + ßgk + (1 − ß)(gλ + a)

(A.III)

Thus the growth rate of per capita income is the sum of the growth of the institutional quality factor Z , of the growth rate of the capital intensity (weighted with ß) and of the growth rate of working efforts plus the rate of non-embodied technological

A.6 Variations on the Solow Model

23

progress (weighted with 1 − ß). For transition countries, in particular those moving from a distorted socialist planned economy—with a poor institutional quality index and a weak labor motivation factor λ (not least due to an expanding socialist shadow economy), one may expect a transitory growth bonus until Z in eastern European countries and λ have achieved quasi-equilibrium values which roughly could be assumed to be equal to EU15 average. Once this growth bonus is fully exploited, growth is simply the weighted sum of the growth of capital intensity k and the growth rate of technological progress. If the basic politico-economic institutional network weakens so that its quality deteriorates, the parameter Z falls. For example, if an integration club such as the EU25 (or individual member countries) should move toward a less consistent politicoeconomic system, this implies a fall of the level of per capita income. Moreover, if the social security system becomes too generous in the sense of weakening λ, the effect on per capita output will also be negative. (In a model with heterogeneous labor, one would have to modify the analysis since the unemployment insurance system allows workers laid off to move to new jobs with relatively high productivity instead of quickly accepting the next best job to come.) Let us adopt the standard assumption of the neoclassical growth model, namely that labor and technology grow with a constant rate, that is L(t) = L0 ent and A(t) = A0 eat (n and a are assumed to be exogenous positive parameters). Within a simple growth equilibrium model which assumes that savings S = sY and imposes the goods market equilibrium condition S = dK/dt (hence there is no deprecation of capital) the steady-state capital ratio k is derived from the differential equation (with y := Y/[AL]): dk  /dt = sy − (n + a)k 

(A.IV)

This gives the steady-state capital stock ratio k as k  # = [sZ λ1−ß /(n + a)]1/(1−ß)

(A.V)

Here (note that # denotes the steady state) we can see that the savings rate s—the crucial variable in the SOLOW model—and both Z and λ will affect the level of the growth path of k . The long-run growth rate of k := K/L and per capita income y will be given, of course, by the progress rate a. An important phenomenon of the 1980s and 1990s is that many Asian countries launched a rather successful economic catching-up process certainly interrupted by the Asian crisis of 1997. The US and Western European countries still are leading countries in terms of per capita income, however, there is some international real income convergence (unfortunately leaving out most of Africa). With respect to the growth rate of per capita income, the EU and the US were roughly at par in the 1980s and 1990s. The US growth rate of real GNP exceeded that of the EU, however, since the US recorded considerable population growth while that of the EU was very low. Germany, France and Japan have almost caught up with the US in terms of per capita income. From the perspective of the neoclassical growth model, catching-up at some point of time t can be brought about by two mechanisms, namely by a rise of the relative

24

Innovations in Macroeconomics

per capita income level (while the long-run growth rate remain constant) and/or by a relative rise of the growth rate of technological progress (while the level of the growth path is unchanged). Both Germany and the US have experienced several shifts in the trend growth rate of progress as has been suggested by JUNGMITTAG (2006 b) and by BEN-DAVID, LUMSDAINE, PAPEL (2003) for the case of the USA. In a world economy in which the ratio of research and development relative to national income is increasing over the long run—while the role of MNCs (often representing technological ownership-specific advantages) is rising at the same time—the progress rate is likely to play an increasingly important role over time. However, it is unclear to which extent the trend of the progress rate is stable across countries. Moreover, product innovations are likely to affect the speed of process innovations, as novel products can often be produced only on new machinery and equipment. If two countries are to have the same level of the growth path and the same long-run growth rate, the neoclassical growth model requires that a whole set of parameters should coincide across countries. It is not really clear which mechanisms could bring about such convergence of parameters, including convergence of the savings rate, the rate of capital depreciation and the growth rate of technological progress. The very existence of MNCs is based on technological advantages of the respective companies, and there is no free lunch for firms (not being a subsidiary) in foreign countries to quickly get access to foreign multinationals’ latest technologies. Here innovations mean process innovations, but equally important are product innovations which allow firms to temporarily fetch higher prices in world markets. The conventional idea of most textbooks that the law of one price is valid in a simple form is not really convincing in a world with heterogeneous products. There are other departures from the standard neoclassical models in reality, namely that there is unemployment in many countries for many years—to which extent can unemployment be considered in a long-run growth model and how will long-run inflation and long-run unemployment interact with economic growth? In the following tables and graphs we take a quick look at selected data which are an interesting background for the subsequent analysis. We can see that per capita GNP growth is relatively similar across countries, while the growth rates of GNP and of population are rather different. As we can see, the growth rate of the population is declining in many countries, but the cross-country differences are considerable. Asia’s economic weight will be reinforced both through high per capita growth and sustained growth of the population.

Foreign Direct Investment and Technology Economic catching-up in Europe was rather impressive for several countries in the 1960s and 1970s, but there were also impressive catching-up dynamics in the period from 1990 to 2005. It is rather unclear which forces explain these phenomena. When one discusses economic catching-up across countries, it is important to make a distinction between GNP per capita and GDP per capita. FDI inflows contribute to

A.6 Variations on the Solow Model

25

Bars: Growth Rate Real GNP per Capita (national currency)

Lines: Growth Rate Real GDP per Capita (national currency)

10 10 8 5 6 0 4 –5

2 0

–10

–2

–15

–4

–20 1980

1985

1990 Ireland Ireland

1995

2000

2005

United States United States

Netherlands Netherlands

Fig. 3 Annual growth rate of real GNP and GNP per capita, 1980–2005 (US, Ireland and Netherlands). (Source: Ameco Database; Own calculations)

Bars/Real GNP pC Growth in %

Lines/Real Population Growth in %

12

2

10

1

8

0

6

–1

4

–2

2

–3

0

–4 1970

1975

1980

1985

1990

1995

2000

2005

–2

–5

–4

–6 DE

FR

IT

UK

US

DE

FR

IT

UK

US

Fig. 4 Growth rate of real GNP per capita and population in selected countries, 1970–2005 (US, UK, France, Germany, UK, Italy). (Source: Ameco Database)

US UK France Germany Italy Turkey China India Pakistan World

5.40 1.73 1.85 0.84 0.72 8.97 4.48 9.14 13.15 6.91

2000

4.95 1.70 2.05 0.42 0.65 7.27 3.29 8.06 10.72 6.23

2005

4.71 1.42 1.72 0.01 0.14 6.68 2.94 7.24 10.92 5.85

2010 4.31 1.49 1.31 −0.23 −0.62 5.84 2.84 6.51 10.41 5.50

2015 3.90 1.75 0.99 −0.28 −1.19 5.00 2.22 5.69 9.45 4.97

2020 3.45 1.88 0.72 −0.38 −1.44 4.37 1.23 4.76 8.34 4.32

2025 3.08 1.62 0.48 −0.56 −1.57 3.66 0.35 3.84 7.40 3.72

2030 2.72 1.20 0.22 −0.77 −1.70 2.87 −0.24 3.12 6.61 3.22

2035

2.38 0.90 −0.10 −0.90 −1.91 2.15 −0.66 2.69 5.86 2.81

2040

2.10 0.79 −0.41 −0.88 −2.22 1.56 −1.15 2.17 5.11 2.37

2045

1.92 0.85 −0.64 −0.87 −2.57 1.02 −1.74 1.59 4.28 1.89

2050

Table 2 UN projections of growth rates of population for US, UK, France, Germany, UK, Italy, Turkey, China, India, Pakistan, World, 2000–2050. (Source: UN)

26 Innovations in Macroeconomics

A.6 Variations on the Solow Model

27

Nominal GNP in Billion PPS other countries

Nominal GNP in Billion PPS USA

2500 11000 9000

2000

7000 1500

5000 3000

1000 1000 –1000

500

–3000 –5000

0 1980

1985 United States

1990 Germany

1995 France

2000 Italy

2005

United Kingdom

Fig. 5 GNP (PPP figures) in the US, UK, France, Germany, Italy, 1980–2005. (Source: Ameco Database)

Nominal GNP in Billion PPS 600 500 400 300 200 100 0 1980

1985 Ireland

1990 Netherlands

1995 Poland

2000 Finland

2005 Sweden

Fig. 6 GNP (PPP figures) in the Netherlands, Sweden, Finland, Ireland, Poland, 1980–2005. (Source: Ameco Database)

a rise of GDP and GNP, but the rise of GNP is likely to be lower, since subsidiaries of MNCs will transfer profits to the parent companies abroad. Therefore, it is an important fact that per capita foreign direct investment inflows differ considerably across countries.

28

Innovations in Macroeconomics

Bars: Real GNP per Capita (national currency)

Lines: Real GDP per Capita (national currency) 40000

40000 Ireland Ireland

35000

Netherlands Netherlands

United States United States

35000

30000

30000

25000

25000

20000

20000

15000

15000

10000

10000

5000

5000 0

0

1980

1985

1990

1995

2000

2005

Fig. 7 Per capita GDP and per capita GNP of the US, Ireland and the Netherlands, 1980–2005. (Source: Ameco Database) FDI Stocks in Mio. 1800000 1600000 1400000 1200000 1000000 800000 600000 400000 200000 0 1994

1995

1996 Germany

1997

1998

France

1999 Italy

2000

2001

Netherlands

2002 UK

2003

2004

US

Fig. 8 FDI stocks per capita in selected countries. (Source: Ameco Eurostat)

A.6.2 Aspects of Empirical Analysis of Economic Development The basic neoclassical growth model—based on a Cobb–Douglas production function Y = Kß (AL)1−ß —and a savings function S = sY(1 – τ), reinvestment δK and an

A.6 Variations on the Solow Model Fig. 9 Empirical aspects of economic development

29

ln y D′ C′

α′ D

C′ B′

A

α

α′ E

B

α

t′

t′′

t

exogenous growth rate of the level of labor-augmenting technology A(t), namely a, and an exogenous growth rate of the population L, namely n, leads to the following steady-state solution for per capita income Y/L =: y y# = {s[1 − τ]/[n + δ + a]}ß/(1−ß) e

at

(A.VI)

If one considers this model as an adequate approach to reality all medium-term changes in y can be explained by the interaction of two basic elements provided that s, τ, n and δ are not correlated with a and also independent of time t: • If there is an increase in the level of per capita income the underlying reason is a rise of s (or ß) or a fall of τ, δ or n. A rise in the level of the growth path must not be confused with a change of the growth path itself—this brings us to the next point. • If there is a structural break in the time series the reason is a change in the growth rate of technological progress; a rise of the progress rate a will go along with a once-and-for-all fall of the level of the growth path and a fall of the progress rate a will go along with a rise of the level of the growth path. An additional test to be performed would look at a (period) sub-sample of the data, namely whether the coefficient for the progress rate has increased in the regression. The following graph makes a clear distinction between a rise of the level of the growth path occurring in period t and a rise of the growth rate occurring in period t (see the arch ED). If both a rise of the level of the growth path and of the progress rate itself should occur we would see a picture such as the arch C D . The initial stage of economic catching-up in poor countries typically is one during which the savings rate is increasing and the growth rate of the population falling which implies that the level of the growth path is raised over time. Often only in a later stage of economic catching-up will technological progress enter the picture and the international transfer of technology through various mechanisms and domestic innovation policy may well interact.

30

Innovations in Macroeconomics

One may study the impact of economic opening up—that is of trade and capital flows—on both the parameters relevant only for the level of the growth path and for the growth rate of technological progress. In the literature this distinction is rarely made.

Population Growth, Progress and Economic Dynamics Population growth increased in Europe after the Industrial Revolution; after the introduction of the modern welfare state it has considerably reduced and few European countries expect long-term population growth. By contrast the US is expected to have sustained population growth and to face ageing problems much later than Japan and the EU (with eastern European population growth falling faster than in EU15). The demographical dynamics and ageing of the population clearly represents mayor challenges for policy makers in Europe and Japan. McMORROW/RÖGER (2004, p. 35) argue that ageing will affect savings in various ways: “On the positive side, ageing would be expected to boost savings rates due to: increased savings for retirement by forward-looking (not liquidity constrained) worker households; lower dissaving in retirement. On the negative side, ageing would be expected to deplete savings due to an increasing share of low savings retirees, higher expected future labor income and lower investment needs. In addition, the overall net effect of ageing on savings is further complicated by the interest rate effects. Regarding the latter, given that lifetime wealth calculations are affected and that the substitution and income effects can be different depending on the level of the intertemporal elasticity of substitution, interest rate changes can easily have positive or negative effects on savings.” A refined neoclassical model is useful when considering some of the key aspects of changes in the growth rate of the population. We assume a standard Cobb–Douglas production function Y = Kß (AL)1−ß and an exogenous growth rate of technology (A; dlnA/dt =: a) and an exogenous growth rate of the population (n = dlnL/dt). By assumption savings S = s(1 − τ)(1 − hu)Y where u is the structural unemployment rate—long-term unemployed have a negative savings rate—and h a positive parameter; τ is the income tax rate. Imposing the equilibrium condition that gross investment (δ is the depreciation rate) equals savings, that is dK/dt + δK = S, we obtain the differential equation for k := K/(AL): dk  /dt = s(1 − τ)(1 − hu)k  − (n + a + δ)k  ß

(A.VII)

The steady-state solution for the ratio of capital to labor in efficiency units is: k # = {s(1 − τ)(1 − hu)/(n + a + δ)}1/(1−ß)

(A.VIII)

Thus y := Y/(AL) in the steady state is given by y # = {s(1 − τ)(1 − hu)/(n + a + δ)}ß/(1−ß)

(A.IX)

A.6 Variations on the Solow Model

31

Wíth e denoting the Euler number we get for labor productivity y := Y/L the result y# = {A0 s(1 − τ)(1 − hu)/(n + a + δ)}1/(1−ß) e

at

(A.X)

A0 is the initial level of technology. Denoting ß/(1 − ß) = ß per capita output in the steady state thus is governed by ln(y(t)) = {lnA0 + ß [lns − τ − hu − ln(n + a + δ)]} + at

(A.XI)

Note that the elasticity of y with respect to the investment-output rate (read s) is ß/(1 − ß) which is 0.5 if we assume ß = 1/3 as is typical for many OECD countries; raising the investment-GDP ratio from 20% to 21% (an increase by 5%) thus—from a theoretical perspective—should result in an increase of per capita income by 2.5% which is in line with empirical findings reported subsequently for the US and the EU. If the empirical findings were larger or smaller the only explanation would be that s is affecting the progress rate; for example the apparent elasticity of y with respect to s could exceed ß/(1 − ß) if the progress rate a were a negative function of the investment-output ratio s (as s is raised it becomes more difficult for firms to organize investment projects in a way that all investment projects reflect a high rate of embodied technological progress—if empirical findings suggest an elasticity much above 0.5 one might indeed assume that such an effect plays a major role; using a as a positive parameter the implication is that a = a0 − a  s and from this perspective raising the savings rate would thus not be a prime task for government since one has to consider the potentially negative effect of s on the progress rate and the trend growth rate, respectively). The semi-elasticity of per capita income with respect to the income tax rate is given by ß and the same applies for the unemployment rate if h is unity. In the latter case a reduction of the unemployment rate by 5 percentage points will raise the long-run level of per capita income by 2.5%; based on an annual per capita income of 20,000 € this implies an increase by 500 € (of which government—including social security—would typically get 200 € in Euro zone countries). The long-run gain would be much larger if one were to assume that the progress rate is a negative function of the unemployment rate u, that is we have a progress function a = a0 – a#u. While it is true that the positive effect of lowering u on the level of the growth rate would be weakened by such a specification of the progress function, the implied increase of the trend growth rate a—after a fall of the structural unemployment rate—will more than offset this effect on the level of the growth path. The expression {. . . } determines the level of the growth path. We have assumed that hu and τ are close to zero, so than we can use the approximation ln(1 + x) ≈ x. The impact of a rise of n obviously is a fall of the level of the growth rate. However, reality is more complex and a particularly important aspect concerns the link between the growth rate of the population n and the progress rate a and the savings rate s. Considering such an impact leads to a quasi-endogenous growth model which is quite simple but offers some interesting insights. Now let us assume that n affects the savings rate and the progress rate. Depending on the social security system, government may influence savings in a way which

32

Innovations in Macroeconomics

amounts to a negative link between the growth rate of the population and the savings rate. We also assume that the growth rate of the population positively affects the progress rate which we model (with a0 and a1 as positive parameters) as a = a0 + a1 n

(A.XII)

The justification for a positive parameter a1 is the idea that a rise of the growth rate of the population will bring more competition and implies that a larger pool of new ideas is available—both effects could raise the progress rate. As an alternative to the specification presented we could introduce an additional term a2 n2 (with a2 < 0) so that there is a critical rate n beyond which n will negatively affect the progress rate— say, because having very many children will undermine the ability of the family to ensure a decent education for all kids. For the sake of simplicity we focus on the simple equation above. As regards the impact on savings we use—assuming n to be positive and using a positive parameter h —the following function for the savings rate: s = s0 e 

h /n

(A.XIII)

The steady state is now determined by ln(y(t)) = lnA0 + ß [lns0 + h/n − τ − hu − ln(n + a0 + a1 n + δ)] + [a0 + a1 n]t

(A.XIV)

To shed more light on the impact of n on the long-run per capita (or labor productivity) we assume that a0 + δ = 1 so that we can write: ln(y(t)) = lnA0 + ß [lns0 + h /n − τ − hu − (n + a1 n)] + [a0 + a1 n]t

(A.XV)

The semi-elasticity of per capita income with respect to n (for the level of the growth rate) thus is given by −h /n2 − [ß/(1 − ß)](1 + a1 ) which is negative; it would be ambiguous if we had considered a function a = a0 + a1 n + a2 n2 ; remember that a2 < 0). Alternatively, we may use the approximation lnX = 1 − b /X; with b chosen as a suitable positive parameter. Hence, we would use the approximation term 1 − [b /(n + a0 + a1 n + δ)] for ln(n + a0 + a1 n + δ), but the qualitative results will not change. A higher growth rate of the population will not only affect the level of the growth rate through the standard capital deepening effect but also via the fall of the savings rate and the increase in the progress rate. The positive effect of n on the progress rate implies that per capita income in the very long run will be positively affected by population growth. By implication a fall of the growth rate of the population implies a one-off increase in the level of the growth path, but a fall of the growth rate of per capita income in the very long run. This is paradox since for OECD countries facing a transition to lower population growth rates the implication is that there will be a transitory increase in per capita income (the modified capital deepening effect) which many consumers and investors—and government authorities—might interpret

A.6 Variations on the Solow Model

33

as a signal for structural economic improvements while the contrary is true: Thus there is the danger that policy makers in ageing societies with falling population growth rates will not adopt timely reforms required to raise the progress rate. At the beginning of the twenty-first century the perspective for the EU and Japan is that a fall in population growth will lead to a fall of the progress rate and labor productivity—relative to previous long-term trends. An interesting question is how the result is affected by considering the role of embodied technological progress; STOLERU (1978, p. 373) has shown that a higher rate of technological progress in a vintage model amounts to a rising of the depreciation rate. His analysis leaves the broader implications unclear. Here we write a = a0 + h δ1 while taking into account that the rise of δ has reduced the level of the growth rate. As regards the increasing role of information and communication technology— that is the relatively rising role of software compared to hardware—one may argue that h (a positive parameter) is higher in the age of modern ICT than in the 1960s or 1970s. A further refinement could be the assumption that the government deficit ratio is a negative function of n so that a fall of n brings a rise of the structural deficit ratio. Denoting net exports as X —and using the function X = x (q∗ )—and reinvested profits of foreign investors as D∗∗ we thus have the equilibrium condition in the goods market (with q∗ := eP∗ /P; e is the nominal exchange rate, P the domestic price level, P∗ the foreign price level): ∗

dK/dt + δK + x (q )X = S + T − G + D∗∗ (q∗ )

(A.XVI)

Note that a permanent net import position of the country considered implies that foreigners will own a share of the capital stock b and obtain thus a share of profits. If we assume competition in goods and factor markets and that factors are rewarded in accordance with the respective marginal product, the share of gross domestic product accruing to foreigners is bß so that D∗∗ = b(q∗ )ßY. Following FROOT/STEIN (1991) we may assume that the desired share b(. . . ) of FDI inflows depends on the real exchange rate q∗ . A rise of q∗ will bring higher net inflows in a world economy with imperfect capital markets and hence we also conclude that the desired share in the capital stock of country I—the home country—depends on q∗ . Foreign investors from country II will want to hold the highest share of K possible; the higher the share of K the easier it is to acquire assets in country I through international mergers and acquisitions. A real depreciation of country I currency will facilitate takeovers by firms from country II. Savings are now assumed to depend on national income which is Z = (1 – bß)Y. Assuming that X = x(q∗ )Y and imports J = j(q∗ )Y and that real government expenditures (G) relative to AL—namely G/(AL) is a positive function of n—we get the following differential equation (where the government surplus ratio is denoted as τ ): dk  /dt = {s[1 − τ][1 − hu][1 − b(q∗ )ß] + τ (n) − x (q∗ ) + b(q∗ )ß}k  − (n + a + δ)k  ß

(A.XVII)

34

Innovations in Macroeconomics

This gives the following steady-state solution (with j =: x denoting the net import ratio):  1  {s[1 − τ][1 − hu][1 − b(q∗ )ß] + τ (n) + j (q∗ ) 1−β k#= + b(q∗ )β}/(n + a + δ) 

(A.XVIII)

In a country with a falling growth rate of the population—and in a setup with n not affecting the progress rate a—we thus can conclude: The level of the growth path is positively affected by the capital deepening effect (the rise of the denominator), but it is negatively affected by the fall of the government surplus ratio. The net effect of FDI is an increase in the level of the growth path. One also may want to consider a setup in which the progress rate positively depends on b so that a = a0 + a b. Then FDI has an ambiguous effect on the level of growth as b is now both in the nominator and in the denominator. However, with a progress function a = a0 + a b (where a is a positive parameter) the trend growth rate will be raised by foreign direct investment. A country with a short political horizon therefore will be hesitant to invest resources in attracting FDI—assuming that there are some sunk costs to be incurred to make the country truly attractive to FDI inflows. Only if the political time horizon is long enough (meaning that the long-run improvement of trend growth through the presence of foreign investors is adequately considered), will there be political reforms conducive to foreign investment. Clearly, if the time horizon is sufficiently long policy makers will perceive a positive net welfare effect from FDI inflows, as the trend growth effect will finally dominate any negative effect on the level of the growth path. Let us come back to the impact of population growth. The new growth theory is not really clear about the impact of population growth and ageing; and the empirical analysis is partly ambiguous although there seems to be clear evidence that falling population growth negatively affects growth dynamics (TEMPLE 1999). The model mechanics in new growth approaches depend on the pattern of knowledge creation. In the new growth theory one basically explains the progress rate by certain efforts, for example the share of R&D personnel (L ) in the overall workforce (L). One could also state that a = a (L /L) where a is a positive parameter. In such a setting the growth rate of A falls parallel to the growth rate of the population and the only way to stabilize the progress rate is through a continuously rising share of R&D personnel. In his theoretical and empirical analysis JONES (2002a) argues that the long-run growth rate of US labor productivity in the period 1950–1993 can be explained through a permanent shift of factor inputs into knowledge activities—read R&D activities and human capital upgrading. The growth rate of educational attainment (human capital) was 0.63% p.a. and that of the R&D labor force 4.8%. Without human capital upgrading and R&D intensification the US labor productivity growth would have been less than 0.5%. From a theoretical perspective it is clear that one will have to consider both policy effects on the level of the growth path and the growth rate itself. In economic policy in OECD countries one hardly finds a broader discussion about these aspects—except in the European Commission and at the Council of Economic Advisors. While JONES

A.7 Technological Progress and the Long-run Price Level

35

estimates for the US the long-run productivity multiplier (level effects after 50 years) to be 2.1% for a 1 percentage point increase of the physical investment share, the European Commission comes up with a similar estimate of 2.4%. An increase by one year in educational attainment brings a 7% increase in the JONES analysis, but a 12.8% increase in the analysis of the Commission. An increase by one percentage point of the R&D share brings a 16% increase in the JONES model, but 17.7% in the EU. A reduction of the working age population growth by 1 percentage point reduces the productivity growth in the US considerably (JONES’ figures indicate a range of −2.5% to −16%); the estimate by the European Commission is −8.7% where the ECFIN analysis uses a slightly different approach than JONES. The overall EU analysis—the reader partly is referred to EUROPEAN COMMISSION (2003b)— also shows a positive impact of openness and market size for the EU and positive effects of European deregulation.

A.7 Technological Progress and the Long-run Price Level A.7.1 Process Innovations In modern economies process innovations are an important element of economic development. It is surprising that the role of process innovations have not been considered much in medium-term macro models. Only in long-run growth models have process innovations played a role. However, the dominant neoclassical growth models are non-monetary models in the sense that money market equilibrium is not considered. Subsequently we will show that combining a growth model with a money market equilibrium condition is quite useful. The following analysis is not only relevant for Schumpeterian innovation dynamics in a monetary economy (and every modern economic system is a monetary economy), we also can state that the role of monetary policy cannot be fully assessed if we do not include the role of technology. As regards the role of monetary policy it has been emphasized that an income elasticity of the demand for money of less than unity has crucial implications for monetary policy, e.g., that the Friedman rule of monetary policy is not optimal and the growth rate of money should be below the growth rate of output in order to achieve price stability. Moreover, monetary aggregates are still important in the new era of inflation targeting (HAYO 1999). Recent empirical work—based on co-integration analysis and error correction models—for broad money in Australia (VALANDKHANI 2005), Germany (BEYER 1998), the Euro zone (COENEN/VEGA 2001) and the UK (ERICSSON), namely for narrow money, all have shown that the longrun income elasticity is rather close to unity which is consistent with the quantity theory of money (if the elasticity were 0.5 the implication is that the Baumol–Tobin transaction approach is applicable, if the elasticity is above unity money is a luxury good). As regards the growth of the demand for money relative to income LAMBSDORFF (2005) has presented empirical evidence for a cross-country approach. We

36

Innovations in Macroeconomics

will show that the income elasticity of the demand for money points to important long-run implications in the context of technological progress. Process innovations which amount to the cutting of costs typically are expected to lead to a fall of the price level. The expansion of the digital economy often is considered as a case where process innovations have played a strong role (AUDRETSCH/WELFENS 2002; WELFENS 2002). This is a typical perspective one might have in an economy in which all sectors are subject to process innovations. However, this apparently convincing insight from microeconomics has a pitfall, as we will show in a simple long-run approach to the quantity theory of money. We will combine the money market equilibrium with the condition of profit-maximization; namely that the real interest rate r should be equal to the marginal product of capital. We will prove that, in the case of the income elasticity of the demand for money being between 0 and 1, there will be an increase in the equilibrium price level. Let us start the analysis with a standard microeconomic perspective of process innovations. Assume that there is a process innovation in market i (see in the following graphthe downward shift of the marginal cost curve K i where i could represent the tradable sector) and an unchanged supply condition in market j. At first sight this will lead to a fall of price pi and hence (with b denoting the share of income spent on good i) a decline of the aggregate price level P = (pi )b p(1−b) . One may introduce j some refinement in the argument, namely that a real income effect associated with the higher output in the i-market and the (potentially transitory) fall of pi will shift the demand curve in the j-market upwards so that the price pj will rise as a consequence of technological progress in sector i; thus the effect on the price level is ambiguous (see the following graph). However, we can prove within a macroeconomic approach that there is no ambiguity at all if the income elasticity of the demand for money is in the range between 0 and unity. If the income elasticity is above unity then the longrun equilibrium price level will fall as a consequence of process innovations. The relevant mechanism partly includes the macroeconomic money market: The demand for money is affected by a rise of the technology level in two offsetting ways as we will see. In a consistent macro model with goods markets and a money market, the relevant mechanism is related to the demand for money and this in turn suggests that there must be a real balance effect in goods markets (or in the aggregate goods market).

A.7.2 The Model A.7.2.1 True Long-run Equilibrium in the Money Market Let us consider the long-run money market equilibrium, namely, real money balances M/P equals the real demand for money md (Y, i) where M is the nominal money stock, Y aggregate output and i the nominal interest rate. As we will assume an expected inflation of zero, we will set I = r (real interest rate). Moreover, we will consider a

A.7 Technological Progress and the Long-run Price Level pj

b

37

pi

a

Kj0′

K i0′

K i1′ H

E

p j1 p i1 G

p j0

F

p i0

DDj1 qj

DD i0

DDj0 q j1 q j0

0

q i0

q i1

qi

Fig. 10 Ambiguous effect of technological progress on price level

Cobb–Douglas production function with a Harrod factor A Y = K ß (AL)1−ß

(A.10a)

and impose the condition of profit maximization so that r = YK = ßY/K

(A.10b)

Here ß is the output elasticity of capital and YK the marginal product of K. In this approach the marginal product of capital determines the real interest rate. Thus we are not following the optimum growth model which leads to f (k ) = θ + n where k is modified capital intensity K/[AL], f the marginal product of capital, θ is the time preference and n the growth rate of the population (modified golden rule; alternatively the golden rule could be used f (k ) = n; see BLANCHARD/FISCHER 1989). For an optimum growth approach one would rather consider n to be endogenous here; one also could argue that the golden rule approach assumes that utility maximizing consumers dominate the capital market while our approach assumes that investors dominate capital markets (in reality both groups will have an influence so that r = b θ + (1 – b )f (k ); b represents that relative impact of consumers—we have a similar problem as with exchange rate determination in the presence of fundamentalist actors and speculators betting on present trends). Next we follow the standard assumption that the real money demand m is a positive function of Y and a negative function of the nominal interest rate i. Money market equilibrium is defined by M/P = m(Y, i)

(A.10c)

38

Innovations in Macroeconomics

Taking a look at the long-run money market equilibrium condition (defined by M/P = m and the equality of the real interest rate and the marginal product of capital) brings an important and surprising insight. It is convenient to define real money demand as M = Yσ σ /i

(A.10d)

Let us point out that with a real money demand function m = Yσ σ /i (or a similar specification; σ > 0; σ > 0) and zero expected inflation (hence the nominal interest rate i = r), we get in an economy with profit maximization and a Cobb-Douglas production function Y = Kß (AL)1−ß the somewhat surprising result that a once-andfor-all rise of the level of technology A could raise the price level P. This can be seen from the money market equilibrium condition M/P = md (Y, i) which is solved here for the steady-state price level P#: σ

P# = MY− ß[Y/K]/σ = [ßMY1−σ /K]/σ

(A.10e)

It is obvious that a rise of M will raise the equilibrium price level while for a given real interest rate and hence a constant ratio Y/K a rise of output will reduce the price level. If the international law of one price is holding, namely P = eP∗ , the nominal exchange rate is given (assuming an exogenous P∗ ) by P#/P. Now let us consider the equation for the price level (true monetary long-run equilibrium condition) in more detail: P =(ß/σ )M(AL)(1−ß)(1−σ) K ß(1−σ)−1

(A.10f)

We can see that a rise in the capital stock will reduce the price level which corresponds to standard results from a model with two markets (or one aggregate goods market) in which there has been an increase in production capacity. ∂P/∂K < 0

(A.10g)

Indeed, this condition obviously is fulfilled since ß is about 1/3 and σ close to unity. The multiplier for K is negative. Note that Eq. (A.10f) can be restated as P = (ß/σ )MA(1−ß)(1−σ) L(1−2ß)(1−σ)+1 k so that one could display a P–k-line for money market equilibrium. As regards the impact of process innovations (dA > 0) (and similarly for dL) we find a rather paradoxical result (one should recall that the monetary approach to the balance of payments is also paradoxical as the Mundell–Johnson argument emphasizes that in a small open economy with a fixed exchange rate a rise of the foreign price level will raise through arbitrage the domestic price level and hence raise the demand for money; The excess demand for money translates into a current account surplus which leads to a rise of the money supply which is consistent with the initial rise of P). We indeed can see: ∂P/∂A > 0 if 0 < σ < 1

(A.10h)

If the income elasticity of the demand for money is slightly below unity, a rise of the technology level (A) will raise the price level. If this elasticity were above unity,

A.7 Technological Progress and the Long-run Price Level

39

process innovations will lead to a lower price level. As is well known from the literature, there has been (at least since Milton Friedman’s argument that money is a luxury good: hence the income elasticity should be above unity) a long debate about the income elasticity of money and the empirical evidence is not always conclusive as to whether the elasticity is below unity or above unity. In our long-run approach the level of technology has an impact both on real income and on the real interest rate: The reason for the interesting paradox presented is the role which the level of technology has on the marginal product of capital and hence on the interest rate; a rise of A amounts to raising the marginal product of capital and hence the interest rate so that the demand for money is reduced. Therefore money market equilibrium (at a given nominal money supply and a given capital stock) can only be restored if the price level is rising (this might be interpreted in a way that the real income effects of technological progress can overcompensate the direct price effect of falling marginal costs). If σ = 1, the price level would remain stable and the positive real output effect associated with the rise of A would generate exactly sufficient additional demand for money to restore the equilibrium. If σ > 1, the income-induced rise of the real demand for money would be so large that it would require a fall of the price level for equilibrium in the money market to be restored. Whatever the specification of the demand for money, there will always be a critical value of the income elasticity below which a rise of A has to be accompanied by a rise of the price level if a new equilibrium is to be achieved in the money market. Basically, we have an interesting empirical question on the one hand and on the other hand the idea presented reinforces the natural skepticism one has when simple analogies from microeconomics are drawn to derive macroeconomic conclusions. Even parallel process innovation in both markets could ultimately lead to a rise of the price level, namely if the real income effect in both markets is strong enough to outweigh the productivity/cost effect related to process innovations.

A.7.2.2 Long-run Growth Perspective Next we recall that k := K/[AL]. Let us rewrite the true long-run monetary equilibrium condition in the following way, where we observe that in the following equation the elasticity of P with respect to AL apparently is negative (this seems to contradict the initial equation for true long-run monetary equilibrium, however, one must take into account that the variable k contains AL in the denominator!): P = (ß/σ )M(AL)−σ k 

ß(1−σ)−1

(A.10i)

Assume that savings S = sY, reinvestment is proportionate to K (parameter δ) and that overall investment I = dK/dt + δK = S. From the standard neoclassical growth model we know that the equilibrium value k # is expressed for the case of a given L and a given A by k # = (s/δ)1/(1−ß) .Thus we get for the long-run price level P#: P# = (ß/σ )M(AL)−σ [s/δ][ß(1−σ)−1]/[1−ß]

(A.10j)

40

Innovations in Macroeconomics

One should note, however, that the assumption that there is profit maximization imposes a restriction on the parameter sets since we have ßk ß−1 = r and hence k # = (ß/r)1/(1−ß) ; and we have k # =[s/δ]1/[1−ß] . This requires a specific savings rate, namely s = (ß/r)δ which could be fulfilled by choice of a specific ß; this effectively implies growth on a razor’s edge. We can state that a rise of M raises the long-run equilibrium price level while a rise of the savings rate will reduce it. An increase in the depreciation rate δ will raise the price level. In a stationary, non-growing economy inflation is always a monetary phenomenon. Next we consider an economy with population growth and sustained progress so that (with e denoting the Euler number, n the growth rate of population and a the growth rate of the technology level A) L = Lo ent and A = Ao eat . We therefore get the following equation which offers some non-monetarist insights about inflation:   (a+n)t −σ (A.10k) P#(t) = (ß/σ )M [s/(a + n + δ)][ß(1−σ)−1]/[1−ß] L0 A0 e Obviously in a growing economy there could be a sustained deflation, namely to the extent that a + n exceeds zero. A rise of the progress rate a will lead to both a rise of the level of P and of the deflation rate respectively (the expression ß(1 – σ) – 1 is always negative, so that the impact for the level of P is unambiguous). For the case of a shrinking population (clearly a future problem of Japan and some other OECD countries) we also have to take into account the case n < 0. Even if in a growing economy there is a potential case for a non-monetary inflation or deflation it is true that monetary authorities could achieve price stability, namely by adjusting the money supply accordingly. This will, however, affect seigniorage revenues for government. We now return to the true long-run monetary equilibrium condition. Let us briefly focus on the case of an open economy which suggests an additional potential paradox. A paradox in an open economy in which there is parallel technological progress in country I and country II (dA > 0, dA∗ > 0; and dA = dA∗ ) will occur if the income elasticity of the demand for money is below unity (in the interval [0, 1]) in the home country and above unity in country II. The consequence of global technological progress is that the price level in country I will rise, while it will fall in country II; implicitly one has to assume downward wage flexibility if unemployment is to be avoided. If the nominal exchange rate is constant the effect is a real appreciation of the home country’s currency and this has to be taken into account in the context of the interest parity which reads in the absence of inflation r = r∗ + dlnq∗ /dt where q∗ is defined as eP∗ /P (e is the nominal exchange rate); hence technological progress will affect capital flows through the logic of the interest parity. While some observers analyzing country I might argue that process innovations (or rises in labor productivity) lead to a real appreciation, the true story is that process innovations per se do not lead to this appreciation, rather it is a mechanism which is related to the money market. Our approach suggests that analyzing long-run price level dynamics in open economies with technological progress should be done in a careful way and must include an analysis of the money market. The common analytical split

A.7 Technological Progress and the Long-run Price Level

41

between pure trade theory (never looking at the money market) and monetary theory of international economic relations is not adequate in certain cases. If one considers the case of flexible nominal exchange rates and process innovations (again with σ in the interval [0, 1] in country I and above unity in country II) one may assume that the nominal exchange rate is rising, so that there is a nominal depreciation of the currency. Speculators and scientists therefore should be interested in the size of the income elasticity of the demand for money. It seems likely that in poor countries the income elasticity of the demand for money is below unity while in countries with a high per capita income it is above unity as the demand for real balances and other wealth assets is rising more than proportionately as income is rising. Economic catching-up of poor countries and thus international real income convergence could thus help to avoid the above paradox. To learn more about the role of this paradox from an empirical perspective, one should particularly study the link between progress and the price level in those countries where the income elasticity of the demand for money is below unity in a certain period and above unity in the following period. Next we take a look at the real exchange rate eP∗ /P while assuming that the above equilibrium equation holds in a similar way abroad: P∗ = (ß∗ /σ∗ )M* (L* 0 A* 0 e(a

∗ +n∗ )t

∗

∗ )−1]/[1−ß*]

)−σ [s∗ /(a∗ + n∗ + δ∗ )][ß*(1−σ

(A.10l) Now we get a much better understanding about the long-run real exchange rate which is given by the following expression: (Denoting s/(a + n + δ) =: s , LoA0 =: Z and [ß(1 – σ) – 1]/[1 –ß] =: ß ) q∗ = e(ß∗ /ß)(σ /σ∗ )(M∗ /M)(Z *e

(a ∗ +n∗ )t −σ∗

)



[s *]ß * /[(Z e

(a+n)t)−σ



[s ]ß ] (A.10m)

If ß = ß∗ we can state that a rise of the foreign savings rate relative to the domestic savings rate will raise the real long-run equilibrium exchange rate; a relative rise of the domestic savings rate will bring about a real appreciation; as −σ < 0 we can add that a relative rise of the sum of the domestic progress rate and the population growth rate will also bring about a real appreciation (both a relative rise of the savings rate and a relative rise of the domestic progress rate are typical of economic-technological catching-up (with Japan being a prominent example in the 1970s and 1980s). One should note that the world real income in terms of country I (home country) is YW = Y + q∗Y∗ . If all goods are homogenous and indeed the array of goods produced in both countries are equal then we would have q∗ = 1, so that the nominal exchange rate can be inferred from the above equation. It is fairly clear that in a multi-product world economy with products a, b, . . . , z the relative import price eP∗ /P will be determined by the weighted average of individual prices. If the range of goods a, b, . . . , z is in ascending order with respect to technology content and if one assumes that the Schumpeterian rent included in individual product prices is a positive function of the technological intensity of the product, a technologically leading

42

Innovations in Macroeconomics

country typically will produce more of the high-technology products x, y, z or be even the only producer, in which case the respective prices will contain a monopoly pricing element. Thus q∗ = 1 will hold only under the condition that there is both free trade and full international technological convergence; or an equivalent technological specialization in exports of both countries is considered. Our findings for the case of a full employment growth model are consistent with a macroeconomic approach to the exchange rate and the current account, respectively. However, we will show later that the production function and the growth model also can be used in the presence of unemployment. Let us get back to the standard literature: In the literature one often finds two contrasting views of explaining the real trade balance X = X – q∗ J (where J is imports); one can argue that since export quantity X = X(q∗ , Y∗ ) – X is a positive function of q∗ and Y∗ and the import quantity J = J(q∗ , Y) the development of the trade balance depends for given Y and Y∗ on the Marshall–Lerner condition or the Robinson condition; X = X (q∗ , Y, Y∗ ). Alternatively one can argue that since the goods market equilibrium condition in an underemployed economy can be written as S(Y) = I(r) + δK + G − T + X − q∗ J one can state (assuming for simplicity G = T) that net exports X are a function of Y and r. Net exports will rise if savings rise relative to planned investment and for given Y, Y∗ , P, P∗ this obviously implies a nominal depreciation. We now also see this for the case of a full employment growth model. Again, as one may argue that the production function and the growth model respectively also work in an economy with a positive unemployment rate, we have shown a clear mechanism according to which the savings rate affects the exchange rate. However, it is clear that the net investment function in a full employment model cannot be I(r), rather we have r = ßY/K and therefore we can state the equation −dr + ß(dY/dt)/K = ß(Y/K2 )(dK/dt). Moreover, to get a stationary real exchange rate we must either have all the goods being identical at home and abroad or that (a + n)σ = (a∗ + n∗ )σ∗ ; if ß = ß∗ and σ = σ∗ the growth rate of the population in the home country must exceed that of the foreign country by exactly the difference in the progress rate in favor of the foreign country. Let us finally take a look at the basic form of the quantity theory of money, namely that MV(Y,i) = PY; we denote with g growth rates and with Ex,z the elasticity of X with respect to Z. Thus we have: gM + EV,Y gY + EV,i gi = gP + gY

(A.10n)

Therefore it follows (without loss of the validity of the basic argument) under the simplifying assumption ß = 1 – ß (and taking into account that r = ßY/K) the following equation: gM = gP +(1 − EV,Y )[ßgKAL ] − EV,i (ß − 1)g(KAL)

(A.10o)

If the price level is to remain constant and hence gP = 0 the central bank must adopt a growth rate of the money supply which is equal to: gM = (1 − EV,Y )[ßgKAL ]+EV,i (ß − 1)g(KAL)

(A.10p)

A.7 Technological Progress and the Long-run Price Level

43

The third term on the right-hand side of the equation has not been considered in standard analysis, rather one has implicitly considered the term through the interest rate. For long-term analysis in open monetary economies it can be quite useful to adequately combine the real sphere and the monetary sphere. Even if short-term dynamics in some markets diverge from the long-run equilibrium pattern (e.g., the case of Dornbusch overshooting in the exchange rate) one should study the long-term equilibrium solution since that solution should guide expectations of rational actors in an economy in which one finds global stability (as regards the latter one always has to analyze the dynamics before one can consider long-run equilibrium solutions as meaningful; provided that the adjustment process is stable). The income elasticity of the real demand for money can change over time and might be related to both per capita income development and financial market innovations. Actually, we do not know very much about the determinants of the income elasticity of the demand for money. Transaction technologies clearly play a role but so do other factors.

A.7.3 Conclusions for Analysis of Process Innovations in a Monetary Economy Process innovations are a standard phenomenon of the economic analysis. In a monetary economy one can, however, not neglect the impact of the money market on the price level. Since process innovations not only affect real output but also the marginal product of capital and therefore the real interest, one has a principal ambiguity with respect to the impact of technology on the price level. There is a critical size of the income elasticity below which a rise of the level of technology implies a rise of the price level; with an elasticity above the critical value, process innovations will bring about a fall of the price level. The impact of technology on the price level in turn will have an impact on capital flows since a change of the real interest rate is part of interest parity. Our analysis suggests that analyzing technological progress requires combining an analysis of the real sphere and of the monetary sphere of the economy. As we have shown, monetary policy could avoid inflation by an adequate choice of the growth rate of the money supply.

A.7.4 Solow Model and Role of Money for Growth As regards growth dynamics in a broader sense, one may focus mainly on macroeconomic aspects or on the topic of the underlying structural change—with respect to the latter see BORBÉLY (2006) who presents for the case of Eastern Europe and EU eastern enlargement an innovative empirical analysis for explaining the dynamics of structural change, export specialization and export unit value dynamics for various sectors, including labor-intensive sectors and technology-intensive sectors. The

44

Innovations in Macroeconomics

macroeconomic analysis which is presented here is more mainstream and an analysis of structural change in open economies. However, it also is complex and it can be quite useful—as is argued here—in combining standard elements of traditional and modern growth analysis with some new thoughts about linking the real sphere of the economy and the monetary sphere. Moreover, in some fields macroeconomic analysis and the analysis of structural change can be combined fruitfully. The Solow growth model is a very useful starting point for the analysis of economic growth, and it can be refined in many interesting ways. It determines the long-run capital intensity k# (k := K/L where K is capital and L is labor) and—in the context of technological progress—of k (k := K/(AL)) through combining a production function and an equilibrium condition for the goods market. For the sake of simplicity, our analysis will at first consider the rather simple case of a Cobb–Douglas production function Y = K ß (AL)1−ß where ß (0 < ß < 1) is the output elasticity of capital, Y is output and A is the level of labor-saving technology. As regards the level of technology, we assume that A(t) = A0 eat ; a is the exogenous progress rate and A0 the initial level of technology. The basic Cobb Douglas function makes the following generalizations rather tractable. We are interested in discussing several generalizations which mainly refer to the savings function and the production function. As a point of reference we assume—as in the original Solow model—that savings S is proportionate to real income Y so that S = sY; the population is L = Lo ent (n is the growth rate of the population). Imposing the equilibrium condition dK/dt = S (and hence [dK/dt]/[AL] = S/[AL]) and taking into account the definition of k , we get the fundamental differential equation: dk  /dt = sy −(n + a)k  = sk  − (n + a)k ß

(a0)

This is a stable Bernoulli differential equation (See Appendix G 4) whose general solution is k  (t)=[C0 e

−(n+a)(1−ß)t

+(s/(a + n))]1/(1−ß)

(a1)

The initial conditions determine C0 . As long as the sum of the growth rate of the population and of the level of technology—that is (n + a)—is not negative the economy will converge to the steady-state value k # =[s/(a + n)]1/(1−ß) and as y = kß we get for the steady-state per capita income: y# = [s/(a + n)]ß/(1−ß) A0 e

at

(a2)

This equation is our basic point of reference. It says that the steady-state level of per capita income is a positive function of the savings rate s and a negative function of the progress rate a and the growth rate of the population n. The initial level of technology affects the level of per capita output. The long-run growth rate is exogenous and is equal to a. Once the steady-state capital intensity k# is achieved, output per capita y will grow at the constant rate a. Starting at k0 , the economy will experience a transitory economic catching-up process characterized by the growth

A.7 Technological Progress and the Long-run Price Level

45

Fig. 11 Standard neoclassical growth model and adjustment path

y′=k′ß (n+a)k′ sy′

dk′/dt

0 k′0

0

k′#

k′

0 lny0 t α

tgα = a

lny

of k over time (dk /dt > 0). The following figure shows the determination of the steady state through the intersection of the (n + a)k line with the sy line. Thus, we basically have a representation of the fundamental differential equation. We also can see the adjustment path in the sense of dk /dt, and we see—assuming that in t0 we have k = k 0 —the adjustment path of lny (y := Y/L). Where does the temporary growth rate of k —and hence of y —reach a maximum? In the fundamental differential equation, we take the derivative with respect to k and set the result equal to zero (remember that dln(k )/dt := [dk /dt]/k ). Therefore dln(k  )/dt = ßsk 

ß−1

− (n + a)

(a3)

This implies a maximum growth rate dln(k )/dt at the value: k

max

= (ßs/(a + n))1/(1−ß) = ß1/(1−ß) k  #

(a4)

The maximum growth is a positive function of ß (obviously taking logarithms gives ln kmax = (1/(1 − ß))(ln[ßs] − ln[a + n]). If we compare two countries (foreign variables are stared) it is clear that in a world economy with capital depreciation—the depreciation rate is δ in country I and δ∗ in country II—the relative per capita income position in the long run will be given (assuming ß = ß∗ ) by y/y∗ = [(s/s∗ )(a∗ + n∗ + δ∗ )/(a + n + δ)(A0 /A0 ∗ )]e

(a−a∗ )t

(a5)

46

Innovations in Macroeconomics

The term in square brackets determines the relative level of the growth path of the domestic economy. As long as the progress rates a and a∗ are exogenous, it is not possible to really discuss options for growth policies. If one further assumes that the income tax rate τ as well as the unemployment rate u negatively affect savings so that the savings function is S = sZ (1 – τ)(1 – u)Y in country I and in a similar formulation S∗ = s∗ Z∗ (1 – τ∗ )(1 – u∗ ) Y∗ , we can modify the equation for relative income and obtain—after including the institutional variable Z : y#/y∗ # = {(sZ (1 − τ)(1 − u)/Z∗ [s∗ (1 − τ∗ )(1 − u∗ )]) · (a ∗ + n∗ + δ∗ )  (a−a∗)t /(a + n + δ)(A0 /A0∗ ) e (a6) The main reason to assume that savings is negatively influenced by the unemployment rate is the fact that unemployed workers do not save, and indeed they often dissave for a certain time period. Economic catching-up in the sense of narrowing the gap with respect to the level of the growth path of country II can now be achieved through various instruments—as viewed from country I: • an improvement of the institutional setup (Z ); • a rise of the savings rate (s); this is in well-known contrast to the message of the standard short-term Keynesian/Mundell–Fleming model according to which a rise of the savings rate will reduce equilibrium income; • a fall of the tax rate (τ); • reduction of the unemployment rate (u); • fall of the population growth rate (n); • fall of the depreciation rate (δ); one should note that economic opening up of a country will bring about a once-and-for-all rise of the depreciation rate, as many firms will experience obsolescence of the capital stock once the economy is opened up to the world market. Hence, economic opening up might bring about a fall of the level of the growth path unless economic opening up helps to upgrade the institutional setup factor Z sufficiently. If the government’s planning horizon is short enough, a fall in the progress rate might be desirable since this will raise the level of the growth path in the short run while reducing the permanent growth rate in the long run. In an open economy, there are further long-run constraints to be observed. In an open economy setting—for simplicity considered under the constraint that there is no government budget disequilibrium, no unemployment, zero inflation, a zero current account and no capital flows—the implication clearly is that a poor country can catch up only if the parameters change in the long run in such a way that the same or at least a similar level of y is achieved as abroad (y∗ ); and international economic convergence requires that the growth rate of technological progress of the initially poor country converge to that of the rich country. Hence if s = s∗ , a = a∗ , n = n∗ and ß = ß∗ —which is in line with the Heckscher–Ohlin assumption that technology is the same in country I (home country) and country II—both countries will converge towards the same long run per capita income, despite all initial differences in the initial per capita income positions.

A.7 Technological Progress and the Long-run Price Level

47

A growth model which fits reality in a world economy with many different countries will naturally consider the empirically well established fact that very poor countries have a very small savings rate while countries with a medium per capita income (among the OECD countries) have a relatively higher savings rate. However, rather rich countries have a relatively low savings rate. We will suggest a rather simple way to deal with different savings rates in the course of economic catching-up. How can we cover this phenomenon? We simply may assume a modified simple savings function (with z denoting a positive parameter in the interval [0, 1]), namely S = s(1 + z dk  /dt)Y

(a7)

Alternatively, one can write S/[AL] = s(1 + z dk /dt)y . A key argument why the savings rate should increase during a rise in k is the fact that a rise in the ratio of capital to labor in efficiency units (AL) generates a desire of private households and entrepreneurial households to benefit from an expected increase in output growth related to positive external output effects of investment; the latter might be related to learning-by-doing effects. The modified fundamental differential equation therefore is dk  /dt = s(1 + z dk  /dt)k  − (n + a)k 

(a8)

(1 − z k  )dk  /dt = sk  − (n + a)k 

(a9)

ß

ß

ß

It is easy to see that the steady-state solution for k # is the same as in the above basic model (note that we assume z k ß  = 1). However, the adjustment speed towards the steady state is now different. Empirical research should tell whether or not the approach suggested is useful. If country I (the relatively poor home economy) were to achieve in the long run the same per capita income as the rich foreign country II, a double convergence is required in the neoclassical growth model (for simplicity we assume zero population growth in both countries). The savings rate—effectively the investment output ratio—must converge to that of the foreign country, and the progress rate would have to be the same as abroad. Referring to the standard SOLOW model, one must therefore assume a mechanism which is reflected in a suitable equation such as (with z standing for a positive parameter in the interval [0, 1])  −1

ds/dt = (s/s∗ )(s∗ 2 sz



− s∗ 1−z )

(a10)

This differential equation basically consists of the first term (s/s∗ ) and a second term on the right hand side, which will bring about s = s∗ in the long term. As regards the savings income ratio, sound financial institutions—ultimately reflected in a relatively high level of real money balances per capita—may be expected to play an important role. If people have no confidence in the banking sector, the savings rate will naturally remain low. We emphasize here that the picture will have to be modified if we take into account FDI which requires making a distinction between gross domestic product and gross national product. One will have to raise—mostly

48

Innovations in Macroeconomics

ignored in the literature—the topic of how the savings function in the source country and the home country is to be modified adequately in a world with foreign direct investment. For the moment, we will disregard the foreign investment issue. Turning to the above differential equation, it is rather unclear which forces will bring about such an international convergence of the savings rates. If one takes into account the possibility of permanent government deficits or surpluses, one may point to the role of government in the convergence of savings ratios. However, in few poor countries is the government known to maintain long-term budget surpluses. Instead of looking for budget surpluses in poor countries, we may instead point out the role of permanent positive deficit-GDP ratios in rich countries which could contribute to international convergence of the savings rate. Growth and the Role of Real Money Balances Another element of generalization in the Solow model refers to the specification of the savings function in the sense that one might want to consider S/(AL) = sy . Moreover, we may consider the role of real money balances m (m is the ratio of the nominal stock of money M to the price level P) for savings and consumption, respectively. We assume that the higher m/(AL), the higher the desired savings, which effectively amounts to saying that a higher stock of m := m/(AL) will go along with a higher real capital stock relative to AL. We thus assume the parameter  to be positive ( is also assumed to be positive; in the Solow model it is zero). We therefore can specify: 

S/(AL) = sy m



(a11)

We thus assume that savings per efficiency unity of labor has a positive effect on (relative) real income and (relative) real money balances. Now let us assume—with i denoting the nominal interest rate; σ and σ are positive parameters—that the real demand for money is given by σ

md /AL = y σ /i

(a12)

With m/AL denoted as m , we can express money market equilibrium therefore as σ

m = y σ /i

(a13)

We insert this equilibrium condition in the savings function and obtain: 

S/(AL) = sy y

 σ



(σ /i)

(a14)

If we assume profit maximization (real interest rate r = ßy /k  = ßk  ß−1 ) and zero inflation and hence i = r, we obtain S/(AL) = sk 

 ß+ ß

(σ /ß)

 σ

; ß := [1 + ß(σ − 1)]

(a15)

A.7 Technological Progress and the Long-run Price Level

49

The fundamental differential equation for k therefore reads: dk /dt = sk 

 ß+ ß

(σ /ß)

 σ

− (n + a)k 

(a16)

This equation—with C0 to be determined by the initial condition k(0) = k0 —has the solution k  (t) = [C0 e

−(n+a)(1− ß− β )t





+ s(σ /ß) /(a + n)]1/(1− ß−

 

β )

(a17)

Assuming that n + a exceeds zero, this equation is stable if 1 −  ß −  ß > 0;  > 1 is a necessary condition that the transitory growth rate of this monetary Solow model exceeds that of the original model. Whether this condition is fulfilled is an empirical question. Assuming the condition to hold, the steady-state value for k is: 



 β )

k  # = [s(σ /ß) /(a + n)]1/(1− ß−

(a18)

If σ > β and  > 1 the steady-state capital intensity in a monetary economy will exceed that of a non monetary economy. As regards the empirical evidence on  the reader is referred to the final chapter. Taking into account the modified savings function, the money market condition and profit maximization thus implies the following: The long-run equilibrium ratio of capital to labor in efficiency units • • • •

positively on the savings rate and negatively on a and n (the standard results); positively on the interest responsiveness of the demand for money (σ ); positively on the elasticity of savings with respect to real money balances ( ); negatively on the income elasticity of the demand for money ( ) if s > σ /ß which points to an interesting empirical question.

A similar reasoning holds with respect to the steady-state value of y . In addition, we can add the traditional result that the level of output relative to labor input in efficiency units is a positive function of ß. However, the exponent for y looks a bit more complex than is traditionally the case; here it is ß/(1 −  ß −  β ) which is identical with the traditional result ß/1−ß if the income elasticity of savings is unity and  = 0. If the exponent ß/(1 −  ß −  ß ) is equal to or greater than ß/(1 −ß), we may assume that the introduction of a monetary economy brings about a higher  capital intensity k than the non-monetary SOLOW model, provided that (σ /ß) exceeds unity. A final remark shall refer to the progress rate. This rate can be endogenized in principle, but it also could be considered as shaped by stable cyclical impulses. For example, we may assume that a(t) = a0 + a1 sin(t) (a0 and a1 are positive parameters). In this case, however, the solution of the fundamental differential equation looks somewhat different as the progress rate a is no longer a constant parameter. At the bottom line, one may consider the possibility that long-term technology cycles overlap with short-term cyclical forces. The latter could include variations of the supply elasticity of input factors.

50

Innovations in Macroeconomics

Money as a Positive External Effect in the Production Function Another way to integrate the analysis of inflation in a long-run growth model is to assume that real money balances enter the production function in the form of a positive external effect. The fact that households hold money and use it in market transactions saves information and transaction costs not only for households but also for firms selling in such markets. Assuming an output elasticity of real money balances of ß , the production function may therefore be written as ß

y = m  k 

ß

(a19)

The savings function S = sY then leads to the fundamental differential equation ß

dk  /dt = sm k  − (n + a)k  ß

(a20)

Obviously the variable m , which can be considered a policy variable in an open economy with flexible exchange rates, must not be ignored for determining the level of the growth path. The steady-state solution for the capital stock relative to labor in efficiency units is: ß

k# = [sm  /(n + a)]1/(1−ß)

(a21)

Again we could integrate the condition for money market equilibrium. In the production function, we have to replace m by yσ (σ /i); y = y

σß

ß

(σ /i) k 

ß

(a22)

This implies ß /(1−σß )  ß/(1−σß )

y = (σ /i)

k

(a23)

If we assume a relatively high inflation rate π we can replace i with π#, which should be interpreted as the target inflation rate of the central bank. Interestingly, the apparent output elasticity of the capital stock is now lower than in a pure nonmonetary growth model (we assume 0 < σß < 1). By contrast, if we assume that the central bank’s inflation target rate is zero, the nominal interest rate can be set equal to the real interest rate r. Now let us assume that firms are profit maximizers, so that 1/r = (1/ß )k  1−ß . We obtain β /(1−σβ )  β /(1−σβ )+(1−β )β /(1−σβ )

y = (σ /β )

k

(a24)

We now have an apparent output elasticity of the capital stock in which the output elasticity of k is determined by two elements: the elasticity of money balances m and the income elasticity of the demand for money. With a standard savings function S = sY, we now get the fundamental differential equation 



dk/dt = s(σ /β )β /(1−σβ ) k 

β /(1−σβ )+(1−β )β /(1−σβ )

− (n + a)k 

(a25)

A.7 Technological Progress and the Long-run Price Level

51

This looks rather similar to the above case of a modified savings function—which includes a real balances effect—in combination with a production function which does not contain real money balances. Thus we have two good arguments to consider the role of real money balances in a long-run growth analysis. The steady-state solution is given by k  # = {[s/(n + a)](σ /β )

β /(1−σβ ) 1/(β (1−σβ ))

}

(a26)

The impact of money on the capital intensity is ambiguous. Money, Transfers, Growth and Real Income If one follows the basic TOBIN approach to monetary growth—we will recall this model in detail subsequently—who has argued that seigniorage should be taken into account in the government budget, one should expect the paradox result that equilibrium capital intensity and per capita output in long-run equilibrium are smaller in a monetary growth model than in the traditional SOLOW model. However, we will show that under plausible assumptions—referring indeed to the core of defining a monetary economy (the production function)—we will not get TOBIN’s result that introducing money in a neoclassical growth model will bring about a fall in both equilibrium capital intensity and per capita income y := Y/L (L is population or labor). Consider that the government budget equation (γ − τ)Y = (dM/dt)/P can be written (with M nominal money stock, P price level, m := ratio of real money balances m to L; γ is government transfers relative to GDP, τ is the income tax rate and μ is the growth rate of money) as (γ − τ)y = μm

(i)

(γ − τ)y  = μm

(ii)

or (with m := m/[AL])

Hence, the income elasticity of money is unity; σ is a parameter indicating the interest responsiveness of the demand for money and i is the nominal interest rate. As regards the production function, we assume that real money balances m raise the productivity of firms so that we have a production function (with y := Y/AL; k = K/AL and ß and ß standing for positive elasticities): y = k  m  ß

ß

(iii)

The goods market equilibrium condition in a closed economy (with G denoting government expenditures as well as transfers, T real tax revenue) is given by S + (T − G) = dK/dt + δK. Thus we get dk  /dt = s[y (1 − τ) + μm  ] − μm − (n + δ + a)k 

(iv)

52

Innovations in Macroeconomics

Taking into account money market equilibrium (where i is the nominal interest rate and σ a positive parameter indicating the responsiveness of the demand for money with respect to i), namely m = y σ /i

(v)

dk  /dt = s[y  (1 − τ)] + (s − 1)μy σ /i − (n + δ + a)k 

(v )

leads to the equation:

Setting dk /dt = 0, we get the equilibrium value for k : β

k  # = {sm [(1 − τ) − μσ (1 − s)/i]/(n + δ + a)}1/(1−ß)

(v )

Here were have the TOBIN result that the steady-state capital intensity in a monetary economy could be lower than in a non-monetary economy, however, per capita income could be higher according to our production function. Indeed, the steady-state income Y/[AL] =: y is given by: β

y # = {sm [(1 − τ) − μσ (1 − s)/i]/(n + δ + a)}ß/(1−ß) m

ß

(vi)

We can rewrite the equation as y

#(1−ß)/ß

= {s[(1 − τ) − μσ (1 − s)/i]/(n + δ + a)} m

ß /(1−β)

(vii)

Necessary conditions for y in a monetary economy to exceed y in a non-monetary  economy are that (1 − τ) > μσ (1 − s)/i and mß /(1−β) > 1. We use the approximation that ln(1 + z) ≈ z, which holds if z is close to zero. Taking logarithms thus gives (1 − ß)/ß lny = ß (1 − ß) ln(m ) + lns − τ − μσ (1 − s)/i − ln(n + δ + a) (viii) It is obvious that in a monetary economy, y in the steady state is higher than in a non-monetary economy if ß /(1 − ß) ln m  > μσ (1 − s)/i

(ix)

m  > exp((1 − ß)μσ (1 − s)/(iß ))

(x)

that is if

It is quite plausible that the introduction of money should raise the level of the growth path; otherwise evolutionary dynamics with open economies would not allow monetary economies to survive (moreover, standard microeconomic analysis suggests productivity-enhancing effects of using money in a market economy). Alternatively, one could argue that money makes the economy more effective in absorbing shocks at relatively low costs. Besides an impact of m  —and the inflation rate—on the level

A.7 Technological Progress and the Long-run Price Level

53

of the growth path, one should in principle also consider the effect of money on the progress rate; that is one should consider monetary endogenous growth models (For a specific approach in a quite different context see GRIES/SIEVERT/WIENEKE 2004). Note that if there is to be zero inflation, we must have the growth rate of the money supply μ = a + n so that the growth rate of the money supply is quasi-endogenous. We thus have an empirical question which refers to the relative size of ß , s and τ where government has a choice of τ. Moreover, we have an interesting set of empirical issues. The more general question of monetary growth modeling refers to a situation with inflation—so that the inflation rate π > 0 and μ = a + n + π. Imposing the  condition of profit maximization requires that the real interest rate is r = ßk  ß−1 mß . This aspect might be an additional element of analysis. The more interesting question concerns the impact of the inflation rate on the progress rate. Denoting the undistorted progress rate as a0 , we can write a = a0 − a1 π if we state the hypothesis that inflation diverts management’s attention from the innovation process so that the progress rate is dampened by inflation. The impact of the inflation rate on the progress rate will dominate the impact of inflation on the level of the growth path in the long run. To the extent that inflation raises the level of the growth path in the short run, thereby reducing the progress rate, a short-sighted government will have a political preference in favor of inflation.

A.7.5 Monetary Growth Model and Tobin Paradox The Solow growth model was modified by TOBIN (1965) in a way which allowed including money in a growth perspective which also is part of the debate about superneutrality of money. While the idea of the classics that money is neutral for the real economy has been discussed under the heading of neutrality the term superneutrality refers to the question whether a positive or negative growth rate of the nominal money supply will affect real variables. In the model of TOBIN (1965) the main result of introducing money in a growth model is a reduction of the per capita capital intensity (k) and hence of per capita output (y) in the steady state. Moreover, a rise of the growth rate of the money supply was found to raise the inflation rate but also to possibly raise the level of the growth path in a simple model with an exogenous growth rate (n) of the population L. In such a model the long-run growth rate of output is exogenous, namely n. Government can, however, affect the steady-state value (denoted by #) of the capital intensity k = K/L (K is the capital stock) and hence the growth rate of output Y; in the simplest case output is described by a neoclassical production function Y(K, L). In summarizing the TOBIN approach in a simple way we partly follow REITHER (1989). Money is introduced through the government budget constraint since the supply of money generates “seigniorage revenues” which consist of the real value of a rise of the nominal money supply. In an equilibrium approach one has to take into account that the nominal money supply M will have to be equal to the nominal

54

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money demand Md = Pmd where P is the price level and md the real demand for money which positively depends on Y and negatively on the nominal interest rate i. The formal setup is as follows; first we consider the government budget constraint where G is real consumption of government, T real tax revenue and H real transfers. (dM/dt)/P = G − T + H

(1)

We define h as transfers per capita (L) so that H = h L which allows to write—with μ as growth rate of the nominal money supply M, m = (M/P)/L and the definition of the government budget deficit ratio [G – T]/Y =: γ —the budget constraint in per capita terms as: μ m = γ y + h

(2)

We assume a per capita savings function (with z denoting disposable per capita income and s a parameter in the interval [0, 1]), namely that savings S relative to L is given by: S/L = sz

(3)

The disposable income is (with τ denoting the income tax rate): z = (1 − τ)y(k) + h

(4)

Equilibrium in the goods market requires that the gross per capita savings S/L finance both per capita investment and the government deficit: s[(1 − τ)y(k) + h ] = [dK/dt]/L + γ y(k) + h

(5)

If we assume that reinvestment is δK and that the growth rate of the population is n we get the following implicit expression for the steady-state value of the capital intensity (k#): {s[1 − τ] − γ }y(k# ) = (n + δ)k# + (1 − s)h

(6)

With a standard Cobb–Douglas production function y = kß we get in the steady state: {s[1 − τ] − γ }k ß = (n + δ)k + (1 − s)h

(7)

The left-hand side of the equation is portrayed as LHS in the subsequent graph, the right-hand side as RHS. TOBIN (1965) assumes that the structural deficit ratio is zero so that h = μm . We can conclude from the graphical analysis that h > 0 shifts the right-hand side curve upward (RHS1 instead of RHS0 ) so that k#0 falls to k#1 . This is obvious since government must finance h while savings per capita is raised only by sh so that the equilibrium capital intensity is reduced. If we had a structural deficit the LHS curve rotates downwards so that the intersection point shifts to the left: k# falls. If one assumes a positive growth rate of the money supply there could be inflation; the inflation rate is π = μ – n (in an economy

A.7 Technological Progress and the Long-run Price Level Fig. 12 Government activity in the TOBIN monetary growth model

55

LHS RHS1

RHS

RHS0

LHS0

LHS1

h′′

n+δ k#2

k#1

k#0

k

with technological progress rate a the steady-state (long-run) inflation rate is given by π = μ − [a + n]). Disregarding technological progress we can state: Printing money generates a “growth seigniorage revenue” nm and an inflation tax πm. As the money supply growth rate μ = π + n in the steady state we can write: h = [π# + n]m #

(8)

If we require a zero structural budget deficit we get the steady-state equilibrium condition: s[1 − τ]y(k) − (1 − s)nm # = (n + δ)k# + (1 − s)π#m #

(9)

With inflation we have to consider the impact of the inflation rate on the inflation tax—here we have to take into account money market equilibrium, too. That is real money supply per capita (M/P)/L must equal real money demand per capita md (r + π, y) which one may specify for the sake of simplicity as yσ σ /[r + π]. A rise of the inflation rate will reduce the per capita money supply so that the value of the starting point of LHS on the ordinate is shrinking. The effect is a rise of the

LHS

E1

RHS

RHS0 LHS1 LHS0

E0 (1-s) π#m′′# (1-s) π#m

′′#

1 Fig. 13 Money supply # ′′# m (1-s) π dynamics and the capital 0 intensity in the TOBIN model

k#0

k#1

k

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steady-state capital intensity: Higher inflation brings a rise from k#0 to k#1 (TOBIN effect). However, the growth seigniorage revenue effect is not the only effect to be considered. Depending on the interest elasticity of the demand for money we could get a rise of π#m#, no change in inflation tax or a fall of π#m#. The latter case could lead to superneutrality of money which means that inflation would not affect the capital intensity. Taking into account process innovations we will have to reconsider the results presented. The crucial question is whether and to which extent inflation negatively affects the progress rate. Since inflation is known to reduce the average maturity of bonds one may argue that inflation generally reduces the decision horizon of economic agents. Innovation projects which generate a high social rate of return in the long run could not be realized in an inflationary environment; at least not if the growth rate of the price level is beyond a critical inflation rate (π #).

A.7.6 Technological Progress Cycles Let us briefly consider the logic of progress cycles in the neoclassical growth model. If we assume that savings S = s(1 − τ)(1 − u)Y where the income tax rate is τ and the unemployment rate is u, we get a simple steady-state condition for per capita income y =Y/[AL]—that is output per efficiency units of labor. Note that the savings function presented assumes that savings is reduced by unemployment. Output Y is determined by a production function Y = Kß (AL)1−ß —with 0 < ß < 1. At first the progress rate is exogenous in the sense that dlnA/dt =: a; the growth rate of the population is given by the parameter n (n = dlnL/dt). The unemployment rate is considered exogenous. In the case of a balanced government budget, the goods market equilibrium condition in a closed economy is given (with δ standing for the rate of capital depreciation) by S = dK/dt + δK

(Ia)

We thus can state—with k := K/[AL]—the differential equation for k : dk /dt = s(1 − τ)(1 − u)k  − (n + a + δ)k  ß

(Ib)

Solving this Bernoulli differential equation or simply setting dk /dt = 0, we get the steady state (symbolized by #) for k , namely: k # = {s(1 − τ)(1 − u)/(n + a + δ)}1/(1 − ß)

(Ic)

Thus y # is given by: y # = {s(1 − τ)(1 − u)/(n + a + δ)}ß/(1−ß)

(Id)

Wíth e denoting the Euler number we get for y := K/L the result y# = A0 {s(1 − τ)(1 − u)/(n + a + δ)}1/(1−ß) e

at

(Ie)

A.7 Technological Progress and the Long-run Price Level Fig. 14 Shifts in the progress function over time

57

ln y

G

α

F

E C

B

0

α

D

t1

t2

t3

t

Thus output per capita is given an expression where the level of the growth path is negatively affected by the progress rate a, while a affects the growth rate positively— indeed dlny/dt = a. This has a straightforward implication if we assume that there is a long-term normal progress rate a# while a can rise in certain periods. If we assume that in t1 there is an increase in the progress rate, we will see a drop of the level of the growth path while the growth path itself becomes steeper (consider the reaction in stock markets: a fall of per capita income in t1 could be interpreted by chartists— people with extrapolative expectations—as a signal that there will be a slowdown of the economy, but the opposite is true and after some time chartists will start noticing this favorable development, possibly after output per capita has increased after t2 beyond the natural growth path). What happens if the progress rate falls back in t3 to the normal level? The level of the growth path will rise and the growth rate will also be reduced. (Consider the potential incipient reaction in stock markets where market participants might anticipate that the one-off increase in output per capita is a signal for accelerated long-run growth while in reality the growth rate has decreased.)

Semi-endogenous Progress We can focus next on a semi-endogenized progress rate and thus consider aspects of population growth and the unemployment rate and hence implicitly of labor market dynamics. Let us assume that we have a progress function a = a# + a1 n − a2 u

(If)

We thus assume the progress rate to positively depend on the growth rate of the population—hence a shrinking population brings a lower progress rate (which could be a major future problem of OECD countries)—and negatively on the unemployment rate. An argument for the latter is the common observation that workers in high unemployment countries are often resistant to outsourcing and rationalization

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investment so that technological progress is slowed down, obviously the result of workers’ fears to be laid off during periods with a high progress rate. With countries such as Germany, Italy and France—as core countries of the Euro zone—facing a fall in population growth and even a negative long run n in combination with a high structural unemployment rate, the result will be a fall in the long-run progress rate and hence in the trend growth rate. If a progress function with a negative impact of the unemployment rate exists, restoring full employment is enormously important since this will raise both the level of the growth path and increase the steady-state growth rate itself.

A.7.7 Equilibrium and Terms of Trade Aspects in a Simple Open-economy Growth Model In an open economy—without foreign direct investment/capital flows—an adequately specified growth model should take into account the fact that products exported become more sophisticated as capital intensity (capital K relative to labor in efficiency units AL) k := K/[AL] rises. Assuming that more sophisticated products will fetch higher prices in world markets, we have to take into account a long-term terms of trade effect, where the real exchange rate eP∗ /P =: q∗ so that—with the assumption for the parameters α > 0 and 0 < α ≤ 1—we specify: dq∗ /dt = dk  /dt α k 

−α

(I)

An investment boom goes along with a real depreciation, and the effect is stronger the lower capital intensity is. By integration we obtain (with C as a constant to be determined from initial conditions) the equation: q∗ (t) = [α/(1 − α )]k 

−α +1

+ C

(II)

For simplicity we assume a balanced government budget and that neither exports X nor imports J depend on q∗ . The result presented is rather robust as we shall subsequently see. The goods market equilibrium condition requires that savings be equal to the sum of gross investment and net exports of goods and services. The quantity imported (J) has to be multiplied by q∗ in order to express imports in units of domestic output. S = dK/dt + δK + [X − q∗ J]

(III)

If we assume—with τ defined as the income tax rate—that imports J = jY (hence J/AL = jy ), exports X = xY (hence X/AL = x y ), savings S = sY[1 − τ], a constant growth rate of progress a (a := dlnA/dt), a constant growth rate of the labor force n (n := dlnL/dt) and output Y = Kß (AL)1−ß —with 0 < ß < 1—we derive from the

A.7 Technological Progress and the Long-run Price Level

59

goods market equilibrium condition a differential equation in which we have inserted  q∗ (t) = [α/(1 − α )]k  −α +1 + C : dk  /dt = s(1 − τ)k  + C jk  − x k  − (n + δ + a)k  + jα/(1 − α )k  ß

ß

ß

ß−α +1

(IV) Assuming that this equation is stable, we get the steady-state solution by setting dk /dt = 0. This equation cannot be solved analytically unless we make two assumptions,  namely that 2(s(1 – τ) + C j − x )1/2 (jα/(1 − α ))(ß−α +1)/2 = (n + δ + a) and that  we have (1 − α + 2ß)/2 = 1—this implies ß > 0.5. In this case, we can express the condition that dk /dt = 0 as a quadratic equation: 0 = [(s(1 − τ) + C j − x )

1/2

k

ß/2

− (jα)/(1 − α )1/2 k 

(ß−α +1)/2 2

]

(V)

We thus get the steady-state solution as 

k  # = {(s(1 − τ) + C j − x)/[(jα)/(1 − α )]}1/(1−α )

(VI)

The stronger the terms of trade improve (see the parameter α ) as a consequence of a rising k —the higher the fall of q∗ as a consequence of a higher capital intensity— the higher the steady-state capital intensity. Note that this implication is based on inspection of the exponent 1/(1 – α ). We can thus argue that the stronger the impact of capital accumulation on the terms of trade, the higher the steady-state capital intensity and hence the level of the long-run growth path. In this context, the remarkable improvement of the US price of industrial products in the 1990s—relative to Germany—is crucial. A sustained improvement of the terms of trade has contributed to a series of rises in the level of the growth path. The growth rate of both per capita output y =Y/L and capital intensity k = K/L might be considered as exogenous. What looks like a rise in the US trend growth rate could thus in fact represent a combination of an increased trend growth rate and several increases in the level of the growth path associated with an improvement in the US terms of trade.

A.7.8 International Macroeconomics, FDI and Fiscal and Monetary Policy A considerable part of modern macroeconomics is devoted to the question of how to optimally stabilize an open economy. The standard result in a Mundell–Fleming model with perfect capital mobility is that monetary policy is ineffective under fixed exchange rates since an expansionary monetary policy will reduce the nominal interest in the short term, leading to massive capital outflows and an excess demand in the foreign exchange market. This excess demand forces the central bank to intervene and buy foreign exchange so that the domestic money supply will fall. In such a manner, monetary policy is not effective. By contrast, an expansionary fiscal policy

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is effective as the associated short-term rise in the interest rate brings about an excess supply in the foreign exchange market—related to rising capital inflows—so that an expansionary fiscal policy indirectly causes an expansionary monetary policy. Under floating exchange rates, the policy assessment is just the opposite. Monetary policy is effective, fiscal policy is not. Expansionary monetary policy causes a shortterm fall in the interest rate and hence a real depreciation which will stimulate net exports of goods and services (provided the Marshall Lerner condition is met). An expansionary fiscal policy will cause a real appreciation, thereby reducing net exports of goods and services so that the expansionary effect is dampened. Now let us include aspects of FDI where we focus on a small open economy which is a host country to FDI inflows but not a source country of FDI. If we integrate the argument of FROOT/STEIN (1991), namely that a real depreciation will cause higher FDI inflows—a rise of the real exchange rate q∗ := eP∗ /P will increase overall investment I and also net capital inflows Q—we have to modify the standard model slightly. Additionally, we assume that output (or GDP) is produced with a Cobb– Douglas function Y = Kß L1−ß so that capital income is ßY. Assuming the FDI capital stock to be a share b of the overall capital stock, K gross national income thus is Z = Y[1 – b(q∗ )ß]; the desired b is a positive function of q∗ , as a real depreciation will make it easier for foreign investors to acquire firms. We assume that consumption is proportionate to gross national income net of taxes (income tax is τ). The consumption function C = cY(1 − b(q∗ )ß)(1 − τ) so that we can write the consumption function as C(q∗ , Y, τ); ∂C /∂q∗ < 0. Overall investment I is composed of investment of domestic firms I(r) and FDI inflows I (q*). We thus have three medium-term conditions for the goods market (X is net exports), the money market—with m representing real money demand—and the foreign exchange market. Y = C(q∗ , Y, τ) + I (r) + I (q∗ ) + G + X (Y, Y∗ , q∗ ) (ISF curve) M/P = m(i, q∗ , Y)

LMF curve

Q(i/i∗ , q∗ ) = −X (Y, Y∗ , q∗ )

BBF curve

(1 ) (2 ) (3 )

If we set U = 1/D Where D is the system determinant: D = − P/P∗ ((1 − CY − XY )(Qe mi − Qi me ) + (Ce + Ie )(XY mi − Qi mY ) + Xe mi (1 − CY ) + Xe mY (Ir − Qi ) + Ir (Qe mY − XY me ))

(4 )

This expression has no unambiguous sign, but if we assume a negative sign we get the following results: dY/dG = −UP/P∗ (mi (Qe + Xe ) − me Qr )

(5 )

which is positive if X e < Qe . If we set mq∗ = (P∗ /P)me = 0, we get:

(6 )

A.7 Technological Progress and the Long-run Price Level

dY/dG = −UP/P∗ mi (Qe + X e )

61

(7 )

which will still be positive if X e < Qe dY/dM = U/P∗ (−Ir (Qe + X e ) + Qr /i∗ (Ce + Ie + X e ))

(8 )

which is negative if Xe < Qe and Xe < −Ie − Ce and positive if Xe > Qe ; and Xe > −Ie − Ce . If we set Cq∗ = (P∗ /P)Ce = 0, we get: dY/dM = U/P∗ (−Ir (Qe + X e ) + Qr /i∗ (Ie + X e ))

(9 )

which is positive if Xe > Qe . Note that we have assumed a real money demand function which negatively depends on the nominal interest rate i and positively on gross national income [Y(1 – b(q∗ )ß] so that we can write m(i, q∗ , Y); with ∂m/∂q∗ ≤ 0. For simplicity, we assume in the subsequent medium-term analysis that exchange rate expectations are static (otherwise such expectations would influence both FDI and net capital inflows). Under flexible exchange rates, an expansionary fiscal policy could now be even less expansionary in the medium term than in the traditional setup, since a real appreciation will reduce consumption through the fall in gross national income, as a higher share of firms is owned by foreign investors so that profit transfers flowing to the source country (II) increases. For a moment, let us disregard the impact of q∗ on I which basically means that all FDI is international mergers and acquisitions. If foreign investment were mainly greenfield investment, the implication is that ∂I/∂q∗ (denoted subsequently as Iq∗ ) is rather high so that a real depreciation will strongly influence investment demand—if ∂I/∂q∗ reaches a critical threshold, the net FDI effect on aggregate demand (the sum of the effect of FDI on consumption and investment) will be positive—this is the standard case assumed subsequently. As regards net capital inflows, we have to take into account that a rise in the interest rate stimulates portfolio capital inflows directly but will indirectly dampen FDI inflows. As such, taking into account FDI implies that the excess supply in the foreign exchange market stemming from expansionary fiscal policy is smaller than without FDI. The consequence is that expansionary fiscal policy will cause a smaller real appreciation than without FDI so that net exports of goods and services are dampened less than in the standard setup of the Mundell–Fleming model. If there is no shift in the money market equilibrium line, we can therefore state that an expansionary fiscal policy is less than expansionary in the presence of foreign investors if the combined effect on investment and consumption is not strongly negative. The presence of FDI dampens the traditionally negative indirect effect of expansionary fiscal policy on net exports. Moreover, we have assumed for simplicity’s sake that a real appreciation will not cause a leftward shift of the money market equilibrium line LMF. We may state that under certain conditions, expansionary fiscal policy is even less effective in a system of flexible exchange rates. The presence of foreign investors undermines the effectiveness of fiscal policy. There is also a serious caveat which

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concerns expected future tax rates. If one assumes that investment not only depends on the current income tax but on the future income tax rate as well, there could be a case in which expansionary fiscal policy causes such a high rise in mediumterm budget deficits that the expected future tax rate τ will increase (a problem not considered in further detail here). We have seen that foreign investment, including the ratio of greenfield investment to international mergers and acquisitions plays a crucial role for the effectiveness of fiscal policy. In a world economy in which FDI has become increasingly important, one should include FDI in a modified Mundell–Fleming model. Expansionary monetary policy will cause a real depreciation and hence increased net FDI inflows. Thus the relative advantage of monetary policy over fiscal policy in a system of flexible exchange rate might not really be affected by taking into account FDI within our asymmetric approach. In an explicit two-country model we could consider the simple case that investment in country 2 is given by I∗ (r, q∗ ) = I∗ (r∗ ) − I (q∗ ) so that foreign investment flows accruing to country 1 imply a fully offsetting reduction of investment in country 2. Depending on the type of FDI one could consider a partial offset coefficient, namely an investment function I∗ (r, q∗ ) = I∗ (r∗ ) – αI (q∗ ) where α is in the interval [0, 1]. If fiscal policy is less expansionary in the presence of FDI the political incentive for conducting expansionary fiscal policy is relatively weak. This could partially explain the success in the field of budget consolidation in countries with high cumulated FDI inflows.

Global Economy Perspective, FDI and International Policy Cooperation The only closed economy in reality is the world economy. Therefore it must hold that the fiscal multiplier for the world economy is the same for a consolidated model with FDI as in a consolidated model without FDI. By implication, the finding that fiscal policy is less expansionary in the presence of inward FDI suggests that the benefits from coordinated fiscal policies (in a two-country setting) must be higher in the presence of FDI than in a model without FDI. If the open economy shows that fiscal policy is more expansionary in the presence of FDI than without FDI, the implication is that coordinated fiscal policies should be relatively less effective than the fiscal policy of the open economy.

Foreign Direct investment and Optimum Currency Areas The role of FDI should be included in the analysis of optimum currency areas. Given that monetary union is a long-term venture, one should not so much focus on mediumterm analysis, rather growth analysis is the appropriate framework. The basic issue is to what extent FDI (net) inflows increase the level of the equilibrium growth path

A.7 Technological Progress and the Long-run Price Level

63

and whether FDI affects the trend of growth rate in an endogenous growth model. If one considers this problem, one would have to ask how savings S is affected in the presence of FDI and how in a model with a production function Y = Kß (AL)1−ß the growth rate of A (A is the level of technology) is affected by the presence of FDI. To the extent that FDI is associated with international technology transfer and that technology is a non-rival input in production functions, in a three-country model with countries I, II and III—possibly all countries being both a source country of FDI and an FDI host country—one will have to ask which combination of countries I/II or I/III or II/III or I/II/III is an optimum currency union. If countries form a monetary union along the lines of traditional optimum currency area literature (Mundell–McKinnon– Kenen approaches), where the monetary union then suffers from a reduced steadystate growth rate or a lower level of the growth path, this negative effect would have to be considered against the advantages in terms of stabilization policy. Key aspects of the TOBIN monetary growth model also would have to be included in a consistent analysis—basically the issue is to which extent alternative exchange rate regimes or various groupings of countries in a monetary union will go along with a higher or a lower steady state inflation rate. If policy makers in each country want to maximize per capita consumption and minimize the variance of consumption, one could combine aspects of optimum growth analysis with aspects of the traditional optimum currency area literature. If theoretical arguments or empirical findings should imply that a higher steady-state growth rate is associated with a higher variance of real per capita income development and consumption, one would have further interesting aspects to consider.

A.7.9 Long-run Phillips Curve in a Growing Economy There has been considerable debate about the link between the inflation rate π and the unemployment rate u. Most economists probably agree that in the short term there is a trade-off between unemployment and inflation. In the long run there is no trade-off since one may assume that the inflation rate is fully anticipated in the long run. In his Nobel lecture, Milton Friedman argued that the natural rate of unemployment is that long-run unemployment rate u# is determined by structural characteristics of labor markets and goods markets. He noted that the long run link between inflation and the unemployment rate could be positive. Here we want to add a straightforward aspect which is linked to the following question: How will long-run unemployment and the long-run inflation rate affect the output elasticity of capital? Put differently, we consider—with parameters ψ and ω —the following modified Cobb–Douglas production function: y = k 

ß(1+ω u)(1+ψ π)

(a26)

A priori we have no clear idea with respect to the impact of the unemployment rate and the inflation rate on the output elasticity of capital. If high unemployment

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Innovations in Macroeconomics

distorts the output responsiveness of the capital stocks (i.e., of firms) in the sense of reducing it, the output elasticity will fall—that is ω < 0. A similar reasoning holds with respect to the inflation rate. Obviously, one cannot rule out a priori that in a situation of unemployment and inflation the output elasticity is that same as in an economy with full employment and zero inflation. This could indeed be the case if the parameters ω and ψ were of opposing value. Taking logarithms yields ln y = ß(1 + ω u)(1 + ψ π) ln k 

(a27)

Taking logarithms again while assuming that ω u and ψ π are rather small in absolute terms—so that we can use the approximation ln(1+x) ≈ x—we get an equation which can be estimated: ln ln y = ln ß + ω u + ψ π + lnln k 

(a28)

In a long-term empirical analysis we should expect non-zero parameters for the impact of both the unemployment rate and of inflation. Such results imply a variable output elasticity of the capital stock variable. One perspective useful with respect to this equation is to ask for the implication of the steady state. This requires the interpretation of u as the natural rate of unemployment (u#) and π as the steady-state inflation target (π#) of the central bank. If the parameter signs for ω and ψ are equal, the result would be a negative slope of the long-run inflation rate. If these two parameters carry opposite values, there will be a long-run steady Phillips curve with a positive slope in the growing economy considered. In an open economy with flexible exchange rates we may consider both the natural unemployment rate and the inflation target as exogenous. We can now consider an additional aspect which implies a quasi-exogenous progress rate: Let us assume that the progress rate (a) is influenced by the inflation rate and the natural unemployment rate. One may assume that the impact of both variables on the progress rate is negative since a higher inflation rate implies that the management often will be absorbed with issues of optimally hedging against inflation risks. Moreover, workers in an economy with a relatively high long-run unemployment rate will put pressure on firms to slow down the adoption rate of new labor-saving technologies. Hence we state the hypothesis (with parameters ω , ψ ): A(t) = A0 e

a(1−ω u)(1−ψ π) t

(a29)

Therefore we have an equation which says that under zero inflation and zero unemployment, we get the traditional SOLOW assumption. Otherwise the progress rate in the presence of unemployment and inflation is lower. ln A(t) = ln A0 + {a(1 − ω u)(1 − ψ π)}t

(a30)

If we normalize ln A0 to unity we can write as an approximation (assuming {. . . } to be close to zero): ln lnA(t) = {a(1 − ω u)(1 − ψ π)}t.

(a31)

A.7 Technological Progress and the Long-run Price Level

65

Combining this hypothesis with the aforementioned idea, we can see that the unemployment rate can affect both the level of per capita income and the growth rate of per capita income. While the idea of suggesting that the output elasticity of capital intensity is not simply equal to ß might look strange at first glance, one should indeed consider this conjecture as a challenge for empirical analysis. Moreover, we will show in a somewhat different setup again that the basic idea can be expressed in a different way.

A.7.10 Variable Output Elasticity of Capital The standard Cobb–Douglas production function has several important implications, and in the case that one would like to diverge from one the implications—considered to be unrealistic—one has to modify the production function accordingly. A more complex production function might be more realistic but often makes the analysis more complex. Let us consider a rather simple suggestion, namely that at the aggregate level of the economy output elasticity of capital is not governed by a Cobb– Douglas production function (consider y = k ß ); the latter implies (dy/dk)(k/y) = ß, so that the average product of capital is proportionate to the marginal product of capital. Instead we will assume at the macroeconomic level that (k/y) (dy/dk) = ß + θk

(a32)

The parameter θ is assumed to be positive. Our assumption implies dy/dk + [−θ − [ß /k]]y = 0

(a33)

This is a linear-homogenous differential equation whose solution is (with C0 determined from the initial conditions): y(k) = C0 k ß e

−θk−ß /(k*k)−

(a34)

If θ is positive, we indeed have a modified case of ROMER (1986), where the output elasticity of capital at the aggregate level is higher than at the level of the individual firm (we may assume that from the individual perspective of the firm, output elasticity is ß). Obviously a large economy should find it easier to achieve a high per capita income level since there are quasi-economies of scale at the level of the economy. Now let us assume that inflation rate π negatively affects output elasticity, which we may express as: 

y(k) = C0 k ß eθk−θ π

(a35)

Per capita output indeed only depends on the capital intensity as becomes clear when we take into account a standard money market equilibrium condition. (For the sake of convenience, we use σ to denote the elasticity of per capita real money demand with

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Innovations in Macroeconomics

respect to per capita income; this should not be confused with σ, denoted previously as the symbol of the elasticity of m d with respect to y ). (M/P)/L = yσ σ /i

(a36)

Here σ is the income elasticity of money and σ a positive parameter which indicates the role of the interest rate as the opportunity cost of holding money. M is the nominal money supply, P is the price level and i the nominal interest rate. The real money balance will be denoted by m. To stay as simple as possible we will consider an economy with hyperinflation so that the real interest rate is neglected and i is set equal to the inflation rate π. We thus can rewrite money market equilibrium as: m/L = k ßσ σ /π

(a37)

Assuming for simplicity that ßσ = 1 and after replacing the inflation rate in the production function, we obtain: y(k) = C0 k ß e

θk−θ k(σ m/L)

(a38)

Indeed, per capita income only depends on the capital intensity; and on m/L which is considered to be a policy variable. It should be clear that we are not considering deflation here. An economy with deflation implies special problems which are not considered in this context. We also assume that the money market is stable as can easily be shown. Denoting the growth rate of a variable by g we see that gy = ßgk + k(θ − θ σ m/L)gk

(a39)

From this perspective, it is quite important to include the role of the money market in the analysis of economic growth.

A.8 Foreign Direct Investment and Innovation A.8.1 Innovation Dynamics and Multinational Companies The main long-term drivers of economic development are captured in the macroeconomic production function Y = Y(. . . ). Gross domestic product typically is considered to be function of capital services—assumed to be proportionate to the respective stock K—, labor input L (one may distinguish between unskilled labor L and skilled labor L ), technology A and some other input factors. The latter could include institutional aspects which indirectly refer to the fact that there is not only one firm producing but there are indeed many firms whose interaction is influenced by institutions which determine transaction costs and risks within the firm and in the market. Moreover, the institutional design also could affect the diffusion

A.8 Foreign Direct Investment and Innovation

67

of knowledge and the size of knowledge spillovers. Hence government is important, namely in the design of the economic system. Moreover, government also is involved directly and indirectly in the provision of infrastructure. The diffusion of knowledge will be influenced by the size of the telecommunications network—and relative telecommunications prices—and the intensity of communications. As regards the latter, an empirical investigation for the Federal Republic of Germany by WELFENS/JUNGMITTAG (1995, 2002) have shown that output can be explained by a production function with capital, labor, technology (patents plus imported licences) as well as the intensity of telecommunications where the latter stands for a diffusion variable. While it is true that there are many small innovative firms it is well established that large MNCs are the main drivers of technological progress in OECD countries. However, the number of MNCs is not constant, and the leading positions in the world economy are changing fast. In the 1950s and 1960s, it took 20 years to replace 1/3 of the Fortune 500. In the 1970s, it took 10 years. In the 1980s, 1/3 of the Fortune 500 firms were replaced within 5 years, in the 1990s within about 3 years. Twelve per cent of the largest 50 US firms—as defined by stock market capitalization—had been created less than 20 years previously against only about 4% in the EU (SAPIR ET AL. 2004; p. 43). From the pool of young dynamic SMEs, new firms have entered the Fortune 500; firms from the sector information communication technology play a particular role in this respect. From a theoretical perspective technological advantages are a major basis of successful multinational activities, and in the evolving knowledge society the role of MNCs—and hence of FDI—is expected to grow. According to the OLI approach of DUNNING (1973), we should expect that firms with relatively strong ownershipspecific advantages—and those indeed are often technology advantages—will have conditions to successfully expand through foreign production in attractive host countries. This is a necessary condition for FDI to be a superior alternative to service foreign markets, that is not to rely on exports or giving licenses to foreign firms. The sufficient condition for FDI outflows to emerge is that international intra-firm transaction costs are lower than international market transaction costs. A typical adjustment pattern in OECD countries could be to assume that for catching-up countries, one can assume that the marginal product of capital z is governed by the simple equation dz/dt = (z − z∗ )2 = z2 − 2zz∗ + z∗2

(Aa)

We consider z* an exogenous benchmark. The solution of this RICATI differential equation is (with Co determined by the initial conditions; consider a differential equation dx/dt = P(t) + Q(t)x + R(t)x2 , where parameter P(t) = z*2 , Q(t) = –2z*, R(t) = 1; as x1 (t) = z* is one solution of the initial equation, and since we can use the transformation Z = x–x1 , dZ/dt = Z2 and the transformation W = 1/Z we then get dW/dt = –1. The latter has the solution W(t) = –t + C0 ; hence Z(t) = (C0 − t); x(t) = (C0 − t)−1 + a. z(t) = (C0 − t) + z∗

(Ab)

68 Fig. 15 Adjustment path in the differential equation

Innovations in Macroeconomics z

z* C0

t

The time path of z is such that it will approach z* from above (at point t = C0 ), thereafter it will be below z*. For a shift in global leadership in a simple world economy, this equation might be an adequate description. However, in a more complex world with many sectors there could be individual sectors which are characterized by some overtaking process while in the leading country new sectors emerge which restore the overall lead at the aggregate level. There also could be a particular relevance for diffusion. In the digital networked economy, diffusion of new knowledge has accelerated, while innovation cycles in some industries have shortened. Accelerated diffusion undermines innovation efforts to the extent that the period of obtaining a Schumpeterian rent in the market is squeezed. At the same time, faster diffusion could stimulate leading innovators to come up with innovations more frequently. As regards the expanding information and communication technology, it is not really clear to which side the new technologies and expanding digital networks will tilt the balance. From this perspective, one may emphasize the firm’s ability to accumulate information, to create new knowledge and to develop new products and services. In some sectors and for some production activities—read production of intermediate products and services—it seems that the move towards a digital economy implies a rise of international intra-firm activities. One should, however, not overlook that due to the internet one also can find sectors with increasing market activities, namely almost perfectly global markets with low transaction costs (e.g., see the example of eBay). A key aspect of MNC activities is that production in the digital age might be shifted abroad rather easily. Research and development, however, are less footloose and typically concentrated in the headquarter country. This does not rule out that some research is conducted abroad (e.g., Opel in Germany for GM, or GE Germany/ GE Hungary in Europe for the US parent company and the respective local markets). However, the headquarters country will represent a disproportionate share in the overall R&D budget of the company (for the US see MARKUSEN 2002). A crucial implication is that international mergers and acquisitions can change the geographical composition of R&D in the triad. For example, if a French firm takes over a German pharmaceutical company, one may expect that part of the German pharmaceutical company’s R&D be shifted to the parent company, that is to France. Moreover, if European MNCs (US MNCs) acquire US firms (EU companies) the US research (EU research) activities might be reduced unless we have the case of asset-seeking

A.8 Foreign Direct Investment and Innovation Fig. 16 Asset-seeking FDI

YK

69 YK*

A YK

YK0

C

B*

YK1*

D

A*

E1 G

r2*

E0

r1*

F

YK0*

YK0* 0→K

K01K0* K2K2* K1K1*

K*←0*

foreign direct investment. The latter means that FDI indeed is motivated by obtaining better access to new technology—and within the OECD this could be a motive in some cases. Foreign subsidiaries account for 1/10 and 1/20 of all R&D expenditures in the computer and electronics industry and the US electrical equipment industry (NSF 2004) in the US. It seems that Swiss and EU firms strongly invested in the US in the 1980s and 1990s in order to better tap the technology pool of dynamics US innovators and of leading US universities. This case suggests a modified McDougall diagram (WELFENS 1987). The initial allocation of capital—before economic opening up in country I and country II (foreign country)—is K0 and K0 ∗ , respectively. The traditional McDougall diagram says that with a given marginal product of capital schedule YK0 and YK0 ∗ (country II), the new equilibrium after economic opening up will be point E0 ; the world income gain is equivalent to the triangle DE0 F. However, if the capital importing country I is specialized in a way that generates international technology spillovers in favor of country II or if country I subsidiaries pick up superior technology, the marginal product schedule of country II will shift upwards. There will be an additional real income gain which corresponds to the area A∗ E0 E1 B∗ . Such developments are particularly relevant in the context of asset-seeking foreign direct investment, and such FDI in turn is more likely in the triad if the ratios of R&D to GDP are rising in the EU, the US and Japan. In an explicit multi-sector model of two countries with high levels of technology, one could also expect two-way FDI which might be associated partly with increased global cooperation among firms in R&D-intensive sectors. In OECD countries there is indeed a long-term tendency towards rising inter-firm R&D partnerships (HAGEDOORN 2002); they allow international technology networking and often are useful for establishing global standards. In many host countries, MNCs could set up local R&D facilities, and the higher the capital stock abroad and the larger the foreign market is, the more likely such offshore R&D activities (VEUGELERS ET AL. 2005). From this perspective, regional integration schemes could be useful to the extent that they raise per capita income and growth. At the same time, one may emphasize that oligopolistic interdependence among rivals from OECD countries is likely to play a considerable role in

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Innovations in Macroeconomics

international FDI dynamics. If smaller MNCs follow the industry leader investing in a certain target country, the host country will receive more FDI inflows than is normally the case, and there indeed could be some temporary overinvestment. The global expansion of the information and communication technology (ICT)—representing a general purpose technology useful in almost all sectors—is stimulating FDI directly, namely to the extent that the ICT sector is strongly technology intensive. In the perspective of the OLI approach, one should expect that the ICT sector is clearly shaped by MNCs. Indeed, NAVARETTI/VENABLES (2004) have found this sector to be second to the chemical industry. As regards one subsector, namely the telecommunications sector it is particularly true that the role of FDI has increased after EU opening up and after privatization in European countries and in many other countries as well. One also should note that the telecommunications sector was a leading sector in terms of patent applications in the 1990s. With increased patent dynamics, the incentive for capital accumulation in technology intensive industries will be reinforced, provided profit rates in such sectors are above average. Such a situation cannot persist under perfect competition. However, innovation dynamics imply that there is no perfect competition—there are market entry costs and risk where the latter naturally includes innovation risks. Investors are eager to benefit from excessive rates of return (in combination with modest risk), and this is a major reason why much capital flow became available for the US in the 1990s. US households have benefited from high capital gains—be it in stock markets or in real estate markets—have reduced savings. At the same time, savings from ageing societies in Europe and Japan have partly been invested in the US which has benefited from high growth and favorable profit dynamics. In a closed economy the role of savings is less complex than in open economies. However, it is useful to take a closer look at the role of savings for growth in the context of a closed economy. The world economy is a closed economy, and the rather simple analytical setup facilitates the consideration of some useful modifications to the savings function.

The Role of Savings for Growth An important variable in the neoclassical growth model is the savings rate s which, however, is difficult to measure for empirical purposes. Disregarding such measurement problems we can see that there are considerable differences among countries—with very poor countries having low savings ratios initially (but China stands for a very high savings ratio). The development of the savings ratio is partly related to per capita income but there is certainly a broad set of influences which in the end come under the catchall heading preferences and institutions. Religious forces as well as psychological aspects (e.g., trust in the stability of government/society and the banking system) play an important role here. Prudential supervision and monetary policy are also crucial. The role of financial markets is rarely considered in growth models; we will make a few suggestions going beyond traditional approaches. Since the ratio of narrow money to income and of broad money to income differs across countries,

A.8 Foreign Direct Investment and Innovation

71

45

Savings Rate in %

40 35 30 25 20 15 10 5 0 1990

1992

1994

1996

1998

2000

2002

2004

2006

Germany

France

United Kingdom

United States

Russian Federation

China

Fig. 17 Savings rates in selected countries: USA, Germany, France, United Kingdom, India, China, Poland, Hungary, Russia. (Source: WDI 2005)

we should consider the influence of the degree of monetary development on savings behavior. From a portfolio-theoretical perspective, there should be two aspects: A rise in opportunity costs of holding money will stimulate a shift in the demand for assets in favor of real capital. Moreover, a rise in the real money stock will increase the demand for complementary real capital whose risks are assumed to systematically diverge from financial assets. Investors eager to minimize risk and to maximize the rate of return of the portfolio will behave in such a way. Finally, a rise of m/Y could indicate an improvement in financial intermediation which stimulates savings. In the final chapter we will take closer look at Eastern Europe and new theoretical arguments. The anticipated inflation rate will affect the nominal interest rate which in turn will affect the demand for money. The role of real money balances is rather unclear in growth analysis. While one assumes in most textbooks that a standard macro model dealing with fiscal policy and monetary policy should include real balance effects in both the consumption function and the savings function, growth models largely ignore the role of real money balances, first by not considering it in the savings function and second by not considering a direct role in the production function. Traditional medium-term analysis has in turn discussed the link between the inflation rate and the unemployment rate, but the long-run growth analysis has not considered both phenomena in combination. Even if one would argue that in a long-run steadystate analysis one should not assume cyclical unemployment, there is a need to ask which role the natural rate of unemployment has. Moreover, taking a look at countries such as Germany, France or Italy in the second half of the century, we have countries which experienced high sustained unemployment rates over decades. This is also an

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Innovations in Macroeconomics

0.5

Bars: M1 / Real GNI in national currency

Lines: M2 / Real GNI in national currency 0.8

0.45

0.6

0.4

0.4

0.35

0.2

0.3

0

0.25 –0.2

0.2

–0.4

0.15 0.1

–0.6

0.05

–0.8 –1

0 1970

1975

1980 DE

1985 FR

US

1990 DE

1995 FR

2000 US

Fig. 18 Ratio of M1/nominal national income and of broad money/nominal national income in selected countries (USA, Germany, France). (Source: IFS Database)

argument to at least basically consider inflation and unemployment in the context of growth. While the level of financial development and hence the stock of real money balances has been important for economic development for centuries, it seems that the technology factor has become increasingly important in the 1980s and 1990s as well as at the beginning of the twenty-first century: The European Commission and the European Council have adopted the Lisbon Agenda which is supposed to make the EU the most competitive knowledge-based economy by 2010, wonderful goals which apparently will not be reached (as emphasized in the Kock Report of 2004). This policy failure comes at no surprise since a solid theoretical analysis was missing prior to the policymakers’ adoption of the ambitious goals. Patent dynamics are different across countries, and we will learn more about this later. National patent applications are also misleading to some extent since many patent applications in Europe and Asia indeed reflect patents of US subsidiaries. As regards US patent applications, it also is obvious that a considerable part comes from subsidiaries from Europe and Japan. In the services sector, the picture is generally more opaque since few services qualify for patenting. Capital stock accumulation has been a major driving force of economic growth in the 1980s and the 1990s as is apparent from the table above. However, one should not overlook the role of human capital formation which shows different rates of return across EU countries and also country-specific differentials—in some cases positive, in some cases negative—between the private rate of return and the social rate of return (DE LA FUENTE 2003).

A.8 Foreign Direct Investment and Innovation

73

Table 3 Inflation rates and unemployment rates in selected countries (moving centered three-year averages). (Source: Ameco Database (1981–1993 West-Germany, Statistisches Bundesamt)) Unemployment Rate

1981 1982 1983 1984 1985 1986 1987 1988 1989 1990 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002

Inflation Rate

United States

Germany

France

Italy

United States

Germany

France

Italy

8.1 9.0 8.9 8.1 7.2 6.8 6.2 5.7 5.5 5.9 6.6 7.1 6.8 6.2 5.7 5.3 4.9 4.5 4.2 4.3 4.8

5.5 7.5 9.1 9.1 9.3 9.0 8.9 8.7 7.9 7.2 7.3 8.5 9.8 10.6 10.4 11.5 12.7 12.3 11.7 10.7 10.4

7.0 7.6 8.4 9.2 9.9 10.3 10.3 10.1 9.6 9.2 9.4 10.0 11.1 11.7 12.0 12.0 12.1 11.9 11.2 10.2 9.2

8.0 8.6 9.3 9.9 10.5 11.2 11.8 12.1 11.9 11.5 11.3 10.9 10.9 10.8 11.3 11.5 11.6 11.5 11.1 10.4 9.7

10.0 6.6 4.6 3.7 3.2 3.1 3.2 4.2 4.7 4.8 4.2 3.4 2.9 2.8 2.8 2.7 2.3 2.0 2.4 2.8 2.6 2.2

6.3 5.2 3.2 2.5 2.0 −0.1 0.2 1.2 2.8 2.6 1.6 5.1 4.1 3.0 2.0 1.7 1.4 1.1 1.0 1.3 1.6 1.5

13.0 11.6 9.7 7.7 5.3 3.9 2.8 3.2 3.2 3.4 3.0 2.6 2.0 1.9 1.8 1.7 1.3 0.8 1.0 1.3 1.8 1.9

18.5 16.3 14.0 11.6 8.6 6.6 5.2 5.4 5.9 6.3 6.0 5.3 4.5 4.6 4.4 3.8 2.7 1.9 2.1 2.3 2.6 2.6

70000 60000 50000 40000 30000 20000 10000 0 1996

1997 1998 1999 2000

2001 2002

2003 2004 2005 2006 2007

EU 27

Germany

France

Netherlands

UK

USA

Fig. 19 Patent applications in selected countries. (Source: Eurostat)

Italy

EU 27 Germany France Italy Netherlands UK USA

13.02 12.28 12.78 9.52 13.14 8.86 13.49

1997

11.24 12.64 10.42 8.73 10.38 13.44 10.50

1998 8.10 6.48 4.72 9.31 12.24 10.88 6.29

1999 5.23 5.32 1.16 7.28 16.67 4.29 2.14

2000 –1.16 –1.40 –0.59 –0.94 12.58 –7.05 –3.07

2001

Table 4 Growth rates of international patents, 1990–1997. (Source: Eurostat)

–0.80 –1.25 0.95 5.38 –11.12 –1.64 3.11

2002 2.28 1.17 6.91 3.31 –0.04 –1.13 1.58

2003 5.64 4.77 6.15 6.39 4.54 –0.29 6.42

2004

1.35 2.72 –1.20 4.71 –5.52 –2.15 1.74

2005

2.89 2.72 3.60 4.37 –0.43 –1.22 3.03

2006

3.08 3.18 2.65 4.66 –0.56 –1.25 3.45

2007

74 Innovations in Macroeconomics

A.8 Foreign Direct Investment and Innovation

75

140000

Capital Stock pC in €

120000 100000 80000 60000 40000 20000 0 1980

1985 Germany United States

1990 France Japan

1995 Italy

2000

2005

United Kingdom

Fig. 20 Real capital stock per capita in selected countries, 1980–2005 (figures are unajusted for quality effect). (Source: Ameco Database)

Growth accounting has become popular in explaining differences in growth performance of Europe and the US in the 1980s and 1990s. The role of information technology IT has also been important in the Euro zone as was shown by SAKELLARIS/VISELAAR (2005). In a broader perspective, growth accounting is of particular interest with respect to Europe and the US. If one assumes a linear-homogenous production function and that factors are rewarded according to the respective marginal product, one can decompose Y(K, L, A) according to growth rate of output (Y) as the weighted sum of the growth rate of capital stock (K) growth and the growth rate of labor (L)— the weights are the respective income shares of capital and labor—plus the growth rate of total factor productivity (A). With respect to empirical analysis, data issues are important here. One may emphasize problems with an overall quality bias of equipment and software as well as embodied technological change (i.e., the role of the quality of capital which has been emphasized by SAKELLARIS/ VISELAAR (2005). Their growth accounting for the Euro area indicates that quality-adjustment of capital goods implies a higher rate of output growth in the period from 1982 to 1990 than the unadjusted figures would indicate. In that period, one also finds—on the basis of quality-adjusted data—a rise of the growth rate of total factor productivity growth, namely of about 1/10. Quality-adjusted data also indicate a higher output growth in the 1990s but no change for total factor productivity growth. The growth accounting results reported indicate—on the basis of quality adjusted output and quality adjusted capital—that the Euro area has suffered a growth deceleration in the

76

Innovations in Macroeconomics

1990s as compared to the 1980s while the US has reported an acceleration. The US lead amounted to 1.8 percentage points in the 1990s while it was only 0.6 percentage points in the 1980s. In the Euro area the long-run growth of capital input—based on quality-adjusted data for the 1980s and 1990s—has been roughly twice the figure suggested by standard statistics. Total factor productivity growth in the Euro area (this includes quality aspects of labor) has been higher in the Euro area than in the US, although this lead was lower in the 1990s than in the 1980s. The consistency of any growth accounting exercise depends on the theoretical approach used (i.e., essentially the production function used and assumptions made with respect to factor remuneration) and on the quality of the data. As regards comparative growth accounting of (SAKELLARIS/VISELAAR 2005; CUMMINS/VIOLANTE 2002) the results can be summarized as follows: While the US had a positive contribution to labor in both decades the growth contribution of labor in the Euro area was negative. The latter is rather surprising since unemployment rates have increased in the Euro area. The contribution of capital has been close to 1 percentage point in both decades in the Euro zone, but more than twice as high in the US. Compared to the 1980s, the contribution of the quality of capital has been higher in the US and the Euro area in the 1990s. The decline in the total factor productivity growth of the Euro area is difficult to interpret, since the 1990s were shaped by strong expansion of information and communication technology in both the US and the Euro area. This suggests an expansion of total factor productivity growth in the 1990s as compared to the 1980s. To some extent, a recent growth and ICT study (with a focus on Germany) of WELFENS/JUNGMITTAG/VOGELSANG (2006) sheds light on the issue, at least with respect to Germany which accounts for roughly 1/3 of the GDP of the Euro area. The results from data envelopment analysis—which is better suited to explain growth than traditional growth accounting which relies on the specific assumption of full employment—indicate a decline of the growth rate of total factor productivity growth in the second half of the 1990s. In particular, North-Rhine Westphalia, West Germany’s largest state, and eastern Germany fell behind the technological frontier as marked by Hamburg closely followed by the state of Baden-Würtemberg in southern Germany (thus, for regions with roughly 45% of the German population total factor productivity growth has declined!). Moreover, the analysis shows that the structure of labor demand partly explains the growth of total factor productivity: Regions with a rising share of employment in high technology manufacturing and high technology services have recorded a relatively high increase in factor productivity growth. Economic growth in industrialized countries is a complex phenomenon as is the topic of economic catching-up where recent empirical findings on economic catching-up dynamics for EU-15 suggest a significant role of trade and the patterns of technological specialization (JUNGMITTAG 2004; 2006). The growth decomposition analysis by JUNGMITTAG is summarized for in the following graph and shows a considerable positive impact of high technology specialization.

Adj. 2.97 0.90 0.11 0.07 0.08 0.43 0.04 0.16 −0.12 2.20 0.59 1.61 0.91

2.49 0.57 0.07 0.07 0.05 0.17 0.05 0.16 −0.12 2.04

Unadj. 2.34 0.96 0.11 0.07 0.12 0.45 0.12 0.09 −0.07 1.45 0.63 0.82 1.07

Adj.

1991–2000

2.34 0.96 0.44 –0.07 1.45

EA

US 3.60 2.04 0.82 1.19 0.35

EA

2.97 0.90 0.32 –0.12 2.20

4.15 2.27 1.10 1.22 0.66

0.63 1.14 0.50 1.31 –1.85

1980s

1.81 1.31 0.66 1.29 –0.79

1990s

−0.59 −0.06 0.00 0.00 0.00 0.00 0.02 −0.08 0.05 −0.58

Difference

Unadj.

Adj. −0.63 0.06 0.00 0.00 0.04 0.02 0.08 −0.08 0.05 −0.75 0.04 −0.79 0.16

Slowdown 1980s vs 1990a

Note: a euro area: this study; US: Cummins and Violante (2002); b Output: average annual change; Contributions: percentage points

Output Contribution of capital Quality of capital Contribution of labor TFP (incl. quality of labor)

1990s

1980s

US

1.90 0.51 0.08 0.07 0.05 0.17 0.06 0.08 −0.07 1.46

Unadj.

Note: Slowdown is the difference between the 1982–1990 figures and the 1991–2000 figures, row by row

Output (i.e., GDP) Capital growth source IT hardware Software Communication equipment Other machinery and equipment Transport equipment Non residential construction Labor growth source TFP (i.e., disembodied technical progress) Equipment and software Rest Memo: embodied technological change

1982–1990

Table 5 Growth accounting: comparison of Euro area and US developments. (Source: SAKELLARIS/VISELAAR 2005)

A.8 Foreign Direct Investment and Innovation 77

78

Innovations in Macroeconomics Knowledge Diffusion Labour Technological Specialisation

70 60

Capital Patent Stock Growth

5 4.5 4 3.5

40

3 30 2.5 20 2 10

Growth Rate

Contribution to Growth

50

1.5

0

1

–10

0.5 0

–20 IE

PT

ES

GR

FI

AT

NL

FR

BE

IT

DK

UK

DE

SE

Fig. 21 Decomposition of average growth rates of GDP in selected EU countries, 1969–1998. (Source: JUNGMITTAG, A. (2006a), Internationale Innovationsdynamik, Spezialisierung und Wirtschaftswachstum in der EU, Berlin und Heidelberg)

A.8.2 Modified Multiplier in Macro Model with FDI Outflows As FDI has become increasingly important in the modern world economy it is useful to refine standard macro models by taking into account FDI while assuming that factors are rewarded in accordance with the marginal product rule; hence profits are given by ßY. Let us assume that foreigners own a share b of the capital stock K in country I (home country) and that output Y is determined according to Y = Kß L1−ß . Moreover, imports J depend on national income Z which is the difference between gross domestic product Y and net profits transferred abroad b bßY where b is the share of MNC subsidiaries’ profits transferred abroad (and b is the share of reinvested profits accruing to foreign investors): J = j(q∗ )[Y − b ßY]

(A.11)

Similarly we assume for exports while denoting the real exchange rate q* := eP*/P and q = 1/q*: X = x(q∗ )[Y∗ − b ßY/q∗ ]

(A.12)

We assume that consumption is proportionate to national income and that investment consists of investment by domestic firms I(r) plus reinvested earnings of foreign investors: Reinvested earnings are proportionate to profits of foreign subsidiaries: b bßY; note that we implicitly take into account the argument of FROOT/STEIN

A.8 Foreign Direct Investment and Innovation

79

(1991) which argue that FDI inflows—relative to Y—positively depend on the real exchange rate q* := eP*/P so that a real depreciation will raise FDI inflows. The FROOT/STEIN argument basically says that in a world of imperfect capital markets a real depreciation implies that foreign firms will have higher equity capital expressed in terms of the potential target country which raises the probability of a successful international merger & acquisition project. Hence firms from country II—which faces a real appreciation—will find it easier and more attractive to invest in country I. According to our approach the short-term condition for the goods market equilibrium equation therefore reads in the FDI host country: Y = cY[1 − b ß] + I(r) + b (q∗ )bßY + G + x(q∗ )[Y∗ − b ßY/q∗ ] − j(q∗ )[Y − b ßY]

(A.13)

Compared to traditional analysis we get a slope of the ISF curve which is flatter for the FDI host country than in a model without FDI (with the traditional IS curve). This effect implies an output expansion if the money demand schedule is given in the conventional form, namely M/P = m(i, Y) unless the LM curve—reflecting money market equilibrium—is vertical; i is the nominal interest rate, and in the absence of inflation i coincides with the real interest rate r. A simple specification of the real money demand function m is m = hY – h i: the parameter h is related to the transaction demand for money, while the parameter h’ is related to the speculative demand for money. If, however, the real money demand depends not on GDP but on GNP the money market equilibrium condition is given by adequately refining the money market demand where we assume that subsidiaries of MNCs typically will use less domestic currency than domestic firms; hence we have introduced the parameter a : M/P = hY[1 − a b ß] − h i

(A.14)

The effect of FDI on the money market is that the equilibrium schedule LMF is flatter than the traditional LM curve so that the money market effect reinforces the real expansion effect of FDI. To put it differently, as the transaction demand for money is weaker in an economy with FDI a given real money supply will be absorbed for a given Y only if the interest rate is lower than before (read: in an economy without FDI inflows). This, however, is rather implausible as FDI inflows typically will raise r and hence the nominal interest rate i. There is a caveat, namely that a sufficient share of FDI inflows concerns banking and financial market services which then indeed might bring about a fall of the interest rate through efficiency gains in financial intermediation. Moreover, one should consider that in the presence of FDI the interest elasticity of the demand for money will increase since the presence of foreign investors should lead to enhanced political stability which in turn leads to financial market broadening: As a broader variety of liquid bonds become available the interest elasticity of the demand for money should increase. In the case of flexible exchange rates the foreign exchange market equilibrium condition can be expressed as follows (with Q denoting real net capital inflows,

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including FDI inflows which are assumed to positively depend on the relative market size Y/Y*; * denotes foreign variables): Q(q∗ , Y/Y∗ ) = −x(q∗ )[Y∗ − b ßY/q∗ ] − j(q∗ )[Y − b ßY]

(A.15)

While the condition for the foreign exchange market equilibrium is identical for country II—the FDI source country—the equilibrium conditions for the goods market and the money market looks as follows where we make the special assumption that profits earned in country I which are not reinvested in country I will be invested in country II: Y∗ = c∗ Y∗ + c∗ b ßy/q∗ + I∗ (r∗ ) + [1 − b (q∗ )]bßYq∗ + G∗ − x(q∗ )[Y∗ − b ßY/q∗ ] + j(q∗ )[Y − b ßY] ∗

∗

∗

∗

 

∗ ∗

M /P = h Y [1 − a b ß] − h i

(A.16) (A.17)

The goods market equilibrium schedule ISF* is steeper than in the standard textbook case, the money market equilibrium schedule LMK* is steeper than in a world without FDI. However, the equilibrium output Y* could well be higher than without FDI, namely due to the investment-enhancing effect of profits accruing from abroad. The results for a two-country model are summarized subsequently. Using the abbreviations: 

 k1 = jq∗ Y − b βY − xq∗ Y∗ − b q∗ bβY + x(q∗ )b βY/q∗2 + xq∗ b βY/q∗ P∗ /P 

k2 = Qq∗ + xq∗ Y∗ +jq∗ Y − b βY − x(q∗ )b βY/q∗ 2 − xq∗ b βy/q∗ P∗ /P  k3 = c∗ b βy/q∗ 2 − jq∗ [Y − b βY] − b βY + x(q∗ )b βY/q∗2  + xq∗ b βy/q∗ +b (q∗ )bβY+b q∗ bβY P∗ /P



k4 = 1 − c 1 − b β −b (q∗ )bβ + x(q∗ )b β/q∗ + j(q∗ ) 1 − b β



k5 = 1 − b (q∗ ) bβq∗ + x(q∗ )b β/q∗ + j(q∗ ) 1 − b ß k6 = Qy − x(q∗ )b β/q∗ − j(q∗ )b β and differentiating Eqs. (A.13), (A.14), (A.15), (A.16) and (A.17) we get the following system of equations: ⎛ ⎞⎛ ⎞ x(q∗ ) K1 Ii 0 K4 dY ∗ ⎟ ⎜−h[1 − a b β] ⎜ 0 0 h 0 ⎟ ⎜ ⎟ ⎜ dY ⎟ ∗ ⎜ ⎟ ⎜ K6 QY∗ + x(q ) K2 0 0 ⎟ ⎜ de ⎟ ⎜ ⎟ ⎝ 1 − c∗ + x(q∗ ) K3 0 II∗∗ ⎠ ⎝ di ⎠ K5 0 h∗ [1 − a b β] 0 0 h∗ di∗ ⎞ ⎛ ⎛ ⎞ 1 0 0 0 dG ⎟ ⎜0 0 1/p 0 ⎟⎜ ∗⎟ ⎜ ⎜ dG ⎟ 0 ⎟ =⎜ ⎟ ⎝ dM ⎠ ⎜0 0 0 ⎝0 1 0 0 ⎠ dM∗ 0 0 0 1/P∗

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81

We assume: 1. 2. 3. 4. 5. 6. 7. 8. 9. 10.

k1 > 0 k2 < 0 k3 > 0 k4 < 0 k5 < 0 k6 > 0 k1 k6 < k2 k4 k1 k5 > k3 k4 1 – c* + x(q*) > 0 1. QY∗ + x(q*) > 0

Furthermore we define: ⎛

k4 x(q∗ ) k1   ⎜−h[1 − a b 1ß] 0 0 ⎜ ∗) ∗ k Q + x(q k U = det ⎜ 6 Y 2 ⎜ ⎝ 1 − c∗ + x(q∗ ) k3 k5 0 h∗ [1 − a b ß] 0

Ii h 0 0 0

⎞ 0 0⎟ ⎟ 0⎟ ⎟ II∗∗ ⎠ h∗

and V =: 1/U < 0 This results in the following multipliers:       dY/dG = −Vh h∗ k3 QY∗ + x(q∗ ) − k2 1 − c∗ + x(q∗ )  + Ii∗∗ k2 h∗ [1 − a b β] > 0    dY/dG∗ = Vh h∗ x(q∗ )k2 − k1 QY∗ + x(q∗ ) > 0 dY/dM = −VIi (h∗ ((QY∗ + x(q∗ ))k3 − k2 (1 − c∗ + x(q∗ ))) + h∗ [1 − a b β]k2 Ii∗∗ )/P < 0   ∗  dY/dM = −Vh Ii∗ x(q∗ )k2 − k1 QY∗ + x(q∗ ) /P∗ > 0     de/dG = Vh k6 1 − c∗ + x(q∗ ) h∗ − Ii∗∗ h∗ [1 − a b β]   − k5 h∗ QY∗ + x(q∗ ) < 0    de/dG∗ = Vh∗ Ii h[1 − a b β] QY∗ + x(q∗ )     + h k4 QY∗ + x(q∗ ) − k6 x(q∗ ) > 0       de/dM = −VIi h∗ k6 1 − c∗ + x(q∗ ) − k5 QY∗ + x(q∗ )  − Ii∗∗ k6 h∗ [1 − a b β] /P < 0    de/dm∗ = −VI∗i∗ Ii h[1 − a  b β] QY∗ + x(q∗ )     + h k4 QY∗ + x(q∗ ) − k6 x(q∗ ) /P∗ > 0

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A.9 Output Dynamics: Interaction of the Demand Side and the Supply Side In macroeconomics the short-run Keynesian model reads for all intents and purposes as follows for the case of the closed non-inflationary economy (using simplified functions, namely consumption C = cY and investment I = b0 – br while real money demand md = hY – h r; Y is real output and r the real interest rate): Y = cY + b0 − br + G (goods market equilibrium condition)

(i)

M/P = hY − h r (moneymarket equilibrium condition)

(ii)

We get the familiar multipliers for fiscal and monetary policy, respectively: dY/dG = −h /[−sh − bh] > 0; dY/d[M/P] = −b/[−sh − bh] > 0 unless h approaches infinity. According to these short-run multipliers both monetary and fiscal policy are effective in the closed economy within a short-run model. However, we will argue that a meaningful medium-term policy perspective comes up with rather different result which point to considerable needs for more empirical analysis. The approach suggested also allows to take into account both demand side impulses (Yd is aggregate demand: the sum of planned consumption and investment plus exogenous government demand plus net exports) and long-run supply side effects (the production potentialYpot as proxied by a simple production function) since we basically will argue that in a medium-term perspective actual output Y is determined according to Y = (1 − α)Yd + αYpot ;

(1a)

Note that α is a weighting parameter in the interval [0, 1] and basically is determined by the dominant type of expectations which assign long-run output potential Ypot a certain weight α—under long run full employment equal to unity—and thus present demand conditions a weight (1 − α). Such a joint impact of Yd and Ypot indeed is obtained if we assume a special variant of the permanent income hypothesis, namely that consumption is determined by the weighted impact of current real income and expected long-run income—this is dubbed a hybrid consumption function—which is assumed to coincide with the production potential (for simplicity we have no discounting here): C = c(1 − α )Y + cα Ypot = cY + cα [Ypot − Y]

(1b)

Thus consumption is proportionate to current real income; if consumers expect longrun income to exceed current income—and hence anticipate real income to rise— current consumption is higher than cY. If α is a flexible variable (not a constant parameter) one may assume that a lasting gap between Y and Ypot will lead to a decline of α ; and the combined impact of a rising gap and a falling α could indeed imply a fall of consumption. Assume that we have aggregate demand in an open economy given by the following simple equation which assumes that consumption C is determined according to

A.9 Output Dynamics

83

a the hybrid consumption function and that investment I and imports J are proportionate to actual income while export X is proportionate to foreign output Y* (γ is the exogenous ratio of government expenditures to output Y): Yd = c(1 − α )Y + cα Ypot + b Y + γY − jY + xY∗ = [c(1 − α ) + b + γ − j]Y + cα Ypot + xY∗

(1c)

Inserting (1c) in (1a), namely dY = (1 – α)dYd + αdYpot we get: dY = (1 − α)[c(1 − α ) + b + γ − j]dY + [(1 − α) + ca + γ]dYpot + (1 − α)xdY∗

(1d)

Let g denote growth rates; then we have (note thatYpot /Y =: u which is the inverse of the degree of capacity utilization U ) in a medium-term perspective with a production function Ypot = Kß (AL)1−ß and defining:

  s = 1 − (1 − α) c 1 − α + b + γ − j





gY = (1 − α) cα + α U /s ßgK + (1 − ß) (gA + gL )

+ (1 − α) x/s Y∗ /Y gY∗

(1e)

Medium-term output growth thus not only depends positively on the growth rate of capital accumulation gK and the growth rate of labor input gL and the rate of (Harrod-neutral) technological progress gA and the growth rate of foreign output gY∗ (the foreign growth rate will affect gY the more, the higher foreign output Y* relative to Y is), but also on the import-GDP ratio j and the export-GDP ratio; this is in line with many empirical studies finding a significant impact of trade intensity on growth. Moreover, growth depends negatively on the term s ; this being said does, of course, not rule out that the savings rate s = 1 – c has a positive impact on the level of the long-run growth path which is in accordance with long-run growth theory. One should note that from a theoretical perspective the growth rate of labor saving technological progress might depend on the trade intensity x + j (or any suitable index reflecting the relative intensity of exports and imports); a more refined view might introduce specific weights for the impact of low, medium and high-technology trade intensity; one also should note in this context the empirical findings of JUNGMITTAG (2004) who finds that the degree of high-technology specialization  has a significant positive impact on economic growth of EU15 countries. If we assume that the growth rate of technological progress depends on the trend innovation input ratio (r  ), namely weighted past R&D-expenditures relative to Y, and on the trend degree of high technology specialization ( ) we can—using positive parameters f  and f  , respectively—replace gA by f  r + f   .

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A.10 Growth Accounting Under Unemployment and Okun’s Law In economic growth, accounting is made under the implicit assumption of full employment. However, this restrictive constraint is, not necessary. Plausible assumptions about the link between unemployment and firms’ factor input decisions shed even light on OKUN’s Law which argues that there is a negative link between the unemployment rate and output growth. Let us start with a brief look at the standard case. Standard analysis tells us for the case of a linear-homogenous production function: Assume for simplicity that Y = Y(K, L) such that output Y = YK K + Y L L

(Ia)

whereYK andYL stand for the marginal product of capital K and labor L, respectively; we therefore also can write gY = EY,K gK + EY,L gK (E denotes elasticities). If we assume competition in goods and labor markets and that production factors capital and labor are rewarded in accordance with the marginal product rule so that the real wage rate w = YL and the real interest rate r = YK we can write (with ß denoting the elasticity of output with respect to capital; g is growth rate): Y = wL + rK

(Ib)

gY = (1 − ß)gL +ßgK

(Ic)

Next we assume that there is a positive unemployment rate u. We will further assume that unemployment occurs in a way that workers with a relatively low productivity are laid off first and that trade unions and employer organizations agree to impose wages below the marginal product according to: w(1 + u) = YL

(Id)

Alternatively, a more complex impact of the unemployment rate on the real wage rate may be considered by assuming that w(1 + u)χ = YL where χ is a parameter related to collective bargaining. However, we stay with our simple approach which basically says that firms in a situation with aggregate unemployment will pay a real wage which is below the marginal product of labor; as an argument for such a behavior one might point to risk averse firms which consider demand uncertainty. In an economy with unemployment they are afraid that the situation might further become aggravated. Moreover, we assume that the unemployment rate reduces the marginal product of capital as compared to full employment. The basic argument for this is that switching from full employment to unemployment typically goes along with situation in which part of the existing capital stock becomes obsolete. However, as firms assume with some probability that some of the idle machinery and equipment could be used during a future economic upswing more capital is employed than would be adequate if the firms strictly would follow the standard profit- maximization condition r =YK . Hence we assume the following capital input condition to hold: r(1 − u) = YK

(Ie)

A.10 Growth Accounting Under Unemployment Fig. 22 Capital input and labor input in an economy with unemployment

85

w Ls F w1 G w2

E0

w0

Ld

a 0

L0

L1

L

YK,r

YK0(K,L0) YK1(K,L1) E1

E0

r0

E2

b

0

K1

K2

K0

K

The corresponding allocation of capital and labor in an economy with unemployment is shown in the following graph where Ld is labor demand andYK shows the marginal product of capital: Firms will hire only L1 and pay w2 (note that w2 exceeds the full employment wage w0 ). which is below w1 and the marginal product of labor, respectively; moreover, firms will realize point E2 (panel b) and employ K2 —which exceeds K1 . Inserting the modified factor input equations into the equation Y = YK K + YL L we thus get: Y = w(1 + u)L + r(1 − u)K

(If)

Under which condition is this equation identical with the full employment case of Y = wL + rK? This obviously is the case if wL = rK since only then wuL − ruK = 0; for the case of a Cobb–Douglas production function Y = Kß L1−ß this would

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imply a parameter value of ß = 0.5. If it should turn out that the true factor market  input conditions rather look like w(1 + u)χ = YL and r(1 − u)χ = YK a different value of ß would be obtained. The relevance of the reflections presented here is that from an empirical point of view standard growth accounting can be useful even in an economy with unemployment. However, it also is true that in a situation of unemployment Data Envelopment Analysis might be more adequate. In our simple modified growth accounting framework the implication is that the standard full employment production function Y = K ß L1−ß can be rewritten—taking into account that there is idle capital in periods of unemployment—in a generalized way as 

Y = (1 − u)χ K ß L1−ß

(Ig)

To put it differently we get an implicit form of Okun’s Law (OKUN 1962); Okun’s Law states—with a denoting a positive parameter—that the difference between the current rate u and the natural rate unatural = a [(Ypot −Y)/Y]100): Taking logarithms while using the approximation that ln(1 + x) ≈ x we have lnY = −χ u + ßln K + (1 − ß)lnL

(Ih)

gY = −χ du/dt + ßgK + (1 − ß)gL

(Ii)

Thus there is a negative link between the growth rate of output and the change in the unemployment rate; note that the existence of structural long-run unemployment implies that one should not consider the actual unemployment rate but the difference between the actual rate and the respective national natural unemployment rate. By implication a generalized Cobb–Douglas “output function” thus may be stated as follows (with e as the Euler number): Y = e

−χ u

K ß L1−ß

(Ij)

In an empirical context on should not use u but the effective unemployment rate u : The variable u is not the actual unemployment rate, rather it is the difference between actual unemployment rate and the natural (long run) unemployment rate. Additionally one might take into account technological progress as proxied by a time trend variable (e at ). Y = e e at

  −χ u

K ß L1−ß

(Ik)

Finally one should note that the unemployment rate can, of course, be partly or fully related to aggregate demand dynamics. Thus the equations (Ig – Ik)—and indeed OKUN’s Law—do not represent a pure supply-side perspective.

A.11 Innovation, Trade and Foreign Investment From an economist’s perspective rising trade should go along with rising specialization and efficiency gains in the medium term and—under certain circumstances— with higher innovation dynamics and an associated rise of firms’ expenditures on

A.11 Innovation, Trade and Foreign Investment

87

research and development. Import competition can contribute to efficiency gains and process innovations, respectively; for such a link there is evidence for several sectors of manufacturing industry in the United States—but not for Germany (MANN 1998). As regards Germany, ZIMMERMANN (1987) found econometric evidence that import competition stimulates innovations in exporting firms and encouraged product innovations. FDI inflows as well as import competition and exports could stimulate innovation dynamics (LOFTS/LOUNDES 2000) as domestic firms react with innovations to the external challenges. SCHERER/HUH (1992) find a negative impact of an increasing import competition on the R&D intensity of US firms. A possible explanation for the negative link between import competition and R&D intensity is a fall in profits which might be associated with a rising share of imports; with profits falling, firms in R&D intensive sectors will find it more difficult to finance innovations and hence, R&D intensity goes down. Note that a rising share of imports could also signal a parallel fall in exports, so that both falling market shares at home and abroad would translate into lower profits. As regards FDI inflows, one may follow DUNNING (1977) who has emphasized that FDI will replace exports if the respective firm can profitably combine owner specific advantages—this typically means high innovation dynamics/a stock of patents—with locational advantages in the prospective home country; profitability is reinforced if intra-company transactions go along with internalization advantages: firm internal transaction costs are lower than costs for arms-length transactions through markets. While there are many studies on the role of foreign competition and innovation in the manufacturing industry there are almost no studies in the field of the services industry. BLIND/JUNGMITTAG (2004) show in their pioneering study for Germany’s service sector that import competition and also export activities and FDI inflows positively affect both product innovations and process innovations. Moreover, the size of the firm is found to have—up to a critical size—a positive impact on both product innovations and process innovations. If firms have the respective headquarter abroad the impact on innovations is negative. In a more general perspective and assuming that the findings for Germany apply to other OECD countries one may conclude: international mergers and acquisitions will reduce innovation activity in the host country unless this goes along with a minimum increase of exporting activities of the newly acquired subsidiary. A familiar theoretical model about the link between foreign competition and innovations is the industrial economics approach of BERTSCHEK (1995) whose analytical framework is as follows: Suppose we have an imperfect competition so that total market volume consists of output (qi ) of firm i plus the quantity offered by other domestic firms (Q) or firms with foreign ownership (Q**); and there can be imports J). Thus the price pi can be written as the following function: pi = pi (q, Qi , Qi ∗∗ , Ji , vi )

(1)

Where a change in qi reflects a move along the demand curve; all other variables are shift parameters. The assumption here is that a rise of Q, Q** or J will reduce

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the price. The output of firms under foreign ownership is assumed to be produced according to the stock of FDI of the previous period t – 1. Marginal costs ci depend on factor prices Wi , product innovations vi and process innovations Vi ; product innovations raise ci , process innovations reduce marginal costs. Ci = ci (Wi ,vi ,Vi ) Assuming fixed costs of process innovations CV profits are thus given by:   i = pi q, Qi, Qi ∗∗ , Ji , vi qi − ci (Wi , vi , Vi ) qi − CV .

(2)

(3)

In BERTSCHEK’s model the domestic firm i is assumed to have the goal of maintaining profits so that the total differential of the above equation can be set zero. From this condition one obtains the following results (we drop the subscript i) with respect to process innovations: dV/dQ∗∗ > 0;

(4)

Hence, a rise of output of foreign subsidiaries will stimulate process innovations. Such innovations help to cut costs and thus counterbalance the negative effect of the expansion of Q** with respect to profit. Note that dV/dQ** = dV/dQ if pQ = pQ∗∗ where we denote partial derivatives with a subscript, e.g., ∂p/∂Q =: pQ . Moreover, one gets: dV/dJ > 0

(5)

Thus a rise of imports stimulates process innovations. A higher output of foreign subsidiaries as well as higher imports stimulate the firm engaged in process innovations. Moreover, and assuming that the marginal return of product innovations is higher than the associated rise of marginal costs, one gets: dv/dQ∗∗ > 0

(6)

dv/dJ > 0

(7)

Both additional import competition and higher output of foreign-owned firms stimulate the firm to come up with product innovations. Finally, the effect of the output of the domestic firm is given by: dv/dq < 0;

(8)

dV/dq < 0

(9)

At the bottom line, both the presence of FDI inflows and import competition should raise both process innovations and product innovations, while a rise of the output of the respective firm will reduce innovativeness. Not really satisfactory is the fact that in the particular case of ∂p/∂Q = ∂p/∂Q** a rise of output of other domestic firms should have the same effect on innovativeness as a rise of foreign subsidiaries. As an interesting extension we suggest the following model in which the firm i is producing both for the domestic market and for export markets; the innovative

A.11 Innovation, Trade and Foreign Investment

89

firm is assumed to also export (e is the nominal exchange rate, p*i the world market price in foreign currency). We introduce a specific assumption here: the innovative firm can affect the foreign price by product innovations so that our model stands for the case of a small open economy with a major innovating company (e.g., Ericsson in Sweden, Nokia in Finland, Philips in the Netherlands or Samsung in Korea)— thus we are not subscribing to the traditional small open economy textbook model in which all firms are pricetakers in the world market. Moreover, our behavioral assumption is that we assume that the company has the goal to raise profit in line with export revenue; possibly because a rising export exposition is considered a risk by banks financing the firm which in turn, amounts to say that there is a required rate of export profitability (parameter n which is in the interval 0, 1; in principle the firm can chose n such that a critical overall profit/sales ratio is achieved). For sake of simplicity fixed costs are assumed to be zero. As regards exports we assume that part of higher output of foreign subsidiaries is exported so that with a given international demand exports of firm i will fall; other domestic firms are assumed not to be exporters. Finally, assuming that the export quantity positively depends on product innovations and on process innovations of firm i—with a given domestic demand a fall in marginal costs will allow larger exports at any given stock of factor inputs—we have the following profit equation i = pi (qi , Qi , Qi ∗∗ , Ji , vi )qi + e(vi )p∗ i (vi )Xi (Q∗∗ , vi , Vi ) ∗

− ci (Wi , vi , Vi )[qi + Xi (.)] = n ep i Xi (.)

(10)

A special assumption made here is that a rise of product innovations (v) can—if the firm considered is critically influential in the perspective of financial market actors— affect the nominal exchange rate e: A rise of v is assumed to bring about an expected appreciation in a flexible exchange rate system as market analysts anticipate a rising current account surplus in the future and hence, a fall of e; and the change in the expected exchange rate will bring about an actual fall of the nominal exchange rate. This assumption makes sense only if the firm considered is a large and dominant exporter (e.g., Nokia in Finland, less so Boeing in the case of the US). The total differential thus reads as follows (we drop the subscript i again. Various alternatives with respect to interdependency of behavior can be analyzed, e.g., dq/dQ** < 0 in the case of an oligopolistic setting—or dq/dQ** = 0 if the firm acts interdependently):

0 = pq dq + pQ dQ + pQ∗∗ dQ∗∗ +pJ dJ + pv dv q + [1 − n ]ep∗ XQ∗∗ dQ∗∗ + Xv dv + Xv dV] + p∗ Xev dv + Xep∗v dv + p(.)dq − c(.)XQ∗∗ dQ∗∗ − [cw dw+cv dv+cv dv][q + x] − c[Xv dv+Xv dv]

(11)



0 = [qpq + p(.)]dq + qpQ dQ+ qpQ∗∗ + (1 − n )ep∗ XQ∗∗ − cXQ∗∗ dQ∗∗  

+ qpv + p∗ Xev + Xep∗v − cv (c + X) + (1 − n )ep∗ − c Xv dv  

(12) + qpJ dJ+ (1 − n )ep∗ − c Xv − cv (q + X) dV−cw (q + x)dW

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A series of impact multipliers—process innovation multipliers and product innovation multipliers—can thus be derived, including different impacts of a rise of Q and Q**, respectively. Note that the behavioral assumption that the firm simply wants to maintain existing profits can be accommodated by setting n = 0.  −1 dV dq = [qpq + p(.)]  ∗ dQ [((1 − n )ep − c)Xv − cv (q + X)] dQ ∗∗

dQ dJ + qpQ∗∗ + (1 − n ) ep∗ XQ∗∗ − cXQ∗∗ + qpJ dQ dQ dW + qpQ + qpv + p∗ Xev+ Xep∗v − cv(c + X) − cw (q + X) dQ   dv + (1 + n )ep∗ − c Xv ] (13a) dQ   −1 dq dV = [qpq + p(.) ∗∗  ∗ dQ [((1 − n )ep − c)Xv − cv (q + X)] dQ∗∗ dq dJ ∗ + qpQ ∗∗ + qpJ ∗∗ + qpv + p Xev +Xep∗v dQ dQ   dv − cv (c + X) + (1 − n )ep∗ − c Xv ] dQ∗∗ 

dW  ∗ − cw (q + X) ∗∗ + qpQ∗∗ + (1 + n )ep XQ∗∗ − cXQ∗∗ dQ

(13b)

  −1 dV dq = [qpq + p(.) dJ [((1 − n )ep∗ − c)Xv − cv (q + X)] dJ

dQ∗∗ dQ + qpQ + qpQ∗∗ + (1 − n )ep∗ XQ∗∗ − cXQ∗∗ dJ dJ   dv ∗ + qpv + p Xev + Xep∗v − cv (c + X) + (1 − n )ep∗ − c Xv ] dJ  dW (13c) − cw (q + X) + qpJ dJ   dV dq −1 = [qpq + p(.)  ∗ dW [((1 − n )ep − c)Xv − cv (q + X)] dW ∗∗

dQ dQ dJ + qpQ∗∗ + (1 − n )ep∗ XQ∗∗ + qpJ + qpQ dW dW dW   dv ∗ + qpv + p Xev + Xep∗v − cv (c + X) + (1 − n )ep∗ − c Xv ] dW (13d) − cw (q + X))

A.11 Innovation, Trade and Foreign Investment

91

Note that the impact of exports reinforces the effect of output from foreign-owned subsidiaries. If the process innovation multiplier is positive it is larger in an economy with exports in the respective sector. Note also: the impact of Q, Q** and J, respectively, could be negative with respect to process innovations if the term [(1 − n )ep∗ − c]XV is positive and exceeds the absolute value of qcV ; the expression is always positive in the case of n = 0 and if exports are profitable (ep* > c). The absolute size of XV , that is the reaction of exports in the case of incipient excess capacities is important; the larger XV is the more negative is the multiplier in absolute terms—if it is negative at all. dv −1

= ∗ ∗ dQ qpv + p Xev + Xepv − cv (c + X) + ((1 − n )ep∗ − c) Xv  dq · [qpq + p(.)] dQ

dQ∗∗ dJ + qpJ + qpQ∗∗ + (1 − n )ep∗ XQ∗∗ − cXQ∗∗ dQ dQ   

dV dW + (1 − n )ep∗ − c Xv − cv (q + X) − cW (q + X) + qpQ dQ dQ (13e) −1 dv

= dQ∗∗ qpv + p∗ Xev + Xep∗v − cv (c + X) + ((1 − n )ep∗ − c) Xv  dQ dJ dq · [qpq + p(.)] ∗∗ + qpQ ∗∗ + qpJ ∗∗ dQ dQ dQ  

dV + (1 − n )ep∗ − c Xv − cv (q + X) dQ∗∗ 

dw  ∗ − cW (q + X) ∗∗ + qpQ∗∗ + (1 − n )ep XQ∗∗ − cXQ∗∗ dQ

(13f)

−1 dv

= ∗ ∗ dJ qpv + p Xev + Xepv − cv (c + X) + ((1 − n )ep∗ − c) Xv 

dQ∗∗ dq · [qpq + p(.)] + qpQ∗∗ + (1 − n )ep∗ XQ∗∗ − cXQ∗∗ + qpJ dJ dJ  

dV + (1 − n )ep∗ − c Xv − cv (q + X) dJ  dQ dW +qpQ − cW (q + X) (13g) dJ dJ

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 dv dQ −1

= qpQ dW dW qpv + p∗ Xev + Xep∗v − cv (c + X) + ((1 − n )ep∗ − c) Xv

dQ∗∗ dJ + qpJ − cW (q + X) + qpQ∗∗ + (1 − n )ep∗ XQ∗∗ − cXQ∗∗ dJ dW   

dV

dq + (1 − n )ep∗ − c XV − cV (q + X) + qpq + p(.) (13h) dW dW An interesting result is that export effects reinforce the multiplier for Q**; that is the more foreign subsidiaries are not only selling in the host-country market but also in the global market, the stronger the incentive will be for product innovations. From the perspective of a two-country model the message is that two-way foreign direct investment—possibly concerning different sectors in country I and II—will stimulate global product innovativeness. Another interesting result is that if[(1 – n )ep* – c] is negative—which requires n to reach a critical threshold value—there is a positive link between higher output of other domestic firms or output from foreign subsidiaries only if the revenue-augmenting effect of product innovations reaches a critical value: The reaction of p, e and p* with respect to v is crucial here. From this perspective internationalization of the economy will lead to long-term product upgrading only if product innovativeness really pays—and this is both a technological and an economic question; and, of course, an empirical issue. The impact multipliers for product innovation and process innovation are crucial for policymakers since government is promoting R&D; government policies so far make no clear distinction between promotion of product innovations and process innovations. Moreover, there is only scant knowledge about the relative significance of external effects; and about the extent to which such effects are international external effects which naturally would raise issues about cooperation in innovation policies. One finally may notice that one also could impose the behavior of profit maximization as a long-run requirement which technically requires to set d/dv = 0 and d/dV = 0 (and checking for additional constraints, including second-order conditions). These and other technical issues can be easily explored. Our analysis of an industrial economics model with imports, exports and FDI raises some doubts about the adequacy of many standard macroeconomic models which so often assume that world market prices are given and which almost never consider product innovations or process innovations. This is all the more doubtful since the twentieth century was characterized by an enormous rise of global innovation activities; and the twenty-first century is poised to be even more a Schumpeterian age than the century before. R&D expenditures relative to GDP (or firms’ sales) are increasing in OECD countries and in newly industrialized countries; and the worldwide expansion of modern telecommunications and the Internet are accelerating the diffusion of new knowledge.

A.12 Conclusions Essentially, one may draw several conclusions within the context of this analysis: • Classification of exports and trade, respectively, is rather difficult.

A.12 Conclusions

93

• The HOS model is a useful analytical tool for certain simple questions, but for the modern world economy with sustained innovation dynamics one should modify the model adequately. • The links between trade, foreign direct investment and growth are not fully understood. For a consistent neoclassical analysis of trade and growth one has to assume that there are external effects of capital accumulation in the consumption goods sector on the investment goods sector. In principle one cannot rule out that the investment goods sector also has cross-sectoral spillover effects. Sectoral spillover effects can contribute to sustained growth in a closed economy. Sectoral spillovers could look more complex in an open economy since one might face in country I both sectoral spillovers from machinery and equipment in the consumption goods sector and from the production of investment goods—which is larger than net investment if there are net exports of capital goods. If positive externality comes only from the use of machinery and equipment a positive RCA in machinery and equipment should not influence economic growth. Positive empirical evidence on a positive link between the overall capital stock of a country and the RCA of capital intensive industry would support the hypothesis of positive external effects of capital accumulation. If there are positive externalities stemming from actual and cumulated output in the investment goods sector it would be less important whether investment goods are sold at home or abroad—the latter aspects are, of course, always important with respect to capital formation as such. We have seen that classification of sectors by capital intensity is difficult if there are cross-sectoral spillovers from the use of capital (or the production of investment goods). Hence, the Leontief Paradox necessarily will occur if capital intensity of the foreign country’s export sector is identified with the capital intensity of the importcompeting industry; unless both countries are of roughly equal size in terms of the capital stock. The overall capital stock might be a more adequate measure for the size of a country than population. Product innovations and process innovations are an important element of the world economy. The associated Schumpeterian dynamics should not be taken into account on the basis of the assumption of fully competitive markets. From a theoretical perspective technological catching-up is a necessary condition for economic catching-up if the world economy would consist of countries of equal size. However, if intersectoral spillovers and economies of scale in domestic markets play a role for international competitiveness the size of the economy matters. Small open economies effectively can enlarge their relevant economic geography by FDI outflows; to the extent that FDI outflows are linked to owner-specific technological advantages sufficient R&D activities—including international R&D in subsidiaries abroad—are crucial for catching-up of small open economies. Regional integration schemes which effectively enlarge the domestic market could help small open economies to offset some of the potential disadvantages which small economies might face.

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Appendix A.1: Aggregation in a Two-Sector Growth Model: A Modified Solow Approach with Cobb–Douglas Production Functions Economic growth represents crucial dynamics in market economies. New growth theory (ROMER 1990, GROSSMAN/HELPMAN 1991; BRETSCHGER 1997; SEGERSTROM 1998) has highlighted some new aspects of economic growth, including the role of technological spillovers. Some models of the new growth theory also generate sustained endogenous growth, where the most interesting approaches are models which endogenize growth in the context of an innovation sector and R&D expenditures (e.g., JONES 1995), respectively. The overall progress in recent growth theory is rather impressive (and emphasizing the role of R&D for technological progress) if one takes the book JONES (1998) as a useful point of reference. From a policy point of view one also finds increasing evidence on the role of technology, but also on the impact of entrepreneurship. The latter variable is only vaguely addressed in neoclassical growth models, namely in the form a SOLOW neutral technological progress. While the many variants of the new growth theory represent important theoretical progress, some crucial questions of the older SOLOW-type growth theory (SOLOW 1956) have not been solved. Here I will focus on a rather simple but important issue, namely two-sector modeling. The standard contribution to this field is UZAWA (1965). However, the results derived are cumbersome and rather ambiguous. We will use the familiar SOLOW one-sector growth model as a benchmark for a two-sector model based on Cobb–Douglas production functions. As is well known, the SOLOW model is based on an exogenous rate of technological progress, the savings rate, and other parameters, including the growth rate of population n, and can only be modified to achieve a higher (or lower) equilibrium capital intensity and a fortiori per capita output in the steady state. The SOLOW model in its basic setup is based on a neoclassical production function with labor L and capital K, a standard savings function S = sY (with S and Y standing for savings and GDP, respectively) and the equilibrium condition investment I = sY. Here we disregard depreciation on capital. Together with the definition d(K/L)/dt = dK/dt/L − nk one can derive the standard results of the model. If we use a Cobb–Douglas function Y = H Kß L1−ß , the important results concern capital intensity k = K/L and per capita output y in the steady state: k = [s/(a + n)]1−ß

(I)

y = Y/L = [s/(a + n)](1−ß)/ß

(II)

The latter result is very straightforward for the case of ß = 0.5. The steady-state per capita output is directly proportionate to the savings rate. The more important the

Appendix A.1: Aggregation in a Two-Sector Growth Model

95

savings rate is for equilibrium capital intensity and per capita output, the more crucial are adequate reforms of the tax system and of the banking system, including the policy stance of the central bank. For any government aiming at raising long-term per capita income the relative merits of measures affecting the savings rate and other relevant parameters are crucial. Moreover, with OECD economies ageing and savings rates falling in the long run, a full appraisal of the role of the savings rate for growth is indeed important. With this background in mind we turn in section 2 to the modeling of a two-sector economy in a setup with Cobb–Douglas production functions. In the final section we draw some policy conclusions and point out potentially important options for future refinements.

Two-Sector Cobb–Douglas Model Let us consider a small open economy with two sectors (sector 1 = production of capital goods) which produce with labor L and capital K where we denote k1 = K1 /L1 , k2 = K2 /L2 , k = K/L, λ = L1 /L and q = PC /PI . q is exogenous, that is it will be taken from the world market since firms are price takers. Assume that both sectors are characterized by a Cobb–Douglas production function Y1 = HKß11 L11−ß1 ; 0 < ß1 < 1 Y1 /L = HKß11 λ Y2 = HKß22 L21−ß2 ; 0 < ß2 < 1 Y2 /L = Hk ß22 (1 − λ)

(1) (1.1) (2) (2.1)

In a long-term equilibrium approach requiring a balanced current account we have for an economy with zero government expenditures the following equilibrium requirement: [I/L] + [C/L] = Y/L = y

(3)

We will use the definition of k = K/L, that is k2 = k + λ(k2 − k1 ) Hλ(k1ß1 ) + qHk ß22 (1 − λ) = y

(4) (3.1)

Due to profit maximization, a condition not taken into account in the standard SOLOW model, we have ß1 I/K1 = r = ß2 C/K2 =ß2 cY/K2

(3.2)

(ß1 I/L)/[(K1 /L)(L1 /L1 )] = ß2 (cY/L)/[(K2 /L)(L2 /L2 )]

(3.3)

ß1 (I/L)/K1 γ] = (ß2 cY/L)/[K2 (1 − γ)]

(3.4)

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Assuming the equilibrium condition I/L = sY/L

(3.5)

ß1 sy/(k1 λ) = ß2 (1 − s) y/(k2 (1 − λ))

(3.6)

k2 = k1 (ß2 /ß1 ) (1 − s) λ/[(1 − λ)s]

(3.7)

we have

Using the definition of k in Eq. (4) we have: {(ß2 /ß1 ) λ [(1 − s) /s] }k1 = k − λk1

(4.1)

k = λ{1 + (ß2 /ß1 )[(1 − s)/s]}k1

(4.2)

Assuming that ß2 = ß1, which is particular sensible when we turn to a comparison of our two-sector approach with the one sector SOLOW equation, we have: K = (λ/s)k1

(4.3)

y = Hk ß11 + (1 − λ)qH{(ß2 /ß1 )(1 − λ)s]}ß2 k1ß2

(3.1 )

Inserting in (3.1) we get:

With ß2 = ß1 = ß we have y = Hk1 ß {λ + q(1 − λ)[(1 − s)λ/((1 − λ)s)]ß }

(5)

y = Hk ß {sß λ1−ß +q(1 − λ)1−ß (1 − s)ß }

(6)

Therefore

We now assume for ease of exposition that s = 0.5. This assumption will not change our results in a qualitative way. We get y = H k ß sß {(λ1−ß + q(1 − λ)1−ß }

(6 )

Note that profit maximization requires that the marginal value product of labor in each sector be equal to the uniform nominal wage rate W, that is (1 − ß1 ) [Y1 /L1 ] PI = W = (1−ß2 ) [Y2 /L2 ] PC

(7)

Using the definition q = PC /PI and taking into account the assumption ß1 = ß2 we have Q = (Y1 /L1 )/(Y2 /L2 )= Hk1 ß /Hk2 ß

(7 )

Taking into account (3.7) we have q = {(1 − λ)s/[(1 − s)λ]}ß

(8)

Appendix A.1: Aggregation in a Two-Sector Growth Model

97

This gives us q1/ß = ((1 − λ)/λ)(s/(1 − s)) or q1/ß (1 – s)/s = (1/λ) – 1 and therefore λ = [1 + q1/ß (1/s − 1)]−1

(9)

Replacing λ in Eq. (6 ) we obtain −1 1−ß

y = Hk ß sß {([1 + q1/ß (1/(s − 1))]

)

+ q(1 − [1 + q1/ß (1/s − 1)]

−1 1−ß

)

} (6 )

This finally results with s = 0.5 in ß

y = Hk ß sß {(1 + q1/ß ) }

(6 )

There is a „correction factor“{. . . } in the above equation which has implications for the neoclassical growth model when comparing this to the standard neoclassical one-sector model, which is y = H k ß . In a model without depreciation and with an exogenous growth rate of technological progress of dH/dt/H = α (here we assume for simplicity α = 0), we have as the familiar equation for the steady-state equilibrium—with equilibrium k denoted as k#: sy = n k#

(10) ß

s H k ß {sß [1 + q1/ß ] } = nk#

(11)

s1+ß H[1 + q1/ß ]ß = nk#1−ß

(12)

The traditional formula for the one sector economy is s = n k 1−ß . Thus our twosector approach shows that the traditional SOLOW model overestimates (recall that s < 1) the role of the savings rate for the equilibrium capital intensity and a fortiori for per capita income. The difference is not trivial. As an illustrative case take ß = 0.5 which comes close to empirical estimates of the share of capital income in poor countries. Changes in the parameters, leaving α aside, will only affect the level of capital intensity and output per capita as is well known from the original SOLOW model.

