International Labor Mobility: Unemployment and Increasing Returns to Scale (Routledge Studies in the Modern World Economy)

International Labor Mobility Migration of workers within and across national boundaries is an important issue in an ag...

Author: Bharati Basu

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International Labor Mobility

Migration of workers within and across national boundaries is an important issue in an age of increasing levels of innovation and invention which economizes cost and helps large-scale production. This book analyzes the implications of migration for the levels of unemployment and distinguishes between unemployment which can be attributed to government policy and that which can be generated by a particular behavior of employers and workers. The discussion also includes the issue of foreign workers’ effects on unemployment levels – a salient issue in today’s climate. With impressive clarity and a scholarly approach, Bharati Basu succeeds in explaining and analyzing an important yet complicated topic. This book will be of use to students, academics and professionals interested in labor economics, industrial studies and international economics. Bharati Basu is Professor of Economics at Central Michigan University, USA.

Routledge studies in the modern world economy

1 Interest Rates and Budget Deﬁcits A study of the advanced economies Kanhaya L. Gupta and Bakhtiar Moazzami 2 World Trade after the Uruguay Round Prospects and policy options for the twenty-ﬁrst century Edited by Harald Sander and András Inotai 3 The Flow Analysis of Labour Markets Edited by Ronald Schettkat 4 Inﬂation and Unemployment Contributions to a new macroeconomic approach Edited by Alvaro Cencini and Mauro Baranzini 5 Macroeconomic Dimensions of Public Finance Essays in honour of Vito Tanzi Edited by Mario I. Blejer and Teresa M. Ter-Minassian 6 Fiscal Policy and Economic Reforms Essays in honour of Vito Tanzi Edited by Mario I. Blejer and Teresa M. Ter-Minassian 7 Competition Policy in the Global Economy Modalities for co-operation Edited by Leonard Waverman, William S. Comanor and Akira Goto 8 Working in the Macro Economy A study of the US labor market Martin F.J. Prachowny 9 How Does Privatization Work? Edited by Anthony Bennett 10 The Economics and Politics of International Trade Freedom and trade: volume II Edited by Gary Cook 11 The Legal and Moral Aspects of International Trade Freedom and trade: volume III Edited by Asif Qureshi, Hillel Steiner and Geraint Parry

12 Capital Markets and Corporate Governance in Japan, Germany and the United States Organizational response to market inefﬁciencies Helmut M. Dietl 13 Competition and Trade Policies Coherence or conﬂict Edited by Einar Hope 14 Rice The primary commodity A.J.H. Latham 15 Trade, Theory and Econometrics Essays in honour of John S. Chipman Edited by James C. Moore, Raymond Riezman and James R. Melvin 16 Who Beneﬁts from Privatisation? Edited by Moazzem Hossain and Justin Malbon 17 Towards a Fair Global Labour Market Avoiding the new slave trade Ozay Mehmet, Errol Mendes and Robert Sinding 18 Models of Futures Markets Edited by Barry Goss 19 Venture Capital Investment An agency analysis of UK practice Gavin C. Reid 20 Macroeconomic Forecasting A sociological appraisal Robert Evans 21 Multimedia and Regional Economic Restructuring Edited by Hans-Joachim Braczyk, Gerhard Fuchs and Hans-Georg Wolf 22 The New Industrial Geography Regions, regulation and institutions Edited by Trevor J. Barnes and Meric S. Gertler 23 The Employment Impact of Innovation Evidence and policy Edited by Marco Vivarelli and Mario Pianta 24 International Health Care Reform A legal, economic and political analysis Colleen Flood 25 Competition Policy Analysis Edited by Einar Hope 26 Culture and Enterprise The development, representation and morality of business Don Lavoie and Emily Chamlee-Wright

27 Global Financial Crises and Reforms Cases and caveats B.N. Ghosh 28 Geography of Production and Economic Integration Miroslav N. Jovanovi´c 29 Technology, Trade and Growth in OECD Countries Does specialisation matter? Valentina Meliciani 30 Post-Industrial Labour Markets Proﬁles of North America and Scandinavia Edited by Thomas P. Boje and Bengt Furaker 31 Capital Flows Without Crisis Reconciling capital mobility and economic stability Edited by Dipak Dasgupta, Marc Uzan and Dominic Wilson 32 International Trade and National Welfare Murray C. Kemp 33 Global Trading Systems at Crossroads A post-Seattle perspective Dilip K. Das 34 The Economics and Management of Technological Diversiﬁcation Edited by John Cantwell, Alfonso Gambardella and Ove Granstrand 35 Before and Beyond EMU Historical lessons and future prospects Edited by Patrick Crowley 36 Fiscal Decentralization Ehtisham Ahmad and Vito Tanzi 37 Regionalisation of Globalised Innovation Locations for advanced industrial development and disparities in participation Edited by Ulrich Hilpert 38 Gold and the Modern World Economy Edited by MoonJoong Tcha 39 Global Economic Institutions Willem Molle 40 Global Governance and Financial Crises Edited by Meghnad Desai and Yahia Said 41 Linking Local and Global Economies The ties that bind Edited by Carlo Pietrobelli and Arni Sverrisson 42 Tax Systems and Tax Reforms in Europe Edited by Luigi Bernardi and Paola Profeta

43 Trade Liberalization and APEC Edited by Jiro Okamoto 44 Fiscal Deﬁcit in the Paciﬁc Region Edited by Akira Kohsaka 45 Financial Globalization and the Emerging Market Economies Dilip K. Das 46 International Labor Mobility Unemployment and increasing returns to scale Bharati Basu

International Labor Mobility Unemployment and increasing returns to scale

Bharati Basu

First published 2004 by Routledge 11 New Fetter Lane, London EC4P 4EE Simultaneously published in the USA and Canada by Routledge 29 West 35th Street, New York, NY 10001 Routledge is an imprint of the Taylor & Francis Group This edition published in the Taylor & Francis e-Library, 2005. “To purchase your own copy of this or any of Taylor & Francis or Routledge’s collection of thousands of eBooks please go to www.eBookstore.tandf.co.uk.” © 2004 Bharati Basu All rights reserved. No part of this book may be reprinted or reproduced or utilized in any form or by any electronic, mechanical, or other means, now known or hereafter invented, including photocopying and recording, or in any information storage or retrieval system, without permission in writing from the publishers. British Library Cataloguing in Publication Data A catalogue record for this book is available from the British Library Library of Congress Cataloging in Publication Data A catalog record for this book has been requested ISBN 0-203-48847-4 Master e-book ISBN

ISBN 0-203-57232-7 (Adobe eReader Format) ISBN 0–415–29825–3 (Print Edition)

To my mother, Karuna, and my father, Ahi Bhuson

Contents

List of ﬁgures List of tables Foreword Preface

xii xiv xv xviii

1

International labor mobility with full employment

2

International labor mobility with exogenously created unemployment

3

International labor mobility with endogenously created unemployment

36

Free trade versus free-labor mobility with increasing returns and unemployment

54

Labor mobility and a dual economy: a case of external economies of scale and unemployment

71

6

Labor migration in European Union countries

84

7

An empirical overview

102

Appendices Notes Bibliography Index

119 163 172 178

4

5

1 21

Figures

1.1 1.2 1.3 1.4 1.5 1.6 2.1 2.2 3.1 4.1 4.2 4.3 4.4 4.5 5.1 5.2 5.3 6.1 A1 A2 A3 A4 A5 A6

Zero effect of migration with one good Zero effect of migration with two goods Loss from migration in a two goods-two factors model Gains from migration in a two goods-two factors model Effects of migration in comparison with effects of trade in goods Effects of migration with non-traded goods Production possibility frontiers for minimum wage Country(I) and non-minimum wage Country(II) Trade offer curves of Country I and Country II Effects of migration efﬁciency wages Equilibrium for type I labor market Efﬁciency wage and effects of migration in comparison with effects of trade in goods Labor market equilibrium with efﬁciency wage and external economies of scale Trade in goods under external economies of scale and efﬁciency wages Migration under external economies of scale and efﬁciency wages Urban labor market equilibrium Labor allocation in a dual economy with minimum wage distortion Labor allocation in a dual economy with efﬁciency wages and external economies of scale Equilibrium with internal economies of scale Factor intensity effect and scale effect for sector 2 Value of marginal product curves of two sectors Effects of a price increase in sector 2 Multiple equilibrium points with increasing returns to scale in one of the sectors Value of marginal product curves with multiple equilibria Effects of a price change on factor prices

7 8 10 11 12 15 25 26 47 60 62 67 67 69 75 77 78 98 122 122 123 124 124 125

Figures xiii A7 Equilibrium with internal economies of scale and declining elasticity of demand for goods A8 Equilibrium with internal economies of scale and constant elasticity of demand for goods B1 Labor supply curve with efﬁciency wages B2 Labor market equilibrium with efﬁciency wages

128 129 139 140

Tables

1.1 Migrant stock by region, and as a proportion of a region’s total population 1.2 Countries with the highest net immigration rates 1.3 Foreign or foreign born population in selected OECD countries 1.4 Unemployment in OECD countries as percentage of labor force 1.5 Employment of foreigners and nationals by industry division 1.6 Workers’ remittances in selected emigration countries 2.1 Nature of specialization in production for different trade equilibria between zones 6.1 Immigration in three EU countries 6.2 Age distribution in some EU countries 6.3 Inﬂow structure by skill level 6.4 Employment and unemployment rate for skilled workers in the European Union 7.1 Effect of unemployment on unionization 7.2 Effect of training on unemployment 7.3 Calibrated values of F 7.4 Calibrated unemployment with no-trade A1 Economies of scale

3 4 4 5 6 7 28 85 86 88 89 105 105 113 116 119

Foreword

Traditionally the theory of international trade is dominated by issues of international movements of goods. International movements of factors of production, such as international labor migration and foreign direct investment, usually receive much less coverage. For example, most theorems in the theory are about international trade in goods, and most textbooks on international trade pay more attention to international movements of goods than to movements of factors. It is often argued that such asymmetric attention to trade in goods is attributed to two things. First, volumes of trade in goods are much larger than those of factor movements in the world markets. After all, there are more restrictions on international movements of factors than on movements of goods, including those due to economic, social, legal, historical and political factors. It is thus natural to ﬁnd that there are more issues about international trade in goods, and also that they draw more attention and receive more analysis from trade economists. Second, in the classical and neoclassical frameworks characterized by constant returns to scale, perfect competition, perfect price ﬂexibility and perfect information (the CPPP assumption), factors of production can be regarded as negative outputs, at least in a mathematical sense. Therefore many theorems and results about trade in goods established in these frameworks can be extended to factor movements, with factors appropriately interpreted. These two justiﬁcations, however, are less convincing now. The past several decades have witnessed a tremendous rise in movements of factors of production across national borders. This is especially true for international movements of capital. With the rapid drop in the costs of information and the costs of sending investment resources abroad, investors and big corporations are more eager now to move their production activities to places where they can ﬁnd cheaper or even better production facilities. As governments were encouraged by the successes in recent rounds of trade talks in removing economic barriers on international ﬂows of commodities, they are working along the same line on international capital ﬂow. For example, recent free trade agreements such as the North America Free Trade Agreement permit liberalization not just in movements

xvi

Foreword

of goods but also in capital ﬂow. Members of the World Trade Organization (WTO) a few years ago signed agreements to liberalize traderelated investment measures (TRIMs). In order to get accession into the WTO in 2001, China agreed to lower its barriers not only on the inﬂow of many types of foreign goods but also on foreign investment in many of its domestic industries. The rise in international labor migration in the past decades was less dramatic, mainly because governments are still reluctant to remove their controls over migration, especially inﬂow of foreign residents. However, that does not mean that international labor migration is not important. The very fact that international labor migration involves the inﬂow or outﬂow of people means that it has many distinct features that need special attention and analysis; for example, illegal migration, border control, guest worker programs and so on. Furthermore, international labor migration is closely related to many domestic issues that are on the agenda of every government; for example, unemployment, education, crime and so on. As international factor movements are rising in volume and importance, one may wonder whether, as some have argued, factors can be regarded as negative outputs and theorems on international trade in goods can be extended to international labor migration. The answer in many cases is in the afﬁrmative as long as one stays in the classical or neoclassical framework. However, anyone who is familiar with the theory of international trade knows well that in the past several decades many developments in the theory involve models characterized by increasing returns, imperfect price ﬂexibility, imperfect information and/or imperfect competition. The analysis developed by many economists so far shows that the symmetry between international trade in goods and international factor movement breaks down in many areas once the CPPP assumption is no longer valid. International Labor Mobility is a delight to those who are interested in international labor migration in the presence of unemployment or increasing returns. It demonstrates appropriately and convincingly why new analysis and analytical tools are needed to address many of the issues when the CPPP assumption is not applicable. Developing models that are very different from the classical and neoclassical frameworks, many of the results derived in the following chapters are not what one would expect in the traditional theory based on the classical and neoclassical frameworks. As Basu argues in the Preface, one needs to incorporate unemployment to bring international labor migration closer to the real world. The distinction is made between exogenously created unemployment such as that due to minimum wage legislations, and endogenously created unemployment caused by efﬁciency wage distortion. Basu raises and investigates many interesting issues in this book. The main part of this book begins with an analysis of international

Foreword xvii labor migration with exogenously created unemployment (Chapter 2). It focuses on the case in which unemployment is created by an exogenously given minimum wage, before moving on to the cases of labor migration for economies that are characterized by efﬁciency wage distortions. Three chapters consider models: those with constant returns (Chapter 3), those with internal increasing returns (Chapter 4) and those with external increasing returns (Chapter 5). Some real world cases are also examined. Chapter 6 analyzes labor migration in European Union countries, which allow very little restriction on the movement of workers within the union. This is a very interesting case for those who want to investigate the empirical implications of labor migration across countries with different economic conditions, cultures and systems. Chapter 7 provides an empirical overview. International Labor Mobility shows clearly why, in many cases, one would want to go beyond the neoclassical framework when addressing issues related to international labor migration. Efﬁciency wages and increasing returns have been used extensively, and many new results are derived. This book also provides welfare analysis and derives many policy implications. Although Basu mentions that she uses a trade theoretic approach in analyzing international labor migration, and although many tools and techniques in the theory of international trade are used extensively, this book does in fact cover many issues related to labor migration. It is my opinion that this book will be a valuable reference not only to international trade economists but also to economists in other ﬁelds and policymakers who are interested in knowing more about the causes and effects of international labor migration and those who plan to do more research in this important ﬁeld. Professor Kar-yiu Wong Department of Economics and Director: Research Center for International Economics University of Washington Seattle, USA

Preface

Any analysis of labor migration should pay attention to existing labor market conditions. When economists started looking into international migration as trade in factors, the focal point of their analyses was to ﬁnd out how migration affects the host and the source country in a world of full employment with perfectly competitive markets. The objective was to ﬁnd an optimum migration policy. This search for a migration policy passed through the stages where we moved from labor migration in a model with one good and one factor to a model with multiple goods and multiple factors. Efforts were also made to ﬁnd out whether free labor migration, i.e. free trade in factors, can be a substitute for free trade in goods. Sideby-side, a separate set of analyses was going on empirically to delineate the causes of migration and to examine the volume of migration empirically by different demographic and location factors. In this book I am not going to focus on that type of empirical analysis. Migration in this book is analyzed from a trade theoretic point of view. The models of international migration that used the trade theoretic approach gradually had to incorporate unemployment to bring them closer to the real world. The focus was still on the search for an optimum migration policy and/or on the debate on whether the outﬂow of labor or inﬂow of capital should be the relevant question in the presence of unemployment. It should be noted though that these analyses of migration in the presence of unemployment mainly dealt with unemployment created exogenously by instruments like minimum wage legislation, union contract, etc. But involuntary unemployment can also be the outcome of the functioning of the labor market itself; for example it can be endogenously determined by an efﬁciency wage, or by a special behavior like job search. According to the efﬁciency wage hypothesis employers, in the presence of shirking and imperfect monitoring, offer a higher than market clearing wage and use this as a discipline device. The analysis of international migration has yet to take this type of endogenous distortion into consideration. Furthermore, most of the analyses of international migration assume a linearly homogenous production technology. Again, in reality, especially

Preface xix with the emerging industrialized countries, a non-constant returns to scale becomes a standard characteristic of production. The focus of this book is to analyze international migration in the presence of unemployment and economies of scale. I have presented the scenarios under both exogenously created and endogenously created unemployment. In the case of exogenous distortion I have used unemployment created by minimum wage legislations. The endogenous unemployment is created by efﬁciencywage distortion. In incorporating economies of scale I have used both external and internal economies of scale in describing the production technology throughout the book. To make readers familiar with the literature, I have presented an overview of the analyses on economies of scale and international trade in Appendix A. Appendix B introduces readers to the analysis of efﬁciency wage-generated unemployment. The motivation behind writing this book lies in the effort of ﬁlling some of the gaps in the literature analyzing international migration from the trade theory point of view. In this book, migration across national boundaries is treated as a ﬂow of a factor of production between countries and I use a trade theoretic approach in analyzing this ﬂow. To provide the readers with a coherent understanding of the issue of international labor migration from that point of view, I focus on migration with full employment in Chapter 1. I analyze international migration in the presence of exogenously created unemployment in Chapter 2. In Chapter 3, I introduce endogenously created unemployment and look into international migration policies in that framework. Chapter 4 incorporates increasing returns to scale to the analysis involving endogenously created unemployment. In doing so it includes both internal economies of scale and external economies of scale. It also examines whether, under the circumstances, free trade in goods will be a substitute for free trade in factors. In Chapter 5, I follow through analyzing migration for a developing dual economy with a labor market distortion generated endogenously in one of its sectors. In Chapter 6, I describe a unique feature of EU migration where migration is endogenously determined by the unions’ bargaining decisions. I describe the empirical signiﬁcance of each topic in Chapter 7 and discuss data that we need to gain more insights about international migration. Throughout the book, as mentioned before, I use the standard techniques used in the analysis of international economics. A basic knowledge of algebra and calculus should be sufﬁcient to understood the book. I want to thank Ron Jones and Kar-yiu Wong for their very helpful comments on the manuscript. Thanks are also due to friends and colleagues for their help during the preparation of this book. Excellent research assistance was provided by Bogdan Birliga and Ling Wang. I also want to thank Debbie Clearwater for her help in the typing of the manuscript. I would like to thank the Korea International Economic Association and Taylor & Francis for their permission to use my previously published

xx

Preface

material. The articles that I have used are ‘Minimum wage, international migration and the effects on welfare’, in International Economic Journal, 9, 2, summer 1995, 33–45: ‘Efﬁciency wages, unemployment and international factor movements’, in Journal of International Trade and Economic Development, 7, 3, 1998, 317–38 (http://www.tandf.co.uk). This book was partially funded by an FRCE grant from ORSP of Central Michigan University.

1

International labor mobility with full employment

This chapter starts with an overview of the literature on the implications of migration between two countries when both of them are enjoying full employment. The chapter takes us from the one-good, one-factor model to the one-good, two-factor model and then ﬁnally to the twogood, two-factor model. In discussing the two-good, two-factor model, it makes a distinction between the case when both goods are traded goods and the case when one of them is a traded good and the other is a non-traded good. It reminds the reader about the result that, under full employment, constant returns to scale and perfectly competitive market structure, trade in goods and trade in factors might be substitutes for each other in the sense that both of them can accomplish the same objective. Finally, in an analysis with interconnected markets, the chapter shows that, even in the presence of a non-traded good, emigration can have favorable effects on those who are left behind not only through favorable terms of trade effects but also through capital enrichment. All these results are established when there is full employment in both the host and the source country.

The world economy is now experiencing an unprecedented level of openness where the term ‘globalization’ is taking a new form. This globalization, which started almost a century ago, is no longer inhibited by high transport cost, or imperfect information and a lack of a well-integrated global ﬁnancial market.1 During the last few decades, labor, capital, ﬁnance and all forms of resources have been ﬂowing across national borders to take advantage of opportunities. New technology is spilling over the countries and the information system is getting more and more integrated. The volume of trade is growing, and more interestingly we are seeing more intra-industry trade. Goods that were considered non-tradable are entering the world market. The development of world organizations (such as the World

2

International labor mobility with full employment

Bank, International Monetary Fund, World Trade Organization and European Central Bank), and the increasingly active role of the United Nations during the twentieth century have only complemented the growth of this new world economy. In his study on technology spillover, Helpman concludes, ‘there are signiﬁcant cross country links that are driven by foreign trade and investments’ (1999: 17–30). In this new world environment international labor mobility creates new implications. International labor mobility is another form of trade among nations. It is trade in factors. Thus it is an important tool for world economic integration. Even when globalization was at its infant stage, labor mobility contributed signiﬁcantly to nations’ growth.2 Of all different types of mobility across national borders, labor mobility is slightly different. Thus, although sometimes labor migration as a substitute for trade in goods has similar economic consequences, it meets radically different political acceptability. International labor migration faces more restriction than international trade in goods. During the 1980s, for instance, the European Union imposed serious restrictions on labor immigration while they followed free trade in goods. Mobility of workers between nations is also different from movement of any other factors of production across national boundaries. For any other factors the owners of the factors of production do not have to move to another country. They can provide their services to the host country while staying in their resident country. This is also true for guest workers who, although they move in person to the host country, are not entitled to many amenities in that country. But international labor migration means a ﬂow of workers together with their services between countries. In this chapter, I will ﬁrst present some tables and graphs to show the importance of international labor migration. Table 1.1 shows the migrant stock by region, and as a proportion of a region’s total population, in 1965 and 1990. In Table 1.2, I present countries with the highest net immigration rates, 1990–1995. Table 1.3 shows the foreign or foreign-born population as a percentage of total population in selected OECD (Organization for Economic Co-operation and Development) countries. These three tables suggest that international labor mobility is becoming more visible. In Table 1.3, we can see that the proportion of immigrants in a country’s population is rising for most of the countries included and it is predicted to increase more in the twenty-ﬁrst century. Since, in this book, my focus is on the relation between unemployment and labor mobility, it is helpful to look at the unemployment rates in different parts of the world and the employment level of foreigners and foreign-nationals in different sectors of the economy (Table 1.4 and 1.5). Since international migration means movement of workers together with their services across national boundaries, the analysis of the effects of international migration needs some special attention. For example, the movement of capital and other resources affects only Gross Domestic

International labor mobility with full employment 3 Table 1.1 Migrant stock by region, and as a proportion of a region’s total population, 1965 and 1990 Estimated foreign-born population Thousands

World total Developed countries Developing countries Africa Northern Africa Sub-Saharan Africa Asia East and Southeast Asia China Other East and Southeast South Central Asiaa Western Asia Latin America and the Caribbean Caribbean Central Americab South America Northern America Europe and former USSR Countries with economies in transitionc Former USSR Other Europe Oceania

1965

1990

75,214 30,401 44,813 7,952 1,016 6,936 31,429 8,136 266 7,870 18,610 4,683 5,907 532 445 4,930 12,695 14,728 2,835 140 11,753 2,502

■

As a percentage of total population of region 1965

1990

119,761 54,231 65,530 15,631 1,982 13,649 43,018 7,931 346 7,586 20,782 14,304 7,475 959 2,047 4,469 23,895 25,068 2,055

2.3 3.1 1.9 2.5 1.4 2.9 1.7 0.7 0.0 1.9 2.8 7.4 2.4 2.4 0.8 3.0 6.0 2.2 2.4

2.3 4.5 1.6 2.5 1.4 2.8 1.4 0.4 0.0 1.2 1.8 10.9 1.7 2.9 1.8 1.5 8.6 3.2 1.7

159 22,853 4,675

0.1 3.6 14.4

0.1 6.1 17.8

Source: Trends in Total Migrant Stock, Revision 4 (POP/1B/DB/96/Rev.4) database maintained by the Population Division of the United Nations Secretariat. Notes a Excluding Armenia, Azerbaijan, Georgia, Kazakhstan, Kyrgyzstan, Tajikistan, Turkmenistan and Uzbekistan. b Including Mexico. c Including Albania, Bulgaria, the former Czechoslovakia, the former German Democratic Republic, Hungary, Poland, Romania and the former Yugoslavia and excluding the former Union of Soviet Socialist Republics (USSR).

Product (GDP), which is the value of total production within the country, while the movement of labor affects both GDP and Gross National Product (GNP), which is the value of total product produced in the country minus the payment to the foreign workers/resources plus the earnings of the country’s citizens residing in the foreign country. The level of GNP is usually used as an indicator of welfare as far as implications of factor mobility is concerned.

4

International labor mobility with full employment

Table 1.2 Countries with the highest net immigration rates, 1990 to 1995 Country

Net immigration (in thousands)

Net immigration rate per 1,000 people

United States Germany Afghanistan Russian Federation Zaireb Yemen Mozambique Canada Guinea Tanzania Israel

4,250a 2,900 2,500 1,800 1,100 1,000 1,000 600 600 550 485

3.3 7.2 29.1 2.4 5.3 15.0 12.7 4.2 18.3 4.0 19.1

Source: http://qsilver.queensu.ca/sps/calender/Gibson.papaLecture.pdf, p. 24. Notes a Includes the one-time only, legalized population from 1986 Legalization Programs. b Now Democratic Republic of Congo.