Conclusions The model has shown that the SOLOW one sector model overestimates the role of savings. On the one hand, the implication is that other variables are relatively underestimated. On the other hand, the secular fall of the savings rate in ageing OECD countries does not seem as dramatic with respect to long- term growth as the original SOLOW model suggests. As regards distinguishing different technologies in the two sectors, it should be pointed out that only for ease of exposition have we made the assumption of identical production functions in both sectors. Different sectoral capital intensities are naturally quite crucial in such a setup. In a more general model with different production

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function in both sectors or both countries the role of technology would receive more emphasis. A useful application a explicit two sector modeling is the analysis of the internet dynamics (WELFENS 2001a). What is the impact of a rise in the exogenous variable q? According to (12) we can state: The higher the relative price PC /PI the higher will be the equilibrium capital intensity k#. According to the Samuelson–Stolper theorem the factor which is intensively used in the good which has become expensive will benefit from an increase in factor reward. If consumption is relatively capital intensive, then capital income should increase relative to labor income. However, this exactly is ruled out by using Cobb–Douglas production functions. This points to the necessity to consider even more complex modeling based on CES functions. A final remark concerns the role of technology, somewhat neglected here. Ideally one could take into account the role of biased technological progress and product innovations. However, while innovations lead us more closely towards the real world, it will make analytics much more cumbersome. In a Schumpeterian setup it is not convincing to assume that technologies are identical in both countries. Moreover, a temporary technological edge will give firms the ability to profitably produce abroad. With FDI flows the setup becomes crucially different form the Heckscher–Ohlin world since with FDI one will have to distinguish between GDP and GNP, and this distinction is important for the issue of international per capita income convergence (WELFENS 1997). These basic conclusions point to a rich field of refined future research, even without taking into account the new growth theory.

Appendix A.2: Two-Sector Model (KHAN/BILGINSOY 1994) Nominal output is Q; we consider a two-sector economy with output I and H, respectively—prices are P in the I-sector and P in the H-sector. Q = P I + P H

(1)

Consider the following two simple production functions (e is the Euler number) I = eψt f(K , L )

(2)

H = eξt h(K  , L , I)

(3)

Competition and profit maximization gives: fK /hK = fL /hL = P /P =: p   fK /hK = fL /hL = 1 + δ p in case of market power

(4)

dQ/dt = HdP /dt + IdP /dt + P dH/dt + P dI/dt

(6)

dI/dt = ψI + fK dK  /dt + fL dL /dt

(7)

(5)

Appendix A.2: Two-Sector Model

99

Note that dK = dK + dK ; and dL = dL + dL . Substituting dH and dI from Eqs. (7) and (8) and using Eq. (5) and Eq. (6) that is we use fk = (1 + δ )[P /P ] hK and fL = (1 + δ )[P /P ] hL dH/dt = ξH + hK dK  /dt + hL dL /dt + hI dI/dt

(8)

dQ = ψP I + ξP H + HdP + IdP + hK P dK + hL P dL + hI P dI   + δ P hK dK + hL dL

(9)

Using (7) and (5) again we get: dQ = ψP I + ξP H + HZdP + IdP + hK P dK + hL P dL + hI P dI + [δ /(1 + δ )]P dI − [δ ψ/(1 + δ )]P I P dH

(HdP

IdP

(10)

P dI)

= dY – + + From Eq. (6) we have By chosing dH/dt as the dependent variable, we obtain from Eq. (9): dH/dt = ξH + hK dK + hL dL + hI dI − [δ /(1 + δ )]pdI − [δ ψ/(1 + δ )]pI

(11)

With ρ := hL L/H and  = hI I/H—the elasticity of the sectoral externality—and s := P I/P H we get: gH = ξ + hK [dK/dt]/H + ρgL +  gI − 1/(1 + δ )s gI + [ψ/(1 + δ )]s

(12)

The output growth rate of H thus not only depends on the sectoral progress rate but also on the relative overall growth rate of the capital stock—the second term on the right hand side (using g for denoting growth rates) can be written also as hK (gK )/[H/K]—and the growth rate of the output of the other sector (with crosssectoral spillovers) and the weighted technological progress rate of the I-Sector. We may add that from (2) and (3) we directly obtain: gI = ψ + Ef,K gK + Ef,L gL

(2 )

gH = ξ + Eh,K gK  + Eh,L gL + Eh,I gI

(3 )

Hence a general finding—ignoring profit maximization (note that  := Eh,I )—is: gH = ξ + Eh,K gK + Eh,L gL + [ψ + Ef,K gK + Ef,L gL ]

(3 )

However, expression (12) is much more revealing. Returning to the result from (12) one may add that in a closed economy (and disregarding capital depreciation) dK/dt is equal to I so that the assumption I = sY and H = cY leads to gH = ξ + hK s/c + ρgL + gI −1/(1 + δ )s gI + [ψ/(1 + δ )]s

(13)

The growth rate of consumption output then is determined by the rate of technological progress plus—assuming that the real interest rate r is equal to hK —the term r s/c plus the growth rate of labor plus the externality element (gI ) from the production of investment goods plus the weighted progress rate of the other sector.

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Appendix A.3: Labor Markets with Tradables and Nontradables We present a simple model for the case of a small open economy. The model setup is with two labor markets, namely for skilled labor earning real wages w and unskilled labor earning a real wage of w . We assume that the nontradables sector employs only unskilled workers L N while the tradables sector employs both unskilled workers L T and skilled workers L . The demand for skilled workers is—denoting the real interest rate as r—assumed to be a negative function of w /r, while the demand for unskilled workers is assumed to be a negative function of w /r. We assumed that the supply of tradables depends on the input of skilled labor, unskilled labor and capital plus the import of intermediate products T** which is assumed to be a negative function of the real exchange rate q* = ePT */PT (e is the nominal exchange rate in price notation, PT is the tradables price and * denotes foreign variables). Assuming that the domestic demand for tradable goods is proportionate to real wage income w L + w L the domestic quasi-equilibrium condition for the tradables sector is written as: Ts (w /r, w /r, T∗∗ (q∗ )) = c [w L + w L ]

(1)

Note that any excess supply in the tradables sector is equivalent to a current account surplus which will bring about a real appreciation, and a real appreciation in turn will raise the tradables output in turn. We define a real wage index w = z w + (1 – z )w —where z is a proxy for the share of workers employed in the tradables sector; the w –w space the slope of the real wage rate line ww0 is negative. Using the definition of the real wage index we can easily write an equilibrium condition for the nontradables market where demand is assumed to be proportionate to real wage income wL (with L : =L + L ). Ns (w /r) = c wL

(2)

In the short-run labor supply of unskilled workers and skilled workers is given, in the medium term on may assume that L is a negative function of w /w while L is a positive function of the relative wage ratio w /w . In w –w space we can draw the LNN curve portraying equilibrium in the nontradables sector and the LTT curve portraying equilibrium in the tradables sector. The intersection point E stands for full employment equilibrium and also for a simultaneous equilibrium in the N-market and the T-market. Above the LNN curve we have an excess demand (EDNN ), below there is an excess supply; and therefore also an excess supply of unskilled workers in the nontradables sector. An equilibrium in the unskilled labor market can be restored either be returning to point E or moving to a situation in which there is an excess demand for unskilled labor in the tradables market (one may assume that a parallel excess demand for skilled workers will be satisfied by training of unskilled workers which qualify as unskilled after a certain training time). Below the TT-curve there is an excess supply (ESTT ) in the tradables market. Denoting the nominal money supply as M, the price level as P and assuming that the demand for money is proportionate to real output Y—and Y = wL + rK (where

Appendix A.3: Labor Markets with Tradables Fig. 23 Wage structure and trade balance (w : wage of unskilled labor, w : wage of skilled labor)

101 Initial Situation

w′

LNN0 (EDNN) (ESTT) w0′

H G

E0 F

LTT0 ww0

a

α w0′′

w′

Effect of Depreciation (Endogenous) w′

E0

w2′

D

w1′

LTT1

w0 ′ E0 LNN0 ww0

α

b 0

w2′′

w0′′

w1′′

LTT0 w′′

K is the capital stock)—and negatively depends on the interest rate money market equilibrium in a non-inflationary modeling setup is given by M/P = n (r)[wL + rK] = n (r)[z w L + (1 − z )w L + rK]

(3)

In w –w space the slope of the money market equilibrium line LMM is negative. A rise of M/P would shift the LMM curve temporarily to the right so that we get an excess supply in the money market so that the demand for bonds will rise which will bring about a rise of bond prices and a fall of the interest rate. Equations (1)–(3) determine jointly w , w and r. The real exchange rate can change only temporarily since for a small country its medium-term value is determined from the outside.

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Appendix A.4: Product Innovations with Schumpeterian Intermediate Products: A Simple Formula Product innovation dynamics in modern economies are internationalized in many respects. An important element concerns the fact that producers of innovative final products (say a good j) will rely on using imported intermediate novel products (say an intermediate good i). One may state the hypotheses that the final goods producer can impose a higher top-up rate on the product—compared to a standard benchmark product (price pj *) in world markets—than the supplier of the intermediate product. What is the effective top-up rate compared to the benchmark final product? We will show that this question analytically is equivalent to the problem of the effective tariff rate in a world with tariff escalation (the tariff rate on the intermediate product is lower than for the final product); furthermore we will show that the well known formula for the effective tariff rate can be written in a simplified version which is quite useful. Value-added of the standard product is Vj * = pj * – αpi * Here α denotes the amount of the intermediate product i needed to produce one unit of the final product j. If we consider an innovative final product which uses an innovative intermediate product value-added is now: vj * = (1 + τj )p∗j − α(1 + τi )p∗i . By assumption the top-up ratio τ for the final product exceeds that for the intermediate product, that is τj > τi . (furthermore we will assume that intermediate producers from poor countries can obtain only smaller top-up rates than rich countries which produce the same intermediate product). The effective top-up rate (τeff ) is defined as  

  τeff = vj − Vj ∗ /V∗j − τj pj ∗ − ατi pi ∗ / pj ∗ − αpi ∗ (A4.1) We denote the share of the intermediate product in a € s worth of the final standard product at free-trade prices by θ := αpi */pj *. Hence we get: τeff = (τj − θτi )/(1 − θ).

(A4.2)

The formula shows that the effective top-up rate is determined by the top up rate for the final product, the top-up rate for the intermediate product and the share θ (we do not assume process innovations in combination with product innovations since this would imply that the innovative product would have α below the case of the standard/benchmark product). This formula exactly is the same as the well known formula for the effective rate of tariff protection. We can go one step further and derive a modified new formula, namely by taking into account that τi = (1 − ρ)τj where ρ is a positive parameter in the interval 0, 1 which indicates the percentage by which the top-up rate for intermediate products is below that of the final innovative product. We therefore can write: τeff = (τj − θ(1 − ρ)τi )/(1 − θ)

(A4.3)

We assume that θ is rather small so that we can use the approximation ln(1 + x) ≈ x. Taking logarithms results in: ln τeff = lnτj +θρ/(1 − θ)

(A4.4)

Appendix A.5: Medium-term Output and Wage Policies

103

This equation says that the logarithmized effective top-up rate—an indicator of profitability—obtained by innovative producers of final products is the larger the higher the (logarithmic) top-up rate for the final product and the higher the differential ρ between the two top-up rates. Taking into account the Amoroso-Robinson equation one might argue that the top-up rate for the final product and the intermediate product, respectively, mainly will reflect the inverse of the absolute price elasticity. (The result for the effective tariff rate is, of course, identical in the sense that the effective tariff rate τeff is the higher the higher the tariff rate on the final product, the higher the parameter θ—the more important intermediate products economically are—and the higher the differential ρ between the tariff for the final product and the intermediate product.) Final goods producers from Schumpeterian sectors thus have a massive interest in international outsourcing/offshoring to poor countries since this raises the effective profit ratio and the effective top up rate, respectively. There is, however, an economic mechanism which limits international outsourcing/offshoring: namely the fact that the higher θ the lower is the feasible τi . People will be willing to pay a premium—compared to standard cars—for a Porsche, Audi or Mercedes, Volvo or Jaguar provided that there is a considerable part of value-added which is undertaken in Germany, Sweden and the UK, respectively. Obviously, the feasible top-up ratio depends on a company-specific premium and a country-specific premium, otherwise final production stage of many premium cars would be relocated to developing countries or eastern Europe which has not been the case. There is a clear conclusion to be drawn, namely that rich OECD countries will be characterized by considerable activities in final goods (and services) production. Economic catching-up in a multi-country model thus requires that poor countries are not only moving up the technology ladder but also grab an increasing share of final goods production in which relatively high Schumpeterian rents can be earned. From this perspective locational competition is particularly hard if international relocation of headquarters takes place since then the country/location will change where the final production stage is realized.

Appendix A.5: Medium-term Output and Wage Policies in an Open Economy In countries with high unemployment rates, one often hears claims that output and employment could be raised through more aggressive wage policies. Higher real income would translate into higher aggregate demand which in turn raises output. We want to shed some light on this argument in a simple one-sector model, while ignoring that a major issue in reality is not just the size of the wage increase (or the wage level) but average wage increases on the one hand and cross-sectoral wage dispersion on the other. We also do not deal much with the issue of whether wage inequality and unemployment affect productivity growth. As regards this link ARNOLD (2006) has presented an interesting new model, namely a non-scale continuous-

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time overlapping-generation growth model which provides an explanation for why economies with relative wage rigidity record higher unemployment but not slower productivity growth than economies with more flexible wages. The result stems from two offsetting effects: (i) the compression of the wage distribution associated with relative wage rigidity slows down human capital accumulation due to negative incentive effects; (ii) high unemployment among the low-skilled workers reinforces the incentives to invest in human capital which stimulates growth. A knife-edge result for productivity growth thus is possible. The author refers to two strands of the literature: The link between innovation, growth and unemployment on the one hand and between innovation and human capital accumulation. As regards the latter the contribution by GROSSMAN/HELPMAN (1991) was crucial who rely on the approach of FINDLAY/KIERSZKOWSKI (1983)—looking at the link between human capital formation and research & development. YOUNG (1993) has analyzed a model with growth and human capital where skill acquisition via learning by doing is costless. EICHER (1996), GALOR/MOAV (2000) and GOULD ET AL. (2001) present approaches on the impact of growth on inter-group and intra-group wage inequality. As regards the link between growth and unemployment an important contribution of the literature concerns search models of the labor market (BEAN/PISSARIDES 1993); AGHION/HOWITT (1994, 1998) have shown with a search framework how growth affects unemployment via a “capitalization effect”—higher growth raises profitability of offering vacancies—and a creative destruction effect (new products destroy jobs in the old industry). While this strand of the literature is quite interesting our focus is more modest and raises the question how wages in an open economy will affect output in a medium-term framework.

Wage Policy in the Mundell–Fleming Model Basically we wish to first consider a small open economy under flexible exchange rates, for which we assume that net exports of goods and services X positively depend on exogenous world output Y* and the real exchange rate q* := eP*/P (e is the nominal exchange rate) and negatively on real incomeY and the ratio of domestic real wages w to foreign real wages w*. The price level is assumed to be sticky. The model determines e, Y and the real interest rate r in a short-term approach. Moreover, we assume that consumption is proportionate to expected future wage income w L (w is expected real wage, L expected employment), current real wage income wL, where employment L is assumed to negatively depend on current real wage and the expected future wage rate w . The current capital stock is given and underemployed so that it is not relevant for labor demand. Future employment is assumed to depend negatively on w but positively on the future capital stock K = K + I. Since we assume investment I to be a positive function of the expected profit rate z and a function of w/r (with an ambiguous sign, as a higher w stimulates substitution of labor through capital but also could boost demand which would raise profitability of investment), we must assume L (w , K, w/r, z ). We denote w/r as ϕ and w/w* as ϕ . To assume that the real wage rate is exogenous in the short run is justified on the basis of the

Appendix A.5: Medium-term Output and Wage Policies

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assumption that the price level P is sticky. Real net capital inflows Q are assumed to positively depend on the ratio of the nominal interest rate i to the foreign rate i* and negatively on the expected nominal devaluation rate a . As regards money market equilibrium, we assume that the real demand for money depends positively on Y, negatively on i and positively on the ratio of w/w# (denoted as ϕ ), where w# is the equilibrium wage rate for the labor market. A rise of w/w# implies unemployment— for the case of w exceeding w#—and a higher unemployment rate will increase the liquidity preference; the demand for money will therefore rise. The parameters c and c are exogeneous, as is government consumption G. Y = cwL(w, w ) + c w L (w , K, ϕ , z ) + I(ϕ , z ) + G + X(ϕ, q∗ , Y∗ , Y)

[IS curve]

M/P = m (Y, i, w/w#) [LM curve]     [ZZ curve] Q i/i∗ , a  = X ϕ , q∗ , Y∗ , Y

(1) (2) (3)

Assuming zero inflation and hence i = r, we get the following result from taking the total differential: dY = cLdw + cwLw dw + cwLw dw + c w L w dw + c w L K dK + c w L ϕ dϕ + c w L z dz + Iz dz + Iϕ  dw/r + dG + Xϕ dϕ + Xq∗ dq∗ + XY∗ dY∗ + XY dY dM/P = mY dY + mi di + [mϕ /w#]dw Qi/i∗ dr/i∗ + Qa da = Xϕ dϕ + Xq∗ dq∗ + XY∗ dY∗ + XY dY

(4)

(5) (6)

We assume that aggregate demand determines output Y and that (with ψ denoting the degree of utilization of the capital stock) the supply side is determined according to Y = F(ψK, L) = ψrK + wL. Hence a rise in Y, which is not fully explained by a rise of w or L or r, must be explained by a rise in the degree of utilization of the capital stock. The case of a closed economy with c’ assumed to be zero-to remain as simple as possible-leads to the following picture. Assuming that Iφ < 0, a rise in the real wage rate will lead to a leftward shift of the IS curve if the labor demand elasticity with respect to labor exceeds unity or is equal to unity. In both an open and a closed economy, Iφ > 0, and Iq exceeding a critical parameter would imply that a rise in w implies a rightward shift of the IS curve, which suggests that real income will increase and the real interest rate will rise for a given LM curve (i.e., with mφ = 0). Only if a rise in the real wage rate brings about a strong reaction on the side of entrepreneurs to raise investment can one expect a positive impact of the real wage rate on real equilibrium output. Even if the IS curve is shifted to the right through a rise in the real wage rate could the equilibrium income be stagnating, namely if there is a sufficient leftward shift in the LM curve as a consequence of a higher wage rate.

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In an open economy under flexible exchange rates and perfect capital mobility— the ZZ equilibrium line horizontal in r–Y space—a rise in the real wage rate will cause a real appreciation of the nominal exchange rate which in turn will cause a leftward shift of the IS curve so that any initial expansion of the wage rate will be undermined provided that the price level remains constant. A rise in the nominal wage rate (implying a rise in the real wage rate) could bring about a rise in price level, which in combination with the nominal depreciation could ultimately trigger a relatively strong rise in the price level and hence a medium term fall in the real wage rate. This would be a rather paradoxical output expansion path generated by an initial increase in both the nominal and real exchange rate. Note that a relatively strong rise in real output implies that the degree of capital utilization will increase. The multipliers for the main cases of interest are shown subsequently where we assume that the system determinant is negative; this requires that the interest elasticity of investment is not exceeding a critical value and that the intertemporal substitution of labor is rather small (Lr which refers to future labor input as a consequence of a change in the current factor price ratio). A rise of the wage rate will raise output in the short term only if the reaction of labor demand with respect to w is rather weak and if the reaction of net exports with respect to w is small. The multiplier expressions for r and M also are indicated. We have shown that a rise of the wage rate could be a way to overcome a recession only if both labor demand and net exports react only weakly with respect to a rise of the wage rate. The more the economy is specialized in high technology products and the higher the share of high technology exports in overall trade is the more likely is the case of a positive multiplier dY/dw. However, as only very few OECD countries indeed are specialized dominantly in high technology the standard case for OECD countries is dY/dw < 0. Empirical analysis can shed more light on this issue. In an open economy there also is an important caveat, namely the reaction of other countries. It is clear that a reduction of wages in country I will not really improve the trade balance if wages abroad are also reduced. Moreover, in certain cases wage reductions could be an element of an undesirable beggar-my-neighbor policy. dY/dw = (Qr (cL + cwLw + c w Lw /r + Iw /r + X w /w∗ ) − (w/r2 Ir + cw L r w/r2 )X w# i∗ /w∗ )/D where D := (Qr (1 − X Y ) + X Y i∗ (w/r 2 Ir + cw L r w/r2 )) dr/dw = (X Y (cL + cwLw + Iw /r + c w Lw /r) + w/w∗ )/D

(7) (8) (9)

 ∗  i mi w#)(1 − XY ) − i∗ (w/r2 Ir + cw Lr w/r2 ) dM/dw = ((Qr w∗ mw + Xw   mY w# − XY mw w∗ ) − (cL + cwLw + Iw /r + c w Lw /r + (Xw   + X w /w∗ )w#w∗ (Qr mY − XY i mi ))/[w#(Qr (1 − X Y)  ∗ i (w/r2 Ir + cw Lr w/r2 ))/Pw∗ ] + XY

(10)

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Flexible Exchange Rates The situation is quite different under fixed exchange rates; endogenous variables are Y, r and the money supply M. Let us briefly consider the new setup. An increase in the real wage rate will bring about a rise in the real interest rate, thereby causing a net capital inflow. This in turn translates into an excess supply in the foreign exchange market, which will bring with it—through intervention of the central bank—a rise in the nominal money supply. This rightward shift in the LM curve could finally bring about a rise in real output. From this perspective, one should not rule out that aggressive wage policies could be more common in a fixed exchange rate regime than in a system of flexible exchange rates. In a more long-term perspective, one will have to raise the question as to whether a rise in the money supply will bring about a medium-term increase in the price level so that the real wage rate might fall after a transitory increase. This also points to the issue of whether a system of fixed exchange rates is more inflationary than a system of flexible exchange rates. Taking into account the Mundell–Johnson monetary approach to the balance of payments, one could essentially argue that the monetary policy in combination with wage policies in the anchor country is the key to answering this question. If we set U = P*/X e P(−mY Qr /i* − mi + mY (w/r2 Ir + cw L r w/r2 )). If Lr < 0 then U < 0 then the multipliers for w are as follows: dr/dw = −UX e P/P∗ (mw Qr /(w#i∗ ) + mi X w /w∗ − (cL + cwLw + Iw /r + c w Lw /r + X w /w∗ )mi − mw wIr /(w#r 2 ) − cw L r wmw /(w#r 2 )) 

(11)

∗





dY/dw = −UX e P/P (mw /w# + mY (cL + cwLw + Iw /r + c w Lw /r)) > 0 (12) ∗



∗



∗

de/dw = −U(Qr mw w − Qr X Y mw w + X w i mi w# − (wIr /r 2 + cw L rw /r 2 )(X w i∗ mY w# − X w i∗ mY w#) + (cL + cwLw + Iw /r + c w L/r + X w /w∗ ) (Qr mY w#w∗ + XY i∗ mi w#w∗ ) − X w X Y i∗ mi w#)/i∗ w#w∗ ∗

 

(13)

dY/dG = mi /(Qr mY /i + mi − mY (Ir w/r + cw L r w/r )) 2

2

(14)

dr/dG = −mY /(Qr mY /i∗ + mi − mY (Ir w/r2 +cw L r w/r2 )) ∗



∗

(15) 



de/dG = −(Qr mY /i + mi XY )/X e (Qr mY /i + mi − mY (Ir w/r + cw Lr w/r 2 )) (16) 2

The fiscal policy multipliers for Y, r and e are positive provided that the system determinant—the denominator—is negative.

B. Savings, Investment and Growth: New Approaches for Macroeconomic Modeling

B.1 Introduction In macroeconomics, there are two contrasting views to the role of the savings rate. In a short-term Keynesian perspective, a rise in the savings rate s reduces the equilibrium income. However, the long-run neoclassical growth model suggests that a rise in the savings rate raises equilibrium real income. Short-term macroeconomic analysis is rarely linked to long-term dynamics, and this can be misleading for policymakers. Moreover, it leaves policymakers, who would like to know under which conditions a rise in the savings ratio shows up in a contractionary or an expansionary impact, confused. The following analysis—for a non-inflationary world—is straightforward and first recalls the simple long-run neoclassical growth model (SOLOW 1956), and the short-run Keynesian macro model before we merge both approaches within a new medium-term model. We present the multipliers for monetary policy, fiscal policy and supply-side policy (rise in the savings rate s). Section B.2 presents the model, and the final section gives some policy conclusions. Several conclusions reached are in marked contrast to the standard Keynesian model and also go beyond the monetarist debate.

Analytical Starting Points There have been various attempts at describing macroeconomic modernization in the literature. Real business cycle economists have emphasized the role of productivity shocks in models where the central bank has almost no options to influence employment and output (PRESCOTT 1986; PLOSSER 1989). New classical theorists have put the focus on the relevance of intertemporal optimization and rational expectations (LUCAS 1981; LJUNGQVIST/SARGENT 2000). Modern Keynesian economists have focused on the effects of monopolistic competition, markups and costly price adjustment (MANKIW/ROMER 1991; ROMER 1993). The new neoclassical synthesis combines elements from both the Keynesian perspective and the classical P. J. J. Welfens, Innovations in Macroeconomics, DOI 10.1007/978-3-642-11909-5_2, © Springer-Verlag Berlin Heidelberg 2011

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approaches into a single framework where GOOD-FRIEND (2004) and GOODFRIEND/KING (1997/2001) have been particularly active—along with others (e.g., CLARIDA/GALI/GERTLER 1999; WOOD-FORD 2003). Combining short-term economic perspectives with long-term economic analysis is done here on the basis of a modified consumption function based on a variant of the permanent income hypothesis: It is assumed that at the macroeconomic level consumers’ spending is a function of current income (Yt ) and the steady-state value (Y#) where weights a for discounted Y# and (1 − a  ) for current income Yt are used: Ct = c(1 − a )Yt + ca Y#/(1 + r). This consumption function may be interpreted as follows: One group of consumers is mainly influenced by current income, a second group mainly by long-term expected steady-state income; or each consumer considers both the current income and long-term expected income. Moreover, we consider a specific net investment function which implies—for a certain parameter set—that investment per capita demand is such that the capital accumulation dynamics are consistent with the capital-market-driven capital supply accumulation implicit in the Solow growth model. Thus, our medium-term model is consistent with the transition dynamics of the capital stock. The investment function used states that net investment dK/dt is proportionate to the difference between the marginal product of capital YK —net of depreciation (depreciation rate δ)—and the real interest rate r; specifically we assume an adjustment parameter b (K) where the adjustment speed is a positive function of the capital stock. The argument for the adjustment speed b to positively depend on K is that in a highly specialized interdependent economic system the adjustment speed for sectoral differentials in the net marginal product of capital, and the real interest rate will be the higher the larger K is. A final goods producer relying on intermediate suppliers would want to avoid a diversion of suppliers from the profit maximization condition—ensuring efficient production. The more complex the supplier network is—in a larger economy (as proxied by K)—the supplier structure becomes more complex and hence the final goods producer faces high sunk costs (if suppliers are not efficient, the economic viability of final goods producers is threatened). An alternative argument would be that with rising K, the number of potential bidders willing to take over a company with unexploited opportunities for profits will increase—an increasing probability of takeovers will stimulate the management to rather quickly eliminate differences between the net marginal product of capital and the real interest rate. To put it differently: While from a microeconomic perspective each firm faces adjustment costs in investment projects, we assume that each firm’s adjustment speed is linked to the overall capital stock. The larger K, the smaller the optimum adjustment speed chosen by the individual firm. The model to be presented combines a sticky price short-term analysis (the output is determined by aggregate demand) with an implicit long-run flexible price model (the Solow growth model); the mixture of Keynesain elements and the Solow growth model is not a contradiction as we will not consider a model with deflation or inflation. The price level is given because the Keynesian perspective implies a constant price level due to underutilization of production capacities in the short run; at the same time the Solow model is consistent with a constant price level as long as we are not considering process innovations (WELFENS 2006).

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One should not easily dismiss that an alternative modeling strategy based on explicit microeconomic foundation and intertemporal maximization analysis for consumers and investors could be a useful alternative to the approach suggested. However, as we rely on the well-established permanent income hypothesis and simply combine the standard Keynesian analysis and well-established results from long-run growth analysis, we are not relying on opaque ingredients for the medium-term model. Moreover, the consumption function presented could indeed be derived from a rather simple two-period model (with period 2 representing the long run, period 1 the short run); intertemporal optimization would bring out the role of subjective time preference. The only shortcoming which might be serious is that we are not considering delayed price adjustment which one could combine with monopolistic competition in a model with n product varieties—but one may emphasize that the simple model presented here already is highly complex in the multiplier analysis. Finally, for policymakers it will be quite useful to have a model which includes both parameters from consumption and investment demand as well as relevant supply-side parameters so that a broad range of options can be carefully considered.

B.2 A Medium-term Keynes–Solow Model For the case of a production function is Y = Kß L1−ß , capital depreciation is δK (depreciation is proportionate to the capital stock K, 0 < ß < 1), savings S = sY and gross investment I = S the standard neoclassical growth model (assuming that the population L is constant) shows that long steady-state equilibrium capital intensity k# and output Y#, respectively, is given by the expression k# = [s/δ]1/(1−ß)

(1a)

Y# = L[s/δ]ß/(1−ß)

(1b)

Here δ is the depreciation rate of capital, s is the savings rate. Taking at first a look at the closed economy (with savings rate s, real interest rate r and output Y and government consumption G), one may at first state the IS curve for goods market equilibrium as Y = (1 − s)Y − br + G. Using the hybrid consumption function suggested (with L[s/δ]ß/(1−ß) representing the modified permanent income component) we get  Y = (1 − s) (1 − α )Y+[α /(1 + r)]L(s/δ)ß/(1−ß) − br + G. (1c) Taking into account the investment function suggested, we are not using the investment demand in the form of b/r, rather—taking into account the production function, namely YK = ßY/K—gross investment is given by δK + b[ßY/K − δ − r]K, and thus the equilibrium condition for the goods market reads Y = (1 − s){(1 − α )Y + [α /(1 + r)]L(s/δ)ß/(1 − ß)} + b[ßY/K − δ − r]K + δK + G

(1d)

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Note here that for comparing the hybrid model with the standard Keynesian setup one should set K = 1. What about the role of real government expenditure G? A rise of G will raise Y and hence consumption will increase—as in the standard case—but the effect on consumption and hence equilibrium medium term output is reduced through the factor (1 − α ). Moreover, the increase in Y implies an increase in the marginal product of capital (as long as K is constant) so that investment is raised. This is a quasi-accelerator effect, and the fiscal multiplier indeed is raised through the term bß. If one endogenizes r, one will have to take into account a crowding out-effect both through lower consumption—see the modified permanent income component—and lower investment. Note also that a rise of the savings rate s has an ambiguous effect since a rise of s reduces consumption with respect to current income (fall of marginal consumption expenditures) but stimulates consumption through the positive permanent income effect. Depending on the various parameters government might indeed consider to raise s as a medium-term supply-side policy alternative to standard Keynesian policy options. Already from the inspection of the simple goods market equilibrium condition, we see that a richer set of parameters is now determining multipliers: Besides the standard Keynesian parameters, we have supply-side parameter such as ß, b, δ and the weighting factor α for modified permanent income. One should note the advantage of the above approach in the sense that it easily allows us to consider various crucial aspects at the same time; for example, in an extended version (with production function Y = Kß (AL)1−ß ; A denoting the level of Harrod-neutral technology) one may consider the role of process innovations easily as a standard vintage approach (STOLERU 1978; p. 405) implies not only that A is rising at a certain rate but the depreciation rate δ, too. The multipliers for a setup with constant level of technology will be studied in more detail subsequently. As the steady-state value Y# is obtained from the differential equation for the change in the capital intensity k := K/L, namely dk/dt = s(Y/L) − δk = sk ß − δk

(1e)

long-run output Y# is obtained by taking t → ∞ or by setting dk/dt = 0. Rational forward-looking individuals with infinite time horizons would thus expect Y to converge toward Y# in the long run. The simple neoclassical growth model has the well-known implication that the higher the savings rate, the higher equilibrium output. Hence in a long-run perspective, a rise in the savings rate will lead to higher equilibrium output.

B.2.1 Capital Accumulation Dynamics and Profit Maximization It is unclear how the neoclassical SOLOW growth model can be reconciled with profit maximization which suggests that dk/dt should depend on the difference between the net marginal product of capital YK − δ and the exogenous real interest rate r (note

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113

that we are considering an economy without inflation here). We briefly suggest a way to resolve the problem. One may interpret Eq. (1c) as the change in the supply of new capital per capita; this typically is represented by the supply of savings in capital markets. The change in the demand for new capital per capita can be written—as proposed here—as dk D /dt = b(YK − δ − r)k

(1 a)

The equation—with b representing a positive parameter—says that net investment per capita is proportionate to • the difference between the net marginal product of capital and the real interest rate, • the capital intensity k. Note that dkD /dt will finally fall as the net marginal product of capital YK − δ is approaching the exogenous real interest rate; however, this effect is mitigated by the rise of k over time until finally YK − δ = r so that net investment demand per capita becomes zero. The adjustment parameter b is exogenous at first glance. However, if the investment goods market is to be in equilibrium all the time, that is dk/dt = dkD /dt, we must have b[r + δ] = δ and s = bß. This follows from rewriting Eq. (1 a) as dkD /dt = b(ßkß−1 − r − δ)k = bßk ß − [br + bδ]k.

(1 b)

Clearly the path for kD # will coincide with the k# in Eq. (1 ) only if bß = s;

(1 d)

b[r + δ] = δ

(1 e)

and

These two equations imply [s/ß][r + δ] = δ and therefore (1 f)

r = δ[(ß/s) − 1]

By implication the real interest rate is positive only if ß > s. If (1 f) is fulfilled, the supply of net investment per capita and the demand for net investment per capita coincide at any point of time. Note that the condition for the case of the golden rule (condition which maximizes per capita consumption) is fulfilled if δ = r, and in the long run r = YK if ß/s = 2, that is s = ß/2. As ß is put for OECD countries typically at around 0.33 the optimal savings rate—maximizing long run per capita consumption—thus would be 16.5%. Note that for the case of a real money demand function m = hY − h r (m is real money balances M/P where M and P stand for the nominal money stock and the price level, respectively; r is the real interest rate relevant in the present setup with zero inflation) the implication is that the central bank must set long run [M/P] per capita such that we have [m/L]# = hk#ß − h k#ß−1

since

r = ßY/K = ßk ß−1 .

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The general solution to (1 b) is—with e denoting the Euler number—given by the solution of the Bernoullian differential (see Appendix G.4) equation dk D /dt = bßk ß − b[r + δ]k; the solution for this is  1/(1−ß) k D (t) = C0 e−(1−ß)b(r+δ)t + ß/[r + δ]

(1 g)

where C0 is determined by initial conditions. The adjustment speed is the higher, the higher b as well as the real interest rate and the lower ß. The adjustment speed for kD (t) is identical with that for k(t) if (1 − ß)δ = (1 − ß)b(r + δ) which requires (r + δ) = δ/b, and this condition indeed is equal to Eq. (1 e). If adjustment speeds on the supply side and the demand side in the capital market are not coinciding, we could have a picture as shown in the subsequent graph where during an initial time period the supply of net investment per capita is higher than the demand for investment per capita such that we will have unemployment while in a second period (after point F) we will have inflation as demand exceeds supply; in principle one also could have a first period of inflation followed by a second transition period of unemployment.

δk E

Fig. 24 Transitory equilibrium (point F) and steady-state equilibrium (“time” 0F = unemployment, “time” FE = inflation)

sy

dkD/dt

F dk /dt 0

kF

k#

k

We thus may argue that the SOLOW growth model could indeed be consistent with profit maximization. Subsequently we will use the net investment function suggested in (1 a) in a medium-term KEYNES–SOLOW model; the above specification is the only formulation which is consistent with the long-run steady-state value of the SOLOW model.

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115

B.2.2 Choosing a Consistent Investment Function and a New Consumption Function An investment function—for net investment—consistent with (1 a) thus is I = b(YK −r−δ)K which will be used subsequently as the function describing investment demand. Whenever net investment is given by this equation we know that investment demand dynamics are potentially consistent with the SOLOW growth model. A possible modification of the case of unemployment (with the unemployment rate   u > 0) or inflation (π > 0) could be formulated as I = b(YK − r − δ)Ke−σ u−σ π where e denotes the Euler number and σ is a the semi-elasticity (in absolute terms) of net investment with respect to the unemployment rate (σ is the semi-elasticity with respect to the inflation rate). Subsequently, we will use the net investment function I = b(YK − δ − r)K. Next we turn to a standard Keynesian model of a closed economy which implies that output is determined by aggregate demand consisting of consumption C, gross investment I and real government expenditures G. We denote reinvestment as IR , net investment as I (r, YK , K), and we also consider a standard consumption function C = cYd (Yd is the aggregate demand). Hence output Y is given by Y = cYd + IR + I (r, YK , K) + G

(2)

It is assumed that net investment I = b(YK − δ − r)K so that total investment I := IR + b(YK − δ − r)K which implies for the goods market equilibrium: Y = cYd + IR + b(YK − δ − r)K + G

(3)

The capacity effect of investment is neglected in the standard Keynesian setup, and thus the marginal product of capital is constant in the short run. Output Y is driven by aggregate demand and thus is given—with s := 1 − c and IR = δK—by the equation: Yd = Y = [δK − by + G + b(YK − δ − r)K]/s

(4)

dY/ds = −[δK − by + G + b(YK − δ − r)K]/s2 < 0

(5)

The conclusion is that the savings rate negatively affects the short-term equilibrium real income: A rise in the savings rate (s > s) implies that at any real income the desired savings S = s Y is higher than before; however, the condition I = S then implies a fall of equilibrium Y. This is in some contrast to the statement that savings from an individual perspective is useful and desirable as it is the basis for the accumulation of wealth. Note that the negative multiplier in (5) strongly differs—according to (1b)—from the neoclassical long-run multiplier which is given by dY#/ds = ß/(1 − ß)L[1/δ]ß/(1−ß) [s]−1/(1−ß) > 0. A straightforward hypothesis which combines the short run and the long run is to assume that output in the medium term is determined by weighted impacts from the demand side and the supply side (here the supply side is set equal to Y#): Y = [1 − a (t)]Yd + a (t)Y#

(6)

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The closer the economy is to full capacity utilization the higher a is. In a situation of extreme capacity underutilization such as the Great Depression 1930–1934—with US output showing a cumulative fall of 27% (Germany 16%, France 11%)—a is close to zero so that aggregate demand indeed determines output. The idea of taking into account both impacts from the demand side and the supply side will be considered subsequently in a formal model whose approach is slightly different from the above equation, but the spirit is the same. Indeed, one may consider a medium-term model which means taking into account that a rise in K will reduce the marginal product of capital (in contrast to the standard Keynesian analysis) and where we use the following modified consumption function, which is a simplified version of the permanent income hypothesis: The consumption function chosen emphasizes that consumption C is influenced not only by the present income but also by the long-run expected income (here Y#); with a consumption function C = ca Y + ca [1/(1 + r)]Y#

(7)

we get the following equilibrium condition for the goods market in the medium term Keynes–Solow model: Y = c{a Y + a [1/(1 + r)]L[s/δ]ß/(1−ß) } + δK + b(ßY/K − δ − r)K + G;

with a  := (1 − a  )

(6 )

The consumption function suggested (for simplicity with a independent of time) here states that C = cY + ca [Y# − Y], and hence consumption will be higher than that implied by the standard consumption function C = cY whenever there is a positive expected difference between long-run output Y# and present output Y. Approaching the steady state, we indeed will see that consumption C is converging toward Ct = cYt . Expected future income—read steady-state income Y# —is discounted by 1/(1 + r); as an alternative, one might want to multiply it by a different discount factor which would also reflect the subjective probability that the economy will converge toward the hypotheticalY#. A more complex approach could take into account both demandand supply-side dynamics over many periods, but the approach presented here catches the basic idea of taking into account both present and future income. In the above equation, we have taken into account that the marginal product is equal to ßY/K. Assuming r to be exogenous, we have medium-term equilibrium output—based on our medium-term approach—given by Y = {ca [1/(1 + r)]L[s/δ]ß/(1−ß) + δK(1 − b) − brK + G} /[s + ca  − bß]

(6 )

Note that the above equation determines Y through medium-term aggregate demand where consumers are forward looking economic agents.

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B.2.3 Multiplier Analysis We now can take a look at the simple multiplier for the goods market (and later we turn to the broader picture with goods market, money market and the foreign exchange market). From (6 ) we get—while assuming that s + ca > bß: dY/dG = 1/[s + ca − bß] > 0

(7 )

In the medium-term model fiscal policy is (ignoring at first the impact of ca ) more effective than in the short-run standard model since a rise of G raises output which translates not only into higher consumption but also into higher net investment since a rise of Y also implies a rise of the average product of capital. If by coincidence Eq. (1 d) is fulfilled so that bß = s the multiplier would be 1/(ca ); note that an economy which is close to the steady-state value of output Y# may be expected to have a close to unity so that the fiscal multiplier is relatively small. If s + ca approaches bß, the multiplier will approach infinity. Whether such a case is of any practical relevance is an empirical question; note that one can dismiss the idea to artificially reduce the capital stock as a means to eliminate an excess supply in the capital market—followed by an expansionary fiscal policy whose multiplier thus is raised as the condition s = bß is fulfilled: An artificial reduction of the capital stock would, of course, reduce expected long-run income. Moreover, one should emphasize that approaching Y# the equilibrium condition for the goods market will become Y = cY# +δK # +G so that withY approachingY# government consumption G is endogeneous. By implication it is clear that a fiscal multiplier—and therefore fiscal policy—makes no sense if the economy is close to Y# (the long-run case). The following multiplier analysis thus is confined to a medium-term policy perspective. The medium-term fiscal multiplier from (7 ) could be smaller or larger than the traditional short-run fiscal multiplier 1/s. If the transitory consumption demand effect as captured by ca exceeds bß, we will have a smaller fiscal multiplier than that the short-run Keynesian model suggests. The higher ß and b are, the higher is the fiscal multiplier. Thus fiscal policy becomes more effective if there is a change in technology which leads to a rise of ß and if the responsiveness of investors with respect to differences between the net marginal product of capital and the real interest rate has increased. The reason is straightforward since for a given interest rate a rise of G which translates into a rise of Y will have the higher an impact of the marginal (and average) product of capital and net investment the larger ß and b, respectively. The increasing role of information and communication technology (ICT) might have raised ß since increasing output is facilitated—at least in those sectors where supply is based on software and digital inputs. From this perspective ICT might have raised the effectiveness of fiscal policy. However, to the extent that expansion of ICT has translated into a rise of a there is an offsetting effect, and only empirical analysis can tell whether the fiscal multiplier has increased or fallen in the digital economy. In a period in which there is a high gap between present and long-term income, a will be relatively high so that the fiscal multiplier is relatively low. From this

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perspective, emphasis on expansionary fiscal policy in a deep recession—such as the case during the Great Depression—is indeed useful, namely to the extent that deep recession is translated by economic actors as falling weight of future long-run income. With massive underutilization of capacity, one could also argue that b—the reaction parameter in the net investment function—will be close to zero which also reinforces the statement that expansionary fiscal policy in a deep recession should be quite useful to raise real income. The fiscal multiplier effect should also be high if the time horizon of people is shortening, as is typically the case in periods of high business uncertainty or in war periods. If the output elasticity of capital is increased (ß goes up)—for example, in the context of the unfolding of the New Economy—the fiscal multiplier is reduced. It is also reduced if investors’ responsiveness to a difference between the marginal product of capital and the real interest rate increases (for example, the parameter b could be raised through reduced information costs about such differences). Again consider the impact of the new economy and information and communication technology which has raised market transparency with respect to investment opportunities in non-ICT fields while the ICT field itself—given its enormous technological dynamics—is rather opaque for outside investors. As regards the multiplier for L it is obvious that a higher L raises the long-run expected equilibrium real income—hence permanent income is raised—and therefore the multiplier is positive provided that s > ca + bß. In an economy with a relatively small capital stock or with a very small responsiveness (sufficiently small b) of net investment with respect to the marginal product of capital, we have a positive multiplier. dY/dL = {ca  [1/(1 + r)][s/δ]ß/(1−ß) }/[s + ca − bß] > 0

(9)

dY/ds = {−(1 + a ){ca [1/(1 + r)]L[s/δ]ß/(1−ß) + (δ − br)K + G} + [(s + ca  − bß)ca [1/(1 + r)]L[ß/(1 − ß)]sß(1−ß) ]/δß(1−ß) } /(s + ca − bß)2

(10)

A sufficient condition for dY/ds to be positive is given by: s + ca > bß, ß > s and ca [1/(1 + r)]L[s/δ]ß/(1−ß) + G < (br − δ)K where there has to be br > δ. These conditions—suggesting under the assumption that br > δ—that a rise of the savings rate raises output if the savings rate and the impact (a ) of the long-run real income on consumption are relatively high—point to interesting empirical issues. Thus a society with a large positive gap between Y# and Y (and hence a high parameter a ) is likely to benefit from government measures which stimulate the savings rate: Medium-term income will rise. To the extent that one interprets ß as a distribution parameter one may conclude that in a country with a critically high ß—as might be observed in developing countries or in some transition economies—a rise of the savings rate might reduce medium-term equilibrium output. The real interest rate can, of course, be endogenized (assuming a zero inflation rate) by taking into account the money market equilibrium condition: M/P = hY − h r

(11)

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r = [hY − M/P]/h

(12)

If we endogenize the interest rate we get from inserting (12) into (6 ) Y = c{a Y + a [1/(1 + [hY − M/P]/h )]L[s/δ]ß/(1−ß) } + δK + b(ßY/K − [hY − M/P]/h )K] + G

(13)

Using Cramer’s rule, we can calculate the multipliers for monetary and fiscal policy from differentiating (6 ) and (11) and the respective equation written in matrix notation: ⎞ ⎛ h −h   ⎟ dY ⎜    ⎠ ⎝ s β(1−β) ca L dr (s + ca − bβ) bK − (1 + r)2 δ ⎛ ⎞⎛ ⎞ 0 1 0 dG ⎜   ⎟ ⎝d(M/P)⎠ =⎝ dY ⎠ 1 0 ds ds   dY dY dY denotes (s + ca  − bβ) with the from Eq. (10). Where ds ds ds And therefore   dY = {−{ca [1/(1 + r)]L[s/δ]ß/(1 − ß) + (δ − br)K + G} ds + [(s + ca  − bß)ca [1/(1 + r)]L[ß/(1 − ß)]s(2ß−1)/(1−ß) ]/δß/(1−ß) } /(s + ca + bß) ⎛ ⎜ det(A) = det ⎝

h (s + ca − bβ) 

bk−



⎞ −h ⎟ ca  L  s β(1−β) ⎠ (1 + r)2

= {([s + ca − bß]h + hbK)[1 + r] δ

δ

2 ß/(1−ß)

− ca Lhsß/(1−ß) }

/[1 + r]2 δß/(1−ß) which implies (1 + r)2 δβ/(1−β) 1 = det(A) ((s + ca  − bβ)h + hbK)(1 + r)2 δβ/(1−β) − ca Lhsβ/(1−β) And therefore the multipliers are as follows: h (1 + r)2 δβ/(1−β) dY = dG ((s + ca − bβ)h + hbK)(1 + r)2 δβ/(1−β) − ca Lhsβ/(1−β)

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(s + ca − bβ)h + hbK < 0 ⇒

dY <0 dG

In a poor country—with very low s and low K—the condition for dY/dG is likely to be met so that fiscal policy is ineffective with respect to output. The condition stated implies that for dY/dG < 0; (s + ca − bß) needs to be negative, but this is not sufficient as in Eq. (7). As well (s + ca  − bß) > 0 does not imply dY /dG > 0 but still is a necessary condition. Empirically, it will be interesting to study whether bß exceeds s + ca . The multiplier dY/dG shows an ambiguous impact of the size of the country considered since a rise of L reduces any positive multiplier result; the same holds for K as long as s + ca − bß is positive. The more strongly investors react to any difference between the net marginal product and r (parameter b) the lower is the fiscal multiplier. The medium-term fiscal multiplier is the larger (assuming that it is positive) the larger the interest elasticity of money and h , respectively, is. Comparing the above fiscal multiplier to the familiar short-run Keynesian multiplier dY/dG = 1/(s + hb/h ) —suggesting that the higher h the larger the multiplier—we have a similar result. However, here we also see the impact of the effect of changes in aggregate demand on the average product of capital and investment, respectively; and we see the impact of reinvestment and of the technology parameter ß. The lower the depreciation rate, the lower is the fiscal multiplier. Compared to our simple fiscal multiplier we can see—as an impact from the money market—that a rise of a , namely the weight consumers attach to long-run income has an ambiguous impact on the multiplier; the impact of ca is positive if h(1+r)2 δß/(1−ß) falls short of Lhsß/(1−ß) ; a low real interest rate and a low income elasticity of the demand for money as well as a low capital depreciation rate make it more likely that the impact of ca’ is positive. The impact of the savings rate is not as strong as the simple multiplier for the goods market suggests: The money demand effect is reducing the denominator. The higher the level of the real interest rate the smaller is the fiscal multiplier (assuming dY/dG > 0) which points to a strategic advantage of countries with low real interest rates—this could, for example, reflect credibility of monetary policy or of fiscal policy. The United States which is known to have the lower real interest rates among OECD countries—except for the special case of Switzerland—thus should have an advantage while the Euro zone has a disadvantage once that the conflicts about the non-fulfillment of the Stability and Growth Pact contribute to higher real interest rates. This points to an interesting paradox, namely that ministers of finance eager to loosen the stability pact in order to get a larger room for manoeuvre in fiscal policy matters ultimately will reduce the effectiveness of fiscal policy. The higher the depreciation rate the smaller is the fiscal multiplier provided that it is positive. This is an important message for developing countries eager to catch up with advanced industrialized countries: (i) in such countries repair management in firms often is relatively poor which implies a relatively high depreciation rate; (ii) choice of technology often is biased by government in favor of importing advanced

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capital equipment from OECD countries which, however, is not only likely to be inconsistent with international relative factor price differentials but also could force the country to pursue a modernization policy which tries to be in line with that in advanced countries; there is pressure to always introduce latest foreign technologies fast so that the effective depreciation rate could be high. bK(1 + r)2 δβ/(1−β) − ca Lhsβ/(1−β) dY = dM/P ((s + ca − bβ)h + hbK)(1 + r)2 δβ/(1−β) − ca Lhsβ/(1−β) dY bK(1 + r)2 δβ/(1−β) = ds ((s + ca − bβ)h + hbK)(1 + r)2 δβ/(1−β) − ca Lhsβ/(1−β)



dY ds



Obviously the multiplier for monetary policy is zero if bK(1 + r)2 δß/(1−ß) is equal to ca Lhsß/(1−ß) . The multiplier for monetary policy will be infinte in absolute terms if ((s + ca  − bß)h + hbK)(1 + r)2 δß/(1−ß) is approaching ca Lhsß/(1−ß) . Note that for the special case that the depreciation rate is zero, the multiplier is unity. Dividing the numerator and the denominator by bK(1 + r)2 δß/(1−ß) , we can see that the multiplier is greater unity—provided that it is positive—if the condition holds that {[s + ca − bß)h ]/bK + h} is smaller than unity. Comparing the above monetary policy multiplier to the familiar Keynesian shortrun multiplier—dY/d(M/P) = 1/([sh /b]+h)—we can see that there is no liquidity trap if s + ca is equal to bß. Monetary policy is the more effective, the higher b—assuming that the multiplier is positive. A supply-side policy, defined as a rise of s, can have a positive or a negative impact where the sign for the multiplier dY/ds depends on a complex set of parameter conditions. The multiplier is zero if the interest elasticity of the demand for money is zero. The multiplier is the higher the higher the depreciation rate is and the higher the size of the capital stock is the lower the multiplier (assuming (dY/ds) to be positive). As regards the impact of real money balances one might want to consider a refined model in which the real output is affected by real money balances so that Y =   (M/P)ß Kß L1−ß−ß ; in addition one might want to modify the savings function by assuming S = sY[Y/(M/P + K)] so that savings per capita fall—assuming a given per capita income—as the income-to-wealth ratio increases. Finally, one should note that from (6 ) we get the slope of the medium-term goods market equilibrium schedule ISM as dr/dY = [s + (ca  − bß)]/[−ca L(s/δ)ß/(1−ß) − b] which can be larger or smaller than the short-run schedule of the familiar IS curve with slope dr/dY = −s/b. If we assume that (i) ca = bß or (ii) ca  < bß while the numerator remains positive the slope of the ISM curve is definitively smaller in absolute terms than the standard IS curve. To put it different: An expansionary monetary policy will raise output in the medium term more strongly than in the short run (see the appendix). However, we have a certain paradox of monetary policy

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since in the long-run monetary policy is endogenous as we have emphasized. Any medium-term monetary policy which reduces in a non-inflationary world the interest rate temporarily below the steady-state equilibrium interest rate—the natural interest rate to use WICKSELL’s term—must adopt in the long run a contractionary monetary policy which brings up the interest rate to the natural level. We thus may conclude that expansionary monetary policy will have an effect on medium-term output only if individuals discount future monetary policy strongly, or if the initial interest rate was above the natural rate.

Open Economy: Mundell–Fleming–Solow Model For the case of an open economy, we have to distinguish the case of fixed exchange rates versus the case of flexible exchange rates. The subsequent model is a hybrid Mundell–Fleming–Solow model (MFS) where—denoting real net capital imports as Q and q = eP*/P (e is the nominal exchange rate, P the price level, * denotes foreign variables) —we have added the following balance of payments equilibrium condition to Eqs. (6 ) and (12): Q(r, r*, q*) = q*J(q*,Y,Y#) − X(Y*,Y*#, q*)

(14)

In the context of an open economy, we also have to modify the investment function I, which now includes—following the model of FROOT/STEIN (1991) who emphasizes the role of imperfect capital markets—the real exchange rate variable, since a real depreciation of the currency of country I (home country) will stimulate the inflow of foreign direct investments: I = δK + b(ßY/K − δ − r) + Hq*, where the parameter H is positive. Therefore, net capital imports depend not only on the ratio of the domestic real interest rate r to the foreign interest rate variable, but also on the real exchange rate eP*/P. As consumption depends on both Y and Y# it is natural to state the hypothesis that imports also depend on both Y and Y#; and that real exports positively depend on both Y* and Y*#. Compared to traditional modeling, the impacts of q* and of Y# and Y*# are new in our statement of the balance of payments equilibrium condition; one may note that in principle one additionally might want to consider the impact of q*#/q* on capital inflows as well as trade, but for the sake of simplicity we will ignore this here. In a small open economy, we can thus state the following equation system with e, Y and r as endogenous variables (case of flexible exchange rates). We can calculate the multipliers for three exogenous variables, namely for expansionary monetary policy (dM) or fiscal policy (dG) or a change of current foreign output (Y*) or a change of long-run foreign output (dY*#) or a change of long run domestic output (dL) as well as the impact of a rise in the savings ratio (ds). In reality, a rise in the savings ratio could be linked to special incentives of government aimed at raising the savings rate and the investment ratio so that ds > 0 can be interpreted as supply-side policy. The medium-term goods market equilibrium condition in an open economy with foreign direct investment

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123

reads the following: Y = c{a Y + a [1/(1 + r)]L[s/δ]ß/(1−ß) } + δK + b(ßY − eK) + Hq* + G + X(Y*,Y*#, q*) − q*J(q*, Y, Y#)

(15)

Differentiating (15), (12) and (14) gives the following system of equations in matrix notation: ⎞ ⎛ k2 −H + J + q*Jq* − Xq* ⎛ s + ca  − bβ + q*JY ⎞ ⎟ dY ⎜ ⎟ ⎜  h −h 0 ⎟ ⎝ dr ⎠ ⎜ ⎟ ⎜ ⎠ dq* ⎝ [M/P] q*JY + Q[M/P]/Y −Qr −Qq* + J + q*Jq* − Xq* 2 Y ⎛ ⎞ a  s β/(1−β) ⎛ dG ⎞ 0 k1 XY* XY*# ⎜1 ⎟⎜ 1+r δ ⎜ ⎟ ⎜ dM ⎟ ⎟ ⎜ ⎟⎜ 1 ⎜0 ⎟ ⎜ ds ⎟ ⎟ 0 0 0 0 =⎜ ⎟⎜ P ⎜ ⎟ ⎜ dY* ⎟ ⎟ ⎜ ⎟⎝ ⎝ ⎠ dY*#⎠ Q[M/P]/Y 0 − 0 0 XY* XY*# dL PY k1 = −Ya −

k2 = bK −

a  L(s − β) β/(1−β)

(1 + r)(1 − β)δ

2β−1

s 1−β

ca L  s β/(1−β) (1 + r)2 δ

This implies ⎛

s + ca − bβ + q*JY

⎜ ⎜ h B = det ⎜ ⎝ [M/P] q*JY + Q[M/P]/Y Y2

k2

−H + J + q*Jq* − Xq*

−h

0

−Qr

−Qq* + J + q*Jq* − Xq*

⎞ ⎟ ⎟ ⎟ ⎠

= (−H − Xq* + J + q*Jq* )(−Qq* h + h (q*JY + Q[M/P]/Y [M/P]/Y2 )) + (−Qq* − Xq* + J + q*Jq* )[−h (s + ca − bß + q*JY ) − h(bK − ca  L[s/δ]ß/1−ß /(1 + r)2 )] Furthermore, we will define U = 1/B. The multipliers for a change in G, M, s and other variables are as follows: dY/dG = −Uh  (−Qq* + J + q*Jq* − Xq* )

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U dY/dM = − k2 (−Qq* + J + q*Jq* − Xq* ) + Qr (−H + J + q*Jq* − Xq* ) P − Uh Q[M/P]/Y [1/P]/Y(−H − Xq* + J + q*Jq* ) dY/dS = −Uk1 h (−Qq* + J + q*Jq* − Xq* ) dr/dG = −Uh(−Qq* + J + q*Jq* − Xq* )  dr/dM = U/P (s + ca − bβ + q*JY − XY)(−Qq* + J + q*Jq* − Xq* )  − (q*JY + Q[M/P]/Y [M/P]/Y2 )(−H + J + q*Jq* − Xq* ) − UhQ[M/P]/Y [1/P]/Y(−H − Xq* + J + q*Jq* ) dr/ds = −Uk1 h(−Qq* + J + q*Jq* − Xq* ) dY/dY* = −Uh XY* (H − Qq* ) dY/dY*# = −Uh XY* #(H − Qq* ) a   s β/(1−β)  dY/dL = −U h (−Qq* − Xq* + J + q*Jq* ) 1+r δ dr/dY* = −UhXY* (H − Qq* ) dr/dY*# = −UhXY*# (H − Qq* ) a  s β/(1−β) h(−Qq* − Xq* + J + q*Jq* ) dr/dL = −U 1+r δ dq*/dY* = UXY* (−hQr + h (q*JY + Q[M/P]/Y [M/P]/Y2 )) + [−h (s + ca  − bß + q*JY ) − h(bK − ca  L[s/δ]ß/(1−ß) /(1 + r)2 )] dq*/dY*# = UXY*# (−hQr + h (q*JY + Q[M/P]/Y [M/P]/Y2 )) + [−h (s + ca  − bß + q*JY ) − h(bK − ca  L[s/δ]ß/(1−ß) /(1 + r)2 )] a   s β/(1−β) dq*/dL = U [−hQr + h (q*JY + Q[M/P]/Y [M/P]/Y2 )] 1+r δ One can see that U is negative if the following conditions are met: s + ca > bß

(I)

q*JY > XY 

(II)

(1 + r) bK > ca L(s/δ) 2

ß/(1−ß)

(III)

J > Qq* + Xq* − q*Jq*

(IV)

J > H + Xq* − q*Jq∗

(V)

As well as:  ∗

Qq∗ h > h q JY

(VI)

B.3 Conclusions and Possible Extensions

125

Or alternatively J < H + Xq* − q*Jq* which is equivalent to H > Qq*

(V )

Qq* h < h q*JY

(VI )

Depending on which set of conditions is met, we can draw the following conclusions about the multipliers: dY/ds > 0, if s < ß. dY/dG > 0. dY/dM > 0, if V and VI are met. dY/dY* depends on the sign of XY* and if V and VI or V and VI are met. dY/dY*# depends on the sign of XY*# and if V and VI or V and VI are met. dY/dL < 0. Note that if s = ß/2—which implies the fulfilment of the golden rule—the multiplier for dY/ds indeed is positive. The medium-term model suggests that fiscal policy can be effective. Monetary policy—under certain conditions—also is effective; namely, if imports are relatively high in comparison to the impact of the real exchange rate on foreign direct investment inflows and the net exports of goods and services, respectively. An important aspect concerns supply-side policy: If the savings rate is smaller than ß a rise of s will raise medium-term output. The impact of a rise ofY* and Y*#, respectively, can differ in the respective sign which suggests that international policy coordination is more complex than that the standard macro model suggests. Governments with an emphasis on the long-run output—hence governments with a more long-run time horizon—thus could favor different policy options than shortrun-oriented political actors. The assignment debate thus is affected. An explicit two-country model could offer more refined results. The multipliers for the exchange rate also are interesting: dr/dG > 0. dr/dM < 0 if V is met. dr/ds < 0. dr/dY* depends on the sign of XY* and if V or V is met. dr/dY*# depends on the sign of XY*# and if V or V is met. dr/dL < 0. A rise of government consumption raises the interest rate which is in line with the standard model. Expansionary monetary policy will reduce the interest rate under certain conditions while a rise of the savings rate will reduce the interest rate. The impact of Y* and Y*# on the interest rate might differ in sign. A rise of long-run employment will reduce the medium-term interest rate.

B.3 Conclusions and Possible Extensions The results show a more differentiated picture than the familiar debate on Keynesianism versus monetarism. The analysis suggested here is a useful medium-term

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analysis bridging in a consistent way short-run standard macroeconomic analysis and long-term growth analysis. Many refinements and modifications are possible, and there is a broad set of empirical issues which emerges in the model suggested. The relative size of s, ß, δ and b are of particular importance. Changes of the technological regime—such as the switch to the New Digital Economy—could alter ß, δ and b. The model presented suggests that policymakers should not only consider monetary and fiscal policy but also policies stimulating the savings ratio (and the investment ratio) as well. The more consumption is influenced by long-run expected steady-state income, the more attractive supply-side policies are. Countries with a stable political system should be able to exploit the impact of policy measures designed to raise long-run output. However, in countries with political instability or with politicians without much reputation government will naturally have a bias in the field of supplyside policy; instead of raising the savings rate, government will be inclined to follow the logic of the short-run Keynesian model and try to raise short-run output by reducing the savings ratio. With only temporary increases in output and a growing stock of public debt, there is a considerable risk that the debt–GDP ratio will increase and hence the anticipated future tax rate τ . Indeed in a two-period approach, it must hold that real government consumption as well as real interest rate payment on the stock of public debt (B) and discounted future government expenditures G# be equal to current tax revenue and discounted future tax revenue: G + rB + G#/(1 + r) = τY + τ Y#/(1 + r).

(16)

In a more elaborate MFS model, taking into account that the current tax rate and the future tax rate will negatively affect present consumption and investment, one could endogenize τ while assuming, for example, that G = G#. Risk-averse taxpayers will calculate τ not simply from (16), rather with G = G# they will calculate it as τ = (1 + r){G + rB + G#/(1 + r) − τY ]}Y# + ωT

(17)

The variable T indicates the credibility of government tax policies, or alternatively, its history in political cheating. If past governments have always kept their promises in the field of taxation and borrowing, T is zero. The more often taxes or deficitGDP ratios were raised in violation of election promises (or international treaties such as the Stability and Growth Pact in the Euro zone) the higher T will be. Thus, T can be considered within a broader approach an endogenous variable which could be explained in the framework of a New Political Economy approach. At the bottom line, a loss in government reputation will therefore reduce present consumption and investment. Moreover, it might reduce net foreign direct investment inflows and hence net capital inflows. The new approach presented can be extended in various ways (WELFENS 2005) and allows us to combine short-run macroeconomic analysis with many of the standard results of modern growth theory—as for example summarized in JONES (1998). The model presented also raises many new issues for the debate about the efficiency of fiscal policy and monetary policy.

B.3 Conclusions and Possible Extensions Fig. 25 Standard IS-LM model vs. Keynes–Solow model

127

r LM0 LM1

E0

r0

E2 E1

ISM0

IS0

0

Fig. 26 Medium-term and Long-run equilibrium

Y0 Y1

Y2

Y

tg α0 = [βY2/K2] /Y2 = β/K2

r

tg α1 = β/K#

E2

E#

r2

α0 0

r = δ [(b /s)–1]

ISM0

α1 Y2

Y#

Y

As regards the money market: note that—with m := M/P—in the long run the condition must hold: (m/L)# = hk #ß − h ßk #ß−1 .

C. Economic Integration, Technological Progress and Growth

C.1 Rich Countries vs. Poor Countries and Economic Integration The world economy consists of many poor countries and a few dozen relatively rich countries. Per capita income differentials across countries were fairly large at the beginning of the twenty-first century. Asian countries did relatively well in catching up with leading OECD countries in the 1970s and 1980s. As respect to the 1990s, several transforming countries from Eastern Europe have also achieved relatively high per capita income ratios, and there is some optimism that EU accession countries could catch up relatively quickly with EU-15. BEN-DAVID (1996) has empirically shown that economic integration has contributed to economic convergence, SACHS/WARNER (1995) have presented evidence on the positive links between trade liberalization and economic growth. LEVINE/RENELT (1992) have also found that economic openness is closely related to growth. MANKIW/ROMER/WEIL (1992) have emphasized the role of human capital for growth and economic convergence; however, below we do not look into the human capital issues—but capital K could be adequately defined to include human capital and thus we include some such aspects, at least implicitly. Various alternative approaches to growth modeling in open economies and the issue of international real convergence have been discussed in the literature (OBSTFELD/ROGOFF 1996), but no convincing general approach has emerged. Much of the convergence optimism in the context of EU eastern enlargement is related to the Heckscher–Ohlin–Samuelson (HOS) theorem which shows for the case of identical linear-homogeneous production functions in a 2country–2goods– 2factor model that moving from autarchy to free trade will bring about relative price equalization that will go along with relative factor price equalization. The ratio of real wage w to the real interest rate r in the home country will become equal to the foreign relative factor price ratio w*/r*. While there are many trade modeling variations in modern Economics— partly taking into account economic integration—(e.g., BRETSCHGER 2002;

P. J. J. Welfens, Innovations in Macroeconomics, DOI 10.1007/978-3-642-11909-5_3, © Springer-Verlag Berlin Heidelberg 2011

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SLAUGHTER 1997), there is no doubt that many economists would emphasize convergence optimism in the context of the HOS model. This holds despite the fact that DEARDORFF (1986) has shown that small deviations in the underlying modeling assumptions can undermine the convergence results of the HOS approach—there could be convergence of relative prices while relative factor prices are diverging. The traditional HOS modeling—based on free trade, absence of international factor mobility and identical technologies in both countries of the model— implies medium term economic convergence. As national income in real terms is Y = wL + rK, for countries I (home country) and II, K/L is denoted as k, Y/L as y and * is used for foreign variables: y = w + rk

(1)

y∗ = w∗ + r ∗ k ∗ .

(2)

Hence, if the factor price ratio w/r is converging toward w*/r*, free trade will bring about partial convergence at given k and k*, respectively. Moreover, in the medium term, profit maximization will drive k toward k* since capital intensity is a function of the factor price ratio. Hence trade can bring about full international economic convergence. However, the HOS model is silent on the accumulation dynamics. By contrast, the neoclassical growth model has explicit accumulation dynamics, but does not consider the role of trade—although both trade and capital accumulation must be considered when analyzing the issue of convergence vs. divergence. Theoretical analysis shows (GRIES/JUNGBLUT 1997) that growth models can be built in which there will be a permanent income differential between two countries. The GRIES/JUNGBLUT model is based on a three sector approach in which a traditional sector, an industrial sector and a research sector interact. This model already raises some scepticism about the prospects for full economic convergence across countries. As regards empirical evidence for international economic convergence, BARRO/SALA-I-MARTIN (1992, 1995) and BAUMOL (1986)—among others—have presented evidence on international economic convergence. ROMER (1986) and DE LONG (1988) have suggested considerable criticism on the Baumol interpretation since there is a sample selection bias problem which leads to overstating the case for convergence. DURLAUF/QUAH (1998) offer new empirical evidence, as it seems that there are certain regional convergence clubs, but one can hardly argue that the world economy has witnessed global convergence. When discussing problems of globalisation or aspects of economic integration, part of economists’ convergence optimism is based on the neoclassical growth model which predicts that relatively poor countries—that is with a per capita capital stock k = K/L which is much below the steady-state value—will experience relatively faster catching-up in the growth of k than medium income countries which in turn might catch-up vis-à-vis the leading country (USA in a global context or Denmark in the EU). Integrating trade theory and growth theory has been rather difficult in Economics, and two-sector growth models indeed are not easy to handle. WELFENS (2002b)

C.1 Rich Countries vs. Poor Countries and Economic Integration

131

has argued that the neoclassical growth model within a two-sector approach suggests that the original Solow model overemphasizes the role of the savings rate. In the following analysis, we want to look at a two-country model where country I, the home country, is small and relatively poor, while country II is large and has a high per capita income and an exogenous growth rate of Harrod-neutral technological progress a* = [dA*/dt]/A*. We will focus on a one-sector growth model but nevertheless integrate important elements from the HOS model, namely the hypothesis that trade will stimulate economic catching-up. To the extent that the two countries considered are engaged in a regional integration scheme—such as EU-15 and the eight Eastern European accession countries—one might point out that the parameters of the model have to be calibrated adequately. Analytical understanding of convergence potentials could indeed become quite interesting for both EU enlargement and for expansion of ASEAN or NAFTA. As is well known, the rate of technological progress plays a role both for the level and the long-term growth rate in the neoclassical model with (exogenous) technological progress. The neoclassical growth model is relatively mechanistic and does not take into account profit maximization. This is much in contrast with HOS models in which profit-maximizing firms in each country will specialize according to the given respective relative factor endowment. The subsequent modifications suggested the desire to reconcile growth theory and trade theory but also the desire to avoid excluding crucial problems from the beginning. We will not consider a third potential avenue of determining the growth rate, namely Ramsey–Cass–Koopmans models, which assume that infinitely lived house holds maximize discounted utility U(C/L)e −ζt dt subject toY/L = w + rK/L where e is the Euler number, ζ is the discount rate, C is the consumption, L and K stand for labor and capital, respectively; w and r denote the real wage rate and the real interest rate, respectively. This leads to optimum growth gC/L (with g denoting the growth rate) of per capita consumption which is equal to [r − ζ]/υ, where υ is the inter-temporal rate of substitution: υ = −U (C/L)[C/L]/U (C/L). This way the optimisation of per capita consumption easily determines long-term growth rates of C/L and, of course, of K/L, where some modification can be built into the approach by opening up the economy so that temporary current account imbalances could affect consumption and capital accumulation, respectively. The country with the lowest time preference would accumulate the fastest and run correspondingly temporary current account deficits—with the output of this country finally exceeding that of its trading partner. In such a setup, real economic convergence in the sense of equal growth rates can be obtained only in a rather artificial way, namely that the time preference rates and the inter-temporal elasticities of substitution at home and abroad would have to adjust endogenously. A first step to go beyond the neoclassical growth model—determining the steadystate level of capital intensity k = K/L and k = K/(AL), respectively—will be to state a hypothesis with respect to the technological catching-up process. We will at first describe this process with a differential equation in which trade intensity on the one hand and government per capita R&D expenditure on the other hand

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will play a crucial role. In a subsequent modification of the technological progress function we will assume that foreign direct investment will also affect international technological catching-up. Hence we will present a model in the spirit of the New Growth Theory, but we will use part of the neoclassical model in our approach. In a quasi-neoclassical growth model, we want to determine the capital intensity on the basis of a modified Solow model that thus—at first glance—is inconsistent with HOS. However, we want to show a way to integrate profit maximization in a model which is asymptotically consistent with (new) growth theory, respectively. The model developed is asymmetric in the sense that we have a small poor open economy (country I) and a large rich country (II) with an exogenous rate of technological progress. In this setup, we can analyze the conditions for technological catching up and economic convergence. The main results derived are as follows: • Trade stimulates economic catching-up; • R&D-expenditures per capita (v) also play a crucial role for technological progress and catching up; moreover, in our model they make the tax rate an endogenous variable so that v indeed is the only government variable with which government has an influence on the convergence process. • We can determine an optimum government R&D–GDP ratio (vopt ) in the sense that vopt will maximize consumption per capita. • Finally, we demonstrate how foreign direct investment will affect the analysis where we point out that the share of foreign direct investment in the capital stock of the host country has an ambiguous effect on convergence. Combining trade analysis and growth analysis should be quite useful for policymakers in all countries with slow growth which consider changes in trade or FDI or innovation policy.

C.2 Setup of the Model At first, we recall the basic neoclassical growth model—here with a Cobb–Douglas production function Y = K ß (AL)1−ß , a depreciation rate δ, savings rate s, income tax rate τ, and growth rate of population n. The technological progress rate AL is dubbed Harrod-neutral, that is labor-saving—a problem with the simple Cobb–Douglas function is that Harrod neutrality cannot be distinguished from Hicks neutrality and Solow neutrality, but as we are not looking into the empirical issues here this issue is neglected here. We assume that savings S are proportionate to disposable national income, so that S = s(1 – τ)Y. The standard model is summarized in a basic set of equations (see the appendix) and the following Bernoulli differential equation for k = K/(AL): dk  /dt = s(1 − τ)k  − (n + a + δ)k  . ß

k  (t) = {C0 e−(n+a+δ)(1−ß)t + [s/(n + a + δ)]}1/(1−ß) .

(3) (3 )

C.2 Setup of the Model

133

The steady-state value for k is k # = [s(1 − τ)/(n + a + δ)]1/(1−ß) .

(4)

Hence the steady-state value for y is y # = k  = [s(1 − τ)/(n + a + δ)]ß/(1−ß) . ß

(5)

Abroad we have—assuming a Cobb–Douglas function Y* = K*ß (A*L*)1−ß —a similar equation for the steady-state variable: y∗ # = k ∗ # ß = [s∗ (1 − τ∗ )/(n∗ + a∗ + δ∗ )]ß/(1−ß) .

(5 )

Hence output per capita in country I and country II is (denoting the Euler number as e ) given by (6) and (6 ): y = [s(1 − τ)/(n + a + δ)]ß/(1−ß) A0 e ; at

y∗ = [s∗ (1 − τ∗ )/(n∗ + a∗ + δ∗ )]

ß/(1−ß)

A ∗ 0 e

(6) a∗ t

(6 )

.

In the subsequent analysis, we will consider a model in which technological progress is endogenous in country I, but for simplicity we assume that it is exogenous in country II. Indeed, we will consider various technological catching-up regimes ranging from the simple HOS assumption that technology is the same at home and abroad to progress functions in which the progress rate is linked to trade intensity and R&D per capita expenditures or to these variables plus FDI. As is well known changes in s, τ, n and δ will affect the level of the growth path, while a change of the progress rate a will affect both the level and long-term growth rate (see Fig. 27): A rise in t1 of the level of the growth path means that the originial curve AA is shifted upwards as shown by BB while an additional rise of the growth rate is displayed as BB . lny B″ B′ B

A

Fig. 27 Level vs. growth effect

0

t1

t

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At the end of this section, we notice that monetary aspects—actually financial market institutions—might be taken into consideration in a simple way. As the efficiency of the banking system, or more generally, of the intermediation process is important for the savings process, one may take into account international differences in the efficiency of the intermediation process through a parameter λ which would be quasi-augmenting for the savings rate. y# = {s(1 − τ)[1 + λ]/[n + δ + a(t)]}ß/(1−ß) .

(7)

In this way one could consider the effects of financial market integration and thus combine trade analysis and financial market analysis. Poor countries often suffer from unstable financial institutions and inadequate prudential supervision, which implies that efficiency parameter λ is low. However, in the following analysis we will disregard financial market aspects.

C.2.1 Convergence in a Hybrid Growth Model with Trade and R&D We will now consider a modified model that follows the spirit of the approach by WELFENS (2002) in which trade intensity has an impact on the growth rate of technological progress. A balanced government budget and a balanced current account are imposed for the long-term analysis by the hybrid growth-trade model. Trade intensity is measured by import-GDP ratios at home (j) and abroad (j*). Moreover, we assume that R&D expenditures per capita (v) have a positive impact upon the speed of technological catching-up. The hypothesis stated here is that a rise in the growth rate of technological progress (a) is more difficult the higher the level of a already achieved; however, da/dt is a positive function of the ratio of a*/a. We will use a simple function to express our catching-up hypothesis—parameter b, σ, ψ, ε are assumed to be positive—where we assume that technological catching-up is a positive function of the technology gap a*/a (we will not look into the potentially interesting case that k enters the parameter for a*/a): da/dt = −ba + (jj∗ )σ vψ (a∗ /a)ε .

(8)

Defining h = (jj∗ )σ vψ we have: da/dt = (h a*ε )a −ε − ba.

(9)

The solution of this equation is: a(t) = {C0 e−b(1+ε)t + (h a∗ε )/b}1/(1+ε) .

(10)

The rate of technological progress will converge with t → ∞ toward a ∗ε/(1+ε) (h /b)1/(1+ε) , where the steady state of a# depends positively on a* and on h = (jj*)σ vψ : the higher the import-GDP ratios j and j* are and the larger government R&D promotion per capita, the higher will be the long term equilibrium value a#. The parameters b and (1 + ε) determine the adjustment speed.

C.2 Setup of the Model

135

Regional integration will raise j and j*, respectively—and regional integration might indeed raise the import ratio of two countries forming a customs union more than it would in a three-country model of global free trade. This conclusion could emerge in the context of a homogenous three-country setup of countries with equal population size but rather different per capita incomes; and the two relatively rich countries joining in a customs union. The elasticities σ and ψ also could be affected through integration. It is unclear whether the deceleration impact of the parameter b will be affected by regional integration. However, we may assume that regional integration stimulates competition on the one hand, on the other hand it could create more technological opportunities for applying innovations; and this would reduce the parameter b. The steady state value of a(t) is given by a# = a ∗ ε/(1+ε) (h /b)1/(1+ε) .

(11)

We note that regional integration and R&D promotion stimulate the long-term growth rate of technological progress. Once a is stable, the neoclassical growth equation can be used in a traditional way, namely to determine the convergence of per capita income: y# = [s(1 − τ)/(n + a∗ε/(1+ε) (h /b)

1/ε

+ δ)]1/(1−β) A0 e

a*[ε/(1+ε)]

(h /b)[1/ε] t. (6 )

The level of the growth rate of per capita income y is negatively affected by technological progress, but the exponential term with technological progress clearly implies that the overall impact of technological progress on y is positive. Note that the government budget constraint vL = τY implies that the tax rate is endogenous once that v is set by the authorities. Finally, we may note that we can derive a modified golden role for maximization of per capita consumption (C/L). Denoting output as Y =Y(K, AL) we can state that the marginal product of capital z in the optimum—in steady-state—must be equal to z(k#) = n + δ + a∗ ε/(1+ε) (h /b)1/ε .

(12)

If it would hold additionally—as suggested later—that z = r = r* in the steady state we have: r ∗ = n + δ + a∗ ε/(1+ε) (h /b)1/ε .

(12 )

The intersection point of the S/L curve with the I/Y curve must occur in the golden age at the point where the slope of the Y-curve is equal to (n + a + δ). Government can indeed influence the intersection point by adquate choice of the tax rate or by directly influencing the savings rate. However, one must not overlook that the government can chose only the tax rate or v to be an exogenous variable, and for government it is rational to strive for a golden rule at the highest possible growth rate of technological progress. Thus the optimization problem for the golden rule is more complex than in the standard approach.

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If from a golden rule perspective s[1 − τ] is too high (low) government could reduce (raise) the tax rate accordingly so that the intersection point between the per capita savings curve and the per capita investment curve is shifted to fulfill Eq. (12). If one would integrate cyclical output movements into the long-term analysis, it may be suggested that a situation marked by recession in which s > sopt will not pose any problem for stabilization and growth policy, respectively. Keynesian logic would suggest reducing the savings rate in order to stimulate demand and output; the golden rule logic also argues in favor of a reduction of s. A serious problem would occur, of course, if s < sopt since stabilization policy and growth policies would want to move in opposite directions. The two-country perspective raises the problem that the golden rule for the two countries will not be identical under profit maximization conditions that imply r = z = r* = z*; however, unless in the case of a + δ = a* + δ* there is indeed full convergence of a toward a*. Full technological convergence a# = a* will be observed under a specific parameter constellation: (h /b)(1/(1+ε))[1−(ε/(1+ε)] = a∗ .

(11 )

If ε is in the range between zero and unity, the exponent of h/z exceeds 1/ε. It may be worth noting that economic integration is likely to raise both ε and h. A priori it is unclear whether integration policy and government policies are sufficient to achieve a sustained progress rate that could bring convergence. However, it is clear that government can influence h through the innovation policy variable v. Full convergene of per capita income will occur—taking into account (6) and (6 )—if in addition to (11 ) which brings about technological convergence (a# = a*) we have: [s(1 − τ)/(a + n + δ)]1/(1−ß) A0 = A∗ 0 [s∗ (1 − τ∗ )/(a∗ + n∗ + δ∗ )]1/(1−ß) . (13) It is clear that (6) and (6 ) are the result of an inhomogeneous differential equation with constant coefficients. However, if a = a# = a*—and if relative convergence speed of a(t) is sufficiently high—we can asymptotically treat a as a constant coefficient so that the steady results are as presented in (5). The adjustment path of y toward the steady-state can be analyzed on the basis of simulations. Equation (13) suggests a crucial role for the savings rate and the tax rate, respectively. Note that the budget constraint vL = τY effectively leaves government only one instrument beyond trade policy (economic integration policies). It is interesting that the convergence of a(t) toward a*—or any other steady-state value a#—implies a twin convergence role for a, since a(t) will affect both the level of the growth path and the growth rate. This suggests that the process of closing the international technology gap is most crucial for real economic convergence. Moreover, all variables entering the technology gap function must be carefully studied. The model developed here suggests that trade—in the spirit of the HOS model—and Schumpeterian innovation policies play an important role for catching-up. However, our model setup is not a full HOS-framework since we have not assumed identical technologies in both (or in all) countries. Reality indeed reveals an obvious

C.2 Setup of the Model

137

truth about technological heterogeneity, with the US having a share of roughly 40% of all international patents. The number of international (or US patents) per capita of EU countries also differs significantly, with Germany and Sweden as EU leaders— upon closer inspection these figures would have to possibly be corrected by the effect of patenting of US subsidiaries in Germany and Sweden; in Belgium, US subsidiaries account for about 40% of all patents granted. In a global perspective, technological heterogeneity is likely to increase as the share of R&D expenditures relative to GDP increases over time and the role of multinational activities grows. MNCs ability to successfully produce abroad is—according to DUNNING—based on ownership-specific advantages—read technological advantages.

C.2.2 Profit Maximization in the Hybrid Growth Model A strange problem in traditional economics is that the HOS model assumes profit maximization—and emphasizes trade as an engine of economic convergence—while the neoclassical growth model does not consider profit maximization. The only exception is that the golden rule, namely marginal product of capital z = n = gY in the basic fundamental model, is often interpreted so that real interest rate r must be equal to the growth rate—but the adjustment of the marginal product of capital and r is opaque. For a consistent link between trade theory, growth modeling, and profit maximization we suggest here a simple approach: The hypothesis is that the marginal product of capital z is governed by an adjustment process according to zt = α(z∗ − z) + zt−1 .

(14)

Equation (14) states that domestic investors want to achieve the same return on investment as firms in the foreign benchmark country. Here, α is the speed of adjustment. With continuous time we have: dz/dt = α(z∗ − z).

(14 )

If a and z* are constant, (14 ) is an inhomogenous differential equation with constant coefficients whose steady-state solution is z# = z* = r*. In our approach, we will see the HOS result that r = z = z* = r* through the indirect mechanism r = z and r* = z*, where convergence of z to z* will bring about r = r* = z*. In the foreign country, we can assume that r* = z* remains constant. Equation (14) implies with domestic profit maximization that z = ßkß−1 , suggesting a corresponding adjustment of k(t) which can be considered the implicit demand for real capital per capita. The idea to reconcile trade and growth theory is that the adjustment speed α be not constant, but that the relative divergence between the steady-state value of capital intensity k # from the hybrid growth model and actual capital intensity k matters for the adjustment speed; k # is interpreted here as the

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implicit capital supply per capita (in efficiency units) offered by those willing to save. We assume α = [k  # − k  ]/k  #.

(15)

Hence the investors act according to dz/dt = {[k  # − k ]/k  #}(z∗ − z).

(16)

The mechanics of the hybrid neoclassical model makes sure that with t → ∞ we have: k = k  #.

(17)

Asymptotically, we will thus also have z = z* = r*, which is consistent with profit maximization. If free trade asymptotically brings about the convergence of factor price ratios (w/r = w*/r*), we also have r = r*. r = r ∗ = z = z∗ .

(18)

This result occurs without international capital mobility. The steady-state solution will thus bring about a result in which the supply of capital is equal to the profitmaximizing demand for capital. Both sides of the implicit capital stock market try to anticipate some elements from the other side: S = I can be interpreted in such a way that the supply side wants to offer savings in line with actual investment; the dynamic Eq. (16) indicates that investors take the logic of capital accumulation resulting from planned savings into account. From an empirical point-of-view, it would be quite interesting to analyze whether the adjustment speed in rich countries and poor countries is different. Such differences could indeed explain part of the observed nonconvergence or conditional convergence observed in reality. Moreover, the various elasticities in the hybrid growth model are also quite interesting; it goes without saying that the impact of trade and innovation could be modeled in various ways so that our model is one of several straightforward approaches.

C.3 Asymmetric Foreign Direct Investment in a Two-Country Growth Model Next we consider an asymmetric two-country model with given populations (L = L0 , L* = L*0 ) where the home country (I) attracts foreign direct investment flows, but country I is not investing abroad. Foreign investors make a once-and-for-all choice to hold a certain share of ϕ as the capital stock in country I (a more complex modeling approach could make ϕ for each period dependent on instantaneous profit maximization). Both countries produce according to Cobb–Douglas functions Y = Kß (AL)1−ß

C.3 Asymmetric Foreign Direct Investment in a Two-Country Growth Model

139

and Y* = K*ß (A*L*)1−ß . Moreover, we assume profit maximization in competitive markets so that profit income accruing for foreign investors is ϕßY, and consequently we have to distinguish between gross domestic product Y and gross national product Z =Y(1 − ϕß) in country I. Similarly, national income in country II is now Z* =Y* + ϕßY =Y* + ϕßY*(Y/Y*). If investors from a country are not repatriating all profits, one should interpret parameter ϕ as the product of the share of foreign investors in the domestic capital stock times the share of MNC subsidiaries’ profits repatriated in the analysis of the said country. Consequently, assuming that savings depends on disposable national income savings per capita, efficiency units in country I and country II is now given by Eqs. (19) and (20), respectively. S/(AL) = s(1 − τ)(1 − ϕß)y β

S∗ /(AL∗ ) = s∗ (1 − τ∗ )(y∗ + ϕßy∗ [k  L0 /k  *β L0 *]) k  = [s(1 − τ)(1 − ϕβ)/(δ − α)]1/(1−β) #

β

k ∗# = [s∗ (1 − τ∗ )[1 + (L0 /L∗0 )ϕß(k  /k ∗ ) ]/(δ∗ + a∗ )]1/(1−β) .

(19) (20) (19.1) (20.1)

At first we consider an exogenous technological progress rate a and a*, respectively. Hence the steady-state solutions for country I and II are: k  = [s(1 − τ)(1 − ϕβ)/(δ + a)]β/(1−β) #

β

k ∗# = [s∗ (1 − τ∗ )[1 + (L0 /L∗0 )ϕβ(k  /k ∗ ) ]/(δ∗ + a∗ )]β/(1−β) .

(19.2) (20.2)

The steady-state per capita income for country I is reduced by foreign direct investment according to (19.1), while that in country II is raised (see 20.1). However, the implausible result of a negative impact of FDI on country I will no longer hold after the next analytical step. We will use a modified technological progress function as we assume that foreign direct investment contributes to technological catching-up, hence for the poor country I, we have: da/dt = −ba + (jj)σ vψ ϕθ [a∗ /a]ε .

(21)

Note that the presence of FDI could bring about an increase of the parameters σ and ψ. However, the size of j will be smaller since a balanced current account requires that jY* − jY −ßϕY= 0. Now the steady-state value of a(t) is given—with h = (jj)σ vψ ϕθ by definition—by a# = a∗ε/(1+ε) (h /b)1/ε .

(22)

Since FDI raises the steady-state value of the growth rate of technological progress, one may assume that FDI indeed contributes to improving convergence prospects

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for the initially poor country where the dynamics of per capita steady-state income is determined in country I according to: y# = A0 e {s(1 − τ)(1 − ϕß)/(a + δ)}ß/(1−ß) . at

(19.3)

The fact that ϕ might negatively affect the level of the growth path—which is influenced by a#(ϕ, . . . )—while ϕ also increases long-term technological progress raises the issue of how long-term the time horizon of policymakers actually is. As the following figure shows, GNP per capita will fall once the country opens up to FDI inflows, however, long-term growth rate of the economy will increase as a result of FDI inflows. ln GNP/L E D B A

Fig. 28 Impact of foreign direct investment on growth (short-term fall of per-capitaGNP level and rise of growth rate as a consequence of FDI inflows)

α1 α0

C

t1

tm

t

Since country II is the source of foreign direct investment and thus obviously has a technological advantage over country II, it is not adequate to assume that technological catching-up will be only positively influenced by ϕ. Rather we have to consider there will be a systematic gap that has to be reflected in a modified Eq. (19) such as: da/dt = −ba + (jj)σ vψ (1 − ϕ)η ϕθ [a∗ /a]ε .

(21 )

Clearly, FDI inflows as modeled here will not affect short-term gross domestic product, rather it will influence the level of GNP per capita and the growth rate of GNP per capita, respectively. Politicians can be expected to be more interested in GNP per capita than in GDP per capita since high GNP per capita is a natural interest of voters. The difference between GNP and GDP can be rather high if the share of cumulated FDI inflows in overall capital stock is large as is the case in Ireland for example. Such long-term progress effects might be heavily discounted in political reality so that the potentially negative impact of FDI inflows on the level of the growth path could encourage politicians to be hesitant in accepting FDI.

Appendix C.1: Basic Neoclassical Model

141

C.4 Policy Conclusions The theoretical analysis has shown that one can integrate trade analysis and new growth theory in a rather simple way. Thus, endogenous growth theory is quite useful and should play a larger role in the policy arena. This holds particularly for relatively poor countries, but also for those OECD countries that have suffered from slow growth for many years. There are at least four policy conclusions to be drawn: • Governments should promote R&D in order to stimulate long-term growth (and regional integration might reinforce the potential for positive technology spillovers). • Regional integration could be useful in accelerating technological catching-up; both the role of regional and of global integration for technological progress should be carefully analyzed. • Effects of FDI inflows on economic catching-up will be positive if the share of FDI in the capital stock of the host country strongly contributes to economic catching-up. • One can calculate a new golden rule in which endogenous technological progress plays a crucial role. In this context, growth policy and stabilization policy are interesting as a simultaneous challenge; if the savings rate s is below the optimum savings rate in a recession, both growth policies and demand-side stabilization policies would suggest the same policy direction, namely to reduce the savings rate. The situation is quite different in a situation when s exceeds the golden rule savings rate since demand-side stabilization policies would entail negative welfare effects associated with the fall of per capita consumption below the optimum level. One would have to distinguish between temporary and permanent deviations from the golden rule. Obviously in our modeling exercise, we deliberately have not considered that the role of the terms of trade which might be affected—according to the Balassa–Samuelson argument—by relative economic catching-up. Here we have one further interesting area of future research. Another interesting question is whether the interaction of trade, FDI and capital accumulation within a fully developed two-country model will raise per capita income in both countries. Another possible extension concerns a monetary growth model in which real money balances would directly enter the production function. Finally, one might want to analyze the role of public capital formation—and of public consumption—which would not only affect the production function but also the budget constraint.

Appendix C.1: Basic Neoclassical Model The following is a standard approach (see, e.g., JONES 1998) Y = Kβ (AL)1−β .

(23)

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The Cobb–Douglas function with capital K, labor L, 0 < ß < 1 L = L0 e 

nt

(24)

(e is the Euler number); S = s(1 − τ)Y; savings function, where τ is the tax rate

(25)

I = s(1 − τ)Y;

(26)

goods market equilibrium reflecting I = S I = dK/dt + δK;

(27)

gross investment is net investment plus depreciations A(t) = A0 e . at

(28)

Harrod-neutral technological progress dk /dt = (dK/dt)/[AL] − (n + a)k  ;

(29)

dk  /dt = s(1 − τ)k  − (n + a + δ)k  .

(30)

ß

Bernoulli-type differential equation in k k  (t) = {C0 e−(n+a+δ)(1−ß)t + [s/(n + a + δ)]}1/(1−ß)

(31)

k#  = (K/AL) = [s(1 − τ)/(a + n + δ)]1/(1−β) steady state for k

(32)

y# = Y/L = A0 e [s(1 − τ)/(a + n + δ)]β/(1−β) steady state for y.

(33)

at

The most fundamental and simple setup is with a = 0 and δ = 0.

Appendix C.2: General Approach and Simulations In the model presented we have the differential equations dk/dt = sk ß − [n + δ + a(t)]k; capital stock accumulation

(34)

da/dt = (ha*ε )a−ε − ba; technological progress function.

(35)

The solution of Eq. (35) is a(t) = {C0 e

−b(1+ε)t

+ (ha∗ ε )/b}1/(1+ε) .

(36)

Appendix C.2: General Approach and Simulations

143

Hence the general equation for capital accumulation is given by dk/dt = sk ß − [n + δ + {C0 e

−b(1+ε)t

1/(1+ε)

+ (ha∗ ε )/b}

]k.

(37)

Profit maximization requires ßk#ß−1 = z = r and hence k  # = (r/ß)1/(ß−1) . This determines the real interest rate r and requires for the steady-state that k  # = (r#/ß)1/(ß−1) = [s(1 − τ)/(n + a + δ)]1/(1−ß) ; therefore, r# = ß(n + a + δ)/[s(1 − τ)].

(38)

Opening up the economy in the context of an asymmetric two country model—the home country being small—brings the problem that profit maximization in the sense of z = r cannot hold instantaneously, rather domestic capital accumulation will be driven by an equation in which the technological progress function and the impact of a* on a are playing a role. We could, however, assume that asymptotically the profit-maximization condition z = r* will be fulfilled. However, the implication is powerful, namely that k # = k *#. However, it remains unclear how the savings rate s could adjust in a way which is consistent with this implication.

Simulation The following simulation is run for the general solution  k(t) =

1−β k0

  1 1−β s s  (n+δ+a(t))(1−β)t − + . e n + δ + a(t) n + δ + a(t)

(39)

We can show a parameter constellation which does not lead to convergence and simulations where convergence will hold. The parameters assumed are as follows. We can consider a simulation on the basis of ß = 0.33, n = 0.02, δ = 0.1, Co = −0.8, h = 0.4, a* = 0.03, ε = 1/2:

144 Fig. 29 Capital formation under endogenous technological progress

Innovations in Macroeconomics k(t) = k(t,a(t))

k 1.25 1 0.75 0.5 0.25 0

5

a 0.25

10

15

20

25

30

a = a(t)

0.2

0.15

0.1

0.05

0

Fig. 30 Endogenous technological progress

5

10

15

20

25

30

20

25

30 t

k 4 k(t) = k(t,a = 2.5) 3

2

1

Fig. 31 Capital formation constant technological progress (progress for 2.5 periods)

0

5

10

15

D. Impact of the Real Exchange Rate on Trade, Structural Change and Growth

D.1 Introduction As regards economic transition countries as well as EU accession countries, one can observe that they have recorded a long-term real appreciation vis-à-vis the Euro and other currencies. Long-term appreciation does not exclude considerable short-term real exchange rate dynamics where stages of temporary nominal and real currency depreciation can be an element of a long-term real appreciation process. One thus has to ask which role volatility—including potential overshooting—plays on the one hand. On the other hand, the focus is on the impact of the real exchange rate trend on economic development. The real exchange rate q∗ is defined here as eP∗ /P (e is the nominal exchange rate in price notation, P the price level, ∗ denotes foreign variables) while the relative price of nontradables (N goods; T is tradables) is denoted as ϕ = PN /PT . It is clear that the international law of one price will not hold strictly for tradables if we take into account transportation costs, tariffs and other trade impediments. However, even without these physical and political impediments, the law of one price does not hold universally across countries. Subsequently, we will take a closer look at potential explanations and the implications. From a theoretical perspective, the real exchange rate affects trade, structural change and economic growth in an interdependent way. In the medium term, the real exchange rate will affect the trade volume, the product mix of exports and imports plus the current account position. Moreover, the structure of output will be affected; this will partly be linked to sectoral productivity growth. In the medium term and in the long run, there will be direct and indirect effects on national income and per capita income. Those changes will in turn affect structural change and trade. In an open economy, the picture would be incomplete if one does not consider the effects of exchange rate dynamics on capital inflows as well as the stock market. To the extent that there is an increase of capital inflows and in particular foreign direct investment (FDI) inflows, there will be effects on the production potential

P. J. J. Welfens, Innovations in Macroeconomics, DOI 10.1007/978-3-642-11909-5_4, © Springer-Verlag Berlin Heidelberg 2011

145

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and productivity growth (see Fig. 32). From a policy perspective, one must ask whether and which impulses are coming from regional integration and economic globalization. Moreover, the question arises as to which EU policy impulses are relevant and which national policy measures could be adopted to spur growth and a stable economic development. Subsequently, we take a closer look at alternative explanations for real exchange rate changes (Sect. 2). Moreover, we consider macroeconomic effects of real exchange rate changes. This concerns the link between the real exchange rate and economic development (Sect. 3.1), selected links between real exchange rate dynamics and structural change (Sect. 3.2), and the links between the real exchange rate and economic growth (Sect. 3.3). In the final section, we present some basic policy conclusions. The appendix presents some innovative modeling related to the topic of exchange rate dynamics and macroeconomic analysis (including smooth linking of supply-side effects and demand-side impulses). Moreover, we emphasize product upgrading and product innovations in a macroeconomic context which includes an approach of an extended open economy model: the Mundell–Fleming–Schumpeter model, which gives new insights for policy options in a broader macroeconomic perspective. A major element of the analysis presented is that we do not assume the law of one price to hold all the time.

OvershootingProblem

Real Exchange Rate

Capital Inflows

Productivity Growth Trade (Inter-/Intra-industrial; Intermediate vs. Final Products)

Structural Change (Product Mix, Innovations)

Impulses from Regional Integration and Globalization

EU Policy Impulses

Stock Markets

Economic Growth (Level of Output and Growth Rate)

National Policy Measures

Fig. 32 Exchange rate dynamics, trade, structural change and growth

D.2 Reputation, Market Size and Relative Price Effects

147

D.2 Reputation, Market Size and Relative Price Effects: A Quasi–Balassa–Samuelson Effect In reality, the law of one price does not always hold on the one hand while the real exchange rate can change considerably over time on the other. In order to focus more closely on the theoretical problems, we first define the price level as 



P = (PT )a (PN )(1−a ) in country I, and ∗

∗

∗

P∗ = (PT )a (PN )(1−a

∗ )

in country II.

(1) (2)

We assume—with 0 < h < ∞—that there is a premium factor h(. . . ) which implies that the law of one price for tradables does not hold universally. PT = hePT∗ .

(3)

Thus, the real exchange rate is given by 

∗

P/(eP∗ ) = h(. . .)[ϕ](1−a ) /[ϕ∗ ](1−a ) .

(4)

The parameter h is an indicator which reflects forces that render the law of one price internationally invalid. If country I is a relatively poor and small open economy, h will be less than unity since the firms’ standing in international markets—especially if said firms are relatively young and unknown—will be weaker than that of firms from country II. Identical products of firms from country I and II will fetch different prices. Alternatively, a situation with h smaller than unity could reflect a gap in product innovativeness in country I (in this case, we enter a world economy with monopolistic competition and truly heterogeneous goods where country II, for example, is producing more varieties than country I). According to Eq. (4), a rise of the real exchange rate—an appreciation—is consistent with a rise of the relative price of nontradables compared to the respective price ratio abroad. However, it is also clear that the parameter h could rise over time. One may assume that the size of the domestic market (Y vs. Y∗ ), and the relative share of high-income people (y∗∗ is the critical high income here, for which simplicity is assumed to be equal to y∗ ) affects product reputation positively so that we can write H = h(Y/Y∗ ; L /L∗ ).

(5)

Here we have assumed that L is the number of people with at least y∗ income in country I and that all people in country II have income y∗ so that the share of highincome people in country I relative to that of country II is L /L (In country I, overall population L = L + L where L is the number of people with income below y∗ ). Denoting L /L as γ and per capita income as y in country I and y∗ in country II, we can rewrite the equation for the case of a linear homogenous function as h = h (y/[γ y∗ ], 1).

(6)

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According to the approach presented here one indeed would expect that the real exchange rate is a positive function of relative international per capita income y/y∗ . This would be in the spirit of the BALASSA–SAMUELSON effect, but the mechanism suggested here is distinctly different. One may note that the reputation of firms in country I might benefit from FDI since a foreign investor brings reputation to the newly acquired firms, and adequate international branding might then help to fetch higher tradable prices abroad. The h function could be specified in such a way that with y approaching y∗ , the value of h converges toward unity. According to the traditional BALASSA–SAMUELSON effect (BALASSA 1965), the relative price of nontradables will increase along with real per capita income. Writing this relative price as PN /PT , it is clear that in principle such a shift can be brought about by a combination of a rise of PN and a stable PT or a stable PN and a fall of PT , which in turn—assuming an exogenous international tradables price PT∗ —can be brought about only by a nominal appreciation, a fall of e. From this perspective, flexible exchange rates are preferable for catching-up countries which aim at a stable overall price level. The combination of a rise of the nontradables with an absolute fall of the tradable price is quite useful here. Let us take a closer look at q = P/(eP∗ ). If the relative price of nontradables in country I rises relative to country II, the implication is that at a given world market price P∗ either P will rise or the nominal exchange rate will fall. In a system of flexible exchange rates, the nominal exchange rate of country I might indeed fall or the price level P could increase—indeed P will rise if the relative price of nontradables rises while the price of tradables is constant. However, if the law of one price holds for tradables, the nominal appreciation in combination with a constant world market price implies a fall in the absolute level of the tradable price. For simplicity we assume that a = a∗ ; thus we can rewrite (4) as 



P/(eP∗ ) = h (y/y∗ )[ϕ](1−a ) /[ϕ∗ ](1−a ) 

= h (y/y∗ ){[PN /PN∗ ][PT∗ /PT ]}(1−a )

(7)

The real exchange rate q := P/(eP∗ ) will increase according to the traditional BALASSA–SAMUELSON effect, because the ratio of the relative price of nontradables increases along with a rising per capita income. Here we have shown a new additional element for a real appreciation along with a rise of relative per capita income—the h function ultimately reflects the impact of relative market size and of the size of relatively affluent people in society. Hence as the country’s economic size and the development of income distribution enter the picture, the relative size of an economy catching-up will increase and income distribution will change in the course of economic catching-up (note that a change of γ will imply a new h function). It is easy to see that there will be a real appreciation if (i) both the premium factor h and y/y∗ (or the share of relatively rich people as expressed in the parameter γ ) increase; (ii) PN /PN∗ should rise more strongly than PT* /PT falls; such a development could occur, for example, if there is a relatively strong demand shift in favor of the

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149

nontradables sector in country I while there is a strong productivity increase in the tradables sector of country II (the latter implies a fall of PT∗ /PT ; the law of one price is not necessarily assumed to hold for tradables); (iii) PN /PN∗ should fall less than PT∗ /PT rises (e.g., because the relative productivity growth of the nontradables sector could be strong in country I while relative productivity growth in the tradables sector is high compared to country II. The latter means that the relative price of tradables will fall and hence PT∗ /PT will rise); (iv) if both PN /PN∗ and PT∗ /PT are rising, but the relative increase of the nontradables price is larger than that of the tradables price ratio. This could occur, for instance, if the demand for nontradables in country I rises relatively strongly (or if the relative productivity growth in the nontradables sector abroad is relatively high) while the relative productivity growth in the tradables sector is relatively high. For EU accession countries, situation (ii) and (iii) should be quite characteristic. We expect particularly strong productivity growth if there are high FDIs and if competition has been reinforced. A long-run real appreciation as measured by official statistics is to a considerable extent an overstatement if there is sustained upgrading in the quality of exports of the appreciating country. With respect to eastern European accession countries, there is indeed evidence of quality upgrading in exports, in particular in Hungary and the Czech Republic (BORBÉLY 2004).

D.3 Real Exchange Rate Dynamics and Economic Effects D.3.1 Real Exchange Rate and Trade The rise of the real exchange rate has effects in transition countries. It affects: • the volume of imports whose growth is reinforced as import goods become cheaper; • the volume of exports whose dynamics are dampened—this does not exclude high export growth to the extent that domestic firms show a rising export orientation or that subsidiaries of foreign multinationals increase exports; • with standard price elasticity assumptions there will be a deterioration of the trade balance which could be reinforced by relatively high growth over time; as one can write net exports (X ) of goods and services as a function of the real exchange rate (with ∂X /∂q < 0), domestic demandY (with ∂X /∂Y < 0), foreign demandY∗ (with ∂X /∂Y∗ > 0), the domestic production potential Y (with ∂X /∂Y > 0) and the foreign production potential Y∗ (with ∂X /∂Y∗ < 0), it is clear that demand-side effects as well as supply-side effects have to be taken into account; • there is an incentive to upgrade export products in terms of quality and technological sophistication which is a strategy to offset the upward price pressure from the appreciation of the currency.

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Real appreciation will reduce the influx of FDI which implies a long-term deterioration of the current account since the increase of the production potential will slow down.

D.3.2 Real Exchange Rate and Structural Change A rise of the real exchange rate will stimulate product upgrading in the export sector and thus contribute to rising national income. This is particularly true if Schumpeterian rents that can be fetched in world markets are a positive function of the level of technological sophistication of products. Assume that we can order all sectors by technology intensity, starting with A as that sector with the lowest intensity (the sector is assumed to have perfect competition and employ only unskilled labor at the nominal wage rate W ), B the second-lowest intensity . . . Z the highest technology intensity. Assuming that the markup factor which can be realized in international markets depends on the level of technology intensity, we can calculate value-added in a three-sector economy—producing products A, B and Z—on the basis of labor inputs L1 , L2 and L3 (with W as the wage of unskilled workers paid in sector A and W paid to skilled workers which are employed in B and Z; foreign capital is only used for Z output) as follows: Ynominal = L1 W + L2 W (1 + B (q, L )) + [L3 W + r ∗ K ∗∗ (q)PK ] · [1 + Z (q, K∗∗ (q))].

(8)

Note that K∗∗ is the stock of foreign capital in country I, PK is the price of capital— this may be approximated by the stock market price index—and B and Z are the parameters for the markup ratio in sector B and Z; B and Z are assumed to positively depend on the real exchange rate. That is, an appreciation of the currency, which brings the prospect of losing market share in existing markets abroad, will encourage firms to move toward higher quality ranges where one can fetch higher profit rates. Note also that sector B s markup ratio is assumed to benefit from network effects among skilled workers and therefore B positively depends on the number of skilled workers L . Thus sector A is (unskilled) labor intensive and might be identified with the nontradables sector, B is skilled-labor intensive and Z is intensively using FDI and hence international technology; here both B and Z stand for tradable goods. Real income is given by Y = w L1 + w L2 (1 + B (q, L ) + [L3 w + r ∗ K ∗∗ (q)PK /P] · [1 + Z (K∗∗ (q), q)].

(9)

The average real wage rate is w = [L1 /L]w + w [1 − L1 ]/L, where we naturally assume w > w . Real output and real income will increase if • training helps to transform unskilled workers into skilled workers;

D.3 Real Exchange Rate Dynamics and Economic Effects

151

• skilled workers move from a sector of medium technology and a low markup factor to a high technology sector with a higher markup factor (Z > B ); • there is real appreciation which stimulates firms in the medium technology sector and in the high technology sector to upgrade product quality which in turn goes along with a higher markup factor (B and Z will rise along with q); however, in the high technology Z-sector, q has an ambiguous effect on the markup ratio Z since a rise of q stimulates product upgrading while reducing the optimum stock of FDI inflows; • the markup factor can be raised by attracting FDI (FDI as well as cumulated FDI = K∗∗ ); real appreciation reduces FDI inflows, while real depreciation raises FDI inflows relative to GDP (FROOT/STEIN 1991). The extent to which unskilled workers can be transformed into skilled workers depends on many aspects, including economic incentives for skill upgrading for both unskilled workers and firms in medium technology and high technology sectors. We thus have pointed out some key aspects of structural change in an open economy: • An excess of unskilled labor in the A sector will translate fully into long-term unemployment unless there is upgrading of both unskilled workers and unemployed people; this is the implication of our assumption that the tradables sector employs only skilled workers. • One may emphasize that any excess supply of skilled labor in sector B (or Z) can be absorbed by Z (or B) if the country considered is a small open economy. However, there is one serious caveat which is normally not considered in the standard model of a small open economy. If one sector produces and exports high technology goods, one may not assume that the international demand for such products is infinitely elastic; this standard assumption would fully contradict the idea of a high technology product (e.g., advanced computers or medical drugs) which face a limited international demand well known to all—the few—producers in the world. If there is real appreciation, technological and economic catching-up might be facilitated not least through a rising import of cheaper sophisticated intermediate imports. At the bottom line, it is clear that the structural perspective of economic dynamics described here is in marked contrast to the broader approaches in growth theory and growth analysis.

D.3.3 Real Exchange Rate and Growth D.3.3.1 Growth and FDI in a Modified Neoclassical Framework If accession countries are characterized by a long-term real appreciation associated with a nominal appreciation, the implication for capital flows is that there will be higher net capital imports than otherwise. We can write interest rate parity prior to

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EU membership in the following form where the domestic economy is the accession area/country (where i stands for the nominal interest rate, zE for the expected depreciation rate and R for the risk premium, ∗ for foreign variables): i = i∗ + zE + R .

(10)

Prior to EU membership there will be a positive politico-economic risk premium for every accession country. Assuming that the nominal interest rate reflects inflationary expectations, we obtain for the case of expectations coinciding with actual inflation rates (π in accession country and π∗ in the EU-15 countries) the equation r = r ∗ + [z + π∗ − π] + R .

(11)

If there is real appreciation, the bracket term for the change of the real exchange rate (with z denoting the actual depreciation rate) is negative so that the cost of capital in accession countries is reduced; profit maximization will drive firms to realize equality of r and the marginal product of capital. The risk premium after EU accession, R , is certainly much smaller than prior to accession. As one may assume that prudential supervision and the ability of firms to survive recessions and phases of temporary strong appreciation (including overshooting phenomena) in accession countries is smaller than in EU-15 and the Euro zone, one may assume that R is positive. If the risk premium were zero, the real interest rate in accession countries would be smaller than in EU-15, which in turn would stimulate both investment and growth. At the bottom line, the real exchange rate appreciation of catching-up countries implies a rise in the level of the growth path. However, as the real exchange rate appreciation zr can be assumed to be a positive function of relative per capita income y/y∗ , the pace of real appreciation will decline over time, and indeed becomes zero if y = y∗ .

Growth Model with Foreign Direct Investment In an open economy, it is important to understand the role of FDI for production and per capita income. Subsequently we consider a simple model of an open economy which receives FDI inflows—those depend on the real exchange rate (FROOT/STEIN 1991)—and produces based upon a Cobb–Douglas function. To understand basic growth dynamics, consider country I and country II which—with K, L and A denoting capital, labor and a Harrod-neutral progress factor, respectively,—both produce according to a Cobb–Douglas function Y = K ß (AL)1−ß and ∗

∗

Y∗ = K∗ß (A∗ L∗ )1−ß .

(12a) (12b)

We will subsequently consider an asymmetric world economy—or integration zone—where one country is a single source of FDI outflows. The home country is the accession area where we will assume for simplicity that a part b of the capital

D.3 Real Exchange Rate Dynamics and Economic Effects

153

stock is owned by foreign investors; b could be determined through a gradual process of FDI inflows or through a set of initial transactions in the course of privatization of a post-socialist economy involving foreign investors as bidders. We denote the real exchange rate as q and assume that b = b(q) which—with ∂b/∂q < 0—is in the spirit of FROOT/STEIN (1991). If technology is identical in both countries, we have A = A∗ and ß = ß∗ . If factor reward is according to the marginal product rule, we have national income at home Z = Y − bßY;

(13a)

ßY is the profit and b reflects the share of the capital stock owned by foreign companies. Abroad—in the source country of FDIs—we have Z∗ = Y∗ + [bßY/q∗ ].

(13b)

It is easy to recognize that asymmetric FDI will lead to sustained differences in per capita income across countries (WELFENS 1997). In the presence of FDI, it is certainly necessary to carefully distinguish between GDP and GNP. We will assume that savings S = s(. . . )Z

(14)

S∗ = s∗ (. . . )Z∗ .

(15)

Let us at first modify standard neoclassical growth theory—assuming a as the rate of exogenous labor-augmenting technological progress, n as the growth rate of L and denoting k = K/[AL]—by considering a savings rate which positively depends on the real interest rate r. Imposing the conditions of a long-term balanced government budget and that investment I (I = dK/dt + δK) is equal to savings S of domestic residents plus foreign investment from part (exogenous parameter b ) of profits (b ßY): S + b ßY = I

(16)

S∗ − b ßY/q∗ = I∗ .

(17)

The differential equation for the home country (country I) is given by: dK/dt + δK = s[1 − b(q)ß]Y + b ßY.

(18)

Taking into account the definition k = K/[AL] and the respective expression for dk /dt = [dK/dt]/AL − [n + a]k and the production function, we obtain from Eq. (18) after dividing by AL: dk  /dt = [s[1 − b(q)ß] + b ß]k  − [n + a + δ]k  . ß

(19)

This is a Bernoullian equation (we assume a constant q and hence constant b) whose steady-state solution—with r = r∗ —is: k  # = {{s(r ∗ )[1 − b(q)ß] + b ß]}/[n + a + δ]}1/(1−ß) .

(20)

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The steady-state value k # can be smaller or larger than in a closed economy. It is larger if ß[b − sb] is positive, that is if b > sb or if S < b /b(q).

(21)

If government is considering FDI as means of raising gross domestic product, it will have to influence the savings rate or b /b; as regards the latter, government might have to influence the real exchange rate adequately—indeed, one may assume that not just b is a function of q but that b /b is a function of the real exchange. Fulfilling (21) is rather likely, especially if b is close to b so that b /b is close to unity. However, a country which loses the confidence of foreign investors might face b /b < s so that gross domestic product would be smaller than in a closed economy. If we assume that imports positively depend on gross domestic product, the fulfilment of condition (21) implies that from a source country perspective, FDI outflows and rising trade rise in parallel. While on a sectoral basis FDI outflows are likely to replace sectors exports, the aggregate effect of FDI inflows in the host country has an offsetting and possibly dominating effect. Equation (20) and (21) basically point to the fact that reinvested earnings of foreign investors contribute to capital accumulation and a higher GDP while profits transferred abroad reduce gross national product. We will still have to consider under which conditions in the steady-state real national income will be higher than in a closed economy. As a simple step to endogenize the growth rate of output, we assume that the growth rate a is composed of the basic growth rate a as well as an endogenous element b b (with parameter b > 0). The share of the FDI in the overall capital stock b thus has a positive impact upon the growth rate. A = a + b b.

(22)

Output per capita (or GDP per capita) in the steady-state (y#) is given—denoting the Euler number by e —by the following equation: y# = e A0 {{s(r ∗ )[1 − b(q)ß + b ß]/[n + a  + b b(q) + δ]}ß/(1−ß) . at

(23)

Note that the adjustment dynamics for k is affected by the expression [n + a + δ] and (1 − ß). The higher both expressions are, the faster the adjustment toward the steady state will be. Hence, part of the benefit of FDI occurs in the form of faster adjustment toward the steady state. As regards the steady state, we can see from (20) that the higher q is, the lower b is and therefore the lower k # is as well. From this perspective, the early initial real depreciation occurring in countries opening up suggests that the level of the long-term growth path is raised through an exchange rate effect which, however, will fade out in the course of the medium- and longterm appreciation. Nevertheless, b has a positive long-term impact upon per capita income since the slope of the lny(t) line is raised by b (see the following figure where b jumps—e.g., in the course of privatization involving foreign investors—from zero to the new equilibrium value in t1 ). Depending on s relative to b/b , this will lower

D.3 Real Exchange Rate Dynamics and Economic Effects

155

or raise the level of the growth path (see point E versus point C). This does not rule out a long-term equilibrium growth gap, namely if a < a∗ . Compared to the existing literature, the proposed model differs since it takes into account both a change in the level of the growth path as well as a rise of the permanent growth rate. The familiar model by BARRO/MANKIW/SALA-I-MARTIN (1995) takes into account international borrowing, where this approach affects the adjustment speed toward the steady state which itself is not affected by capital flows. F′

lny

α′

F

E D′ B α A

Fig. 33 Effect of FDI on the level of per capita income and the growth rate

D α′

C

0

t1

t

The ability to generate a higher growth rate in the presence of foreign investors is likely to be reinforced if government expenditures on research and development is relatively high; the R&D policy variable is denoted as  and one may assume a(b, ). Hence the degree of supply-side government fiscal policy matters (the higher the share of  relative to output or to overall government expenditures, the higher the degree of supply-orientation in government fiscal policy). Steady-state national income (Y ) per capita is given by: (Y /L)# = [1 − b(q)ß]y# = [1 − b(q)ß]{s[1 − b(q∗ )ß] + b ß}e ∗

· {s(r )/[n + a(b(q)) + δ]}

ß/(1−ß)

.

a(b(q))t

A0 (24)

Whether GNP per capita is larger than in a closed economy depends (ignoring the question whether opening up changes the real interest rate) on [1 − b(q∗ )ß]{s[1 − b(q)ß] + b ß} > s

(25)

s[1 − b(q)ß]2 + b ß > s + bb ß.

(26)

[1 − b(q∗ )ß]2 > 1 − b ß/s.

(27)

Dividing by s gives

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Assuming that bß and b ß/s are both close to zero, we can use the approximation that ln (1 − x) ≈ −x and thus obtain—quite interesting also for empirical analysis—as a critical condition for GNP per capita to be larger than in a closed economy: s > b /2b(q).

(28)

More empirical analysis needs to be done. From Eq. (28), we can only conclude that a rise of q which reduces b makes it less likely that s exceeds the right-hand side of the equation. A government of an open economy interested in raising the level of the growth path of per capita GNP should encourage savings as we can see from Eq. (28). One should also note that real appreciation reduces the burden of foreign debt, which often is considerable in poor countries. Thus long-term real appreciation is welcome by many poor countries. D.3.3.2 Negative International Spillovers? It is interesting to take a look at appreciation dynamics within the context of a threecountry perspective: Country I is a poor country while country II is a high income country. Both country I and II are part of a regional customs union. We assume that the catching-up country I records a gradual long-term real appreciation of the currency. At the same time, we assume that productivity growth in the tradables sector is higher than the appreciation rate so that the price of exported goods falls from the perspective of the (net) importing country II. We now have to distinguish two cases in the context of a three-country perspective: 1. Country II imports intermediate products built into products exported to third country markets. Here, country II could ultimately benefit from rising net exports, higher profits and higher employment. 2. Country II imports final products which puts strong downward pressure on the price of tradables (much more than in the case of cheaper intermediate products) and hence implies downward inflation pressure. The welfare effect will be ambiguous since lower prices of final consumer goods will benefit consumers. At the same time, lower prices of tradables imply lower profits in the tradables sector—and in the case of wage rigidity also lower employment. Unemployment problems will be reinforced if the implied rise in the real interest rate in country II reduces the equilibrium capital intensity and hence investment. From an EU-15 perspective, the implication thus is the following with respect to rising imports from EU accession countries: The mix of imported products is quite crucial—namely intermediate products versus final products—as is the relative productivity effect in accession countries. If the productivity growth effect is so strong that the relative price of imported tradables falls in EU-15, further analysis will have to focus on the above-made distinction. To identify such patterns is quite difficult since product upgrading in Eastern Europe makes price measurement rather cumbersome.

D.5 Wages, Prices and the Real Exchange Rate

157

D.4 Real Effective Exchange Rate (p/ep∗ ) Dynamics in Selected EU Countries

140 120 100 80 60 40 20

93 19 94 19 95 19 96 19 97 19 98 19 99 20 00 20 01 20 02 20 03 20 04 20 05 20 06 20 07 20 08

92

Source: WDI 2010

19

91

19

19

19

90

0

Poland

Portugal

Ireland

Hungary

Spain

Czech Republic

Fig. 34 Real effective exchange rate (p/ep∗ ) dynamics in selected EU countries: Poland, Hungary, Czech Republic, Portugal, Spain, Ireland, 1990–2002. (Source: WDI 2010)

D.5 Wages, Prices and the Real Exchange Rate Assuming that accession countries face long-term real appreciation pressure—eP∗ /P falls over time—the implication is that relative wage costs increase over time. The latter is an implication of the assumption that prices are determined through a markup J on wage costs so that P∗ = J∗ W∗ and

(29)

P = JW.

(30)

With a constant markup ratio a and a∗ , respectively, a real exchange rate appreciation will always go along with a relative rise of domestic wage: [1/e][P/P∗ ] = [1/e][J/J∗ ][W/W∗ ].

(31)

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We assume that the nominal wage W and W∗ will both be determined by expected price dynamics (PE and PE∗ represent the expected price level at home and abroad) and labor productivity growth, which is in line with profit maximization on the part of firms. They all are assumed to use a Cobb–Douglas production technology ∗ ∗ Y = AKß L1−ß and Y∗ = A∗ K∗ß L∗1−ß . W := PE w = PE (1 − ß)A[Y/L]

(32)

W∗ = P∗ E w∗ = P∗ E (1 − ß∗ )A∗ [Y∗ /L∗ ].

(33)

Hence for the relative wage ratio we get: W/W∗ = [PE /P∗ E ]{(1 − ß)[A/A∗ ][Y/L]/[1 − ß∗ ][Y∗ /L∗ ]}

(34)

[1/e][P/P∗ ] = [1/e][J/J∗ ][PE /P∗ E ]{(1 − ß)[A/A∗ ][Y/L]/[1 − ß∗ ][Y∗ /L∗ ]}. (35) From this perspective a real exchange rate depreciation—assuming a constant nominal exchange rate—will occur if there is • • • •

a relative increase in the markup ratio (a/a∗ ), a rise of the relative expected price level, a rise of the foreign relative output elasticity of capital (ß∗ /ß), a rise of relative labor productivity.

In countries of a customs union area which have opened up toward free regional trade and FDI, one can expect high growth in investment, output and per capita income. This holds all the more the more politically stable the country under consideration is. Structural change will go along with a rise of relative labor productivity while in a context of rational expectations, the expected relative price increase is largely linked to relative money supply.

D.6 Towards an Integrated Macroeconomic Approach We will emphasize that for certain analytical purposes it is useful to take a look at the macroeconomic impact of both supply-side and demand-side impulses. In every economy, output dynamics can be understood to be a mixture of the impact of the supply side—its macroeconomic equivalence is the production potential Ypot = Kß L1−ß (K is the capital and L is the labor)—and of aggregate demand Yd . In transition countries, both supply-side dynamics and the demand side are important with some sectors being dominated by supply-side developments while others are shaped by demand-side dynamics. If one were to include labor-saving technological progress (stock of knowledge is A), the production function Ypot = Kß (AL)1−ß would be used. Taking into account both the impact of the supply side and the demand side, a hybrid equilibrium approach for the goods market can be written as follows: Y = αYpot + (1 − α)Yd .

(36)

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159

An important question is what determines α (in the interval [0, 1]), the size of the relative supply-side impact parameter. It reflects various forces, including expectations. The most simple way to think about α is to consider it as identical with 1 − u (with u denoting the unemployment rate). In a full employment economy, u is zero and hence only the supply-side dynamics—that is the accumulation of input factors—will determine actual gross domestic product. If u were rather high, it would be clear that supply-side dynamics would hardly influence actual output while the demand side would have a strong impact on Y. A more refined way would be to replace a with uχ , where the parameter χ is assumed to be positive. In a small open economy—which asymptotically faces a totally elastic world demand curve—the impact of the supply side should be relatively high. It is obvious that for the case of a closed economy, the fiscal multiplier for the case of standard specification of the demand side is smaller than the standard textbook case of 1/s; with α = 1 − u the fiscal multiplier is dY/dG = 1/[1 − uc].

(37)

An exogenous increase in the production potential raises actual output by dY/dYpot = (1 − u) + u∂Yd /∂Ypot > 0.

(38)

For the special case of an increase of the production potential through one unit of net investment and assuming an exogenous real interest rate, we have ∂Yd /∂K = r and hence dY = [(1 − u)Kß−1 L1−ß + ur]dK.

(39)

If one simply assumes that the impact of aggregate demand reduces over time while that of aggregate supply increases in the long run, one might restate Eq. (36) as follows (with e denoting the Euler number): Y = [1 − e

−bt

]Ypot + e

−bt

Yd .

(36 )

Output and Wage Pressure in a Hybrid Supply & Demand Macro Model One also should note that the hybrid approach suggests an interesting answer to the question of how a rise of the real wage rate will affect both output and employment. Consider a small open economy which can raise exports in accordance with the growth the potential output—here we assume that all output is tradable. We can rewrite Eq. (36) as follows if one assumes that consumption C = cY—with Y = wL + rK# (assuming that factors labor L and capital K are rewarded in accordance with their respective marginal product; K# is the equilibrium capital stock, r the real interest rate, w the real wage rate); investment I = I(r) and government consumption G is exogenous, net exports X are a negative function of the international

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real wage ratio (∗ denotes foreign variables), a negative function of the real exchange rate q = P/(eP∗ ), whereby P is the price level, e the nominal exchange rate, W the nominal wage rate and the real wage rate is defined as w = W/P. Y = αYpot (W/P) + [1 − α]{c[wL + rK # ] + I(r) + G + X (W/eW∗ , q)}.

(37)

We assume that the real interest rate r and the exchange rate e are exogenous; denoting eW∗ as W∗ and W/W∗ as ϕ we obtain from differentiation: dY/dW = α∂Ypot /∂W + [1 − α]{c[L + r∂K # /∂W] + ∂X /∂ϕ dW/W∗ }. (38) By assumption, the partial derivative ∂X /∂ϕ is negative. Given P, the rise of the nominal wage rate is, of course, equivalent to a real wage increase. The impact of a higher wage rate on consumption is positive, namely c[L + r∂Kopt /∂W]; the overall sign for dY/dW is thus unclear. In a small open economy, the net export effect may be expected to outweigh the domestic consumption effect (and also the effect ∂Ypot /∂W if it should be negative). Moreover, if α = 1 − u and u = u(w/[Y/L]) the total differential for (1 ) yields even a somewhat more complex result for dY/dW (if dY/dW is negative, the sign for du/dW should be positive). The ambiguity of dY/dW remains, but we can learn from the approach presented that the risk of adopting an excessive wage rate is higher the less open the economy is. One should, however, not rule out that net exports could be a positive function of W/W∗ , namely if the quality and innovativeness of the export base is a positive function of the relative wage ratio. Such a function implicitly assumes that the country considered can sufficiently move up the quality ladder in line with the rise of the international wage ratio. Analytically, we thus enter a world of imperfect competition, where the export price P∗∗ might well diverge from domestic price P for the same good. Assume that export quantity X = X( ), that is X negatively depends on the ratio of the wage rate W to marginal market revenue per worker P∗∗ ßY/L—relative to the respective foreign indicator. We thus consider a relative cost pressure indicator  = {[W/P∗∗ ]/[ßY/L]}/{[W∗ /P∗ ]/[ß∗ Y∗ /L∗ ]}.

(39)

Note that real exports are XP∗∗ /P while real imports, expressed in domestic quantity, are q∗ J, where J is the quantity of imports. Now let us assume that we have the following pricing rule (with v as a quality index or novelty index; σ is a positive parameter): P∗∗ = W(1 − ß) + σ v.

(40)

We furthermore assume (with parameter σ > 0) that the quality index realized by exporters is a positive function of the international nominal wage ratio because a relative rise of wage costs stimulates firms to move up the technology and quality ladder (an argument which, however, might be doubtful in the case of technologically leading countries where R&D expenditures as well as global product innovations are quite important). v = σ W/[eW∗ ].

(41)

D.6 Towards an Integrated Macroeconomic Approach

161

Hence,

P∗∗ = W(1 − ß) + σ σ W/[eW∗ ] = W (1 − ß) + σ σ /[eW∗ ] .

(42)

For the foreign country, we have (implying a specific effective relative international price P∗∗ /eP∗ ): P∗ = W∗ (1 − ß) + σ∗ σ∗ W∗ /[e∗ W] = W∗ [(1 − ß∗ ) + σ∗ σ∗ /[e∗ W]]. Thus we can write      = 1 − ß + σ∗ σ∗ e/W [ß∗ Y∗ /L∗ ]/ 1 − ß + σ σ /eW∗ [ßY/L].

(43)

(44)

Real imports are qJ and J is assumed—with W/W∗ denoted as ϕ —to be a function of J(q, ϕ , Y). With respect to J, all three partial derivatives Jq, Jϕ and JY are positive; Jq reflects a demand shift effect since the quantity of imports will reduce when their price is raised relative to domestically sold goods; Jϕ reflects the relative importance of wage income in overall income. JY is the familiar increase of imports resulting from higher aggregate income. Hence, we paradoxically find that the ratio of real exports to real imports [XP∗∗ /P]/[qJ] could be positively influenced by the international nominal wage price ratio. A critical assumption here is that the price of exports indeed can be raised which is possible only under imperfect competition in international goods markets and if the firms of the countries considered sufficiently move up the quality ladder. Quality here includes product innovativeness. A simplified case in which we assume the quantity of imports not to be reacting to Y and q∗ (q∗ = 1/q)—more or less the case in a country whose imports are dominated by natural resources (as is the case of Japan and a few other countries). We assume that the quantity exported is X = X(ϕ ), where X is a negative function of ϕ and a positive function of process innovations v ; the quantity imported J is a positive function of ϕ . Net real exports X are given by X = [P∗∗ (ϕ , v )X(ϕ )/P] − eP∗ J(ϕ )/P.

(45)

Denoting E as an elasticity we get dX /dϕ = [X/P][P∗∗ /ϕ ]EP∗∗ ,ϕ + P∗∗ ∂X/∂ϕ /P − q∗ ∂J/∂ϕ .

(46)

The expression dX /dϕ (note that the elasticity ϕ might fall in absolute terms if ϕ is increased again and again, which implies that there is an optimum wage pressure!) is positive only if the elasticity exceeds a critical value:



Ep∗ ,e > − ϕ /X ∂X/∂ϕ + P/P∗∗ q∗ ∂J/∂ϕ . (47) Whether this inequality is fulfilled is an empirical question. One may assume that this will only be the case if the firms of the respective country have strong performance

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in product innovations (OECD countries—or some of them). Even if dX /dϕ is positive, it is clear that there will be a positive link between Y and ϕ only if a rise of ϕ has no critical negative effect on domestic absorption (e.g., a rise of ϕ could cause unemployment in the nontradables sectors). Assume that the unemployment rate negatively depends on process innovations A and positively on wage pressure as captured by ϕ . Denoting absorption by H (u, ϕ )—where u is the unemployment rate and for simplicity we may assume u = u(ϕ , A), with ∂u/∂ϕ > 0, ∂u/∂A < 0—we have in a “Schumpeterian demand-oriented approach”: Y = H (u(ϕ , A), ϕ , r) + [P∗∗ (ϕ , A)X(ϕ )/P] − eP∗ J(ϕ )/P.

(48)

This equation is a quasi-equilibrium condition for the goods market. Denoting with lower case suffix a partial derivative, we get dY = H r dr + H u uA dA + X/PP∗∗ A dA + {H ϕ + H u uϕ + [X/P][P∗∗ /ϕ ]EP∗∗ , ϕ + P∗∗ Xϕ /P − q∗ Jϕ }dϕ .

(49)

Within a simple framework, one may set dr = 0 and dA = 0 and then solve for dY/dϕ . This expression in a nutshell suggests that there is an optimum wage pressure in countries catching-up: set dY/dϕ = 0 which yields the output-maximizing wage rate (where we assume that the second derivative is negative). Note also that in the case that ∂P∗∗ /∂ϕ = 0—so that EP∗∗ ,ϕ = 0—net real exports are always negatively affected by wage pressure. Taking into account a simple real money demand equation m(Y, i, u)—where we assume mu > 0 (as a rise of the unemployment rate signals higher uncertainty and hence a rising real demand for liquidity: see ARTUS 1989)—and stating the money market equilibrium condition, we have M/P = m(Y, i, u).

(50)

As prices are sticky, we have assumed that process innovations will not reduce the domestic price level in the short run. For a constant domestic price level, we get after differentiation: dM/P = mY dY + mi di + mu du.

(51)

Assuming zero inflation—in line with the assumption of a stable domestic price level P—and hence real interest rate r = nominal interest rate i, we obtain dr = [1/mi ]dM/P − [mY /mi ]dY − [mu /mi ]du.

(52)

Inserting this finding from the money market equilibrium in the goods market quasiequilibrium condition, we get dY = [H r /mi ]dM/P − H r [mY /mi ]dY − H r [mu /mi ][uϕ dϕ + uA dA] + [H u uA + XA X/P]dA + {H ϕ + H u uϕ + [X/P][P∗∗ /ϕ ]EP∗∗ , ϕ + P∗∗ Xϕ /P − q∗ Jϕ }dϕ .

(53)

D.6 Towards an Integrated Macroeconomic Approach

163

Ignoring for the moment any impact from the foreign exchange market, we can thus see some of the impact on Y. It is an empirical question of whether process innovations have a positive impact on Y, that is whether dY/dA > 0. It is straightforward to determine the endogenous variables r, q and Y on the basis of the equilibrium conditions for the goods market, the money market and the foreign exchange market. The latter is given (using Q to denote real net capital imports which are assumed to positively depend on r/r∗ and q) by Q(r/r∗ , q) = qJ − P∗∗ X (· · ·)/P.

(54)

In a short-term model, one would use the equilibrium condition as stated in (48); in the context of a medium-term approach one would replace (48) by (36) and in a long-term perspective (36 ) which converges toward the traditional neoclassical model. One should note that in the medium-term framework and in the long-term analysis we have to consider the impact of technological progress (A) on both the demand side and the supply side. The model would look more complex if one would relax the assumption of a small open economy which faces no restrictions in exports to the world market. We thus have a fairly general macroeconomic approach which can accommodate different time horizons in a consistent way. A serious problem could be that the optimum wage pressure is not necessarily consistent with full employment. However, government can be assumed to be able to also influence P∗∗ , namely by R&D promotion measures designed to stimulate product innovations in the tradables sector. With the goal of full employment it certainly is important to avoid excessive wage pressure (ex ante) and rather raise the marginal value-added in the tradables sector through adequate R&D promotion. Wages will then adjust ex post to the rising marginal value-added. Finally it is interesting that a change of the real exchange rate q will affect net exports and investment in different ways. In a period of a fall in the real exchange rate—due to a relatively slow increase of the domestic price level—one will have a rise of net exports. At the same time, there will be a dampening effect on inflation, which drives up the real interest rate. In countries which are catching up economically, the real exchange rate is likely to temporarily increase so that net exports are dampened while domestic investment increases. This development should not be interpreted as simply a loss of international competitiveness since a major driver behind this development is, according to the BS effect, the natural adjustment of relative prices within a long-term economic adjustment process. For small open economies acting in a system of flexible exchange rates there will be the long-term policy option to adopt a restrictive monetary policy so that domestic absorption will be reduced through rising real interest rates; at the same time net exports will increase. Economic catching-up (associated with both supply-side effects and demand dynamics) is subsequently understood as moving up the technology ladder of products (i.e., the adoption of more sophisticated quality products over time). Product innovation rates will largely be considered as exogenous so that we leave open the explanation as to why and at what time firms in the respective countries will upgrade product assortments (e.g., this may be linked to FDI inflows or to a rise in the ratio

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of government expenditures on research and development relative to GDP). The analytical focus will be on a one-sector model or a two-sector approach with tradables and nontradables. Moving up the technology ladder thus means that the share of high-quality products in overall exports or total output is increased in the respective transition country. An interesting theoretical challenge is to consider both product and process innovations which we will undertake in one simple model—a more refined approach includes endogenous process innovation (and possibly endogenous product innovations). While political reforms in transition countries affect opportunities for economic growth, there are naturally favorable prospects of economic catching up in the context of economic opening up. Once those countries have opened up for trade and capital flows they can benefit from the following: • competitive pressure from world markets stimulating efficiency-enhancing economic restructuring; • productivity-stimulating effects from OECD imports of intermediate products used for the production of final goods, including export goods; • import of investment goods with embodied technological progress; • exploitation of scale economies in the context of rising exports in scale-intensive industries; • inflows of FDI which raise the capital stock in the case of greenfield investment and raise factor productivity in the context of international mergers and acquisitions. For economic analysis, it is rather useful to make a distinction between the nontradableses (N-) and the tradables (T-) sector. • Rising trade will naturally only affect the tradables sector; however, the tradables sector will typically be the main impulse for structural change. • FDI inflows can be in both the T-sector and the N-sector. A major effect of FDI inflows should be productivity growth. The structure of FDI inflows will thus partly determine the relative price of tradables, namely to the extent that productivity determines the relative price. If FDI affects both sectors in a parallel way with respect to productivity growth, we should expect a smaller rise in the relative price of nontradables compared to the case that FDI inflows are concentrated in the tradables sector.

D.7 Medium-Term Approach to Product Innovations, Output and the Exchange Rate As countries catch up, the export–GDP and the import–GDP ratio will grow while the share of intra-industrial trade increase. Moreover, FDI inflows will rise and in the long run there will typically be two-way FDI flows. Firms will become more innovative and will emphasize product innovations; the rate of product innovations will be denoted as v. Note that the term product innovation is understood here in the sense that the respective product is new from the perspective of the respective

D.7 Medium-Term Approach to Product Innovations, Output and the Exchange Rate

165

catching-up country (from the perspective of a global technology leader country this looks like product imitation). The term v may be understood as the country’s product innovations relative to that of foreign countries: v is a stock variable, that is the share of product innovations given the overall number of products no . In the following analysis, we will raise the issue of how product innovations will affect output, the interest rate and the exchange rate. The following macroeconomic model set up is a “Schumpeter–Keynes” approach in the sense that product innovations are integrated into the familiar Mundell–Fleming model. Hence the price level at home and abroad is given. As regards the goods market our basic assumption is that investment I is a function of the real interest rate at home I and abroad (r∗ ), the real exchange rate q∗ (i.e., eP∗ /P)—following the FROOT/STEIN argument—and the product innovation rate v, which is exogenous in the model. Hence we implicitly assume a model with FDI inflows. Moreover, we basically assume that new products can be produced only with new equipment so that investment is a positive function of v. Consumption is also assumed to be a positive function of v; and a positive function of disposable income Y(1 − τ) and of real money balances M/P so that we have a real balance effect in the consumption function. Net exports X are assumed to be a positive function of Y∗ , q∗ and v, but a negative function of Y. As regards the money market we assume that the real demand for money m depends positively on Y and v—the latter as a higher rate of product innovations suggests that the marginal utility of holding liquidity increases for consumers looking for shopping opportunities of innovative goods; m depends negatively on the nominal interest rate I which is equal to r plus the expected inflation rate (assumed here to be zero). The foreign exchange rate market equilibrium requires here that net capital imports Q(i/i∗ , v, q∗ )—with positive partial derivatives of Q with respect to both i/i∗ , q∗ and to v—plus net exports of goods and services are equal to zero. Net capital imports react positively to a real depreciation in line with the FROOT/STEIN argument. Net capital imports are assumed to depend positively on v because a higher rate of product innovations will stimulate FDI inflows. Foreign investors become more active as they anticipate higher profit opportunities. Linearizing the consumption function as C = c(1 − τ)Y + c (M/P) + c v

(55a)

and using a simple investment function for an open economy (with FDI inflows so that investment depends both on the domestic real interest rate and the foreign interest rate and the real exchange rate in line with the FROOT/STEIN argument) I = −hr − h r∗ + h v + h q∗

(55b)

X = xq∗ + x Y∗ /Y + x v

(55c)

and a net export function

we have the following three Eqs. (56–58) as the equilibrium condition in the goods market, the money market and the foreign exchange market, respectively (G is the

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real government expenditures): Y = c(1 − τ)Y + c (M/P) + c v + G − hr − h r ∗ + h v + h q∗ + xq∗ + x Y∗ /Y + x v M/P = m(Y, r, v) Q(i/i∗ , v, q∗ ) + xq∗ + x Y∗ /Y + x v = 0.

[IS]

(56)

[LM]

(57)

[ZZ]

(58)

Product innovations shift the IS curve to the right, the LM curve to the left and the ZZ curve downwards. The latter holds since net exports of goods and services increases as a consequence of a higher v. An initial negative trade balance will thus be reduced so that required net capital imports fall. If one assumes that FDI inflows and hence Q depends positively on Y/Y∗ —that is the relative size of the market—the implication is that the balance of payments equilibrium curve (ZZ) can have a zero slope even if ∂Q/∂(i/i∗ ) is not infinite in absolute terms, and hence the domestic interest rate could diverge from the foreign interest rate. If mv is zero, the LM curve is not directly affected by a change of v so that product innovations clearly raise both equilibrium output and the interest rate. Under flexible exchange rates, there will be an appreciation of the currency in point E1 —as this point is above the ZZ line—so that the IS1 curve (driven by reduced net exports of goods and services) shifts a little to the left (IS2 ) while the ZZ1 curve shifts upwards (ZZ2 ). It remains true that product innovations raise the output level and the real interest rate and contribute to a current account surplus. This situation could continue until a new intersection point in the initial equilibrium Eo (note that in a system of fixed exchange rates, point E1 implies higher net capital inflows and an excess supply in the foreign exchange market) is observed. The stock of money M will increase, and the LM-curve and the IS-curve—the latter due to higher consumption—will shift to the right). This, however, does not mean that government promotion of policy innovation is inefficient since in a medium-term perspective, the capital stock K will increase as the consequence of net investment—actually increased net investment in the context of product innovations. Indeed, a modified simple medium-term model could consider that consumption C = c(1 − τ)Y + c [(M/P) + (P /P)K] + c v where the term c [. . . ] is a broader real wealth effect on consumption, namely including the real value of capital stock; P /P is the ratio of the stock market price index P to the output price index P. A consistent medium-term export function would read X = xq∗ + xY∗ /Y + x v + x K where the term x K (with x > 0) is a supply shift variable in the export sector. This term will then shift both the IS curve to the right and the ZZ curve downward as K is raised. Thus the general equilibrium point in our diagram will shift to the right over time where we assume that monetary policy raises the money supply in parallel with the capital stock K so that medium-term money supply equilibrium is given for the case of an income elasticity of output of unity by the simple equation (M/P)/K = [Y/K]m (i, v). In a non-inflationary economy, it is equal to the real interest rate r which under profit maximization and a Cobb–Douglas production function Y = KßAL1−ß (with L standing for labor and A for Harrod-neutral technological progress) is equal to ßY/K so that Y/K = r/ß. Hence

D.7 Medium-Term Approach to Product Innovations, Output and the Exchange Rate Fig. 35 Rise of product innovations in the Mundell–Fleming model

r

167

LM0

ZZ2 E1

ZZ0

r1

ZZ1

E2 r0

E0

IS2

IS1

IS0

0

Y0

Y1

Y

a monetary policy strategy which aims at a constant ratio [M/P]/K is then consistent with a constant money demand {[r/ß]m (i, v)}—assuming that v, i and r are constant; they have reached an equilibrium value. An interesting long-term question concerns the relation between product innovations v and the process innovations A. If A is a positive function of v—since new products can often be produced only with new equipment (and the innovation system may be assumed to be responsive to the higher demand for A)—an exogenous rate of product innovations dv/dt > 0 would indeed generate a continuous growth process. A more realistic picture would emerge if we would also consider a quasi-depreciation rate of the stock of product innovations or a vintage-type approach to product innovations so that in each period the oldest product generation is removed from the shelf and production. As endogenous variables we haveY, r and e (changes in e stand for a real exchange rate change as long as P or P∗ do not change). So we are interested in the mediumterm multipliers for Y, r and e with respect to v, the product innovation rate. Using Kramer s rule we obtain (with ζ = i/i∗ ) after differentiation of (II), (III), (IV): dY/dv > 0 (sufficient condition is mv = 0)

(59a)

dr/dv > 0 (sufficient condition is mv = 0)

(59b)

de/dv < 0 if (see the appendix; the system determinant is negative; the following expression reveals that the nominator expression of the multiplier de/dv) Qϕ and mr are sufficiently small so that    x  Y∗ 1 − c (1 − τ) + 2 mr (Qq∗ + x) − hmY (Qq∗ + x) Y    x Y∗  (60) > (h + x) mQ Qζ − mr 2 Y

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and Y∗ exceeding Y0 ∗ (home country is relatively small). Product innovations will bring about a real appreciation; one may also note that it raises equilibrium output. This is much in line with the original reflections of Schumpeter who argued that firms facing the pressure of economic recession will launch new products in order to generate more sales. From a policy perspective, our analysis suggests that government could stimulate product innovations in recessions in order to raise output; indeed one may split government expenditures G into government consumption G plus government R&D support (G ) for product innovations. Such an approach is certainly rather appropriate in countries catching-up, as for them a higher rate of product innovations largely means to accelerate the speed of international imitations of foreign product innovations. As regards advanced countries it is questionable whether higher government R&D subsidies could strongly stimulate product innovations in the short term so as to easily overcome a recession. At the bottom line, the model presented clearly suggests that the structural breakdown of government expenditures is crucial. Since the ratio of R&D expenditures to GDP has increased over the long run in OECD countries, it is obvious that innovation issues have become more important while standard macroeconomic modelling largely ignores innovation issues.

Total Multiplier Effect The distinction between different types of government expenditures is crucial as we will subsequently show and is totally ignored in the traditional macro models. Real government expenditure G is split here into government consumption G and expenditures G on the promotion of product innovations: G = G + G .

(61)

Expenditures on the promotion of product innovations mean in the case of leading OECD countries that development of true product innovations is stimulated and no short-run results can be expected. However, for catching-up countries this could mainly refer to the acceleration of imitation of foreign product innovations which in many cases should be possible within one or two years. We subsequently assume that there is a link between government expenditures on R&D—with a focus on product innovations—that can be described by v = G .

(62)

Hence we have a link between two exogenous variables. As regards multipliers for G they clearly differ from that for G since a change in G will not only affect aggregate demand (direct impact) but also the product innovation rate v (indirect impact) so that the overall multiplier for any endogenous variable Zi (=Y, r, e) can be written as dZi /dG = [dZi /dG] + dZi /dv

(63)

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169

is the same for dG = dG and dG = dG , but the second term is relevant only with respect to a change of G . The output multiplier dY/dG for a rise of G is clearly larger than that for a rise of government consumption G . There is another link between exogenous variables in the context of product innovations which imply an effective fall of the price level P—a problem which theoretically comes under the heading of hedonic price measurement. Using a simple approach—with the hedonic parameter H(H > 0)—we can thus write dP = −Hdv.

(64)

Product innovations are indeed a non-monetary aspect of the price level. At the bottom line the complete multiplier analysis for the impact of a rise of G is given by dZi /dG = [dZi /dG] + dZi /dv − HdZi /dP.

(65)

The following graphical analysis shows both the direct effect of a rise in government expenditures promoting product innovations and the indirect effects of this policy which consists of a double rightward shift of the IS curve related to the impact of G on v and of v on P and M/P, respectively; the effective rise of M/P amounts to a hedonic real balance effect. Moreover, there is a rightward shift of the LM curve which is to say that product innovations are equivalent to a rise of M/P unless there is a dominant money demand effect. In a more general perspective, it is true that the impact of v on P must be considered with respect to all multipliers dZi /dv so that these multipliers are composed of a direct effect and an indirect effect related to a change of the price level. Thus a consistent analysis of the multipliers for Y, r, and e is achieved. As regards the change in the “hedonically adjusted” real exchange rate, one has to take into account that d(eP∗ /P) is given for a constant foreign price level P∗ , normalized to unity by (1/P)de/dv − (e/P2 )dP/dv. Our analysis offers a new and broader analytical picture of important policy issues.

D.8 Economic Catching-up and Long-Term Real Exchange Rate Dynamics From a theoretical perspective, we expect a long-term real appreciation of the currency of accession countries which are assumed to catch up in economic and technological terms with EU-15. Thus, the BS effect would work. However, how will this effect indeed be realized? One may ask whether it is mainly a nominal appreciation which brings about the BS effect, thereby requiring flexible exchange rates or whether it is a rise in price level relative to the foreign price level (in a setting with a constant or stable nominal exchange rate). A rise in the domestic price level could bring problems with respect to the inflation convergence criterion and the interest rate convergence criterion of European Economic and Monetary Union. From

170 Fig. 36 Direct and indirect effects of product innovation

Innovations in Macroeconomics r

LM0 LM1

E1 r1

ZZ0

E0 r0

ZZ1 IS3 IS2 IS0 Y0

0

Y1

IS1

Y

this perspective, it is clear that countries eager to join the monetary union quickly might prefer an extended period of flexible exchange rates and enter the Euro zone only after a transition period of several years.

A Simple Long-Term Approach In the following approach, we assume that net exports X positively influence the real exchange rate q := [P/eP∗ ] (parameter b > 0) and that it is a negative function of the relative innovation differential a∗ . On the link between the real exchange rate and the current account, consistent models are available. A relative rise of innovativeness abroad (country II)—we focus here mainly on product innovations—will lead to relatively lower export prices of country I. The prospects for technological catchingup depend on technology policy and education policy, and both can be expected to negatively depend on the share of the natural resource sector in the overall economy. As regards the link between q and a∗ , one may also note that net capital exports will be larger the higher our a∗ is (i.e., a technological progress differential in favor of the foreign country). Here we assume a∗ to be an exogenous variable. Hence we find the following: dq/dt = bX − a∗ q.

(66)

We furthermore assume that net exports negatively depend on q where the elasticity η is negative. Hence, we have X = qη (with η ≤ 0).

(67)

D.8 Economic Catching-up and Long-Term Real Exchange Rate Dynamics

171

This leads to the following Bernoullian differential equation for q(t): dq/dt = bqη − a∗ q.

(68)

In the subsequent graph, we have drawn the first-right hand side expression as the BB line and the second expression as the AA line. For given parameters, there will be a monotonous real appreciation (see the QQ line). With C0 determined from initial conditions and e denoting the Euler number, the solution of the differential equation is: ∗ (1−η)t

q(t) = {C0 e−a

+ b/a∗ }1/(1−η) .

(69)

This equation is convergent for q. Hence we have an equation for the long-term real exchange rate with q converging and thus has the steady-state value (for t approaching infinity) q#: q# = (b/a∗ )1/(1−η) .

(70)

For a small, open—non-innovative (!)—economy facing an infinite price elasticity in export markets, the equilibrium real exchange rate is clearly unity (see Eq. (70)). If the export demand elasticity is zero, thereby reflecting the extreme case of a country exporting a very large share of high technology goods, we find that q# = (b/a∗ ) (case of high technology dominance in exports).

(71)

If the absolute value of η is unity, we would get as the steady-state value q# = (b/a∗ )1/2 . Clearly, technological catching-up with a∗ being reduced will lead to downward rotation of the AA curve (AA1 in Fig. 37b). Technological upgrading could also go along with a fall in the absolute value of the price elasticity. Both elements could occur simultaneously. Take E0 as the starting point. If there is only a fall in price elasticity (in absolute terms), the rotation of the hyperbola indicates that there will be a real depreciation effect. Next we take a look at the fall of a∗ . Taking E0 as the starting point, we observe a real appreciation in point E01 . Catching-up of the home country is also associated with a rise in the share of technology intensive goods. Should catching-up go along with a higher share of (medium-) technology intensive goods (e.g., due to foreign investors increasingly producing product cycle goods in modern plants for exports to world markets), we find a rotation of the BB curve, since the price elasticity—in absolute terms—of exports is falling (BB1 ). This elasticity effect will dampen the real appreciation so that E1 is the final equilibrium point. If, however, the reduction of the technology gap is relatively strong (intersection point of AA is to the right of point F), the reduction of the absolute price elasticity will reinforce the real appreciation effect. Note that there may be cases when a∗ rise and the price elasticity falls in absolute terms. From an empirical perspective, we may expect that countries opening up will liberalize trade and adopt internal modernization measures which help to raise per

172

Innovations in Macroeconomics BB0

BB1

QQ BB0

AA0(a0*′q) AA1(a1*′q)

E0

AA0(a*′q)

E′0 E01 E1

E0

AA2(a2*′q) F

dq /dt

E2

bqn

0

a

q#

q

0

q

#

00

q

#

0

q

#

1

q

#

01 1

#

q

2

q=p/(ep*)

b

Fig. 37 a Real exchange rate dynamics. b Model of the long-term real exchange rate (dq/dt = bqη − a∗ q)

capita income in the medium term. This would help to stimulate capital inflows (in particular FDI inflows) so that per capita output will further increase. (Per capita GNP might increase more slowly than per capita GDP, however, since rising FDI inflows could raise the share of profit transfers relative to GDP.) As per capita income y rises, the share of intra-industrial trade should increase, accompanied by intensified competition. The latter, in turn, should stimulate static efficiency gains as well as innovation, and government policy may then stimulate innovation through subsidies for research and development. As a possible further analytical step, consider the following modifications. We restate our basic equation by focusing on x which is per capita net exports and assuming that b is a function of the capital intensity k – where k = K/(AL) which is the capital per efficiency unit of labor (A standing for Harrod-neutral technological progress) because net exports will contribute to an appreciation the higher the capital intensity for a given net export x is. We thus have dq/dt = b(k  )[x ] − a∗ q.

(66 )

b(k  ) = b k  .

(66 )

We specify 

Moreover, we state a modified neoclassical accumulation dynamic which includes FDI inflows F per unit of labor in efficiency unit which we assume to be proportionate to y = −Y/(AL) in the following way: F/(AL) = f(q)y = qλ y .

(67 )

The parameter λ is—in line with the FROOT/STEIN argument—negative. Assuming a simple savings function S (where the real exchange rate affects savings but we

D.8 Economic Catching-up and Long-Term Real Exchange Rate Dynamics

173

make no a priori assumption about the partial derivative; with a net foreign debt position, a rise in q reduces the burden of the debt and thus might raise the ability to save, with an international net creditor position a rise in q could reduce the savings rate—ultimately, all this is an empirical issue) we have S = sqσ Y.

(68 )

The modified neoclassical equilibrium condition is therefore δK + (dK/dt) = sqσ Y + F .

(69 )

Dividing by AL and taking into account (II ) and using a Cobb–Douglas production function y = kß (this production function might include—as a kind of positive external effect of household’s money holdings—real money balances M/P if M/P = 1) yields dk  /dt + [n + a + δ]k = sqσ k ß + qλ k ß .

(70 )

Note that using the equilibrium condition Eq. (III ) implies that investment is linked to output and the real exchange rate, but one should note that this equilibrium perspective is also fully compatibly with an investment function I(Y, q) in a disequilibrium approach. We define x as net exports per efficiency unit of labor and now assume that x = qη . The accumulation dynamics for the capital stock are governed by: dk  /dt = [sqσ + qλ ]k  −[n + δ + a]k  . ß

(71 )

An analytical solution of this pair of differential equations is quite complex. If a steady state for k, q exists, then we can solve this by setting dk /dt = 0 and dq/dt = 0: q# = [b k  /a∗ ]1/(1−η) . 

(72)

A solution of (VI ) is rather easier if we take a look at the special case σ = λ: k  # = {[(s + 1)qσ ]/[n + δ + a]}1/(1−σß) k  # = {[(s + 1)(b k  /a∗ ) 

η σ

]/[n + δ + a]}1/(1−σß) ;

(73) (74)



we define 1/(1 − η) = η . From this we have 

η σ

k  # (1−σß)/ση = {[(s + 1)(b /a∗ )

]/[n + δ + a]}1/(1−σß) .

(75)

There is a problem with the interpretation of outputY(orY/AL) when we have product innovations. However, one may assume that true output Y —a hedonically deflated nominal output variable—can be written asYqμ , since q is strictly a negative function of a∗ (the parameter μ is positive). A potential variant of this model would be to endogenize the rate of product innovations (e.g., by making it dependent on the per capita income and the real exchange rate). This would be a new line of research in endogenous growth modeling. Moreover, the model can be linked to endogenous growth theory based on endogenous process innovations (e.g., BARFIELD/HEIDUK/WELFENS 2003).

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D.9 Policy Implications Policy conclusions can be drawn on the basis of theoretical analysis and empirical analysis. As regards the latter, WELFENS/BORBÉLY (2004) have pointed out links between the foreign exchange market and the stock market. From this perspective both overshooting phenomena in foreign exchange markets and in stock markets can cause considerable temporary volatility. Moreover, it has been shown (JUNGMITTAG 2004) that poor countries such as Spain and Ireland have been able to catch up technologically over time, while Portugal and Greece stand for a much more modest catching-up record in the EU-15. From this perspective, it is obvious that there is no easy path toward sustained technological and economic catching-up in Europe. According to the approach presented here, the size of markets/countries and the share of relatively rich households in overall households is important for quasi-BS effects. Hence the price of tradables in poor countries will not show a uniform pace of convergence toward the price of tradables across leading EU or OECD countries. Government should stimulate and encourage the upgrading of human capital and cross-sectoral labor mobility as well as FDI inflows. The upgrading of export products could take place not only through the presence of multinational companies and R&D promotion—of national or supranational policymakers—but also through a rising share of sophisticated intermediate imports (in this respect, EU-15 offers broad opportunities for EU accession countries in eastern Europe). Theoretical analysis has shown that a real appreciation of the currency—in a country catching-up economically—can have several major effects (see Fig. 38): • it reduces the costs of capital; • it reduces FDI inflows, but it has an ambiguous effect on output per capita; • it stimulates product upgrading in the tradables sectors. However, it is unrealistic to assume that firms can quickly upgrade export products in terms of quality or product innovativeness. The adjustment time or learning phase required typically depends on the general ability of firms to adjust, the level of technological sophistication already acquired (and hence the presence of foreign investors) and

Fiscal Policy Real Appreciation

Exchange Rate Regime

Monetary Policy

Lowers Cost of Capital

Reduces Inflation

Reduces Real Foreign Debt

Fig. 38 Effects of a real appreciation

Discourages FDI Inflows

Stimulating Upgrading in the Tradables Sector and Raising Net Imports

D.9 Policy Implications

175

the share of skilled workers available. A sudden strong real appreciation should be avoided, as the supply-side responsiveness of firms can cope only with limited exchange rate pressure. Moreover, as real appreciation tends to reduce FDI inflows, phases of sudden and strong real appreciation could become a problem for an accession country (and this all the more the higher initial trade balance deficit is); • it raises net imports of goods and services in the medium term—after the initial negative J-curve effect; • it could reduce the inflation rate (a topic not much dealt with here); • it reduces net foreign debt.

E. Macroeconomic Aspects of Opening up, Unemployment, Growth and Transition

E.1 Introduction Economic opening up has been a natural element of systemic transformation in the former Soviet Union and the smaller post socialist countries of Eastern Europe. Anticipating EU eastern enlargement, eastern European transition countries have reoriented the regional focus of trade toward the EU-15 countries. The change in regional orientation coincided with changes in the structure of output and trade. As regards structural change of exports, several countries underwent rapid structural change and achieved gradually improved revealed comparative advantages (RCAs) in non-labor intensive sectors (BORBÉLY 2004). After high inflation rates and a massive transformational recession in the early transition stage—reflecting obsolescence of part of the capital stock and adjustment costs in the course of restructuring—in the first transition stage, most transition countries have achieved considerable economic growth. Countries with relatively low per capita income, a well-educated labor force, and a functioning banking system should indeed be able to record considerable economic growth if stable and efficient institutions, competitive pressure and opening up are combined in a sustained manner. It is not easy for transition countries with a young democracy to come up with the right combination of constitutional foundations and efficiency enhancing political learning, in particular since governments eager to generate quick improvement in some fields might favor short-term political action over long-term growth strategies. The analysis will focus on economic catching-up in the sense that we consider economies which become open for trade, foreign direct investment flows, and technology transfer. Attracting rising FDI inflows—those often are associated with international technology transfer—has been not only a major element of EU eastern enlargement but of southern EU enlargement as well. FDI inflows have two major effects for the host country: It raises capital intensity and thus—according to the Rybczynski theorem—implies that the production of capital intensive goods should increase. If such sectors dominate wage bargaining, the parallel increase in labor productivity should lead to high general wage increases which in turn could lead

P. J. J. Welfens, Innovations in Macroeconomics, DOI 10.1007/978-3-642-11909-5_5, © Springer-Verlag Berlin Heidelberg 2011

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to unemployment outside of capital intensive sectors. From an EU-15 perspective, high FDI outflows toward the transition countries imply a continuous outsourcing of manufacturing value-added in tradables sectors Ti (i = 1, 2, . . . , n) toward EU accession countries (as well as Ukraine and Russia). This vertical FDI outflow from Western Europe is likely to improve global international competitiveness of firms from EU-15 countries. Thus one may anticipate that RCAs of EU-15 countries in transatlantic trade are positively correlated with those fields n, n , n in which accession countries have a positive RCA in trade with EU-15. At the same time, growing vertical FDI could lead to a convergence of sectoral export specialization—a process which is likely to be reinforced by economic catching-up in Eastern Europe and the associated relative rise of intra-industrial trade. The relative rise of the nontradables price in accession countries will, however, raise the relative share of nontradables production so that the development of production specialization in Eastern Europe could diverge from export specialization. We assume that the first stage of economic opening up is accompanied by a rise of price elasticities, however, in a second transition stage during which firms increasingly specialize in more technology intensive (and less price sensitive) products, requiring a higher share of sunk costs in investment, labor demand elasticity will be assumed to fall. As regards innovations, we will focus partly on process innovations, but more important here are product innovations in countries catching-up. Product innovations are new for the respective poor country but not new to the world economy so that from the perspective of a leading global economy we focus on international diffusion phenomena. The following analysis presents certain analytical building blocs but not an integrated model, although one may combine the various blocs to a consistent meta model. Moreover, there will be no microeconomic foundations of behavior at the macroeconomic level; this certainly is possible but as we will consider only minor—but powerful—modifications of well-known models we are not so much interested in the aspects of microeconomic foundations. We will not deal much with the issue of international economic convergence— that is convergence of per capita national income across countries—except for an important observation: Since GDP (Y) is equal to real wage income wL (w is the real wage rate, L is the employment, K is the capital, k := K/L and * denotes foreign variables) it holds for per capita income y : = Y/L and y*, respectively that y = w + rk

(1)

y* = w* + r*k*.

(2)

Assume that country I (home country which is assumed to have a relatively low per capita income) and country II product according to a Cobb–Douglas production function, then we will have y = kß

(3)

y* = k*ß* .

(4)

The only explanation for temporary international differences in per capita income is a difference in capital intensity. If we consider an open economy with free trade and free

E.1 Introduction

179

flows of technological knowledge such that ß = ß* (a mysterious implication of the Heckscher-Ohlin-Samuelson [HOS] approach which assumes that there is no factor mobility), we will have—according to the HOS approach—convergence of relative factor rewards which in combination with the assumption of profit-maximization leads to w = YL (YL is marginal product of labor; YK is the marginal product of capital) and r = YK and w* = YL * = w and r* = YK * = r. Since the optimum capital intensity k depends on w/r (abroad: k* depends on w*/r*), it is clear that—in line with neoclassical growth theory—there will be a convergence of capital intensities across countries. Which adjustment mechanism will bring about this result? We suggest that the mechanism is the Balassa–Samuelson (BS) effect which says that the relatively poor country—with the relatively low capital intensity—will witness a real appreciation in the course of economic catching-up, and the real appreciation in turn is linked to changes in the relative price of nontradables (the nontradables price relative to the tradables price in a poor country is lower than in a rich country: as relative per capita income rises the relative price of nontradables will rise, too). The real exchange rate eP*/P will fall over time, which in a system of flexible exchange rates could mean that there is a fall of the nominal exchange rate (e) of country I while the foreign level (P*) and the domestic price level (P) are constant; alternatively both e, P* and P could change adequately. From the perspective of country II which is capital abundant (initially k* > k), the profit rate  for an investment in country II and in I are in the case of constant price levels: r* = YK * = 

(5) 

{[de*/dt]/e*}P/P* + YK =  *.

(6)

Profit-maximization in a model with both capital mobility and foreign direct investment implies  * =  . The real depreciation of the country II currency—the rise of e*—implies that investment of firms from country II in country I will generate a higher profit rate than for domestic investors from country I. As long as the real depreciation of the country II currency continues as long will there be a special incentive for foreigners to invest in country I. Until finally y approaches y* and hence YK = YK * = r* = r. From this perspective, a new open economy model with trade in investment goods and asymmetric foreign direct investment lets one expect that convergence will take place faster than without foreign direct investment (in the HOS model the convergence of relative and absolute factor rewards can occur even if the two tradable goods considered are consumption goods). As regards the links between trade and growth, the HOS model might be misleading to the extent that the real world is characterized by high mobility of capital, namely foreign direct investment. Moreover, part of the changes in Eastern Europe and Russia take place in a period of a strong rise of oil and gas prices—those prices increased strongly after 2000. According to the Samuelson Stolper theorem the price of capital—which we assume to be the factor intensively used in the oil and gas sector—will increase in Europe. This in turn could stimulate investment in the long run.

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E.2 Growth, Trade and Innovation E.2.1 New Production Function for Open Economies Economic growth in open economies is only partly understood, and modeling it in a consistent way is not easy. Consistent modeling is, however, crucial if one is to understand the dynamics of international economic catching-up. The standard neoclassical growth theory is a consistent analytical tool for simple growth analysis in closed economies, however, is unsatisfactory with respect to the role of trade and some other key aspects. A straightforward way to improve growth modeling—for the case of a country catching-up—and to combine the supply side with the international demand side may be suggested as follows: • Consider the fact that import competition in many countries contributes to competitive pressure which in turn stimulates specialization as well as efficiency gains. Hence output should be a function not only of capital and labor inputs but of the ratio of imports J to national income Y. We assume that J = V(q*)Y where q*  is the real exchange rate eP*/P. Specifically we can specify J = jq*λ Y where  λ ≤ 0. Subsequently we will use for simplicity J = jY, and jχ indicates the impact of import competition on output. • Take into account that the higher the share of exports X in national income Y the higher competitive pressure from global markets will be. This implies that we will use a production function in which not only capital K and labor L enter but also x := X/Y. We will assume as a simple export function that X = q*λY*χ so that X/Y = q*λY*χ /Y. • Take into account that the use of telecommunications stimulates the diffusion of knowledge so that telecommunications density T (a proxy variable for the use of telecommunications)—the number of access lines per capita—has a positive impact on national output Y. • Consider the impact of (cumulated) R&D expenditures F . For the sake of simplicity, we will ignore the problem of accumulation of R&D expenditures. Moreover, to stay as simple as possible, we will assume that F is an exogenous variable chosen by government—effectively we have government R&D promotion here. Thus we can state as (assuming Harrod-neutral technological progress A(t) and f as a parameter to indicate the impact of F on output) the macroeconomic production function where we assume ß = 1 − ß 





Y = Ff K ß Tσ [AL]ß xχ jχ .

(7)

Hence 



Y[1+χ] = Ff K ß Tσ [AL]ß Xχ jχ .

(8)

We denote ß /[1 + χ] =: ß, f/[1 + χ] =: f  , χ2 /[1 + χ] =: χ , χ /[1 + χ] =: χ , σ/[1 + χ] =: σ , χλ/[1 + χ] =: λ . 







Y = Ff K ßTσ [AL]1−ß [q*λ Y*χ jχ ].

(10)

E.2 Growth, Trade and Innovation

181

Thus we have a production function which looks like a Cobb–Douglas function with both a Harrod-neutral progress A and a Hicks-neutral technological progress;      the relevant “parameter” for the latter is [Ff Tσ q∗λ Y∗χ jχ ]. Note that per capita income y := Y/L is (with k := K/L) given by 









y = Ff k ß Tσ [A]1−ß [q∗λ Y∗χ jχ ].

(11)

As one can see, the import–GDP ratio j will only affect the level of per capita output y, but not the growth rate— unless one would specify that A = A(j, . . . ); note, however, that the balance of payments equilibrium constraints implicity suggests that trade positively affects both the level of output and the growth rate. Output per efficiency unit of labor (y := Y/[AL]; and k := K/[AL]) is given by f

σ







y = F k  T [q*λ Y*χ jχ ]. ß

(12)

Assuming a constant growth rate of A(t), namely dlnA/dt = a, per capita income grows (with e denoting the Euler number) according to: f

σ







y = A0 e F k  T [q*λ Y*χ jχ ]. at

ß

(13)

Assuming a constant import–GDP ratio j, this equation implies for the growth rate (g) of per capita income y := Y/L (the exogenous growth rate of L is denoted as n): gy = a + f  gF  + σ gT + ßgK − ßn + λ gq* + χ gY* .

(14)

We assume profit-maximization so that the marginal product of capital YK –under Cobb–Douglas it is equal to ßY/K—is equal to the real interest rate, or r = ßY/K.

(15)

Since we can rewrite [dK/dt]/K as [[dK/dt]/Y][Y/K] and since we assume that savings S are proportionate to national income Y—that is S = sY—and that S equals gross investment dK/dt + δK (δ is the depreciation rate of capital) we have gy = a + f  gF  + σ gT + ß[sr/ß − δ − n] + λ gq* + χ gY* .

(16)

If one assumes that the savings rate depends on the real interest rate r and on the ratio of real money balances per capita to real income per capita so that s = s(r, m/Y)— namely that s is rising until a critical ratio m/Y is achieved, beyond this point s is a negative function of m/Y—we can state gy = a + f  gF  + σ gT + s(r, m/y)r − ßδ − ßn + λ gq* + χ gY* .

(17)

Note that since the real demand for money balances m is assumed to depend on the nominal interest rate i which in turn is the sum r and the anticipated inflation rate π —assume the inflation rate to be zero here—we can restate the above equation as gy = a + f  gF  + σ gT + s (r, y)r − ßδ − ßn + λ gq* + χ gY* .

(18)

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A simple specification for the function s is s = s (r)/y

(19)

gy = a + f  gF  + σ gT + s (r)r/y − ßδ − ßn + λ gq* + χ gY* .

(20)

and hence we have

In a small open economy with free capital flows, r will be equal to r*. The above equation is a differential equation in y. dy/dt − [a + f  gF  + σ gT − ßδ − ßn + λ gq* + χ gY* ]y = s (r*)r*.

(21)

Hence we have (with C denoting a constant to be obtained from initial conditions) y(t) = C e

[a+f  gF +σ gT −ßδ−ßn+λ gq* +χ gy* ]t

− s (r*)r/[a + f  gF + σ gT − ßδ − ßn + λ gq* + χ gY* ]

(22)

The growth rate of per capita income is higher the higher parameter a is, the higher the growth rate of R&D expenditures is, the higher the growth rate of telecommunication density is, the higher foreign output growth is and the higher the real depreciation rate is. Note that according to the Balassa–Samuelson effect, there will be a continuous real appreciation in an open economy with tradables and nontradables, which would therefore slow down economic growth. There will be permanent growth of per capita income if [a + f  gF  + σ gT + λ gq* + χ gY* ] > ß[δ + n].

(23)

Besides empirical issues, the only major theoretical issue is to endogenize parameter a. However, it is obvious that government has an impact on economic growth, in particular through the growth rate of real R&D expenditures and the growth rate of telecommunications services, which will depend not least on government policies with respect to the allocation of scarce spectrum for mobile telephony. As regards the initial condition we have in t = 0 y0 = C − s (r*)r/[a + f  gF  + σ gT − ßδ + λ gq* + χ gY* ].

(24)

C = {yo + s (r*)r/[a + f  gF  + σ gT − ßδ + λ gq* + χ gY* ]}.

(25)

Hence

Thus the savings rate s positively affects the level of the growth path so that we have a familiar element of standard neoclassical growth theory.

E.2 Growth, Trade and Innovation

183

E.2.2 Foreign Direct Investment It is an interesting question as to whether asymmetric FDI inflows—for example, a dominance of FDI in the tradables sector—will cause any problems for the economy. More generally put, to what extent large differences in productivity growth could be a problem for balanced growth and full employment? Furthermore, to what extent will the production elasticity of domestic capital affect the long-term ratio of domestic capital to foreign capital (K**) employed? We consider the production potential to be given. We take up the latter question first and assume that output is determined on the basis of domestic capital input K and the stock of foreign capital K** (production function and gross domestic product, respectively, is Kß K**1−ß ) while demand consists of domestic investment—assumed to be proportionate to national income—and net exports X which we assumed to be proportionate (proportionality factor z ) to cumulated foreign direct investment inflows K** in country I: the higher the stock of cumulated FDI inflows the better the access to the world market will be—to provide just one simple reasoning for the proposed specification. ßKß K**1−ß = z K ß K**1−ß + z K**.

(27a)

Here we have assumed that both domestic capital K and foreign capital K** are rewarded in accordance with the marginal product rule so that national income is ß times gross domestic product. (1 − z )ßK ß K**−ß = z .

(27b)

[K/K**] = {z /[1 − z ]ß}1/ß .

(27c)

Hence it holds

The ratio of domestic to foreign capital employed in the country is therefore positively correlated with z /(1 − z ) and negatively correlated with the output elasticity of domestic capital ß. One should emphasize that a combination of trade and FDI liberalization— observed in the reality of catching-up economies—takes us outside of the familiar Heckscher–Ohlin model, and we clearly have a lack of modeling when it comes to taking into account both trade and FDI effects. There are also other potential problems associated with economic opening up, in particular there could be the problem of: • High current account imbalances; indeed high deficit-GDP ratios can be a problem as foreign indebtedness is rising—however, a large sustained current account surplus also can be a problem since it will go along with “unnatural” net capital exports and a strong temporary boom which could raise the price of nontrables relative to tradables strongly. • Volatile short-term inflows which raise the exposure of the respective country in the sense that high outflows might follow in the future: An exceptional period is

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represented by election years as these may be associated with political instability and large ideological swings in the case of a change in power. • Transition countries differ in many ways including the size of the respective country and factor endowment. Russia, Romania and Kazachstan are resource-rich countries while other transition countries are relatively richly endowed with labor (and in some cases capital—taking into account countries which have attracted high FDI inflows). Countries which are relatively abundant in natural resources should clearly benefit from economic expansion in periods in which the relative price of resources is high—as was the case in the late 1990s. 200 P_Oil (USD)*e/PPI

P_Oil (USD)*e/CPI

180 160 140 120 100 80 60 40 20 0 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010

Fig. 39 Relative price of oil. (Source: www.recep.org, Eurostat/IFS Database)

One should not overlook that many resource-abundant countries have a tendency for artificially low prices—for instance oil and gas prices in countries with rich oil or gas sites. If prices were raised to the world market price level, their income levels from the natural resources sector would be high, however a fast price convergence would undermine the viability of energy-intensive firms and could raise unemployment. Countries rich in oil and gas also tend to have high nontradables prices and strong Balassa–Samuelson effects in the sense of a relative rise of nontradables prices. The latter may, however, not so much reflect technological economic catching-up but rather a pure natural resources boom effect. As regards the impact of a relative rise of energy prices on employment, the effect will be negative in the non-energy sector and positive in the oil and gas sector. Assume that the energy sector uses only capital K and labor L while the non-energy sector (NE) uses factor inputs capital   K and labor L, namely according to YNE = Kß Eß L1−ß−ß . In the short term we can assume a constant capital stock and obtain from profit-maximization and assuming competition in goods and labor markets so that factors are rewarded according to the marginal product rule (we denote the energy price as P , output price in the

E.2 Growth, Trade and Innovation

185

non-energy sector as P) 





w = [1 − ß − ß ][K/L]ß/(1−ß ) (ß /[P /P])ß /(1−ß )

(28)

Hence, labor demand in the non-energy sector is a positive function of capital intensity and a negative function of the real energy price P /P. However, in the energy   sector—with output E = Kß L1−ß —we will have (defining W/P = w ) 

w = [1 − ß ][K /L ]1/ß .

(29)

Overall labor demand is L = L + L. For countries which are richly endowed with natural resources, a rise of the oil price could indeed raise overall labor demand and overall real income which is, expressed in terms of the non-energy good: Y = (P /P)E +YNE . The option is all the more attractive if the country considered enjoys alone or with other countries together—as in the case of OPEC—some international market power (then profit-maximization leads to a slightly modified labor demand schedule). Transition and Unemployment As regards the dynamics of unemployment in transformation countries the unemployment rate is high in many transition countries (e.g., in Poland it has risen continuously in the first twelve years of transformation reaching a specific unemployment rate of close to 30% in 2004). In the following table, countries are ranked according to the degree of economic openness: It seems that small open economies face less problems in the field of unemployment than large economies—except for Russia which has benefited after the 1998 crisis from strong economic growth, stimulated strongly by high real oil prices. A typical phenomenon of transition countries is that the specific unemployment rate of unskilled labor is rather high, although labor markets seem to be quite flexible in most of these countries. This has to be explained, and our analysis will present a simple model which is mainly related to the interaction of the tradables and nontradables sectors. Another element of transition and economic catching-up is that firms will upgrade in terms of technology and specialize according to comparative advantages—here analysis shows that RCA is changing relatively quickly in countries with high foreign direct investment inflows. Shifts in RCAs of different types of industries, ordered in accordance with technology intensity, are observed (BORBÉLY 2004). In the course of technological upgrading and specialization one may expect that factor demand becomes more inelastic; which consequences this might have for labor has to be analyzed. Unemployment also has other effects crucial for macroeconomic analysis, as will be shown subsequently. Patterns of economic catching-up are difficult to reconcile with HOS modeling. Successful catching-up seems to be comprised of two elements where one indeed is HOS-compatible. A typical pattern of economic catching-up in the context of EU

Estonia Slovak Republic Czech Republic Belarus Hungary Bulgaria Slovenia Latvia Lithuania Romania Russian Federation Poland

6.4 2.2 2.9 5.8 5.2 5.8 4.6 6.6 3.9 1.6 8.3 4.0

14.8 18.9 8.8 NA 6.5 16.3 7.5 8.4 11.1 10.8 11.4 16.7

182.5 156.5 144.2 137.1 150.2 118.7 116.5 100.0 107.3 74.4 59.8 59.8

Openness (%)

172.2 149.6 146.6 137.2 129.2 122.5 121.8 100.1 96.7 73.9 70.7 61.8

2001 Unempl. Rate (%)

Openness (%)

GDP growth (%)

2000

6.5 3.3 3.1 4.7 3.8 4.1 2.9 7.9 6.5 5.3 5.0 1.0

GDP growth (%) 12.6 NA NA NA 5.7 NA 5.9 7.7 12.9 NA NA 16.2

Unempl. Rate (%) 177.7 152.7 132.7 143.4 131.1 112.9 114.4 101.5 113.9 76.7 58.7 59.5

Openness (%)

2002

6.0 4.4 2.0 4.7 3.3 4.8 3.0 6.1 6.7 4.3 4.3 1.4

GDP growth (%)

NA NA NA NA 5.8 NA 13.8 NA NA NA NA 17.8

Unempl. Rate (%)

Table 6 Openness (trade/GDP), growth and unemployment in transition countries. (Source: WDI 2002, WDI online (openness and GDP growth 2001, 2002), IFS (unemployment rate 2001, 2002))

186 Innovations in Macroeconomics

E.2 Growth, Trade and Innovation

187

southern and EU eastern enlargement (EU eastern enlargement effectively started with the EU association treaties with postsocialist countries of eastern Europe) is that poor countries specialize in labor intensive products which is consistent with the HOS approach. Poor countries are relatively labor abundant and thus should specialize in labor intensive products—economic opening up will raise the share of labor intensive production and exports will concern labor intensive products. Indeed countries such as Spain, Portugal, the Czech Republic, Poland and Hungary show a RCA and high export unit values in part of labor intensive production: This combination of a high RCA and high export unit values in labor intensive production represents profitable exports in this field. However, there is a second element of successful catching-up, namely a gradual rise of the RCA in science-intensive and human-capital intensive products: If in such sectors a high and rising export unit value can be obtained this will stimulate long-term expansion of these sectors (narrowly defined) and related sectors into which firms might move in the course of product differentiation (broadly defined) and catching-up. Such developments are associated with product innovation dynamics where a product innovation in a poor country typically will stand for diffusion when defined from the perspective of a leading OECD country. It is unclear whether the ability to achieve positive RCA in technology-intensive and science-intensive goods and differentiated goods (largely electronics) depends mainly on domestic human capital formation or mainly on foreign direct investment. A quick product upgrading and hence rising RCAs can hardly be expected without foreign direct investment inflows in those sectors unless there is considerable domestic research and development; and it requires active human capital formation policies and government support for research and development. Such traits are not only found in catching-up dynamics of Spain and Portugal in the 1980s and Hungary, Poland and the Czech Republic in the 1990s but also in Asian Newly Industrializing Countries in the 1970s and 1980s. One may argue that this second element of catching-up—it may be dubbed the DUNNING–SCHULTZ–SCHUMPETER element—is of general importance for product innovation and technological upgrading: Once labor intensive profitable production contributes to reducing unemployment and rising technology-intensive plus human-capital-intensive production contributes to growth of net exports of goods and services there is a broad potential for future structural change and shifts toward high-value added sectors. This amounts to favorable prospects for sustained longterm economic growth. A crucial sustainability test for economic catching-up is the phase of continuous real appreciation which will stimulate firms to upgrade product quality and to move toward industries which are more technology intensive and hence less price sensitive. Taking simply a look at the output structure of countries in eastern Europe or Asia can be misleading, particularly if there is a high share of technology intensive production and positive RCAs in this field (positive RCA means that it should exceed unity if it is defined as sector export–import balance relative to the national export–import balance or exceed zero if one uses the natural logarithm of this variable). There is a caveat which concerns vertical multinational investment: For example, even if computers were manufactured in Hungary or Poland one must analyze whether

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production statistics showing computer manufacturing are not hiding the fact that high-tech components are imported and that value-added is mainly from “screwdriving factories” so that ultimately there is labor-intensive production taking place. Production and export of intermediate inputs can, however, lead to more complex long-term production and upgrading: For example, Portugal initially developed intermediate product assembly for the automotive industry abroad, but later was able to attract final assembly in the automotive sector—not least because it had developed a competitive supplier industry. From this perspective technological upgrading does not only mean to switch to more advanced products but also to shift more into final product assembly. Another example is Toyota in Japan which started out decades ago as a producer of textile machinery before it became a very innovative and profitable automotive firm. We leave open here how upgrading in production takes place—in subsequent modeling the idea is basically that it is associated with foreign direct investors and that international technology transfer occurs (for simplicity) at zero marginal costs. In the following analysis, we want to highlight selected macroeconomic problems of transition and economic opening up. In particular, we are interested in innovation issues. We suggest new ideas in three different fields of transformation 1. We state the hypothesis that there is a link between the Balassa–Samuelson effect and unemployment of unskilled labor. 2. We argue that product innovations are crucial in the course of economic catchingup and opening up—and we show how product innovations can be integrated into the Mundell–Fleming model. 3. It is shown in a simple dynamic model how the current account and relative innovation performance affect the long-term real equilibrium exchange rate. In addition our analysis recalls standard sceptical approaches to high output growth in resource-rich countries when they based growth largely on depletion of nonrenewable natural resources. As regards policy conclusions, government promotion of product innovation seems to be rather important in transition countries and NICs.

E.3 Growth, Resource Dynamics, Balassa–Samuelson Effects and Unemployment E.3.1 Growth, Natural Resources and Economic Welfare Before we take a closer look at innovation aspects of catching-up, we briefly look into the issue of countries which are abundant with natural resources. In transition countries, aggregate output can typically be described by a standard production function which for simplicity can have the arguments capital K, labor L, technology A—assumed to be labor augmenting—and natural resources dR/dt where R is the stock of natural resources. In the case of a Cobb–Douglas production function we

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can write  

Y = Kß R ß (AL)1−ß−ß .

(30)

Hence output growth is—with g denoting growth rate and R = dR/dt—given by gY = ßgK + ß gR + (1 − ß − ß )[gL + gA ].

(31)

As we have a homogenous production function we also can write Y = YK K + YAL (AL) + YR |dR/dt|.

(32)

If factors are rewarded according to the marginal product rule we have Y = rK + w[AL] + [PR /P]|dR/dt|.

(33)

If resources are non-renewable resources an adequate measure of welfare—or of “modified net national product”—would be (assuming that capital depreciation is proportionate to K) the following term Z : Z = Y − δK − A |dR/dt|.

(34)

A is a real shadow price variable which reflects the value of resource depletion in terms of consumption goods; a should be determined on the basis of a sustainable growth model—at a given level of technology (not discussed here). In a broad perspective this concept corresponds to the logic of net value added. One has to deduct capital depreciations and resource depletion if one wants to focus on value added along with maintaining the stock of capital and natural resources, respectively. The term adR/dt catches the depletion of natural resources which are considered as a natural asset here. Combining Eqs. (33) and (34) yields Z = rK + w[AL] + {[PR /P]|dR/dt| − A |dR/dt|} − δK

(35)

If the relative price of natural resources were identical to the parameter a, an adequate welfare measure would be simply the sum of capital income and labor income. The analysis is rather complex in reality since the first element in the term {[PR /P]|dR/dt| − A |dR/dt|} refers to the physical use of resources while the second term dR/dt should effectively be corrected by a factor (1 − b ), where b is a technological progress parameter allowing a better exploitation of existing stocks of resources. As b can be assumed to be relatively large in transition countries, one should not overemphasize the problem of natural resources depletion in the medium term. However, in the long run this aspect is clearly important. Z = rK + w[AL] + {[PR /P]|dR/dt| − A (1 − b)|dR/dt|} − δK

(35 )

If the relative price of oil is increasing (as was the case in the late 1990s) we can expect a rise of Z .

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In any case we may emphasize that resource rich countries are well advised to take into account the problem that early growth dynamics can only be sustained if there is long-term industrial diversification in production and exports. This view does, of course, not rule out that proceeds from the export of natural resources can be quite useful to finance the import of machinery and equipment as well as technology useful for the expansion of manufacturing exports in the long run. There is also a risk that strong wage growth from the resource sector—in periods of high international resource prices—spills over to other sectors and thus could raise unemployment. Russia, Kazakhstan, Azerbaijan and Romania are crucial countries in this respect.

E.3.2 The Balassa–Samuelson Effect, Unemployment and Exports The catching-up process of poor countries will be accompanied by relatively high growth rates which in turn will raise the relative price of nontradable (N) goods. The relative price of nontradables—including rents—will increase in the course of rising real per capita income; this is the Balassa–Samuelson (1964) effect which we assume to work in transition countries. The price index is P = (PN )b (PT )(1−b) . If we assume a fixed exchange rate and an exogenous and constant world market price of tradables the domestic price of tradables is exogenous—the price level is determined by the Balassa–Samuelson effect and the rise of the nontradables price. The assumption of a constant exchange rate might be inadequate in resource abundant countries, which in a regime of flexible exchange rates will face considerable appreciation pressure in periods of a rise of the world market price of natural resources. Rather, one would expect long-term appreciation—bringing about a rise of the nontradables price in the context of stable nontradables prices and a fall of the domestic price of tradables (due to strong appreciation)—in combination with high volatility of the exchange rate. Now let us take a look at the labor market for unskilled workers. A first issue concerns the size of the true unemployment rate; if state-owned firms have a policy of not laying off excessive workers such firms stand for hidden unemployment. Other distortions also could be important: In poor countries government and state-owned firms, respectively, tend to distort international trade by buying—often for pure prestige reasons—the latest technology in OECD countries while a private company often would have preferred instead to buy older vintages of machinery and equipment because this is cheaper and represents a higher labor intensity (with labor abundance it makes no economic sense to buy the latest technology which is developed in capital intensive countries) than ultra-modern equipment. From this perspective one should not be surprised if empirical analysis of international specialization would not exactly find Hecker–Ohlin dynamics in poor countries. Tradables and Nontradables Next we turn to the role of tradable goods versus nontradable goods. Assuming that consuming nontrables is a basic necessity for survival—think for instance of

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191

housing—one may argue that the reservation wage (the beginning of the labor-supply curve) is determined by the absolute price of nontradables. Hence the Balassa– Samuelson effect will shift up the labor-supply curve over time. At the same time we may assume that there is labor saving technological progress in both the tradables and the nontradables sector. We have sectoral neoclassical production functions for T (sector 2) and N (sector 1) with the inputs unskilled labor L, capital K and labor augmenting technological progress A; in addition we assume that skilled labor H is employed in the T-sector (an alternative would be to assume that only skilled labor is employed in the T-sector, then full employment in the presence of any excess supply of L in the nontradables sector can be only eliminated through retraining efforts and skill-upgrading which is costly) Ts = T(LT , H, KT , AT )

(36)

Ns = N(LN , K N , AN )

(37)

where AN is assumed to be governed by positive spillover effects from AT because the tradables sector typically is the more dynamic sector and indeed often has technology spillover effects. Let LNs denote the short-term labor supply of unskilled labor in the N-sector which is supposed to depend positively on the sectoral nominal wage rate WN and negatively on the price level and the nontradables price PN . We will consider a rise in the price of nontradables which implies a leftward shift of the labor-supply curve in WN , LN space. Assume a constant capital stock KN in the nontradables sector, then the—exogenous or endogenous (for instance determined by the level of international trade relative to output in the tradables sector)—spillover effect from technological progress in the T-sector: labor-saving progress in the T-sector, AT , is assumed to have a positive spillover to AN , that is to trigger labor-saving progress in the N-sector, and this rise of AT implies a leftward shift of the labor-demand curve in the N-sector. In the subsequent diagram we assume this leftward shift to dominate the rightward shift associated with a rise of the nontradables price. The effect is a reduction in employment in the N-sector and to the extent that in the short run labor is immobile across sectors (or regions in the case that N and T are located in different regions), we will have quasi-unemployment, namely the differN ence between initial employment LN 0 and L1 . Strictly speaking we have voluntary unemployment but those losing their job will certainly register as unemployed although they do not want to work at the going wage rate in the official economy. They might, however, be interested in working in the unofficial economy provided that the official economy is subject to considerable burdens in terms of income taxes and social security contributions. If there is full labor mobility across sectors one might argue that unemployed workers from the N-sector could find a job in the T-sector. However, this argument is not very convincing if physical capital and human capital are strongly complementary—hence the expansion of the tradables sector is accompanied with only a modest increase in the demand for unskilled labor. The result could be that there is an economic growth and poverty at the same time, and indeed a high share of the population may suffer from malnutrition. The rise of

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the relative price of nontradables will not only be a problem for unemployed people but also for pensioners who cannot expect to automatically get annual increases of benefits in line with inflation. As regards medium term labor dynamics, labor is assumed to be mobile across sectors, and in the long run a certain fraction of unskilled workers can be transformed through training and education into skilled workers. Retraining efforts require investment in human capital, however, it is unclear whether there are financial resources available for this. If there are low mobility costs and excess unskilled labor from the N-sector can easily move toward the T-sector, unskilled labor unemployment should decline over time. There is, however, a problem if production in the T-sector is using skilled labor intensively and if government is unable or unwilling to subsidize training and human capital upgrading adequately. Moreover, if there are barriers to mobility, for example, excess demand in regional housing markets or administrative barriers, this will make unemployment of unskilled labor a sustained problem. Moreover, to the extent that structural change, stimulated by economic opening up and FDI inflows, favors expansion of sectors with a relatively high demand for skilled labor, the excess unskilled labor from the N-sector will find it difficult to get a new job. The real adjustment dynamics in poor countries opening up in a world with trade and FDI flows indeed does not often show a general expansion of labor intensive production which would absorb unskilled labor. Rather we see some expansion and positive RCA in labor-intensive sectors, while sectors with high FDI inflows are often sectors which are technology-intensive or skill-intensive. In a nutshell, these problems are found in many transition countries and certainly also in many Newly Industrializing Countries and in developing countries.

L1Ns (P1N,WN) N

W

L0NS (P0N,WN)

E1

N

W1

E0

N

W0

L0Nd (P0N,K0N,A0N,WN)

Fig. 40 Balassa–Samuelson Effect, technological progress and quasi unemployment

0

L1N

L0N

L1Nd (P1N,K0N,A1N,WN)

LN

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193

E.3.3 Wage Bargaining as Inherent Source of Unemployment? The reasons for long-term high unemployment in transition countries are not well understood, and it is unclear how economic and institutional developments in the course of catching-up will affect employment and unemployment, respectively. Keynesian models suggest that a lack of effective demand is a major reason for high unemployment as neoclassical models emphasize a lack of investment and problems in labor markets. The following analysis emphasizes problems of wage bargaining and argues that it might be rather difficult to implement a policy framework which gives incentives to trade unions to target full employment. An important point of departure is that trade unions represent both employed and unemployed workers where for an individual trade union organization (Oi in sector i) an unemployed member might be more important in terms of membership fees than a member with a job who will change with a certain probability from sector i to sector j and thus leave the initial trade union organization Oi and join Oj instead. It is clear that unemployed members pay a lower membership fee to the trade union since membership fees typically are proportionate to income. It is often argued that trade unions have a tendency—in particular in large countries—to lobby for excessively high wage rates. If wage bargaining leads to a wage rate w1 above the market-clearing wage rate wE , we have a situation in which workers obtain wages w(1−τ)L—with the tax rate τ partly or fully determined by the costs of unemployment and unemployment benefits paid; in addition unemployed workers will obtain unemployment benefits which are proportionate to their former income (see the shaded area in the following graph). As regards unemployed workers, an alternative assumption considered subsequently is to assume for simplicity that unemployment benefits are proportionate to the wage rate fixed in the bargaining process, and indeed this simplifying assumption will not change the basic results as long as labor supply is inelastic. While we will not consider an explicit model with tradables and nontradables, this assumption can be defended on the grounds that with wages fixed above the market-clearing rate the (overall wage) income is higher than under market-clearing which in turn leads to higher nontradables prices, for example, housing prices and rents, than under market-clearing so that government and parliament will have a natural incentive to consider a rule under which unemployment benefits are implicitly proportionate to the going wage rate. The incentive for trade unions to strive in wage bargaining for a wage rate above the equilibrium wage rate will increase over time if technological upgrading and specialization makes labor demand less elastic. The graphical analysis in panel a) shows that in the case of labor-demand curve Ld0 switching from a market-clearing wage rate to a higher real wage rate w1 has two effects: It reduces labor income due to the fall in employment, namely by the area GE0 L0 L1 , but labor income will be raised in line with the rise of the wage rate (area FGwE0 w1 ). The net effect of the fall in employment and the rise in the real wage rate is ambiguous, however, if the labor demand becomes more elastic the income-enhancing effect from the rise in the real wage will become more important (the theory of efficiency-wage bargaining

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suggests that firms also may have a tendency to support strong wage pressure—we will, however, not consider these effects here).

Ls0 F′

w2

Ls0

Ld0

H

w1 +

wE

F

+ F E0

0

G -

J

w1

E0

wE0

Ld0

-

a

0

L1

L0

L

b

0

L1

L0

L

Fig. 41 Wage rate fixing above the market-clearing rate

Economic caching-up of the transition countries is associated with increasing specialization of firms—partly reflecting the very impact of opening up and international competition—the demand for labor becomes less elastic and hence the risk is rising that wage bargaining will lead to excessive wage rates and unemployment. Part of the problem is, of course, related to the degree of wage centralization and the strength of trade unions and employer organizations. The problem considered might effectively be rather negligible in small open economies where fixing wage rates above marginal labor productivity will lead to large visible losses in world market shares which renders part of the capital stock obsolete and thus shifts the labor-demand curve to the left: Labor income and national income will reduce in parallel. However, in a large economy the trade-GDP ratio is much below that in small open economies which implies—along with a home bias of consumers with respect to tradables goods—that a period of excessive wage fixing will not be followed by as quick a fall of overall market shares of firms in the tradables sector as in a small economy. Since incentives in a large economy to fix the wage rate at the equilibrium level are weaker than in a small economy the risk of neoclassical unemployment is rather strong in large transition economies. This holds except for large countries in which wage bargaining is rather decentralized and in which trade unions are relatively weak (see for instance the US). A priori it is unclear, in transition countries, whether the influence of trade unions will rise over time and how their behavior will develop. The Model Taking a closer look at a simple model of wage bargaining can shed some light on the issues raised. In the following analysis we assume that firms are profit-maximizing

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195

and the economy is characterized by a Cobb–Douglas production function Y = Kß L1−ß , where Y is output and capital K and labor L, respectively. Labor demand L is derived from profit-maximization of the firm. Those unemployed (L which is equal to labor supply minus labor demand) get unemployment benefits which are proportionate to the average gross real wage paid (w); unemployment benefits are assumed to be w(1 − z)[L0 − L] where L0 is the exogenous labor supply and 0 < z < 1. Unemployment benefits are financed by taxes on labor income where the tax rate is τ. We will assume that the tax rate depends on w—alternatively wL might be considered—where the partial derivative is positive. τ = τ(w).

(38)

With a Cobb–Douglas production function profit-maximization leads to labor demand L given by L = [(1 − ß)/w]ß K.

(39)

The elasticity of labor demand with respect to the real wage rate is –ß which in absolute terms is below unity. Pure gross wage income is wL = [1 − ß)]ß Kw1−ß so that the elasticity of pure labor income—income earned in the market—is below unity. Trade unions are assumed to aim at maximizing the sum Z of net wage income w(1 − τ)L and the quasi-income of unemployed which is defined as w(1 − z)(L0 − L); however, as trade unions are averse to unemployment we will use a slightly modified expression, namely αw(1 − z)(L0 − L). The parameter α indicates how strongly the trade union weighs the unemployment benefits and unemployment. If this parameter were zero or the effective replacement ratio (1 − z) = z zero, the trade union would disregard the income accruing to unemployed workers. Trade unions are thus assumed to maximize (see also the appendix) Z = w[1 − τ(w)]L + αw(1 − z)(L0 − L).

(40)

The solution for maximizing Z is shown in the appendix. This solution has to be compared to the full employment wage rate so that one can draw conclusions with respect to an adequate replacement parameter z = (1 − z)—the parameter has to be fixed by the political system—which would lead to full employment. To the extent that the full-employment enhancing z is very low and imply an income of unemployed below a critical minimum, government may want to consider giving unemployed workers a fixed per capita unemployment benefit—regardless of the previous income of those who lost their job. There are also other ways of providing an incentive compatible labor market regime: For example, those regions and sectors which exhibit unemployment rates below average would have lower contribution rates to the unemployment insurance system than regions and sectors with unemployment rates—or job loss rates—above the national average; or some other benchmark figure.

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Unemployment and Current Account Position Economic catching-up is associated with growing exports and imports, where poor countries typically record net imports for an extended period—later a current account surplus emerges as firms in the tradable sector become more competitive. However, we will argue that macroeconomic developments play a role for the current account, too. We assume that there is a move from full-employment to a situation with a high unemployment rate. How does this affect the current account? An answer to this question should help us to understand changes in current account positions. In particular we will see in a simple model—with all goods assumed to be tradable—that a high current account surplus is not always an indicator of high competitiveness of countries. The basic point can be shown in four equations: Assume that consumption C and Investment I are proportionate to real income Y and are negatively affected by the number of unemployed L (the unemployment rate u is defined as the ratio of unemployed L to those employed L). Furthermore real government expenditures G are written as G = γY + n L

(38a)

G/L = γ[Y/L] + n u

(38b)

Hence

where n is the replacement ratio paid by the unemployment insurance system to the unemployed. Hence we have two behavioral equations for real consumption C and real investment I plus the equilibrium condition for the goods market where X denotes net exports of goods and services, Ypot is the production potential, while actual output supplied is assumed to be (1 − ωu)Ypot which implies that with a positive unemployment rate u (u is defined as unemployed L over employed L) there will also be underutilization of capital and labor in firms—this is quite a realistic assumption. Our approach—with parameter ω > 0 and ωu < 1—implies that output supply will be equal to the production potential once u converges toward zero. Moreover, the proposed specification allows the building of models that represent medium term approaches for a situation with unemployment and looking in a consistent manner at long-term growth. The term (1 − ωu) affects the level of output but not growth as for example, the fall of the number of unemployed must be equal to the rise in the number of new jobs (du is zero!). Our simple consumption function and the investment function are as follows: C = cY − fL ; I = b Y − a L ;

f>0 a  > 0.

(38c) (38d)

Note that one might introduce the assumption that a = a(r, q) so that the investment function to some extent becomes more similar to the traditional investment function

E.3 Growth, Resource Dynamics, Balassa–Samuelson Effects and Unemployment

197

in Mundell–Fleming models; and to take into account the impact of FDI inflows along the lines suggested by (FROOT/STEIN 1991). Moreover, in an open economy with FDI inflows and outflows it would be adequate to assume that investment depends on the ratio of the marginal product of capital at home to that abroad which implies— relying on the case of a Cobb–Douglas production function which has proportionality of marginal product and average product of input factors—that I = I[Y/K]/[Y*/K*] so that I = I(q, Y, Y*. . . ): This would imply a net export function X(q, Y, Y*) with familiar partial derivatives! In Addition to the goods market one might, following (ARTUS 1989, p. 45), consider the money market equilibrium and assume a money demand function where the demand for real money balances m depends on output, the interest rate and the unemployment rate; the partial derivative for the unemployment rate is positive since higher unemployment raises the demand for liquidity: higher u means higher uncertainty. Thus a modified Mundell–Fleming model in r–u-space could be drawn where a fall in u implies a rise of Y. The approach proposed also easily lends itself to combining a goods market quasi-equilibrium condition with Phillips-curve analysis; moreover, the capacity effect of investment could be incorporated as well, however, these possible extensions are not pursued here. We state our basic idea for output supplied as follows: Ys = (1 − ωu)Ypot .

(38e)

Equation (40) states that output supplied is proportionate to the production potential but also is negatively affected by the unemployment rate u; if there is a positive unemployment rate firms will realize some labor hoarding for various reasons so that output is less than the number of employed people normally would suggest. Potential output is defined as follows: Ypot = K ß L1−ß .

(38f)

The quasi-equilibrium condition—output is not at the full employment level—for the goods market can be written as follows: (1 − ωu)Ypot = (b + c + γ)Y − (f + a − n )L + X .

(38g)

Dividing Eq. (38g) by L and taking into account the production function—and denoting K/L as k—we get for net exports per worker X /L = [1 − ωu − c − b − γ]k ß + (a + f − n )u.

(38h)

Hence net exports per capita are—for a given capital intensity—a positive function of the unemployment rate if (a + f − n ) > ωkß . Therefore a rise of net exports per worker thus must not simply be interpreted as a rise of competitiveness. It simply may reflect a rise of the unemployment rate and the associated fall in domestic absorption—corrected for supply effects related to changes in the unemployment rate. This case of a positive impact of the unemployment rate on net exports per worker is shown in the subsequent graph.

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Innovations in Macroeconomics

Fig. 42 Net exports and unemployment rate

X′/L

XU0

U

E.4 Product Innovation and Macroeconomic Developments: Schumpeter and the Mundell–Fleming Model E.4.1 The Role of Risk and Innovation An important aspect of innovation dynamics concerns risk. As a simple way to take into account risk and innovation one may proceed as follows. We consider a consumption function C where consumption depends on income on the one hand and on wealth A on the other hand. The expected rate of return on innovation is μ, the variance is σ. There are only two assets considered, namely real capital K and real money balances m (m = M/P). We chose deliberately a specification where K/AL and [M/P]/AL (denoted as m ) both enter the consumption function as a variable to the power ß since otherwise the mathematical calculation would become very intricate. All exponents are assumed to be positive. Hence a higher variance of innovation (and investment) yield imply a higher consumption since saving obviously brings relatively uncertain rewards; a higher expected yield on innovation reduces consumption and indeed stimulates savings as the reward for those saving is increased. C/[AL] = cy + c [σ/μ]ε [k  + m ]. ß

ß

(60)

As regards the term [kß + mß ] this formulation is rather unusual at first sight; an ideal specification would indeed use [kß + mß ]2 but for ease of exposition we will drop the square. Our basic reflection in this context will focus on a special case where A = A0 = 4 and L = L0 = 1. Assume that ß = 1/2 and the production function contains real money balances M/P as a positive external spillover effect, where real balances factor in as (M/P)ß ; hence we have output as Y = Kß (M/P)ß Lß0 . One may then indeed state a simple consumption function (with c adequately defined) as C/[AL] = cy + c (K0.5 + m0.5 )2 = cy + c [K + 2K 0.5 m0.5 + m] = c y + c [K + m].

(61)

We will use the Cobb–Douglas output function to replace kß by y and a simple CAGAN-type real money demand equation to replace m , namely (with the Euler

E.4 Product Innovation and Macroeconomic Developments

199

number written as e and the semielasticity of the nominal yield on investment denoted as ψ and the expected inflation rate denoted as π ): m  = e d

ψ [μ+π ]

y.

(62)

Let us assume that both σ and μ are positive functions of the product innovation variable v. The corresponding savings function is therefore as follows: S/[AL] = {1 − c − c [σ(v)/μ(v)]ε [1 + e

ψ [μ(v)+π ]

]}y .

(63)

We assume that the partial derivative of the expected rate of return with respect to v is higher than that for the reaction of the variance with respect to changes in v. This assumption is sufficient to bring about a rise of savings if v is increased. If we insert this equation in the familiar neoclassical growth model we will get the following steady state result for k # (note we we use v/v* instead of a *): 

k #ση /(1−σß) = ({1 − c − c [σ(v)/μ(v)]ε [1 + e 

ψ [μ(v)+π ]

· (b /[v/v*])η σ /[n + δ + a]1/(1−σß)

]} + 1) (64)

This result includes both process innovations and product innovations and represents a much richer approach than traditional models. Domestic product innovations clearly raise the optimum capital intensity and output per efficiency unit of labor.

E.4.2 Endogenous Product Innovations in Countries with Similar Development Levels Which research perspective is useful for countries which are of similar sophistication in product innovations? Let us consider two open economies of a similar technological level which are exporting goods and importing goods. Households consume domestic and foreign goods, including new products launched at home and abroad; in addition there is a kind of consumption technology which allows households to develop novel consumption patterns which depend on the interaction of v and v* in the market. The stock of product innovations abroad is v*, in the home country it is v. We assume that there are network effects (in commercial novelties) N in country I which can be described as follows: N = (v2 + v*2 + 2vv* )α .

(65)

The rights hand side term says that the stock of novelties available depends on domestic product innovations (v), foreign product innovations (v*), and a third term which represents the interaction of both terms. We can rewrite the above quation as N = (v + v*)2α .

(66)

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Abroad we may assume a similar network effect N * = (v2 + v*2 + 2vv*)α *. The next question to be raised is how v and v*, respectively, can be explained. Research expenditures H is obviously one relevant variable. How can we define true quality-adjusted output? One useful definition would be  

Y = YN α .

(67)

If the term a is unity (and abroad a * is unity) we can calculate relative qualityadjusted output as Y /Y * = [Y/Y*]N /N *.

(68)

There are indeed considerable differences across countries when it comes to the willingness of households to use new products as was shown.

E.5 Conclusions and Policy Implications We have analyzed some key issues of transition countries from a theoretical point. From an analytical perspective it is clear that the familiar HOSframework has to be refined if the challenges of opening up and transition are to be understood. Transformation is not a quick process where a country can jump from the distortions of the old system toward a new full employment market economy. First, it is important to take into account that transition countries differ in important aspects, for example, the degree of natural resource abundance. Second, there has been high unemployment in many transition countries over decades, particularly high amongst unskilled workers. The analysis presented argues that economic and technological catching-up—accompanied by increasing specialization—will make labor demand less inelastic. This in turn reinforces the problem that wage negotiations may lead to a wage rate above the market-clearing rate where we suggest that government should fix unemployment benefits in a way which effectively leads to full employment. Unemployment in a small open economy (by assumption it can export the excess supply of the tradables sector) in turn is likely to raise net exports so that an improvement in the current account is not necessarily related to an improvement of technological competitiveness. Misinterpretation of the net export position by government and international organizations can have very serious consequences. As regards medium term modeling of output development in transition countries we focus on the role of product innovations within a Schumpeter–Mundell–Fleming model (product innovations effectively means—from the perspective of leading OECD innovators—diffusion). We argue that the law of one price will not hold in such a model and show that product innovations raise output and bring about a real appreciation. To the extent that government innovation policy (with a focus on promotion product innovations and diffusion, respectively) can stimulate product innovations there is an important policy variable beyond traditional fiscal policy and monetary policy. It would be interesting to have empirical analysis for various

Appendix E.1: Maximization of Total Quasi-Income of Workers through Trade Unions

201

countries which shows how important the share of product innovations in overall (net) exports is and how strongly government R&D promotion affects the product innovation rate. As regards policy conclusions government promotion of product innovation seems to be rather important in transition countries and NICs. Finally, we take a look at real exchange rate dynamics in a setup in which the current account position and the relative rate of product innovation is affecting the real exchange rate. The approach presented argues that catching-up means a reduction of the price elasticity of net exports and a fall of the foreign relative innovation rate. Both effects contribute to a real appreciation of the currency. The contribution has presented analytical building blocs relevant for transition countries. It is beyond the scope of our analysis to integrate those blocs into one coherent model. However, we have raised several crucial issues relevant for economic catching-up and transition countries. There certainly is need for further research which should help to reconcile real world dynamics with standard economic wisdom.

Appendix E.1: Maximization of Total Quasi-Income of Workers through Trade Unions (labor supply L0 is exogenous, parameter 0 ≤ α ≤ 1) Z = w[1 − τ(w)]L + w(1 − z)α[L0 − L]

mit

z = 1 − z

= wL − wτ(w)L + wz αL0 − z αL = (1 − ß) w ß

1−ß



(69) (70)



K(1 − τ(w) − z α) + wz αL0

(71)

dZ = [(1 − ß)(1 − ß)ß w−ß K(1 − τ(w) − z α)] − τw (1 − ß)ß w1−ß K − z αL0 dw (72) = [(1 − ß)(1 − ß)ß w−ß K(1 − τ(w) − z α)] − τ(w)ετ,w (1 − ß)ß w−ß − z αL0 (73) = K[(1 − ß)1+ß (1 − τ(w) − z α) − τ(w)ετ,w (1 − ß)ß ]/z αL = wß wß = K(1 − ß)ß [(1 − ß)(1 − τ(w) − z α) − τ(w)ετ,w ]/z αL0

(74) (75)

The optimum w# is obviously a negative function of ß. (Note that ßln = lnK + ß(–ß)[–ß – τ(w) – z – α) – t(w)ετ,w ) − ln (z αL0 ). The larger ß (the lower 1 – ß), the lower the optimum wage set by trade unions will be. Note, the term [(1 – ß)(1 – τ(w) – z – α – t(w)ετ,w ]) is assumed to be positive—otherwise the real wage rate would be negative. The wage rate set by trade unions depends negatively on the tax rate, labor supply, the parameter α and z (w# depends positively on z!): A rise of α which indicates that trade unions weigh the unemployment element in the target function relatively higher implies a lower wage rate; and indeed higher employment. Government can induce trade unions to attach a higher weight to unemployment if government assigns funds to trade unions, for instance, earmarked for training programs, that should be a negative function of the unemployment rate.

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Compare (75) to profit-maximization and full employment, respectively, namely the equation L0 = [(1 − ß)/w]ß K;

or

w = (1 − ß)(K/L0 )1/ß .

(77)

Comparing (75) and (77) Eq. (75) will coincide with (77) only if [(1 − ß)(1 − τ(w) − z α) − τετ,w ]/z α = 1

(78)

[(1 − ß)(1 − τ(w)) − τ(w)ετ,w ]/z α − 1 + ß = 1

(79)

[(1 − ß)(1 − τ(w)) − τ(w)ετ,w ]/z α = 2 − ß.

(80)

Taking logarithms we have—assuming ß and τ(w)(1 + τ(w)ετ,w ) and z to be close to zero—we have the following approximation: −ß(τ(w) − 1) − τ(w)(1 + τ(w)ετ,w ) = −z + lnα + ln(2 − ß).

(81)

Hence government policy should set z according to z = τ(w)(1 + τ(w)ετ,w ) + lnα + ß(τ(w) − 1) + ln(2 − ß).

(82)

The larger α, the larger should government choose z in order to obtain full employment. So if trade unions attach a high weight to unemployment benefits, government should counterbalance this by reducing unemployment benefits. Unemployment benefits should be the smaller (hence z would rise) the larger the tax rate and the elasticity ετ,w . If z would be so small that the survival of unemployed would be difficult one may consider a system which basically gives a fixed per capita payment to all the unemployed. Finally, note that maximization of Z requires conditions to be considered that guarantee that the second derivative of Z with respect to w is negative. However, we rather will focus on a refined approach in the next section and then look at both the necessary and sufficient condition for a maximum.

Rational Trade Unions Next note that the government budget constraint is as in Eq. (69 ), and we assume that trade unions take this also into account—this is most likely in small open economies in which there are transparent macroeconomic feedback effects on wage setting. The budget constraint is τ(w)wL = w[1 − z][L0 − L]

(69 )

where on the left-hand side we have tax payments (read: contributions to the unemployment insurance system), on the right-hand side we have expenditures on the unemployed. We rewrite the above equation {τ(w) + [1 − z]}L = (1 − z)L0 .

(69.1 )

Appendix E.1: Maximization of Total Quasi-Income of Workers through Trade Unions

203

Denote 1 − z = z , divide the equation by L and separate τ(w) τ(w) = z (L0 /L − 1).

(69.2 )

Trade unions maximize the following Eq. (83) while taking into account (69) and profit-maximizing labor demand—see (70 ) L = [(1 − β)/w]β K

(70 )

Trade unions now maximize the equation while taking into account (69 ) and (70 ) Z = w[1 − τ(w)]L + wz α[L0 − L]; we replace the tax rate by (69.2 )

(83)

Z = w[1 − z (L0 /L − 1)]L + wz α(L0 − L)

(83 )

= w[L − z (L0 − L)] + wz α(L0 − L)

(83 )

Z = wL[1 + (1 − α)z ] − (1 − α)wz L0 ; we next insert L from (70 ) Z = (1 − ß)β K[1 + (1 − α)z ]w1−β − (1 − α)z L0 w

(84) (85)

Next we take a closer look at dZ/dw = 0 to obtain the optimum w# dZ = (1 − ß)1+β K[1 + (1 − α)z ]w−β − (1 − α)z L0 = 0, dw 1  (1 − ß)1+ß K[1 − (1 − α)z ] ß w# = (1 − α)z L0

(86)

(87)

The larger ß is, the higher will be the optimum w#. The smaller a (that is the higher 1 − a), the smaller w# which is rather paradox: The less the trade union cares about income accruing to the unemployed the less it will push for a high real wage rate. The larger z —that is the smaller z—the lower the desired wage rate w#. This also is rather paradox since it suggests that governments with a generous unemployment system (that is wage replacement regime) will face less the risk of excessive wage pressure. There is, of course, a caveat here since we do have inelastic labor supply and thus are not analyzing how the unemployment insurance system will affect effective labor supply. Compare (87) to profit-maximization and full employment, respectively, namely the equation L0 = [(1 − ß)/w]ß K

or

w = (1 − ß)(K/L0 )1/ß .

(88)

Hence (87) is consistent with this only if {(1 − ß)1+ß [1 − (1 − α)z ]/[(1 − α)z ] = 1; w# will exceed the full employment wage rate if (1 − ß)1+ß [1 − (1 − α)z ]/[(1 − α)z ] > 1.

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From (87) in combination with (70 ) we can derive the z # which government should chose. If z # is politically not feasible there will be no full employment. (1 − ß)1+ß [1 − (1 − α)z ] = [1 − α]z .

(87.1)

We now assume that ß and −(1 − α)z and α are rather small so that we can use the approximations ln (1 + x) ≈ x and ln(z ) ≈ z − 1. (1 + ß)(−ß) − (1 − α)z = −α + z − 1

(87.2)

α + 1 + (1 + ß)ß = z [2 − α].

(87.3)

Hence we obtain the full employment preserving z# as z# = [α + 1 + (1 + ß)ß]/[2 − α].

(87.4)

There is only a certain range of parameters under which z falls in the interval [0, 1]. If ß is rising and hence (1 − ß) is falling z should fall. However, it is unclear whether government will be able to impose a corresponding z#. The second order condition for a maximum of Z is negative: d2 Z = −ß(1 − ß)1+ß K[1 + (1 − α)z ]w−(1+ß) < 0 dw2

(88)

Appendix E.2: Mathematical Appendix dY = c (1 − τ)dY + c d(M/P) + c dv − hdr + c mr dr + h dv + h de + xde −

x Y* dY + x dv Y2

  x Y*  = 1 − c (1 − τ) + 2 dY+(h − c mr )dr − (h + x)de Y

(89) (90)

= c d(M/P) + (c + h + x )dv d(M/P) = mY dY + mr dr + mv dv

(91a)

mY dY + mr dr = d(M/P) − mv dv

(91b)

Qϕ dr + Qv dv + Qq* de + xde +

x Y* dY + x dv = 0 Y2

x Y* dY + Qϕ dr + (Qq* + x)de = −(Qv + x )dv Y2

(92a) (92b)

Appendix E.2: Mathematical Appendix

205

The equation system in matrix notation is ⎛

k1

⎜ ⎜ mY ⎜ ⎜  ⎝ x Y* Y2

h − c mr mr Qϕ

⎞ −(h + x) ⎛ ⎞ ⎛  ⎟ dY c ⎟ 0 ⎟ ⎝ dr ⎠ = ⎝ 1 ⎟ ⎠ de 0 Qq* + x

k1 = 1 − c (1 − τ) +

⎞  c + h + x  ⎠ d(M/P) −mv dv −(Qv + x )

x Y* Y2

Define k1 = 1 − c (1 − τ) +

(93)

x Y* , then we have the system determinant Y2

|A| = {k1 mr (Qq* + x) − (h − c mr )mY (Qq* + x)}    x Y*  + −(h + x) mY Qϕ − mr 2 Y If {. . . } exceeds [. . . ] : |A| < 0; if Qϕ and |mr | are sufficiently small, then |A| < 0. ⎛

h − c m r

k1

c + h + x

⎞

⎟ ⎜ ⎟ ⎜ m de 1 m −m Y r v ⎟ ⎜ (94) = det ⎜ ⎟ dv det(A) ⎠ ⎝ x Y* Qϕ −(Qv + x ) Y2  1 k1 [mr (−Qv − x ) + mv Qϕ ] − (h − c mr )mY = (95) |A|     x Y* x Y* <0 · −mY (Qv + x ) + 2 mv + b mY Qϕ − mr 2 Y Y Whereas b = c + h + x . For Y* > critical Y0 * (home country is relatively small), second term in squared brackets then is positive. ⎛

h − c m r

−(h + x)

−mv

mr

0

−(Qv + x )

Qϕ

Qq* + x

⎜ dY 1 ⎜ = det ⎜ ⎝ dv det(A)

c + h + x

=

⎞ ⎟ ⎟ ⎟ ⎠

1 ((c + h + x )mr (Qq* + x) + hmv (Qq* + x) det(A) + (h + x)(mv Qϕ − mr (Qv + x )))

(96)

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Innovations in Macroeconomics

    dY > 0 is that mr Qv − mv Qϕ  > mr x  . dv ⎛ ⎞ c + h + x −(h + x) k1 ⎜ my ⎟ dr 1 −mv 0 ⎟ = det ⎜  y* ⎝ ⎠ x dv det(A)  −Qv − x Qq* + x 2 y  = −k1 mv (Qq* + x) − bmY (Qq* + x) + (h + x)

Sufficient condition for





· mY (Qv + x ) − mv



x Y* x + 2 Y 

 (97)

Appendix E.3: Reflections on EU Eastern Enlargement Eight transition countries will join the EU in 2004: On May 1, 2004 there will be an EU Eastern enlargement, and this will be the largest EU expansion to date. The population of the EU will increase by 1/5, national income of the EU by some 5% (of EU-15 GDP) at face value and by about 10% if purchasing power standards, which take into account the fact that the prices of nontradables are still relatively lower in accession countries compared to EU-15, are used. The accession countries have benefited from pre-accession EU transfers and also from asymmetric trade liberalization in Europe. The Commission has estimated that the growth rates of the accession countries will be in the range of 4.5% to 6% in the period from 2005 to 2009, which is clearly above the estimated 3% growth projected in a simulation without accession (SOLBES 2004). EU accession countries will benefit from adopting the EU legal system—the acquis communautaire—which makes investment less risky but some business ventures also more complex to organize. EU accession countries of Eastern Europe are former socialist countries which adopted a very broad range of new institutions and policy patterns in the transformation decade of the 1990s when they also opened up to the world economy and reoriented trade strongly toward Western Europe. Accession countries will benefit from EU transfers for decades which go particularly to regions with per capita income below 75% of EU average (at purchasing power parity), with the average per capita income level of accession countries of Eastern Europe in 2004 close to 45%. With eastern enlargement, there will be ten new countries in the EU—eight from Eastern Europe—plus Malta and Cyprus, whereby the latter is a Mediterranean island divided between a Greek population in the West and a majority of Turkish people in the East. Cyprus is a difficult political turf, but it also is the home of Russia’s largest expatriate banking community. The 1990s were a period of massive capital flight from Russia and the echo effect particularly found root in the dynamic banking

Appendix E.3: Reflections on EU Eastern Enlargement

207

scene in Cyprus and massive “Cyprian” (read: Russian) foreign direct investment in Russia. EU eastern enlargement also brings major changes for the Community and Russia as the latter will suffer from trade diversion. Russia’s exports of industrial goods—disregarding oil and gas—will decline, in particular due to the protective nature of EU standards. Moreover, the people of the new Russia face exclusion in the sense that almost all European countries are no longer accessible for Russians without a visa. The situation will become worse after Bulgaria and Romania join the Community in 2007. Russia also feels threatened by Nato enlargement which is organized on the side of Western Europe and the US with utter disregard for Russian interests, creating a feeling of alienation in the new Russia. Nato enlargement is also an eastern enlargement, but while Brussels is the center of gravitation of EU eastern enlargement, it is Washington which is steering Nato enlargement. The Bush administration obviously wants to get Nato involved in many new hot spots, including Iraq where some new Nato members from Eastern Europe are already active. Poland, whose president obviously expected to gain in prestige and political clout from following the Bush administration into Iraq, is one example. Foreign adventure to compensate for social tensions at home is not a new motive in politics. The borrowed prestige is in stark contrast to the weak economy in Poland. EU accession countries might, however, be tempted to follow the US in military adventures in more regions, and this brings Europe back to Africa and Asia in a second wave of quasi-colonial activities, this time under the US umbrella. Germany has so far been hesitant to follow the US, but there is little doubt that a future conservative government might close ranks with the US again. The enlarged Community is a new mixture of advanced OECD countries and relatively poor countries which are characterized by wage rates that are roughly 1/9 of that in Germany. Certainly, productivity of firms in Germany is higher than those in EU accession countries, but it is clear that there will be a new international division of labor in EU-25. Labor-intensive production and partly capital intensive production as well will be relocated to accession countries which therefore naturally become important markets for German exports of investment goods. As EU enlargement goes along with heavy investment in upgrading infrastructure in accession countries, both eastern European supplier firms and exporters will find faster and cheaper access to EU-15 markets in the future. From an EU-15 perspective, it holds that import competition from EU accession countries will therefore grow. At the same time, firms in high wage countries such as Germany, France, Austria or Sweden will have to specialize more on goods using technology and human capital intensively. The EU enlargement of 2004 means that the Community population will increase by some 70 million inhabitants, whereby Poland is the largest country with 39 million people. In 2002, per capita income relative to EU-15 was 73.7% for the leading country, Slovenia, followed by 59.8% for the Czech Republic and Hungary with 55.9%. At the bottom level were Poland, Lithuania and Latvia which stood at 39.4%, 39.1% and 35.2%, respectively. Figures for Bulgaria, Romania and Turkey were 24.7, 24.5 and 22.9%, respectively; for 2006 the forecast figures (EUROPEAN COMMISSION 2003c) are 28%, 27.6% and 24.5%, respectively. Except for Slovenia

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and Hungary with inflation rates of 7.5% and 5.3% in 2002, inflation rates were low in accession countries in 2002 and are expected to remain low in 2006 with the relevant range between 0% and 3%. In line with relatively low per capita income, the consumer price level in Eastern European accession countries in 2002 was around ½ of EU-15, except for Slovenia and Poland where the price level stood at 70 and 61, respectively. The unemployment rate was very high in Poland in 2002/03, namely close to 20%; in the Slovak Republic and in Lithuania it reached about 18% and 14%, respectively. At the same time, Poland had the highest participation rate, namely 76%. Current account imbalances are not a major problem for accession countries, except for Estonia and Poland. If Poland’s current account deficit should grow over time, the country might face a major depreciation and a confidence crisis associated with sudden capital outflows and hence rising interest rates. One-third of Poland’s government debt is foreign debt. If Poland should face a major crisis in the future, both Germany and the Euroland will have to find an answer to the question addressing the extent to which a problem of a major neighbouring country is considered a common interest worth solving. If such a problem should emerge, neither the German government nor the ECB is likely to be very forthcoming with financial and political support to stabilize the country; there is no pretext with respect to this. However, as much as the US has always helped its neighbouring country, Mexico, through a financial crisis, there are good reasons why Germany and the EU should not treat Polish problems with a benign neglect attitude. From the perspective of EU-15 countries and Germany, current account deficits in accession countries are rather welcome if they remain manageable for the respective countries; the mirror position of EU-15 countries are net exports of goods and services which stimulate the rise of national output. If EU accession countries’ import growth would mainly reflect higher imports of investment goods, a current account deficit would be only a temporary problem since one may assume that rising production potential will contribute to higher production and exports in the future. The EU will face quickly massive internal problems if serious financial market problems in accession countries should emerge in a period of slow growth in EU15 core countries. Germany together with Italy is the weak core of the EU in the first decade of the twentyfirst century. Both countries are aging rapidly and both countries have serious problems in their political systems for adopting adequate political reforms. What the North–South divide is for Italy is more or less the East– West divide of Germany. Moreover, the fact that Germany’s per capita income (at figures based on purchasing power parity) fell below the EU average in 2003 is shocking news for the largest EU economy. The longer slow growth continues, the more EU partner countries in Western and Eastern Europe will suffer from this.

Appendix E.3: Reflections on EU Eastern Enlargement

209

Table 7 Selected macroeconomic indicators for EU accession countries and Turkey. (Source: European Commission, 2010 Pre-Accession Economic Programme of the Acceding and Other Candidate Countries: Overview and Assessment)

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Table 7 (continued)

Poland is the largest accession country with close to 40 million people. However, the country is weak in economic terms with its unemployment rate reaching 20% in 2004. This is not intended to overshadow the considerable growth rate of 3–4% p.a. in recent years. However, for a poor country which reaches less than 50% of EU-15 per capita income, one should indeed expect high growth rates in the context of economic and technological catching-up. The Polish economy made enormous progress after a bold comprehensive transformation in the early 1990s. Successive governments have been slow to modernize infrastructure, however, where for instance building a highway between Warsaw and Berlin is moving forward at a snail’s pace. On the positive side, one should emphasize that the inflation rate is very low and the trade balance deficit does not present a serious problem. Rather Poland has recorded a surplus vis-à-vis Germany in 2003 for the first time in a decade. At the same time it is true that Poland is facing rising social tensions as its society is divided in young dynamic strata with rising real incomes and a large number of poor—and often—unemployed people. The creation of more firms is of utmost importance for Poland, but indigenous entrepreneurial dynamics are likely to suffer in the context of EU accession as regulations will become more complex and costly. In addition, access to bank loans could become more difficult as Polish banks will have to obey the stricter rules of Basel II principles of prudential supervision. Warsaw is a very dynamic city with many students in private and public universities with many foreign students, including a minority from Arab countries (and it has been stated that for years Palestinian students attended Polish universities, in most cases studying seriously, however in certain cases students came simply to recover from “action” in

Appendix E.3: Reflections on EU Eastern Enlargement

211

the Middle East). On both sides of the German–Polish border, unemployment rates are very high, namely close to 20%. It is not only Poland which is having problems stimulating growth and employment. There are indeed similar problems in eastern Germany where productivity levels in 1991 stood at 1/3 of western Germany, but at 2/3 in 1999. Since then the productivity gap has not closed. There has been some industrial revival in 2003/04 in eastern Germany, but East Germany suffers from a lack of entrepreneurs, a declining population—there is continuing East–West migration within Germany—and insufficient government spending on public investment and promotion of innovation. At the same time, East Germany is spending too much on civil servants, as there is overstaffing in parts of the government bureaucracy. EU accession countries have adopted very low corporate tax rates (e.g., 15% in the Slovak Republic) which in turn forced Austria to reduce its corporate tax rate to 20% in 2003. A major weakness of EU eastern enlargement is that the EU-15 has not imposed a minimum corporate tax rate which would be binding for all accession countries after a transition period. Indeed, it is strange that German taxpayers contribute heavily to the EU budget which in effect means that accession countries— getting EU structural funds of up to 4% of gross domestic product—use German taxes to artificially reduce corporate tax rates. As a consequence, there will be accelerated relocation of industry from EU-15 to accession countries. With corporate tax rates effectively reduced to below 20% in the Community, the implication is that mainly workers of EU-15 countries finance tax reductions for corporations with their tax payments. Worse yet, strange tax competition in the EU leads to a weakening of growth and employment in EU-15 which must not be the ultimate goal of EU enlargement. If the strange tax competition would allow accession countries—representing roughly 1/10 of EU GDP—to raise output growth by one percentage point while the growth rate in EU-15 would be reduced by 1/5 of a percentage point the net effect for the community would clearly be negative. To avoid any misunderstanding: Countries which are not obtaining major EU transfers should be free to have low corporate tax rates, but it is inappropriate for countries obtaining massive transfers to adopt low rates. Germany and other EU countries—including those of Eastern Europe—could benefit from a certain growth acceleration effect associated with the expansion of information and communication technology (WELFENS 2003; VAN ARK/PIATKOWSKI 2004). In Germany, the government has adopted several initiatives including a private public partnership project (D21) which has stimulated reforms. It is noteworthy that the head of the advisory committee, Chancellor Schröder, has participated in all sessions of the committee which is a clear signal the he takes this field quite seriously. At the bottom line, Germany has adopted many new reforms, but only a few of them really meet the challenges ahead—setting adequate priorities has not been a hallmark of government. EU eastern enlargement will bring new pressure to accelerate reforms. However, short-sighted politicians are not very likely to adopt those reforms which are most necessary. Germany is unlikely to record high growth in the coming years unless the government adopts a more professional and consistent set of policy elements.

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If Germany should continue to face rising unemployment and slow growth over many years as well as the prospect of EU membership for Turkey, one should not rule out the possibility of debate about a reunited Germany leaving the enlarged community. One can only warn against illusory policy as supported by EU Commissioner Verheugen, who would support Turkey’s quick accession into the Community. Neither Germany, the EU-25 nor Turkey are in good shape, and international politics have become quite complicated not least of which is due to the problems of terrorism. Responsible policymakers interested in preserving a stable and dynamic Community should first successfully digest EU eastern enlargement before embarking upon new enlargement dreams. The enlargement of the Federal Republic of Germany, that is German unification, has shown everybody how difficult the merger of two very different countries really is. With Turkey the situation is even much more difficult, not least because the Turkish population is growing by about 1 million p.a.; the country will have some 120 million inhabitants by 2050. Germany alone can be expected to attract some 5 million Turkish immigrants in the period 2020–2050 (assuming that Turkey were to become a full EU member by 2020). Mr. Verheugen’s view that full EU membership of Turkey could be combined with restrictions on labor mobility in the EU is illusory since the European Court of Justice has stated in its rulings that restrictions on labor mobility can only be temporary for EU member countries.

Appendix E.4: Fiscal Multiplier in a Hybrid Approach A hybrid approach can be written as follows: Output is a weighted sum of the production potential and aggregate demand. Y = αYpot + (1 − α)Yd .

(98)

To see the implication of a medium term analysis—with α = 1 − u—one may consider the case of closed economy with consumption C = cY, investment I(r) and exogenous government consumption G; and production potential Ypot = Kß L1−ß (K is capital, L is labor, 0 < ß < 1). Hence we can rewrite Eq. (1) as follows: Y = [1 − u]Kß L1−ß + u{cY + I(r) + G}

(98 )

dY/dG = 1/[1 − uc].

(98 )

Only if the unemployment rate approaches unit we get the familiar Keynesian multiplier dY/dG = 1/[1 − c]. For any positive unemployment rate below unity the multiplier for fiscal policy is smaller than the standard textbook result.

Appendix E.5: Reconsidering Aggregate Output in a Two-Sector Approach

213

Appendix E.5: Reconsidering Aggregate Output in a Two-Sector Approach Assume that aggregate demand consists of tradables demand T and nontradables demand N, the relative price between tradables and nontradables is φ. We can thus state, as an equilibrium condition for the goods market (with Ypot denoting potential aggregate output) in a fully employed economy: Ypot = N + ϕT.

(99a)

Instead—and assuming for simplicity φ = 1—we may state [Ypot ]

σ (N,T)



= Nσ (N,T) T1−

σ (N,T)

.

(99b)

The elasticity σ depends on N and T in a way which is not clear here (more on this subsequently). We can thus state σ (N, T)lnYpot = σ (N, T)lnN + [1 − σ (N, T)]lnT.

(99b )

Thus the elasticity of potential output with respect to N-demand is unity and with respect to tradables demand is (1 − σ)/σ. This elasticity should not be confused with the pure output elasticity for the case of a production function (say Ypot = Kß L1−ß where K and L are respectively, capital input and labor input). Why can we state Eq. (99b)? Note simply that for any two variables A and B (A = 0; B = 0) the following equation holds—with a specific exponent α: [A + B]α = Aα Bα .

(99c)

α{ln[A + B] − lnA + lnB} = 2lnB.

(99d)

Taking logarithms results in:

Hence the above Eq. (99d) holds for α = {[ln[A + B]/2lnB] − [lnA/2lnB] + 0.5}−1 .

(99e)

A useful approximation is ln[A + B] − lnA ≈ lnB − n lnA. α = {1 − [[1 − n]lnA/2lnB]}−1 .

(99e )

Moreover, for the special case that A + B are normalized to unity α is even simpler α = {−[lnA/2lnB] + 0.5}−1 .

(99f)

An interesting application of this theorem in mathematics—with many useful applications in Economics—is the familiar goods market equilibrium condition in macroeconomic analysis (C is consumption, I investment, Y real income) Y = C + I.

(99g)

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Without loss of generality we can state instead Yα = Cα + I1−α .

(99h)

lnY = lnC + {[1/[1/α] − 1}lnI.

(99i)

Hence

If we assume a consumption function C = cY we can state: lnY = lnc + lnY − [2−[1 − n][(lnc + lnY)/lnI]lnI.

(99j)

Hence we can easily calculate the elasticity of Y with respect to a change in exogenous investment I. Alternatively one can consider an investment function (with e denoting the Euler  number) I = e−μ r . Basically the equilibrium line for the goods market can be drawn in lnY–r space.

F. Productivity Shocks, Innovations, Stock Market Dynamics and Growth

F.1 Introduction The banking business in the late twentieth century has undergone profound changes. A first aspect is that the speed of adjustment in financial markets has increased in the course of digitization, computer expansion and the internet revolution, at the same time bringing down heavily prices of transactions in financial markets and thus contributing to the internationalization of financial markets and banking. A second key aspect is economic globalization with the result that for many financial products there exists a global market in which only a few large banks compete. A third element is that prudential supervision has started to emphasize risk-based equity requirements—indeed, Basel II rules will bring about broader spreads across different classes of loan risk. A fourth element is the increasing role of investment banking and the role of international mergers & acquisitions which accounted for roughly 3/5 of foreign direct investment (FDI) in the 1990s. This in turn reinforces the role of stock markets on whose dynamics our analysis will focus. Moreover, in the presence of imperfect capital markets there is a renewed interest in the development of the real exchange rate since it will affect FDI: FROOT/STEIN (1991) have emphasized that a real depreciation of the currency of the host country implies that equity capital of foreign bidders—expressed in terms of the currency of the host country—is increased so that a successful leveraged international M&A will become more likely; FDI inflows will increase. Defining the real exchange rate of country I (home country) as q = P/eP∗ or q∗ = eP∗ /P where e is the nominal exchange rate and P the price level (∗ denotes foreign variables), it is clear that both nominal exchange rate dynamics and changes in the sticky price level at home and abroad will affect the real exchange rate. Our analytical focus will be partly on short-term stock market dynamics in open economies which we define as having trade and FDI inflows. We will present a new short term model which models the interaction of money market, stock market and foreign exchange rate. Moreover, a medium term model based on the capital asset pricing model (CAPM) will be presented and finally we will plug the stock market

P. J. J. Welfens, Innovations in Macroeconomics, DOI 10.1007/978-3-642-11909-5_6, © Springer-Verlag Berlin Heidelberg 2011

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into a modified growth model. Indeed, we will emphasize the role of stock markets for short-term and long term dynamics. As regards the potential relevance of research on stock markets—and related wealth effects—it is clear that the impact of changes in the real wealth of stocks is rather small in many countries. For example, as regards the impact of changes in stock market prices empirical analysis points to only a minor impact on consumption in cross-country analysis. However, observing individual countries could reveal a different story; a priori one would expect a relatively large impact on consumption and savings, if the share of stocks in overall wealth is relatively large and if a sizable share of the population owns stocks: This is for instance the case in the US, the UK and Sweden. One may, however, also raise the issue as to why theoretical and empirical analysis finds investment dependent on stock market dynamics—in a simple equilibrium growth model this implies that savings must also be affected by the stock market. For example, a simple approach is to assume that savings depends on the real interest rate r and the ratio of (exogenous) target wealth AT to actual wealth A which for simplicity one may consider as to be comprised of real money balances M/P and the real value of stocks P K/P where P is the stock market price level, K is the capital stock—equal to the number of stocks—and P is the output price level. A sustained increase in P /P should translate into a fall of savings as the gap between the wealth target and actual wealth has fallen. Since stock markets are very volatile, it is clear that people will discount stock market prices strongly. Another caveat to the relevance of the stock market is that when considering wealth, real estate is more important than stock market dynamics for macroeconomic development. In many OECD countries, real estate is somewhat higher than the value of stock market capitalization. While it is true that real estate is an important variable, in particular in countries with a high share of owner-occupied housing (e.g., US, UK, France, Spain), one should not overlook the fact that stock market capitalization relative to GDP has increased considerably in the 1990s. Taking a look at the Great Depression also reveals a strong impact of stock markets, although one should emphasize that the respective dynamics could be covered adequately in a disequilibrium model. Stock markets have strongly shaped economic growth in the 1990s as real stock prices and real GDP growth increased in most OECD countries and emerging markets; and when stock market prices collapsed in 2001/2002 there was also a considerable fall in output growth. As regards international links among stock market developments, empirical analysis suggests that the US stock market dominates EU stock market developments. From this perspective any overshooting or bubble phenomenon on the US stock market translates into similar movements in other OECD countries. However, it is not fully understood why we observe such international correlations. Within a simple medium-term model, we will suggest a simple transmission channel which is linked to product innovations and network effects. The model we present is for an innovative small open economy with full capital mobility in the sense that FDI inflows are allowed. A special aim of the analysis presented concerns economic catching up on the one hand, on the other hand we want to better understand the links between stock market and exchange rate dynamics with real economic development in leading

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217

OECD countries and follower countries. Our analysis presents a model for combining stock market dynamics, the real exchange and capital accumulation dynamics plus product innovations. The paper thus looks into some unchartered waters of modern Economics. As regards policy options we emphasize that governments should try to avoid overshooting in stock markets and foreign exchange markets. Cooperation among leading OECD countries in the field of stock market regulation could be useful. The real exchange rate in catching-up countries typically is expected to increase in the long-term (BALASSA–SAMUELSON effect); however, it is unclear how shortterm dynamics will affect exchange rate development. In this context, one must bear in mind the implications of the DORNBUSCH model which emphasizes that in a system of flexible exchange rates there can be overshooting stemming from the interaction of sticky prices and fast adjusting exchange rates. There is a link between the real exchange rate and the burden of the debt. A real depreciation is particularly important for a country with foreign debt since it raises the burden of foreign debt; this effect offsets the stimulating effect of a depreciation of the currency on net exports of goods and services. The literature on pricing to market has undermined previous elasticity optimism—at least in a more short-term view. Pricing to market implies that an exchange rate change will not go along with a full exchange rate pass-through. With respect to potential overshooting the problems associated could be more likely than with full pass-through. There is also a link between the real exchange rate and capital flows, in particular FDI. A real appreciation, namely a fall of eP∗ /P, implies that home firms will find it easier to acquire foreign assets. In imperfect capital markets (FROOT/STEIN 1991), a fall of eP∗ /P implies that at a given relative price of stocks (ratio of stock market price P to output price level P) both home and abroad, foreign firms (in country II) can be acquired more easily after an appreciation; firms from country I can put up more equity capital as expressed in terms of the foreign currency. Hence they will be able to obtain more loans in the target country than previously so that there is a higher likelihood to outbid rival firms in the target country. A rarely considered implication—not considered by FROOT/STEIN—is that in open economies investment depends on the real exchange rate. With respect to short-term analysis, with P and P∗ considered as sticky variables, nominal exchange rate changes are equivalent to real exchange rate changes. Over a long-term perspective price levels are flexible, however, so that discussing the real exchange rate requires us to take a look at both the nominal exchange rate as well as the price level at home and abroad. In a world with tradable (T) goods and (N) nontradable goods, the internal exchange rate is defined as PT /PN . It can be shown—we pick up on this point subsequently—that the real exchange rate, q, is related to both the internal exchange rate and relative international sectoral productivity differentials. Economic opening up and economic growth are associated with considerable sectoral changes and hence productivity shifts. Not all countries which have opened up to the world economy have achieved both high productivity growth and real income growth. It will be interesting to focus on this issue and to raise some issues related particularly to productivity growth and the nominal and real exchange rate.

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While arbitrage in a two country model with homogeneous traded goods implies that PT = ePT∗ the analysis looks different in a setup with product innovations and heterogeneous goods: It will hold PT = V ePT∗ where V = 1 in equilibrium. In our analysis we are interested in looking into a world with Schumpeterian product innovations. Firms and countries differ in terms of product innovations. In certain countries, the size of the market and consumer preferences might be particularly appealing for launching new products, and the large market with high per capita incomes in the US is therefore often an important lead market; this is all the more true since many US multinational companies have a strong record in product innovations and since in new niche markets innovative young firms can often be found. As regards Western Europe there are clearly differences across countries when it comes to per capita income and patenting per capita; and one may distinguish between large and small countries. However, there are also considerable differences in terms of response time to innovative products: Time-to-takeoff in years (average time between product introduction on the national market and sales takeoff) was found to be around four years in Denmark, Norway and Sweden, around five years in Finland, Ireland, Belgium, Switzerland and the Netherlands, about six years for Austria and Germany, seven years for Italy, Spain and France and roughly nine years for the UK, Greece and Portugal (TELLIS/STREMERSCH/ YIN 2003). Finland and Sweden also are among the leaders in the EU’s European Innovation Scorebord (EUROPEAN COMMISSION 2003a, p. 27) when it comes to questions such as: 1. What is the percentage of “new to market products” of all turnover in manufacturing and of all turnover in services, respectively? In the 2003 scoreboard the EU-15 average (with missing data in the case of Ireland, Luxembourg and Netherlands) was 10.5 in manufacturing, while it was 27.2 for the top-leader Finland followed by Italy, Portugal and Denmark with 18.7, 16.0 and 14.3, respectively. In the field of services the EU-15 average was 7.4 (with missing data in the case of Ireland, Netherlands and the UK), while the leaders were Greece, Spain, Finland and Italy with 17.9, 13.7, 12.2 and 11.6, respectively. In the leader countries the price of tradables—in the field of manufacturing and services—should be higher than the EU average to the extent that novel products can fetch higher prices in the market. The data must be interpreted with caution since many products are newly introduced in the national market while this product does not necessarily stand for a global product innovation. If we concentrate on manufacturing products— typically all tradable—in high income countries where products new to the market should normally also mean new to the world market, Denmark has a clear lead, trailed by France and the UK with 9.5 for both countries, followed by Austria and Germany with 8.4 and 7.1, respectively. As a general hypothesis we expect that an increase in the share of new products to the market—relative to the EU average—will go along with a relative rise of the tradables price in the respective country. From a Schumpeterian perspective, it is thus not adequate to assume the law of one price to hold strictly.

F.1 Introduction

219

2. What is the percentage of “new to the firm but not new to the market products”, namely as a percentage of all turnover in manufacturing and of all turnover in services, respectively? In manufacturing, the EU-15 average (data missing for Ireland) was 28.6, while leaders were Germany, Sweden, Finland and Italy with 40.3, 32.1, 31.1 and 30.1, respectively; they are followed by Spain, Denmark and the Netherlands (25.8, 24.2 and 23.8, respectively). In services the EU-15 average (data missing for Ireland) was 18.8, while leaders were Greece, Spain, Sweden and Belgium scoring 37.1, 26.4, 23.7 and 23.5, respectively. Leading countries here indicate a high ability for imitation. It is, however, not ruled out that relatively poor countries have a relatively high score in the imitation index simply because they are catching-up. As regards relatively poor countries one should not underestimate the role of diffusion in economic catching-up. In the context of EU eastern enlargement this implies that firms in accession countries should perform well in imitation in the medium term. Over the longer term, the role of true innovations should gain importance, and this should become visible in international patent statistics. In the literature the traditional analysis of the link between catching-up and relative price changes is the Balassa–Samuelson effect. This effect—narrowly defined—suggests that the relative price of nontradables will increase along with a rise in per capita income (BALASSA 1964; SAMUELSON 1964). Basically, the reason could be that income elasticity for nontradables is higher than for tradables or that during economic catching-up productivity growth in the tradables sector is higher than in the nontradables sector. An alternative definition of the Balassa–Samuelson effect—broadly defined—is that the real exchange rate will rise along with the growth of per capita income. As is well known, the two types of Balassa–Samuelson effect are linked to each other, and we will pick up on this later. Under flexible exchange rates the foreign exchange market determines—as part of an interdependent system of macro markets—the nominal equilibrium exchange rate. The short-term exchange rate is consistent with a long-term fundamental equilibrium exchange rate only if all other macro markets (including the goods market and the labor market) are also in equilibrium. Hence there are different analytical time horizons with respect to exchange rate analysis. Moreover, if we look at a given economy, it is important to consider the goods market and the labor market first; if these markets are in equilibrium and the exchange rate clears in a situation of a roughly balanced current account, we have an equilibrium real exchange rate. Very short-term models are based on the analysis of financial markets, where the Branson model is a standard approach. A well-known medium-term analytical framework is the Mundell–Flemming model for an economy with unemployment. A simple full employment model is the model from MUNDELL (1968), who emphasized the distinction between tradable goods and nontradable goods. More recent contributions to the literature with a particular focus on the Balassa–Samuelson effect, are from DE GREGORIO/WOLF (1994), HALPERN/ WYPLOSZ (1997), CHIN/JOHNSTON

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(1997), MALISZEWSKA (1997), KRAJNYAK/ZETTELMEYER (1998), CANZONERI/CUMBY/DIBA (1999), GRAFE/WYPLOSZ (1999), CIPRIANI (2000), ROTHER (2000), SZAPARY (2000). It is worth mentioning that the real exchange rate can increase relatively quickly during economic catching-up, e.g., the case of Spain in the European Monetary System by 25% between 1986 and 1993. Several eastern European EU accession countries have also recorded phases of high real appreciation in the late 1990s. Many accession countries have also recorded a rise of the relative price of nontradables. There are, however, no models considering the long-term link between growth/technology and the real exchange rate. As such, we will present the first such model. At the same time there is also no model dealing with very short-term financial market analysis and economic catching up which marks—along the time axis—the other extreme. Short-term exchange rate developments can have considerable effects, possibly including foreign debt problems if there is a strong short depreciation such as overshooting effects in a country with high foreign debt. Thus we will present both a very short-term financial market model (namely an augmented BRANSON model) and a long-term model of the real exchange rate. Additionally we will present some new ideas on the role between economic catching-up and the exchange rate in the context of a modified perspective on Balassa–Samuelson effects related to the rise of the real exchange rate and the relative price of nontradables in the context of economic catching-up. We will first present the very short-term financial market analysis, followed by a refined medium-term model for Balassa–Samuelson effects in the context of product innovation; moreover, we suggest a basic approach for analyzing the long-term real exchange rate, where relative innovativeness also plays a key role. As a medium-term approach we consider a modified Mundell–Fleming model: We integrate product innovations into the model. We model innovativeness as changes in total factor productivity, product innovations and capital productivity changes. In the very short-term model the focus is on productivity shocks, while the medium-term and long-term analysis put the focus, respectively, on product and process innovations. The analysis suggests that relative international innovativeness is a crucial determinant for both the short-term exchange rate, the medium-term rate and the long-term rate. As the medium-term model suggests that the equilibrium nominal exchange rate could rise or fall as a consequence of a relative rise in per capita income (y/y∗ ; with y standing for per capita income) there are some doubts about a system of fixed exchange rates—in particular for countries catching up. As the ratio of research and development expenditures to GDP is increasing in OECD countries and Newly Industrializing Countries so that innovation dynamics intensify globally, one may indeed argue that in a world with stronger Schumpeterian innovation dynamics there are arguments for adopting more flexible exchange rate systems. As regards the 1980s and 1990s, it is noteworthy that relative innovativeness— as proxied by patent applications per capita and other variables—has witnessed considerable shifts in Europe and across OECD countries (JUNGMITTAG 2003, 2003a).

F.2 Traditional and New Approaches to the Exchange Rate

221

F.2 Traditional and New Approaches to the Exchange Rate and Stock Market Dynamics F.2.1 Stylized Facts of Exchange Rates and Stock Market Prices Let us first take a closer look at the links between the exchange rate e and stock market price at home P and abroad P∗ . As regards nominal exchange rate dynamics and stock market fluctuations, it is not surprising that the growth rate of the exchange rate is strongly positively correlated to the growth rate of the price of the stock market— such linkage reflects a kind of interest parity in the sense that international arbitrage requires that the growth rate of the stock market price at home should be equal to the expected sum of the growth rate of the stock price index abroad plus the anticipated relative change of the exchange rate (WELFENS 2001b): Due to such arbitrage it will hold (g denotes growth rate): gP = ge + gP ∗

(1)

There is empirical evidence (WELFENS 2001b)—including a nice out-of-sample forecast—that a simple model of the euro-dollar exchange rate based on the independent variables nominal interest rate at home and abroad plus the change of stock prices at home and abroad can explain exchange rate development; and the modeling brings indeed a nice out-of-sample forecast. According to (1 ) it must be true that for a given percent change of the foreign stock price index, there must be a parallel movement of the domestic stock market price and the exchange rate e. Indeed, if foreign (read US) stock market price dynamics strongly influence domestic (read: e.g., European) stock market price dynamics—for example, for simplicity gP = (1 − x)gP∗ where x is between 0 and 1—it is clear that the depreciation rate must run rather parallel to the stock market price changes. The US and Japan seem to indicate such a link while German dynamics are more difficult to interpret. What we can also see is that the stock market volatility on the basis of three-months-moving averages of monthly average figures is greater than the exchange rate variability. What is, of course, interesting is the covariance of the exchange rate and the stock price index. Taking a closer look at Eastern European countries and Newly Industrializing Countries, one also finds a high volatility of stock market prices, while the volatility of the exchange rate is rather limited: This is probably due to the fact that central banks have adopted some implicit pegging of the exchange rate. As regards levels of the stock market indices of various countries it is obvious that the US dominates many foreign stock markets. A traditional approach to exchange rate dynamics is the DORNBUSCH model— which assumes sticky prices and instantaneous exchange rate movements in a system of flexible exchange rates—in which overshooting plays a crucial role. In our modified DORNBUSCH model which assumes that the price of stocks (P ) has a

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8 6

EUR/USD S&P500

4 2 0 –2 –4 –6

Ap

r O 93 kt Ap 93 r O 94 kt Ap 94 r O 95 kt Ap 95 r O 96 kt Ap 96 r O 97 kt Ap 97 r O 98 kt Ap 98 r O 99 kt Ap 99 r O 00 kt Ap 00 r O 01 kt Ap 01 r O 02 kt Ap 02 r O 03 kt Ap 03 r0 4

–8

Fig. 43 Exchange rate and stock market dynamics in the US (three-month moving average) 18 USD/EUR DAX 30 14 10 6 2 –2 –6

Ap r O 93 kt Ap 93 r O 94 kt Ap 94 r9 O 5 kt Ap 95 r O 96 kt Ap 96 r O 97 kt Ap 97 r O 98 kt Ap 98 r O 99 kt Ap 99 r O 00 kt Ap 00 r O 01 kt Ap 01 r O 02 kt Ap 02 r O 03 kt Ap 03 r0 4

–10

Fig. 44 Exchange rate and stock market dynamics in Germany (three-month moving average)

positive impact on the demand for money can be summarized by a set of equations which represents the Phillips curve (1a), aggregate demand—in a logarithmic approximation—(1b), money market equilibrium (1c), capital market equation ((1d): full capital mobility and full substitution of domestic and foreign bonds, that is interest parity will hold where E is the expectation operator) and expectation formation

F.2 Traditional and New Approaches to the Exchange Rate

223

14 USD/EUR Eurostoxx 50 10

6

2

–2

–6

Ap

r O 93 kt Ap 93 r O 94 kt Ap 94 r O 95 kt Ap 95 r O 96 kt Ap 96 r O 97 kt Ap 97 r O 98 kt Ap 98 r O 99 kt Ap 99 r O 00 kt Ap 00 r O 01 kt Ap 01 r O 02 kt Ap 02 r O 03 kt Ap 03 r0 4

–10

Fig. 45 Exchange rate and stock market dynamics in Europe (three-month moving average) 10 8

YEN/USD Nikkei 250

6 4 2 0 –2 –4 –6

Ap r O 93 kt Ap 93 r O 94 kt Ap 94 r O 95 kt Ap 95 r O 96 kt Ap 96 r O 97 kt Ap 97 r O 98 kt Ap 98 r O 99 kt Ap 99 r O 00 kt Ap 00 r O 01 kt Ap 01 r O 02 kt Ap 02 r O 03 kt Ap 03 r0 4

–8

Fig. 46 Exchange rate and stock market dynamics in Japan (three-month moving average)

(1e). We will assume that the foreign stock market dominates P so that in the money demand equation for simplicity one may replace P through the foreign stock market price index P∗ times e: The condition eP∗ = ξ P could also be read as a kind of arbitrage condition—with E(eP∗ ) = E(e)E(P∗ ) + Cov(e, P∗ ) = E(e)E(P∗ ) +

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700

BUX

600 500 400 300

Forint

200 100

Q 2 9 Q 4 4 9 Q 4 2 9 Q 5 4 9 Q 5 2 9 Q 6 4 9 Q 6 2 9 Q 7 4 9 Q 7 2 9 Q 8 4 9 Q 8 2 9 Q 9 4 9 Q 9 2 0 Q 0 4 0 Q 0 2 0 Q 1 4 0 Q 1 2 0 Q 2 4 0 Q 2 2 0 Q 3 4 0 Q 3 2 04

0

Fig. 47 Exchange rate and stock market dynamics in Hungary (annual data) 250 200

Zloty

150 WIG 20

100 50

4 9 Q 4 2 9 Q 5 4 9 Q 5 2 9 Q 6 4 9 Q 6 2 9 Q 7 4 9 Q 7 2 9 Q 8 4 9 Q 8 2 9 Q 9 4 9 Q 9 2 0 Q 0 4 0 Q 0 2 0 Q 1 4 0 Q 1 2 0 Q 2 4 0 Q 2 2 0 Q 3 4 0 Q 3 2 04

Q

Q

2

94

0

Fig. 48 Exchange rate and stock market dynamics in Poland (annual data)

σe σP∗ ρ(e, P∗ ) and variance VAR (eP∗ ) ≈[E(e)]2VAR(e) + [E(P∗ )]2VAR(P∗ ) + 2E(e)E(P∗ )Cov(e, P∗ )—for stock markets of open economies with a similar level of technology and hence profitability of firms; for simplicity we set ξ = 1 (P∗ could itself be subject to overshooting; moreover, one may note that a priori the sign of the correlation ρ(e, P∗ ) is unclear; policy makers could restrict the covariance by declaring a maximum acceptable variance of the exchange rate). We will use the following simple (with Y# denoting full employment output): dlnP/dt = f  (lnYd − lnY#)

(1a)

lnYd = δ (lne − lnP) − ϕ lnY + lnG

(1b) ∗

ln M = ln P + μ lnY − σ i + ω [lne + lnP ]

(1c)

F.2 Traditional and New Approaches to the Exchange Rate

225

160 140 120 Koruna

100 80

PX 50

60 40 20

Q 2 9 Q 4 4 9 Q 4 2 9 Q 5 4 9 Q 5 2 9 Q 6 4 9 Q 6 2 9 Q 7 4 9 Q 7 2 9 Q 8 4 9 Q 8 2 9 Q 9 4 9 Q 9 2 0 Q 0 4 0 Q 0 2 0 Q 1 4 0 Q 1 2 0 Q 2 4 0 Q 2 2 0 Q 3 4 0 Q 3 2 04

0

Fig. 49 Exchange rate and stock market dynamics in the Czech Republic (annual data)

i = i∗ + E(dlne/dt) 

E(dlne/dt) = θ (lne# − lne)

(1d) (1e)

An alternative to adaptive expectations as stated in (1e) would be perfect foresight (we will disregard this for the moment): E(dlne/dt) = dlne/dt

(1f)

Note that all parameters are positive and that e# and Y# denote, respectively, the equilibrium exchange rate and full employment output. Combining (1c), (1d) and (1f) gives an equation for the monetary sector (M M line) showing an inverse relationship between lnP and lne. The economy will be characterized by this M M line at any moment of time since adjustments in the fast variables i and e will keep the system on the M M line. ∗

lnP = lnM − μ lnY + σ i∗ − ω lnP + σ θ (lne# − lne) − ω lne

(1g)

The slope in lnP–lne space is determined by −σ θ − ω which is negative: The absolute interest rate elasticity of the demand for money and the “learning” parameter θ (in the expectation equation) are crucial which indicates how quickly the actual exchange rate adjusts toward the equilibrium value e#. The smaller both parameters are, the flatter the negatively sloped M M curve—and the smaller the learning parameter is the closer is the location toward the origin. The flatter the M M curve is, the higher is the overshooting phenomenon; a low value for ω reinforces the overshooting problem. Conversely, the higher the learning speed and the higher in absolute terms the interest rate of the interest elasticity (the steeper M M ), the smaller is exchange rate overshooting; and the higher ω the smaller is the overshooting problem. This points to potential stabilizing properties of stock market transaction (one may state the hypothesis that the larger the long-term stock market capitalization is the higher is ω ). Government can influence the interest elasticity of the demand for money by

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encouraging the development of an efficient financial sector offering a broad variety of financial market instruments: The larger the range of liquid short term investment alternatives in the market, the higher (in absolute terms) the interest elasticity in the demand for money. Note that overshooting is critical for developing countries with high foreign debt since it will bring the risk that excessive transitory (overshooting) devaluation will raise the foreign debt level to a critical value: To the extent that investors will not agree on the relevance of overshooting a potential liquidity problem then might translate into a solvency problem—the country is considered to have such a high foreign debt that default is expected in the near future. Combining (1a) and (1b) gives—with dlnP/dt = 0—a medium-term equilibrium condition for the real sector of the economy (I S curve which has slope unity in lnP–lne space): lne# = lnP# + [1/δ ] lnG − [(1 − ϕ )/δ ]lnY

(1h)

Expansionary monetary policy leads to overshooting (see the following figure) in the sense that the exchange rate will jump from e0 to e01 immediately, while the long-run equilibrium value of the exchange rate is e1 . The long-run depreciation is smaller than the medium-term depreciation of the currency. lnP M′M′1

I′S′

M′M′0 E1 E0

E01

lnP0

Fig. 50 Financial market equilibrium (M M ) and real economy (I S )

lne0

lne1

lne01

lne

An increase in the foreign stock market price—reflecting for instance intensified innovation dynamics and hence higher expected profits and higher stock market prices—will shift the M M curve upwards. Hence there will be a strong short-term depreciation and a more modest long term depreciation. If foreign stock markets are characterized by a series of upward price increases we can expect to see a zigzag exchange rate movement which will reflect the overshooting phenomenon. One might include additionally on the demand side in the goods market the variable P /P— Tobin’s q (denoted here as Q ): This means introducing a real “Tobin Q demand effect” in the goods market equilibrium by adding a term δ P /P in (1b)) which

F.2 Traditional and New Approaches to the Exchange Rate

227

would mean that the overshooting effect is reinforced since the I S curve will shift to the left if the stock market price P and P∗ , goes up: The long-term depreciation effect is reduced—assuming that there is a depreciation at all—and in this sense the relative overshooting has increased. If the “Tobin Q demand effect” were very strong, there could even be the case that short term depreciation will be accompanied with long-term appreciation; here we touch upon an empirical issue where one may anticipate a priori only rather limited relevance of such a case. The long-term equilibrium solution is obtained by inserting (1h) in (1g) to replace lnP (which is equal to lnP ) and by setting lne = lne#:   lne#(1 + ω ) = lnM + σ i∗ − ω lnP∗ + [1/δ ] lnG − μ + [(1 − ϕ )/δ ] lnY. (1i) Clearly, this equation can be estimated empirically. Note that a rise of the foreign stock market price will bring about a nominal depreciation. If the stock market price index abroad is positively influenced by product innovations v—and associated improved profitability of firms—the effect of product innovations abroad is a nominal long-term depreciation. Moreover, in the long run the elasticity of e with respect to P is unity. An expansionary monetary policy will shift the M M curve to the right; and the nominal exchange rate will react immediately and jump—as a short-term reaction (only the M M curve is binding) to a higher nominal exchange rate; in the short-run dlne/dlnM will exceed unity so that there is overshooting. If we replace the adaptive expectation process by perfect foresight, that is E(dlne/dt) = dlne/dt

(1f)

we will get a differential equation from combining (1c), (1d) and (1f) which reads dlne/dt = [1/σ ]/[1 + ω ][lnP + μ lnY − lnM] − 1/[1 + ω ]i∗ + ω /[1 + ω ]lnP *

(1j)

Note that (1a) and (1b) can be combined to the following differential equation for the dynamics: dlnP/dt = [−f  δ ]lnP + [f  δ ]dlne/dt + f  [lnG − (1 − ϕ )lnY]

(1k)

The phase diagram for the system of two Eqs. (1j) and (1k)—the curves EE (for (1j)) and PP (for (1k))—shows that there is a saddle path so that there is only one unique trajectory (the M M line) to the equilibrium point. Again it is true that shifts in exogenous variables will lead to an overshooting of the nominal exchange rate so that the long-term equilibrium exchange rate differs from the short-term exchange rate. Imperfect capital mobility could reduce, but not necessarily eliminate, the phenomenon of overshooting.

228 Fig. 51 Saddle point stability in a perfect foresight model

Innovations in Macroeconomics lnP I′S′ (dlnP0 /dt=0)

lnP#0

E0

lne#0

EE0 (dlne/dt=0)

lne

F.2.2 A Short-Term Analysis of Financial Market Dynamics and Technology Shocks A look at the effective real exchange rate of several countries shows that the real exchange rates show a long-term rise—parallel to output per capita. This is true both for Asian NICs (until 1997, the year of the Asian crisis) and selected EU accession countries in the 1990s as is shown in the subsequent graph. Such a longterm appreciation trend does, however, not rule out that there can be considerable short-term depreciation periods; e.g., in the context of expansionary monetary policy and falling interest rates or as a consequence of investors’ fears with respect to the sustainability of government debt policy. In addition to this, oil price shocks could affect short-term nominal and real exchange rate development. Now let us turn to some modeling analysis. Over the short term, all stock variables—such as the capital stock K—and the price level P are given. There can however be productivity shocks, namely changes in the marginal or average capital productivity. As for a Cobb–Douglas production function, the marginal productivity is proportionate to the average productivity. Interesting cases to consider are changes in expectations and in productivity growth and in the price level, capital stock and the stock of money, where the latter is a policy variable.

New Open Economy Approach: Augmented Branson Model A well-known model of financial markets in open economies is the BRANSON model, which focuses on the money market as well as the short-term domestic bonds market and the short-term foreign bonds market, with foreign bonds being denoted as F∗ (in foreign currency). Essentially, the model allows for the simultaneous determination of the exchange rate and the nominal interest rate in a setting with a domestic bonds market (BB line), a foreign bonds market (FF line) and the money market (MM line). This model determines the nominal exchange rate e and the nominal interest rate i.

F.2 Traditional and New Approaches to the Exchange Rate

229

180 Czech Republic

Hungary

Poland

160 140 120 100 80 60 40 20 0 20

08

07

06

09

20

20

20

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03

02

01

00

99

98

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96

95

94

04

20

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20

20

20

19

19

19

19

19

19

Fig. 52 Real effective exchange rates for selected EU accession countries in the 1990s, Jan 1990 = 100. (Source: Eurostat)

Subsequently we will modify the approach by dropping the domestic bonds market and adding the stock market. This allows for a convenient graphical exposition. The more complex augmented BRANSON model, which includes the original three markets of the seminal model and the stock market, could be discussed analytically. e BB0 MM0

E0 e1

FF0

Fig. 53 Portfolio equilibrium in the simple basic Branson model

0

i0

i

The simple augmented BRANSON model, with i∗ representing the foreign interest rate and aE the exogenous expected exchange rate change, can be written as follows (with V representing the marginal utility of money, z capital productivity,  expected growth rate of the stock market price; M is the nominal money stock, K the capital

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stock, P the stock market price and A = [M/P] + [eF∗ /P] + P K/P is overall real wealth): A = (M/P) + (eF∗ /P) + P K/P [budget constraint]

(2a)

M/P = n(V, i∗ + a E , z, )A ; n1 > 0, n2 < 0, n3 < 0, n4 < 0 [MM curve] (2b) eF∗ /P = f(V, i∗ + a E , z, )A ; f1 < 0, f2 > 0, f3 < 0, f4 < 0 [F∗ F∗ curve] (2c) P K/P = h(V, i∗ + a E , z, )A ; h1 < 0, h2 < 0, h3 > 0, h4 > 0 [KK curve] (2d)

We have dropped the domestic bonds market for convenience; in principle there is no problem in also taking into account the domestic bonds market. The system for Eqs. (2c) and (2d) can be written in matrix form (remember that only two of the three Eqs. (2b)–(2d) are independent as n + f + k = 1) and determine—using Kramer’s rule and taking into account the budget constraint Eq. (2a)—the multipliers for e and P ; while e and P are endogenous variables, the other variables are exogenous. Thus we differentiate the system and look at interesting multipliers such as • • • • • • • • • •

de/dz > 0 de/d < / > 0 de/dK = 0 de/dM > 0 de/di∗ > 0 dP /dz > 0 dP /d > 0 dP /dK < 0 dP /dM > 0 dP /di∗ < / > 0.

A rise of capital productivity will raise the stock market price level, and it—under certain parameter constellations—brings about a nominal depreciation. In such a case, we cannot easily infer whether the domestic stock price has increased P relative to the price of foreign stocks (eP∗ ). Only if the percentage rise of P exceeds that of the nominal exchange rate would this be the case. One may dub such a case as an improvement in the international terms of capital where the latter is defined as P /(eP∗ ); in an open economy with two-way FDI and portfolio investment in stocks, a rise of the terms of capital implies that the amount of foreign real capital per unit of domestic real capital has increased. Such a perspective implicitly goes one step beyond the existing model in the sense that we would have to also consider foreign stocks—at a given price of stocks abroad—so that domestic investors can trade domestic stocks for foreign stocks. In an e–P diagram, we can display the equilibrium line (MM) for the money market, which has a negative slope since a rise in e (increase in the demand for money) must be combined with an adequate fall of the stock market price if money

F.2 Traditional and New Approaches to the Exchange Rate Fig. 54 Foreign bonds market, stock market and money market

231

e KK

FF e0

MM 0

P0 ′

P′

market equilibrium is to be maintained. The equilibrium line for the stock market (KK) has a positive slope, as a rise in P (its impact is a net supply effect) must be combined with a rise in e, namely an increase in the demand for stocks if stock market equilibrium is to be maintained. The slope of the equilibrium curve for the foreign bonds market is also positive and smaller than that of the KK curve. A rise of e causes a net supply effect—indeed an excess supply—in the foreign bonds market. This excess supply is eliminated if the stock market price and hence the real value of wealth is adequately increased. e KK0 KK1 FF1

E1 e1

FF0

e0

Fig. 55 Effects of an increase in capital productivity in the modified Branson model with stock market

E0

MM1

MM0 0

P0′

P1′

P′

An expansionary monetary policy implies an upward shift of the MM curve so that we observe depreciation and a rise in the stock market price. Net investment (i.e., a rise in K) will shift the KK curve upward so that we can learn from the new

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intersection point with the MM curve that the nominal exchange rate will increase and the stock market price will fall in the short run. A rise in capital productivity (as occurs in the course of both structural change and economic catching-up) implies a downward (upward) shift of the KK (FF) curve and a rightward shift of the MM curve. From our multiplier analysis one may derive some ideas with respect to the correlation coefficient ρ(e, P∗ ). The short-term result of an expansionary monetary policy is nominal depreciation and a rising stock market price. In the medium term, however, one must take into account that for foreign investors from country II, depreciation in country I is equivalent to an appreciation of the currency of country I, allowing the purchase of assets more cheaply. This, however, does not hold for either stocks (or real capital) if the percentage increase in stock prices is higher than the depreciation rate of the currency in country I. Based on this perspective, a modified Branson model suggests that FDI could fall over the medium term. In the long run, the situation is different if one assumes that a relative rise of the stock market price will stimulate emission both of new stocks and net investment. The KK curve will shift upward, thereby dampening the medium-term increase in stock market prices. This, in turn, will stimulate FDI inflows over the long run.

F.3 Hybrid Model: Combining Interest Parity and Augmented Money Market Equilibrium A simple approach to exchange rate modeling is to combine “interest parity” with money market equilibrium; we will augment traditional approaches not least by assuming that the demand for money is not only a function of output and the nominal interest rate but also of the stock market price index P —assuming that the higher P the higher the transactions financed in stock markets. According to open interest parity, we should have (with e as the nominal exchange rate, i as the nominal interest rate, ∗ to denote foreign variables and R as the risk premium): Eet+1 − et = i − i∗ − Rt 

(3)

[Eet+1 /et ] = 1 + (i − i∗ ) − Rt 

(4)

Assuming that (i−i∗ )−Rt is relatively small we can use the approximation ln(1+x) ≈ x and write: lnEet + 1 − lnet = (i − i∗ ) − R

(5)

lnet = lnEet+1 + (i∗ − i) + R

(6)

We will assume that the risk premium R depends on the sustainability of fiscal policy as proxied by the debt–GDP ratio d : lnet = Eet+1 + (i∗ − i) + R(d )

(7)

F.3 Hybrid Model

233

The expected exchange rate is supposed to be determined according to another part of the book: lnEet+1 = lnet−1 + ß(lnY − lnY∗ ) + ß (lne♦t − lnet ) + ß (lnet − lnet−1 ) = −ß(lnY∗ − lnY) + (1 − ß )lnet−1 + ß lne♦ − (ß − ß )lnet

(8)

This equation—where we assume 0 < ß < 1, (ß − ß ) ≤ 1—states that the expected exchange rate is based on the past spot exchange rate plus three factors, namely the current account impact-related net exports of goods and services and hence the differential lnY/Y∗ , the difference between the hypothetical long term (read purchasing power: PPP) equilibrium exchange rate e♦ and the actual exchange rate; and the difference between the present exchange rate and the exchange rate of the previous period. This learning pattern may reflect pragmatic learning in the sense that economic agents consider the present exchange rate with a certain probability as an equilibrium exchange rate (perfectly rational if the equilibrium exchange rate were characterized by a random walk), but also consider the relevance of the rational component e♦; and e♦ is based on purchasing power parity. Inserting (8) into (7) gives lnet [1 + (ß − ß )] = −ß (lnY∗ − lnY) + (1 − ß )lnet−1

(7 )

+ ß lne♦ + (i∗ − i) + Rt (d  ) As regards the hypothetical equilibrium exchange rate—according to PPP—we follow the monetary approach to exchange rate determination in a modified form. The modification concerns the role of the stock market price index P  which is assumed to positively affect real money demand as transactions on stock markets will rise along with P . The expected exchange rate is assumed to depend on relative money supply. Hence we assume the law of one price (in its weak form, that is V = 1), that is purchasing power parity, and hence Pt = V e♦t Pt∗

(9)

lnPt = lnV + lne♦t + lnP∗t

(9 )

We assume money market equilibrium at home and abroad; and we denote real money demand m = m(Y, i, P ) and m∗ = m∗ (Y∗ , i, P ) abroad. P is the stock market price index (real income is denoted as Y, the income elasticity of money demand denoted as α and the semi-interest elasticity denoted as α and the elasticity with respect to the stock market price index as α ). The real money supply is M/P in the home country and M/P∗ in the foreign country so that the equilibrium conditions read as follows (with e denoting the Euler number): 



Mt /Pt = Yt α Ptα e−α it ∗

Mt ∗ /Pt ∗ = Yt ∗ α P t

∗α∗ −α∗ i∗ t

e

(10) (11)

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Innovations in Macroeconomics

lnMt − lnPt = αlnYt − α it + α lnPt 

(10 )

lnMt ∗ − lnP∗t = α∗ lnYt ∗ − α∗ it ∗ + α∗ lnPt ∗

(11 )

Inserting from (10 ) and (11 ) P and P∗ into the equation for purchasing power parity (9 ), we have lne♦t = −ln V + ln Mt − ln Mt∗ + α∗ lnYt∗ − α∗ it∗ + α∗ lnPt∗ 

(12)



− αlnYt + α it + α lnPt Inserting (12) in (7) we get [1 + (ß − ß )]lnet = −ßlnY/Y∗ + (1 − ß )lnet−1 − ß lnV

(13)

+ ß lnMt − ß lnMt ∗ + α∗ ß lnYt ∗ − αß lnYt + (1 − α∗ ß )it ∗ − (1 − α ß )it     + ß α∗ lnP∗ t − ß α lnPt + Rt

Defining [1 + (ß − ß )] as b we obtain lnet = (1 − ß )/b · lnet−1 − ß /b · lnV + ß/b · lnMt − ß /blnMt ∗ ∗ 

∗

(14)



+ [(α ß + ß)/b]lnYt − [(ß + αß )/b]lnYt + {[1/b][1 − α∗ ß ]it ∗ − [1/b][1 − α ß ]it }     + [ß /ß]α∗ lnP∗ t − (ß /b)α lnPt + (1/b)Rt

If we assume that the semi-interest elasticity for the demand for money is the same at home and abroad, we can replace the expression {. . . } by the interest differential i∗ −i. Equation (14) is a testable hypothesis, which takes into account both short-term dynamics from the capital account and more long-term dynamics related to the current account and purchasing power parity, respectively. For an empirical analysis with respect to transition countries see WELFENS/BORBÉLY (2004) who find positive empirical evidence for Eq. (12).

F.4 Capital Asset Pricing Model and Product Innovations The CAPM focuses on the behavior or risk-averse investors who have a choice between bonds and stocks here understood as a promise for paying out future profits of the respective firms. The contemporaneous yield of stocks consists of the dividend yield plus the percentage change in the stock market price P . What is the minimum rate of return sE an investor in stocks will require? The CAPM is straightforward in that it considers the risk free bond interest rate i, the expected variance of stock

F.4 Capital Asset Pricing Model and Product Innovations

235

market prices Eσ2t+1 and the market price of risk λt+1 which reflects the degree of risk aversion of investors: sE = i + λt+1 Eσ2 t+1 .

(15)

Investors in the stock market will raise the required yield if there is a rise in • the opportunity rate of return (i): Here the Growth and Stability Pact of the EU— assuming that it enjoys creditability—contributes to low interest rates as does the very size of the Euro area which allows more easily economies of scale in the issuing of debt instruments. • the degree of risk aversion λ : The degree of risk aversion is likely to rise with the median age of the population—in the long run the age level is rising considerably in the EU and Japan, but hardly in the US. • or stock market volatility σ2 : The variance of stock prices is affected by the variance of the underlying fundamentals, including, e.g., innovation dynamics and the price of energy. If we additionally take into account that the real money balances M/P will affect the demand for stocks as well as the role of Tobin’s Q (P /P: the ratio of the stock price—reflecting the existing capital stock—to the price of investment goods/the price of newly produced goods) and the FROOT-STEIN argument relevant in an open economy, we get a simple long-term demand function for stocks Z: Zd = Zd (i, M/P, Eσ2 t+1 , v, λ , Q , q∗ )

(16)

The partial derivatives (denoted a0 , a1 , . . . , a6 ) of the first and third variable, the degree of risk aversion and of Q are negative, while M/P and q∗ will positively affect the stock demand. From the perspective of a small open economy, the volatility is determined by the US stock market dynamics. The degree of product innovativeness v will positively affect the demand for stocks since product innovation will allow firms to fetch higher prices in goods markets and thus to raise profitability. In the medium term, the market price of risk can be assumed to be exogenous. The nominal interest rate is affected by—domestic and foreign—bonds markets while M/P is a policy variable to the extent that the nominal money supply is concerned. P is a predetermined variable to the extent that medium-term dynamics of national output Y are governed by the existing stocks of factor inputs (for a given trajectory of M and Y we can implicitly determine P). The real exchange rate is endogenous under flexible exchange rates, but exogenous in a fixed exchange rate system; in a mediumterm perspective, we might even consider the exchange rate as pre-determined if purchasing power parity is remains steady, which will be done here. As regards the supply of stocks Zs we will use the following simple function (partial derivatives denoted as b1 , b2 , . . . , b6 ) which assumes that supply is determined by the interest rate and Kopt (the profit-maximizing capital stock; if actual K falls short of this optimum investment I will stimulate the supply of new stocks) the rate of product innovation v—the higher the innovation rate the higher anticipated profits-, the corporate income tax rate τ, Tobin’s Q and the real exchange rate q∗ . The partial

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derivative of i, Kopt , v, Q and q∗ are positive where a rise of q∗ is assumed to translate into higher export profits. The tax rate will negatively affect the supply of stocks: Zs = Zs (i, K opt , v, τ, Q , q∗ )

(17)

Using a linearized function for the demand and the supply side in the stock market, medium-term equilibrium Zd = Zs in stock markets is therefore given by a rather simple equation (where we replace domestic volatility by foreign volatility): P /P[b5 − a5 ] = (a0 − b0 )i + a1 Eσ∗2 + a2 (M/P) + (a3 − b3 )v + a4 λ − b2 [Kt−1 + Iopt ] − b4 τ + (a6 − b6 )q∗

(18)

Note that a similar equation will hold abroad. Indeed the equation is an implicit twocountry model for a small open innovative economy. The term [b5 − a5 ] is positive, the term (a0 − b0 ) is negative and (a6 − b6 ) is positive. We can thus state that a rise of the interest rate negatively affects the real stock market price (read Tobin’s Q ). There is also a negative impact of volatility, risk aversion, the capital stock and the tax rate. The real exchange rate has a positive impact on the real price of stocks. With sticky output prices it holds that a rise of the nominal exchange rate e will raise the stock market price P , which is consistent with our basic short-term financial market model. As regards the impact of right-hand side variables on the real stock price one should note: The only unclear sign is for v, namely [a3 − b3 ]/[b5 − a5 ]. Before we look closer into the innovation variable, one may emphasize the role of structural similarities of countries considered here. If the home country and the foreign country are of equal size and composed of equal firms, the law of one price must hold for stock prices: P = ξ eP∗

(19)

or (assuming constant ξ with g for the growth rate) gP = ge + gP∗ which reads that the expected capital gains rate on domestic stocks must equal the expected capital gains rate on foreign stocks plus the expected currency depreciation rate, that is: [E(P 1 )/P 0 ] − 1 = [E(e1 )/e0 − 1] + [E(P∗ 1 )/P∗ 0 ] − 1

(19 )

In a setting characterized by (19) and a given real exchange rate, the endogenous variable in the above equation is investment, which no longer can be determined by autonomous domestic firms, rather investment follows immediately from the law of one price for the stock market. The law of one price for the stock market will hold in the long run only for countries with a similar technology basis and across which knowledge flows rather freely. This amounts to saying that there must be some factor mobility (and the internet creating broad transparency). In the subsequent analysis, we will not consider this special case of stock market price arbitrage. Finally, note that with given K and sticky output prices Eq. (18) can be rearranged and solved for e, namely for the case of a small open economy whose stock market price dynamics are determined by the foreign stock market price according to P = ξ eP∗ : The real

F.4 Capital Asset Pricing Model and Product Innovations

237

and nominal exchange rate thus would be a positive function of i, a positive function of the variance of stocks and of the risk premium as well as a negative function of real money balances and a positive function of the capital stock and the price of (foreign) stocks relative to the price level; the impact sign of the product innovation variable is unclear. With a focus on Eq. (18), we turn to the innovation variable: If the innovation variable affects the demand side more strongly than the supply side, namely [a3 > b3 ], we will have a positive impact of v on Q . There could be periods of irrational exuberance when investors anticipate a wave of exogenous product innovations— see the internet bubble or a potential future bubble centered on nanotechnologies—to strongly stimulate future profitability and thus raise the demand for stocks (for this case we assume a3 > b3 ). A simplifying assumption is that such a wave of product innovations will not affect volatility in the market. One should note that the interdependency of financial markets suggests that the nominal exchange rate and the stock market price should be determined simultaneously. WELFENS (2002) has argued that the real demand for money should be specified in a way which includes the contemporaneous stock market price: The demand for money m does not only reflect transactions in goods markets but also transactions in stock markets so that m = m(Y, i, P ) for country I and m∗ (Y∗ , i∗ , P∗ ) for country II; the partial derivative of m with respect to the stock market price P is expected to be positive. Using purchasing power parity e = P/P∗ and replacing P and P∗ from an explicit money demand function at home and abroad, one should expect the nominal exchange rate to depend on Y, Y∗ , i, i∗ , P and P∗ —note that in a case of global dominance of the US stock market (that is the US S&P 500 development determines P ), the elasticity of P would be the same as that for P∗ ; and this seems to be relevant for both countries in Western Europe and Eastern Europe. A two-stage least-square estimation (WELFENS and BORBÉLY 2004) for Hungary has shown domestic and foreign stock market price indices to be significant variables for the nominal dollar exchange rate; for Poland the domestic stock market price was a significant variable, the foreign stock market price index was only weakly significant. Adequate Durbin–Watson statistics and a high R squared underline that the approach chosen is useful. A more extensive modeling could endogenize v, e.g., by assuming that some path dependency in innovation in accordance with dv/dt = f(. . . )vt−n + B E(P ) where f(. . . ) is a density function for past innovations (B is a positive parameter); moreover, a rise in v may be assumed to be associated with a rise of volatility. Here we are not so much interested in such extensions, rather we want to consider another impact, namely that domestic innovations and foreign innovations are interacting through network effects: We assume that the effective domestic rate of product innovations v (v replaces thus v in the demand-side function and the supply-side function) is determined by interaction of product innovations launched by domestic firms (v) and by foreign firms (v∗ ) where we have positive efficiency parameters λ , λ∗ and a simple multiplicative term included which makes sure that there are positive marginal

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cross fertilization effects from innovations: v = λ v2 + λ∗ v∗ 2 + 2λ λ∗ vv∗

(20)

We thus have a real Schumpeterian channel which implies a positive cross-country correlation of stock market prices (note we define [b5 − a5 ] = b ): P /P = (a0 − b0 )/b i + a1 /b Eσ∗2 + a2 /b (M/P) + a3 /b λ − b2 /b [K] (21) − b4 /b τ + (a6 − b6 )/b q∗ + b3 /b [λ v + λ∗ v∗ ]2 Equation (21) seems to be adequate for the US but an estimation for any other country would have to add a term b7 P∗US /P∗US which reflect the global dominance of the real US stock market index; the sign of b7 should be positive for OECD countries and any other country where the structure of the stock market index reflects a set of industries similar to that in the S&P500 index of the US. If one were to estimate the dynamics of the stock market and the exchange rate simultaneously the implication for any non-US country is an ambiguous sign for the impact of the foreign stock market variable. From an industrial economics perspective, it would be interesting to consider countries where both goods markets are shaped through international oligopolistic interdependence in technology intensive innovative industries. A term such as that associated with b3 should then be highly relevant.

F.5 Consumption, Volatility and Growth In the following analysis, we will turn toward the problem of modified neoclassical growth modeling with labor-augmenting technological progress A(t). This approach implies that dK/dt is now determined by a goods market equilibrium condition for an open economy. We are mainly interested to understand how volatility will affect respectively output and growth. To simplify matters we impose the long-term interest parity condition in the form i = i∗ ; as we will not consider inflation we indeed have real interest rate parity in the form r = r∗ . There is one modification which must be additionally considered, namely that instead of M/P and K we will use (M/P)/(AL) =: m and K/(AL) =: k , respectively. We do so as we want to focus on an economy with process innovations in the production function Y = Kß (AL)1−ß , that is a =[dA/dt]/A > 0 and population whose exogenous growth rate is n. P /P = (a0 − b0 )/b i + a1 /b Eσ∗ 2 + a2 /b m − b2 /b k  + a3 /b λ

(21 )



− b4 /b τ + (a6 − b6 )/b q∗ + b3 /b [λv + λ∗ v∗ ]2 Now consider the following consumption function which basically states that consumption per efficiency units of labor C/[AL] is proportionate to income per efficiency unit of labor (y ), the real stock price and real wealth which we deliberately write in a somewhat unusual form. A standard model derived from utility

F.5 Consumption, Volatility and Growth

239

maximization would be to assume that consumption is proportionate to income and proportionate to real wealth where the expected rate of return and the variance of yields play a role for the real wealth variable (DIXIT 1998). Here we use a modified approach: Real wealth per efficiency unit of labor consists of real money balances per efficiency units of labor m and the stock of real capital per efficiency units of labor k . The consumption function assumes in particular that volatility of investment returns has a positive impact on consumption—a higher volatility is discouraging savings—and that a higher expected yield has a negative impact on consumption. A rise of Tobin’s Q is assumed to have a positive impact on consumption: ϕ

C/[AL] = cy + {c (r ∗ )[σ/μ]ε [k  + m ]Q } ß

ß

(22)

Assume that all investment is in innovative projects associated with product upgrading. The expected rate of return on innovation is μ, the variance is σ. There are only two assets considered, namely real capital K and real money balances m (m = M/P). We chose deliberately a special specification where K/AL and [M/P]/AL (denoted as m ) both enter the consumption function as a variable to the power ß since otherwise the mathematical processes would become very intricate (ß also is the supply elasticity of capital here). All exponents are assumed to be positive. As regards the term [kß + mß ] this formulation is rather unusual at first sight; an ideal specification would-as we will show—indeed use [kß + mß ]2 but for ease of exposition we will drop the square. Our basic reflection in this context—with setting Q unity for simplicity (and Q∗ = Q )—will focus on a specific case where A = A0 = 4 and L = L0 = 1. Assume that ß = 1/2 and the production function contains household’s real money balances M/P as a positive external spillover effect, where real balances factor in as (M/P)ß ; hence, we have output as Y = Kß (M/P)ß Lß0 . One may then indeed state a simple consumption function as follows, namely: C/[AL] = cy + c (K0.5 + m0.5 )2 = cy + c [K + 2K 0.5 m0.5 + m] = C y + c [K + m] Here C = c + 2c . We will use a somewhat different Cobb–Douglas output function to replace kß by y and a simple CAGAN-type real money demand equation to replace m , namely (with the Euler number written as e and the semi-elasticity of the demand for money with respect to the nominal interest rate denoted as   —defined as negative—and the expected inflation rate denoted as π ): m  = e d

  [μ+π ] 

y

(23)

Let us assume that both σ and μ are positive functions of the product innovation variable v: The corresponding savings function is therefore as follows: ϕ

S/[AL] = {1 − c − c [σ(v)/μ(v)]ε Q [1 + e

ψ [μ(v)+π ]

]}y

(24)

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In the presence of FDI inflows F the modified neoclassical equilibrium condition is (with S denoting savings and depreciation rate on capital δ). δK + (dK/dt) = S + F

(25)

Dividing by AL and taking into account that we assume that FDI inflows F are proportionate to output—we assume F /[AL] = qλ kß while depending on q (in accordance with FROOT/STEIN we assume that the higher q the lower FDI inflows so that λ < 0) and using a Cobb–Douglas production function y = kß (this production function might include—as a kind of positive external effect of household’s money holdings—real money balances M/P where M/P is normalized to unity) gives dk  /dt + [n + a + δ]k = sk  + qλ k  ß

ß

(26)

The accumulation dynamics for the capital stock are governed by dk  /dt = [s + qλ ]k  − [n + δ + a]k  ß

(27)

We assume that the real exchange rate reaches a steady-state value q# relatively quickly so that we can treat q# asymptotically as a constant in the above Bernoullian equation. The steady-state value for k (denoted as k #) is k# = {[s + qλ ]/[n + δ + a]}1/(1−ß)

(28)

The openness of the economy—as far as associated with FDI inflows and captured in the term q—allows reaching a higher steady-state level of growth; however, the higher q#, the lower is the positive effect on the level of the growth rate. We emphasize that s need not to be a constant. One may assume that the partial derivative of the expected rate of return with respect to v is lower—ultimately, this is of course, an empirical question—than that for the reaction of the variance with respect to changes in v: This assumption is sufficient to bring about a rise of the savings rate and S, respectively, if v is increased; note that we must take into account that s :=[1    – c – c [σ(v)/μ(v)]ε Qϕ [1 + eψ [μ(v)+π ] ]}. Thus, we have both process innovations and product innovations as well as stock market dynamics. The long-term real exchange rate q = 1/q∗ can be determined within a simple analytical approach (WELFENS 2004a); it should also be noted that the growth rate of technological progress can be endogenized (WELFENS 2004b). It certainly would be useful to have more empirical research along the lines suggested by our modeling approach.

F.6 Policy Issues and Conclusions A first policy issue is overshooting, respectively, in stock markets and the foreign exchange market. It would be useful to avoid strong overshooting effects, most importantly in the case of countries with relatively high foreign debt. For a country

F.6 Policy Issues and Conclusions

241

with a high foreign indebtedness—relative to GDP—there is a risk that what might at first glance be considered as temporarily excessive devaluation become a systemic risk once a critical level of foreign debt has become relevant. If the respective country is close to a critical limit in foreign debt, overshooting can translate liquidity problems into serious solvency problems. It will not help the country much if an expert would state publicly that the massive devaluation which has occurred was only a transitory problem on the way toward a mild long-term devaluation. Hence there is critical interest on the part of heavily indebted countries to avoid overshooting problems. Slowing down the adjustment speed of financial markets or raising the speed of goods and factor markets principally are potential policy options. The adjustment speed in financial markets could fall endogenously, e.g., as there is a graduation toward a higher average maturity in the bonds market which in turn could be stimulated by reducing inflation rates. An interesting problem are international spillovers which on the one hand can occur both through network effects in product innovations; on the other hand there could also be international external effects in the sense that the foreign variance of stock market yields enter the equation for the domestic economy. This is not a major problem as long as regulation in the dominant country(ies) makes sure that there is no bias in stock market dynamics; e.g., as fraudulent investment bankers in the US publicly recommended certain stocks of firms in the ICT (information and communication technology) sector in the 1990s—while privately saying that one should simply sell such stocks as they had attained non-sustainable levels—this did not only amount to US stock market manipulation, rather it also affected other OECD countries as the US stock market bubble influenced other stock markets abroad. The considerable covariance of stock market dynamics and exchange rate changes also raises the issue as to whether or not stock market bubbles tend to contribute to market instability in foreign exchange markets. It would be interesting to consider policy options that help to avoid excessive short-term fluctuations of stock market prices and exchange rates. A useful policy option would be to impose—for both private and corporate customers (so far some OECD countries have such rules only for private households which is the smaller part of the market)—“time-progressive” yield taxation. The longer customer X holds a certain stock, the lower will be the tax rate applied to earnings. If owners of firms are not to be favored unfairly, one should consider imposing a minimum corporate tax rate as well. There are some key links between the monetary/financial sector of the economy and the real economy. Stock market dynamics will feed into the consumption market—obviously the higher the stock market capitalization is relative to national income. There is a lot of empirical research to be done; and simulations to be run. It is not really understood how strong exchange rate dynamics and exchange rate chances are intertwined. Moreover, it is unclear whether a kind of stock market parity holds over the long run, namely eP∗ = P . The analysis—based on an ADF test—suggests that there has been, in some countries, non-stationarity of the term eP∗ /P over the decade following 1992. One can, however, not rule out that adjustment needs

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more than a decade when it comes to international stock market comparisons. There finally is the issue of causality, namely to what extent exchange market dynamics dominate the stock markets; or vice versa. Hence there is a broad research agenda for open economies with capital mobility and innovation under flexible exchange rates.

Appendix F.1: Slope of Equilibrium Lines MM-Kurve:   P K M M eF∗ ∗ E = n(V, i + a , z, ) + + P P P P ⇔ −n(V, i∗ + aE , z, )

  eF∗ M P K M = n(V, i∗ + aE , z, ) + − P P P P

⇔ n(V, i∗ + aE , z, )eF∗ = −n(V, i∗ + aE , z, )(M + P K) + M ⇔ eF∗ = −(M + P K) + K ⇔ e = − ∗ P + F



M n(V, i∗ + aE , z, )

K M − F∗ n(V, i∗ + aE , z, ) F∗



K de =− ∗  dP F

(29)

F∗ F∗ -Kurve:

  P K eF∗ M eF∗ ∗ E = f(V, i + a , z, ) + + P P P P

  eF∗ eF∗ M P K − f(V, i∗ + aE , z, ) = f(V, i∗ + aE , z, ) + P P P P   ∗  M PK eF ∗ E ∗ E (1 − f(V, i + a , z, )) = f(V, i + a , z, ) + ⇔ P P P ⇔

⇔ eF∗ (1 − f(V, i∗ + aE , z, )) = f(V, i∗ + aE , z, )(M + P K) ⇔e=

Mf(V, i∗ + aE , z, ) Kf(V, i∗ + aE , z, ) + P F∗ (1 − f(V, i∗ + aE , z, )) F∗ (1 − f(V, i∗ + aE , z, ))

de Kf(V, i∗ + aE , z, ) = ∗  dP F (1 − f(V, i∗ + aE , z, ))

(30)

Appendix F.2: International Bonds Market Integration, Interest Rates

243

KK-Kurve:

  M eF∗ P K P K = h(V, i∗ + aE , z, ) + + P P P P ⇔ P K = h(V, i∗ + aE , z, )(M + eF∗ + P K) ⇔ −eF∗ h(V, i∗ + aE , z, ) = h(V, i∗ + aE , z, )(M + P K) − P K ⇔ −e =

−h(V, i∗ + aE , z, )(M + P K) + P K F∗ h(V, i∗ + aE , z, )

⇔e=−

P K P K M − ∗ + ∗ ∗ ∗ F F F h(V, i + aE , z, )

K K K(1 − h(V, i∗ + aE , z, )) de =− ∗ + ∗ =  ∗ E dP F F h(V, i + a , z, ) F∗ h(V, i∗ + aE , z, )

(31)

Appendix F.2: International Bonds Market Integration, Interest Rates and Stock Market Volatility In the last quarter of the twentieth century financial market integration has made enormous progress as capital flows have been liberalized and privatization and lifting restrictions to FDI inflows have created new opportunities for cross-border capital flows. Changes in exchange rate regimes also have affected international financial market integration, but we will ignore this aspect here. The issue we are interested in is simply the following: How will an increase in international bonds market integration affect stock market prices and interest rates—and in particular we would like to know how changes in the capital stock will affect the model. The model is simple and consists of the domestic bonds market, the domestic money market, the foreign bonds market and the domestic stock market. With respect to the impact of asset yields we assume that all assets are gross substitutes. Money has a yield of v (marginal utility of money—this is exogenous here), short-term domestic bonds carry interest rate i, foreign bonds F the foreign interest rate i∗ . The nominal exchange rate is e. B is the stock of domestic bonds, M the stock of money, K the stock of capital, P is the price level of goods, P is the stock market price index. The marginal product of capital is z , and the demand for stocks is a positive function of z , a negative function of the two interest rates and of v. The desired shares of assets in total wealth are denoted by n , b, f and h; namely for money, domestic bonds, foreign bonds and stocks, respectively. Moreover, we assume that demand for each asset is proportionate to real wealth A = M/P + B/P + eF∗ /P + P K(1 − δ)/P; thus it holds that n + b + f + h = 1. We assume for simplicity an instantaneous capital depreciation whose rate is δ. Only three equations out of the four equilibrium conditions for the four asset markets are independent. We will consider only the two bonds markets (BB line for domestic bonds market equilibrium, FF line for equilibrium for foreign bonds) and the stock market (KK line). For simplicity,

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we assume that expected stock market price changes are zero and expectations are static. The endogenous variables in this implicit two-country model—with flexible exchange rates—are the domestic interest rate i, the exchange rate and the domestic stock market price index P . We will assume that FDI flows are the only type of capital flows existing. As it is interesting to consider the role of FDI inflows D in the home country (country I)—where we only focus on international mergers & acquisitions; according to FROOT and STEIN (1991) D is a positive function of the real exchange rate q∗ := eP∗ /P as in imperfect capital markets a real depreciation of the exchange rate raises the amount of potential foreign investors’ equity capital expressed in terms of country I currency. Additionally we assume that foreign investors taking over a publicly quoted stock company will transform it into a limited liability company which is the typical pattern observed in OECD countries. Moreover, we assume that any excess supply of stocks will result in higher FDI inflows (the home country is small relative to the world real capital market). Hence the real value of stocks—with the number of real capital units initially being equal to the number of stocks—is reduced in accordance with D. Note that we have assumed that there is instantaneous capital depreciation where the depreciation rate is δ. The equilibrium conditions for the four markets are given (with the left-hand side denoting the supply side) by M/P = n (v, i, i∗ , z )A

(1)

B/P = b(v, i, i∗ , z )A

(2)

eF∗ /P = f(v, i, i∗ , z )A

(3)

P K[1 − δ]/P − D (q∗ , excess supply in stock market) = h(v, i, i∗ , z )A

(4)

Appendix F.2: International Bonds Market Integration, Interest Rates P′

245

FF1′

BB0

FF1

H P′2

FF0

D′

G

D

P′0

E

F

P′1

F′ C

KK1 KK0

KK2

i1 i 3

0

i0

i4 i2

i

Fig. 56 International bonds market integration, stock market volatility and interest rate volatility

dP /di = ni /K(1 − δ) + 1/K(1 − δ)((1/ni − 1)dM/di ∗



(1)

∗



− dB/di − deF /di − A P(nv dv/di + ni∗ di /di + nz dz /di)) dP /di = bi /K(1 − δ) + 1/K(1 − δ)((1/bi − 1)dM/di ∗



(2)

∗



− dB/di − deF /di − A P(bv dv/di + bi∗ di /di + bz dz /di)) dP /di = fi /K(1 − δ) + 1/K(1 − δ)((1/fi − 1)dM/di − dB/di ∗



∗



(3)



− deF /di − A P(fv dv/di + fi∗ di /di + fz dz /di)) The system determinant is: U = F∗ K(1 − δ)(bi n − ni b)/P2 < 0

(4)

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This leads to the multiplier: de/dM = −(bi f − fib)/F∗ (bi n − ni b) < 0

(5)

The slope of the KK curve in P –i space is negative as is the slope of the BB curve. The slope of the FF curve is positive. Concerning cyclical aspects, we assume that during unanticipated recessions the deprecation rate will increase while during booms it will fall. This implies that in P –i space a boom is indicated by an upward shift of the KK line—from KK0 to KK1 ; in a recession there is a downward shift from KK0 to KK2 . A rising degree of international financial market integration in the sense of domestic bonds becoming closer substitutes to foreign bonds implies that the absolute value of the partial derivative ∂f/∂i has increased. Hence the FF curve becomes steeper—and indeed the FF0 curve is rotating upwards in point C which will cause a rise of the stock market price and a fall of the interest rate: The instantaneous intersection point is G; however, as G stands for an excess supply in stock market which will translate in higher FDI inflows so that the KK curve shifts to the right (not shown in the graphic): Point H is the final intersection point; the effect of a higher FDI inflow is a rise of stock market price and a slight increase in the interest rate—but the interest rate still is lower than initially. Note that a rise of FDI inflows might have occurred endogenously through a nominal and real exchange rate depreciation (this will cause a rise of the real supply of foreign bonds). Thus increasing financial market integration reduces the nominal interest rate; and it raises the stock market price and FDI inflows. If inflation remains constant the real interest rate also will fall. From an EU perspective the creation of the Euro has contributed to raising the substitutability between $ denominated bonds and Euro denominated bonds—the size of the Euro zone is closer to that of the US than the previously relevant pair DM zone compared to the US. In the perspective of the simple model presented the impact of greater substitutability of domestic bonds and foreign bonds is a fall of the interest rate and a rise of the stock market price index. However, we also are interested to understand the pure effect of the FF curve becoming steeper so that we draw the new FF curve through the initial intersection point of all three curves. This initial equilibrium point determines P0 and i0 . It is interesting to consider the case that monetary authorities will embark upon an expansionary open market operation (leaving real wealth unaffected). If one compares the impact of cyclical movements in the KK curve for the case of FF0 and FF1 the conclusion is clear: • International bonds market integration will increase stock market volatility (compare points D and F with F and D). • International bonds market integration will reduce interest rate volatility. This raises the question what the impact of greater stock market volatility and lower interest volatility will be. One should note an important caveat here, namely that monetary policy might change its strategy once it has noted the increased international bonds market integration.

G. Innovation Dynamics and Optimum Growth

G.1 Introduction Standard and New Growth Theory In all industrialized countries, achieving sustained economic growth in the sense of a long-run increase of output or output per capita is a crucial goal. From a neoclassical perspective, the basic growth models of SOLOW (1970) emphasize the role of the production function—and the respective input factors capital and labor—and the savings rate, respectively. Growth is modeled as a steady-state equilibrium phenomenon which is characterized by accumulation dynamics for capital and certain parameters of the utility function (DIXIT 1976). Modern growth theory to some extent has added emphasis on the role of human capital formation (LUCAS 1979), but the mechanics of the basic neoclassical growth model can be retained if one interprets capital as human capital or skilled labor. Standard growth theory suggests that accumulation dynamics of capital determine long-run equilibrium output per capita. The simplest model is based on the assumption that savings S = sY (with Y standing for real income) and that the growth rate of the population L is n while per capita output y = f(k); k is the capital intensity K/L (K is the capital stock) and the production function is well-behaved, that meets Inada conditions. Imposing the equilibrium condition that investment I = S we can summarize the accumulation dynamics in such an economy as follows: dk/dt = sf(k) − nk

(1a)

If we assume that f(k) = kß —so that output is determined by a Cobb–Douglas production function (with 0 < ß < 1)—we can easily solve for the steady-state solution by setting dk/dt = 0: skß = nk.

(1b)

Hence the steady-state solution for k is given by k# = [s/n]1/(1−ß) P. J. J. Welfens, Innovations in Macroeconomics, DOI 10.1007/978-3-642-11909-5_7, © Springer-Verlag Berlin Heidelberg 2011

(1c) 247

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y# = [s/n]ß/(1−ß)

(1d)

As population dynamics (with e denoting the Euler number) are given by L(t) = L0 ent we have equilibrium output determined by Y(t) = L0 ent [s/n]ß/(1−ß)

(1e)

In the long run—in the steady state—output Y grows with the exogenous growth rate n; the level of the growth path is higher, the higher s and the lower n are.

Technological Progress If one assumes that savings S = sY, a stationary population and that savings S equals investment I = dK/dt while there is labor-augmenting Harrod-neutral progress in the production function so that output Y = Kß [AL](1−ß) , one obtains—with a denoting the exogenous growth rate of A(t)—a slightly modified equation for the accumulation dynamics of k := K/[AL] where k is dubbed capital per efficiency unit of labor: dk  /dt = sk  − ak  ß

(1f)

We might further refine this equation by introducing population growth (growth rate n) which leads to [a + n]k as the second right-hand side term in the equation for the accumulation dynamics: dk  /dt = sk  − [a + n]k ß

(1f )

The solution of this Bernoullian differential equation is (with C0 to be determined from the initial conditions and e denoting the Euler number; see appendix) k  (t) = {C0 e

−[a+n](1−ß)t

+ [s/[a + n]]}1/(1−ß)

(1f )

Clearly, there is a convergence for k as long as ß < 1; and one should add: As long as the growth rate n is not critically negative, that is the shrinkage speed of the population must not exceed a—obviously a problem which a priori cannot be dismissed for the case of ageing societies with declining population. The steady-state value for k is k  # = [s/[a + n]]1/(1−ß)

(1g)

Per capita consumption in the steady state is given by the difference of per capita output and investment per capita (I/L), that is C/[AL] = f(k ) − [I/L]#; as [I/L]# is equal to (n + a)k maximizing per capita consumption requires—with c := C/[AL] as a necessary condition: dc /dk  = f  (k  ) − (n + a) = 0

(1g )

G.1 Introduction

249

f  (k  #) = n + a

(1g )

Let us point out one important aspect: In the case of a Cobb–Douglas production function, the marginal product of capital is given by f (k ) = ßkß−1 . If one assumes that firms also maximize profits and hence f (k ) = r, the optimum growth policy is defined by the condition: r = ßk

ß−1

=a+n

(1g )

Therefore, k

opt

= {ß/[a + n]}1/(1−ß)

(1g )

Obviously this coincides with (1g) only if s = ß. Since ß in industrialized countries roughly is 1 / 3 and since savings ratios in most OECD countries are only around 20% it seems that the major challenge for a government interested in maximizing long-run per capita consumption is to indeed raise the national savings rate. From an empirical perspective it is, however, unclear to which extent ß is changing in the course of technological development; as regards the expansion of the digital “New Economy” one may anticipate that the ß, the production elasticity of capital, will increase. We also could add capital depreciation at rate δ so that the second right-hand term in the above equation becomes [a + n + δ]k ; this will not affect the mechanics of the model in a critical way. All this is in the framework of standard textbook growth analysis (see, e.g., JONES 1998), and it is indeed a good starting point for some theoretical progress and certain refinements and theoretical innovations. Before we take a look at those it is useful to briefly recall some key insights from the optimum growth theory in the traditional sense, namely of neoclassical growth models that have been used to derive optimum growth policies (PHELPS 1961; WEIZSÄCKER 1962): In those models, government can achieve maximum per capita consumption if the savings rate is manipulated in a certain way; in an economy with a constant growth rate of the population (n), profit-maximizing firms, no technological progress and zero capital depreciation the optimum growth policy is characterized by the equality of n and the real interest rate r. Since output growth in the steady state is equal to n the implication is that the growth rate of output is equal to r. GROSSMAN/HELPMAN (1991) have presented broad analytical progress in growth modeling, however, the issue of optimum growth was not picked up. AGHION/HOWITT (1998) presented new ideas about endogenous (New) growth; in particular they have emphasized the role of innovation. The result in a model in which consumers discount utility—thus going beyond the traditional approach—is not much different since maximizing the welfare function F (with U denoting Utility relevant for an integral from 0 to infinity, per capita consumption c , e the Euler number and ρ the rate of time preference) to be maximized is F = U(c t)e − ρtdt subject to dk /dt = f(k ) − c − (n + a)k  which gives—with denoting the current-value shadow price—the Hamiltonian:

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Innovations in Macroeconomics

 H = U(c t)e −ρtdt + λ[f(k )−c −(n+a)k  ]. The optimality conditions (∂H/∂c = 0 and ∂H/∂k = −dλ/dt) give the Ramsey rule: r = −dlnU (c )/dt + ρ + n + a. In the steady state—where c is constant and hence the growth rate of the marginal utility U is zero—we thus get r = ρ + n + a. As we are not so much interested in the role of the time preference, we will not rely on the complex Hamiltonian approach. Rather a simple graphical model is sufficient to bring out the main critical results. The reader interested in the role of time preference can replace in the relevant steady-state condition n through n + ρ if he wants to highlight the role of ρ. One may also note that adjusting the utility function in a way which contains both c and k —or more generally wealth—gives only a minor modification. The optimum steady-state k# is rises in comparison with traditional optimum growth approaches. In the subsequent analysis, we at first are interested in endogeneizing technological progress. The following section takes a closer look at some key issues of endogenous growth and proceeds with combining optimum growth approaches and endogenous growth modeling; we also will consider the role of long-run relative price changes in the context of technological progress. The analysis presented then leads to several interesting policy conclusions related to growth policy and innovation policy, respectively. The main conclusions clearly go beyond the standard analysis in the literature and basically suggest considerable changes in economic policy in both advanced and catching-up countries.

G.2 Endogenous Growth, Innovation and Maximum Consumption per Capita G.2.1 Optimum Endogenous Growth The standard optimum growth literature of PHELPS (1961) and WEIZSÄCKER (1962) has established for the case of a closed economy that within a neoclassical growth model the optimum growth—defined by maximization of steady-state per capita consumption C/L—is determined by the condition that in the absence of technological progress, the growth rate of the population n is equal to the marginal product of capital YK ; moreover, in a world of implicit profit maximization and zero capital depreciation this also implies the real interest rate r = F (k) = n, where F (k) is the marginal product of capital (alternatively we denote the marginal product of capital asYK ); the function y = F(k) is linear homogenous, y =Y/L is per capita output and k := K/L capital intensity. From an optimum growth perspective, a government’s growth policy should aim to manipulate the savings rate s—establishing indeed a new adequate savings rate s —in a way such that the intersection point of the curve nk with sF(k) is such that for the respective k# the slope of the F(k) curve is equal to n.

G.2 Endogenous Growth, Innovation and Maximum Consumption per Capita

251

Similarily, if there is Harrod-neutral technological progress we have a production function Y/[AL] = f(k ) where k = K/[AL]; graphically the steady-state value k # is determined by the intersection of [n + a]k and the curve sf(k ) as shown in point E0 . In the steady-state output, Y will grow at the rate n + a. Again, government could consider the topic of optimum growth, namely maximizing consumption per capita in the steady state. As y = C/[AL] + I/[AL] it is clear that point kopt is the optimum (DE1 is parallel to the curve [n + a]k ), and it will be achieved—see the subsequent figure— if government reduces the savings rate to s . In the implicit case of profit maximization the optimum is characterized by the equality of r and the marginal product of capital f (k ) and hence by r = f (k ) = a + n. Note that in the model profit maximization is introduced here in an ex post fashion, there is no endogenous mechanism which drives the economy toward kopt . dk'/dt C/(AL)

f(k') [n + a]k' E1

E0

sf(k')

D s'f(k') F

Fig. 57 Optimum growth in the standard model

α 0

k'opt

k0#'

k'

The standard optimum growth approach takes the population growth rate n as given and suggests that government should adjust the aggregate savings rate s; indeed government could do so by adjusting the government budget deficit–GDP ratio in an appropriate way.