Table 1.3 Foreign or foreign-born population in selected OECD countries

Australia Austria Belgium Canada Denmark Finland France Germany Ireland Italy Japan Netherlands Norway Portugal Spain Sweden Switzerland UK

1988

1998

22.3 4.5 8.8 16.1 2.8 0.4 6.8 7.3 2.4 1.1 0.8 4.2 3.2 1.0 0.9 5.0 15.2 3.2

21.1 9.1 8.7 17.4 4.8 1.6 6.3 8.9 3.0 2.1 1.2 4.4 3.7 1.8 1.5 5.6 19.0 3.8

Source: OECD International Migration Database; OECD Labor Force Statistics.

To analyze the effects of international migration, we have to consider the effects on the host country, effects on the source country and also the effects on the migrants themselves. Furthermore, the effects on the host and source countries will vary depending on whether each of them is including migrant’s welfare in the national welfare. It is also important to

International labor mobility with full employment 5 Table 1.4 Unemployment in OECD countries as percentage of labor force Average 1988–1998 North America Canada Mexico United States Asia Japan Korea Europe Denmark Finland Norway Sweden Greece Italy Portugal Spain Austria France Germany UK EU

Projections 1999

2000

2001

2002

9.4 3.7 5.8

7.6 2.6 4.2

6.8 2.3 4.0

1.2 4.6 4.6

1.2 5.0 5.0

2.8 2.8

4.7 6.3

4.7 4.1

4.9 4.2

4.8 4.0

7.5 10.6 4.8 5.4 9.0 10.5 5.7 19.6 5.0 10.9 7.5 1.9 9.6

5.2 10.2 3.2 5.6 12.0 11.5 4.4 15.9 5.3 11.2 8.3 6.0 9.1

4.8 9.8 3.4 4.7 11.3 10.7 4.0 14.1 4.6 9.7 7.8 5.5 8.2

4.7 9.1 3.4 4.1 10.8 10.0 4.1 13.2 4.6 8.6 7.3 5.4 7.7

4.8 8.6 3.3 3.9 10.0 9.2 4.2 12.6 4.4 8.1 6.8 5.5 7.3

Source: OECD (2002C) Economic Outlook, No. 9, June.

know whether migration is permanent or temporary. A permanent migration means that migrants are not planning to go back to their source or origin country, i.e. there is no return migration. A temporary migration, on the other hand, means that migrants move knowing that they will have to go back (in some cases the return migration can be state contingent). In this book, I will focus on permanent migration. It is important to remember that the absence of return migration does not preclude reverse migration. Reverse migration does not guarantee that the original migrants will move back. It is difﬁcult to evaluate the effects of state-contingent return migration. Here migrants will return if a certain state occurs and they will stay in the host country if they face the alternate state. This involves uncertainty and, for the purpose of this book, I have decided not to bring it in. Since the effect of immigrants on the host and the source country depends on the remittance sent by the migrants, Table 1.6 gives us an idea about workers’ remittance payment in selected emigrating countries. In this chapter, I will focus on labor migration where there is full employment of labor in both the countries. As mentioned before, in this chapter production technology is linear and homogenous and both the product and the factor markets are perfectly competitive. The preference

6

International labor mobility with full employment

Table 1.5 Employment of foreigners and nationals by industry division (proportion of total employment of foreigners to nationals)

Australia Austria Belgium Canada Denmark Finland France Germany Greece Ireland Italy Japan Luxembourg Netherlands Portugal Spain Sweden UK USA Total

Agriculture

Industry

Services

F

N

F

N

F

N

2.2 1.3 1.1 2.4 4.4 3.6 3.2 1.4 3.9 3.7 6.8 0.3 1.6 2.1 1.9 7.5 1.5 0.7 4.2 3.3

5.8 7.6 2.7 4.7 3.9 7.7 4.8 3.1 19.9 11.0 6.6 5.5 3.8 3.8 12.8 8.5 3.3 1.9 2.4 4.3

26.7 42.0 35.9 24.6 22.9 23.5 38.2 46.3 41.3 25.2 34.9 64.1 28.3 28.3 38.8 20.7 27.2 20.2 26.2 29.2

20.7 29.2 27.1 19.6 26.6 27.6 26.0 34.1 22.5 28.3 32.2 61.6 22.9 22.9 32.5 30.1 25.7 27.4 22.6 27.4

71.1 56.7 63.0 73.0 72.7 72.9 58.7 52.3 54.7 71.2 58.3 35.6 70.1 69.7 59.3 71.8 71.3 79.1 69.5 67.5

73.4 63.2 70.3 75.7 69.5 64.7 69.3 62.8 57.6 60.8 61.2 33.0 76.2 73.4 54.7 61.4 71.0 70.7 75.0 68.4

Source: Euro stat, U.S. Bureau of Census, Statistics Canada, Japan’s Ministry of Justice, Australia Bureau of Statistics, OECD labor force Stat. Note F = foreigners; N = nationals.

pattern is homothetic for each individual in each country, i.e. inferiority in consumption is not allowed. After analyzing the implications of international migration with full employment in this chapter, I add unemployment in Chapter 2. Furthermore, once we are familiar with the implications of migration under constant returns to scale and perfectly competitive market structure, I plan to introduce variable returns to scale and imperfect competition in the subsequent chapters.

1.1 Zero effect of migration on the host and the source country Suppose there are two countries, the home country and the foreign country. Each of these countries has labor as its only factor of production and produces only one good. The value of the marginal product of labor (VMPL) curve in each country is downward sloping following the law of diminishing returns (see Figure 1.1). Originally in the home country, OL2 labor was producing OCAL2. Let’s suppose that L1L2 workers move to the foreign

International labor mobility with full employment 7 Table 1.6 Workers’ remittances in selected emigration countries (remittances as a percentage of exports of goods and services) Albania Jordan Bangladesh Egypt Nicaragua India Morocco Jamaica Greece Dominican Republic Sri Lanka Pakistan Ecuador Nigeria Guatemala Turkey Honduras Tunisia Peru Mexico Total

153.5 42.5 27.3 26.9 26.3 20.7 20.2 19.5 18.9 17.7 17.7 17.1 16.8 16.0 13.1 9.8 9.2 8.5 5.3 4.3 12.1

Source: IMF (1999) Balance of Payments Statistics Yearbook, Part I.

country and, after migration, the country’s total production is OCBL1. The total loss of production is L1BAL2 of which L1L2 AD is taken as migrants’ wages. So L1L2 amount of migration results in a loss equal to ABD, and as the magnitude of migration becomes inﬁnitesimally small, emigration does

Figure 1.1 Zero effect of migration with one good.

8

International labor mobility with full employment

not have any effect on the home or the source country. By similar reasoning, an inﬁnitesimally small immigration will not have any effect on the host country. But assuming that migration is triggered by an economic incentive, emigrants will gain. In other words, migrants will move because they expect to get a wage in the host country that is higher than OW1 and it will make the migrants better off compared to their situation in the source country. This analysis will also hold good if each of these two countries has both labor and capital, and each one of them is producing only one good. Holding capital supply ﬁxed, the declining value of marginal product curve will result in the same conclusion. For the inﬁnitesimally small migration, the presence or absence of the migration does not make any difference. Let’s now suppose that each country produces two traded goods with two factors of production. In the home country, AB is the country’s production possibility frontier (PPF) before any migration takes place (see Figure 1.2) and CD is the PPF of non-migrants before migration. We are assuming homothetic preference pattern. Note that CD (relative to AB) is showing that X is a relatively labor-intensive good. The pre-migration welfare of the non-migrants is given by Ua. In the post-migration situation, the terms of trade are not changing for this small, open economy and, as a result, the remaining residents of the source country (i.e. non-migrants) are staying on the same utility function (Ua = Ub). Thus we see that emigration of a part of the labor force does not affect the source country even in a two-good, two-factor model when the terms of trade do not change due to the small country effect.

Figure 1.2 Zero effect of migration with two goods.

International labor mobility with full employment 9

1.2 Non-zero effect of migration on the host and source countries Again, I will ﬁrst look into a scenario involving only two factors and one good. For the source country, if we look at Figure 1.1, then for any ﬁnite amount of emigration, say L1L2, the loss of total product is equal to the area ABD plus ADL1L2. In the post-migration period, wages of the existing workers will go up and they will earn a larger share of the country’s total product. The capital owners on the other hand will lose. Putting aside this income distribution effect and assuming ADL1L2 area is taken by the emigrant workers, the loss of the source country is ABD (Berry and Soligo 1969; Tobin 1974). This is the famous Harberger triangle in the migration literature (see Wong 1986a; Quibria 1988). As far as the effect on migrants is concerned, it is very reasonable to think that migrants move because of an economic incentive, i.e. they expect to get a wage higher than the wage they are receiving in their home country. In terms of Figure 1.1 it means that emigrants will get a wage higher than W1 or in this case at least W2 in the foreign country. If the home country takes emigrant’s gain in income as a part of its national gain then in addition to the loss of ABD and ADL1L2, the home country also gains the area AEB.3 Following the same logic, according to Figure 1.1, the host country will gain in total product (area ABD) with a ﬁnite amount (L1L2) of migration. Declining marginal product range of production reminds us that this is also the range for declining average product. If workers in the source country are paid by average product in the pre-emigration period, the emigration will raise the average product of those left behind and it might be considered as a gain. But that should not be considered as a gain because (1) this is not an increase in per capita income and (2) workers are paid according to their marginal product unless it is an economy resembling family farming (Bhagwati and Rodriguez 1975; Basu 1985). Let us now look at the situation when each of the two countries produces two goods with two factors of production without trade or the open small economy assumption. Good X is relatively labor intensive. In the pre-migration period PP is the PPF (see Figure 1.3) and residents in the source country were getting U0 level of utility at price level AB. Premigration PPF of non-migrants is given by P′P′ and their production equilibrium will be at E′ where EE′ presents the Rybczynski line. Following the assumption of non-inferiority in consumption, non-migrants’ consumption level was at point F before any migration occurs. After migration, assuming stability, the price of the relatively laborintensive commodity will rise and that of the relatively capital intensive commodity will fall. Thus, at new price line CD, non-migrants will be consuming at point G on U2. This loss in welfare for those left behind is either due to the fact that non-migrants lose the trading opportunity with the

10

International labor mobility with full employment

Figure 1.3 Loss from migration in a two goods-two factors model.

migrants because of migration or, if they engage in trade with the foreign country, the terms of trade will move against them. If the source country engages in trade and it is not a small economy, it is possible for this country to experience a change in its terms of trade following migration (since both production and demand change). If the terms of trade change, whether non-migrants lose or not depends on whether they were importing or exporting the good whose price rises in the world market. In Figure 1.4, non-migrants are importing Y, the relatively capital-intensive good. The terms of trade change after migration is in favor of good Y. So people left behind gain from emigration as they move from C to D. If it were a small open economy as in Figure 1.2, the non-migrants would not lose the trading opportunity, i.e. they could trade with the foreign country and, as a result, at the unchanged terms of trade, they will be on the same utility curve both before and after migration. The analysis of the loss of non-migrants when they lose trading opportunities with the migrants is used by Rivera-Batiz (1982) to explain what will happen if one of the goods is a non-traded good. Since the price of the non-traded good is determined in the home market, Rivera-Batiz’s model resembles this one. In this case we will look at a closed economy although residents can trade with each other. The host country for the same reason will have a gain in welfare. As for the migrants, again they have an economic incentive to move. They will be better off (see Section 1.4 for a different effect of migration with non-traded goods and full employment) as a result of migration (Jones et al. 1986).

International labor mobility with full employment 11

Figure 1.4 Gains from migration in a two goods-two factors model.

1.3 Factor mobility versus trade in goods One of the objectives of this book is to examine the issue of whether free labor migration can be a substitute for free trade in goods in the sense that they can accomplish the same objective. Under full employment and linearly homogeneous production technology Mundell has studied this in the mid-twentieth century. According to Mundell (1957), under some assumptions, free international labor migration is a perfect substitute for free trade and, in the absence of free labor migration, free trade in goods will accomplish the objectives of free factor movement (in this case labor migration). In the literature, this has been referred to as a demonstration of a full equivalence between trade in goods and factor mobility (Wong 1986b). In the absence of migration cost, either one of them will equalize commodity and factor prices between the nations, provided both countries have identical constant returns to scale production technology, i.e. marginal productivities depend, absolutely and positively, on the proportions in which factors are employed, factor endowments do not allow complete specialization in either of the countries and, in a two-goods world, one commodity needs a greater proportion of one factor relative to the other commodity at all factor prices and at all levels of production. Suppose two countries, A and B, are producing steel and cotton using labor and capital. Production technology is linear and homogenous and

12

International labor mobility with full employment

there is full employment in each of these countries. Cotton is a relatively labor-intensive good and steel is a relatively capital-intensive good. A is labor-abundant and B is relatively capital-abundant and if free trade in goods is allowed, A will export cotton and B will export steel since cotton is a relatively labor intensive commodity. I will assume that B represents the rest of the world and A is just a small open economy whose factor endowments or production conditions do not have any effect on prices in the world market. Before trade, A was producing and consuming at D in Figure 1.5. The price of cotton relative to steel was cheaper in A compared to that in B. Thus the marginal product of labor (MPL) and wage rate in A was lower than that in country B. Let’s suppose now that there is no mobility of factors. If trade opens up, the international price or terms of trade A′B′ will replace A’s domestic price AB. This will stimulate cotton production in A, since AB is steeper than A′B′. Resources will be moved from steel to cotton production and since cotton is a labor-intensive product it will make the labor relatively scarce (although it was the abundant factor) and the MPL and wage rate will go up in A. The international price is established by the two countries such that country A sells cotton at a price higher than its domestic price and B sells steel at a price equal to its domestic price. Resources in A therefore move towards cotton production from steel production. Since steel is a capital-intensive commodity, this creates a surplus of capital in A and marginal product of capital as well as interest falling in A, although capital is a scarce factor in A. Thus, factor prices move in opposite directions in country A and this results in international factor price equalization. When factors cannot move, trade in goods reallocates the utilization

Figure 1.5 Effects of migration in comparison with effects of trade in goods.

International labor mobility with full employment 13 of factor endowments in each country by moving the goods between countries. If, on the other hand, there is a partial impediment to trade, but labor can move freely between countries, then factor and commodity prices will also be equalized. For example, let’s start with a tariff on cotton in the cotton-importing country, B. This will increase the domestic price of cotton and cotton production will increase in B. Since cotton is a relatively labor-intensive commodity, at constant factor prices this will create an excess supply of capital. To maintain full employment, the marginal product of capital as well as its price will go down and wages will rise in B. With free labor mobility, workers will move out of A. Country A will now produce on the new production possibility frontier T′T′. This will reduce the MPL in B. Note that the after tariff, terms of trade is A′′B′′ and the new production point in A is H when MPLA < MPLB. The migration will continue until MPLA = MPLB i.e. until the old free-trade price is established. When the new production equilibrium is reached at this price, cotton production in B is less than its post-tariff cotton production and A still imports steel, but its volume of imports will be reduced since the demand has been reduced by the demand of emigrants. The new consumption equilibrium in A will be the consumption equilibrium of the non-migrants before the emigration. The volume of trade for the non-migrating residents will go back to its original position and factor prices will be equalized across nations. This relation between trade in goods and factor mobility also has been studied later by several authors (Purvis 1972; Markusen 1983; Svensson 1984) to show that the equivalence relation will not hold if the HeckscherOhlin assumptions such as identity of production functions are relaxed. Wong (1986b) has examined the relation by showing whether an increase in the level of one will increase the volume of the other. In a general equilibrium analysis he in fact has developed the necessary and sufﬁcient conditions for substitutability and complementarity. In an earlier work, Wong (1983) has also rank ordered different regimes involving different combination of free trade in goods and free factor mobility.

1.4 Migration and non-traded goods: an interconnected market approach In Section 1.1, I have shown that in a standard two-good, two-factor model, emigration is of no concern to the non-emigrants if the nonmigrants do not engage in trade or the terms of trade do not change. This is true when the country of emigration is small and faces exogenously given terms of trade. But if one of these goods is a non-traded good, emigration then may result in possible welfare loss to the remaining residents. According to the Rivera-Batiz model (1982), for example, this welfare loss is due to a loss of trading opportunity the non-migrants had with the migrants, in terms of exchange of traded for non-traded commodities.4

14

International labor mobility with full employment

Rivera-Batiz shows that migration forces the remaining residents to adjust the imbalance in the non-traded good market resulting from the loss of trading opportunities with the migrants. Consequently, the domestic price ratio changes after migration, and the remaining residents suffer a welfare loss, while the terms of trade remain constant. In this section, I will present the effects of migration in the presence of a non-traded goods sector when the terms of trade are determined endogenously. It is assumed for this study that each country in a threegood, two-country model produces only its non-traded good and its exportable good and consumes only its non-traded good and its importables.5 It is also assumed that when migrants move to the host country, they adapt to the consumption pattern of their new country.6 In this model, due to production changes and changes in the demand pattern of migrants after migration, the source country (country of emigration) experiences an excess demand for its exportable good and the host country experiences an excess supply of its exportables. This affects the source country’s terms of trade favorably. Although non-migrants still lose their trading opportunity with migrants after migration, they experience this favorable movement in the terms of trade. This favorable change results in a change in the domestic production price ratio as well as an improvement in the domestic consumption price ratio for the source country.7 Therefore, the non-migrants may end up better off as a result of migration. If substantial migration occurs from the non-traded goods sector of the economy, then, in addition to these favorable price effects, the remaining residents may experience another favorable effect: the capital-enrichment effect. The presence of the capital-enrichment effect shows that nonmigrants experience a signiﬁcant increase in their capital stock because migrants are unable to move or sell capital resources they own due to institutional, legal or cultural reasons.8 I will show that in the presence of a non-traded good sector in a small open economy, emigration results not only in the loss of trading opportunities for non-migrants (described by Rivera-Batiz 1982), but also in favorable changes in the terms of trade. The changes in the terms of trade and the gift of capital from migrants to non-migrants can increase the remaining residents’ welfare shortly after migration takes place. Other favorable effects of migration, e.g. remittance effect (Djajic 1986) and the effects of return migration by a subgroup of migrants, are not considered here. Thus, migration of people from the non-traded goods sector is not necessarily a cause for major concern as far as the immediate loss in the welfare of nonmigrants is concerned. Terms of trade effect and capital enrichment effects The source country produces two goods, Xn and X1, with two factors of production, labor (L) and capital (K), both of which are mobile between

International labor mobility with full employment 15 the industries. Xn is the non-traded good and X1 is the exportable good. There is perfect competition, both in the product and in the factor markets, and the production function is assumed to be linear and homogenous. Under these assumptions, the pre-migration production possibility frontier (PPF) for the entire economy is presented by TT in Figure 1.6a. Since the labor-abundant developing countries usually comprise a large part of international migration, it is assumed that the source country is the

Figure 1.6 Effects of migration with non-traded goods.

16

International labor mobility with full employment

labor-abundant country and X1 is the labor-intensive good relative to Xn, which is a capital-intensive good. The categories of goods produced by these countries go from one extreme of labor-intensive exportables to the other extreme of producing (although to a limited extent) capital-intensive import substitutes. The non-traded goods, being the commodities with relatively higher cost of production, can be assumed to be more capital intensive compared to the exportable goods. The host country produces X2 and X *n, its exportable goods and nontraded goods, and consumes X1 and X *n, its importable and non-traded goods. Production conditions in the host country are similar to those of the source country. The host country is a capital-abundant country and X2 is a capital-intensive good relative to X *n which is a labor-intensive good. The taste patterns are different in the two countries and can be presented by the usual bowed-in, non-intersecting indifference curves. The source country consumes X2 and Xn, where X2 is the imported commodity. The host country does not have uses for X2 and the source country does not have uses for X1. There are three price ratios which concern the source country: P1/Pn, the ratio that guides production; P2/Pn, which, along with income, determines the consumption bundle; and P2/P1, the terms of trade, which affect the demand by affecting real income. Any two of these price ratios determine the third one. As laborers migrate from the source country, leaving some or all of their capital resources behind for social, cultural or institutional reasons, the remaining residents are affected in two ways: 1. 2.

by the gift of migrants’ capital: the capital-enrichment effect; by the favorable change in the terms-of-trade caused by changes in the demand pattern by migrants from X2 to X1 and by production changes in both countries: the terms-of-trade effect.

An analysis of the capital-enrichment effect9 Prior to migration, suppose the total labor supply (L) in the source country is made up of potential migrants (L1) and non-migrants (L2). The total capital resource (K) is made up of capital resource owned by migrants (K1) and capital resource owned by non-migrants (K2). Given these factor endowments, the pre-migration production equilibrium for the entire economy is shown by point E on TT at price ratio PP (Figure 1.6a). If migrants had taken all of their capital following migration, non-migrants as well as the entire economy will be on NN (see Bhagwati and Brecher 1980; Rivera-Batiz 1982). This also is the hypothetical production-possibility curve for non-migrants in the pre-migration situation. It shows where non-migrants would be in the pre-migration situation if a separate PPF could be drawn for them. This allows one to

International labor mobility with full employment 17 compare pre- and post-migration situations of the non-migrant population when migrants move with their entire capital resource. At the prevailing price ratio of the economy, PP, the production equilibrium point for the non-migrants is shown by point F on NN. Prior to migration, the non-migrants’ total income (Y2) can be expressed as the sum of the returns to the factors owned by them or the sum of the values of output produced by them. That is: Y2 = wL2 + rK2 = P1x1 + Pn xn, where xi is the output level for i = 1, n, which the non-migrants could have produced alone. This also represents non-migrants’ income after the migrants leave with their capital. At constant terms of trade, Y2 only changes if factor supply changes. If migrants leave all of their capital behind, the non-migrants’ new income, Y2′ (= wL2 + r(K1 + K2)), will be greater than Y2 as a result of migration. Or dY2 = (Pxˆ 1 x1 + xˆn xn) dK > 0 (see Equation (8) in Appendix C). Therefore, with the gift of the migrants’ capital, non-migrants will move to N′N′. At constant terms of trade, the new production equilibrium will be at point H, while remaining residents enjoy an increase in their income. An analysis of the terms-of-trade effect Although the source country is assumed to be a small open economy in this model, it can affect the world terms of trade following emigration of its workers because of the pattern of production specialization and the nature of consumption. Changes in the terms of trade following migration are brought about by two sets of factors, namely, factors responsible for changes in production and factors responsible for the shift in demand. The hypothetical production possibility schedule for the non-migrants (Figure 1.6a) shows that, prior to migration, non-migrants were producing qF of X1 and Oq of Xn at point F. The migrants, on the other hand were producing qE′′ of Xn and EE′ of X1. The total amounts of exportables and non-tradables produced by these two groups then match the aggregate level of production at the pre-migration equilibrium for the entire economy shown by point E on TT (Figure 1.6a). Suppose that the nonmigrants had exchanged qF of X1 (Figure 1.6a) for q′F ′ of X2 in the world market (Figure 1.6b) before migration and the potential migrants had exchanged EE′ of X1 (Figure 1.6a) for q′′F ′′ of X2 (Figure 1.6b). The new endowment point resulting from these exchanges is shown by point F ′ in the Edgeworth Box Oq0q′′q′′′ (Figure 1.6b). The hypothetical consumption of both the migrants and the non-migrants and the trade between these two groups before migration also occurred is shown in this Edgeworth Box. The pre-migration endowment of consumables for the non-migrants therefore consists of Oq′ of Xn and q′F ′ of X2 and that for the migrants consists of q′q0 of Xn and and q′′F ′′ of X2 (Figure 1.6b). The pre-migration consumption point for both the groups, on the other hand, is shown by

18

International labor mobility with full employment

point A (Figure 1.6b). This shows the trading opportunity (in terms of the exchange of traded for non-traded commodities) enjoyed by non-migrants and migrants inside the country before migration occurred. After migrants leave, non-migrants lose this trading opportunity and face the imbalance between demand and supply in the non-traded goods market. If the migrants do not take all or part of their capital resource, then, as labor supply goes down, after migration, aggregate production of X1 falls and that of Xn goes up compared to the non-migrants’ premigration production equilibrium. The non-migrants reach point H on N′N′ as their new production equilibrium point, which reﬂects the magniﬁcation effect (Jones 1965) for the source country, where |Xˆ1| > |Xˆ n| after migration. Although this new equilibrium point reﬂects an increase of non-migrants’ income, the source country’s aggregate income Y(= wL + rK = P1X1 + PnXn) declines after migration because the factor endowments decline in supply, and/or the decline in the output of X1 is greater than the increase in the output of Xn. Following migration, therefore, while the supply of Xn increases due to the change in the source country’s factor endowments (shown by ekˆn(kˆ )), the demand for Xn goes down due to the decline in the source country’s aggregate income (dY). The price of the non-traded good, Pn, therefore declines. This decline in Pn causes substitution both in the domestic production and in the domestic consumption (shown by the terms enn and Enn). The ﬁnal change in Pn is given by:

(

{

(

Pˆn = −  ( mn P1dY ) / Pn DX n − Enn + enn 

)}) + e (kˆ ). n kˆ

(See Equation (4) in Appendix D for derivation of Pˆn.) Resources start shifting from production of non-tradables to production of exportables, and the demand shifts away from importables. If substitution in production is smaller than substitution in consumption, then P1 or the exportable price will rise following the adjustment in the non-traded goods market. (It should be noted here that even if Pn rises, depending on the size of mn, the substitution in production works favorably to raise P1 and the terms of trade must move favorably for the source country.) The immigration of workers in the host country, on the other hand, raises the production of X n* and reduces the supply of X2 when |Xˆ n*| > |Xˆ 2|. The host country, therefore, enjoys an increase in income. While the repercussions in the host country’s non-traded good market shows an increase in the supply of X n*, the demand for X n* also increases because of the gain in the country’s income. Hence, Pn* will increase if the marginal propensity to consume the non-tradables in the host country, i.e. m n*, are very high. This change in Pn*, i.e. Pˆn* is given by:

(

)

(

(

))

()

* * * Pˆn* =  mn* P1dY * / Pn* DX n* − Enn + enn  − e(nkˆ ) kˆ .  