G.2.1.1 Role of Government Consumption In the case of a constant Harrod-neutral progress rate a, the mechanics of the neoclassical growth model remain the same as in the basic model. An interesting refinement suggested here is to analyze the role of government consumption G under the simple assumption that G = γY and that private consumption and government consumption are full substitutes while γ negatively affects the progress rate as we assume a = a1 (1 − b γ) where a1 is the progress rate which would hold without government consumption and b is a positive parameter in the interval [0, 1]. Progress is still exogenous here as γ is exogenous. Ruling out government deficits and therefore taking

252

Innovations in Macroeconomics

into account that γ = τ (where τ is the income tax rate) the accumulation dynamics now are given by dk  /dt = s[1 − γ]k − [a1 (1 − b γ)]k  ß

(1m)

The effect of government consumption on long-run growth and technological progress is negative. However, the effect of γ on the level of the growth path is ambiguous since the steady-state solution is given by k  # = {s[1 − γ]/[a1 (1 − b γ)]}1/(1−ß)

(1n)

The numerator in the above expression is reduced by rising government consumption so that the s[1 − γ]k ß curve—in dk /dt − k space—is bending the more downward the higher γ is. However, the ray OF (for γ = 0) showing [a1 (1 − b γ)]k is also rotating downward (see OF for a certain γ in the interval [0, 1]) so that k # could rise or fall as the consequence of relatively higher government consumption. Our analysis thus raises some interesting questions about the role of government in a neoclassical growth model. Politically optimal growth obviously can diverge considerably from what is optimal from a situation in which perfectly informed rational economic agents are interacting. If the government in an economy with profit maximization wants to maximize long-run per capita consumption while ignoring the link between γ and the progress rate the optimum k is given by the condition: r = [a1 (1 − b γ)]

(1n )

dk'/dt

H

H'

f(k') F sf(k')

E0 E1

Fig. 58 Government consumption and the steady state in a neoclassical growth model

0

k0#'

k1#'

F' s(1 – γ)f(k')

k'

G.2.1.2 New Political Economy From the perspective of New Political Economy, the case of a rise of the level of the growth path is particularly interesting. Under a myopic government or in the presence of myopic voters, one could not rule out that government will adopt a kind

G.2 Endogenous Growth, Innovation and Maximum Consumption per Capita

253

of short-run maximization of consumption (either pure consumption of households or the sum of private and public consumption), taking into account effects of γ on the level of the growth path and on long-run growth rate itself: Government would adopt a policy—based on raising the ratio of government consumption to GDP— which raises the level of the growth path while lowering the long-run growth rate; the initial per capita output path VJ would be given up in point t in order to switch to the new path V J . If voters are sufficiently myopic and thus consider the increase in output as sufficiently attractive, government will be reelected through a policy which dampens long-run growth. There is some critical time horizon of voters marked by t  beyond which the trajectory with the low long-run growth path certainly would look inferior to voters when compared to VJ (the starting point here). A government aiming to realize V J would hope that for ordinary voters and even experts the overlap of changes in the level of the growth path and in the long-run growth rate is opaque on the one hand and on the other hand that the time horizon of voters is sufficiently short. Periods of war are particularly known to be characterized by a shortening of time horizon of individuals/voters, so that indeed the strategy described is particularly likely to be realized during war times (there is well-known positive historical evidence on this); and the existence of ratchet effects would then suffice to make the rise of γ a permanent phenomenon for a considerable time—until new generations of voters increasingly gain influence and start to look more critically at the choices at hand. The mechanism described would amount to an endogenous rise of γ and thus could be an explanation for the size of government in a growing economy. Note that if V J is the initial trajectory the adoption of a policy that raises the progress rate would—with effects realized after time t —lead to a transitory fall of the level of y which is followed by a higher y after time t (remember that in the standard growth model with exogenous progress and population growth the steady-state value of per capita income is y# = A0 eat (s/[a + n])ß/(1−ß) ).

lny

J' H

G

E0

α'

V

Fig. 59 Change of the level of growth path vs. growth rate

J

α

V'

0

t'

t''

t'''

t

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Innovations in Macroeconomics

Within the strategy described here politicians thus could exploit the bounded rationality of voters and economic actors, respectively. Since ROOS (2005) has provided empirical evidence that private households to a large extent disregard the opinion of experts on macroeconomic forecasting, it also is plausible that voters will widely ignore the message from empirical growth analysis that a high share of government consumption in GDP is undermining long-run growth. However, one may assume that in an economy with an increasing share of well-educated people the information costs about processing the information of experts will fall so that the resistance against an excessive government size will rise along with human capital. From this perspective, there might be a two-pronged impact of human capital formation on growth • The efficiency of production increases or the growth rate of technological progress rises; • The increase in the share of skilled workers reinforces the resistance against high government consumption, and the fall of government consumption—relative to output—will then translate into higher long-run growth. The second point should be expected to be relevant in democratic societies, not in countries with an authoritarian regime. From this perspective, the switch from autocracy to a democratic society, combined with increased human capital formation, could raise long-run growth.

G.2.1.3 High Population Growth vs. Ageing Societies Let us consider the role of the growth rate of the population in a quasi-endogenous growth model (here government variables can affect the progress rate). We assume that the growth rate of the population will reduce the savings rate since in industrialized countries with a rising growth rate of the population governments tend to adopt a pay-as-you-go public pension scheme so that private savings is reduced. Thus we get a modified equation for the accumulation dynamics in which the factor [1 − αn] indicates the impact of population growth on the savings rate (with s0 denoting the savings rate in a society with zero growth of the population). Moreover, we assume that the growth rate of Harrod-neutral technological progress is affected by the growth rate of the population—it is likely to negatively affect the progress rate since a higher n means a greater abundance of labor and thus less incentives for research and development with a focus on labor-saving progress. At the same time, we assume that (modest) tax pressure stimulates innovation since firms will try to evade labor-intensive sectors in which high social security contributions are part of production costs. Denoting the progress rate at zero population growth with a0 , we can describe the progress rate as a = a0 − a1 n + a2 τ (a1 and a2 are positive parameters). The accumulation dynamics is now given by dk  /dt = s[1 − αn][1 − τ]f(k  ) − [n + a0 − a1 n + a2 τ]

(1o)

G.2 Endogenous Growth, Innovation and Maximum Consumption per Capita

255

In the case of a Cobb–Douglas function y = kß we get as the steady-state value k #: k  # = {s[1 − αn][1 − τ]/[n(1 − a1 ) + a0 + a2 τ]}1/(1−ß)

(1p)

The s[1 − τ][1 − αn] curve is the more bending downward the higher n and a are; and the higher the tax rate τ—necessary to financing social security benefits—is. At the same time, the denominator in the above expression is reduced through the term a1n but raised through the tax pressure effect so that the effect of population growth on the long-run capital intensity and the progress rate—and hence growth—is ambiguous. Only careful empirical investigation can clarify the issues raised here. Countries with ageing societies and declining population growth, respectively, are facing two key problems: • n becomes negative; • the tax rate (social security contribution rate) for financing public pensions systems rises. The level of the growth path is thus reduced, but the progress rate could increase. The net effect of both influences on the level of the growth path and the growth rate itself has to be analyzed also in empirical studies. Assuming that government is myopic and thus neglecting the impact of its policy on the progress rate a quasi-optimum growth policy thus is defined by the condition: r = [n(1 − a1 ) + a0 + a2 τ]

(1p )

Government can use tax policy to achieve this. A rise of the real interest rate thus would have to be accompanied by a rise of the tax rate. If government takes into account the short-term cyclical dynamics of the economy and the likely negative effects of such a policy mix—read restrictive monetary policy and restrictive fiscal policy—government will fail to adopt the suggested long-term strategy. It is indeed an interesting finding that there is a potential trade off between short-term cyclical strategies and long-run growth policy options of government. G.2.1.4 Unemployment and Growth Finally we take a look at basic unemployment aspects within a growth model. We assume that unemployed people are not saving or even dissaving so that aggregate savings S is given by S = s(1 − u u)Y where u is the unemployment rate—defined as unemployed L relative to all workers L—and u a positive parameter. The unemployment rate is determined by collective bargaining decisions which are exogenous here. As there is an unemployment insurance there also must be taxes to finance benefits for the unemployed. The benefits are assumed to be proportionate to the per capita income Y/L; u (falling in the interval [0, 1]) is a positive parameter. Government expenditures thus are given by uLuY/L; and these are the only government expenditures considered here. Denoting tax revenues as T the accumulation dynamics are now determined by S + T = dK/dt + uLu (Y/L)

(1q)

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Assuming that tax revenue T = τy and dividing by AL gives S/[AL] + τY/[AL] = [dK/dt]/[AL] + uu (Y/[AL])

(1r)

Hence the accumulation dynamics read for the case of zero population growth and an exogenous unemployment rate u and a negative link—reflecting increased workers’ resistance against technological progress in a society with unemployment—between the progress rate a and u (expressed as a = a0 − U u where the parameter U falls in the interval [0, 1]; a0 is the progress rate at full employment). dk  /dt = sk  + τk  − uu k  − [a0 − U u]k  ß

ß

ß

(1s)

Note here that we have used Y = Kß [(1 − u)L]1−ß so that y = kß (1 − u)1−ß and thus S = skß (1 − u)1−ß . The steady state for k# is now given by k  # = {[s(1 − τ) + τ − uu ](1 − u)1−ß /[a0 − U u]}1/(1−ß)

(1t)

If the unemployment rate would not affect the progress rate, the implication simply would be that that the unemployment rate reduces the steady-state k and hence the level of the growth path of the per capita income y. However, here we focus on the progress function a = a0 − U u. As regards the impact of the unemployment rate on steady-state capital intensity the result is clear: There will be an upward rotation of the per capita investment curve and hence the nominator in the above expression is raised. At the same time the denominator is reduced. From a welfare economic perspective the unemployment rate has, however, two negative effects: Unemployment itself is undesirable from the perspective of workers—and even of those who are employed as they interpret positive unemployment rates as a risk of losing the job in the future; moreover, the unemployment rate reduces the progress rate and hence long-run growth. In an economy with unemployment, it is difficult to define an optimum growth policy. Only as a second-best policy one may consider that government adopts a policy which is characterized by the equation r = [s(1 − τ) + τ − uu ](1 − u)1−ß = [s + τ(1 − s) − uu ](1 − u)1−ß

(1t )

Government can respond to a change in the long-run real interest rate by adequate changes in the tax rate: A rise of r must go along with a rise of the tax rate, however, this policy mix is likely to undermine cyclical growth and hence government might instead prefer to reduce unemployment benefits (parameter u”).

G.2.2 Optimum Growth and Endogenous Growth Modeling in Open and Closed Economies The traditional optimum growth model assumes a given rate of population growth, a given relative price of capital goods and is assuming that the aggregate savings rate

G.2 Endogenous Growth, Innovation and Maximum Consumption per Capita

257

should be manipulated by government intervention, namely for the sake of maximizing long-run per capita consumption. Subsequently we will at first assume that the savings rate of private households indeed is the result of individual optimization approaches and that the government budget is fully determined by government expenditures on research and development (R&D); thus there is no room for manipulation of the savings rate. Moreover, as we will assume endogenous growth in the sense that the progress rate is explained by certain variables, including government policy, we can develop a new concept of an optimum growth model. One variant presented will also relax the assumption of a constant relative price of capital goods. In an extension of the traditional model—and using for simplicity the Cobb– Douglas production function Y = K ß [AL](1−ß) and δ as the capital depreciation rate—we can introduce (endogenous) Harrod-neutral progress and capital depreciation so that the dynamic equation now is dk  /dt = sk  − (a + δ + n)k  ß

(1)

Optimum growth is achieved if the condition holds that (a + δ + n) = YK

(2)

r + δ = YK

(3)

As profit maximization requires

we obtain from both equations the condition relevant for optimum growth: a+n =r

(4)

Aspects of Taxation If government imposes an income tax rate τ, profit maximization in a closed economy requires r = [YK − δ][1 − τ]

(3 )

Note that in an open economy we would have instead r = [YK − δ][1 − ψ τ] where ψ reflects the degree of capital mobility; ψ approaches zero under infinite capital mobility, but in a closed economy it is equal to unity (0 ≤ ψ ≤ 1). Assuming that τ is small so that 1/[1 − ψ τ] ≈ [1 + ψ τ] we get r[1 + ψ τ] + δ = YK

(3 )

Opening up the economy will reduce the parameter ψ and thereby stimulate a transitory expansion of the economy, as the marginal product will tend to fall and hence

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k tend to rise. This might hold even more if (with * denoting foreign variables; E is the expectation operator and e the exchange rate) interest parity holds in the form r = r∗ + dlnE(e)/dt where the home country faces a nominal and real appreciation so that dlnE(e)/dt < 0. As YK is a negative function of k , it is clear that imposing a tax on capital income implies that the profit-maximizing k is lower than without taxation. The condition relevant for optimum growth is a = r(1 + ψ τ) − n

(4 )

The problem looks, however, somewhat different if the progress rate is positively affected by the tax rate since either tax rate pressure stimulates—below a critical threshold τ —innovativeness or as government uses tax receipts to promote research and development. Denoting the neutral progress rate as a0 —this is the progress rate in the absence of taxation—we get a0 (1 + a ψ τ) = [r(1 + τ) − n]

(4 )

Here the impact of the tax rate now is not much different from the world without government, so that the income tax rate here is rather neutral. Finally, we may have to consider that opening up—both in the form of trade and in the form of capital mobility—affects the progress rate positively; this case (with a  and a representing positive parameters and x and j standing for the export–GDP ratio and the import–GDP ratio, respectively) may be expressed for an initial situation of 0 < ψ < 1 as a0 (1 + a [x + j] + a /(1 − ψ ) + a ψ τ) = [r(1 + τ) − n]

(4 )

Impact of Capital Intensity on the Progress Rate We return to the situation of a closed economy. For simplicity let us assume here that the progress rate a depends on k and on the cumulated ratio (R) of research and development expenditures to national output, namely over the past from a distant point T to the present t = 0: a = T R + a k  ;

(5)

This is a simple progress function which has an exogenous part in the form of the first term where government determines once and for all R; and an endogenous part which is a k. A potentially interesting modification of this progress function could be to assume that the progress rate a depends negatively on the growth rate of the population: a = T R + a k  − a n. This variant—not further emphasized subsequently—implies that

G.2 Endogenous Growth, Innovation and Maximum Consumption per Capita

259

ageing societies will face a long-run decline of the progress rate unless government R&D promotion is raised adequately. With respect to open economies one also could include a technology gap element (a∗ is the progress rate abroad) in the sense that the progress function becomes a = T R + a  k  − a n + a  (a ∗ − a)

(6)

Let us now turn back to the simple approach a = T R + a k . For simplicity we assume that all R&D expenditures are indeed government expenditures. Thus then we have to replace s in the basic differential equation for k through s(1−τ) where τ is the average tax ratio on income; our specific assumption that real government expenditure (G) consist only of R&D expenditures indeed implies that S = I is consistent with the condition that the sum of savings plus tax payments (T), namely S + T = I + G. Note that the budget constraint for each period is τ=R

(7)

The optimum growth condition reads is now difficult to determine since the growth rate is no longer constant; a is a function of k ; however, we know that in the steady state T R + a  k  # + n = r

(8)

Policy Perspective This implicit condition for the optimum endogenous growth requires government to chose R in such a way that this condition is fulfilled. As ageing societies in Japan and the EU will face a medium term decline of n (see e.g., McMORROW/RÖGER 2004). Since the long-run world nominal interest rate i∗ may be considered as exogenous from the perspective of the EU and Japan, respectively, the Euro zone and Japan face a specific real interest rate r∗∗∗ consistent with nominal interest rate parity i = i∗ +ge where ge is the long-run depreciation rate of the Euro and the Yen, respectively (this rate could be considered as exogenous or related to differences in national savings rates). The real interest rate then is derived by subtracting the inflation rate from i. We may recommend to Japan and the Euro zone—both facing a long-run fall of n— to raise the progress rate through adequate long-run R&D promotion; deregulation and stricter competition policies as well as government support for venture capital also might be useful in this respect. From the perspective of the Euro zone the challenge would be for individual member countries to realize an optimum progress rate in the respective country (a special problem also is that national inflation rates differ considerably in the Euro zone so that a constant nominal global interest rate i not automatically will imply a uniform real interest rate for each member country). Given the findings of JUNGMITTAG (2004), who demonstrates that innovation

260

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dynamics are not generally converging across countries of the EU/the Euro zone, one could indeed consider a stronger emphasis on national innovation policies as useful from the perspective of an optimum growth policy in the Euro zone and the EU, respectively. To the extent global or regional competition bring about sustained pressure on governments to reduce the tax rate, there could be a critical divergence from the optimum growth policy; this then would give a rationale for cooperation in tax policies. From this perspective, the growth-enhancing strategy of the EU’s Lisbon Agenda neglects the issue of a common tax policy. There is a critical caveat: Greater cooperation in tax policies could, however, lead in reality not so much to higher R&D–GDP ratios but to higher expenditures on social security expenditures—relative to GDP— in ageing OECD countries. Another caveat concerns the challenge of integrating monetary aspects in the optimum growth model (see appendix). If one takes an illustrative look at the period 1960–2000, we have some interesting observations in the OECD. The implied optimum progress rate aopt —calculated on the basis of long-term real interest (r) rate minus population growth rate (n)—was low in has the 1960s in the technologically leading US, but it fell then in the 1970s under rather irregular circumstances, namely two oil price shocks and the inflationary policy of the FED (partly reflecting the impact of the Vietnam War). As regards the 1970s, a similar finding holds for the EU-15, while the implied optimum progress rate in Japan was positive (1%). In the 1980s the optimum progress rate reached rather high levels of slightly above 3% in the US and Japan and even 3.6% in the EU-15. In the 1990s, the optimum growth rate fell by almost a full percentage point in the EU-15, as the growth rate of the population increased while the real interest rate fell slightly. In the US, where the real interest rate fell a full percentage point as compared to the 1980s, the optimum growth rate fell to 2%. With the growth rate of the population in Japan reaching only 0.26% p.a.—a quarter of the figure in the 1960s and 1970s—and a fall of the real interest rate to slightly below 2%, the optimum progress rate fell to 1.7%. As regards the optimum progress rate, the differences across EU-15-USA-Japan were modest in the 1980s but much higher in the 1990s, which could imply considerable policy conflicts among OECD countries and within the TRIAD. As regards the actual rate of technological progress, there is a broad range of estimates of factor productivity growth. Here we rely on those of the European Commission which shows progress rates for the US of around 1% in all four decades of the period 1960–2000. The EU-15 performed better than the US in the 1980s, but it was slightly weaker in the 1990s. Japan had a very low progress rate in the 1990s. If the actual progress rate exceeds the optimum rate the implication is that profit maximization leads to a capital intensity below the social optimum; if the actual progress rate is smaller than the optimum progress rate profit maximization will lead to an excessive capital intensity (which is the case for the US in the 1970s and 1980s). The figures presented suggest that the growth rate of progress was close to the optimum in the US in the 1990s—but there was a large gap in the 1970s and 1980s; and as regards the EU it witnessed a relatively small gap in the 1990s—but the gap still was 1.6% points. Japan was relatively close to the optimum in the 1970s and 1990s. This suggests that economic policy could generate considerable benefits

G.2 Endogenous Growth, Innovation and Maximum Consumption per Capita

261

in OECD countries if the concept of optimum growth would be taken seriously. Judging by the figures for the 1990s the US and Japan should raise the progress rate and thus should increase public R&D support. The EU-15 had every reason to further stimulate the progress rate. If one would assume that the first decade of the twenty-first century will be similar to the 1990s it is obvious that the strong emphasis of the EU’ Lisbon Agenda on technological progress seems adequate despite the fact that the growth rate of the population is expected to slightly decline (as compared to the 1980s and the 1970s, the 1990s show a slight improvement for the EU, but the EU shows a large gap with respect to the optimum progress rate when compared to the case of the US and Japan in the 1990s). Table 8 Real interest rates∗ , population growth rates and progress rates in selected OECD countries (annual average growth rates). (Source: German Council of Economic Experts and AMECO databank (European Commission), own calculations) EU-15

1960–1970 1970–1980 1980–1990 1990–2000 ∗ Long-term

USA

Japan

r

n

aopt

r

n

aopt

r

n

Na −0.42 3.90 3.67

0.82 0.51 0.28 0.81

−0.93 3.62 2.68

1.54 −0.50 4.02 3.02

1.34 1.11 0.98 1.01

0.20 −1.61 3.04 2.01

na 0.18 3.69 1.92

1.12 1.18 0.56 0.26

aopt 1.00 3.13 1.66

nominal interest rate minus growth rate of GDP deflator; a opt = r − n

Table 9 Actual vs. optimal total factor productivity growth in selected OECD countries. (Source: AMECO Database, own calculations) TFP Growth Rates

1960–1970 1970–1980 1980–1990 1990–2000

EU-15

USA

a

aopt

3.10 1.63 1.09 1.05

− −0.93 3.62 2.68

a−

aopt

− −2.56 −2.53 −1.63

Japan

a

aopt

−aopt

A

aopt

1.79 0.72 0.83 1.14

0.20 −1.61 3.04 2.01

+1.59 −2.33 −2.21 −0.97

6.91 1.98 1.67 0.35

− 1.00 3.13 1.66

a − aopt − +0.98 −1.46 −1.31

G.2.3 Biased Technological Progress and Optimum Growth The New Economy—with digital products and ever-cheaper computers—has been characterized by an enormous long-run fall of relative prices of computer equipment and more generally of capital goods (disregarding real estate and land). From this perspective it is interesting to consider the impact of biased technological progress which is defined here by its impact on the relative price of capital goods: Assume that the Harrod-neutral progress rate will lead to a relative fall of the price of capital goods p = PK /P(PK is the price of capital goods and P the price of newly produced output which in a two-sector economy will consist of a sub-price index for consumption

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goods and a sub-price index for investment goods). We subsequently assume that the change in the relative price is given by dlnp/dt = −a0 a;

where 0 ≤ a0 < 1

(9)

Profit-maximization requires that YK = r + δ − dlnp/dt

(10)

As the change of the relative price is (using a positive parameter a 0 in the interval [0, 1]) governed by dlnp/dt = −a0 a, we get YK = r + δ + a 0 a

(10 )

(a + δ + n) = YK

(11)

a[1 − a0 ] + n = r

(12)

Optimum growth requires that

The optimum progress rate now is given by a opt = [r − n]/[1 − a0 ]

(13)

As an illustrative initial example, assume that the long-run real interest rate r is 3%, long-run population growth 1% and a  0 = 0.5, then the optimum growth rate of technological progress is 4%. If, however, a  0 is 2/3 the optimum progress rate would be 6%. Thus—and adopting a normative perspective—the switch to a New Economy in the 1990s (AUDRETSCH/WELFENS 2002; BARFIELD/HEIDUK/WELFENS 2003) which brought a rise of the impact of a on the relative price change (a 0 increased to a 0 )—should go along with a rise of the optimum progress rate. To date, governments have not responded to the relative fall in capital goods prices in the 20 years after 1985. If the population growth rate falls to −1% the optimum progress rate—with ao assumed to be 0.5—is increasing: 8% is now the optimum growth rate of technological progress. This points to the need that governments in ageing societies (with n falling in the long run) should strongly reinforce R&D promotion. No such policy strategy has been adopted thus far in OECD countries, except for the EU’s Lisbon Agenda perhaps, which aims to stimulate innovation dynamics by lifting the Community’s R&D–GDP ratio to 3% (the EU approach has, however, never made any reference to optimum growth approaches).

G.2 Endogenous Growth, Innovation and Maximum Consumption per Capita

263

G.2.4 Efficient vs. Optimal International Specialization In the traditional optimum growth theory (following the golden rule established by PHELPS and VON WEIZSÄCKER) it is emphasized that the steady-state ratio of capital to labor in efficiency units is not necessarily identical to that ratio k #opt which maximizes long-term per capita consumption and the level of the growth rate of per capita consumption. As per capita consumption is maximized if k # is such that at this ratio the slope of the tangent at the production function is equal to n + a + δ we face an interesting problem—not treated in the literature thus far—with respect to international specialization once we implicitly consider a two-sector economy: The ∗ initial “non-golden intersection points” of the curve sk ß and the (n + a + δ)-line in country I and of s∗ k ∗ß∗ and the (n∗ + a∗ + δ∗ )-line in country II could be such that k  #0 exceeds k ∗ #0 so that—according to the Heckscher–Ohlin–Samuelson approach— the home country should specialize in capital-intensive goods and country II in labor-intensive goods; while a corresponding adjustment might bring specialization gains for both countries and thus effectively raise the progress rate in both countries. In an open economy there is, however, the topic of optimum international specialization which is not trivial at all since—as is argued here—it is not easy to determine which country has a relatively higher capital intensity: The term relative capital intensity indeed might refer to the actual capital intensities abroad or at home; alternatively, one may want to focus on the capital intensities occurring in a (hypothetical) global state of the golden age which maximizes per capita consumption in both countries. Global golden state is defined here in that way that both countries are in the golden age; that is the golden rule has been realized in all countries (the respective capital intensity of this optimum state is denoted as k opt ). If the respective golden rule capital intensities k opt and k ∗opt , respectively, are such that the relative ordering changes, namely k opt < k ∗opt (alternatively, initially k  #0 < k ∗ #0 while in simultaneous golden rule states: k opt > k ∗opt ), we have an interesting ambiguity about efficient international specialization (here we are not dealing with the relatively trivial case that there is no qualitative difference between initial ratios in a steady state and the ratio of steady states in the golden global age). While initial non-golden steady states in both countries have implied that country I should specialize on capital-intensive goods while country II should specialize on laborintensive goods, the global golden rule suggests just the opposite: Country I should specialize in labor-intensive goods production while country II should specialize in capital-intensive production (see the subsequent graph). A global golden state may be dubbed Golden Optimal Specialization. If adjustment costs from switching from capital-intensive specialization to laborintensive specialization would be rather high it might be even advisable—assuming a rather short political capitalization horizon in both countries—to stick to the initial non-golden specialization. As a policy implication one may conclude that government planning intervention in catching-up countries are wise to consider options to realize the golden rule from the outset; and this all the more the poorer the respective country is. If more developing countries were to follow the golden rule there

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Fig. 60 Issue of efficient specialization vs. golden optimal international specialization. a country I, b country II

F

k'β

F' α G

E

E’

(n + a + δ)k' s0k'β s1k'β

α

a

k'opt

0

k0'#

F'*

E'* E*

b

0

k0'*#

k'*opt

k'

k'*β

(n*+ a* + δ*)k'* s1*k'*β s0*k'*β

k'*

obviously would be less starvation and malnutrition (and migration) in the world economy since per capita consumption levels in poor countries would be higher than otherwise. For development policy the topic discussed here also could be quite interesting since it does not make much sense to give high development aid to poor countries whose governments are unwilling to move the economy into the gold age as defined by growth theory. It would be a useful task of the World Bank to calculate the conditions for fulfilling the golden rule in various countries. Countries willing to indeed implement the golden rule should get a bonus in development aid. In a broader perspective it would be useful if all OECD countries and indeed many other countries would calculate the golden rule capital intensity. If both firms and countries undertake specialization according to the golden age rule abroad and at home we have “golden efficient specialization” and such a state of the world economy indeed is desirable from a normative point of view— assuming that governments (and indeed voters) want to maximize sustainable per capita consumption.

G.3 Policy Implications If the business community brings about a socially optimum progress rate by itself there is, of course, no need for government intervention. This holds particularly

G.3 Policy Implications

265

because government intervention itself typically entails certain costs to society, including rent-seeking activities. If, however, the business community does not bring about an optimum progress rate, government should carefully consider efficient ways to promote research and development/technological progress, respectively. In an open economy with a low per capita income this typically will also include incentives for diffusion and foreign direct investment, respectively (JUNGMITTAG/WELFENS 2003). In addition, trade liberalization might contribute to efficiency gains. Enhancing trade could stimulate competition and thus can enhance international diffusion of new technology so that the level of technology A(t) in the relatively poor country will catch up more quickly with the level of technology A∗ (t) of the leading economy. Foreign direct investment is also known to be an important route for international technology transfer. Governments in ageing societies should reinforce promotion of innovation dynamics where measures could include impulses for broader and better human capital formation and higher R&D expenditures as well as better exploitation of global technological progress through raising inward foreign direct investment and outward foreign direct investment—the latter in leading industrialized countries, as only in those countries does the sourcing of advanced technologies through subsidiaries seem to be relevant. Growth policy should be adequately redefined in OECD countries, namely within the framework of optimum growth models under endogenous technological progress. This would be a major step forward to making the traditional and the new growth theory more fruitful for policymakers. Within a G-8 framework, it is rather obvious that there will be considerable differences in preferred strategies since the optimum progress rates implied for individual countries differ. As regards the role of international organizations such as the the World Bank or the IMF—or the EU and the EBRD in a regional (European) context—it would be wise to place emphasis on aspects of optimum growth policies. The benefits of optimum growth policies could be considerable not only in OECD countries but in newly industrializing countries as well. As the goal of optimum growth policy is to raise consumption per capita—in many poor countries implying a higher survival rate and hence endogenous growth of the population—there should be clear benefits in catching-up countries. However, there are three caveats as regards the role of optimum growth policy: • Politicians interested in optimum growth policy should adopt a long-time horizon, and it is unclear whether such a long-time horizon can realistically be expected; • policymakers in many countries will be tempted to translate a stronger emphasis on innovation policy in expansion of protectionist industrial policy which favors selected sectors—possibly including decline ones—and impairs free trade and a level playing field of foreign investors; due to growing economic inefficiencies such a policy is likely to impair growth and maximum long-run per capita consumption; • there will be serious problems with data forecasting over a long-time period relevant for growth policy; within an optimum growth policy one will have to

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rely on solid empirical data and modeling. Here policymakers should invest more in empirical analysis. As regards the EU the SAPIR Report (SAPIR ET AL. 2004) has made useful proposals on how to enhance European economic growth and innovation, respectively: Stronger promotion of R&D, opening up of markets and deregulation as well as reforms of the EU budget were key aspects discussed in that report. The analysis presented here adds new elements to the options for growth-promoting economic policy—both in Europe and elsewhere. Our analysis suggests that governments which adopt an optimum growth approach will realize major benefits for consumers and voters, respectively. The paper also has raised interesting empirical issues, including the question about the progress function. Here, the aspect of declining population growth is of particular interest.

Appendix G.1: Optimum Quantity of Money Traditionally, growth models have rarely been linked to monetary policy issues, although PATINKIN on the one hand and TOBIN and JOHNSON on the other introduced money in growth models from the supply side and the demand side, respectively (survey: SIJBEN 1977). Monetary policy has been discussed mostly in the context of cyclical issues in the literature. The role of inflation in growth models was first considered by SIDRAUSKI (1967), SINAI/STOKES (1972) emphasized the role of money in the production function and fiscal policy issues in a growing monetary economy were introduced in the literature by STEIN/ INFANTE (1980). Our perspective is different since our starting point is a model with technological progress and since we focus on linking money and growth through the optimum growth condition, which requires in the simple form that the real interest rate r = a + n. Hence we raise the question of how long-run monetary policy must be conducted to be consistent with optimum growth in a closed economy. If we assume that real money demand per efficiency unit of labor (md := [Md /P]/[AL] where M is the nominal stock of money and P the price level; i is the nominal interest rate) is given by md = [y ]σ /[σ i]—with σ and σ (both parameters > 0) denoting the income elasticity of the demand for money and a parameter related to the interest elasticity of money (Em,i = −[y ]σ /[m σ i]), respectively, we can focus on equilibrium in the money market: m = [y ]σ /[σ i]

(a.1)

We assume that the central bank wants to achieve an inflation rate of zero, so that i = r. Taking into account that under profit maximization r = ßk ß−1 , we can write m = [k  ]σ /[σ ßk  ß

ß−1

] = k

1+ßσ−ß

/σ ß

(a.2)

Appendix G.1: Optimum Quantity of Money

267

Replacing k through the steady-state value k  = [s/(a + n)]1/(1−ß) , the optimum money stock therefore is given by m #opt = [s/(a + n)](

1+ßσ−ß)/(1−ß)

/σ ß

(a.3)

Hence in the steady state it holds that M(t)/P = [s/(a + n)](1+ßσ−ß)/(1−ß) /σ ßL(0)e A(0)e nt

at

(a.4)

We assume that 1 + ß(σ − 1) > 0 since empirical evidence is known to suggest an income elasticity of the demand for money around unity, indeed exceeding unity if one follows the hypothesis that money is a luxury good. Note that the parameter σ is the lower the higher the absolute value of the elasticity of the demand for money (Em,i = −[y ]σ /[m σ i]). Hence the level of real money supply in the steady state is higher • • • • •

the higher the interest elasticity of the demand for money (the lower σ ), the higher the savings rate, the higher the income elasticity of the demand for money, the lower the progress rate, and the lower the population growth rate.

One may point out that financial innovation and regional economic/financial integration could bring about changes in the interest elasticity. In a larger integrated market there will be more liquid financial assets which are good substitutes for holding money, and thus a rise of the interest elasticity of the demand for money would once-and-for-all require the reduction of the real money stock. The optimum growth perspective therefore presents a challenge for both the monetary and fiscal policy. The growth rate of the nominal money supply should be equal to the sum of a and n. We thus have a new perspective on the old topic of the optimum quantity of money. Here it is that money stock brings about the golden rule of capital accumulation and maximum growth of per capita consumption. The concept proposed here is clearly different from that of FRIEDMAN (1969), and given the specification of the money demand chosen here we indeed cannot apply the FRIEDMAN condition that the inflation rate (π) be set equal to −r so that i = 0. We finally note that introducing money in a growth model with government clearly requires stating the government budget constraint in an adequate way, namely: γy = τy + πm . We measure the inflation we obtain for the equilibrium money [k ß ]σ /[σ (π + ßk ß−1 )] so that (γ − τ) = πk σ /[σ (π + ßk ß−1 )]: The long-run budget deficit ratio outside the golden rule age then is a function F(k, π), whereby the function allows us to determine a revenue-maximizing inflation rate, including the potential modification to assume that k is a function of the inflation rate and other variables. From this perspective, one could extend the research perspective suggested here in many ways.

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Appendix G.2: Specialization, Technological Progress and Factor Price Ratios In a closed two-sector economy with labor mobility we can characterize the economy in a straightforward manner if we assume that there is one sector producing consumption goods and the other is producing investment goods. Both sectors produce with labor L and capital K, namely according to Cobb–Douglas functions: Investment output is given by 



YI = [K I ]ß [LI ]1−ß

(A.I)

and consumption output by 



YC = [K C ]ß [LI ]1−ß

(A.II)

Aggregate GDP—expressed in units of the consumption good—is given by the sum of output of the consumption goods sector (C) plus output of the investment goods sector where Y = C + pI where p = PI /PC ; and per capita incomey = yC + pyI . Goods market equilibrium in the standard sense requires S = sYP = PI YI . As P = [PI ]v [PC ]1−v we can write Ip1−v = sY

(A.III)

It is assumed that the capital intensity of the consumption goods sector exceeds that of the investment goods sector which is a necessary condition for stability of the model. With linear-homogeneous production function we can (see for a summary JUNGMITTAG (2006)) write (with v : = 1 − v; ω := W/r which is the ratio of the nominal wage to the real interest rate r): 

yI : = I/L = sy/pv = sf  I (kI (ω))(k + ω)

(A.IV)

dlnk/dt = sf  I (kI (ω))[(k + ω)/k] − [n + δ]

(A.V)

and

The long-run steady state—in analogy to the one-sector model—is given by sf  I (kI (ω))[(k + ω)/k] = [n + δ]

(A.VI)

With respect to the short run it can be shown that dω/ds > 0 and that dyI /dω > 0 so that an increase of the relative factor price ratio raises the share of investment per capita output.

Appendix G.3: Endogenous Progress in the Capital Goods Sector Fig. 61 One-sector economy and the factor price ratio

269

y

OA = w OB = w/r y = (W/P) + rk

y(k) E0 A α B

α 0

E1

k1

k2

k

Appendix G.3: Endogenous Progress in the Capital Goods Sector In a one-sector economy—with a given level of technology—we have to consider y = y(k) and y = w + rk (y is per capita income, k the capita intensity; the factor price ratio is w/r; w is the ratio of nominal W to price level P). Graphically we have a production function in which the distance OA indicates for the production y(k) where OA indicates w, and the distance OB is equal to w/r. If the real interest rate is equal to tgα the line BA determines the optimum capital intensity k2 (see point E0 ). If the factor price ratio falls—and the income line shifts toward the origin—we get a new equilibrium point E1 , the optimum capital intensity has fallen (k1 ): Transitorily firms will drop reinvestment plans in order to achieve the lower capital intensity k1 so that there will be transitory unemployment and an excess supply in the goods market, respectively. Next we turn to a two-sector economy where capital and labor are mobile across sectors so that we have a uniform factor price ratio. Graphically we have two production functions for sectors C and I where equilibrium output is determined by the line BA (slope α) which is tangent to both production functions, namely in E0 and in E1 ; the capital intensity (kII ) of the consumption goods sector is higher than that of the investment goods sector (kI0 ); L and L will denote labor employed in the C-sector and the I-sector, respectively. Note that y0 is I/L and y1 is C/L (see the following graph). Denoting the initial Hicks-neutral progress factor as A 0   and using a simple Cobb–Douglas function I = A 0 [K /L ]ß and C = [K  /L ]ß while defining overall (exogenous) labor supply L = L + L we can write—setting  A0 = 1 : C/L = [1 − α ](K  /L )ß and I/L = α (K /L )ß where α = L /L. What happens if the factor price ratio falls (see the new income line starting in point B )? It is clear that the new optimum would be characterized by lower capital intensity in both sectors so that an adjustment process toward the lower capital intensities will have to be brought about—possibly by dropping previously planned reinvestment. This is not what the investment goods producing sector will want since any excess supply of capital will reduce the price of investment goods and hence the profitability and hence the share price of firms producing investment goods. What is the alternative for profit-maximizing firms in the investment goods sector? For that sector in particular it makes sense to try to achieve some technological progress

270 Fig. 62 Two-sector economy

Innovations in Macroeconomics y

yi = (Wi /P) + rk i OA = w0 OB = (w/r)0

y01

E1

y1 y0

E0

E2 A E01 α B

α' B'

0

kI1

kI0

kII

k

which amounts to raising the level of technology from A0 to A1 such that the production function in the investment goods industry becomes steeper (an alternative could be to raise ß , the output elasticity of capital in the I-sector). The new equilibrium point shown in the graph—see point E2 —requires only a modest fall of the sectoral capital intensity; point E2 is in marked contrast to the solution suggested by traditional adjustment patterns, namely point E01 (with a given level of technology). To the extent that economic globalization reduces the factor price ratio there will be a strong incentive for firms in OECD countries to become more innovative in the investment goods sector, and as almost all machines are customer-taylored anyway it is indeed plausible to expect that producers of investment goods—facing changing factor price ratios—will explore new technologies in the production process. One may also consider besides the Harrod-neutral technological progress A(t) in the I-sector a progress rate in the I-sector, too (dlnB(t)/dt). In this case we can express output relative to efficiency units of labor.

Appendix G.4: Simple Differential Equation and Bernoulli Differential Equation Let us consider for X(t) the following simple differential equation with constant coefficients a and b, written in the “elementary form” dX/dt + aX = b

(A.I)

The solution of this equation is (with e for Euler number; C0 determined by the initial condition X(0)) X(t) = C0 e

−at

+ b/a

(A.I )

If a > 0 there is long-term convergence to X#, that is with t → ∞ we get the long-run value (“steady-state value”) X# = b/a. From t = 0, the value for C0 is easily obtained: X(0) = X0 , so that: [X0 − (b/a)] = C0 . This elementary form of a differential equation will be used subsequently to solve a more complex equation, namely the Bernoulli differential equation.

Appendix G.5: The Macroeconomic Foundation of Microeconomics

271

Let us write the Bernoulli differential equation in a specific way so that we can recognize a simple similarity with the above differential equation: dX/dt = bXß − aX

(A.II)

X−ß dX/dt + aX1−ß = b

(A.II )

Dividing by Xß gives

We make the substitution: X1−ß = V so that dV/dt = (1 − ß)X−ß dX/dt and hence we can restate the above equation as follows: (1/(1 − ß))dV/dt + aV = b

(A.II )

Dividing by (1/(1 − ß)) results in dV/dt + [a(1 − ß)]V = b(1 − ß)

(A.II )

With respect to the variable V(t) this is exactly the simple differential equation in the elementary form so that the solution is V(t) = C0 e

−a(1−ß)t

+ b/a

(A.III)

As X1−ß = V we finally get as the solution of the differential equation X(t) = [C0 e

−a(1−ß)t

+ b/a]1/(1−ß)

(A.IV)

If a is positive and ß < 1 we have convergence of X(t) toward the steady-state value X# = (b/a)1/(1−ß)

(A.V)

C0 is determined from the initial equation as X0 = [C0 + b/a]1/(1−ß)

(A.VI)

X0 1−ß = C0 + b/a

(A.VII)

C0 = X0 1−ß − b/a

(A.VIII)

Appendix G.5: The Macroeconomic Foundation of Microeconomics In Microeconomics a standard result is that demand for a certain good (say good i) is a positive function of per capita income (y), the number of demanders (L) as well as a negative function of the relative price: pi /pj (j represents an alternative good which is a substitute for good i).

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We can state the demand function in a simple linear way (with positive parameters v, v , v ) as qi = vy + v L − v pi /pj

(I)

In neoclassical growth theory—denotingY for real income, K for capital, L for labor, A for knowledge (labor augmenting)—we have as standard ingredients a savings function S = sY (0 < s < 1) and also (0 < ß < 1) a simple production function Y = K ß (AL)1−ß ; we assume that the depreciation rate of capital (δ) is constant and that labor growth at an exogenous rate n while knowledge growth at rate a. Finally, we impose the goods market equilibrium condition S = investment I (I = dK/dt + δK) which gives as the steady-state result for per capita incomeY/L =: y (# denotes steady state, e the Euler number): y# = [s/(δ + a + n)]ß/1−ß e

at

(II)

In the simplest case we can set a = n = 0 and get y# = [s/δ]ß/1−ß

(III)

Hence for consistency reasons—and this is the macro foundation of microeconomics—the following demand function for market i should hold in this very simple case: qi = v[s/δ]ß/1−ß + v L − v pi /pj

(IV)

The demand for good i is a positive function of the aggregate savings function, a positive function of employment L and a negative function of the savings rate. The role of L suggests that unemployment will reduce the demand in market i. Testing for such demand functions could reveal to which extent households really think long term.

H. Trade, Structural Change and Growth in an Open Monetary Economy

H.1 Introduction As regards structural change in Eastern Europe, it is clear that one should expect considerable structural change in the initial transition stage and possibly also once high foreign direct investment inflows occur. This occurred early on in Hungary, and the Slovak Republic, but only with a considerable delay in Poland. The various subsequent indicators show different intensities of structural change, and the intensity of change is not equal across the various indices. On theoretical grounds (see appendix), one should focus mainly on the Lilien index and the modified Lilien index. As the features of those two indicators consider the sectors’ relative weights, and also meet other standard requirements. As we can see in the subsequent table, the various indicators which summarize the intensity of structural change in the period from 1993 to 2001/2002, the statistics point to rather strong structural change in several accession countries. Ideally, workers move out of sectors with low productivity growth toward sectors with high productivity growth, the latter often being found in sectors with high foreign direct investment inflows (FDI). FDI and investment of domestic firms will increase capital intensity and this, along with improved technology, will raise productivity. A positive gap between the growth rate of the wage rate and sectoral productivity growth will reinforce sectoral profit rates which in turn should stimulate sectoral FDI inflows. To the extent that economic catching-up and modernization is associated with high cumulated FDI inflows, one should expect that a considerable part of trade is shaped by FDI. Intra-company trade accounts for roughly 1/3 of trade in OECD countries. By contrast, the degree of structural change in Germany was rather low, though this might be an artifact related to rather rough sectoral decomposition. For example, if international outsourcing to Eastern Europe takes place this can be associated with considerable structural change although at the two-digital level one would not note that less automotive parts are produced in Germany in the early twenty-first century than a decade ago. As regards structural change this is partly related to technologies, while also partly to other factors—including real exchange rate changes. There are two alternative P. J. J. Welfens, Innovations in Macroeconomics, DOI 10.1007/978-3-642-11909-5_8, © Springer-Verlag Berlin Heidelberg 2011

273

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Table 10 Various indicators measuring structural change based on production data at the NACE 2-digit level (LI = Lilien index; MLI = modified LI). (Source: OECD STAN Database, own calculations) Deutschland Griechenland Ungarn Polen Portugal Slowak Rep. USA

1993–2002 1995–2002 1993–2001 1995–2001 1995–2001 1993–1999 1993–2001

NaV

EuN

SRD

IG

GRP

LI

MLI

0.1727 0.2181 0.5903 0.2601 0.1503 0.2749 0.0825

0.076 0.0737 0.1967 0.0656 0.0409 0.1119 0.0222

4.0043 5.742 20.7673 9.5737 4.5519 8.7107 2.6044

0.0434 0.0529 0.4593 0.0756 0.0236 0.1933 0.0097

0.0731 0.0912 0.2248 0.1146 0.064 0.0994 0.0364

0.1097 0.1222 0.4124 0.1427 0.082 0.2766 0.0497

0.0327 0.0318 0.0814 0.0282 0.0177 0.0442 0.0096

definitions of the real exchange rate q = P/(eP*)—with * denoting a foreign variable and P and e representing the price level and the nominal exchange rate, respectively; P represents a basket of goods which is composed of tradables and nontradables. An alternative for defining the real exchange rate is λ = PT /(ePT *) where T stands for tradables. A rise in q or a rise in λ can be identified with a real appreciation. Subsequently, we take a closer look at alternative explanations for real exchange rate changes which must include an analysis of the links between nominal exchange rate dynamics and the real exchange rate (Sect. 2). We demonstrate within a monetary growth model that the real money demand does not depend on the real interest rate unless the savings rate is a function of the real interest rate. Moreover, it is shown that the real interest rate will affect both the level of the growth rate and the growth rate itself. We use a rather simple growth model with trade, endogenous innovation and FDI. In Sect. 3 we highlight an alternative approach to generating a Balassa–Samuelson effect which is linked to income distribution at home and abroad. Section 4 is on the real exchange rate and economic development, trade, structural change and growth where we also focus on a new structural model with product and process innovations but also on some aspects of the more complex HANSEN/RÖGER model. Our analysis also takes a look at the links between the real exchange rate and economic growth, including aspects of optimum economic growth. In the final section, we present some basic policy conclusions. The appendix presents some innovative modeling related to the topic of exchange rate dynamics and macroeconomic analysis (including smooth linking of supply-side effects and demand-side impulses). At the bottom line, there is a strong emphasis on the fact that the dynamics of exchange rate development and growth should simultaneously consider trade and FDI. With reference to both the OECD countries in general as well as to Eastern Europe and Asian countries in specific, a considerable share of trade is intra-company trade. The perspective adopted here is a mixture of Schumpeter and Dunning, namely in the sense that innovation and FDI are emphasized. Both trade and FDI depend on the real exchange rate, however, as the FDI stock contributes to the overall capital stock in the host country the net trade position— more precisely the current account—depends on cumulated FDI: The difference between output produced and domestic absorption (sum of consumption, government consumption and investment, including FDI inflows) is equal to net exports. There

H.2 Exchange Rate Dynamics, Relative Prices, Employment and Growth

275

also is a geographical coincidence in the sense that the gravity equation for FDI and trade typically shows similar patterns. This applies to Eastern Europe for which Western Europe represents the main export markets and also the main source of FDI inflows. Such inflows contribute to product upgrading over time. The analytical focus has various time horizons and brings some new insights, including the fact that in a non-inflationary economy the demand for money does not depend on the (long term) real interest rate. Indeed ambiguous results from empirical analysis in this field are well known. We also develop a rather convenient graphical model to focus on the issues of structural change and competitiveness, and we propose new ways of how to include the optimum growth literature in the analysis of Schumpeterian economic dynamics. From a policy perspective, it becomes clear that analyzing macroeconomic topics can hardly be done adequately without taking into account structural change and innovation dynamics. While innovation and structural adjustment are a natural element of EU eastern enlargement both in Western Europe and Eastern Europe (or in a North–South perspective), not much is known about the adjustment costs of firms and countries when moving up the technology ladder.

H.2 Exchange Rate Dynamics, Relative Prices, Employment and Growth H.2.1 Nominal Exchange Rate, Real Exchange Rate and True Long-Run Money Market Equilibrium Naturally, there is a link between the nominal exchange rate and the real exchange rate q*. It holds that E(lne) + E(lnP*) = E(lnP). As regards the variance VAR it holds that VAR(lne + lnP*) = VAR(lne) + VAR(lnP*) + 2cov lne, lnP* = VAR lnP. If one were to assume that VAR lnP = VAR lnP*, it is clear that for any variance of lne and of lnP*, there must be negative cov lne, lnP*. It indeed is plausible that a depreciation of country I’s currency will go along with a fall in country II’s price level as goods imported from country I will become cheaper in country II. From the perspective of a small open economy, the short-term nominal exchange rate e is determined by the interest rate parity i = i* + aE where aE denotes the expected depreciation rate, and i is the nominal interest rate. In the long run, the interest rate at home and abroad is given by i = r + π (sum of the real interest rate r and the inflation rate π) and i* = r* + π* which implies with profit maximization r =YK and r* =Y*K , respectively: (r − r*) + (π − π*) = a E . If there is free capital mobility and domestic and foreign bonds are perfect substitutes—but no free movement of FDI—it holds that r = r* which makes the interest parity fully consistent with long-run purchasing power parity P = eP* if there is no (systematic) difference between expected and actual devaluation rate. The real exchange rate q* := eP*/P is determined in the short run by nominal exchange rate dynamics, in the long run P and P* plays a role as

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well. Overshooting phenomena of the short-term nominal exchange rate thus will affect the real exchange rate temporarily. If domestic and foreign bonds are not perfect substitutes while we have full mobility of FDI, the marginal products at home and abroad will be equal in the long run: YK =Y*K . Hence profit maximization in both countries will indirectly bring about the condition r = r* in the long run. However, there is not really a long run in a strict sense if one does not consider a growth model and some other aspects. A specific aspect will refer to the fact that FDI flows will be a function of the real exchange rate as argued by FROOT/STEIN (1991). We will turn to this later and at first focus on the issue of a long-run equilibrium real exchange rate. If we are to make a prediction about the domestic price level, we could use a model that predicts the nominal exchange rate (WELFENS/BORBÉLY 2004) and combine this with a model which explains the foreign price level P*. As regards, the latter one may consider a rather simple approach based on four elements: • Money market equilibrium: This must be considered in long-run growth modeling of a monetary economy. • Profit maximization: In the long run, the real rate of interest must be equal to the marginal product of capital (with a standard Cobb–Douglas production function Y = Kß (AL)1−ß the marginal product of capital YK = ßY/K where K is the capital, L is the labor, and A is the level of labor-saving technology). • A simple growth model: In a neoclassical growth model—with a growth rate dlnA/dt =: a, a Cobb–Douglas production function (as above) and a savings function S = sY—the steady-state solution for per capita output y# = A0 eat (s/n)ß/(1−ß) ; here e denotes the Euler number. Hence the level of the growth path of y is a positive function of the initial level of technology A0 and the savings rate s, and the growth rate a. We will show that in an open economy with trade and FDI— and monetary transactions—the equilibrium solution looks more complicated and suggests new empirical approaches. • An assumption with respect to the strategy of monetary policy. At first we are interested in the level of P* which is not really exogenous here. One can show—as an innovative feature of the model—that the long-run demand for money is independent of the real interest rate unless the savings rate depends on the real interest rate. Money market equilibrium requires that real supply (M/P; M is the nominal money stock) equals real money demand m*(. . . ): M*/P* = m*(Y*, i*)

(H.1)

The equilibrium condition for the money market is fairly general as we will see. Indeed, it is reasonable both for a narrow definition of the money supply (M1 ) and for a broad money supply (M3 ). If we consider M1 , cash balances plus deposits, one should expect a close medium term link with the price level. In an underemployed economy, a rise in the money supply will raise output Y, and as the capacity utilization rate is increased, the price level P will increase with a certain delay. If one wants to

H.2 Exchange Rate Dynamics, Relative Prices, Employment and Growth

277

express (A.1) in a kind of a quantity-theoretical framework, we can simply write: M1 = V (i, Y)PY, with V denoting the inverse of the income velocity of money. While it often is claimed that M3 (M1 plus term deposits plus savings deposits) is linked with the price level, there are no serious arguments why a rise in broad money M3 should raise the price level unless one argues that there is a strong real balance effect. A serious argument would look different: A rise in M2 -here defined as M3 minus M1 —would increase within a portfolio-theoretical approach with the demand for stocks as real capital being complementary to money balances. Combining a higher stock of M2 with a higher value of stocks P K (P is the stock market price level and K the capital stock) reduces the portfolio risk. To the extent that P is positively correlated with P, one may expect that empirical investigations on the long-term demand for money come up with positive evidence for a link between M3 and P. This point is easily understood if we assume that the fundamental value of stocks reflects discounted future profits which are—in a very simple two-period perspective (with  denoting unit labor costs and E the expectations operator)—given by the straightforward expression: (Pt − t )Yt + (E(Pt+1 ) − E(t+1 ))Yt+1 /(1 + i) = P . Assuming for simplicity that market participants expect E(Yt+1 ) = Yt , that unit labor costs are constant, that output Y = KlnL (we will, however, later switch to Cobb–Douglas) and that firms finance all investment through the stock market, we can state the following equation: M2 = V (i, Y)P K and—assuming that  = P ω— thus M2 = V (i, Y) (P(1 − ω))(1 + (1 + i)−1 ) Y/lnL. We can then add M1 and M2 and state—with ω := 1 − ω—the long-term money market condition: M3 = V (i, Y)PY + V (i, Y)(Pω (1 + (1 + i)−1 )Y/lnL = PY(V (..) + V (..)ω (1 + (1 + i)−1 )/lnL.

(H.1 )

This now looks more or less like the quantity theory of money MV(Y, i) = ψPY. We therefore can indeed return to (H.1) while specifying for country II a specific money demand function: M*/P* = Y*σ* σ* /i*

(H.1 )

∗

Thus the real money demand m* is specified as Y*σ σ∗ /i* where Y* is the foreign real output and i* the foreign nominal interest rate which in turn is the sum of the expected inflation rate plus the real interest rate r. The parameters σ and σ stand for the apparent income elasticity of the demand for money and the implicit interest responsiveness of the demand for money, respectively. However, we will show that in a long-term perspective that σ* is not really the income elasticity of the demand for money and the domestic real interest rate, respectively. Assuming (with K*, A*, and L* denoting capital, the level of technology and labor input) a Cobb–Douglas production function abroad, we have Y* = K*ß* (A*L*)1−ß*

(H.2)

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Moreover as we assume that factors are rewarded in accordance with the marginal product rule, it holds that r* = ß*Y*/K*

(H.3)

In the absence of inflation/deflation, we can thus write that the money market equilibrium for country II is as follows: M*/P* = Y*σ* σ* /(ß*Y*/K*) = K*Y*σ* −1 σ* /ß*

(H.4)

Here we have taken into consideration that i = r and that under profit maximization r = ßY/K. Taking logarithms we get lnP* = lnM* − (σ* − 1)lnY* + ln(ß*/σ* ) − lnK*

(H.5)

As is obvious that the long-run income elasticity of the demand for money is not σ*, rather it is σ* − 1. We can rewrite the equation in per capita terms (actually in efficiency labor units AL) on the right-hand side, and this will be dubbed true long-run money market equilibrium: lnP* = ln(M*/A*L*) − (σ* − 1)ln(Y*/A*L*) + ln(ß*/σ* ) − ln(K*/A*L*) − (σ* − 1)ln(A*L*).

(H.6)

Note that in the case of flexible exchange rates, the nominal money supply is exogenous, and this is the main case we want to consider subsequently. The problem looks different under fixed exchange rates (in the case of Eastern European accession countries this largely corresponds to the situation of moving to the European Exchange Rate Mechanism II). If we assume that savings S = sY, no population growth, a zero rate of capital depreciation and that technological progress rate (dA/dt)/A = a is exogenous, we get—with y := Y/(AL) and k := K/(AL) and # for steady state—the standard neoclassical steady state solution, namely y # = (s/a)ß(1−ß) and k  # = (s/a)1/(1−ß) . Thus it is obvious that in the long-run demand for money, the savings rate and the progress rate will enter into play. The interest elasticity of money should be zero. If empirical analysis on the long-run money demand finds a significant impact of r, it effectively confuses r* and r, that is the condition r = r*! (In an inflationary world one may, of course, have to consider the inflation rate as an additional variable determining the demand for money.) Only in the case that one assumes that the savings rate depends on the interest rate would the long-run money market equilibrium depend on the interest rate. For the case that monetary policy maintains a constant m *#(with m * := M*/(A*L*)), we get lnP* = lnm *# − {[1 + (σ* − 1)ß]/(1 − ß)}ln(s*/a*) + ln(ß*/σ* ) − (σ* − 1)ln(A*L*).

(H.7)

H.2 Exchange Rate Dynamics, Relative Prices, Employment and Growth

279

The long-run equilibrium therefore is a positive function of the central bank’s target money stock m . Assuming that the apparent income elasticity of the demand for money (σ) is smaller than unity, the price level is a negative function of the level of technology and of the size of the labor force. Moreover, it is a negative function of the ratio of the savings rate to the progress rate provided that ((1+(σ*−1)ß*)/(1−ß*)) is positive. Note that the price level is stationary only if labor input declines with the same growth rate as the level of technology rises or if the apparent income elasticity of the demand for money is unity. The long-run expected price level depends only on exogenous parameters, in particular the savings rate and the progress rate. In an open economy we may assume—now considering the world from a country I perspective—that savings S = s(Y + q*r* Fn **/P*), where F* is nominal net claims on the rest of the world. Hence q*r* Fn **/P* is the interest income accruing in terms of domestic goods. We assume that net real foreign assets q*Fn **/P* expressed in domestic goods are proportionate to Y. Defining f** := q*Fn **/P*AL = q*Fr **/AL, assuming that f** = νy and assuming a constant progress rate in country I, namely a, and a production function Y = Kß (AL)1−ß

(H.8)

y # = (s(1 + r*ν)/a)ß/(1−ß)

(H.9)

we get a steady-state value

If we define Fr**/AL = ν and assume that households consider ν as a target ratio we can write y # = (s(1 + r*q*ν )/a)ß/(1−ß)

(H.9 )

Per capita income therefore is—denoting with e the Euler number—given by y# = A0 e s(1 + r*q*ν )a) at

ß/(1−ß)

(H.9 )

Hence the long-run steady-state value of y # depends on the real exchange rate. Moreover, long-run money market equilibrium will also depend on the real exchange rate as is obvious if we plug in (H.9) into (H.6 ); Eq. (H.6 ) is the corresponding equation for the domestic economy: lnP = lnm − (σ − 1)lny + ln(ß/σ ) − lnk  − (σ − 1)ln(AL)

(H.6 )

lnP = lnm − {[1 + (σ − 1)ß]/(1 − ß)}ln(s(1 + r* q*ν )/a) + ln(ß/σ ) − (σ − 1)ln(AL).

(H.6 )

If we assume for simplicity that r*q*ν /a is close to zero, we may use the approximation that ln (1 + r*q*ν )/a) ≈ r*q*ν /a. A rise in the real exchange rate—hence a real depreciation—will increase the price level if (1 + (σ − 1)ß) < 0. This now points to an empirical issue.

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H.2.2 Real Exchange Rate, Growth Path and Steady State Let us get back to (H.9 ). A real depreciation will raise the level of the growth path. This implication is, however, not robust if we assume that the progress rate depends negatively on q*, for example, if we assume that imported licenses or technology intensive intermediate products play an important role for the country considered. Then we may state the hypothesis (with a1 denoting the progress rate in a closed economy). A = a1 − B q*; assumption: a1  = B q* where B is a positive parameter related to ν .

(H.10)

We now also get an ambiguous result with respect to the impact of q* on the price level (see H.6 ). It still holds that the level of the growth path is positively influenced by q* (see H.9 ). However, the growth rate is negatively influenced, and the sum of both effects on real per capita income will become negative after some critical time t = t . We have a quasi-endogenization of growth and the progress rate, respectively, since from a traditional small country perspective, the real exchange rate—in a world in which only tradables exist—is exogenous. This, however, is no longer true if there are nontradables and differentiated tradables. For every product variety sold in the world market, increasing exports will correspond to a fall in the price of the respective product; this problem will be neglected for now. Rather we turn to the accumulation dynamics of foreign assets where an important aspect to consider is that dFn **/dt = r*Fn ** + PX/e − P*J so that (dFn **/dt)/P* = r*Fr ** + X/q* − J = r*Fr ** + xY/q* − jY (dFr **/dt)/Fr** = r* + x(Y/q*)/Fr** − jY/Fr** = r + x/ν − jq*/ν

(H.11) (H.12)

In the next section, we take a closer look at the real exchange rate from a mediumterm perspective, where the link between the real exchange rate and investment will be considered. Before we turn to this aspect, let us briefly consider the case of an open economy with FDI inflows and a production function where real money balances and the ratio of per capita imports j = J/(AL) and export intensity x = X/(AL) enter the production function: 





Y = Kß (AL)1−ß (J/AL)ß (X/AL)ß (m/AL)ß

(H.13)

The specific assumption here is that the output effect of imported intermediates/imported machinery and equipment—only those should be included in J here—is diluted if there are more workers in efficiency units. This mechanism could be associated with learning-by-doing in the sense that importing, say machinery, brings a one-off productivity increase for workers dealing with the sophisticated imports. If one assumes that imported machinery and equipment is employed with a lag of one period, the current import J would also show up in a higher K. A similar reasoning holds with respect to X/(AL) to the extent that one assumes that X/AL is a measure of the exposure of workers to world market dynamics. It is debatable whether or not

H.2 Exchange Rate Dynamics, Relative Prices, Employment and Growth

281

m or m := m/(AL)—or m/L—should enter the production function; only empirical analysis can solve the issue. Here we use m , as one may argue that liquidity on a per capita basis is relevant for saving transaction costs and actually contributing to labor productivity. Finally, note that in a model with both inward and outward FDI, one might also have to include the stock of outward FDI, namely to the extent that there is considerable asset-seeking investment which implies international transfer of technology from the subsidiaries to the parent company. Firms in technology-intensive industries which invest abroad—namely in technologically leading countries so that new technologies can be picked up rather easily—will benefit from a company-wide technology transfer which is not just from the company headquarters to the subsidiary but also from the subsidiary back to the parent company. Instead of using J/AL =: j and X/AL = x in the production function, one might chose a production function with 1 + j and 1 + x in the production function so that zero imports and zero exports imply a consistent output for the case of the closed economy. However, we use j in the production function on the basis of the assumption that the country considered has become so specialized that it requires indispensable foreign inputs (in empirical investigations only the import of intermediate products and capital goods should be considered). For the sake of simplicity, we also use x and not (1 + x ). One may assume that real money balances enter the production function through a positive external effect of households using money in all transactions in the goods market. Therefore, ß ß

ß

y = k  j x  m 

ß

(H.14)

The accumulation dynamics is given by ß ß

ß

dk  /dt = s(1 − bß)k  j x m

ß

− ak 

(H.15)

Here we have assumed that foreign investors have a share b of the capital stock; and as capital income is ßY, the national income is GDP minus bßY. Savings S is proportionate to national income and therefore we have S = sY(1 − bß) = sY. As we assume J/AL = j(q*)Y/AL and X/AL = x (q*)Y*/AL or more conveniently X/AL = x (q*)y * A*L*/AL so that we get ß

ß

ß





ß

y # = [s(1 − bß)j y x y *ß (A*L*/AL)ß m /(n + δ + a))]ß/(1−ß) (H.16) If one were to impose a strict long-run trade balance requirement one might want to impose in (H.15) the long-term equilibrium condition that X = q*J so that x = q*j which, however, is not done here. Taking into account the money market equilibrium condition (H.6 ) in an appropriate way, namely m = y1/ß+(σ−1) (AL)σ−1 σ/ß we obtain with  := (A*L*/AL): ß

ß

ß



ß

y # = [s(1 − bß)j y x y *ß  y 

· (σ/ß)ß /(n + δ + a)]ß/(1−ß)

(1/ß+(σ−1))ß

(AL)(σ−1)ß



(H.17)

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Innovations in Macroeconomics

The implicit solution for the steady-state output therefore is: 

y#1−(1/ß+(σ−1))ß

−ß









= s[(1 − bß)jß xß y *ß ß (AL)(σ−1)

ß



· (σ/ß)ß /(n + δ + a)]ß/(1−ß) 







y# = {[s(1 − bß)jß xß y *ß ß (AL)(σ−1)ß

(H.18)





· (σ/ß)ß /(n + δ + a)]ß/(1−ß) }1/(1−(1/ß+(σ−1))ß



−ß)

(H.19)

We will assume that bß is close to zero so that ln(1 − bß) ≈ bß. If we take logarithms and define ß# := 1/(ß/(1 − ß))(1 − (1/ß) + (σ − 1))ß − ß) we have a testable production function, namely for per capita income y :=Y/L 

lny = ß#lns − ß#bß + ß#ß lnj + ß#ß lnx + ß#ß lny * + ß#ß ln(A*L*) + ß#((σ − 1)ß − ß )ln(AL) + ß#ß ln(σ/ß) − ß#ln(n + δ + a) (H.20) Taking a look at (H.19) we can see that the level of the growth path positively depends on the effective savings rate s , x , y * and the relative technology level (A*L*/AL); note that the y * variable effectively reflects the impact of exports. The steady-state equilibrium output per capita—in efficiency units—therefore is a positive function of the income elasticity of the demand for money provided that σ < 0. As regards the impact of q* one has to consider b(q*), x (q*) and j (q*), which is not unambiguous. Only empirical research can give a clear answer. The growth rate of per capita income y =Y/L is a, and one could consider how FDI, government expenditures (consumption vs. R&D promotion) and trade will affect the progress rate which raises many new interesting issues. We will pick up the issue of government expenditures and discuss the impact on the level of growth and growth itself. An interesting refinement is to assume that S = sY(1 − bß)(1 − u)(1 − τ) where u is the structural unemployment rate and τ the income tax rate. We get for y in the steady state: ß

ß



ß

y# = {s(1 − bß)(1 − u)(1 − τ)j x y *ß  (AL)(σ−1)ß 

· (σ/ß)ß /(n + δ + a)ß/(1−ß) }1/(1−(1/ß+(σ−1))ß



−ß)



(H.21)

We thus could consider the impact of unemployment and the income tax rate—both a higher tax rate and a higher unemployment rate will reduce the level of the growth path—as well as that of j and x on the level of the growth path. Moreover, we can also discuss the effects of the unemployment rate and the tax rate—making specific assumptions how tax revenues are used (public consumption vs. R&D financing)—on the growth rate. Finally, we should take into account the requirement that in the long run the current account must be balanced. For the simple case of no FDI we have XP = eP*J

(H.22)

H.2 Exchange Rate Dynamics, Relative Prices, Employment and Growth

283

We will assume that X = j*(q*)Y*

(H.23)

J = j(q*)Y

(H.24)

Therefore we get—while multiplying the left hand side of (H.22) by A*L*/[A*L*] and the right hand side by AL/[AL]—the equation XP = eP*J or j*Y*P = eP*jY

(H.22 )

[A*L*]j*Y*P/[A*L*] = ALeP*jY/[AL]

(H.22 )

[A*L*]/[AL] = q*jy /j*y*

(H.23)

Thus we obtain

Note that there is a relation between j and j since J/(AL) =: j = jy ; this applies in a similar way to the foreign country, namely j * =: x = j*y *. Replacing in (H.17) the expression  := A*L*/AL from (H.23) we get 











y # = [s(1 − bß)jß y2ß xß y*ß [q*jy /j*y*]ß y(1/ß+(σ−1))ß (AL)(σ−1)ß · eß



σ/ß



(H.17 )

/(n + δ + a)]ß/(1−ß)

Therefore we can write ß

y # = [s(1 − bß)j y · e

ß σ/ß

ß +ß  ß  2ß

x

y*



[q*j/j*]ß y

(1/ß+(σ−1))ß

/(n + δ + a)]ß/(1−ß)

(AL)(σ−1)ß



(H.17 )

We thus could derive a similar equation to (A.21) where the elasticity ψ of y with respect to the modified expression {. . . } is higher than in (A.21); note that we make the assumption that y * actually is foreign steady-state per capita income in efficiency units. Moreover, one can see that the elasticity of y # with respect to  the real exchange rate also will have to consider the expression [q*j(q*)/j*(q*)]ß which reflects a modified Marshall Lerner impact. The overall effect of q* on y can, however, not be assessed without considering that b, j and j also are a function of q*. At the bottom line one may consider to allow a permanent trade balance surplus in our model with asymmetric FDI, and this leads to a minor modification: j*Y*P = eP*jY + bßYP

(H.22 )

On the right-hand side, we have nominal imports plus nominal dividends accruing to the foreign parent companies. Obviously we can write j*Y* = [q*j + bß]Y

(H.24)

It also is debatable whether or not an adequate import function should not read J = jZ (with national income Z := Y − bßY); and an adequate export function X = jZ* = jY* + bßY/q*.

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Innovations in Macroeconomics

H.2.3 Investment, Real Exchange Rate and Employment As is well known the real exchange rate (q* = eP*/P) has an impact upon the trade balance; however, the real exchange rate also will affect FDI as was emphasized for the case of imperfect capital market by FROOT/STEIN (1991). Foreign investment inflows in the recipient country—say an EU accession country or a newly industrializing economy—can be expressed as a share ψ in overall investment where ψ(q*); the partial derivative of ψ with respect to q* is positive since a depreciation of the host country currency effectively makes it easier for foreign investors to be successful in mergers and acquisitions. We thus assume that the overall investment output ratio I/Y is a positive function of the real exchange rate (in empirical analysis a positive correlation between I/Y also will catch the impact of improving net export expectations on the side of investors). Assuming profit maximization in an open economy in the form that the marginal product of capital YK is equal to the foreign real interest rate r* we can write for the growth rate of real output: gY = (I/Y)r*

(I)

Denoting the investment output ratio as z = z(q*) and recalling Verdoorn’s Law, namely that the growth rate (g) of labor productivity Y/L is a positive function of the growth rate of output (V and V are positive parameters) we have gY/L = Q + Q gY

(II)

According to Verdoorn’s law, the growth rate of employment will be a positive function of output growth gL = −Q + [1 − Q ]gY

(III)

gL = −Q + [1 − Q ]z(q*)r*

(IV)

hence

If we assume that the parameter Q is a positive function of the productivity-wage lag—meaning the time it takes for the real wage to fully catch up with marginal labor productivity YL (the long-run equilibrium values are denoted by #)—we have in the case that the marginal product is proportionate (1 − ß is a parameter in the interval [0, 1]) to the average labor productivity (YL = (1 − ß)y; ß is the output elasticity of capital): gL = −Q + Q ([y#/w#]/[y/w])z(q*)r*

(V)

The parameter Q := 1−Q thus depends positively on the steady-state productivity– wage ratio relative to the current productivity wage ratio. Hence outside the steady state—according to which (1 − ß)y would be equal to the real wage rate w—the growth rate of labor demand will be a negative function of the current real wage rate and a positive function of per capita income y. An interesting case is to assume that

H.2 Exchange Rate Dynamics, Relative Prices, Employment and Growth

285

Q —we have assumed Q to be smaller than unity—follows an inverted logistical adjustment path as y/w approaches y#/w#. The following figures show the growth rate of employment and the annual change of investment/GDP ratio for the EU-15 countries, Germany, Hungary, Poland and the Czech Republic.

Percent, Percent Points, resp.

2.0 1.5

d. Inv.q: EU–15 g. Empl: EU–15

1.0 0.5 0.0 –0.5 –1.0 –1.5 1960

1970

1980

1990

2000

Note: Until 1991: Growth rates of Western Germany, since 1992: Unified Germany, also in E–15–Aggregates

Fig. 63 EU-15: Growth rate of employment and annual change of investment/GDP ratio

15 10 5 0 –5

Fig. 64 Germany: Growth rate of employment and annual change of investment/ratio

–10 –15 1970

1975

1980

1985

1990

1995

2000

2005

286

Innovations in Macroeconomics

6 4 2

Change in investment

0 –2

Change in employment

–4 –6 –8 –10 –12

1992

1993

1994

1995

1996

1997

1998

1999

2000

2001

2002

2003

Fig. 65 Hungary: Growth rate of employment and annual change of investment/GDP ratio. (Source: Transition report, EBRD, various issues) 6 4 2

Change in investment

0 –2 –4 –6 –8 Change in employment –10 –12 1992

1993

1994

1995

1996

1997

1998

1999

2000

2001

2002

2003

Fig. 66 Poland: Growth rate of employment and annual change of investment/GDP ratio. (Source: Transition report, EBRD, various issues)

H.2.4 Technology, Exchange Rate Changes and the Relative Tradable Price In the following analysis, we will take a closer look at the role of technological progress—while sectoral capital stocks are assumed to be given in the short run—

H.2 Exchange Rate Dynamics, Relative Prices, Employment and Growth

287

6 Change in investment 4 2 0 –2 Change in employment –4 –6 –8 –10 –12

1992

1993

1994

1995

1996

1997

1998

1999

2000

2001

2002

2003

Fig. 67 Czech Republic: Growth rate of employment and annual change of investment/GDP ratio. (Source: Transition Report, EBRD, various issues)

which for simplicity we assume to only occur in the tradables sector (T). Tradables and nontradables are gross substitutes on the demand side and the supply side. There is a technology shift parameter in the tradables market, namely A. In addition, the demand for tradables is assumed to negatively depend on the relative price of nontradables (PN /PT =: φ) and positively on the real money balances M/P—a proxy for wealth. M denotes the nominal money supply and P the price level. We assume that the quality of N-goods is given and does not change, but the quality index Q of tradables could change through product innovations in the tradables sector. Hence the hedonic price index is given by α

P = PN PT1−α /Q = ϕ1−α PT /Q the parameter α is in the interval [0, 1]. Due to arbitrage, we have PT = eλ PT * where e is the nominal exchange rate, λ is a parameter reflecting trading costs (before full regional integration λ > 1, full integration λ = 1). Supply in both sectors depends on ϕ and labor as well as on capital stocks. We can state a straightforward equilibrium condition for the tradables sector, namely tradables supply T = T where T denotes tradables demand. Any excess supply in the tradables sector is equivalent to a current account surplus since we are considering a small open economy. Equilibrium in the nontradables market is given by the equality of nontradables supply N and nontradables demand N = N (. . . ) + G where N (ϕ, τ, M/P) is the private sector demand for nontradables and G government consumption of nontradables; τ denotes the tax rate. Note that the nominal exchange rate e enters the demand for both goods since M/P can be written as M/(ϕ1−α eλ PT* /Q). The initial equilibrium is determined by the intersection of the

288

Innovations in Macroeconomics

NN curve-which portrays equilibrium in the nontradables markets-and the TT curve which portrays equilibrium in the tradables sector-as well as a balanced current account. Technological progress in the tradables sector, that is a rise in the supply parameter A, will shift the TT curve upward (TT1 ) so that there is a rise in the relative nontradables price and a nominal depreciation. The price level remains constant if the nominal appreciation rate −ge = (1 − α)gϕ where g denotes growth rates. A given price level P0 is here indicated simply by the curve ϕ = (QP0 /PT *e)1/(1−a) ; the PP0 line indicates a given price level in ϕ–e space. Thus it depends on the slope of the NN curve whether or not technological progress in the T-sector brings about a fall in the price level or a rise in the price level. If the nominal wage is inflexible, a falling price level will bring about classical unemployment which in the context of empirical analysis should not be misinterpreted as technological unemployment! If there is no downward wage flexibility points below the PP line, an excess supply in the labor market is indicated. If the composition of tradables is increasingly characterized by product innovations, the tradables supply will become less price elastic as a higher share of product innovations typically will require more specialization and indeed higher sunk costs on the tradables supply side. Moreover, the demand for tradables becomes less price elastic; that is ∂T /∂ϕ will fall and the slope of the TT curve will rise. Hence a depreciation will bring about a higher current account than previously. This is somewhat surprising as one might think that a lower relative price elasticity makes the trade balance (or the current account) less price sensitive. However, one has to take into account that a rise in the relative price level of nontradables will cause less supply-switching on the supply side of the economy. An expansionary fiscal policy in the sense of raising G would shift the NN curve to the right and hence bring about a higher relative nontradables price and a depreciation of the currency. A fall in trading costs will shift the NN curve upward and the TT curve downward which in any case will bring about a nominal depreciation while the effect on the relative price of nontradables is unclear. An expansionary fiscal policy in the form of a cut in the tax rate τ will bring about a rightward shift of TT and an upward shift of NN. In the lower part (b) of the following graph we have drawn—for an exogenous expected exchange rate E(e1 )—the interest parity line according to i = i ∗ +[E(e1 ) − e]/e. The short-term impact of an expansionary monetary policy would be a fall in the nominal interest rate and hence a nominal and real depreciation. As prices are assumed to be sticky, there would be a price reaction only in the medium term. An expansionary monetary policy therefore moves the economy (see panel a) from point E0 to point F so that we have an excess supply in the tradables market—with a temporary current account improvement—and an excess supply in the N market. The rise in the real money stock shifts the NN curve and the TT curve to the right and finally also will raise the price level (which implies that the long-run rightward shift of NN and TT will be smaller than in the medium term). Hence we will get a new real equilibrium point which might be between E0 and F . Assuming that money market equilibrium can be written as M = V (i)PK, a rise in M will shift the PP line upward; a rise in i dampens the shift. The approach is more complex if we consider the HANSEN/RÖGER (2000) model. In the HANSEN/RÖGER model, the real exchange rate is determined through

H.2 Exchange Rate Dynamics, Relative Prices, Employment and Growth

289

the intersection point of the domestic equilibrium line and the foreign equilibrium line. In that model, consumption is assumed to depend positively on real income Y and negatively on the gap between the desired stock of wealth (F) and actual real financial wealth f. It also depends negatively on the real interest rate r relative to the long-run equilibrium level r# (in a small open economy equal to r*). Interest parity together with the domestic equilibrium condition gives a differential equation in q, while the current account equilibrium equation is given by df/dt = CA = rf + TB (with CA and TB denoting current account an trade balance, respectively). Setting dq/dt = 0 and df/dt = 0 gives two equilibrium lines (qq and ff) which jointly determine general equilibrium. We will pick up some aspects of this model subsequently. Tradables supply is T, demand T ; T(ϕ, A, KT ) = T (ϕ, τ, M/P); with PN /PT =: ϕ; M = PV(i)K; P = ϕ1−α PT /Q; arbitrage: PT = eλPT *; nontradables equilibrium: N(ϕ, KN ) = N (ϕ, τ, M/P) + G; interest parity i = i ∗ +[E1 (e) − e]/e.

φ TT1

PP0 F φ1

E1

φ0

TT0

H E0 H'

F'’

F' '

NN0

a 0

e1

e0

e2

i1 i0

Fig. 68 Equilibrium in the (a) tradables market (TT) and nontradables market (NN) and interest parity (b); model can track fiscal and monetary policy & supply shocks

i

b

E1' E0'

e

IP0

290

Innovations in Macroeconomics

There is one particular instability area in part (a) of the figure, namely between the PP curve and the NN curve (starting at point E0 : the area where NN0 is written). We observe in this area both an excess supply in both goods market and an upward real wage pressure—at a given nominal wage—so that the risk of unemployment is quite high unless workers who lost their job in the Nsector easily find a new job in the T-sector which in turn would have to generate a rather high trade balance surplus. If there is product innovation in the tradables sector both the TT curve and the NN curve will become steeper.

H.3 Real Exchange Rate Dynamics and Economic Effects Among the policy implications, we find that government in poor countries—such as EU accession countries—should stimulate savings and encourage FDI. It also would be wise to avoid early fixing of the nominal exchange rate, since the normal rise in the relative price of nontradables can no longer be achieved through nominal and real appreciation but only through an increase of the nontradables price which must be stronger than the price increase of the tradables price. That is, combining low inflation rates and the long-term increase of nontradables prices is difficult to achieve unless one has flexible exchange rates. There is, however, some risk that flexible exchange rate regimes could be associated with temporary overshooting. Since the exchange rate is an international relative price, the reason for overshooting dynamics could be internal or external. Strong and sudden real appreciations should be avoided. If the real appreciation comes not through a fall in the nominal exchange rate but through a very low inflation rate, this could create serious problems in an economy with insufficient downward wage flexibility. Moreover, the relative rise in the nontradables price to normally be expected along with a process of economic catching-up requires a fall in the nontradables price which could be difficult to achieve. While FDI inflows are basically a welcome ingredient for economic catching up, governments in host countries should be careful to avoid unnecessary concentration tendencies which could undermine the flexibility and innovativeness needed in an open economy exposed to temporary or permanent real appreciation of its currency. The EU Eastern enlargement will bring a medium-term real appreciation for the accession countries, which will affect FDI, trade and the current account. From a EU-15 perspective, Eastern Europe generates pressure for structural change and international outsourcing on the one hand, while driving high wage countries to increasingly specialize in technology-intensive goods on the other. For the governments of EU-15 countries, this could encourage promotion of technological progress through R&D subsidies. From an optimum growth perspective, both national governments and supranational EU policy should consider opportunities to bring about optimum growth. There clearly is a special challenge for the Euro zone due to uniform interest rates: The long-term dynamics of the current account, FDI growth and structural change require further analysis. It is not easy to design a consistent economic policy which stimulates the overall growth of EU-25 while maintaining economic stability.

H.3 Real Exchange Rate Dynamics and Economic Effects

291

The EU would be well advised to seriously consider the implications of endogenous growth theory and of the optimum growth theory. National governments in leading EU countries could indeed try to influence the progress rate, and in the Euro zone achieving optimum growth could be a challenge for the cooperation between national governments of the Euro zone’s member countries—adjusting R&D promotion policy adequately—and the ECB with its opportunities to adjust the interest rate. Eastern European accession countries should also carefully study the options of an optimum growth policy. A major challenge for EU-25 is that an efficient modernization and innovation process requires that the adjustment in EU-15—especially in high-wage countries— should be structural change toward skill-upgrading and product innovations which normally go along with a relative rise in export unit values (“relative” means in comparison to the USA, which is the leading OECD country). In a triangular economic perspective, rising EU-15 outsourcing toward EU accession countries in Eastern Europe should strengthen global competitiveness so that EU-15 RCAs in the global market should improve in particular in sectors in which EU-15 countries have rising imports from accession countries. Whether the overall development of EU-25 terms of trade will be positive in the medium term is unclear. As regards Germany, it is remarkable that the weighted average export unit value for industrial products stayed flat in the 1990s while that of the US strongly increased. Hence, the relative German export unit value has fallen considerably.

0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 1999

2000

2001

2002

2003

2004

2005

2006

2007

2008

Fig. 69 Relative export unit value of German industry (Germany relative to US, weighted). (Source: Comext Database)

292

Innovations in Macroeconomics

The developments in Germany suggest that it is facing declining profit rates in world markets and might therefore face an intensified struggle for income (i.e., social conflicts between workers and capital owners). If Germany is forced by the interplay of domestic dynamics and global structure change to move more toward less profitable sectors, the German current account balance might improve if import demand is sufficiently elastic. It will in any case be important to conduct further research on European and global economic dynamics in the future.

Appendix H.1: Statistical Measures of Structural Change According to STAMER (1999), the degree of structural change between the time points or time periods, 1 and 2, can be measured by the following indicators (for output X) if we distinguish sectors i = 1, . . . , n, n 

Xi = X

(1)

Xi = 1

(2)

i=1

and xi = Xi /X n  i=1

1. Norm of absolute values (NAV): NAV1,2 =

n 

|Xi,2 − Xi,1 |

(3)

i=1

2. Euclidean norm (EuN):

EuN1,2

  n  = (Xi,2 − Xi,1 )2

(4)

i=1

3. Sum of relative differences’ absolute values (SRD):   n     Xi,2 − Xi,1     , Xi,1 > 0 SRD1,2 =   X i=1

(5)

i,1

4. Information gain (IG): IG1,2 =

n  i=1

   Xi,2   , Xi,1 > 0, Xi,2 > 0  Xi,2 ld  Xi,1 

(6)

Appendix H.1: Statistical Measures of Structural Change

293

5. Growth rate parameter (GRP): GRP1,2 =

n

Xi,1 |gi,2 − g2 |,

i=1

that is with gi,2 = lnXi,2 − lnXi1 , g2 = lnX2 − lnX1 GRP1,2 =

n

  Xi,1 ln

i=1

(7)

 Xi,2  Xi,1  , Xi,1 > 0, Xi,2 > 0

6. LILIEN Index (LI) (see LILIEN 1982a, b):   n    Xi,2 , Xi,1 > 0, Xi,2 > 0 Xi,2 ln LI1,2 =  Xi,1

(8)

i=1

7. The modified LILIEN Index (MLI) (see STAMER 1999, p. 42–44):   n    Xi,2 2 Xi,1 Xi,2 ln , Xi,1 > 0, Xi,2 > 0 MLI1,2 =  Xi,1

(9)

i=1

Some important features of these indicators of structural change are summarized in Table 1. Note that the first three properties are necessary (and sufficient) conditions for an indicator to be a metric space. All indicators mentioned above have advantages and drawbacks. The choice of an indicator has to be made on the basis of the goals of the respective research. For many purposes, the norm of absolute values and/or the Euclidean norm are frequently used measures. A useful indicator as a measure of diversification is the index proposed by LILIEN (1982a). Some drawbacks of this indicator are remedied by the Modified LILIEN Index of STAMER (1999). This, however, comes at the cost of a more complex interpretation. Table 11 Features of structural change indicators. (Source: STAMER (1999, p. 53))

Norm of absolute values Euclidean norm Sum of relative differences’ absolute values Information gain Growth rate parameter LILIEN Index Modified LILIEN Index

Zero distance in case of identity

Symmetry in respect of time direction

Fulfillment of triangular inequality

Measure of dispersion

Consideration of sector’s weights

yes

yes

yes

no

yes

yes yes

yes no

yes no

no yes

yes no

yes yes

no no

no no

no yes

yes yes

yes yes

no yes

no yes

yes yes

yes yes

Austria Belgium & Luxembourg Bulgaria Croatia Cyprus Czech Republic Denmark Estonia Finland France Germany Greece Hungary Ireland Italy Latvia Lithuania Malta Netherlands Poland Portugal Romania Russia Slovak Republic Slovenia Spain Sweden Turkey UK

0.0282 0.0649 −0.0957 0.1755 −0.2069 −0.0921 −0.1066 −0.4466 0.2072 0.0696 0.0202 0.2293 −0.5494 −0.0376 0.0090 −0.6174 −0.6986 0.1057 −0.1648 0.0589 0.0851 0.0188 0.0496 −0.3409 −0.0613 0.0764 0.0107 −0.0547 −0.0016

Div NaV 0.0070 0.0380 −0.0584 0.0605 −0.1975 −0.0071 −0.0607 −0.1878 0.0843 0.0404 0.0050 0.0914 −0.1816 0.0209 0.0020 −0.3150 −0.3804 0.0405 −0.0787 0.0602 0.0184 −0.0055 0.0131 −0.1297 −0.0314 0.0380 −0.0043 −0.0298 −0.0013

Div EuN

Div IG 0.0568 0.0068 −0.0652 0.3429 −0.4727 0.0815 −0.0621 −1.8960 0.1243 0.0288 0.0100 0.2469 −0.8139 −0.0090 0.0121 −0.7041 −0.9331 0.2840 −0.0468 0.0225 0.1498 0.0527 0.0730 −0.6989 0.0738 0.0157 −0.0239 −0.0181 −0.0016

Div SRD −17.4023 −1.7611 2.1720 25.0527 −10.8361 3.2848 −2.4890 −1108.0745 −4.3084 1.0470 1.2968 7.0727 −20.5246 −1.1866 2.0360 −1095985614.4010 −120.0675 1.4643 −0.8003 −2.6743 44.1747 9.3168 11.8606 −36.6218 −52.7684 −5.9234 −14.2139 −6.2853 0.8464 0.0236 0.0352 −0.0692 0.0209 −0.0511 −0.0639 −0.0344 −0.0219 0.1531 0.0342 0.0086 0.1065 −0.1937 −0.0222 0.0085 −0.1577 −0.4341 0.2601 −0.0472 0.0260 0.0161 0.0127 0.0515 −0.0743 −0.0343 0.0362 0.0231 −0.0300 −0.0019

Div GRP 0.0482 −0.0016 −0.0350 0.3068 −0.2426 0.0978 −0.0915 −1.1023 0.0365 0.0387 0.0192 0.1867 −0.4597 −0.0057 0.0135 −0.3684 −0.3363 0.0441 −0.0777 0.0051 0.1505 0.0518 0.0336 −0.4170 0.0955 0.0274 −0.0422 −0.0068 −0.0006

Div LI

0.0023 0.0165 −0.0241 0.0217 −0.0754 −0.0075 −0.0260 −0.0680 0.0351 0.0174 0.0021 0.0368 −0.0670 0.0089 0.0008 −0.1372 −0.1342 −0.0094 −0.0352 0.0256 0.0059 −0.0030 0.0022 −0.0386 −0.0158 0.0165 −0.0015 −0.0148 −0.0005

Div MLI

Table 12 Various indicators measuring structural change based on export data to the EU-15 at the NACE two-digit level (difference between indicators in the time periods 1998–2003 and 1993–1998). (Source: Own calculations)

Appendix H.2: Indicators Measuring Structural Change

294 Innovations in Macroeconomics

I. Innovations in the Digital Economy: Promotion of R&D and Growth in Open Economies

I.1 Introduction Starting in the 1980s, a new wave of economic globalization has brought about a relative increase of foreign direct investment and hence a risig role of multinational companies (MNCs). MNCs are crucial for the diffusion of new knowledge, and those firms are also key actors in research and development (R&D). With China and a new Russia—plus the smaller former socialist CMEA countries of Eastern Europe—opening up to the world economy, new players have entered global markets and competition has intensified. The end of the Cold War has intensified the global innovation race for civilian products as the share of military R&D expenditures in the USA, France and the UK has fallen to close or less than 50%. There is a long-term upward trend in the ratio of expenditures on R&D to national income. While the ratio of R&D to GDP was close to 1% in OECD countries in the 1960s, it reached about 2% in the 1980s and is moving toward 3% at the beginning of the twenty-first century. Technological competition has increased since expenditures on R&D have grown relative to GDP. While process innovations have reduced production costs, product innovations stand for novel goods for which consumers (or investors) show a higher willingness to pay than for standard products. Product innovations also tend to raise profitability of firms and hence stimulate investment. While innovations in industry are often reflected in patents, innovations in services are more difficult to protect through intellectual property rights. A special case is software which enjoys copyright protection and more recently patent protection in the USA. Technological competition also increased in the 1990s and the early twenty-first century, because global diffusion of new knowledge accelerated due to the expansion of the internet. With the expansion of the digital economy, there is an increasing role of innovative services whose significance is rather difficult to assess since patenting is relatively rare. Moreover, while a rise of export unit values (corrected for inflation) is, to some extent, a useful indicator for assessing the novelty of a product, a similar analytical category for services is not available. First, many tradable services are

P. J. J. Welfens, Innovations in Macroeconomics, DOI 10.1007/978-3-642-11909-5_9, © Springer-Verlag Berlin Heidelberg 2011

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intra-company services for which transfer prices are applied which might reflect the tax considerations of MNCs rather than the novelty of the service provided. Second, many services are nontradable, thereby bringing identification problems in the context of the Balassa–Samuelson effect, which suggests that the relative price of nontradables will increase parallel to the rise of per capita income. (There is also the more general problem that the effects of process innovations which reduce costs and product innovations—which raise the willingness to pay—often overlap in reality). This structural relative price effect makes it difficult to relate price increases in services to the degree of innovativeness in the provision of services. Thirdly, productivity measurement in services is more difficult than in industry, which makes the distinction between product innovations and process innovations cumbersome. Finally, many services are provided by government which has a particularly weak record in measuring productivity growth and in developing innovations. In a modern services society, it is hardly conceivable to fully exploit technological dynamics without carefully nurturing and stimulating innovativeness in the services sector, a point which has largely been overlooked in the Lisbon agenda of the EU aimed at making the union the most competitive economy in the world by 2010. As regards technologically leading countries, the USA saw an acceleration in both economic growth and patenting in the 1990s. With respect to the EU, growth was slower than in the USA in the 1990s, but the combination of the single market and EU enlargement in 2004 should allow higher growth in the EU-25. According to the Lisbon summit, the EU is to become the most competitive knowledge-based economy by 2010, a goal which includes the aim of raising employment rates considerably. The Lisbon goal cannot be achieved if EU member countries do not see improvements in the growth of output and employment. Germany, France, Italy and the UK play a key role here. The smaller open economies achieved a solid performance in the late 1990s with a higher growth, higher employment and reduced budget deficits or even surpluses being achieved. (The latter holds true even for Finland, which had a record high 18% unemployment rate in 1993 yet only 9% in 2004.) While the UK achieved full employment and sustained growth in the 1990s, the three core countries of the Euro zone still have to make progress. High unemployment rates in France, Italy and Germany are key problems with close to 30% unemployment in Southern Italy and Eastern Germany. A wide range of policy reforms in Germany in 2003/2004 (Hartz reforms) is likely to yield positive effects in terms of both lower unemployment and higher employment ratios within a medium-term adjustment period. However, restoring sustained growth is a different issue, as is overcoming the economic West–East divide in Germany. The German government has declared that raising expenditures on R&D promotion relative to GDP is a medium term policy priority. It is unclear whether the German states, which account for roughly a half of the government R&D expenditures, will contribute significantly to this goal. Both national and regional governments face the constraints of the Stability and Growth Pact, with Germany having exceeded the 3% deficit ratio in 2002, 2003 and 2004 (the latter year judging by the deficit ratio of the first half of 2004). Hence, Germany—and other EU countries with similar problems—will face serious dilemmas in raising R&D expenditures.

I.1 Introduction

297

EU enlargement and economic globalization mean a changing international division of labor. The new international division of labor at the beginning of the twenty-first century is characterized by economic catching-up processes in newly industrializing countries ofAsia—including China—and in Eastern Europe and Russia. Asian NICs are richly endowed with labor and have achieved rising capital intensity due to domestic investment and foreign direct investment. Former socialist countries in Eastern Europe and Russia are richly endowed with unskilled labor and human capital. Western Europe’s high-wage countries must increasingly specialize in technology-intensive and knowledge-intensive products. Focusing on the ratio of R&D expenditures to GDP, Sweden as the OECD leader reached 4% at the beginning of the twenty-first century. As regards the ratio of expenditures on higher education to GDP, Sweden is No. 2 behind the USA. As regards R&D expenditures, Germany achieved 2.4% of GDP in 2003, slightly higher than in the years before but much lower than the 2.9% of 1989. Germany’s problems with the 3% deficit ceiling impair efforts to raise expenditures on R&D and education, and similar problems can be found in Italy and France. While the USA spends about 2.5% of GDP and Sweden (and Finland) about 1.7% of GDP on higher education, Germany spends only 1% of its GDP in this field for which German states are almost exclusively responsible. The latter also contribute to roughly 50% of public R&D expenditures. Skilled labor is largely complementary to R&D (and R&D requires skilled labor inputs itself). As regards skilled labor, this category is not only represented by university graduates, rather skilled labor is also related to training activities in firms. With workers’ tenure falling gradually in large firms in Europe, the incentive for firms to invest in training and retraining is falling. The New Growth Theory has emphasized the role of R&D, skills and differentiated products. Economic globalization forces firms to relocate production more often on an international scale, and the risk to train workers for domestic and foreign competitors also fails to encourage firms to reinforce training activities. To the extent that globalization places stronger pressure on capital markets to come up with a high return on investment in the short term, this could also undermine firms’ long-term activities to invest in human capital. This could be a particular problem for Germany and Austria (as well as Switzerland) whose firms have a long record of investment in training and retraining. As international competitiveness always reflects relative competitive advantages, it is also noteworthy that many countries in the EU have caught up with the Federal Republic of Germany in terms of infrastructure capital, R&D expenditures and education expenditures (relative to GDP). EU eastern enlargement has opened up new opportunities for the relocation of industry, and often supplier firms—they are expected to deliver on-time innovative high-quality inputs (“complex subsystems”)—follow the foreign investment of large companies, thereby accelerating the international transfer of know-how and knowledge. Moreover, the internet reinforces the international diffusion of knowledge so that first mover advantages could fade away more quickly. These developments as well as the long record of high unemployment raise many questions in terms of raising innovativeness, accelerating structural change and launching adequate policy reforms for high-wage countries. The careful

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exploitation of opportunities to raise productivity in the information and communication technology (ICT) could be a new and important policy element (BARFIELD/HEIDUK/WELFENS 2003). Raising labor productivity has been an important element of high growth in the USA and several EU countries in the 1990s. While there is no debate about the productivity-enhancing role of ICT production, it is less clear that the use of ICT—linked to ICT capital accumulation—strongly contributes to higher growth of output and productivity. (A strange case is productivity measurement in the USA retail sector where a firm with ten employees selling ten standard PCs in 1999, but ten more modern PCs in 2000—worth five times as much, according to hedonic price measurement, as a 1999 PC—shows up as a productivity growth of 500%!) Production of computers or telecommunication equipment seems to be crucial for growth. Given the increasingly important role of innovation dynamics for international markets, the promotion of R&D becomes a crucial part of economic policy. The traditional argument in favor of R&D promotion is the existence of positive external effects which imply that marginal social benefit exceeds marginal private benefits of R&D expenditures. However, some new developments in innovation dynamics have to be taken into account when raising the issue as to which role government should assume in the promotion of innovation and skills.

I.2 Innovations and New Economic Structures in the Digital Economy I.2.1 Selected Innovation Traits in OECD Countries Product innovations allow for the increase in product prices in world markets and hence the earning of high incomes (wages and profit). Process innovations are equivalent to cost reductions and allow firms to fetch higher market shares and high incomes, in particular if price elasticity is larger than unity or if increased market share also allows for the exploitation of dynamic scale economies (e.g., learning by doing effects). Innovation dynamics can be assessed in different ways: • Innovation expenditures, usually scaled by sales (“R&D intensity”); this in an R&D input indicator • Patents per capita (R&D output indicator) • Product innovation rate (new products to the market in % of sales, survey data, innovation output indicator) • Diffusion rate (new-to-the-firm products, figures are from surveys) Taking a closer look at selected EU countries as well as the USA and Japan, one finds that Sweden, Germany and Finland were leading in R&D intensity in manufacturing (6.4, 4.7 and 3.9, respectively, in 2003; EU average 3.45). France and the Netherlands achieved 3.1, the UK 3.0. Germany’s R&D intensity in the services sector was much weaker, namely 1.6 compared to the EU average of 1.8. Sweden was a clear leader

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in this field. France and the UK recorded 1.6 and 1.4, respectively. It is interesting to observe that in the field of product innovations in manufacturing, Germany was below the EU average despite its leading position in R&D intensity. Finland, Sweden and France were leading countries in the field of product innovations. This suggests that the German innovation system might have considerable efficiency problems. A similar picture is found in production innovation in the services market. As regards diffusion indicators, Germany is a leading EU country. Moreover, Sweden and Germany recorded a high ratio of New-to-firm to New-to-market in the manufacturing industry, which points to relatively fast diffusion (this could reflect strong competition). Table 13 European innovation scoreboard 2003—selected member states. (Source: EUROPEAN COMMISSION (2003a), Staff Working Papers, European Innovation Scoreboard 2003, p. 27, Brussels and own calculations) Innov exp manuf Innov exp serv New-to-mark prods manuf New-to-mark prods serv New-to-firm prods manuf New-to-firm prods serv New-to-firm/New-to-mark prods manuf New-to-firm/New-to-mark prods serv

EU-15 3.4 1.8 10.5 7.4 28.6 18.8 2.7

DE 4.7 1.6 7.1 3.7 40.3 16.4 5.7

FR 3.0 1.5 9.5 5.5 17.5 17.1 1.8

NL 3.0 0.7 – – 23.8 13.9 –

AT 2.8 0.9 8.4 4.3 23.1 12.8 2.8

FI 3.9 0.9 27.2 12.2 31.1 18.8 1.1

SE 6.4 19.1 3.5 9.3 32.1 23.7 9.2

UK 2.9 1.3 9.5 – – – –

2.5

4.4

3.1

–

3.0

1.5

2.5

–

DE = Germany, FR = France, NL = Netherlands, AT = Austria; FI = Finland; SE = Sweden; UK = United Kingdom

Against such apparent innovation weakness, one might consider it surprising that Germany has such a high current account surplus, e.g., 5% of GDP in 2002. However, 90 billion net exports recorded in 2002 would quickly melt away if full employment could be restored; investment would increase by about 10% or by about Euro 20 bill., consumption also by about 5% or 60 bill., which would leave net exports down at Euro 10 bill. The assumption here is that consumption is a positive function of disposable income and a negative function of the expected unemployment rate uE . Investment is assumed to depend negatively on the real interest rate and the expected unemployment rate. To put it differently, a high net export position of a country with a high unemployment rate cannot simply be considered an indicator of high international competitiveness. Rather, it largely reflects weak domestic demand. The reduction of net exports in the case of rising employment and hence a falling expected and actual unemployment rate will hold even if one takes into account the expansionary impact of higher employment on the supply side. This perspective is, of course, not to deny that in a situation of high net exports (and also in the case of net imports: see the USA in the 1990s), certain sectors are positively successfully specialized in production and export of technology-intensive or innovative products. International competitiveness in specific sectors can be assessed on the basis of revealed comparative advantage indicators (RCA: sectoral export–import balance

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relative to overall export–import balance in the EU-15 single market with an indicator above 1 indicating a positive sectoral competitive advantage) or with respect to export unit values. Higher RCAs and higher export unit values in certain sectors are likely to contribute quite strongly to output growth in the long run. Scale-intensive sectors and science-intensive sectors are obviously two potentially relevant sectors. In a highwage economy, emphasis on science-based products can strengthen competitiveness through product innovations which will temporarily lead to rising export unit values and hence higher profitability. This is a Schumpeterian perspective which leads away from perfect competition. Scale-intensive products also imply that the perfect competition model does not hold. In some cases, scale-intensive products exhibit both static and dynamic scale economies so that high production volumes could be combined with first mover advantages. As regards export unit values and the change of export unit values over time, one should also take a look at weighted export unit values so that the relative economic significance of certain sectors can be understood. As regards Germany, it is well-known that the country has a positive RCA—read RCA above unity—in both the automotive industry and in other transport equipment (NACE 34 and 35). Taking a closer look at German industry, one can see that specialization in terms of RCA changed slightly in the decade after 1993. There is a high RCA in the manufacturing of fabricated metal products (NACE 28, not including machinery and equipment). It is also noteworthy that the export unit value has increased over time for this product group. In the field of office machinery and computers (NACE 30)—a sector which (together with NACE 32: telecommunications equipment) is considered highly relevant for productivity growth—Germany has a negative RCA. Worse yet, the export unit value in this sector has declined. NACE 32 has improved over time. The overall picture with respect to the long-term development of export unit values in German industrial export reveals that export unit values—average revenue per quantity unit (e.g., kilogram of steel etc.)—showed few changes over the period from 1993 to 2001. Which sectors are most important for economic dynamics: In a narrow sense those sectors which show a positive RCA and a high-weighted export unit export value; this at least is the concept presented here. As regards the economic significance of export unit values it is indeed useful to take a closer look at weighted unit values where sectoral shares in overall manufacturing exports are taken as weights: considering only weighted indicators reaching at least 0.75 (hence export unit value must be high or the share of the respective sector in overall export of manufacturing)—see the bold figures in the respective tables—we see that 29, 30, 32, 33, 34 and 35 are crucial sectors for Germany; 32, 33, 34 (33 and 34 stand for the automotive sector; 32 is medical, precision and optical instruments, watches and clocks) are important sectors in each of the three countries considered, 35 and 29 only in Germany and the UK, 31 only in Hungary. Note that the change in the weighted export unit value of 32, 33 and 34 was positive in Germany, the UK and Hungary over the period 1992–2001; and this should translate into relatively rising wages for skilled workers as we may assume that these sectors are using skilled labor intensively. Interestingly, 18 (wearing apparel) which stands for labor-intensive production is important in both the UK and in Hungary. Moreover, 18 stands indeed

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for a positive RCA both in the UK and in Hungary (figures underlined in the subsequent tables). As regards Germany 29, 33, 34 and 35 stand for an economically significant positive RCA, in the UK we have 29, 34 and 35 (note that 29 and 34 both stood for a positive RCA in the UK and Germany in 2000/01); as regards Hungary we find 18, 30, 31, 32, 34 as positive RCA: 34 is an overlap with the UK and Germany. The fact that Hungary could improve the weighted export unit value strongly in 34, the automotive sector, points to a strong catching-up process in the Hungarian automotive sector. To the extent that this finding is representative for accession countries in eastern Europe Germany’s automotive firms acting in the lower quality segments of the market might face profitability problems in their German plants. The new international division of labor in Europe suggests that mass production of standard cars will be largely relocated to Eastern Europe’s low wage countries. Hence the respective regions will face serious labor reallocation challenges in the early twenty-first century. In sector 18 there is an overlap of Hungary with the UK, 30, 31 and 32 indicate successful Hungarian specialization. However, note that 31 and 32—differentiated goods (this also includes 29)—stand for relative footloose industries: The manufacturing of office machinery and computers (30) and of electrical machinery and apparatus n.e.c. (31) could internationally be relocated relatively quickly. As regards Germany it is important to note that the country—in contrast to the UK (whose labor productivity has reached about 80% of the German level in the 1980s and 1990s), has no positive RCA in labor-intensive industries—and this is surprising in a country which has more than four million unemployed, most of which are unskilled workers. One may consider this finding as an indicator for insufficient wage differentiation in Germany. Obviously in all three countries medium technology fields are important for export dynamics and RCAs, respectively. One should point out that RCAs typically follow relative sectoral patent positions. A rising share in global patents in the respective sector translates with a time lag of 3 to 4 years into an improved sectoral RCA. Hence expenditures on R&D and innovation policies are important. Compared to the apparently stable German industrial specialization pattern, Hungary has launched a rather impressive catching-up process since reinforcing the RCAs in some technology-intensive sectors and was also able to fetch higher export unit values—a proxy for its ability to extract high prices in competitive EU market—in EU-15 markets. The British industry, whose relative size has declined over decades, still has certain fields in which it shows considerable strength. Interestingly, RCA and export unit values in labor-intensive production increased in the period between 1993 and 2001, which obviously is consistent with the improved employment record of the UK. At the same time, the UK has also improved its position in science-intensive products. Particularly important is NACE 30 (office equipment and computers), where the export unit value has improved over time while the RCA remained fairly stable below unity. The UK has shown a strong weighted improvement of the export unit value in NACE 32, the manufacturing of radio, television and communication equipment. With respect to the UK, considerable employment growth in the overall economy must, however, be explained largely by the expansion of the services

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sector. To some extent, it seems surprising that the UK has a positive RCA (exceeding unity) in only a few sectors. Moreover, where RCA is above unity, it is only weakly so. By contrast, Germany’s industry shows some clear fields of comparative advantage as does Hungary, an interesting case of new economic dynamics in an EU accession country. It is quite noteworthy that Hungary achieved higher export unit values in several sectors. The table shows that weighted improvements of export unit values were strong in 30, 32 and 34, essentially electronic products which represent scale-intensive goods, science-based goods and differentiated goods (Classification of Industries follows OECD; (See BORBÉLY 2006) RCA is modified RCA). 1.2

7000

1.0 5000

0.8 0.6

3000 0.4 0.2

1000

0.0 –1000

–0.2 –0.4

–3000 –0.6 –0.8

–5000

–1.0 Labor Intensive

Resource Intensive

–1.2

Ress. Scale

Scale Intensive

Scale Science- Differentiated Goods Sci. based

–7000

17 18 19 28 36 15 16 20 23 26 27 21 22 24 25 34 35 30 33 29 31 32

1999

2000

2001

2002

2006

2007

2008

EUV 1999

2003

2004

2005

EUV 2008

Fig. 70 Germany—RCA and export unit values. (Source: Comext database)

I.2.2 Innovation System and Innovation Record From a microeconomic perspective, the innovation process is clearly affected by incentives for the firm and the interdependency within the market. Key drivers of the innovation process are: • Adequate governance of the firm which is a crucial challenge particularly in large companies and in small companies growing fast.

RCA 2000/2001

0.24 0.07 0.28 0.11 0.16 0.79 0.50 1.10 0.29 0.91 0.57 0.49 0.53 0.56 1.24 1.40 1.31 1.93 3.64 0.20 4.73 0.97

NACE (2-digit)

15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36

0.40 2.04 6.85 28.16 9.17 1.37 0.84 14.21 0.11 3.95 8.00 3.91 7.35 12.57 20.61 144.80 35.90 252.70 150.70 9.73 299.90 22.27

EUV 2001

0.26 1.64 5.28 17.75 11.17 0.82 0.50 9.48 0.09 2.25 6.13 2.66 4.33 8.64 14.22 117.80 25.52 125.40 84.41 6.96 76.10 12.45

EUV 1993

0.01 0.00 0.04 0.06 0.02 0.01 0.01 0.14 0.00 0.52 0.14 0.03 0.21 0.18 2.61 22.11 1.60 27.94 13.41 0.32 53.81 0.44

EUV 2001 Weighted (exp. share) 0.01 0.00 0.06 0.11 0.04 0.01 0.01 0.11 0.00 0.32 0.13 0.02 0.14 0.13 1.57 20.29 1.01 8.35 7.53 0.22 10.36 0.23

EUV 1993 Weighted (exp. share) 0.00 0.00 −0.02 −0.05 −0.03 0.00 0.00 0.03 0.00 0.20 0.00 0.01 0.07 0.05 0.59 1.82 0.58 19.59 5.88 0.10 43.45 0.22

Weighted (exp. share)

dEUV

Table 14 Germany—RCA, EUV, EUV weighted with the sectoral export shares of manufacturing

0.16 0.02 0.95 1.25 0.39 0.21 0.29 3.07 0.02 11.56 3.09 0.65 4.75 3.90 48.12 492.20 35.52 622.00 298.50 7.06 1197.00 9.89

EUV 2001 Weighted (GDP share) 0.11 0.01 0.67 1.23 0.48 0.14 0.12 1.20 0.01 3.50 1.49 0.24 1.54 1.43 17.43 225.10 11.22 92.67 83.58 2.43 114.90 2.50

EUV 1993 Weighted (GDP share)

0.06 0.00 0.28 0.02 −0.09 0.08 0.16 1.87 0.00 8.06 1.61 0.41 3.21 2.48 30.70 267.00 24.29 529.30 214.90 4.63 1082.00 7.39

Weighted (GDP share)

dEUV

I.2 Innovations and New Economic Structures in the Digital Economy 303

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Innovations in Macroeconomics

6

40

35 5

4

RCA

25

3

20

15 2 10 1 5

0

0 17

18

19

28

36

15

Labor Intensive

16

20

23

26

Resource Intensive

27

Res. + Scale

21

22

24

25

Scale Intensive

1993

1994

1995

1996

1999

2000

2001

EUV 01

34

35

30

33

29

31

32

Scale Science Differentiated + Science -based Goods

1997 EUV 93

Fig. 71 Hungary—RCA and export unit values. (Source: Comext database)

Fig. 72 UK—RCA and export unit value. (Source: Comext database)

1998

Export Unit Value (€/kg)

30

RCA 2000/2001

0.46 0.00 0.85 2.11 1.42 1.05 0.25 0.19 0.51 0.31 0.70 0.65 0.60 0.87 0.73 1.28 2.83 2.59 0.82 1.46 0.18 0.92

NACE (2-digit)

15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36

1.45 0.00 5.72 28.39 17.21 0.37 0.84 2.32 0.27 1.09 3.04 0.73 0.56 2.40 4.51 29.81 11.36 29.91 34.83 9.93 5.96 4.69

EUV 2001

1.27 3.19 6.29 29.41 13.31 0.38 0.75 1.89 0.18 0.56 1.93 0.53 0.29 1.69 3.16 9.74 8.32 18.76 22.37 4.68 4.54 2.50

EUV 1993 0.05 0.00 0.11 1.05 0.28 0.00 0.01 0.00 0.00 0.04 0.07 0.01 0.02 0.05 0.29 3.59 1.10 5.06 0.80 2.35 0.05 0.09

EUV 2001 Weighted (exp. share) 0.04 0.00 0.12 1.09 0.21 0.00 0.01 0.00 0.00 0.02 0.04 0.01 0.01 0.04 0.20 1.17 0.81 3.17 0.51 1.11 0.03 0.05

EUV 1993 Weighted (exp. share) 0.01 0.00 −0.01 −0.04 0.06 0.00 0.00 0.00 0.00 0.02 0.02 0.00 0.01 0.02 0.09 2.42 0.29 1.89 0.29 1.24 0.01 0.04

dEUV Weighted (exp. share)

Table 15 Hungary—RCA, EUV, EUV weighted with the sectoral export shares of manufacturing

19.29 0.00 48.85 494.80 118.30 1.62 2.72 1.69 1.59 22.93 27.75 2.89 8.56 21.86 113.70 2503.00 489.90 1624.00 198.10 941.10 6.85 37.21

EUV 2001 Weighted (GDP share) 16.37 0.00 26.15 438.10 70.66 0.63 0.50 0.83 0.29 5.09 4.43 1.46 1.76 6.41 26.54 9.06 74.79 35.17 20.40 20.94 2.63 8.30

EUV 1993 Weighted (GDP share)

2.92 0.00 22.70 56.65 47.72 0.99 2.22 0.87 1.30 17.85 23.32 1.44 6.80 15.45 87.21 2494.00 415.10 1589.00 177.70 920.10 4.23 28.91

dEUV Weighted (GDP share)

I.2 Innovations and New Economic Structures in the Digital Economy 305

RCA 2000/2001

1.54 0.41 1.57 1.47 2.45 7.05 2.30 0.99 0.48 0.74 1.11 1.22 0.74 1.09 1.10 0.68 1.07 0.83 0.96 1.53 1.15 1.56

NACE (2-digit)

15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36

1.42 9.48 9.72 43.62 31.73 0.52 0.91 3.31 0.28 2.02 3.72 0.68 0.88 4.37 10.12 59.74 12.73 71.05 89.80 9.10 35.19 6.82

EUV 2001

1.09 6.53 5.33 27.33 14.65 0.37 0.82 3.33 0.13 1.25 3.44 0.48 0.75 4.05 9.26 81.05 9.98 32.98 53.50 7.36 14.48 6.72

EUV 1993 0.10 0.01 0.22 0.75 0.39 0.01 0.03 0.03 0.00 0.22 0.10 0.01 0.03 0.09 0.81 9.10 0.43 5.88 2.05 1.51 1.16 0.15

EUV 2001 Weighted (exp. share) 0.08 0.01 0.12 0.47 0.18 0.00 0.03 0.03 0.00 0.14 0.09 0.01 0.03 0.09 0.74 12.35 0.33 2.73 1.22 1.22 0.48 0.15

EUV 1993 Weighted (exp. share) 0.02 0.00 0.10 0.28 0.21 0.00 0.00 0.00 0.00 0.08 0.01 0.00 0.01 0.01 0.07 −3.25 0.09 3.15 0.83 0.29 0.68 0.00

dEUV Weighted (exp. share) 10.51 5.47 14.20 50.97 9.44 0.14 1.79 9.62 1.27 33.81 10.91 0.98 4.67 8.67 55.21 1637.00 52.73 984.80 175.40 98.09 169.50 14.48

EUV 2001 Weighted (GDP share)

Table 16 United Kingdom—RCA, EUV, EUV weighted with the sectoral export shares of manufacturing and of GDP

8.35 0.62 10.73 32.08 6.13 0.08 1.24 6.64 0.58 17.26 6.70 0.61 2.41 4.09 45.32 395.70 21.90 134.20 108.40 47.35 63.42 8.24

EUV 1993 Weighted (GDP share)

2.15 4.85 3.47 18.89 3.31 0.06 0.55 2.98 0.69 16.55 4.21 0.37 2.26 4.58 9.88 1242.00 30.82 850.50 66.95 50.74 106.00 6.23

dEUV Weighted (GDP share)

306 Innovations in Macroeconomics

RCA 2000/2001

1.19 0.27 0.92 0.78 0.45 0.74 0.78 0.85 0.75 0.97 1.07 0.95 1.12 0.81 0.83 0.68 1.06 0.88 0.80 1.34 1.72 0.74

NACE (2-digit)

15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36

0.99 7.03 4.20 13.40 11.10 0.37 0.81 3.14 0.34 1.46 3.45 0.56 0.56 2.78 6.91 36.65 6.92 31.66 23.99 7.27 86.05 5.18

EUV 2001

1.07 4.75 5.84 33.46 13.97 0.32 0.69 4.48 0.17 1.02 3.72 0.49 0.47 2.79 7.08 82.90 8.29 29.68 49.62 7.24 72.65 2.52

EUV 1993 0.09 0.01 0.09 0.19 0.06 0.00 0.02 0.02 0.01 0.21 0.11 0.01 0.03 0.06 0.49 2.70 0.25 1.59 0.47 1.56 5.62 0.08

EUV 2001 Weighted (exp. share) 0.16 0.00 0.20 0.72 0.12 0.00 0.02 0.03 0.00 0.17 0.14 0.01 0.03 0.07 0.50 4.11 0.29 1.11 1.12 1.13 4.83 0.10

EUV 1993 Weighted (exp. share)

EUV 2001 Weighted (GDP share) 13.09 1.28 12.59 27.65 8.73 0.36 2.87 3.48 0.84 30.50 16.61 1.19 5.07 8.31 72.10 398.10 36.60 234.80 69.53 229.60 829.90 11.61

dEUV Weighted (exp. share) −0.07 0.01 −0.12 −0.54 −0.06 0.00 0.00 0.00 0.00 0.04 −0.03 0.00 0.00 −0.01 −0.01 −1.41 0.04 0.48 −0.65 0.43 0.80 −0.02

Table 17 France—RCA, EUV, EUV weighted with the sectoral export shares of manufacturing and of GDP

11.13 0.32 12.83 47.64 7.73 0.17 1.33 2.56 0.18 11.16 10.57 0.76 2.38 4.68 38.88 285.90 21.68 74.82 70.81 91.59 347.00 3.03

EUV 1993 Weighted (GDP share)

1.96 0.97 −0.24 −19.98 0.99 0.19 1.54 0.92 0.66 19.34 6.04 0.43 2.68 3.63 33.23 112.10 14.92 159.90 −1.28 138.00 482.80 8.58

dEUV Weighted (GDP share)

I.2 Innovations and New Economic Structures in the Digital Economy 307

RCA 2000/2001

0.84 0.01 2.79 1.85 3.76 0.62 0.68 0.89 0.49 0.65 1.46 2.00 0.92 1.72 1.99 0.29 1.10 0.45 0.72 0.77 0.95 2.39

NACE (2-digit)

15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36

1.07 0.70 9.53 15.80 17.62 1.30 1.12 2.69 0.28 1.79 2.95 0.59 0.71 2.58 6.19 56.58 6.54 24.50 20.28 6.32 24.99 3.89

EUV 2001

1.04 0.75 10.83 29.77 11.43 1.49 0.99 2.88 0.15 1.30 2.90 0.65 0.57 2.57 6.35 89.47 5.67 19.24 24.72 5.81 21.79 5.20

EUV 1993 0.07 0.00 0.59 0.52 0.78 0.01 0.02 0.02 0.00 0.17 0.13 0.02 0.04 0.11 1.04 1.81 0.24 0.63 0.36 0.78 0.90 0.19

EUV 2001 Weighted (exp. share) 0.07 0.00 0.96 1.36 0.68 0.01 0.02 0.02 0.00 0.10 0.13 0.02 0.02 0.10 0.96 4.88 0.19 0.42 0.43 0.48 0.82 0.29

EUV 1993 Weighted (exp. share) 0.00 0.00 −0.37 −0.83 0.11 0.00 0.01 0.00 0.00 0.07 0.00 −0.01 0.01 0.01 0.08 −3.06 0.05 0.21 −0.08 0.30 0.09 −0.10

dEUV Weighted (exp. share)

Table 18 Italy—RCA, EUV, EUV Weighted with the sectoral export shares of manufacturing and of GDP

7.93 0.01 69.33 61.52 92.16 0.84 2.72 2.51 0.36 19.81 15.50 2.10 4.23 13.07 122.20 212.80 28.73 73.63 41.91 91.19 105.90 22.38

EUV 2001 Weighted (GDP share) 4.70 0.00 65.67 92.67 46.23 0.53 1.24 1.48 0.11 7.00 8.73 1.70 1.71 6.92 65.92 333.20 13.04 28.80 29.62 32.51 55.71 19.76

EUV 1993 Weighted (GDP share)

3.23 0.00 3.67 −31.14 45.93 0.31 1.48 1.02 0.25 12.82 6.77 0.39 2.52 6.14 56.40 120.30 15.69 44.83 12.29 58.68 50.25 2.62

dEUV Weighted (GDP share)

308 Innovations in Macroeconomics

RCA 2000/2001

0.24 0.07 0.28 0.11 0.16 0.79 0.50 1.10 0.29 0.91 0.57 0.49 0.53 0.56 1.24 1.40 1.31 1.93 3.64 0.20 4.73 0.97

NACE (2-digit)

15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36

0.40 2.04 6.85 28.16 9.17 1.37 0.84 14.21 0.11 3.95 8.00 3.91 7.35 12.57 20.61 144.80 35.90 252.70 150.70 9.73 299.90 22.27

EUV 2001

0.26 1.64 5.28 17.75 11.17 0.82 0.50 9.48 0.09 2.25 6.13 2.66 4.33 8.64 14.22 117.80 25.52 125.40 84.41 6.96 76.10 12.45

EUV 1993

0.01 0.00 0.04 0.06 0.02 0.01 0.01 0.14 0.00 0.52 0.14 0.03 0.21 0.18 2.61 22.11 1.60 27.94 13.41 0.32 53.81 0.44

EUV 2001 Weighted (exp. share) 0.01 0.00 0.06 0.11 0.04 0.01 0.01 0.11 0.00 0.32 0.13 0.02 0.14 0.13 1.57 20.29 1.01 8.35 7.53 0.22 10.36 0.23

EUV 1993 Weighted (exp. share) 0.00 0.00 −0.02 −0.05 −0.03 0.00 0.00 0.03 0.00 0.20 0.00 0.01 0.07 0.05 0.59 1.82 0.58 19.59 5.88 0.10 43.45 0.22

Weighted (exp. share)

dEUV

Table 19 USA—RCA, EUV, EUV weighted with the sectoral export shares of manufacturing and of GDP

0.16 0.02 0.95 1.25 0.39 0.21 0.29 3.07 0.02 11.56 3.09 0.65 4.75 3.90 48.12 492.20 35.52 622.00 298.50 7.06 1197.00 9.89

EUV 2001 Weighted (GDP share) 0.11 0.01 0.67 1.23 0.48 0.14 0.12 1.20 0.01 3.50 1.49 0.24 1.54 1.43 17.43 225.10 11.22 92.67 83.58 2.43 114.90 2.50

EUV 1993 Weighted (GDP share)

0.06 0.00 0.28 0.02 −0.09 0.08 0.16 1.87 0.00 8.06 1.61 0.41 3.21 2.48 30.70 267.00 24.29 529.30 214.90 4.63 1082.00 7.39

Weighted (GDP share)

dEUV

I.2 Innovations and New Economic Structures in the Digital Economy 309

310

Innovations in Macroeconomics

• The expected rate of profit which is partly determined by first mover advantages, patenting performance and R&D subsidies. • The intensity of competition and the growth of the overall market—intensive competition will typically stimulate innovations, and such innovations are easier to finance if the overall market is growing. • Technological dynamics—the 1990s witnessed an acceleration of patents of several countries in the USA, above all of the USA itself. • Locational advantages which include the availability of skilled labor and the associated tacit knowledge (codified knowledge is easily transferable, while tacit knowledge is immobile to the extent that skilled workers cannot be easily moved abroad). As regards immobility of industries, one should point out that few technologyintensive industries are really immobile, namely those where R&D activities and production activities cannot easily be separated geographically. This is typically the case in the air & space industry (high technology intensive which is a typical trait of the US industry and of part of the French industry) and in the production of specialized machinery and capital equipment (medium technology intensive which is a typical trait of German industry). High technology production is not generally immobile as the case of the chip industry clearly illustrates (e.g., one can develop the blueprint for a new generation of chips in California or Bavaria or Scotland, but after the first innovation stage, the production can be relocated to countries with low wage costs in Eastern Europe or Asia). Countries have different innovation systems as the interaction of government institutions, firms, universities and research labs has evolved within different countries in various ways. Innovation dynamics is not only a matter of specialization and human capital formation. In the case of integrated countries—e.g., in the case of the EU, ASEAN or NAFTA—it is important to launch novel final products tailored to regional and global markets. What also matters at the level of the firm is the ability to adequately use the knowledge of specialized suppliers whose ability to develop novel subsystems is a crucial asset in the automotive industry of many countries. Moreover, using novel intermediate products imported from countries with successfully innovative firms is also an element of competitiveness in open economies. What matters more in the long run is the dynamics of the overall innovation system, which not only includes firms and their innovative suppliers but also specialized R&D firms, the innovative potential of researchers and labs at universities and the availability of modern infrastructure (roads, railways, airports, telecommunications). The incentives for innovation are partly intrinsic, partly in the form of expected rewards for which intellectual property rights and R&D promotion by government are important. Moreover, innovation is associated with a certain degree of risk, so that sustained high innovation dynamics require favorable access to equity capital including venture capital. Continental EU countries have traditionally relied much on the banking system which, in turn, financed most investments and innovation projects on the basis of collateral. In a modern digital service economy, the availability of collateral, however,

I.2 Innovations and New Economic Structures in the Digital Economy

311

Public R&D Investment

Input of Technology Private R&D Investment

Education System

R&D Capital Stock R&D Facilities

Skilled Labor (Tacit Knowledge) Immigration of Skilled Labor

Product Innovations Process Innovations Import of Intermediate Products

Production of Goods and Services

GROWTH OF OUTPUT & PER CAPITA INCOME

Infrastructure

GROWTH OF EMPLOYMENT

Fig. 73 Actors and institutions in the innovation system

becomes a problem since knowledge and software play an increasing role for existing and new innovative firms. Compared to the continental banking system, Anglo-Saxon capital markets—with a strong tradition in venture capital financing—are easier sources of financing innovative projects in the services sector. This could undermine the dynamics of modern industry in continental EU countries to the extent that innovative services are crucial inputs for manufacturing products or a key element for optimum after-sale service. To the extent that US multinational services companies invest in Europe or Asia, innovative services might become available despite weaknesses of the respective domestic services sector. However, high profits earned in innovative service firms will then accrue in the USA which, in turn, could thereby strengthen digital US growth. In high-wage countries of the EU, it seems to be quite important that nurturing innovative services not be neglected.

I.2.3 High Technology, ICT Growth and Modernization of the Economic System The EU has adopted a strong focus on ICT in the 6th framework program. The Community has thereby stimulated cross-border ICT research in the EU. However, it

312

Innovations in Macroeconomics

is unclear that the Community adequately emphasizes the ICT sector and that the interplay between national R&D policies and supranational R&D policy is optimal. R&D policy is optimal if positive external effects are internalized efficiently. National external effects can be internalized mainly at the national level, international external effects could be internalized through R&D policy in partner countries or through adequate supranational policy. If there is insufficient international cooperation (within the EU or within the OECD) the level of innovation policy will be lower than optimal. From the perspective of the respective government it is clear that positive growth effects and the associated additional tax revenues provide an incentive for R&D promotion. R&D intensities in the EU do not seem to converge across countries—only for a subgroup of early leading EU countries and Finland there is convergence, at the same time one finds empirical evidence for a convergence of trade structure among EU-15 (JUNGMITTAG 2006). It is, however, unclear what convergence really means here: One may state the hypothesis that through increasing vertical trade—within industries—there is some structural convergence in the EU (or in the world economy). If convergence should mean that intermediate products with low profit rates are more and more concentrated in Spain and Portugal while final goods production is in Germany, France, the UK and the Benelux group plus Scandinavian countries plus Ireland one would not really expect economic convergence in terms of per capita income. The main reason for non-convergence or divergence is that final goods producers in technology-intensive industries will appropriate a Schumpeterian rent in their respective profit rates. In a Heckscher–Ohlin approach to international trade technologies are the same across countries and Schumpeterian profit differentials across countries therefore cannot play a role. In reality Schumpeterian profits indeed play a crucial role; this holds not only for countries with high patent intensities but also for countries with a specialization in sectors shaped by high progress rates. ICT is such a sector; the OECD (2001) has emphasized that it is one of the most important fields of innovation dynamics in the USA and some other OECD countries. From a theoretical perspective international network effects are of particular relevance in ICT innovations in certain fields; network effects are positive demand-side externalities which are rather unusual. ICT R&D is likely to have positive cross-sector spillover effects and one also may anticipate considerable international spillovers; either in the ICT sector itself or through increasing use of ICT capital in other sectors. One should, however, carefully distinguish sub-sectors of ICT; e.g., chip production is scale intensive and knowledge intensive (referring to the overall product not the rather simple chip production as such) as is software. However, many digital services have to be very customer specific so that economies of scale play a limited role; to some extent economies of scale can be exploited for the basic product—say the core algorithm—while customization requires specific adjustment involving the employment of skilled labor. While ICT facilitates international outsourcing it is not true that leading OECD countries are natural losers from outsourcing; BAILEY/LAWRENCE (2005) have shown that the US software sector has outsourced some 100,000 jobs in the period

I.2 Innovations and New Economic Structures in the Digital Economy

313

2000–2003, however, the overall number of software personnel in the USA has increased in that period; mainly rather simple programing jobs were outsourced, often to Asian countries. This suggests that international outsourcing of standardized services will allow advanced countries with relative abundance of skilled workers to specialize increasingly on advanced services. The EU-15 also should benefit in a similar way as leading software firms become globally more competitive by outsourcing to Eastern Europe or Asia. At the beginning of the twenty-first century, OECD countries are shaped by intensified innovation dynamics and the need for flexible adjustment in a world economy with a high rate of technological progress and in which Newly Industrialized Countries—including China and India—are becoming increasingly important players in international markets; China particularly has become a major host country for foreign investment and FDI indeed has stimulated modernization and economic opening up of the Chinese economy (GRAHAM 2004). Both Asian countries benefit technologically mainly by imitating foreign technologies, however, they can combine incipient innovation with strong imitation dynamics and economies of scale in many sectors which should help to achieve considerable economic growth. As regards links between the USA, the EU and Japan one should emphasize the role of international R&D alliances which have become rather important in the 1980s and 1990s in OECD countries—not only in ICT. As regards international alliances the emphasis is more on EU-15 countries than on EU accession countries. Strategic R&D alliances played an increasing role in the EU in the late 1980s as globalization and the run-up to the single market program as well as higher EU funds for cooperative R&D projects stimulated the internationalization of European R&D (NARULA 1999); the IT sector and biotechnology played a particular role. Moreover, there also have been renewed dynamics in R&D in the form of both asset-exploiting and asset-seeking FDI in the EU and the USA (CRISCUOLO/ NARULA/VERSPAGEN 2005) argue that R&D facility’s capacity to exploit technological competences is a function not just of its own resources, but the efficiency with which it can utilize complementary resources associated with the relevant local innovation system; the empirical analysis indicates that both EU (USA) affiliates in the USA (EU) rely strongly on home region knowledge sources, although they appear to exploit the host knowledge base as well. The crucial emphasis on home knowledge suggests doubts about a potential R&D strategy of the EU which would neglect the EU countries as prime locations for leading edge R&D in technologically dynamics sectors, in particular the ICT sector. One also must raise the issue to which extent the expansion of ICT requires reforms of the innovation system and in particular a stronger role of virtual research networks and “Digital Universities”; optimal linkages between R&D facilities and firms in technology-intensive sectors are crucial which naturally will include foreign investors. Both the USA and the EU belong to the group of major source countries and host countries while Japan is mainly a source country of FDI—at least if one is to believe Japanese statistics (note: according to US FDI outflow statistics Japan should have high US FDI inflows). In the USA and the EU innovation plays a crucial role for economic growth. The USA and several EU countries have achieved

314

Innovations in Macroeconomics

rather high growth rates of per capita income and total factor productivity in the 1990s, and the expansion of ICTs has played a particular role. From a theoretical perspective one may emphasize the endogenous growth model of ZON/MUYSKEN (2005) who have highlighted in a refined LUCAS model the role of ICT in a modern growth model where the ICT capital intensity has a positive impact on the knowledge accumulation process; ICT is important both in final goods production and in knowledge accumulation.The expansion of knowledge and the rise of ICT capital intensity contribute to higher steady-state growth of output. Knowledge accumulation thus plays an important role for economic growth. The implication is that the long-run increase of ICT capital intensity in OECD countries and NICs—fuelled by falling relative prices of ICT capital goods—will reinforce the role of knowledge in production. As regards long-term dynamics one should, however, not overlook the problems of information markets themselves which suffer from market imperfections. The special aspects of ICT and growth will not be analyzed here as many special aspects would have to be emphasized, including the considerable role of intangible assets, network effects as a dynamic demand side-effect and static as well as dynamic economies of scale in several subsectors. ICT seems to facilitate the outsourcing of services as it supports virtual mobility of the supply- and the demand side. With the role of digital services increasing in modern economies one might find at the aggregate level that the macroeconomic production function is characterized by economies of scale. However, there is no clear evidence about this. The EU has adopted the Lisbon Agenda in 2000 which has emphasized the need for higher innovation, higher growth and higher employment so that the EU should become the most dynamic knowledge based economy by 2010; interim results are rather sobering according to the KOK (2004) report. With EU eastern enlargement the EU is facing additional challenges. The EU is increasingly moving toward a digitally networked high technology knowledge society. Western Europe’s highwage countries are particularly facing the need to adjust to globalization and EU eastern enlargement in a way which requires increasingly the use of ICT. ICT is one of the most dynamic fields in terms of technological progress in OECD countries and therefore it is of prime importance for economic growth, productivity increases and employment. ICT markets in Europe and worldwide are growing at a pace which exceeds regional and global economic growth, respectively. The ICT sector also has become a major driver of the innovation process and of productivity growth. High Schumpeterian dynamics are not only observed in ICT production but also in the use of ICT. Hence ICT investment relative to overall investment may be expected to grow continuously, not least because falling relative prices of software and hardware stimulate ICT investment. With digital (broadband and narrowband) networks expanding in Europe, North America, Asia and in other regions of the world economy one may anticipate a further acceleration in digital knowledge creation and information as well as e-commerce—often also associated with favorable network effects. With so many changes shaped by ICT the question arises whether traditional economic systems, historically shaped by industry, should adjust in order to optimally support—digital—economic growth. Liberalization of

I.2 Innovations and New Economic Structures in the Digital Economy

315

EU telecommunications in 1998 (UK already in 1984) has stimulated product innovations and possibly innovations in the overall telecommunications sector. The picture for telecommunication network operators is inconclusive as one finds some firms with rising R&D–sales ratios and other with falling R&D–sales ratios. One can, however, not overlook that the R&D–sales ratio of the equipment industry has increased which suggests that in the course of restructuring of telecommunications network operators—in the post-1998 period—R&D activities were effectively shifted to a considerable extent to the equipment industry which is both knowledge intensive and scale intensive. The more competition drives e-communication toward global technological standards the higher will be the pressure in the equipment industry to consolidate. It is noteworthy that R&D–sales ratios of telecommunications operators are lower than in the continental EU where the liberalization of the telecommunications sector occurred only 14 years after the market opening up in the USA. Taking a broader look at R&D expenditure in ICT—relative to overall business R&D expenditure—one can considerable differences across countries: Ireland and the Scandinavian EU countries were leaders at the beginning of the twenty-first century. The three top OECD countries Ireland, Finland and Korea have spent 70%, 64% and 50% of total business R&D expenditures on ICT in 2003. Canada, the Netherlands, the USA and Japan followed with an ICT share of about 35%; France had 31%, the UK 24 and Germany, Italy and Spain about 22%. Ireland, the UK, Norway, Denmark, Australia, Spain and the Czech Republic had a relatively high share of R&D ICT expenditures in the service sector. The ranking in terms of ICT patents looks rather similar to that in ICT R&D expenditures. The top countries are Singapore, Finland, Israel, Korea, Netherlands and Japan, Ireland, the USA, Canada and Sweden which recorded an ICT patent share—based on figures at the European Patent Office—of close to or above 40% (top scorers Singapore and Finland close to 60%); follower countries are the UK, Chinese Taipei, China, Australia, Hungary, France, EU, Russia, Germany, Norway, Switzerland, Denmark, New Zealand, South Africa, Belgium Spain, Austria, Italy, India and Brazil. It is clear that the ICT patent position of US firms—with subsidiaries in many of the top countries—is much stronger than that of the USA as a country. Moreover, taking a look at US figures shows a clear lead of the USA even if one assumes that there is a home bias (in the USA in favor of US firms, in the EU in favor of EU firms). As regards ICT goods Japan is very strong in global markets; this also becomes apparent from the fact that the share of Japan in EPO patents was very close to the share of the USA—see the subsequent figures. Based on methodology developed in Chap. 6 of the Information Technology Outlook 2004. See also van Welsum and Vickery (2004), New perspectives on ICT skills and employment, Information Economy Working Paper DSTI/ICCP/IE(2004)10, OECD. (2) 2002 instead of 2003 (3) 1997 instead of 1995. (4) Estimates.

Telefonica used a different methodology to calculate R&D prior 2001.

Table 20 R&D Expenditures for PTOs (USD millions). (Source: OECD Communications Outlook 2009) 316 Innovations in Macroeconomics

I.2 Innovations and New Economic Structures in the Digital Economy Fig. 74 R&D expenditure in selected ICT industries, 2003 or latest year available as a percentage of business enterprise sector R&D expenditure. (Source: OECD, ANBERD Database, March 2005)

317

R&D expenditure in ICT manufacturing industries (1) R&D expenditure in ICT services industries (2) Ireland (4)

70.2

Finland

64.3

Korea

55.1

Canada

38.5

Netherlands (3)

36.3

United States (3, 6)

35.5

Japan (3)

34.4 32.8

Sweden Denmark (3)

31.5

France (3)

30.6

Norway

28.3 26.8

Australia (3)

24.2

United Kingdom (3) Italy

22.5

Belgium (3)

22.4

Spain (3)

21.8

Germany (4, 5)

21.7 14.4

Czech Republic

12.1

Poland (3) 0

10

20

30

40 %

50

60

70

80

As regards ICT employment—narrowly defined—it has increased in most OECD countries in the period 1995–2003; Ireland is a negative example. The share of ICTrelated occupations in the total economy was in a range of 3–5%; Sweden was the OECD leader in 2003; the USA was ahead of the EU by almost one percentage point. This finding points to a transatlantic lead of the USA which is well ahead of the EU in terms of patenting, R&D–sales ratio and employment. Given the relatively small employment shares it is impressive to see how important ICT patents are in comparison with other sectors. As regards EU innovation dynamics one might want to consider a broader coordinated R&D effort in the ICT sector, in particular some form of coordinated international R&D program; the latter should not mean that all EU countries or very many are embarking upon coordinated projects under the

318 70

Innovations in Macroeconomics

% 2000

60

1991

50 40 30 20 10 0 Brazil India Italy Austria Spain Belgium South Africa New Zealand Denmark Switzerland Norway Germany Russian Federation European Union France Hungary Australia China Total ICT patents Chinese Taipei United Kingdom Sweden Canada United States Ireland Japan Netherlands Korea Israel Finland Singapore

Fig. 75 ICT patents (the provisional definition of ICT patents is presented in Annex B of the OECD Compendium) as a percentage of national total (EPO) in selected countries(cut-off point: countries with more than 100 EPO applications in 2000). According to the residence of the inventors, by priority year. (Source: OECD, Patent Database, September 2004)

% 5 1995

2003

4 3 2 1 Belgium

Portugal

Greece

Spain

Italy

France

Ireland

Germany

Luxembourg (2)

United Kingdom

Austria

Finland (3)

Netherlands (2)

Denmark

Sweden (3)

Korea (2)

EU-15 (4)

Australia (3)

USA (2)

Japan (2)

Canada

0

EU-15

Fig. 76 ICT employment across the economy—share of ICT-related occupations in the total economy in selected countries, 1995 and 2003, narrow definition (1). (Source: OECD Information Technology Outlook 2004)

heading of EU programs. Rather it would be desirable that several countries team up under the heading of a multi-country ICT R&D program of excellence. The typical EU R&D program which effectively requires involving countries/partners from Western Europe, Eastern Europe and the Cohesion countries makes ICT project

I.2 Innovations and New Economic Structures in the Digital Economy

319 Germany 14.4

European Union 38.2

France 5.7 United Kingdom 5.5

United States 29.5

Other countries 8.9

Japan 23.5

Netherlands 4.1 Sweden 2.2 Finland 2.0 Other European countries 4.3 Switzerland 1.7 Canada 1.5 Korea 1.5 Israel 1.2 Australia 0.8 Other countries; 2.1

Fig. 77 Share of countries in ICT patents’ (the provisional definition of ICT patents is presented in Annex B of the Compendium of patent statistics 2004) at the EPO, according to the residence of the inventors, by priority year. (Source: OECD, Patent Database, September 2004)

unnecessarily complex and often undermines efficiency. The EU might well want to subsidize employment of R&D researchers from relatively poor countries in leading EU R&D countries. There could be a particular role for EU-funded R&D projects but overemphasizing EU projects is damaging for European innovation dynamics. Political control of EU R&D policy is rather weak which implies inefficiency risks. The EU might want to consider a special role for the supranational policy level in stimulating diffusion and in financing R&D centers of excellence in the Community. Finally, there is a major inconsistency in the EU R&D projects which typically require 50% co-financing. As regards university research institutes one should expect that national government or special R&D funds with partial government funding would provide the co-financing for successful bidders. This is not the case and indeed is adequate for industrial R&D consortia. However, only a rather limited number of R&D projects are dominated by the business community, namely in applied R&D. Fundamental R&D should be financed mainly by government; in Germany and several other EU countries—including EU accession countries in eastern Germany—there is no adequate co-financing from government for projects in fundamental research. Moreover, the broad lack of private universities in most EU countries means that there is insufficient funding of higher education and insufficient R&D activities at the same time (e.g., Germany spends only 1% of its national income on university funding and has very few private universities—which all are very small). The ICT sector has a special feature which makes adequate financing of innovation projects difficult in the continental EU countries. Many sub-sectors of ICT are char-

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acterized by a high share of intangible assets which undermines bank financing—the typical bank will always want collateral and neither intangible assets (e.g., software) nor computer equipment whose price is absolutely falling over time can serve as collateral for bank financing. This implies for many Eurozone countries that one has enormous problems with financing innovative young ICT firms. Interestingly, there are some big companies, including, e.g., Siemens, SAP and Deutsche Telekom, which have set up special venture capital funds. However, the general conclusion is that the Euro zone countries should move more toward a capital market system and thus become more Anglo-Saxon in terms of the financial market system. Financial markets are important for growth and structural change (WELFENS/WOLF 1997). Mutatis mutandis, this also holds for university financing where continental EU countries have underdeveloped banking markets for students; part of EU underfunding of the university system actually is a lack of private universities on the one hand and of adequate university study financing on the other hand. As one may argue—from a theoretical perspective—that adequate financial market deepening will contribute to a higher level of growth and potentially to a higher trend growth rate (namely to the extent that the structure of financial markets influences R&D intensity and human capital formation and hence contributes to endogenous growth dynamics) one should make serious efforts in the new EU knowledge society to develop financial institutions that are up to the challenges and opportunities of the digital age. These arguments do not imply that one should underestimate the risks from volatile stock markets. Slow growth in the Eurozone over many years—in particular in Germany and Italy—should be a wake-up call for many continental EU countries to modernize the innovation system and to put more emphasis on R&D funding which at the same time should become more efficient. Conditional tax credits should play a larger role than traditional subsidies which effectively favor large firms which can afford to spend much money on active lobbying. R&D tax credits would be less distorting in the sense that large countries and SMEs are acting in a more level playing field. Since innovative SMEs are so important in R&D in the ICT sector—and since Germany/the Eurozone is lagging behind the USA—one should seriously consider the reform proposals made here.

I.3 Theory of Innovation Policy I.3.1 The Standard Case Why should government support R&D? This is obvious when it has a particular individual interest in innovations as is the case in the field of defense. Besides this special sector, it is only in case of positive intersectoral or intrasectoral effects that R&D subsidies are adequate. Assume that the demand for an innovative product is given by the demand curve AZ (DD0 )—expressing private benefits—while social benefits are reflected by the demand schedule A Z (DD01 ). As there are positive

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external effects of using the innovative product (or service), the optimum quantity will not be brought about by private markets themselves. The market would bring q0 while the optimum quantity is q1 ; the latter would be produced if government reduces marginal costs by a fraction, b, so that there should be R&D subsidies. The price would fall to p1 instead of p0 in the simple market equilibrium. However, R&D subsidies would then amount to the area HGFD, which can only be financed through (income) taxes, in turn shifting the AZ curve downward. Taxation in turn will impose deadweight losses—that is, reduce economic welfare—unless the tax is on activities with a negative external effect. Since the latter case can be assumed to be relatively rare, the optimum R&D subsidy is slightly smaller than indicated by the subsidy rate, b. Moreover, subsidization of R&D makes sense only if the increase in net welfare is higher than the costs of subsidization. These costs could ultimately include the costs of other sectors calling for equal treatment: read subsidization (while not showing positive external effects). In addition, there is a risk that government combines R&D subsidies with interference in the business sector which can cause efficiency losses. As a practical issue, one also has to look into the issue of granting subsidy payments or offering tax credits for R&D intensive firms. Subsidy payments appeal to the lobbying and rent-seeking efforts, particularly of large firms. Tax credits are a superior instrument to the extent that R&D intensive small and medium-sized firms can also benefit from this relatively easily. The government also plays a role in the field of intellectual property rights. In the digital economy, intellectual property rights have come under pressure because the violation of copyrights is rather easy (see, e.g., the Napster trial). A'

k',p

k'0 k'1 (1-b)

A p0

D

F E

H G

Fig. 78 Product innovation with positive external effects and R&D promotion

0

q0

q1

Z

Z'

q

Making profits by selling digital contents is not easy. There are technical reasons for this problem, but there also is a lack of adequate legislation in some countries. Germany has introduced national legislation that is supposed to implement the EU e-commerce directive. As regards copyrights, Germany’s new laws clearly weaken the copyrights of authors, thereby reducing the incentive to develop quality contents for traditional and digital publications. In an open economy, it is important to understand that subsidies can influence trade (following figure). If the world market price is p*0, the initial situation without R&D

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subsidies implies net imports of AB. If country I (home country) subsidizes R&D so that the marginal costs schedule shifts downwards, we would have net exports equivalent to the distance BC. If country II (“the rest of the world”) also introduced subsidies—pointing to the positive external effects of R&D—the world supply curve would shift downwards so that country I would be a net importer again. The quantity imported would thereby be equivalent to the distance DF. The problem with R&D subsidies and trade is that such subsidies are adequate to the extent that the subsidy rate reflects positive external effects (at home and abroad). Since the size of external effects of innovation is very difficult to assess, subsidization in technology-intensive tradables sectors naturally presents a potential field of controversy. Country I—assuming it to be a globally leading country in the respective sector— might argue that R&D subsidies in this sector abroad are adequate since positive external effects in other countries should be relatively small. Yet country I might argue that other countries aim at catching market shares by way of unfair subsidization. If the sector concerned has dynamic scale economies in the long run or is characterized by an international oligopoly, there are additional aspects to be considered. International rent-shifting opportunities will particularly accrue to first movers and large aggressive firms which, in turn, should enjoy particular opportunities if the home market is large and characterized by high per capita income. In a large home market, it is fairly easy to exploit static- and dynamic-scale economies. Countries such as the USA, Japan, the EU—and in the future, China or India—offer special opportunities in this respect. Thus, it would not be surprising if trade conflicts emerge between these large economies. p

k′0 k′1 E B

A

C

D

p0*(k′0*) F

k′0*(1-b*)

DD0

Fig. 79 R&D promotion, production and trade

0

q1

q2

q3

q

I.3.1.1 Intermediate Traded Products, R&D Subsidies and Rent-Shifting Another neglected field of R&D promotion in open economies concerns the case of an intermediate technology-intensive product produced in country I and exported as

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an intermediate input to country II. We will subsequently consider the case of traded intermediate product innovations whose use in country II raises the marginal willingness in the market for the final product. Assume that the government in country I offers R&D subsidies, largely reflecting thereby the positive external effects in country II, so that q1 of the intermediate product is produced in country I instead of the natural market solution, q0 . R&D subsidization allows for the production of a higher quality of the intermediate product so that the demand curve for the final product shifts outward in country II. As intermediate products are obtained at subsidized costs from producers in country I, we have a downward shift of the k* curve abroad (see panel b). The positive welfare effect accruing for country II is given by the area A*B*C*F*G*D*. However, the costs of R&D subsidies in country I are equivalent to the area FGHI. p*

b k*′1

k*′0

p

a

A*

B*

C*

D*

p0*

G

F*

k′0

F G* I q*

q*1

q*0

k′ (1-b)

H DD0 q0

q1

DD1 q

Fig. 80 International external effects of domestic R&D promotion (technology-intensive inputs for tradable products)

Under which conditions would country I be interested in providing an R&D subsidy for an intermediate product when the main welfare effect is observed abroad (as shown in our simple partial equilibrium model in the above figure)? 1. If country II could offer country I an adequate share in income taxes as a compensation for the R&D costs. 2. If the firms in country II are largely owned by residents of country I—at least with respect to higher profits in country II (sent to country I as profit remittances), there

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is effective taxation in country I; the profit increase in country II is equivalent to the area, C*F*G*D*. 3. If a large share of demand abroad effectively represents users from country I (e.g., in the case of tourism or in the case of mobile internet services). 4. If there are positive effects not only for country II but also for other sectors in country I so that part of the shift from DD0 to DD1 represents domestic positive external effects. The latter could explain why Korea subsidizes R&D in Boeing, intermediate inputs manufactured in Korea. In the EU-25 single market where technology-intensive intermediate inputs are partly produced in EU countries catching-up, there are indeed arguments that rich countries which dominate the final assembly of technology-intensive products should transfer an adequate share of income taxes to those countries which deliver intermediate products developed on the basis of R&D subsidies in the respective country. Since one may assume that this typically concerns cases in industry and that the main producers of technology-intensive final products are Germany, France, Sweden, Finland and the Netherlands, we have a new argument that these countries contribute over-proportionately to the EU budget. It is, however, unclear that countries producing much technology-intensive intermediate inputs really obtain an adequate share of EU transfers. So far, the EU transfer scheme does not consider the case of technology-intensive intermediate products. In a more general sense, the existence of the single EU market and the ongoing globalization imply that there could be an increasing role of the internationalization of R&D, including the production of innovative intermediate products. This internationalization of R&D and the associated positive international external effects could imply that all governments spend less on R&D than would be optimal. The simple reason for this is that an international tax revenue sharing scheme has not yet been developed by the OECD. (As the basis for such a scheme, one would have to analyze the size and direction of technology spillovers, which could be quite cumbersome). Network Effects In the digital economy, there are more fields with network effects than in the traditional industrial economy. Network effects can be understood as an endogenous outward rotation of the demand curve (alternatively, as a rightward shift of the demand curve) in the process of network expansion. For example, the marginal utility of having access to the telephone network will increase for the initial users if more users—read potential communication partners—are switched on the network, at least as long there are no additional congestion costs. This is also the case for advanced software and novel internet services. A monopolistic supplier facing the demand curve DD0 would impose under the standard Cournot monopoly solution the monopoly price p2 which goes along with output q0 . For simplicity, we assume that a conservative monopoly firm would neither be willing nor able to exploit network effects, that is, to anticipate that the dynamic demand curve—including network effects—is DD2 and not DD1 . If government offered a one-off R&D subsidy for process innovations

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(shifting the marginal costs curve from k0 to k1 ) to several firms under the condition that network effects be jointly exploited, the conditional competitive solution would be point G. The positive welfare effect from the network effect is the area AEF plus the effect seen by cost cutting, namely EFGH. An additional welfare benefit—not related to network effects—would come in the form of the area p0 EHp1 . Thus, network effects represent a neglected and interesting field of R&D subsidies (for a broader partial equilibrium analysis, also see appendix 2). p A

p2

E

C

F

k′0

p0 G

k′1

p1 R′0

H Z

DD0

p q0

q1

q2

DD1 q3

V q

Fig. 81 Network effects and cost-saving progress

I.3.1.2 Macroeconomic Approach: A Schumpeter– Mundell–Flemming Model The familiar Mundell–Fleming model suggests that fiscal policy is effective under fixed exchange rates, while monetary policy is ineffective. Under flexible exchange rates, it is monetary policy which is effective while fiscal policy is relatively ineffective. In the following analysis, we suggest that supply side oriented fiscal policy—namely raising R&D expenditures in order to promote product innovations—can have positive effects on output and employment within the framework of an extended model. The basic arguments have been presented in WELFENS (2004), where a key idea is that consumption C, investment I and (net) exports X positively depend on product innovations v. In reality, a higher export unit value could be obtained due to product innovations, and the quantity shipped abroad might increase as well. The larger the tradables sector affected relative to the overall economy, the larger the effect on net exports of goods and services. Through an innovation-promoting fiscal policy—with a focus on product innovations—we basically get a rightward initial shift of the IS curve since

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government R&D expenditures and hence aggregate demand increase. In the medium term, we get more product innovations v so that investment and consumption increase; net exports also increase. While the ensuing real appreciation of the currency dampens the net export effect (the IS curve shifts back to the left, while the balance of payments equilibrium curve ZZ shifts upwards), the overall effect on output and employment is favorable as is shown in the following graph. A minor complication in a model with product innovation is that in applying the logic of hedonic pricing, we implicitly get a fall of the price level, thereby shifting the LM curve to the right (not shown in the graph). There also is the potential problem of considerable time lags. Higher R&D promotion could translate into more product innovations only after several years. However, as investors will anticipate this effect, improved profit expectations should already stimulate output after a short period. From a policy perspective, there could also be a problem stemming from strategic R&D behavior of firms which cut R&D expenditures more strongly in recessions with the hope that government R&D support will effectively allow for the substitution of company funds through governmental subsidies. Government could cope with this problem by using an adequate base year.

r

LM0

ZZ2

E1

ZZ0

r1 E2 r0

ZZ1

E0 IS01 IS1 IS2 IS0

Fig. 82 Expansionary fiscal policy promoting product innovations

0 Y0

Y1

Y

If government raises R&D expenditures in order to promote process innovations, we get a less favorable result to the extent that technological progress is labor-saving. Labor in efficiency units is AL and the production function is Y(K, AL), where Y is output, L is labor, and K is capital. Depending on the strength of the upward shift of the production function, labor-saving technological progress might indeed lead to a new equilibrium in which the demand for workers is lower than initially the case. There are less jobs available than in the initial equilibrium (L3 < L0 : see the graph).

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r IS2 IS1

LM0

IS3

LM1

IS0

E2

E1

(-ΔP due to process innovations/R&D promotion)

E3 E4 r*0=r0

ZZ0 E0

(IS3: net exports fall in the medium term due to appreciation) Y0 0 Y3

Y1

Y

Y4 Y2

L3 L0

L

Y(K0,A0,L)

Y(K0,A1,L)

Fig. 83 Expansionary fiscal policy with a focus on promoting process innovations

In the above model setting, we have assumed that net capital imports Q = Q(i, i*, v, q*), where v is the rate of product innovations, raises profitability and hence foreign direct investment inflows. The impact of the domestic and foreign interest rate i and i*, respectively, requires no further comment. Not so apparent is the

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positive impact of q* = eP*/P (e is the nominal exchange rate, P and P* the domestic and foreign price level, respectively). The link is explained by the FROOT–STEIN argument, which emphasizes the role of imperfect capital markets for foreign direct investment inflows. The ZZ line has a slope of zero if the interest elasticity of capital flows (∂Q/∂i) is infinite. Note that the balance of payments equilibrium line (ZZ) does not only have a slope of zero when the interest elasticity of capital inflows is infinite; it could also have a slope of zero if we assume—a realistic case in view of empirically significant gravity equations of foreign direct investment—a net capital import function Q(i, i*, v, Y,Y*), where the partial derivative ∂Q/∂Y is positive and ∂Q/∂Y* is negative. Both ∂Q/∂Y and ∂Q/∂Y* reflect the impact of domestic and foreign output on net foreign direct investment inflows on net foreign direct investment inflows. If ∂Q/∂Y is equal to ∂J/∂Y—with ∂J/∂Y denoting the marginal propensity to import goods—the slope of the ZZ curve is zero, even if the interest elasticity of capital mobility is low. In the case of poor countries opening up to trade and foreign direct investment—e.g., in the case of Newly Industrializing Countries or post-socialist transition countries—the marginal propensity to import will at first increase. After some time, ∂Q/∂Y will increase and the special case ∂Q/∂Y = ∂J/∂Y could occur and hold for some time, thus leading to an interesting empirical question.

I.3.1.3 Empirical Insights from the Analysis of Innovation, Growth and Structural Change Recent empirical analysis (JUNGMITTAG 2004) shows that a macroeconomic production function is useful in which not only labor, capital and technology enter into play, but also the degree of economic specialization in high-technology products. An alternative specification in which specialization as such—Smithian specialization—matters did not yield significant results for the production function. We assume that the pressure to specialize more strongly in technology-intensive products is reinforced if there is increasing import competition of countries which are catching-up technologically (e.g., as measured by R&D input indicators or R&D export indicators). According to this line of reasoning, measures to liberalize trade could have long-term benefits in terms of both higher per capita income and higher growth rates. In the context of EU Eastern enlargement, it was shown (BORBÉLY 2004) that accession countries have specialized in different ways while also recording specific performance with respect to the development of export unit values. Hungary and the Czech Republic recorded positive RCA dynamics in both medium technology-intensive products and in selected high-technology sectors. Moreover, in some sectors, improvements in export unit values were recorded in the decade after the early transition recession. This ability to move up the technology ladder and to obtain higher prices in world markets might be strongly related to foreign direct investment inflows.