International labor mobility with full employment 19 (See Equation (5) in Appendix D for the derivation.) These disturbances in the non-traded goods markets therefore change the world’s terms of trade by affecting the production levels of X1 and X2. Furthermore, since the migrants change their taste pattern after they are in the host country, there will be a shift of demand from X2 to X1. This raises demand for X1 and reduces demand for X2 which also affects the terms of trade favorably. The following equation summarizes all these effects on the terms of trade:

{(

) (θ ( − E ) + α (e ))}P m 

)

( ))m P dY

P2 d( DX 2 − X 2 ) = dY  − m − θ x 2 E2n /   n* +   α n 2  − e 2   / θ x n − Enn + α x n enn   

( (

n n

xn

* n 1

()

xn

*

n n

1

n

  

n* − P2 DX 2 E2n e nkˆ − P2 X 2  − e 2  ekn * kˆ

()

(See Equation (8) in Appendix D for the derivation.) The favorable movement in the terms of trade changes Pn/P1 and Pn/P2 also moves favorably. In Figure 1.6, at unchanged terms of trade PP, the movement from point F on NN to point H on N′N′ shows the gain of the remaining residents when they enjoy the capital resource left by the migrants. Corresponding to point F in Figure 1.6, the domestic consumption price for the source country was aa when the population consumes at point A in Figure 1.6b. Following the change in the demand pattern, production changes and the adjustment in the non-traded goods market in the post-migration period, the non-migrant will face a change in the production price ratio from PP to P′′P′′. This change can be described as:

(Pˆ − Pˆ ) = {(E + m − 1) / (E + e)}(Pˆ − Pˆ ) n

1

2

1

(See Equation (11) in Appendix E for derivation.) The new production equilibrium would be at point I on N′N′. The corresponding consumption price ratio would be a′′a′′ when the non-migrants consume at C.

(

) (

)(

)

(

E Pˆ2 − Pˆn + Pn / P2 M 1 − m dy = e Pˆn − Pˆ1

)

(See Equation (8) in Appendix E for derivation.) Note that if there were no gift of capital, the terms of trade would still change and migrants would move from point F on PP to point G on P′P′. In sum, non-migrants become better off due to the gift of migrants’ capital and, furthermore, they are favorably affected because of the change in the terms of trade. This improvement in the terms of trade is brought about by production changes and shift in migrants’ demand. The production changes involve a decrease in production of the source

20

International labor mobility with full employment

country’s exportables and an increase in production of the source country’s importables. Only if the migrants move with no capital is there a chance that production of the source country’s importables will go down. If this fall in production of importables washes out the terms-of-trade effect brought by other production changes, then the terms of trade effect due to the shift in the demand pattern, and the capital-enrichment effect will still make the non-migrants better off. We see that emigration does not always reduce the welfare of the source country producing the non-traded good. Depending on the pattern of production specialization and the nature of consumption, it can increase the welfare of the source country. When the source country, although small in size, is the only seller of its exportables and the only buyer of its importables, the world terms of trade can change in its favor following the emigration of its workers. The change in the terms of trade results in changes in the domestic production price ratio between the non-traded good and the export good (only goods produced). This also improves the domestic consumption price ratio between importables and its non-traded good (only goods consumed). Hence, the non-migrants’ welfare will increase. This favorable effect continues to exist with the capitalenrichment effect, through which the remaining residents enjoy an increase in their domestic capital due to the gift of the migrants’ capital. Therefore, it can be said that, although non-migrants lose their trading opportunity with migrants in the post-migration period, favorable movement in the terms of trade opens up more opportunities with the rest of the world. This, together with the effect of the increase in capital input, improves the non-migrants’ welfare.

2

International labor mobility with exogenously created unemployment

This chapter evaluates migration policies for an open economy in the presence of unemployment resulting from a minimum wage. Migration between countries is triggered by an expected wage differential that depends on both the market wage and the level of unemployment. Workers therefore can move in either direction. It is shown that labor outﬂow raises employment and welfare. Distortion-ridden free trade with this out-migration is therefore better than distortion-ridden free trade with no migration. It might also be better than autarky. Under the scenario, free migration is an alternative to restricted trade often recommended to deal with this type of distortion. A labor inﬂow, on the other hand, generates unfavorable terms of trade, raises national and global unemployment, and reduces welfare.

Having looked into possible effects of international migration under full employment in the ﬁrst chapter, I bring in unemployment in the analysis of international migration in this chapter. Unemployment is created by an exogenously ﬁxed wage that is also higher than the market-clearing wage (as in the case of minimum wage legislation). Although the analysis of the welfare effects of factor mobility in the presence of unemployment has been the focus in a few studies of international factor movements (Brecher and Choudhri 1987) and Brecher (1989), this chapter focuses on a different aspect of this issue. Brecher and Choudhri (1987) for the ﬁrst time deal with international factor movements in the presence of unemployment and conclude that free movement of factors is not desirable if there is unemployment. The objective of Brecher and Choudhri’s paper is to evaluate the effects of labor inﬂow against those of capital outﬂow in the presence of unemployment. Labor migration in their model therefore represents only labor inﬂow and the optimum labor inﬂow in the presence of unemployment is zero according to their analysis. In a broader search for migration policies (e.g. free versus restricted migration and/or labor outﬂow versus labor

22

Mobility with exogenously created unemployment

inﬂow) for an open economy in the presence of unemployment, this chapter explores the effects of free international labor migration for a country where unemployment results from a binding minimum wage. In Brecher and Choudhri’s model, unemployment is created by an unemployment beneﬁt package. It implies that everybody in the labor force will receive at least a required minimum. A binding minimum-wage law will on the other hand provide a guaranteed amount only to the employed worker. Unlike in Brecher and Choudhri’s analysis, in this chapter it is not the difference in the market wage rates that induces migration across national borders; international migration is guided by the difference in the expected wage rates that depend on the market wage as well as the level of unemployment in each country. Depending on the level of unemployment in the economy, both in-migration and out-migration are therefore feasible in this model. The study allows unemployment caused by a real-wage ﬂoor that is institutionally imposed throughout the entire labor market of the home economy within a two-country, two-good, two-factor model of a world engaged in free international exchange of goods. The model is then used to permit unrestricted labor movements across national borders. This chapter agrees with Brecher and Choudhri (1987) in concluding that the optimum labor inﬂow in the presence of unemployment is zero, since it reduces national employment and welfare. But in comparison to their analysis, in this model the labor-importing country suffers more severely in terms of its national welfare and also relative to the rest of the world. Furthermore, labor inﬂow in this model signals a special type of social engineering in the country with distortion in its factor market in comparison to the model analyzing factor inﬂow with full employment of all the factors of production (Jones 1984). The high minimum wage attracts the factor that is already suffering from unemployment. In Brecher and Choudhri’s (1987) model, labor inﬂow only increases the size of the unemployment pool by the number of migrants.1 In the model of this chapter migrants not only join the existing pool of unemployed workers but they also reduce the domestic employment rate. So the number of unemployed workers as a result of migration will be higher in my model. This implies that the rate of unemployment for the non-migrants (or the residents) will always go up in this model, whereas the employment rate for residents will be affected in Brecher and Choudhri’s model only when migrants are not eligible for the unemployment beneﬁt package.2 This chapter also shows that, although the optimum labor inﬂow in the presence of unemployment is zero, free outﬂow of labor across national borders in the presence of unemployment is desirable. Such factor movement raises employment and welfare and therefore reduces the severity of damage from domestic distortion caused by the binding minimum wage. Although Brecher and Choudhri (1987) acknowledge the possibility of such out-migration, this out-migration according to them is only possible

Mobility with exogenously created unemployment 23 by a migration subsidy and it cannot therefore be a part of free-migration policy. In the model of this chapter, out-migration is triggered by the difference in expected wages resulting from initial minimum-wage law. Furthermore, when Brecher and Choudhri refer to the possibility of reducing or eliminating unemployment by out-migration of workers, they imply a movement of either some or the entire pool of unemployed workers out of the country. In my model, the level of unemployment goes down not only because some of the unemployed workers move out of the country, but a favorable change in this country’s terms of trade resulting from out-migration also raises the level of employment within the country. This can ultimately generate full employment for workers in this country. The literature on international trade theory suggests that, in the presence of distortion in the domestic factor market (such as unemployment due to a wage ﬂoor), free trade may be inferior to a no-trade situation. This chapter shows that distortion-ridden free trade with free-labor outﬂow is better than distortion-ridden free trade with no labor migration, and it might also be better than a no-trade situation. Under the scenario, free-labor migration can be used as an alternative to other regulatory measures (such as a trade tax or a trade subsidy), which are often recommended to deal with this type of distortion. In the following, I will very brieﬂy describe the pattern of production and trade potentials of two countries when one of the countries has a binding wage ﬂoor in its labor market.3 It is followed by a description of both the short-run and the long-run equilibrium between these two countries.4 In this section, I also show how the nature of these long-run equilibria varies according to the direction of labor migration and the pattern of specialization, and how these different long-run equilibria will have different effects on welfare and unemployment in both countries.

2.1 The basic model I begin with the standard Heckscher–Ohlin–Samuelson model, where two countries produce two goods, X and Y, under constant returns to scale with two factors of production, capital (K) and labor (L). The producers’ objective is proﬁt maximization under perfect competition. Two factors of production are perfectly mobile between industries so that each factor’s reward is the same in both sectors of the economy. Domestic factor endowments are perfectly inelastic. Good Y is the labor-intensive good, and there is no factor-intensity reversal. Under these conditions, following the standard general equilibrium production model (Jones 1965), full employment of the existing factor endowments in one of these two countries, e.g. Country II, implies that: * * aLx X * + aLy Y * = L*

(2.1)

24

Mobility with exogenously created unemployment * * aKx X * + aKy Y * = K*

(2.2)

where X * and Y * represent Country II’s production of goods X and Y. L* and K * show Country II’s endowment of both the factors of production. a *ij shows the amount of factor i going into the production of commodity j, where i = L*, K * and j = X *, Y *. The competitive equilibrium implies: * * w*aLy + r *aKy = Py*

(2.3)

* * w*aLx + r *aKx = Px*

(2.4)

The input coefﬁcients are deﬁned as: aij* = aij* (w* /r * )

(2.5–2.8)

where w* and r* are wage and rent in Country II, and Py* and Px* represent the prices of goods Y * and X *. Community taste patterns are homothetic, and taste patterns of individuals are identical. Both goods are normal in consumption. Note that ratio of demand here depends only on price. Under the speciﬁcation, Country II will have a standard production possibility frontier and the offer curve, as shown by a′c′ in Figure 2.1c and OF (or OF ′) in Figure 2.2. For Country I, a real-wage ﬂoor in terms of, say, good Y is now – is the added to its entire labor market.5 Let’s suppose that wx /P = wy ≥ w y minimum-wage constraint where wj ( j = X, Y) is the real wage in terms of good j, and P is the relative price of the second good, Y, in terms of the ﬁrst good X. Assuming that this minimum-wage rate is institutionally set above the full-employment level, there will be unemployment, i.e. L = E + U where L is the total labor supply in Country I, E is the number of workers employed and U represents the number of unemployed workers. Capital, K, is always fully employed. Therefore the production equilibrium of this country can be described as: aLx X + aLyY + E

(2.9)

aKx X + aKyY = K

(2.10)

waLx + raKx = Px

(2.11)

waLy + raKy = Py

(2.12)

The input coefﬁcients are deﬁned as:

Mobility with exogenously created unemployment 25

Figure 2.1 Production possibility frontiers for minimum wage Country(I) and nonminimum wage Country(II).

aij = aij (w / r )

(2.13–2.16)

where Y and X are the two goods produced by Country I; w and r are wage and rent in Country I, and Px and Py are the prices of the two goods produced in Country I. aij shows the amount of factor i going into the production of commodity j, where i = L, K and j = X, Y. To close the model, I bring in the demand condition:

26

Mobility with exogenously created unemployment

Figure 2.2 Trade offer curves of Country I and Country II.

 Py  Y   = f  X  Px 

(2.17)

These seventeen equations, together with the equation of the demand condition in Country II and L = E + U, will determine X *, Y *, X, Y, w*, r*, r, E, U, the ratio of the demand for X to that of Y in each country, (X/Y) and (X/Y)*, and all the aij’s in the system. To describe the production possibility frontier (PPF) of this country, let’s now start from a position where the level of the binding minimum wage and the corresponding price ratio, say P′, is such that X = 0, and Y > 0. (From Brecher (1974a; 1974b) it is known, moreover, that if the minimum wage is binding, the product transformation curve and the trade offer curve of the minimum-wage economy are both linear in the region of incomplete specialization and the slope of the PPF is greater than that of the price line.)6 At the same price (P′) as E goes down (because of unemployment from the binding wage constraint) and the original PPF moves

Mobility with exogenously created unemployment 27 downward from Z2′′ Z1′′ to Z2′′′ Z1′′′ etc. (Figure 2.1a), Y/X goes down until at that price incomplete specialization is not proﬁtable, i.e. Y = 0, and X > 0. – ≥ (w /P)), Now, since the minimum wage is ﬁxed in terms of good Y(w y x an increase in the prices of X (at this complete specialization point) is a rise in the real wage in terms of X (Stolper-Samuelson Theorem) and more workers are employed to bid this wage down to the ﬂoor level. The output of X, therefore, increases until E = L and Y still equals zero.7 The PPF and the offer curve of Country I will look like S 20 S 01Z1 in Figure 2.1a, and U2A2U1A1 in Figure 2.2, respectively. At autarky, if Country I has demand for both goods, then equilibrium would be somewhere between S 02 and S 01, say e 0, in Figure 2.1b. In Figure 2.2 this autarky point is represented by the origin. At a particular product–price ratio or terms of trade, Country I’s offer for export of the labor-intensive good on the perfectly elastic segment OA2 responds to the level of employment determined by the imposition of the minimum-wage law. An upward movement on this part of the offer curve implies that employment and welfare increase in Country I, and that this country becomes more and more specialized in the labor-intensive good. Once complete specialization is reached, Country I’s offer becomes highly elastic where, although output and employment cannot be increased, Country I enjoys a welfare gain via improvements in the terms of trade. On the other hand, when the imposition of a minimum wage has resulted in the fall of employment to such an extent that Country I is moving more toward the specialization of the capital-intensive good, the perfectly elastic segment OA1 of the curve shows how the minimum-wage country’s offer for export of the capital-intensive good is determined by the volume of actual employment in Country I. Once the complete specialization of the capital-intensive good is achieved, a further rise in the price of the capitalintensive good raises the real wage in terms of that good, and employment, output and welfare go up. In Figure 2.1b, Zone 1 presents the point of complete specialization in Y, and Country I exports the labor-intensive good. Zone 2 shows incomplete specialization and export of Y. The point e0 is the autarky point. Zone 3 shows incomplete specialization and export of the capital-intensive good, and Zone 4 is completely specialized and is exporting X. Zone 5 is also completely specialized and exporting X, but employment here is higher than that at e0. Zone 6 is the point of complete specialization in good X, with full employment of both factors.

2.2 Analysis of migration In analyzing the effects of international factor movements in the presence of unemployment, so far two different means have been used in the literature to introduce exogenously created unemployment in the analysis. For

28

Mobility with exogenously created unemployment

Table 2.1 Nature of specialization in production for different trade equilibria between zones Trade equilibrium

Type of specialization CC

1C′ 1b′ 2b′ C′2 3b′ a′3 4b′ a′4 5b′ 5a′ 6b′ 6a′

II

CI

X X X X X X X X X X X X

Notes CC: both countries are completely specialized. II: both countries are incompletely specialized. CI: one is completely specialized and the other is incompletely specialized.

example, Brecher (1989) discusses policy-induced ﬂow of capital when unemployment in the domestic labor market is allowed by setting a minimum-wage ﬂoor. In Brecher and Choudhri’s (1987) model, unemployment is created when workers are offered an unemployment-beneﬁt package. This package provides at least a guaranteed minimum for everybody in the labor force (migrants or non-migrants). Home unemployment does not have any bearing on the foreigners’ expectation of wages (compensation or beneﬁts) in their model. In this chapter, unemployment results from a minimum-wage law in the country. This minimum wage provides a guaranteed amount only for the employed workforce. So the migrants as well as the non-migrants will receive the same wage if they are employed. Migration is caused by the expected wage differential between the two countries, which considers actual wages as well as the level of unemployment.8 Expected wages are deﬁned as we = w(E/L) (for Country I), and we* = w*(E */L*) = w* (for Country II). Since E * = L* for full employment with ﬂexible wages in Country II, the actual real wage in Country II is always equal to the expected real wage. Immigration or out-migration of workers does not affect we* through the employment level. The actual wage, w*(= we*), changes after migration as a result of changes in the value of the marginal product of workers. This change in w*(= we*) and the corresponding change in we(= w(E/L)) in Country I following migration enable the dynamics of the adjustment process to reach equilibrium. Here, w is the binding minimum wage and both w and we are expressed in terms of good

Mobility with exogenously created unemployment 29 Y. Since the expected wage, we, takes the probability of employment into consideration, we < w. It should be noted that we is the wage based on which workers make their migration decision, rather than the actual wage migrants receive in the host country.9 Free trade without movements of factors between these two countries can lead to any of the equilibria described in Table 2.1. In the analysis of this chapter when migration is allowed, some of these equilibrium situations become short-run situations because they are not sustainable. Migration will drive these economies toward long-run equilibria. The nature of these long-run (i.e. no migration) equilibria will depend on the pattern of production (specialization or non-specialization) and the direction of migration. With an economy-wide wage ﬂoor, E in Country I is exogenously ﬁxed by the level of the binding wage. As long as this country is incompletely specialized on the straight-line part of its PPF where P or the terms of trade remain constant, the level of E (once determined by the binding wage) remains unchanged. But when this economy is completely specialized in the capital-intensive good, E becomes endogenous and is directly related to the relative price of the capital-intensive good. So a favorable movement in the terms of trade (Py/Px) will increase E on this part of the PPF (see Appendix F for changes in terms of trade resulting from labor migration). When Country I is perfectly specialized in the capital-intensive good, X (for example, in Zone 5 of PPF in Figure 2.1b), but it has unemployment, and Country II is incompletely specialized and exporting the laborintensive good while enjoying full employment (in Zone b′ of PPF of Figure 2.1c), actual wages in Country I are higher than actual wages in Country II. But labor could move in either direction because migration is triggered by the difference in the expected wages. If unemployment in Country I is so high that it makes Country I’s expected wage lower than Country II’s expected wage, unemployed labor starts moving out of Country I (the higher actual wage region). Since only unemployed workers move out, this does not change the production pattern of Country I. But this emigration to Country II affects its actual labor supply and consequently the production of labor-intensive good goes up and that of capital-intensive good goes down in Country II following the employment effect (the Rybczynski theorem). Consequently, the world price of the labor-intensive good falls and the rate of employment starts rising in Country I. Migration to Country II does not impose any additional burden because wage-price is fully ﬂexible there. In Country I, the price of that good decreases in line with which the minimum wage is ﬁxed; so actual wages can be bid down and employment increases. As a result, we(= wE/L) goes up, w*(we*) on the other hand goes down due to inﬂow of additional workers who reduce workers’ marginal product in Country II. This will start eliminating the expected wage differential, and eventually the long-term equilibrium will be achieved.10

30

Mobility with exogenously created unemployment

We therefore observe that free mobility of workers across national boundaries, even in the presence of unemployment, is sometimes desirable. It may reduce the intensity of the damage caused by the binding minimum-wage ﬂoor. Depending upon the pattern of trade or the nature of specialization in production, outﬂow of workers or emigration from the minimum-wage country will increase its employment and welfare. If the nature of trade equilibrium is such that this labor outﬂow fails to increase the home country’s employment (e.g. when Country I is incompletely specialized and exporting the capital-intensive good, i.e. in Zone 3, and Country II is completely or incompletely specialized and exporting the labor-intensive good), free-labor mobility is still desirable because labor outﬂow will raise the global employment and output, and reduce the domestic unemployment rate. This conclusion also holds for another possible equilibrium situation when Country I is completely or incompletely specialized and exports the labor-intensive good, i.e. either in Zone 1 or in Zone 2, but the other country is completely or incompletely specialized and exporting the capital-intensive good.11 Under the circumstances, outmigration cannot affect the domestic employment, but out-migrants ﬁnd jobs in Country II and thus global employment goes up. Proposition 1: Any migration from a minimum-wage country to a nonminimum-wage country when the minimum wage is ﬁxed in terms of the labor-intensive good, and the minimum-wage country is completely specialized in and exporting the capital-intensive good while the nonminimum-wage country is completely or incompletely specialized in and exporting the labor-intensive good, will move the terms of trade in the minimum-wage country’s favor; the output and employment of this country as well as the global output and employment will go up. ˆ* > 0 Proof : Migration from Country I to Country II implies that L (where a ‘ˆ’ over a variable denotes the rate of change of that variable). To trace the effect on the world’s terms of trade, let’s look at the changes in the global demand and supply of the goods. Following the deﬁnition in 2.1, and assuming that the demand pattern is the same in both countries,12

(Yˆ

wD

)

(

− Xˆ w D = − δ D PˆyW − PˆxW

)

(2.18)

ˆ w and X ˆ w are the rates of change in the world demand for Y and where Y D D X good, δD = elasticity of substitution in consumption. Pˆj w stands for proportionate change in the world price of good j = X, Y. On the supply side, the relative rate of change in the world supply of goods Y and X can be shown as:

(Yˆ

w

) (

)

(

)

Y * /X * Y /X − Xˆ w = Yˆ * − Xˆ * + Yˆ − Xˆ Yw /X w Yw /X w

(2.19)

Mobility with exogenously created unemployment 31 ˆ W and XˆW are the rates of change in the world supply of Y and X where Y ˆ, Y ˆ * and X ˆ * are the rates of change in the supply of good Y and good. Yˆ, X good X in Country I and Country II. After appropriate substitution (see Appendix F),

(Yˆ

w

Lˆ * Y * /X *  *  Y * /X *  Y /X  ˆ  Py − Pˆx − Xˆ w = * + δ s   + ( − eE δ s ) w w Yw /X w  λ Yw /X w   Yw /X w 

)

(

) (2.20)

The change in the commodity price ratio is then given by the mutual interaction of demand and supply.

(Pˆ

yw

− Pˆxw

)

Y /X Lˆ * Yw /X w =−   Y * /X *  Y /X  λ  δ D + δ *S  + − δ ( e )   E S  Yw /X w   Yw /X w 

(2.21)

where  Y * /X *   Y /X  δ *S   > δ S eE    Yw /X w   Yw /X w  The terms of trade therefore move in Country I’s favor, and employment in Country I goes up. To show that welfare of the country of emigration will increase, I deﬁne the welfare of its residents as: V = U ( DY ,DX )

(2.22)

where V is the welfare and U is the concave function of the consumption of good Y and good X. Welfare, V, is maximized subject to: R = PDY + DX = PX + Y

(2.23)

where R is the real income of the people in the country of emigration in terms of good X. Dx and Dy stand for aggregate demand for good X and good Y. X and Y are the production of good X and good Y. Now by totally differentiating the above equation and through some manipulations, it is possible to determine the factors which can give rise to a change in V: dR = PdY − PdDY + (Y − DY )dP + dX − dDX = 0 because of complete specialization in good X.

(2.24)

32

Mobility with exogenously created unemployment dV = (Y − Dy )dP + dX = P (Y − Dy )Pˆ + dX

(2.25)

where dX > 0 and (Y – Dy) < 0. Substituting the value of Pˆ, we can see dV/dL* is positive.

Q.E.D.