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I.4 Policy Conclusions I.4.1 General Policy Conclusions for Innovation Policy in Open Economies In open economies, there is some risk that R&D promotion is smaller than would be optimal under global welfare considerations. If there are symmetric international R&D spillover effects, one would have little reason to wonder about optimum R&D support. However, reality is likely to show asymmetric positive international external effects since countries trading with each other have different technology levels and since the degree of openness and trade in intermediate technology-intensive products differs across countries. Obviously, it would be useful for countries with high technology-intensive tradables output to cooperate in R&D policies which might include international tax revenue sharing. Assuming that the difference between private and social benefits of innovation is even larger at the level of the world economy than at the national level, one may raise the question of whether the internationalization of business has not brought about an increased divergence between existing and optimum R&D subsidies. (While the EU might be considered a supranational player in R&D promotion, one must point out that the share of R&D promotion in the budget is very small and that the current transfer system is not rewarding countries which support R&D in firms which produce technology-intensive intermediate products.) Innovation systems differ across countries. However, some key ingredients can be identified: There are public R&D funds and there are private R&D funds, whereby the latter typically has a focus on applied R&D while the former emphasizes basic research. Funds have to be partly invested in R&D facilities. At the same time, hiring highly skilled workers and dynamic researchers is crucial for high innovation performance. Skilled workers represent tacit knowledge, which often make international relocation of R&D-intensive production difficult. In addition to this, a modern education system as well as the import of technology-intensive imports and government R&D promotion must be considered. This should then result in sustained innovation dynamics and growth of output and employment. Countries have specialized in certain technology-intensive fields which typically show a positive RCA over time. Facing economic globalization and intensified global competition, it makes sense for governments to focus their R&D support within internationally competitive sectors. This seems to be even more the case the larger the backward linkages and forward linkages are and the larger the respective sector is itself. Such a strategy of supporting existing fields of comparative advantage and also fields of rising export unit value would, however, leave open the question to which extent relatively new sectors—such as nanotechnology or biotechnology or ICT— should be supported. Obviously, it is useful to support such sectors to the extent that the respective country is richly endowed with complementary human capital and that the capital markets encourage creation of technology-intensive innovative start-up companies. (In the field of digital services, Germany faces particular problems since

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the dominance of banks and the relative weakness of venture capital funds impairs the creation and expansion of firms which offer little collateral.)

I.4.2 Specific Policy Conclusions for Germany I.4.2.1 R&D Promotion for Medium Technologies and High-tech Industry Germany’s traditional strength is in medium intensive technologies such as automobiles, machinery and equipment. The government should continue to encourage R&D in medium intensive technologies, provided there are good arguments in favor of positive external effects. There are long established cooperations between universities and firms in the automotive industry and in the capital goods sector. However, one might want to broaden cooperation across borders and also internationalize the German university system in a way that teaching and conducting research abroad would be a normal element of a long-term strategy of achieving excellence in research and teaching and of creating networks allowing for the finance of innovative projects in both teaching and research. As regards international activities of German universities, there are only a few exceptions. State-owned universities would find all kind of bureaucratic barriers if they wanted to expand internationally. Thus, privatizing several universities and giving more autonomy to universities would be highly desirable, but in the political arena no such initiatives have been adopted. Given the medium term technological catching-up of EU accession countries in Eastern Europe and of Asian and some Latin American countries, the highwage economy of Germany would be well-advised to increasingly specialize in knowledge-intensive and technology-intensive sectors; this should include hightechnology sectors. Germany must move up the technology ladder and undertake serious efforts to modernize the education system accordingly. There have been very few efforts in the field of modernizing the education system. The PISA shock which saw bad results for Germany has encouraged some reforms in basic schooling. However, there are few efforts to really modernize the education system on a broader basis. Such commitment could be visible with the creation of new universities, tax incentives for the creation of private universities and tax incentives for adults to engage in advanced training and retraining. Such measures have not been undertaken thus far in Germany. One should also note that Germany, with its ageing society, could face a long-term decline in output growth unless the rate of technological progress and the quality of human capital formation are improved in a sustained way. Short-sighted politicians are also sometimes inclined to impair innovativeness simply to get additional short-term revenues. A prime example in this respect involves the Ministry of Health, which forced leading pharmaceutical companies to pay an extra lump sum tax as a contribution aimed at alleviating the funding problems of the health care system. Such a policy is a wonderful starter for gradually killing the once globally leading German pharmaceutical firms. At the bottom line, the government obtained a few hundred million Euros yet thereby undermined innovation dynamics worth billions of Euros.

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I.4.2.2 Skill Upgrading and Reform of the Education System Facing economic and technological catching-up in Eastern Europe, Russia, Asia and Latin America (plus a few countries in Africa), the German economy will have to increasingly emphasize the production of technology-intensive and skill-intensive or knowledge-intensive products. More training and retraining as well as the modernization of the basic education system are major challenges for Germany. As regards incentives for firms and employers to engage more in training and retraining/skillupgrading, the government could introduce adequate conditional tax benefits. Given Germany’s budget problems, higher expenditures or reductions in tax revenues are only acceptable if new sources of tax revenue become available. Since Germany has a very low VAT rate among EU countries, one could consider raising the VAT rate as a means to finance incentives for the training, retraining and modernization of the education system. As regards the university system, it would be useful to not only step up competition among universities but also to encourage foreign universities to set up satellite centers in Germany. A broader and more international supply side in the academic system would be quite useful not only for Germany but for other EU countries as well. A major weakness of the German university system is the low share of female graduates in engineering and informatics. The low share of female graduate in informatics (about 15% at the beginning of the twenty-first century) is a serious disadvantage for a country which is facing an ageing of its society in the long run and modest economic growth in the short term. The USA and many countries in the EU have been relatively successful in raising the share of female graduates and in encouraging a high share of female entrepreneurship. Germany has a long way to go in this respect.

I.4.2.3 Problems with Immigration of Unskilled Labor The specific unemployment rate of unskilled workers was roughly twice the national average. Among immigrant workers, the specific unemployment rate is even higher. This poor result is partly due to the weakness of the German schooling system at successfully integrating foreigners. Since foreign workers have below average skills, it is not surprising that they become unemployed more often than workers born in Germany. The situation in Sweden (and some other EU countries) is different. Sweden in particular has emphasized and facilitated the immigration of skilled workers. The free movement of labor has been restricted in the enlarged EU-25 until 2011 (at the latest). Germany is likely to attract a high degree of unskilled labor after 2011, since youth unemployment and overall unemployment rates in many accession countries of Eastern Europe are high. Economic geography—Germany’s proximity to the accession countries—and economic incentives, namely high German wage rates and low social integration costs due to a large stock of foreigners (from eastern Europe) from previous immigration waves, make Germany a natural target country for those wishing to emigrate from eastern Europe. Such immigration will include

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citizens from Bulgaria and Romania, where relative per capita income (at purchasing power parity relative to EU-15) was only about 22% in 2003. If the EU were to seriously consider Turkish membership, one would have to anticipate a large wave of additional Turkish immigrants in the future. The population in Turkey is growing at a pace of about 1 million per year, with the population growing from roughly 70 million in 2004 to 120 million by 2050. The high-wage economy of Germany would thus face millions of Turkish immigrants once Turkey— with a per capita income of about 20% of EU-15 average in 2003—enjoys full membership. Immigrants from Turkey would be largely unskilled workers which would reinforce unemployment problems in Germany. Against this background, it is doubtful that German politicians would quickly embrace EU membership for Turkey. If EU leaders were to quickly move toward EU membership, this might signal an integration overstretch, which could even result in a future German government leaving the EU under the heading “we want control of immigration, want to save funds used inefficiently by the EU and prefer having the D-Mark again.” One should remember that the very purpose of creating the EU in 1957 was to firmly anchor the Federal Republic of Germany in Western Europe, and it would be historically tragic if enlargement to include Turkey drove Germany out of the Community (in the accession year 2004, the EU is hardly able to work effectively since there are so many new politicians and inexperienced bureaucrats in Brussels).

I.4.2.4 Improving Knowledge Transfer from University to the Business Community Traditionally, there have been close links between firms and universities in Germany. However, universities have been relatively reluctant to promote early entrepreneurship of graduates. Moreover, many public universities are highly inflexible, bureaucratic and reluctant with respect to innovation and internationalization. Incentives to improve knowledge transfer from the university system to the business community would be much stronger if half of the universities were private universities which were more competitive in acquiring research funds from industry and public institutions. Privatizing a considerable number of universities and attracting foreign private universities could be interesting policy options to accelerate knowledge transfer. The existing transfer institutions are rather bureaucratic and slow, the incentives from the slow marketing of patents obtained by professors at the universities are weak. While the three leading US universities had revenues of about 15% from patents and licensing at the beginning of the twenty-first century, the leading German universities had a revenue share in this category of not more than 2%. While the links between the university and large MNCs in Germany are well established, such networking hardly exists with respect to most SMEs. Here, the internet offers new platforms and opportunities. However, local telecommunications is relatively expensive in Germany, not least due to the quasi-monopoly which the Deutsche Telekom AG (still largely government-owned) has maintained in traditional fixed-line telecommunications. Moreover, the German government allowed

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Deutsche Telekom AG to establish a dominant market position in the DSL market with the market share of the state-owned firm having been close to 90% in 2003. Germany cannot really deliver an optimum contribution to the Lisbon process if government does not strongly promote competition in both fixed-line telecommunications and the DSL market. DSL competition in France is much stronger than in Germany, and consequently France has overtaken Germany in terms of the absolute number of DSL lines in late 2004 when France reached a level of about 5 million lines. The share of households with broadband internet connection was close to 30% in Belgium, Denmark and the Netherlands (largely due to cable TV) in early 2004. In Sweden, Finland and Austria, it was in the range of 15–20%. Spain, France and Portugal had close to 15%, while Italy, the UK and Germany had only 12–13%. From this perspective, neither Italy, the UK nor Germany currently have an ideal starting point for developing and marketing innovative digital services. However, large countries always enjoy the benefit of a large home market.

I.4.2.5 Keeping Skilled Workers and Innovation Leadership in the Region Facing the new international division of labor in Europe and worldwide, it is obvious that a high-wage country such as Germany should specialize more on producing knowledge-intensive and technology-intensive goods and services. Advanced services seem to be particularly underrepresented in Germany with part of the problem being a lack of competition in retail banking, telecommunications and energy. These sectors have been sheltered from international competition for many years, and productivity growth has been relatively slow except for the post-1998 period in fixed-line telecommunications. Universities should be encouraged to focus more on these potentially dynamic liberalized sectors. At the same time, regional government or national government could provide tax incentives for venture capital funds set up by large companies in these sectors (and other sectors). A rising share of venture capital funds should go to young firms created by university graduates. Regional government could provide R&D facilities and modern infrastructure for young technology-oriented firms centered around a business park. Regional governments would be wise to promote existing clusters of excellence as well as new dynamic fields with growing long-term demand and a high rate of technological progress. Regional government can try to keep potentially mobile innovative companies in the respective region by offering generously modern facilities for innovators. Promoting innovative supplier clusters is also an option to reduce the mobility of innovators. An important ingredient in gluing innovative companies to a region is a network of highly innovative and flexible universities and R&D labs. Germany faces major financial problems in university and public research funding, and this could become a serious impediment for implementing adequate policy priorities.

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I.4.2.6 A European Policy Perspective Germany would be wise to embrace the best-practice approaches of other EU countries. Among the interesting new developments are open innovation systems such as the R&D park in Eindhoven where Philips is the leader in a large network of innovative firms. Cross-licensing is a typical element of networking in this R&D park. A major strategic goal of Philips is to nurture international R&D networking in a way that helps to set global standards quickly. Revenues from international licenses increasingly contributed to Philips’ revenue in the 1990s and in the beginning of the twenty-first century. As industry becomes increasingly mobile in the EU-25 and as accession countries catch up over time, it is natural that research activities also become more footloose. In a dynamic open economy, nobody should expect to easily earn high income in traditional fields of specialization. Rather, it will be necessary to react relatively flexibly and to move into new markets and niches. For firms, the challenge is to develop flexible, efficient and innovative-enhancing structures. For national policymakers and the EU, the medium-term challenge is to shift the focus of R&D policy more toward success-promising new fields. Both the national and the supranational policy level should become more efficient and effective in R&D promotion. Moreover, at both the national and the supranational level, a strong emphasis on competition and open markets is essential. While better digital intellectual property rights seem to be necessary in general, the special case of software patenting raises serious doubts. In a sector in which network effects automatically become an endogenous barrier for market entry, software patents are quite doubtful. It is true that the software market is not homogenous, but easy patenting of software should certainly be avoided if the policy goal is to encourage digital innovations in the long run. One should take the Lisbon process seriously in all EU member countries, in particular in large Eurozone countries such as Germany, France and Italy. There is little doubt that Germany and Italy have underestimated the challenges of achieving sustained growth for many years. The heated public debate of 2003/04 between politicians and researchers in France—the latter pointing out a massive funding gap for top R&D institutions and projects—shows that not only Germany (or Italy) has serious problems in allocating sufficient funding to promoting innovations. Regular monitoring of national and regional R&D policies could be quite useful in generating more pressure on member states to adopt efficient R&D policies and to increase spending on innovation and human capital formation.

Appendix I.1: Optimum Product Innovation under Uncertainty As regards innovation efforts, firms can undertake R&D at fixed costs H, where one may assume that the probability to obtain a (temporary) monopoly depends on H. Let us assume that without product innovations we have a linear demand function p = a −bq; we assume that R&D costs H reflect efforts in product innovations which

Appendix I.1: Optimum Product Innovation under Uncertainty

335

raise the willingness to pay, so that denoting α as the parameter to indicate the rise in the willingness to pay for innovative products and α as the probability of successful innovation, the expected demand function in the case of a product innovation is p = a + α(H) − bq.

(1a)

Here α is the probability to successfully launch a product innovation and thus also the probability to obtain a monopoly provided that competitors are expected to remain passive as is assumed here. Production costs are assumed to be proportionate to q and to include R&D costs which are fixed costs H (an alternative would be to assume that R&D costs for product innovations are equal to H + [n/q]): Z = hq + H.

(1b)

Under standard competition, the market is characterized with p = h and q = (a −h)/b; standard monopoly theory suggests a monopoly quantity qM = (a −h)/2b and monopoly price pM = (h + a)/2. Denoting α as the probability of a successful product innovation, r as the revenue under monopoly, RC under competition, RE as expected revenue and Q as profit we assume that the firms wants to maximize the profit function: Q = RE − Z = {α(H)r  + [1 − α(H)Rc ]} − [hq + H].

(2)

Expected revenue in our approach is RE = α(H)[aq + α(H)q − bq2 ] + [(1 − α(H)[aq − bq2 ]] = [aq − bq2 ] + {α2 (H)q}.

(3)

The term {. . . } makes the difference to the standard approach in profit maximization. The monopolist will equal marginal production costs k (q) and marginal expected  revenue RE which is 

RE = a − 2bq + 2α(H).

(4)



Optimum output is given by h = RE and therefore q# = [a − h + 2α(H)]/2b.

(5)

The corresponding price—enforceable in the case of successful product innovation is p# = a + α(H) − b[a − h + 2α(H)]/2b.

(6)

Compared to standard monopoly theory, the approach presented shows a marginal revenue which is higher so that optimum output in a Schumpeterian economy will indeed be higher in every market with product innovations than in a non-innovative economy. The optimum H can be determined from dV/dH = 0, which yields: 

 (7) Q = aq − bq2 + α2 (H)q − [hq + H].

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∂Q/∂H = 0.

(8)

2α(H)αH q = 1.

(9)

2α(H)αH [a − h + 2α(H)]/2b = 1.

(10)

Inserting optimum q implies

Denoting the elasticity of α with respect to H as Eα,H we can write 2 (1/H) Eα,H [a − h + 2α(H)]/2b = 1.

(11)

Implicitly from this function, the optimum H can be derived. Note that the optimum H—which is a fixed cost here—must be below the expected profit from product innovation, because the firm is otherwise squeezed out from the market. One should also note that the market will be characterized by excess capacity if the product innovation cannot be launched successfully. The reason for a tendency to overcapacity in the market is that the firm will decide about optimum q in advance. If the product innovation cannot be launched successfully, the firm can still cut back production— and hence avoid marginal costs of initially planned production—in a way that excess production in the market is avoided. Finally, it should be noted that in innovative sectors temporary excess capacity should not be identified with signs of a recession since it simply is a by-product of product innovation under uncertainty. If a rise of per capita income goes along with a rising degree of product differentiation and hence a stronger tendency toward product innovation the problem of apparent excess capacity in the overall economy could gradually become more important during certain periods. If government promotes product innovation, an unwelcome by-product could be temporary excess capacity in some sectors. Moreover, government measures to promote growth (raising per capita income) could indirectly stimulate product innovations and hence bring about the problem of temporarily idle capacities. In an open economy, such excess capacity might lead to unplanned net exports in the respective sector. If the exporting country is large, this will entail a temporary reduction of world market prices.

Appendix I.2: Product Innovations and Network Effects in a Simple Model Assume that willingness to pay depends on the degree of product innovation V, which in turn is proportionate to innovation efforts H, while production costs positively depend both on the quantity produced q and the innovation efforts H. In the following simple model, we will look at some interesting aspects of product innovations in sectors with network effects. We will consider the behavior of an experienced innovator who is certain that innovation expenditures on product innovation will translate into a temporary monopoly position. For simplicity, we assume V = H and that the  demand function is q = Hα a/p (where a and α are positive parameters; and by assumption α > 0. Note Ey,x will denote the elasticity of variable y with respect to

Appendix I.2: Product Innovations and Network Effects

337

variable x). Note that such a demand function implies that revenue is constant since  R = pq = Hα a. Thus for the profit-maximizing firm undertaking product innovations, we demand the following expressions for the function and for profit Q, respectively: 

Q = Hα a/p

(1)

Q = p(H)q − k(q, H)

(2)

Maximization of this function requires in a competitive framework dQ/dq = p − k  (q, H) = 0

(3)

p = k (q, H)

(3 )

Hence

under competition (a minor problem occurs with maximization due to the constancy of revenue for any given H!) R (q, H) = k (q, H)

(3 )

under monopoly; with revenue R = p(q, H)q and dQ/dH = ∂p/∂Hq − ∂k/∂H = 0

(4)

Inserting the demand function we have: 

∂p/∂HHα a/p = ∂k/∂H

(5)



Ep,H Hα −1 a = ∂k/∂H

(6)

Hence the optimum product innovation effort H# is given by the necessary condition 

H# = {[∂k/∂H]/aEp,H }−1/(1−α )

(7)

After choice of H#, the firm can choose output q in a way that the condition marginal revenue equals marginal costs is fulfilled. According to the above equation, the product innovation effort will be the higher the lower the marginal costs of innovation ∂k/∂H and the lower the elasticity Ep,H of the price with respect to innovation (efforts) and the lower the basic willingness to pay as expressed by a is. How will network effects affect the elasticity of p with respect to H? If the market is characterized by network effects, we may assume that the elasticity of p with respect to product innovation effort H is lower than in a normal market (this effect could be estimated empirically), because network effects stimulate competition which in turn drives down the market price. Hence the optimum product innovation effort would be higher—every round of product innovation is a new starting point to escape the move toward low competitive prices. At the same time, there could be scale effects

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whose exploitation is facilitated in the presence of network effects. If there is only one firm, it should be easy to anticipate the positive network effect. However, the firm will charge not only a temporary monopoly price—which is a natural side-effect of the product innovation itself—but it will charge a monopolistic price even in the long run; it also will adopt a lower rate of product innovation. With many firms in the market, the firm which launches a product innovation only has a temporary monopoly. As soon as there is broad imitation, the innovating firm can no longer fetch a monopoly price in the market. It must accept a price which is equal to long-term marginal costs (assumed to be constant in the subsequent graph where we show an initial monopoly price plus a situation with a product innovation in the context of monopoly pricing as an analytical starting point). If there are quasi-scale economies in the sector considered, the marginal costs of product innovation will be negatively influenced by the size of the market, which in turn is positively affected by network effects. The latter thus bring about a positive external costs effect for all competitors. The assumption that network effects reduce the marginal costs of innovation can be justified only if the size of the market is a positive signal for attracting more researchers to R&D activities in which learning by doing or intra-sector spillovers plays a role. Note that under monopoly, we have price pN for the product innovation both in the short term and in the long term, but under competition, it would be the lower price p1 in the long run. Hence government should encourage competition and help high barriers to entry from occurring. Endogenous barriers resulting from strong network effects in industry (e.g., in the software sector) could also be a problem which would not always justify standard patent protection. Our line of reasoning can also be seen from the following graph where we show an initial marginal costs curve k0 and a new marginal cost curve k1 which is relevant in the context of the product innovation. The initial equilibrium point under monopoly and the initial demand schedule DD0 is point C and hence output is q1 and the monopoly price pM . Now we turn to product innovation. There will be a rise of the cost curve stemming from product innovation efforts, and this reduces consumer welfare. At the same time, there will be an upward rotation of the demand curve (see DD1 ) reflecting the increased willingness to pay for the novel product; the latter effect is associated with higher consumer welfare. A positive network effect is reflected in the graph as a rightward shift of the demand curve (see DD2 ). If there are quasi-scale effects, there will also be a downward shift of the k curve. For simplicity, we can assume that this shift effect fully offsets the initial shift from k0 to k1 : Hence taking into account quasi-scale effects associated indirectly with network effects results in k0 so that the long-term competitive equilibrium is point H, output q5 and price p0 (without scale effects output would be q2 ). Transitorily, there could be a monopoly situation with a monopoly price p0 and output q6 . There are cases when industry itself is able to exploit network effects fully (e.g., when leading firms in the sector agree on a new standard in the context of a product innovation). Setting standards in an environment of open interfaces of equipment allows for the exploitation of both network effects and scale effects. Modern electronics offers many examples of successful standard setting through industry itself.

Appendix I.3: NACE (EU classification) rev. 1.1 Classification

339

p,k′ A′′

A′

R′2 PO

O

R′1

A N

pN C pM R′0

p0

L

E

p1 R

F

k′1 H

K D

G

k′0

DD1

DD0

DD2 Z

V 0 q1 q4 q6

q3

q2

q5

q

Fig. 84 Product innovation and network effects

There are, however, well known examples of competing proprietary standards as well, as was the case with video recorders.

Appendix I.3: NACE (EU classification) rev. 1.1 Classification at the 2-Digit Level (in Parts) D Manufacturing • • • • •

15 Manufacture of food products and beverages 16 Manufacture of tobacco products 17 Manufacture of textiles 18 Manufacture of wearing apparel; dressing and dyeing of fur 19 Tanning and dressing of leather, manufacture of luggage, handbags, saddlery, harness and footwear • 20 Manufacture of wood and of products of wood and cork, except furniture;

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• • • • • • • • • • • • • • • • •

Innovations in Macroeconomics

21 Manufacture of pulp, paper and paper products 22 Publishing, printing and reproduction of recorded media 23 Manufacture of coke, refined petroleum products and nuclear fuel 24 Manufacture of chemicals and chemical products 25 Manufacture of rubber and plastic products 26 Manufacture of other non-metallic mineral products 27 Manufacture of basic metals 28 Manufacture of fabricated metal products, except machinery and equipment 29 Manufacture of machinery and equipment n.e.c. 30 Manufacture of office machinery and computers 31 Manufacture of electrical machinery and apparatus n.e.c. 32 Manufacture of radio, television and communication equipment and apparatus 33 Manufacture of medical, precision and optical instruments, watches and clocks 34 Manufacture of motor vehicles, trailers and semi-trailers 35 Manufacture of other transport equipment 36 Manufacture of furniture, manufacturing n.e.c. 37 Recycling

Appendix I.4: Market Entry of Digital Good Producers in a General Equilibrium Model The following model (VOGELSANG 2006) puts the focus on the role of R&D in intermediate production and uses a Dixit-Stiglitz utility function where we quote from WELFENS/VOGELSANG (2006, pp. 120–123):Consider “a general equilibrium model with two sectors and simultaneous Cournot and Betrand-Competition“ which follows the approach of GROSSMAN/HELPMAN (1991). The main point of the model is described by the following characteristics: • The aspatial character of digital companies is stressed, as these companies are located in the “rest of the world.” The model describes their decision to enter a (new) market of a small, open economy. • The expected profits are crucial for the internationalization strategy. • The revenues are influenced by the quality of the products. • Only one input factor is significant, labor. This stresses the low capital intensity of digital goods production function. First the framework of a closed economy is developed. For a representative household, a standard CES-utility function is assumed ⎛ U=⎝

n 

⎞1

j=1

with elasticity of substitution σ =

1 1−ρ

ρ

Xj ⎠

> 1.

ρ

(1)

Appendix I.4: Market Entry of Digital Good Producers

341

In the model each of the n different industries produce a final product x. The final products are imperfect substitutes which means that monopolistic competition is predominant in the final goods markets. The budget constraint reads E = xj pj = wH LH + wI LI + 

(2)

with LH and LI representing the labor employed in the sectors sales/marketing H of the final goods and intermediates production I, respectively, wH and wI signifying real wage rate in the sectors, p showing the prices of the n different final products x and profits  summed up over all companies and sectors. With regard to the standard assumptions of monopolistic competition (free-entry, Cournot-Competition), a markup λ results, so that the prices for the final products xj exceeds their marginal costs by λ = 1/ρ

(3)

Variable costs of assembling the final goods xj out of intermediates q and fix costs for marketing add up to the total Cost function C: Cj = HwH + vπj xj

(4)

with H illustrating fixed sales and marketing costs, π the price of the intermediates. The input factor v results from the production function for the final products xj =

vj  1 i=1

v

zj,i (qj,i )

(5)

assuming that vj = v = v¯ . For mathematical convenience and without loss of generality, the input factor 1/v balances the number of v different intermediate products z, so that for the production of x units of final product j, exactly z units of the intermediates are used. qj,i indicates the quality of intermediate product zj,i . Following Grossman and Helpman (1991b), a quality ladder as seen in the graph below represents the enhancements achieved when producing the intermediates. The horizontal axis represents the intermediate producers of industry j indexed by i. The quality level q of the intermediates is shown on the vertical axis. Improving quality means developing a next generation version of an intermediate. By assumption, a next generation intermediate provides exactly κ times as much quality (or services) as the product of the generation before it. κ > 1 is constant and exogenous. The production function to produce the intermediates z has a fixed component α and variable component with a fixed input factor 1/β: var /β zj,i = α + Lj,i

(6)

Bertrand competition in the market of intermediates for industry j leads to the result that only the company offering the best quality adjusted price will survive: Consider two companies A and B which both offer intermediate i for industry j. They may

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Fig. 85 Quality ladder for Industry j. (Source: Grossman and Helpman 1991b)

q

κ

κ

κ

i=1

v

produce intermediates of quality qj,i,A and qj,i,B , respectively. Quality adjusted prices Q are Qj, i =

πj,i qj,i

(7)

The intermediates i for industry j are perfect substitutes. The quality adjusted price is the only criterion for the final goods producer to decide which company should supply the intermediates. With equal quality adjusted prices, it chooses the higher quality product for convenience. Therefore results zj,i,k = 0 with k ∈ B, C, D, . . . when Qj,i,A < Qj,i,k for every k. So company A sells all z, j,i at price Qj,i,B = κQj,i,A , which reflects Bertrand competition in this market segment. Introducing marginal cost pricing for company B, which yields βwI with wI for the real wage in the intermediates producing sector according to (6) the price which has to be paid by the final good producer of industry j to company A, yields marginal costs of B times the factor κ: πj,i = Qj,i,B qj,i,A = κβwI

(8)

For determining a general solution, some symmetry assumptions are now introduced: (1) βj,i = β, (2) wI,j,i = wI and (3) κj,i = κ for all j,i. The quality of an intermediate depends on the amount invested in R&D, which is measured by α. To agree on producing zj,i , company A must achieve a non negative profit A ≥ 0:     α α A = zj,i πj,i − wI − βwI = zj,i wI κβ − −β zj,i zj,i = zj,i wI [(κ − 1)β] − α

(9)

Appendix I.4: Market Entry of Digital Good Producers

343

The equilibrium conditions for the labor market finish the description of the closed economy L = LH + LI

(10)

LH = nH

(11)

LI =

vj n  

(zβ + α)

(12)

j=1 i=1

The next step is to transform Eq. (9) so that profit can be expressed with exogenous variables of the closed economy only. Then the expected profit function of potential new intermediate suppliers can be examined when the closed economy is opened. First, the cost-function is amended by the industry’s j pricing model. The expenditure per industry is calculated, which gives solutions for x and z. Assuming symmetry of all n v industries, a general cost-function can then be determined. The total costs involved in producing and selling final products xj are Cj = HwH + νπj xj = HwH + νβwI κxj

(13)

Marginal costs amount to ∂Cj = νβκwI ∂xj

(14)

In equilibrium, the price of the final product equals the marginal costs times the mark-up λ: pj = λνβκwI

(15)

In each industry j the difference between the price and marginal costs is used to cover the fixed costs: HwH = xj (vβκwI − vβκwI )

(16)

Assuming labor flexibility between all sectors wH = wI = w leads to xj =

H (λ − 1)νβκ

(17)

The number of industries n is given by the standard solution of monopolistic competition: xj =

p(j)1/(ρ−1) n 0

p(y)1/(ρ−1) dy

E=

p(j)−σ n

(18)

p(y)−σ dy

0

Symmetry with P(j) = p for all j would directly lead to xj = E/(np(j)). Assuming symmetry for all i it directly follows xj = zj,i from the production function since

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the input coefficient 1/v balance the number of digital goods. Inserting the equation determining xj in the profit function:   Hw(κ − 1) 1 1 A = − α = Hw − −α (λ − 1)νκ (λ − 1)ν (λ − 1)νκ

(19)

When w = 1 is chosen as numeraire the equation express the expected profit in terms of exogenous variables only. The model specification leads to the result that the marginal costs β are irrelevant, which reproduces a main characteristic of a digital economy. The interpretation of the equation is intuitive: • Technological leadership positively affects profits. ∂A >0 ∂κ • The higher the number of intermediate goods producers in an industry, the lower the profit will be. ∂A <0 ∂ν • The higher the fixed costs of the final goods provider the more profitable are investments in R&D by the digital goods producer: ∂(∂A /H) >0 ∂κ Opening the economy changes the perspective to consider a single company F outside this country, whose headquarters is located “somewhere” in the rest of world (or is aspatial in this sense). The production function of F corresponds to (6). Moreover μ denotes the additional marketing and sales costs for market entry in the closed economy and ψ describes the probability of having success, which means that the domestic competitor A for variety I can be squeezed out:1 1. Strategy 1: F enters the market and offers its own digital products as intermediates. Transport costs are neglected because of the special characteristics of digital goods. Assuming that the product is developed already, which means the fixed costs α are not relevant for the decision on market entry, the profit function then yields: 

foreign 1 For

 H(κ − 1) =ψ −μ (λ − 1)νκ

(20)

convenience, it is assumed that the company F is the only potential competitor and that F is “small” in the sense that possible disequilibria in the balance of payments can be neglected.

Appendix I.4: Market Entry of Digital Good Producers

345

2. Strategy 2: The foreign company F buys domestic company A. K is the price of ∗ the acquisition, ρ the discount factor for the next period’s profits and (1 − ψ)it describes the probability that not one of the competitors will be successful till t. foreign = K −

 H(κ − 1) − α ρ−t (1 − ψ) (λ − 1)νκ

∞   t=1

it∗

(21)

3. Strategy 3: Do nothing. foreign = 0

(22)

Equations (20) to (22) predict the internationalization strategies of digital goods producers: • A high H and a low λ are preferred by foreign digital goods producers to enter in. Interpreting the necessary marketing constants H as a proxy for the size of the country leads to the result, that larger countries are more attractive for foreign digital goods producers. • Strategy 2 (acquisition) is chosen, when technological leadership of the domestic price-quality leadership is dominant and sustainable and the risk of not achieving the leader position oneself is high. The price–quality competition is pivotal in this model. Interpreting the enhancement process of versions as raising the knowledge intensity of a product, the model predicts that competition drives digital goods producers to the right upper corner of the knowledge-scale-intensity diagram introduced above. In reality all strategies can be observed. Anecdotic evidence may be that Microsoft tends to conduct strategy 1 since it has a strong technological leadership position in operating systems (high κ) and therefore prefers growing through trade. Whereas eBay in the early years pursued a mixed strategy; in countries with competitors in its market segments (e.g., Germany), it prepared the ground through acquisitions. Whereas the hypothesis for SAP may be that it prefers large countries due to a high μ.

J. EU Innovation Policy: Analysis and Critique

J.1 Introduction Economic globalization has accelerated the innovation race among leading OECD countries as foreign direct investment (FDI) in Newly Industrializing Countries (NICs) plus China and India have created a new international division of labor. Indeed, globalization went along with a more intensive innovation race (JUNGMITTAG/ MEYER-KRAHMER/REGER 1999). Moreover, in the 1990s increased R&D expenditures in China and many NICs as well as Russia have reinforced the ability of economic and technological catching-up. There is a certain minimum R&D expenditure requirement—relative to GDP—if countries are to be able to effectively adopt foreign technologies. Both innovation and fast diffusion can contribute critically to international innovativeness. Improving the international competitiveness of the overall EU-15 has been an explicit goal of the EU Lisbon summit of 2000. This summit has proclaimed the goal to make the EU the most competitive economy by 2010; exploitation of the digital information society is to play a crucial role in this respect as the Heads of State and Government of European Union endorsed the idea of a European Research Area (ERA) and declared the creation of a European knowledge-based society a crucial element of the political strategy. With the expansion of digital networks and the internet, respectively, there are also new global channels for technology diffusion on the one hand, on the other hand modern digital networking also facilitates cooperation among researchers and engineers which enhances the effectiveness of the innovation process in leading OECD countries; this also applies to the EU-15 which has emphasized building a European Information Society early on. The European Commission has considered some broad reforms in EU innovation policy in the document “Towards a European Research Area (ERA)” (EUROPEAN COMMISSION 2000b). The European Parliament has supported the project in a Resolution adopted on May 18, 2000. The new strategy accepts that national innovation policy is crucial but it seeks a well-defined complementary role of supranational innovation policy. Key elements of the new strategy are:

P. J. J. Welfens, Innovations in Macroeconomics, DOI 10.1007/978-3-642-11909-5_10, © Springer-Verlag Berlin Heidelberg 2011

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• Better and more flexible co-ordination of national innovation policies. • Creating Networks of Excellence (NoE) which aim at reinforcing excellence on a research topic by creating large networks of R&D actors with a common focus on a joint program of activities. • Establishing Integrated Projects (IP) which stand for multi-partner ventures which aim at bringing together a critical mass of resources to reach a specific research objective—with a strong focus on combining new knowledge for launching product innovations and process innovations. According to the EU the Networks of Excellence and Integrated Projects, respectively, should reflect the following idea (Extract from the Decision No. 1513/002/Ec. of the European Parliament and of the Council of 27 June 2002 as quoted in CARACOSTAS 2003, p. 39): The purpose of Networks of Excellence is to strengthen and develop Community scientific and technological excellence by means of the integration, at European level, of research capacities currently existing or emerging at both national and regional level. Each Network will also aim at advancing knowledge in a particular area by assembling a critical mass of expertise. They will foster co-operation between capacities of excellence in universities, research centers, enterprises, including SMEs, and science and technology organizations. The activities will be generally targeted towards long-term, multidisciplinary objectives, rather than predefined results in terms of products, processes or services. . . Integrated Projects are designed to give increased impetus to the Community’s competitiveness or to address major societal needs by mobilizing a critical mass of research and technological development resources and competencies. Each Integrated Project should be assigned clearly defined scientific and technological objectives and should be directed at obtaining specific results applicable in terms of, for instance, products, processes or services. (. . . ) Subject to conditions to be specified in the specific programs and in the rules for participation, the Integrated Projects will have a high level of management autonomy including, where appropriate, the possibility to adapt the partnership and the content of the project. They will be carried out on the basis of overall financing plans preferably involving significant mobilization of public and private sector funding, including funding or collaboration schemes such as EUREKA, EIB and EIF.

Taking into account the principle of subsidiarity it is clear that EU R&D programs must have extra EU-value added, for example positive mutual—unilateral or reciprocal—spillover effects in a joint innovation project. To some extent the idea of creating networks of excellence certainly is adequate in the sense that in a single EU market there should be international R&D joint ventures organized within the framework of top R&D groups from several countries; this typically would bridge various national systems of innovations and also various languages in the community. To some extent it also could bring useful cross-country R&D spillover effects, in particular for relatively backward countries which under different circumstances would find it more difficult to catch-up in terms of innovativeness. To the extent that successful R&D consortia applying for EU funds have integrated partners from EU countries with a relatively low per capita income—e.g., cohesion countries—one may anticipate accelerated diffusion of new technology in the community. It remains, however, an open question whether partners from lowincome countries can make considerable contributions to top R&D performance.

J.2 Innovation Policy in the EU

349

Whether or not this is the case clearly will depend on stable networking and hence sufficient learning and cumulation effects. Establishing integrated projects also is a useful approach to the extent that university R&D (or similar external R&D centers) and R&D centers of firms cooperate smoothly.

J.2 Innovation Policy in the EU In the EU innovation policy is mainly a policy task faced at the national level. National innovation policies of EU member countries must take into account the “national innovation system” which is defined as the respective set of institutions, agencies and cultures relevant for the innovation process (LUNDVALL 1992; HOLLINGSWORTH/BOYER 1997). The EU has two elements of innovation policy at the level above national government: • There are Framework Programmes (FP 1–FP 6) which aim at stimulating joint research efforts. The first FP of 1984 has emphasized industrial technologies, information technology, telecommunications and biotechnology. Subsequent Framework Programmes have broadened with respect to the scope of research topics and technologies. • Outside the Framework Programmes the Commission has launched a range of regional innovation policy initiatives. For example in 1993 a special initiative termed Regional Technology Plans (RTP) was started, where the idea was to nurture regional innovation and growth in disadvantaged regions. Such pilot programs can help to stimulate growth. The Commission is mainly playing a mentor role in RTP, the regions which finally were selected to enter with their projects the experimental stage are mainly responsible for the success of the respective program. In addition, there are transnational programs such as COST and EUREKA. The latter, starting in 1985, includes not only the EU countries but countries from Eastern Europe and Russia as well. These programs are intergovernmental initiatives which are mainly bottom-up programs and emphasize international networking in R&D. All this does not mean that the EU has a strong comprehensive innovation policy. Major problems in this respect refer to: • Availability of rather limited funds at the level of the EU: Supranational funds have not reached more than roughly 4% of expenditures at the national level. • Conflicting interests among high-income countries with a high share of medium and high technology in manufacturing output as compared to low-income countries with a high share of low and medium technology in manufacturing output. Low-income countries anticipate that they will get a disproportionate share of EU R&D funds which implies considerable resistance against raising the relative share of supranational R&D expenditures in the overall EU budget. With EU eastern enlargement this problem might be reinforced. • Problems in creating an integrated innovation system.

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Despite all these problems one should not overlook the impact of the single-market dynamics which include emergence of a large integrated capital market in the Euro area.

J.3 Innovation Dynamics in OECD Countries J.3.1 Innovation, Specialization and Growth: Empirical Analysis for EU-15 and USA Comparing economic development in the USA and the EU and individual EU countries, respectively, there are various differences which might explain the relatively high dynamics of the USA and the more modest growth in the EU in the 1990s. Superior US innovation dynamics is only one aspect, a relatively high rate of population growth of the USA is a second factor; and the growth of information and communication technology (ICT) is a third element where the USA has benefitted both from increasing production of ICT goods and increasing use of ICT—based on the accumulation of ICT capital. It is well known that the expansion of ICT production has strongly contributed to technological progress in the USA; it seems that most of the rise of total factor productivity in the 1990s indeed is attributable to ICT production (JORGENSEN 2002). The issue of spillover effects and a more detailed analysis of total factor productivity growth thus remains on the agenda. Taking a closer look at the EU requires to focus on individual countries and their respective catching-up and innovation dynamics. From an analytical perspective an augmented production function is useful in which capital, labor, technology and telecommunications play a role (WELFENS/JUNGMIITAG 2002). Moreover, there is an additional growth bonus from specialization itself which can be divided into general specialization effects and high technology specialization effects. As regards technological catching-up dynamics within the EU there is clear empirical evidence that specialization effects matter, in particular in high technology (JUNGMITTAG 2004). Moreover, there is evidence that some EU countries have made considerable progress in technological catching-up in the period 1970–95, this holds in particular for Finland and Ireland, but there is also some modest catching-up of Spain. The following figure shows some of the relevant catching-up dynamics in the EU where we leave open to which extent diffusion, enhanced human capital formation and gross fixed capital formation plus innovation—strictly defined (and partly linked to FDI inflows) have contributed to convergence.

Percentage contribution of technology diffusion to growth

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351

Specialization in R&D-intensive technologies 30% 20% ES SE

FI

y = –1,1663x – 0,018

IE

R2 = 0,4166

10%

AT

BE

UK

0% –15%

–10%

– 5%

0%

5%

GR –10%

DK

FR

PT 10%

15%

IT NL

–20%

DE

–30% – 40% Percentage contribution of specialization to GDP growth Specialization in leading-edge technologies

Percentage contribution of technology diffusion to growth

50% FI ES

y = –1,1936x – 0,0155

30%

R2 = 0,8158

IE

10%

AT

–40%

–30%

–20%

DK

PT

BE SE

–10% 0% –10% IT –30%

DE

10%

20%

30%

40%

UK

GR FR

–50% Percentage contribution of specialization to GDP growth

NL

Fig. 86 Correlations between contributions of transferable technical knowledge and technological specialization to GDP growth. (Source: Jungmittag (2004), innovations, technological specialization and economic growth in the EU, Brussels)

J.3.2 Comparative Innovation Dynamics Innovation dynamics can be measured in various ways. There are two key figures to be considered crucially: • As regards input in the R&D process one is interested in R&D expenditures relative to GDP or R&D expenditures per capita. If one is interested in a refined analysis one may take a look at expenditure figures on the basis of purchasing power parity which mainly reflects differences in the absolute price of nontradables across countries (e.g., construction prices in Spain are lower than in Germany or France or Scandinavia so that building a new research lab is relatively cheap in Spain—and other low-income countries).

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• As regards innovation output there is a natural interest in patent applications— and patents granted—on a per capita basis. Not all patents are equal so that there is particular interest in medium technology and high technology patents; and in those patent classes which show the highest growth rate. High growth rates reflect strong innovation dynamics. Not all innovations can, of course, be patented; in the case of innovative services and software trademarks and copyrights are important to some extent; alternatively, one might want to take a look at the share of new products in overall sales. As regards patenting one might have to consider two special problems: There seems to be an international tendency of leading firms to generally seek more patents where patent applications to some extent are used as a strategic means to deter rivals in the innovation race. In some high technology fields patenting might not be attractive as innovation cycles are so short that patenting does not give effective protection. Finally, there can be a rise in patent applications due to the fact that one patent at time t goes along with more “follower patents” in t + 1 than in previous periods. Comparing the EU with the USA and Japan we find that the share of EU-15 in overall patent applications at the European Patent Office (EPO) has gradually declined in the 1990s. By contrast the share of the USA has increased considerably. If the trend would continue for another twenty years the natural home bias—read: home lead—of EU countries would no longer exist. 50 45

EU-15

40 35

USA

30 25 20

Fig. 87 Percentage shares of patent applications at the European patent office

Japan

15 10 1990 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001

As regards the number of patent applications at the EPO per one million inhabitants the USA and Japan were ahead of the EU-15 at the beginning of the twenty-first century. This also points to a certain weakness of EU innovation dynamics. From this figures it is fairly clear that the EU will be unable to reach the Lisbon target and become the world’s leading economy in terms of competitiveness. A particular problem is Germany where the stock of national patents has been declining in the 1990s. While taking a look at patent applications relative to applications of other countries means to consider marginal patenting dynamics the focus on the stock of patent gives a much broader picture. If we assume that the stock of knowledge enters the production function and if we approximate that variable by the stock of patents it is obvious that a declining stock of patents indicates a dampening vintage effect in the field of technology; moreover, if Schumpeterian rents are proportionate to the stock of patents—we assume that products made on the basis of

J.3 Innovation Dynamics in OECD Countries 180

353 Japan USA EU-15

160 140 120 100

Fig. 88 EU-15, Japan and USA: Number of patent applications per one million inhabitants at EPO

80 60 1990 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001

patented technology can fetch relatively high prices in world markets—a decline in the stock of patents should indeed go along with reduced income growth.

56000 54000 52000 50000 48000 46000 44000

Fig. 89 Stock of patents at the German patent and trade mark office (1960–2001)

42000 40000 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007

As regards per capita patent applications at the EPO several small EU countries were quite successful in terms of raising the respective figure, however, Germany, France and Italy have only a modest record. As regards EU accession countries patenting dynamics are relatively low, however, this is not surprising since they still have low per capita income and still modest ratios of R&D expenditures relative to GDP. There are, however, good prospects that continuing growth and FDI inflows in combination with rising public R&D expenditures—plus EU support—will raise patenting performance. For the accession countries there is still need to emphasize to some extent diffusion of new technologies and adoption of advanced technology. Generating higher innovation dynamics and technological upgrading is a necessary element of the medium term adjustment and growth process. There are indeed new empirical findings which show that Hungary, the Czech Republic and Poland (BORBÉLY 2004) have embarked upon a process of structural change and economic and political catching-up. The analysis of trade between the EU-15 and selected accession countries by means of a modified Revealed Comparative Advantage Index in the context of R&D expenditure shows, that Poland mainly specializes in the expor-

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400 Sweden Finland Germany

300

Netherlands Luxemburg Denmark

200

Austria Belgium France UK

100

Ireland Italy Spain Greece Portugal

0

1990 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001

Fig. 90 EU 15: Number of patent applications per one million inhabitants at the EPO

45 Slovenia

30

Hungary

15 Estonia Czech Rep. Latvia Slovakia Poland Lithuania

0 1990 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001

Fig. 91 Central and eastern European accession countries: number of patent applications per one million inhabitants at the EPO

tation of low and medium R&D intensive sectors, whereas the Czech Republic has clusters both in medium and high R&D intensive sectors, and Hungary specializes mostly in high technology products already. Although R&D expenditure ratios are still much lower in eastern European countries than in the current EU member states, the sectoral distribution of R&D expenditures is, however, similar.

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As regards R&D expenditure per capita Japan and the USA have shown a considerable growth in the 1990s while EU-15 has achieved only modest growth at the end of the decade.

340 USA 290 Japan 240

190 EU-15 140

90 1991

1992

1993

1994

1995

1996

1997

1998

1999

2000

2001

Fig. 92 R&D expenditure per capita in EU-15, Japan and the USA (EUR, current prices)

As regards R&D expenditure in percent of GDP in the EU-15, Japan and the USA, it is obvious that Japan and the USA have a clear lead compared to the EU, and the gap has not really narrowed in the 1990s.

3,5 Japan 3 USA 2,5

EU-15

2

1,5 1992

1993

1994

1995

1996

1997

1998

1999

2000

Fig. 93 R&D expenditure in percent of GDP in EU-15, Japan and the USA

2001

2002

2003

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J.3.3 Acceleration of Innovation Dynamics The OECD countries have witnessed considerable differentiation in economic growth in the 1980s and 1990s on the one hand, on the other hand the rate of innovation—as measured by patent applications—has increased in the USA and Europe in the 1990s (COUNCIL OF ECONOMIC ADVISERS 2000; WELFENS/AUDRETSCH/ADDISON/GRIES/GRUPP 1999). The USA has achieved a considerable lead in economic growth and technological progress vis-àvis the EU in the 1990s which was characterized by an unusual increase in labor productivity in the second half of the economic cycle in the USA (COUNCIL OF ECONOMIC ADVISERS 2001). US labor productivity growth in the period 1973– 1995 was 1.4% p.a., but in 1995–2000 it reached 3.1%. It is unclear what the reasons for the robust US productivity growth is. The Council of Economic Advisers has argued that falling computer prices and rising computer expenditures of wholesale trade, banking and the ICT sector itself play a crucial role for US growth in the 1990s. Moreover, there was a strong rise of multifactor productivity growth in the 1990s, and to a considerable extent this is related to ICT; in the USA both the production of ICT and the use of ICT—this is associated with ICT investment—have contributed to a strong growth of labor productivity in the 1990s. The picture for EU countries is heterogeneous: There are countries in which labor productivity growth in the services sector is more affected by ICT dynamics than in manufacturing industry (OECD 2003). The growth of the ICT sector (ICT) in the 1990s has considerably contributed to growth in the USA, especially in the second half of the 1990s. According to estimates by the US Department of Commerce (see the study DIGITAL ECONOMY) the ICT sector represented 8.3% of US output in 2000, but the sector contributed almost 1/3 of real GDP growth in the period 1995–99. Even more impressive is the contribution of ICT to investment in the USA; it is noteworthy that computer prices have fallen strongly in the 1990s. In 1999 business spending for ICT equipment and software represented more than three-fourths of the 12 percent real growth in total equipment and software spending. The contribution of the ICT sector in percentage points increased from 0.8% in 1994 when overall US growth was 4.2% to 1.6% in 1999 when the overall growth rate was close to 5%. In Europe only Finland and Sweden as well as Ireland, have an ICT sector which directly contributes significantly to economic growth. In 1989 Swedish Ericsson stood for about 0.5% of total Swedish GDP, but in 1999 the company stood for 2.6% of GDP and contributed 0.5 percentage points to economic growth. In Finland Nokia stood for 4% of GDP—and 1/5 of Finnish exports—and contributed a full percentage point to growth in 1999 (EUROPEAN COMMISSION 2000a). The ICT sector (as defined by EITO 2000) consists of IT-spending which reached 2.7% of GDP in the EU in 1999, but 4.5% in the USA. Telecommunications accounted for 2.8% of 3.1% of GDP in the EU in 1999, for 2.8% in the USA. Assuming that prices in the EU for telecommunication equipment and services are slightly higher

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than the USA one may argue that the transatlantic differential in ICT spending is almost zero in telecommunications, but that the EU is far behind in the IT sector. The use of telecommunications has contributed considerably to economic growth in the 1970s and 1980s in Germany, and the expansion of the internet could lead to a similar effect if it contributes to accelerating diffusion of information and knowledge, respectively (WELFENS/JUNGMITTAG 2000; 2001; WELFENS 2001a). Network effects play a role both in the use of telecommunications and PCs (the internet). As regards the USA, GORDON (1999) has argued that US growth acceleration in the second half of the 1990s—ignoring the cyclical effects—can fully be explained by the growth of output and productivity growth, respectively, in the computer producing sector and in the output of other durables. GORDON argues that there were no spillover effects in productivity to other sectors. GORDON argues that falling computer prices signal a falling marginal product of computer equipment. Subsequently, we will raise some doubts about this view. We also will look into the problem of modeling certain spillovers in a straightforward way. Indeed, we will address several aspects of the new economy and emphasize the potential role of spillover effects and network effects. One may also consider the GORDON (2000) argument about the limited role of computer expenditures in the USA as flawed: He argues that the expenditure on computers as a share of nonfarm private business has stagnated at 1.3% in the late 1990s, however, he completely overlooks that the USA is the leading country in terms of software expenditures which accounted for 2.7% of GDP in 1995—for comparison France 0.9% (OECD 1998). Analyzing the role of computers—and semiconductors—without taking into account software expenditures obviously is inconsistent. The 2003 European Innovation Scoreboard (EUROPEAN COMMISSION 2003a; SEC (2003) 1255)—the fourth Scoreboard realized, namely as part of the Lisbon strategy—has shown that the EU lags the USA for ten out of eleven indicators available in both the EU and the USA. Only in the field of science and engineering graduates did the EU beat the USA. Fields with a gap were: • • • • • • • • • •

High-technology patents at the US Patent and Technology Office (USPTO) USPTO patents Early stage venture capital in percent of GDP High-tech patents at the European Patent Office (EPO) Population with tertiary education High-tech manufacturing value-added Business R&D expenditures in percent of GDP Expenditures on ICT in percent of GDP Public R&D expenditures in percent of GDP EPO patents

On the basis of an Overall Summary Innovation Index which combines a look at the average change in SII trend indicators with the level of the indicator—in the range 0–1—for the respective country Finland and Sweden are clear leaders while Germany, Netherlands and France are losing momentum; Italy is falling behind. The fact that except for the UK all large EU countries are facing problems raises serious

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worries. An important field in which, however, the EU is indeed catching-up with the US concerns ICT as is noted in the 2003 European Innovation Scoreboard (EUROPEAN COMMISSION 2003a): “The only encouraging example of a long lasting catching-up process is in ICT expenditures (gap cut by 50% since 1996). Reaping the full benefits of this positive trend would require acceleration of organizational innovation following investment in ICT hardware.” The 2003 summary innovation index (SII-2 which covers the 12 most widely available indicators from the Community Innovation Survey) shows that Greece, Portugal and Spain are catching-up while the Netherlands, France and Germany are losing momentum. Another interesting finding is that there is a rising role of R&D expenditures in the services sector: For the overall EU the share of services in business R&D was 13% in 1999 which was 5 percentage points above the 8% in 1992. In Japan R&D in services represented 2% in 2000, up from 0.2% in 1992. In the USA the share of business R&D has increased from 24% in 1992 to 34% in 2000. EU-25 countries which were found to rank high in terms of innovativeness also ranked high in terms of diffusion. As regards the response time of markets to innovative products the Scandinavian countries had relatively short response periods while Germany, Italy, Spain, France, the UK, Greece and Portugal had long response periods (TELIIS/STREMERSCH/YIN 2003, in Marketing Science 22, 188–208; data for USA and Japan not available).

J.3.4 Specialization in Innovation and ICT Network Perspectives Analyzing the ICT sector means to look into technological dynamics, output-GDP shares and expenditure-GDP shares. Let us start with the simple observation that ICT is a highly dynamic sector of the economy. Judging by figures from the European

Canada

Sweden

Italy

Netherlands

UK

18 −52 −26 −62 −56 −29 48 −36 −69 35

France

−67 −96 0 −41 10 −20 −44 −7 −13 −65

Germany

70 −7 −19 85 −12 32 −52 13 −53 10

Japan

50 −84 −22 30 −71 −64 42 −53 52 −19

USA

Telecommunication 13.6 10 −3 −34 −7 17 −75 Turbines 10.6 −8 −74 −40 87 8 83 Railway Systems 8.5 −74 −41 67 9 −67 58 Paper−Making Equipment 7.6 −4 −88 28 −71 −43 −54 Automobiles 6.7 −47 −14 57 35 −31 −84 Medi. Sector, Instruments 6.6 46 −80 −38 −36 −7 38 Advanced Electronics 6.4 −18 46 1 −21 −18 −52 Power Distribution 6.4 −20 8 16 34 −23 −27 Agrochemicals 6.1 35 −59 0 −3 5 22 Medi. Sector, Electronics 5.8 42 −31 −47 −64 −9 −48

Growth

Switzerland

Table 21 Specialization (relative patent share in interval −100, +100) in 1995–1999 in technologyintensive fields with high growth rates in patents* (Source: FhG-ISI, Karlsruhe, preliminary)

*Average annual growth of patent applications at the European patent agency in 1989–1997

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Patent Agency the telecommunication sector has become that sector which has the highest growth rate of all patent groups; the growth rate in the period 1989–1997 was 13.6% p.a., the growth rate of advanced electronics was 6.4% which made it No. 7 in the field of the ten fastest growing technology fields. This means that ICT is rather technology intensive and has some potential for technology spillovers (in the sense of the New Growth Theory à la Romer or else). The USA plus Canada, the UK, Sweden and the Netherlands are positively specialized in telecommunications; they should strongly benefit from the global telecommunications boom which, however, will face some saturation problems in the long term when almost everybody has a mobile phone. In advanced electronics we find the USA plus Canada and the Netherlands again, but also and strongly Japan. According to these figures the USA, Canada and the Netherlands stand to gain particularly from the ICT boom worldwide. Japan is likely to benefit mainly on the electronics side. In the New Economy, there is, however, one caveat with respect to patent figures; many internet-based services cannot be patented—copyrights and trademarks play an important role here. Network Effects As is well known the use of computers and modern telecommunication equipment often is characterized by network effects. For the initial users the network becomes more useful with additional users linked to it. Therefore users might actively promote the use of their network, but more importantly, networks—say AOL, MSN or YAHOO (giving some incentive to existing users)—have an incentive to encourage users to convince friends and family to also use the network. Network effects also can play a role in industry, especially if there are strategic technology alliances in technology intensive industries. Indeed, the number of technology alliances is particularly strongly in the USA in the 1990s (COUNCIL OF ECONOMIC ADVISORS 2001, p. 117). A logistical function can be used to model network effects in the new economy, that is we can use the standard innovation diffusion model. Assume that Z(0) = 1, the adoption rate for the innovation Z is given by the differential equation: dZ/dt = aZ (L − Z)

(1)

where L is the exogenous population, Z the number of persons using the innovation— say a mobile phone, a PC or the internet—and L – Z the number not using it. Whenever pioneer users meet nonusers there is an “infection” effect which is described by the positive parameter a. In an economy which also is a heavy producer of the innovative product the diffusion parameter a is likely to be higher than in a setting where the innovative product is only used. The solution of the above equation is given (see BECKMANN/KÜNZI 1984, p. 130) by a logistical equation for the stock variable Z(t): Z(t) = L/[1 + (L − 1)e−at ]

(2)

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Note here that in an open economy the parameter a might be influenced by both the export-GDP ratio (x) and the import-GDP ratio (j) to the extent that the “infection” rate in the tradables sector is more intensive than in the nontradables sector; a simple suitable function could be a = a0 (1 + x + j). If the presence of FDI at home and abroad reinforces international diffusion of knowledge an FDI stock proxy K”/Y and K”*/Y* for the stock of FDI at home and abroad relative to GDP might also affect the diffusion rate. Moreover, one could study an export function with standard products (1, . . . , n) and innovation products (m. . . z) where the innovation products are ranked according to novelty—with novel products assumed to fetch higher prices than standard products; innovation products are increasingly adopted by firms in the export sector. After some critical time T innovation products become standard products with no premium in the world market, that is prices are equal to marginal costs. The terms of trade thus will depend on the percentage of innovation products in the overall basket of export goods. We will not look in these special problems here. Rather we will continue with Eq. (2). Denoting Z/L as z we have z(t) = 1/[1 + (L − 1)e−at ]

(2 )

Assume that there is a dual use good (dual here refers to its double nature as consumption and investment good)—here mobile telecommunication devices that are first bought as consumption goods—whose diffusion is described by Eqs. (1) and (2), respectively; we use the following modified production function in which positive spillover effects from mobile telecommunication devices Z are entering: Y = K β L1−β Zσ

(3)

The basic assumption here is that the use of computers in households has positive spillover effects in industry; there are knowledge spillover effects into output of firms whose aggregate value-added is Y. A special case which is easy to handle is where σ = 1: Y = Kβ L1−β L/[1 + (L − 1)e−at ]

(4)

In per capita terms we have (with y =Y / L and k = K / L): y = kβ Lz(t)

(4 )

Interestingly, the size of the country plays a positive role for per capita income here. From this perspective there could be an advantage for large countries—with large markets (USA or EU or other regional integration areas)—in the era of the New Economy. In such a model setup the size of the country matters. Comparing the NAFTA and Europe there is no reason to believe that Europe cannot benefit from size effects as much as North America plus Mexico. An important aspect concerns the impact of the ICT boom on the wage-real interest rate-ratio. If ICT is partly Solow-neutral capital augmenting technological progress the ratio of wages to interest rates will increase which will stimulate US firms to

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relocate ICT production abroad. Say to Mexico, Ireland, Hungary or Malaysia. This means that ICT production in low-income countries will grow so that the growthenhancing effects of strong productivity growth in ICT finally arrives outside the pioneer country (USA, partly Japan). If the host countries for FDI in ICT should reflect as small a group of host countries as for FDI in general in the 1980s and 1990s only two dozen countries worldwide will benefit from ICT product cycle trade. In a Schumpeterian economy there will be a series of innovations coming to the market. If such innovations are not evenly distributed over time they can cause a spurt in growth when a cluster of innovations is entering the diffusion stage, later the growth rate will slow down. If this stimulates entrepreneurs to come up with new innovations—again being realized in a cluster-type fashing at some point t—there will be another economic upswing. Instead of using a single differential equation for one innovation, one will have to use a system of logistical equations for all products i (i = 1,. . . , n). The new economy is generating logistical diffusion patterns both in the household sector—namely in the case of mobile telecommunication equipment and PCs plus internet use—and in industry (computers, internet use). The GORDON view of computers and ICT is doubtful for several reasons. But further research is needed. From the human capital growth model it follows: Europe will fall behind the USA in terms of per worker income if EU countries are not reducing unemployment rates and reducing tax rates and raising efforts on human capital formation. The most difficult problem in Europe is to finance higher education in private universities. European governments will find it very difficult to generate higher tax revenues in the era of globalization and the internet; unfortunately the idea of private universities (and vouchers) is unpopular in Europe. The competition of private universities would not only mean a higher stock of educational capital but also would stimulate the efficiency of teaching and research efforts in public universities. An economically meaningful investment-output ratio in the knowledge society should be defined as the weighted sum of the traditional investment-output ratio, the R&D–GDP ratio, the software expenditure–GDP ratio and the education expenditure–GDP ratio. In the latter three fields the USA has a clear lead over Euroland and Germany, respectively.

J.3.5 Openness, Taxation and Growth Several authors have dealt with the issue whether openness affects growth. An interesting indirect route is suggested—and empirically tested—by BRETSCHGER (2005). His theoretical point of departure is an optimum taxation framework which aims at equalizing marginal benefits of taxation and marginal costs of taxation. In an open economy overall marginal costs are equal to private marginal costs M plus marginal capital outflows (M ). If the economy is characterized by a Cobb–Douglas production function Y = AKβ L1−β the marginal product of capital is ∂y/∂k = (1 − τ)βA1/β y[β−1]/β so that inserting this expression in the Keynes–Ramsey

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rule gives the following expression for the per capita growth rate (g as symbol for growth rate; η is the intertemporal elasticity of substitution): ! " gy = [1/η] (1 − τ)β A1/β y[β−1]/β − (a + n + δ) . The empirical estimation for 18 OECD countries then proceeds under the assumption that the tax rate is a negative function of economic openness, and the results indeed show such a negative impact and thus indirectly a positive impact of trade on the level of the growth path. As an alternative we may consider the following—standard—setup which relies on a production function with Harrod-neutral technological progress). We will assume that the income tax rate is a negative function of the sum of the import ratio j at home and abroad (j*); and that the government budget constraint is given by γY − τY = μ[M/P] so that γy − τ y = μ[M/P]/[AL]; as we impose money market equilibrium under the assumption that money demand (with m := [M/P]/[AL] is given by m d = y σ /i (i is the nominal interest rate which is equal to r in the absence of inflation, σ is a positive parameter) we obviously can write γ = τ + σ / r. Hence, we get the following differential equation for k :=Y/(AL) as we use the goods market equilibrium condition [s(1 − τ) + τ − γ]Y = dK/dt + δK and assume that the real interest rate is a positive function of j/j* while the tax rate is a negative function of openness (with τ defined as a positive parameter):   (5) dk  /dt = s(1 − τ/[τ (j + j∗ )] + σ /r(j/j∗ ) k  β − [n + a + δ]k Hence we have for a central bank with a non-inflationary (and non-deflationary) monetary policy and a progress function a = a0 + a (j + j*)–with a denoting a positive parameter and a0 autonomous technological progress—the steady state solution for y :=Y/[AL]: y # = {[s(1 − τ/[τ (j + j∗ )] + σ /r(j/j∗ )]/[n + a0 + a (j + j∗ ) + δ]}ß(1−ß)

(6)

The effect of trade openness—the combined effect of j and j*—on the level of the growth path is ambiguous while the impact of trade openness on long run trend growth is positive. It thus depends on the length of the political capitalization horizon whether the positive trend growth effect is sufficiently taken into account. One major challenge for international organizations such as the IMF/the World Bank and the WTO is to help poor countries quantifying the empirical side of the approach presented and to support a political strategy which adequately takes into account both the aspects of changes in the level of the growth path (already requiring a long term view) and in the trend growth rate. While the USA stands for the leading global innovator country and may be expected to build its progress function mainly on domestic sources—the education system, the US innovation system and ICT capital accumulation—small open economies’ progress function indeed may be expected to be rather strongly affected by international trade dynamics: in particular if technology-intensive imports on the one hand and on the other hand technology-intensive products with considerable economies of scale play a role.

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International Alliances As regards international alliances the emphasis is more on EU15 countries than on EU accession countries. Strategic R&D alliances played an increasing role in the EU in the late 1980s as globalization and the run-up to the single market program as well as higher EU funds for cooperative R&D projects stimulated the internationalization of European R&D (NARULA 1999); the IT sector and biotechnology played a particular role. Moreover, there also have been renewed dynamics in R&D in the form of both asset-exploiting and asset-seeking FDI in the EU and the USA (CRISCUOLO/NARULA/VERSPAGEN 2005) argue that R&D facility’s capacity to exploit technological competences is a function not just of its own resources, but the efficiency with which it can utilize complementary resources associated with the relevant local innovation system; the empirical analysis indicates that both EU (US) affiliates in the USA (EU) rely strongly on home region knowledge sources, although they appear to exploit the host knowledge base as well. The crucial emphasis on home knowledge suggests doubts about a potential R&D strategy of the EU which would neglect the EU countries as prime locations for leading edge R&D in technologically dynamics sectors, in particular the ICT sector. One also must raise the issue to which extent the expansion of ICT requires reforms of the innovation system and in particular a stronger role of virtual research networks and “Digital Universities”; optimal linkages between R&D facilities and firms in technology-intensive sectors are crucial which naturally will include foreign investors.

J.4 Recommendations for Future EU Innovation Policy The existing experience with EU framework programmes has shown that they are an important stimulus for internationalization of research in the Community. At the same time it is obvious that the lessons from the mid-term of the 6th framework raise some doubt in term of efficiency. One major challenge in terms of research efficiency in the 6th framework programme is that Integrated Projects have been introduced which consists of 15–25 partners and thus are very complex to administer for the coordinator in the research projects. The efficiency of such projects is thus rather limited. The benefit of integrated projects for the Commission is that it facilitates work for the EU authorities—in the sense that a rather limited number of projects has to be evaluated— but this is offset by efficiency losses in research itself as a high number of partners implies enormous coordination efforts (unless partners work together over many years). Therefore very large integrated projects—unless there specific reasons to aim at involvement of many countries and partners, respectively—stand for a doubtful approach which should be replaced by a new strategy with emphasis on: • Specific Large Integrated Groups (SLIG) with a large number of partners should be continued; there are clear arguments in favor of a broad network.

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The Commission—and its advisors—should identify a limited number of areas deemed as suitable for Specific Large Integrated Projects. Areas earmarked as suitable for SLIP should not be exclusive so that other types of projects—in particular compact projects—should be allowed to compete. • Many compact projects with a carefully selected small number of players could be quite successful. Small Integrated Projects (SIP) with not more than five partners; this requires that the Commission and the European Parliament, respectively, put up more resources for project evaluation. A relatively large share of resources should go to those projects. If projects reach high marks in evaluation the research group should be allowed to increase the number of partners provided that it has indicated such plans in a mid-term report. This would then result in two-stage Integrated Projects. • Networks of Excellence should continue, but start on a rather limited number of actors (not more than 10). Research groups applying should indicate a two-stage plan for Network Extension in the Final Report; and networks with high marks in evaluation should then be allowed to apply for a Large Network of Excellence. However, the budget allocation for an enlarged network of excellence should be required to reflect growth in the number of partners under proportionately as the very idea of network effects suggests that efficient networks will be able to exploit economies of scale. • For both networks of excellence and for integrated projects there should be standardized contracts available for research groups which bring together partners from industry and outside industry. The available experience from NoEs and IPs indicates that legal problems raised by industry partners in prospective international R&D groups impair the realization of both NoEs and IPs. The proposed organizational improvements will bring enhanced R&D efficiency. However, this is not the most crucial issue when it comes to the topic how the EU could catch up with the USA. There is no doubt that the EU has fallen behind the USA in the 1990s in terms of innovativeness as measured by patent applications and share in high technology trade. A relatively weak performance has been measured in Germany whose poor economic performance after German unification raises many unpleasant questions. From an EU perspective it is crucial that the transatlantic digital technology gap should be closed relatively quickly. At the same time the EU might want to maintain its lead in mobile telecommunications which seems possible in the medium term provided that UMTS services are quickly rolled out and that the USA is not catchingup very fast in 2G mobile telecommunication density. Taking a look at the main budget items of the European Community—with No. 1 agriculture (share about 45%) and No. 2 structural funds (share about 1/3)—we do not find adequate priorities. Agricultural subsidies should be reduced to less than 20% of the EU budget while structural funds should be reformed in a way that would support more strongly retraining, education and support for research and development. If both the production of ICT and the use of ICT are important for economic growth there could be two ways for high growth. Trying to become a country that has successfully specialized in ICT production or encouraging firms and households

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to quickly use the new technologies. As regards the use of new ICT and promotion of the diffusion process governments could have a role in countries which are not leaders in ICT production—namely to the extent that government can substitute for the diffusion impulses which come from ICT production in other countries. The Scandinavian countries, the Netherlands and Germany have embraced telecommunication liberalization energetically after 1998, the UK already before. This lets one expect that part of the EU could be a driving force in the European and global ICT revolution. However, while the EU partly looks strong in the field of telecommunications its role in the fields of computer and software looks relatively modest when compared to the USA. It would be useful to study the user patterns of internet users more closely—both with respect to the time budget and the structure of use. Moreover, the size of network effects and the significance of the role of spillover effects from household computer use should be estimated empirically. Part of the problems encountered here will refer to data problems as neither government nor industry has straightforward data which could tell where computers sold finally are used. But the data issue should be solved by survey analysis and other methods. With EU eastern enlargement there will be pressure on EU-15 countries to move up the technology ladder. This should go along with increasing human capital formation which, however, raises the issue how the system of state-run universities will be able to cope with this challenge. The mixed US system—with private and public universities—has been impressive in its supply-side elasticity in the 1990s when more than two million new jobs were created in the education system. Serious problems for EU countries could also emerge in education since the Maastricht criteria have increased the pressure for budget consolidation. This raises some critical questions for an adequate future policy mix in the EU. There is a broader need for more comparative US–EU research—such research certainly could be helpful for identifying policy options to improve economic policy in all relevant fields of Schumpeterian dynamics.

K. Financial Market Integration, Interest Rates and Economic Development

K.1 Introduction Economic globalization progressed considerably in the 1990s with the opening-up of post-socialist eastern European countries for trade and capital flows as well as with the completion of the single EU market. Part of the single EU15 market introduced in 1993 was the liberalization of services including financial services. With EU eastern enlargement in 2004, there were steps towards an EU25 single market. However, free movement of labor was postponed for most EU15 countries until 2011 (at the latest). In ASEAN countries, financial integration resumed after the 1997/1998 crisis, and a broader integration strategy was envisaged. Both the EU and ASEAN are facing economic globalization in the sense that there is a long run increase in the trade of financial services, in foreign direct investment (FDI) in the banking and insurance sector and a growing influence from global international organizations such as the IMF and the Bank of International Settlements. Financial markets are important for economic development for many reasons, including the financing of capital accumulation, innovation and human capital formation. In his survey, TSURU (2000) points to several channels through which financial markets can affect growth. Competitive financial markets contribute to • The efficient allocation of capital • Efficient intermediation so that savings flow to those investment projects with the highest yield • A rise in the savings rate (under certain circumstances) In their empirical analysis, KING/LEVINE (1993) have emphasized that several traits of the financial market contribute to higher growth. For example, liquidity relative to output and the share of private credits in total credits are important for growth; the emphasis on the share of private credits implicitly is an argument that a high share of public credits is not only crowing out private investment in a way which is neutral to output but that it indeed reduces real income. LEVINE/ZERVOS (1998) have pointed out that several variables affect growth of output: P. J. J. Welfens, Innovations in Macroeconomics, DOI 10.1007/978-3-642-11909-5_11, © Springer-Verlag Berlin Heidelberg 2011

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• Stock market capitalization, stock market liquidity and the degree of international capital market integration were found to have a positive impact on real output. • The volatility of stock returns negatively affects output. Thus empirical findings suggest that international capital market integration—in particular to the extent that it raises stock market capitalization (relative to GDP)— increases stock market liquidity and reduces the volatility of stock returns—will positively contribute to economic development. There is, however, a causality problem in the sense that we cannot exclude that capital markets stimulate growth, which stimulates the development of financial markets, since one may argue that wealth accumulation typically grows faster than output, leading to a situation in which the long-run growth of asset accumulation will naturally stimulate the expansion of financial markets and the respective services. (Granger causality analysis could shed some light on this, however, the causation could also be a phenomenon of interdependency.) One also cannot be certain that capital market liberalization and regional capital market integration will go along with reduced stock market volatility. To the extent that the US stock market dominates regional stock markets in the EU and Asia, the key issue is the speed and scope of international transmission of US stock market impulses. Moreover, while the US financial market system is the result of an evolutionary market development in which aspects such as stock markets, bonds markets, banks and prudential supervision interact in a useful way, one should expect that financial market institutions in other countries reflect their own specific evolutionary development. Therefore it would be no surprise if temporarily high US stock market volatility causes few problems in the USA or Western Europe, but this can have rather destabilizing effects in Eastern Europe, Asian NICs and other regions. Instability in major regions could occur as the consequence of unequal economic globalization so that not modern globalization is the key problem; rather critical international differences in the respective modernization of national financial markets and institutional developments seem to be a critical challenge. EU countries have recorded sustained growth since the creation of the single EU market at the end of 1992. However, growth was slower than in the USA. This broad comparison obscures the more detailed picture in the Euro zone, namely that medium-term growth performance was rather different across countries. As regards the late 1990s, this is particularly the case across member countries of the Euro zone which started on 1 January 1999 when the European Central Bank (ECB) and the European System of Central Banks (ESCB = ECB + national central banks) started. The 11 starter countries of the Euro were a rather heterogeneous group in terms of per capita income and debt–GDP indicators; most starter countries faced considerable unemployment problems in 1999, and the large member countries of the Euro zone still had serious unemployment problems in 2005. By contrast, the non-Euro countries in the EU15 group—UK, Denmark and Sweden—had low unemployment rates. Attributing differential unemployment figures to the Euro is not adequate, however, as several countries in the Euro zone had favorable development in terms of employment and growth. Regional monetary integration does, however, require an adequate degree of wage flexibility and labor mobility.

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With financial market integration making considerable progress in the Euro zone, visible for instance through the convergence of nominal interest rates, there was hope that economic growth in the Euro zone would accelerate and unemployment be reduced. This has hardly been the case since growth accelerated mainly in small open economies of the Euro zone while it fell in Germany and Italy. Italy—having a high debt–GDP ratio of close to 110% in the run-up to the start of the Euro—was to benefit from falling nominal and real interest rates as well as from interest rate convergence. Hence Italy should benefit from higher growth/better economic development, as should Germany, provided that domestic policies adopted were growth-enhancing and increasing trade with member countries of the Euro area stimulated growth through higher trade dynamics and technology diffusion. From a theoretical perspective, trade creation was to be expected from monetary integration. This holds despite the fact that the Euro area of 11 starter countries (France, Germany, Italy, Austria, Belgium, Netherlands, Luxemburg, Spain, Portugal, Finland, Ireland) could not be considered as representing an optimum currency area as defined by traditional criteria from the literature. There was considerable economic heterogeneity which led to the creation of cohesion funds for the relatively poor countries, Portugal, Spain, Ireland and Greece, with the latter joining the Euro area in 2001. Weak current account positions of Portugal, Spain and Greece indicate that even within a monetary union a country’s external position is a useful indicator of economic dynamics and prosperity. Relatively high growth of unit labor costs has been a major problem for several countries in the Euro zone. Between 1995 and 2005 the increase was 4.2% in Portugal, but −14.3% in Ireland; the figures for Spain and Greece were −8.5% and −2.4%, respectively. The Czech Republic recorded 6.4% which signals incipient competitiveness problems, Poland recorded −7.9%, Hungary −9.6%. Germany recorded −4%, but Austria did even better at −8.6%. Sweden and the UK witnessed an increase in unit labor costs, namely 5.8% and 2.3%, respectively. As rise of unit labor costs in industry would not be a problem if the relative degree of product innovations would increase or if the rise of wage costs would be driven by a strong expansion of the services sector; as regards the latter the UK has been rather successful, in particular in the financial services sector.

Financial Market Integration in Western Europe Financial market integration was hoped to deliver some of the expected economic benefits through the creation of the Euro and the ECB. Such integration could reinforce specialization in production and exports which should translate into higher productivity and output growth. However, following the KENEN criterion of optimum currency areas such reinforcement of specialization would undermine the case for a common monetary area (the KENEN criterion basically argues that a more diversified economy will be subject to international shocks which more or less cancel out, a strongly specialized economy faces a high risk of external shocks which amount to serious stability problems). JUNGMITTAG (2006) has shown that export

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Table 22 Growth of unit labor costs in selected OECD countries (Source: Ameco Database) Countries

1995

2000

2005

Change 2006 to 1995

Belgium Czech Republic Denmark Germany Estonia Greece Spain France Ireland Italy Cyprus Latvia Lithuania Luxembourg Hungary Malta Netherlands Austria Poland Portugal Slovenia Slovakia Finland Sweden United Kingdom

100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100

97.8 104.6 99.8 99.6 89.2 99.6 97.2 98.4 87.1 94.6 95.3 94.1 108.7 87.9 90.5 95.1 99 95.2 100.7 109.1 92.4 99.4 94.9 105.3 100.6

96.6 106.4 100.5 96 88.1 97.6 91.5 98.3 85.7 96.9 93.9 90.4 101.1 94.1 90.4 95.4 99.3 91.4 92.1 104.2 91.4 99 98.9 105.8 102.3

−3.4 6.4 0.5 −4 −11.9 −2.4 −8.5 −1.7 −14.3 −3.1 −6.1 −9.6 1.1 −5.9 −9.6 −4.6 −0.7 −8.6 −7.9 4.2 −8.6 −1 −1.1 5.8 2.3

structures have converged across EU15 while there is increasing specialization in production across countries. BORBÉLY (2006) comes up with similar findings for EU accession countries. This difference in international structural convergence of trade and output could explain why business cycles still differ considerably across countries—even within the Euro zone. However, the implication also is that vertical trade (trade within sectors/trade in intermediate products) plays only a limited role since otherwise convergence of trade and convergence of output specialization would occur in parallel. Monetary integration creates larger markets allowing the exploitation of economies of scale and the reduction of transaction costs. If one defines financial market integration through the weighted nominal interest rate convergence—with the relative share of loans across the spectrum of maturities as the weight for that convergence—one could indeed measure financial market integration. As financial market integration might go along with financial market deepening, which amounts to a yield curve with a longer time horizon than before, we have to take into account an additional aspect. Finally, the whole yield curve might be shifted upwards or downwards through monetary integration so that we have at least one additional aspect to be considered. A downward shift, which amounts to reduced costs of capital and in turn should raise the investment output ratio, should increase real income.

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As regards benefits from monetary union, one may emphasize the reduction of international transaction costs within the union, the reinforcement of competition via higher price transparency, the increase in liquidity in bonds markets, benefits from achieving a broader reserve currency status and achieving a high degree of price stability in all member states of the monetary union. ROSE (2000) has argued in an empirical paper that a one percent rise in trade between countries in a monetary union will lead to a rise of per capita income of one-third of a percent. FARUQUEE (2003) has emphasized that monetary union has raised trade volumes among member countries by 10% so that there should be considerable benefits for countries in the Euro zone. It is, however, less clear which benefits come from increased fiscal policy surveillance and the Stability and Growth Pact which impose new restrictions on fiscal policy. If deficit ratios hover over many years close to the 3% deficit–GDP ratio, member countries might have insufficient room to maneuver in times of slower growth and also might face a long-term increase of the debt–GDP ratio whose longterm dynamics are determined by the ratio of the long-run structural deficit–GDP ratio to the trend output growth rate. To the extent that real interest rates in the Euro zone are reduced one may anticipate higher investment in the overall Euro area, however, this could still go along with asymmetric intra-Euro zone and extraEuro zone inflows so that economic divergence and lack of social cohesion could be a major effect. Moreover, it is unclear how innovation dynamics and indeed the innovation system is changing under the twin pressure of: • Limited fiscal policy options which could impair R&D financing in some countries. • Larger capital markets which raise the required rate of return in some countries of the monetary union so that long-term innovation financing might become more difficult. Another important effect which concerns both cohesion countries and potential Eastern European Euro member countries refers to structural change where financial market integration could reinforce specialization. Increased specialization would be not in line with the KENEN criterion of optimum currency areas, so that entering the Euro zone could bring problems. Moreover, if there are strong Balassa–Samuelson effects—meaning a rise of the relative price of nontradables along with per capita income—the inflation rate in catching-up countries could be much higher than in the Euro zone/in Euro zone partner countries. The real interest rate could become very low, which in turn could distort the investment and innovation process in a way which weakens productivity gains, profitability and growth in the long run. Bubbles in the stock market and the real estate market also could become more likely. A rather neglected aspect concerns the issue of increased international bond substitutability in the context of the creation of the Euro zone and the enlargement of the Euro zone. If Euro denominated bonds and US Dollar denominated bonds become closer substitutes one may anticipate lower interest rates and higher stock market prices.

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Perspectives of the Lisbon Agenda The EU’s Lisbon Agenda 2010, which put forward the goal of making the EU the most competitive and dynamic knowledge-based economy by 2010 points to the prominence of setting growth goals. Therefore it is important to focus on some of the potential links between information and communication technology (ICT) and financial markets. From a practical perspective, one may point out that the European Council—here, the heads of governments and presidents of EU member countries—has not raised this topic. Moreover, the European Council has adopted a strange policy goal with the “Lisbon Agenda 2010” in the sense that it has defined a supranational goal for which the European Commission has hardly any power in laying these foundations. It is the EU member countries which have in principle the means to stimulate economic growth (and some countries fail in this respect; notably is Germany which runs a high current account surplus but has achieved only slow economic growth in the decade after 1994—except for 2000 when growth was 3.1%). The following analysis describes the stages of financial market integration and monetary integration in the EU and presents basic theoretical reflections on financial market integration and about the links between regional financial market integration and growth. As regards the potential link between financial market dynamics and economic growth, we rely partly on traditional arguments from literature, but we also look at the problem from an endogenous growth perspective. In principle this requires that we • look at the level of the growth path, with the neoclassical growth model suggesting that one examine the impact of financial market integration on the savings rate; • look at the growth rate of output as explained by various elements of financial market integration. It seems to be rather unclear as to whether regional financial integration in the Euro area has strongly fostered economic growth in the Euro area thus far. Part of the problem is that regional integration effects are superseded by globalization effects on the one hand. On the other hand, policymakers in some EU member countries have adopted economic policies which did not promote growth and employment. Moreover, interesting effects of financial market integration can also be studied in the context of EU eastern enlargement. From the perspective of accession countries, membership brought with it the advantage of reducing the political risk premium to almost zero so that higher FDI inflows could be anticipated. High FDI inflows could be particularly stimulating for growth if FDI were significant and entering those sectors crucial for economic modernization, including the financial market sector. Banking and insurances are, however, traditionally considered sensitive sectors so that there are considerable impediments for taking over banks or other financial intermediates. At the bottom line we must ask which policy options could be useful for promoting growth and employment. We find that financial market integration has not yet been completed in the EU and that both national policymakers and the supranational

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policy level of the EU could contribute to higher growth. Political interference in goods markets and political obstacles to inward FDI as well as to outward FDI are key problems which must be overcome. If the Euro area does not adopt a more coherent set of policy measures, the Euro zone might disintegrate in the long run. The creation of an economic and monetary union in the EU has opened a window of opportunity in Europe, however, it is unclear whether policymakers will come up with consistent policies and the necessary set of reforms to stimulate productivity growth and innovation in the Euro area. Those EU countries which are not yet members of Economic and Monetary Union can be expected to closely watch the dynamics of integration and growth in the Euro area and outside. It also is interesting to focus on issues of future enlargements of the Euro zone which effectively began with German unification in 1990. The negative referenda on the EU constitution— in France and the Netherlands—raise doubts about broad political support for EU deepening and EU widening. It is clear that integration projects normally have the support of broad strata of the population if integration contributes to higher growth and employment. This also reinforces the ability of politicians to pursue EU interests abroad. Thus the question rises as to whether the EU still has a consistent set of goals, strategies and means. Achieving sustained growth will not, however, be easy in an ageing society, which naturally brings about a decline in long-term growth rates of the respective country (McMORROW/ROEGER 2004). Much will depend on the process of financial market integration which in principle could stimulate higher long-run growth.

K.2 Financial Market Integration in the EU K.2.1 From Basic Theory to Endogenous Growth Approaches From an economic perspective, globalization is mainly shaped by intensified trade dynamics, rapid growth of capital flows and the expansion of the digital economy. For a better understanding of the links between financial markets and growth, one should take into account standard theoretical elements as well as some new aspects related to, for example, the role of ICT, which is a critical sector in several ways. As regards ICT, one should note that productivity growth in the US banking sector is strongly influenced by sectoral accumulation of ICT capital, while the productivity impact of ICT in the EU is—for unclear reasons—more modest (INKLAAR/O’MAHONY/TIMMER 2003). Impediments to intra-EU FDI in the banking sector could be part of the explanation. Moreover, it is important to consider the link between financial market development and technological progress. In an economic system with innovating firms, there is a basic information asymmetry between the innovating firm and the institution financing the respective project (and related investment). Depending on the type of financial system, it is more or less difficult to finance innovation projects, with small and medium-sized firms having particular problems. In a system with

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universal banks, it is relatively difficult to finance international innovation projects of a firm unless there is a long-term relationship between a major bank and the respective firm, with the bank also being active in those markets/countries—and thus getting relevant information—within which the innovating firm has partners. If the innovating medium-sized firm has high profit rates and retained earnings, it can signal credibly to the banking community that it is willing to adequately share risks in the innovation project. The alternative to bank-financed innovation projects is to rely on stock markets while building up reputation as a successful innovator. This in principle requires taking a firm public. The more technologically advanced the country is, the more it should rely on stock markets as a source of financing innovation and investment projects. International stock market listings can help innovating firms from small countries get broader access to global risk capital. However, listing a European or Asian company in New York is relatively costly. Regional integration of stock markets is thus an alternative for both EU and ASEAN countries. If the respective firm is a newly-created high-technology company, it will not immediately be able to rely on stock markets, rather it will need adequate access to venture capital. As regards venture capital, regional integration of venture capital markets could also stimulate both dynamic start-ups and long-run growth. However, one should not really expect sweeping economic benefits from financial market integration if this is not embedded in a broader concept. The overall economic system consists not only of financial markets, and therefore benefits cannot be fully realized if there are stumbling blocks for growth in other factor markets. Moreover, one should raise the issue as to whether there is a critical minimum degree of financial market integration—say, as defined by full interest convergence across 2/3 of the maturity spectrum (starting with short-term markets), and one may well debate whether there is full integration if mortgage markets are not truly integrated, which national regulations often impair. From a theoretical and empirical perspective, one may state that output Y positively depends on (WELFENS/JUNGMITTAG 1996, 2002) not only on the input of capital, labor and technology (technology input as measured by patents and real expenditures on the import of licenses), but also on the use of telecommunications which is a proxy for the intensity of the diffusion of new technology. An interesting empirical approach was conducted by JUNGMITTAG (2004), who finds that not only capital, labor and patents are empirically significant for the growth of output for the EU15, but also the degree of high-technology specialization ( ). From this perspective, it is not simply technological specialization—emerging in an open economy under the joint pressure of trade, foreign investment and financial market dynamics—which is relevant for growth, rather it is specialization in hightechnology sectors. A standard reference in empirical economic growth analysis is MANKIW/ROMER/WEIL (1992) who explain growth of real income by the investment output ratio and human capital. Their approach is, however, somewhat doubtful, since they impose the assumption that the growth rate of technological progress is the same across all countries of the sample which is highly unrealistic (indeed, the assumption amounts to ignoring the existence of multinational

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companies whose very existence is related to ownership-specific advantages, read: technological advantages!). This is important for the link between financial market analysis and growth to the extent that financial market development or financial market integration contributes to long-term technological progress. The MANKIW/ROMER/WEIL approach—in line with some other studies—points to the relevance of the (net) investment output ratio I/Y. As I/Y times the marginal product of capital ΔY/ΔK is equal to the growth rate of real gross domestic product, one must take into account that I/Y has a trend component and a cyclical component—related to the real interest rate r, the cyclical unemployment rate uc and expectations about future profits—while the marginal product of capital is determined by capital intensity, technology and human capital. In the following graph, we can see that output growth rates in the Euro zone went through a cyclical increase in the five years after 1995 but have fallen after 2000. The ratio of the long-run interest rate to the short-term rate increased after a transitory fall after the start of the both Euro zone and the ECB. After 1995, there was a fall in the real interest rate in the Euro zone and most member countries of the Euro zone. The Netherlands and Spain recorded a strong fall in the real interest rate in the four years after 1999, while Germany faced a temporary rise in the real interest rate; in a trade gravity modeling perspective it is clear that Germany, Austria and Finland—compared to France, Spain or Portugal—will be strongly exposed to import competition from eastern Europe which tends to reduce the inflation rate; hence the real interest rate in Germany (and Austria and Finland) will be higher than in other countries of the Euro zone. After a temporary real appreciation in the early years of the Euro zone, the Euro faced a period of real appreciation, which reduced the real and nominal interest rate below the US level for some time. With monetary integration, it is also clear that the rest of the world will benefit considerably from higher capital outflows from the Euro zone. The reason for this is that from an investors’ perspective, there are no longer opportunities for currency diversification within the Euro zone. This should have contributed to an early depreciation of the Euro in the starting phase of the ECB and the Euro. There is another long-term aspect which is related to the ageing of societies in the EU; ageing should raise the savings rate of the population. However, financial market integration could dampen this development in the Euro zone, since households are likely to face less borrowing constraints in integrated markets. One should also note that empirical findings and most analyses in the literature suffer from a problem in that one rarely makes a clear distinction between the level of output and the growth rate of output. Within the context of a standard macroeconomic growth model (JONES 1998) in the steady state, output per capita (y) is given by the following formula if one assumes—with Y denoting output, K capital, L labor and ß a parameter in the interval [0, 1]—that the macroeconomic production function is Y = Kß (AL)1−ß and that the growth rate of the population is n, the exogenous growth rate of the Harrod-neutral factor A is a and the depreciation rate on capital is δ (e is the Euler number, s the savings rate, A0 the initial value of A, t the time index, # for

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steady state): 

y#(t) = A0 e at {s/[n + a + δ]}ß/(1−ß)

(1)

Taking endogenous growth into account is interesting from a theoretical perspective. If one assumes that the progress rate a(t) is endogenous in the transition to the steady state for the variable real income relative to labor in efficiency units—this is the variable y # := Y/[AL]—we must ask how financial market integration will affect endogenous growth and innovation dynamics, respectively. It also would be interesting to consider an endogenous savings rate. With respect to explaining the progress rate, endogenous growth theory has emphasized the role of human capital (LUCAS 1988), positive external effects from capital accumulation (ROMER 1990), R&D expenditures and innovation (GROSSMAN/HELPMAN 1991) and intermediate products—allowing firms the production of a greater variety of final products which stimulates both demand and real output growth (ROMER 1990; GROSSMAN/HELPMAN 1991; BRETSCHGER 1998). One may summarize the link between financial market integration and growth as follows: • Financial market integration may affect the savings rate s and hence the level of the growth path. In principle it could dampen the savings rate as households face less borrowing constraints (a phenomenon obviously relevant in the Euro zone), but it could also stabilize the savings rate to the extent that the monetary union imposes new constraints on government borrowing (such as the constraints envisaged in the Stability and Growth Pact of the Euro area; as they have not been implemented, however, they are likely to undermine the creditability of the Euro zone and may sooner or later trigger a risk premium on international capital flows into the Euro zone. This particularly reflects doubts about bonds in Italy, Portugal or Greece, which have very high debt–GDP ratios as well as high internal euro area current account deficits). • Financial market integration can also affect endogenous growth in various ways. Examples of this include facilitating human capital formation (banks facing more competition and becoming more innovative become more willing to engage in university studies financing), influencing the share of firms undertaking innovations (and influencing the type of innovations pursued), encouraging more foreign investors to come—also more MNCs to emerge within the country—and thus to contribute to international technology transfer and increased international outsourcing. FDI will contribute to higher capital intensity in the host country, and hence to a higher output and a higher income per capita, respectively; one thus should not be surprised to find a positive correlation between FDI and trade. As regards empirical findings, it is obvious that we know rather little about the links between financial market integration and growth. As regards transitory economic catching-up in open economies one should consider the role of temporary net capital inflows for which relative yields on investment are expected to play a major role.

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y(t) = A0e’at [s/(δ+n+a)] ß/1-ß

Level of Growth Path

Growth Rate

EXOGENOUS GROWTH RATE

ENDOGENOUS GROWTH

Human Capital

R&D

Reinvested Earnings

FDI & Trade Intermediate Products/ Outsourcing/Product Varieties

Household Savings

Government’s Budget Surplus Repatriated Profits

Financial Market Integration

Fig. 94 Financial market integration and growth

K.2.2 Current Account Dynamics: A New Approach The current account Z is the difference between private savings S plus the government surplus T − G minus investment I. [S + (T − G)] − I = Z

(2)

One may consider Z as a distinct economic function or assume that taking a closer look at the left hand side of the above equation—if specified adequately and if consistent behavior of economic agents is assumed—will finally allow to specify the equation for Z . We will consider the indirect specification of the equation for Z . Assume that savings S = S(Y , M/P, r, q*)—where Y is real national income (Y is real GDP and Y =Y[1 − b], where b is the share of the capital stock owned by foreign investors), M/P is real money balances, r the real interest rate r and q* the real exchange rate eP*/P. Savings will rise with Y and r and with M/P (m =: M/P) as

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a rise of broad real money indicates financial market development and hence better opportunities to earn high yields. If the country is indebted abroad a real depreciation will raise foreign debt expressed in real domestic terms and hence savings will rise provided we assume an exogenous wealth target (or a target ratio A /Y where A is net private sector wealth). Let us assume that the share of the capital stock owned by foreign investors is a positive function of b which is an implication of the arguments of FROOT/STEIN (1991). Moreover we assume that investment I is proportionate to output; and a negative function of the real interest rate r and a positive function of the real exchange rate q* (the latter reflecting the FROOT/STEIN argument). Thus we can write on the basis of a savings function s (r, q*)Y[1 − b(q*)] + s [M/P] and an investment function I = z(r, q*, YK /YK *)Y—where YK is the marginal product of capital, * denotes foreign variables, τ the government surplus–GDP ratio and s a positive parameters—the following equation for the current account: Z = s (r, q*)Y[1 − b(q*)] + s (M/P)y + τYy + {−zr + z q*y + z ([Y*/K*]/[Y/K])}Y

(3)

Note that z, z are positive parameters. We have assumed that both countries considered produce under Cobb–Douglas functions so that the respective marginal product of capital and the average products of capital are proportionate to each other. The term β[Y*/K*]/(β[Y/K]) indicates the international marginal product ratios and hence the capital intensity gap between the rich capital abundant country II and the poor home country I; the latter is a host country for FDI. FDI inflows thus are a positive function of the marginal product ratios. Assume that both countries are characterized ∗ ∗ by Cobb–Douglas productions function Y = Kß (AL)1−ß , Y* = K*ß (A*L*)1−ß we then know that the marginal product of capital in country I is ßkß−1 and in coun∗ ∗ try II it is ß*k∗ß −1 ; and y = Akß and y* = A*k *ß (k := K/AL and A is the level of technology). Denoting per capita income as y we thus can write z (y/y*, A*/A) where z is a positive function of y/y* and of A/A*: Dividing the current account equation byY we get an empirically testable equation for the current account–GDP ratio Z /Y Z /Y = s (r, q∗ ) + s m/Y + τ − zr + z q∗ + z (y/y∗ , A∗ /A)

(4)

Thus we have the missing theoretical basis for an empirical analysis published by DEUTSCHE BUNDESBANK (2006) in its January monthly report, however, in the view presented here (with Eastern Europe standing for country I and Western Europe or Germany being country II) one additionally should include the relative level of technology. The two ambiguous signs from a theoretical perspective is the impact of the real interest rate and the real exchange rate. Let us simply quote from the Bundesbank’s research findings which has presented a study on the determinant of current accounts in the eastern European accession countries (the following quote also refers to theoretical underpinnings which, however, are rather opaque; note that the Bundesbank approach uses 1/q* as the real exchange rate):

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“As part of a panel analysis, major determinants of the current account balances in the new EU member states of Central and Eastern Europe (Czech Republic, Estonia, Hungary, Latvia, Lithuania, Poland, Slovakia and Slovenia) were examined on the basis of quarterly data for the years 1994 to 2004. The starting point for this was the following regression equation for the current account balance or savings–investment gap. CAGDPi,t = γ0 + γ1 RELGDPi,t + γ2 FINGDPi,t + γ3 INVGDPi,t + γ4 REERi,t + γ5 RIRi,t + γ6 M2GDPi,t + εi,t

(5)

CAGDP denotes the ratio of the current account balance to gross domestic product, while RELGDP is defined as a logarithm of relative per capita income in relation to Germany. The government budget balance (FINGDP) and investments (INVGDP) are measured as ratios to gross domestic product and are thus comparable between the countries. The logarithm of the real effective exchange rate (REER) rises in the event of a currency appreciation and falls in the event of a depreciation. The real interest rate (RIR) and the money stock in relation to gross domestic product (M2GDP) were included in the study as financial market variables. Positive signs are expected for γ1 , γ2 and γ5 and a negative sign for γ3 . According to theoretical considerations, the relationship between the real exchange rate and the current account (γ4 ) is a priori just as indeterminate as the net effect of a growing financial sector (γ6 ). The absolute values of γ2 and γ3 should lie between zero and one since the associated variables, as components of the savings–investment decision, have a direct influence on the current account but can be at least partially offset by adjustments to private saving. Panel unit root tests confirm that the variables are stationary. Two estimation methods are compared. A feasible generalized least squares estimate (FGLS) takes into account fixed country effects, panel-specific autoregressive terms, a heteroscedastic error structure and a contemporary correlation between the countries. By contrast, an instrument variable estimator (IV) allows an explicit modeling of the dynamics by means of a lagged endogenous variable. In this way, the Nickell bias, which arises in the static estimate when calculating the autoregressive terms, can be avoided. Furthermore, selecting the appropriate instruments means that any endogenous results, i.e., repercussions which the current account has on the independent variables, are accommodated in the model. These advantages of the dynamic estimator contrast with it being less efficient than the static model. The table shows the results of the FGLS estimate and dynamic IV estimator.” Our theoretical approach presented is consistent with the empirical findings of Deutsche Bundesbank research. Only the relative technology variable is missing here (and our theoretical reflection suggests replacing the investment output ratio through r, q*, y*/y and A/A*); the approach presented clearly suggests that this variable should play a role. It is surprising that γ2 in the Bundesbank model is not unity, as this is expected on theoretical grounds.

380 Table 23 Macroeconomic determinants of the current account

Innovations in Macroeconomics Determinant

FGLS estimate

IV estimate

CAGDP (−1)

–

RELGDP

0.02700*** (5.40) 0.0831** (2.20) −0.2375*** (−6.93) −0.0381* (−1.94) 0.0009** (2.09) 0.0062 (1.02)

0.4608*** (2.75) 0.0147*** (2.75) 0.1420*** (2.75) −0.2891*** (−6.66) −0.0264 (−1.15) 0.0014*** (2.71) 0.0138*** (3.19)

FINGDP INVGDP REER RIR M2GDP

***, (**), [*] means significant on the 1%, (5%), [10%] level; t-values in parentheses

K.2.3 Monetary Integration, Financial Market Integration and Welfare Effects As regards financial market integration in the Euro zone, we clearly can measure this through interest rate convergence. High interest rate countries should converge to the low interest rate of Germany. (In the period of the Deutsche Mark, Germany almost always had the lowest nominal interest rate in the EU.) Thus, a country previously known for high interest rates (e.g., Italy) will experience a fall in the interest rate as the Euro zone starts and also during the run up to the start of the Euro and the ECB. Let us call Germany country I and Italy country II (with starred variables). Italy will have a considerable once-and-for-all welfare gain as the nominal interest rate falls form i*0 to i*1 , which is equal to the (unchanged) German interest rate (i0 = i1 ). As the real money demand m is a positive function of Y and a negative function of the interest rate, the historically high-interest rate country will have a welfare gain equivalent to the area CDEE . If financial market integration and associated financial innovations bring about a higher substitutability of money and bonds in the country with previously high interest rates, there will be an additional welfare gain since the money demand becomes flatter. These additional gains are equal to the area AF E . As such, the real money stock M/P =: m in equilibrium would not only rise from m*0 to m*1 but to m*2 . Note that a lower nominal interest rate implies a rise of the equilibrium real money stock; if the fall in the nominal interest rate is brought about by a fall of the inflation rate there must be an additional once-and-for-all increase in the real money stock which could be achieved through a lower price level (onceand-for-all fall of the equilibrium level of the price path which might go along with a higher real wage rate which could translate into higher unemployment) or a higher level of the nominal money supply path.

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b Country I

a Country II A i*

md’(Y*,i*) F

F’

E

i

md*(Y*0,i*) i*0

E’

md(Y0,i) D

C

H

i*1 Z m*

m*2

m*1

m*0

0

m0

m

Fig. 95 Static effects and medium-term effects of monetary union. a Country II. b Country I

Indeed, the real money stock can increase in only two ways. First, the new central bank can increase the nominal money supply at a given price level, which implies that the European Central Bank could have considerably increased the money stock in the early years of the Euro zone without inflation effects. (The ECB will have to reduce monetary growth at a later date if inflation is not to become a problem.) The associated positive wealth effect should stimulate consumption and investment so that there is a favorable one-off effect on the unemployment rate. The alternative way of raising the real money stock would be a fall of the nominal price level at a given stock of the nominal money stock, which is likely to bring about a rise of unemployment. The two alternative policy options are shown for the simple case of a non-growing economy with constant trend inflation. There will be a one-off increase in real output if the central bank brings about a rise in the real money balances through an expansion in the nominal money supply (b). If the central banks sticks to its pre-monetary union expansion path of the money supply, the monetary union will bring about a one-off rise in unemployment and hence a fall in the equilibrium output level (a) (assuming a given degree of wage flexibility). Hence, a temporary expansionary monetary policy of the ECB is clearly preferable, and it seems that the Euro zone has indeed adopted such a policy—however, obviously not as part of a deliberate strategy. Analysts worried about the allegedly excessive growth in the stock of money simply overlook the analytical aspects discussed here. As regards the empirical analysis of the link between inflation and the growth of the money stock in the Euro zone (hypothetical Euro zone prior to 1999) in the period from 1980 to 2005, one should expect a statistical break around 1999/2000/2001. Of course, it will be difficult to clearly separate the effect identified from the switch to the new monetary regime as well as the ECB.

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Innovations in Macroeconomics

ln M

M(t)

ln Y ln P

P(t) m(t)

Y(t)

0

t t mon. union

u0 u(t) u

a

M(t)

ln M P(t)

ln Y ln P

m(t)

Y(t)

t mon. union t

0 u(t) u0 u

b Fig. 96 Monetary union, inflation and unemployment: structural break from switching to monetary union

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383

In a more medium-term perspective it is quite important to focus on real income development. If due to monetary union output in country II in the monetary union would be lower (Y*2 ) than without monetary union (Y*0 ), there is a welfare loss of BE1 E3A*2 . In country I monetary union could lead to a rise in real output (Y1 >Y0 ) so that for the overall monetary union, the net welfare effect is unclear. There would be a clear welfare gain if output in the monetary union were higher in country I and country II (Y*1 , Y1 ). If country I indeed had a higher real output, the existence of positive spillover effects could then indeed raise output in country I to Y2 (a similar reasoning applies to the analytical framework of a growing economy). Whether output is raised by the switch to a monetary union is an empirical question and depends—from a theoretical perspective—largely on wage flexibility in the monetary union on the one hand and the degree of financial market innovations on the other. With low or even reduced wage flexibility, increasing price competition in the monetary union is likely to increase the unemployment rate (u) and hence reduce output. A higher degree of financial market innovations—particularly if geared towards venture capital markets, commercial paper markets and stock markets—should stimulate the creation and expansion of new firms, thus leading to increased output. Finally, one should raise the question as to whether the European Central Bank takes opportunities to stimulate output expansion more or less than the average national central banks in the pre-Euro area into account. Clearly, a central bank should avoid long-term inflationary policy since this will not only raise inflation to critical levels but distort managers’ attention from product and process innovations toward more innovative liquidity and asset management in order to exploit inflation dynamics. The crucial point here is that this type of financial engineering does nothing to raise consumption output per capita or the quality of consumption goods available.

i*

i A2

A*1

A*0 E0

A0

(Y*0,i*)

E2 md1 (Y1,i)

F G A*2

i*1

E*1 md*0

E3 md2 (Y2,i)

E*2 md*1 (Y*1,i*)

A1

H

E0=E1 md0 (Y0,i)

i0

i*0

md*2 (Y*2,i*) m*

m*1

m*0

m*2

0

Fig. 97 Dynamic welfare effects of monetary union

m0=m1

m

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There is one more interesting aspect of monetary union in a dynamic perspective. If per capita income positions differ strongly in the monetary union, there will be considerable differences in the national inflation rate (the price index is composed of tradables and nontradables prices), where differences are on the one hand related mainly to the Balassa–Samuelson effect; this means that the relative price of nontradables will rise relative to tradables as per capita income rises. On the other hand, considerable differences in per capita income imply different degrees of intraindustrial trade, which in turn affects the inflation dynamics. A country with high per capita income will have a relatively high share of intra-industrial trade which acts as a disciplinary force on inflation as consumers have a broader choice among domestic and foreign tradables which are close substitutes. This effect is likely to be underestimated in empirical analysis, as a rising share of intra-industrial trade and a rising per capita typically go along with a higher degree of product innovations which will raise prices at face value—but not if improvements in quality are adequately taken into account in the context of hedonic price measurement approaches. By implication, the inflation rate should fall with a rise in per capita income. This perspective is reinforced, if one assumes that stock market capitalization—and stock market turnover—relative to GDP should increase in a more innovative economy. As relatively rising stock market turnover absorbs more liquidity, a given growth rate of the money supply should translate into a lower inflation rate—of newly produced goods—in the long run.

K.3 Integration of Financial Markets in the Euro Zone and Global Dynamics In both the EU and ASEAN, there is an increasing overlap of regional integration and economic globalization. As regards regional financial market integration, we expect interest rate convergence and actually a fall in the nominal and real interest rate if financial market integration is embedded in a stability-oriented monetary union of countries with a similar per capita income. We also expect maturity deepening in bonds markets and should witness volume growth of bond emissions in the integrated bonds market where economies of scale in intermediation will be easier to exploit than before. All this contributes to lower interest rates. At the same time (see the following figure), there are international impulses possibly leading to higher interest rates. Globalization pressure implies that required rates of return are on the increase in EU and ASEAN stock markets. In particular, banks come under pressure to generate higher profit rates which will—along with the pressure from the BIS’s Basel II package requiring more risk-differentiated credit pricing of banks— reduce the growth rate of loans. Medium-sized firms in Europe and Asia facing problems as bank credits become more expansive will consider therefore the option to finance investment and innovation through the bond market with greater interest.

K.3 Integration of Financial Markets in the Euro Zone and Global Dynamics

Bond Markets

Loan Markets

Country 1 Country 2

Banks

Interest Rate Convergence

Maturity Deepening

(Elimination of Currencies)

Relative Volume Growth (Reduction of Transaction Costs)

385

Political Pressure I / II

Globalization Pressure

Pressure from Basel II

Innovation Dynamics

Higher required Rate of Return

(Prudential Supervision)

ICT Growth

Economies of Scale

Firms Reduces Nominal and Real Interest Rates

Undermines Financing of SMEs & Digital Firms

Requires Venture Capital & Stock Market Financing

Investment and Innovation Dynamics

Fig. 98 Integration of financial markets and globalization

(Governments in Europe have not done much to encourage SMEs to take this route, and the ECB as well as the BIS have done much to downplay the impact of Basel II). Finally, there are increasing global innovation dynamics in OECD countries and Newly Industrialized Countries on the one hand and an expansion of the ICT sector largely based on the use of modern computers and software on the other. The latter is particularly poor collateral from a banker’s perspective, which implies that countries with a strong reliance on a universal banking system have disadvantages in financing the expansion of ICT. This could be a major problem in continental EU countries which heavily rely on universal banking and are obviously lagging behind in ICT expansion relative to the USA and the UK (as well as to Sweden and Finland). A rising role of global innovation dynamics and of ICT requires a greater role of venture capital financing and a relative expansion in the role of stock markets. The latter is, however, not without risks, as there are considerable overshooting problems in stock markets and foreign exchange markets. The standard DORNBUSCH overshooting problem from exchange rate markets can indeed have mirror effects in the stock market, and both markets are interdependent as has been shown in the empirical analysis by WELFENS/BORBÉLY (2004).

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Innovations in Macroeconomics

K.4 Policy Conclusions We can draw a number of policy conclusions from our analysis above. Financial market integration and economic growth are characterized by a number of interesting links on which one should shed more light through empirical analysis. If one considers the interdependencies of the overall economic system, it is not very realistic to expect major benefits from financial market integration if there are blockades to structural change in labor markets. The high unemployment rate in the Euro area represents a blocking factor in this respect. For example, while raising factor productivity and the yield on investment might well require outsourcing in many sectors, the resistance of trade unions in countries with high unemployment is likely to slow down such outsourcing in some countries of the Euro zone (also compared to the USA). Uniform minimum wages—without regional differentiation—in France and Italy as well as certain social security elements in Germany seem to be crucial problems for the labor market in the Euro zone. At the same time, one should take into account that more integrated financial markets—in a period of global financial market liberalization as enshrined in GATS—could be subject to larger shocks and more extreme bubble problems than was previously the case. To the extent that stock market bubble problems are related to short-sighted speculations, it is worthwhile to consider strong tax incentives for long-term investment while short-term yields could be taxed more heavily. Such a development is unlikely to happen unless OECD countries agree upon some joint framework in this respect. In the Euro zone, the governments in Germany, France and Italy should carefully consider their serious and long-lasting unemployment problems. Financial market integration will be a complementary measure towards full employment if this integration stimulates the creation of new firms and encourages investment and innovation in existing firms as well. The latter will, however, not come easily. Governments have many possibilities—including tax policies—to stimulate the expansion of venture capital markets and to encourage the growth of stock markets. Moreover, social security reforms should be done in such a way as to give stock markets a greater role. However, one should not overemphasize the expansion of this pillar for savings toward retirement, since stock markets are quite volatile. An important problem in the Euro zone is the Commission’s emphasis that state-owned savings banks in several member states (including Germany) should no longer earn privileged backing by government, since this would not allow for the establishment of a level playing field with private banks. To some extent this is a valid argument, but at the same time it is not really clever for government to throw away the economic benefit of a triple-A rating from which state-owned banks can benefit. Given the rather limited engagement of private banks in start-up financing, one may instead argue that state-owned banks should not only enjoy a privilege with respect to capital costs but also have special obligations in the field of local venture capital financing; such banks should also have an information advantage in this respect. One might well consider allowing private banks to acquire a majority stake in local and regional

K.4 Policy Conclusions

387

state-owned banks. However, there could indeed be reasons to require that government keep a certain minority stake in certain regions (say, below 1/3 of overall capital). It seems quite important that governments in the Euro zone remove barriers to FDI since there can be no truly integrated financial market if the convergence of capital costs is not facilitated by broad FDI activities. Moreover, there might be FDI diversion effects in the context of EU eastern enlargement and Euro area enlargement toward Eastern Europe. It also seems adequate to encourage foreign investors from outside the Euro zone to invest more in the EU. This, however, requires that the Stability and Growth Pact in the EU truly be respected, which is not the case thus far; one might have to adopt a new pact. Higher FDI inflows into the Euro zone also depend on a consistent and growth-enhancing policy of the European Central Bank. It is not clear whether the ECB really exploits opportunities to stimulate growth and employment. International confidence in the Euro would benefit from a more consistent framework in prudential supervision in the Euro area. Once the first crisis hits the financial markets in the Euro zone, national governments—which in many member countries are strongly involved in supervision—and the ECB as well as some national central banks involved in supervision will finally want to cooperate (or to cooperate more than in the first seven years of the Euro period). Yet this cooperation will then come at a premium price. Governments in member countries of the Euro zone should commission studies to highlight not only the problems in venture capital financing but also to better understand the problems of ICT financing. It is naturally a challenge for the universal banking system to finance investment and in particular innovation in an increasingly digital world. The risk that benefits from an innovation will not accrue to the ICT investor but rather diffuse to other countries is only one problem; the lack of collateral in the digital services sector is another. One can only hope that the Euro zone will proceed slowly with an eastern enlargement of the Euro area. There is still considerable need for exchange rate flexibility in eastern European accession countries. However, at the same time the ECB should carefully analyze the dynamics of financial market development and growth in Eastern Europe, and prudential supervision agencies in the euro area and in accession countries would be wise to cooperate. If there is ever a crisis in Poland its neighbor, Euro country (or Germany) cannot be indifferent to such negative dynamics. At the bottom line, one may hope that financial market integration in Europe can contribute to both higher growth and a higher level of the growth path. There are many interesting issues for both theoretical and empirical analysis. The necessary bridging between real economics and monetary economics is an enormous challenge, as there has been a long tradition that most researchers in their respective fields have worked in splendid isolation for many years. The contribution presented thus is only a modest step towards building such a bridge.

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Innovations in Macroeconomics

K.5 FDI and Information and Communication Technology in the Dornbusch Model K.5.1 Basics of the Dornbusch Model Overshooting of exchange rates has become an important analytical issue since the seminal paper of DORNBUSCH (1976) who has emphasized that importance of considering differential adjustment speeds in goods markets and financial markets. The implication of this is that the short-term exchange rate dynamics can establish a temporary equilibrium solution in the foreign exchange market which is above the long-term exchange rate (overshooting). A key feature of the Dornbusch model is simple: The adjustment speed in financial markets—here the foreign exchange market and the bond market—is high, while prices in goods markets are sticky. The analysis of the DORNBUSCH model is interesting not only in terms of money supply shocks which imply overshooting but also in terms of supply shocks, where the former in some cases could bring about overshooting problems. In the following analysis we use an extended model of DORNBUSCH (1976); we will partly follow the basic setup of GÄRTNER (1997) who considers a small open economy with trade and portfolio capital flows. In addition, we want to focus on the role of FDI flows. In the following analysis, # denotes long-run equilibrium, E the expectation operator, e the nominal exchange rate, P the price level, G real government expenditures, M the nominal money supply and e the Euler number. A useful alternative approach is HANSEN/RÖGER (2000) who focus on the asset accumulation dynamics of the current account, a Phillips curve and the aggregate demand side in combination with a price index for tradable and nontradable goods (hence there is an internal relative equilibrium price in both countries). The intersection of the equilibrium locus for external equilibrium and the schedule of internal equilibrium—with zero output gap—then determines the medium-term equilibrium real exchange rate which is influenced by the net asset position of the respective country. The original Dornbusch model ignores the accumulation dynamics and puts the focus on the differential adjustment speeds in goods markets and financial markets. Here we are interested in taking a closer look at the Dornbusch model which we extend in a simple way to include FDI flows (in a more elaborate model we could combine the modified Dornbusch model with accumulation dynamics where one option would be to replace Y# by the solution of the Solow growth model which). A major problem tackled here is how to state a logarithmically consistent aggregate demand function and to discuss some key aspects of money supply shocks versus supply-side shocks. We will focus on the role of FDI flows in the Dornbusch model and also discuss the impact of product innovations as well as ICT: Both FDI and ICT affect various parameters of the model and thus the dynamics of adjustment and the role of overshooting, respectively. Important results are a consistent formulation of a logarithmically-stated specification of aggregate demand (with the elasticity param-

K.5 FDI and Information and Communication Technology in the Dornbusch Model

389

eter for Y being negative and not positive as stated in hundreds of articles published in the literature). Moreover, we shed additional light on the overshooting debate.

K.5.2 The Modified Dornbusch Model Subsequently we consider a simple system of six equations: Eq. (1) is a kind of Phillips curve, where Y# is full employment long-run equilibrium output: An excess in demand will lead to an increase in price level. Equation (2) is logarithmically-stated specification of aggregate demand—partly following GÄRNTER (1997); however, we insert several extensions including the impact of product innovations which are assumed to raise net exports; in the original formulation of GÄRTNER there also is a term related to real income lnY (and a term related to trade and the exchange rate); however, the sign of the parameter of lnY is negative—as we will show—and not positive; in spite of hundreds of articles using ad hoc logarithmically stated demand curves where the elasticity of lnY is positive while it actually is negative as the relevant parameter reflects the impact of a change in lnY on real net exports and imports, respectively. Moreover, there often also is lnG in the aggregate demand but we will replace lnG by the ratio G/Y which is more consistent as will be argued subsequently. It is assumed that the foreign price level P* is constant and equal to unity so that ln(eP*/P) = lne − lnP; we define q* = eP*/P. To the extent that we consider a model with FDI, the parameter ψ does not only reflect the link between trade balance (ψ) and the real exchange rate but also the impact (ψ ) of the real exchange rate on FDI and hence on the overall investment–GDP ratio: A real depreciation will bring about higher net FDI inflows—relative to GDP—and hence higher overall investment according to the theoretical arguments and empirical findings of FROOT/STEIN (1991). The perspective suggested here implies that ψ = ψ + ψ . The variable e is the current nominal exchange rate, e# denotes the long-run exchange rate. As regards the logarithmic formulation of aggregate demand (lnYd ) it is not easy to reconcile the commonly used formulation (e.g., see GÄRTNER) lnYd = alnq* + a lnY + a lnG (the parameters a, a , a all are positive) with the standard expression of the uses side of GDP: Y = C + I + G + X − q*J where C is consumption, I investment, X exports and J imports (τ is the tax rate, v product innovations, * for foreign variable). One may, however, consider a consistent setup where C = cY(1 − τ), G = γY, I = λY; and λ = λ(lnq*, γ, lnv, τ), the net export function is X = x (ln[eP*/P], lnY, lnY*, lnv)Y*; we then will use the function lnx (. . . ). The investment output ratio λ is assumed to be a positive function of the real exchange rate as we follow FROOT/STEIN (1991) who argue that in a world with imperfect capital markets foreign firms will find it easier to take over companies in country I (host country) since a real depreciation of country I’s currency will raise the equity capital expressed in terms of the potential host country so that leveraged international takeovers will become easier; hence we assume that the overall investment–GDP ratio is a positive function of the real exchange rate eP*/P (or lnq*); the partial

390

Innovations in Macroeconomics

derivative of λ with respect to lnq* therefore is positive (ψ > 0). With respect to the government expenditure–GDP ratio γ the partial derivative ω is ambiguous (will be positive if a rise of γ mainly falls on investment goods), with respect to product innovations v the partial derivate is positive (η > 0), and with respect to the income tax rate it is negative (in absolute term ω ). We also define 1 + ω =: ω . Furthermore, we assume that lnx is a function of all the four arguments shown in the function x(. . . ). Thus we can write a consistent version of the aggregate demand side: Yd {1 − c[1 − τ] − γ − λ(lnq*, γ, lnv, τ)} = x (. . . )Y*

(2 )

Assuming for simplicity that −c − γ − λ is rather small so that we can use the approximation ln(1 + z) ≈ z we can rewrite the equation as: lnYd − c[1 − τ] − γ − λ(lnq*, γ, lnv, τ) = {lnx (lnq*, lnY, lnY*, lnv)} + lnY*

(2 )

Using linearized functions λ(. . . ), lnx (. . . ) we can write—with derivatives ∂lnx /∂lnq* =: ψ , ∂lnx /∂lnY* =:  , ∂lnx /∂lnv =: η and ∂lnx /∂lnY =: − < 0— the equation as follows: lnYd = c − cτ + γ + ψ ln(lne − lnP) + ωγ + ηlnv + ω τ + {ψ(lne − lnP) − lnY +  lnY* + η lnv} + lnY*

(2 )

This then leads to subsequent Eq. (2) where ψ := ψ + ψ, η = η + η and = 1+ ; we also define 1 + ω =: ω . The money market is characterized (with ϕ denoting the income elasticity of the demand for money, σ the interest semi-elasticity  and e the Euler number) by nominal money demand Md = PYϕ e−σ i which implies for equilibrium lnM = lnP + ϕlnY − σ i. While money market equilibrium is fairly standard, the subsequent capital market equilibrium condition is rather unusual as it modifies the interest rate parity condition by taking into account portfolio-theoretical considerations relevant in a setup with FDI—the latter is not considered in the Dornbusch model. Note that an alternative way to express the aggregate demand in a logarithmically-stated function is based—with j denoting the import-output ratio (imports J = jY)—on Yd ([1 − c − γ − λ(. . . ) + q*j(lnq*)] = x(lnY, lnq*, lnv*)Y* where we have assumed in the spirit of the gravity equation that exports are not only a positive function of real income abroad but of domestic real output or actually of lnY as well (in an empirical context the assumption that c + γ + λ − j is close to zero is more convincing than assuming that c + γ + λ is close to zero). Capital market equilibrium is given by two interacting factors (i is the nominal exchange rate), namely the impact of portfolio investors guided by the interest rate parity (i = i* + E(dlne/dt)) and foreign investors who focus on long-run differences in the marginal product of capital; (as we assume that both the home and the foreign country (* denotes foreign variables) produce according to a ∗ ∗ Cobb–Douglas function Y = Kß (AL)1−ß and Y* = K∗ß (A*L*)1−ß , respectively, the relevant variable for foreign investors is the difference in marginal products

∗

K.5 FDI and Information and Communication Technology in the Dornbusch Model

391

of capita (YK# , YK *#) namely ßY#/K minus ß*Y#*/K#* where # denotes longrun values. From a portfolio-theoretical perspective, real capital and bonds are complementary in terms of risk as risks faced by holders of K are negatively correlated with that of holding bonds. Hence, we state the rather simple equilibrium condition i + ζ(ßY#/K# −YK *#) = i* + E(dlne/dt). Thus a positive international differential of marginal products in favor of the home country requires for a given sum i* + E(dlne/dt) that domestic interest rates fall. To put it differently, given the domestic and the foreign interest rate the required expected exchange rate depreciation rate E(dlne/dt) must rise along with a positive differential of marginal products since bond investment abroad would otherwise be insufficiently attractive now that holding domestic bonds has become more attractive. The expected devaluation rate is assumed to be proportionate to the difference between the equilibrium exchange rate e# and the actual exchange rate e; or expressed in logarithms, we have Eq. (6). Goods Market: dlnP/dt = π (lnYd − lnY#)

(1)

lnYd = c + ψ [lne − lnP] − lnY# + [1 + ω]γ − [c + ω ]τ

(2)

+ η lnv + *lnY* Money Market: lnMd = lnP + ϕlnY − σ i

(3)

lnMs = lnMd = lnM

(4)

i + ζ(ßY#/K# − YK *#) = i* + E(dlne/dt)]

(5)

E(dlne/dt) = θ(lne# − lne)

(6)

International Capital Market:

Note that in the very long run (defined by equality of marginal products of capital across countries), Eq. (5) boils down to the standard interest rate parity condition. Here we focus on the short term and the long run where the latter is defined by a response of the price level P. We now can draw in lnP–lne space, the positively sloped equilibrium line for the goods market (ISP; slope is unity). The ISP line is obtained by combining Eqs. (1) and (2) and imposing dlnP/dt = 0 which also implies Yd =Ys . The equilibrium line ISP—the goods market equilibrium schedule—represents the equation: lnP = lne + c/ψ + ω γ/ψ − [(1 + )/ψ ]lnY# − [(c + ω )/ψ ]τ + (η /ψ )lnv + (*/ψ )lnY*

(7)

The slope in lnP–lne space is unity. To the right of ISP, we have an excess demand; above the ISP line there is an excess supply. In the third quadrant, we have drawn

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Innovations in Macroeconomics

money market equilibrium. In the forth quadrant, we have the CME line which indicates international capital market equilibrium. The LM curve represents money market equilibrium and hence the equation: i = (1/σ )[lnP − lnM + ϕlnY#]

(8)

The CME line is obtained by combining the equations for the capital market which results in i = [i* + θ(lne# − lne)] − ζ(ßY#/K# − YK *#)

(9)

The logic of Eq. (9) basically says—disregarding the term relevant for foreign investment for the moment: • A rise in the domestic interest rate—given i*—must go along with a rise in the effective yield of a portfolio investment abroad which requires an expected depreciation rate. Such an expected depreciation rate will occur only if there has been an excessive initial appreciation. • A fall in the domestic nominal interest rate—given the foreign interest rate i*— will have to go along with a decline in the effective yield on investments abroad so that the expected rate of change of the exchange rate must be negative. An expected appreciation can, however, only occur if the initial depreciation has been excessive (i.e., stronger than required in terms of the long run equilibrium exchange rate). Now let us take into account FDI term. If a positive differential between the domestic marginal product of capital and that of country II (foreign country) emerges for any interest rate differential, a lower expected depreciation rate is required than before. Note also that in the absence of inflation and assuming profit maximization, we will have YK # =YK *# in the long run. Assume that we have initial equilibrium in all markets where i = i*, equality of marginal products across countries and that the actual exchange rate is equal to the equilibrium exchange rate e#. Let us consider the short-term and long-run impact of an expansionary monetary policy which leads to an upward shift of the LM schedule and a rightward shift of the CME schedule. In the short term the price level does not change so that the adjustment takes place only through the response of the exchange rate and the interest rate. In long-run equilibrium, we must have i = i* again, and points A2 , C2 and B2 indicate overall equilibrium. In the short run, however, the excess supply in the money market leads to a strong reduction of the nominal interest rate I (see point A1 ) which implies an interim exchange rate of e1 which is higher than e2 . The phenomenon that the short-term exchange rate reaction exceeds that which is required by long-term equilibrium is called exchange rate overshooting. If we plug Eq. (9) into (8)—that is combine the capital market with the money market in a financial market subsystem—we get σ i* + σ θ(lne# − lne) − σ ζ(ßY#/K# − Y*K* #) = [lnP − lnM + ϕlnY#] (10) ln P = lnM − ϕlnY# + σ i* + σ θ(lne# − lne) − σ ζ[(ßY#/K# − Y*K* #) (11)

K.5 FDI and Information and Communication Technology in the Dornbusch Model (II)

ISP

lnP

45°

(I)

B2

lnP2

lnP0

lnP2

393

B

lne#0

lnP0

lne#2

lne1

lnP

lne

i

A1

1

C1 A2

A

C

C2

i0=i0* LM1 (III)

LM0 i

CM E0

CME1 (IV)

Fig. 99 Goods market, money market, international capital market

In an economy in which the marginal product of capital exceeds that abroad the long-term effect of net FDI inflows on the price level obviously is negative. Only in the very long run—when there is international equalization of marginal products of capital—will there be no effect of FDI inflows on the price level. By implication a temporary net inflow of FDI will dampen the price level in the host country and raise it in the host country. This equation is crucial in the sense that it represents short-term adjustment dynamics in financial markets. In lnP–lne space we have a negatively sloped FMS curve while the ISP curve is positively sloped. An expansionary monetary policy will shift the FMS curve to the right so that—at given ln P—a new temporary exchange rate equilibrium is immediately established. This is above the long-run equilibrium value, and adjustment then continues along the FMS curve. In long-run equilibrium, lne# = lne andYK# =Y*K∗ # so that the long-run financial sector equilibrium can be written as: lnP# = lnM − ϕlnY# + σ i*

(12)

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Innovations in Macroeconomics

Fig. 100 Financial market equilibrium and goods market equilibrium in the Dornbusch model (slope FMS = −σ θ)

lnP FMS1

ISP

FMS0 E1

lnP#

1

lnP#0

E0

F

0 lne#0

lne#2

lne#1

lne

Hence, the long-run price level is a monetary phenomenon and we can conclude (12 )

dlnP#/dlnM = 1. Moreover, note that the long-run multiplier for an increase of lnY# is given by dlnP#/dlnY# = −ϕ < 0.

(12 )

Hence, a positive supply shock will reduce the equilibrium price level in the long run. Inserting the long-run solution of Eq. (12) in Eq. (7) and assuming e = e#, gives ∗

ln M − ϕlnY# + σ i = lne# + c/ψ + ω γ/ψ − [(1 + )/ψ ]lnY# − [(c + ω )/ψ ]τ + η /ψ lnv + (∗ /ψ )lnY∗

(13)

ln e# = ln M + ϕlnY# + σ i∗ − c/ψ − ω γ/ψ + [(1 + )/ψ ]lnY# + [(c + ω )/ψ ]τ − η /ψ lnv − (*/ψ )lnY* = lnP# − c/ψ − ω γ/ψ + [(1 + )/ψ ]lnY#

(14)

+ [(c + ω )/ψ ]τ − η /ψ lnv − (∗ /ψ )lnY∗ Hence dlne#/dlnP = 1 and dlne#/dlnM = 1. Product innovations will bring about a nominal and real appreciation in the long run. As regards the impact of the government–GDP ratio on the long-run exchange rate the model implies a real depreciation as long as we assume that ω < 1 and are not considering the need to balance the budget—that is to combine a rise of γ with a rise of the income tax rate. As regards the impact of tax policies a rise of the tax rate will bring about a nominal and real

K.5 FDI and Information and Communication Technology in the Dornbusch Model

395

depreciation. Note that one might consider within a modified model the case that ζ is a function of q* and the tax rate. If there is a parallel supply-side shock abroad (rise of Y*) and at home (rise of Y#) the net effect is ambiguous. Moreover, the long-run real exchange rate lne# − lnP# thus equal to lnq*# = −c/ψ − ω γ/ψ + [(1 + )/ψ ]lnY# + [(ω + c)/ψ ]τ − η /ψ lnv − (*/ψ )lnY*

(14 )

Note that product innovation will bring about a real appreciation as dlnq*/dlnv = −η /ψ

(14 )

The short-run reaction of the exchange rate can be obtained from Eq. (11): lne = lne# + [lnM − lnP − ϕlnY#]/(θσ ) + i∗ /θ − [ζ/θ](ßY#/K# − Y∗ K ∗ #)/θ

(11 )

Therefore, we have in the short run the following result which confirms exchange rate overshooting: dlne/dlnM = dlne#/dlnM + 1/(θσ ) = 1 + 1/(θσ ) > 1.

(15)

Monetary policy is unanticipated here (if one changes the formation of expectations the impact effects will differ; e.g., one may set E(dlne/dt) = E(dlnM/dt) or switch to adaptive expectations, namely Et (lnMt+1 ) = Et−1 (lnMt) + Et−1 (lnMt) + ε[lnMt t − Et−1 (lnMtt )] = (1 − ε)Et−1 (lnMt ) + εlnMt we would have a share of ε of monetary policy which is considered as permanent; and the short-term reaction would become dlne/dlnM = 1 + 1/(θσ ) − (1 − ε)/θ; the last term indeed then could imply that there is no overshooting at all or that there is indeed an appreciation followed by a depreciation(see GÄRTNER (1997)). Moreover, note that the long-run exchange rate reaction of a supply-side shock is given from Eq. (14) as: dlne#/dlnY# = −ϕ + [(1 + )/ψ ]

(15 )

As the real exchange rate is lne − lnP and since dlne#/dlnP = 1 the change in the equilibrium long-run real exchange rate will be given by: dlnq*#/dlnY# = [(1 + )/ψ ] > 0

(15 )

A supply-side shock—standing for a kind of process innovation—will cause a real depreciation in the long run. However, as product innovations will bring about a real

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Innovations in Macroeconomics

appreciation a period of intensified innovation dynamics has an ambiguous effect: If product innovations dominate so that the investment–GDP ratio and the net export– GDP ratio increase sufficiently strongly one should expect a real appreciation of the currency of the Schumpter lead country. Note that if we want to consider the very long run in the sense of equalization of marginal products of capital, the impact of a supply-side shock on the nominal exchange rate is only −ϕ +[(1 + )/ψ ]; without the transitory FDI impact the more likely is a depreciation. From Eq. (11 ), we have the following short-term reaction of the nominal exchange rate (note: for a variable y = f(x) it generally holds: df/dlnx = [df/dlnx] [dx/dx] = [df/dx][dx/dlnx] = [df/dx][1/(dlnx/dx)] = x[df/dx] and hence for f(x) = ax we have—with a as a constant parameter—df/dlnx = ax): dlne/dlnY# = dlne#/dlnY# − [ϕ/(θσ )] − [ζß/?K#]Y# = −ϕ[1 + (1/θσ )] + [(1 + )/ψ ] − [ζß/θK#]Y#

(15 )

A positive supply-side shock is the more likely to cause a real appreciation in the short term, the larger the income elasticity of the demand for money is and the higher the output elasticity of capital is (and the lower the capital stock is). A positive supply shock is reinforced by the impact of FDI which reinforces the tendency towards a short-term appreciation. Note that in the context of a supply-side shock the long-run change in the real exchange rate is given by (dlne# − dlnP#)/dlnY# = dlne#/dlnY# − dlnP#/dlnY# which is zero only if the expression [(1 + )/ψ ] is zero which requires that ψ approaches infinity. As regards the short-term reaction of the exchange rate there will be a real appreciation as a consequence of a supply-side shock under certain parameter constellations—indeed a sufficiently high role of FDI in capital markets (parameter ζ) will bring about this result unless expectation formation is characterized by θ→∞. Moreover, we should note that FDI unambiguously reduces dlne/dlnY# since the role of FDI is to raise the denominator ψ (without FDI the denominator would be ψ = ψ − ψ ); and FDI is visible in the expression −[ζß/θK#]. The comprehensive analysis of monetary-policy shocks and supply-side policy shocks leads to an important conclusion: Whether a system of flexible exchange rates brings rather strong instability of the exchange rate depends on the relative weight of monetary-policy shocks and supply-side shocks. The presence of foreign investment seems to dampen overshooting problems. Moreover, to the extent that flexible exchange rates stimulate innovations and hence positive supply-side shocks, the system of flexible exchange rates will bring a double benefit: Higher innovations and rather limited exchange rate volatility, provided that monetary policy is accommodating in the sense that positive supplyside shocks are adequately combined with expansionary monetary policy. However, one cannot rule out that a system of flexible exchange rates will bring about less innovation performance than a system of fixed exchange rates. All which we can say here is that empirical analysis is lacking in this regard.

K.5 FDI and Information and Communication Technology in the Dornbusch Model

397

Turning back to the standard analysis of monetary policy: The stronger foreign exchange markets react to a temporary divergence between expected long-run equilibrium exchange rate and the current exchange rate and the higher the semi-interest elasticity is, the lower the overshooting effect. The short-run adjustment dynamics in the goods markets are obtained from combining Eqs. (1) and (2), which results in: dlnP/dt = π [ψ (lne − lnP) − (1 + )lnY# + ω γ + η lnv + *lnY* − (c + ω )τ + c]

(16)

From Eq. (14) we have ψ [lne# − lnP#] = −ω γ + [1 + ]lnY# − *lnY* + (c + ω )τ − c − η lnv (17) and therefore we get in combination with Eq. (16): dlnP/dt = π [ψ (lne − lne#) − ψ (lnP − lnP#)]

(18)

Inserting Eq. (12) in Eq. (11 ) gives lne − lne# = (lnP# − lnP)/[θσ ] − (ζ/θ)[ßY#/K# − Y*K #]

(19)

If we assume that the foreign marginal product of capital is equal to the domestic marginal product we get after inserting this result into Eq. (18): dlnP/dt = −π (ψ /σ θ + ψ )(lnP − lnP#) = −α (lnP − lnP#)

(20)

Here we have simply defined π (ψ /σ θ + ψ ) = α . The above equation is (setting P# = 1) a homogeneous differential equation of first order and has the solution lnP(t) = C0 e−α

 t

(21)

This implies (having solved for C0 by considering t = 0): lnP(t) = lnP# + (lnP(0) − lnP#)e

−α t

(22)

Note that −1

lne(t) = lne# + [θσ ]

(lnP# − lnP)e

−α t

(23)

Thus we can state lne(t) = lne# + (lne(0) − lne#)e

 −α t

(24)

The adjustment speed for the exchange rate variable is therefore the same as for the price level. Obviously, the adjustment speed α is faster the higher π and ψ are (i.e., the faster goods market react to excess demand and the stronger trade and

398

Innovations in Macroeconomics

(foreign direct) investment react to the real exchange rate). The lower the semiinterest elasticity of the demand for money (σ) and the slower the foreign exchange market reacts to divergences between the long-run equilibrium value and the current exchange rate (parameter θ), the faster the adjustment process of the price level towards the equilibrium price level. However, we have seen that low parameters θ and σ imply a large overshooting in case of a monetary supply shock so that these two parameters are ambivalent. If they are low, the overshooting effect will be large, but adjustment to the new equilibrium value will be fast. FDI raises the adjustment speed. International coordination and the intervention rules of central banks will affect the adjustment parameter θ. There are some arguments that governments and international institutions should work in favor of a high parameter θ, since this means only modest overshooting (and a slow adjustment speed). One may also argue that the presence of foreign investors will affect the learning parameter θ.

Information and Communication Technology and the Dornbusch Model How will the expansion of ICT affect exchange rate dynamics and the overshooting/undershooting effects? The price adjustment speed in goods market is likely to decrease, as the global supply-side elasticity in an internationally networked society will be relatively large, in particular in the field of digital services whose share in aggregate demand is likely to increase in time. Since ICT facilitates access to various kinds of financial market instruments, the interest elasticity of the demand for money may be expected to increase. Monetary overshooting problems should thus be reduced unless the learning speed in the field of exchange rate expectations should decrease. However, ICT might indeed facilitate the learning process in markets and hence ICT expansion will go along with a higher adjustment parameter θ (concerns formation of exchange rate expectations). This implies that ICT will lead to reduced overshooting problems; at the same time the adjustment speed to the new long-run exchange rate equilibrium will slow down. From this perspective, the opportunities of an activist monetary policy have improved, namely in the sense that exchange rate overshooting problems are less severe than in the traditionally industrialized OECD countries. This holds all the more since one has to take into account that ICT expansion is equivalent to a positive supply shock which itself implies a dampening exchange rate movement.

K.5.3 Conclusions Exchange rate overshooting depends on several parameters, including the learning dynamics of exchange rate expectations and the interest elasticity of the demand for money; the adjustment speed to the new equilibrium is influenced by the responsiveness of the trade balance and FDI. ICT and FDI will affect the nominal and

K.5 FDI and Information and Communication Technology in the Dornbusch Model

399

real exchange rate dynamics. There are several arguments why FDI could reduce the problem of overshooting; from this perspective economic globalization—in the sense of a rising share of FDI in overall investment—is likely to contribute to less exchange rate instability. If ICT for technological reasons is raising the learning speed in the foreign exchange market the size of overshooting is reduced, at the same time one might expect that ICT raises the price adjustment speed in goods markets which reinforces the speed of adjustment towards the new equilibrium. Monetary policy would then generate less overshooting than in the time of the Old Economy so that a more activist monetary policy could be considered. From an empirical perspective it would be important to find out more about the effect of the exchange rate regime on innovation dynamics. A fixed exchange rate regime basically transmits the domestic price level to those countries which have pegged the currency to the anchor country. If a fixed exchange rate regime helps to diffuse price stability worldwide—under the assumption that the anchor country pursues a stability-oriented monetary policy leading to a low-inflation rate— firms in all countries might find it relatively easy to conduct R&D policies which require a long-term perspective; bond maturities (as a proxy for the representative time horizon) are known to be relatively long in periods of low inflation rates. The counter-argument in favor of a flexible exchange rate regime is that it establishes full individual responsibility in monetary policy in each country so that the weighted world inflation rate could be lower under flexible exchange rates than in a system of a fixed exchange rate. However, there other aspects which are rather unclear: Will multinational companies be more active innovators in a system of fixed exchange rates than in a system of flexible exchange rates? More research is needed here. As regards regional integration several parameters of the (modified) Dornbusch model will be affected: The price adjustment parameter in goods markets should increase as this would be natural to expect in a single market—and to the extent that monetary union is reinforcing this adjustment speed the argument is even more valid. From a Eurozone perspective there is the crucial issue whether or not dollar exchange rate volatility in the sense of overshooting risks will be reduced; indeed, less overshooting problems should be expected if regional integration—in particular monetary integration—raises the interest elasticity of the demand for money (in a monetary union one should expect more liquid alternatives to holding money than in fragmented national markets). Moreover, the learning speed (parameter θ) in the foreign exchange market also should increase. The main risk occurring in a monetary union involving countries with high sustained budget deficits is that there is a considerable risk that tax rates will go up. If such tax increases are not mainly invested in the form of higher public investment—relative to GDP—and higher R&D expenditure–GDP ratios the impact on GNP could be negative in the long run; not least because an increasing share of GDP will accrue to foreign investors (from country II) which will benefit from a real depreciation through cheaper access to the stock of capital abroad. Finally, one should notice that the expansion of ICT is likely to reinforce the role of FDI as firm-internal transaction and management costs are reduced. Thus the findings with respect to FDI are reinforced through the expansion ICT. The loga-

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rithmic formulation of the aggregate demand side suggested here should encourage new options to consistently develop macro models. Supply-side shocks and product innovations will affect the exchange rate in the long run, and in a world economy with increased innovation dynamics the respective topics need to further explored and also require additional empirical analysis.

Appendix K.1: Aspects of Transition and Trend Growth in a Setup with Technology Shifts We consider our refined neoclassical model with the standard Cobb–Douglas production function Y = Kß (AL)1−ß and an exogenous growth rate of technology (A; dlnA/dt =: a) and an exogenous growth rate of the population (n = dlnL/dt). We make the assumption that savings equals, S = s(1 − τ)(1 − hu)Y where u is the structural unemployment rate and h a positive parameter; τ is the income tax rate. Imposing the equilibrium condition that gross investment (δ is the depreciation rate) equals savings, that is dK/dt + δK = S, we obtain the differential equation for k := K/(AL): dk  /dt = s(1 − τ)(1 − hu)k  − (n + a + δ)k  ß

(AK.1)

The steady-state solution for the ratio of capital to labor in efficiency units is: k # = {s(1 − τ)(1 − hu)/(n + a + δ)}1/(1−ß)

(AK.2)

As regards transition dynamics of the Bernoulli equation (see Appendix G.4) for k — and similarly the dynamics for per capita income y—the transitory adjustment speed is given by (n + a + δ)(1 − ß) provided that we use the simplifying assumption that ß = 0.5. If the unemployment rate negatively affects the rate of progress in such a way that we have a progress function a = a0 − a#u (a0 is a kind of autonomous progress rate) the implication is that both the speed of adjustment towards the new steady state is reduced and the long-run growth rate is reduced. Conversely, countries with high initial structural unemployment stand to benefit twice from reducing unemployment: First by achieving a higher speed of adjustment towards the new steady state and secondly by a higher-trend growth rate. There is also a negative effect, namely the reduction in the level of the growth path. In the context of a modified quasi-monetarist Phillips curve this implies that a fall in the natural rate of unemployment will go along with a fall in the inflation rate which is consistent with Milton Friedman’s conjecture in his Nobel lecture. At the same time one should expect a one-off rise in the price level since the level of the growth path is reduced.

Appendix K.2: Uncertainty, Savings and Product Innovations The impact of the expected yield (r)—and of the standard deviation σ of the interest rate—on consumption is ambiguous (DIXIT 1991, p. 175). DIXIT considers an

Appendix K.2: Uncertainty, Savings and Product Innovations

401

infinitely long living consumer who owns wealth A that earns a random total return (principal plus interest) of r per period; there is no other income. The impact of uncertainty depends on parameters of the consumption function which may differ—as emphasized here—across countries so that a rise of E(r) could raise the optimum consumption–wealth ratio C/A (C is consumption, A is net wealth) in country I while country II (foreign country) has a fall of the ratio of C*/A *. Before we consider the impact of product innovations we recall here the basic analysis of DIXIT who assumes the following utility function: U(C) = C1

−ε

/(1 − ε); ε > 0

(Z.1)

The utility discount factor δ = 1/(1 + r) and the objective over time is to maximize the mathematical expectation of the discounted present value of utility. In the initial period the household starts with wealth A , if the household consumes C and saves A − C his random wealth at the beginning of the following period will be r(A − C). The Bellman equation then leads to the following optimum: C/A = {1 − δ E[r1

−ε 1/ε

]}

(Z.2)

Thus the optimal rule for consumption out of wealth is a proportional one, but the proportion critically depends on δ and ε and the distribution of the random variable ε. The special case of a lognormal distribution of r – ln r is normally distributed with standard deviation σ—yields the following result: E[r1−ε ] = {E[r]}1−ε exp(−ε(1 − ε)σ2 /2)}

(Z.3)

Hence, we get C/A = {1 − δ E[r]}1−ε exp(−ε(1 − ε)σ2 /2)}

1−ε

(Z.4)

Let us consider the case ε < 1: A rise of E(r)—with σ fixed—reduces the optimum consumption–wealth ratio; a rise of σ will raise this ratio. The opposite result holds if ε > 1. If country I is characterized by ε < 1 while II has ε > 1 the asymmetric twocountry model—in which the large economy (in a system of fixed exchange rates) dominates real interest rates in both countries—implies the following result of a rise of r* and r, respectively: As the desired ratio C/A has fallen while C*/A * has increased abroad country I will run a current account surplus and country II a current account deficit: This could mean that country II acquires part of country I wealth through FDI. In this case monetary policy in country II causes an international reallocation of wealth.

Role of Product Innovation on the Consumption–Wealth Ratio In addition to the analysis of DIXIT (1991) we may consider the particular role of ε more closely. Here let us assume that ε is below unity in both countries and that

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Innovations in Macroeconomics

there is a wave of product innovations which raises ε so that consumers get a higher benefit from C(t). How will this affect the optimum C/A ? Let us assume that C/A is close to unity (that is δ E[r1−ε ] is close to zero) so that we obtain: ln(C/A ) ≈ −(1/ε)δ E[r1−ε ] 

= −(1/ε)δ {E[r]}

1−ε

(Z.5) exp(−ε(1 − ε)σ /2)} 2

dln(C/A ) ≈ (1/ε2 )δ{E[r]}1−ε exp(−ε(1 − ε)σ2 /2) − (1/ε)δ dδ − (1 − ε)(1/ε)δ{E[r]}−ε exp(−ε(1 − ε)σ2 /2) + ε(1 − ε)σ2 /2(1/ε)δ{E[r]}1−ε exp(−ε(1 − ε)σ2 /2)

(Z.6)

= {(1/ε) − (1 − ε) + ε(1 − ε)σ2 /2}ε−1 δ E[r]1−ε exp(−ε(1 − ε)σ2 /2) Therefore the sign of dln(C/A )/dε depends only on the expression {(1/ε) − (1 − ε) + E(1 − ε)σ2 /2} and it holds that {(1/ε) − (1 − ε) + ε(1 − ε)σ2 /2} > 0 ↔ dln(C/A )/dε > 0

(Z.7)

We can see that ε > 1—the critical case for the impact of a change of E(r) and of σ—is not generally leading to a switch of the sign of dln(C/A)/dε; the sign for this impact multiplier is less likely to be positive than in the case of ε < 1. Let us return to our standard case of ε < 1. If the variance of the interest rate becomes critically large the expression (Z.7) always is positive for the assume parameter range 0 < ε < 1. And conversely: if the variance σ2 is relatively small product innovations will reduce the ratio of C/A . If we assume that product innovations will go along with a higher expected real interest rate and a higher standard deviation— more product innovations indeed could imply a higher variance of the failure rate of firms (over time) so that the variance of bond prices and hence that of interest rates will increase—the impact of product innovations on C/A is unclear as three impulses are overlapping. Thus we have an interesting empirical issue where clarification is needed not least with respect to the link between product innovations and E(r) and the variance of r, respectively. As a hypothesis (assuming a priori ε < 1) one may state that a higher rate of product innovations raises both r and the variance of r; if the variance effect—raising the ratio C/A —dominates the effect of the rise of E(r) the net effect would be a rise of the consumption–wealth ratio provided that there is no sufficiently strong offsetting effect through the rise of ε.

Appendix K.3: A Macro-Model with Unemployment and Endogenous Taxation We now want to focus on an economy with expected unemployment rate u where the s unemployed—the difference between (one period ahead) expected supply L and

Appendix K.3: A Macro-Model with Unemployment and Endogenous Taxation

403

expected labor demand L —get a transfer which by assumption is proportionate to current per capita income y = yA (y :=Y/[AL] where A is the level of technology and Y is real income); we basically assume that unemployment insurance pays an income replacement ratio U is in the interval 0,1. Hence the government budget— with government consumption and tax revenues denoted by G and T, respectively—is given by d

G + [L − L ]U y A = T s

d

(X.1)

With γ and τ denoting the ratio of G/Y and T/Y, respectively, we can write: γY + [Ls − Ld ]U y A = τY

(X.2)

Denoting population (or workforce) by L and using the definition u := (L – L )/L and y :=Y/(AL) we get s

γy + u U y = τy 

d

(X.3)

Therefore we get for the tax rate τ: τ = γ + u U

(X.4)

The tax rate is the higher the higher γ and the higher the replacement ratio U and the higher the expected unemployment rate u is; note that u is at first considered to be exogenous and basically is determined by past wage policies and productivity dynamics. We assume that consumption C = cY(1 − τ) or equivalently C/[AL] = cy [1 − τ]. The investment output ratio λ := I/Y (I is investment) is assumed to depend on the expected unemployment rate u and the real interest rate r (the partial derivative of λ with respect to r is assumed to be negative); as regards the impact of the expected unemployment rate u we assume that a rise of the expected unemployment rate stimulates capital deepening (positive parameter λ ) and hence the investment rate to a certain extent, but that u also has a dampening effect (parameter λ ) on the investment output ratio: Hence we have λ = λ u − λ , u − λr r. The import function J = jY and the real exchange rate q* := eP*/P. Therefore the goods market is characterized by the equation Y[1 − c(1 − τ) − γ − λ(u , r) + q*j] = xY*

(X.5)

Y* denotes foreign real income and exports X = x(. . . )Y* so that we obtain after division by AL: y [1 − c(1 − τ) − γ − λ + q*j] = xy *(A*L*/AL)

(X.6)

The level of technology at home and abroad is considered as exogenous as is the population in both countries. Taking logarithms (while assuming that c(1 −τ) −γ −

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Innovations in Macroeconomics

λ(u , r) − q*j =: z to be close to zero so that we use the approximation ln[1 + z] ≈ z) we can write: lny = c[1 − τ] + γ + λ(. . .) − q*j + lnx + lny * + ln(A*L*/AL)

(X.7)

We can write the condition for a goods market equilibrium as follows (where x := ∂lnx/∂u > 0, x = ∂lnx/∂(A/A*); the import ratio j is linearize as j = j lnq* where j := ∂j/∂lnq*): lny = c − c(1 − γ − u U ) + γ − λr r + λ u − λ u − q*j + x u + x (A/A*) + lny * + ln(A*L*/AL)

(ISU curve) (X.8)

The parameters x and x are assumed to be positive; with respect to u the implication is that firms intensify activities in exports markets as soon as they anticipate a rise of future unemployment and hence less opportunities to sell in domestic markets. As regards the money market we assume that the demand for money is a positive function of income and the expected unemployment rate (as regards the latter we partly follow ARTUS 1995: however, here not current unemployment but expected unemployment is relevant) and a negative function of the nominal interest rate. The money-market equilibrium is given by ϕ



[M/P]/[AL] = y (1 + u )ϕ e

−σ i

(X.9)

Hence, lnM − lnP − lnA − lnL = ϕlny + ϕ u − σ i (MU curve)

(X.10)

The current account equilibrium under flexible exchange rates—with Q denoting real net capital imports (depending on domestic yield i, foreign yield and A/A*) and J denoting net imports which are assumed to be a positive function of lnY and a negative function of u, q* and lnY*—is given by Q (i, i* + E(dlne/dt), A/A*) = J (lnq*, lny , lny *, u)

(X.11)

If the expected depreciation rate E(dlne/dt) is assumed to be zero and net capital imports (Q is assumed to be a positive function of i*, A/A*) and the net imports function (J ) are linearized we can write in a world without inflation the condition for equilibrium in the foreign exchange market as: Q r r + Q r r* + Qα A/A* = J q* dlnq* + J y lny + J y* lny * + J u u lny space the slope of the ZZU curve is positive.

(ZZU) (X.12)

L. Natural Resources, Oil Prices and Innovation Dynamics

L.1 Introduction In the wake of the two oil price shocks of the 1970s—each bringing with it a quadrupling of the oil price—the Economics of exhaustible resources became an important research field (e.g., STIGLITZ 1974; DASGUPTA/HEAL 1979; SINN 1981). Oil and gas are particular examples of non-renewable resources, and they are politically sensitive since the main deposits are concentrated regionally, in the case of oil in politically rather sensitive Arab countries as well as Iran and Russia. In addition major oil producers have formed the OPEC which became a powerful cartel in the 1970s when it controlled about 60% of the world market for oil. As transportation costs for oil are very small, the oil price is a true world market price since equilibrium is determined by world oil supply and global oil demand. There is considerable short-term oil price volatility in the short run and there have been major shifts in oil prices over the medium term. Changes in market structure will affect the optimum rate of depletion of resources (KHALATBARI 1977). The oil and gas sector has a long history of high Schumpeterian dynamics, where analysis by ENOS (1962) suggests there is a time lag of about 11 years between invention and innovation. By implication, R&D promotion in this industry will go along with considerable time lags with respect to innovation—this is also a challenge for policy makers, who would have to apply a relatively long-time horizon. As regards R&D Promotion, FURTADO (1997) found that differences in the degree of appropriability between upstream and downstream of the oil industry had a great impact on effect of R&D promotion. There are regional case studies on the dynamics of innovation in the oil and gas industry—concerning Stavanger and Aberdeen (HATAKENTA/WESTNES/GJELSVIK/LESTER 2006)—which show that different approaches to R&D Promotion can have similar effects. It is also noteworthy that the energy sector has been a leading early user of information technology (WALKER 1986). A rising relative price of non-renewables is often considered inevitable since there is long-term global population growth and also high aggregate output growth

P. J. J. Welfens, Innovations in Macroeconomics, DOI 10.1007/978-3-642-11909-5_12, © Springer-Verlag Berlin Heidelberg 2011

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since the 1990s in the world economy. The use of fossil energy sources has not only economic aspects but is also relevant in terms of global warming problems. The Stern Report (STERN et al. 2006; NORDHAUS 2006) has raised international attention about the dynamics of the use of energy and the associated CO2 emissions as have the policy activities and UN reports with a focus on the Kyoto Protocol. There is long-term concern that high economic global growth will strongly stimulate the demand for energy and hence raise emissions, at the same time there are also medium-term concerns about the potential negative impact of oil price shocks: While higher real oil prices might be useful to encourage a more efficient use of energy resources there also could be inflation and unemployment problems linked to sudden rises of nominal oil prices. Among the economic aspects linking the oil price and economic development, the volatility of oil prices (see Fig. 101) is important. YANG/HWANG/HUANG (2002) have empirically analyzed the price volatility of crude oil markets by focusing on the demand structure—impacts of prosperity and recession of the world economy—and oil prices where the authors use the income effect to evaluate future prices. Moreover, the oil price is of considerable macroeconomic importance since rising oil and gas prices imply inflation pressure and a somewhat reduced output for the EU (e.g., ROEGER 2005) as well as high current account surplus positions of OPEC countries; the US and some EU countries plus Japan as well as many non-oil producing developing countries in turn face high current account deficits in periods of high oil prices. Since most of the international oil and gas trade is billed in US$,

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Fig. 101 Rate of change in WTI oil prices, 1986–2010 ($/Barrel) (Y/Q/M). (Source: www.eia.com)

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a rise in oil prices also leads to a medium-term appreciation of the US$. A real appreciation in turn will reduce the inflow of foreign direct investment in the USA as emphasized by FROOT/STEIN (1991): foreign firms will find it more difficult to take over US firms through a leveraged takeover once the equity capital of European and Japanese multinationals—expressed in US$—has declined. At the same time, US firms will find it easier to take over foreign firms in those countries whose currency has depreciated. The reserve-to-production ratio for oil is about 40 so that one can expect—at current relative prices and given technologies—that oil reserves will meet world demand for about four more decades. However, with relative oil prices rising in the medium term (or even in the long run) and with technological progress to be expected in exploration on the one hand and in the use of energy on the other hand, the reserveto-production ratio could stay at 40 for much more than four decades and could even increase over time. In the period from 1980 to 2007 it indeed increased every year (BP 2007). Natural gas is a substitute for oil, but it is not a perfect substitute—the demand for oil mainly reflects transportation needs while gas is used mainly for electricity generation and heating; it rarely is used in transportation. The reserve-to-production ratio for gas is about 60. Prices of oil and gas have strongly increased since 1999 when they had fallen to US$ 10 per barrel in the wake of the Asian economic crisis 1997/1998 (see Fig. 102). In early 2008, the oil price passed the US$ 100 threshold, but these price observations are, of course, all nominal dynamics. A typical perception in the general public is that relative oil prices are expected to increase strongly over the long run. The expansion of the world economy in terms of population—1.5 bill. in 1900, 6.5 bill. in 2000 and about 9 bill. in 2050—and economic output are indicators of a long-run growth of global demand. Indeed, with China, India, Brazil and Russia being new growth poles in the world economy at the 2.0

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Fig. 103 Relative oil prices (current price and price with constant exchange rate respectively to the USA—price level 2002). (Source: BP (2007))

beginning of the twenty-first century, one may argue that global demand for oil will grow strongly over the next decades. One should, however, not ignore the fact that real oil price which had been very high in the early 1880s—when the industry was quite young—has remained at a rather stable level for the following decades. This holds throughout the twentieth century during which the global population increased from 1.5 bill. at the beginning of the century to 6.5 bill. in 2000 as stated above. Indeed, one should not overlook that historical experience does not demonstrate a long-term increase in real oil prices in the twentieth century; corrected for US inflation the real oil price has largely hovered around US$ 25 in 2002 prices (see Fig. 103). This finding for the twentieth century does not rule out, of course, that price dynamics in the twenty-first century could differ considerably from that in the previous century. In any case, one has to explain the long-term stability of the relative oil price in the twentieth century. The oil price shocks of the 1970s seem to be only a temporary deviation—caused by the Middle East conflict—from a long-term equilibrium value determined by demand developments, technology dynamics and a rise in the number of oil producers as well as changes in the market structure. A key question to be raised here concerns the role of technological progress. Within the context of a macroeconomic production function Y(K, L, E, A), one might want to consider the role of knowledge A in combination with input factors capital K, labor L and energy E; if knowledge is energy augmenting, one may write a Cobb–Douglas type production function as Y = Kß Lß (AE)1−ß−ß where ß and ß are in the range between zero and unity. Technological progress could then be considered in analogy

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Table 24 Effect of the 50% increase of oil prices on EU output and prices. (Source: ROEGER (2005)) Price Level* AWM (1) QUEST (2) NIGEM (3) Interlink (4) Multimod (5)

GDP*

Year 1

Year 2

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Year 2

Year 3

0.5 0.3 0.3 0.6 1.6

0.9 0.5 0.5 0.8 2.7

1.0 0.6 0.5 0.9 3.2

−0.1 −0.5 −0.8 −0.4 −0.1

−0.3 −0.6 −0.8 −0.2 −0.4

−0.4 −0.7 −0.7 0.1 −0.3

*All numbers are deviations from baseline levels

with a conventional neoclassical growth model. A more microeconomic approach which is preferred here considers changes in exploration technology (in a narrow sense) and the aspect of a quasi resource-augmenting technological progress which allows for the extraction of a higher percentage of a resource site’s physical deposit; in reality firms from the oil and gas industry manage to extract only about 50% of the physical deposit at a given site and it is only over time—as technology improves—that the percentage of the exploitable physical quantity at that site increases. Relative energy prices increased strongly over the 1970s and in the first decade of the twenty-first century. However, it is unclear to what extent one should expect sustained increases in the relative oil price and the relative gas price. As regards the macroeconomic impact of oil price increases, their effects on the EU economy in the 1990s obviously were smaller than in previous decades, which largely might reflect both the fact that the energy intensity of GDP has reduced and that backstop technologies have become more available over time. If the oil price increases by 50%, various models suggest that the reduction in real income would be less than 1% in the first year and between 0.2 and 0.8 in the following two years (see Table 24). The effect on inflation would be about 1% in year 2 and 3 (disregarding the multimod model). It is, of course, quite interesting to not only consider the effect of oil price dynamics on inflation in OECD countries but also to consider the effect of inflation on oil price dynamics.

L.2 Theory of Natural Resource Pricing The theory of non-renewable natural resource pricing is rather straightforward and considers the alternative of leaving a finite resource in situ versus extracting it. Thus from a theoretical perspective, the basic approach to natural resource prices can be determined from the following simple arbitrage condition: If the owner of a nonrenewable resource exploits one unit of this resource, the cash flow is—with P (t) denoting the price of the resource, h(. . . ) denoting the unit costs of extraction, V the stock of resources and resource extraction R = −dV /dt—given by the expression P R − h(V )R = R[P − h(V )]. Assuming a nominal interest rate I, the profit from

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a current extraction of the natural resource is determined by multiplying the cash flow times the interest rate i obtained from portfolio investment that is iR[P − h(V )]. In the standard literature one often finds the argument that postponing resource extraction yields a marginal profit of dP /dt. This, however, is not correct if there is technological progress—and such progress will subsequently be considered indeed. Without technological progress the alternative of extraction versus non-extraction of one unit of a non-renewable resource leads to the equilibrium condition that i[P − h(V )] = dP /dt.

(1.1)

dP /dt − iP = −hi

(1.1 )

If h is constant we can write

which gives—with e denoting the Euler number—the solution P (t) = C0 eit + h.

(1.1 )

From this equation, we can determine C0 = (P0 − h) where C0 is positive as P0 > h is assumed; the main insight from this equation is that the price P will grow at the rate i and since i is the sum of the real interest rate r and the inflation rate π, it is clear that the real oil price grows at rate r. Let us return to Eq. (1.1). Dividing by the aggregate output level P, denoting the inflation rate by π, h/P by h and P /P by ϕ and noting that dϕ/dt = [(dP /dt)/P] − ϕπ = ϕ(π − π) gives: i[ϕ − h (V )] = dϕ/dt + ϕπ.

(1.2)

As the real interest rate r = I − π we can write ϕr − ih (V )] = dϕ/dt.

(1.3)

r − i[h (V )/ϕ] = [dϕ/dt]/ϕ.

(1.4)

L.2.1 Technological Progress in the Oil Industry In the following analysis we will distinguish between two types of technological progress: • Progress in pure costs of exploitation: This means a fall in the real marginal/average production costs of exploiting a given resource site—with no change in the exploitable amount of resources in a given field; thus we consider a site X in which a profitable amount x could be exploited (say x0 is 50% of the physical amount contained in site X). • Progress in pure exploration technology: This represents a rise in the exploitable amount of resources in a given field (at given pure real costs of exploitation); this

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type of progress is quasi-resource augmenting in the sense that the share of x in the site X has increased while pure unit exploitation costs remained constant. While in reality both types of technological progress might occur, it seems to be useful to at first consider both types of progress separately.

Pure Technological Progress of Exploitation Let us recall the above equation in the following form: r − ih /ϕ = [dϕ/dt]/ϕ.

(1.4 )

The growth rate of the real oil price ϕ thus should be equal to the real interest rate minus the term ih /ϕ; the lower h is, the more the growth rate [dϕ/dt]/ϕ of the real oil price will be below the real interest rate. For the special case of zero inflation and hence i = r, the condition for a stationary oil price is r = rh /ϕ which implies that the real oil price is equal to the unit exploitation cost. An alternative way to express the above equation is r − (r + π)(h /ϕ) = dlnϕ/dt.

(1.5)

r(1 − h /ϕ) = dlnϕ/dt + πh /ϕ.

(1.6)

r(ϕ/h − 1) = (ϕdlnϕ/dt)/h + π.

(1.7)

r(ϕ/h − 1) − π = (ϕdlnϕ/dt)/h .

(1.8)

Thus dlnϕ/dt will be zero if π = (ϕ/h − 1) where (ϕ/h − 1) > 0 since h < ϕ.

Quasi-Resource-Augmenting Technological Progress Next we turn to technological progress in the sense of a quasi-augmenting technological progress: Firms can extract from a given physical maximum a higher share x than was previously the case. One should be well aware that the rate of technological progress is relatively high in the oil and gas industry and progress to a large extent is quasi-resource augmenting. Progress is high not least since the oil and gas industry is one of the sectors with the highest ratio of computers used per employee. For example, computer simulations are often employed to simulate alternative extraction options and thus to optimize extraction, thereby effectively saving on exploitation cost. In a setting with resource-augmenting technological progress, the alternative to postponing extraction yields a profit of [dP /dt][1 + λ], where λ is the technologyrelated “apprication rate” of the exploitable stock of natural resources. By waiting and

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postponing exploitation by one period, the owner of the site enjoys the benefit of a rise of the price and the appreciation effect through technological progress in resource extraction (physically, one can never, of course, exploit more than 100% of the resource; however, in reality the starting point is often only about 50% of the physical resource, and the general technological progress rate of 3% considered typical for many OECD countries allows for an increase in the degree of exploitation of the existing physical resources). The optimum resource exploitation thus is implicitly determined by the condition (dubbed “fundamental equation”):



 (2) dP /dt 1 + λ = i P − h(V ) . The standard equation in Resource Economics is written with δ = 0 and written as





(3) i = dP /dt 1 + λ / P − h(V ) . If λ is zero and unit extraction cost were zero, we get the well-known Hotelling rule according to which the growth rate of the resource price is determined by the condition: [dP /dt]/P = i.

(4)

Assuming only that unit extraction costs are zero and considering λ > 0 we can write [using the approximation (1 − λ) = 1/(1 + λ)]: [dP /dt]/P = i(1 − λ).

(5)

If the non-renewable resource considered is oil we may state: The oil price inflation rate is reduced by technological progress. The interesting point is to consider an endogenous innovation model in which the appreciation rate λ is a positive function of the real oil price change. Moreover, one may additionally consider the fact that the nominal interest rate i is the sum of the inflation rate π and the real interest rate r— which is a negative function of P /P =: ϕ if one considers the effect of international “oil profit recycling” (the fact that high profits in the oil and gas sector of many OPEC countries are largely invested in OECD countries)—so that we can write dlnϕ/dt = r(ϕ)[1 − λ(ϕ)] + πλ.

(6)

One cannot rule out that the real increase in the oil price increase is zero, namely if both r is relatively small as a consequence of a high relative price ϕ which in turn also raises λ; and if at the same time the term πλ is very small which requires the output inflation rate π to be close to zero. The world inflation rate is largely determined by the difference between the growth rate of the money supply μ and the trend growth of output (a); in a neoclassical growth model with technological progress the growth rate of output is exogenous. Here one may assume, however, that in the long run λ = a[1 + b] where b is a positive parameter—in the interval [0,1]—which depends on the relative price ϕ. Note that one could replace (assuming that the inflation rate is determined by the difference

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between the growth rate of the money supply and output growth) here the term π by the approximate term {μ − λ[1 − b]} so that we have the following: dlnϕ/dt = r(ϕ)[1 − λ(ϕ)] + {μ − λ(ϕ)[1 − b]}λ.

(7)

If the impact of the relative price ϕ on technological progress is relatively strong, the  right-hand term could be summarized in an approximate way by the term ϕ−ß ; if we now consider in addition the existence of synthetical substitutes (or green substitutes; e.g., ethanol) for oil we would have to add—with δ denoting a positive parameter— a term on the right-hand side—δγ, where γ stands for the exogenous expansion rate of developing synthetical or green substitutes (this rate could be influenced by government R&D expenditures relative to GDP). Using a positive parameter ε and assuming a specific set of parameters, we thus can rewrite the above equation as the following Bernoulli equation: 

dϕ/dt = εϕ1−ß − δγϕ.

(8)

If 1 — ß =: ß is in the interval [0, 1] we get the following steady-state solution (#): 

ϕ# = [ε/(δγ)]1/(1−ß) .

(9)

In such a setup, there is no eternal growth of the relative price of the non-renewable resource. Technological progress and the expansion of substitution products contribute to this result.

L.2.2 Non-Stationarity of Oil Prices? Let us consider resource-augmenting technological progress whose rate is assumed to be constant, namely λ; we will not assume that is a positive function of 1/V but rather we will focus on h/P which we will consider as constant. A straightforward approach for analyzing the dynamics of the oil price P is given by the following basic equation while taking into account that the overall inflation rate is the weighted sum—with α denoting the weight of non-oil products—of the inflation rate π of nonoil products and the percentage change of oil price (π ); we also take into account that the nominal interest rate is the sum of the real interest rate r and the aggregate inflation rate. From this it follows that the growth rate of the oil price is a positive function of the real interest rate and a positive function of the non-oil products’ inflation rate. The oil price inflation rate is also a negative function of the resource-augmenting progress rate λ and a negative function of the extraction costs h relative to P . If the ratio h/P should fall as a consequence of an increased monopoly degree in the oil market, the oil price inflation rate will increase. For any combination of a positive real interest rate and positive non-oil product inflation rate, the oil inflation rate will be positive, and there will therefore be a non-monetary inflation pressure, unless the progress rate in the non-oil sector is high enough to bring about a continuous fall in

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the price of non-oil products. An interesting aspect of technological progress is the case when the economy-wide progress rate is also λ and hence prices in the non-oil sector will fall at rate λ, that is π = −λ which implies a constant oil price for the case r/α = λ.   h   (10) (P − h)i = P (1 + λ) ⇒ 1 −  (r + π) = π (1 + λ) P π = απ + (1 − α)π

(11)

i=r+π

(12)





h (r + απ + (1 − α)π ) = π (1 + λ) P       h h 1 + λ − 1 −  (1 − α) π = (r + απ ) 1 −  P P     h h h λ +  + α −  α π = (r + απ ) 1 −  P P P   r  (r + απ ) 1 − Ph α +π π =  =        1 + λ + Ph / 1 − Ph λ + Ph + α 1 − Ph 1−

(13) (14) (15)

(16)

Clearly, the oil price inflation is zero only if the non-oil price inflation rate is negative, namely if we have π = −r/α. Moreover, the oil price inflation rate is a negative function of λ and a negative function of h/P ; under monopoly pricing P exceeds h by a term which depends on the price elasticity—based on the Amoroso–Robinson relationship; under full competition h = P so that moving from a monopoly toward competition reduces the oil price inflation rate (assuming that it is positive). The non-oil inflation rate is determined in a quasi-monetary setting through the difference between the growth rate of the money supply and the growth rate of (USA/world) output which in a modified neoclassical growth model in turn might be approximated by the growth rate of knowledge (WELFENS 2000). At the bottom line we thus may conclude • that there could be a positive oil price inflation even under competition (h = P ); • the oil price inflation is zero if the inflation rate of non-oil products achieves a critical negative value; • that the nominal oil price inflation rate is a positive function of the real interest rate and the non-oil price inflation rate; • that the oil price inflation rate is a negative function of the resource-augmenting rate of technological progress and the ratio h/P . Also one might want to include political risk in the sense that governments of oil-rich countries are afraid of internal revolution which could be modeled by adding in a basic equation on the right-hand side, a term (1 − R ) where R is a proxy indicator for political risk.

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L.2.3 Which Interest Rate Is Relevant? It is interesting to analyze whether the short-term interest rate i or the long-term interest rate i is relevant. In a rather uncertain political and economic environment, one may assume that the short-term interest rate is relevant, while in a stable and safe politico-economic environment the long-term interest rate is relevant. In the presence of a normal yield curve, the long-term interest rate is higher than the short-term interest rate and hence political uncertainty should translate—paradoxically—into a lower growth rate in the oil price (and other non-renewable natural resources). As the nominal interest rate i is the sum of the real interest rate r and the expected output inflation rate π, we can write the simple Hotelling rule—with π =: [dP /dt]/P — as π − π = r.

(17)

The growth rate of the real price of natural resources d(lnP /P)/dt thus should be equal to the real interest rate. Subsequently we will basically look at oil prices as a proxy for natural resource prices. Note that we can modify this equation if we assume that the oil price inflation rate π affects π since the general output price level can be expressed—with P denoting non-oil prices—as P = Pα P(1−α) ; here α which is in the interval[0, 1] denotes the share of household spending on nonrenewable natural resources. Hence P = [P/P ]α P , and therefore we can write π = α dln(P /P ) + π . Thus it must hold for the relative oil price increase: d(ln(P /P ))/dt = r/α.

(18)

Note that the real interest rate can be positive, zero or negative; it is, of course, important whether one considers the short-term or long-term interest rate—and the US or Eurozone interest rate (see Figs. 104 and 105). Given the temporary differences between the US real interest rate and the euro zone interest rate, it is indeed crucial which interest rate is the relevant benchmark for oil producers. As long as the foreign exchange reserves of OPEC countries are mainly in US$-denominated assets it is, of course, natural to consider the US interest rate as the relevant one. One should not overlook that the Euro’s weight in global currency reserves has increased from about 25% in the year of its introduction (1999) to about 35% in 2006. However, none of the major Arab oil producers thus far has declared that they will favor foreign exchange holdings in the Euro in the future. In a period of a zero real interest rate, the relative price increase of non-renewable natural resources should be zero. What happens if a rising real oil price brings about a fall in the global real interest rate through international oil money recycling? For example, the profits of OPEC countries in 2004 were estimated at some € 350 billion, of which a considerable amount has flown to the USA and the EU. Let us assume— with a positive parameter σ—that r = R[P /P ]−σ . The impact of the OPEC on the real interest rate in OECD countries has been considerable in the post-1974 and post-1979 oil price recycling when the current account surplus of OPEC countries

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effectively translated into high investment in bonds and stock markets in OECD countries; from this perspective there is not just a link between oil prices and the interest rate but the interest rate in turn could be affected by oil price changes and the dynamics of the current account surplus position of major oil and gas producers. In the above graph the real oil price (annual data) largely follows—with an apparent time lag—the US real long-term interest rate. It is noteworthy, however, that real oil prices rose in the period from 2002 to 2004 while the real US interest rate fell. The September 11 shock and a gradual rift between the USA and some key Arab OPEC countries—plus Venezuela and Iran (both OPEC countries) which have

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adopted an anti-USA course—could play a role here. With part of the OPEC countries more inclined to effectively base pricing on the Euro, one should indeed expect a transition period in which the depreciation of the dollar is added to the standard price formula. As long as OPEC pricing is mainly in US$, a rise in the world market price increases the global demand for the dollar and therefore reduces the nominal interest rate of dollar-denominated bonds; and it brings about a depreciation of other currencies. It is noteworthy that the US dollar has experienced a sharp nominal and real depreciation in the period 2004–2007. Only in 2006/2007 did the real price dynamics seem to follow the theoretically expected pattern with respect to the impact of the real interest rate. In the empirical part of this analysis, we will take a closer look at the variables considered in the theoretical section, and we observe that the model fit is quite good. The empirical part in the appendix is in line with the analysis presented here (the expected inflation rate approximated by the growth rate of the money supply M3 in the USA). In addition, the role of the US Stock Markets (Dow Jones) index is considered as is the price of gold.

L.2.4 Long-term Macroeconomic Aspects of Oil Price Dynamics The oil and gas prices are so important in the world economy that it makes sense to analyze some broader macroeconomic aspects of oil price dynamics. It is useful to consider the long-term macroeconomic aspects of oil price dynamics by taking into account that the price index contains the oil price. The overall price level P = Pα P1−α so that the aggregate inflation rate π can be expressed as π = απ + (1 − α)π . Thus, after dividing by P , we obtain from our fundamental equation (P − h)i = dP /dt(1 + λ) while taking into account that the interest rate i = r + π (in a strict analytical perspective it is not the actual inflation rate which affects the nominal interest rate but the expected inflation rate): (1 − h/P )[r + α(π − π ) + π ] = π (1 + λ).

(19)

π = (1 − h/P )[α(π − π ) + r]/(h/P + λ).

(20)

This gives

As h ≤ P , the above expression is positive—as a sufficient condition—if π > π . In addition we could consider a modified setup in which λ is a positive function of (π − π ); and we might want to also consider that OPEC-$-recycling could bring about a fall in the international real interest rate which may be proxied by the US real interest rate. Taking into account a technological progress function—with a positive parameter a (exogenous component of progress) and a parameter a > 0 as well as a as a component driven by h/P —we can write λ = [a + a h/P + a (π − π )].

(21)

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π = (1 − h/P )[α(π − π ) + r]/[a + a  h/P + a (π − π )].

(22)

Finally, we consider that the resource owners have not only the alternative of investing in bonds (at interest rate i) but also in stocks, where the stock price index is denoted as P . For simplicity we assume that the shares invested in bonds and stocks, respectively, are exogenous, namely ψ and ψ (where ψ =: 1 – ψ < 1; the split between stocks and bonds could, of course, be explicitly analyzed within a portfolio-theoretical approach). Assuming in our long term analytical framework that the real interest rate r equals the real growth rate in output (dY/dt)/Y, we can write the modified fundamental equation now as ψ dP /dt(P − h) + ψ(P − h)[(dY/dt)/Y + (dP/dt)/P] = dP /dt(1 + λ). (23) Dividing by P gives ψ (1 − h/P )dP /dt + ψ(1 − h/P )[(d ln Y/dt + d ln P/dt]

(24)



= d ln P /dt(1 + λ). Integration with respect to time t and assuming that h/P and λ are constant (while denoting the integration constant as C which can be determined from the initial conditions), we get for the long-run equilibrium price level P #: ln P # = [(1 − h/P )/(1 + λ)][ψ (1 − h/P )P + ψ(ln Y + ln P)]

(25)



/(1 + λ) + C . Thus the long-run equilibrium price of oil lnP # • is a positive function of the stock market price index, world output and the output price level; • is a negative function of the growth rate of resource-augmenting progress; • is a positive function of market power as measured by P /h; or alternatively: the degree of competition as expressed by h/P negatively affects the equilibrium price level. Finally, one may consider gold as an additional alternative investment so that the owners of non-renewables are considering bonds, equities and gold as alternatives to leaving—at the margin—an extra unit of resources in the site for future exploitation. This broader investment menu could be considered both in the context of a long-run analysis—in which the growth rate of international output is equal to the real interest rate—and within the context of a medium-term analysis. The empirical analysis will pick up this perspective. Note that the above equilibrium equation derived from both inter-temporal optimization and inter-temporal arbitrage is easily reconciled with a fairly standard demand equation (Q denoting the quantity of oil; v, v and v standing for positive parameters; Q0 denoting autonomous demand) and standard supply equation. Indeed, one may state the global demand equation for oil as Qd = Q0 + vY − v P /P + v P /P.

(25 )

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419

Here aggregate global demand Y and a global wealth effect as proxied by v P /P positively affect demand, while the relative oil price P /P negatively affects demand for oil. One may note that strictly speaking the global wealth effect should be covered by the variable (P /P)K where K is the global capital stock. However, with a global   production function Y = K ß Lß Qß , one can basically replace the variable K with an adequate combination of Q and L, respectively. The supply curve may be written in a conventional manner as (with h =: h/P ; z and z denoting positive parameters): Q = z P /P − z h /λ. s

(25 )

This approach implies an equilibrium price which looks quite similar to the result obtained from inter-temporal optimization. The theoretically more elegant approach is inter-temporal optimization.

L.3 Oil Price Regression Analysis Can the theoretical approach be supported by empirical evidence? The approach is rather straightforward, and it seems useful to ignore the 1970s with their extreme oil price hikes which were largely determined by political events such as the YomKippur War of 1973 and the following shift of OPEC’s pricing regime. The focus here is on the period from 1991 (January) to 2004 (May). A broad investment menu containing equities, bonds and gold is considered for the subsequent medium-term empirical analysis, which explains—based on monthly data—the link between the oil price and the gold price (“gold”), the composite variable (ip) which effectively is i(1- λ), that is the nominal interest rate multiplied by the technological progress indicator (the number of patent applications per capita at the European Patent Office) and the US money stock (M3) which is a proxy for the expected US price level. The stock price index considered is the US Dow Jones Industrial Index. The empirical analysis—with the second step based on co-integration analysis carried out with the Johansen approach—show that a long-term relationship between these variables exist (trace statistic value is bigger than the critical value) with one cointegrating vector. The conitegrationg vector is (1 –1.314 1.94 1.71 3.70) and therefore the cointegrating equation can be expressed—the coefficient of the variable oil is normalized and should not interpreted as endogeneous—as follows: ln(oilt−1 ) = 23.76 − 1.31*ln(goldt−1 ) + 1.94*ln(ipt−1 ) + 1.71*ln(usdjit−1 ) + 3.71*ln(usm3t−1 ). Note that the t-values do not follow a t-distribution in the case of non-stationarity of variables. Therefore, no definitive conclusion can be drawn with respect to the significance of the coefficients in the cointegrating vector. However, in the long run the oil price is negatively linked with the gold price and positively linked with the other variables. Obviously disequilibrium is reduced by the coefficients of the variables ln_usdji and ln_usm3, respectively. These coefficients (see the Error Correction variables) express the speed of adjustment to the long-term equilibrium.

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Table 25 Oil price regression and cointegration analysis (Vector error correction model). (Data Source: Eurostat, own calculations) ADF test statistic Variable

t-Statistic

Prob.*

Test critical values: 1% level 5% level 10% level

−3.4697 −2.8787 −2.576

ln(oil) ln(gold) ln(ip) ln(usdowji) ln(usm3)

−1.1132 −0.5454 −0.8148 −1.3374 3.1449

0.7102 0.8779 0.812 0.6115 1

1% level 5% level 10% level

−3.4699 −2.8788 −2.5761

dln(oil) dln(gold) dln(ip) dln(usdowji) dln(usm3)

−12.2387 −10.4048 −5.2003 −11.2633 −3.6919

0 0 0 0 0.0051

Trace 0.05 Statistic 53.883 22.2244 5.9838 0.3004

Critical Value 47.8561 29.7971 15.4947 3.8415

Prob.** 0.0122 0.2862 0.6975 0.5837

∗ MacKinnon(1996)

one-sided p-values d: differenced variable Cointegration Analysis Vector Error Correction Model Sample Size: 4161 Series: ln(oil), ln(gold), ln(ip), ln(usm3) Lags intervall: 1 to 2 Unrestricted Cointegration Rank Test (Trace) Hypothesized No. Of CE(s) None* At most 1 At most 2 At most 3

Eigenvalue 0.1816 0.0977 0.0353 0.0019

Trace test indicates 1 cointegrating eqn(s) at the 0.05 level ∗ denotes rejection of the hypothesis at the 0.05 level ∗∗ MacKinnon-Haug-Michelis (1999) p-values

Vector Error Correction Estimates Sample Size: 4161 Standard errors in ( ) & t-statistics in [ ] Cointegrating Eq. CointEq1 ln(oil)(−1) ln(gold)(−1) ln(ip)(−1) ln(usdji)(−1) ln(usm3)(−1) 1 1.3144 −1.9396 −1.7058 −3.7077 (1.1716) (0.9675) (0.7279) (1.2348) [1.1219] [−2.0049] [−2.3435] [−3.0027] Error Correction: CointEq1

d(ln(oil)) −0.0172 (0.0093) [−1.8577]

d(ln(gold)) −0.0045 (0.0035) [−1.3009]

d(ln(ip)) −0.0018 (0.0038) [−0.4721]

C 23.7627

d(ln(usdji)) d(ln(usm3)) 0.0099 −0.0018 (0.0040) (0.0003) [2.4625] [−5.2236]

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421

Table 25 continued Vector Error Correction Estimates Sample Size: 4161 Standard errors in ( ) & t-statistics in [ ] Cointegrating Eq. CointEq1 ln(oil)(−1) ln(gold)(−1) ln(ip)(−1) ln(usdji)(−1) ln(usm3)(−1) 1 1.3144 −1.9396 −1.7058 −3.7077 (1.1716) (0.9675) (0.7279) (1.2348) [1.1219] [−2.0049] [−2.3435] [−3.0027] d(ln(oil)(−1))

d(ln(oil)(−2))

d(ln(gold)(−1))

d(ln(gold)(−2))

d(ln(ip)(−1))

d(ln(ip)(−2))

d(ln(usdji)(−1))

d(ln(usdji)(−2))

d(ln(usm3)(−1))

d(ln(usm3)(−2))

C

R-squared Adj. R-squared Sum sq. Residuals S.E. equation F−statistic Log likelihood Akaike AIC

0.0039 (0.0792) [0.0487] −0.1310 (0.0786) [−1.6666] 0.1430 (0.2148) [0.6658] −0.0785 (0.2163) [−0.3632] 0.3741 (0.2015) [1.8567] 0.3010 (0.2105) [1.4296] 0.0164 (0.1917) [0.0858] 0.4791 (0.1851) [2.5886] −3.1582 (2.2761) [−1.3875] 0.1576 (2.1948) [0.0718] 0.0165 (0.0129) [1.2844]

0.0227 (0.0299) [0.7591] −0.0371 (0.0296) [−1.2506] 0.1054 (0.0810) [1.3013] −0.2130 (0.0816) [−2.6113] 0.0389 (0.0760) 80.5117] 0.0892 (0.0794) [1.1240] 0.0052 (0.0723) [0.0713] −0.0193 (0.0698) [−0.2764] −0.6746 (0.8584) [−0.7859] −0.2794 (0.8277) [−0.3376] 0.0051 (0.0049) [1.0597]

0.0608 (0.0324) [1.8756] 0.0758 (0.0322) [2.3570] −0.1735 (0.0879) [−1.9731] 0.0089 (0.0886) [0.1008] 0.2730 (0.0825) [3.3092] −0.0719 (0.0862) [−0.8343] 0.0698 (0.0785) [0.8898] 0.0277 (0.0758) [0.3658] 0.0622 (0.9320) [0.0667] −0.1735 (0.8987) [−0.1931] −0.0054 (0.0053) [−1.0307]

0.1580 0.0945 0.8388 0.0758 2.4897 189.6380 −2.2486

0.1017 0.0340 0.1193 0.0286 1.5023 343.7230 −4.1990

0.1716 0.1092 0.1406 0.0310 2.7498 330.7219 −4.0345

−0.0511 (0.0342) [−1.4935] 0.0074 (0.0339) [0.2191] 0.0191 (0.0928) [0.2056] 0.1068 (0.0934) [1.1439] −0.0594 (0.0870) [−0.6824] 0.0945 (0.0909) [1.0394] 0.1914 (0.0828) [2.3123] −0.0881 (0.0799) [−1.1025] 1.3875 (0.9830) [1.4116] 0.5980 (0.9478) [0.6309] −0.0005 (0.0056) [−0.0811]

C 23.7627

0.0004 (0.0029) [0.1361] −0.0015 (0.0029) [−0.5112] −0.0056 (0.0080) [−0.7023] −0.0006 (0.0080) [−0.0761] −0.0197 (0.0075) [−2.6319] −0.0194 (0.0078) [−2.4848] 0.0009 (0.0071) [0.1272] −0.0023 (0.0069) [−0.3417] 0.1222 (0.0845) [1.4456] 0.0646 (0.0815) [0.7920] 0.0030 (0.0005) [6.3359]

0.1076 0.3940 0.0404 0.3484 0.1564 0.0012 0.0327 0.0028 1.6007 8.6298 322.3058 709.9284 −3.9279 −8.8345

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Table 25 continued Vector Error Correction Estimates Sample Size: 4161 Standard errors in ( ) & t-statistics in [ ] Cointegrating Eq. CointEq1 ln(oil)(−1) ln(gold)(−1) ln(ip)(−1) ln(usdji)(−1) ln(usm3)(−1) C 1 1.3144 −1.9396 −1.7058 −3.7077 23.7627 (1.1716) (0.9675) (0.7279) (1.2348) [1.1219] [−2.0049] [−2.3435] [−3.0027] Schwarz SC Mean dependent S.D. dependent Determinant resid covariance (dof adj.) Determinant resid covariance Log Likelihood Akaike information criterion Schwarz criterion

−2.0160 0.0043 0.0797

−3.9664 0.0004 0.0291

−3.8019 −0.0060 0.0329

−3.6953 −8.6019 0.0078 0.0040 0.0334 0.0035

3.63E-17

2.45E-17 1900.7810 −23.2377 −21.9778

Data sources: Eurostat., IMF Financial Statistics, EIA Calculations based on E-Views software Variable: ln(oil) with natural logarithm of the oil price in $ Variables: ln(gold), ln(ip), ln(usdji), ln(usm3) ln: natural logarithm gold: gold price in US dollar ip: long-term nominal interest rate (government bonds with 10 years maturity) multiplied with 1 minus technological progress (defined as patent applications per capita for the EU-15; this is the proxy used here for technological progress) usdji: US Dow Jones Industrial Index usm3: US money stock M3; average oil price in the regression period was $20.90 All variables are indexed (1996 = 100); monthly data (for the period from 01/1991; 05/2004) are used. Note that the data used for the patent applications had to be transformed by linearization from annual into monthly data.

The short-term part of the Vector Error Correction Model (VECM) shows that oil has a significant positive impact on the composite variable ip. On the other hand, ip has a strong negative impact on the US money stock m3 (Table 25). The empirical results obtained from VECM Approach clearly indicate that the variables considered are cointegrated. Cointegration means that all the included variables are integrated of the same order—in this case I(1)—and at lest one linear combination of these variables is stationary, i.e., I(0). Relevant long-term links therefore exist between the variables considered. A new element presented here is the role of technology, and we clearly find the theoretically derived variable i(1 + λ) to be significant at least in the short term. The regression results–based on VECMs– indicate that the Dow Jones Index (US), the proxy for inflation pressure (M3) and

L.4 Policy Implications

423

the composite innovation variable are significant; however the R2 is rather modest so that further research is needed. Part of the problem could be related to the quality of the innovation variable used—ideally one should use a variable which reflects innovation dynamics in the oil and gas sector. One major conclusion from the analysis presented is that a fall in the nominal interest rate and a rise in the progress rate will dampen the price of oil. However, from this we may not conclude that oil-rich countries would prefer for leading OECD countries to adopt an inflationary monetary policy since the real oil price growth is the rate of increase of the nominal oil price minus the aggregate inflation rate.

L.4 Policy Implications Nurturing innovations is important in a policy perspective. Governments in OECD countries—especially the major importers of oil and gas—have a strategic interest in promoting resource-augmenting innovations. A broader perspective of the oil and gas industry suggests that a high overall progress rate of the economy will dampen the oil price dynamics to the extent that resource-augmenting innovations are an important element of such Schumpeterian dynamics. For OECD countries with a large financial sector, recycling of OECD profits could be quite important. Assuming that OPEC countries mainly focus on the interest rate of US bonds— which is natural if oil prices are mainly denominated in US$—the course of US monetary policy is quite important; an inflationary policy which reduces the real interest rate is not in the interest of OPEC countries and to the extent that oil price shocks trigger accommodating inflationary policies, there is a trade-off for OPEC in its long-term desire to raise the prices of oil and gas. At the same time, the enhanced currency competition between the US$ and the € gives OPEC countries some leverage in the sense that their decision with respect to the choice of currency for central bank foreign exchange reserves has important implications as to whether the US interest rate or rather the Eurozone interest rate will be relevant. The oil-producing Arab countries apparently have a strong preference for the US dollar since even in a period of strong dollar depreciation—2004–2008—the share of reserves held in $ has not much changed. This might reflect largely political considerations and indeed points to the fact that the oil business is strongly shaped by political dynamics; as long as the USA can credibly guarantee continuation of the rule of certain autocrats in the OPEC group—that is as long as the US military can offer a sufficient number of helicopters to evacuate the ruling families and has adequate military forces to intervene in the case of revolution on the Arab peninsula—there is a strong bias of Arab OPEC countries to hold currency reserves in US$. This contributes, of course, to a low real US inflation rate, but this might not be considered a strong problem in the perception of ruling families in some countries. A short-term strong increase in oil prices might indeed not be welcome for political reasons since would-be revolutionary groups might translate high current oil prices into a signal that the politico-economic prey for revolutionary attackers has been raised.

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The EU has emphasized its ambitions with respect to fighting global warming; however, the community has not adopted a specific focus on the role of innovation in the oil and gas industry. The EU’s Lisbon Agenda should indeed add an explicit goal in the field of innovation dynamics in the energy sector broadly defined; moreover, the EU energy policy should put a stronger focus on innovation in the energy sector, and this would include both the use of energy and natural resource exploitation as well as transportation and storage of energy—the latter possibly also for CO2 in the context of novel sequestration technologies. It is quite important that the major oil and gasproducing countries in the European Economic Area (this includes Norway) adopt adequate R&D promotion programmes. Furthermore a joint transatlantic effort (e.g., within the Eureka programme) would be useful if oil price inflation is to be reduced in the long run. Such policy measures would not undermine efficient internalization of CO2 emissions provided that the EU emission trading system is reinforced and adopted at the level of the OECD countries, possibly including countries from the OECD International Development Centre. As regards inflation analysis, it is obvious one cannot rule out that in a world with non-renewable natural resources there could be inflationary pressure despite money supply growth being in line with the growth rate of output. The puzzle can be solved on the basis of an augmented quantity equation (with V denoting velocity which negatively depends on the i) which reads: MV(i) = PY + P R(P /P).

(26)

If the flow of resources used (R) is a positive function of P /P—until a critical threshold of the stock of resources V has been exceeded—then a long-term rise in the real price P /P could temporarily go along with a rise in R ; beyond the critical point a rise in P /P will go along with a fall in R. Since output Y is a positive function of capital K, labor L, energy use R and knowledge A, we can write for the case of linear-homogenous production function Y = bK + b L + b R + b A where b, b , b and b represent the marginal product of capital, labor, natural resources and knowledge, respectively. With positive autonomous oil price inflation, velocity is higher than in a non-inflationary world, namely if the nominal interest rate i correctly reflects the inflation rate which is composed of an oil price component and a non-oil price component. As P /P is rising over time the ratio of R to real output will decline in the long run so that output becomes less resource intensive. Note that knowledge A could be seen to represent a complete backstop technology which at some point will effectively replace the natural resource. In such a perspective, the relative oil price will achieve a stable ratio and then the standard logic of the (modified) quantity equation holds once again. Those analysts which forecast a long-term inevitable rise in the real oil price have few convincing arguments unless they would argue that technological progress will decline over time. With the effective opening up of China and India in the late twentieth century, the long-term impact of those countries’ integration into the world economy could be rather that the growth rate of technological progress will increase and thus one cannot rule out that the global real oil price will remain more or less

L.5 Sustainability Issues

425

constant in the long run. One can, of course, not rule out that there are relevant shift parameters which will affect the steady-state real price level of oil and natural gas. An important question is to which extent technological progress in the oil and gas industry is influenced by relative prices and how long the lag between inventions and innovations really is. The model presented suggests that those concerned about global warming should not simply rely on some automatic long-term rise in the real oil price as a stimulus for saving fossil fuels. From this perspective, it is quite useful to expand the market for tradable emission permits and to indeed use market forces to internalize negative external effects.

L.5 Sustainability Issues Considering the topic of long-term growth and sustainability—in a broader sense— one will have to take into account several aspects: • Even if relatively high long-term growth can be achieved there is the potential problem of inequality dynamics; growth might lead to a higher inequality which normally is not a problem unless it exceeds a critical dimension and unless government is not engaged in adequate redistribution policies. In a normative perspective one may state that such policies should try to avoid negative incentives for investors and innovators. From a more philosophical perspective—picking up the Theory of Justice of RAWLS (1985) who argued in his “difference principle” that inequalities should be accepted provided that they also contribute to improving the economic position of the poorest strata—one might emphasize that growth should go along not only with a rise in average per capita income but also in per capita income of the poorest strata in society. • High growth over some decades will not be sustainable if there are high and growing emissions of particulates or CO2 and other greenhouse gases. From this perspective the concept of sustainable growth leads to the issue of emissions but also to some other questions, including those related to energy issues. There is hardly any doubt that the ratio of global reserves to global consumption is likely to be rather stable for many years to come—according to statistics of BP (2007) that ratio is about 40 for oil and about 60 for gas. However, there are opportunity costs to the depletion of natural resources and those often are not considered, and we will see that one may argue that depletion of natural resources affects the true net savings ratio. As regards the level of the growth path the savings ratio is decisive. The higher the savings rate the higher the level of the growth path in the steady-state/the long-run equilibrium. While it is true that other variables also influence the level of the growth path one should emphasize that the savings rate clearly is a variable which government can influence in various ways. Moreover, economic integration can affect the savings ratio: With a more integrated system of banks and financial markets—e.g., as

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30

25

20

15

10

5

0 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007 2008

Germany

USA

EU 12

Fig. 106 Savings ratios in the USA, Germany and the Euro Area (in % of GDP) (Y/Q/M). (Source: Ameco Database (2007; annual figures))

in the euro area and the EU, respectively—one should anticipate a fall of the savings ratio, namely for two reasons: • In a more integrated market, competition is more intensive and this will lead to reduced intermediation costs and hence a rise of the effective savings rate (in a growth model one may argue that savings S = s(1 − ρ)Y where ρ—in the interval [0, 1]—is a measure of inefficiency). • In a more competitive integrated market, it will be easier for both firms and households to obtain loans so that savings of private households are likely to fall. • If financial market integration amounts to a positive impulse for economic expansion so that real asset prices increase, one should expect that savings—indeed the savings ratio S/Y—will fall, namely if one assumes that real wealth negatively affects savings (current savings typically are used to bridge the gap between current real wealth and an exogenous wealth target). We can see that after the start of the Euro, the national savings rate decreased slightly in both Germany and the euro area. But after 2005, we have seen a rise in the savings rate over several years which, however, mainly reflects government budget consolidation efforts (in the subsequent graph the sum of private savings and government savings relative to GDP are shown (Fig. 106)). The neoclassical model will lead for the case of a production function Y = Kß (AL)1−ß and a gross savings rate s and population growth rate n to the following term for the level of the per capita income growth path (under the equilibrium conditions savings equals investment which is the sum of dK/dt and δK, where δ is the depreciation rate): A0 [s/(a+n+δ)]ß/(1−ß) ; this can approximately be rewritten for the simple illustrative case n + a = 1 as A0 s(1 − δ). Clearly, the higher the depreciation

L.5 Sustainability Issues

427

rate of capital, the lower the level of the growth path. Since net GDP Y := Y − δK, we have (with y := Y/(AL), k  := K/(AL)) for the steady state: y # := Y /(AL) = y − δk  = k − δk  ß

= [s/(a + n + δ)]ß/(1−ß) − δ[s/(a + n + δ)]1/(1−ß) .

(27)

For the special case of ß = 0.5, we get y = [s/(a + n + δ)] − δ[s/(a + n + δ)]2 .

(28)

y /[s/(a + n + δ)] = 1 − δ[s/(a + n + δ)]2 .

(29)

If δ[s/(a + n + δ)]2 is close to zero—that is if the depreciation rate is rather small—we can use the approximation: ln y − ln[s/(a + n + δ)] ≈ −δ[s/(a + n + δ)]2 .

(30)

ln y ≈ ln[s/(a + n + δ)] − δ[s/(a + n + δ)]2 .

(31)

ln Y /L ≈ e {ln[s/(a + n + δ)] − δ[s/(a + n + δ)]2 }A0 .

(32)

at

We can thus clearly see that the depreciation rate strongly affects the level of net GDP per capita. Net GDP per capita (y ) is a crucial economic variable since it is only y whose production can be sustained, namely if there is adequate reinvestment which must be equal to capital depreciations (in the former GDR this condition was neglected in many years and in some years the government decided to manipulate the capital stocks statistics by effectively imposing a negative depreciation rate so that mysteriously the capital stock had increased). The traditional economic analysis looks only at capital depreciations, but this is an incomplete picture of reality; particularly if the country considered is exploiting non-renewable natural resources. At the same time, the traditional concept of savings—as applied in the System of National Account—is incomplete since private expenditures on education are not considered. Hence it holds: If there are other input factors which are depleted—such as nonrenewable energy or mineral resources—the concept of sustainable growth will have to not only consider depreciation of capital but also the depletion of energy resources and of mineral resources. To put it differently, the true net savings rate—referring to our illustrative case—differs from s(1 − δ): The true net savings rate will be lower, and hence the level of sustainable growth is lower, than simply looking at capital depreciation suggests. At the same time a true net savings rate will have to include private expenditure on education as an item which raises true savings above the traditional savings ratio (as shown in the systems of national accounts). Indeed, there can be sustained growth of both output and consumption only if there is adequate reinvestment. Reinvestment in standard growth models refers strictly to capital, that is, equipment and machinery plus buildings/real estate. If one wishes to assess the long-term consumption opportunities of a closed economy—with a given population—he or she must subtract reinvestment per capita from per capita

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production. True net savings of many countries are much lower if one not only considers allowances for capital depreciation but also the depletion of non-renewable energy resources plus mineral resources and allowances for emissions of particulates and CO2 ; at the same time it is important to add expenditures of human capital formation if one is to derive true net savings as calculated by the WORLD BANK (2006) in its study, “Where is the Wealth of Nations? Measuring Capital for the 21st Century.” True savings relative to real income is 12.7% in Canada instead of 11.5%, the official number published for 2004. For the USA true savings is 8.2%, which is somewhat higher than the official figure of 5.7%. In France the true savings ratio is 14.3% which is much above the official figure of 9.4%. In Kuwait the official figure was 33.5%, while the true net savings rate was −12.9% which indicates that economic expansion in Kuwait is not sustainable in the long run. Taking a look at EU figures we generally see rather favorable growth prospects in many EU-15 countries in terms of sustainability as proxied by the true savings ratio of the World Bank. China, which has a very high true savings rate, could face some problems in the future as the burden of emissions of particulates and CO2 will rise; at the same time one may expect China to spend more on education in the future. While the growth rate of many OECD countries does not seem to be very high compared to newly industrializing countries, one should not overlook that EU growth is rather sustainable. This suggests that Europe faces favorable prospects for longterm growth. The only caveat concerns the long-term decline in population and the problem of aging societies. As the “leading aging” OECD country, Japan has shown at the beginning of the twenty-first century; however, even with an aging and declining population a country can achieve sustained per capita income growth. As regards the problem of sustainable social security financing the EU has come up with broad suggestions for pension reforms which allow for a reconciliation of financial and macroeconomic stability with long-term growth (McMORROW/ROEGER 2004; ROEGER 2007).

Financial Market Integration Financial stability is likewise important for sustainable economic growth (broadly defined). Competitive financial markets and financial innovation can contribute to a more efficient allocation of capital and risk management. Hence financial market integration in the EU could contribute to long-term economic expansion. The European Commission has emphasized the need to achieve a more competitive single market in the financial sphere and considerable benefits have been suggested. The creation of the euro area is in itself a major step toward financial market integration, which should reduce intermediation cost and thus allocate savings more efficiently. In a growth perspective one may argue that savings S = s[1 − ρ]Y where ρ (in the interval [0, 1]) stands for transaction costs; hence financial market integration— reducing ρ—implies a higher level of the growth path in the context of a neoclassical growth model. At the same time, one should consider the potential problem that financial market integration creates a more liquid financial system so that precau-

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Table 26 Official savings and true savings relative (World Bank concept) to gross national income in selected countries, 2000. (Source: WORLD BANK (2006)) Use of Capital (3a)

Emissions (4)

Gross Exp. on Fixed Mineral Forests Energy Parti- CO2 Net (5) True Savings Education Capital Resources (c) Depletion culates Savings (6) Net (1) (2) (a) (b) (3d) 1-3a Savings 1+2−3−4 Canada USA Mexcico Russia France Germany UK Italy Kuwait Indonesia China

24,6 17,4 21,0 37,1 22,0 20,3 15,0 20,1 40,0 21,0 38,8

4,9 4,2 5,0 3,5 5,1 4,3 5,3 4,4 5,0 1,4 2,0

13,1 17,4 10,6 10,0 12,6 14,9 11,5 13,7 6,5 5,6 8,9

0,2 0,0 0,1 0,4 0,0 0,0 0,0 0,0 0,0 1,4 0,3

0,0 0,0 0,0 0,0 0,0 0,0 0,0 0,0 0,0 0,0 0,1

4,9 1,2 5,9 39,6 0,0 0,1 1,1 0,1 48,7 12,5 3,6

0,2 0,3 0,5 0,6 0,0 0,1 0,1 0,2 2,0 0,5 1,0

0,4 0,3 0,4 3,4 0,2 0,2 0,2 0,2 0,6 1,1 1,6

11,5 5,7 10,4 27,1 9,4 5,4 3,5 6,5 33,5 15,4 29,8

12,7 8,2 8,4 −13,4 14,3 9,3 7,3 10,3 −12,9 1,3 25,5

tionary savings are likely to drop, which in turn negatively affects the savings ratio. In the first seven years after the creation of the euro zone, the savings rate dropped— despite the fact that the population has become increasingly aware of the need to increase savings in a new period—indeed with an aging and declining population— in which traditional pay-as-you-go public retirement schemes look much less sound and stable than before. However, there are also considerable medium-term risks in the financial sector in some countries—particularly where prudential supervision is rather weak as is obviously the case in Germany. (Two public banks, Berliner Bank and WestLB as well as a private bank, the IKB Deutsche Industriebank which is No. 4 among German banks, faced major problems and billions of unanticipated losses in the first decade of the new century; Sachsen LB, a state-owned bank in Saxony, also incurred major problems in the context of investment in the USA and the subprime mortgage crisis.) Government is partly to blame for this as the Ministry of Finance has pushed for cost-cutting in the Deutsche Bundesbank and eliminated the traditional Bundesbank remuneration bonus which would be important to attract top talents for the Bundesbank; furthermore, the federal agency BaFin which institutionally share prudential supervision with Deutsche Bundesbank is also unable to offer competitive remuneration and thus largely lacks adequate highly-skilled staff, and this is quite dangerous in a period of rapid internationalization of banks and accelerated financial innovations in the EU single market—this concerns both EU-15 and EU Eastern European accession countries. There is, however, a broader problem of insufficient international accounting standards. The international accounting standard-setting bodies have not really made their homework properly in the wake of the Enron crisis: It was Enron which created special financing entities—active with business outside the Enron balance sheet—to conceal high risks is unacceptable for a joint stock company.

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After the Enron debacle new accounting standards were introduced which should shed more light on the true state of risk and the structure of financing, but for unclear reasons an opaque transition period was introduced which allowed bank and firms to continue for several years in concealing major off-balance sheet activities and their associated risks (top of the weak points is that some short-term financing of bank activities did not even have to be indicated in the notes at the end of the accounting reports). While German law on joint stock companies requires bank management to establish an early warning system—in particular for risks that could endanger the survival of the bank—it is obvious in the case of IKB Deutsche Industriebank and Sachsen LB that managers did not implement a reliable early warning system. With more and more banks becoming engaged in international investment and risk management within EU, the failure of adequately up-stepping the quality of the bank management in many OECD countries has created new problems.

Appendix L.1: Data Sources Three data sources have been used for the regression analysis. The time series of gold price (given in US dollar) is obtained from IMF Stat., time series of long-term interest rate (bonds with 10 years maturity), US Dow Jones Industrial Index and patent applications (per habitant) from Eurostat; and US money stock M3 data are obtained from OECD Stat. All raw (monthly) data have been transformed into indices with the base year 1996.

M. Portfolio Modeling and Growth in Open Economies

M.1 Introduction Open economy Macroeconomics has made considerable progress in recent years— e.g., with the analysis of output, inflation and trade in the context of DSGE models. As regards exchange rate analysis, there has been limited progress: The standard workhorse for the analysis of short-run dynamics is the BRANSON (1977) portfolio model—with money (M), domestic bonds (B) and foreign bonds (F*) which jointly explains the exchange rate (e: in price notation) and the nominal interest rate (i). Net wealth of the private sector is A = M/P + B/P + eF*/P and the desired share of assets are assumed to be proportionate to A (P is the output price level). In a system of flexible exchange rates the portfolio model determines e and i on the basis of given stocks M, B and F* (denominated in foreign currency); F* will rise if there is a current account surplus. A simple, long-term approach to exchange rate determination is the purchasing power parity P = eP*, where  = 1 for the case of heterogeneous tradable goods (* denotes foreign variables). A useful intermediate model for exchange rate determination is the model of DORNBUSCH (1976), which explains overshooting of the exchange rate—the fact that the short-term reaction is higher than the long-run reaction—in the context of fast adjustment of the money market and slow adjustment of the goods market. It is interesting to look for an analytical bridge between the short run and the long run, however the long-term developments of the real economy cannot be considered without taking into account accumulation dynamics such as captured by the neoclassical growth model (or endogenous growth models). In this context it is useful to focus on a modified version of the BRANSON model, in which the domestic bonds market has been replaced by the stock market (WELFENS 2007, 2008a). The stock market price index is denoted by P , the number of stocks is assumed to be equal to the number of capital units K. Such a modified portfolio approach is a useful starting point for combining the portfolio model with a long-run neoclassical growth model. As regards the growth model, we assume that knowledge A(t) grows at a constant rate a, while the growth rate of labor (L) is equal to n. It will be assumed that output is produced according to a Cobb–Douglas function Y = K ß (AL)1−ß —with capital output elasticity ß in the interval (0,1). It will be useful to define k := K/(AL) and P. J. J. Welfens, Innovations in Macroeconomics, DOI 10.1007/978-3-642-11909-5_13, © Springer-Verlag Berlin Heidelberg 2011

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y := Y/(AL) where AL is labor in efficiency units. With respect to the portfolio model we will consider money, foreign bonds and a third asset which could be stocks or oil; in principle one could consider a model with N assets, but keeping the analytics tractable suggests focusing on only three assets (indeed, an explicit solution will be presented subsequently). As regards the link between innovation dynamics and stock market prices, one may point out that GRILICHES et al. (1991) have presented important empirical findings, however, the theoretical basis has remained somewhat opaque. The paper first looks into two variants of the BRANSON model where one modification puts the focus on the role of stocks and the other modification considers the role of oil/non-renewables, which have became a preferred focus on investors in recent decades. The portfolio model with oil—as one of the assets where the exchange rate and the oil price can be analyzed simultaneously—is contrasted with an alternative approach, namely a modified Hotelling approach in which the pivotal role of oil price inflation expectations is more clearly highlighted than in the 238 P.J.J. Welfens portfolio approach which implicitly assumes that a new stable steady state exists, and hence comparative statics and multiplier analysis are meaningful. The modified Hotelling approach shows, however, that a new steady state for the oil price will exist only if the oil price inflation expectation is below a critical value. (In the portfolio approach there is an oil price inflation expectation rate but no a priori critical value is imposed; it is noteworthy that the portfolio model with oil—as one of the assets considered—can explain some of the observed stock market price dynamics and oil price dynamics in the US financial market crisis in 2007/2008). The endogenous variables considered always are the exchange rate and “the asset price”. An important aspect of the broader modeling approach—including growth aspects—concerns the role of product innovations which enter the model as an exogenous variable, but studying the multiplier results for the exchange rate and the stock market price reveals important insights as to how the long-term multipliers differ from the traditional short-term Branson model (with our without the stock market). When combining portfolio modeling with a standard growth model the growth rate of knowledge is considered to be exogenous, so that we can conveniently focus on explicit solutions in our analysis of comparative statics. The new theoretical approach presented does not only show how the production function and capital accumulation dynamics interact with the standard elements of the Branson model; rather we also have a principal starting point from which further future modeling, including endogenous growth aspects. For example, one might assume that the growth rate of knowledge depends on the ratio of R&D expenditures which in turn could be assumed to be proportionate to the value of stocks (this ratio basically would mirror the relative size of the R&D sector; and in a potential extension of the basic modeling presented here, one could include a production function with capital, labor, energy and knowledge and study in turn how a hypothetical link between relative oil price dynamics and energy saving knowledge creation—R&D expenditures financed through the capital market—works). Moreover, the model presented also offers a theoretical

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starting point for considering the relationship between international financial flows and productivity growth or output growth. Kose/Prasad/Terrones (2008) have found some empirical evidence for a positive link between financial openness and total factor productivity—there is clear evidence that foreign direct investment and portfolio equity liabilities boost TFP growth while external debt is negatively correlated with TFP growth. Subsequently, we first look at the modified BRANSON model (Sect. 2). In Sect. (3) the BRANSON model is combined with the neoclassical growth model. Moreover, it is shown that the portfolio model is useful for analyzing asset market dynamics, including a setup with oil as one of the assets considered—and one also can show some similarity with the Hotelling pricing rule for non-renewables. Section (4) presents the multiplier analysis and Sect. (5) draws key conclusions.

M.2 Combining the Portfolio Model and Growth Analysis A useful point of departure is growth theory, namely the neoclassical model which we will consider for the case of a given savings rate, zero capital depreciation, a constant growth rate (n) of the population and a constant growth (a) rate of knowledge. Combining the equilibrium condition for the goods market—in a closed economy (and in the absence of foreign bonds)—dK/dt = sY, one can determine the steady-state solution for the capital intensity K/(AL) as (JONES 2002a): k  # = [s/(a + n)]1/(1−ß)

(1)

Here # denotes the steady state. The production function then implies for output relative to labor in efficiency units: y # = [s/(a + n)]ß/(1−ß)

(2)

In the steady state, the growth rate of output Y will be equal to the sum of a + n. For the case of an open economy, the growth model will have to be modified. The standard BRANSON model assumes that the demand for each asset is proportionate to real wealth (A ) of the private sector, and the desired shares of each asset (j = 1, 2, 3) depends on the domestic interest rate (i) and the foreign interest rate as well as the expected depreciation rate (i* + a ). Due to the budget constraint, it must hold that the shares of the assets add up to unity. As regards the portfolio bloc, a modified BRANSON model is proposed here. It is assumed that the demand for each asset Xj (j = 1, 2, 3 refers to real money balances M/P, real value of foreign bonds eF*/P and a third asset, e.g., the real value of stocks: P K/P) can be expressed as follows (with α > 0) α

Xj = xj (. . . )A Y1−α

(3)

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For a given ratio A /Y, the demand for each asset is proportionate to real income. With respect to empirical issues, an important question concerns the question whether α > 1. Hence, one could express the demand for each asset as follows: Xj /(AL) = xj (. . . ){[A /(AL)]/y }α [Y/(AL)].

(4)

Before the combined approach of the portfolio model and the growth model is considered in broader detail—including the multiplier analysis—we take a brief look at an augmented three asset model with money, foreign bonds and oil (quantity is denoted as V ; we also define i∗ = i* + a and denote the expected growth of the oil price by π ; a is the expected devaluation rate). In a long-term perspective, the basic portfolio-growth model of a closed economy—with money (M), short-term bonds (B) and oil (V )—reads: A = M/P + eF*/P + P V /P

(5)

(M/P)/(AL) = v(i, i *, π )[A /(AL)]α (s/(a + n))ß/(1−ß)

(6)

(B/P)/(AL) = b(i, i *, π )[A /(AL)]α (s/(a + n))ß/(1−ß)

(7)

(P V /P)/(AL) = u(i, i *, π )[A /(AL)]α (s/(a + n))ß/(1−ß)

(8)

The desired ratio of real money balances in total assets is v(Y/A )1−α and a similar reasoning holds for the other assets. There is a long-term restriction, namely 1 = [v + b + u]{[Y/(AL)]/[A /(AL)]}1−α where long-term stationarity of y , (M/P)/(AL), (B/P)/(AL) and (PV /P)/(AL) implies that only two of the three equilibrium conditions for the asset markets are independent. Open Economy In an open economy, the portfolio bloc will include in a simple set-up money, foreign bonds (F*, denominated in foreign currency; e is the exchange rate) and stocks—or oil or other additional assets. As (eF*/P)/(AL) is constant in the steady state, it must be also true that (eF*/P)/Y is constant in the steady state and hence [d(eF*/P)/dt]/(eF*/P) = n + a. This implies that there will be a permanent current account surplus and thus—strictly speaking—one must also make a distinction between GDP and GNP, where the latter is GDP plus net foreign profits (or interest payments) accruing from abroad. This distinction between GDP and GNP has indeed been made in recent analysis of open economies, in particular in the context of foreign direct investment (WELFENS 2007). While we will neglect for simplicity the distinction between GDP and GNP, the more important aspect of stating the equilibrium condition for the goods markets must be fully considered: In the open economy the condition for goods market equilibrium must hold: sY = dK/dt + (edF/dt)/P and hence—with f := F/(AL)—we can write (taking into account df /dt = (dF/dt)/(AL) − f  (a + n)): sk  = dk  /dt + k (a + n) + (e/P)[df  /dt + f  (a + n)] ß

(8 )

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This is the differential equation for capital accumulation in an open economy with capital flows. Later we will consider a portfolio model with stocks (instead of oil) so that the equilibrium condition for the stocks market will read (with P for stock market price index; K is the number of stocks which equals the number of capital units K): P K/P = h(. . . )[A /(AL)]y1−α . Without considering the explicit solution of the above differential equation—there basically is no problem as one may assume that financial market equilibrium is relatively quickly established (compared to goods market equilibrium)—one may restate the above equation by taking into account the asset market equilibrium conditions for the stock market and the foreign bonds market which jointly imply [(eF*/P)/(AL)]/[P K/(AL)] = f/h so that we have f = (f/h)k /(e/P) and hence the steady-state conditions dk /dt and df /dt = 0 imply sk  = k (a + n) + k (1 + (f/h))(a + n) ß

(8 )

Thus the steady-state solution k # for the open economy—with foreign bonds held by domestic residents—is given by (with f/h := ϕ ): k  # = {s/[(a + n)(1 + ϕ )]}1/1−ß

(8 )

The steady-state solution y # for the open economy is, of course, y # = k ß/(1−ß) . This condition must be considered for the subsequent multiplier analysis in the portfolio growth model. It should be emphasized that in the open economy—with a structural current account surplus (and ignoring for the moment the distinction between GDP and GNP)—the steady-state solution for k implies that the capital intensity k # is smaller than in a closed economy. However, this should not be considered a problem since holding foreign bonds brings benefits in terms of risk diversification (explicit analysis could focus on this aspect in the framework of the standard approach CAPM and welfare analysis—with a utility function containing both per capita consumption and per capita wealth—could also be enriched by additional aspects as could be the traditional optimum growth approach); moreover, one might consider an endogenous growth approach, namely assuming that (with a0 denoting the exogenous progress rate,  is a positive parameter) the progress rate a = a0 +  f as international portfolio diversification allows for the raising of innovation intensity. In such a setup, the reduction of the steady-state level of the growth path will be offset by a rise in the trend growth rate. In a growing economy, the monetary policy variable is M/(AL). It will be interesting to consider supply-side parameter changes, including the savings rate s, the progress rate a and—in an enhanced approach—the product innovation rate V as well.

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M.3 Oil Price Dynamics in a Double Perspective Modified Hotelling Rule: Critical Role of Oil Inflation Expectations Before we consider the combination of portfolio approach and growth model, let us focus on a simple portfolio model which sheds new light on the well-established debate about the pricing of non-renewable natural resources (on that debate see, e.g., STIGLITZ 1974; DASGUPTA/HEAL 1979; SINN 1981; ROEGER 2005). The basic insight of the traditional debate is an intertemporal decision rule, which says that there will be indifference between producing today—yielding cash flow expressed in $, namely P − H (where H is the unit price of producing oil in $ units; P is the oil price in $)—and producing tomorrow. We assume that the producer of the natural resource-we will assume that this is oil-wants to invest the cash flow abroad. Producing today will bring (with i* denoting the world nominal interest rate; E stands for expectation, * for foreign variables) at the period’s end a unit revenue of i*[P − H ] if one assumes that the cash flow is invested abroad/in the USA; producing tomorrow (we denote the expected oil price as PE ) will generate a yield of (dPE /dt) per unit. Take the simple case of perfect foresight and we can derive from the equilibrium equation i*[P − H ] = dP /dt the equilibrium expression—after dividing by P : dlnP /dt = i*[1 − H /P ]. For the case of H = 0 this expression is the Hotelling rule, namely that the oil price inflation rate will be equal to nominal interest rate. If the ratio H /P were constant over time, the implication simply is that the growth rate of oil prices will be equal to the world interest rate times[1 − H /P ]. To the extent that monetary policy is expansionary, we should expect a short-term fall in the nominal interest rate, but a long-term rise in the interest rate, provided that the expansionary policy course raises the expected inflation rate. Moreover, if (denoting the US inflation rate of non-oil products as π * and the share of non-oil products on the price index by α *), we assume that the world real interest rate i* in the long run will be equal to the real growth rate of global output (dlnY*/dt) and we have i* = dlnY/dt + α *π * + (1 − α *)π *. Thus, we can indeed restate the equation as π α *[1 − H /P ] = [dlnY*/dt + α *π *][1 − H /P ]. From this equation, the profit-maximizing growth rate of the oil price inflation is obtained as π = [dlnY*/α ] + π . Turning back to the fundamental equation, we can write dlnP /dt = (dlnY*/dt + dlnP*/dt)[1 − H /P ] and assuming that H /P is constant (H := H /P ) the integration of that equation—with C denoting a constant to be determined from the initial period—yields (WELFENS 2008b, c): ln P (t) = [1 − H ][ln Y*(t) + ln P*(t)] + C

(8 )

From this we have that the elasticity of P with respect to world output and to the global price level (read US price level), respectively, is[1 − H ], which is smaller than unity. Therefore the growth rate of global oil price inflation should be influenced by global output growth and the global inflation rate. Note that our fundamental equation could be modified to include technological progress in the sense that over

M.3 Oil Price Dynamics in a Double Perspective

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time a higher share of the oil reservoir in a given resource site can be extracted. If the relevant progress rate—which must not be confused with a reduction of H in real terms—is denoted as a , we can write i*[P − H ] = dPE /dt[1 + a ]; assuming that H = ß R (R is resource extraction) and using the approximation 1/[1 + a ] ≈ 1 − a , we can state the equation i*(1−a )(1−ß R/P ) = (dPE /dt)/P . Let us assume for simplicity that ß R/P is close to zero (close to reality for the case of Quwait); we thus can take logarithms and use the approximation that ln(1 + x) ≈ x so that we get the crucial equation lni* − a − ß R/P = lnπE , where lnπE denotes the logarithm of the expected oil price inflation rate (taking logarithms requires to impose the assumption that the oil price inflation rate is positive). Thus in a supply-side perspective, we have for a given R in the short run the optimum price P = ß R/(lni*− a − lnπE ). In P −R space the supply curve is a ray through the origin. Hence the current oil price will be higher, the lower the interest rate i* (read: the US interest rate), the higher the rate of technological progress a , and the higher πE are. This is a simple supply-side perspective of the oil market and suggests that expansionary US monetary policy— reducing i*—will raise the oil price. Obviously, the best policy to reduce the oil price in the short run is to try to raise the progress rate on the side of energy users and thus to start policy activities which reduce the expected oil price inflation rate (e.g., an OECD initiative which would encourage substitution of oil through other energy sources or a global program to improve energy efficiency through more intensive research and development could be useful here). The above equation can also be rearranged in a way that the medium term optimum supply is determined, namely as a function of P , the world interest rate, the growth rate of technological progress in terms of "site deepening" and the expected oil inflation rate: Hence R = P (lni* − a − lnπE )/ ß . We will assume (with the parameter ζ > 0) that the change in the oil price is a positive function of the excess demand: dP /dt = ζ(Rd − Rs ). If one assumes that the current demand Rd for oil is a negative function of the oil price P and a positive function of wealth [A := M/P + eF*/P + P K/P], we can write Rd = −  P + A + R0 ( and  are positive parameters, R0 is autonomous demand for oil, e is the Euler number, t the time index; C , a constant to be determined from the initial conditions); and we get: dP /dt = ζ[− P +  (M/P + eF*/P + P K/P) + R0 − P (ln i* − a  − lnπ )/ß ] E

(9)

Here it is assumed that R0 , wealth and the term (lni* − a − lnπE )/ ß are exogenous P (t) = C e exp{−ζ[ + (lni* − a − lnπ )/ß ]t} E

+ {R0 +  (M/P + eF*/P + P K/P)}/

(9 )

[ + (lni* − a  − lnπ )/ß ]. E

This solution of the differential equation converges toward a stable steady-state solution {. . . }/[. . . ] if ζ[ + (lni* − a − lnπE )/ ß ] > 0; in this case we have a nonHotelling rule with the special case of a long-term price increase of zero. Moreover,

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the implication is that a critically high expected oil price inflation rate implies that that there is no steady-state solution, namely if lnπE > ß  + lni* − a : the price P (t) will rise at a constant rate; thus we have established a modified Hotelling rule for this specific set of parameters. As i* is equal to the real interest rate r* plus the expected inflation rate which in turn (with π denoting the inflation rate of non-oil products) is α πE + (1 − α )πE the critical condition can now be written—assuming for simplicity that α + [(r + α πE )/πE ] is close to zero—as[(r + α πE )/πE ] < −ß  + a + α : The critical condition thus reads πE > (r + α πE )/(a + α − ß  ) and hence a fall of the real interest rate or a exceeding a critical value or ß or  falling to a critical value could trigger a shift to an unstable regime in the sense that the economy moves from a setting with a stationary price P # toward a regime with a sustained oil price inflation. The model presented suggests that P will be stable over time for a specific set of parameters, however, if there is a critical change of parameters—including the expected oil inflation rate (which could be manipulated by various players in the global oil markets and certainly could be affected by major international political shocks)—there could be a phase of sustained oil price inflation. Oil price inflation expectations thus play a very critical role for current oil price dynamics. The steady-state solution—if there is one—depends on autonomous demand for oil, real money balances, the real price of stocks P /P and the real stock of capital K as well as on the net real claims on the rest of the world (eF /P). The higher e/P—we assume P* as given—the higher the equilibrium oil price level will be. Thus we have a positive long-term relationship between P and e. Portfolio-theoretical Approach to Oil Markets An alternative model with which to understand the oil price developments involves a portfolio-theoretical approach, and it is interesting to consider to which extent the implications are in line with the modified Hotelling rule established here. Let us consider such a portfolio approach in a US perspective so that all assets are denominated in $. We thus consider foreign bonds, money and oil as the three relevant assets. We assume that the share f of foreign bonds is a negative function of i and the expected oil price inflation rate π ; and a positive function of i* := i* + a (a is the expected depreciation rate). The desired share of oil (u ) in the portfolio is a positive function of π , a negative function of i and a negative function of i * (here the budget constraint is n + f + u = 1). The budget constraint reads A = M/P + eF*/P + PV /P so that in the modified portfolio model which contains the money market equilibrium line (MM curve), the equilibrium line for foreign bonds (FF* curve) and the equilibrium line for the oil market (VV curve), only two of the three equations are independent. Thus one can determine in the short-run market—ignoring the production function—the exchange rate e and the resource price P .

A = M/P + eF*/P + P V/P M/P = n (i, i *, π )A

(10) (10 )

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439

eF*/P = f  (i, i *, π )A

(11)

P V /P = u (i, i *, π )A

(12)

In an e−P diagram, the MM curve has a negative slope while the VV curve— showing the equilibrium in the oil market—has a positive slope. An expansionary monetary policy (through an expansionary open market policy: dM is raised as the central bank buys foreign assets) will bring about a depreciation and a rise in the oil price P . If we assume that the oil producer in country II has a target price (in domestic currency) of P0 * , there is a problem to the extent that dlnP /dM < dlne/dM: The price in foreign currency is P* = P /e; as P = eP * a target price line P0 * implies that E1 cannot be a stable new equilibrium point (see Fig. 107). Rather, as the oil producer from country II is assumed to have market power, it would rather fix the oil price in $ at the price P2  instead of P1  . Disregarding this strategic aspect of market power, one may argue that our portfolio-theoretical approach to oil price determination is in line with the logic of the modified quasi-Hotelling rule established above. VV0

e

p0*’’

E1 e1

F E0

e0

Fig. 107 Exchange rate and oil price determination in the hybrid portfolio model

MM0

B 0

p0’’ p1’’

p2’’

MM1 p’’

M.4 Stock Market Analysis and Hybrid Portfolio Growth Model Here we will consider a portfolio model with money, foreign bonds and domestic stocks whose number is assumed to be equal to K, the stock market price index is denoted by P . In e−P space, the equilibrium line for the money market—under standard assumptions—has a negative slope while the stock market equilibrium line has a positive slope (thus we have an analogy to the portfolio model with money, foreign bonds and oil). In the subsequent model both process innovations and product

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innovations (V ) will be considered. It is assumed that the demand for money is raised (parameter λ > 0) if V is on the rise, because a higher range of diversified products implies a higher utility of holding money balances. A rise in V will also lead to an increase (parameter λ > 0) in the demand for stocks, since profits are expected to be raised by said rise in V. The demand for foreign bonds is a negative function of V (parameter λ < 0). The following model presents a new approach bridging portfolio analysis and growth analysis. The modified portfolio model puts the focus on the money market, the foreign bonds market and the stock market, and the basic assumption is that v, f and h—the quasi-shares in assets—depend on i, i * and z (the expected growth rate of the stock market price). For the case of a zero inflation rate, we will replace i by r. Methodologically, the steady-state analysis developed should not be confused with a non-evolutionary perspective of economic dynamics, rather the real world can be understood as being shaped by various shocks, including technology shocks. Calculating the steady-state solutions thus indicates a sequence of consistent, long-term equilibrium solutions. Moreover, as already emphasized it is possible to endogenize the progress rate and in particular to focus on the role of international capital flows (or trade). It is important to emphasize that the subsequent setup is for an open economy with capital flows. Thus in the growth model, the steady-state solution for the capital intensity k := K/(AL) and for output per unit of labor in efficiency units (y :=Y/AL)) must be considered. If one wants to consider an explicit portfolio bloc—with a focus on money, foreign bonds and stocks—with the interest rate i, the yield abroad i and the expected growth rate (z ) of the stock market price index, one will have to consider the subsequent system (13)–(16). Equations (13)–(18) are the basic system and deserve no further comment. The goal is to have an explicit solution. Equation (19) is derived by considering (14) and (16) in combination with (13) and (18); Eq. (15) can, of course, be ignored due to the budget constraint. Next we reformulate the Eqs. (14) and (16) in such a way that we have only {. . . }α on the right-hand side: Equating and reformulating gives (19) which indicates the equilibrium stock market price. A = M/P + P K/P + eF*/P

(13)

α

λ

α

λ

M/P = v(i, i *, z )A Y1−α V

eF*/P = f(i, i *, z )A Y1−α V α

P K/P = h(i, i *, z )A Y1−α V

λ

(14) (15) (16)

k  # = (s/(a + n)(1 + ϕ ))1/(1−ß)

(17)

y # = (s/(a + n)(1 + ϕ ))ß/(1−ß)

(18)

M.4 Stock Market Analysis and Hybrid Portfolio Growth Model



M/P + P K/P + eF*/P (P /P) = h AL 



M/P AL





α 

M/P + P K/P + eF*/P =v AL

(a + n)(1 + ϕ ) s

α 

441 αβ 1+ 1−β

s (a + n)(1+ϕ )

 (1−α)β 1−β

V

λ

V

λ

(19)

(20)

Rearranging and equating (19) and (20) yields   1 h M (a + n)(1 + ϕ ) 1−β  λ −λ V P = v AL s 

dP M d AL

=

  1 h (a + n)(1 + ϕ ) 1−β  λ −λ V >0 v s

  β dP h M 1 (a + n)(1 + ϕ ) (a + n)(1 + ϕ ) 1−β  λ −λ V >0 =− ds v AL 1 − β s2 s

(21)

(22)

(23)

  β h M 1 1 + ϕ (a + n)(1 + ϕ ) 1−β  λ −λ dP V <0 = da v AL 1 − β s s

(24)

  β dP h M 1 1 + ϕ (a + n)(1 + ϕ ) 1−β  λ −λ V <0 = dn v AL 1 − β s s

(25)

1    1−β   dP   h M (a + n)(1 + ϕ )  λ −λ −1 = (λ − λ ) V dV v AL s

(26)

the sign depends on λ and λ. Inserting (21) in (19) yields ⎡  1   β(1−α) α(1−β) λ s AL ⎣ 1 M α − α V e= P F* vP AL (a + n)(1 + ϕ )

(27)

&' %   2 M h (a + n)(1 + ϕ ) 1−β  λ −λ − V 1+ AL v s ⎡

de M d AL

=

  1−α   β(1−α)  α(1−β) s AL ⎣ 1 1 M α −λ V α  F* αv vP AL (a + n)(1 + ϕ ) %

&'   2 h (a + n)(1 + ϕ ) 1−β  λ −λ − 1+ V v s

(28)

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The sign is ambiguous. ⎡  1   β(1−α) −1 α(1−β) λ s AL⎣ P β(1 − α) 1 M α de − α V = ds F* (a + n)(1 + ϕ ) α(1 − β) vP AL (a + n)(1 + ϕ ) ⎤   1+β (a + n)(1 + ϕ ) 2 M h (a + n)(1 + ϕ ) 1−β  λ −λ ⎦ >0 (29) + V s2 1 − β AL v s ⎡  1  β(1−α) −1 α(1−β) β(1 − α) 1 M α de s AL ⎣ sP =− da F* (a + n)2 (1 + ϕ ) α(1 − β) vP AL (a + n)(1 + ϕ ) ⎤ 1+β    )  1−β   λ M 2 1 + ϕ h (a + n)(1 + ϕ λ −λ ⎦ ×V α + V <0 (30) AL 1 − β s v s ⎡  1   β(1−α) α(1−β) λ s AL ⎣ Pλ 1 M α de  − α −1 = − V dV F* α vP AL (a + n)(1 + ϕ ) ' 1   )  1−β   (a + n)(1 + ϕ M  h λ −λ −1 (λ − λ ) + V AL v s

(31)

The sign of the above equation is ambiguous: If λ > λ ; the sign for de/dV is positive. Explicit solutions are derived, and it is interesting that we get unambiguous multiplier results for many policy cases. The term h/v is interesting and a rather simple specification will give more insight: Assume that h = 1/(σr) and v = 1/(ε r) (with parameters σ > 0, ε > 0) so that h/v = ε /σ; in this simplified set-up, we ignore i * and z . One of the partial derivatives of the quasi-shares must be positive if at least one derivative is negative, since the adding-up constraint is otherwise not met. Here, we are not concerned with this aspect, since in a further step we will indeed include the bond market; thus, a negative partial derivative of h, v and f with respect to r is not a problem, as the partial derivative of b with respect to r is positive. If one assumes—in the context of a non-inflationary economy (with a positive parameter ε )—that f = 1/(ε r) and h = 1/(σr), one can replace ϕ with σ/ε . As regards the above multiplier analysis, we find that a rise in M/(AL) will bring about a devaluation if the savings rate is sufficiently high, while a rise in the savings rate will always bring about a devaluation. However, as regards the latter, one may well have to consider the case that a higher savings rate is the basis for financing more innovation projects and hence to raise innovativeness. A rise in the process innovation rate will bring about a (real) devaluation. If λ > λ , a higher degree of product innovativeness will bring about a devaluation; if λ < λ a rise in V could bring about—conditional on a certain parameter set—an appreciation. One should

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443

note that the case of inflation could be considered in the context of i = r + expected inflation rate, which is determined by the growth rate μ , (μ : = dln[M/(AL)]/dt) minus the growth rate of output which is equal to a + n. If one wants to consider a production with real balances (M/P)/(AL) := m entering firms’ production functions as a positive external effect of households holding money (WELFENS 2007), the production function (with ß denoting the output elasticity     of money) is given by Y = mß Kß (AL)1−ß−ß or equivalently Y/(AL) = mß k ß . Hence we have the following result for y in the steady state: 

y # = mβ {s/[(a + n)(1 + ϕ )]}β/(1−β)

(18 )

Inserting this equation in the portfolio growth model we get some modifications in the results: 

(P /P) = hm 

M/P AL

m

 β(1−α)

 = vm

 1−β(1−α)



 β(1−α)

M/P + P K/P + eF*/P AL



α 

M/P + P K/P + eF*/P AL



M/P + P K/P + eF*/P =v AL

α 

(a + n)(1 + ϕ ) s

α 

αβ 1+ 1−β

s (a + n)(1 + ϕ )

s (a + n)(1 + ϕ )

λ

(19 )  (1−α)β

 (1−α)β 1−β

V

1−β

V

λ

(20 ) V

λ

(20 )

Basically, the implication is that Eq. (21) is not changing and that the multipliers with respect to P remain unchanged. The real money balance m will raise the real stock market price in the steady state while the effect on e is ambiguous. Inserting (21) into (19 ) gives ⎡  1   β(1−α)  α(1−β) s AL ⎣  − αβ (1−α) m α −λ V α (27 ) Pm e=  F* v (a + n)(1 + ϕ ) % −Pm



&'   2 h (a + n)(1 + ϕ ) 1−β  λ −λ 1+ V v s

One could change the multipliers accordingly, but there are no qualitative changes. Next we explicitly specify—in a setup in which domestic bonds also are considered— the desired quasi-shares of assets (parameters: σ < 0, σ < 0, σ > 0, σ < 0), the bonds market equilibrium condition is given in Eq. (V): A = M/P + B/P + P K/P + eF*/P 

α

M/P = r σ A Y1−α V

λ

(I) (II)

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α

λ

α

λ

α

λ

eF*/P = rσ A Y1−α V P K/P = r σ A Y1−α V 

B/P = r σ A Y1−α V

σ



(P /P) = r m



M/P AL



B/P AL



σ

 β(1−α)

=r m



σ



 β(1−α)

=r m

M/P + P K/P+eF*/P AL



 β(1−α)

α 

M/P + P K/P+eF*/P AL



M/P + P K/P+eF*/P AL

(IV) (V)

(a + n)(1 + ϕ ) s

α 

(III)

1+ αβ

s (a + n)(1 + ϕ )

α 

1−β

V

λ

(19 )  (1−α)β

s (a + n)(1 + ϕ )

1−β

V

λ

(20 )  (1−α)β 1−β

V

λ

(32) Equating and rearranging (19 ) and (20 ) yields P =

  1 M (a + n)(1 + ϕ ) 1−β σ−σ  λ −λ r V AL s

Inserting (21 ) in (19 ) yields ⎡  1  β(1−α) α(1−β) λ s AL ⎣  − αβ (1−α) 1 M α − α V Pm e=  F* r σ P AL (a + n)(1 + ϕ )

(21 )

(27 )

&' % 2   )  1−β   M (a + n)(1 + ϕ  λ −λ − V 1 + r σ−σ AL s Equating and rearranging (20 ) and (32) gives  r=

M B



1 σ −σ

λ −λ

V σ −σ

(33)

Thus the real interest rate r is a positive function of B/M. Moreover, it is a negative function of V , provided λ > λ . The structure of (21 ) and (27 ), respectively, is similar to (21) and (27) and hence there is no change in the sign of the multipliers. From (33) we have as multipliers dr M d AL

  1−σ +σ −λ B M σ −σ  σλ −σ 1  =  V <0  σ − σ AL B

(34)

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445

dr dr dr = = =0 ds da dn   1 dr λ − λ M σ −σ  λ −λ −1 =  V σ −σ dV σ − σ B

(35)

(36)

the sign depends on λ and λ . An important result is dr/da = 0 and dr/dn = 0, as this shows neutrality of growth with respect to the real interest rate. Under the assumption λ > λ , a higher intensity of product innovations brings about a fall in the real interest rate. If we have profit-maximization in the steady state such that r = ßk ß−1 , the implication is that B/(AL)—according to Eq. (33)—is endogenous. Moreover it must hold that the value of stocks is equal to the discounted value of profits, so that we have P K = ßPY/r. Therefore, it holds that the price of existing capital (P ) is equal to the price (P) of newly produced investment goods. From (21 ) we find that we can thus rewrite the equation as (M/(AL))P =   V(Y/(AL))1/(1−ß) , where V is quasi-velocity which is defined as V := rσ−σVλ −λ . Hence we have derived a modified Fisher equation—with an income elasticity of the demand for money exceeding unity. A rise in the product innovativeness variable will increase velocity, provided that λ > λ . Note that in a set-up considering inflation, it would be necessary to replace in the portfolio equilibrium equations r by the nominal interest rate i; and i would also enter V. Hence, we have derived some important new results.

M.5 Conclusions This approach provides new insights into long-term economic dynamics of open economies and innovation. For the first time, the portfolio model of an open economy has been linked to the growth model of an open economy, and both process and product innovations have been analyzed. These findings give a theoretical basis for some of the empirical literature, with a focus on the links between stock market pricing and innovation dynamics. Basic arguments for considering oil markets in a portfolio balance approach were also discussed; linking such an approach with the production function would, however, be fruitful in a broad sense if one should consider a production function with labor, capital, knowledge and oil (or another non-renewable resource). Thus, we have presented some new thoughts on key problems of macroeconomic analysis. Based on these first steps we need, of course, more comprehensive and refined models. It is noteworthy that one could include welfare theoretical analysis in such new approaches, to the extent that the utility function contains both consumption and wealth. Furthermore, this also opens up new approaches to the optimum growth theory. Finally, the theoretical approaches presented explain global asset market dynamics—including oil price dynamics—in the context of the US banking crisis 2007/08.

N. Transatlantic Banking Crisis: Analysis, Rating, Policy Issues

N.1 Introduction The Transatlantic Banking Crisis has raised many critical questions. Standard economic analysis has assumed that financial markets are efficient and that there are few reasons to assume that financial market dynamics could derail the real economy seriously. Instead, the international banking crisis—starting in the USA in summer 2007—has shown that there are temporary bubble phenomena in the housing and asset markets: Financial markets are not efficient during critical periods. Financial market efficiency means that current prices and ratings reflect all relevant information and that a single interest rate is sufficient to describe the system of financial markets adequately. Instead, the crisis of 2007–2009 in the USA and Europe has revealed that one needs a broader analysis of various financial markets. As regards ratings, it has turned out that looking only at current ratings is not sufficient to reflect Value at Risk of banks (a synthetic indicator which summarizes exposure to risk), rather empirical analysis has shown that “rating momentum”— past changes of ratings—has to be included into the analysis (GÜRTLER/RAUPACH 2008). The fact that financial markets are imperfect has been emphasized by various authors, and the implications have been highlighted clearly with respect to crucial economic variables, not least foreign direct investment (FDI) inflows of the USA, which were empirically found to be a positive function of the real exchange rate (FROOT/STEIN 1991). In imperfect capital markets, a real devaluation of the US$ implies that equity of foreign bidders, expressed in $, is increased so that foreign bidders are more likely to be successful bidders in an international takeover bid. Moreover, shocks in 2007/2008 were strong enough to cause a global recession and thus the worst economic global decline since the 1930s. The downward dynamics were mitigated by exceptional policy measures in the USA and the EU; not only were massive fiscal policy measures applied but also unusually designed monetary policy—including quantitative easing—and massive injections of government capital to save big banks that often came close to bankruptcy either because of inherently weak risk management or simply because the end of Lehman Brothers (going into

P. J. J. Welfens, Innovations in Macroeconomics, DOI 10.1007/978-3-642-11909-5_14, © Springer-Verlag Berlin Heidelberg 2011

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Chap. 11 in mid-September 2008) destroyed the already weak confidence in the interbank market, so that sharp liquidity problems emerged and several banks were on the brink of bankruptcy. Stocks declined massively and there was some risk of a bank run in several countries. Governments intervened massively and government capital injections into banks plus massive interest rate cuts of central banks saved the system in the short term. The Transatlantic Banking Crisis is a historical shock that raises serious issues: • About the design of market economies and the role of economic policy; which institutional design is required to achieve stable and efficient national and international capital markets and a stable financial system? • How could the US financial system—banks and insurance companies, as well as hedge funds—achieve a share of 40% of all profits at the beginning of the twentyfirst century while the share of output of this sector reached only about 10%? One should expect that such a relatively high share of profits would attract a high rate of market entries; however, this has not been the case and thus, barriers to entry seem to play a role in the US financial system. At the bottom line, one also may be skeptical about such enormous profitability since this gives motivation and opportunity for fierce lobbying against reforms that are needed to achieve sustainable economic growth. • Are problems in US big banks and the subprime securitization business— subprime mortgage loans had been packed into a bundle of securities (“MBS: mortgage-backed securities”)—the main cause of the US financial market crisis of 2007/2008 or are hedge funds and biased ratings also crucial elements of the problem? The fact that hedge funds faced problems only in 2008/2009 might suggest that these funds did not play a major role in the crisis; however, subsequently there are indeed arguments for a key role of hedge funds—putting pressure on big US banks to raise the required rate of return—and biased ratings in causing the systemic crisis. Indeed, in the USA the pressure on banks to come up with higher rates of return that would match those of major unregulated hedge funds was so strong that the Swiss UBS set up its own hedge fund in the USA. • What is the dimension of the cost of the banking crisis? Marking down assets— often asset-backed securities (ABS)—has been a key feature in most big banks in 2007/2008, but there could also be a certain recovery rate on “toxic assets” where no market price was quoted for quite some time, as the underlying structures of the respective financial product innovations ’were quite unclear, and the respective markets were almost illiquid. While part of ABS are likely to recover and as stock market prices have also recovered in an unusual environment of nearly zero interest rates in most OECD countries in 2008/2009, there is considerable risk of further down-writing of assets, namely of government bonds: With spreads on government bonds of Greece, Spain, Portugal and some other countries rising strongly in 2009/2010, the implication is that the market price of the stock of bonds from these countries—largely held by financial institutions in France, Switzerland and Germany—will decline. Hence, banks and funds could suffer further massive declines in asset values and new losses, which in turn undermine the equity–loan ratio and hence the ability of banks to give loans to firms in the real economy.

N.1 Introduction

449

• Based on estimates of the IMF and the EU, one may argue that the cost of the Transatlantic Banking Crisis will reach 5–10% of the GDP of OECD countries— and much more in some other countries. Why did economists not anticipate this crisis—except for very few economists—and why did few macroeconomists understand that the massive financial system crisis would bring about a world recession; with strong peak to trough GDP reductions of about −8% in Japan in 2007–2009 and −6% in Germany and Italy, −5% in the UK, −4% in the USA and −3% in France and Canada (these latter figures are based on Global Insight data). At the beginning of 2010, the EU countries have devoted public expenditures close to 44% of GDP to support the banking system—most of these funds were guarantees; only 2.5% of GDP had actually been injected into the banking system, which is not very high if one considers the IMF’s estimate of € 900 billion in impaired assets (EUROPEAN COMMISSION 2009). The historical experience from banking crises suggests that the costs are typically about 13% of GDP, in extreme cases even slightly more than 50% (Indonesia in 1997). The European Commission has argued that the costs of rehabilitating the banking system of the EU could reach about 16% of the EU’s GDP. As regards the fiscal costs of the banking crisis, there are particular costs, namely the rise of debt–GDP ratios and the associated costs of higher interest payments. The rise of debt–GDP ratios caused by the Transatlantic Banking Crisis could reach about 20 percentage points in the US and the Euro zone, which—at a hypothetical 4% real interest rate—implies a permanent rise in government’s interest payments of about 1 percentage point of GDP. A paradox is that big banks placing government bonds in capital markets will draw considerable profits from this rise in the debt–GDP ratio; an increase that many of these big banks have caused in the first place by aggressive expansion strategies associated with excessive risk. The extreme reductions in central bank interest rates implies that the burden of a higher debt– GDP ratio is not really felt in OECD countries in the short run, but in the medium term, there will be a much higher real interest rate. Moreover, the very low interest rates of 2009/2010 in the USA and the EU have brought about high stock market price levels. The overall economic situation in the EU and the USA at the beginning of the second decade of the twenty-first century is unstable since the nominal and the real interest rate is unusually low. Moreover, one has to ask to what extent is there an additional potential for financial instability, namely in the Asian countries which after the Asian crisis of 1997/1998 largely followed the pressure of the IMF to implement western rules and regulations of financial markets (EICHENGREEN 2009). Not only monetary policy and financial market regulations of OECD countries will have to be analyzed in new detail. As deficit–GDP ratios increased sharply in many EU countries and the USA, as well as in some developing countries affected by the global recession, there was a strong rise in debt–GDP ratios—causing new problems in the EU with the Stability and Growth Pact and the convergence criteria, respectively. The international banking crisis has led to an economic crisis in the USA and Europe on the one hand, on the other hand a series of national, supranational and

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multilateral policy reforms have been adopted within a few quarters. This includes setting up the G20—standing for new unclear international governance structures— and also a series of measures adopted in individual countries and in international organizations to stabilize OECD countries and the world economy, respectively. While many countries have experienced a certain economic recovery in 2009/2010, it is unclear whether the reforms adopted and discussed are adequate to avoid future repetition of a transatlantic banking crisis; moreover, there are also new problems, e.g., finding an exit strategy for central banks that have adopted extremely low interest rates and quantitative easing; moreover, spreads on sovereign debt in several EU countries have risen strongly in 2009/2010. Obviously, bubble dynamics have played a certain role in the Transatlantic Banking Crisis. Modern Economics has only looked at the problem of bubbles in some fields; e.g., BERNANKE/GERTLER/GILCHRIST (1999) have looked at variants of the financial accelerator and KIYOTAKI/MOORE (1997), who have emphasized that real estate prices can have negative effects on aggregate demand via collateral constraints. SHILLER (2007) has argued that the housing bubble in the USA was the key source of the financial market crisis in the USA, along the contagion of price expectations that were too optimistic (survey by CASE ET AL. 2003). A somewhat different view from KAHN ET AL. (2007, 2009) argued that since 2004 there was a decline in US productivity growth and the associated expectations might have weakened growth dynamics, thus leading to the economic downturn in the USA. Inflated credit ratings were also considered as a contributor to the financial market crisis by many observers and it is, therefore, important to develop an approach that can explain the role of rating, particularly in the context of complex assets that give an incentive for rating shopping (SKRETA/VELDKAMP 2009). ARTUS/VIRARD (2005) and WELFENS (2009) have argued that excessive required rates of return on equity of US banks and hedge funds, respectively, have been driving forces of excessive risk-taking; weak risk management systems in some major banks in the OECD were already observed by the BIS (2000). Other key elements of the transatlantic banking crisis have also been identified, including loose US monetary policy, but it is not fully clear why risk premiums have fallen so strongly in the later stage of the credit expansion in the USA (GOODHART 2007). There is, however, a rather clear pattern of international contagion—but the global recession following the financial turmoil in the USA and the EU is explained by traditional macroeconomic models only to some extent. Recent improvements in model building include the Commission’s QUEST III model in which collateral constraints and bubble dynamics have been included (RATTO/ROEGER/VELD 2009). DSGE models continue to be a useful workhorse for international macroeconomics to some extent, provided that such models are adequately modified so that they can e.g., explain US economic dynamics and allow one to focus on fiscal policy efficiency in the new setting of quantitative easing or a zero interest rate policy of the central bank (TURRINI/ROEGER/SZEKELY 2009). However, there are good reasons to also consider alternative modeling approaches. Financial market globalization was reinforced in the decade following 1995, and one might expect major benefits from sustainable globalization. There is no doubt

N.1 Introduction

451

that securitization of loans and FDI of banks as well as internationalization of the banking business has intensified over time (DEUTSCHE BUNDESBANK 2008; ECB 2008); the home bias in the use of savings—emphasized in earlier empirical analysis of FELDSTEIN/HORIOKA (1980)—has reduced over time, particularly in the EU (JUNGMITTAG/UNTIEDT 2002). While one should expect considerable benefits from financial globalization organized in a consistent framework, such globalization can have negative national and international collateral effects if the institutional framework is incomplete and inconsistent: a low degree of transparency resulting from this could raise systemic risks and generate negative international external effects. The international banking crisis which started in 2007 in the US subprime mortgage market shows that the institutional framework is incomplete and that there is a broad challenge for the EU countries and other OECD countries as well as China, India and other NICs in implementing a new global financial architecture. On the one hand, the transatlantic banking crisis is a historical shift associated with considerable internal contradictions in the US economic system, on the other, 2008/2009 marks the end of the rule by the G8 and the switch to a much broader G20 group. The analysis takes a look at the dynamics of the banking crisis (Sect. 2), considers some critical reform proposals (Sect. 3);—moreover, Sects. 4–6 look at theoretical aspects of financial globalization and macroeconomic modeling. Section 7 draws key policy conclusion. One key element of reform suggested here is a new tax system which is based on taxation of both profits and the variance of the rate of return on equity: This would encourage bankers to take a more long-term view—such an institutional innovation is considered to be a key element of five crucial reform steps which are presented as an alternative to the long list of reforms adopted at the G20 summits. A critical issue also concerns the role of rating whose role has been reinforced under Basel II. However, there has thus far been no adequate analysis of the role of rating in a macroeconomic perspective, and without such a perspective, it is impossible to fully assess the role of rating; both micro prudential and macro prudential aspects have to be considered. As regards the role of bubbles, tax policy could have a larger role than monetary policy. Part of the neoclassical paradigm is useful, however, there also some doubts about standard approaches: The Transatlantic Banking Crisis suggests that bounded rationality often is a better concept than strict long-run profit maximization approaches; moreover, excessive short-term speculation, lack of rational prudential supervision and a poorly organized financial innovation system in the USA and the EU have contributed to the international crisis (Goldman Sachs’s financial innovation of a currency swap for the government of Greece, based on a fictitious forward exchange rate is one of the problems encountered in international financial innovations). The approach presented here draws on several analytical elements and is a modest contribution to overcoming certain paradigms in Economics which have turned out to be unconvincing. Rigor without relevance is doubtful.

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N.2 The Dynamics of the Banking Crisis There are several questions one has to raise and some approaches to the US dynamics present strange explanations for the US banking crisis. Let us consider a few examples: • One possible version of the ultimate cause of the US subprime crisis in 2007/2008 is that previous governments, including the Clinton Administration, had emphasized that a higher share of the US population should realize the American dream—not just the middle class but also the lower income strata of society should be able to buy a house, meaning that more long-term and cheaper mortgage financing would be needed. Given the modest financial literacy of low-income households and opaque financing schemes in the mortgage market—often based on teaser interest rates in the early years of the mortgage contract—too many loans were given to subprime customers, resulting in the overexpansion of the loan market and the securitization business, respectively, which finally brought about the collapse of the subprime market, and from there on started the destabilization of the whole financial system. There is no doubt that the US subprime market has played a crucial rule, but the deregulation of the US financial system (which started under the Clinton Administration) had broader flaws, that were not discovered and criticized by leading economists within the US administration— say those working at the Council of Economic Advisors. Rather, one had to read it in a report by the US DEPARTMENT OF DEFENCE (2006), which pointed out that predatory lending had become an increasing challenge for people in the army, as problems for soldiers to get security clearance dramatically rose in the period between 2000 and 2005: The number of problematic cases increased by 1600% and 90% among the non-clearances were related to serious financial problems (alcohol and drug abuse were responsible for most other cases). It is absolutely unclear why the US political system did not react to these dramatic figures. In principle, larger strata of society could have realized the American dream, but more transparent markets and stricter supervision would have been required, along with other measures, in favor of financial stability and sustainability, respectively. • There are economists who argue that the massive fall of the US interest rate under Greenspan—in the wake of the dotcom bubble and the September 11 attack in 2001—are mainly to blame for the overheating of the loan market. There might be a grain of salt to it, namely in the sense that the Taylor rule would have suggested a rise of central bank interest rate already in 2002/2003. However, the question is why a postponed rise of the US interest rate then triggered such a disaster, not only in the USA but in Europe as well. • Some bankers in the EU claim that bad luck and a sudden confidence shock in the summer of 2007 are to blame for the Transatlantic Banking Crisis. At the same time, certain bankers argue that 25% rate of return on equity is required as a normal competitive benchmark—set by successful competitors in the USA. This view, however, is quite doubtful, since the US benchmark is one that is established by big banks that are too big to fail; therefore, there is no true competitive bench-

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mark. Few economists voiced their criticisms early against such a high required rate of return: ARTUS/VIRARD (2005) in their French book, indeed pointed out that such a high yield can only be obtained by incurring higher risks than in previous periods. Looking at rates of return on equity in industry in OECD countries in 1970–1994, one would typically find them to be 15–18% (OECD 1995), and with respect to most industries, one may emphasize that those yields were achieved under competitive conditions. Bankers in the EU certainly are right in pointing out that there are risks to be taken by US banks with mega profits—leading to relatively high stock market prices—however, the correct economic argument, it seems, is to point out that US big banks facing soft budget constraints (this is the “too big to fail” problem) are causing negative external effects in the USA and the world economy; the costs of the US/transatlantic banking crisis in the Eurozone is, among other things, an increase of government debt–GDP ratios of 3 percentage points within less than two years and—based on EU projections—about at least 10 percentage points within five years after the outbreak of the crisis. Such negative external effects generated by US banks do not only imply that the true US rate of return on capital is lower than banks’ report indicated. Such negative external effects also require countermeasures by government(s) and a Pigou tax in the US or EU capital import levies, which would be adequate policy options within a ‘second best’ concept. Since capital markets are so important for financing innovations and since effective implementation of capital flow taxation is difficult and costly one may rather consider the alternative, namely to adjust the institutional framework in the USA and the EU in such a way that taxation on capital flows can be avoided. The widespread fervor of proponents of free international capital flows overlooks the fact that a world economy with lack of competition in the banking sector of various big countries occasionally creates serious spillovers and dangerous instabilities within the world economy. The switching to aggressive bonus schemes in so many banks and pressure from stock markets—calling for higher rates of return on equity—which encouraged international diffusion of such incentives implied an interesting self-selection process: Risk-loving new traders joined banks and funds and economists who could have told what a realistic rate of return could be were rarely hired, but instead physicists with no idea about Economics but with strong mathematical and statistical capabilities joined ranks in banks. It was the Queen of England who asked during her visit to the London School of Economics in November 2008 the question “why did nobody foresee the crisis?”. In a letter to the Queen, the British Academy gave an answer that basically argues that “many people did foresee the crisis. However, the exact form what it would take and the timing of its onset and ferocity were foreseen by nobody.” This is a way to say that not many people really foresaw the crisis and it points to obvious problems in Economics as represented by standard paradigms. • A crucial element of building wealth and raising value added in market economies is trust and confidence. Interbank markets strongly relied on confidence among banks whose top managers trusted that market partners operated as solid banking partners—historical records and the information conveyed by reliable balance sheets were two pillars for such confidence, that are immaterial production fac-

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tors in the financial community and financial markets, respectively. Confidence is important in markets operating with asymmetric information. It is indispensable in markets in which moral hazard is a potential problem (raising equity stakes of market participants could be an alternative but it comes at considerable cost). Why governments allowed increasing off-balance sheet activities to have destroyed the value of information obtained from banks’ balance sheets is unclear—the consequence was a self-inflicted market for lemons problem, which contributed to the collapse of the interbank market in the summer of 2008, when managers in most banks started to become suspicious of the effective asset quality in the total portfolio of other banks (including their special entities). The end of Lehman Brothers was a signal to everybody that obviously no bank was safe in principle, and the collapse of the interbank markets in the USA and Europe was the visible short-term consequence thereof. The economic disaster, which was now to be anticipated, made governments on both sides of the Atlantic come up with a clear message that all systemically relevant banks would be bailed out if necessary. This message stabilized the banking sectors; however, it reinforced the structural inefficiencies in the banking sector and the insurance sector—in the USA, the mainly concerned AIG, whose payments to Deutsche Bank, Goldman Sachs and others were effectively secured by the US government’s rescue packages for AIG. Prudential supervision of AIG in the USA and the UK was extremely weak and together with other blunders of prudential supervision of banks is almost like cabaret: Rating agencies pretended to work hard but in reality worked poorly (USSEC, 2008), prudential supervisors achieved world class format while e.g., the head of the German supervisory agency, Mr. Sanio, explained in his preface to BAFIN’s annual report of 2008 that his agency was largely surprised by the developments in financial markets—many economists knew since early 2006 that many US developments were quite doubtful; managers of major banks emphasized in reports to their stockholders that their expansion strategies were conservative while in reality they were seeking top yields in combination with high risk. The US government argued that a Financial Sector Assessment Program (FSAP) on the USA was not necessary and that the IMF should indeed rather invest resources for looking into countries with weak financial markets—it was only in 2007 that the Bush Administration agreed on an FSAP but the world still is waiting for this report which shows how weak the IMF obviously is. At the same time many economists argued that the wisdom of free international capital markets was reflecting rational decision-making of banks and hedge funds which thus guided investment decisions in an optimal way. Rarely has one seen such great contradiction between reality and Modern Economics. • For many economists, the Transatlantic Banking Crisis holds an unwelcome analytical message: Financial markets are not efficient during certain periods, and one may argue that this is not surprising given the many legal battles over insider trading in the US and other OECD countries. Insider trading is concerned with the problem that banks give information in a preferential way to big customers (repeatedly a problem in the USA) and that top managers buying or selling stocks of their own companies can manipulate stock prices and result in considerable

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excess rates of return for about two weeks—until other market participants finally realize the publication of insider transactions and that they adjust their own portfolios; the UK has introduced a one month blackout prior to the publication of quarterly company results, in order to minimize insider trading problems, and this seems to be quite adequate given empirical results by BETZER (2009). • Securitization is not really a new approach in banking. However, securitization at the beginning of the twenty-first century in the USA became increasingly more complex, since ABS were repackaged into ABS-CDOs, which typically would consist of a senior ABS-CDO with about 90% of assets rated A to AAA and a mezzanine ABS-CDO in which, still about 65% of assets had top ratings; the share of residential MBS packed into the ABS-CDOs strongly increased in the seven years after 2000, from about 1% to 37%, but neither markets nor supervisors complained—to the surprise of many observers, risk premia fell even in the period from 2003 to 2006 in the USA, and this suggests that markets were not really working. Rating agencies with often-sloppy work obviously have contributed to this “wonder on Wall Street” and the partially artificial boom associated with the fabulous low costs of capital. In principle, rating gave somewhat general information about the probability of default, but it did not effectively consider the potential problem of an increasing positive correlation between yields and risks of underlying assets. If such correlation dynamics should occur, there would be insufficient diversification (unless the majority of market participants quickly reacted, which they did not), the value of assets would decline and the price of risk associated with the respective portfolio should increase. The junior tranche of ABS-CDO might even outperform the senior tranche in periods of turbulence, in the sense that the value of the senior tranche might fall even more than that of the junior tranche, as exemplary results for periods with rising correlations of yields show (MÄHLMANN 2009)—a mystery to many bankers and supervisors unfamiliar with professional risk analysis. As a result of the naïve understanding of ratings in many banks and the lack of adequate risk management in most big banks in the USA, the UK and some continental EU countries—all of these weak points were ignored by prudential supervisors—the start of the subprime crisis in the USA quickly derailed the whole financial market system of European countries, including Switzerland. Losses of banks in 2007–2010 certainly will exceed $ 2000 bill., with more to come in the near future. As monetary policy in the USA and UK has become quite expansionary—partly based on quantitative easing—since the nominal interest rates in the USA and the UK were close to zero in 2009, there is a new challenge, namely that the $ becomes subject to carry trade, while speculative capital flows out into Asian countries and other countries create new bubbles and instabilities in the world economy. The standard perception up until the US financial market crisis was that the USA had the most integrated and liquid financial markets in the world. And what about Western Europe? Due to the combination of the EU single market and the introduction of the Euro, the Euro zone has made progress in financial integration. Just a few years after the start of the Euro zone and the ECB, it was argued

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by GILCHRIST/HERAULT/KEMPF (2002, p. 10) that risk-free financial markets had fully converged within the Euro zone so a unique, risk-free market had emerged. Still financial markets—broadly defined—remained somewhat fragmented (GROSS/LANNOO 1999), and compared to the USA, there was a predominance of bank credits relative to securities. In the Euro zone, economic activities rely more on bank credits than in the UK or the USA. HURST/PEREE/FISCHBACH (1999) have shown that banking credit accounts for more than 50% of financial intermediation in the Euro zone, which clearly exceeds the UK and US figures of 32% and 20%, respectively. CECCHETTI (1999) has highlighted considerable differences across countries in the Euro zone. For example, banking credits represented 80% of financial intermediation in Ireland and 39% in Finland. Hence, the structure of financial systems differs across countries in the Euro zone, which should, in turn, affect the transmission of monetary policy. To the extent that frictions in financial markets exist—a prominent topic since the Transatlantic Banking Crisis—there could indeed be negative impulses from disturbances in the financial sector to the real economy; in principle, the financial accelerator (BERNANKE/GERTLER/GILCHRIST 1999) could, thus play a role in the Euro zone (GILCHRIST/HERAULT/KEMPF 2002). However, the European Commission has, to some extent, tried to create a more homogeneous EU single-financial market, namely by adopting the Basel II rules, which emphasize minimum capital requirements of banks based on risk-weighted liability indicators. The incentives provided under Basel I rules (still relevant in the USA in 2009) are doubtful to some extent; e.g., there was a strong incentive for banks to sell the first loss-piece of structured products—requiring high coverage through equity capital—which in turn implied a weak incentive for banks to consider what type of assets were really contained in the structured products related to securitization. Big banks in many OECD countries were ready to take all kinds of risk, but the risk management of banks was poor in many cases. The BIS (2000) report on stress testing reveals that not all big banks had stress testing. This is surprising, and one would have liked to get such information—including the disclosure of the respective bank’s name. It seems natural to think that stockholders of such banks would be entitled to get all relevant information on the quality of corporate governance of the respective bank. Even the results of supervisors looking into banks have not been disclosed to stockholders. Then how could owners of such banks be expected to be responsible shareholders? Had managers known that weak risk management would quickly become known to the shareholders or the general public, those managers would have been likely to adopt a more sound strategy for their respective banks. The USA postponed the adoption of Basel II until 2010/2011 and, thus, the run-up to the banking crisis in 2007/2008 was based on the standard capital requirement of the Basel I rules. At first sight, even under Basel I rules there should not be much reason to worry about the stability of the banking system, since regulations require internationally active banks to fulfill a minimum equity capital–loan ratio of 8%. However, the 8% requirement is costly for banks, in the sense that bank managers might wish a higher leverage—thus raising the rate of return on

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equity—and could, therefore, seek raising the share of off-balance sheet activities, something to be regarded as attractive. This problem indeed occurred in the run-up to both the US banking crisis and the international banking crisis. Few economists have considered the role of bank regulation on macroeconomic development. For instance, BLUM/HELLWIG (1995) have presented a model in which a negative shock to aggregate demand lowers the ability of firms to service their debts to banks, and this, in turn, could reduce equity capital of banks and—because of capital adequacy requirements—thus, reduce bank lending and investments of the industry. Under Basel II, there is a more differentiated approach with regards to minimum capital requirement. The new approach measures bank capital and portfolios on the basis of risks, so that 8% applies to a risk-weighted portfolio of the bank. Moreover, there is a distinction between tier-1 capital, tier-2 capital (8% requirement) and tier-3 capital. Based on the method chosen for risk assessment—external rating or two alternative internal rating approaches—the capital requirements will slightly differ. The basic logic of the Basel I/II approach is that an individual bank will face favorable survival prospects if its equity capital–loan ratio is sufficiently high; with regards to an individual bank, a high equity ratio is considered to serve as a cushion against adverse shocks. This logic, however, is flawed at the aggregate level, as can easily be shown (WELFENS 2010). The euro zone’s financial market stability was relatively satisfactory in 2008/2009, while the epicenter of the banking crisis was in the USA and to some extent in the UK, where banking supervisors had followed a similar benign neglect-attitude as their counterparts in the USA. In the euro zone, Spain (CALVO-HORNERO/SANCHEZ 2010) and to some extent Italy pursued rather strict regulatory approaches, which have helped them avoid facing major subprime problems. However, the large share of the construction sector and the high share of foreigners—often from financial centers—investing in Spain made the country vulnerable to the crisis of the real estate sector in the leading OECD countries. The US subprime mortgage markets were the trigger of the financial market crisis in August 2007, but there is no doubt that the whole US banking system was off-course with respect to sustainable banking in 2007. It is quite important to understand what went wrong, since successfully fighting the crisis requires measures based on adequate theoretical analysis. While the G20 meeting in Washington, DC in November 2008 came up with a long list of 47 measures to be considered, it is doubtful that the key reform elements necessary were on the radar screen of policymakers. Overcoming the strange confidence crisis among banks is one of the key challenges as is a more realistic and more long-term profit maximization strategy of banks and other actors in financial markets. Better regulation and more regulation for big banks in the USA and other OECD countries are also high on the agenda. Beyond the financial sector—shaped by high innovation dynamics, high volatility in 2008 and declining confidence among banks—the focus of policymakers is on the real economy: Restoring high growth in OECD countries might be difficult. Financial markets are crucial for financing investment and innovation; thus, they are indispensable for economic growth (SAINT-PAUL 1992). Asymmetric informa-

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tion and moral hazard problems are specific aspects of financial markets and thus financial markets are not working perfectly. There could be credit rationing under specific circumstances (STIGLITZ/WEISS 1981). The risk of bank runs is specific to the banking sector and hence the confidence of depositors and depositor protection are crucial elements of the institutional setup in the banking industry (DIAMOND/DYBVIG 1983). From a theoretical perspective, there are sound arguments for why there should be ex-ante rules—regulations—for banks (DEWATRIPONT/TIROLE 1995) and not simply an application of the general competition law whose rules apply ex post, except for the field of merger control. Central banks are interested in systemic stability, as turbulences could undermine the effectiveness of monetary policy, and certainly investors and the general public have a strong interest in systemic stability (DE BANDT/HARTMANN 2000). For EU countries eager to create capital-based pension systems—as a complementary element to pay-asyou-go systems—the stability of financial markets is also quite crucial. While many banks run stress tests, it is unclear to what extent such tests are tailored adequately. From an economist’s perspective, one may wonder whether prudential supervisors run simulations on the bankruptcy of individual banks. Part of the Economics research community was not really good in understanding the problems of the US subprime financing. For example, PEEK/WILCOX (2006) argued on the basis of empirical analysis that the growth of ABS markets had contributed to stabilizing housing investment in the USA. An important aspect of financial market developments concerns the links between financial innovations, investment and instability, which is a Schumpeterian perspective on financial and real instability (MINSKY 1990). Financial innovation such as securitization and asset splitting had already been created in the 1980s (BIS 1986). An increasing role for private equity funds has been observed since the 1990s, and such funds have reinforced the adjustment and innovation pressure on firms. In certain cases, however, they have also weakened the long-term ability of firms acquired to survive in the market (VAN DEN BURG/RASMUSSEN 2007). The innovation dynamics of the real sector in turn affects asset markets, in particular stock markets; patents affect the stock market prices significantly (GRILICHES/HALL/PAKES 1991). In imperfect capital markets, equity capital is important not least for financing international M&As, and a real depreciation of the currency—implying that foreign investors have a larger amount of equity capital expressed in the currency of the target country—will bring about higher FDI inflows relative to GDP (for the case of the USA see FROOT/STEIN 1991). Thus, the international banking crisis must be explained in a broader context. An interesting feature of the US crisis is the fact that the USA could still attract high capital inflows in 2007/2008, although its current account–deficit GDP ratio had reached 5–6% in that period. While conventional modeling suggests that high cumulated current account deficits imply a depreciation of the exchange rate (HANSEN/RÖGER 2000), the USA has experienced a rather strong appreciation of its currency in the second half of 2008, where a nominal appreciation reinforced the effect from the rise in the price level (followed by more deflationary pressure in 2009).

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These puzzling effects as well as other issues must be analyzed, and one may ask to which extent the USA is able to stabilize its economic system. While the USA as a large economy should indeed be able to stabilize its banking system through adequate policy measures, it is nevertheless obvious that a further acceleration of the banking crisis in 2010/2011—fueled by a strong US recession weakening banks further—could bring serious problems, as neither private US investors nor private investors from OECD countries are likely to be willing to recapitalize US banks on a broad scale. The US government had more or less provided $ 200 billion as a government capital injection—financed through the $ 700 billion TARP program—into US banks in late 2008, but already by early June 2009, the new US Administration allowed major banks to repay $ 68 billion. Since most banks had favorably passed stress tests organized by the government and the US Central Bank, banks anticipated opportunities to tap the stock market. Moreover, they wanted to get rid of the restrictions on manager contracts, which were part of the strings attached to government capital injections. Such strings were unwelcome, as foreign competitors not relying on US government capital injections could exploit the crisis, namely luring away skilled traders and top managers from major US banks. The transatlantic banking crisis intensified after the USA decided to let Lehman Brothers go bankrupt on September 15: A decision which was totally inconsistent given the previous bailout of the smaller investment bank Bear Stearns in March 2008; and taking into account that a few days later AIG, the giant insurance company, was to be saved by the US government. The bankruptcy of Lehman in the midst of the banking crisis has fully destroyed confidence in OECD interbank markets and thus represents a doubtful step on the part of the Bush administration. Freddie Mac and Fannie Mae had been rescued by government, not least under the pressure of China whose central bank held large amounts of bonds issues by those two semi-public mortgage banks.

N.3 Banking Crisis and Critical Reform Proposals At first glance, the US banking crisis started in subprime mortgage financing, as house prices started to fall in absolute terms in 2007; this unexpected fall of the housing price index reflected a change in the relative price dynamics in the sense that the real housing price index had increased over a decade after 1997. However, the strong rise of the real housing price index was followed by a sharp fall of the ratio of the housing price index to the GDP deflator in the USA (see Fig. 108). The absolute fall of the OFHEO housing price index in the USA implied serious doubts about the value of MBS largely held by special purpose vehicles (SPVs) of banks which had organized increasing off-balance sheet activities through SPVs. Most SPVs held large positions of ABS which represented loan portfolios which had been sold in national and international capital markets. The originate-to-distribute model which became popular in the late 1990s assumed that banks could easily sell loan portfolios in the capital market; banks created SPVs to unload ABS and to

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Fig. 108 Relative house price index (1991 Q1 = 100 for the house price index and the US GDP deflator). (Source: OFHEO and IMF, own calculations)

widen off-balance sheet activities—this seemed to be an ideal way to pursue via an unregulated subsidiary relatively aggressive expansion strategies in the sense that they aimed at achieving a high rate of return on equity. Hence the incentive for banks to broaden risk management was weakened and this held all the more as banks alternatively could not sell a loan portfolio but rather only the risk associated with that portfolio (we will refer to the relevant credit default swaps—the insurance instruments part of which was traded in the market— subsequently). As SPVs relied on refinancing through short-term commercial papers, the collapse of the US commercial paper market in summer 2007 forced banks to take the portfolios of their respective SPVs back into their own books—the credit lines which banks had given to their respective SPVs when setting up the SPVs were enormous and had not really been meant to be drawn upon. The very purpose of the large credit line was to get a top rating for the SPV and to thereby make sure that the SPV had low refinancing costs. A potentially dangerous effect of the originate-anddistribute approach (create a bundle of loans and sell it through the capital market) refers to the fact that selling or reselling ABS in the capital market to unregulated hedge funds implied the risk—from a macro-prudential perspective—that the respective hedge fund might have a large leverage ratio based to a considerable extent on loans from the banks which had sold the original ABS. The bank would argue that the loans were no longer on its books, as they had been sold through an ABS, but effectively the loans had entered the balance sheet of the bank through the rear entrance. Effective risk management of banks and consistent prudential supervision would have ruled out that such a case could happen at all.

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Falling house prices in the USA had undermined confidence of investors into MBS held by SPVs and problems with refinancing MBS indicated serious problems in the ABS market. The price of portfolios representing MBS related to the mortgage subprime market in the USA fell quickly in summer 2007. However, the crisis was not confined to the USA. In the UK, a bank run on Northern Rock occurred in 2007, and the government quickly decided to save the bank whose problems could have been anticipated if the regulator had more carefully studied the aggressive expansion strategy of that mortgage bank (MULLINEUX 2007). In early 2008, the UK government decided to nationalize Northern Rock and this became the starting point to heavy government involvement in the UK banking crisis. British banks had largely adopted similar business models as their US counterparts and several banks were involved in the markets for MBS/ABS. As refinancing of SPVs became more and more difficult in summer and autumn 2007 the prices of the respective assets fell strongly: Lack of liquidity in the markets became a major problem: Even A-rated papers obviously could fall strongly in the market price once liquidity was drying out. The British financial markets were largely following the US market developments. British banks were strongly active in the USA, but London was also the place where AIG FP, an AIG subsidiary specialized in CDS transactions was most active. Selling CDS for a bundle of loans—not for individual loans—had become a new business of AIG in 1998, and a few years later US investment banks were eager to get CDS for Collateralized Debt Obligations (CDOs), which in effect represented a bundle of loans. In the notes to the 2007 balance sheet, one finds information verifying that AIG FP had sold a large volume of CDS: $ 562 billion. It was only in October 2005 that AIG managers in New York became suspicious about AIG FP activities whose CDS transaction included about $ 80 billion on CDOs partly associated with subprime loans; while AIG FP stopped the subprime business in late 2005, other AIG subsidiaries continued with subprime investment—poor governance of AIG is visible here, and the largest quarterly loss ever recorded in the USA was one of the results of weak management: $ 61.7 billion in 2007.IV. The US government had to take over AIG in September 2008, with the federal government investing $ 85 billion in the first round and more in the year following, so that the price tag for the US taxpayer figured at about $ 180 billion by early 2009 (the market value stood at only $ 6 billion in mid-2009, which is a large discount compared to the top value of a market capitalization of $ 240 billion in December 2000). AIG had grown partly on the back of temporary hyper growth of US investment banking. In 2004, Wall Street Investment Bankers achieved a softening of SEC regulations, namely that the permissible leverage ratio was raised to 40—but in the end this softening only raised the speed of high-risk investment banking, and all major investment banks went under or were merged with traditional banks in 2008. There are serious doubts that value-added of investment banks on Wall Street were positive in the period 2002–2008; the losses incurred and losses imposed on other banks, firms and countries most likely have exceeded profits and wages paid in that period. Moreover, big banks in the USA—all too big to fail—obtained government capital and thus it seemed that those banks faced a soft budget constraint, a phenomenon

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which had been emphasized by KORNAI (1980) in his book about socialist command economies. While his argument referred to banks and firms, the US case is mainly limited to the banking system (and the problem of banks which are too-big-to-fail), but if ailing automotive firms and other sectors would also come under the umbrella of the US government, the soft budget phenomenon would gain in relevance. The $ 700 billion rescue package offered by the US Congress for saving the banks and insurance companies—to this sum one must also add some $ 250 billion for rescuing Bear Stearns and Fannie Mae and Freddie Mac—will have been spent by mid-2009, and there is some risk that the US government will have to come up with even higher amounts of capital injections, guarantees and subsidies in the coming years. The recession of 2008/2009 has to some extent aggravated the problems of banks and insurance companies, and depreciations of portfolios will become a serious problem again.

Market-for-Lemons-Problems Banks have lost confidence in each other, and the starting point was the growing tendency of bankers in the USA (and Europe) to avoid regulatory equity requirements by transforming loans into ABS which could be sold in the capital market and often ended up in the special investment vehicles created by the banks themselves. The banks’ expansion of off-balance sheet activities have thus created a market-forlemons problem; that is, there was increasing quality uncertainty among bankers who could no longer draw reliable information from balance sheets about the financial status of potential partner banks: The classical lemons problem (AKERLOF 1970) which had been identified as a potential source for market failure in goods markets is now visible in financial markets; with confidence among banks declining liquidity for many financial products has dried up. TAYLOR (2009) has argued that crisis management of the FED should be guided by clear principles and that the FED’s policy to simply swamp markets with central bank liquidity is doubtful in a situation in which confidence problems in interbank markets signal that solvency problems in the banking sector are part and parcel of the problem: This can be seem from the spread between the three-month LIBOR (relevant for short-term interbank lending) and the Overnight Index Swap (proxy for expected central bank rate in the coming three months): The spread was minimal— 0.1 percentage points—in early summer 2007, in August it jumped and reached about 1 percentage point as confidence among banks fell sharply, in October 2008, after the Lehman shock, it had reached 3.5 percentage point, by January 2009 the spread had fallen to 0.92%. Solvency problems cannot be solved by massive liquidity injections of the central bank, rather recapitalization of banks and measures that improve the quality of financial reporting of banks are required—the latter has not been emphasized by the G20 on the London summit of April 2, 2009, indeed, several OECD countries have softened accounting standards which artificially raise equity capital and create “accounting uncertainty” as banks are allowed to switch from

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quarter to quarter between different valuation standards. Even with some banks reporting profits in early 2009 one cannot be sure that this is reflecting sound banking since at the beginning of the twenty-first century Credit Default Swap growth was enormous—with the US company AIG being a global leader in the CDS market— while risk pricing was distorted (GOODHART 2007). High capital inflows in the USA and expansionary monetary policy also have played a role here. It is widely accepted that the US banking crisis started in the summer of 2007 when the housing prices started to fall and doubts about the substance of MBS spread, thus making the refinancing of special investment vehicles—with a strong focus on ABS/MBO—increasingly difficult. However, the sources of the fragility of US banks and financial markets dates back to the late 1990s when hedge funds with high rates of return on equity created enormous pressure for Wall Street Banks: • The unregulated hedge funds with their high rates of return—about 20% in the late 1990s—put enormous pressure on banks to come up with similar rates of return on equity. Twenty-five percent became a kind of magic number announced by top managers of US banks and with some delay also by bankers in the EU. Raising the return on equity became a top priority of bankers and stock markets, and the owners of banks quoted on the stock market cheered when top managers announced ever higher target rates of return—although basic Economics suggests that even a rate of return on equity of 15% would be quite remarkable if achieved over an extended period of time. The UBS in the USA has indeed created its own hedge funds. Many banks in the USA and the EU created off-balance sheet activities and SPVs to raise the rate of return; SPVs invested in ABS/MBS and CDOs—CDO are repacked bundles of ABS with specific tranches in terms of risk profiles—and relied on short term commercial paper for refinancing. This model collapsed once the participants in commercial paper market faced doubts about the inherent value of mortgage-based securities (MBS). With US real estate prices falling in 2007, doubts emerged quickly, and banks had to take the papers of their respective SPVs back into the balance sheet. The basic point is not that house prices can fall over time; the key problem is that hedge funds were unregulated and their indirect role for systemic instability was not recognized. Most critics looked only at the problem of leverage in hedge funds, but the associated high pressure on banks to come up with higher returns was largely ignored. US government representatives have argued that hedge funds were not part of the problem, as these funds faced refinancing problems only in 2008—rather late in the crisis— but this perception is flawed. If hedge funds could continue their activities in an unregulated way, the main trigger of the (US) banking crisis would remain intact. • Banks packed dozens of loans in ABS and sold ABS and related papers in the capital market. In many cases, the banks wanted to maintain the loans on their books but wanted to get rid of the risk associated with the loans; the financial innovation used for this purposed were the Credit Default Swaps, which banks bought from special service providers and insurance companies—but CDS in term were traded in the capital market, mostly in over the counter market. This market lacks transparency for both the prudential authorities and for the market as such.

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Regulators indeed allowed the CDSs to be sold around the world, and no one kept track of these transactions, although it would be wise to know those market participants representing the counterparty risk and whether they would be able to fully pay once the insurance case became reality. As lack of prudential supervision created a global veil of ignorance with respect to the allocation of CDS—there was no clearing house or global registry—currency markets and bonds markets are not only facing an impossible challenge, namely to correctly assess risk premia for various countries (it makes a big difference if most CDS were held within the US, the euro zone, the UK or China). Moreover, the market value of the underlying loan portfolios also became difficult to assess as it makes a big difference whether there is credible insurance for the loan and low counter-party risk, respectively. Allocation of CDS across countries remained opaque, and hence the efficiency of financial market pricing remained low. • Time horizons of managers and traders were rather short, and there were inadequate incentives for long-term investment horizons in banks. Many top bankers pursued high-risk strategies and generated high bonus payments for managers and traders as long as the economic boom—along with rising asset prices—continued in the USA and Europe. In the medium term—as asset prices fell—many banks, however, suffered high depreciations and losses from such “front-loaded” investment strategies. The typical assumption of most textbook Economics—namely that investors maximize a profit function over a very long (infinite) time horizon— was not realistic, rather a hit and retire approach was often observed. As long as the boom continued, one could hit high goals, and once a crisis befell the market, early retirement was the ideal option for managers naturally willing to incur big risks for their respective big banks. The following figure summarizes the key dynamics of the US banking crisis which resulted not only in the collapse of the commercial paper market and the interbank market in late 2007, but also in the US central bank and the ECB providing emergency liquidity to banks which no longer could obtain loans in the money market and the interbank market. Mistrust among banks in the euro zone is so great that more than € 100 billion in excess reserves were kept at the ECB during several weeks in 2008, although market rates in the interbank markets were higher than what could be earned at the ECB account. It is not surprising that the problems in US real estate market and US banks brought about a fall of the stock market price index in 2008; stock market prices in the euro zone also fell strongly in autumn 2008. Coping successfully with the banking crisis and avoiding repeating this crisis within a few years can only be achieved if the causes of the banking crisis are recognized and adequate policy reforms be adopted. The problems in the US and European banking sectors are not really surprising if one considers the early warnings emphasizing the risk of falling house prices in the USA—and ARTUS/VIRARD (2005), who warned that high rates of return on equity implied a high risk premium and hence incurring high risks. In fact the banking crisis is not a real surprise, and one has to blame both banks themselves and prudential supervisors in the USA and the EU to have allowed such

N.3 Banking Crisis and Critical Reform Proposals

Hedge Funds: High Rate of Return

6

S T O P

Refinancing through commercial papers Top ratings

USstock markets

US Real Estate Market; fall of house prices undermines confidence for ABS/MBS

1

465

US Banks: Required Rate of Return on Equity is Raised

2

EU Banks: Rate of Return is Raised

3 4a Creation of Special Investment Vehicles (SIV): Increasing Off-balance activities through asset-backedsecurities (ABS) and mortgage-backed-securities (MBS) 4b

7 8

9

Banks must take back ABS/MBS into their books; massive downwriting on assets

Write-downs on portfolios reduces confidence into banks 10

5 Central bank intervenes

11 Interbank market collapses

Fig. 109 Dynamics of the interbank market

chaos in financial markets to emerge. The US dynamics largely show that the big banks no longer understood the system they had created and that US policymakers had failed to implement a clear system of supervision—instead the USA had refused to adopt the Basel II rules which would have imposed at least a small amount of equity capital for extending large credit lines to special investment vehicles (in this perspective the UK banking sector looks better positioned than the USA). By refusing to adopt Basel II, the USA not only created an uneven transatlantic playing field for banks, but it also prevented greater transparency—in a world economy with high growth—from being achieved. The priority reforms are therefore obvious; they must correspond to the problems identified and should be adopted by the relevant policy layers: • Regulation of hedge funds: Hedge funds—largely active from tax havens—with more than € 0.5 billion should be required to register with the Bank of International Settlements; BIS must reserve the right to raise equity requirements if deemed necessary, and trading in CDS could be restricted. Hedge funds which do not

466

Innovations in Macroeconomics

comply with BIS rules must not be permitted to trade government bonds in any member country of the IMF; this clause might require that government bonds be traded only through international clearinghouses, thus excluding over-the counter trade—in this manner, tax havens would be subject to rules and guidelines set at the European and global policy level. • Banks must establish fully consolidated balance sheets, in the sense that a total balance sheet includes all off-balance sheet activities; banks which do not comply must face sharply restricted access to central bank liquidity. The ECB (the central bank) should encourage interbank activities by according different discount rates, namely a low discount rate to banks strongly active in the interbank market; banks with low activities in the interbank market would face higher discount rates. Thus one would have an incentive for banks to engage in the interbank market. The enormous expansion of ECB liquidity provision in euro zone interbank markets is a doubtful exercise if it were to continue in the long run; this would undermine both the efficiency of monetary policy and the incentive of banks to engage in the interbank market, which is normally a market important for the efficiency of the banking system—monitoring and signaling are crucial elements of the normal competition process in the interbank market. • A strange problem of the transatlantic banking crisis concerns the uncertainties about valuation of assets and the opaque term toxic assets clouds the serious problem that financial markets are expected to price assets perfectly as markets are efficient—but all of a sudden bankers have told the general public that no (adequate) price can be found for many financial assets, some of which are allegedly “too complex”. The critical economist understands, of course, that poor incentives for bank managers result from the standard procedure that bankers quickly repackage loans and sell them in the market under the ABS heading. What could be done to cope with the various problems? ABS products should be standardized in order to avoid complex pricing problems, and all CDS should be registered in a global data bank; a bank issuing ABS should keep 20% of the equity tranche in its books (this gives a strong incentive to really consider the risks contained in the loans which back the ABS) and declare its willingness to buy back the ABS product at 50% of the original price at any point in time, thereby avoiding pricing uncertainty even in the critical case that markets for specific financial products should collapse; the underestimation of liquidity risks, which was a serious element of the US/transatlantic banking crisis, must be avoided in the future. The 50% rule gives a strong incentive to bankers to carefully consider which loans they are bundling into a particular package and to whom the product is sold. New transactions with CDS should be possible only through a clearinghouse, and previous CDS transactions should be required to register worldwide—otherwise, confidence in markets cannot be restored (the EU/the USA have adopted steps into this direction in 2009). • Rating agencies must face new rules and should be required to obtain a license as proposed by the European Commission; in addition, there should be random checks and fines for poor rating accuracy. Conflicts of interests (in the traditional regime, banks placing a bond issue have paid the respective rating agency) must

N.4 Theoretical Aspects of Sustainable Financial Market Globalization

467

be avoided. Specifically, a two-stage financing procedure would be useful; banks, firms or governments wanting to place bonds in the market should pay into a pool, and this pool then would finance the rating process on the basis of competitive tenders. • A new tax regime is necessary for banks, funds and insurance companies. Taxing the profits () of banks should be only one basis for taxation; in addition, the variability of the rate of return on equity should be considered. The higher the variance (V  ) on the rate of return, the higher the overall tax rate to be applied should be. The tax (T ) to be paid by an individual bank j (subscript is suppressed subsequently) would thus be given by subsequent formula ( stands for profit, τ is the standard corporate tax rate relevant for profits and τV is the tax rate applied to the variance of the rate of return on equity). The tax formula would apply only for the profit exceeding one currency unit as the ln is part of the tax base for the variance tax—one element behind this formula is that an excessive variance translates into abnormally high profits, and this is taken into account by the second term in the subsequent tax formula. Banks anticipating such a tax burden would have an incentive to take a more long-term view and consider which sustainable business strategies are useful and attractive—as bank managers have an incentive to avoid very high rates of return on equity this automatically will encourage a lower propensity to incur excessive risk; this also implies less negative spillovers in the banking sector which will be more stable. The subsequent tax formula does not discourage growth of banks as such since the marginal tax rate approaches the standard corporate tax rate τ as profits approach infinity; the tax formula proposed here is: 1. T = τ + τV [V ln]; marginal tax rate dT /d will approach τ with  → ∞. Thus the tax proposed would not discriminate against economies of scale of banks. A variance tax would be a true innovation in the OECD tax systems, but such a tax is indeed quite useful since it would help to avoid excessive short-term decision-making which results in excessive risk-taking and high negative national or international external effects (i.e., international instability spillovers and problems related to systemic instability causes by non-sustainable bankers’ strategies). Indeed, a variance tax could be considered a special PIGOU tax which helps to internalize negative external effects. There could be a minor problem in recessions when the rate of return on equity falls, hence making the variance tax pro-cyclical; however, government could introduce a partial or full waiver for variance taxation in recessions.

N.4 Theoretical Aspects of Sustainable Financial Market Globalization International capital flows and financial market globalization is widely expected to stand for an efficient process which raises economic welfare worldwide. Should one

Balance Sheets: Full disclosure of bank’s activities: including all off-shore balance activities

AIM: Restoring Confidence

Hedge Funds: must register with BIS; equity requirement; hedge funds which do not comply with rules cannot trade in government bonds markets

AIM: Controlling Risk from HFs

AIM: Transparency, reduced transaction costs

ABS and CDS: Standardization of ABS products; 20% of the equity tranche remains at the bank and bank must declare that it is willing to buy back the ABS at 50% of the original price

Priority Reforms for Overcoming the International Banking Crisis

Table 27 Structural reforms to be adopted

AIM: Improving the quality of the ratings process; raising the quality of information

Rating Agencies: Agencies should face new rules such as obtaining a license; agencies should be subject to random checks, fines for poor work; two-stage financing

AIM: Encouraging long term time horizon of banks, funds and insurance companies (avoid short-term hit and retire strategy & inadequate bonus systems)

New Twin Tax Regime: Taxing profits and taxing the variability (variance) of the rate of return on equity

468 Innovations in Macroeconomics

N.4 Theoretical Aspects of Sustainable Financial Market Globalization

469

have some doubts here given the many distortions that have become apparent in the transatlantic banking crisis? Empirical evidence has to be established, but some theoretical reflections also are useful here. Let us consider a simple two-country approach to risk markets (a special niche of insurance markets: think of the CDS markets) where demand in country 1 is given by DD0 (see Fig. 4 ) and supply by SS0 ; in country 2 demand and supply are given by DD∗0 and SS∗0 . There is a market for risk (σ) in the home country (panel a) and a market for risk in the foreign country (panel b). Under autarchy, the price of risk p in the home country (country 1; e.g., the USA) is p0 and p∗0 in country 2. If countries should open up for both trade and capital flows, there will be excess supply in country 1 and excess demand in country 2. The world market price for risk—for credit default swaps for bundles of securities packaged in banks—is pW 0 . Country 1’s insurance industry has expanded (q2 is the supply instead of q0 in the closed economy). However, if there are negative national external effects in country 1—e.g., due to inadequate regulation or a confidence crisis in the medium-size banking sector, caused by big banks—the social costs of providing insurance against risk is given by SS01 instead of SS0, and hence the optimal allocation of resources would be different (at the initial global price for risk the welfare loss in country 1 is given by the area KJBA). Instead of being a net exporter of risk insurance services country 1 would be net importer of insurance services. Country 2 would be a net exporter. Moreover, the price of risk under efficient international allocation of resources would increase, the new price is pW1 (one may also note: An efficient allocation of resources implies a real devaluation of the currency of country 1 which makes FDI inflows into country 2 more likely; this at least is in line with the standard argument of FROOT/STEIN (1991) on the link between FDI inflows and the real exchange rate). If country 2 would like to offset the negative external effect in country 1, it might consider subsidization of the supply side in country 2. The problem is that the effect of this kind of quasiinternalization leads to a fall in the price of risk. To the extent that risk premia in various asset markets are interdependent, such a solution would cause an artificially low-risk premium in the stock market and hence there would be overinvestment. In a two-country model, the negative external effect in country 1 potentially implies a negative external effect in country 2 since comparing the social surplus at the initial world market price with the situation in which the price is pW 1 implies that the consumer surplus is reduced by A*E*B* while the producer surplus is raised by E*C*D*. There is a redistribution effect between consumer surplus and producer surplus which is equal to the area P*0 *E*C* pW 1 ; this effect is, of course, not neutral in terms of economic welfare if the risk insurance industry in country 2 is fully owned by firms from country 1 (to consider a special case which is quite interesting). As the supply curve in country 2 starts at a point G* which is above point G in country 1 the implication is that the cost competitiveness of country 1 is superior to country 2—as long as negative external effects in country 1 are not internalized. As long as there is no internalization in country 1 one may assume that there is a considerable likelihood that insurance firms from country 1 take over firms from country 2 (recall the logic of the FROOT/STEIN argument). This is inefficient in a crucial sense; corporate governance from firms from country 1 will dominate the initial type of governance

470

Innovations in Macroeconomics

in firms in country 2. If governance of firms in country 1 is a source of negative external effects in country 1 FDI has now become a bridge for creating negative external effects also in country 2 (the associated supply curve is not shown in the diagram). If ineffective regulation of the financial sector in country 1 is the source of negative externality, international regulatory competition—assuming dominance of country 1—will transmit the externality to country 2. Therefore, the standard question in the international regulatory debate is flawed, namely whether there might be a race to the bottom in terms of standards or regulation. The more important issue is whether or not a regime with negative external effects has the opportunity to dominate other regimes with no or small external effects. In the context of a system with flexible exchange rates, there are specific risks to be considered additionally. This concerns not only the problem of potential (Dornbusch-type) overshooting of the exchange rate. There also is the more general question as to why banks—after the failure of the Herstatt Bank in 1974—in Germany faced restrictions in holding open positions in the foreign exchange markets: The argument for the new framework introduced by the Deutsche Bundesbank obviously emphasized the risk of foreign currency speculation. From this perspective, it is absolutely unclear why individuals in EU accession countries could obviously take major exchange rate risks when taking loans in foreign currencies such as Euro or Swiss Franc (the majority of those financing cars or homes certainly are risk-averse, and thus it is absolutely unclear why banks would sell a loan denominated in a foreign currency—unless one assumes that banks have speculated that liability rules in the banking sector are not valid). Depreciations and in particular exchange rate overshooting could bring illiquidity, which for some individuals or firms indeed can bring insolvency once

p

p*

SS01

J

M*

M

SS*0

K SS0 pW1

D C

C*

D*

p* 0 A

pW0

B

A*

B*

H* p0 DD*0

G* G 0

a

F σ1 σ0

DD0 σ2

σ

0

σ1* σ0* σ2*

b

Fig. 110 Asymmetric negative external effects and international capital flows

σ*

N.4 Theoretical Aspects of Sustainable Financial Market Globalization

471

spreads are sharply increasing in destabilized markets (indeed in a global market system in which one finds a strange phenomenon such as “distressed markets”— dead markets—which, according to standard theory of a market economy, should not exist at all). If there is no level international playing field of financial services and if there is a serious too big to fail problem in many countries, the banks from the biggest country are likely to dominate with their standards the world economy. The role of the home bias in financial market services implies that the size of the home market will matter and the more economies of scale play a role in banking, the role of large banks from big countries is more important (the UK would have a larger home market if it were part of the euro zone). It is not obvious that big banks really have economies of scale or other advantages which generate a systematic advantage in terms of the rate of return on capital as the following figures for the USA suggest Fig. 5—the rate of return on assets was highest for medium-sized banks, not for the big banks in the period 1999–2007 (except for 2005 and 2006). Big banks might have advantages in the sense that they are politically well connected and thus the survival probability is higher than for small and medium-sized banks. Moreover, it is rather surprising to see that during the banking crisis the US dollar has weakened only transitorily—save heaven effects paradoxically support the source country of the transatlantic banking crisis. The US banks have dominated international financial markets for decades and the Washington consensus—as long as it was relevant (until the US banking crisis)—has reinforced the role of US banks. Asian countries and other countries were pushed to open up for banks from the USA and other countries and US banks were often strong enough to impose their standards—some weak ones, some good ones—on banks abroad. In a world with open capital markets, banks in the rest of the world will always face the challenge of being taken over by leading competitors, and for decades, the USA conveyed the impression that US banks were global leaders. Since the US banking crisis of 2007/2008, there have been serious doubts about this view; the fact that US investment banks were almost completely eliminated in 2008—and that value-added in this sector probably was negative in the decade following 1998 (taking into account all negative external effects)—is an indicator that the US banking system faced considerable inefficiencies. Will there be a sustained globalization process if the US banking system is so unstable and if the deleveraging of banks forces so many banks to cut back on the international business? A stable global market economy might be achieved if one has at least five ingredients: • A stable political system in major countries—this question is partly related to economic stability and sustained growth in the respective countries. • Clear property rights and full competition, including in the banking sector. There are considerable doubts that full competition in the banking sector can be established within the OECD or even worldwide. Larger integrated markets typically go along with bigger banks and if the too big to fail argument holds for many big banks in such markets, there is no effective competition. Rather bank managers

76 1.28 318 1.49 3029 1.36 5157 1.01 8580 1.27

Greater than $ 10 Billion

* Figure in brackets is without 2008

Total/ weighted average

Less than $ 100 mil.

$ 100 million to $ 1 Billion

$ 1 billion to $ 10 Billion

1999

Institutions/Asset Size

82 1.16 313 1.29 3078 1.28 4842 1.01 8315 1.19

2000 80 1.13 320 1.31 3194 1.20 4486 0.91 8080 1.16

2001 106 1.31 450 1.45 4118 1.17 4680 1.00 9354 1.31

2002 110 1.42 471 1.42 4211 1.18 4390 0.95 9182 1.38

2003 117 1.28 480 1.44 4285 1.19 4093 1.01 8975 1.29

2004 118 1.30 512 1.28 4339 1.24 3863 1.00 8832 1.28

2005 119 1.32 530 1.22 4399 1.17 3633 0.93 8681 1.28

2006

119 0.82 549 0.99 4425 0.99 3440 0.75 8533 0.86

2007

114 0.13 562 −0.15 4498 0.33 3131 0.31 8305 0.12

2008

104 1.12 (1.22) 451 1.17 (1.32) 3958 1.11 (1.06) 4171 0.88 (0.95)

2009*

Table 28 FDIC-Insured institutions by asset size categories: numbers, and returns on assets in percentage (1998–2008). (Source: FDIC quarterly banking profile, Table III-A December 31. 1999–2008, http://www2.fdic.gov/qbp/1999dec/qbp.pdf through http://www2.fdic.gov/qbp/12008dec/qbp.pdf)

472 Innovations in Macroeconomics

N.4 Theoretical Aspects of Sustainable Financial Market Globalization

473

will have every incentive to take big risks—while hunting for high rates of return on equity—and speculate that “adverse market developments” will open up the option to save the bank by economic nationalization through taxpayers’ money. The allocation of resources in such a setup will be inefficient, and it is doubtful that liberalization of capital flows under such conditions brings major economic benefits. One must consider the problem that there could be an increased problem of negative international spillover effects which might fully offset the traditional benefits from free capital flows. • Clear liability rules so that incentives encourage efficient allocation of resources. Liability rules in the US system of mortgage financing are incomplete since homeowners simply can move out and leave the key at the bank once the market value of the house is exceeding the mortgage. With 19 million empty houses at the end of 2008, the US economy represents an abnormally large excess supply in the housing market, and many of these houses will disintegrate over time as no responsible owner takes care of the house—in terms of economic welfare, the USA would have been better off if one had built fewer houses in the decade after 1997 than actually was the case. Strangely, during this decade the relative price of houses strongly increased in the USA (to some extent it is, of course, in line with the logic of the market that more houses are built if the relative price of houses is rising). In the EU, those who buy a house with a mortgage would face the risk that the bank can put claims on part of labor income earned by the buyer of the house if he/she fails to serve the mortgage. Nontransparent mortgages at low initial teaser interest rates and other marketing tricks common in nontransparent US mortgage markets represent doubtful developments in US real estate and mortgage markets. • Internalization of internationally relevant external effects should be realized. Markets can be quite useful as a means of internalizing certain external effects as is known, for example, from trading CO2 emission certificates. However, such internalization could not take place without governments adopting a broad international agreement under the heading of the Kyoto Protocol in a first step and the EU (and some other OECD countries) setting rules for trading of emission certificates. Emission certificate trading amounts to a market-driven flexible international Pigou tax which normally could not be imposed as government from country I (II) cannot tax producers or consumers in country II (I). To the extent that inadequate national regulations of financial markets lead to distorted market signals and hence negative international external effects, it is desirable to adjust national regulations in such a way that national and international negative external effects are internalized. • In the context of financial markets, part of the problem with regulation concerns potentially large international external effects which could, for instance, occur in the course of a bankruptcy of a major international bank. A full theoretical understanding of competition dynamics must include the probability of future bankruptcy and the direct and indirect effects of bankruptcy rules. There is an interesting paper available from the Swiss Banking Commission which has warned that the current rules and regulations in place within banks in OECD countries imply massive international negative external effects if there were a bankruptcy

474

Innovations in Macroeconomics

of any major bank with strong international business (EIDGENÖSSISCHE BANKENKOMMISSION 2008). As regards sustainable financial market integration, one can expect long-term globalization only under certain conditions. Financial market integration can generate considerable benefits by reducing international transactions costs, stimulating financial product innovations and efficiency gains as well as through a better diversification of risks. However, those benefits will not be generated automatically; in a multi-country world economy, the leading countries must implement a consistent international framework which creates a competitive level playing field on the one hand and establishes clear responsibilities on the other hand.

N.5 Macroeconomic Modeling Aspects The Transatlantic Banking Crisis has raised many unpleasant issues. One key aspect concerns the fact that standard DSGE models cannot explain the dynamics of the crisis and also ignore some key aspects: • New Keynesian DSGE models (survey CLARIDA/GALI/GERTLER 1999) explain deviations from equilibrium in the context of a setup in which stochastic disturbance variables affect aggregate demand and aggregate supply—in addition, there are nominal rigidities (e.g., sticky nominal wages) or real rigidities. If the variance of the stochastic process should strongly increase, nothing would happen in the DSGE models except that the variance of output would increase, but the expected value of the equilibrium real output would not be affected. This is highly implausible. An alternative approach is the hybrid medium-term macroeconomic model which combines Keynesian ideas with the long-run Solow growth model through a hybrid consumption function, according to which households determine current consumption on the basis of current real income and the expected future steady state (long-run) real income (WELFENS 2008a, b). • Similarly, in the discussion about risk and the required minimum equity–loan ratio, there is confusion between microeconomic analysis and macroeconomic perspectives. While a higher required equity–loan ratio of banks brings about a broader umbrella—or buffer—against adverse shocks from a microeconomic perspective, a simple modeling exercise shows that the ratio of credit supply to the stock of money will increase if the equity–loan ratio should increase. A rise in credit supply to the stock of money—or to GDP (the demand for money is assumed to be proportionate to GDP)—implies that banks face more risks in the sense that a rising investment–GDP ratio typically will go along with more risky investment projects, and hence, a higher risk for the banking system: The individual bank has a bigger umbrella, but a higher equity–GDP ratio also raises the probability of rain. From this perspective, there is an optimum equity–loan ratio. Prudential supervisory agencies’ approach to banking systems is traditionally fo-

N.5 Macroeconomic Modeling Aspects

475

cused much on microeconomic aspects but largely ignores macroeconomic and systemic analysis. • Ratings play an enormous role for financial markets and investment financing, respectively. However, ratings so far have not been integrated into macroeconomic models—except for a first approach by WELFENS (2010), which looks at the phenomenon of rating in an open economy macro. A key insight from this model is that a worsening of the rating variable R is not necessarily raising the aggregate real interest rate. This is the “rating-paradox” since one might expect that a worsening of firm’s individuals ratings should bring about a rise in the real interest rate—a higher real interest rate should reflect the rise in default risk of individual firms in a higher risk premium; however, it is not adequate to draw a simplifying conclusion in a macro model, which implies a confusion of the microeconomic perspective and the macroeconomic analysis. If a lower R reduces the demand for money, there is an expansionary effect that might over-compensate the concretionary effect that a lower R has on investment and aggregate demand, respectively. • The main starting point for controlling risk in the banking system is not necessarily raising the equity–loan ratio (this is adequate only if the system is below the optimum ratio), rather a better quality of the risk management system and better incentives for bank managers to think long term are success-promising for effectively coping with key problems in international financial markets.

N.5.1 A Macro Model with Foreign Direct Investment and Rating The subsequent model follows the earlier work of WELFENS (2008a), who has considered an open economy with inflows of FDI, which is a key phenomenon of modern globalization. We, thus, have to make a distinction between gross national income Z and gross domestic product Y; Z in country I (home country) is equal to Y minus the total profit of subsidiaries, which accrues to parent companies in country II (foreign country). As profits in the home country will be equal to ßY, the profits accruing to parent companies abroad is equal to α*ßY, where α* is the share of capital owned by investors from country II; ß is the output elasticity of capital. The model is asymmetric in the sense that the home country is not active as a foreign investor in country II. Since we will assume that production is characterized by a standard Cobb–Douglas production function, we get in a setting with competition in goods and factor markets, Z =Y(1 − α*ß). The production function is Y = Kß (AL)1−ß where K, L and A denote capital, labor and labor-augmenting knowledge, respectively. It is assumed that net investment is a positive function of the difference between the marginal product of capital ßY/K and the real interest rate (b is a positive parameter); moreover, investment is assumed to be positively depend on rating (positive parameter b ) and also to be a positive function of the international difference in marginal products of capital (φ is a positive parameter). As the foreign production function is ∗ Y* = K*ß (A*L*)1−ß* , the foreign marginal product of capital can be expressed as

476

Innovations in Macroeconomics

ß*Y*/K*, the marginal product in the home country is ßY/K. Finally, investment— which includes FDI inflows—is assumed to positively depend on the real exchange rate q* := eP*/P (e is the nominal exchange rate, * for the foreign variable; τ will denote the income tax rate), which is in line with the arguments on FDI inflows presented by FROOT/STEIN (1991). The basic argument of FROOT/STEIN is that for international mergers & acquisitions, it will matter how much equity capital expressed in currency units of the target country bidders can be put within the context of a leveraged M&A—a real depreciation of the currency of country I will make it easier for foreign bidders (from country II) to successfully take over firms in country I. Reinvestment is δK where δ is the depreciation rate. As regards trade, it will be assumed that the elasticity of exports X with respect to q* is unity, while the elasticity of imports J with respect to q* is –1; hence net exports of goods and services expressed in domestic units read Xnet = xZ*q* − q*jZ/q*; foreign national income Z* is the sum of Y* and α*ßY/q*. With consumption C = c(1 − τ)Z and with G denoting real government expenditures and assuming X = xZ* and J = jZ (both x and j are in the interval (0,1)), we can express the equilibrium condition in the goods market as follows: Y = c(1 − α*ß)(1 − τ)Y + [b(ßY/K − r)

(1)

+ϕ (ßY/K − ß*Y*/K*) + ϕ q* + b R + δK] + G + {x(Y* + α*ßY/q*)q* − jY(1 − α*ß)}; The slope of the IS curve in the host country of (cumulated) FDI is—with α* > 0—smaller than in a standard Keynesian macro model, as can be seen from the inspection of this equation (this statement holds strictly for the special case: x = j). It is assumed that the slope of the IS curve is negative, which is always the case if K is sufficiently large and x is close to j. The following equation for equilibrium in the money market assumes that we consider ratings of firms/corporate bonds for the case of h > 0, while for rating of government bonds the respective parameter is h < 0 which is line with portfolio theoretical analysis: An improved rating on corporate bonds means that the capital stock of firms will expand and corporate bonds to a large extent share risk characteristics of stocks: The argument of Tobin (1958, 1961) that different risks of money and real capital makes real money balances and real capital complementary is considered here (in this case h > 0); however, money and government bonds are substitutes with respect to risk-minimization of a portfolio so that an improved rating of sovereign bonds which raises the demand for such bonds will reduce the demand for money (h < 0). Besides the rating variable, there is an impact of the nominal interest rate (actually the real interest rate r if the expected inflation rate is zero) and the real income on the demand for money (h and h are positive parameters). M/P = hY − h r + h R; r = (h/h )Y + [(h /h )R − (1/h )M/P]

(2) (2.1)

N.5 Macroeconomic Modeling Aspects

477

The slope of the LM curve is given by h dr =  dY h Next, we turn to the equilibrium condition of the foreign exchange market. Net capital imports and FDI inflows, respectively, are assumed to positively depend on rating. The slope of the ZZ curve—portraying equilibrium in the foreign exchange market— is relatively small due to the presence of (cumulated) FDI: The larger α*, the smaller the slope of the ZZ curve; one may point out that the responsiveness of portfolio net capital imports with respect to the international interest rate differential i − (i* + a ) could change through the presence of subsidiaries of multinational companies. The equilibrium condition for the balance of payments is written as follows: ϕ[r − (r* + a  )] + {ϕ (ßY/K − ß*Y*/K*) + ϕ q* + ϕ R} = jY(1 − α*ß) − x(Y* + α*ßY/q*)q*

(3)

Note that foreign direct inflows are captured by the terms in the bracket term {. . . } which covers a first term reflecting the international differential in marginal products of capital, and the term ϕ q* indicates the FROOT/STEIN approach, according to which a real depreciation will raise FDI inflows (ϕ, ϕ , ϕ , ϕ are positive parameters). The term ϕ R reflects the impact of rating on net capital inflows; the way we have stated it here allows us to consider the special case that risk-averse economic agents are to be considered in the market for international portfolio investment: namely in the case that we set ϕ = ϕ. By implication, the real interest rate in a (historical) host country of cumulated FDI is not identical to the foreign interest rate even if the interest elasticity of net capital inflows is approaching infinity. We can solve for r and determine the slope of the ZZ curve—portraying balance of payments equilibrium—in the r–Y-space. r = {r* + a  − [ϕ q* + ϕ R − ϕ ß*Y*/K* − xY*q*]/ϕ} + {[j(1 − α*ß) − α*ß + ϕ (ß/K)]}Y/ϕ

(3.1)

As can be seen from Eq. (3.1), an improvement of the rating will shift the ZZ curve downward in the r–Y-space. The slope of the ZZ curve is given by the following expression: dr/dY = (1/ϕ)[j(1 − α*ß) − α*ß + ϕ ß/K]. The higher the share of the capital stock owned by foreigners (α*), the smaller the slope will be. Normal parameter values are defined as j + ϕ ß/K > α*ß (1 + j) or equivalently: α* < [j + ϕ ß/K]/(ß(1 + j)). From this, it follows that the slope of the ZZ curve could be zero even if the interest elasticity of portfolio capital flows is finite—this is the case when α* = [j + ϕ ß/K]/(ß(1 + j)) = [1 + ϕ ß/Kj]/[(ß/j)(1 + j)] or approximately lnα* ≈ ϕ ß/Kj − ln(ß/j) − j.

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Looking at reality, one may assume that a rise in α* goes along with a rise in the responsiveness of the net portfolio capital inflows (parameter ϕ): With a higher presence of foreign subsidiaries, it seems natural to expect that international portfolio capital flows will be enhanced, not least because the presence of subsidiaries reinforces the international exchange of information and because multinational companies are themselves often active in bonds markets in both the headquarter country and the host country of FDI. The endogenous variables of the model are r, Y and q* (indeed e as P and P* are assumed to be given and sticky). The subsequent multiplier analysis highlights all of important key variables.