However, under a similar type of production pattern, if the existing unemployment in Country I is not high enough to reduce its expected wage, we, below the expected wage of the other country, we*, labor migrates ˆ * < 0). The production transformation from Country II to Country I (i.e. L curve and the offer curve of Country II move inward. As a result, a new equilibrium will put Country I somewhere to the left of the starting equilibrium position along Zones 5 and 4. The price of the labor-intensive good rises (if L* < 0, Equation 2.21 says (Pˆ y w – Pˆxw) > 0),13 and there will be loss of employment and welfare (dV < 0 in Equation 2.25) in Country I.14 The expected wage difference would be wiped out gradually, and another long-run equilibrium is achieved via migration. Country II also suffers from loss of employment and output, and global unemployment therefore increases. But Country II will experience an improvement in the terms of trade after migration. If the trade equilibrium reached by the countries is such that this labor inﬂow cannot cause any change in the home country’s employment (i.e. when Country I is incompletely specialized and exporting the capitalintensive good, i.e. Zone 3 where terms of trade remains constant even after migration, and Country II is completely or incompletely specialized and exporting the labor-intensive good), the level of unemployment increases in the minimum-wage country, eventually eliminating expected wage differences, and long-run equilibrium is achieved. Here free-trade equilibrium is worse than autarky equilibrium. Free international mobility of labor does not improve the situation at all, and it reduces total world output and increases global unemployment. Proposition 2: Any migration from a non-minimum-wage country to a minimum-wage country when the minimum wage is ﬁxed in terms of the labor-intensive good and the minimum-wage country is completely specialized and exporting the capital-intensive good while the non-minimum-wage country is completely or incompletely specialized and exporting the laborintensive good, will move the terms of trade in the non-minimum-wage country’s favor. However, there will be loss of output and employment in both countries and the welfare of the country of immigration would go down. Proof: The proof of Proposition 1 can be repeated with changes in country subscripts to prove this proposition. These effects of labor inﬂow in this model are similar to the effects

Mobility with exogenously created unemployment 33 described by Brecher and Choudhri’s (1987) model where unemployment is introduced by an unemployment-beneﬁt package and migration is caused by actual wage differences. But compared to their model, the damages are more severe in this model because inﬂow of labor not only adds the migrants to the existing pool of unemployed workers, but also reduces the number of employed people. The rate of unemployment for the residents and the global unemployment rate rise. When we focus on the foreign country’s welfare, as it is observed with the ﬂow of capital in the presence of unemployment (Brecher 1989: 376–88), free ﬂow of labor has a positive impact regardless of the direction in which labor moves. But only when there is outﬂow of workers from the minimum-wage country, global welfare, output and employment go up as well. In the case of labor inﬂow, foreign welfare goes up and welfare in the home country goes down, worsening the home country’s relative position in the world. In that sense, as Brecher and Choudhri (1987) suggest, the optimum labor inﬂow in the presence of unemployment is zero. It should be noted that, unlike the analysis of policy-induced ﬂow of capital in the presence of unemployment (Brecher 1989) and the analysis of capital movement under full employment (Jones 1984), this chapter allows the movement of the factor that is already unemployed in the domestic market. In Jones’s (1984) model, the introduction of a tariff on the capital-intensive import commodity affects the home country’s welfare in two different ways: (1) following the small country effect of a tariff, it reduces the welfare of the home country; (2) as a secondary effect, when the foreign capital is attracted to the home country, a rise in the production of the capital-intensive import-competing good reduces the home country’s welfare further. In this chapter’s model, labor inﬂow reduces domestic welfare, but in a completely different way. Labor immigration here reduces the production of both the labor-intensive import-competing good and the export good. Production of the import-competing good falls more than that of the export commodity. The unemployment of residents, overall national unemployment and global unemployment go up. It provides a danger signal to the economy because the taxpayers will bear the burden of this labor inﬂow to face a reduction in their welfare. To summarize, in this chapter I have evaluated the effects of free international migration between two trading partners in the presence of unemployment in one of the countries when this unemployment results from a binding wage ﬂoor. The analysis departs from Brecher and Choudhri’s (1987) study of international migration with unemployment on two different issues. In this chapter’s model migration is caused not by the difference in the market wages but by the difference in the expected wages that depend on the market wages as well as the prevailing unemployment rates. In my model, depending on the level of unemployment, both immigration and outmigration are therefore feasible, when in Brecher and Choudhri’s (1987)

34

Mobility with exogenously created unemployment

model labor migration represents only inﬂow of labor. Furthermore, in Brecher and Choudhri’s analysis of migration, unemployment is introduced by offering an unemployment-beneﬁt package that provides a guaranteed minimum for everybody in the workforce. In this chapter, the use of a minimum-wage law (to describe unemployment) only provides a ﬁxed minimum for the employed workforce. This has important implications for labor migration in my model, that are not present in Brecher and Choudhri’s model. Since there is distortion in the labor market of one of these countries, free trade no longer acts as a substitute for free-migration in this model (i.e. trade cannot equalize the expected wages). So the consideration of migration along with trade becomes crucial to check if it can be used as an effective measure to deal with this type of distortion. As mentioned already in this chapter, in analyzing free international migration in the presence of unemployment, Brecher and Choudhri (1987) have focused only on immigration. Since, in this chapter’s model, migration in any direction is feasible, it is shown that free-labor mobility in the sense of labor outﬂow from the minimum-wage country reduces the severity of damage caused by the binding wage ﬂoor. It not only raises both the national output and employment in the minimum-wage country, but the foreign country also enjoys an increase in output, and employment and the world’s volume of trade go up. Does this conclusion do more than provoke the comment, ‘Anything could happen in a second-best situation?’ By way of answer, it can be said that, while the existence of commodity trade with distortion in the domestic factor market presents a realistic picture, free trade no longer remains superior to autarky. The standard rule for reducing the factor market distortion by trade policies (such as a trade tax or a trade subsidy) leads to the substitution of one distortion with the other (see Bhagwati and Ramaswami 1963) and, depending on the type of the policies, it involves a high cost on the part of the distortion-ridden country. Under the circumstances, instead of pursuing a regulatory policy (such as a trade tax or a trade subsidy), no restriction on migration will lead to equilibrium solutions better than the distortionridden equilibrium without migration.15 As regards the debate (relevant mostly for the developed countries) about choosing free-labor inﬂow over capital outﬂow, the analysis in this chapter conﬁrms the earlier reservation (Brecher and Choudhri 1987) that the optimum labor inﬂow in the presence of unemployment is zero. But in comparison to Brecher and Choudhri’s model, damages are shown to be much more severe in my model. This hints at a special type of social engineering when a factor that is already suffering from unemployment in the domestic market is allowed to move in. It not only raises the overall national level of unemployment, but also the unemployment rate for the non-migrants (i.e. residents of the country) as well as global unemployment. The total world output goes down. A binding minimum wage not

Mobility with exogenously created unemployment 35 only creates unemployment for resident workers, but by offering a temptation for the foreign workers it further intensiﬁes the problem and places a severe burden on the taxpayers of the country. This labor inﬂow unambiguously raises foreign welfare, while domestic welfare goes down. Compared to the rest of the world, the minimum-wage country therefore ﬁnds itself in a worse situation. In the analysis of international factor movements with full employment of factors of production, a policy induced capital inﬂow has been observed to reduce the welfare of the capital-importing country by increasing this country’s production of the imported commodity intensive in this factor. In this chapter’s model, labor inﬂow reduces the world production of the imported commodity intensive in this factor, and it also reduces the production of the exported commodity. The fall in production of the imported commodity is greater than the fall in production of the export good. This, in addition to increasing the unemployment level, turns the world’s terms of trade against the country with the wage ﬂoor. In the case of capital movement under full employment, factor inﬂow is harmful because it prevents the country from taking advantage of trade. In the case of labor migration in the presence of unemployment, free-factor inﬂow does not prohibit trade, but it reduces welfare by turning the terms of trade against the country.

3

International labor mobility with endogenously created unemployment

This chapter examines the implications of unemployment resulting from efﬁciency wages for international factor movements in a standard Heckscher–Ohlin model, where the relative size of the endowments of skilled and unskilled workers and the efﬁciency-wage induced unemployment level in the unskilled-labor market are simultaneously determined given the population, supply of capital and its distribution in the economy. Capital in the economy is used only to train individuals for the skilled-labor market, where workers are fully employed. It is shown that the optimum labor inﬂow in the market with domestic distortion and the optimum capital inﬂow are always positive because they reduce the severity of distortion by raising employment and income for the residents. The income and employment of foreigners also increase. Under this situation the optimum labor or capital outﬂow, on the other hand, is always zero. These conclusions directly contradict the result obtained for international factor movements in the presence of exogenously determined unemployment described in Chapter 2.

The existing literature on international factor movements in the presence of unemployment (Brecher and Choudhri 1987; Brecher 1989; Altonji and Card 1991; Hazari 1994; Basu 1995; Djajic 1995) deals with distortions that are exogenously introduced in the economy. This chapter analyzes international factor movements in the presence of unemployment when the distortion in the economy is endogenously introduced by using efﬁciency wages in one of its factor markets. The basic proposition of the efﬁciency-wage hypothesis (Shapiro and Stiglitz 1984; Yellen 1984; Katz 1986) is that, in the absence of perfect monitoring technology when workers tend to shirk, employers offer a wage higher than the market-clearing wage to induce non-shirking. In analyzing its implication for an open economy (Copeland 1989; Das 1989; Brecher 1992), some of the models use the resulting unemployment as a worker discipline device, while others use a shirking-free sector in the

Mobility with endogenously created unemployment 37 economy to absorb unemployed workers from the other sector and deal with a wage-gap distortion. It is interesting to note that, in the development of the efﬁciency-wage hypothesis, no distinction has yet been made between the skilled and the unskilled workers’ desire to shirk. The use of unemployment as a discipline device in the absence of perfect monitoring technology suggests that the skilled workers will have a higher rate of unemployment because their jobs are more difﬁcult to monitor. But the observed low rate of unemployment in the skilled workers’ market makes economists think about other aspects of the problem such as skilled workers’ commitment to work. For example, in justifying this low rate of unemployment in the skilled workers’ market, Akerlof and Yellen (1986) argue that ‘[i]n fact, it is usually thought that workers’ commitment to work varies positively with the skill requirements of their jobs . . .’ Thus, if workers who are more skilled, or jobs requiring more skill, are also associated with a reduced desire for shirking, efﬁciency-wage models might well predict the observed negative correlation between skill (or education) and unemployment.1 This line of argument ﬁts well with the notion that jobs requiring unskilled labor are usually dirty, dangerous and monotonous, whereas jobs requiring skilled labor are clean, safe, interesting and more rewarding (in the sense of having fun with innovation or invention). So there is less disutility of work effort and less desire for shirking in the skilled-workers’ market. This chapter focuses on an open economy with a dual labor market separated by the skill level of workers. Assuming that skilled workers do not shirk, the skilled-workers’ market is allowed to have full employment. Workers’ tendency to shirk in the unskilled-workers’ market, on the other hand, induces employers to offer efﬁciency wages in that market. The distortion in the form of this efﬁciency wage in the unskilled-workers’ market creates unemployment. Unlike other dual labor market models with efﬁciency wages, this unemployment in the shirking sector is not absorbed by the shirking-free sector of the economy and this affects the relative supply of skilled and unskilled workers in the economy. The economy starts with given endowments of labor and another special input. Each of the individuals can be trained for the skilled labor market. The cost of acquiring skill depends on the individual holdings of the special input. Individuals in the economy like goods. The disutility of work effort is job-speciﬁc in the sense that there is disutility of work effort in the unskilledlabor market, but there is no disutility of work effort in the skilled-labor market. It is shown how, given the initial factor endowments of labor and the special input, and given the distribution of this special input in the economy, the total supplies of skilled and unskilled workers are determined when there is a distortion in one of this economy’s factor markets. Two goods are produced in the economy using these two types of workers. Although the model maintains the Heckscher–Ohlin (H–O) structure and some of its characteristics, it is important to note that the pattern of production depends

38

Mobility with endogenously created unemployment

not only on initial factor endowments of labor and the special input but also on the distribution of this special input in the economy. Within this H–O structure, this chapter analyzes the effects of international factor movements in the presence of endogenously determined unemployment by investigating two questions: (1) Is the free ﬂow of factors in the presence of unemployment of workers at all desirable? (2) Is a policyinduced ﬂow of factors an option to reduce the distortion in the economy? In the analysis of labor ﬂows in this model, unlike the existing analysis of migration with unemployment, (1) migration is triggered by the expected wage differential that considers the market wage as well as the probability of employment, and (2) migrants and domestic workers face similar distortions in the unskilled-workers’ market, i.e. migrants are not allowed to work at a wage inﬁnitesimally less than the wage at which domestic workers are employed. The analysis of international factor movements in this model brings out the following conclusions: •

•

•

•

•

If the economy has different types of labor markets, it is necessary to evaluate the implication of the migration of each type of worker for an effective migration policy for this economy. In a small open economy the optimal inﬂow of workers into the market where workers are suffering from unemployment due to efﬁciency wages (as unskilled workers’ market in this model) is always positive since it raises employment, and output of the residents. The outﬂow of unemployed workers, on the other hand, is never desirable since it reduces the level of employment and income (for the nonmigrant unskilled workers) in the country. The inﬂow of workers only in the market with full employment does not have any economic consequences (Bhagwati and Rodriguez 1975) in the sense that each migrant enjoys his or her own marginal product, and the gross domestic income (i.e. the national income net of payments to migrants) of the host country remains unchanged. The outﬂow of workers from this market reduces the size of the national income from its pre-migration level although the income of the nonmigrant skilled workers remains unchanged. The best policy to induce a factor ﬂow for reducing the severity of distortion is to provide a capital subsidy that will raise employment and income of the country. In the debate over free-labor immigration versus direct foreign investment, this chapter suggests that the optimum capital outﬂow is always zero.

These effects of factor movements stand in sharp contrast with the effects of factor movements in the presence of exogenously determined unemployment (e.g. by a binding minimum wage) where (1) in an

Mobility with endogenously created unemployment 39 economy with homogeneous labor, the optimal labor inﬂow is always zero (Brecher and Choudhri 1987), and outﬂow of workers is desirable because it not only reduces the severity of distortion by reducing unemployment, but it can also generate full employment depending on the nature of specialization and trade (Basu 1995) and (2) in an economy where the labor market is separated by the skill level of workers, immigration raises unemployment of unskilled workers and reduces wages of employed skilled workers while the effect on welfare measured by total income of native workers remains ambiguous (Djajic 1995). Or the effect of outmigration of skilled workers on both the employment of unskilled workers and employment in general will depend on the factor intensities of commodities produced on the economy (Hazari 1994).2 Furthermore, the analysis of factor movements in this chapter opens up avenues to revisit Altonji and Card’s (1991) empirical investigation where labor immigration does not have any severe effects on less-skilled natives, although the effects may vary by sex and race groups. The effects of policy-induced capital inﬂow with the exogenously introduced distortion remain ambiguous (Brecher 1989), while the effects of policy-induced capital outﬂow are the same as they are in the present model.

3.1 Model H–O production structure with unemployment The country produces two goods, X and Y, under constant returns to scale using both skilled and unskilled labor (L1 and L2). The production conditions can be written as:

( ) Y = G(L , L ) X = F Lx1 , Lx2 Y 1

Y 2

(3.1) (3.2)

where L ji denotes Li worker going into the production of jth commodity, Li = L1 and L2 and j = X and Y. The competitive proﬁt conditions for the economy can be expressed as: C x (W1 , W2 ) = Px C x (W1 , W2 ) = PY The employment conditions in this economy are: C1x (W1 , W2 ) X + C1Y (W1 , W2 )Y = L1

(3.3)

C 2x (W1 , W2 ) X + C Y2 (W1 , W2 )Y = L2

(3.4)

40

Mobility with endogenously created unemployment

Where Wi is the wage of each worker in Li, Pj is the price of the commodity j and C ij denotes the partial derivative of C j with respect to Wi and shows the unit input coefﬁcient. L1 is the total number of skilled workers. L2 is the number of unskilled workers who are employed. There is perfect competition in both commodity and factor markets. This description will perfectly ﬁt the H–O framework except that in the unskilled-labor market, L2 = E2 – U2, where E2 is the total supply of unskilled workers and U2 is the number of unemployed workers in the unskilled-labor market. This unemployment results from a wage higher than the market-clearing wage in the unskilled-labor market. The above-equilibrium wage and the resulting unemployment are used to induce non-shirking in this market. The economy actually starts with N individuals and a special resource, K, which is the sum of individual holdings of this resource. We can identify this special input with capital in the broad sense of Kenen (1965) and Findlay and Kierzkowski (1983).3 This resource is used for training a part of the population that is willing to join the skilled labor market.4 The rest of the population comprises the unskilled labor force. Each individual likes to consume goods and each individual, I, in the economy has φi (= RKi/RK) share of this special input where R is the price at which K can be marketed. The individual cost of acquiring skill varies with φi, e.g. the higher is φi the lower will be the cost of training. The disutility of work effort is job speciﬁc, i.e. there is disutility from work effort in the unskilled-labor market but there is no dislike for work in the skilled-labor market. So there is no tendency for shirking in the skilled-workers’ market, but in the unskilled-workers’ market, workers tend to shirk. Each individual maximizes utility according to U (X, Y, e) where X and Y are the consumption goods and e denotes effort. U (X, Y, e) is a homothetic quasi-concave utility function. The corresponding indirect utility function is V (W, P, e), where W is the wage and P is the index for the prices. In order to determine the number of employed and unemployed workers in each of these markets, we need to look at workers’ effort decision (i.e. whether e = 0 or e > 0; this e summed over all the workers in the market gives total labor hours supplied) in each market and workers’ participation decision (i.e. whether to be in the skilled- or in the unskilledworkers’ market) for either of the markets. Workers’ effort decision in the unskilled- and skilled-labor market I follow Shapiro and Stiglitz (1984) to show workers’ effort decision in each market.5 Workers select an effort level to maximize their discounted utility stream. For simplicity we assume that the utility function is separable. The effort decision of individuals is such that they provide either e = 0 (shirking) or e > 0 (non-shirking), i.e. some ﬁxed positive amount.6 We assume that a worker contributes one unit of effective labor if the worker

Mobility with endogenously created unemployment 41 does not shirk; otherwise the worker contributes nothing. In the unskilledworkers’ market, if workers decide to shirk, then: rV 2s = ((W2 + φ i ) / P ) + ( b + q)(V u2 − V 2s )

(3.5)

where V 2s is the expected lifetime utility for a shirker in this market. W2 is the market wage for unskilled workers, b is a normal exogenous turnover rate of workers and r is the given market rate of interest.7 The probability of getting caught while shirking is exogenously given by q, and Vu2 is the expected lifetime utility if unemployed in the unskilled-labor market. Equation (3.5) implies that the return on asset in the unskilled-labor market, rV 2s, is equal to the ﬂow return (i.e. current utility) plus the expected capital loss. This loss occurs because workers enter into unemployment when there is normal turnover of workers and/or when workers are caught while shirking. If workers do not shirk, then: rV N2 = ((W2 + φ i )/P ) − e + b(V 2u − V N2 )

(3.6)

where VN2 is the expected lifetime utility for a non-shirker. If workers are unemployed, then the expected lifetime utility is: rV U2 = ((W2 + φ i )/P ) + a(V2 − V U2 )

(3.7)

where V2 is the expected utility of an employed worker (which is equal to VN2 in equilibrium), 苶 W2 is the unemployment beneﬁt (ﬁnanced by the ﬁrms at the minimum allowable level and available when workers lose their jobs; see Shapiro and Stiglitz 1984), VU2 is the expected lifetime utility of an unemployed worker and a is the probability of getting out of the pool of unemployed workers. If bL2 is the number of workers going into the unemployment pool and a (E2 – L2) is the number of workers getting out of the unemployment pool, then in the steady-state equilibrium a (E2 – L2) = bL2. So a = (bL2/E2 – L2). Workers will not shirk if rVN2 ≥ rV2s . By manipulating Equations (3.5), (3.6) and (3.7), the non-shirking condition (NSC) for the unskilled labor market can therefore be derived as: W2 /P = e + ((W2 + φ1 )/P ) + ( e/q)({ bE2 /( E2 − L2 )} + r ).8

(3.8)

This suggests that wages will have to be as least as great as the RHS of Equation (3.8) if employers do not want their workers to shirk. Let us suppose (W2/P)i = ωi is individual I’s non-shirking wage; i.e. the value of W2/P that equates two sides of Equation (3.8) for individual I. According to Equation (3.8), ωi will be positive and will vary across individuals due to the difference in φ i. Let us suppose ωi is a continuous random variable with density function f(ωi), which all ﬁrms are assumed to

42

Mobility with endogenously created unemployment

know. Since all ﬁrms will expect shirking when W2/P < W, the expected efﬁciency of a worker ﬁred by a ﬁrm will equal W2 / P

e=

∫

f (ω )d (ω ) = F (ω )

0

where F (0) = 0 by assumption. Assuming also that the f-function is single peaked, the distribution function F represents the familiar S-shaped relation between e and W2 /P. Since a portion q(1 – e) of total labor force employed will be ﬁred for shirking, L2 = (1 − q(1 − e ))E2

(3.9)

will be the net labor. Suppose e* is the expected efﬁciency of L2, so that e*L2 = eE2. Then from Equation (3.9), e* = e/[1 – q(1 – e)] where F *(W2/P) = F(·)/{1 – q[1 – F(·)]} and F * satisﬁes the property of F. With cost-minimizing ﬁrms, Equation (3.8) will be solved as an equality in equilibrium and ﬁrms will set W2/P to minimize W2/Pe* which is the wage per unit of effective labor. Given wages, this implies that NSC, will determine the equilibrium level of employment. For future use we rewrite Equation (3.8) as: W2 /P = e + (W2 + φ i )/P + ( e/q){[ bE2 /( E2 − L2 )] + r }

(3.10)

Wage being given by the commodity price, equilibrium in the unskilledlabor market determines the equilibrium level of employment L2. Any equilibrium in this market will have to be non-shirking equilibrium. Since, while non-shirking, a worker provides one unit of effective labor, NSC in Equation (3.8) gives economy’s total supply of unskilled workers at different wage levels, given b, q, r and an effort level, e > 0. The point with NSC = W2/P shows the equilibrium level of L2. In the skilled-workers’ market workers do not shirk. Employers do not need to use unemployment as a worker discipline device and equilibrium is determined where the marginal product of workers is equal to wages. Since, in the unskilled-workers’ market, workers dislike work and tend to shirk, there will always be unemployment in that market. From Equation (3.10) it is obvious that full employment is not consistent with nonshirking. In the skilled-workers’ market, on the other hand, there is always full employment. Workers’ participation decision in the unskilled- and skilled-labor market9 In this model, along with their effort decisions in each market, workers’ decisions about participation in each market need to be followed to deter-

Mobility with endogenously created unemployment 43 mine explicitly the level of employment and unemployment in each market. Each individual has the same homothetic preference pattern. The cost of acquiring skill Cs is also dependent on φi; thus Cs = Cs(φi), C′s < 0, Cs′′ > 0. The individual will decide to join that market which provides higher net discounted expected utility stream with a discount rate of r > 0, i.e. the individual will compare utility from the unskilled-labor market with that of the skilled-labor market. Workers are assumed to maximize expected lifetime utility: ⬀

(

)

V ′ = E[ ∫ V P t , Wi t , e t , φ ti , W t exp( − rt )d 0

where P t is the price level, W it is the wages, et is the disutility from work, φit is individual holding of special resource K and W t is the unemployment beneﬁt. The discounted expected utility stream for a participant in the unskilled-workers’ market is given by: rV'2 = {[(W2 + f )/P ] − e } + (1 − a)(Vu − V2 ) where a is the probability of getting a job, {[(W2 + φ)/P] – e} is the return if employed and (1 – a)(V u′ – V 2′) is the expected loss if unemployed.10 If unemployed, then rVu′ = (W 2 + φ)/P) + a (V 2′ – V′u). Using rVu˙ we can then write: V'2 = ({[(W2 + φ)/P ] − e ]}( r + a) + (1 − a)(W2 + φ)/p)/r ( r + 1) The discounted expected utility stream from the skilled-labor market is given by:  W1 φi  rV'1 =  − c( φ i ) +  P  P where c(φi) is the cost per period when C(φi) is distributed over the entire working period. An individual will be indifferent between these two markets when V′2 = V′1. So, given the distribution of the capital resource, and given wages, there will be an equilibrium level of φ, i.e. ~ φ for which V′2 = V′1. The total number of participants in the skilled-workers’ market is given by:   φ˜ L1 = N 1 − ∫ f ( φ)dφ  (3.11)   0 where 1 – ∫ 0φ˜ f(φ)dφ will give the proportion of total population willing to be in the skilled-workers’ market. The total number of workers in the unskilled-labor market is given by:

44

Mobility with endogenously created unemployment N − L1 = E2 , where E2 = L2 + U 2

(Equilibrium achieved by the effort decision in the unskilled-workers’ market, i.e. Equation (3.10) would determine L2 and U2.)11 The distortion in the factor market in this model originates from workers’ desire to shirk, which creates unemployment. This distortion then channels itself through the allocation of labor resources between the skilled and the unskilled-labor markets. For the dual-labor market in this model, actual wages show the difference in the skill level of workers, e.g. W1 = αW2 when, α > 1, but due to the distortion, the income difference expected by the workers considers more than the difference in the skill level of workers. Characteristics of the H–O structure The economy now has two types of labor, L1 and L2, to produce two commodities, X and Y, where X is the relatively skilled labor-intensive good. This framework resembles the H–O model. But unlike the H–O model, the pattern of trade will depend not only on the availability of factor endowments, N and K, but also on the distribution of K.12 More unequal distribution will result in a smaller number of skilled workers. If the supply of factor endowments is similar, then the country with a more equitable distribution of the special input will export the skilled labor-intensive good. Alternatively, the size of the endowment will be effective in determining the pattern of trade if the two countries have a similar distribution. Changes in commodity prices Assuming that the country is producing both goods, an increase in the commodity prices will affect actual wages in the same way as in the standard H–O model.13 The elasticity of output with respect to commodity price changes is different in this model compared to that in the H–O model because factor supply in this model responds to factor price changes resulting from commodity price changes.14 If the elasticity of relative supply (L1/L2) with respect to the ratio of the expected wages, W1e /W2e, is positive, this implies that, once trade opens up, if the country imports the unskilled labor-intensive good, it will ﬁnd it economically more meaningful to increase its imports and use the released resources for increasing the production of the good which is intensive in the skilled labor. This happens because as PX /PY goes up, the supply of skilled workers increases. Although any increase in the price of the skilled labor-intensive good will raise the proportion of skilled workers, the economy, because of its special input requirements, will resist any price

Mobility with endogenously created unemployment 45 change that might transform the entire labor force into a skilled-labor force.15 Changes in factor supply The effects of changes in K will have the usual Rybczynski effect in this model, in the sense that it will change the relative supply of the skilled workers. As K changes without any other changes in the economy, the equilibrium level of φ, i.e. ~ φ changes dφ˜

dL1

= −( φ˜ /K );

dK dE2 dK

< 0;

dL2 dK

dK

=

()

f φ˜ Nφ˜ dL1 φ˜ >0 = dφ˜ K K

<0

The production of skilled labor-intensive good will go up as K increases.16 A change in N, keeping the nature of distribution the same, on the other hand, will not change the relative supply of the unskilled and skilled workers. The absolute size of each labor market changes. But (L1/L2) remains unchanged.   φ L1 = N 1 − ∫ f ( φ)dφ    0 φ

dL1

= 1 − ∫ f ( φ ) dφ > 0

dN

0

E2 = N − L1 φ˜

= N ∫ f ( φ ) dφ 0

dE2 dN

φ˜

= ∫ f ( φ ) dφ > 0 0

 φ  φ˜ = N 1 − ∫ f ( φ)dφ  /N ∫ f ( φ)d( φ) E2  0  0 L1

Since E2 is dependent on N, differentiating Equation (3.12) we get

(

d L1 /E2 dN

) = 0.

(3.12)

46

Mobility with endogenously created unemployment

3.2 International factor mobility In analyzing international factor movements in the presence of endogenously determined unemployment I will focus on two issues: (1) whether free ﬂow of labor or free ﬂow of capital is at all desirable with this type of unemployment; (2) in the absence of free international factor mobility, how the policy-induced ﬂow of factors would eliminate or reduce distortion. While discussing factor movements I will also focus on how the analysis in each one of these cases differs from the analysis of factor movements with exogenously determined unemployment in the economy. Free-factor mobility Migration in this model is caused by the expected wage differences. I will ﬁrst focus on the situation when there is no international movement of capital or when migrants do not bring any capital with them. Labor migration without any capital movement I will denote L1m as the number of skilled migrants and E2m as the number of unskilled migrants. When international factor movements are allowed, there will be various possible scenarios. Let’s suppose that wages of the home country and the foreign country are such that E2m > 0 and L1m < 0. From the equilibrium condition (Equation 3.10) of the unskilled-labor market we see that any changes in E2 or total labor supply in the unskilled-labor market will create less disincentive for shirking for fear of unemployment and, as a result, at a given wage the economy will be able to supply more labor, i.e. NSC will shift downward. Thus from Equation (3.10) we can write:  A − eb  L2 = E2    A  where A = 0<

W2 q

∂L2 ∂E2

P

− eq − er −

(3.13) W2 q P

<1

or ∂U 2 ∂E2

= 1−

∂L2 ∂E2

>0

This implies that any increase in E2 or the size of the unskilled-labor market will increase the number of both employed and unemployed workers. Thus, when the unskilled immigrants join the pool of existing

Mobility with endogenously created unemployment 47 unemployed workers, they raise both employment and unemployment levels in the economy.17 If both foreign workers and domestic workers have the same probability of getting a job, then the rate of employment for domestic workers goes up as well.18 In Figure 3.1, the ﬁrst and the second quadrants show labor migration in the unskilled- and the skilled-labor market respectively when no capital movement is allowed. When, E2m(E2 E *2 ) > 0, in the unskilled-workers’ market, total employment increases by L2L*2 (caused by the shift of NSC to NSC*) and total unemployment increases from L2E2 to L*2 E *2 . Since the residents and the migrants have the equal chances of getting a job (L′2 or L2m = 1/2(L2L*2 )) the rate of employment for residents will go up.

Figure 3.1 Effects of migration efﬁciency wages.

48

Mobility with endogenously created unemployment

As a result of out-migration of skilled workers, i.e. when L1m(L1L*1) < 0, although total employment in the skilled-workers’ market goes down, the remaining residents do not lose anything. In Figure 3.1, SS shows a premigration supply curve for all the skilled workers and S′S′ is the premigration supply of non-migrant residents. According to Equation (3.13), both L2 and E2 rise as a result of an inﬂow of unskilled workers and thus levels of both employment and unemployment goes up in the unskilledlabor market. The steady-state unemployment rate for unskilled workers (who are now a part of total labor supply) remain unchanged, since L2 and E2 rise in the same proportion. But the unemployment rate for domestic unskilled workers who are now a part of the total labor force will go down. So, for the economy as a whole, although the steady-state unemployment rate does not change, labor movement under the circumstances reduces the unemployment rate for non-migrating residents. In order to ﬁnd out the effect on the national income, let’s deﬁne this country’s income as:19 I = PX X + PY Y

(3.14)

differentiating the production functions, and using the proﬁt-maximizing conditions, dI = W1 dL1X + W2 dLX2 + W1dLY1 + W2 dLY2 since dLi – dLXi + dLYi dI = W1dL1 + W2 dL2

(3.15)

where dL1 = L1m < 0 dL2 = L2′ + L2 m > 0 The emigration of skilled workers will result in the loss in national output and employment, although income and employment of resident skilled workers remain unchanged. Since a domestic, unemployed unskilled worker has the equal chance of getting a job as an unskilled migrant, the addition to the unskilled labor employment following immigration of unskilled workers will come from migrants as well as from domestic unemployed workers where L 2′ shows the newly employed domestic unskilled workers and L2m is the portion of unskilled migrants who are employed. Furthermore, although unemployment of domestic workers goes down, ﬁrms in the unskilled-labor market will have to provide unemployment beneﬁt for unemployed immigrants (U 2′ ). Then: dI = W1L1′m + W2 L2′ + W2 L2 m + W2U 2′

Mobility with endogenously created unemployment 49 It is obvious that gross domestic income (gross national income net of payments to the migrants) will go up if W2L 2′ > W1L1m + 苶 W2U′2. In other words, the loss in national income resulting from the emigration of skilled workers can be offset if there is a large volume of immigration of unskilled workers. With regard to the effect on a country’s income, whether freelabor ﬂow is desirable under the scenario will depend on the volume of out-migration and immigration as well as the wage gap in the economy. This happens because out-migration of skilled workers will reduce domestic output while immigration of unskilled workers will have the opposite effect. The income and employment of the residents will go up. Since a portion of migrants will be employed, foreigners’ income will go up as well. So labor inﬂow is beneﬁcial for this country and desirable for the world economy. Under the alternative scenario when the expected wage of unskilled workers is less than that of the rest of the world, dE2 < 0, and let us suppose that wages of the skilled workers result in dL1 > 0. When unemployed workers move out, the non-shirking condition in the unskilledlabor’s market suggests that the labor supply curve will move upward. At a given wage the equilibrium level of employment will therefore go down. Since 0 < (dL2/dE2) < 1, i.e. the number of out-migrants exceeds the number of unskilled workers who lose their jobs, the level of unemployment will go down. However, total employment and gross domestic income (following Equation 3.15) will go down as well. So this type of labor outﬂow is not desirable for the economy. This is shown again in the ﬁrst two quadrants of Figure 3.1. When E2m(E2E 2**) < 0 and L1m(L1L** 1 ) > 0, in the unskilled-labor market, employment goes down from L2 to L2** and unemployment changes from L2E2 to L2**E 2**. In the skilled-workers’ market, employment increases from L1 to L** 1 . In comparing this analysis of factor movements with the similar analysis in the case of exogenously determined (by a minimum wage) unemployment, it is important to remember that, in the case of exogenously determined unemployment in an economy with homogeneous labor, it is possible to attain full employment with a binding minimum wage if there is complete specialization in the commodity which is different from the commodity in terms of which minimum wage has been ﬁxed (Basu 1995). In the present model, full employment is not at all desirable since it is inconsistent with non-shirking in the unskilled-labor market. Keeping this in mind, we can say that, in the case of exogenously determined unemployment in the economy (Brecher and Choudhri 1987; Basu 1995), free-labor inﬂow is never desirable but free outﬂow can sometimes raise the national level of employment as well as global employment and output. It is even feasible to achieve full employment. Furthermore, in the case where the labor market is separated by the skill level of workers, both labor inﬂow (of unskilled workers) and labor outﬂow (of skilled workers) are

50

Mobility with endogenously created unemployment

considered to be undesirable (Hazari 1994; Djajic 1995) when distortion is exogenously introduced in the economy. In the case of endogenously determined unemployment, free-labor inﬂow is always desirable and the optimum labor outﬂow is zero. The choice of migration policy in the presence of unemployment will therefore depend on whether unemployment is exogenously or endogenously determined in the economy. Labor migration when migrants are allowed to bring their capital I now allow migrants to bring their capital with them. Under the ﬁrst scenario (L1m < 0, E2m > 0) migrants will use a portion of their capital to pay migration-tax or a fee for immigrating to this country. This will raise the capital supply of the host country. This increased capital supply will have relevant effects on the economy if it alters the utility of the marginally skilled resident workers. For a marginally skilled worker it will mean a change of working status because dφ˜ dK dL1 dK

( )

= − φ/K =

()

f φ˜ φ˜ N dL1 φ˜ . + >0 dφ˜ K K

If the extra capital which came with the migrants allows more workers to enter the skilled-workers’ market, and if the unskilled unemployed domestic workers and unskilled migrants have an equal chance of being trained for the skilled-labor market (i.e. there is no discrimination between migrants and non-migrants and this additional capital can be made available for anybody who wants to be trained for the skilled-labor market), then dL˜ 1 = L1m + E2′ m + E2′ ˜ 1 denotes the change in the supply of skilled workers after immiwhere dL grants have moved in with their capital resources. Since, L1m < 0, the new supply of skilled workers is now comprised of a portion of domestic unskilled workers who now can enter the skilled-labor market, E 2′ , and a part of unskilled immigrants who will be eligible to enter the skilled-labor force, E 2m ′ , less the number of emigrants from the skilledlabor market. In this case, if E2m > E′2m + E′2 then dE2 > 0 and, therefore, (using Equation 3.12), where dL2 can again be described as: dL2 = L2′ + L2 m

Mobility with endogenously created unemployment 51 L′2 = newly employed domestic unskilled workers, L2m = portion of unskilled migrants who are employed. From Equation (3.15):

(

)

(

)

dI = W1 L1m + E2′ m + E2′ + W2 L2′ + L2 m + W2U 2′ Therefore the change in the domestic income can be described as W1E′2 + W2U′2. So if W1E′2 + W2L′2 > W1L1m + W 苶2U′2, the domestic W2L′2 + W1L1m – 苶 income will go up.20 The third and fourth quadrants of Figure 3.1 show the effects of labor migration when migrants are allowed to bring their capital with them. When E2m > 0, and L1m < 0 in the fourth quadrant we see that, although E2E *2 migrants move in, only a part of that, E2Ek, will add to the existing unemployment pool because another part will go to the skilled-labor market. The increase in the level of total employment (L2L2k versus L2L*2) as well as the employment of resident workers (L′2k versus L 2′ ) in the unskilled-workers’ market under the situation will be less than when migrants cannot bring their capital with them. But the level of employment will go up in the skilled-workers’ market from L*1 to L1k. In spite of out-migration of skilled workers, the ratio of employed skilled to unskilled workers for the country as a whole, as well as for the residents, may go up depending on how much additional capital can be used for training additional skilled workers. If E2m = E′2m + E′2, dL2 = 0; but the change in gross domestic income will still be positive, if W1E 2′ – W1L1m > 0. If E2m – E′2m < E′2, dE2 < 0, and dL2 < 0. Since (dL2/dE2 < 1), dL2 < E′2, W2 < W1, and W2dL2 < W1E′2. If W1E′2 – W2dL2 > W1L1m + 苶 W2U′2 then dI > 0. If E2m > 0 and L1m > 0, migration tax or a migration fee on the immigrants to the skilled-labor market will allow some unskilled workers to move to the skilled market. This labor movement to the skilled-labor market (say E′2), in addition to unskilled-labor emigration (E2m < 0), will intensify the effects in the unskilled-labor market that follow when, under the same scenario, migration is allowed without capital movement. However, since one part of the existing unskilled workers is now in the skilled-labor market, it is possible for domestic income to go up depending on the volume of immigration and out-migration, the wage gap and the extra capital that have been generated from this labor ﬂow. For example, newly trained, skilled workers, say E′2, will be earning W1 in the skilledlabor market, and suppose L 2′ workers lost their jobs in the unskilled-labor market because of the labor outﬂow, then domestic income will go up if W1E′2 – W2L 2′ > 0. The conclusions will remain the same if an emigration tax were allowed.21

52

Mobility with endogenously created unemployment

Capital inﬂow without labor migration Let’s now consider free ﬂow of capital when there is no labor migration. If the rate of return of capital is higher in the home country, free-factor mobility will result in inﬂow of capital until returns on capital in these two countries are equalized. If, for the marginally skilled worker, the cost of training c(~ φ) goes down because inﬂow of capital makes capital less expensive, the ratio of skilled to unskilled workers will go up. The outﬂow of capital will on the other hand reduce the ratio of skilled to unskilled workers (see Calvo and Wellisz 1983 and Minabe 1974 for analyses of international capital movement in a different context). Policy induced ﬂow of factors Since the country is already suffering from unemployment, luring labor directly is not politically desirable. Any capital outﬂow is going to reduce the supply of skilled labor more than the increase in the supply of employed unskilled workers (since dL2/dE2 < 1). It will therefore reduce employment and income of the country. The only option the country can use is to have a policy-induced inﬂow of capital. The trade policy cannot be used for inducing capital inﬂow because capital does not enter the production directly. To induce capital inﬂow when a capital subsidy is offered, r * = r + δ where r * is the return received by the foreign capital in this country, δ is the subsidy and r is the return received by the domestic capital. The effect of this subsidy will be similar to the situation when free inﬂow of capital is allowed except that an additional payment of δ∆K will ~ have to be made for this subsidy. Suppose ∂L1 = L 1′ is the addition to the skilled-labor force. Increased participation in the skilled-labor market will imply that W1L 1′ – W2L 2′′ – r *(∆k) > 0, where ∆k is the capital used for training L 1′ workers, and L 2′′ is the total number of unskilled workers who became unemployed as a result of the movement of L 1′ workers to the skilled-labor market. National income and employment deﬁnitely increase and the proportion of skilled to unskilled labor goes up. In the case of policy induced capital ﬂow with exogenously determined unemployment, welfare consequences for capital inﬂow are ambiguous. The consequences of capital outﬂow with exogenously determined unemployment conﬁrm the conclusions of this chapter. This chapter focuses on the labor market distortion caused by efﬁciency wages, adapts that to a model of dual labor markets separated by the level of skill of workers and analyzes how effects of international factor movements in a small, two-goods, two-factors H–O world with unemployment endogenously determined by this efﬁciency wage will vary accordingly.22 The dual labor market in this chapter is different from dual markets used

Mobility with endogenously created unemployment 53 in other analyses of efﬁciency wages (Bulow and Summers 1986; Jones 1987; Copeland 1989) because the shirking-free sector in this model does not absorb unemployed workers from the shirking sector. As a result, the domestic distortion unfolds itself in two different ways: (1) it creates unemployment for the shirking sector as well as for the entire economy and, (2) by inﬂuencing the expected wage differential it affects the equilibrium labor-force participation in the skilled- and unskilledworkers’ market. Unlike the existing analysis of open economy models with exogenously determined unemployment, it is not feasible for this economy to attain full employment. In that perspective, the analysis of the debate of free-labor inﬂow versus direct foreign investment in this model suggests that the optimum labor inﬂow in the market with unemployment is always positive because it reduces the severity of distortion by raising national income and employment. The income and employment of foreigners go up as well. Capital outﬂow, on the other hand, is never desirable for the economy with endogenously determined unemployment. These conclusions directly contradict the results obtained from the existing analysis of international factor movements with exogenously determined unemployment where the optimum labor inﬂow is always (with or without homogenous labor) zero. Unlike in the economy with homogenous labor and exogenously determined distortion, where labor outﬂow not only lowers unemployment but can also generate full employment depending on the nature of specialization and trade, labor outﬂow in this model always leads to lower output and employment. Interestingly, however, the output and employment effects of labor emigration of unskilled workers in this model resemble that of skilled-labor emigration in an economy with exogenously determined unemployment and a labor market segregated by the skill level of workers (Hazari 1996). As regards the policy induced ﬂow of factors, the best option for this economy is to provide a capital subsidy which will raise output and employment in the economy while the effects of policy induced capital inﬂow remain ambiguous for an economy with exogenously determined unemployment. Thus, the analysis in this chapter suggests that, for an economy with a distortion in its factor market, the migration policy and/or the policy inducing capital ﬂows will depend on whether the distortion is endogenously or exogenously introduced.

4

Free trade versus free-labor mobility with increasing returns and unemployment

After examining how labor mobility across national boundaries in the presence of endogenously created unemployment (Chapter 3) can have implications different from that with exogenously created unemployment (Chapter 2), I extend the boundary of our analysis by adding non-constant returns to scale technology to production. I focus on increasing returns to scale. Increasing returns to scale can happen either due to an increase in the production by the ﬁrm (internal economies of scale) or due to the increase in the size of the industry when economies of scale are deﬁned to be external to the ﬁrm. This chapter compares free trade in goods with free-labor mobility in the presence of unemployment and increasing returns to scale production technology. Unemployment here is introduced using the efﬁciencywage hypothesis. It is shown that, with internal economies of scale, it is possible to develop reasonable conditions where free trade in goods ceases to be a substitute for free international labor mobility in the sense that free trade and free-labor mobility will not have similar effects on employment and output. Under the scenario, free trade in goods becomes a more desirable policy objective. With external economies of scale on the other hand, they can be substitutes.

Trade theorists have always been very interested in the comparison between free trade in goods and free ﬂow of factors. Their research has helped us to look at the comparison from different angles.1 For example, in examining whether free trade can be a substitute for free-factor mobility, these studies differ in deﬁning the terms ‘substitutes’ and ‘compliments’ and their analyses vary accordingly. They also have shown how results will vary if traditional Heckscher–Ohlin assumptions are removed by incorporating the difference in technology and/or difference in preferences. But most of these studies assume full employment and constant returns to scale technology.2

Free trade versus free-labor mobility 55 Changes in the nature of international trade and global economic condition have long reminded us to move beyond full employment and constant returns to scale technology assumptions of traditional trade theory. This chapter compares trade in goods with factor mobility in the presence of unemployment and economies of scale and thus brings us closer to the real world. The factor mobility here refers to labor mobility or migration among nations. Unemployment in this chapter is related to efﬁciency wages. Furthermore, since economies of scale can be both internal and external, the chapter compares free trade with free-labor mobility in each situation separately. I deﬁne trade in goods and trade in labor to be substitutes if each of them has similar effects on world employment and output without the other. The analysis of the comparison in this chapter suggests that: 1.

2.

3.

4.

with unemployment endogenously created by efﬁciency wages and internal economies of scale, free trade in goods and free-labor mobility cannot be substitutes in terms of their effects on global employment and output. Free trade in goods creates a favorable employment and output effect that cannot be achieved with free-labor mobility alone. however, if economies of scale are external in nature, they can be substitutes in generating favorable output and employment effects under very reasonable conditions. Thus, under external economies of scale, free-labor mobility is not inferior to free trade in goods. because of a special type of imperfectly competitive market structure, free trade in the presence of internal economies of scale generates a ‘love of variety’ effect for the consumers that cannot be obtained with free-labor mobility under a similar situation. Furthermore, external economies of scale will never have such effects, irrespective of whether trade is in goods or in factors. but under external economies of scale, free-factor mobility will have favorable output and employment effects which are not possible with free migration under internal economies of scale.

4.1 Internal economies and unemployment As already mentioned, in this chapter unemployment exists because of efﬁciency wages. Also, since economies of scale in this section are internal in nature, the market structure cannot be perfectly competitive. Thus in this section we use a model of monopolistic competition developed by Dixit and Stiglitz (1977) and adapt it to a model of efﬁciency wages (Shapiro and Stiglitz 1984).3

56

Free trade versus free-labor mobility

Producers and consumer There are two industries in the economy, each producing a large number of products – each of which enter symmetrically into demand; the industries themselves also play symmetric roles. All individuals in the economy will have the same utility function:  n1 θ  V = 1 n  ∑ C1 i   i =1 

1 /θ

 n2 θ  + 1 n ∑ C 2 j   j =1 

1 /θ

− e0

(4.1)

where C1i represents the consumption of ith variety of industry 1, C2 j represents the consumption of the jth variety of industry 2 and e0 represents the disutility of work effort. Thus consumers’ utility increases as variety increases, because consumers love variety. For simplicity, I assume that an individual either supplies work effort, in which case e0 is positive, or does not supply work effort, in which case e0 is zero. Two factors of production available in this economy are type I labor and type II labor, each of which is fully speciﬁc to an industry. I deﬁne l1,i as the amount of type I labor used to produce χ1,i of variety i of the ﬁrst industry product and l2,j as the amount of type II labor used to produce χ2,j of variety j of the second industry product, i = 1 . . . . n1, and j = 1 . . . . n2, l1i = α + βχ1i l 2 j = α + βχ 2 j

(4.2)

α, β > 0 The total cost of producing a variety, therefore, is obtained by multiplying each ﬁxed cost and each marginal cost by its corresponding wage (w1 or w2). I assume that average cost declines but at a diminishing rate. Because of the special nature of demand, there will not be any strategic interdependence among ﬁrms. If the number of the goods (varieties) is very large, then the price of one variety will have negligible effect on the demand for other goods. So each ﬁrm can ignore the effect of its actions on other ﬁrms’ behavior and thus indeterminancy of oligopoly is ruled out. Also, no ﬁrm will produce the exact same variety in equilibrium because of the special nature of demand and the existence of ﬁxed costs of production. The production of goods, therefore, is characterized by increasing returns to scale in a monopolistically competitive market. n1

∑l i =1 n2

1i

= L1 = n1l1i =

L1 α + βχ1i

∑ l 2 j = L2 = n2 l 2 j = j =1

L2 α + βχ 2 j

(4.3)

Free trade versus free-labor mobility 57 where Li = number of type i employed workers i = 1, 2, ni = number of ﬁrms or variety in each industry, i = 1, 2. Each producer is small relative to the market and therefore the elasticity of demand in each case is given by 1/1 − θ. Proﬁt maximization in the production shows P1 =

β θ

w1 and P2 =

β θ

w2

(4.4)

where w1 and w2 are the wage rates of the two types of workers and P1 and P2 are the product prices of the two industries.4 Because of the symmetry of the set up, prices of all the varieties in each industry will be the same in equilibrium. Finally, the absence of entry barriers drives proﬁts to zero. This zero proﬁt condition shows

( ) = (α + βχ )w

P1 χ1i = α + βχ1i w1 P2 χ 2 j

2j

2

(4.5)

This allows us to express the size of each ﬁrm as:  θ χ1 =   θ/(1 − θ) = χ 2  β

(4.6)

We now see that the size of the ﬁrm and the real wage do not depend on the employment level (Equations 4.4 and 4.6), but the number of ﬁrms is positively related with the level of employment (Equation 4.3). The utility function can now be written as:   w  1−θ    w  1−θ  V = 1n  k  n1 θ  + 1n  k  n2 θ  − e0   2 P2     2 P1  

(4.7)

where k = 1 or 2. The fact that the number of ﬁrms increases in employment implies that worker utility is also increasing in employment. This follows the ‘love of variety’ assumption in our utility function. The labor market In the labor market for type I workers, it is assumed that work effort generates disutility. It is a type of market where workers cannot be perfectly monitored, and thus they will tend to shirk. Employers therefore offer wages higher than the equilibrium wage to deter shirking and dismiss workers caught shirking. This results in non-shirking equilibrium with higher wages and unemployment. The fear of losing high wages and the possibility of being unemployed keep the workers from shirking. This is the efﬁciency-wage model as posited by Shapiro and Stiglitz (1984).

58

Free trade versus free-labor mobility

Workers select an effort level to maximize their discounted utility stream. The effort decision of individuals is such that they provide either e = 0 (shirking) or e > 0 (non-shirking) or a ﬁxed positive amount.5 I assume that a worker contributes one unit of effective labor if the worker does not shirk. Otherwise the worker contributes nothing. In the type I labor market if workers decide to shirk then:   w  1−θ    w  1−θ  rV 1s = 1n  1  n1 θ  + 1n   1  n2 θ  + ( b + q)(V 1u − V 1s )   2 P1     2 P2  

(4.8)

where V1s is the expected lifetime utility for a shirker in this market. Let b > 0 denote a normal exogenous turnover rate, r is the given market rate of interest, and q is the probability of being caught if shirking.6 Vu1 is the expected lifetime utility if unemployed in the type I labor market. Equation (4.8) implies that the return on asset in the type I labor market of a worker who shirks, rV1s, is equal to the ﬂow return (i.e. current utility) plus the expected capital loss. This capital loss occurs because workers enter into unemployment when there is normal turnover of workers and/or when workers are caught while shirking. If workers do not shirk, then:   w  1−θ    w  1−θ  rV 1n = 1n   1  n1 θ  + 1n   1  n2 θ  − e0 + b(V u1 − V 1n )   2 P2     2 P1  

(4.9)

where V1n is the expected lifetime utility for a non-shirker. If workers are unemployed, then the expected lifetime utility is: rV 1u = a(V 1n − V 1u )

(4.10)

where a is the probability of getting out of the pool of unemployed workers. Workers will not shirk if V1n ≥ V1s . Using the above three equations, the no-shirking condition (NSC) for type I workers can be written as:7   w  1−θ    w  1−θ  ( r + b + a) 1n   1  n1 θ  + 1n   1  n2 θ  − e0 ≥ e0 q   2 P1     2 P2  

(4.11)

If the inequality in Equation (4.11) holds, then more firms will enter into the production process, creating employment for more workers who are committed to provide the required work effort. If Equation (4.11) does not hold, workers shirk, and their firms will have negative profits and quit. So ultimately Equation (4.11) will be strictly binding in equilibrium. In steady-state equilibrium, the job-acquisition rate, a, is determined by equating the flows into and out of the unemployment pool. If E1 represents the total labor force, then there are E1 – bL1 unemployed; therefore:

Free trade versus free-labor mobility 59 a=

bn1l1i

(4.12)

E1 − n1l1i

In equilibrium, Equation (4.11) can be written as:   w  1−θ    w  1−θ  e r b  E1  1n   1  n1 θ  + 1n   1  n2 θ  = e0 + 0 +   e0 q q  E1 − L1    2 P1     2 P2  

(4.13)

For future reference, from Equation (4.13) we derive:  A − e0 b  L1 = E1    A  where:    w  1−θ    w  1−θ   A =  1n   1  n1 θ  + 1n   1  n2 θ   q − e0 q − e0 r .    2 P1     2 P2     Therefore: 0<

∂L1 ∂E1

<1

or ∂U1 ∂E1

= 1−

∂L1 ∂E1

>0

where U1 is the number of unemployed in the type I labor market. Furthermore, note that unemployed workers ﬁnd employment according to poisson process, so that the expected duration of a spell of unemployment, d, is given by 1/a. Using u as the unemployment rate, it follows that: d=

u b(1 − u)

.