N.5.2 Multiplier Analysis and Key Conclusions on Ratings Based on our simple model, we can determine the multipliers, and indeed, the multipliers are quite interesting. One key question is whether or not an improvement in R will translate into a lower real interest rate r; to put it differently, whether a lower R should translate into a higher real interest rate, which should, indeed, reflect the higher probability of default signaled by a fall of R. However, as it will be shown, only under certain parameter restrictions will a fall of R go along with a rise in the real interest rates—and therefore, we have an interesting empirical question related to certain parameters. The equation system is indicated subsequently—with all relevant multipliers. ⎛

b −h ϕ

k1 ⎝ h k2 ⎛

b = ⎝ −h ϕ

⎞⎛ ⎞ dY −ϕ − xY * ⎠ ⎝ dr ⎠ 0 ϕ + xY * dq* 0 1 −c (1 − α*ßY ) 1 0 0 0 0 0

k1 = 1 − c(1 − α*ß)(1 − τ) − ϕ ß/K > 0, k2 = ϕ ß/K − j (1 − α*ß) + xα*ß > 0,

⎞

⎛

−ϕ ⎜ ⎜ 0 ⎠⎜ ⎜ ⎝ 0

dR d(M/P ) dG dτ da 

⎞ ⎟ ⎟ ⎟ ⎟ ⎠

for sufficiently large K if ϕ ß/K > j (1 − α*ß) − xα*ß

k1 + k2 = 1 + xα*ß − (1 − α*ß)(c(1 − τ) + j ) > 0, if 1 + xα*ß > (1 − α*ß)(c(1 − τ) + j ) U = −(ϕ + xY *)[h(b + ϕ) + h (k1 + k2 )] < 0 dq* 1 = (k1 (h ϕ + ϕh ) + b(hϕ − h k2 ) + b (hϕ + h k2 )) < 0, dR U h if  ϕ > k2 h

N.5 Macroeconomic Modeling Aspects

dr (ϕ + xY *) =− [h(b − ϕ ) + h (k1 + k2 )] > 0, dR U dY (ϕ + xY *)  = [h (b + ϕ) − h (b − ϕ )] dR U (ϕ + xY *)(k1 + k2 ) dr = <0 d(M/P ) U

479

if b > ϕ

dY (ϕ + xY *)(b + ϕ) =− >0 d(M/P ) U dr dG dY dG dr dτ dY dτ dr da  dY da 

h(ϕ + xY *) >0 U h (ϕ + xY *) =− >0 U hc(1 − α*ßY )(ϕ + xY *) = <0 U h c(1 − α*ßY )(ϕ + xY *) = <0 U ϕh(ϕ + xY *) = <0 U ϕh (ϕ + xY *) = <0 U =−

• A rise in R will shift the IS curve in an augmented Mundell–Fleming model to the right and downward, which brings about an excess supply in the foreign exchange market. This in turn causes an appreciation in the currency market, which consequently dampens net exports of goods and services, and thus, shifts the IS curve backward; if h” is negative, the LM curve shifts downward. An improved rating will bring about a real appreciation if (h/h )ϕ > k2 (for the definition of k2 see above); the term (h/h )ϕ only contains parameters from financial markets where a rise in h —assuming that a higher rating raises the demand for money—makes the condition > k2 more difficult to meet. If there is a strong reaction of net capital inflows to a change in ratings (see the parameter ϕ ), there will be a real appreciation as a consequence of a rise in R. This statement is made under the assumption that the system determinant is negative. If there is an induced real appreciation, net export of goods and services will increase. If we consider a rating for government bonds—so that h is negative—an improvement of R always goes along with a real devaluation. • A rise in the expected depreciation rate (a ) will reduce the domestic interest rate, while interest parity would suggest the opposite. • It is noteworthy that the impact of rating on the real interest rate is ambiguous. There is a positive interest rate multiplier (dr/dR > 0) if the investors should react strongly to changes in the rating—the condition is that the relevant parameter

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b exceeds the parameter φ , which is relevant for net capital inflows: domestic firms’ reaction to a change in the rating, thus, must be stronger than that of foreign investors, but this is not plausible if there is a home bias of investors and as long as α* is relatively small. If α* is relatively high, the reaction of foreign investors is likely to dominate the overall reaction of net investment with respect to a change in R. Thus, the impact of ratings in countries that are dominated by foreign investors might differ from the interest multiplier sign in countries with a low share of cumulated FDI inflows. A positive multiplier would be a paradox, since it means that a worsening of rating (−dR) goes along with a fall in the real interest rate; hence, a higher risk of default at the aggregate level does not show up in a higher real interest rate. The interest rate multiplier could be negative if ϕ > b , which is the typical case of a small open economy with a high foreign indebtedness; it is also noteworthy that the output multiplier is always positive if ϕ > b . In the context of a banking crisis, one may point out that rating changes could be exogenous in the sense that once ratings for structure products have worsened in the USA (country II), there might be a parallel rating spillover for the Eurozone (country I). • If the interest rate elasticity of the demand for money reaches a critical high finite value, an improvement in the rating will always bring about a higher real GDP. This might be interpreted as partly being a self-fulfilling prophecy mechanism: With an economic upswing (read: the rise of GDP), the default probability of firms should indeed decline, and hence, a modified model might even look into some endogenous rating development and the associated economic dynamics. Disregarding the extreme case of an infinite elasticity of the demand for money, it may be argued that the multiplier presented shows that rating improvements do work. To the extent that government guarantees contribute to raising the ratings of banks, such guarantees could indeed be considered to be an important instrument during a financial crisis. • A high responsiveness of net capital imports—read the parameter ϕ which indicates the response of net inflows with respect to R—raises the multipliers of fiscal policy and monetary policy, respectively. From this perspective, the effectiveness of fiscal policy and monetary policy can be raised through organizing the financial markets in a way that domestic and foreign investors would react swiftly to changes in rating. Conversely, if the parameter ϕ should reduce—e.g., because market participants assign reduced credibility to the ratings from big rating agencies—the effectiveness of monetary policy and fiscal policy will reduce. It may also be noted that the presence of (cumulated) inward FDI reduces the tax multiplier, as can be seen from the parameter α*. Moreover, it may also be mentioned that a setup could also be considered in which better rating affects the expected currency depreciation rate. As regards implementation of any model one may point out that a rating variable is somewhat tricky since a country that is already in a top rating cannot improve the rating; at the same time, it is clear that moving from a status of junk bonds to an even lower status means a default of the respective bonds. If one were to consider wealth as an argument of the consumption function, such

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481

a critical rating step (−dR) would have to be analyzed on the basis of taking into account both the standard rating impact and the fall of the stock of real bonds as well. An important aspect of rating concerns the issue whether rating should be organized as a private or a public good. The subsequent analysis considers a simple case, namely two demanders I and II. Marginal costs are assumed to be positive. If rating is organized as a public good, the economic welfare is always greater than in the case of a private good. From the regulation of telecommunications, we know that organizing universal services through a universal fund, into which firms have to pay on the basis of market shares, will work well. A similar approach could work for a two-stage approach in rating and to help create a better rating system: Those who plan a placement of bonds will have to contribute to a financial pool and the pool managers will organize auctions which help allocating the ratings jobs in a way which does not generate a conflict of interest. Public Goods

p

Private Goods

p

A˝ k´0

DD0 A´

A´

DDII

DDII

E

A p2 F

DDI 0

q0 q1 q2

C

p2

G

B

a

k´0

Z

E

B Z´

q

DDI 0

b

q0 q1 q2

Z

Z´

DD0 Z˝

q

Fig. 111 Public goods vs. private goods

N.6 The Effects of a Banking Crisis in a Hybrid Macroeconomic Model Linking the Short Run and the Long Run A considerable challenge in macroeconomic modeling concerns the link between the short run and the long run—read economic growth models. A new mediumterm hybrid growth model (WELFENS 2008a, 2010) gives new insights through an approach that emphasizes that consumption is proportionate to hybrid income, which is defined as a weighted sum of current income and discounted future steady

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state income (Y#; # for steady state). Aggregate production is characterized by a Cobb–Douglas production function Y = Kß (AL)1−ß , so ßY/K is the marginal product of capital; s is the savings rate and c is the average consumption rate, τ is the tax rate and the exogenous growth rate of A is denoted by a, the rate of capital depreciation by δ and θ (0 ≤ θ ≤ 1) is the weight attached to Y# (or the probability that Y# is realized in t: This is an alternative interpretation for θ). The discounted value of Y# can be expressed as Ly#/(1 + r) where y# is the steady-state per capita income as derived, and r is the real interest rate (a more complex discounting formula could be used but this will not yield qualitatively new results; e will denote the Euler number, G is real government expenditures, A0 is the initial knowledge, K is the capital stock, L is the labor); indeed, the expression obtained in a standard growth model is as follows:  y# = [s(1 − τ)/(δ + a)]}ß A0 eat . According to the hybrid model—assuming a given population L—the medium-term condition for equilibrium in the goods market reads (with ß := ß/(1– ß); using 1/(1 + r) ≈ (1 – r)) is given by the following: 

Y = (1 − θ)c(1 − τ)Y + θ{[c(1 − τ)]L{[s(1 − τ)/(δ + a)]}ß A0 } + δK + I(. . .) + G.

(4a)

The bracket term {. . .} indicates steady-state income, I is the net investment, and G is the government consumption. In this closed economy, medium-term approach, multipliers can be derived, which include effects of the banking crisis on the initial level of knowledge (A0 ) and on steady-state income (e.g., through a change in the savings rate and the tax rate). Consumption could be rewritten (using t as an explicit time index) as Ct = c(1 − τ)Yt + θc(1 − τ)[Y#(1 − rt ) −Yt ] so that current consumption is proportionate to current disposable income and to a second term {. . .} which is a kind of a weighted expected Solow windfall income gain. The approach presented allows us to bridge the short term and the long run—the latter covered by a steady-state growth mode. The consumption function presented may be considered to be a variant of Friedman’s permanent income approach; there is strong empirical evidence between consumption and expected future income (POUNDER 2009); and households which are strongly risk-averse tend to consume less out of future income in the USA. The world economy is a closed economy and thus, we may draw key conclusions with respect to the banking crisis from this model once we combine it with an equilibrium condition for the money market and an equilibrium condition for the foreign exchange market. In a broader perspective, the medium-term hybrid model presented is not a true equilibrium model since income is not the steady-state income. It is quite interesting to derive various multipliers, including dY/dA0 , dY/da and dY/dδ so that one can indeed take a closer look at the effect of various technology shocks: The banking crisis will undermine refinancing of investment of many firms and this effectively amounts to a fall of the initial level of technology unless all firms are equal. Moreover, the banking crisis could undermine venture capital dynamics and this in turn will reduce a—the effect is a reduction in the trend growth rate of per capital income and a rise of the level of the growth path. The Transatlantic Banking Crisis has raised serious doubts whether standard macroeconomic models can be easily used to understand the sources of the his-

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torical international crisis of 2007/2008 or to get valid conclusions about the impact of the international banking crisis on the real economy. Among the many disappointing reports, one may point to the IMF October 2008 World Economic Outlook (IMF 2008) which has suggested that the Euro zone would suffer a decline in the growth rate but no recession. Instead, the Euro zone has suffered a serious recession in 2009. The following hybrid macro model—based on (WELFENS 2008a, 2010)—is an approach that allows for the understanding of several major effects of the Transatlantic Banking Crisis: this medium-term model bridges demand side aspects and long-run supply-side aspects (as shown in the neoclassical macro model). What are the key effects of a major international banking crisis? Here is a list of effects considered as crucial a priori: • The banking crisis has brought major losses. Private households that have suffered considerable loss in wealth will raise their savings rates. • The many recapitalizations of banks implemented by various governments in the Euro zone, the UK and the USA will raise the medium-term debt–GDP ratio and hence, current and future tax rates. • There is also some probability that venture capital financing will become more difficult in many OECD countries in the long run, since the risk premiums have increased and since private equity funds will become less eager to finance technology-oriented firms, so the growth rate of technology will reduce—this holds true particularly when venture capital financing activities should weaken in the aftermath of the international banking crisis. • A key element of the banking crisis has been the undermining of confidence in interbanking markets—even prior to the failure of Lehman Brothers—as banks had increasingly engaged in opaque out-of-balance sheet investment activities, banks’ willingness to lend each other (without collateral) seriously reduced. As confidence in the financial sector is an immaterial production factor, the output in this sector will reduce; and as financial services are intermediate inputs for all firms. The transatlantic banking crisis amounts to a negative supply shock to the overall economy. • The banking crisis has been associated with considerable relative price shocks, which in turn, have destroyed the profitability of certain industries and technologies, respectively: This amounts to a negative technology shock as the stock of existing technologies has diminished (downward shift of the level of the growth path). Can traditional macroeconomic models cover these negative effects? This is obviously not the case; particularly Keynesian demand-oriented models, in which real income is determined through aggregate demand—the sum of planned consumption C(. . .), planned investment I(. . .) and exogenous government demand G—are hardly able to take any of the key points mentioned above into account. New Keynesian Models which basically look at deviation from an exogenous equilibrium value are also inadequate here: If there is a strong shock it is unclear why the old equilibrium value should be unchanged. There is, however, a rather easy modification of the Keynesian approach, which allows, within a medium-term framework, to almost fully

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cover economic reality, namely to consider both the short term demand side and the impact of changes in future steady-state values: The hybrid macro model (WELFENS 2008a) is useful here, namely a model that considers a variant of FRIEDMAN’s permanent income hypothesis—planned consumption is a function of current disposable income and of discounted future long-run steady-state income.

The Basics of the Hybrid Macro Model The hybrid macro model (WELFENS 2008a, 2010) is a medium-term setup in which consumers’ planned consumption depends on a weighted average of current real disposable income and future steady-state income—actually the level of the growth path of a neoclassical growth model. Let us consider a simple neoclassical growth model with a macroeconomic production function Y = Kß (AL)1−ß ; where K denotes capital, A represents the level of knowledge, and L stands for labor (0 < ß < 1). Savings S is specified as S = sY(1 − τ). Imposing the goods market equilibrium condition dK/dt + δK = S (δ is the depreciation on capital), we get the following long-run equilibrium condition/steady state condition (# denotes the steady state, y refers to per capita income, n represents the exogenous growth rate of the population, and a stands for the exogenous growth rate of knowledge, e is the Euler number): y# = {[(s(1 − τ)/(n + a + δ)]ß/(1−ß) A0 }e . at

The level of the long-run growth path is determined by the expression in the bracket {. . .}, while the trend growth rate of per capita income is determined by the exogenous growth rate a. Thus, we can easily understand part of the negative effects of the Transatlantic Banking Crisis: 1. Let us consider an illustrative case—reflecting leading EU countries in the Euro zone to some extent—where the savings rate is 10%, the tax rate is 30%, the growth rate of the population is 0, the rate of technological progress (a) is 4%, the depreciation rate (δ) is 10%, ß = 1/3 and A0 = € 40,000: This implies that the level of the growth path is equal to € 28,284. Let us assume that after the crisis, the savings ratio will increase to 0.105 and the tax rate will rise to 0.34, as governments of so many countries had to inject enormous amounts of government capital into various banks in order to stabilize the banking system. Moreover, one may assume a higher depreciation rate, which is related to the bankruptcies of banks and firms, respectively—the new depreciation rate is 11%. The new lower level of the growth path is € 27,188 and thus, about 4% lower than the initial level. 2. If one considers the fact that the Transatlantic Banking Crisis is associated with relative price shocks undermining the economic viability of certain existing technologies, one may assume that A0 falls by 10%. This then reduces the level of the growth path by a further 10%, meaning that the level of the growth path will be € 24,469.

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3. There is a paradox effect on the level of the growth path if the progress rate falls from 4% to 3%; the trend growth rate will fall, of course; however, the level of the growth path is raised, as it can be seen from the expression s(1 − τ)/(n + a + δ). 4. The effects relevant to the growth model refer to the long run, while the more interesting effects concern the medium-term economic dynamics. Taking a look at the medium term, a hybrid model, which combines Keynesian demand aspects and long-term supply aspects, may be considered: The critical point in the hybrid macro model is to formulate a modified hypothesis from FRIEDMAN’s permanent income hypothesis that has emphasized that consumers will not only consider current income but future income as well; as a pragmatic approach—in a setup with a constant population L—it is suggested to use a consumption function where real consumption Ct (t is the time index; it will be suppressed later for ease of exposition) is simply a positive function of hybrid income, namely a linear combination of current disposable income (1 − θ)Yt (1 − τ) and the steady-state income level θ(1 − τ)Ly# where θ—assuming 0 < θ < 1—is a weighing factor for the steady-state income (the per capita steady-state income y# is obtained from the growth model). Division of the steady income level by (1 + r) is made in order to take some form of income discounting into account—a more complex discounting formula could be applied but does not change the qualitative results. Net investment is assumed to be proportionate to the difference between the net marginal product of capital ∂Y/∂K—δ and the real interest rate r (b is a positive parameter) and reinvestment is proportionate to K while the anticipated unemployment rate u will dampen reinvestment (λ is a positive parameter). Thus, the equilibrium condition for the goods market can be stated in a compact form, namely Y = C(Yhybrid ) + {δ[1 – λ u ]K + b[ßY/K – δ – r]} + G, where G is the government consumption; note that we have assumed that aggregate production is characterized by a Cobb–Douglas production function Y = Kß (AL)1−ß , so ßY/K is the marginal product of capital. Subsequently we assume that parameter c is in the interval 0.1; the exogenous growth rate of A is denoted by a, and the rate of capital depreciation by δ. The hybrid consumption function Ct = (1 − θ) c(1 − τ)Yt + θc(1 − t)Y#/(1 + r) can be interpreted (# stands for the steady state) as reflecting an aggregate consumption function where the individual per capita function is formulated as Ct /Lt = (1−θ) c(1− τ)Yt /Lt + θc(1 − t)y#/(1 + r) where y# is per capita steady state income; moreover, θ could alternatively be interpreted as the probability that the (expected) steady state income will be realized in the current period; 1 − θ then is the probability that a transitory per capita income yt (at the aggregate level: Yt ) will be realized in the current period. If one would drop the discounting element—the division of Y# by (1 + r)—the aggregate consumption function reads Ct = c(1 − τ)Yt + [θc(1 − t)(Y# − Yt)] so that current consumption Ct can be described as the sum of a standard Keynesian consumption function plus an additional windfall component [θc(1 − t)(Y# −Yt)]; once the steady state is reached—that is Yt = Y# consumption is, of course, C# = c(1 − τ)Y#.

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According to the hybrid model presented here for the case of a closed economy— and a given population L—the medium-term condition for equilibrium in the goods market reads (with ß := ß/(1 − ß) and 1/(1 + r) ≈ (1 − r)): 

Y = (1 − θ)c(1 − τ)Y + [θc(1 − r)]L{[s(1 − τ)/(δ + a)]}ß A0 + {δ[1 − λ u ]]K + b[ßY/K − δ − r]} + G(1b)

(4b)

It should be noted that consumption Ct (we use the time index explicitly here) is considered here as the sum of a traditional component c(1 − τ)Yt plus an additional component—weighted by θ—which refers to the difference between the discounted long-run income and the current income: the second element is the term  [θ{c(1 − r){(1 − τ)L[s(1 − τ)/(δ + a)]}ß A0 −Yt }]. In the r–Y space the above equation is portrayed by the ISA curve, which has a negative slope (for K exceeding a minimum critical value), namely, dr/dY = −{1 − (1 − θ)c(1 − τ) − bß/K} 

/{[θc]{(1 − τ)L[s(1 − τ)/(δ + a)]}ß A0 + b}. The simplified equilibrium condition for the money market (with M and P denoting the stock of money and the output price level, respectively) is assumed to be given by M/P = b Y/(b i) Here, b is a positive parameter, and i is the nominal interest rate, which is equal to the real interest rate in a setup with zero expected inflation. The intersection point of the LM curve–reflecting the condition for money market equilibrium–and the ISA curve stands for a higher real interest rate and a higher real income than the intersection point (E0 ) of the IS and the ISA curve. The above graph shows an initial situation with output Y0 while the real interest rate is r0 . The medium-term equilibrium income results from the intersection of the ISA curve (Eq. (1)) and the LM curve (equilibrium in the money market): Point E1 marks the medium-term equilibrium. The level of the long-run growth path is given by Y0 . The level of long-run growth path is Y2 # and can be written as the product of the given population L and long-run steady-state per capita income A0 [(1 − τ)s/(δ + a)]ß/1−ß . For the simple case ß = 0.5 we get a long-run per capita income that is simply determined by A0 , the numerator (1 − τ)s and the denominator δ + a. In the case where the economy is characterized by equilibrium in the money market, the adjustment path from Y0 to Y#2 is characterized by the LM0 curve. The coordinate of the IS curve on the r-axis is given by the expression [G + δ(K(1 − u ) − b)]/b, the respective coordinate of the ISA curve is higher and is given by {G + δ(K(1 − u ) − b) + θ(1 − s − τ)(1 − τ)[s(1 − τ)/(a + δ)]ß/(1−ß) A0 }/b. It is obvious that the medium-term equilibrium curve for the goods market (ISA) will be shifted to the left if

N.6 The Effects of a Banking Crisis in a Hybrid Macroeconomic Model Fig. 112 ISA–LM Model: medium-term macroeconomic model

487

r LM0 ISA0

E2

r2 IS0 r1 r01 r0

E1 E3 E0

Y(lnYt) 0

• • • • • • •

Y0

Y1

/(1−)

⎛ ⎞ Y#2 = L0y#0 = L0A0 ⎜(1−)s ⎟ +a ⎝ ⎠

a rise in the expected unemployment rate (u ) is predictable; the capital stock (K) falls; there is a fall in the level of technology (A0 ); confidence about the future diminishes (fall of θ); the rate of depreciation (δ) rises; the tax rate (τ) rises; the growth rate of technology (a) increases.

All of the above variables—except for u —are elements of the expression for the slope of the ISA curve. One might also want to consider the case that Y# is affected by the inflation rate, as a result of which the ISA curve (actually a modified ISA curve) is shifted to the right; one aspect here is related to the link between inflation, —as long as it is below a critical upper limit—which raises the firms’ profits and hence, brings about a rise in gross investment: It = δ(1 − λ u )Kt + b(ßYt /Kt − δ − rt ) + v (π# − πt ); if the expected unemployment rate is equal to the actual unemployment rate u and if we insert this investment function into our medium-term equilibrium condition Y = cYhybrid + δ(1 − λ u )Kt + b(ßYt /Kt − δ − rt ) + v (π# − πt ) + G we have an implicit Phillips curve. As an intermediate result, we may also point out that the nominal interest rate—which is relevant for the real demand for money—will be r2 , while the real interest rate is r01 (the associated point is E2 ). The inflation rate will be equal to the distance E2 E3 , namely the difference between the nominal interest rate and the real interest rate. Now, we will consider the case of zero inflation (price stability) and μ = a, respectively; and we will use the approximation 1/(1 + r) ≈ 1 − r; therefore, we can insert the equilibrium condition of the money market and the associated equilibrium interest rate into the goods market equilibrium condition, which in turn, can be used

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to derive key multipliers: %

   s(1 − τ) β θ(1 − s − τ)b L A0 Y 1 − (1 − θ)(1 − s − τ)(1 − τ) + b M/P δ+a  bβ b − −  K b M/P    s(1 − τ) β   A0 − bδ (4c) = δ[1 − λ u ]K + G + θ(1 − s − τ)L δ+a

The multiplier for G is positive if the expression {. . . } on the left-hand side of the equation is positive. For the sake of simplicity we may assume G = 1 and a specific K in the initial state, such that (1 − λ u ) = b; taking logarithms now yields—using the approximation ln(1 + x) ≈ x for small x:    θ(1 − s − τ)b bβ s(1 − τ) β b ln Y − (1 − θ)(1 − s − τ)(1 − τ) + A − L − 0 b M/P δ+a K b M/P    s(1 − τ) β A0 (4d) ≈ θ(1 − s − τ)L δ+a 

Hence we get the multiplier dlnY/dA0 = θ(1 − s − τ){L[s(1 − τ)/(δ + a)]}ß [1 − b /b (M/P)], so that the multiplier is positive if b (M/P) > b . This seems to be a realistic parameter constellation—and the positive multiplier for the level of technology always holds in the liquidity trap (b → ∞). If the level of technology should shrink—for example, due to a negative technology shock (this could refer to a massive banking crisis in the wake of which many technology-intensive firms face problems in refinancing current investment and innovation projects—medium-term output will fall. The technology multiplier is the bigger • • • • •

the larger the weight of long-run income in the consumption function; the smaller the tax rate; the smaller the savings rate; the smaller the rate of capital depreciation; the smaller the trend growth rate of technological progress.

It is quite interesting to note that in this medium-term hybrid model—strongly shaped by aggregate demand—the supply side has a particular impact. It is noteworthy that  one may divide Eq. (1) by θ(1 − s − τ)L{[s(1 − τ)/(δ + a)]}ß A0 := z so that we get    with the definition λ := 1 − λ u : * * * Y{[1 − (1 − θ)(1 − s − τ)(1 − τ)] z + b (b M P) − [bß/K + b /(b M/P)]/z} = δ[λ ]K/z + G/z + 1 − bδ/z(1a  )

(4a )

Considering the Transatlantic Banking crisis—or any other case of a major international banking crisis—it is quite obvious that the hybrid model allows insight into many important issues:

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• What is the role of the weights—and a change in relative weights—for current income and for future long-run income (1 − θ and θ, respectively)? • What impact should be expected from a rise in the anticipated unemployment rate; the answer is clearly that aggregate demand will fall along with lower reinvestment. • What is the effect of a rise in the depreciation rate of capital? • What outcome will result from erosion in the initial stock of knowledge, that is by a fall in A0 ? We get an answer to this set of questions, and other questions as well, in the hybrid model, which assumes that aggregate consumption demand depends on hybrid income—consumption C depending on a linear combination of current income and future long-run income (the steady-state income and the level of the growth path, respectively). The ISA equation can be solved forY and one may define ß := ß/(1 − ß)), while c = 1 − τ + s needs to be considered (s is the savings rate, τ is the income tax rate and δ is the depreciation rate of capital; gross investment is assumed to be given by the expression δ[1 − λ u ]K + b[ßY/K − δ − r], where the net investment is proportionate to the difference between the net marginal product of capital ßY/K—r and the real interest rate r. It is noteworthy to assume that reinvestment is proportionate to K, at the same time, reinvestment will be affected negatively by the expected unemployment rate u , since firms facing a higher expected unemployment rate will not realize the normal amount of reinvestment; λ is a positive parameter in the interval 0.1. By effectively using a modified version of FRIEDMAN’s permanent income, we have stated an adequate formulation of the medium-term goods market equilibrium condition, which gives a much broader picture of the real economy than either the traditional Keynesian approach or the long-run neoclassical growth model. The above equation can be read as a modified goods market equilibrium condition, which implies that aggregate demand determines actual output; an alternative view, however, is that medium-term real income is determined by both aggregate demand and by supply-side effects—the latter is related to expected steady-state income. The weight factor θ for long-run expected income (actually the level of the growth path of per capita income) can change over time. Depending on the degree of confidence about the future, θ could either be high or low—with a confidence shock such as the one that occurred in the Transatlantic Banking Crisis, the weight attached to long-run income has declined transitorily (in a Keynesian system θ → 0; whereas in a neoclassical economy we have θ → 1). With regards to money market equilibrium, we will use a simple equation for real money demand, namely Md /P = bY/[b i], where b and b are positive parameters, and i denotes the nominal interest rate, which is the sum of the real interest rate r and the inflation rate. Thus, money market equilibrium is given by M/P = bY/{b [r + μ − a]}, where it has been assumed that the expected inflation rate π is equal to the difference between the growth rate of the money supply (μ) and the output trend growth rate (a). A fall of the real interest rate—for example in the context of central banks reducing bank rates through monetary easing—will stimulate consumption through the discounting effect: future income will be worth

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more, at the same time, medium-term gross investment will be stimulated (the longrun-investment demand function will be, of course, dK/dt + δK and under special conditions one also may assume that ßY/K − δ = r in the steady state). Considering an economy of zero inflation and μ = a, respectively, and taking 1/(1 + r) ≈ 1 − r and 1 = c + s + τ into account, some policy multipliers may be derived by inserting the money market equilibrium condition into the goods market equilibrium condition (thus, r can be replaced), obtaining the key equation: * Y{1 − (1 − θ)(1 − s − τ)(1 − τ) + (θ(1 − s − τ)b * * * * *  (b M P))L{[s(1 − τ) (δ + a)]}ß A0 − bß K − b (b M P)} *  = δ[1 − λ u ]K + G + θ(1 − s − τ)L{[s(1 − τ) (δ + a)]}ß A0 − bδ. (4e) The multiplier for G is obviously positive if one assumes that the bracket term {. . .} on the left-hand side is positive (so K has to exceed a critical value); setting δ = 0, G = 0 for simplicity and assuming that K is relatively large bß/K ≈ 0; therefore, we get a compact equation that allows us to easily obtain the multiplier dY/dA0 : 

dY = dA0 with



θb (1 − s − τ)L {s(1 − τ)/a}β k1 (b M/P) k22 

θ(1 − s − τ)L{s(1 − τ)/a}β k2 −

 k1 = 1 − (1 − θ)(1 − s − τ)(1 − τ) + (θb (1 − s − τ)/  β (b M/P))L s(1 − τ)/(δ + a) A0 − bβ/K  β k2 = δ[1 − λ u ]K + G + θ(1 − s − τ)L s(1 − τ)/(δ + a) A0  b k1 β θ(1 − s − τ){Ls(1 − τ)/a} k −  2 (b M/P) dY = dY0 k22    b 1 k1 = θ(1 − s − τ){LS(1−τ)/a}β − k2 k2 k2 (b M/P)    b Y θ(1 − s − τ){LS(1−τ)/a}β 1−  = k2 (b M/P)

Hence, the multiplier for A0 is positive if bY < (b M/P) and it holds * * * Y = {1 − [(θ(1 − s − τ)) (b M P)2 ]} *  {1 − (1 − θ)(1 − s − τ)(1 − τ)} L{{[s(1 − τ)/a]}ß A0 }.

(4f)

Thus, it is obvious that the multiplier for A0 is positive; therefore, a fall in A0 will go along with a fall in medium-term equilibrium output Y. Massive financial market

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shocks, which have brought about relative price shocks, and therefore destroyed— in an economic sense—part of the existing technology, will thus, go along with a fall in real output. It is fairly obvious that the hybrid approach is quite useful since it can be easily understood why long-term supply-side shifts affect the economy’s medium-term output. It can be seen from the above equation that the multiplier for monetary policy is positive.

N.7 Policy Conclusions The US administration faces a serious challenge in overhauling the financial system and prudential supervision. So does the Euro zone and the EU. Western OECD countries will pay a price for lack of an adequate institutional framework for financial globalization. Replacing the G8 more or less by the G20 already represented a power shift in favor of Asian countries, according to which China could be the main winner if the government develops its own consistent understanding about prudential supervision and market deregulation in the context of WTO membership. Chinese bankers—from Shanghai over Hong Kong to those dominating the financial community in Singapore—stand to benefit also, although embracing financial globalization has its own risk. If OECD countries should be unable to come up with adequate restrictions on hedge funds and private equity funds, the next round of a banking crisis is ante portas. At the bottom line one will have to anticipate that big banks will again face enormous pressure from unregulated hedge funds to develop a shadow banking system and the next banking crisis will develop sooner or later. One should not anticipate that the banking crisis simply will be a remake of the Transatlantic Banking Crisis of 2007– 2009; changing the rules of the financial game will bring about new financial products and new fields into which liquidity will flow and on which financial entrepreneurship will focus on. There is a serious risk of delayed and incomplete financial sector reforms—and this would come at a high cost to society if Japan’s banking crisis of the 1990s should be repeated in a modified form (KAMADA/TAKAGAWA 2005; KAWAI 2005; FUKAO ET AL. 2005; AHEARNE/SHINADA 2005; SAXONHOUSE/ STERN 2005; HAMADA/NOGUCHI 2005; HORI/SHIMIZUTANI 2005; IHORI/NAKAMOTO 2005; FUKAO 2005; SAXONHOUSE 2005; ITO 2005; FATUM/HUTCHISON 2005; MCKINNON 2005). If “wash sales” are no longer allowed and those investing in derivatives must hold the underlying assets, one may expect less volatility in certain markets in the short run. However, a change in the rules will set new incentives for new activities (e.g., Goldman Sachs has acquired Metro International Trade Services, which operates large inventory houses for storing metals; Goldman Sachs is an active trader at the London Metal Exchange and there are—even if physical volumes of metals traded should be required—no big barriers for metal traders to become very active in the respective derivatives market). Politicians and firms in the real economy should carefully consider what should be the role of financial markets; maybe, there are good arguments for establishing a lib-

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eral framework, but there are also good arguments for requiring that financial firms be encouraged to generally take a longer view. A financial Pigou tax which tries to internalize negative national and international effects is a serious point to consider for international policy reforms. While a global Tobin tax is unlikely to generate much economic benefits—as it does not discriminate among various financial services—a more refined tax system is more success-promising. At the same time, one should not rule out that innovative financial market participants generating positive external effects could get R&D subsidies, but it should be clear that providers of financial services would have to come up with a more refined innovation system. Bubbles in financial markets are a key issue of economic stability. Monetary policy has its role in helping to avoid bubbles, namely by not keeping the interest rate at artificially low levels. However, the momentum of a financial market bubble— in a two-country model it may occur in country I or country II (as a spillover from country I or a joint phenomenon or just by coincidence)—typically is strong: Relative price increases can be double-digit over several years, and the rise of interest rates necessary to punctuate the bubble would be very high so that the social costs of a drastic monetary policy intervention could be considerable. There probably is no general instrument for fighting bubbles, but in the important case of a real estate market bubble—often a trigger for a wave of excessive lending and for a subsequent banking crisis—the standard way to fight such a bubble obviously is tax policy. Government(s) could impose a temporary levy on profits from real estate markets. Compared to financial innovation dynamics, the standard policy mix is too rigid and taking into account the cost of a banking crisis policy makers often are too hesitant in considering temporary policy interventions which help mitigating the overall burden of adjustment. The euro zone if going to face a test in the aftermath of the banking crisis. Broad analysis of key fiscal and monetary policy aspects of the Euro zone has shown mixed results (RYAN; HORSEWOOD 2009; POGHOSYAN 2009; HALLETT; RICHTER 2009; KORONOWSKI 2009; LANGWASSER 2009). There is also abroad discussion on enhanced regional cooperation and prudential supervision in the EU (WOLF 2008). A broader issue concerns the dynamics of financial innovations and information flows—the ability to control the diffusibility of knowledge and the degree of turbulence related to obsolescence of knowledge has been identified in the innovation literature as an important element of information dynamics (BOISOT/MACMILLAN/HAN 2007); this approach could be a useful starting point for a better understanding of financial innovation dynamics and the so far vague role of property rights in the financial sector. The rise of CDS premia on “Club Med countries” in 2009/2010 shows that speculators are going to test the stability of the Euro zone, whereby several countries face potential problems with sovereign debt. Taking a critical look at debt–GDP ratios of up to 125% in Greece does not suggest that there is a serious problem with government debt. However, the very high share of revenue spent of the service of public debt is worrying, and there is no doubt that Greece has, among many problems on the supply side (related to productivity growth and international competitiveness), a serious revenue problem. Rising spreads on countries with debt problems will bring new

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write-downs of sovereign bonds as well as of weakly rate corporate bonds. Weaker rating of Club Med countries will bring weaker rating of banks in these countries and there could be a vicious circle. It is the task of both national governments and the EU to stabilize the Euro zone. Taking a closer look at the Mexican debt crisis is inspiring—if Germany, France and Switzerland would join forces to give a special bridging loan and if the IMF and the BIS would support national and EU programs, this would be sufficient to avoid new regional and global instabilities. Financial globalization will not be sustainable if there are not enough clever reforms at the national policy level and in the international financial architecture.

O. International Banking Crisis and Innovation

O.1 The Effects of a Banking Crisis in a Hybrid Macroeconomic Model Linking the Short Run and the Long Run A considerable challenge in macroeconomic modeling concerns the link between the short run and the long run—read economic growth models. A new medium-term hybrid growth model (WELFENS 2010) gives new insights through an approach that emphasizes that consumption is proportionate to hybrid income, which is defined as a weighted sum of current income and discounted future steady-state income (Y#; # for steady state). Aggregate production is characterized by a Cobb–Douglas production function Y = Kß (AL)1−ß , so ßY/K is the marginal product of capital; s is the savings rate and c is the average consumption rate, τ is the tax rate and the exogenous growth rate of A is denoted by a, the rate of capital depreciation by δ and θ (0 ≤ θ ≤1) is the weight attached to Y# (or the probability that Y# is realized in t: this is an alternative interpretation for θ). The discounted value of Y# can be expressed as Ly#/(1 + r) where y# is the steady-state per capita income as derived and r is the real interest rate (a more complex discounting formula could be used but this will not yield qualitatively new results; e will denote the Euler number, G is real government expenditures, A0 is the initial knowledge, K is capital stock, L is the labor); indeed, the expression obtained in a standard growth model is: y# = [s(1 − τ)/(δ + a)]}ßA0 eat . According to the hybrid model—assuming a given population L—the medium-term condition for equilibrium in the goods market reads (with ß := ß/(1 − ß); using 1/(1 + r) ≈ (1 − r)) is given by: Y = (1 − θ)c(1 − τ)Y + θ{[c(1 − τ)(1 − r)] *  × L{[s(1 − τ) (δ + a)]}ß A0 } + δK + I(. . . ) + G.

(1a)

The bracket term {. . . } indicates steady-state income, I is net investment and G is government consumption. In this closed economy, medium-term approach, multipliers can be derived, which include effects of the banking crisis on the initial level P. J. J. Welfens, Innovations in Macroeconomics, DOI 10.1007/978-3-642-11909-5_15, © Springer-Verlag Berlin Heidelberg 2011

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of knowledge (A0 ) and on steady-state income (e.g., through a change in the savings rate and the tax rate). Consumption could be rewritten (using t as an explicit time index) as Ct = c(1 − τ)Yt + θc(1 − τ)[Y#(1 − rt ) − Yt ] so that current consumption is proportionate to current disposable income and to a second term {. . . } which is a kind of a weighted expected Solow windfall income gain. The approach presented allows to bridge the short term and the long run—the latter covered by a steady-state growth mode. The consumption function presented may be considered to be a variant of Friedman’s permanent income approach; there is strong empirical evidence between consumption and expected future income (POUNDER 2009); and households which are strongly risk-averse tend to consume less out of future income in the USA. The world economy is a closed economy and thus, we may draw key conclusions with respect to the banking crisis from this model once we combine it with an equilibrium condition for the money market and an equilibrium condition for the foreign exchange market. In a broader perspective the medium-term hybrid model presented is not a true equilibrium model since income is not the steady-state income. It is quite interesting to derive various multipliers, including dY/dA0 , dY/da and dY/dδ so that one can indeed take a closer look at the effect of various technology shocks: The banking crisis will undermine refinancing of investment of many firms and this effectively amounts to a fall of the initial level of technology unless all firms are equal. Moreover, the banking crisis could undermine venture capital dynamics and this in turn will reduce a—the effect is a reduction in the trend growth rate of per capital income and a rise of the level of the growth path. The Transatlantic Banking Crisis has raised serious doubts whether standard macroeconomic models can be easily used to understand the sources of the historical international crisis of 2007/08 or to get valid conclusions about the impact of the international banking crisis on the real economy. Among the many disappointing reports, one may point to the IMF October 2008 World Economic Outlook (IMF 2008) which has suggested that the Euro zone would suffer a decline in the growth rate but no recession. Instead, the Euro zone has suffered a serious recession in 2009. The following hybrid macro model—based on (WELFENS 2010)—is an approach that allows for the understanding of several major effects of the Transatlantic Banking Crisis: This medium-term model bridges demand side aspects and long-run supply-side aspects (as shown in the neoclassical macro model). What are the key effects of a major international banking crisis? Here is a list of effects considered as crucial a priori: • The banking crisis has brought major losses. Private households that have suffered considerable loss in wealth will raise their savings rates. • The many recapitalizations of banks implemented by various governments in the Euro zone, the UK , and the USA will raise the medium-term debt–GDP ratio and hence, current and future tax rates. • There also is some probability that venture capital financing will become more difficult in many OECD countries in the long run, since the risk premiums have increased and since private equity funds will become less eager to finance

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technology-oriented firms, so the growth rate of technology will reduce—this holds true particularly when venture capital financing activities should weaken in the aftermath of the international banking crisis. • A key element of the banking crisis has been the undermining of confidence in inter-banking markets—even prior to the failure of Lehman Brothers—as banks had increasingly engaged in opaque out-of-balance sheet investment activities, banks’ willingness to lend each other (without collateral) seriously reduced. As confidence in the financial sector is an immaterial production factor, the output in this sector will reduce; and as financial services are intermediate inputs for all firms. The transatlantic banking crisis amounts to a negative supply shock to the overall economy. • The banking crisis has been associated with considerable relative price shocks, which in turn, have destroyed the profitability of certain industries and technologies, respectively: This amounts to a negative technology shock as the stock of existing technologies has diminished (downward shift of the level of the growth path). Can traditional macroeconomic models cover these negative effects? This is obviously not the case; particularly Keynesian demand-oriented models, in which real income is determined through aggregate demand—the sum of planned consumption C(. . . ), planned investment I(. . . ), and exogenous government demand G—are hardly able to take any of the key points mentioned above into account. New Keynesian Models which basically look at deviation from an exogenous equilibrium value also are inadequate here: If there is a strong shock it is unclear why the old equilibrium value should be unchanged. There is, however, a rather easy modification of the Keynesian approach, which allows, within a medium-term framework, to almost fully cover economic reality, namely to consider both the short-term demand side and the impact of changes in future steady-state values: The hybrid macro model (WELFENS 2008a) is useful here, namely a model that considers a variant of FRIEDMAN’s permanent income hypothesis—planned consumption is a function of current disposable income and of discounted future long-run steady-state income.

The Basics of the Hybrid Macro Model The hybrid macro model (WELFENS 2010) is a medium-term setup in which consumers’ planned consumption depends on a weighted average of current real disposable income and future steady-state income—actually the level of the growth path of a neoclassical growth model. Let us consider a simple neoclassical growth model with a macroeconomic production function Y = Kß (AL)1−ß ; where K denotes capital, A represents the level of knowledge, and L stands for labor (0 < ß < 1). Savings S is specified as S = sY(1 − τ). Imposing the goods market equilibrium condition dK/dt + δK = S (δ is the depreciation on capital) we get the following long-run equilibrium condition/steady-state condition (# denotes the steady state, y

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refers to per capita income, n represents the exogenous growth rate of the population and a stands for the exogenous growth rate of knowledge, e is the Euler number): y# = {[(s(1 − τ)/(n + a + δ)]ß/(1−ß) A0 }e ; at

The level of the long-run growth path is determined by the expression in the bracket {. . . }, while the trend growth rate of per capita income is determined by the exogenous growth rate a. Thus, we can easily understand part of the negative effects of the Transatlantic Banking Crisis: 1. Let us consider an illustrative case—reflecting leading EU countries in the Euro zone to some extent—where the savings rate is 10%, the tax rate is 30%, the growth rate of the population is 0, the rate of technological progress (a) is 4%, the depreciation rate (δ) is 10%, ß = 1/3 and A0 = € 40,000: This implies that the level of the growth path is equal to € 28,284. Let us assume that after the crisis, the savings ratio will increase to 0.105 and the tax rate will rise to 0.34, as governments of so many countries had to inject enormous amounts of government capital into various banks in order to stabilize the banking system. Moreover, one may assume a higher depreciation rate, which is related to the bankruptcies of banks and firms, respectively—the new depreciation rate is 11%. The new lower level of the growth path is € 27,188 and thus, about 4% lower than the initial level. 2. If one considers the fact that the Transatlantic Banking Crisis is associated with relative price shocks undermining the economic viability of certain existing technologies, one may assume that A0 falls by 10%. This then reduces the level of the growth path by a further 10%, meaning that the level of the growth path will be € 24,469. 3. There is a paradox effect on the level of the growth path if the progress rate falls from 4% to 3%; the trend growth rate will fall, of course; however, the level of the growth path is raised, as it can be seen from the expression s(1 − τ)/(n + a + δ). 4. The effects relevant to the growth model refer to the long run, while the more interesting effects concern the medium-term economic dynamics. Taking a look at the medium term, a hybrid model, which combines Keynesian demand aspects and long-term supply aspects, may be considered: The critical point in the hybrid macro model is to formulate a modified hypothesis from FRIEDMAN’s permanent income hypothesis that has emphasized that consumers will not only consider current income but future income as well; as a pragmatic approach—in a setup with a constant population L—it is suggested to use a consumption function where real consumption Ct (t is the time index; it will be suppressed later for ease of exposition) is simply a positive function of hybrid income, namely a linear combination of current disposable income (1 − θ)Yt (1 − τ) and the steady-state income level θ(1 − τ)Ly# where θ—assuming 0 < θ < 1—is a weighing factor for the steady-state income (the per capita steady-state income y# is obtained from the growth model). Division of the steady income level by (1 + r) is made in order to take some form of income discounting into account—a more complex discounting formula could be applied but does not change the qualitative results.

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Net investment is assumed to be proportionate to the difference between the net marginal product of capital ∂Y/∂K − δ and the real interest rate r (b is a positive parameter) and reinvestment is proportionate to K while the anticipated unemployment rate u will dampen reinvestment (λ is a positive parameter). Thus, the equilibrium condition for the goods market can be stated in a compact form, namely Y = C(Yhybrid ) + {δ[1 − λ u ]K + b[ßY/K − δ − r]} + G, where G is government consumption; note that we have assumed that aggregate production is characterized by a Cobb-Douglas production function Y = Kß (AL)1−ß , so ßY/K is the marginal product of capital. Subsequently we assume that parameter c is in the interval 0.1; the exogenous growth rate of A is denoted by a, and the rate of capital depreciation by δ. The hybrid consumption function Ct = (1 − θ) c(1 − τ)Yt + θc(1 − t)Y#/(1 + r) can be interpreted (# stands for the steady state) as reflecting an aggregate consumption function where the individual per capita function is formulated as Ct /Lt = (1 − θ) c(1 − τ)Yt /Lt + θc(1 − t)y#/(1 + r) where y# is per capita steady-state income; moreover, θ could alternatively be interpreted as the probability that the (expected) steady-state income will be realized in the current period; 1−θ then is the probability that a transitory per capita income yt (at the aggregate level: Yt ) will be realized in the current period. If one would drop the discounting element—the division of Y# by (1 + r)—the aggregate consumption function reads Ct = c(1 − τ)Yt +[θc(1 − t)(Y# − Yt)] so that current consumption Ct can be described as the sum of a standard Keynesian consumption function plus an additional windfall component [θc(1 − t)(Y# − Yt)]; once the steady state is reached—that is Yt = Y# consumption is, of course, C# = c(1 − τ)Y#. According to the hybrid model presented here for the case of a closed economy— and a given population L—the medium-term condition for equilibrium in the goods market reads (with ß := ß/(1 − ß) and 1/(1 + r) ≈ (1 − r)):



ß Y = (1 − θ)c(1 − τ)Y + θc(1 − r) L s(1 − τ)/(δ + a) A0 



 + δ 1 − λ u K + b ßY/K − δ − r + G.

(1b)

It should be noted that consumption Ct (we use the time index explicitly here) is considered here as the sum of a traditional component c(1 − τ)Yt plus an additional component,—weighted by θ—which refers to the difference between the discounted long-run income and the current income: The second element is the term  [θ{c(1 − r){(1 − τ)L[s(1 − τ)/(δ + a)]}ß A0 − Yt }]. In r—Y space the above equation is portrayed by the ISA curve, which has a negative slope (for K exceeding a minimum critical value), namely dr/dY = −{1 − (1 − θ)c(1 − τ) − bß/K} 

/{[θc]{(1 − τ)L[s(1 − τ)/(δ + a)]}ß A0 +b}.

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The simplified equilibrium condition for the money market (with M and P denoting the stock of money and the output price level, respectively) is assumed to be given by: M/P = b Y/(b i). Here, b is a positive parameter and i is the nominal interest rate, which is equal to the real interest rate in a setup with zero expected inflation. The intersection point of the LM curve—reflecting the condition for money market equilibrium—and the ISA curve stands for a higher real interest rate and a higher real income than the intersection point (E0 ) of the IS and the ISA curve. r LM0 ISA0

E2

r2 IS0

E1

r1 E3

r01 E0

r0

Y(lnYt ) 0 Y0

Y1

Y#2

=

L0y0#

⎛(1− ) s⎞ = L0A0 ⎜ ⎟ ⎝  +a ⎠

/(1−)

Fig. 113 ISA–LM model: medium-term macroeconomic model

The above graph shows an initial situation with output Y0 while the real interest rate is r0 . The medium-term equilibrium income results from the intersection of the ISA curve (Eq. 1) and the LM curve (equilibrium in the money market): Point E1 marks the medium-term equilibrium. The level of the long-run growth path is given by Y0 . The level of long-run growth path is Y2 # and can be written as the product of the given population L and long-run steady-state per capita income A0 [(1 − τ)s/(δ + a)]ß/1−ß . For the simple case ß = 0.,5 we get a long-run per capita income that is simply determined by A0 , the numerator (1 − τ)s and the denominator δ + a. In the case where the economy is characterized by equilibrium in the money market, the adjustment path from Y0 to Y#2 is characterized by the LM0 curve. The coordinate of the IS curve on the r axis is given by the expression [G + δ(K(1 − u ) − b)]/b,

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the respective coordinate of the ISA curve is higher and is given by {G + δ(K(1 − u ) − b) + θ(1 − s − τ)(1 − τ)[s(1 − τ)/(a + δ)]ß/(1−ß)A0 }/b. It is obvious that the medium-term equilibrium curve for the goods market (ISA) will be shifted to the left if • • • • • • •

a rise in the expected unemployment rate (u ) is predictable; the capital stock (K) falls; there is a fall in the level of technology (A0 ); confidence about the future diminishes (fall of θ); the rate of depreciation (δ) rises; the tax rate (τ) rises; the growth rate of technology (a) increases.

All of the above variables—except for u —are elements of the expression for the slope of the ISA curve. One might also want to consider the case that Y# is affected by the inflation rate, as a result of which the ISA curve (actually a modified ISA curve) is shifted to the right; one aspect here is related to the link between inflation—as long as it is below a critical upper limit—which raises the firms’ profits and hence, brings about a rise in gross investment: It = δ(1 − λ u )Kt + b(ßYt /Kt − δ − rt ) + v (π# − πt ); if the expected unemployment rate is equal to the actual unemployment rate u and if we insert this investment function into our medium-term equilibrium condition Y = cYhybrid + δ(1 − λ u )Kt + b(ßYt /Kt − δ − rt ) + v (π# − πt ) + G, we have an implicit Phillips curve. As an intermediate result, we may also point out that the nominal interest rate—which is relevant for the real demand for money—will be r2 , while the real interest rate is r01 (the associated point is E2 ). The inflation rate will be equal to the distance E2 E3 , namely the difference between the nominal interest rate and the real interest rate. Now, we will consider the case of zero inflation (price stability) and μ = a, respectively; and we will use the approximation 1/(1 + r) ≈ 1 − r, therefore, we can insert the equilibrium condition of the money market and the associated equilibrium interest rate into the goods market equilibrium condition, which in turn, can be used to derive key multipliers: % Y 1 − (1 − θ)(1 − s − τ)(1 − τ) &   bβ s(1 − τ) β b θ(1 − s − τ)b A0 − L −  + b M/P δ+a K b M/P    s(1 − τ) β A0 + bδ = δ 1 − λ u K + G + θ(1 − s − τ) L δ+a

 

(1c)

The multiplier for G is positive if the expression {. . . } on the left-hand side of the equation is positive. For the sake of simplicity, we may assume G = 1 and a specific K in the initial state, such that (1 − λ u ) = b; taking logarithms now yields—using

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the approximation ln(1 + x) ≈ x for small x,    s(1 − τ) β θ(1 − s − τ)b A0 L lnY − (1 − θ)(1 − s − τ)(1 − τ) + b M/P δ+a    b s(1 − τ) β bβ −  ≈ θ(1 − s − τ) L − A0 K b M/P δ+a

(1d) 

Hence we get the multiplier dlnY/dA0 = θ(1 − s − τ){L[s(1 − τ)/(δ + a)]}ß [1 − b /b (M/P)], so that the multiplier is positive if b (M/P) > b . This seems to be a realistic parameter constellation—and the positive multiplier for the level of technology always holds in the liquidity trap (b → ∞). If the level of technology should shrink—for example, due to a negative technology shock (this could refer to a massive banking crisis in the wake of which many technology-intensive firms face problems in refinancing current investment and innovation projects—medium-term output will fall. The technology multiplier is the bigger • • • • •

the larger the weight of long-run income in the consumption function; the smaller the tax rate; the smaller the savings rate; the smaller the rate of capital depreciation; the smaller the trend growth rate of technological progress.

It is quite interesting to note that in this medium-term hybrid model—strongly shaped by aggregate demand—the supply side has a particular impact. It is noteworthy that  one may divide the Eq. (1) by θ(1 − s − τ){L[s(1 − τ)/(δ + a)]}ß A0 := z so that we    get with the definition λ := 1 − λ u : Y{[1 − (1 − θ)(1 − s − τ)(1 − τ)]/z + b /(b M/P) − [bß/K + b /(b M/P)]/z} = δ[λ ]K/z + G/z + 1 − bδ/z.

(1a )

Considering the Transatlantic Banking crisis—or any other case of a major international banking crisis—it is quite obvious that the hybrid model allows insight into many important issues: • What is the role of the weights—and a change in relative weights—for current income and for future long-run income (1 − θ and θ, respectively)? • What impact should be expected from a rise in the anticipated unemployment rate; the answer is clearly that aggregate demand will fall along with lower reinvestment. • What is the effect of a rise in the depreciation rate of capital? • What outcome will result from erosion in the initial stock of knowledge, that is by a fall in A0 ? We get an answer to this set of questions, and other questions as well, in the hybrid model, which assumes that aggregate consumption demand depends on hybrid income—consumption C depending on a linear combination of current income and

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future long-run income (the steady-state income and the level of the growth path, respectively). The ISA equation can be solved forY and one may define ß := ß/(1−ß), while c = 1 − τ + s needs to be considered (s is the savings rate, τ is the income tax rate and δ is the depreciation rate of capital; gross investment is assumed to be given by the expression δ[1 − λ u ]K + b[ßY/K − δ − r], where the net investment is proportionate to the difference between the net marginal product of capital ßY/K − r and the real interest rate r. It is noteworthy to assume that reinvestment is proportionate to K, at the same time, reinvestment will be affected negatively by the expected unemployment rate u , since firms facing a higher expected unemployment rate will not realize the normal amount of reinvestment; λ is a positive parameter in the interval 0.1. By effectively using a modified version of FRIEDMAN’s permanent income, we have stated an adequate formulation of the medium-term goods market equilibrium condition, which gives a much broader picture of the real economy than either the traditional Keynesian approach or the long-run neoclassical growth model. The above equation can be read as a modified goods market equilibrium condition, which implies that aggregate demand determines actual output; an alternative view, however, is that medium-term real income is determined by both aggregate demand and by supply-side effects—the latter is related to expected steady-state income. The weight factor θ for long-run expected income (actually the level of the growth path of per capita income) can change over time. Depending on the degree of confidence about the future, θ could either be high or low—with a confidence shock such as the one that occurred in the Transatlantic Banking Crisis, the weight attached to long-run income has declined transitorily (in a Keynesian system θ → 0; whereas in a neoclassical economy we have θ → 1). With regards to money market equilibrium, we will use a simple equation for real money demand, namely Md /P = bY/[b i], where b and b are positive parameters and i denotes the nominal interest rate, which is the sum of the real interest rate r and the inflation rate. Thus, money market equilibrium is given by M/P = bY/{b [r + μ − a]}, where it has been assumed that the expected inflation rate π is equal to the difference between the growth rate of the money supply (μ) and the output trend growth rate (a). A fall of the real interest rate—for example, in the context of central banks reducing bank rates through monetary easing—will stimulate consumption through the discounting effect: future income will be worth more, at the same time, medium-term gross investment will be stimulated (the long-run-investment demand function will be, of course, dK/dt + δK and under special conditions one also may assume that ßY/K − δ = r in the steady state). Considering an economy of zero inflation and μ = a, respectively, and taking 1/(1 + r) ≈ 1 − r and 1 = c + s + τ into account, some policy multipliers may be derived by inserting the money market equilibrium condition into the goods market equilibrium condition (thus, r can be replaced), obtaining the key equation: Y{1 − (1 − θ)(1 − s − τ)(1 − τ) + (θ(1 − s − τ)b /(b M/P)) 

{L[s(1 − τ)/(δ + a)]}ß A0 − bß/K − b /(b M/P)} 

= δ[1 − λ u ]K + G + θ(1 − s − τ){L[s(1 − τ)/(δ + a)]}ß A0 − bδ. (1e)

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The multiplier for G is obviously positive if one assumes that the bracket term {. . . } on the left-hand side is positive (so K has to exceed a critical value); setting δ = 0, G = 0 for simplicity and assuming that K is relatively large bß/K ≈ 0, therefore we get a compact equation that allows to easily obtain the multiplier dY/dA0 : 



θ (1 − s − τ) {Ls (1 − τ)/a}β k2 −

θb (1 − s − τ){Ls(1 − τ)/a}β k1 (b M/P)

dY = dA0 k22 with   1 − (1 − θ)(1 − s − τ)(1 − τ) + (θb (1 − s − τ)/(b M/P))  k1 = {Ls(1 − τ)/(δ + a)}β A0 − bß/K 

k2 = δ[1 − λ u ]K + G + θ(1 − s − τ){Ls(1 − τ)/(δ + a)}β A0 Hence, the multiplier for A0 is positive if bY < (b M/P) and it holds Y = {1 − [(θ(1 − s − τ)/(b M/P) ]}/{1 − (1 − θ)(1 − s − τ)(1 − τ)} 2



/{{L[s(1 − τ)/a]}ß A0 }.

(1f)

Thus, it is obvious that the multiplier for A0 is positive, therefore a fall in A0 will go along with a fall in medium-term equilibrium output Y. Massive financial market shocks, which have brought about relative price shocks, and therefore destroyed— in an economic sense—part of the existing technology, will thus, go along with a fall in real output. It is fairly obvious that the hybrid approach is quite useful since it can be easily understood why long-term supply-side shifts affect the economy’s medium-term output. It can be seen from the above equation that the multiplier for monetary policy is positive.

O.2 Financial Innovations, Banking Crises, and Schumpeterian Growth Dynamics O.2.1 Introduction: Financial Innovations Dynamics versus Industrial Innovations While product and process innovations in the manufacturing industry have been analyzed in much detail from both a theoretical and an empirical perspective (e.g., BRETSCHGER 2004, JUNGMITTAG 2006; survey: FAGERBERG/MOVERY/NELSON 2006; GRUPP 2008) and links between innovations and growth are well understood, there is only superficial research on the role of financial innovations; this holds despite the fact that insights from Economic History clearly reveal the enormous role of financial innovations in economic growth (e.g., TILLY 2003). Product innovations in the financial sector (survey: RAMSER/STADLER 1995; GOWLAND 1991; JOHNSON 1988) will raise the liquidity of financial assets or reduce the risk of certain transactions. It may also be added that certain

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financial innovations will generate network effects so that the private and social benefit from using certain financial innovations is much higher than initially perceived; credit cards can be considered as such an example. Credit cards also stand for the case of two-sided markets where the expansion of credit cards reduces the transaction in all goods markets and therefore indirectly contributes to the expansion of overall output. In open economies, there are specific sources of shocks, which in a system of flexible exchange rates will to some extent be reflected in nominal exchange rate changes. Flexible exchange rates bring the advantage of establishing a clear responsibility of monetary authorities—the central bank can control the stock of money and the monetary base respectively so that achieving low inflation rates (assuming here that this is the target of the central bank) could be a credible goal of monetary policymakers. If price stability is achieved, relative price signals will work clearly so that allocation of resources—including the use of resources for innovation—will be efficient; this statement, however, assumes that the positive external effects of innovations are internalized through adequate government R&D support. One more aspect related to the open economy under fixed exchange rates and flexible exchange rates; under fixed exchange rates there is the risk of misalignment, namely that the nominal exchange rate is not in line with the relative price level development P/P* (P is the price level, * refers to foreign variables); furthermore, a fixed exchange rate regime could generate a higher world inflation rate than a system of flexible exchange rates—thus, the nominal exchange rate would be higher than otherwise. This goes along with a welfare loss as the demand for money is a negative function of the nominal interest rate. There are also certain risks associated with flexible exchange rates, for example, overshooting effects in the sense that the shortterm reaction of the nominal and real exchange rate is greater than it will be in the long run: This at least is the message from the Dornbusch model, which shows that overshooting could occur due to differences in the speed of adjustment in financial markets—read: The response of the interest rate i—and the goods market (read: the price level), which is assumed to be sticky so that only slow adjustment of the price level P will be realized. Overshooting will occur in the Dornbusch model if the interest elasticity of the demand for money and if the adjustment process of price expectations reach a critical level. If one simply wants to focus on financial innovations from the perspective of individual banks, the typical assumption in a partial equilibrium analysis is that innovations generate positive external effects. At the same time, it may be asked to what extent potential too-big-to-fail problems will be reinforced. From a microeconomic or Industrial Economics perspective, financial innovations are enhancing productivity and profitability—the latter in many cases through raising the willingness to pay and therefore, the marginal value product. At the same time, financial innovations can have side effects that are problematic in the perspective of policymakers: • National or international prudential supervision could be impaired (e.g., KANE 1978, 1988; WELFENS 2009).

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• Monetary policy control could be undermined (e.g., AKHTAR 1984; IZGIKOGAR 1995). • There could be distortions in international capital markets, namely to the extent that positive or negative international external effects could occur; certain problems will also come from increasing information asymmetries and in particular cases also from new problems emerging in the field of moral hazard. Subsequently, we take a closer look at the link between financial innovations and growth so that one gets a better understanding of the role of innovations in the monetary sphere of the economy. At the same time, some key links between the financial services sector and the innovation dynamics of the real economy are discussed.

O.2.2 Financial Innovations and Growth In a historical perspective, financial market liberalization has stimulated financial innovations—many of which are welfare enhancing. The 1970s brought about the liberalization of portfolio capital flows in the OECD countries and this in turn stimulated competition; competition in turn encouraged product and process innovations. In the 1980s, foreign direct investment inflows and outflows increasingly played a role and FDI increased in particularly in banking. Countries that have liberalized early on while maintaining adequate regulations have benefited much: the UK, the USA and the new financial centers in Asia, in particular Hong Kong and Singapore. Diffusion of new knowledge was facilitated by the use of modern information and communication technology. As regards financial globalization, there is little doubt that both the expansion of information and communication technology and the growth of FDI in banking have contributed to more dynamic financial markets; the new traits also concern the role of more differentiated investment funds whose number was growing over many years in OECD countries. A first securitization wave took place in the 1980s when the growth of sovereign debts was often organized in combination with packaging banks’ loans to governments into new papers that were sold in the capital market. It was only in the late 1990s that financial globalization increasingly went along with a new wave of securitization, which brought many doubtful aspects with it: Loans were packed into financial products over several layers of packaging and repackaging; and banks thought they could easily get rid of risks, namely by buying credit default swaps (CDS) (DEUTSCHE BUNDESBANK 2008; WELFENS 2009); consequently there was an incentive on the side of banks to invest less in risk management while the securitization process, certain financial services innovations, and a partly weak rating process reinforced the potential role of risk. Counterparty risk was rarely considered in this new world of modern finance although such risk played a role in the growing market for credit risk insurance—read: the market for CDS. In some countries, high concentration ratios in the banking sector also pointed to the potential relevance of counterparty risk (e.g., the case of the UK). The wave of securitization reinforced on the side of many banks that giving loans would not require much attention on associated risk since getting rid of risk associated with

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certain loan packages seemed to be so easy: Sell asset-backed securities (ABS) in the capital market and then the risk management of the respective assets/loans are no longer a task of the bank. However, there is not much risk management in the capital market except for some activities—for example, due diligence (mainly assessment of investment plans) in the case of creation of new companies or in the case of takeovers, private information and then on top, the information conveyed through ratings. The securitization process has been driven in OECD countries, as well as in some other countries, through the rules of Basel I and Basel II. The minimum regulatory equity capital stipulated by Basel II differs in accordance with the risk of individual positions in the balance sheet and from this perspective the incentive for securitization has become stronger under the Basel II rules—compared to the uniform 8% required equity ratio of Basel I: Securitization means that the respective bank takes a bundle of loans out of its balance sheet and sells the bundle in the capital market as an ABS so that the equity–loan ratio will increase, which in turn makes additional loan business possible. The EU has implemented Basel II through a directive so that all EU member countries would have implemented Basel II by 2008. Switching to the more differentiated Basel II rules should generate an excess of regulatory capital in many countries (RYAN 2007) and thus an expansion of credit volume along with higher growth of output might occur. Securitization is a process that shifts credit risk from banks to the capital markets, in which ABSs are off-loaded from banks. Those banks that keep large positions of loans in the balance sheet can still get rid of the associated risk, namely by buying a CDS, which is effectively an insurance against such risk. After buying such risk insurance, the respective loan position is classified as less risky, and required regulatory capital will typically fall so that the bank’s loan business can expand further. Assuming that regulation of the insurance business and of banks is consistent, effective and efficient, a smooth process of financial innovations should be expected since banks will mainly focus on two options for enhancing the growth of the banking business: • Securitization that requires the packaging of bundles of loans into a product, dubbed ABS—the default risk of the ABS will be assessed by rating agencies so that the capital market gets clear signals about the risk profile of each and every ABS; provided that rating agencies are properly doing their job. The socalled structured financial products (read: ABS) consisting of layers of loans with different profiles, where the senior tranche stood for top ratings, while the lowest tranche was the equity piece (the first loss piece) effectively had no rating. There is, however, a potential problem for the financial system, namely to the extent that ABS I—which emerged from packaging loans into a bundle in stage I—can be combined with other ABS so that a more complex ABS II product is created; ABS I could even be combined with a bundle of CDS so that one would again obtain a more complex and potentially also a more risky ABS II. One key problem occurs in the capital market as certain funds, including unregulated hedge funds, will buy the various ABS; however, the hedge funds in turn have taken loans from banks and by coincidence, they might have indeed taken the loans to buy ABS from

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those banks that have created the ABS so that the risk is back into the balance sheet of the bank—without the prudential supervisors or the market participants knowing anything about this; In countries with a highly concentrated (investment) banking system this could become a serious problem of intransparency of risk. How then could stock markets adequately price stocks of banks? The more opaque the ABS process is and the weaker the work of rating agencies, the more opaque the fundamental price of stocks of banks—the variance of such stocks could increase but this would happen only if there is some broad mistrust spreading in the stock market. If market participants are unaware of the true risk position of banks and get the message that the risk of the banks’ credit portfolios has reduced, the relative stock market price of banks will go up and the financial services sector will expand. • The bank keeps the loans in the bank and buys CDS from one of the big insurance companies. The bank has the alternative to keep the CDS and to sell the CDS at a market price. Selling CDS in the market makes sense for the bank if there are market partners that are highly specialized in the business of risk management and will, therefore, be willing to pay more for the CDS than the bank has paid to the insurance company. Again, there is a potential macro prudential problem if selling and buying and re-selling of CDS is not organized in a transparent way—there is, again, counterparty risk (this concerns the question whether those who have bought the CDS will be able to pay once a default of the relevant loans should occur). Any over-the-counter-trading is inadequate since the transparency of markets and hence the competitions process is impaired. Moreover, it will not be easy to assess the market for risk in the presence of dominant over-the-countertrading prudential supervisors; if there should be distortions and inefficiencies in the market for risk, the complementary market for credits will be distorted too. From this perspective, the indifference of prudential supervisors to allow the emergence of over-the-counter-trading of risk is one source of the Transatlantic Banking Crisis; only after the crisis have OECD countries switched to a more transparent system with clearing houses. Thus, it is fairly obvious that the organization of financial markets is an important challenge for policymakers; in a rather internationalized setup of financial markets this, of course, implies considerable international coordination. In a democratic perspective, one then wonders to what extent is there adequate international democratic control over the relevant actors and international organizations, respectively. As regards the United States subprime crisis and the destructive financial dynamics that has consequently occurred, there is only weak consensus about the main drivers of the Transatlantic Banking Crisis; there is a weak consensus that the United States housing market has been a major trigger of the crisis (ELLIS 2008). The fragmentation of banking supervision in the USA and indeed weak overall supervision of banks in an era of high financial services innovation dynamics seems to have been part of the problem (WELFENS 2009). It may be argued that prudential supervisors responsible for micro prudential analysis should have kept a more critical eye on the financial services industry, at the same time, it may also be argued that the macro

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prudential implications of financial innovations were neither well observed nor really understood by the authorities, including ministries of finance that should have had a natural interest in avoiding big losses of banks and chaos in financial markets (a modest description of the month after September 15, 2008). The bursting of the bubble in the US housing market was only one element in the international crisis; many banks from the EU that had invested in US subprime—that is in certain mortgage-based securities—suffered large losses from their respective US investment.

Pecuniary Externalities and Non-pecuniary Externalities Modeling financial innovations has put the focus on the specifics of financial systems, which includes information asymmetries, moral hazard and externalities including potential contagion dynamics; an interesting model is by GAI/MILLARD/PEREZ (2008), who present a model of intermediation, which considers financial constraints as well as state contingent contracts—in the case of fire sales there will be pecuniary externalities. However, one may add: If the pecuniary externalities are relatively strong so that a serious financial shock occurs, the result could be a confidence crisis—and this amounts to a non-pecuniary externality: For example, the demand for risky assets shifts downwards so that private marginal utility is now below social marginal utility in financial market segments related to financing innovations. Such links between pecuniary externalities and non-pecuniary externalities have not been discussed so far. From a normative economic perspective, government should intervene only in the case of non-pecuniary externalities, which refers to spillovers from firm i’s production activities to the production function of j (there can also be externalities that enter the utility function of households). If certain financial innovations are poorly organized and not well-monitored, destructive market dynamics as well as negative output effects or enhanced variance of output could occur through self-fulfilling prophecies. Bubble phenomena might also be stimulated along this line. Financial market innovations can be considered in various ways: • Of particular interest is the modeling of JERMANN/QUADRINI (2006), who focus on the variance of the equity–capital ratios of firms and thus explain the volatility of the financial structure of firms—with potential implications on the aggregate variance of output at the aggregate level. • A different perspective comes up in the analysis of VALVERDE/DEL PASO/FERNANDEZ (2007), who have focused on the role of regional growth differential in Spain—and the underlying role of financial innovations in the banking sector. • Approaches can be found among the interesting macroeconomic aspects, which look into the links between financial innovations and the efficiency of the intermediation process—there could be an effect on the level of the growth path or on total factor productivity and the trend growth rate, respectively (e.g., PAGANO 1993; CHOU 2007). The question of to what extent the financial sphere is affecting the growth process could be analyzed in various ways, one analytical avenue being the perspective of a monetary growth model (WELFENS 2008a).

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A specific analytical challenge concerns the link between innovative financial services and the financing of innovative new firms in manufacturing industry and the services sector. This analytical perspective mainly concerns the venture capital industry and innovation (e.g., ENGEL 2002; GOMPERS/LERNER 1999, 2001; on Japan see SCHULZ (2005)), but to some extent, it may also concern financing of investment in established high-technology industries—here, one might also find collateral damages from financial market crises that undermine the ability of innovative firms to obtain adequate long-term financing for investment (with embodied technological progress) so that a maturity mismatch will emerge in the economy which makes the real sector more vulnerable to real interest rate shocks (e.g., after 2007/2008 some big telecommunications firms in the EU have faced problems in getting the standard long-term financing for investment). Venture capital financing was found to matter more than patents for United States economic growth (KORTUM/LERNER 2000), so a financial crisis that undermines venture capital financing may negatively affect economic growth. From a macroeconomic perspective, it will have to be asked to what extent financial innovations contribute to higher productivity in the financial sector as well as in the overall economy and whether financial services innovation stimulate innovation in the real economy and in overall economic growth. There is also the reverse angle, namely to ask to what extent does the long-term rise of R&D–GDP ratios in OECD countries and elsewhere imply a rising share of high-technology goods and high-technology services relative to GDP that have to be financed through banks and capital markets; with long-term rise of Schumpeterian innovation dynamics one should expect to see a growing role of venture capital. However, there is a serious caveat, namely that most venture capital investment will seek an exit strategy at some point—typically the venture capitalist that engaged itself in the seed financing stage will try to sell the company with a profit in stock markets. If stock market prices stagnate or even fall, this exit option is hardly available anymore and the dynamics of the venture capital business will be negatively affected. Here lies one of the potentially negative long-term collateral damages of the Transatlantic Banking Crisis: Stock market price developments could stagnate over several years. Moreover, if there should be a general and lasting increase in the risk premium in international financial markets, venture capital firms will only be able to come up with the funding for a reduced pool of innovative firms—as compared to the pre-crisis decade. This could then lead to an equity gap and this in turn could undermine innovation dynamics and economic growth, respectively.

O.2.3 Policy Issues: Financial Innovations and Government R&D Support? There is an established literature that has looked at links between financial market development and economic growth (e.g., LA PORTA et al. 2002; DEMIRGÜC-KUNT/LEVINE 1999; LEVINE/ZERVOS 1998; for a skeptical view see EDISON 2002; for the EU context see BAELE et al. 2004), but the role of finan-

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cial innovations has not been discussed intensively in the literature. Rather, there is a general perception that innovations in financial markets are useful and not much critical discussion is warranted; this view is an implication of the hypothesis that financial markets are efficient—a view that has been started to be questioned seriously after the Transatlantic Banking Crisis. There is no doubt that financial innovations have played an important role in market economies over many years. To the extent that banks undertake serious R&D in financial services, one may well consider that governments should subsidize innovation activities and R&D, respectively. Research and development could be encouraged for example, through some form of R&D-related tax bonuses for companies conducting R&D. In contrast to manufacturing, industry governments in OECD countries do not really subsidize innovations in the financial services industry. There is, however, an implicit subsidization through two channels: (i) Governments to a large extent accept big banks that are too-big-to-fail; if R&D activities and financial innovations, respectively, are proportionate to the size of the bank, the implicit government guarantee—bringing lower costs of capital for big banks compared to smaller banks—could coincidentally be high enough to internalize the positive external effects of big banks’ financial product innovations (one should not underestimate the capital cost advantage of big banks: when WestLB, one of Germany’s biggest public banks, decided to setup a bad bank in 2009 and finally had reduced the size of its toxic assets. Moody’s comment (from December 8, 2009)—according to a press report from Financial Times Deutschland of December 9, 2009 (www.ftd.de/unternehmen/finanzdienstleister/:bonitaet-der-landesbankbad- bank-be...)—was that WestLB was on the brink of being downgraded since it no longer fell into the category of a system-relevant big bank. The implication is that indeed big banks enjoy an implicit subsidization of capital costs since the rating agencies anticipate in their rating that in a situation of crisis a system-relevant big banks will be saved by governments: The incentives for big banks to come up with top class governance are weakened by this mechanism and the overall competition process in the financial services sector is distorted. (ii) Governments are likely to have an implicit home bias when buying financial services from banks (e.g., placing governments bonds in capital markets might show such a home bias): If the relative mark-up is proportionate to the market share of the respective bank—as suggested by standard oligopoly models—this home bias could implicitly amount to an incentive that internalizes positive external effects from innovation. There is, however, a serious caveat for this type of implicit subsidization of financial innovations: Obviously, the above mentioned indirect form of internalization of positive external effects from innovation is not really well targeted and the main effect of (ii) could simply be to reinforce the average size of big banks. Secondly, any too-big-to-fail problem is a potential threat to effective competition in the banking sector and lack of competition—at least in critical fields of banking—will undermine the overall innovativeness of the banking system. Moreover, if any of the big banks has to be rescued by government, there will not only be enormous costs to the taxpayer, but there is also the risk that there will be a confidence shock that will

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negatively affect all other banks so that the cost of capital or the costs of insurance for certain bank activities will go up—the price of CDS for a standard loan bundle of the respective bank is one potential indicator of the price of insurance against bankspecific risk. This means that with some probability ωi , big bank i will be successful and survive—generating positive external effects E in the context of its innovations, while the probability for not surviving is ωi . In this case, there are negative external effects where the costs in the home market is Ci and the external costs abroad is Ci  . The expected net external effect of a big bank i is thus given by the expression: E i

net

= ωi E + ω i (Ci  + Ci  ).

(1)

If policymakers anticipate a negative external effect in the banking sector, one should consider measures to trim the size of the banking system. Whether policymakers really would be determined enough to dismember overweight banks is somewhat doubtful. The lobbying pressure from big banks can be quite heavy and is often very influential. It is noteworthy that the sector value-added can be negative: Denoting value-added at market prices in the banking sector j by Yj the “true net value-added” in sector j is given by Yj net = Yj + ωj Ej  + ω j (Cj  + C j ).

(2)

One cannot rule out that the true net value-added of United States investment banks plus Freddy Mac and Fannie Mae—the two large semi-public mortgage banks of the USA that were nationalized in 2008—was negative in the 2002–2008 period. Part of the capital injections into the United States semi-public banks are reflecting negative external effects from the activities of Freddy Mac and Fannie Mae themselves, which were echoed in a confidence crisis whose repercussions also affected these two banks in the end. According to estimates of the US Congressional Budget Office (from August 2008) the costs of nationalization of Freddy Mac and Fannie Mae reached $ 291 billion. As regards financial services innovation, it may be pointed out that the innovations system created in the USA and the UK and in other OECD countries in the financial services sector is much more opaque than in the case of manufacturing industries. The screening and testing undertaken in the financial services sector is much weaker than the procedures applied in the manufacturing industry. The quality control mechanisms through the financial market itself is rather weak: Many financial services are complex and certainly stand for “confidence goods” or experience goods that will only reveal their true effective utility with the course of time. There is no national or international industry body that has established itself for testing new financial services or for standardizing financial services (compared to the international electronics industry). While industrial clients of banks may to some extent be expected to have relevant knowledge and access to international benchmarks— including comparisons of financial services provided abroad—households are in a relatively weak position. Financial literacy is low, the ability to engage in costly litigation with banks that have delivered “faulty” new financial services is quite limited

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and the willingness of losers in the capital market game is also quite limited. Those who suffer for example, high losses by inadequate diversification or from misunderstanding of the characteristics of new financial services bought will often not reveal anything to friends and relatives since the loss of social reputation would come as a consequence of such public information; while exit is a mechanism supporting quality improvements in financial markets “voice” will hardly work as too many clients will be hesitant to engage themselves in the public. Banks that have launched faulty new financial products will occasionally hear in public about the fortunes made by the happy few investors thriving on the financial innovations, however, the negative news on bad experiences of clients with the new financial service will hardly be heard in public ever: The mechanism of exit might work in the financial services industry (with some delay), but the mechanism of voice is hardly existing. A minor counterexample are the standardized tests conducted by FINANZTEST, which is effectively a public foundation in Germany that tries to raise the awareness on the quality of banking services and related services. However, the bad results of FINANZTEST obtained in early 2010 in Germany—repeating a test with similar bad results during the Transatlantic Banking Crisis—suggest that banks have not learned much from the crisis. Moreover, the government is quite hesitant to impose any consequences on banks that fail to deliver even the most basic quality in standard financial services for private households. The task was to give advice to a risk-averse private customer who wished to invest € 30,000 over a medium-term period: One bank came up with the advice to invest the total amount into gold. A useful sanction to consider would be that wealth management services of banks failing to reach a minimum score in standardized tests should be closed down at rather short notice and all of the banks’ clients should get immediate information on this. As long as the incentives in the banking system of OECD countries are not changed, the misery for millions of customers and the poor average innovation performance of the banking sector is likely to continue. One question immediately arises if one is to consider the problem of external effects in the banking sector: What institution is to take care of adequate internalization of external effects in the banking sector? At first, focus has be put on competition and regulatory policy, respectively, which should bring about competitive behavior in all banks, including big banks. If one wants to subsidize positive external effects of financial innovations in a way analogous to that of other industries, for example, the option of an R&D tax rebate has to be considered; such a rebate could be obtained by a specific bank only to the extent that the bank provides proper specification of its innovation activities on the one hand—from this perspective the policy option to explicitly give conditional public subsidies for financial innovations should be carefully considered, as this is a way to finally get some transparency on the Schumpeterian dynamics in financial services. On the other hand, scientific analysis would have to shed light on the prospective size of positive external effects in the banking industry so that governments could roughly determine adequate subsidizations for innovative banks. There are internationally integrated financial markets, and therefore, we face positive external international effects. Governments from both countries (if we capture the world economy in the standard simplified two country model) would

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have to negotiate about joint subsidization of innovations on the one hand; on the other hand countries should jointly impose some form of Pigou tax on the bank for its negative international external effects. The latter is quite difficult to imagine in reality—obviously the country whose big banks (or other financial entities) have caused the negative international external effects should compensate those countries that are suffering from these negative external effects. However, if the USA—or any other big country—is the source country of the international banking crisis and international shocks, respectively, it is not very likely that the small partner countries of the USA (actually their citizens/investors/depositors) would get any compensation. The bankruptcy of Iceland’s leading banks in 2008 is an interesting case study for the topic of compensation of foreign depositors. If the interest rates of Icelandic banks had offered a risk premium for the risk of default, then it seems quite doubtful that the British and Dutch government would have decided to fully compensate the losses suffered by British and Dutch depositors of Icelandic banks, which had been nationalized by the government of Iceland. The governments of the UK and of the Netherlands then put considerable diplomatic pressure on the Icelandic government to reimburse the governments of the UK and the Netherlands for their compensation schemes.

P. New MARSHALL–LERNER Condition and Economic Globalization

P.1 Introduction High current account deficits have been a major challenge for US policy makers since the 1990s; many other countries have also occasionally faced problems with the current account deficit. Such deficits often give rise to protectionism, and it is therefore quite important to understand which policy options exist for correcting a trade balance deficit or a current account deficit. With respect to the United States, OBSTFELD/ROGOFF (2005) have raised the problem that even a considerable adjustment of the real exchange rate might be insufficient to cope with the high current account deficit. Instead, the internal relative price—the ratio of tradables to nontradables prices—would also have to adjust in a way which stimulates net exports of goods and services. The authors also emphasize that the asymmetric structure of the capital account is important, since US investment abroad is mainly in the form of equity investment and foreign direct investment (FDI), while the share of foreign investment in the United States is dominated by investment in bonds and other assets, which are less risky than equities and therefore carry a relatively low yield. The rate of return from United States foreign investment is higher than the average return foreign investors in the United States have obtained. While FDI has become a common fact of economic reality, economists have not fully taken account of its implications; one crucial implication concerns international profit transfers from subsidiaries to the parent company. One may add that for many countries in Europe, Asia, and Latin America, high cumulated FDI contributes to a considerable difference between GDP and gross national income—for example, Ireland transfers more than 1/10 of its GDP in the form of profits to parent companies of foreign MNC subsidiaries. Subsequently, we will show that (cumulated) FDI affects the reaction of both the trade balance and the current account balance. Modern globalization—characterized by high FDI flows and increasing activities of multinational companies—affects the impact exchange rates have on the external balance. While economic globalization and FDI have become a common trait of the world economy, economic modeling largely ignores the distinction between GDP and GNP

P. J. J. Welfens, Innovations in Macroeconomics, DOI 10.1007/978-3-642-11909-5_16, © Springer-Verlag Berlin Heidelberg 2011

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(as an exception see e.g., WELFENS 2008a), and this is not likely only to bring about inconsistent multiplier results, but it also implies a bias in many empirical analysis of import functions, export functions, and whole macro systems (e.g., Germany’s export function can be estimated with standard approaches in a satisfactory way; however, for many years it’s well-known that estimating Germany’s import function yields rather poor results). It is straightforward to show that the traditional derivation of the Marshall–Lerner condition brings inconsistent results for a world economy characterized by economic globalization. One should, however, not overlook that in a broader macroeconomic approach both the real exchange rate and real income will affect the current account—as has been emphasized by McKINNON (2005) in his analysis on the current account of Japan and China. Subsequently, it will be argued that the real exchange rate indeed has a direct impact on real income in the home country and the foreign country; with trade depending on GNP at home and abroad on the one hand and, on the other hand, savings and consumption depending on GNP and investment depending on the real exchange rate we get new multiplier results for the case of an FDI-augmented macro model (see the Appendix). The well-known Marshall–Lerner condition states that a real devaluation (a rise of the real exchange rate q∗ : = eP∗ /P where e is the nominal exchange rate, P the price level, and ∗ denotes foreign variables) will improve the real current account if the absolute sum of the import elasticities at home and abroad exceed unity. Alternatively, one may define a Marshall–Lerner condition as the reaction of the nominal trade balance to a change in the nominal exchange rate. This definition is useful if one wants to study pricing to market behavior which concerns the case that markups that exporting firms make vary with movements in the exchange rate—the market structure (DORNBUSCH 1987), the product-demand curve (MARSTON 1990), and the technology of the firm (BUGHIN/MONFORT 1993) imply different degrees of exchange rate pass-through so that a change in the home currency leads to between zero and a more-than-proportionate change in the foreign-currency price (BUGHIN 1996). Denoting real exports, the real exchange rate, and foreign GDP as X, q∗ and Y∗ , respectively, and assuming—with ϕ∗ being the elasticity of exports with respect to q∗ and x representing a positive parameter—the Marshall–Lerner condition can be derived by considering a standard export function X = q∗ϕ∗ xY∗ and a standard import function J = q∗−ϕ jY (J is real imports, ϕ is the absolute elasticity of J with respect to the real exchange rate, and j is a positive parameter). The current account in real terms is X = X – q∗ J. It is convenient to derive the Marshall–Lerner condition by taking a look at the equivalent ratio X = X/[q∗ J]: We get the familiar result that dX /dq∗ > 0 only if ϕ∗ + ϕ > 1. In the standard two-country model (with home country 1 and foreign country 2), the export elasticity ϕ∗ is, of course, equal to the foreign import elasticity. In the modern world economy, one should, however, not overlook that both FDI flows and multinational companies can considerably change the picture, since a realistic approach will have to consider that savings are proportionate to gross national income (and not to GDP). Moreover, imports of goods and services are proportionate to gross national income and not to GDP—the latter being the standard assumption

P.1 Introduction

517

in models without FDI. The standard literature indeed puts emphasis on the GDP. It suffices to point out that the IMF-methodology used for calculating equilibrium real exchange rates (FURUQUEE 1998, p. 56) clearly states that one considers the equilibrium savings–investment balance and the current account balance as a share of GDP and thus implicitly ignores the distinction between GDP and GNP. With FDI inflows strongly rising relative to GDP in many Newly Industrialized Countries and in many OECD countries since the mid-1980s, one should carefully consider the distinction between GDP and GNP; many OECD countries are both major source countries of FDI and host countries of FDI at the same time. These aspects imply that the modified Marshall–Lerner condition stated here—for the case of an economy with FDI and multinational companies—is stricter than the traditional Marshall–Lerner condition. It will be useful to define X as the ratio of real exports to real imports and to denote the elasticity of X with respect to the real exchange rate q∗ as EX ,q∗ . For a two-country setup—with both countries producing in accordance with a Cobb–Douglas production function and with two-way FDI— one may express the modified condition for an improvement of the current account (with ϕ, ϕ∗ denoting import elasticities in the home country and the foreign country) indirectly as ϕ∗ + ϕ − 1 > EX ,q∗ > ϕ∗ + ϕ − 2. One should note that with FDI, one has to make a distinction between the reaction of the trade balance with respect to the real exchange rate and the reaction of the current account balance with respect to the real exchange rate as profit income accruing from abroad (or paid to parent companies abroad) is part of the current account; only under the special condition that all profits earned abroad are reinvested could one ignore this distinction. One should also note that the relative size of the home country to the foreign country affects the results. In order to shed more light on the sometimes complex formula, we will consider interesting limit conditions. With both multinational companies and FDI playing an increasing role in the world economy since the mid-1980s, one may conclude that real exchange rate adjustments might have become rather ineffective in correcting current account imbalances. Given the fact that multinational companies are typically active in technology intensive production in OECD countries, it is almost natural that a real depreciation hardly helps in reducing a current account deficit. This is already obvious if one assumes that multinational companies—dominating trade within the OECD—have specialized on exports of Schumpeterian technology-intensive goods whose price elasticity is relatively low. An offsetting effect might work on the import side if there is an increasing range of intermediate products which can be imported from many producers in many countries worldwide. (If we additionally consider pricing to market, namely that the foreign price level/the import price P∗ is a negative function of e, because exporters in country II will want to dampen the loss in market share—associated with a fall of the nominal exchange rate—by lowering the national offer price in national currency units, the problem looks slightly different; considering the negative link between P∗ and e and the positive link between P and e the nominal depreciation rate required to correct a current account deficit would rise even more.) The following analysis considers the impact of FDI inflows and FDI outflows and shows that the presence of FDI requires higher import elasticities in absolute

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terms than stated in the standard Marshall–Lerner condition (in the simple setup presented we focus on a two-country model where ß stands for the share of profits in GDP of country 1 and ß∗ for the share of profits in GDP of country 2—using a Cobb–Douglas function in both countries facilitates the analysis considerably, but the arguments presented can easily be generalized). Following the mathematical derivation in Sect. 2, the final section presents key policy conclusions.

P.2 FDI, the External Balance and the Real Exchange Rate With inward FDI and outward FDI, one has to make a distinction between real gross domestic product (Y) and real gross national product (Z). For ease of exposition, the following analysis assumes that both the home country and the foreign country produce on the basis of a Cobb–Douglas function where K denotes capital, L labor, and ∗ ∗ A knowledge. Hence, we haveY = Kß (AL)1−ß in country 1 andY∗ = K∗ß (A∗ L∗ )1−ß in country 2 (∗ denotes foreign variables; 0 < ß < 1). It also is assumed that there is competition in goods market and factor markets so that profit income in country 1 (home country) is equal to ßY, in country 2 equal to ß∗Y∗ . Thus we can—denoting the share of country 1 capital stock owned by foreign investors as α∗ and the share of country 2 capital stock owned by investors from country 1 as α—express Z and Z∗ , respectively, as follows: Z∗ = Y∗ (1 − αß∗ ) + α∗ ßY/q∗

(1)

Z = Y(1 − α∗ ß) + q∗ αß∗ Y∗

(2)

α∗ ßY

will accrue to investors in As ßY stands for profits in country 1 the amount country 2; profits accruing from 1—expressed in units of country 2’s output—thus is given by α∗ ßY/q∗ . A real devaluation will reduce the real GNP in country 2, as real profits (expressed in units of country 2’s output) accruing from country 1 have reduced. As regards real gross national income in country 1, we clearly see that a real devaluation will raise Z which in turn stimulates imports of goods if real imports J are proportionate to Z. Note that α is in the interval 0,1; and the same holds for α∗ . The next analytical step to consider is the assumption that exports of goods and services depend on the real exchange rate and the real foreign GNP—not on GDP as stated traditionally. Similarly, imports depend on real GNP; we will assume imports are proportionate to real GNP. Thus we will derive a Modified Marshall–Lerner condition (as a first step in a setup without international profit transfers): X = X(q∗ , (1 − αß∗ )Y∗ + α∗ ßY/q∗ );

(3)

J = J(q∗ , Y(1 − α∗ ß) + q∗ αß∗ Y∗ );

(4)

We specify the following modified equations for exports and imports, respectively (x and j are positive parameters as are ϕ and ϕ∗ ): ∗

X = q∗ ϕ x[Y∗ (1 − αß∗ ) + α∗ ßY/q∗ ]

(5)

P.2 FDI, the External Balance and the Real Exchange Rate

J = q∗−ϕ j[Y(1 − α∗ ß) + q∗ αß∗ Y∗ ]

519

(6)

If one computes X = X/[q∗ J] and calculates dX /dq∗ we get a modified Marshall– Lerner condition. Here it should be noted that a real depreciation reduces real income of the foreign source country and thus dampens exports of goods; conversely, the denominator in X is raised through the term q∗ αß∗Y∗ . It therefore will not come as a surprise that the following mathematical derivation shows that the import elasticities in the foreign country and the home countries have to exceed the range defined by the standard Marshall–Lerner condition. It will be straightforward to show that for the special case of a small open home economy and for the case of a dominant home economy the Marshall–Lerner condition reads dX /dq∗ > 0 if ϕ∗ + ϕ > 2; the same condition is obtained for the case of “symmetrical long-term FDI involvement” in the sense of αß∗ = α∗ ß (while not considering the additional constraint that Y =Y∗ ). For the special case of a symmetric world economy—with equal size of countries (Y =Y∗ and the initial q∗ being unity) and symmetric cumulated FDI involvement of both countries (αß∗ = α∗ ß)—the modified Marshall–Lerner condition looks rather similar to the standard Marshall–Lerner condition: The elasticity EX ,q∗ = ϕ∗ + ϕ − 1 − 2α∗ ß. Considering that the output elasticity of capital typically is 1/3 and that the ratio of α (or of α∗ ) rarely will exceed 0.5 the implication is that in this extreme case we have to consider that EX ,q∗ will be positive if ϕ∗ + ϕ > 1,33. Before we turn to the formal analysis, one should note that FROOT/STEIN (1991) have argued that FDI—in a world of imperfect capital markets—should positively depend on q∗ ; the authors have presented empirical evidence for the United States that the ratio of FDI inflows to GDP positively depends on the real exchange rate. A fortiori one may consider the case that α and α∗ depend on q∗ . In the formal analysis, we will ignore the FROOT/STEIN argument at first and only later we will take into account that α∗ is a positive function of the real exchange rate while α is a negative function of q∗ .

Formal Analysis The formal analysis starts by considering the ratio of real exports to real imports and taking logarithms. We then calculate the elasticity of X with respect to q∗ (see Eq. 10). It should be noted that we will refer to the relative size of the foreign economy through the parameter : =Y∗ /Y. One may indeed use such a parameter here while a general equilibrium approach—in which Y and Y∗ also would depend on q∗ —does not require us to stipulate any given ratio Y∗ /Y. The interesting point in deriving the subsequent modified Marshall–Lerner condition is that the limit case of  approaching infinity represents the case of a small of economy (Y relative to Y∗ is very small), while the case of  approaching zero means that we consider a setup in which the home economy is dominant (Y∗ is very small relative to Y). The first step in our analysis is to consider the effect that real exports are proportionate to foreign GNP; and that real imports are proportionate to real GDP—an aspect which

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already has been raised in WELFENS (2008) in the context of an asymmetric general equilibrium model (FDI flows only in one direction). As X : = X/(q∗ J) we have: ∗

q∗ ϕ x[Y∗ (1 − αß∗ ) + α∗ ßY/q∗ ] X = ∗1−ϕ q j[Y(1 − α∗ ß) + q∗ αß∗ Y∗ ] 

= q∗ϕ

∗ +ϕ−2

x[q∗ Y∗ (1 − αß∗ ) + α∗ ßY] <0 j[Y(1 − α∗ ß) + q∗ αß∗ Y∗ ]

(7)

Using the parameter  from the implicit definition Y∗ = Y gives: ln(X ) = ln(q∗ϕ

∗ +ϕ−2

) + ln(x[q∗ Y∗ (1 − αß∗ ) + α∗ ßY])

− ln(j[Y(1 − α∗ ß) + q∗ αß∗Y∗ ]) = (ϕ∗ + ϕ − 2)ln(q∗ ) + ln(x) − ln(j) + ln(q∗ Y∗ (1 − αß∗ ) + α∗ ßY) − ln(Y(1 − α∗ ß) + q∗ αß∗ Y∗ ) = (ϕ∗ + ϕ − 2)ln(q∗ ) + ln(x) − ln(j) + ln(q∗ Y(1 − αß∗ ) + α∗ ßY) − ln(Y(1 − α∗ ß) + q∗ αß∗ Y) = (ϕ∗ + ϕ − 2)ln(q∗ ) + ln(x) − ln(j) + ln(q∗  − αß∗ q∗  + α∗ ß) − ln(1 − α∗ ß + q∗ αß∗ )

(8)

The elasticity EX ,q∗ is calculated using the equivalence: E

x ,q∗

Ex ,q∗

  d ln(X ) d ln(X ) ∗ d ln(X ) d ln(q∗ ) −1 = = q (9) = d ln(q∗ ) dq∗ dq∗ dq∗ + ' 1 − αß∗ αß∗ ∗ = ϕ + ϕ − 1+ − 1−α∗ ß − 1 < ϕ∗ + ϕ − 1 ∗ ∗ 1 − αß∗ + qα∗ ß + αß ∗ q  (10)

The inequality holds because [.] is negative: 1 − αß∗ 1 − αß∗ +

α∗ ß q∗ 

1 − αß∗ 1 − αß∗ +

−

α∗ ß q∗ 

αß∗ 1−α∗ ß q∗ 

+ αß∗

−1<0

αß∗ < 1+ 1−α∗ ß ∗ q∗  + αß

1 − α∗ ß 1 − α∗ ß ∗ + αß∗ − αß − αß∗ αß∗ ∗ q  q∗     1 − α∗ ß α∗ ß ∗ ∗ < + 2αß 1−α ß+ ∗ q∗  q 

P.2 FDI, the External Balance and the Real Exchange Rate

αß∗ − 1 <

0<

1 − α∗ ß (q∗ )2

521

+2

α∗ ß q∗ 

α∗ ß 1 − α∗ ß + 2 + (1 − αß∗ ) q∗  (q∗ )2

With α = 0 this gives Ex ,q∗ = ϕ∗ + ϕ − 1 −

1 ∗ 1+ qα∗ß

(10 )

With α∗ = 0 this gives: Ex ,q∗ = ϕ∗ + ϕ − 1 −

1 1+ αß∗1q∗ 

(10 )

For 1 − α∗ ß − αß∗ > 0 it also holds that ϕ∗ + ϕ − 1 > Ex ,q∗ > ϕ∗ + ϕ − 2 as: α∗ ß 1 − α∗ ß > ∗ ∗ q αß (1 − αß∗ )q∗  (1 − α∗ ß)(1 − αß∗ )q∗  >q∗ αß∗ α∗ ß q∗  − α∗ ßq∗  − αß∗ q∗  > 0 1 − α∗ ß − αß∗ > 0 For the limit processes  → ∞ and  → 0 it holds that: Ex ,q∗ =ϕ∗ + ϕ − 2

(11)

In the case of αβ∗ = α∗ β = 0.5 the elasticity is as well given as: Ex ,q∗ =ϕ∗ + ϕ − 2

(12)

Let us also consider the special case of two rather similar countries with symmetrical two-way FDI. In the case of q∗  = 1 and αβ∗ = α∗ β, the elasticity is given by: Ex ,q∗ =ϕ∗ + ϕ − 1 − 2αβ∗

(13)

So far we have analyzed a setup in which there is a distinction between GDP and GNP, namely because there is FDI. Implicitly, however, we have focussed on a situation in which there are no effective international profit transfers (so all profits obtained abroad are invested in the host country). Alternatively, we could say that the conditions derived so far refer to the reaction of the trade balance to the real exchange rate. Let us now consider the current account in the case that there are international profit transfers. In the following analysis, we want to consider profit

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transfers received (and transferred to the source country) as an explicit element of ˜ overall exports X (and similarly on the import side) so that X is substituted by X ∗

˜ = q∗ ϕ x[Y∗ (1 − αß∗ ) + α∗ ßY/q∗ ] + αß∗ Y∗ /q∗ X

(14)

J˜ = q∗−ϕ j[Y(1 − α∗ ß) + q∗ αß∗ Y∗ ] + q∗ α∗ ßY∗

(15)

This gives a new condition for the ratio of overall exports to overall imports: q∗1+ϕ x[Y∗ (1 − αß∗ ) + α∗ ßY/q∗ ] + αβ∗ Y∗ >0 q∗2−ϕ j[Y(1 − α∗ ß) + q∗ αß∗ Y∗ ] + q∗3 α∗ βY∗ ∗

X =

(16)

ln(X ) = ln(q∗1+ϕ x[Y∗ (1 − αß∗ ) + α∗ ßY/q∗ ] + αβ∗ Y∗ ) 2−ϕ −ln(q∗ j[Y(1 − α∗ ß) + q∗ αß∗ Y∗ ] + q∗3 α∗ βY∗ ) ∗

∗

E −

x ,q∗

(17)

(1 + ϕ∗ )q∗ ϕ xY∗ (1 − αß∗ ) + ϕ∗ q∗ϕ α∗ ßY = ∗1+ϕ∗ q x[Y∗ (1 − αß∗ ) + α∗ ßY/q∗ ] + αß∗ Y∗ ∗−1

(2 − ϕ)q∗1−ϕ j[Y(1 − α∗ ß) + q∗ αß∗ Y∗ ] + q∗2−ϕ jαß∗ Y∗ + 3q∗2 α∗ βY∗ q∗2−ϕ j[Y(1 − α∗ ß) + q∗ αß∗ Y∗ ] + q∗3 α∗ βY∗

(18)

In the case of Y∗ = Y and α∗ = 0 this gives: Ex ,q∗ = (1 + ϕ∗ )q∗−1

1 ∗ 1+ ∗ϕ∗−1αß q x(1−αß∗ )

− (2 − ϕ)q∗−1 + q∗−1

1 1 αß∗ q∗ 

+1

(19)

If Y∗ = Y and α = 0 this gives: ∗−1

Ex ,q∗ =

(1 + ϕ∗ )x + ϕ∗ q α∗ ß (2 − ϕ)q∗−1−ϕ j(1 − α∗ ß) + 3α∗ β − (20) x[q∗  + α∗ ß] q∗−ϕ j(1 − α∗ ß) + α∗ β

Even considering purely asymmetric cases does not yield clear results.

The FROOT–STEIN Aspect FROOT/STEIN (1991) have argued that in a world of imperfect international capital markets, FDI inflows will be a positive function of the real exchange rate, and international bidding games are influenced by the amount of equity capital a foreign bidder can put up—the higher the amount is, expressed in units of the host country’s currency, the higher the loan which can be obtained for a leveraged international mergers & acquisition. A real depreciation of the host country currency implies that foreign bidders will have more equity capital and thus are more likely to take over firms in country 1 (host country). Let us go back to Eq. (10) and assume that indeed α

P.3 Policy Conclusions

523

and α∗ are a function of q∗ . Note that considering the FROOT/STEIN (1991) effect, namely that α is a negative function of q∗ and α∗ is a positive function of q∗ only slightly modifies the result obtained. Ex ,q∗ = ϕ∗ + ϕ − 2 + −

 − αß∗  − αq∗ ß∗ q∗ +αq∗ ß q∗ − αß∗ q∗  + α∗ ß

−α∗ q∗ ß+ αß∗  + q∗ αq∗ ß∗  1 − α∗ ß + q∗ αß∗ 

(21)

The general case with FDI inflows and FDI outflows is, however, quite cumbersome. Even the simple case of asymmetric FDI outflows does not yield straightforward analytical results so that empirical analysis will have to shed more light on the results derived.

P.3 Policy Conclusions Taking into account FDI and the role of multinational companies implies a modified Marshall–Lerner condition. Compared to the original Marshall–Lerner condition one may state the general finding that the sum of the absolute elasticities must exceed unity by an additional term. This is an interesting insight, but it should not be considered a general implication that real exchange rate movements will be less powerful in a world of globalization—a two-country model with FDI—than in a world without factor mobility. No such implication can be stated without looking at least a simple macro model (this is done in the Appendix, namely for a specific parameter constellation). However, it is clear that in a consistent Mundell–Fleming model with FDI a real depreciation (appreciation) would shift the IS curve less to the right (left) than the traditional Mundell–Fleming approach suggests. The effectiveness of fiscal policy and monetary policy under alternative exchange rate regimes thus will be affected. As regards the need to modify the Marshall–Lerner condition in a world with FDI—and international profit transfers—a general analysis with inward FDI and outward FDI does not easily yield unambiguous results. More straightforward are the analytical findings for certain special parameter constellations. The special case of asymmetric pure FDI outflow (and no profit repatriation) has shown that the requirements for the sum of the import elasticities in the home and the foreign countries are sharper than the original Marshall–Lerner condition. This case is approximately represented by the combination United States and non-OECD countries (as country 2) so that a real depreciation of the US currency would have to be stronger than the traditional Marshall–Lerner condition suggests (also the EU in combination with non-OECD countries are a similar case). Interestingly, a sharper condition than the original Marshall–Lerner requirement also holds in the case of a rough internationalization symmetry, which roughly is the United States and the EU. If the US current account deficit is largely vis-à-vis Asia and the EU—as is the case in reality—the elasticity requirements are clearly sharper than Marshall–Lerner suggests. There is, however, no reason for a general elasticity pessimism. While it is true

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that modern economic globalization brings about a larger role for both FDI and multinational companies, one should also consider the growing role of an international splitting up of the value-added chain, which includes a rising share of intermediate products exported by Newly Industrialized Countries (e.g., Mexico, Brazil, Asian NICs). Since exporters from developing countries and NICs can hardly pursue pricing to market behavior—as opposed to innovative exporters of final products in OECD countries—the changing international division of labor could lead to an increase in import price elasticities. With respect to the United States, there is considerable evidence that pricing to market behavior has weakened—and US import price elasticities have increased—in the context of rising imports from Mexico in the period 1985– 2005 (BUSSIERE/PELTONEN 2008, p. 24). The BUSSIERE/PELTONEN analysis highlights several influences on the import elasticities and comes up with several key insights, namely that the elasticity of trade prices in NICs is not significantly higher than in OECD countries; elasticities are mainly determined by macroeconomic influences such as the inflationary environment and the exchange rate regime—product differentiation also plays a role. Moreover, elasticities are found to be strongly correlated across countries. Exchange rate pass-through to import prices has reduced in the United States and in some other countries, which is consistent with an increase in pricing-to-market in several NICs and particularly with a change in the geographical composition of imports of the United States. As regards the role of international profit transfers, one may, on the one hand, consider periods of tranquility in which a normal share of profits made abroad is repatriated. On the other hand, periods of crisis in which firms in FDI source countries—facing a liquidity shock—tend to reduce new outward FDI might therefore want to repatriate a larger share of profits. (In periods of tranquility profits abroad, this will typically be reinvested to a large extent.) The case of asymmetric pure FDI inflow (and not profit repatriation) implies weaker elasticity requirements than the Marshall–Lerner condition. A typical case of such an asymmetric FDI inflow pattern is China. By implication, real exchange rate adjustments by China should be a relatively powerful instrument to affect China’s current account. There are several issues which could be crucial in future research: (i) Calculating a fundamental equilibrium exchange rate will have to take into account—current and cumulated—FDI inflows and FDI outflows. (ii) In a macro model with rational expectations and a fixed exchange rate regime, economic agents will want to anticipate the time path of all policy variables. This, however, creates a difficult problem, since it is doubtful that nominal exchange rates can be credibly fixed on the one hand. On the other hand, one would have to anticipate both the time path of the foreign price level relative to the domestic price level, which in turn puts the focus on domestic monetary policy and monetary policy in the anchor country. Moreover, there also could be a certain probability of a change in the exchange regime, which makes modeling rather complex—at the same time this raises new empirical issues. (iii) The enormous asymmetry of the world economy in terms of inward (cumulated) FDI– GNP shares and outward (cumulated) FDI–GNP shares raises some doubts about

Appendix P.1: Macro Model with FDI

525

the notion of a real effective exchange rate, since this is related only to geographical patterns of trade but does not consider relative FDI stocks. Key concepts in international macroeconomics—for example, the fundamental real equilibrium exchange rate—will have to be reconsidered in the modified context emphasized here. Export functions should be stated in a way that the quantity of exports depends of real foreign GNP (not on foreign GDP) and imports should be considered as depending on real GNP. Finally, one may note that FDI is typically linked to international technology transfer and future research might look into these aspects. For example, it is quite interesting to consider an asymmetric, two-country model—with country 1 being the only source country—in which the level of technology abroad (A∗ ) is a positive function of α. Such a perspective corresponds to the FDI approach of DUNNING (1977) and is also in line with empirical findings for some countries (e.g., GÖRG ET AL 2006). As FDI outflows will reflect ownership-specific advantages (read: technology advantages) of the respective firms in the source country, FDI inflows in country 2 will bring about an international technology transfer. Finally, one may note that within a macro model, capital flows and certain model parameters affect trade dynamics in several important ways: (1) the net asset position of the private sector may affect savings, imports and exports; (2) the structure of capital flows—the share of FDI in total capital flows—will be affected by the real exchange rate (FROOT–STEIN argument); and the parameters of the money demand function and the adjustment speed of learning in the equation describing exchange rate expectations—for example, in the context of the DORNBUSCH model—will affect the degree of nominal and real exchange rate overshooting. If there is an excessive, temporary depreciation, this will bring about higher FDI inflows, which in turn will affect both GDP and GNP. Thus, there is a broad array of new issues to be considered in further theoretical and empirical research.

Appendix P.1: Macro Model with FDI The role of multinational companies has increased in the global economy over many years, and hence (FDI) has therefore become an increasingly important aspect of real economic life. As multinational companies are major drivers of technological progress, FDI is not only affecting capital formation in host countries but also international technology transfer and supply-side dynamics. In the presence of FDI, one has to make a distinction between real gross domestic product (Y) and real gross national income (Z). The difference can be considerable as is known from countries such as Ireland, Hungary, or China, which represent small countries and a large country, respectively, ranking among leading host countries—with not much outward FDI. The United States, Germany, France, the United Kingdom, and the Netherlands as well as Switzerland are key players in both a host country perspective and a source country perspective. A simplified model with asymmetric FDI (the home country is the only source country) brings out some new ambiguities with respect to the multiplier

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analysis: The modified Mundell–Fleming model with FDI looks more complicated than the traditional setup. In a simple, two-country model—where both countries produce according to a Cobb–Douglas function, namely Y = Kß (AL)1−ß and Y∗ = —with K, A, L, and ∗ denoting capital, knowledge, labor, and foreign variables, respectively (0 < ß < 1)— the GNP of the single source country 1 (home country) is Z =Y + αß∗Y∗ q∗ ; here α is the share of country 2’s capital stock owned by investors from country 1 and q∗ is the real exchange rate eP∗ /P where e is the exchange rate and P the price level. It has been assumed that in both countries there is competition in goods markets and labor markets so that production factors are rewarded in accordance with the marginal product rule, and hence profits from abroad, expressed in units of country 1’s output, are ß∗Y∗ q∗ . If one wants to understand the role of FDI inflows, it is crucial to point out that GNP is given by Z = Y(1 − α∗ ß), where α∗ is the share of the host country’s capital stock owned by investors from country 2; again for the sake of simplicity the setup is asymmetric so that we consider only capital inflows in country 1. Does FDI make a difference in terms of the Mundell–Fleming model? It does for various reasons where one assumption adopted here is that investment is a positive function of the real exchange rate q∗ ; this link between the real exchange rate and FDI inflows was pointed out in the context of an approach with imperfect capital markets by FROOT/STEIN (1991) who presented positive empirical evidence for the United States. Moreover, one has to consider that consumption is proportionate to GNP and that imports are proportionate to GNP; and one has to add an additional element, namely that net capital imports are a positive function of q∗ so that the augmented Mundell–Fleming model reads for the case of a non-inflationary world (τ is the tax rate, b, b’ and b as well as j and x are positive parameters, G is government consumption; by assumption real exports X = jZ∗ /q∗ so that the elasticity of X with respect to q∗ is unity and real imports J = jZ/q∗ so that the respective elasticity is minus one: Y = c(1 − τ)(1 − α∗ ß)Y + [bq∗ − b r + b (ßY/K − ß∗Y∗ /K∗ )] + G − q∗ jY(1 − α∗ ß)/q∗ + xq∗ [Y∗ + α∗ ßY/q∗ ] (goods market equilibrium) 

M/P = hY − h r

(I)

(money market equilibrium)

(II)

 ∗

n r − n r∗ + [b (ßY/K − ß∗Y∗ K ∗ ) + n q ] = q∗ jY/q∗ − xq∗ [Y∗ + α∗∗ ßY] (equilibrium condition for the foreign exchange market /external equilibrium)

(III)

The consumption function thus is C = c(1−τ)(1 − α∗ ß)Y, the investment function I = I(q∗ , r, ) where r is the real interest rate and  the differential between the domestic marginal product of capita YK (YK = ßY/K) and Y∗ K ∗ (abroad Y∗ K = ß∗Y∗ /K∗ ). As regards the demand for money, it has been assumed that the real demand for money is proportionate to real GDP and a negative function of the interest rate; an alternative specification would be the case that the money demand is not proportionate to

Appendix P.1: Macro Model with FDI

527

Y but to Z. The modified investment function—taking into account the arguments of FROOT/STEIN with respect to the link between FDI inflows and q∗ —implies that a real depreciation will bring about a stronger rightward shift of the new IS curve than the standard Mundell–Fleming model; a real depreciation will not only affect net exports of goods but also raise FDI inflows. With respect to the medium term there is, however, a theoretical caveat which concerns the distinction between international mergers and acquisitions—the type of FDI emphasized by FROOT/STEIN—and greenfield investment. (q∗ also will affect FDI inflows here because acquiring land for building a new factory is facilitated if there is a real depreciation of the currency of the host country, but the medium-term effect could be rather a future excess supply in the goods market—if the capacity effect of investment were considered.) Real net capital inflows are assumed to be a positive function of r − r∗ ∗ (r : = r∗ + a where a is the expected depreciation rate of the currency which is assumed to be zero; n and n are positive parameters) and a positive function of both q∗ and ; the square bracketed term on the left hand side of the equilibrium condition for the foreign exchange market stands for FDI inflows while n (r − r∗ ) represents portfolio capital inflows. It is only for the sake of simplicity that we consider the simple case that the absolute elasticity of imports with respect to q∗ and the elasticity of goods exports with respect to q∗ are assumed to be unity. Next let us solve for the special case of exports inelastic with respect to q∗ for the real exchange rate (in this case any real exchange rate change will leave net exports of goods unaffected) so that we get: ∗

q∗ = [n r − n r + b ß∗Y∗ /K∗ − xY∗ ]/n + [(j + xα∗ ß − b ß/K)/n ]Y

(IV)

If one considers only the foreign exchange market and ignores the goods market equilibrium condition, the implication is that the real exchange rate is a positive function of Y—provided that j + xα∗ ß > b ß/K—and a negative function of Y∗ ; the latter holds if x > b ß∗Y∗ /K∗ . It is noteworthy that the slope of the balance of payments equilibrium line EE—not shown here—could have a zero slope in r − Y space, namely if n approaches infinity (the traditional case) and if j + xα∗ ß = b ß/K. The latter case implies that a marginal rise in goods imports generated by a rise in Y—net of the effect of higher exports generated by the rise of GNP abroad—would automatically be offset by rising FDI inflows, which will react to a higher Y as (at given K) this represents a rise in the marginal product of capital. Note that in principle, a real depreciation not only affects net goods imports but also net capital inflows. If the parameter n is relatively large, there is a strong financing impact of a real depreciation, since not only a rise in q∗ will dampen net imports of goods and services, but net imports of capital will increase at the same time through higher FDI inflows. Subsequently, we summarize the whole set of equations and derive the multipliers. Y = cY − b r∗ G + xq∗ Y∗ − jY

(V)

M = hY − h r P

(VI)

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u r − u r ∗ = jY − xq∗ Y∗ ⎛

1−c+j ⎝ h −j

b −h u

⎞⎛ ⎞ ⎛ dY 1 0 −xY 0 ⎠ ⎝ dr ⎠ = ⎝ 0 1 dq∗ xY∗ 0 0 ⎛

1−c+j h U = det ⎝ −j + xY∗



b −h u

1−c+j h

xq∗ 0 −xq∗

(VII) ⎛ ⎞ ⎞ dG 0 ⎜ dM/P ⎟ ⎟ (VIII) 0 ⎠⎜ ⎝ dY∗ ⎠  u dr ∗

⎞   −xY h −h 0 ⎠ = −xY∗ −j u xY∗

b −h



(IX)

= −xY∗ (h(u + b) + (1 − c)h ) < 0 dY h xY∗ =− >0 dG U

(X)

xY∗  dY =− (b + u ) > 0 dM/P U

(XI)

dY =0 dY∗

(XII)

dY u h xY∗ >0 = dr∗ U

(XIII)

dr hxY∗ =− >0 dG U

(XIV)

(1 − c)xY∗ dr = <0 dM/P U

(XV)

dr =0 dY∗

(XVI)

dr u hxY∗ >0 = −  dr∗ U

(XVII)

dq∗ hu − h j = dG U

(XVIII)

(1 − c + j)u + b j dq∗ =− >0 dM/P U

(XIX)

q∗ dq∗ = − <0 dY∗ Y∗

(XX)

Appendix P.1: Macro Model with FDI

529

dq∗ u = − ((1 − c + j)h + b h) > 0  dr∗ U

(XXI)

Y = c(Y(1 − α∗ β) + αβ∗ q∗ Y∗ ) + c τ (G , G )Y# + I(r, q∗ , βY/K − β∗ Y∗ /K ∗ ,  ) + G + G + x(q∗ )(Y(1 − α∗ β) + αβ∗ q∗ Y∗ ) − q∗ j(q∗ )(Y(1 − α∗ β) + αβ∗ q∗ Y∗ )

(XXII)

M = h(Y(1 − α∗ β) + αβ∗ q∗ Y∗ ) − h r P

(XXIII)

Q(r,r ∗ ,q∗ , βY/K − β∗ Y∗ /K ∗ ,  ) = q∗ j(q∗ )(Y(1−α∗ β) + αβ∗ q∗ Y∗ ) − x(q∗ )(Y(1−α∗ β) + αβ∗ q∗ Y∗ ) ⎞⎛ ⎞ ⎛ k4 dY k3 −Ir ⎝−h(1 − α∗ β) h −hαβ∗ Y∗ ⎠ ⎝ dr ⎠ Qr k6 dq∗ k5 ⎞⎛ ⎞ ⎛   dG c τG + 1 c τ G + 1 k1 0 0 hαβ∗ q∗ ⎠ ⎝ dG ⎠ =⎝ 0 0 k2 dY∗

(XXIV)

(XXV)

k1 = cαβ∗ q∗ − β∗ IY∗ /K ∗ + x(q∗ )αβ∗ q∗ − q∗ j(q∗ )αβ∗ q∗ k2 = β∗ QY∗ /K ∗ − x(q∗ )αβ∗ q∗ + q∗ j(q∗ )αβ∗ q∗ k3 = 1 − c(1 − α∗ β) − IY β/K − x(q∗ )(1 − α∗ β) + q∗ j(q∗ )(1 − α∗ β) ∗

∗

k4 = −cαβ∗ Y∗ − Iq∗ − (xq∗ αβ∗ q Y∗ + x(q∗ )αβ∗ Y )   ∗ ∗ j (q∗ ) (Y(1 − α∗ β) + αβ∗ q Y∗ ) + q∗ jq∗ (Y(1 − α∗ β) + αβ∗ q Y∗ ) + ∗ + q∗ j (q∗ ) αβ∗ Y k5 = QY β/K − q∗ j(q∗ )(1 − α∗ β) + x(q∗ )(1 − α∗ β) ∗

∗

k6 = Qq∗ + (xq∗ αβ∗ q Y∗ + x(q∗ )αβ∗ Y )   j(q∗ )(Y(1 − α∗ β) + αβ∗ q∗ Y∗ ) + q∗ jq∗ (Y(1 − α∗ β) + αβ∗ q∗ Y∗ ) − ∗ ∗ + q∗ j(q∗ )αβ Y ⎛

⎞ k3 −Ir k4 U = det ⎝ −h(1 − α∗ ß) h −hαß∗ Y∗ ⎠ k5 Qr k6 = k3 h k6 + Ir hαß∗ Y∗ k5 − k4 Qr h(1 − α∗ ß) + k3 hαß∗ Y∗ Qr − k4 k5 h − Ir h(1 − α∗ ß)k6

(XXVI)

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⎛ dY 1 = det ⎝ dG U =

c τ G + 1 0 0

−Ir h Qr

⎞ k4 −hαβ*Y* ⎠ k6

(c τG + 1)(h k6 + hαβ*Y*Qr ) >0 U

(XXVII)

We assume U is positive. ⎛   c τ G + 1 1 dY ⎝ 0 = det dG U 0 =

⎞ k4 −hαβ*Y* ⎠ k6

(c τG + 1)(h k6 + hαβ*Y*Qr ) >0 U

⎛ k1 −Ir 1 dY ⎝ hαβ∗ q∗ h = det dY∗ U k2 Qr =

−Ir h Qr

(XXVIII)

⎞ k1 hαβ∗ Y∗ ⎠ k6

k1 h k6 +Ir hαβ∗ Y∗ k2 +k4 Qr hαβ∗ q∗ +k1 hαβ∗ Y∗ Qr −k4 k2 h +Ir hαβ∗ q∗ k6 <0 U if k1 h k6 < 0 (XXIX)

Q. Trade, Innovation and Output Dynamics

Q.1 Introduction There is a broad range of research on trade and growth and there is also considerable empirical evidence on the range of the link between trade and the level of GDP and GDP per capita, respectively. The evidence is relatively clear for OECD countries, namely that there is a positive link between the two variables, however, looking at developing countries (and some newly industrializing countries), the evidence is negative (JUNGMITTAG 2009; HERZER 2009); it is noteworthy that the analysis of JUNGMITTAG simultaneously considers the links between trade, foreign direct investment (FDI), and real income. HERZER finds in his extended heterogeneous panel data analysis that the share of natural resources in exports negatively affects real income per capita; so for a certain group of countries, higher trade goes along with higher GDP per capita. However, according to JUNGMITTAG (2009), the positive effect of trade for certain countries seems to be conditional on FDI inflows. However, to some extent, there is a lack of theoretical analysis with respect to the link between trade and GDP and between trade, FDI, and GDP. As regards economic globalization, both trade dynamics and international investment dynamics play a crucial rule—moreover, innovation dynamics that are both related to trade and FDI are part of modern globalization. Standard trade theory suggests that economic opening up brings about specialization gains. In a macroeconomic supply-side perspective, it seems natural to translate this in an adequate way into a production function; this is done here in alternative ways. The basic insight from the analysis—based on Cobb–Douglas’ production functions both in country I and country II (foreign country)—is that the role of trade can be easily incorporated into the macroeconomic production function.It should be emphasized that both specialization effects and trade-related technology transfer effects may be considered. Those could be related to trade in technology-intensive products—a channel for which there is ample empirical evidence. Moreover, it can also be shown that both trade and FDI can be considered in a straightforward manner; at least the asymmetric case of cumulated FDI is rather easy to consider.

P. J. J. Welfens, Innovations in Macroeconomics, DOI 10.1007/978-3-642-11909-5_17, © Springer-Verlag Berlin Heidelberg 2011

531

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From a theoretical perspective, there are basically two elements to consider the link between trade and GDP: • Trade can directly enter the production function; the idea that trade stimulates technological specialization in a model with two goods and two production factors (or n goods and N factors), therefore, the fact that specialization gains from opening up of the economies can be exploited and real income gains are realized has a corollary in the macroeconomic production function: If the production function ∗at home and∗ abroad under autarchy are given by Y = Kβ (AL)1−β and Y∗ = K∗β (A∗ L∗ )1 − β , respectively, opening up implies that output elasticities change or that effective factor inputs are raised. • Trade can also affect key parameters of the neoclassical growth model; for example, the growth rate of technological progress can be affected by trade. Subsequently, we will take a look at both possibilities. Further research—mainly empirical research—would have to shed light on the question of what analytical approach is most adequate. There is, however, also a standard empirical approach, namely the gravity equation to trade, which looks doubtful against the background of the analysis developed here. The popular gravity equation basically states that imports of country i from country j is a positive function of country i’s GDP and of country j’s GDP and a negative function of the transportation costs and distance between country i and j, respectively. If, however, imports (or more generally: trade) contribute to GDP, there is an endogeneity problem in the standard specification of the trade gravity equation. Imports between country I and II—to focus on a simple two-country setup—are not simply a function of GDP in country I/country II and the distance between the countries considered; so what is the alternative approach that duly takes account of the endogeneity problem described here. While the gravity equation has emphasized that the trade volume will react with respect to both the GDP of the importing country and that of the partner country, which delivers the relevant goods, the question of links between trade and output developments/economic growth is relatively complex. In the 50 years since 1960, global trade has grown strongly since trade barriers have been dismantled among the OECD country group and also in many other countries. Tariffs were reduced and this has amounted to effectively falling trading costs. Rising trade volumes have contributed to higher global output, not least since many imports stand for embodied technological progress; moreover, rising trade in intermediate products also stands for a broader sharing of knowledge and technology, respectively—and this has contributed to real income gains. Moreover, the growth of real income worldwide and the rise of per capita income—the latter stimulating trade in differentiated products—have contributed to high growth rates of trade. Regional integration schemes in Europe, North America, Latin America, and Asia (EU, NAFTA, MERCOSUR, ASEAN) have also contributed to higher trade, at least in a regional context. The increasing use of information and communication technology (ICT) in the 1980s and 1990s has stimulated the growth of output and trade, where international outsourcing and off-shoring has played a considerable role (MEIJERS/DACHS/WELFENS 2007). As regards EU eastern enlargement, it should also

Q.1 Introduction

533

be noted that over time trade within EU-25 has become more similar in the field of industry, which suggests that vertical trade has increased over time (BORBÉLY 2006). The empirical analysis of JUNGMITTAG (2006) suggests that non-international specialization (“Smithian specialization”) contributes to higher output per capita in EU countries, and it is rather high-technology specialization (“Ricardian specialization”) that generates higher per capita income through higher trade. Empirical analysis of trade in a cross-section of countries should work fairly well since for a given observation period, it may be assumed that real incomes Yi and Yj are not affected by trade in the short run. EGGER/LARCH (2007) have presented a cross-section of some 16,000-country pairs for 2005: empirical evidence shows that a membership of countries in preferential trading agreements stimulates other countries to also participate in such trading clubs or to create new trading clubs. A more difficult issue concerns the role of panel data analysis for the gravity model of trade, which, of course, requires GDP in the importing country and the trading partner country to be exogenous. Here, we will shed new light on the issues and it will be argued that panel data analysis can be quite misleading; for example, the analysis of ROSE (2000), which has found that the WTO has no positive impact upon trade sufferers from the endogeneity problem. The endogenous variable volume of imports—or trade—must not be explained by the same variable on the right-hand side of the equation; misspecification of the regression equation will lead to confusing and inconsistent results, which could then induce policymakers to take doubtful decisions. Various authors have analyzed the impact of certain variables on economic growth: RAHMAN/MUSTAFA (1997) and JIN/YU (1995) have presented empirical evidence on the link between exports and growth; moreover, HESS/PORTER (1993) have explored the impact of money on growth and CASELLI ET AL. (1996) and CARROLL/WEIL (1994) have looked at the link between savings and growth. This perspective clearly suggests a look at bridging growth modeling and trade modeling, which is also crucial for theoretical reasons (WELFENS 2007). FRYGES/WAGNER (2007) have analyzed the link between exports and output growth: Based on the newly developed generalized propensity score methodology, the authors estimate the link between a company’s export–sales ratio and its growth rate of labor productivity on the basis of a sample of German firms—there is a causal effect of companies’ export activities on the growth of labor productivity (but exporting raises labor productivity growth only within a sub-interval of the range of companies’ export–sales ratios). Trade has grown enormously in the 50 years after 1958, when convertibility was re-established in Western Europe. A major newcomer in world trade after 1978— the year of economic opening up—was China, which has become a leading trading country in merchandise trade within three decades (see Table 1); this new role of China is largely coupled with high economic growth, opening up for FDI (GRAHAM 2004), and modernization of infrastructure plus WTO memberships at the beginning of the twenty-first century. FDI inflows were to some extent coupled with portfolio capital inflows—the latter often being the frontrunner of overall capital inflows (with FDI following only after confidence of foreign investors had been nurtured to a critical extent). Stock market capitalization in China and other Newly Industrialized

2

1

27.9 20.2 7.5 3.7 2.6 2.7 1.3 0.3 1.7 1.2

30.1 21.9 11.6 4.9 4.6 2.4 1.8 1.7 1.6 1.5

2001–2005 15.7 21.2 8.5 6.9 1.2 5.7 0.5 0.7 0.7 1.3

1971–1975 11.6 18.5 7.4 4.7 7.2 4.4 2.7 3.1 1.0 1.2

2001–2005

1971–1975

20.5 15.7 6.7 3.1 14.0 1.9 1.8 1.6 5.7 2.7

2001–2005

1971–1975

22.5 21.3 8.0 4.3 3.0 2.1 1.7 0.6 3.5 2.7

Exports

At market exchange rates

At PPP exchange rates

Excluding intra-euro trade area Data in column 1971–1975 are for 1976–1980

US Euro area1 Japan UK China2 Canada Mexico Korea India Brazil

Merchandise Trade

GDP

15.6 21.2 7.9 7.9 1.3 5.5 0.8 0.9 0.8 1.9

1971–1975

Imports

19.7 16.9 5.8 5.6 6.2 4.0 2.9 2.7 1.2 0.9

2001–2005

Table 29 Role of large economies in the global economy. (Source: IMF 2007, World Economic Outlook, Washington DC, pp. 122–123)

44.4 15.3 9.4 7.5 1.9 2.8 0.5 1.1 0.8 0.8

2001–2005

Stock Market Capitalization

534 Innovations in Macroeconomics

Q.2 Trade and the Production Function

535

Countries has increased in the decade prior to the Transatlantic Banking Crisis. China as a new regional economic gravity center should stimulate regional trade expansion in Asia, but also trade with the EU (new key trading partner of China) and the United States. By contrast, India’s share in world trade is relatively low and protectionism, as well as barriers to FDI inflows, might play a role in this. It is well known that in OECD countries roughly 1/3 of trade is intra-company trade so that lack of multinational companies—that is insufficient FDI inflows and FDI outflows—implies that trade opportunities are not fully exploited; this in turn means that specialization gains as well as gains from international economies of scale are not fully used and intra-company technology flows across borders are also smaller than they could be. At the bottom line, dynamic trade—including trade in productcycle goods—will stimulate structural change and hence productivity growth and economic growth, respectively. While high imports of machinery and equipment are typical for countries catching-up, a major driving force linking trade and output dynamics are intermediate products that play an increasing role in the context of international fragmentation (MEIJERS/DACHS/WELFENS 2007). The implication is that links between trade and economic dynamics can be different for different groups of countries. In the subsequent analysis, the focus will be on the link between trade and output development (and vice versa). The basic idea is to modify the macroeconomic production function in a way that it takes the role of trade into account; moreover, this modified production function for an open economy can be integrated into a modified (neoclassical) growth model—here, the focus will be on international technology transfer as well. Moreover, the modified growth model allows us to consider the role of FDI, too. At the bottom line, we get a better theoretical understanding of the interaction of trade, FDI and technology dynamics in open economies. The paper is organized as follows: Section II looks at the integration of trade in the production function; Sect. III is a critical look at the gravity equation. Finally, it will be shown that a modified neoclassical growth model allows to restate the optimum growth literature in an important way: It can be shown that there is an optimum income tax that maximizes per capita consumption in the steady state of an open economy with technological progress—the elasticity of technological progress with respect to the income tax rate and some other parameters play a critical role here.

Q.2 Trade and the Production Function: Growth in Open Economies Looking for a consistent link between trade activities and output requires focusing on various alternatives; the import–GDP ratio could be decisive for the level of output or the level of the growth path in a modified open economy growth model; or the import relative to labor in efficiency units; or some other well founded specification. A basic insight from a neoclassical growth model with labor L, capital K, and laboraugmenting knowledge A is that the steady-state solution (# for steady state) can be

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derived, namely for k := K/(AL) and for y :=Y/(AL). Assuming a Cobb–Douglas function, Y = Kβ (AL)1 − β (0 < β < 1), a savings function S = sY(1 − τ) and a constant growth rate of labor (n) and a constant growth rate of knowledge (a), the steady-state solution—with δ being the depreciation rate of capital—reads as follows (WELFENS 2007): • k  # = {(s/(a + n + δ)}1/1−β • y # = {(s/(a + n + δ)}β/1−β • Therefore (with e denoting the Euler number, t the time index) for the longrun per capita income, we have y# = {A0 [(s/(a + n + δ)]β/1 − β }eat ; the term {. . . } determines the level of the growth path, while the term indicates that the trend growth rate of per capita income is equal to a-and for Y it will, of course, be equal to a + n (it is noteworthy that a rise in “a” will reduce the level of the growth path, while the trend growth rate will be raised!). Thus, the interesting questions in a two-country open economy growth model will refer to the issues of how trade and FDI affect the solution on the one hand, on the other hand, international technology transfer will also be an interesting issue: For example, if the foreign country ∗ ∗ (∗ denotes foreign variables) produces according to Y∗ = K ∗ β (A∗ L∗ )1 − β , will foreign technology affect technology in country I (home country), where a special case is a = a∗ , so that the foreign country fully determines the growth rate of technology in country I? Let us take a look at a production function first, in which the export ratio X/Y and the import ratio J/Y both enter the production function; both exports and imports of goods raise the production potential, however, it is only the ratio X/Y and J/Y that matters (according to the assumption made here; in the end, only empirical analysis can clarify which one is the relevant specification). X/Y is a quasi-input that reflects specialization gains in the open economy, J/Y could also be a quasi-input factor, namely to the extent that intermediate products from abroad are used in production— and again, the argument of specialization gains has to be considered. Alternatively, J/Y could be considered as a proxy for the intensity of import competition, which in turn contributes to efficiency gains. To stay it as simply as possible, we will use equal exponents for x and j, but in principle there is no problem in considering different weights for x and j, respectively. It will be assumed that X = x(. . . )Y∗ and imports of goods are J = j(. . . )Y. At the bottom line, a direct link can be established between Y and Y∗ , as will be shown subsequently; the production function is as follows (with ϕ denoting a positive parameter): Y = Kβ [(X/Y)(J/Y)]ϕ (AL)1−β

(1a)

The particular assumption made here is that both the export–GDP ratio and the import–GDP ratio contribute to a higher GDP; moreover, for the sake of simplicity, it is assumed that the output elasticity of X/Y is the same as for J/Y; however, the alternative case of different elasticities could also be considered. Whether this specification is adequate can only be determined on the basis of empirical analysis. It is noteworthy that an alternative convenient formulation is (1a) Y = Kβ [1 + (X/Y)(J/Y)]ϕ (AL)1 − β ,

Q.2 Trade and the Production Function

537

which would have the advantage of implying that X = J = 0, making the function boil down to the case of the closed economy; but in order to avoid tedious mathematical calculations, the function has been chosen as shown in Eq. (1a). One also may point out that a more refined version of (1a) can be stated asY = Kβ (X/Y)ϕ (J/Y)ω (AL)1 − β which allows to include the case that the import–GDP ratio contributes less to aggregate output than the export–GDP ratio; moreover, allowing the parameter ω to be in the interval (−∞,1) one could consider a setup in which the import–GDP ratio negatively affects output. The subsequent export function X and the import function J are fairly standard (x and j are parameters in the interval 0, 1) and rather simple since x and j are not assumed to depend on the real exchange rate q∗ = eP∗ /P (e is the nominal exchange rate, P is the price level, and P∗ is the foreign price level). In principle, taking q∗ into account is not posing special problems, but the impact of q∗ is indeed not in the focus of the following analysis. So we have as the export and import function, respectively: X = xY∗

(1b)

J = jY

(1c)

Inserting (1b) and (1c) into (1a) we get Y = K β [xjY∗ /Y]ϕ (AL)1−β

(1d)

Y = K β [xjY∗ /Y]ϕ (AL)1−β

(1e)

Y1+ϕ = K β (xjY∗ )ϕ (AL)1−β

(1f)

Y = {[(xjY∗ )]ϕ/(1+ϕ) }K β/(1+ϕ) (AL)(1−β)/(1+ϕ)

(1g)

Note that the modified output function (1g) is not homogenous in K and AL and the output elasticities of K and labor in efficiency units (AL) have diminished. At the same time, there is a supply-side multiplier effect in the term {[(xjY∗ )]ϕ/(1+ϕ) }, which implies that a rise in foreign output by 1% will raise GDP by [ϕ/(1 + ϕ)] percent: the cross-output elasticity of Y with respect to Y∗ is smaller than unity. The term {. . .} looks like a quasi-Hicks-neutral progress factor. Empirical analyses that use a production function with Hicks-neutral technology could, therefore, identify a significant impact of such a technology element, while in reality trade is behind the argument (!). Moreover, it is noteworthy that trade intensity in the production function implies positive externalities of foreign knowledge A∗ , L∗ , and K∗ since ∗ ∗ the foreign production function is assumed to be Y∗ = K ∗ β (A∗ L∗ )1 − β . One should notice that a current account surplus—more specifically: x exceeding j by an adequate size—implies a positive impact on the production potential here. Next we take a look at the expression for Y/(AL), where AL is labor in efficiency units: y = {[(xY∗ j)]ϕ/(1+ϕ) }k 

β/(1+ϕ)

(1h)

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Taking a closer look at this quasi-production function, we may state that the export– import ratio and foreign output have a magnifying effect on the GDP.As the exponents for both K and AL are reduced, there will be a positive net effect on national output only if the term {[(xY∗ j)]ϕ/(1+ϕ) } is sufficiently large, therefore Y∗ must exceed a critical minimum size (note that one may also consider the case that X/Y and J/Y have different exponents in the production function, but the general insight is not affected by this modification). A very important aspect is concerned with growth accounting. Taking the natural logarithm for the quasi-production function Y(. . .) yields (with the definition ϕ := ϕ/(1 + ϕ)) lnY = ϕ (lnx + lnj + lnY∗ ) + [β/(1 + ϕ)]lnK + [(1 − β)/(1 + ϕ)] ln(AL) (1i) Since x and j are constant, taking the derivative with respect to time (with g denoting growth rate; and using the approximation 1/(1 + ϕ) ≈ (1−ϕ), which is valid for small ϕ), yields gY ≈ ϕ gY* + [β(1 − ϕ)]gK + [(1 − β)(1 − ϕ)](a + n) = βgK + (1 − β)(a + n) + [ϕ gY* − ϕ(βgK +(1 − β)(a + n)]

(1j)

Comparing this growth accounting to the result of a closed economy, namely the equation gY = βgK + (1 − β)(a + n), implies that trade will raise the growth rate compared to the case of a closed economy if ϕ gY* > ϕ(βgK + (1 − β)(a + n))

(1k)

This insight points to a potential problem in empirical growth accounting where the progress rate (a) is taken as the residual; however, in a growth accounting exercise, the effective residual in an open economy is (a + ϕ gY∗ )—at the same time, it should also be noted that the elasticities for the growth rate of labor and capital, respectively, will not add up to unity.

Different Elasticities for Export–GDP Ratio and Import–GDP Ratio If we consider different elasticities of the export–GDP function and the import–GDP function (elasticity ω which in principle could be negative) we have to consider the production function: Y = Kβ (X/Y)ϕ (J/Y)ω (AL)1−β

(1a )

The case that J/Y has a negative impact on Y (ω < 0) clearly has to be distinguished from the case of a positive impact. From the production function we get, Y(1+ϕ) = Kβ (xY∗ )ϕ (j)ω (AL)1−β

(1b )

Q.2 Trade and the Production Function

Y = [(xY∗ )ϕ/(1+ϕ) (j)ω/(1+ϕ) ]Kβ/(1+ϕ) (AL)(1−β)/(1+ϕ)

539

(1c )

Obviously: ∂Y/∂j > 0 if ω > 0. The second derivative is negative if ω < (1 + ϕ); this raises an interesting empirical question. For the case of ω < 0 the second derivative is negative. The equation obtained for the growth model looks as follows: gY ≈ βgK + (1 − β)(a + n) + [ϕ(1 − ω)gY∗ − ω(βgK + (1 − β)(a + n))] (1j ) Comparing this growth accounting to the result of a closed economy, namely the equation gY = βgK + (1 − β)(a + n), implies that trade will raise the growth rate compared to the case of a closed economy if ϕ(1 − ω)gY* > ω(βgK + (1 − β)(a + n))

(1k )

In the steady state, we will have gK = (a + n) so that the inequality reads the following: gY* > [(a + n)]/{ϕ[(1/ω) − 1]}

(1k )

In the steady state gY = a + n (assumed to be positive) so that 1/ω should be in the interval (0, 1) if the right-hand side is to be positive. In order to meet the requirement of the inequality, the foreign growth rate of GDP will have to exceed the home growth rate by a critical margin if the term {ϕ[(1/ω) −1]} exceeds unity. Note, however, that the inequality holds always if ω is negative. The latter case points to a paradox since ω < 0 implies that the average import-GDP ratio negatively affects Y while the growth rate of Y is raised more intensively through the international growth link (the term [ϕ(1 − ω)gY∗ − ω(βgK + (1 − β)(a + n))]). The empirical results for the United States and Germany (WELFENS/ISLAMI 2010)—based on OLS for yearly data for the period 1983–2007—show that trade has a positive significant effect on GDP: • The regression for the logarithm of GDP shows for the case of the United States that the current capital stock, the current hours of labor worked and imports affect (endogenous variables are all in logs) are relevant variables for the sample period 1983–2006. The fact that lagged capital stock—the lag is one year—has a negative impact on GDP can be assumed to reflect a dampening effect of a capital stock adjustment process on real output. The elasticity of output with respect to the current capital stock input is 1.9%, the elasticity for hours worked (lagged by one period) is 0.2%, while that for the current import–GDP ratio is 0.09. Such a positive impact for the trade variable (weakly significant here) suggests that intermediate goods are a crucial element of overall imports. The adjusted R2 is 0.72. • As regards Germany, the current capital stock variable as well as the export– GDP ratio have a significant impact on GDP in the sample period 1992–2007. The lagged capital stock has a negative impact and the lagged patent applications also; the latter points to adjustment costs on raising the level of knowledge. The import–GDP ratio has a negative elasticity with respect to output, and this might point to the fact that foreign firms that successfully sell products in Germany impose adjustment costs on the overall real economy.

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Regression Results for GDP, Trade, Capital, Labor, and Technology: The United States and Germany Endogenous is GDP (D at the beginning of the variable means first difference); CS is capital stock, IMPQ is the ratio of imports to GDP, HL is hours of labor worked, EXPQ is the ratio of exports to GDP, PAT is patent application at the European Patent Office and the US patent office—equal weights for patent applications in Europe and the United States (No. in bracket behind variable indicates lag). The tables show the best-fit “final equation” of the basic setup lnGDP = f(lnCS, lnIMPQ, lnEXPQ, lnPAT). Country: United States Method: Least Squares Sample (adjusted): 1983 2006 Included observations: 24 after adjustments Variable

Coefficient

t-Statistic

Prob.

DCS DCS(−1) DIMPQ DHL(−1) R-squared Adjusted R-squared

1.8861 −1.1322 0.0860 0.2167 0.7545 0.7177

6.1634 −4.0162 1.7539 2.5121

0.0000 0.0007 0.0948 0.0207

Country: Germany Dependent Variable: DGDP Method: Least Squares Sample (adjusted): 1992 2007 Included observations: 16 after adjustments Variable

Coefficient

t-Statistic

Prob.

DCS DCS(−1) DEXPQ DIMPQ DPATENT(−1) R-squared Adjusted R-squared

3.1957 −2.2096 0.1497 −0.1832 −0.1038 0.8026 0.7308

5.7909 −4.4420 2.3107 −2.4929 −2.9713

0.0001 0.0010 0.0412 0.0299 0.0127

Patent: number of patent applications Source: WELFENS/ISLAMI (2010), Trade Dynamics and Economic Growth: An International Empirical Approach, European Institute for International Economic Relations (EIIW) at the University of Wuppertal/Schumpeter School for Business and Economics, EIIW Paper No. 180, March 2010

In an analytical perspective, one may argue the ratio of exports to imports is the implicit result of an international tournament on international goods market—read: markets for tradable goods. Exports stand for companies which have won the contest against their foreign rivals, imports stand for fields in which foreign firms have a

Q.2 Trade and the Production Function

541

comparative advantage. One may, however, note that exports to some extent will contain imported intermediate products (containing specialization gains and embodied technological progress) and those intermediates stand for inputs which facilitate exporting firms to conquer foreign markets. Therefore the “net interpretation” of trade effects on GDP growth is not really easy. Ideally, the empirical approach should consider two types of imports, namely final goods and intermediate goods, but getting adequate data is quite cumbersome.

Foreign Direct Investment The standard MacDougall model of foreign direct investment shows that—with a given world capital stock—opening up for FDI in a two-country model will result in an increase in GNP in both countries; labor will benefit in the host country of FDI, while capital will benefit in the source country of FDI. An easy way to translate this insight into a macroeconomic production function is the following formulation (where α is a positive parameter in the interval (0, 1) and α∗ denotes the share of the overall capital stock in country I owned by foreign investors): β

Y = [K(1 + α α∗ )] (AL)1−β

(1l)

Taking into account that ln(1 + z) ≈ z for small z, we get the followig after taking logarithms: lnY ≈ β lnK + β α α∗ + (1 − β)ln(AL)

(1m)

Obviously, the production function can be rewritten as  ∗

Y ≈ K β (AL)1−β eβ α α

(1n) α α∗

Hence, FDI will bring a real income gain provided that eβ > 1; this is an interesting  ∗ empirical issue. Subsequently we will define eβα α := e . There is, however, an additional aspect to be considered: One may indeed easily include the role of (cumulated) FDI inflows. If α∗ denotes the share of the capital stock owned by foreign investors—assuming that there is competition in goods and factor markets (hence profits will be βY and the share accruing to subsidiaries from abroad is α∗ ), therefore, the savings function is S = s(1 − τ)Z (Z is GNP =Y − α∗ βY. Hence the savings function is S = s(1 − τ)(1 − α∗ β)Y and the solution for a growth model would read (with β := β/(1 + ϕ): y # = {[s(1 − τ)(1 − α∗ β)]e [(xY∗ j)]ϕ/(1+ϕ) /(n + a + δ)}β/1−β

(1o)

Note that for the sake of simplicity the setup considered is asymmetric; there are FDI inflows in country I but there is no FDI flowing into country II. We can now see at first sight that the steady state per capita income is raised through trade, while cumulated FDI inflows have an ambiguous impact (there is a negative impact from

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Innovations in Macroeconomics

α∗ , but e stands for positive impact provided that e > 1). However, a broader reflection suggests an important caveat: The growth rate of technology a is likely to be positively affected by the presence of FDI so that a = a(α∗ ); thus the trend growth rate is raised through cumulated FDI inflows, while the level of the growth path is reduced. A crucial question now concerns the time horizon of policymakers and voters, respectively: If they are not too short-sighted, they will be in favor of FDI inflows as the long-run effect on the trend growth rate will dominate the short-term fall in the level of the growth path. It is noteworthy that the exponent for {. . .} is the same as in a closed economy, which makes the role of trade and FDI easy to identify, respectively: y # = {[s(1 − τ)/(n + a + δ)]}β/1−β {[(1 − α∗ β)]}e [(xY∗ j)]ϕ/(1+ϕ) }β/1−β (1p) The first bracket term is exactly the term obtained in a neoclassical growth model of a closed economy. However, we are interested in a broader analysis with trade, FDI and foreign technology; all these elements are included in the second term {(1 − α∗ β)]e [(xY∗ j)]ϕ/(1+ϕ) }β/1−β . We can rewrite the above equation in a way that we solve for Y(t): Y(t) = {[s(1 − τ)/(n + a + δ)]}β/1−β {(1 − α∗ β)e [(xY∗ j)]ϕ/(1+ϕ) }β1−β A0 e

(a+n)t

(1q)

Taking into account that Y*(t) will grow over time—assuming that the progress rate abroad is a*, while the growth rate of the population is n*—basically implies that the growth rate of output in the steady state is given by the term; this is obvious from taking logarithms and looking at the derivative with respect to time: gY # = (a + n) + [ϕ β/(1 − β)]

(1r)

This is an interesting new result as it has been shown that both the level of growth path and the steady state growth rate are affected by economic opening up. The statement for the steady growth rate is unambiguous: The growth rate is higher than in a closed economy.

Structure of Trade In this subsection, we want to consider the role of the structure of trade—and the role of FDI will be ignored for the moment. Here, it has to be first considered that the savings function in a closed economy is S = s(1 − τ)Y, where s is the savings rate and τ is the income tax rate: In an open economy, the savings function could be affected by the structure of trade (in a two-sector model this could be modeled in an explicit way); for example, the share of x of natural resources exports in total exports could negatively affect savings since natural resource prices are strongly volatile— translating into high volatility of profits in the natural resources sector—therefore, (at the aggregate level) risk-averse individuals will wish to reduce their savings rate

Q.2 Trade and the Production Function

543

as a function of x . Thus—with χ denoting a positive parameter in the interval [0, 1]—the savings function will read S = s(1 − τ)(1 − χ x  )Y. Note that we will assume that Y* is constant. Imposing the goods market equilibrium condition S = dK/dt + δK (δ is the depreciation of capital) and a constant growth rate (a) of knowledge A, the steady state income y # (with y :=Y/(AL) and # denoting the steady state) will be determined according to the following equation: y # = [s[(xY∗ j)]ϕ/(1+ϕ) (1 − τ)(1 − χ x )/(a + δ)](β/(1+ϕ))/(1−β(1+ϕ))

(1s)

Thus, per capita income (y) in the steady state is given—with A0 denoting the initial level of technology—by the following equation: y# = A0 [s[(xY∗ j)]ϕ/(1+ϕ) (1 − τ)(1 − χ x )/(a + δ)](β/(1+ϕ))/(1−β(1+ϕ)) e

at

(1t)

Disregarding the elasticity effect on K and AL, we can state: Opening up will raise per capita income if {[(xY*j)]ϕ/(1+ϕ) (1 − χ x )} > 1 the potentially negative impact χ x from natural resources exports should, therefore, remain below a critical limit if there is to be a positive link between trade and the steady-state per capita income. Using the approximation that ln(1 + z) ≈ z for z being close to zero, the condition {[(xY∗ j)]ϕ/(1+ϕ) (1 − χ x )} > 1 can be restated as[ϕ/(1 + ϕ)](lnx + lnY∗ + lnj) − χ x > 0; therefore it holds that x < {[ϕ/(1 + ϕ)](lnx + lnY∗ + lnj)}/χ has to be fulfilled, if the share of natural resource exports x is larger than the critical boundary, per capita output will not benefit from opening up for trade—there is a negative trade impact related to a quasi-Dutch disease effect. A high share of natural resources in production and exports is likely to bring about a reduced investment–GDP ratio (or a reduced savings rate), because the relative prices of natural resources are rather unstable which in turn translates into a reduced aggregate investment–GDP ratio. Moreover, a high share of natural resources exports and a high share of the natural resources sector are likely to go along with corruption—HERZER (2009) finds empirical evidence for both institutional weakness/corruption and a high share of natural resources in exports to explain the negative link between trade and per capita income in relatively poor countries.

Q.2.1 Alternative Asymmetric Model for Trade and Growth Let us consider the following alternative specification (with ϕ standing for a positive parameter) that highlights the impact of exports on GDP in an open economy: 

Y = K β (1 + lnX/Y)ϕ (AL)1−β

(2a)

X = xY∗

(2b)

ln Y ≈ β ln K + ϕ ln(xY∗ /Y) + (1 − β) ln(AL)

(2c)

(1 − ϕ ) ln Y = β ln K + ϕ ln(xY∗ ) + (1 − β) ln(AL)

(2d)

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Defining β : = β/(1 − ϕ ) and ϕ = ϕ /(1 − ϕ ) ln Y = β ln K + ϕ ln(xY∗ ) + (1 − β )/(1 + ϕ ) ln (AL)

(2e)

Obviously we have β < β, therefore, trade and exports, respectively, amount to reducing output elasticities of both capital and labor in efficiency units; but there  is quasi-Hicks-neutral external progress component xY∗ϕ . The implied production function is thus 





Y = K β (xY∗ )ϕ (AL)1−β

(2f)

the case 0<ϕ<1 The elasticity of Y with respect to Y* is unity if ϕ∗ = 1; here, ∗ ∗ ∗β ∗ ∗ 1−β is considered as realistic. Assuming that Y = K (A L ) in country II—the foreign country (here, I and II are thus asymmetric in terms of the impact of exports on output)—we have 

Y = xϕ K ∗β

∗  ϕ

 (1−ß∗ )

(A∗ L∗ )ϕ



K β (AL)(1−β



)/(1+ϕ )

(2g)

Obviously the output elasticity of capital is larger than in a closed economy, while the output elasticity of labor (in ∗efficiency units) ∗could be smaller than in a closed   economy; assuming that xϕ" K ∗β ϕ (A∗ L∗ )ϕ (1−β ) exceeds units, is a rather weak “minimum requirement” for output in an open economy with trade to be larger than in a closed economy. If theoretical analysis can clearly establish that output in an open economy with trade is higher than in a closed economy-this is a standard textbook result (except for the empirically not really relevant case of “immiserizing growth”, which brings a critical deterioration of the terms of trade/the relative goods price as a consequence of opening up; at the same time, the output expansion is biased in favor of the good whose relative price is falling after opening up the economy)-then ∗  βϕ  the term xϕ K ∗ (A∗ L∗ )ϕ (1−β ) should exceed unity by a critical margin. If we assume, however, an almost symmetric production function for country II    (compared to country I), namely Y∗ = K ∗β * (jY)ϕ∗ (A∗ L∗ )1−β * in country II— exports of country II are, of course, equivalent to imports of country I—then the explicit production function for country I becomes: 

Y = Kβ [xK∗ ∗ ϕ )

Y = {[x1/(1−ϕ



(AL)(1−β

K∗

β∗

β ∗ /(1−ϕ∗ ϕ )

∗







(jY)ϕ (A∗ L∗ )1−β ∗ ]ϕ (AL)1−β ∗ /(1−ϕ∗ ϕ )

jϕ

 ∗

(A∗ L∗ )(1−β

(2h)

)/(1−ϕ∗ ϕ ) ϕ



] }K β

)/(1−ϕ∗ ϕ )(1+ϕ )

/(1−ϕ *)

(2i)

Taking the definition of β = β/(1 + ϕ ) into account and using—for small ϕ —the approximation β ≈ β(1 − ϕ ), we get: lnY = {ϕ (1/(1 − ϕ∗ ϕ )) lnx + ϕ β∗ (1 − ϕ∗ ϕ ) lnK ∗ + ϕ [ϕ∗ /(1 − ϕ∗ ϕ )] lnj + +ϕ (1 − β∗ )(1 − ϕ∗ ϕ ) ln(A∗ L∗ )} + β(1 − ϕ )/(1 − ϕ∗ ) lnK + (1 − β(1 − ϕ ))/[(1 − ϕ∗ ϕ )(1 + ϕ )] lnAL (2j)

Q.2 Trade and the Production Function

545

Whether or not trade raises output can be determined on the basis of two elements: • The bracket term {. . .} should exceed unity; to put it differently: Taking logarithms implies that the sum of the elasticities for lnx, lnK*, lnj, and lnA*L* should exceed unity. • The sum of elasticities for K and AL, respectively, should exceed unity; a neutral case would be that the output elasticity of capital is equal to β and the elasticity of labor in efficiency units (AL) is equal to 1 − β. Assuming that ϕ and ϕ * are in the interval (0, 1), the output elasticity of capital and labor will be raised through trade under certain parameter conditions. At first, we take a look at the output elasticity of capital K and we can see that the condition for the elasticity to be higher than in a closed economy (namely β) is given by the condition: β /(1 − ϕ∗ ) > β

(2k)

β/[(1 + ϕ )(1 − ϕ∗ )] > β

(2l)

ϕ (1 − ϕ∗ ) > ϕ∗

(2m)

lnϕ > ϕ∗ + lnϕ∗

(2n)

A useful approximation is

Recalling that ϕ∗ := ϕ∗ /(1 − ϕ∗ ), it may be stated that the above condition is only met if the impact of the export–GDP ratio on output is much larger than that of the import–GDP ratio. The condition for the output elasticity of AL to exceed 1−β (the case of a closed economy) is rather complex (see the appendix): ϕ [1 − ϕ∗ ϕ (1 + 1/ϕ )] > (2β − 1)/(1 − β) 2

(2o)

If 0 < β < 0.5 (which is a realistic case for OECD countries), we must additionally have that ϕ∗ ϕ (1 + 1/ϕ2 ) > 1. To get a better understanding, we consider the expression ϕ [1 − ϕ∗ ϕ (1 + 1/ϕ )] > [−(1 − β)2 + β2 ]/(1 − β)

(2p)

1 + ϕ [1 − ϕ∗ ϕ (1 + 1/ϕ )] > [β2 /(1 − β)]

(2q)

2

2

As an approximation, we consider (after taking the logarithm) ϕ [1 − ϕ∗ ϕ (1 + 1/ϕ )] > β + 2lnβ

(2r)

ln ϕ − ϕ∗ ϕ (1 + 1/ϕ ) > ln(β + 2lnβ)

(2s)

2

2

This condition cannot be fulfilled since ϕ := ϕ /(1 + ϕ ) < 1. We, therefore, conclude that trade can raise—under specific parameter constellations—the output elasticity of capital (compared to the case of a closed economy), while the output elasticity of

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labor is reduced through trade. This is quite important since this finding suggests that trade is not a full substitute for international labor movements—an inflow of foreign workers into country I (or country II) will typically not only shift the labor supply curve to the right, but labor supply could also become elastic—particularly if labor inflows are more skill-intensive than domestic labor supply. At the bottom line, we may state that trade amounts to a quasi-Hicks factor in the production function; disregarding the output enhancing effects of higher output elasticities of capital, it may be stated that the level of output is raised by the factor {. . .}. Foreign output becomes a quasi-positive external effect for domestic output.