The type II labor market will have full employment with wage w2. Equilibrium There will always be full employment equilibrium in the labor market of type II workers. In the type I labor market (given a ﬁxed labor force), the job acquisition rate is increasing in employment. Therefore, the minimum

60

Free trade versus free-labor mobility

Figure 4.1 Equilibrium for type I labor market.

utility that a ﬁrm must offer to a worker in order to deter shirking increases as employment increases in this market (Equation (4.11)). Equation (4.7) suggests that actual worker utility also increases as employment increases. Therefore, both sides of Equation (4.13) are monotonically increasing functions of employment. In Figure 4.1, the left-hand side of Equation (4.13) is depicted by the curve GG and the right-hand side is depicted by the curve LL. The curve GG is concave in L1 (θ denotes elasticity of substitution and, in monopolistically competitive market, it is high). As drawn, there are two points of intersection; but if GG > LL, then more ﬁrms will enter and the right-hand side will grow at a higher rate until equilibrium is achieved at both higher utility and higher employment levels. If LL > GG, ﬁrms will exit and equilibrium will ﬁnally be achieved. The higher employment equilibrium is thus the stable equilibrium. Therefore, the economy in equilibrium will enjoy full employment in a type II labor market and, although in a type I labor market there will always be unemployment, the equilibrium level of employment is the highest level that can be sustained with no shirking of the workers. Trade in goods Let’s suppose that the goods are tradable and there is a foreign country. The foreign country is exactly like the home country except for the relative size of the endowment. The variables of the foreign country are denoted by an asterisk. Let us suppose that the home country is relatively abundant in type II workers and the foreign country is the mirror image of the home country. This implies that (E1/E2) < (E1/E 2)*, and E1 = E *2, E2 = E *1.

Free trade versus free-labor mobility 61 Due to unemployment induced by efﬁciency wages L1 < E1, L*1 < E *1 and L1 < L*1, when E1 and E *1 are the actual numbers of type I workers in the home and in the foreign country respectively and L1 and L*1 are the numbers of employed type I workers in these two countries. With trade, the condition necessary to deter shirking in type I labor market in the home country becomes: 1−θ  1−θ   w    w1  e0 r b  E1  * θ * θ 1 n  +   ( n1 + n1 )  + 1n    ( n2 + n2 )  = e0 +  e0 q q  E1 − L1    2 P1     2 P2  

or 1−θ    w  1−θ   w  e r b  E1  1 n  1  N 1 θ  + 1 n   1  N 2 θ  = e0 + 0 +   e0 q q  E1 − L1    2 P2     2 P1  

(4.14)

where n1 + n*1 = N1 and n2 + n*2 = N2. The left-hand side of Equation (4.14) is increasing in N1 and N2. In Figure 4.1, the GG curve shifts upward as N1 and N2 increase, increasing the equilibrium value of n1 and L1. This, in turn, increases n*1 and L*1. Thus, trade increases employment in one country that, in turn, increases employment in the other country. The minimum utility that a type I worker should get in each country will be equalized (at P′ and Q′ in Figure 4.2). In the type II market, workers enjoy higher utility because they can have more varieties, but since there is full employment, no employment effect is observed. Trade in factors as an alternative If this free intra-industry trade is not allowed, then there will be free-ﬂow factors. We know that ( E1 /E2 ) < ( E1 /E2 )* ,

E2 L*1

>

E2* L1

, E2 = L2 and E2* = L*2

Proﬁt income is zero and increases in the wages are spent equally on two goods, i.e. w1l1n1 = w2l2n2. So the ratio of wages of two types of workers in each country is equal to the reciprocal of the ratio of the corresponding number of employed workers, i.e. (w1 /w2 ) = ( L2 /L1 ) and (w1* /w2* ) = ( L*2 /L*1 ). Thus,

w1 w2

>

w1* w2*

and type I workers from the foreign country will move into the home country and type II workers will move out of the home country to the foreign country. Unlike the trade in goods, trade in factors will shift both

62

Free trade versus free-labor mobility

Figure 4.2 Efﬁciency wage and effects of migration in comparison with effects of trade in goods.

LL and GG curves. In the home country, immigration of type I workers will shift the LL curve downward. Following migration, because of the relative size of the labor markets and the efﬁciency-wage distortion in the type I labor market, the decline in E2 (thus L2) is higher than the increase in L1.8 Any increase in L1 will raise n1, and decline in E2 will reduce n2. Since the decline in E2 is larger than the increase in L1, the decrease in n2 will be higher than the increase in n1. As a result, the left-hand side of Equation (4.13) will go down and GG will shift downward. In the foreign country, the decline in L*1 is less than the rise in E *2. So G*G* shifts upward

Free trade versus free-labor mobility 63 and utility for type I workers rise. This is shown in the south-east quadrant of Figure 4.2. Before type I workers start moving, equilibria in the home and in the foreign country are at Q and P. The NSC and NSC* in the south-west quadrant show the respective non-shirking constraints in each of these countries. As international migration starts, LL moves to LmLm and L*L* moves to Lm* Lm* . The GG and G*G* curves move to GmGm and Gm*Gm* respectively. The NSCs also change in each of the countries. Since 0 < (∂L1/∂E1) < 1, the new equilibrium is reached at utility level where employment and output of type I workers in the foreign country has gone down (L1 m* ) and that in the home country has gone up (L1m). The scenario for type II workers will show the standard factor price equalization under full employment. The utility level of type I (and also of type II) workers will go down in the home country. The foreign county will experience the exact opposite movement. (The increase in world utility resulting from increased variety cannot be realized in the case of free factor mobility as it can be achieved under free-trade.) The labor movement will continue until the utility levels obtained by workers in both countries are equalized. Notice that free trade in goods is able to generate favorable employment effects in both countries. But free-labor mobility in the absence of free trade increases employment of type I workers in one country (home country) and reduces their employment in the other country (foreign country). It is obvious that movement of factors instead of free intraindustry trade will not be able to generate a favorable employment effect globally for type I workers. There will always be full employment in type II workers’ market. Because of the difference in the size of the labor markets, under free labor mobility total employment in the home country will go down, even though employment of type I workers increases. Total employment will go up in the foreign country even though type I workers suffer from unemployment. We thus see that, under internal economies of scale and unemployment created endogenously with efﬁciency wages, free trade in goods and freefactor mobility cannot be substitutes in terms of their effects on global output and employment. It deviates from the conclusion that Krugman derived with internal economies of scale and full employment. Under this scenario, the argument for having free trade becomes more forceful not only because of its favorable employment and output effects, but there is also no other alternative that can achieve the same result. Furthermore, if we want to compare distributional effects of free trade with that of free-factor mobility, we can focus on gains or losses of utility of each type of worker. Following Krugman (1981), it is obvious that, under free-factor mobility, both types of workers in the home country will be worse off relative to the free trade situation. Even though factor returns are equalized, there is no gain from additional variety as it is under free trade. It happens because, while n1 goes up, n2 goes down and n2 > n1.

64

Free trade versus free-labor mobility

Workers in the foreign country will enjoy an increase in utility because of increased variety. Under free trade, though, workers in both countries will enjoy an increase in utility. In order to focus on the question about country size, we can look at the situation when relative factor proportions in the countries, E1/E2 and E1*/E2*, remain the same as before where each country is relatively abundant in different types of workers. The only difference is that the size of the home country’s total labor force is bigger than that of the foreign country, i.e. E1 + E2 > E *1 + E *2 . In that case, free trade in goods without free-factor mobility will increase global welfare (see Equation (4.14)) because of the love of variety assumption, and the nature of global equilibrium under free-factor mobility without free trade in goods will remain the same. But the disparities between the countries as far as the level of employment is concerned will grow further. In the case when each country is of the same size, total employment in the home country decreases (the decline in L2 affects the increase in L1) and that in the foreign country increases. When the home country is bigger, in the sense that E1 and E2 are greater than E *1 and E *2 , change in the employment level follows the same direction but the increase in the foreign country may be much higher in this case (because they don’t lose much of E *1 and get a bigger boost in E *2 ).

4.2 External economies and unemployment Under the scenario, the commodity market is somewhat different from that in the previous section in the sense that one of the two commodities produced in the country enjoys external economies of scale. This implies that, unlike in the case with internal economies of scale, we will be able to use the perfectly competitive structure in the commodity market. There is still distortion in the factor market because one of the labor markets suffers from unemployment created endogenously by a non-shirking wage. Commodity market There are two industries producing two goods, χ1 and χ2.9 As in the previous section, χ1 uses type I labor and χ2 uses type II labor in its production. The production function is given by L11 χ1 = L1 L22 χ 2 = L2 where L1 and L2 are the total amount of labor employed in each of the labor markets, Lij, i, j = 1,2 is the unit of type i labor needed to produce one unit of the j good. The sector producing χ1 enjoyed increasing returns

Free trade versus free-labor mobility 65 to scale (IRS) of the external type (see Mayer 1974). The χ2 sector enjoys constant returns to scale (CRS).10 Labor market11 As described in the previous section, in a type I labor market, work effort generates disutility. Since workers cannot be perfectly monitored, they will tend to shirk. Employers therefore offer wages higher than the equilibrium wage to deter shirking and dismiss workers caught shirking. This will result in non-shirking equilibrium with higher wages and unemployment. The fear of losing high wages and being unemployed will keep the workers from shirking. This is the efﬁciency-wage model as posited by Shapiro and Stiglitz (1984). Let b > 0 denote an exogenous turnover rate, r is the market rate of interest and q is the probability of being caught shirking, as in the previous section. Deﬁne V1u, V1s and V 1n respectively as the expected lifetime utilities of the unemployed, shirking and non-shirking employees in type I labor market. Furthermore, deﬁne a as the probability of getting out of the pool of unemployed workers. Assuming risk neutrality, the asset value equations applicable to these three types of workers are: rV 1u = a(V 1n − V 1u ) rV 1s = ( b + q)(V 1u − V 1s ) + (w1 /P )

(4.15)

rV = (w1 /P ) − e0 + b(V − V ) n 1

u 1

n 1

where e0 is the disutility of effort. rV1s is equal to the ﬂow return (i.e. current utility) plus the expected capital loss. This capital loss occurs because workers enter into unemployment when there is turnover of workers and/or when workers are caught while shirking. In rV1n, V1n is the expected utility of an employed non-shirking worker and Vu1 is the expected lifetime utility of an unemployed worker. Workers will not shirk if V 1n ≥ V1s. Using the above three equations, the no-shirking condition (NSC) for type I workers can be written as: (w1 /p) ≥ e0 +

e0   bE1   r +   q   ( E1 − L1 )  

(4.16)

If the inequality in Equation (4.16) holds, more ﬁrms will enter into production, creating employment for more workers who are committed to provide the required work effort. If Equation (4.16) does not hold, workers shirk. Then ﬁrms will have negative proﬁts and the ﬁrms will quit. So ultimately Equation (4.16) will be strictly binding in equilibrium. In steady-state equilibrium, the job-acquisition rate, a, is determined by equating the ﬂows into and out of the unemployment pool. If E1

66

Free trade versus free-labor mobility

represents the total labor force, then there are E1 – bL1 unemployed; therefore, a = (bL1/E1 – L1). In equilibrium, Equation (4.16) can be written as: (w1 /p) = e0 +

e0 r q

+

b  E1    e0 q  E1 − L1 

(4.17)

From (4.17) we can write:  A − e0 b  L1 = E1    A 

(4.18)

where A = (w1q/p) − e0 q − e0 r Therefore: 0<

∂L1 ∂E1

<1

(4.19)

or ∂U1 ∂E1

= 1−

∂L1 ∂E1

>0

where U1 is the number of unemployed workers in the type I labor market. In Figure 4.3, the non-shirking condition on the workers’ behalf is represented by the NSC curve. The equilibrium employment in the type I labor market is L1 and L1E1 is the unemployment in this market. The equilibrium real wage is given by w1. The characteristic feature of the type I labor market is that there will always be unemployment. Also, any increase in the labor supply will push the NSC curve down. The type II labor market would always have full employment. Trade versus factor mobility Let’s suppose that there are two countries. They are otherwise similar except that the home country has a larger supply of type II labor, i.e. (L2/L1) > (L2/L1)*. All the variables of the foreign country are presented with asterisks. From Equation (4.17), we can say that, in Figure 4.4 the NSC curve in the type I labor market in the foreign country will lie below that of the type I labor market in the home country (L*1 > L1). Demand conditions are

Figure 4.3 Labor market equilibrium with efﬁciency wage and external economies of scale.

Figure 4.4 Trade in goods under external economies of scale and efﬁciency wages.

68

Free trade versus free-labor mobility

such that the pre-trade price ratios show that the foreign country has comparative advantage in good χ1. If we allow trade in goods, the foreign country will enjoy a rise in relative price of χ1 from autarky price P a* to free-trade price PT. Accordingly value of the marginal product curve will shift upward in the foreign country (Figure 4.4) and that of the home country will shift downward. As a result, employment in the foreign country will go up from L*1 to L*1T and employment of type I labor in the home country will go down from L1 to L1T. Since the NSC curves show that ∂w1/∂L1 > 0 and ∂2w1/∂L21 > 0, and assuming a constant elasticity of economies of scale in the χ1 sector, the increase in employment in the foreign country will be more than the fall in employment in the home country (note that since the foreign country was already producing at a higher level of NSC, the change in wage is higher in the foreign country) so global employment will rise. Now suppose that there is no free movement of goods but there is free mobility of factors (labor). The type II labor market will have usual full employment with w2 equalized across countries. In the pre-migration period w*1 < w1, type I labor will start moving out of the foreign country. Under the scenario, NSC* will move upward and NSC will move downward. Since, to start with, E *1 and therefore L*1 are higher than E1 and L1, the proportionate increase in the supply of type I labor in the home country will be higher than the proportionate decrease in the labor force in the foreign country. Accordingly, as shown in Figure 4.5, the downward movement in NSC in the home country will be bigger than the upward movement of the NSC* in the foreign country. Following this migration, the demand for χ1 rises in the foreign country and falls in the home country (the number of type II workers that move to the foreign country is larger than the number of type I workers migrating out of the foreign country. This happens because elasticity of employment with respect to migration is different in two types of labor markets). Since the supply of χ1 falls following migration, there will be an excess demand of χ1 in the foreign country and, as a result, P *1 rises. Similarly P1 falls in the home country. The magnitude of these changes will depend on the volume of migration or the elasticity of wage with respect to unemployment in the type I labor market in each country. If the prices change by the same magnitude, the shifts in the value of marginal product curves will be the same, although in opposite directions. Thus, the increase in employment in the home country will be more than the fall in employment in the foreign country. So, again, global employment will rise. Therefore, in the sense of whether free-factor mobility will have a similar effect on unemployment as has the free trade in goods, we can say that they can be substitutes as far as the global employment effect is concerned. But, from the perspective of the country that has more unemployment, free trade might be more desirable. It ceases to be a substitute for free-factor mobility for that country.

Free trade versus free-labor mobility 69

Figure 4.5 Migration under external economies of scale and efﬁciency wages.

If we allow both factor mobility and free trade at the same time, and deﬁne them to be substitutes (complements), when trade in goods reduces (augments) factor mobility and vice versa, then they are substitutes. This is a deviation from the results under full employment where trade in goods complements factor mobility under similar circumstances (Bhagwati, Panagariya and Srinivasan 1998). Let’s now consider the situation when the home country has the same endowment ratio as the foreign country, but the foreign country is slightly bigger than the home country. In that case, the foreign country will export good χ1. Free trade is due to the comparative advantage resulting from the IRS (not just from the divergence in factor prices). As trade in goods starts, w*1 in the foreign country will move up and, if factor mobility is allowed at the same time, type I labor will move in and eventually all the prices will be equalized. If we start with free mobility of factors, then type I labor will move out (because of the relatively bigger size, w*1 will be lower). Factor prices will be equalized and trade in goods will be reduced. Under the scenario, both free trade and free-factor mobility reduce each other. With wage rates ﬁxed endogenously by the efﬁciency-wage hypothesis, and also having external economies of scale at the same time, free trade in goods can be a good substitute for free-factor mobility in the sense that

70

Free trade versus free-labor mobility

they can produce the same effects on global employment and output. But individually the country with a larger volume of unemployment might prefer free trade over free-factor mobility. We compared trade in goods with free-factor mobility under both internal and external economies of scale. While under external economies of scale, each one of them can accomplish similar results, the effects are not the same under internal economies of scale. It may be due to the fact that the production structure has to be imperfectly competitive with internal economies of scale. That special structure, together with a restriction on demand in this chapter’s model, generates with free trade a ‘love of variety’ effect for the consumers that cannot be possible either under external economies of scale or under free-labor mobility. Thus with increasing returns to scale and unemployment, the superiority of free trade in generating favorable employment and output effect or the strength of free trade in general depends on whether economies of scale are external or internal.

5

Labor mobility and a dual economy A case of external economies of scale and unemployment

This chapter focuses on an endogenous wage distortion in a developing dual economy where an efﬁciency wage in the urban sector triggers rural–urban migration. The urban sector is also allowed to have external economies of scale. Because of the endogenous nature of the distortion, this migration reduces the severity of distortion by creating more jobs. This is in sharp contrast to the exogenous wage distortion of Chapter 2 (minimum wages) where rural–urban migration increases the severity of unemployment and calls for costly policy mechanisms that might be either politically or economically difﬁcult to implement. This migration also reduces the sectoral wage differential. The presence of economies of scale helps to reduce that further and changes the effects of factor accumulation and commodity price changes in a way that is different from the effects under migration with exogenous wage distortion.

A vast majority of the analysis of labor mobility in the presence of unemployment in a developing dual economy focuses on rural–urban migration, with a rigid wage in the urban sector. The pioneering work by Harris and Todaro (1970) on this topic has used this exogenous wage distortion, such as minimum-wage legislation, to explain urban unemployment that persists in a developing dual economy. This wage is ﬁxed above the equilibrium level and it is also higher than the existing rural wage. The Harris–Todaro model shows how this wage rigidity and the resulting sectoral wage difference can trigger rural–urban migration in spite of unemployment in the urban sector. A large number of studies (Corden and Findlay 1975, and references there) following Harris and Todaro have discussed the issues related with this migration. The focus of all these studies is that rural–urban migration makes the situation worse by raising the pre-migration urban unemployment level. Migration eventually stops when expected wages (actual wage times the probability of employment) in the two sectors become equal and an

72

Labor mobility and a dual economy

equilibrium is reached with urban unemployment. In order to reduce the severity of this unemployment resulting from the wage distortion, these studies (Corden and Findlay 1975, and references there) have suggested different policies. Many of these policies are usually either politically or economically difﬁcult to implement and thus this distortion is considered to be a problem for a developing dual economy. However, wage distortion in a developing economy can very well take an endogenous form. With an underdeveloped information system, perfect monitoring of the workers is not feasible. Employers in the urban sector, therefore, use efﬁciency wages to prevent shirking in the work place. The higher wage and the possibility of being dismissed if caught shirking, and therefore, becoming unemployed, act as control mechanisms. The model in this chapter uses an efﬁciency wage which is set above the wage level that clears the labor market and it is also higher than the existing rural wage. The level of this wage, and the resulting unemployment level, are determined endogenously in the economy. This efﬁciency wage and unemployment serve as discipline devices to control shirking. In the case of the exogenous wage distortion, a desired wage level is achieved but unemployment is its disturbing consequence. In the model of this chapter, both the level of the efﬁciency wage and the corresponding unemployment are desired, as they serve as substitutes for a perfect monitoring system. In addition to this endogenous form of wage distortion, the urban sector in this chapter also has an additional feature. Production here enjoys economies of scale. These economies of scale are external in nature. The assumption of economies of scale or increasing returns to scale (IRS) is very reasonable for a developing urban sector. In the initial stages of development, the urban sector is at its infant stage of production and is ready to exploit the potentials of the existing factors of production. As the growth process thrives, the newly developed infrastructure facilities and technology reduce the transport cost and makes it possible to produce with economies of scale. Goldstein and Moses (1973) in fact have criticized the assumption of constant returns to scale in the urban sector. According to them, urban growth is intimately related to scale and agglomeration economies. This chapter analyzes the implications of rural–urban migration in the presence of external economies of scale and endogenously created unemployment in the urban sector. The analysis in this chapter suggests that: 1.

2.

inter-sectoral labor mobility actually increases employment in the economy when the urban wage is endogenously determined by the efﬁciency wage. This stands in sharp contrast with the employment effect of exogenous wage distortion. this migration also reduces the sectoral wage differential and the distortion that results from it. Furthermore, because of economies of scale, this reduction in sectoral wage differential could be bigger than it would have been in the absence of economies of scale (i.e.

Labor mobility and a dual economy

3.

4.

73

economies of scale make the value of marginal product curve in the urban sector ﬂat). growth in the supply of capital will help the manufacturing sector grow, but by less than it would have been in the absence of efﬁciency wages. This growth also intensiﬁes initial sectoral wage differential. an increase in the price of manufacturing goods will increase both wages and returns to capital in the urban sector. This is in contrast to what we have seen in models with IRS and exogenously ﬁxed wages.

5.1 Model In this dual economy the urban sector produces the manufacturing good and the rural sector produces the agricultural good. Two factors of production capital, K, and labor, L, are completely mobile between the sectors, and both of them enter into the production of each of the commodities. The total output of the manufacturing sector is given by: X m = h( X m ) Fm ( Km , Lm )

(5.1)

where Xm = output, Km(Lm) = total capital (labor) employed in the manufacturing sector. Fm is assumed to be linear and homogenous in its arguments and has the usual properties of a standard production function. The function, h, captures the scale economies. The industry output, Xm, is the sum of the outputs of all the ﬁrms in the manufacturing industry. The production function of a typical ﬁrm, k, in this industry is written as: X mk = h( X m ) Fmk ( Kmk , Lkm ), where X km, Kkm and Lkm represent the total output, capital and labor associated with ﬁrm k. Let’s deﬁne  h   dX m  ε≡    X m   dh 

(5.2)

as the scale elasticity. We assume that 0<ε<1 i.e. although there are economies of scale, to produce more output ﬁrms still need more inputs. When economies of scale are external in nature, the perfectly competitive structure of the market is maintained. Thus, as price takers, ﬁrms equate the private value of marginal product of each factor to the factor’s price. All ﬁrms are identical, and thus:

74

Labor mobility and a dual economy  ∂F   ∂F  Pm h( X m )  mk  = Pm h( X m )  m  = Wm  ∂Lm   ∂Lm   ∂F   ∂F  Pm h( X m )  mk  = Pm h( X m )  m  = rm  ∂Km   ∂Km 

(5.3)

where Pm represents the price of manufacturing good and Wm and rm denote the wage rate and rental rate in the manufacturing sector. In addition, the labor market in the urban sector follows the nonshirking condition (NSC) since workers tend to shirk and cannot be perfectly monitored. Employers therefore offer wages higher than the equilibrium wage to deter shirking and dismiss workers caught shirking. This will result in non-shirking equilibrium with unemployment and higher wages. The fear of losing high wages and being unemployed will keep these workers from shirking. This is the efﬁciency-wage model as posited by Shapiro and Stiglitz (1984). Let b > 0 denote a normal exogenous turnover rate, i is the discount rate and q is the probability of being caught if shirking. Deﬁne VmU, VmS and VmN respectively as the expected lifetime utilities of the unemployed, shirking employees and non-shirking employees in the urban sector. Furthermore, deﬁne a as the probability of getting out of the pool of unemployed workers. Assuming risk neutrality, the asset value of equations, applicable to these three types of workers are: iVmU = a(Vm − VmU ) iV mS =

Wm

iVmN =

Wm

P P

(5.4a)

+ ( b + q) (VmU − VmS )

(5.4b)

− e0 + b(VmU − VmN )

(5.4c)

where e0 is the disutility of effort. Vm is the equilibrium wage and is equal to VmN. Workers will not shirk if VmN ≥ VmS. Using the above three equations, the non-shirking condition (NSC) can be written as: Wm P

= e0 +

e0  bEm     + i q  Em − Lm  

(5.5)

where Em is the total labor in the urban sector and Lm is the employed workers in the urban sector. According to the efﬁciency-wage hypothesis, there will always be unemployment if the non-shirking condition is satisﬁed. In Figure 5.1, W m* is an above-equilibrium wage and the size of the unemployment is LmEm. In the rural sector, we will have constant returns to scale in agricultural production, i.e.:

Labor mobility and a dual economy

75

Figure 5.1 Urban labor market equilibrium.

X a = Fa ( Ka , La ).

(5.6)

where Xa = total output of the agricultural good Ka = total amount of capital in the rural sector La = total amount of labor in the rural sector.  ∂F  Pa  a  = Wa  ∂La   ∂F  Pa  a  = ra  ∂Ka 

(5.7)

where Pa, Wa and ra respectively denote the commodity price, wage rate and rental rate in the rural sector. Inter-sectoral mobility of capital ensures that, in equilibrium, we will have: ra = rm .

(5.8)

As regards the labor market, free inter-sectoral mobility allows labor to move from the rural sector to the urban sector because the manufacturing sector’s wage is higher than the rural sector’s wage. Eventually equilibrium is established when expected wages of the sectors are equalized (i.e. W me , the expected wage of the urban sector is equal to, Wa, the rural

76

Labor mobility and a dual economy

sector’s expected wage). This expected wage is deﬁned to be the actual wage multiplied by the probability of being employed, i.e.: Wm

Lm Em

= Wme = Wa .

(5.9)

Finally, the total endowment of the economy is divided between the two sectors: Km + Ka = K Lm + La + U m = L = Em + La

(5.10)

Remember that Lm < Em and Em – Lm = Um where Em is the total number of workers available, in the urban sector. After deﬁning λ = Um/Lm, Equation (5.9) can be written as: Wm = Wa (1 + λ) Given K, L, Pa, Pm, b, i, q and e0 the system of equations will solve for Xm, Xa, Lm, Em, La, Um, Km, Ka, Wa, Wm, ra and rm.

5.2 Migration equilibrium To describe how the migration equilibrium works we ﬁrst start with Corden and Findlay’s (1975) geometric presentation of the Harris–Todaro model. Total labor supply in the economy is presented by the horizontal distance OmOa in Figure 5.2. Lm is measured to the right from Om and La is measured to the left from Oa. The Vm curve represents the value of the marginal product in the manufacturing sector and the Va curve represents the value of the marginal product in the agricultural sector. In the absence of any distortion, the equilibrium is obtained at C. But due to the rigid minimum wages (exogenously given), the urban employment is now OmLm. Since Wm is higher than Wa, there will be migration until expected wages of both the sectors are the same, i.e. Wme = Wa. The expected wage equality also suggests that WmLm = WaEm. Therefore, rectangular hyperbola through T such as qq would represent all the points whose value is WmLm. If the Va curve cuts this qq curve then we will have WmLm = WaEm. Migration equilibrium will then be reached, with LmEm being the size of the unemployment. The migration equilibrium is shown in Corden and Findlay’s (1975) analysis, when there is CRS in both the sectors (see also Neary 1981). In this chapter, we have IRS in the urban sector. Accordingly, we need to look at Equation (5.3), representing the value of the marginal product of labor.  ∂F  Pm h( X m )  m  = Wm .  ∂Lm 

Labor mobility and a dual economy

77

Figure 5.2 Labor allocation in a dual economy with minimum wage distortion.

Differentiating this with respect to Lm, we can obtain:

[

]

eLm = (Vˆm /Lˆ m ) = − (θ Km /δ m ) + ε/(1 − ε ) θ Lm .

(5.11)

eLm is the elasticity of the value of marginal product curve with respect to a change in labor employed in the manufacturing sector. As Lm rises, Lm/Km rises, and this will reduce the marginal product of labor. This is the factor endowment effect depicted by the ﬁrst term in Equation (5.11). But, as output rises due to the increase in labor, we see the scale effect presented by the second term in the above equation. The scale effect will make the curve look ﬂatter and, if it is strong enough, we will have a positively sloped Vm curve. Thus, we might not have the existence of a stable equilibrium. To avoid that problem, we are assuming that, in spite of the presence of IRS, the Vm curve is negatively sloped to give us a stable equilibrium. In Figure 5.2, we have Wm exogenously given. In this chapter, Wm is ﬁxed endogenously by the intersection of the NSC curve and the Vm curve, as shown in Figure 5.3. To start with, the urban sector has Wm and rural sector has Wa. The employment level in the urban sector is OmLm and in the rural sector is OaEm. If Wm(Lm /Em) > Wa , labor starts moving from the rural sector. According to the non-shirking condition, Equation (5.5), the NSC curve

78

Labor mobility and a dual economy

Figure 5.3 Labor allocation in a dual economy with efﬁciency wages and external economies of scale.

moves downward to NSC′. Wm consequently moves to W′m, Lm moves to L′m and Wa moves to W′a. The employment in the urban sector rises. But the rise in Lm is less than the increase in Em. In this case, Wm(Lm /Em) > Wa or Wme goes down, while Wa goes up. Eventually, they would be equal at T′, when migration equilibrium with unemployment will be reached. The difference between the usual Harris–Todaro model with full factor mobility and the model in this chapter is that the rural–urban migration in this model helps to increase employment in the urban sector, even though the unemployment rate might not go down. So, either the decline in urban wage or decline in both the urban wage and the probability of getting a job in the urban sector helps to bring the equilibrium following migration. In fact, urban wage in this model is not fully rigid. By forcing the wage to go down, migration reduces the distortion brought in by the wage differential. Proposition: An increase in Em increases equilibrium Lm i.e. rural– urban migration increases urban employment.

Labor mobility and a dual economy

79

Proof : The equilibrium condition in urban labor market is given by: e0 +

e0 i q

A+ B

+

e0 bEm q( Em − Lm )

Em

Lm = ∂Lm ∂Em

= Vm

Em − Lm

where A = e0 +

e0 i q

= Vm

and B =

(5.13) e0 b q

Em ( A + B − Vm ) A − Vm = =

A + B − Vm A − Vm

(5.12)

(5.14)

 ∂V  B + Em  m .  2  ∂Em ( A − Vm ) 

( A + B − Vm )  A − Vm  Vˆ  + B  Vm  Eˆ m

(5.15)

The second term is very similar to the elasticity of the marginal product of labor that includes both scale effect and the factor-intensity effect. Thus:  A + B − Vm  1 θ km  ε  = − +  ( A − Vm )  θ Lm > 0 ∂Em  B Vm σ m  1 − ε   ∂Lm

(5.16)

From Equation (5.13), we know that the ﬁrst term on the right-hand side will be positive and, for a large value of σm and ε, the expression in Equation (5.16) will be positive. That may also be true, even when ε is not large enough so that the factor intensity effect θkm/σm will dominate the scale effect (ε/1 – ε)θLm to keep the Vm curve negatively sloped. Q.E.D. As a result of immigration, employment in the urban sector increases, ∂Lm /∂Em < 1, because of the NSC condition which leaves some workers unemployed, or ∂(Em – Lm )/∂Em < 0. From Equation (5.5), it follows that: ∂ (Wm /P ) ∂ ( Em − Lm )

<0

Thus, in this model, following rural–urban, urban employment increases and the sectoral wage difference goes down because of the decline in the urban wage. This reduces the severity of distortion.

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5.3 Comparative static analysis In a regional economy with labor market distortion (such as in Harris– Todaro economy), Panagariya and Succar (1986) have shown that the Rybdzynski effect will be valid with IRS. In this chapter, I examine the effects of factor endowment changes in the presence of IRS, when wage distortion takes an endogenous form. A growth in capital supply increases manufacturing output, as it does in the case of exogenous wage distortion, i.e.: Xˆ m /Kˆ = ( ∏ 22 ∏ 33 − ∏ 23 ∏ 32 )/ ∏ > 0 where ∏ 22 = λ La

[

∏ 33 = (θ Lm − θ La + θ Km δ m θ La )/(θ Lm − θ La )

[

(

)] [

]

(

)]

∏ 23 = αλ Lm θ Km δ m θ La / θ Lm − θ La + λ La θ Ka δ a θ Lm / θ Lm − θ La + λ Lm α ∏ 32 = 0

(See Appendix H for detailed derivation and the comparative static analysis for other factor endowment changes.) In my analysis |Π| > 0 and all Πi’s except Π32 are positive (see Appendix H), i.e. the modiﬁed Harris–Todaro model is stable. The changes in factor supply will affect the factor prices in a paradoxical way, e.g. an increase in K will raise r. However, it will be less paradoxical compared to the case where production enjoys economies of scale and the labor market has an exogenously ﬁxed wage. Wˆ m  ( A22 A33 − A23 A32 )  >0 =   Kˆ A   A A −A A  rˆ 23 31 = −  21 33  > 0  ˆ K A   Wˆ a  ( A21 A32 − A22 A31 )  <0 =   Kˆ A   where  1− ε λ LaT ′X m θ Lm A21 = αλ Lm  − αλ LmθKmδ m + λ Lmα  θ Lm + Xa ε  ε 

Labor mobility and a dual economy

81

 1− ε λ LaT ′X m θKm θKm A22 = αλ Lm  + (αλ LmθKmδ m + λ LaθKaδ a )  θKm + Xa ε θ Lm − θ La  ε    1 A23 =  − (αλ LmθKmδ mθ La + λ LaθKaδ aθ Lm ) − λ Lmα  θ − θ La  Lm  A31 = A32 =

(θ Lm − θ La + θKmδ mθ La ) (θ Lm − θ La )

 [(1 − e )(θ Lm − θ La ) − θKmδ mε ]  θ Lm +  (θ Lm − θ La )   ε

θKm  [(1 − ε )(θ Lm − θ La ) − θKmδ mε ]    (θ Lm − θ La ) ε  

 (θ − θ La + θKmδ mθ La )  A33 =  Lm  θ Lm − θ La  

In the analysis of this chapter, a part of the scale effect is outweighed by the endogenous nature of the distortion in the labor market. As K increases, Xm expands. For an exogenously ﬁxed Wm, rm would increase by a large amount to take care of IRS and Wa would fall when ra increases to match with rm. In this chapter, as Km rises, the Vm curve shifts to the right and NSC allows for a higher Wm. So rm and ra will not rise as much as they would have in the absence of this labor market distortion. As Wm and Lm rise, the expected wage in the urban sector goes up and more labor starts ﬂowing to the urban sector. Since ∂Lm /∂Em < 1, Wme in the long run equilibrium may move in either direction, but the new equilibrium wage would be higher than the initial one. As far as changes in the commodity prices are concerned, the results deviate from what we have seen with exogenously ﬁxed wages in the urban sector. When Pm goes up and there is IRS in the urban sector with Wm ﬁxed exogenously, the rise in production is larger than what it could be under constant returns to scale. If Wm is ﬁxed, the entire beneﬁt goes to rm, i.e. capital enjoys a much higher return compared to that under CRS. Then, Wa falls to compensate for ra. This, together with a fall in La and Ka, reduces Xa. In this chapter, though, as Pm goes up, Wm changes. This happens because the value of marginal product goes up, i.e. the Vm curve moves upward. As Wm goes up, the increase in rm will be less than it would have been with IRS and exogenously ﬁxed urban wage. But the increase in rm causes ra to go up, and Wa falls from its equilibrium level. This, together with the increases in Wm and Lm, causes agricultural workers to move to the manufacturing sector, so agricultural production falls. In the long run, equilibrium Wa will be lower compared with its original level and r will be higher. As in the exogenous case, La, Ka and Xa will go down. It should be noted that because of endogenous wage distortion in the urban sector, the

82

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fall in Wa and the increase in r will be much less than is seen under IRS and exogenous wage distortion. In the long run, Lm will rise, but since the size of the urban labor market rises more, the unemployment rate will increase too. The original Harris–Todaro model has showed a migration equilibrium in a dual economy with exogenously given wage in one of the sectors. This equilibrium is an unemployment equilibrium because of the labor market distortion created by the rigid wage in the urban sector. Similar unemployment equilibrium is also observed when external economies of scale are added to the labor distortion in the urban sector (Panagariya and Succer 1986; Choi 1999). In this chapter, I show that a wage distortion that is tied to work efﬁciency or shirking by workers in the urban sector also generates a migration equilibrium with unemployment even when it works along with external economies of scale in that sector. Did we gain anything by looking into this new type of wage distortion? I have shown that the equilibrium resulting from free rural–urban migration in this model raises the level of employment in the urban sector. The developing dual economy proceeds towards the desired structural transformation as the share of industrial income in the gross domestic product goes up. However, this structural transformation might not be welfare enhancing because employment and output for the economy might decrease. This can happen when the increase in the urban sector’s output cannot make up for the loss of output in the rural sector. Whether the economy will suffer this loss will depend on the elasticity of wage with respect to unemployment that, in turn, depends on the elasticity of employment with respect to migration.1 In Chapter 7, I derive this elasticity in terms of the detection rate, q, the discount rate, i, and the turnover rate, b, and calibrate the values of the elasticity with given parameter values. I show that it is possible to have a socially desirable level of migration by controlling the detection rate, the discount rate or the turnover rate in the economy. This might have fewer budgetary consequences compared to any tax or subsidy policies. The addition of IRS to this new type of distortion reduces the severity of the unemployment problem further. The value of the marginal product of labor curve will be relatively ﬂat in the urban sector and it intersects the new NSC curve that has moved downward. Another important implication of migration in this distortion-ridden economy is that a change in the factor endowment changes factor prices in a paradoxical way. For example, an increase in capital supply raises return to capital as it does in the case of the Harris–Todaro model with IRS (Panagariya and Succar 1986). However, the paradox is less severe in this chapter because of the endogenous nature of the labor market distortion. This is due to the fact that the labor market takes a part of the gains from economies of scale. Furthermore, as far as the distributional effect is concerned, both labor and capital can gain from capital accumulation that is not possible in the

Labor mobility and a dual economy

83

presence of an exogenous distortion. As regards the effect on the rate of unemployment, we see that the unemployment rate may rise as it does in the case of the Harris–Todaro model with IRS, but interestingly in this model, the employment rate also rises. It would be interesting to see how this dual economy behaves when we make a distinction between the formal and informal sectors in the city and bring both skilled and unskilled workers into the analysis. That will be an important topic for further research in this area.

6

Labor migration in European Union countries

In the previous chapters I have presented the implications of international migration under different types of unemployment. In particular, Chapter 5 presented an analysis of migration in the presence of an endogenous labor market distortion to show how migration can reduce the severity of unemployment in a developing dual economy. This chapter focuses on the migration in European Union countries. One special feature of the labor market in the European Union countries is that labor unions play a dominant role in deciding workers’ wages. These unions are also becoming increasingly aware of the presence of unskilled immigrant workers and the related problems of unemployment. This chapter shows how, under some reasonable conditions, migration can affect unions’ strategy in deciding workers’ compensation that can reduce unemployment.

In earlier chapters, I have discussed the implications of migration between two countries when there is a labor market distortion in either one or both the countries. I have focused on two types of distortions that result in unemployment. One of these distortions is introduced by exogenously ﬁxed wages. The other is an endogenous distortion that is created by efﬁciency wages. The efﬁciency-wage distortion is a semi-ﬂexible wage distortion. The semi-ﬂexible wage distortion can also be introduced using a union-bargained wage. In this chapter I will focus on this union-bargained wage distortion and the implications of migration in European Union (EU) countries. Although union-bargained wage distortion exists in many countries of the world, one of the notable aspects of labor-market behavior in EU countries is that it has to deal with the strong presence of workers’ unions. For example, in Germany, labor-market decisions are not unilateral (government or otherwise) decisions. Rather, it goes through a tripartite system where workers’ unions play a signiﬁcant role. We can use either a monopoly union model or a right-to-manage with monopoly union

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85

Table 6.1 Immigration in three EU countries EU 1997 Germany UK Netherlands 1998 Germany UK Netherlands 1999 Germany UK Netherlands

Non-EU

150,583 100 19,779

(24.61%) (0.17%) (22.70%)

461,213 57,350 67,366

135,908 360 20,429

(22.57%) (0.53%) (21.19%)

466,121 67,890 75,994

135,268 0 20,857

(20.22%) (0%) (22.07%)

533,848 95,730 73,639

Source: www.migrationinformation.org, a project of Migration Policy Institute.

model where unions usually make decisions about wages. Following the union-wage level, employers decide on the level of employment and the government takes care of the unemployment pool through a transfer payment mechanism.1 Before analyzing the implications of migration in EU countries, I want to point out some special features of immigration in the EU countries. Immigrants in EU countries are classiﬁed as EU immigrants and nonEU immigrants. EU immigrants make up the immigrants from the member countries (France, Italy, Germany, UK, Luxembourg, Belgium, the Netherlands, Greece, Sweden, Ireland, Denmark, Spain, Portugal, Austria and Finland); immigrants from any other countries are called nonEU immigrants. Historically, most of these non-EU immigrants come from the developing world of Africa and Asian countries and they form a larger part of total immigration to EU countries. In the Western European countries, the inﬂux of foreign labor is not really a ‘brain drain’ from the developing areas of the world. Most of these immigrants join the unskilled-labor market. This happens even when these European countries face a high level of unemployment in the unskilled-workers’ market. It could be due to the fact that even after considering the possibility of being unemployed and the cost of migration, the potential migrants from the Asian and African countries ﬁnd it lucrative to move because the unemployment beneﬁts are higher than their earned wages in the home country. Although studies have shown that this migration does not have much effect on the unemployment of the native workers, it deﬁnitely creates tension and complicates socio-economic life in general. The usual belief is that resident unskilled workers lose their jobs and face reduced wages because of this huge inﬂow of workers, while skilled workers’ wages tend to increase. This creates a sense of disparity, not only between unskilled residents and unskilled migrant workers, but also between skilled and

86

Labor migration in European Union countries

unskilled workers. The debate ultimately focuses on the question of whether the governments of these EU countries should have speciﬁc migration policies. This problem must be viewed by taking into consideration the fact that workers’ unions have dominated the European labor market for a while. The post bargained wage does not work like an exogenously ﬁxed wage. It is a semi-ﬂexible wage. It is important for the government to see how, in bargaining for their members, unions react to the issues related to immigration. As an alternative policy, the government might provide incentives to the bargaining units to make them responsive to the problems of unemployment and immigration in the unskilled-workers’ market. To understand the implications of immigration for unions’ bargaining strategy, one must pay attention to the integration of two types of immigrants (EU immigrants and non-EU immigrants) to the economic system of EU countries. In that respect one needs to focus on the labor market behavior in the EU countries. One notable feature of the labor market of the EU countries is that it is characterized by different level of wages, different labor market regulations, different educational requirements for speciﬁc jobs and, of course, language and cultural barriers. It is rather surprising that, even though in the Treaty of Rome of 1957 (which is the beginning of the European Union), free labor mobility was encouraged among the member nations, the labor market adjustment process was rather slow (Zimmermann 1995). One explanation is that the European population is aging and labor market adjustment is not usually smooth for an aging population. One of the objectives of forming the EU was to encourage labor mobility among the member countries. Policies aimed at fast assimilation of EU workers were formed. EU members started having different policies with respect to EU migrants and non-EU migrants. After 1993, EU immigrants are allowed to move freely within member countries, but non-EU immigrants still have to stay in their host country. Table 6.2 Age distribution in some EU countries Age Group 0–19 20–44 45–54 55–up Age Group 0–19 20–44 45–54 55–up

Germany 1999 2000 21.36 21.21 36.72 36.46 12.46 12.77 29.46 29.55

2001 21.02 36.20 13.21 29.57

France 1999 25.52 35.63 13.74 25.10

2000 25.37 35.37 14.04 25.22

2001 25.21 35.14 14.16 25.50

Italy 1999 19.54 38.00 13.01 29.45

2001 19.18 37.67 13.27 29.88

Spain 1999 21.58 39.58 12.09 26.74

2000 21.00 39.76 12.15 27.06

2001 20.61 39.81 12.25 27.33

2000 19.34 37.86 13.21 29.59

Source: US Bureau of the Census, International Database.

UK 1999 25.37 35.80 13.12 25.71

2000 25.21 35.83 13.12 25.85

2001 25.03 35.80 13.13 26.04

Labor migration in European Union countries

87

Although this policy reduces the economic opportunities for the nonEU migrants, and in the long run works as a disincentive for immigration, in the short run it does not remove the pressure on the labor market. If the labor market in a particular member country feels pressure, and the nonEU immigrants cannot move, then either the native residents or the EU migrants will spill over to the other member countries, who will have to share the burden of immigration. Thus in the absence of a uniform policy of external border control, a non-EU immigrant in any of the member countries has the potential of affecting the labor market of all the member countries. Putting aside the question of whether immigration causes signiﬁcant unemployment of resident (natives) workers, workers’ unions in the EU countries in recent years have been paying increasing attention to unemployment and immigrant workers’ problems when setting the wage level. Unions’ concern about unemployed unskilled workers and especially about unemployed unskilled immigrant workers has in recent years changed unions’ views of immigration. In both France and Germany, instead of supporting the government’s restrictive immigration policy, unions are working to integrate the unemployed immigrant workers into the labor market.2 While working both for the skilled and unskilled workers, unions realize that the majority of immigrant unemployed workers are unskilled workers and they create pressure for the unskilled native workers. The conventional wisdom is that labor unions are in favor of restrictive migration policy. During the 1980s and 1990s, in spite of high levels of unemployment, unions did not want governments to have a restrictive migration policy. Studies (Haus 1999) have shown that this change in preference from the earlier decades is due to the fact that unions believe that their government only has the capacity to inﬂuence migration but that cannot completely control it. Unions want to integrate immigrants and create a broader base for their bargaining power. Keeping this in mind, it will be interesting to see how migration can affect the strategy of unions. Schmidt et al. (1994) have shown that in a heterogeneous unionized labor market, immigration will encourage unions to restrain wage demands to bring in favorable employment effects if skilled and unskilled workers complement each other. This analysis of migration in the absence of a perfectly competitive market structure is somewhat different from the analysis of migration under strictly enforced minimum wage law or government-run unemployment insurance. This insight does add to the analysis of migration in the presence of unions by Calvo (1978) and Burda and Funke (1991), who have shown how migration might affect union strategy and thus can affect wage outcomes when labor is homogenous. All of these analyses of migration and labor unions have focused only on the unions’ role in determining monetary compensation. Yet unions in all types of labor markets may bargain not only for money wages but also

88

Labor migration in European Union countries

Table 6.3 Inﬂow structure by skill level

1993 France Denmark Sweden Switzerland UK 1999 France Denmark Sweden Switzerland UK

Skilled (%)

Unskilled (%)

28.00 12.00 0 26 41

72.00 88.00 100 74 59

15.00 10.00 1 34 46

51.70 39.40 99 66 54

Source: OECD: International Mobility of the Highly Skilled, p. 54, Table 1. Available at: www1.oecd.org/publications/e-book/9202011E.PDF.

for non-monetary beneﬁts. Can unions use non-monetary wages or other beneﬁts as part of their negotiation strategy and, in turn, produce beneﬁcial results for the labor market as a whole? In this chapter I allow unions to focus on both wage and non-wage beneﬁts for their workers. I show that unions as a dominant partner of a tripartite system in the presence of migration, can bargain effectively to (1) change the composition (skilled or unskilled) of the labor market; (2) help foster economic growth; and (3) reduce the severity of the unemployment problem, while achieving unions’ traditional objective of income maximization for the active labor market.