Q.2.2 Quasi Economies of Scale in a Simple Two-Country Model To some extent, economic benefits from trade are related to international economies of scale; both countries produce at least one export product under economies of scale, opening up of countries generates real income gains that are related to the existence of a large integrated world market and the associated efficiency gains (e.g., reduction of X-inefficiencies in the sense of Leibenstein) or economies of scale. How can we consider this effect in a macroeconomic production function? The following equation suggests a straightforward way to solve the challenge at hand: ρ

Y = Kβ (AL)1−β (1 + ρlnY + ρ lnY∗ ) Y1/

ρ



(3a)



= K β/ρ (AL)(1−β)/ρ (1 + ρlnY + ρ lnY∗ )

(3b)

Let us assume that ρlnY + ρ lnY∗ is very small, therefore, we can use the approximation ln(1 + z) ≈ z. Thus taking logarithms yields (1/ρ ) lnY ≈ (β/ρ ) lnK + ((1 − β)/ρ )[lnA + lnL] + ρlnY + ρ lnY∗

(3c)

Next we can solve for lnY and finally we will get the new quasi-production function, which is not linear-homogenous under various parameter constellations (the case of economies of scale can be identified on the basis of certain parameter restrictions). [(1/ρ ) − ρ]lnY = (β/ρ )lnK + ((1 − β)/ρ )[lnA + lnL] + ρ lnY∗  )/(1−ρ ρ )

Y = Kρ(β/ρ

 )/(1−ρ ρ )

(AL)ρ((1−β)/ρ



  )

Y∗ (ρρ )/(1−ρ ρ

(3d) (3e)

Let us define β := ρ(β/ρ )(1 − ρ ρ ), therefore, we can write 





  )

Y = K β (AL)1−β Y∗ (ρρ )/(1−ρ ρ

(3f)

The elasticity ofY with respect toY* contains all the (semi-) elasticities used for covering the impact of international economies of scale or the role of international market integration. It is interesting to consider the above type of international integration—or

Q.2 Trade and the Production Function

547

economies of scale effect—since it is obviously not easy to disentangle trade-related output effects and the type of international integration effects (or scale effects) of the kind just covered here. Again, standard growth accounting is misleading in the sense that the standard analysis will argue that the growth of output can be decomposed into the growth rate of the capital stock and the growth rate of labor on the one hand, on the other hand, there is the progress rate (multi-factor productivity growth rate a); according to the approach presented here, the growth rate of output gY = β gK + (1 − β )(a + n) + (ρρ )(1 − ρ ρ )gY∗ . The standard growth accounting mistakenly lumps the terms (1 − β )a and (ρρ )(1 − ρ ρ )gY∗ , which is a rather serious problem since gY∗ = β∗ gK∗ + (1 − β∗ )(a ∗ + n∗ ). Therefore, the multifactor productivity of country I measured empirically in the traditional growth accounting approach implies an inconsistent mixture of domestic technological progress and the rate of technological progress plus the terms with gK∗ and n∗ . Interestingly, international economies of scale are rather easy to cover in a macroeconomic production function; the production function is still linear-homogenous in K and (AL), however, foreign output now enters country I’s GDP as a quasi-scale factor; the exponent of Y* exceeds unity, therefore, for foreign output exceeding unity, opening up of country I and country II will yield a positive real income effect for country I.

Q.2.3 Open Economies Growth Model: The Role of Technological Progress In an open economy, the output of the partner country could affect the development of technology. One possibility to be considered is to assume that the change in the level of knowledge is proportionate to lndY*/dt; the larger the change of output abroad, the more technology spillovers and international network effects among firms may be assumed to occur—and this technology spillover is assumed to be related to the export–GDP ratio x ; moreover, similar network effects may also be assumed in the home country, therefore lndY/dt could also affect dA/dt. Thus—with positive parameters x , j and λ” (j might represent the share of imported intermediate imports in technology-intensive sectors)—we want to consider the following technological progress function: dA/dt = λ x lndY∗ /dt + j lndY/dt; dY*/dt > 0; dY/dt > 0

(4a)

A = λ x lnY∗ + j lnY + Z

(4b)

Without loss of generality, we can subsequently set Z = 1. Next consider the production function Y = K β (AL)1−β

(4c)

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Innovations in Macroeconomics

Inserting the result from the technology function, we get Y = Kβ [(λ x lnY∗ + j lnY + 1)L]1−β

(4d)

Y1/(1−β) = Kβ/(1−β) [(λ x lnY∗ + j lnY + 1)L]

(4e)

For simplicity of exposition, we assume that λ x lnY* + j lnY is relatively small, therefore, we can use the approximation ln(1 + x) ≈ x: [1/(1 − β)]lnY ≈ [β/(1 − β)]lnK + (λ x lnY∗ + j lnY) + lnL

(4f)

So that we get [(1/(1 − β)) − j ]lnY ≈ [β/(1 − β)]lnK + λ x lnY∗ + lnL

(4g)

Defining [(1/(1 − β)) − j ] := β we get an implicit logarithmic production function that can be estimated: lnY = {[β/(1 − β)]/β ]}lnK + (1/β )λ x lnY∗ + (1/β )lnL

(4h)

The production function—defining β = {[β/(1 − β)]/β }—is thus given by lnY = ß lnK + (1/ß )λ x lnY∗ + (1/ß )lnL

(4i)

The function is not linear-homogeneous in K and L. Foreign GDP will positively affect domestic GDP; the elasticity (EY,Y∗ ) of Y with respect to Y* is given by the expression EY,Y∗ = {(1−β)/[(1/(1−β))−j ]}λ x ; this expression is assumed to be larger than unity. Obviously Y and Y* will grow at the same rate only if the following condition holds: 1 = {(1−β)/[(1/(1−β))−j ]}λ x . This elasticity is larger • • • •

the larger the impact of β on EY, Y* the larger j the larger x the larger λ

The explicit production function can be written as 





Y ≈ K{β/[(1−β)β ]} L[(1−β)/β ] Y∗[(1−β)/β

]λ

(4j)

With a standard savings function S = s(1−τ)Y and imposing the equilibrium condition S = dK/dt + δK, the requirement for a steady state to exist is {β/[1−β)β ]} < 1 and we recall that the definition of β = [(1/(1−β))−j (1−β)]. Assume that the population abroad is constant and that the growth rate of knowledge A* is exogenous, therefore, the foreign GDP is determined according to: Y∗ = K ∗ β (A∗ L∗ )1−β

(4k)

Q.2 Trade and the Production Function

A∗ (t) = A∗ 0 e

549 a∗ t

(4l)

Taking the growth model for country II into account, the interdependency of the steady state for countries I and II can then be considered; there can be dependency or interdependency and the main aspect is whether A determines A* or vice versa; alternatively, we may assume that the growth rate of technology in country I is given by a = a + αa*, where a is the exogenous home component of technological progress in country I, while αa* (with α∗ denoting a positive parameter) reflects the impact of the large foreign country on the progress rate of country I. A truly interdependent model of two big economies requires more complex modeling since the assumption that the progress rate is exogenous and constant will no longer hold.

Q.2.4 Growth Modeling of Open Economies: Technology Spillovers and the Role of Trade The role of technological catching-up has been studied in various ways (e.g., HERZER 2009) and the empirical studies have shown some asymmetric technological catching-up within the EU (JUNGMITTAG 2006). Two types of exports will be considered, namely X and X ; we assume that X depends on Y, which, therefore, could to some degree represent product innovations (if L is given the rise ofY/L := y should go along with increasing production of certain goods—those for which the income elasticity is positive—and part of these goods will be exported). X is assumed to be driven by foreign ∗GDP. In country II, output ∗ is determined by a simple production function Y∗ = K∗β (A∗ L∗ )1−β . We will consider a setup in which both countries (country I and country II) are producing according to Cobb–Douglas production functions. The role of asymmetric international technology spillovers will be considered—such spillovers could occur in the context of the networks of multinational companies on the one hand, on the other hand, an increasing international technology spillover through digital networks and ICT could be relevant (WELFENS 2010b). Specifically, it will be assumed that production in country I is based on the use of capital K and labor L; there is Harrodneutral technological progress (labor-augmenting) and the multiplier for L consists both of a home component A (“domestic knowledge”) and part of foreign knowledge A*; only a fraction ψ of foreign knowledge is used in country I and ψ is in the interval (0, 1).

Asymmetric International Technology Spillover Let us now consider the case of direct international asymmetric technology spillovers where foreign knowledge A* reinforces the knowledge A of country I (ψ is a positive and will be dubbed technology transfer parameter): Y = Kβ (ψA∗ AL)1−β

(1)

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Defining ψ := ψ1−β , we can write Y = ψ K β (A∗ AL)1−β

(2)

As regards the change of knowledge (with positive parameters λ , λ , and λ∗ ), we use a simple technological progress function: A specific avenue through which trade and output in country I (home country) could be linked, concerning technological progress. ∗

dA/dt = λ dln(X /L)/dt + λ dln(X /L)/dt + λ dln(J/L)/dt

(3)

According to this function, learning is shaped by three elements, which stand for declining marginal products of learning in each element: We make a distinction, namely exports X and exports X that might simply reflect two different sectors (or exports going to two different countries with differing import profiles) with different international learning-by-doing intensities—X /L and X /L affect the change of the level of knowledge. At the bottom line, more exports per capita will enhance knowledge. Per capita imports also contribute to raising labor-augmenting technology where λ∗ is higher the higher the share of imported technology-intensive goods is. Taking the integral (and defining y := Y/L) and considering the per capita import   function J/L = yθ and the export-per capita functions X /L = yθ and X /L = yθ , respectively, we get ∗

A(t) = λ ln(X /L) + λ ln(X /L) + λ ln(J/L) + C0

(4)

The term C0 has to be determined from the initial conditions and we can set it equal to unity (for ease of exposition) without affecting the validity of the subsequent analytical results. Hence the production function now reads ∗

Y = ψ K β (A∗ L)1−β {1 + [λ ln(X /L) + λ ln(X /L) + λ ln(J/L)]}1−β

(5)

Using the definitions y := Y/(A∗ L) und k  := K/(A∗ L), we can write β

∗

y = ψ k  {1 + [λ ln(X /L) + λ ln(X /L) + λ ln(J/L)]}1−β

(6)

Defining ψ := ψ1/1−β , we get the following as the implicit production function: y

1/1−β

= ψ k 

β/(1−β)

∗

{1 + [λ θ lny + λ θ lny∗ + λ θlny]}

(7)

For simplicity, we assume that the expression is close to zero so that we can use the approximation ln(1 + x) ≈ x; hence we get the following after taking the following logs: ∗

[1/(1 − β)]lny ≈ lnψ + (β/(1 − β))lnk  + [λ θ lny + λ θ lny∗ + λ θlny] (8) Defining β =: 1/(1 − β) we obtain ∗

[β − (λ θ + λ θ)] lny ≈ lnψ + [β/(1 − β)] lnk  + [λ θ lny∗ ]

(9)

Q.2 Trade and the Production Function

551

The implicit production function reads—with the parameter β := (β/(1 − β))[β − (λ θ + λ∗ θ)] as follows (0 < β < 1 by assumption; the assumption β < 1 is necessary to make sure that the relevant differential equation is convergent): y ≈ {ψ [(λ θ )lny∗ ]

[1/[β −(λ θ +λ ∗ θ)]]

}k 

β

(10)

Now let us consider the goods market equilibrium in the sense that savings S = dK/dt + δK (δ is the depreciation rate on capital) and that the savings function is S = (1−τ)Y; we assume a constant foreign progress rate a* := dlnA*/dt and a constant population L. Using the definition k := K/(A*L) and taking into account that dk /dt = (dK/dt)/(A*L)−a*k” we can firstly state the goods market equilibrium condition and also obtain the following equation: S/(A∗ L) = (dK/dt)/(A∗ L) + δK/(A∗ L)

(11)

And 

∗

 

dk  /dt = s(1 − τ){ψ [λ θ lny∗ ][1/[β −(λ θ +λ

θ)]]

}k 

β

− (a∗ + δ)k 

(12)

At first, we consider the special case of a constant a*. This implies the following solution for the Bernoulli differential equation (# denotes steady state): 

 

 ∗ θ)]]

k # = {s(1 − τ){ψ [λ θ lny∗ ][1/[β −(λ θ +λ



}/(a∗ + δ)}1/(1−β 

 

From the production function y ≈ {ψ [λ θ lny∗ ][1/[β −(λ θ the following steady-state solution: (β +1)

y # ≈ {ψ [λ θ lny∗ ]

+λ∗ θ)]]



}[s(1 − τ)/(a ∗ + δ)]β

)

(13) 

} kβ , we get

/(1−β )

(14)

Hence, the per capita income in the steady state is given by (β +1)/[β −(λ θ +λ ∗ θ)]

y# ≈ {ψ [λ θ lny∗ ]



}[s(1 − τ)/(a ∗ + δ)]β

/(1−β )

A#

(15)

Trade will generate—here, disregarding the term β /(1 − β )—a positive effect on the level of the growth path, namely as shown by the term {ψ     ∗ [λ θ lny∗ ](β +1)/[β −(λ θ +λ θ)] ; this term includes the technology spillover parameter as well as the export parameter λ ; and the logarithm of foreign per capita income. Assuming that β is 1/3—a typical empirical finding—and that ß >0, it is obvious that trade will raise the level of the growth path in the steady state. Taking into account (with y: =Y/L) that C/L = c(1−τ)y, the old issue of maximizing per capita consumption in the steady state (C/L)# may be considered in a modified way. For simplicity, let us assume that technological progress abroad is ∗ exogenous and constant (we define dlnA∗ /dt =: a∗ ) so that A∗ (t) = A0 ea t (e is the Euler number; ∗ for foreign variable). Note that in Eq. (12) the factor in front of k β contains lny∗ ; since lny∗ = β∗ lnk∗ + (1−β∗ )lnA∗ , an increase of A∗ will raise lny∗ so that, in our interdependent growth model, the foreign growth of per capita output will have an influence on the solution for a maximum steady state per capita consumption in the home country.

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Q.3 The Gravity Equation in a Long-Term Analytical Perspective Empirically, trade dynamics have often been analyzed in the context of the gravity equation which has brought adequate regression results for explaining trade in EU15, EU-25, and global trade for certain periods of time: Imports J between country i and j can be explained by real income in country i and output in country j (Yi and Yj) , while distance (Dij )—or more exactly, transportation costs between i and j—will negatively affect imports (J). Distance is a proxy for transportation costs. A basic form to specify the gravity equation for imports Jij is Jij = αYi β Yj β Li ϕ Lj ϕ Dij ψ Uij 







(1)

where Uij is a lognormally distributed error term with E(lnU(ij ) = 0; we have parameters α, β , β , ϕ , ϕ , ψ (all parameters are positive). If k different goods were to be explicitly considered, we would have to state the gravity equation accordingly for Jijk -with αk and suitably adjusted variables Y and L—and Uijk as a lognormally distributed error term. If countries from a free trade area or a customs union are involved, a dummy variable will obviously have to be added for the integration effects (as regards empirical implementation, the standard distance data often come from the internet data source, http://intrepid.mgmt.purdue.edu/TRADE.Resources/Data/Gravity). An alternative formulation of the equation has real income in countries and per capita income in country i and j plus the distance variable on the right-hand side. Monetary integration could also affect trade intensity through a reduction of trading costs and BALDWIN (2006) has estimated that Euro integration has stimulated intra-trade in the Euro zone by 5–10%. As regards trade within countries—here the United States and CANADA—WOLF (1997) and McCALLUM (1995) have used the gravity model for highlighting the role of national borders; HEAD/MAYER (2001) who have carefully modeled the distance variable, have used the gravity model to empirically highlight border effects within the context of the EU single market and have indeed shown that the single market program has not generally undermined market access for US producers. However, in a sectoral perspective, some EU sectors have shown signs of a Fortress Europe effect. The gravity equation, so useful in modern International Economics, is originally based on LINNEMANN (1966), and the inspiration for the gravity approach is from Newtonian physics (ZHANG/KRISTENSEN 1995). An important theoretical contribution in the field of the gravity equation is from ANDERSON (1979) who has shown that this equation can be derived from the properties of an expenditures system of an open economy; the implications are that this equation is an “alternative method of doing cross-section budget studies” as ANDERSON (1979, p. 114) stated. One should, however, also take an alternative approach into account, which—in a simple two-country perspective stated here—interprets the gravity equation as an implicit formulation of the goods market equilibrium in an open economy. This is the implication of assuming—following DIXIT (1990)—that savings is a function of private sector wealth A (where ε is the marginal utility elasticity of the consumption

Q.3 The Gravity Equation in a Long-Term Analytical Perspective

553

function U1−ε/1−ε) and of income and that imports (of intermediate products) are related to outward foreign investment (WELFENS 2007). Many other authors have made important theoretical contributions (e.g., LEAMER/STERN 1970, 1974; BALDWIN 1994; ASILIS/RIVERA-BATIZ 1994; EVENETT/KELLER 1998), and have applied this approach to explain trading patterns in Europe (e.g., BRADA/MENDEZ 1985; ENDOH 1999; GROS/STEINHERR 1995) or to anticipate future trade after economic opening up of post-socialist Eastern Europe (e.g., HAMILTON/WINTERS 1992), while other researchers have looked into a joint analysis of international trade dynamics and foreign direct investment dynamics (e.g., FONTAGNE/FREUDENBERG/PAJOT 1999; EGGER et al 2006). The study by JUNGMITTAG/WELFENS (2001) has looked at the role of international telecommunications in trade within a gravity model—with significant results of an augmented gravity equation in which international telecommunications plays a significant role. Moreover, PROJAN (2001) has emphasized that spatial econometrics should be applied for the problems studied and comes up with interesting results in the context of the gravity equation, which uses distance and per capita GDPs on the right-hand side of the equation: Taking the inherent spatial effects of the model into account, affecting the magnitude of the estimated parameters. A remarkable feature of many empirical studies is that the elasticity for the (relative) distance variable is constant over time (see, e.g., HEAD/MAYER 2001, who cover six sub-periods and find a highly significant parameter for the distance variable where the sample period starts with 78–80 and ends with 93–95). In the following analysis, we put the gravity approach into a long-term perspective and basically argue that popular panel data analysis of the gravity equation is likely to be flawed due to a serious endogeneity problem, which is brought out here on the basis of a simple compact model. In a nutshell, the presented arguments state that the fact that trade affects output should not be overlooked—in all countries involved in international trade and hence, domestic and foreign GDP for any pair of countries cannot be taken as exogenous in long-run analysis. The analysis presented subsequently has broad implications for the long-run gravity equation, modeling and understanding the dynamics of trade and globalization, respectively. In the following analysis, we will take a closer look at the logic of the gravity equation in the context of a growth model (Sect. 2); this allows highlighting the problems that occur in a panel data analysis of the standard gravity equation. The presented theoretical arguments suggest a different long-run approach for trade dynamics, namely to reconcile a growth model of an open economy—with trade entering the production function—with the gravity equation. Moreover, a new explanation for the apparently missing death of distance result is offered, namely the fact that regression analysis of the standard gravity equation suggests that the coefficients for the distance variable are more or less constant over time; in any case, the coefficient has not been found to systematically fall over time.

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Q.3.1 Towards a Consistent Long-Run Gravity Trade Model The Standard Gravity Approach The standar d empirical approach to trade can be expressed through a simple gravity equation, which—taking the simplest case—in a two country perspective, suggests that we can express imports J as follows (with ε denoting a white noise error term and b, b , and b positive parameters; and * denoting foreign variables): ∗

J = b0 + bY + b Y − b D + ε

(2)

It is obvious that J is proportionate to domestic real output Y; it is also a positive function ofY* since it may be assumed that the higher the economic size of the trading partner—as proxied by Y*—the larger the number of product varieties available and the larger the role in scale economies in certain sectors; these are standard theoretical arguments. However, it may be added that bY* might effectively cover exports contained in imports, namely the impulse that the share of exports used as intermediates in imports is larger the higher the GDP of the trading partner/country II actually is (a larger country will offer a richer array of sectors using imports from country I that will be used for products to be exported to country I). Distance has—at a given technology—a negative impact on the volume of imports; ε is a normally distributed error term with zero expected value. Let us consider the respective equation for the foreign country, while assuming for obvious reasons that b * is equal to b . ∗

J∗ = b∗0 + b∗ Y∗ + b Y − b D + ε∗

(2 )

The trade balance X —which is net exports—can be written as ∗

X = (b∗0 − b0 ) + (b∗ − b )Y∗ + (b − b)Y + (b − b )D + ε∗ − ε

(3)

For the trade balance, the distance variable, of course, plays no role if exports and imports are symmetric. Obviously, we will get a familiar result for the trade balance— namely that net export positively depends onY* and negatively onY—if imports react less to foreign output (Y*) than exports and if foreign imports react more strongly to national output of country I than exports of country II. These are rather conventional assumptions that are not causing major problems in an analytical perspective. For the trade balance, distance obviously cancels out, and the only variables remaining are national income and foreign income (plus the error terms and the absolute term). As regards long-run analysis of trade and growth, Eqs. (1) and (2) must be carefully considered, namely because Y and Y* are obviously not independent from imports and trade, respectively. If specialization gains or economies of scale associated with trade or a link between trade intensity and technological progress are considered, Y and Y* can no longer be considered as exogenous variables. We will pick this problem up subsequently in a simple setting.

Q.3 The Gravity Equation in a Long-Term Analytical Perspective

555

Q.3.2 Combining the Gravity Equation and Growth Modeling Before we consider the link between economic growth and the gravity equation, we want to shed more light on the distance variable in the gravity equation. The distance variable is a proxy for trading costs. Taking a look at a representative market for imported goods and assuming that the average per unit trading costs T (costs per tonkilometer) are proportionate to the average distance for the representative imported good, we can see that imports are determined by the world market price ep∗ (with e standing for the nominal exchange rate and p∗ for the exogenous world market price level) times[1 + T ]. We will assume that the average distance relevant for imports is a positive function of the level of technology A(t) = A0 eat (with e denoting the Euler number), which is assumed to be both labor-saving and distance-enhancing so that progress stimulates international fragmentation of production. In the following analysis, we will consider a symmetrical two-country model with technological progress and trade. At first, we turn back to the gravity model of imports of country I and divide all of the variables by AL, where A(t) is the level of know-how and L is the population, which is assumed to be constant and identical in both countries (L = L∗ ). Denoting imports per unit of labor in efficiency units (AL)—with L denoting labor and A knowledge—we can divide the gravity equation by AL and obtain (with y =:Y/(AL); y∗ =Y∗ /(A∗ L∗ ) and j = J/(AL): ∗

j = by + b y − b D/[AL]

(4)

Imports relative to workers in efficiency units are a positive function of y and y∗ and the distance variable (D/(AL) =: d ). We now turn to the link between distance and technological progress, which is assumed to facilitate fragmentation of production in such a way that the average transportation distance is raised; hence A(t) is a true driver of globalization. Let us assume that the average transportation distance is a positive function of A so that D = D0 eat . Thus, the third right-hand distance term becomes D0 /L = d”, which, for a given population L, is truly exogenous; note that D0 /L is a kind of average distance per person. For simplicity, we will assume that b is proportionate to j , that is b = j λ , which implies that there are iceberg-type transportation costs. ∗

j = by + b y − j λ d

(5)

This corresponds to the idea of iceberg transportation costs according to which part of the goods shipped is melting away through transportation, therefore, effective imports are indeed j (1−λ d ). Defining d=:1−λ d , we can alternatively write: j = (b/d)y + (b /d)y∗ where it should be noted that multiplying the equation by AL yields the equation J = (b/d)Y + (b /d)Y∗ (AL/A∗ L∗ ); if AL = A∗ L∗ , the last term becomes (b /d)Y∗ . As we are interested in a long-run perspective, we have to focus on a growth model with trade. We will use a simple Cobb–Douglas production function, where we assume that all imports are intermediate products and thus contribute to higher

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output; and we also assume that exports—through the competitive pressure from world markets—contribute to higher output; therefore (adjusting the exponent for AL, namely assuming that in an open economy it will be smaller than in a closed economy which implies at first sight that labor income share falls via opening up the economy), the production function can be easily expressed (WELFENS 2007): 







Y = Kβ Jβ J∗β (AL)1−β−β −β

(6)

Capital K, imports J, exports J∗ and labor in efficiency units (AL) are entered into the production function, where we assume that all exponents are in the interval 0, 1. With respect to J as an import factor, it is only intermediate goods imported that matter; as regards the impact of exports J∗ on Y, it may be emphasized that the larger J∗ is, the more embedded the economy in the world market competition, which in turn implies that J∗ is a quasi-input in the macroeconomic production function. We will assume Harrod-neutral progress and that knowledge A develops (with e denoting the Euler number) according to A(t) = A0 e

at

(7)

We can—using y =:Y/(AL)—rewrite the production function as β β



y = k j j∗β

(8)

If we wanted to make sure that the closed economy production function is y = k β — the standard approach—we could alternatively consider the alternative formulation: β





y = k  (1 + j )β (1 + j∗ )β

(9)

This formulation has the advantage that with j = 0 and j∗ = 0 the production function boils down to the function for a closed economy; however, for ease of exposition, we will subsequently use j and j∗ as input variables; it is, however, no problem to redefine j := 1 + J/(AL); and this is indeed useful if wanted to make sure that output per unit of labor in efficiency units is higher in an open economy—with trade—than in a closed economy. As regards empirical findings for a link between trade and per capita GDP, the empirical findings of JUNGMITTAG (2006) should also be taken into account, who shows that rising (intra-EU) trade has contributed to enhanced diffusion of knowledge and hence higher output for the EU-15. For simplicity, we will use the formulation of Eq. (8) subsequently. An important issue is whether trade not only contributes to a higher level of per capita income in the steady state; it might also contribute to a higher growth rate of output (WELFENS 2007). Here, we have an issue that requires empirical analysis. Let us assume that savings S is proportionate to Y, therefore, S = s(1−τ)Y; τ is the income tax rate, and s is the savings rate (we will define s(1−τ) := s ). The conditions of a balanced government budget and a balanced current account are also imposed,

Q.3 The Gravity Equation in a Long-Term Analytical Perspective

557

thus, the goods market equilibrium requires (with δ denoting the rate of capital depreciation; we assume δ = δ*): S = I = dK/dt + δK

(10)

The accumulation dynamics for k =: K/(AL) is thus given by β β



dk  /dt = s k  j j *β − (a + δ)k 

(11)

Note that the implication of a balanced current account—and taking the assumptions L = L∗ , A = A∗ , and β = β into account—implies j = j∗ and therefore, dk  /dt = s j

2β  β

k − (a + δ)k 

(12)

We obtain the following as a steady-state value for k and y , respectively: k  # = [s j

2ß

/(a∗ + δ)]1/1−ß .

(13)

2β

/(a∗ + δ)]β/1−β

(14)

y # = [s j

Compared to the traditional neoclassical growth model, the equilibrium capital intensity and the equilibrium per capita income y =:Y/L are higher now. Taking the assumption β* = β into consideration, we have the following equation for the foreign country: ∗

∗ 2β

y = [s j

/(a∗ + δ∗ )]β/1−β

(15)

Therefore, the long-run gravity equation should read—with s∗ = η*s (η* is a positive parameter, which indicates the relative size of the savings rate abroad relative to that in the home country) and δ = δ* as well as a = a*: j = b[s j

2β

/(a* + δ*)]β/1−β + b η*β/1−β [s j j = (b + b η*β/1−β )[s j

j

1−2β β/(1−β)

2β

2β

/(a* + δ*)]β/1−β − j λ d (15 )

/(a + δ)]β/(1−β) − j λ d

= (b + b η*β/1−β )[s /(a + δ)]β/(1−β) /(1 + λ d )

(15 ) (15 )

Defining b = 1 + b (b is a parameter) and using—for very small x—the approximation ln(1 + x) ≈ x, we obtain the following: lnj = −(λ /β )d + (1/β )(b + b η*β/1−β ) + (β/(1 − β)β )lns − [β/(1 − β)β ]ln(a + δ)

(16)

The gravity equation thus simply reads: lnJ = lnA + lnL − (λ /β )d + (1/β )(b + β/1−β b η∗ ) + (β/(1 − β)β )lns − [β/(1 − β)β ]ln(a + δ); assuming β > 0, it still has a negative impact on the modified distance variable; the level of knowledge positively

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affects the logarithm of imports, but the progress rate (a) will negatively affect the level of imports. The larger the parameter η*, the higher the volume of imports: The larger the level of the foreign growth path (country II), the higher the imports of country I (home country). Let us now consider a fully symmetrical two-country world: The long-run gravity equation is—now assuming that a* = a and δ = δ* (and in the next step s = s* and b = b , which stands for a symmetrical two-country world)—given by j = b[s j

2β

/(a + δ)]β/(1−β) + b [s *j

2β

/(a + δ)]β/(1−β) − j λ d

(16 )

Assuming that b = b and s = s∗ we have 2β

j = 2b[s j /(a + δ)]β/(1−β) − j λ d

(16 )

This gives 2β

(1 + λ d )j = 2b[s j /(a + δ)]β/(1−β)

(16 )

Therefore we have 2β

(1 + λ d ) = 2b[s j /(a + δ)]β/(1−β) /j j

1−2β β /(1−β)

= 2b[s /(a + δ)]β/(1−β)/(1 + λ d )

(17) (18)

We assume that λ d is close to zero, therefore, the approximation ln(1 + λ d ) ≈ λ d will hold. Denoting[1−2β β/(1−β)] =: β and assuming β > 0, we obtain the following expression after taking the logarithms: lnj = −(λ /β )d + (1/β )ln2b + (β/(1 − β)β )lns − [β/(1 − β)β ]ln(a + δ) (18 ) We can conclude that the volume of imports relative to AL is a negative function of d”; and it is a positive function of the savings rate and a negative function of the progress rate. For a constant savings rate s and a constant progress rate a, the ratio J/(AL) is stationary. We can write lnJ = lnA + lnL + (1/β )ln(2b) − (λ /β )d + [β/(1 − β)β ]ln(s /(a + δ)) (19) It is fairly obvious that the traditional gravity equation, therefore, cannot be estimated within a long-term approach: IfY andY* were to be used on the right-hand side of the equation, there would be misspecification problems for the long-run gravity equation, since the volume of trade affects the level of the growth path of output. The picture would become more complex if we wanted to explicitly consider the case of international technology catching-up, in which trade plays a positive role (WELFENS 2007). Indeed, it is an empirical question whether trade affects the level of growth or the trend growth rate or both.

Q.3 The Gravity Equation in a Long-Term Analytical Perspective

559

An important issue concerns the variable d =: D/(AL). This variable is not stationary unless we impose certain conditions—and indeed the augmented growth model will not deliver a stationary value for y unless we do so; otherwise, we get a new case of endogenous growth. To make d a stationary variable, it must hold that the average distance D is increasing at rate a, the growth rate of technological progress. From this perspective, it is not surprising that the death of distance is not found in empirical analysis, since—according to the hypothesis stated here—technological progress raises the average transportation distance over time. Such an increase in transportation distance can indeed be observed for many products in the context of international off-shoring which in turn is strongly linked to the expansion of ICT (and ICT in turn strongly affects total factor productivity growth in OECD countries). ICT facilitates international fragmentation, namely the trade of intermediate products so that more components are traded over a larger geographical radius (MEIJERS/DACHS/WELFENS 2007). Even in financial services, we observe a rise in trading distance in the context of the use of ICT, where the study of PETERSEN/RAJAN (2002) refers to intra-US trade in banking services; however, a rising distance of trade in services was also found in an international context, for example, in the case of the US software industry (BAILEY/LAWRENCE 2005).

Q.3.3 Implications We have shown how the link between the economic growth in an open economy and the gravity equation can be conveniently modeled. The implication is clearly that panel data analysis must be carefully applied. Using the standard gravity equation should be avoided, because there are serious endogeneity problems. Instrumental approaches or other adequate changes for the empirical analysis are thus required. As regards long-term economic catching-up in the world economy, an implication is that countries with a relatively high ratio of trade-to-labor in efficiency units should have a higher per capita income. Thus, it is not surprising to find that land-locked countries that face higher transportation costs and hence, lower trading opportunities are relatively poor (SACHS/WARNER 1997). From an empirical perspective, complex co-integration analysis will be required in any case. It seems important to analyze both the import functions and the production function—with imported intermediates as a specific input and exports of certain (technology-intensive) products as another specific input. It is fairly clear that assessing the role of international organizations such as the IMF or the WTO cannot be assessed in the context of the standard gravity equation. Rather, it should be tested whether or not IMF membership—allowing to cope with potential and actual balance-of-payments problems more easily—and WTO membership raises the share of intermediate products traded in overall trade. Moreover, it will be quite interesting to empirically assess to what extent trade is conducive of technological progress and diffusion, respectively.

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At the bottom line, it may also be concluded that the role of trade and globalization dynamics, respectively, cannot be adequately assessed if the theoretical framework underlying the empirical analysis is not consistent. This points to considerable challenges in terms of future research on the empirical implementation of the gravity analysis. A particular problem refers to technological progress in transportation. There is not much theoretical and empirical research at the aggregate level of OECD countries or the world economy as such. The best available data material—and hence studies that have used such material—refers to the United States and the EU, respectively. It may be emphasized that the European Commission has argued for many years that the EU Eastern Enlargement will bring about an enormous increase in truck and railway transportation. Figures on international shipping are also rather difficult to find, although it should be said that a limited body of research is indeed available. From this perspective, it would be useful if the WTO and the OECD could establish broader evidence of transportation dynamics in a systematic way.

Q.4 Growth, Optimum Taxation, and Innovation Policy Q.4.1 A New Optimum Taxation Approach The traditional optimum neoclassical growth theory states that per capita consumption becomes maximal if the marginal product of capital is equal to the growth rate of output. To achieve this result, governments might try to manipulate the savings rate or the tax rate in an adequate way. The following analysis is a modified approach and it is new in the sense that it is able to accommodate the case of open economies with regards to trade and foreign direct investment. Before we turn to the open economy, we consider the simple case of a closed economy: Consider an economy that produces capital K, labor L and knowledge A, which is labor augmenting. The depreciation rate of capital is δ and the production function is Cobb Douglas, namely Y = Kβ (AL)1−β ; 0 < β < 1. We assume that the government imposes an income tax where the tax rate is τ; the ratio of government expenditures to GDP is γ. It is assumed that the government budget is balanced. Subsequently, a closed economy is considered and it is assumed that savings S = s(1−τ)Y; s is a positive parameter in the interval (0, 1). Net investment is dK/dt, where t is time. Imposing the goods market equilibrium condition S = dK/dt + δK, considering the production function and taking the definition k := K/(AL) and y :=Y/(AL), as well as the mathematical rule into account (while defining n := dlnL/dt; n := dlnA/dt) that dk /dt = dK/dt−(n + a)k , we obtain the following differential equation β

dk  /dt = s[1 − τ]k  − [n + a(τ) + δ]

(I)

This equation has the steady-state solution (# denotes the steady state): k# = {s[1 − τ]/[n + a(τ) + δ]}1/[1−β]

(II)

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Hence y# = {s[1 − τ]/[n + a(τ) + δ]}β/[1−β]

(III)

We have to consider that 1 = c + s + τ (c is the consumption–GDP ratio) and it will be assumed that the growth rate of knowledge a = a(τ); by assumption, the partial derivative is negative. Consumption per unit of labor in efficiency units C/(AL) := c in the steady state is given by c # = (1 − τ)(1 − s − τ){s[1 − τ]/[n + a(τ) + δ]}β/[1−β]

(IV)

If the government wants to maximize C/(AL), it is useful to consider dlnc /dτ = 0 as the necessary condition for optimum tax policy. For the sake of simplicity, it will be assumed that n + δ = 1, so that we can use the approximation ln(1 + x) ≈ x for x close to zero. Taking the logarithms yields lnc # ≈ (−τ) + (−s − τ) + (β/(1 − β)){lns + [−τ] − a(τ)}

(V)

dlnc #/dτ = −[(2 − β)/(1 − β)] − [β/(1 − β)]∂a/∂τ = 0

(VI)

Denoting the elasticity of a with respect to τ as Ea,τ , we can write [2 − β] = β|Ea,τ |τ/a

(VII)

Therefore, the optimum tax rate is given by τopt = a[2 − β]/[β|Ea,τ |]

(VIII)

This will bring about a maximum C/(AL) provided that the second derivative of a, with respect to the income tax rate, is negative; this is obviously the case. The optimum tax rate is a negative function of the output elasticity of capital and of the elasticity of the progress rate with respect to the tax rate; it is a positive function of the initial progress rate. To get an idea about the order of magnitude for the optimum tax rate, it may be assumed that the initial growth rate is 0.02, β = 1/3 and Ea,τ = 3; in this case, the optimum tax rate is roughly 33%. Implicitly, we also have information about the optimum innovation policy, namely to the extent that using a relatively higher share of government expenditures for R&D promotion, the absolute magnitude of the elasticity Ea,τ will fall. To the extent that government’s promotion of research and development is stimulating Schumpterian dynamics—read: raising a—the overall increase of the tax rate associated with a rise in the government R&D expenditures-GDP ratio will reduce the relevant elasticity. The optimum R&D policy is characterized by a mixture of R&D promotion expenditures relative to GDP (τ ) and general government expenditures relative to GDP (τ : this reflects costs of running the economic and political system) that minimizes Ea,τ it must hold that τ = τ + τ”. Hence, there is an interesting range of new empirical issues to be considered. It should, however, be noted that governments that want to raise long-term per capita income might not be—in a specific initial situation—very interested in the proposed

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solution, namely if the government and voters, respectively, have a very long timehorizon: If the implication of the solution is that the tax rate should be increased, the subsequent implication is that the trend growth rate in the steady state will fall; unless voters or government representatives are very short-sighted, the negative effect on the trend growth rate could more than offset the short-term per capita increase, that resulted from the rise in the level of the growth path. If, however, the initial situation is such that the tax rate has to be reduced in order to realize the optimum tax rate, there is no such “dynamic steady-state conflict”. The presence of cumulated FDI inflows—in an asymmetric setup (only FDI inflows in country I, no FDI in country II) will not change the results obtained here. A different savings function would have to be considered, namely S = s(1−τ)(1−α∗ β)Y, where α* is the share of capital owned by foreigners; the savings function used here is S = sZ, where Z is GNP and the difference between GNP and GDP in this asymmetrical setup is profits accrued from country I to investors from country II.

Q.4.2 Optimum FDI Policy in an Open Economy with Subsidiaries from Abroad Finally, we consider an open economy with trade and FDI. The considered economy is asymmetric in the sense that country I faces (cumulated) FDI inflows but there is no outward FDI of country I. We have to make a distinction between GDP and GNP (Z). Obviously, in an economy with competitive goods markets and factor markets, it will hold that Z =Y(1−α∗ β), where α∗ is the share of the capital stock owned by foreign investors; to the extent that the host country has an influence on α∗ , one might want to consider the issue of maximizing consumption per capita through an adequate FDI policy. Now savings is given by the following function S = s(1 − τ)(1 − α*β)Y

(VIII)

The rate of technological progress is assumed to be a negative function of the income tax rate τ and a positive function of α*; obviously we have assumed that the presence of foreign investors brings about an international transfer of technology—that is a(τ, α*)—so that the steady state condition for k will read: k# = {s(1 − τ)(1 − α∗ β)/[n + a(τ, α∗ ) + δ]}1/[1−β]

(IX)

It may be noted that it would easily be possible to specifically consider some of the modified production functions derived above. For the sake of simplicity, the analysis is based on the standard production function. The equation for C/(AL) now reads c#  = (1 − τ)(1 − s − τ){s(1 − τ)(1 − α∗ β)/[n + a(τ, α∗ ) + δ]}1/[1−β]

(X)

(C/L)# = (1 − τ)(1 − s − τ) {s(1 − τ)(1 − α∗ β)/[n + a(τ, α∗ ) + δ]}β/[1−β] A0 e

a( τ,α∗)t

(XI)

Q.5 Conclusions

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With respect to α*, there is no simple maximization problem for C/(AL) since a rise in α* will always reduce the level of the growth path—provided that ∂a/∂α* is positive. The problem here is rather one of political economy. Raising α* by accepting foreign investors to raise the share of ownership in the capital stock will raise the trend growth rate a; if the time-horizon of policymakers and voters, respectively, is long enough that the expected discounted rise in per capita income from the higher trend growth rate will at least offset the short-term reduction of the level of the growth path, which occurs with a rise in α*, policymakers will make a decision that increases the weighted increase of current and discounted future per capita income. In principle, trade and FDI aspects may be combined as presented in the various sections. The main impact of trade in the production function concerns the savings function and the key differential equation for k . The main results can be found in WELFENS (2010a).

Q.5 Conclusions It has been shown that trade and FDI can be integrated in an augmented production function of an open economy and that both trade and FDI can be integrated in a consistent way in growth models of open economies. A new optimum tax formula has been derived and the issue of an optimum innovation policy in a growing open economy has been analyzed. There is a broad range of new empirical issues to be analyzed in further research. Considering the issues raised under different production constraints—for example, within a CES production function in both countries— could also be quite interesting. As regards economic policy, there are clear conclusions to be drawn: Sustained opening up can contribute to output dynamics, and both trade and FDI contribute to this. Further research could highlight both symmetric and asymmetric growth interdependencies in a multi-country system, in which countries are linked with each other through trade, FDI, and international technology flows. As it is well known, international technology flows are partly related to trade on the one hand and to FDI on the other hand—read: multinational companies. Empirical analysis can shed more light on the relevant issues. The concept of a technological progress function has been shown to be useful for analysis in open economies; the Kaldorian concept of a progress function could, of course, be combined with modified production functions developed here so that trade and FDI aspects could also be considered.

R. New Open Economy Policy Perspectives: Modified Golden Rule and Hybrid Welfare

R.1 Introduction Economics is facing serious challenges after the Transatlantic Banking Crisis, which has almost brought the capitalist system to a financial meltdown in the wake of the Lehman Brothers crisis. Why did so few economists from the USA or Europe anticipate this crisis—some notable exceptions were RAJAN (2005) andARTUS/VIRARD (2005) whose warning against excessive required rate of return on equity of banks was published in French in the book “The Current Self-Destruction of Capitalism”—went unheard? The sharp global recession of 2009 caused by the Transatlantic Banking Crisis was followed by a strong recovery in 2010 on the one hand, on the other hand the massive recapitalization expenditures of several governments of OECD countries for ailing banks and the massive cyclical deficits occurring in the context of expansionary fiscal policies brought a confidence crisis among the sovereign debt market, with Greece being the first victim—partly due to the fact that the outgoing conservative Greek government had produced fake statistics for deficit–GDP ratios in 2009 and in earlier years, therefore the confidence crisis shaking the government bonds markets brought Greece to the brink of bankruptcy. I would like to add that in my book Transatlantic Banking Crisis published in early 2009—the German manuscript was finished in 2008—the section of conclusions clearly mentioned the likely scenario of a Greek debt crisis and the Euro crisis, respectively. Mailing the file and later also the book to the German Chancellor’s chief economist obviously did not ring a bell in the economic advisor team and so the German government stumbled in the Greek and Euro crisis in early 2010 without any preparations and this has certainly raised costs for the German and European taxpayer, respectively. The Transatlantic Banking Crisis is shocking to the extent that the enormous advances in economic modeling since the 1960s lets one expect that the Economics profession—at least a broader subgroup—should have been able to send out analytical warning signals in the late 1990s or a bit later since there were so many strange developments in the USA and partly also in the EU financial markets. Moreover, the Transatlantic Banking Crisis was not the only big surprise for economists and

P. J. J. Welfens, Innovations in Macroeconomics, DOI 10.1007/978-3-642-11909-5_18, © Springer-Verlag Berlin Heidelberg 2011

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international organizations, respectively. It is indeed noteworthy that the IMF has delivered considerable analytical insights during the Transatlantic Banking Crisis, but it also is remarkable that the October 2008 forecast (in the World Economic Outlook) did not anticipate the economic recession of the Euro zone in 2009 when output strongly fell in real terms. This poor forecasting from the IMF might not be considered as a problem since so many other forecasters came up with modest results in their forecasting exercises. However, the IMF stood for its own policy blunder in the early 1990s when its poor advice to Russia, namely to adopt fixed exchange rates, indirectly contributed to the Russian crisis which partly emerged as an echo effect to the Asian crisis. As a personal note, I may mention that I had been invited to a high level IMF workshop on Russia in 1998 and Mr. Stanley Fischer kindly welcomed the group of about 30 economists as the leading experts on Russia. In my own introductory statement, I expressed my gratitude for the invitation but I pointed out that at the table no leading experts on Russia were present since nobody from BOFIT had been invited—the Finnish Central Bank’s research institute renowned for timely and excellent analysis on Russia (including a paper on Non-Sustainability of Russian public finances which had been written in late 1997). One may take these events, pitfalls and problems to raise a few key questions on the role of modern Economics at the turn of the century. What went wrong? What is the problem with modern Economics? These questions are very difficult to answer, but rather than ignoring the analytical challenge, the following reflections try to give some answers on the basis of certain key questions and facts. One of the facts that has to be critically considered with respect to the Transatlantic Banking Crisis is related to the finding that European economists seem to be catching up with the so-far leading US academic community, which is, however still dominant in the leading Economics journals (CARDOSO/GUIMARAES/ZIMMERMANN 2010). This suggests that in a transatlantic perspective there is increasing competition but there is also—according to CORDOSE/GUIAMARAES/ZIMMERMANN— increasing cooperation in writing scholarly articles in Europe. European and certainly also Asian economists are trying to meet the US standards in Economics and there has been some success in this respect. The troubling question however is, whether or not Europeans and other researchers aspire to meet the right benchmark? And are we focusing on relevant issues, do we have a realistic perception of the US economy and the EU, respectively? If a community of economists and the paradigms represented by their large majority are so outstanding why did so few researchers anticipate the historical shocks of the US banking crisis and the Transatlantic Banking Crisis? It is clear that there is intensive discussion among US economists as well as among European economists, but given the emphasis on the robustness of paradigms which has been emphasized by Thomas Kuhn in his book The Logic of Scientific Revolutions, it is not obvious whether a new convincing paradigm will emerge from the USA—but one may hope that the discussion will develop momentum in North America and elsewhere. There is a need for a new paradigm which one may dub Double Sustainability: There is a need for environmental sustainability on the one hand, on the other hand investment and innovation should be sustainable—the accumulation dynamics

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should lead to a long-run equilibrium (read: steady state) and ideally indeed to a situation with an optimum economic welfare, namely a maximum per capita consumption. Or is anybody really interested in roughly quadrupling asset prices and equity prices within 12 years—the case of Ireland 1995–2007—and then losing this increase in wealth and suffering a sharp recession, a massive drop of consumption per capita? Something is wrong with the modern market economy and the market dynamics which generate doubtful risk premia and enormous price bubbles which under restrictive assumptions are dubbed rational.

Developments in Economics Modern Economics has certainly been characterized by several different elements of progress as perceived by the community of Economists: • Economics has become more tuned towards Mathematical Economics: This suggests that there is scope for better modeling, improved analytical tools, and better forecasting. To some extent, this is indeed what we have seen in some fields, including Business Cycle Analysis and including Auction Rules for frequency auctions in mobile telephony and for new regulatory approaches in telecommunications. In Business Cycle Analysis, DSGE models have played a prominent role and they have been useful to some extent—more in explaining certain dynamics, less in short-term forecasting. An approach that might bring some fresh ideas to analysis is agent-based modeling, which is, however, even more complex than DSGE models. This Schumpeterian approach to economic dynamics might, however, contribute with some very useful insights since this approach allows to combine principles of economic analysis, learning theory and some principles of bounded rationality that seem to be acceptable to a broader group of economists. • Economics has become more specialized as is visible, for example, in the splitting up of the American Economic Review into several specialized reviews. This raises the question: which group of economists—if at all—should work as system integrators, that is pull together key insights from a specialized group of economists. Specialized chairs in Economic Policy seem to be the natural way for such an analytical integration that is highly relevant for economic policymakers. • With the increasing role of international organizations after 1995,—such as the IMF, the Bank of International Settlements, the World Trade Organization, and the World Bank or in a European context the European Commission and the European Bank for Reconstruction and Development—the role of economists in such organizations has also become more important. While few of them show up at national or regional meetings, there is no doubt that they are quite influential. Did international organizations stand up to the challenges? Often yes, but there were very notable exceptions such as the IMF in the Asian Crisis and in the Russian Crisis of 1998. • There is a key problem with the increasing role of mathematical modeling and the rising role of economists in key international organizations. The traditional

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link in part of the Economics community with legal experts and faculties of law has become much weaker. It is quite obvious that this is a problem for economic policymaking in the sense that institutions and rules shape incentives for firms and banks, for regulators and other bureaucrats, for investors and innovators. While modern economists have picked up some key issues in the joint realm of Economics and Law, it is fair to say that this area is of declining importance in Economics. The increasing emphasis on mathematical modeling makes cooperation between economists and legal experts often quite cumbersome. The fact that the Transatlantic Banking Crisis has partly been caused by very obviously doubtful financial innovations—which were easy to recognize (such as the multi-stage opaque repackaging of loans through Collateralized Debt Obligations or opaque over-the-countertrading of Credit Default Swaps)—is a good example to recognize the limited ability of mathematical modeling to contribute to understanding straightforward pitfalls in the banking sector and the financial community. It is plausible to assume that a better cooperation of economists and legal experts could have identified some of the key problems of CDOs and CDS early on. One may point out that indeed it was the US DEPARTMENT OF DEFENCE (2006) whose report on the over-indebtedness of army officers alarmed at least part of the US political establishment. At the same time, the USA practice of state prosecutors to not take most of the doubtful banks to court but rather to hammer out an out-of-court settlement has weakened the economic system in the USA and the credibility of institutions and rules. Economists face a serious analytical problem which has been unsolved for decades, namely to reconcile short-term Keynesian analysis with long-run growth modeling. Worse, while open economy macroeconomics has looked into short- and mediumterm models, there has hardly been a serious body of research on open economy growth analysis in an explicit two-country model with trade and foreign direct investment. This is strange since this is exactly the real world in which economic actors have been active since the 1970s. While there has been progress in the understanding of economic globalization, it is unclear to what extent the Economic profession has a broader understanding of long-run economic dynamics. An important approach to long-run economic analysis is neoclassical growth theory. In the growth theory of the 1960s, the neoclassical Solow growth model was developed, from which several economists derived the golden rule (Phelps and von Weizsäcker), which indicates the condition under which the steady state— characterized by a constant long-run capital intensity—goes along with a maximum per capita consumption C/L (C is consumption, L is population). The neoclassical full-employment growth model was subsequently modified as the role of human capital was analyzed (e.g., LUCAS 1988). Growth modeling has remained largely an analysis which puts the focus on the real economy, and only few economists have looked into monetary growth modeling (e.g., TOBIN 1965). Another refinement was to consider open economies and the role of foreign direct investment (FDI) have also been analyzed (e.g., WELFENS 2008a).

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Certainly modeling became more complex in endogenous growth models that explained technological progress, for example, through the share of the workforce employed in the R&D sector. The golden rule aspects were dropped in the growth modeling after the 1960s and 1970s although it is not just a fable for economists but stands for a very important aspect when we take a broader welfare perspective into account. Such a broader perspective is adopted subsequently, including environmental aspects and global warming, respectively.

R.2 From the Traditional Model Toward a New Approach Let us briefly recall the basic neoclassical growth model before we consider several crucial modifications, which in the end bring new insights with respect to monetary and fiscal policy as well as innovation policy. In a nutshell, the neoclassical growth model (SOLOW 1956) consists—with Y, K, L, A denoting output, capital, labor and labor-augmenting knowledge—of a neoclassical production function Y(K, L, A), a simple savings function S = sY and an equilibrium condition for the goods markets, namely sY = dK/dt + δK (δ is the capital depreciation rate). As the subsequent new theoretical and political considerations will refer to a setup with the Cobb– Douglas production function Y = Kß (AL)1−ß , the neoclassical standard model can be characterized for the case of such a production function as follows: • In a setup with an exogenous population growth rate n and labor-augmenting progress rate a and a given capital depreciation rate δ, the standard assumption of a savings function S = sY (with Y standing for output; s denoting a positive parameter in the range between 0 and 1) the steady-state solution k # := K/(AL)— with AL denoting labor in efficiency units (A is knowledge, L is labor, K is the capital stock)—can be written for the case of the above Cobb–Douglas production function as follows: k # = [s/(a + n + δ)]1/(1−ß) ; hence the level of the growth path in the steady state (denoted by #) is given by y # :=Y/(AL) = [s/(a + n + δ)]ß/(1−ß) ; the growth rate of per capita income y :=Y/L in the steady state is equal to the progress rate a. The long-run growth rate of output is a + n, the growth rate of per capita income in the steady state is equal to a. The golden rule requires the marginal product of capital, namely ßkß−1 = a + n + δ; this implies that the net marginal product of capital is ßkß−1 − δ = a + n: the net marginal product of capital is equal to the growth rate of output. We will return to this case of technological progress subsequently. • In the case that the exogenous growth rate of the population is n, while A = 1 and there is no technological progress, the differential equation for capital accumulation is dk/dt = skß − (δ + n)k, where k := K/L and dk/dt = (dK/dt)/L − nk has been used. Thus the equilibrium capital intensity in the steady state (with dk/dt = 0) is given by k# = [s/(n + δ)]1/(1−ß) and per capita output is y# = k#ß . In this setup, the golden rule requires that the marginal product of capital is equal to (δ + n), that is ßkß−1 = (n + δ) and this in turn implies k = [ß/(n + δ)](1/1−ß) ; considering k#

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the implication is that government should manipulate the savings rate in such a way that s = ß. This might be interpreted as the case of a classical economy in the sense that the share of capital income—assuming competition in goods markets and factor markets—is ß and if all profits are saved and workers do not save, we have ß = s.

Politico-economic Aspects of the Golden Rule One politico-economic extension is appropriate here which already points to a problem: If workers have savings rate s and capitalists have savings rate s , we still can get an equivalent result of S = s ßY + s (1 − ß)Y = [s + ß(s − s )]Y; one may assume s > s . Hence the golden rule now requires ß = s + ß(s − s ), which implies the condition: ß(1 + s − s ) = s and after taking logs this gives the condition (as an approximation where we use the rule ln(1 + x) ≈ x) lnß ≈ lns + (s − s ). Thus governments would have to manipulate the savings rate of the workers or the capitalists accordingly. If it is assumed that k# is below k#gold initially, governments would have to raise the overall savings rate, which is s + ß(s − s ). A conservative government might have a preference for raising s if it is assumed that owners of capital have conservative voting preferences. A left government, however, is rather likely to raise s since this would imply that workers—largely voting for the left government—will own a larger share of the capital stock than if s is raised. Such a perspective implicitly assumes that owning capital generates specific utility, not just consumption as is assumed in the standard literature. If k# is above k#gold , the government would have to discourage savings. In an international context, this would also affect the current account, namely to the extent that the current account-GDP ratio reflects the difference between the average savings ratio and the domestic investment ratio. Discouraging savings implies that the current account will worsen. If, however, the country considered has already reached a critically high foreign debt-GDP level, there will be international pressure to raise the savings rate and this in turn implies a loss of economic welfare in a setup in which only consumption per capita is considered as relevant in the utility function. Profit maximization which is often considered to be a natural element of neoclassical analysis raises awkward questions: In the setup with technological progress, the golden rule in combination with profit maximization, namely ßkß−1 − δ = r = a + n. The capital intensity in the steady state is then k # = [ß/(a + n + δ)]1/(1−ß) . By implication, it may be argued that profit maximization is consistent with the golden rule. In terms of economic welfare, considering profit maximization makes sense if it is assumed that households interested in maximizing per capita consumption are not identical to the group of households owning the capital stock. In a small open economy, it might be assumed that profit maximization is imposed through the pressure of free capital flows and profit maximization abroad—in a dominant foreign economy.

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If the money-market equilibrium (M is the nominal stock of money, P the price level of newly produced goods, r is the real interest rate, and ε is a positive parameter) is also to be considered, it can be defined by the equation: (M/P)/(AL) = (Y/AL)/(εr)

(1)

The real interest rate thus implies an endogenous monetary policy since we have zero expected inflation in this setup—and denoting (M/P)/(AL) as m —it will hold: m  # = [ß/(a + n + δ)]ß/(1−ß) /[(a + n)ε].

(2)

Here we have taken into account that r = a + n. The equation presented stands implicitly for the optimum money supply, however, in the setup presented here money has no direct role for production. For the special case of ß = 0.5 and δ = 0, the result in the steady state (starting with t = t ) is: [M/P](t  ) = {0.5/[ε(a + n)2 ]}Ao Lo e

(a+n)

(3)

The level of the optimum money supply is a negative function of the growth rate and the interest elasticity, but it also is a positive function of ß (here ß was set equal to 0.5). An increase of the growth requires reducing the real money supply. A somewhat different setup makes more sense in economic terms, namely if an economy is considered in which the holding of money by households generates positive external effects on output so that money enters the production function, which now reads: ß

y = m  k ß

(4)

The marginal product of capital is now influenced through the stock of money; the MPC is given by: ß

∂y /∂k  = ßm k ß−1

(5)

The marginal product of capital is raised through the stock of real money balances relative to labor in efficiency units (AL). The golden rule in the case of an economy with technological progress and population growth thus becomes: ß

ßm k ß−1 = (a + n + δ);

(6)

Hence we have: ß

k gold = [ßm  /(a + n + δ)]1/(1−ß)

(7) 

The golden capital intensity is higher than in a non-monetary economy if mß exceeds unity; this also implies that per capita consumption in the golden state in a  monetary economy exceeds that of a non-monetary economy if mß exceeds unity.

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While in OECD countries, (M/P)/(AL) may be assumed to exceed unity, it is unclear how big ß really is. The implication of the golden rule here is that s = ß. This  follows from the steady-state condition dk /dt = 0 = smß k ß − (a + n + δ)k and thus  k# = [smß /(a + n + δ)]1/(1−ß) ; note that it has been assumed that m is a policy variable which the central bank can control so that m may be assumed to be constant. As C/(AL) = (1 − s)k # ß per capita consumption in a monetary economy could be higher—compared to a non-monetary economy—for two reasons in the golden state: The savings could be higher, and the capital intensity exceeds that of a nonmonetary economy (with respect to the role of the capital intensity, the alternative Tobin-approach may also be considered for the case of a monetary economy). The goal of government and the central bank in the long run could be to implement the golden rule—with zero inflation. The zero inflation condition or the condition that nominal interest i (the opportunity costs of holding money balances) equals to the real interest rate r is not automatically an obvious choice, but in a broader context it may be argued that zero inflation implies an optimum working of markets so that transaction costs in financial markets and goods markets are minimized. This could be covered by considering a savings function S = s(1 − θπ)Y(1 − τ) where θ is a positive parameter and π is the inflation rate and τ is the income tax rate. The political system thus wants to maximize C/L under the side constraint that π is zero, where the central bank is responsible for zero inflation and the government has to choose the tax rate τ that brings about the golden rule.

R.3 Endogenous Population Growth Let us consider poor countries in which the population growth rate n is a positive function of C/L; for the sake of simplicity the level of knowledge is assumed to be given. Hence the relevant differential equation for k in a society with zero technological progress is given by: dk/dt = sk ß − [n(C/L) + δ]k

(8)

In low-income countries the growth rate of the population may be assumed to be a positive function of C/L, beyond a critical level of C/L—and a certain level of education—one may assume that the growth rate of the population is a negative function of C/L. In advanced societies with high per capita income, we may assume that n is a negative function of C/L; defining a positive parameter n the follow may be specified: n = n − n /[C/L]

(9)

and as we assume C/L = cy, we can write n = n − n /(ckß ) and inserting this in the above equation gives: dk/dt = sk ß − [n + δ]k + [n /c]k1−ß

(10)

R.4 Economic Welfare, Golden Rule and CO2 Emissions in the Context

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We can easily solve the equation for the special case of ß = 0.5 for which we get (using c := 1 − s): k# = {[s + n /(1 − s)]/[n + δ]}2

(11)

y# = {[s + n /(1 − s)]/[n + δ]}

(12)

The insight from this equation is: In a society with an endogenously shrinking population growth—linked to per capita consumption—it is all the more important to achieve a high savings rate as can be seen from the nominator expression in the above equation; if we set n to zero, the steady state would be characterized by a stationary population.

R.4 Economic Welfare, Golden Rule and CO2 Emissions in the Context of a Modified Growth Model Economic welfare has traditionally been measured through the Systems of National Accounts and gross national income (GNI); GNI is defined as gross domestic product plus net factor income from abroad and per capita income is a standard measure of international economic comparisons. One key problem with GNI per capita is that international comparisons will have to rely on corrected data in the sense that international differences in nontradables prices—such prices are relatively low in poor countries compared to rich countries—have to be taken into account: This standard correction brings GNI per capita at purchasing power parity. A traditional critique of GNI as a welfare measure points out that depreciations on capital have to be considered if one is interested in a long-term perspective—capital depreciations or equivalently reinvestment is necessary to maintain the existing stock of capital and the capital intensity (K/L), respectively (K is capital, L is labor); if population L is growing at rate n, the necessary per capita investment to maintain capital intensity is nk + δk, where δ is the rate of capital depreciation. The standard economic approach here is the neoclassical growth model. Hence in a traditional model approach net national income is a useful concept to measure economic welfare. However, microeconomic approaches always emphasize that economic agents maximize utility and utility is a function of (per capita) consumption—and possibly also of leisure. The neoclassical growth model emphasizes the role of maximum per capita consumption in the context of the so-called golden rule, which is defined by capital intensity that maximizes long-run per capita consumption. As regards depreciations, a more refined approach—for example, partly adopted by the WORLD BANK—has not only to take into account physical capital depreciations but should also consider depreciations of non-renewable natural resources and human capital as well as the role of negative external effects: The World Bank has coined this broad approach in a genuine savings rate. This concept in turn has been used as one of the pillars for the EIIW-vita Global Sustainability Indicator (GSI), which takes a closer look at two other pillars, namely revealed comparative advantage in

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environmental-friendly products—the relative export position of a country in the field of green products in world markets—and the share of renewable energy in total energy (WELFENS/PERRET/ERDEM 2010). Modeling of economic growth has at first ignored the problem of the use of energy and the associated emissions that stand for negative external effects,—for example, in the context of global warming. There are, however, several authors who have considered the role of energy in growth and growth simulations (e.g., GRIES 2011). Assuming that CO2 emissions are proportionate to real gross domestic product, the golden rule of traditional growth theory can be modified in an important way.

The Traditional Growth Model Assume that the aggregate savings function is S = sY (with 0 < s < 1; Y is GDP) and that the production function is a well-behaved neoclassical function with positive marginal products of the respective input factors—the second derivative is negative; a standard function with these properties is the Cobb–Douglas production function Y = Kß (AL)1−ß , where A is labor-augmenting knowledge; hence Y/(AL) = kß where k := K/(AL). It will be assumed that the population growth at rate n and that the growth rate of knowledge is given by dlnA/dt = a (t is the time index). Moreover, we impose the condition that goods market equilibrium holds, namely S = I = dK/dt + δK (t is the time index); dK/dt + δK is gross investment where δK stands for reinvestment. If capital per unit of labor is defined in efficiency units, namely K/(AL): = k , the accumulation dynamics of k can be expressed by the differential equation dk /dt = skß − (a + n + δ)k  . This leads to the steady-state solution for k # = [s/(a + n + δ)]1/(1−ß) ; # denotes the steady state and the long-run equilibrium, respectively. Hence y # :=Y/(AL) = [s/(a + n + δ)]ß/(1−ß) and per capita income—with e denoting the Euler number and recalling that A(t) = A0 eat —in the steady state is y# = {A0 [s/(a + n + δ)]ß/(1−ß) }eat so that the growth rate is given by the progress rate a, while the level of the growth path is determined by the expression A0 [s/(a + n + δ)]ß/(1−ß) . To the extent that production is associated with CO2 emissions, there are specific challenges since such emissions contribute to global warming and climate problems. The standard golden rule according to which the marginal product of capital is equal to (a + n + δ) is not valid any more, rather a modified condition will have to be derived.

New Data on CO2 –GDP Ratios In the following table the effective CO2 –GDP ratios are indicated where for the first time the impact of the shadow economy is considered. The updated figures for the shadow economy are taken from the research group of FRIEDRICH SCHNEIDER (2010) and it is obvious that ignoring the shadow economy, which is not recorded in the System of National Accounts, means ignoring a considerable part of the effective value-added in most countries.

R.4 Economic Welfare, Golden Rule and CO2 Emissions in the Context

575

Energy intensity without shadow economy (BTU per constant 2005 PPP US $) 30000 Canada China India

25000

United States Russian Federation Brazil

20000 15000 10000 5000

19 90 19 91 19 92 19 93 19 94 19 95 19 96 19 97 19 98 19 99 20 00 20 01 20 02 20 03 20 04 20 05 20 06 20 07

0

Energy intensity with shadow economy (BTU per constant 2005 PPP US $) 25000 Canada China India

20000

United States Russian Federation Brazil

15000

10000

5000

02 20 03 20 04 20 05 20 06 20 07

01

20

00

20

99

20

98

19

97

19

96

19

95

19

94

19

93

19

92

19

91

19

19

19

90

0

Fig. 114 Energy intensity of selected countries with/without shadow economy (SCHNEIDER et al. 2010)

Hybrid Economic Welfare Maximization A pragmatic way to consider the maximization task in the context of a golden rule approach is to assign Y and Y/L, respectively, a negative imputed utility linked to emissions—the relevant positive parameter is . Thus—in a setup with a given level

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Innovations in Macroeconomics

of technology—we still want to maximize C/L but the constraint and the relevant equation, respectively, look somewhat different than in the standard model: C/L = y(1 − ) − (δ + n)k

(13)

Maximization of C/L requires a necessary condition: d(C/L)/dk = (1 − )ßk ß−1 − (δ + n) = 0

(14)

(1 − )ß k ß−1 = (δ + n)

(15)

kgold = [(1 − )ß/(δ + n)]1/(1−ß)

(16)

The golden capital intensity that maximizes per capita consumption in an economy with CO2 emissions causing negative external effects is, therefore, lower than in an economy without CO2 emissions. As k# = [s/(δ + n)]1/1−ß , we have the implication that we should have s = (1 − )ß

(17)

Thus the savings rate should be lower than in a CO2 -free world. Moreover, if there is technological progress that allows the reduction of specific CO2 emissions—hence  falls—the optimal savings rate (leading to the golden capital intensity) will increase. From this perspective, it is obvious that it is useful to also consider a world with technological progress. Next let us consider an economy with an exogenous “embodied” progress rate a, but we want to take the vintage effects into account, which are associated with capita-embodied technological progress; as STOLERU (1978) has shown, the case of the Cobb–Douglas production function with embodied technological progress means that the depreciation rate is a positive function of the progress rate a (one may dub this the Stoleru effect). Thus the steady-state equilibrium for k := K/(AL) is given by: k  # = [s(1 − )/(a + n + δ(a))]1/(1 − ß)

(18)

y # = [s(1 − )/(a + n + δ(a))]ß/(1 − ß)

(19)

A rise in the progress rate will cause a larger fall in the level of the growth path than without considering the vintage effect. Moreover, if  is assumed to be a negative function of progress rate a, we have the following steady-state condition for y : y # = [s(1 − (a))/(a + n + δ(a))]ß/1−ß

(20)

Now the progress rate has an ambiguous role in the level of the growth path: • A rise in the progress rate reduces  and therefore the nominator will increase • At the same time a rise in the progress rate raises the size of the denominator.

R.5 Open Economy and Economic Growth

577

We can state for the impact of a change in the progress rate on y #: dy /da = [ß/(1 − ß)][(−sa )/(a + n + δ(a))] + s(1 − (a))/(a + n + δ(a))2 (1 + δa );

(21)

If technological progress has a strong green bias in the sense that a is strongly falling, the sign of dy /da could be positive. The golden rule condition in this setup with the Stoleru effect reads: ß = (a + n + δ(a))

(22)

Thus the modified golden steady-state capital intensity requires: ß = s(1 − (a))

(23)

If government imposes an income tax rate, the condition of the golden rule is modified, namely ß = s(1−τ) provided that the CO2 emissions are ignored. The following figure shows that the steady state realized is not necessarily in line with the golden rule which requires that the marginal product of capital is equal to the depreciation rate of capital (assuming that the population growth rate n = 0 and that the rate of progress a is zero); the tax rate has to be τ1 if the golden rule is to be realized. If one takes into account the CO2 emissions the condition for the golden rule has to be modified accordingly. Modified Growth Model and the Environment: Technological Progress with the Stoleru Effect and CO2 Emissions (level of knowledge A = 1).

R.5 Open Economy and Economic Growth In an open economy, economic growth models have to be modified in an adequate way. Basically, five key aspects have to be considered: • The production function: If knowledge from abroad (country II) and the foreign progress rate affects the progress rate in country I (a country with an income and technology gap vis-à-vis country II) the production function needs to be specified adequately. One possible way to express the fact that the exports x—while assuming that X = xY*—contribute to GDP in the home country (country I) through specialization is to specifyY = Kß (xY*)η (AL)1−ß ; by implication that the growth rate of GDP, namely gY , is determined according to gY = ßgK + (1 − ß)(a + n) + ηgY* (* denotes foreign variables, η is a positive parameter in the interval [0,1], g denotes growth rates; note that it has been assumed that x is constant). Hence trade brings an international growth bonus which is expressed here by ηgY* . If there is international symmetry, the foreign production function—with j denoting the foreign export ratio and assuming that exports X* = jY—can be written ∗ ∗ as Y* = K∗ß (jY)η∗ (A*L*)1−ß and therefore we can restate the production func∗ tion for country I as Y = Kß [x K*ß∗ (jY)η∗ (A*L*)1−ß ]η (AL)1−ß and—defining

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Innovations in Macroeconomics

Fig. 115 Growth model: golden rule

stationary economy y(k) F

F‘ T

φ

δk

E0

s[1– τ0] y (k) s[1– τ2] y (k)

E‘

s[1– τ1] y (k)

E1 φ

a

k = K/L k#gold

0

k 0#

Population Growth n (n<0) y(k) F‘ T

φ‘

E1

(δ+n)k s[1– τ0] y (k)

E‘‘ φ‘

b

k k#gold

0

k#1

y (k) δ (a) + a

F‘

s [1– τ0] y (k) φ‘‘

E2

φ‘‘

0

k#gold

Fig. 116 Golden rule in a growth model with technological progress and the Stoleru effect

J‘ CO2 /L J

k#2

k‘ = K /(AL)

H‘ H

ß = ß/(1 − η*η), ß * = ß*/(1 − η*η), η = η/(1 − η*η), η * = η/(1 − η*η)—  ∗ ∗  ∗ ∗ ∗ thereforeY = Kß xη jη K∗ß (A*L*)(1−ß )/(1−η η) (AL)(1−ß)/(1−η η) . Thus foreign capital accumulation and foreign knowledge and labor input effectively contribute to domestic output—read: output in country I.

R.5 Open Economy and Economic Growth

579

• The impact of the foreign progress rate (a* in country II) on the progress rate of the poor country (country I) also needs to be considered. There will be some international technology spillover—partly related to trade and also to FDI inflows and outflows. • If there is FDI, the impact of inward and outward FDI needs to be considered. From an analytical perspective, it also needs to be taken into account that cumulated FDI inflows imply that part of the domestic capital stock—say in country I which has attracted FDI inflows—is owned by foreign investors; hence the difference between gross domestic product and national income needs to be considered. If only international dividend payments are considered and it is assumed that production factors—in the traditional production function Y = Kß (AL)1−ß in ∗ country I and Y* = K∗ß (A*L*)1−ß* in country II—are rewarded in accordance with the marginal product rule, we can state (with α* denoting the share of capital K owned by foreign investors) that national income in country I(Z) is equal to Z =Y(1 − α*ß), since ßY is the share of GDP accruing to the owners of capital. In this simple case, we have assumed asymmetric foreign direct investment, namely investors from country II invest in country I, but there are no FDI flows from country I to country II; in this setup, the foreign national income Z∗ = Y* + αßY/q*, where q*: = eP*/P (e is the nominal exchange rate, P is the price level, * stands for foreign variable). The case of two-way FDI flows can, of course, also be considered, where α denotes the share of K* owned by investors from country I. As long as no specialization gains from trade are considered in the production function, the respective function in country II is given by the expression Y* = K∗ß (AL)1−ß . • One may want to consider maximization of global economic welfare, namely in the simple sense that consumption per capita should be maximized in both countries: That is the conditions for the golden rule can be identified in both countries. • Transition and adjustment dynamics could also be considered, including those that occur if the steady-state capital intensity differs from the capital intensity in line with the golden rule (kgold ): We have to focus on three different cases: (i) k # > kgold and k#* > k*gold so that both countries will want to reduce the savings rate; this implies a deterioration of the current account balance for the country that proceeds quickly and strongly with a policy that reduces the savings rate— and most likely there will be international conflicts over adjustment policies. (ii) k # > kgold and k#* < k*gold . Country I will want to reduce its savings rate—this implies a transitory deterioration of the current account position—and country II will want to raise its savings rate—this implies a transitory improvement of the current account position, which in principle is compatible with the desired adjustment dynamics of country I. (iii) k # < kgold and k#* < k*gold : Both countries will want to raise the savings rate, but this could again imply conflicts over inconsistent desired current account dynamics in both countries. Let us first consider the simple case of no effect of trade on the production function, while there is asymmetric FDI in the sense that country I faces cumulated FDI inflows—but there are no FDI outflows from country I toward country II; the share

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Innovations in Macroeconomics

of the capital stock owned by foreigners is α, which is in the range (0,1). It is adequate, of course, to consider that savings is proportionate to gross national product so that S = sZ and hence the savings function in country I (with technological progress rate (a) and a constant growth rate of the population (n)) reads S = s(1 − α*ß)Y

(24)

Hence the steady-state solution for y is given by y = [s(1 − α*ß)/(a + n + δ)]ß/(1−ß)

(25)

An interesting question concerns the issue to what extent progress rate a is a positive function of α: If a(α*), an increase in α* will go along with a fall in the level of the growth path and a rise in progress rate a; a stronger presence of foreign subsidiaries thus raises the progress rate, which is plausible to the extent that multinational companies are characterized by ownership specific advantages, namely technology advantages. Whether or not the government is eager to promote FDI inflows depends on the political time horizon and discount rate applied in the political process. This is due to the fact that y will fall in the short run but will be higher in the presence of FDI in the long run. If there are two-way FDI flows, for Z (with q* denoting the real exchange rate and α being the share of foreign) we have to write: Z = Y(1 − α*ß) + q*αß*Y*; (and Z* = Y*(1 − αß*) + α*ßY/q*)

(26)

Here αß*Y* stands for country I’s profits accrued from abroad and multiplying the term with the real exchange rate q* translates such profits into domestic goods units of country I. In such a setup, it is not easy to state the equation that governs the accumulation of k . Let us consider the current account equilibrium which states that the sum of exports plus profits accruing from abroad must be equal to imports plus profits of foreign subsidiaries accruing to parent companies abroad (we denote the export–GDP share by x and the import–GDP share by j): xY* + q*αß*Y* = q*jY + α*ßY

(27)

[x + q*αß*]Y* = [q*j + α*ß]Y

(28)

Y* = {[q*j + α*ß]/[x + q*αß*]}Y

(29)

Hence we have

Thus national income in country II can be expressed as follows: Z = Y(1 − α*ß) + q*αß*{[q*j + α*ß]/[x + q*αß*]}Y

(30)

Hence a setup with savings S = sZ can be written as S = s{(1 − α*ß) + q*αß*{[q*j + α*ß]/[x + q*αß*]}}Y

(31)

R.5 Open Economy and Economic Growth

581

Thus the steady state for k becomes k # = {s{(1 − α*ß[1−[x + q*αß*]−1 ] + q*αß*q*j/[x + q*αß*]}/(a + n + δ)}1/(1−ß)

(32)

In principle, the right hand side term can be larger or smaller than in a closed economy with the solution k # = [s/(a + n + δ)]1/(1−ß) . Thus, the empirical aspects will have to be looked at carefully. The situation looks even more complicated if we include trade-related effects in a monetary economy. If the savings function is S/L = s(1−τ)Y/L—with τ denoting the income tax rate— the government has a simple tool, namely the tax rate, to manipulate the effective savings rate s(1 − τ). In the case of a constant population size—with a savings rate s(1 − τ0 )—we initially have equilibrium point E0 , while the distance E0 F stands for per capita consumption C/L in the steady state. The golden rule requires that the slope of the production function—the marginal product of capital—be equal to the capital depreciation rate: Hence point T on the production function is relevant and point E1 is the desired optimal intersection point of the curve δk and the savings function. In this case, it would be adequate to raise the income tax rate and the maximum per capita consumption—equivalent to the distance TE1 —obtained. A fall in the effective savings rate and hence a rise in the income tax rate was adequate here since the initial steady-state capital intensity exceeds that of the golden rule capital intensity (k#gold ). In an open economy, country I could have FDI outflows equivalent to the distance k#0 − k#ggold without any welfare loss; on the contrary, there would be an increase in national income and hence national economic welfare. It is, however, an issue whether country II will benefit from such outflows; if country II’s capital intensity is below the golden rule capital intensity, FDI inflows will be welcome. The basic problem setting is not changing much if we consider (as in the next diagram) a situation with positive or negative population growth—for many OECD countries declining population growth rates might be characteristic in the future. In the case of a model with technological progress and the Stoleru Effects, an interesting situation is shown in the subsequent diagram, which refers to an economy with CO2 emissions. The steady-state capital intensity exceeds the golden rule capital intensity. If the government can reduce the effective savings rate, the economy will move to the golden rule situation; at the same time, there will also be an increase in welfare from the reduction of CO2 per capita emissions.

Reconciling the Short-term Keynesian Model and the Long-Run Growth Model In qualitative terms, one can move from the core result of the Keynesian model to the neoclassical growth model through a sign-switching function s(t), where (t) has the characteristic to switch from s in t0 to 1/s for t approaching infinity. From

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mathematical signaling theory we can plug in an appropriate sign-switching function. There is, however, a theoretical challenge, namely to explain exactly why such a sign-changing function is generated through the economic system, namely in the sense that dY/ds > 0 in the short run, while dY#/ds > 0 in the very long run. Logically the existence of such a sign-switching function may be postulated; moreover, the multipliers for various policy instruments, including monetary policy and fiscal policy might also change over time and we might indeed find a good new way of understanding the short-run, medium-term, and long-run economic dynamics on the basis of such a sign-changing function. The proposed way is useful for achieving a more consistent macroeconomic modeling approach. Moreover, one has a new starting point for considering both short-term stabilization gains from economic policy and long-term effects on the level of the growth path (and the trend-growth rate if a model with progress is considered). There is more research to be conducted, but we have indeed found a new avenue for analytical progress. In an analytical perspective, the short- and medium-run approach of New Keynesian Macroeconomics could be a starting point for the short-run/long-run link, namely in the following way: A typical element is a technology shock which implies—in an initial situation with constant relative prices—that the mark-up will increase and the unemployment rate will rise; in the long run, relative prices are flexible, including the relative price of nontradables whose development is not only important for the sectors (nontradables, tradables) but also for current account equilibrium and full employment. However, it is not clear to what extent this changes the role of the savings rate in a qualitative way. One option to link the short run and the long run in a consistent way is to define an operator FLEX, which is the frequency of price adjustments per period, where we assume that the price adjustment frequency is increasing when approaching the market equilibrium. In a two-sector economy with constant knowledge, the divergence k# − k(t) = λ FLEX pi /P, where pi is the price of investment goods and P is the general price level so that pi /P is a relative price indicator; λ is a positive parameter. Here we face a formidable challenge in Economics. It is quite unsatisfactory that so far there is no consistent analytical link between the short-run (New) Keynesian macroeconomic equilibrium and the long-run equilibrium as established in the neoclassical growth model. One proposal suggested here is the hybrid Keynes–Solow approach presented.

R.6 A Broader View on the Golden Rule and Innovation in Open Economies Let us assume that savings S is composed of a domestic component and a foreign component related to profits made in country I. The setup is asymmetric in the sense that country I has net FDI inflows, but there are no FDI outflows from country I. The

R.6 A Broader View on the Golden Rule and Innovation in Open Economies

583

savings function (with s * for the savings rate of foreign subsidiaries in country I) is S = sY(1 − τ)(1 − α*ß) + s *α*ßY(1 − τ) = [s(1 − α*ß) + s *α*ß](1 − τ)Y

(33)

Hence overall savings consist of domestic savings (in a narrow sense) and of savings from subsidiaries from abroad [(s *α*ß)(1 − τ)Y]. Moreover, it is assumed that there is an exogenous element of technological progress a0 , as well as a foreign element, which is related to share α that foreign investors hold in the overall capital stock. Thus the following progress function is used (assuming that a* is constant and using a positive parameter α ): a = a0 + α α*a*.

(34)

Thus the steady state in an economy with population growth rate n (n can be positive or negative) and a Stoleru effect based on a positive link between the depreciation rate and a*, a0 and α (the presence of cumulated foreign investment and spillovers contributes to vintage effects): k  # = {[(s(1 − α*ß) + s *α*ß)(1 − τ)]/(a0 + α α*a* + n + δ(α*a*)}1/(1−ß) (35) Taking a look at the golden rule issue we now have to consider that C/L = c(1 − α*ß)(1 − τ)y

(36)

In an open economy with FDI and net income transferred abroad, the income use side reads (in the case of income taxation and with s αßY(1 − τ) denoting the savings of foreign subsidiaries): Y = C + S + T + α*ßY = cY(1 − τ) + sY(1 − α*ß)(1 − τ) + s *α*ßY(1 − τ) + τY + αßY

(37)

Alternatively we can write Y[(1 − α*ß) − c(1 − τ) − τ] = [s(1 − α*ß) + s *α*ß](1 − τ)Y

(38)

The task of maximizing C/L now has to take into account that the distance between the (1 − a*ß) line and the investment line (a + n + δ)k has to be maximized. Hence we must have (1 − α*ß)ßk 

ß−1

= a0 + α α*a* + n + δ(α*a*)

(39)

Taking the steady-state condition for k # into account, we get (1 − α*ß)ß = [s(1 − α*ß) + s *α*ß](1 − τ)

(40)

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Innovations in Macroeconomics

In this setup, it is obvious that the level of maximum consumption per capita is affected through the presence of foreign investors: The required income tax rate that brings about the maximum consumption per capita can be derived as follows (after division of the above equation by s(1 − α*ß) and after taking logarithms while using the approximation ln(1 + x) ≈ x): τ ≈ s *α*ß/s(1 − α*ß) − ln(ß/s)

(41)

A special case of parameter sets brings the result that τ = 0. Remember that the steady-state capital intensity is simply determined by the ratio k# = {[(s(1 − α*ß) + s *α*ß)(1 − τ)]/(a0 + α α*a* + n + δ(α*a*)}1/(1−ß) (42) Hence if s * sufficiently exceeds s, the negative impact of foreign subsidiaries on the denominator term, the level of the growth path is increased; as the presence of foreign investors has increased the progress rate—according to our assumptions (which imply sustained competition in all sectors of the host economy)—the case considered here unambiguously implies that foreign investment inflows raises long-run consumption per capita: As C/(AL) is constant in the steady state C/L = [(C/L)0 A0 ]eat . However, if s * is sufficiently smaller than s, the level of the growth path will fall as a consequence of cumulated FDI inflows; it should also be pointed out that foreign investors are likely to pay lower effective income tax rates so that savings S = s(1 − α*ß)(1 − τ) + s *α*ß(1 − τ ), where τ is the effective income tax rate applied to foreign investors. Such a change in the average income tax rate might raise long-run debt–GDP ratios and will hence bring about a real depreciation in the currency, which in a world of imperfect capital markets according to FROOT/STEIN (1991) implies higher FDI inflows relative to GDP. If the presence of foreign subsidiaries reduces the level of the growth path, the effect of cumulated foreign investment on the progress rate still has to be considered: As the growth rate a is increasing, it is only a question of time until the progress effect will dominate the level effect. However, it is unclear whether policymakers’—or voters’—time horizon is long enough to open up the economy adequately for foreign investors. Moreover, the presence of foreign investors in the model setup presented here implies less policy autonomy since governments can only directly influence part of the savings rate, namely the domestic component; the foreign component s *αß might also be influenced through adequate tax policies or other incentives, but a small open economy might not find it easy to affect this part of the savings ratio. A big economy—with considerable political and economic leverage (e.g., China)—will find it easier to have an impact here.

Innovation, R&D Sector and Semi-endogenous Growth in Open Economies The R&D sector has to be considered more explicitly and to do so we first take a look at the simple closed economy setting before we switch to the open economy.

R.6 A Broader View on the Golden Rule and Innovation in Open Economies

585

Innovation takes place in an R&D sector, where a fraction of GDP is spent on research and development so that capital accumulation in a closed economy is given by: dK/dt + δK + ϕY = sY

(43)

Hence with a Cobb–Douglas production function Y = Kß (AL)1−ß and a constant growth rate of labor and a progress rate a = ϕ ϕ (ϕ is a positive parameter; assumption ϕ < s), we get the steady-state solution: k  # = [(s − ϕ)/(ϕ ϕ + n + δ)]1/1−ß

(44)

Thus per capita output in the steady state is determined by y = A0 [(s − ϕ)/(ϕ ϕ + n + δ)]ß/(1−ß) e

ϕ ϕt

(45)

Therefore, we see it more clearly than in a standard model with exogenous R&D that a rise in the output share of the R&D sector will reduce the level of the growth path. In an open economy with cumulated FDI inflows and income taxation and a savings function S = s(1 − τ)(1 − α*ß) + s *(1 − τ)α*ß, we have—also considering the vintage effect of the progress rate—the solution: k  #{[(s(1 − α*ß) + s *α*ß)(1 − τ)]/(a0 + ϕ ϕ + α α*a* + n + δ(α*a*, a0 + ϕ ϕ))}(1/1−ß)

(46)

Thus it has been assumed that a = a0 + ϕ ϕ + α α*a*, therefore beside autonomous technological progress, the size of the R&D sectors matters as well as international spillovers. Denoting the export–GDP ratio by x and the import–GDP ratio by j, one may consider to add the term λa* + λ x + λ ja* in the progress function where λ, λ , and λ are positive parameters: λ is truly exogenous international technology spillovers, λ indicates how demanding foreign markets are in terms of (induced) technological sophistication and λ indicates how strong the embodied innovation dynamics in trading partner countries is from which the country is importing goods and services. Looking at the progress function a = a0 + ϕ ϕ + α α*a* + λa* + λ x + λ ja*

(47)

we see that the long-run growth rate of per capita output depends both on the size of the R&D sector, technological progress abroad, and the intensity of trade relations. The parameter ϕ is basically chosen by firms and industry. The only task for governments is to internalize external effects and if they do so, there will be an optimum progress rate, which may be indicated by a parameter ϕ (instead of ϕ ). In this case, per capita GDP in the steady state—with a = a0 + ϕ ϕ + α α*a* + λa* + λ x + λ ja*—is given by y# = {[(s(1 − α*ß) + s *α*ß)(1 − τ)]/(a0 + ϕ ϕ + α α*a* + λa* + λ x + λ ja* + n + δ(a))}ß/(1−ß) e

at

(48)

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One further potentially useful modification should be noted with respect to savings function: “Foreign savings” from subsidiaries might not be given by s *α*ßY but rather by s *α*ßY + s *ß*Y*q*, where s * indicates the willingness of the parent company to devote part of its profits in country II (the headquarter country) to investment projects in country I. Moreover, the case might have to be considered that ϕ positively depends on the share of the capital stock owned by foreign companies— the higher the share owned by foreign subsidiaries, the higher the share of GDP in the host country, which is devoted to R&D; however, in principle we cannot rule out the perverse effect that ϕ negatively depends on the presence of foreign investors (e.g., a leading biotechnology from Denmark took over a privatized Brazilian biotechnology company at the beginning of the twenty-first century—and closed down the R&D activities in Brazil as the key interest was simply to get a hold of the Brazilian company’s biotechnology patents; moreover, foreign investors might accelerate the consolidation of certain sectors and indeed weaken actual and potential competition in certain sectors in the long run). In the above setup, the golden rule requires that (1 − αß)ßk ß−1 = a0 + ϕ ϕ + α α*a* + λa* + λ x + λ ja* + n + δ(a)

(49)

The size of the golden capital intensity is a negative function of ß and a negative function of α, however, it must not be overlooked that the progress rate and hence the long-run growth rate of per capita consumption is a positive function of α*.

R&D and Outward Foreign Direct Investment Let us consider the following asymmetric case of an open economy: Country I has invested abroad but there is no inward foreign direct investment. Hence national income is given by Z = Y + αß*q*Y*

(50)

S = s(Y + αß*q*Y*)

(51)

The size of the domestic R&D sector in GDP is ϕ and hence we can write the accumulation dynamics of k as follows: dk  /dt = s[y + αß*q*y*(A*L*)/(AL)] − (n + a + δ)k  y* = [s*(1 − αß*)/(n* + a* + δ*)]ß*/(1−ß)*

(52) (53)

dk  /dt = s{y + αß*q*(A*L*)/(AL)[s*(1 − αß*)/(n* + a* + δ*)]ß*/(1−ß)* } − (n + a + δ)k 

(54)

This shows that there is international economic interdependence in the long run, namely based on growth interdependency.

S. Employment in the R&D Sector, Economic Policy and the Golden Rule

S.1 Introduction Macroeconomics has been dominated for many years by models looking at deviations from the equilibrium—with Dynamic Stochastic Equilibrium Models becoming quite prominent in the late 1990s and at the beginning of the twenty-first century. A complementary line of research is the theory of economic growth, which puts the focus on the level of the growth path and the long-run trend growth rate. This research has suffered, however, from certain problems despite the fact that attempts to explain technological progress have enriched growth models under the heading of endogenous growth in the 1990s. Traditional neoclassical growth theory (SOLOW 1956) has intensively influenced Economics in the 1960s and the 1970s; with the Golden Rule maximizing long-run consumption per capita (PHELPS 1961; VON WEIZSÄCKER 1962), growth analyses have established the condition which requires—under the assumption of profit maximization—that the growth rate of output be equal to the real interest rate; this result can be brought about through the government’s choice of a specific savings rate. However, neoclassical growth approaches have not really been very influential in the field of economic policymakers, perhaps except for growth accounting exercises which have, for instance, become prominent in explaining the surge of US growth in the 1990s when information & communication technology rapidly expanded. The fact that monetary policy has become quite influential since the 1960s in OECD countries has probably contributed to the rather limited role of traditional growth models that have neglected the role of money and real balances, respectively. Moreover, there is still a large analytical gap between short-run Keynesian models and long-run Solow-type growth models and it is still quite unclear how a consistent bridge between the two analytical worlds could be built. Growth analysis has remained largely a body of research that looks into the real economy, although some monetary considerations have occasionally been presented (e.g., TOBIN 1965; WELFENS 2008a). The fact that growth models typically do not contain the stock of real money balances is a problem, since without money there is no potential link to the financial sector and this in turn makes it difficult to

P. J. J. Welfens, Innovations in Macroeconomics, DOI 10.1007/978-3-642-11909-5_19, © Springer-Verlag Berlin Heidelberg 2011

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understand the problems and implications of banking crises. Subsequently some of the problems mentioned will be picked up and several new ideas will be presented. With endogenous growth modeling, (survey and new approaches, e.g., BRETSCHGER 1999, 2002) new perspectives have been introduced into the economic analysis, but the link to the traditional growth analysis has remained weak. At the same time, there is no doubt that research and development (R&D) plays an increasingly important role for both industrialized economies and newly industrialized countries. The key elements in modern growth analysis are the production function, the savings function and the progress function used for covering the innovation dynamics. In open economies there are further aspects, which include trade and inward foreign direct investment (FDI) as well as outward FDI. Models dealing with FDI have to make a clear distinction between gross domestic product and gross national income, and this distinction must indeed be picked up if a consistent result is to be established for the analysis of the golden rule, which maximizes per capita consumption in the steady state. Subsequently, it is shown that it is rather easy to implicitly incorporate an R&D sector—with a share of workers active in R&D activities—into the neoclassical growth model and to also take the role of real money balances into account. There are several new insights that are derived in this way, including key conclusions for golden rule policies. A rise in the share of workers active in the R&D sector will reduce the level of the growth path, but it raises the rate of technological progress. At the same time, a higher share of workers active in the R&D sector goes along with a higher optimum income tax rate. There are also key insights to be derived on monetary policy. Moreover, it may be emphasized that the golden capital intensity is not an opaque theoretical concept but it should be used to bring about an optimum long-run economic development. It can be shown that governments and decisionmakers, respectively, will consider raising employment in the R&D sector only if there is no problem of extreme discounting the future growth bonus—the short-term impact of a rise in the share of workers in the R&D sector on the level of the growth path is negative. This implies that we also have some interesting aspects in the context of the New Political Economy. The subsequent sections look into a monetary growth model with an R&D sector whose output is an intermediate input in final goods production. The role of the golden rule in this new setting will be analyzed. Moreover, an alternative approach of a monetary growth model is considered which is based on a savings function in which both disposable income and the ratio of wealth to income enters. Finally, the question is raised under what parameter constellations of short-run Keynesian modeling are compatible with the neoclassical growth model—here the concept of a harmonious savings rate is developed. The assignment suggested here for monetary policy and tax policy is also new and the overall approach opens up new ways for a more realistic analysis. The golden rule capital intensity is considered to be a key concept for economic policymakers—governments should carefully evaluate whether the actual capital intensity falls short or exceeds the golden capital intensity. Indeed it might be suggested that in reality there are political cycles that are characterized by policymakers favoring the rise of capital intensity during certain periods through

S.2 Towards a New Model

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tax policies and monetary policy—possibly beyond the golden rule capital intensity. Going beyond this capital intensity implies that per capita consumption falls short of the possible maximum and this will generate frustration. If such a period is followed by expansionary government policy stimulation consumption, this need not just be interpreted as a measure for a cyclical recovery but it might also stand for a much desired shift toward maximum utility of consumers, namely achieving the maximum long-run consumption per capita.

S.2 Towards a New Model The standard Solow growth model builds on a neoclassical production function Y(. . . ) with factor inputs of labor, capital and knowledge; plus a simple savings function S(. . . ) and an equilibrium condition for the goods market in a closed economy, namely S(. . . ) = dK/dt + δK, therefore, the right-hand side stands for gross investment (δ is capital depreciation). These three elements lead to a differential equation in k (capital intensity k := K/L where K and L denote capital and labor, respectively) and k (k := K/(AL)), respectively: The latter is relevant if growth of knowledge (A) is considered over time. The product AL is dubbed labor in efficiency units. Basically, it can be shown that in an economy with a growing population and a positive technological progress rate (a), the differential equation in k leads to a stable solution where k # is the so-called steady-state solution (# denotes the steady state). As a point of reference it is useful to recall that in the neoclassical model with a production function Y/(AL) := y = kß , an exogenous growth rate (a) of A and an exogenous population growth rate gives—with a savings function S = sY (and therefore S/(AL) = skß )—the steady-state capital intensity k # = (s/(a + n + δ))1/1−ß and steady-state y # = (s/(a + n + δ))ß/1−ß . The so-called golden rule-maximizing the per capita consumption-is characterized by the condition that the marginal product of capital ßkß−1 = a + n + δ and hence k = [ß/(a + n + δ)]1/(1−ß) , which together with k # implies that ß = s: By implication the savings rate would have to be close to 30% if one considers standard estimations of the output elasticity of capital in OECD countries. To the extent that government can manipulate the savings ratio s, this golden steady state will indeed be achieved. If the savings function is S = s(1 − τ)Y where τ is the income tax rate, the requirement for the golden rule is s(1 − τ) = ß. Subsequently, the focus will to some extent be on the golden steady state, which is not considered here as a fable for growthmen—to use part of the original title of the Phelps paper—rather it will be argued that as microeconomics suggests that households want to maximize per capita consumption, it should be taken very seriously by macroeconomists and policymakers, respectively. Many modern macroeconomic models simply consider deviations from long-run equilibrium but this is not convincing if the long-run equilibrium is not adequately defined and the golden steady state seems to indeed be a natural point of reference. Let us consider a neoclassical growth model on the basis of a Cobb–Douglas production function; we also consider a sector with R&D that delivers inputs for the

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production of final goods—the share of workers in efficiency units in the R&D sector is ρ (0 < ρ < 1) and therefore the share of the effective labor force AL working in the final goods sector is 1 − ρ. We consider inputs as real money balances M/P (M is the stock of money, P the price level, ß is a positive parameter), physical capital K, labor L and labor-augmenting endogenous knowledge in the production function which is written here as 



Y = (M/P)ß K ß (AL(1 − ρ))1−ß−ß ;

ß + ß < 1;

0 < ß < 1;

(I)

Real money balances are held by households and enter the production function of firms as a positive external effect; real money balances raise gross domestic product as using money saves on transaction costs and information costs, and there should indeed be no doubt about it in a monetary economy with a zero inflation rate. It is noteworthy that a rise in the share ρ reduces the level of the growth path of per capita income Y/L, however, the subsequent progress function should not be overlooked, which implies that a rise in ρ will increase the rate of technological progress dlnA/dt and in the steady state of the growth model, per capita consumption will grow with the rate of technological progress. We will denote (M/P)/(AL) as m and consider it to be—at first—to be an exogenous policy variable; the production function can be expressed as ß



y = m  (1 − ρ)1−ß−ß k 

ß

(II)

Thus the marginal product of capital and labor is given by the two subsequent equations: ß



∂Y/∂K = ßm (1 − ρ)1−ß−ß k  ß

ß−1

(III.I) 

∂Y/∂L = (1 − ß − ß )m (1 − ρ)1−ß−ß k ß

(III.II)

As the marginal product is proportionate to the average product, it may be stated that both average and marginal labor productivity is a positive function of real money balances per unit of labor in efficiency units; and labor productivity is a negative function of the share of workers employed in the R&D sector, however, when this statement is made, the subsequent progress equation should not be overlooked, which states that A(t) and hence labor in efficiency units A(t)L(t) is a positive function of the share of workers employed in the R&D sector. Taking a closer look at the production function, it may be emphasized that: The ratio of gross domestic product (Y) relative to labor in efficiency units (AL) is not simply kß as in the standard model where Y  = KßAL(1−ß) . Rather, we have a term mß , which indicates a positive role of real money balances for y . At the same time the existence of an R&D sector, which can be understood to represent productivity—enhancing roundabout processes (in the classical sense of Böhm-Barwerk), reduces the level of gross domestic product per unit of labor in efficiency units. The standard Cobb–Douglas function would have been y = kß . Hence the real money balance effect implies an upward rotation of  the y-curve provided that mß exceeds unity; at the same time the existence of an

S.2 Towards a New Model

591 

R&D sector implies a downward rotation of the y-curve since (1 − ρ)(1−ß−ß )/(1−ß) is smaller than unity. From this perspective there are clear changes in the golden rule that maximize per capita consumption C/L and (C/(AL)), respectively. Since   the savings function now is S/(AL) = s(1 − τ)[m ß (1 − ρ)1−ß−ß ]kß the equilibrium for the goods market condition S/(AL) = (dK/dt)/(AL) + δK/(AL) implies for the case of an economy with a progress rate a and a population growth rate n that capital accumulation is governed by the following equation: ß



dk  /dt = s(1 − τ)[m (1 − ρ)1−ß−ß ]k  − (a + n + δ)k  ß

(IV)

This Bernoulli differential equation is stable and has the following solution (setting dk /dt = 0): ß



k  # = {s(1 − τ)[m (1 − ρ)1−ß−ß ]/(a + n + δ)}1/(1−ß) ß



y # = m (1 − ρ)1−ß−ß k 

ß

(V) (VI)

In the steady-state investment per unit of labor in efficiency units (AL) is characterized by (a + n + δ)k and the maximization of per capita consumption and the C/(AL), respectively, requires that the slope of the output graph be the same as (a + n + δ); that   is we must have [mß (1−ρ)1−ß−ß ]ßkß−1 = (a + n + δ). Obviously, the square bracket   term [mß (1 − ρ)1−ß−ß ] could be smaller or larger than unity; if it exceeds unity, the slope that determines the golden rule will be larger and hence k maximizing C/(AL) will be smaller than in the traditional setup. If the square bracket term falls below unity, the slope is lower than in the standard case and this means that k maximizing C/(AL) is higher than in the traditional setup; however, the golden rule still requires s   = ß (1−τ) since the steady-state capital intensity k # = {s(1−τ)[mß (1−ρ)1−ß−ß ]/(a + n + δ)}1/(1−ß) and taking a look at the golden rule condition the implication indeed is s = ß (1 − τ). The positive effects of the share of labor employed in the R&D sector on the rate of technological progress (a) should, of course, not be overlooked here. In the case of a constant progress rate a (dlnA/dt = a or A(t) = A0 eat ; e is the Euler number, t is the time index) and a constant growth rate of labor (n) per capita gross domestic product is given by ß



y = A0 m  (1 − ρ)1−ß−ß k ß e

at

(VII)

Denoting the growth rate of the nominal monetary stock by μ and the inflation rate by π, the growth rate of per capita GDP (gy ) can be expressed as follows: gy ≈ ß [μ − (π + a + n)] + (1 − ß − ß )dρ/dt + ßgk + a

(VIII)

The term is derived by taking the logarithm in the previous equation and taking into account that ln(1 − ρ) ≈ ρ for small ρ. Subsequently, the following progress function (with ρ being a positive parameter; ρ is the depreciation rate of knowledge) is assumed: dA/dt = ρ ρA − ρ A;

(IX)

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This progress function indicates a positive feedback effect between the change of knowledge and the level of knowledge, where the intensity of the feedback effects depends on the share of workers active in the R&D sector and the parameter ρ . The higher the share of workers active in the sector R&D the greater the positive feedback effect will be. The progress rate a := (dA/dt)/A can be expressed as a = ρ ρ − ρ

(X)

It will be assumed that ρ ρ ≥ ρ ; clearly we have a constant A if the share of workers in the R&D sector ρ = ρ /ρ . By assuming that the capital depreciation rate is δ and the savings function S = sY(1 − τ)—with τ standing for the income tax rate—from the equilibrium condition S = dK/dt + δK we get the following differential equation (using dk /dt = (dK/dt)/(AL) − (n + a + δ)k ): ß



dk  /dt = [s(1 − τ)m  (1 − ρ)1−ß−ß k  ] − (ρ ρ − ρ + n + δ)k  ß

(XI)

The square bracket term is similar to the production function, except for a multiplying factor s(1 − τ). The investment per AL necessary to maintain the capital intensity k is indicated by the term (ρ ρ −ρ + n + δ)k which, of course, is equal to (a + n + δ)k . The starting point for the subsequent figureis the intersection point of the savings function s[1 – τ0 ]y and the line (a + n + δ)k (see point E2 ). In neoclassical growth theory, the golden rule characterizes the condition under which per capita consumption in the steady state is maximized: If y = kß , the condition is given by the equality of the marginal product of capital ßkß−1 and (a + n + δ). With our modified production function, the golden rule is affected by both money balances mß and by the term (1 − ρ)1−ß−ß in the production function and this is shown in the subsequent graph where it has been assumed that the net effect of real money balances and the R&D sector effect is an upward rotation of the traditional production function y = kß in y -k  space; in the traditional setup, the maximum consumption per capita is graphically obtained by looking for the point on the production function y = kß where the tangency has the same slope as the curve (a + n + δ)k . With our new monetary production function—with an implicit R&D sector—the maximum consumption per capita ratio is no longer given by F I but by the distance F I and thus we can see that the role of real money balances on the maximum per capita consumption can be positive. It should also be noted that the savings function S/(AL) is rotating upward if the function for y is rotating upward due to the introduction of real money balances. To put a grain of salt in this perception, the lower part of the diagram shows a positive link between production and CO2 per capita emissions which is an important element in the debate about sustainability and true long-run equilibrium. This then raises again the question of optimum sustainable consumption per capita, that is a broader economic perspective has to be addressed in which CO2 emissions stand for a negative external effect and it is not really clear that a conventional golden steady state is indeed an adequate perception of a stable steady state; however, subsequently we will ignore the emission aspects as they have been covered elsewhere (WELFENS 2010c, d).

S.2 Towards a New Model

593

Fig. 117 Golden rule with real money balances and R&D sector employment

y‘ = m’ß‘(1 – ρ)1 – ß – ß’k‘ß F‘‘ y‘(k‘) = k‘ß (δ + a + n)k‘

F‘ G φ‘‘

E2 I

k‘#gold J‘

CO2/L

I‘‘

φ‘‘

0

s[1 – τ0] y‘(k‘)

k‘#2

k‘ = K / (AL)

H‘

J

H

Obviously governments should manipulate the term s(1 − τ) in such a way that the intersection of the curve s(1 − τ)y with the curve (a + n + δ)k is exactly where the distance between y and the line (a + n + δ)k becomes maximal: then C/(AL) is maximal in the steady state; the associated capital intensity k is dubbed kgold . The above equation is a Bernoulli differential equation in k , which is stable and has a simple solution: The steady-state solution (denoted by #) is therefore given by ß



k  # = [s(1 − τ)m (1 − ρ)1−ß−ß /(ρ ρ − ρ + n + δ)]1/(1−ß) 





(XII)



y # = mß (1 − ρ)1−ß−ß [s(1 − τ)mß (1 − ρ)1−ß−ß /(ρ ρ − ρ + n + δ)]ß/(1−ß) (XIII) Hence y # = m 

(ß /(1−ß))



(1 − ρ)(1−ß−ß )/(1−ß) [s(1 − τ)/(ρ ρ − ρ + n + δ)]ß/(1−ß) (XIV)

In the expression one can see that the output elasticity of real money balances per unit of labor in efficiency units is higher than simple inspection of the production  function y = mß kß suggests. The effective output elasticity of m —referring to the level of the growth path—exceeds ß since (1 − ß) is smaller than unity. We get for per capita income y in the steady state: y# = m

(ß /(1−ß))



(1 − ρ)(1−ß−ß )/(1−ß) [s(1 − τ)/(ρ ρ − ρ + n + δ)]ß/(1−ß) e

  ( ρ ρ−ρ )t

(XV) It is noteworthy that a rise in m can shift the y -line upward in the y -k-space and also the y-line in the y-k-space; therefore, the golden rule question is affected by real money balances and monetary policy, respectively.

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Money Market Equilibrium Considering the money market equilibrium condition in its most basic form, namely m = ε y (ε is a positive parameter in the demand function) implies that there is no degree of freedom of monetary policy unless the central bank wants to realize inflation or deflation which is an issue not to be considered here. Thus we get y # = ε

(ß /(1−ß))  (ß /(1−ß))

y



y #(1−ß−ß )/(1−ß) = ε



(1 − ρ)(1−ß−ß )/(1−ß) [s(1 − τ)/(ρ ρ − ρ + n + δ)]ß/1−ß (XVI)

(ß /(1−ß))



(1 − ρ)(1−ß−ß )/(1−ß) [s(1 − τ)/(ρ ρ − ρ + n + δ)]ß/1−ß (XVII)

Whether or not real money balances raise the level of the growth path now depends on ε and the term (1 − ß − ß )/(1 − ß). Hence y # = ε

(ß /(1−ß−ß ))





(1 − ρ)[s(1 − τ)/(ρ ρ − ρ + n + δ)](ß /(1−ß−ß ))

(XVIII)

Real money balances will raise the level of the growth path of y in the steady state under plausible conditions. The level of the growth path is lower, the larger the share ρ of employment in the R&D sector is. However, raising ρ also has the effect that the long-run growth rate of per capita output will increase. Using the basic money market equilibrium condition—assumed to hold any  time—the effective production function reads: y = (εy )ß kß and hence we have 



y = εß /(1−ß ) k 

ß/(1−ß )

(XIX)

In a monetary economy the effective output elasticity of capital is larger than in a non-monetary economy.

Real Money Balances and Distribution Aspects 

If real money balances enter the production function as a term (M/P)ß the question arises how this will affect the income distribution with respect to labor and capital.   Using a production functionY = (M/P)ß Kß (AL)1−ß−ß implies that holders of money get an implicit share of gross domestic product which reflects the marginal utility of real money balances, that is liquidity services of money; at the same time it has been assumed that the share of labor in GDP will fall as money is introduced in the production function. In a fundamental economic sense money is not neutral here. This somewhat arbitrary redistribution effect can analytically be avoided if we specify the   production function as: Y = mß Kß (AL)1−ß and hence y = mß kß (AL)1−ß . However, it is not fully convincing to assume that the monetary quasi-scale factor  in the production function is [(M/P)/(AL)]ß which implies that the aggregate output

S.3 Policy Conclusions

595

effect of a given stock of real money is reduced if labor input grows in efficiency units—say in the context of a growing population. If one considers a monetary economy as a system in which economic agents build networks of production and exchange on the basis of using money—whose value is stable—one might rather argue that there will be network effects if more workers and hence more firms (given the optimum firm size) are engaged in producing output: The productivity of money— of a given currency—will increase if more people use the same money and typically network effects (e.g., in telecommunications—to use an analogy) are a function of the square of the number of users in the network. A partial solution of the problem could be that one takes into account the rising productivity of money in a broader network of exchange in the exponent of m which may be specified as ß (1 + ζ n) where ζ is a positive parameter. The implication for the steady-state solution k # would be that a rise of n is no longer unambiguously reducing the level of the growth path of k and y , respectively. Here we face new empirical issues for both growth analysis and Monetary Economics.

S.3 Policy Conclusions Does it make sense for society to shift part of the workforce into the R&D sector? The answer is a conditional yes: If the time-horizon of decision makers and policymakers, respectively, is not too short, society will bring about this structural shift; a rise in ρ reduces the level of the growth path and thus has a negative short-term effect (short term in the context of a change in the steady-state regime) on per capita GDP and on per capita consumption. However, in the medium term, the dynamic effect of a rise in ρ—the rise in the long-run growth rate—will more than outweigh the short-term negative effect on the level of the growth path. Only if decision makers would apply a very high discount rate would one stick to a suboptimal share of ρ.

ln y

H

G

F D



Fig. 118 Impact of a rise in the R&D employment share on the level of the growth path and the growth rate

0

E

t1

t3

t4

t

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If there were positive external effects of R&D, it would be adequate for the government to subsidize innovation efforts to some extent. Value added in the R&D sector—net of any subsidies—is ρwAL, where w is the real wage rate. Denoting τ as the subsidy rate (equivalent to marginal positive external effects from R&D) we can write that taxes are levied only for the purpose of R&D subsidies and we will have τY = wρALτ

(XX)

Therefore, under the assumption that the real wage rate w is equal to the marginal   product of labor (1 −ß −ß )mß (1 − ρ)1−ß−ß kß , we can write ß



τY = (1 − ß − ß )m  (1 − ρ)1−ß−ß k ß ρALτ 

(XXI)



As y = mß (1 − ρ)1−ß−ß kß we get τ = (1 − ß − ß )ρτ

(XXII)

ρ = τopt /[τ (1 − ß − ß )]

(XXIII)

The optimum tax rate is derived from the golden rule and this then determines—along with the other parameters of the above equation—the size of the R&D employment share; for ρ to be positive τ also must be positive. The next issue to be raised concerns the modified golden rule in our setup with employment in the R&D sector and a monetary growth model.

Modified Golden Rule 



If we take into account the condition τopt = (1 − ß −ß )mß (1 − ρ)1−ß−ß ρτ we have to insert this as an a priori requirement into the savings function so that we have ß

ß





S/(AL) = s[1 − (1 − ß − ß )m (1 − ρ)1−ß−ß ρτ ]m (1 − ρ)1−ß−ß k  (XXIV) ß

If the condition for monetary equilibrium is ignored we get ß



y # = {s[1 − (1 − ß − ß )m ρ(1 − ρ)(1−ß−ß ) τ ] ß



× m (1 − ρ)(1−ß−ß ) /(ρ ρ − ρ + n + δ)}2ß/(1−ß)

(XXV)

Assuming for the sake of simplicity that n + δ = 1 we can take logarithms and use the approximation: ß



lny  # ≈ [2ß/(1 − ß)]{ln s − (1 − ß − ß )m ρ(1 − ρ)(1−ß−ß ) τ + ß lnm − ρ(1 − ß − ß ) − (ρ − ρ ρ)}

(XXVI)

S.3 Policy Conclusions

597

Now we can see that the derivative of lny # with respect to ρ is ambiguous as: ß



dlny /dρ = [2ß/(1 − ß)]{−(1 − ß − ß )m (1 − ρ)(1−ß−ß ) τ ß

+ (1 − ß − ß )2 m ρτ − (1 − ß − ß ) + ρ }

(XXVII)

This expression is positive if 

ρ > (1 − ß − ß ) > (1 − ρ)(1−ß−ß ) /ρ

(XXVIII)

A word of caution on the government budget constraint is appropriate. Note that here we have implicitly assumed that seigniorage μm in the steady state (μ is the growth rate of the nominal money stock M and in the steady state μ = a + n so that m is constant; remember that the inflation rate is zero) is needed to run the central bank as well as the government. The explicit government budget constraint reads—with G denoting real government expenditures on the institutions of the politico-economic system: τY + μM/P = wρALτ + G

(XXIX)

G is the cost to run the politico-economic system, which basically consists of the central bank and government institutions. Dividing the equation by AL, (with g := G/(AL)) while considering that we have μ = a + n in the steady state with price stability, we can write: τ + (a + n)m = (1 − ß − ß )ρτ + g

(XXX)

Monetary Policy in a Setup with an Interest-elastic Demand for Money As the real stock of money enters the production function, it is clear that money matters in the monetary growth model. Subsequently the role of monetary policy will be considered; to avoid tedious mathematical calculus, it will be assumed that δ = 0. Now let us take into account the standard condition for the golden rule, namely that ß = s(1 − t) and hence τ = 1 − (ß/s); the government budget constraint becomes 1 − (ß/s) − (1 − ß − ß )ρτ + (a + n)m  = g

(XXXI)

If the condition for money market equilibrium is to be considered, namely that the demand for real money balances is equal to the real money supply we get—while assuming (with ε standing for a positive parameter and r for the real interest rate) that real monetary demand (M/P)d = εY/(εr) or md = ε y /(εr)—a modified equation will hold for the budget constraint, provided that we also consider the condition for profit maximization, namely β



r = ßm (1 − ρ)1−β−β k ß−1 .

(XXXII)

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The modified budget constraint reads—see the subsequent expression for m — 

1 − (ß/s) − (1 − ß − ß )ρτ + (a + n)[ε /(εβ)](1−ß)/(1−ß−ß ) 

× {[s(1 − τ)]/(ρ ρ − ρ + n)}1/(1−ß−ß ) (1 − ρ) = g

(XXXI)

It is obvious here that the condition for money market equilibrium can be written as: β



β



m = ε m  (1 − ρ)1−β−β k  /(εßm (1 − ρ)1−β−β k  ß

ß−1

(XXXIII)

)

m = [ε k  /(εβ)] 

(XXXIV) 

Using the solution for k # = {s(1 − τ)[mß (1 − ρ)1 − ß−ß ]/(a + n)}1/(1−ß) we can write m

(1−ß−ß )/(1−ß)



= [ε /(εβ)]{s(1 − τ)(1 − ρ)(1−ß−ß ) /(a + n)}1/(1−ß) 

(XXXV)



m = [ε /(εβ)](1−ß)/(1−ß−ß ) {[s(1 − τ)]/(ρ ρ − ρ + n)}1/(1−ß−ß ) (1 − ρ) (XXXVI) This then is the expression which was used in the modified budget constraint. Looking at the equation for m one may conclude that a non-inflationary money supply rule must set M in the steady state according to: 



M(t) = [ε /(εβ)](1−ß)/(1−ß−ß ) {[s(1 − τ)]/(ρ ρ − ρ + n + δ)}1/(1−ß−ß ) × (1 − ρ)P0 A0 L0 e

(a+n)t

(XXXVII)

One may assume that monetary policy could adopt a once-and-for-all change in the level of the money supply—with the price level P0 rising once and for all accordingly. The real money supply relative to labor in efficiency units M/(AL) in the steady state is a positive function • • • • • • • •

of the income elasticity of the demand for money (see the parameter ε ); of the savings rate. Moreover, m is a negative function of the share of employment in the R&D sector; the interest elasticity of the demand for money (see the parameter ε); the income tax rate; the population growth rate; the capital depreciation rate.

A key implication then is that an external shock which raises the rate of capital depreciation is calling for a long-run fall of the level of (M/P)/(AL); it is obvious that the central bank could try to reduce M relative to AL so that the growth rate of M would temporarily fall short of the long-run output growth rate n + a. Alternatively, the central bank could try to reduce M/P through an inflationary monetary policy (the opportunity cost of holding money is, of course, the nominal interest rate I which is the sum of r and the inflation rate)—this, however, will go along with a negative welfare effect to the extent that M/P enters individuals’ utility function directly. Moreover, the equilibrium output relative to AL will fall as a consequence of inflation and hence there will be a fall of consumption per capita in the steady state which stands for a negative welfare effect.

S.3 Policy Conclusions

599

Savings Function with Wealth Subsequently we return to the standard production function y = kß in order to keep the analysis simple—the focus will be on the role of wealth in a modified savings function. An alternative way to incorporate monetary aspects into a modified growth model is to assume that the savings function S consists of two terms: one which is proportionate to disposable income, the other which indicates that savings is also a negative function of the wealth income ratio, where wealth consists of real monetary balances and physical capital (given a potential exogenous wealth target, a rise in (m + k )/y implies that there is lower pressure for households to save; this second term can be modified to include real estate capital Hp , where H/(AL) is defined as h and p is the relative price of real estate). The savings function used subsequently is S/(AL) = s(1 − τ)Y/(AL) − s (m + k )/y or equivalently S/(AL) = sy (1 − τ) − s (m  + k  )/y

(XXXVIII)

Note that here S/(AL) can be interpreted as a savings function that is positively related to disposable income and the average productivity of real money balances and physical capital, respectively (since average productivity and marginal productivity are proportionate to each other one may also refer to the marginal productivity of real money balances and capital, respectively and if the real interest rate r = marginal product of capital the ratio k /y is, of course, proportionate to the inverse of r). Additionally we consider money market equilibrium in the form of (with positive parameters ε , ε; zero inflation is assumed) m  = ε y /(εr)

(XXXIX)

With a simple standard production function y = kß , and assuming zero depreciation of physical capital, as well as profit maximization, r = ßk 

ß−1

(XL)

So we can write m = ε y /(εßkß−1 ) = k ε /(εß)

(XLI)

To keep the analysis tractable, the following reflections are at first based on the simple standard production function y = kß ; also note the analytical advantage that we can identify the specific role of a modified savings function with the additional term (m + k )/y . The ratio (m + k )/y can be written as s (1 + ε /(εß))k /kß = s (1 + ε /(εß))k1−ß . Hence for the case of ß = 0.5 and given growth rates a and n, we get a differential equation—on the basis S/(AL) = (dK/dt)/(AL)—which incorporates permanent money market equilibrium: dk  /dt = [s(1 − τ) − s (1 + ε /(εß))]k 0.5 − (a + n)k 

(XLII)

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Hence k  # = {[s(1 − τ) − s (1 + ε /(εß))]/(a + n)}2

(XLIII)

Compared to the standard result {s(1 − τ)/(a + n)}2 —with ß = 0.5—the capital intensity in the steady state is now smaller and the effect is stronger, the larger the income elasticity of the demand for money (see the parameter ε) and the smaller the interest elasticity of the demand for money (see the parameter ε ).

R&D Sector and the Use of Capital An interesting modification of the model setup would be to focus on an R&D sector which does not use labor as an input factor but rather relies on K so that a share ρ  is used for the R&D sector. So the production function would read Y = (M/P)ß [(1  − ρ)K]ß (AL)1−ß−ß and the progress function is here again dA/dt = ρρ A − ρA. A crucial implication is that the steady-state capital intensity k is not fully available for the production of final goods and this also will affect the golden rule. It is largely an empirical question how an adequate specification of the aggregate production function should look like.

Monetary Production Function and the Golden Capital Intensity 

Note that if an enhanced monetary production function y = mß kß were to be con sidered under the side-constraints of profit maximization (r = ßmß kß−1 ) and money  market equilibrium m = ε y /(εr) we get m = ε y /(εßmß kß−1 ) and therefore we can write 

m  = [k  ε /(εß)]1/(1+ß ) ;

(XLIV) 

And if we insert this in the enhanced production function y = mß kß , the effective production function reads 



y = [ε /(εß)]ß /(1+ß ) k 

ß+ß /(1+ß )

.

(XLV)

Thus, we get a Romer-type positive externality of capital formation, but the mechanism is quite different here—real money balances matter (!). The output elasticity of capital exceeds ß which is also the individual firm’s capital elasticity if all firms are identical. On the basis of the standard savings function S = sY(1 − τ), the accumulation   dynamics can be described by (with ε := ε /(εß)]ß /(1+ß ) and ß := ß + ß /(1 + ß )) 

dk  /dt = s(1 − τ)ε k ß − (a + n)k  .

(XLVI)

S.3 Policy Conclusions

601

Thus for the steady-state solution we get on the basis of savings equals investment (for the sake of simplicity with δ = 0) 

k  # = {[s(1 − τ)ε ]/(a + n)}1/(1+ß

)

(XLVII)

The condition for a golden state now reads ß ε k  k

gold

ß −1

= (a + n)

(XLVIII) 

= {ß ε /(a + n)}1/{1−ß

}

(IL)

This implies from setting k # = kgold s(1 − τ) = ß + ß /(1 + ß )

(L)

τ = 1 − ß /s

(LI)

Therefore we can write

In principle we cannot rule out that the optimum tax rate is negative; but under reasonable parameter conditions it will be positive. In principle this is identical to the optimum tax rate in the standard case. Compare this result to the standard setup: The optimum tax rate in the standard case defined by a setup with y = kß , S/(AL) = s(1 − τ)y and the equilibrium condition sY(AL) = (dK/dt)/(AL) = dk /dt + (n + a)k : In this case the golden rule requires that ßkß−1 = (a + n) and therefore it follows that the golden tax rate is defined by the condition ß = s(1 − τ) and hence τgold = 1 − ß/s. It is noteworthy to emphasize that the optimum tax rate is positive only if s exceeds ß which is not very realistic for OECD countries (China might, however, stand for such a state and Korea in the 1970s and 1980s as well; ß typically is assumed to be around 0.3 in OECD countries). From the condition of profit maximization r = ßkß−1 = (a + n) we get the observable condition for the golden age, namely that r = (a + n). If r exceeds (a + n), the capital intensity k exceeds the kgold and hence consumption per capita cannot be at its maximum, and if r falls short of (a + n), k is below kgold and again consumption per capita cannot be at is theoretical maximum. In an open economy with free capital flows and no political risk premia for countries I and II it is unclear whether both countries could simultaneously realize a golden capital intensity since the condition (a* + n*) = r* = r = (a + n) will be fulfilled just by concidence—even if one might assume that a = f(a*) where the foreign country is assumed to be Schumpeterian dominant country so that a* will positively affect a. However, the demographic variables n and n* might be subject to distinct influences and it indeed unclear whether in the long run we will have a + n = a* + n* unless we have a theoretical approach which basically assumes that international migration in the end will bring about a + n = a* + n*. It should be pointed out (again with δ = 0) that introducing the condition of money market equilibrium plus the condition of profit maximization has a strong impact on the golden rule result. If we would only consider a production function

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y = mß kß and a savings function S/(AL) = s(1 − τ)Y/(AL) as well as the goods market equilibrium, we would get the steady-state condition: ß

k  # = [s(1 − τ)m  /(a + n)]1/(1−ß)

(LII) 

The golden rule condition is ßmß kß−1 = a + n and hence we get kgold =[ßmß /(a + n)]1/(1−ß) and hence the standard result for the golden age, namely ß = s(1 − τ). While so far we have focused much on the long-run economic equilibrium, it is unclear how short-term economic (Keynesian) analysis and the growth model can be reconciled. It is, of course, in principle also possible to consider a modified production function with real money balances or energy as inputs and to determine the steady-state solution for k# and y#. In a broader perspective, one wonders whether—or under which circumstances—short-run economic equilibrium and long-run equilibrium is compatible. If the short-term equilibrium is unstable a long-term equilibrium might never be achieved. This question of an “overlap” of short-term equilibrium and long-run equilibrium is considered in the following subject. Harmonious Savings Rate: Short- and Long-Run Equilibrium If a short-run Keynesian approach and a long-run growth model are considered, there is one key question which is of particular analytical interest: As the short-run model implies that a rise in the savings rate s will reduce equilibrium output, while the long-run growth model implies an increase in equilibrium output, it should be asked whether there is a unique savings rate which is compatible with both the short- and long-run equilibrium. To get an answer to this question it is adequate to consider— without an R&D sector—two basically equivalent model specifications in a simple setup: • For the short term, we considerY = c[1 − τ]Y + ψM/P + δK + G as the equilibrium condition, where the consumption function is c[1 − τ]Y + ψM/P (ψ > 0). Dividing by AL we have y = c[1 − τ]y + ψm + δk + g , therefore the equilibrium real income per unit of labor in efficiency units can be determined as y =[ψm + δk + g ]/s and therefore—with given A and L—the equilibrium income is Y = A0 L0 [ψm + δk + g ]/[s(1 − τ)]. In Y-s-space this is obviously a hyperbola with the nominator A0 L0 [ψm + δk + g ]/(1 − τ). • For the growth model, we use (with ß > 0 and g := G/(AL)) a production   function y = gγ mß kß , where g can be considered to stand for infrastructure investment that has a 100% depreciation rate. The equilibrium condition for the case of zero technological progress and a given population L reads: k # = [s(1   − τ)/δ] 1/(1 − ß) and therefore y # = mß gγ (1 − ρ)1 − ß − ß [s(1 − τ)/δ] ß/(1 − ß) ;   hence Y# = A0 L0 mß gγ (1 − ρ)1 − ß − ß [s(1 − τ)/δ] ß/(1 − ß) ; in Y#-s-space, this is a graph through the origin with a positive slope. Note that long-run consumption per unit of labor in efficiency units is obviously given by C/(AL) = c(1 −     τ)gγ mß [s(1 − τ)/δ]ß/(1 − ß) ; hence consumption C = A0 L0 c(1 − τ)gγ mß [s(1

S.3 Policy Conclusions

603

− τ)/δ] ß/(1−ß) which is basically equivalent to the Keynesian perspective, where aggregate consumption—including government consumption—is a function f(τ, M/P, G. . . ). • What is the implication of the short-run Y being equal to the long-run Y#? Setting A0 L0 [ψm + δk +g ]/[s(1 − τ)] = A0 L0 [s(1 − τ)/δ] ß/(1 − ß) leads to ln [ψm + δk + g ] − lns + τ ≈ ß/(1 − ß)[lns − τ − lnδ] after taking the logarithm and therefore we can now write that lns ≈ (1 − ß)ln[ψm + δk + g ] + (1 − ß)τ + ßlnδ. Hence under certain parameter constellations there is a unique savings ratio, which is consistent with both a short-term equilibrium and a long-run growth equilibrium. An economy that is characterized by such a “harmonious savings rate” sh should face minimal medium-term adjustment dynamics—short-term equilibrium output and long-term equilibrium output do not differ which, however, does not rule out medium-term relative price adjustment dynamics if the analytical horizon is broadened to include an explicit two-sector approach. The subsequent graph shows the Short-Run Equilibrium Locus SEL and the LongRun Equilibrium Locus LEL in Y#(Y)-s-space. The intersection point of SEL and LEL is point E and the associated savings rate is dubbed to be the harmonious savings rate sh . If the economy is on the short-run equilibrium locus—with s > sh or s < sh —it is interesting to analyze the adjustment trajectory toward the point E, however, this issue will not be addressed here. It is noteworthy that an initial situation with s < sh implies that real output exceeds Y0 and an adjustment along SEL will go along with a fall of Y and a rise of s.

Fig. 119 Determining the harmonious savings rate

Y#,Y

E

LEL (Long-Run Equilibrium Locus)

Y0 SEL (Short-Run Equilibrium Locus) 0 sh

s

If people consider volatility of output to negatively affect economic welfare, policymakers might want to target a savings rate, which is partly in line with the golden rule (not far away from the respective savings rate) and partly in line with the harmonious savings rate. If by coincidence a country is in the golden state and at the same time realizes the harmonious rate, this might be dubbed as the harmonious golden state of the economy. Thus we have new analytical and empirical challenges that seem to be quite interesting to be explored further.

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As regards economic policy, it should be pointed out that we may consider the impact of a rise in government expenditures and g , respectively. Alternatively, we may want to consider a rise in m , that is expansionary monetary policy. A rise in g and m , respectively, shifts both the SEL and the LEC schedule upward, which raises an interesting issue: What is the optimum g ? This is a question that will not be addressed here.

Some Thoughts on Open Economies with FDI, Trade and Technological Progress It should be noted that the role of FDI flows—or of FDI outflows—can easily be considered. If foreigners hold a share of α* in the total capital stock of country I (home country), it is clear that national income Z is no longer identical to gross domestic product Y. Assuming, for simplicity, that country I has no FDI outflows, we can state that Z = Y(1 − α*ß) since the share of profits is ßY. This is quite important since the savings function will not read S = sY but rather S = sZ; if there are also FDI outflows Z =Y(1 − α*ß) + αß*Y*q* where q* is the real exchange rate. Thus we have an implicit two country growth model if S = sZ—that is S/(AL) = sZ/(AL)—is considered and  a foreign production function y * = m *ß ∗ k *ß . Open economy growth analysis thus is an interesting analytical challenge. The analysis becomes more complex as we have to solve a system of two differential equation, namely dk /dt and dk */dt. Thus a growth model with FDI inflows—or with both FDI outflows and FDI inflows—can be considered (WELFENS 2008a). The role of trade and FDI in the progress rate a may also be discussed, which may be assumed to be a positive function of the export-GDP ratio x and the import-GDP ratio j as well as of α* and α (α is the share of the capital stock in the foreign country II owned by investors from country I); a simple specification of the progress function (with positive parameters ϕ , ϕ , ω , ω , ζ , ζ ) could be a = ρρ − ρ + ϕ x + ϕ j + ω α* + ω α + ζ a* − ζ σ where the parameter ϕ depends on the share of intermediate technology-intensive imports; ζ indicates direct international technology spillovers, σ stands for the volatility of the political system (considered to be exogenous) so that ζ is a parameter which reflects the impact of volatility. Furthermore, vintage effects on the capital depreciation rate can easily be taken into account which imply that the capital depreciation rate is a positive function of the progress rate a as was shown by STOLERU (1978) in the case of a Cobb–Douglas function. This, of course, also suggests new extensions for golden rule analysis in open economies. Further research has to be conducted and it will be quite interesting to find out in a further analytical step whether or not capital intensity—in certain periods—has in reality exceeded the golden rule intensity. Given the fact that production and the use of capital is associated with CO2 emissions and global warming problems, respectively, exceeding the golden capital intensity is a double problem: Per capita consumption falls short of the maximum per capita consumption and the CO2 emissions are higher than is desirable. If it is assumed that CO2 emissions per unit of AL are proportionate to y , one will no

S.3 Policy Conclusions

605

longer want to maximize the difference between y and investment per unit of labor in efficiency units in the steady state. Rather, y (1 − ) minus the investment relative to AL will be considered, where  stands for the imputed marginal negative CO2 welfare effect of y . These and other refinements can be studied in more detail. At the bottom line, we have presented—within a rather simple approach—several new interesting results concerning the role of the share of R&D employment, the role of the stock of money for the level of the growth path and for the Golden Rule; the Golden Rule is modified in our semi-endogenous growth model. Moreover, two different ways to incorporate money in a growth model have been analyzed, and of course, both approaches could be combined. There is still some empirical work to be done and policymakers have to be convinced that tax policies should be governed in one crucial aspect by golden rule considerations. As regards the theoretical and empirical analysis, we should be careful to consider a production function (e.g., CES type) that allows making a distinction between the Harrod-neutral progress, the Solow-neutral progress and the Hicks-neutral progress. Considering the effect that CO2 emissions are a positive function of the capital intensity, it is all the more important that society avoids capital accumulation beyond the golden rule capital intensity. There is no principle problem within our basic model in taking CO2 emission problems into account and hence additional welfare aspects. It is time to rejuvenate the traditional growth theory in a very broad way.

T. Some Remarks on Growth Analysis on the Basis of CES

T.1 Introduction The CES function is a production function which is more general than the Cobb– Douglas function; one advantage of the CES function is that the income shares of input factors, say labor and capital, are not fixed but depend on the respective factor productivity and the parameter ρ which in principle can be negative or positive and indirectly indicates the elasticity of substitution between the two (or n) production factors considered. A disadvantage of the CES function is that is more complex to handle mathematically. One interesting question is to explicitly consider a CES function in the context of a neoclassical growth model—be it a one-country model or a two-country model. Subsequently the focus is on a CES production function in a closed economy so that real output is given by the expression Y = [c1 (AL)−ρ + c2 (K)−ρ ](−1/ρ)

(1)

where c1 and c2 are positive parameters and ρ is a paramter which indirectly stands for the elasticity of substitution σK,(AL) of capital K and labor AL (AL is labor in efficiency units where A is knowledge). One can define the elasticity σK,(AL) = −1/(1 + ρ); ρ is in the range between –1 and infinity so that the elasticity of substitution is in the range between minus infinity and zero; for the special case that ρ = 0 the substitution elasticity is minus unity which is the case of the Cobb–Douglas function.

T.2 Neoclassical Growth Model with CES: Ambiguous Role of the Savings Rate Assuming that production factors are rewarded in accordance with marginal products the substitution elasticity can be expressed here as dlnk /dln(r/w) where k := K/(AL) and r and w stand for the real interest rate and the real wage rate, respectively. We can rewrite the production function as follows: ρ

ρ

ρ

Y− = [c1 (AL)− + c2 (K)− ] P. J. J. Welfens, Innovations in Macroeconomics, DOI 10.1007/978-3-642-11909-5_20, © Springer-Verlag Berlin Heidelberg 2011

(2) 607

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The marginal product of labor in efficiency units is given by ∂Y/∂(AL) = c1 [Y/(AL)]ρ+1

(3)

∂Y/∂K = c2 [Y/K]ρ+1

(4)

Therefore the expression for the labor income share—assuming that margional product rule holds for factor rewards—is given by. [∂Y/∂(AL)]AL/Y = c1 [Y/(AL)]ρ

(5)

The share of capital income in Y is given by [∂Y/∂K]K/Y = c2 [Y/(AL)]ρ

(6)

Labor income (with w denoting the real wage rate) is equal to wAL = c1 [Y/(AL)]ρ Y

(7)

Gross capital income—including depreciations (δ denoting the capital depreciation rate)—is [r + δ]K = c2 [Y/K]ρ Y (if δ is zero we can write the condition for profit maximization as: r = c2 [Y/K]ρ+1 ). If input factors are rewarded in accordance with the marginal product rule of we can write for the factor price ratio: (r + δ)/w = (c2 /c1 )[(AL)/K]ρ+1

(8)

As is well known the ratio of gross capital income (r + δ)K to wage income w(AL) is given by (r + δ)K/[wAL] = (c2 /c1 )[K/(AL)]−

ρ

(8 )

If the ratio of K/(AL) rises the capital income-wage income ratio will fall the more the higher c2 /c1 and the larger ρ in absolute terms is (assuming here that ρ is positive). For a negative ρ—and hence σ between –1 and 0—the result is that a rising K/(AL) will raise the ratio of capital income to wage income. Using the definitions y = Y/(AL) and k = K/(AL) we can write y−ρ = c1 + c2 k −ρ

(9)

(y /k  )−ρ = c1 /k −ρ + c2

(10)

(y /k  ) = [c1 k −ρ + c2 ]−1/ρ

(11)

Consider a neoclassical growth model with a savings function S/(AL) = s(1− τ)y and an exogenous technological progress rate a and exogenous population growth n and a capital depreciation rate δ. Imposing the goods market equilibrium condition that savings per efficiency unit of labor (AL) be equal to gross investment per efficiency unit of labor, namely S/(AL) = (dK/dt)/(AL) + δk , yields the equation: dk /dt = s(1 − τ)y − (a + n + δ)k 

(12)

T.2 Neoclassical Growth Model with CES: Ambiguous Role of the Savings Rate

609

Dividing by k yields: dlnk  /dt = s(1 − τ)y /k  − (a + n + δ)

(13)

The steady state is obtained from the condition: dlnk  /dt = s(1 − τ)[c1 k −ρ + c2 ]−1/ρ − (a + n + δ) = 0

(14)

[s(1 − τ)]−ρ [c1 k −ρ + c2 ] = (a + n + δ)−ρ

(15)

[s(1 − τ)]−ρ c1 k −ρ = (a + n + δ)−ρ − [s(1 − τ)]−ρ c2

(16)

k  # = {[(a + n + δ)−ρ − [s(1 − τ)]−ρ c2 ]/[s(1 − τ)−ρ c1 ]}(1/−ρ)

(17)

Thus the steady state capital intensity is given by the equation: k  # = {(a + n + δ)−ρ /[[s(1 − τ)]−ρ c1 ] − c2 /c1 }(1/−ρ) 

+

k#=

a+n+δ s(1 − τ)

−ρ

1 c2 − c1 c1

'− 1

ρ

+ '− 1+ρ    ρ c2 1 a + n + δ −ρ ρ−1 a + n + δ −ρ 1 dk  # s − =− ds c1 1−τ s(1 − τ) c1 c1  a + n + δ −ρ 1 c2 < s(1 − τ) c1 c1 −ρ  a+n+δ < c2 s(1 − τ)   a + n + δ −ρ 1 < s−ρ 1−τ c2   a+n+δ ρ c2 > sρ 1−τ

dk  # >0 ds

(18)

(19)

(20)



if

 s<

a+n+δ 1−τ

(21)

(22)

(23)

(24)

1

ρ

c2

(25)

Thus we have a condition under which the standard result holds that a rise of the savings rate s raises the level of the growth path. The condition derived—based on the definition δ = 1− δ—and taking logs—reads (in an approximate way) as follows: lns < (1/ρ)[(a + n + δ ) + τ + lnc2 ] and since c + s + τ = 1 we can replace lns by ln(1− c − τ) ≈ −c − τ and hence –c < (1/ρ)[(a + n + δ ) + lnc2 ] + τ(1 + (1/ρ)); if ρ is in the interval 0,∞ (and hence the elasticity of substitution between –1 and 0) this

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condition is always fulfilled. However, if ρ is in the interval –1, 0 (and hence the elasticity of substitution is between –∞ and –1) it is not clear a priori that a higher savings rate will raise the level of the growth path: Here only empirical analysis can clarify the issue. For a negative parameter ρ we might get a quasi-Keynesian world since the level of the growth path is a negative function of the savings rate; one might indeed argue that the short-run elasticity of substitution is relatively low in the short run, but as soon as this elasticity reaches minus one or a higher negative value the savings rate has a positive impact on k # and hence on y # and hence on y and Y, respectively. Empirical analysis will have to clarify which range of the substitution parameter within which time frame is relevant. There is an interesting question also to economic historians, namely whether economic history does provide cases where a decline of the long run savings rate was associated with a higher level of the growth path—this case at least is not very plausible and would indirectly indicate that the elasticity of substitution between labor and capital was relatively high. In modern economies with highly specialized capital equipment and increasingly highly specialized workers (in industrialized countries) the degree of substitution between capital and labor—indeed labor in efficiency units—seems to be rather low so that a positive ρ is a plausible. Inserting k # in the implicit production function y−ρ = c1 + c2 k−ρ yields the following expression: y−ρ = c1 + c2 {(a + n + δ)−ρ /[s(1 − τ)c1 ] − c2 /c1 ]} y # = {c1 − c2 /c1 + c2 {(a + n + δ)−ρ /[s(1 − τ)c1 ]}}

(26)

(1/−ρ)

(27)

Per capita income y# in the steady state therefore is given by the equation: y#(t) = {c1 − c2 /c1 + c2 {(a + n + δ)−ρ /[s(1 − τ)c1 ]}} Y#(t) = {c1 − c2 /c1 + c2 {(a + n + δ)−ρ /[s(1 − τ)c1 ]}}

(1/−ρ)

(1/−ρ)

A0 e 

A0 L 0 e 

at

(28)

(a+n)t

(29)

The impact of the parameters c1 and c2 on y # (and hence on y# andY#) is ambiguous. Let us consider the special case that c1 − c2 /c1 = 1 and hence c2 = (1 − c1 )c1 (it also is assumed that 0 < c1 < 1) so that we have: y # = {1 + (1 − c1 ){(a + n + δ)−ρ /[s(1 − τ)]}}(1/−ρ)

(30)

Assuming that (1 − c1 ){(a + n + δ)−ρ /[s(1 − τ)]} is relatively small we can use the approximation that ln(1 + x) ≈ x. Hence lny # ≈ (1/−ρ)(1 − c1 ){(a + n + δ)−ρ /[s(1 − τ)]

(31)

Thus it is obvious that a rise of a, n or δ will raise the level of growth path of y in the steady state provided that ρ is positive. If production abroad also is characterized by a CES function—namely ∗ ∗ ∗ Y∗ = [c∗1 (A∗ L∗ )−ρ + c∗ 2 (K∗ )−ρ ](−1/ρ ) –and if savings S = s∗ (1 − t)Y∗ , the rate of

T.3 Two-country Macro Model with CES Functions

611

capital depreciation is δ∗ and if the growth rate of L∗ and A∗ is n∗ and a∗ , respectively foreign GDP in the steady state thus is given by (∗ denoting foreign variables) ∗)

y∗ # = {c∗1 − c∗ 2 /c∗ 1 + c∗ 2 {(a∗ + n∗ + δ∗ )−ρ∗ /[s∗ (1 − τ∗ )c∗1 ]}}(1/−ρ

(31 )

For the special case that c∗ 1 − c∗ 2 /c∗ 1 = 1 we can write lny∗ # ≈ (1/−ρ∗ )(1 − ∗ c∗ 1 ){(a∗ + n∗ + δ∗ )−ρ /[s∗ (1 − τ∗ )] and hence for the international relative income position: ∗

lny #/lny # ≈ (1/−ρ)(1 − c1 ){(a + n + δ)−ρ /[s(1 − τ)]/ −ρ∗

{(1/−ρ∗ )(1 − c∗ 1 ){(a∗ + n∗ + δ∗ )

/[s∗ (1 − τ∗ )]}

(31 )

Defining δ =1− δ we can write (while assuming y # > 1 and y∗ # > 1): ln[lny #/lny∗ #] ≈ ρ − c1 − ρ(a + n − δ ) − lns + τ − ρ∗ + c∗ 1 ∗

+ ρ∗ (a∗ + n∗ − δ ) + lns∗ − τ∗

(32)

∗

ln[lny #/lny #] ≈ −c1 − ρ(a + n − δ) − lns + τ + c∗ 1 + ρ∗ (a∗ + n∗ − δ∗ ) + lns∗ − τ∗

(32 )

It is important to note that the role of the capital depreciation rate is different when compared to a growth model with a Cobb-Douglas production function. Moreover, it also is obvious that the sign of the parameter ρ plays a crucial role for both the impact of a, n and δ as well as of a∗ , n∗ and δ∗ .

T.3 Two-country Macro Model with CES Functions Let us consider a two-country model with production functions Y = [c1 (AL)−ρ + c2 (K)−ρ ](−1/ρ) and for country II: Y∗ = [c∗ 1 (A∗ L∗ )−

ρ∗

ρ∗

+ c∗ 2 (K∗ )− ](−1/ρ∗

)

(2 )

Denoting the share of capital in country I owned by foreign investors as α∗ the real GNP (Z) can be written in the case of asymmetric foreign direct investment inflows (only II is a source country of FDI) as Y{1 − α∗ c2 [Y/K]ρ } = Z

(33)

The foreign national income Z∗ =Y∗ + α∗ c2Y[Y/K)]ρ /q∗ . Subsequently we want to focus on a small open economy under flexible exchange rates, namely an economy which has cumulated foreign direct investment inflows. Assuming that consumption C = c(1− τ)Z, real exports X = xq∗ Z∗ and J = jZ/q∗ the goods market equilibrium

612

Innovations in Macroeconomics

conditionY = C(. . .) + {b(∂Y/∂K − r) + b (∂Y/∂K − ∂Y∗ /∂K∗ ) + b q∗ } + G + X − q∗ J can be written as: Y = c(1 − τ)Y{1 − α∗ c2 [Y/K]ρ } + b[c2 (Y/K)ρ+1 − r] ∗

+ b (c2 (Y/K)ρ+1 − c∗ 2 (Y∗ /K ∗ )ρ

+1

) + b q∗ + G

+ xq∗ {Y∗ + α∗ Yc2 [Y/K]ρ /q∗ } − jY{1 − α∗ c2 [Y/K]ρ }

(34)

Assuming no capital depreciations here the three terms b[. . .] + b (. . .) + b q∗ stand for short-term investment; hence investment is a positive function of the difference between the marginal product of capital and the real interest rate and a function of the difference between the home marginal product of capital and the foreign marginal product of capital. The term b q∗ reflects the argument of FROOT/STEIN (1991) according to which FDI inflows in a world of imperfect capital markets should be a positive function of the real interest rate; however, one may note that in a two-country world with symmetric FDI flows—both countries are source countries of FDI—one might argue that FDI inflows are proportionate to relative GNPs (assuming the relative size of income partly determines the attractiveness of producing abroad) or the difference Z − Z∗ and hence—with b denoting a positive parameter—FDI inflows = ß [Z − q∗ Z∗ ] = ß [Y(1 − α∗ ß) + αß∗Y∗ q∗ − q∗Y∗ (1 − αß∗ ) − α∗ ßY]; here we are considering the simple case of a Cobb–Douglas function in both countries (in ∗ the home country Y = Kß (AL)1−ß and abroad Y∗ = K∗ß (A∗ L∗ )1 − ß∗ ) and as we can see an empirical finding of a positive impact of q∗ on FDIinflows simply might reflect the fact that a real devalutation raises the relative size of the home country’s GNP. Money market equilibrium is written here—assuming zero (expected) inflation—as: M/P = hY/(h r)

(35)

Foreign exchange market equilibrium—in a system of flexible exchange rates—is given by the condition that net capital imports (with portfolio capital inflows assumed to be v [r − r∗ ] where v is a positive parameter) are equal to the net imports of goods and services: ∗ +1

v (r − r ∗ ) + b [c2 (Y/K)ρ+1 − c∗ 2 (Y∗ /K ∗ )ρ

] + b q

∗

= j Y{1 − α∗ c2 [Y/K]ρ } − xq∗ {Y∗ + α∗ c2 [Y/K]ρ /q∗ }

(36)

Note that it has been assumed that international profits transferred in this model— with unemployment assumed to exist in both countries—are zero; if there were profits in both countries (or in one of the two countries) one would have to modifiy the right-hand side accordingly. Differentiating the equilibrium conditions for the goods market, the money market and the foreign exchange market we get: ⎛ ⎞⎛ ⎞ ⎛ ⎞ k1 b −b − xY∗ dY 1 0 k4 k3 k2 ⎝ h/(h∗ r) −hY/(h r2 ) ⎠ ⎝ dr ⎠ = ⎝ 0 1 0 0 0 ⎠ 0 0 0 −k4 k6 −k2 dq∗ v b + xY∗ k5 (37)

T.3 Two-country Macro Model with CES Functions

613

k1 = 1 − c(1 − τ){1 − α*c2 [Y/K]ρ } + α∗ c2 ρ[Y/K]ρ−1 c(1 − τ)Y{1 − α*c2 [Y/K]ρ }/K − (b + b )c2 (ρ + 1)(Y/K)ρ /K − xα∗ c2 (ρ + 1)[Y/K]ρ + jYα*c2 ρ[Y/K]ρ−1 /K

(38) ∗

K2 = b c∗2 (ρ∗ + 1)(Y∗ /K ∗ )ρ /K ∗ > 0

(39)

k3 = c(1 − τ)α*c2 ρ(Y/K)ρ+1 − (b + b )c2 (ρ + 1)(Y/K)ρ+1 /K − xα∗ c2 ρ(Y/K) − jα*c2 ρ(Y/K)ρ+1

(40)

k4 = xq∗ − (Y∗ /K∗ )k2

(41)

k5 = b c2 (ρ + 1)(Y/K)ρ /K − j(1 − α*c2 (ρ + 1)(Y/K)ρ ) + xα*c2 ρ(Y/K)ρ−1 /K

(42)

k6 = b c2 (ρ + 1)(Y/K)ρ+1 /K + jα*c2 ρ(Y/K)ρ+1 + xα*c2 ρ(Y/K)ρ+1 > 0 (43)

Assumptions: k1 > 0, k3 > 0, k4 < 0, k5 < 0 ⎛ k1 b U = det ⎝ h/(h*r) −hY/(h r 2 ) k5 v

⎞ −b − xY∗ ⎠ 0 b + xY∗

∗

= −(b + xY )(hv /(h*r) − k5 hY/(h r2 )) ∗

−(b + xY )(hYk1 /(h r2 ) + hb/(h*r))

(44)

dY hY(b + xY∗ ) >0 =− dG Uh r2

(45)

(b + xY∗ )(b + v ) dy =− >0 d(M/P) U

(46)

dY =0 dY∗

(47)

hY(b + xY∗ )(k3 + k6 ) dY >0 =− dk Uh r2

(48)

dY =0 dK ∗

(49)

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Innovations in Macroeconomics

dr h(b + xY∗ ) =− dG Uh*r

(50)

(b + xY∗ )(k1 + k5 ) dr =− d (M/P) U

(51)

dr =0 dY∗

(52)

dr h(b + xY∗ )(k3 + k6 ) =− >0 dK Uh*r

(53)

dr =0 dK ∗

(54)

hv /(h*r) + k5 hY/(h r2 ) dq∗ = dG U

(55)

dq∗ k1 v  − k5 b =− >0 (56) d(M/P) U      /(h*r) + hYk /(h r 2 )  r 2 ) + hb/(h*r) ∗ hv hYk /(h k k 2 5 2 1 dq = + (57) dY∗ U U     k3 hv /(h*r) + hYk5 /(h r 2 ) k6 hYk1 /(h r2 ) + hb/(h*r) dq∗ = − (58) dK U U      /(h*r) + hYk /(h r 2 )  r 2 ) + hb/(h*r) ∗ hv hYk /(h k k 4 5 4 1 dq = + (59) ∗ dK U U Assumption: U < 0 The various multipliers show that the supply side determines policy multipliers even in a short-term quasi-Keynesian open-economy model. The model with symmetric FDI inflows is a bit more complex, the model for an explicit two-country model is much more complex and only empirical analysis can clarify some of the issues raised by the multiplier analysis. It should, however, be noted that almost all traditional macro models ignore the impact of FDI. This is not adequate in a world of economic globalization.

T.4 Conclusions There is urgent need to generally put more focus on macro models with FDIs. As has been shown it is also important to consider the role of technical parameters of production function—even in the model based on aggregate demand. Finally, it should be pointed out that a modified concept of the production function could even consider immaterial input factors such as confidence (e.g., in financial markets and banks) and patents/copyrights.

Appendix T.2: The Role of Domestic and Foreign Sovereign Debt

615

Appendix T.1: Further Considerations on CES Let us consider the implicit production function and the special case that c1 = 1 and hence: y−ρ = 1 + c2 k −ρ

(60)

Moreover, let us also assume that c2 is very small so that we can use the approximation ln(1 + x) ≈ x. Hence taking logs gives: lny ≈ (−c2 /ρ)k −ρ

(61)

y ≈ exp(−c2 /ρ)k −ρ

(61 )

Hence:

It is particularly interesting to consider the special cases of ρ = −1, ρ = 0 and ρ = ∞ and to draw the respective graphs of the production function y = f(k ). dk  /dt = s(1 − τ) exp (−c2 /ρ)k −ρ − (a + n + δ)k 

(62)

Setting dk /dt = 0 we get s(1 − τ) exp (−c2 /ρ)k −ρ = (a + n + δ)k 

(63)

(−c2 /ρ)k 

−ρ

≈ ln(a + n ++ δ) + lnk  − lns + τ

(64)

(−c2 /ρ)k 

−ρ

≈ ln(a + n ++ δ) + lnk  − lns + τ

(65)

Appendix T.2: The Role of Domestic and Foreign Sovereign Debt in a Simple Medium-term Macro Model with Flexible Exchange Rates Consider the goods market equilibrium where consumption depends on disposable income which is defined as Y plus interest payments obtained on domestic bonds (rB) plus the interest payments obtained on foreign bonds (r*B*; by assumption foreign debt B* is denominated in the same currency as the stock of domestic government bonds B which are indexed bonds). Gross investment is given by [δK−br] where b is positive parameter and δ is the capital depreciation rate; ϕ is the share of foreign bonds which is owned by domestic residents (residents of the home country I). G is real government consumption; in the uses side GDP is equal to the sum C + Igross + G + X − q*J; here we assume that real exports X = xY*q* and real

616

Innovations in Macroeconomics

imports J = jY/q* where q* is the real interest rate and x and j stand for positive parameters. Hence the equilibrium condition in the goods market is given by: Y = c(Y + rB + ϕr ∗ B∗ )(1 − τ) + [δK − br] + G + xY∗ q∗ − jY

(I)

The money market equilibrium condition is given by (in a setup with stability of the price level): M/P = hY/(h r)

hence

r = hY/(h M/P)

(II)

Equilibrium in the foreign exchange market is given by the condition that the ratio of net capital imports to capital exports—this can be expressed as v r/r* where v is a positive parameter—must be equal to the ratio of goods imported to goods exported. v r/r ∗ = jY/(xY∗ q∗ );

r = r ∗ [jY/(xY∗ q∗ v )];

∗

r = r∗ jY/(xY∗ v q );

q∗ = r ∗ jY/(xY∗ v r)

(III)

While we already have obtained r from the money market equilibrium here we can obtain the real exchange rate q* := eP*/P from the equilibrium condition for the foreign exchange market. Thus we can substitute r and q* in the goods market equilibrium condition so that we obtain an explicit solution for the short-run macroeconomic equilibrium: Y(1 − c(1 − τ)) = c(1 − τ)[hY/(h M/P)] B + cϕr ∗ B∗ (1 − τ) + δK ∗

− bhY/(h M/P) + G − jY + xY∗ r∗ jY/(xY∗ v r [jY/(xY∗ q∗ v )]) 

(IV)



Y = [(1 − c(1 − τ)(1 + hB/(h M/P)) + bh/(h M/P) + j)] = cϕr ∗ B∗ (1 − τ) + δK + G + xY∗

Y = cϕr ∗ B∗ (1 − τ) + δK + G + xY∗ /       

1 − c(1 − τ) 1 + hB/ h M/P + bh/ h M/P + j

(V)

(VI)

The equilibrium real GDP will fall if B*, r*, K, G or Y* fall; it also falls if M/P is reduced or if the income tax rate τ is raised and if the stock of domestic debt relative to real money balances M/P is falling. In a symmetric setup with two countries we can write for country II: ∗

Y∗ = [c∗ ϕ∗ (1 − ϕ∗ )r∗ B∗ (1 − τ∗ ) + δ∗ K + G∗ + jY/q∗ ]/ [(1 − c∗ (1 − τ∗ )(1 + h∗ B∗ /(h∗ M∗ /P∗ ) + b∗ h∗ /(h *M*/P*) + x)] ∗

:= [c∗ ϕ∗ (1 − ϕ∗ )r ∗ B∗ (1 − τ∗ ) + δ∗ K + G∗ + jY/q∗ ]/z

(VII)

Y = {cϕr∗ B∗ (1 − τ) + δK + G + x[c∗ ϕ∗ (1 − ϕ∗ )r∗ B∗ (1 − τ∗ ) + δ∗ K∗ + G∗ + jY/q∗ ]/z}/[(1 − c(1 − τ)(1 + hB/(h M/P)) + bh/(h M/P) + j)]

(VIII)

Appendix T.2: The Role of Domestic and Foreign Sovereign Debt

617

Hence Y = {cϕr ∗ B∗ (1 − τ) + δK + G + x[c∗ ϕ∗ (1 − ϕ∗ )r ∗ B∗ (1 − τ∗ ) + δ∗ K∗ + G∗ + jY/q∗ ]/z}/[1 − c(1 − τ)(1 + hB/(h M/P) + bh/(h M/P) + j)]

(IX)

Y(1 − xj/{q∗ z[(1 − c(1 − τ)(1 + hB/(h M/P) + bh/(h M/P) + j)]}) = {cϕr ∗ B∗ (1 − τ) + δK + G + x[c∗ ϕ∗ (1 − ϕ∗ )r ∗ B∗ (1 − τ∗ ) ∗

+ δ∗ K + G∗ ]/z}/[(1 − c(1 − τ)(1 + hB/(h M/P) + bh/(h M/P) + j)] (X) Y = {cϕr ∗ B∗ (1 − τ) + δK + G + x[c∗ ϕ∗ (1 − ϕ∗ )r ∗ B∗ (1 − τ∗ ) + δ∗ K∗ + G∗ ]/z}/{[(1 − c(1 − τ)(1 + hB/(h M/P) + bh/(h M/P) + j)] (1 − xj/{q∗ z[(1 − c(1 − τ)(1 + hB/(h M/P) + bh/(h M/P) + j)]})}

(XI)

If we additionally consider FDI and thus consider the distinction between GDP and gross national product (with country I being a host country of FDI; no FDI inflows into country II) the basic specification—assuming that investment is given by b(∂Y/∂K − r) + b (∂Y/∂K − ∂Y∗ /∂K ∗ )—reads: Y = c(1 − τ)Y{1 − α∗ c2 [Y/K)]ρ } + b[c2 (Y/K)ρ+1 − r] ∗ +1

+ b (c2 (Y/K)ρ+1 − c∗ 2 (Y∗ /K ∗ )ρ

) + b q

∗

+ G + xq∗ {Y∗ + α∗Yc2 [Y/K)]ρ /q∗ } − j Y{1 − α∗ c2 [Y/K)]ρ }

(XII)

For the sake of simplicity the rate of capital depreciation is set equal to zero. Subsequently capital inflows will be assumed to depend both on the difference of the domestic interest rate to the foreign interest rate and on the term b (∂Y/∂K − ∂Y∗ /∂K∗ ) where b is a positive parameter. Hence the money-market equilibrium condition and the foreign exchange market equilibrium condition read: M/P = hY/(h r)

(XIII) ∗ +1

v (r − r∗ ) + b [c2 (Y/K)ρ+1 − c∗2 (Y∗ /K ∗ )ρ

] + b q

∗

= j Y{1 − α∗ c2 [Y/K)]ρ } − xq∗ {Y∗ + α∗Yc2 [Y/K)]ρ /q∗ }

(XIV)

Based on this setup a medium-term macro model of a small open economy with CES function can be considered. Even in a medium-term macro model—with aggregate demand determining real GDP—supply-side parameters will play a crucial role for the determination of multipliers and medium-term equilibria, respectively.

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