6.1 Model The economy starts with N individuals and a special resource, K, which is the sum of individual holdings of resources. We can identify this special input with capital in the sense of Kenen (1965) and Findlay and Kierzkowski (1983).3 This resource is used for training a part of the population that is willing to join the skilled-labor market.4 The rest of the population comprises the unskilled-labor force. Each individual likes to consume goods and each individual, i, in the economy has αi(=RKi/RK) share of this special input where R is the price at which K can be marketed. The country produces a good, Z, using both skilled and unskilled labor (L1 and L2). In the production of Z, a certain ratio of L1 and L2 must be maintained to have a positive level of output. The production function can be written as Z = F(L1,L2). Wages are equal to the values of marginal product of the respective workers, i.e. W1 = Pz F1 and W2 = Pz F2. Here Pz is the given price of the good, Fi, i = 1,2 is the marginal product of the respective workers and Wi,i = 1,2 are the wages in the respective markets. In the skilled-workers’ market there is full employment, but in the

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89

unskilled-workers’ market there is unemployment, i.e. L2 + U2 = E2, where E2 is the total number of unskilled workers, and L2(U2) is the number of employed (unemployed) workers in the unskilled-labor market. This unemployment results from a wage higher than the market-clearing wage in the unskilled-labor market. This above-equilibrium wage is the result of bargaining between the union and the employer. Unions’ bargaining usually involves both skilled and unskilled workers. They are concerned about the ratio of skilled to unskilled workers in the economy, wages of both types of workers, the unemployment level in the unskilled-labor market and the effects of migration on the labor market in general, especially on the unemployment. The unions are also aware of the distortion created by bargaining. For the purpose of this model, we are assuming that unions do not directly bargain for skilled workers’ wages. However, unions take the welfare of the skilled-labor market into consideration in their bargaining process. As we can see from Table 6.4, the employment rate in the skilled-workers’ market is high. Since there is no threat of a huge supply of unemployed workers to push the wage down Table 6.4 Employment and unemployment rate for skilled workers in the European Union (percentage of working population) Countries

Unemployment rate

Employment rate

Austria Belgium Bulgaria Cyprus Czech Republic Denmark Estonia Finland France Germany Hungary Ireland Italy Latvia Lithuania Luxembourg Netherlands Poland Portugal Romania Slovakia Slovenia Spain Sweden UK EU

2.3 3.2 9.0 4.9 4.8 3.3 8.0 5.0 5.5 4.2 1.2 2.0 6.0 10.2 1.8 5.6 2.1 5.8 3.0 4.0 5.5 2.5 10.5 3.8 2.2 4.2

87.0 84.5 75.0 88.5 87.5 87.5 77.5 86.0 80.0 84.0 83.0 87.0 83.5 79.0 85.0 83.0 87.5 84.0 92.0 84.0 86.0 86.0 77.0 83.5 88.0 83.0

90

Labor migration in European Union countries

in the skilled-labor market, unions’ bargaining about wages is focused on the unskilled-workers’ market. In their effort to maximize beneﬁts, unions propose for a nominal wage, W2, in the unskilled-workers’ market. In addition to the wage beneﬁt for the unskilled workers, the unions also bargain for some additional non-wage beneﬁts, the money value of which equals β. This is a payment for training to acquire more skill.5 The 1994 Organization of Economic Cooperation and Development (OECD) job study (part II) has noted that the generation and distribution of skills is an important focus for policy-makers. It also acknowledges that large segments of education and training take place outside the formal sector. Currently, more training is provided in skilled labor-intensive industries. This justiﬁes an approach to start training in the unskilled sector and/or unskilled-workers’ market.6 The non-wage beneﬁt, β, will depend on the duration of employment and therefore will vary from individual to individual. The money value of the total amount negotiated by the unions for unskilled workers is written as 苶 W2 = W2 + β. The total amount bargained could have been just the nominal wage if the union did not want to go for the beneﬁts for acquiring more skill. The union is aware that, for the majority of the unskilled workers, αi is too small to accommodate training costs. The employed unskilled workers will now have αi + βi = φi to ﬁnance the training if they want to join the skilled workers’ market. For the employed unskilled workers, the cost of acquiring skill, Cs, is dependent on βi; thus Cs = Cs(βi), C′s < 0, C′′s > 0. The employed unskilled workers will decide to join the skilled-workers’ market if the net discounted expected utility stream with a discount rate r(> 0) is higher for that market compared to the net discounted expected utility in the unskilled-workers’ market. The discounted expected utility stream for an employed unskilled worker is given by rV2 = (W2 + αi)/P where P is the price level and rV2 shows the return on asset in the unskilled-labor market, which is just equal to current utility.7 The discounted expected utility from the skilled-labor market is given as rV1 = [(W1/P) + αi – c(βi)] where c(βi) is the cost per period when C(βi) is distributed over the entire working period.8 An individual will be indifferent between these two markets when V1 = V2. So, given the distribution of the capital resource and given wages, there will be an equilibrium level of ~ βi, i.e. βi for which V1 = V2. The total number of participants in the~skilled~ workers’ market is given by L1 = N[1 − ∫ β0 f(β)dβ ] where 1 – ∫ β0 f(β)dβ would give the proportion of the total population willing to be in the skilled-workers’ market. The total number of workers in the unskilledlabor market is given by N – L1 = E2, where E2 = L2 + U2. In the pool of unemployed workers, each native worker has αi. When they think about getting training, they compare the return from the skilled-workers’ market with their return from the unskilled-workers’ market. For an unemployed worker, the return from the unskilled-workers’ market is given by rV′2 = a[(W2 + αi)/P] + (1 – a)(Vu – V2) where a is the probability of getting

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91

a job, (W2 + αi)/P is the return if employed and (1 – a)(Vu – V2) is the expected loss if unemployed (Vu is the utility of an unemployed worker). With this information about how unskilled workers decide to join a particular labor market, the unions will choose a particular combination of W2 and β to maximize the total wage bill. After unions ﬁx the 苶 W2, employers decide on the employment level. Thus β and W2 enter as arguments in the L2 function. Since L1 and L2 need to be employed in a ﬁxed proportion, the size of L1 also becomes a deciding factor in the demand for unskilled workers.

[

L2 = L2 W2 , β, L1 (β)

]

dL2 / dW2 < 0 Keeping W2 constant:  ∂L2 dL2 =   ∂β  (− )

+ L1

∂L2 ∂β

+ L2

(+ )

  dβ ∂β  L1   L2   (+ )

∂L2

The ﬁrst term is the usual effect of an increase in the cost of hiring workers. This will have a negative impact, reducing the demand for unskilled workers. The non-wage beneﬁt, β, actually helps workers to move to the skilled-workers’ market. The second term shows the increase in demand for L2 because vacancies will be created when a number of unskilled workers move to the skilled-labor market. When the number of skilled workers increases, there will be an additional demand for unskilled workers to maintain the ﬁxed proportion, (L1/L2), and this positive effect is shown by the third term. The last two terms thus generate favorable effects for employment of unskilled workers. If the elasticity of the marginal product of the labor curve is not high, as a result of an upward change in β the employment of unskilled workers will go up, i.e. ∂L2/∂β > 0. Unions, interested in the maximization of wage bills, will maximize ψ  Max λ[(1 − ∏1 )W1L1 (W1 , W2 , β)] + [(1 − ∏ 2 )W2 γL2 + βγL2 − bγL2 ] −  ( N − γL2 ) 2  2  

(6.1) with respect to W2 and β, subject to the constraints L2 = L2 [W , β, L1 (β)] γ=

NU NU + M

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Labor migration in European Union countries

where λ = the weight attached to the skilled-workers’ market in union decision-making Π1 = tax on skilled workers’ income Π2 = tax on unskilled workers’ income γ = proportion of natives in unskilled-workers’ market NU = the number of unskilled resident workers M = the number of unskilled migrants in the total population b = unemployment beneﬁts ψ = weight for unemployed people in unions’ decision-making The ﬁrst term presents the wage bill from the skilled-workers’ market; the wage bill of the unskilled workers is presented by the second term. And the third term presents the loss in income due to unemployment in the unskilled market. First order conditions are presented by:

[(

)

)] [(

(

)(

]

)

λ 1 − ∏1 W1L1W2 W1 , W2 , β + 1 − ∏ 2 γ L2 + W2 L2 W2 + γβL2 W2 − b γ L2 W 2

(

)

+ ψ N − γL2 γL2 W2 = 0

(6.2)

[( ) ( )] [( + [ψ ( N − γL ).γL ] = 0

)

(

λ 1 − ∏1 W1L1β • + 1 − ∏ γ W2 L2 β + γ L2 + βL2 β − bL2 β 2

2β

)] (6.3)

The increased wage bill due to any increased wage beneﬁt for the unskilled workers will have to be strong enough to offset the negative effects on the total ‘wage bill’ from the skilled-labor market and the unemployment pool. The negative effects are shown by the ﬁrst and the third term of Equation (6.2). The unions are raising wages on the relatively elastic part of the labor demand curve. If labor unions dislike unemployment, unions’ choices will have to be restricted on the inelastic part of the labor demand curve. If the labor demand is elastic with respect to money wages, it will pay off if unions try to reduce wage beneﬁt, W2, and increase non-wage beneﬁt, β. The optimal combination of W2 and β will be the one where Equation (6.2) will be equal to Equation (6.3). In studying unions’ strategy in setting the wages, Schmidt et al. (1994) have noted that the wage elasticity of unemployment has to be greater than one when unions were only maximizing the unskilled-labor market income. This is referring to the problem that a higher wage brings in higher unemployment. In this chapter we see that a higher non-wage beneﬁt opens up the possibility of reducing unemployment. The direct effect of a higher non-wage beneﬁt, which is similar to the wage elasticity of unemployment in Schmidt, Stilz and Zimmermann’s (SSZ) model, still

Labor migration in European Union countries

93

produces unemployment. But it has to be weighed against two other effects, namely training effect and complementary in production effect. Both of these effects increase employment of unskilled workers. When unions can bargain for a combination of wage and non-wage beneﬁt they can go for a higher increase in β than that in W2, so that they don’t need to worry about the elasticity of employment with respect to wage. Looking at Equation (6.3) we see that even when unions focus only on the unskilledworkers’ market, i.e. even when λ and ψ equal zero, the elasticity of employment with respect to the non-wage beneﬁt does not need to be greater than one. Furthermore, in SSZ model the bargained or union-determined wage works as a competitive fringe on the inelastic part of the labor demand curve. I have shown that an increase in β or the non-wage beneﬁt will have a positive effect on employment irrespective of the elasticity value of the labor demand curve. Unlike the SSZ model, this result is maintained even when unions focus on unemployment and the skilled-workers’ market, i.e. even when λ and ψ are greater than zero. In fact, for the purpose of maximizing the total wage bill, the unions will be encouraged to include all three labor markets (skilled labor, unskilled labor and the unemployed).

6.2 Migration Let us suppose that migration is caused by the expected wage (actual wage multiplied by the probability of unemployment) difference. We will focus on the situation where migrants do not bring any capital with them.9 The total population is represented by N(= N S + N U + M) where N S is the number of skilled workers, N U is the number of unskilled resident workers and M is the number of unskilled migrants in the total population. The employment share of each type of unskilled worker is assumed to be determined by their respective sizes in the total unskilled-labor force, i.e. (N U/N U + M) = γ is the employment share of resident unskilled workers. Following immigration, γ goes down. As a result, the marginal gain from W2 and β declines. Following the ﬁrst order conditions, Equations (6.2) and (6.3), it is obvious that this decline in gain is larger for a change in W2 than it is for a change in β. In other words, if the unions’ objective is to maximize the total wage bill it does not help when there is migration. The gain in the total wage bill goes down as γ goes down. This suggests that, in their negotiation, the labor unions shufﬂe the weights between W2 and β, i.e. they do not change the nominal wage but, instead, try for a reasonable increase in the training cost beneﬁts. When more unskilled employed workers opt for training, the total number of skilled workers goes up. This has two favorable effects on the unskilled-labor market: (1) it directly creates vacancies in the unskilled-labor market; and (2) since the unskilled workers work as complements to the skilled workers, it indirectly creates an additional demand for unskilled workers as the newly

94

Labor migration in European Union countries

trained skilled workers need them. Although there will be direct negative effects from an increase in β (pure price effect) the direct and indirect effects together raise the employment of unskilled workers by offsetting the negative effect. Consequently, unemployment goes down. These effects can thus be described using the comparative static analysis. β˜   L1 = N 1 − ∫0 f (β)dβ   

where f (β) represents the population with a certain β. dL1 dβ

()

= − Nf β˜ > 0

[

]

L2 = L2 W2 , L1 (β) dL2 =

∂L2 ∂W2

dW2 +

∂L2 ∂L1

()

dL1 β

when dW2 = dW2 + dβ  ∂L2 dL2 = dW2 +  ∂W2  ∂β ∂L2

( −)

  + +  L  dβ   ∂ β ∂ β  L1 L2  L2  

( −)

∂L2

∂L2

( +) ( +)

Note ∂L2 ∂L1

dL1 (β) =

∂L2 ∂β

 L1     L2 

.

The unions will opt for redistributing the weights between W and β when it will have a favorable effect, i.e. when the last two terms of the expression for dL2 will dominate the ﬁrst two terms and increase employment. After migration, if unions choose not to change W2 at all and just increases β, the favorable effect becomes stronger.  β˜  E2 = N − N 1 − ∫ f (β)dβ   0    dE2 dβ dL2 dβ 2

()

= − Nf β˜ < 0 >0

Labor migration in European Union countries

95

U 2 = E2 − L2 dU 2 = dE2 − dL2 < 0  L1  d  − N 2 f (β )  E2  = >0 2 dβ   β  N ∫ f ( β ) dβ   0  Thus, we see that not only does the level of unemployment go down, but also the number of skilled workers, and the ratio of skilled to unskilled workers go up. The country will enjoy a higher level of national income, and the resident workers’ share in national income goes up too. This share can be described as W1dL1 + W2dLR2 where LR2 = γL2. When L2 rises, even considering a decline in the share of resident unskilled workers in the total number of unskilled workers from γ to γ ′, there will be an addition to resident workers’ (γ′L′2) income when L′2 presents the total number of unskilled workers after the bargaining. The above analysis just focuses on the employment of the resident-workers’ market. It is shown that immigration will affect the host country’s labor market via γ and the share of resident workers in the total workforce. If we look at the labor market as a whole (that includes both resident and immigrant workers), then in Equations (6.2) and (6.3), γ will vanish. The implied assumption is that both resident and immigrants have equal chances of being employed. Under the scenario, immigration will cause a reshufﬂing of weights between W2 to β through N. The effect of an increase in N on the employment of each type of worker and on the size of the unskilled-workers’ market will depend on the equilibrium value of β after N increases. The effects of an increase in N through immigration can be shown as: β    dφ  =  1 − ∫ f (β˜ )dβ F ( φ)  dN   dN  0 

dL1

β    dφ  =  1 − 1 + ∫ f (β)dβ F ( φ)  dN   dN  0 

dE2

Note that φ = α + β.

6.3 Two-goods, two-factor model I will now take another look at this issue of migration and the problem of unemployment in the European Union countries in a two-goods, twofactor framework. Suppose the country produces two goods, X1 and X2.

96

Labor migration in European Union countries

There are two factors of production: skilled labor, L1, and unskilled labor, L2. Each of these factors is speciﬁc to the production of one of the goods. Thus production function can be written as: X 1 = F ( L1 ) X 2 = F ( L2 ) The X2 sector is subject to constant returns to scale. But the X1 sector enjoys internal economies of scale. Before I describe the nature of production in the X1 sector, let’s talk about the factor market. In the skilledworkers’ market, there is full employment.10 But in the unskilled market, there is unemployment following labor union bargaining. The size of the unskilled-labor market is given by E2 and the number of employed workers in the unskilled market is given by L2. The number of unemployed workers in the unskilled market is given by U = E2 – L2. The unions play the same role in the labor market as they do in the onegood model and the workers’ decision about whether to participate in the skilled or in the unskilled market is made in the same fashion as in the one-good model. As mentioned before, the X1 sector enjoys internal economies of scale. Actually, the X1 sector has a large number of ﬁrms. The behavior of this sector is described by a model of monopolistic competition developed by Dixit and Stiglitz (1977) and later used by Krugman (1979) in the analysis of trade with differentiated product. This sector actually produces a differentiated good with a large number of potential varieties. Each variety has the same weight in consumers’ utility function, which is given by: N

U = ∑ u(Ci ) i =1

u ′(Ci ) > 0,

u ′′(Ci ) < 0

when N = potential varieties. The actual number of varieties, n, is less then N. Each of the varieties uses only L1 to produce the good. The cost function is given by: l i = α + δx i i = 1L ⋅ n where α = ﬁxed cost δ = marginal cost xi = amount of output, or the size of ﬁrm i li = total amount of labor used in the production in ﬁrm i So α and δ are identical across i and with α > 0, each ﬁrm enjoys a declining average cost as its output increases. The demand for each variety is given by xi = LCi. The full employment condition is given by

∑l i =1

i

= L1 .

Labor migration in European Union countries

97

We need to determine the size of each ﬁrm, xi, the price of each variety in terms of wage rate, Pi/W, and the number of varieties produced, n. Since there is symmetry in production and consumption, price and output of all the ﬁrms will be the same. We can thus have three unknowns, P/W, x, and n, to decide on. Note that consumers love variety and each consumer will consume each of the varieties. There is also perfect symmetry in the production. Since production carries a ﬁxed cost (though declining), no producer will produce more than one variety. Each producer thus works as a monopolist. The price determination therefore requires that marginal cost equals marginal revenue. Marginal cost is δW and to decide on marginal revenue we have to ﬁnd elasticity of demand since  1 MR = P  1 −  .  ε From the ﬁrst order condition of utility maximization we know that u′(C) = ηP or P = u′(C)/η. η here depends on prices and income. But there are a large number of ﬁrms. So the price policy of one ﬁrm does not affect the other. We can thus take η as given. The elasticity of demand of each ﬁrm and of the industry as a whole is given by: ε(C ) =

P dx x dP

=

u ′(C ) c ⋅ u ′′(C )

.

Elasticity is assumed to be a declining function of consumption.11 The proﬁt maximizing condition is given by: P=

ε(C ) ε(C ) − 1

δW

or P W

=

ε(C ) ε(C ) − 1

δ

This shows a positive relation between C and P/W which is shown by AA curve in the Figure 6.1. Since we are dealing with monopolistic competition, we also need an average cost pricing condition that will drive the proﬁt to zero. This zero-proﬁt condition is given by: Px − (α + δx)W = 0 or

98

Labor migration in European Union countries P W

=

α x

+δ

or P W

=

α CL

+δ

This gives us a negative relation between P/W and C which is shown by BB curve in Figure 6.1. The intersection of AA and BB satisﬁes both MC = MR, and AC = AR conditions where we get an equilibrium value of C, and P/W . From n = L /α + δx we get the equilibrium number of ﬁrms, n. In this economy, as more unskilled workers become skilled, the size of L1 goes up. As L1 rises, the BB curve shifts to the left and C and P/W go down. Since a 1 percent increase in L1 produces less than a 1 percent fall in C (rising AA curve), n has to go up. The real wage of the skilled-workers’ market also goes up. In the unskilled-workers’ market, unions bargain to set the compensation level for the workers. As in the one-good, one-factor model, this compensation includes both wage and non-wage beneﬁts. Under the scenario, when unions bargain with an objective of maximizing the total wage bill, they maximize Equation (6.1) subject to:

Figure 6.1 Equilibrium with internal economies of scale.

Labor migration in European Union countries L2 = L2 (W2 , β) and γ =

NU NU + M

99

.

The ﬁrst order conditions for income maximization with respect to W2 and β are given by:

[(1 − ∏ )γ (L 2

{(

λ 1 − ∏1

]

+ W2 L2 w 2 ) + γβL2 w 2 − bγL2 w 2 + ψ ( N − γL2 ) γL2 w 2 = 0 (6.4)

2

)[(W

1β

[(1 − ∏ )W γL 2

2

L1 (β) + W1L1β (β)

2β

)]} +

] [ (

)

]

+ γL2 + βγL2β − bγL2β + ψ N − γL2 γL2β = 0

(6.5)

It is interesting to note that, unlike the one-good model, changing the wage beneﬁt by the union does not affect the skilled-workers’ market. This is due to the fact that there is no interaction between skilled and unskilled workers in this model. Furthermore, when unions change the non-wage beneﬁt, β, the income maximization objective gets an additional boost because it not only increases the size of that market but it also increases wages in the skilled-workers’ market. The ﬁrst term in Equation (6.5) is bigger than the ﬁrst term in Equation (6.3). So this will have a larger impact on the labor market as well as on the economy as a whole. There is also an additional factor working in this two-factor, two-good model. I have already mentioned that the functioning of the labor market depends on unions, employers and the government. The government operates through the transfer payment system for the unemployed workers and raises taxes for that purpose. If the government’s total tax revenue is deﬁned as: R = ∏1Y1 + ∏ 2Y2 and expenditure for a ﬁxed amount of unemployment:

(

E = b N + M − L*

)

where N = total number of resident workers M = total number of migrant workers L* = total number of employed workers. then the budget residual (surplus or deﬁcit) can be deﬁned as B = R – E. Since, as a result of changing β, Y1 goes up and E goes down, it will create an additional incentive for the government to support this plan. Finally it has been observed that most of the EU countries are engaged in intra-industry trade. This implies that the member countries engage in export and import of goods within the same industry. Since opening up trade pushes the BB curve further to the left by opening up a larger market, it will create another favorable effect. There will not be any

100

Labor migration in European Union countries

incentive for the skilled workers to move around within the EU countries. The unskilled workers might also ﬁnd it more beneﬁcial to stay in one place and evaluate the possibility of being employed than to move to other EU member countries in search for employment. In that sense, the difference in non-wage beneﬁts across member countries might play an important role in reducing unemployment and preventing the spillover of unskilled unemployed immigrant workers from one EU country to another. Since, in the model of this chapter, unions’ policy of increasing nonwage beneﬁts stay the same, irrespective of whether they are paying attention only to the unskilled-workers’ market, unions will follow the same policy in the event of immigration. Following immigration γ goes down, and to offset the effect of that decline in the resident unskilled workers’ share in the national income, unions might opt for a higher β. Noticing that unions’ policy has a favorable impact on unemployment, the government might come up with some incentives for the employers to settle for a higher β than the employers would have agreed to otherwise. The government can afford to do this because the total government expenditure on transfer payment goes down as unemployment decreases. In that case, the bargaining power of the unions is not weakened in the presence of immigration inﬂux. If unions attach equal importance to natives and immigrants, the chances of getting a job will be the same for both the natives and the immigrants. The favorable outcome will still hold and the unions’ policy will remain the same. As I have mentioned before, in European Union countries the governments cannot affect the wages or employment levels directly because of institutional factors. Unions and employers decide on the wages and employment levels either through bargaining or following the unions’ monopoly decisions. However, the government can deﬁnitely control the factors that indirectly affect unions’ and employers’ decisions. Governments are engaged in transfer payment through taxation and unemployment beneﬁts. The governments’ budget in the absence of migration can be given by: B = ∏1W1L1 + ∏ 2 W2 L2 − bU ∂B ∂M

= ∏1W1

∂L1 ∂M

+ ∏ 2 W2

∂L2 ∂M

(6.6) −b

∂U ∂M

(6.7)

As long as the effect of the ﬁrst and the second terms exceed that of the third term in Equation (6.7), the government will not discourage migration. If, for political and other reasons, the government does not want to raise taxes or lower unemployment beneﬁts, it can go for a restrictive migration policy when ∏1W1

∂L1 ∂M

+ ∏ 2W2

∂L2 ∂M

=b

∂U ∂M

.

Labor migration in European Union countries

101

If migration restriction seems unwarranted with regards to global welfare, the government can still support migration as long as the elasticity effects of unions’ beneﬁts are favorable. In the case of intra-industry trade, the impact on the government’s budget becomes more favorable because skilled workers’ wages also go up following the free-trade policy. Thus, the alternative policy option is to encourage intra-industry trade.

7

An empirical overview

In the previous six chapters I have shown how the relation between labor migration and unemployment can vary depending on the nature of production, specialization, pattern of trade and how unemployment is generated in the countries involved. This chapter provides information about the data available for testing some of the propositions, calibrates and/or test a few of them and makes suggestions about the types of data that are needed for empirically testing the hypotheses about international factor mobility that could be developed from the previous chapters.

In the analysis of international trade, very few attempts have so far been made to empirically test the hypotheses of international factor mobility. Students and researchers had to wait a long time for an empirical veriﬁcation of Mundell’s (1957) proposition after he established the classic relation between factor mobility and trade in goods. He has shown that, under some conditions, trade in goods and factor mobility are substitutes in the Heckscher–Ohlin framework. Wong (1988) for the ﬁrst time has examined the empirical relationship between factor mobility and trade in goods in a general equilibrium context. In this chapter my aim is to empirically investigate the propositions that I have established in the previous chapters. However, this by no means suggests that I am going to provide test results of all the propositions. That is an enormous task. I will present empirical testing of the propositions established in Chapter 6 and I will calibrate some of the results of Chapters 4 and 5. For the rest of the chapters, I will analyze the types of data available, if necessary provide suggestions for data that need to be collected and comment on the testing procedure in the absence of the correct data set. Before looking into the empirical testing of the propositions of the previous chapters, it will be helpful to become familiar with two types of empirical testing that are related directly to established propositions of international migration literature.

An empirical overview 103 The ﬁrst of these is the empirical testing of Mundell’s (1957) proposition about the comparison between trade in goods and international factor mobility. Using Samuelson’s (1948; 1949) factor price equalization theorem, Mundell (1957) has shown that, in the Heckscher–Ohlin framework, trade and factor mobility can be substitutes. In a general equilibrium framework, Wong (1988) has tested this theory by estimating the effects of movements of capital and labor on the level of exports and imports and factor prices in the United States. Wong’s (1988) most important contribution in this empirical work is to follow a technique that exploits the theory he is testing. This is very much in contrast to many other empirical studies that just establish a form of relationship among the variables used in the basic propositions. Wong (1988) has estimated an indirect trade utility (ITU) function for the United States using yearly data from 1948–1983. This ITU function presents a country’s total expenditure as a function of commodity prices and factor endowments. By taking the derivatives with respect to commodity prices and factor endowments, one can get exports of goods and factor prices. After calculating the elasticities from these functions, Wong (1988) has measured the effects of factor ﬂows on trade and factor prices. He has concluded that labor accumulation is pro-trade and labor migration is trade-augmenting (1986a). The second important form of empirical contribution for the theory of international migration comes from the analysis of the ‘brain drain’ literature. A good part of international migration that presents migration of Professionals, Trained and Kindred (PTK) is deﬁned as ‘brain drain’. The literature on ‘brain drain’ is huge and one specially should look into Bhagwati’s (1976) book for a comprehensive survey. In this book, along with a section on theoretical analyses of ‘brain drain’, Bhagwati has included both an econometric section and an empirical section analyzing the propositions of ‘brain drain’ literature. The former section has presented estimations using regression analysis and the latter has presented tables and charts showing the calculated values of descriptive statistics of variables relevant for ‘brain drain’ analysis. In these two sections, Bhagwati’s main point is that available data are not adequate to carry out the testing of theories appropriately. In Chapter 2 of that book, Bhagwati and Krugman have evaluated the existing econometric works on ‘brain drain’. Most of the studies that they have looked into, have dealt with the estimation of the values of the determinants of migration across national boundaries (mostly from less developed countries to developed countries). The most important determinant is considered to be the ‘Income’ variable. Bhagwati and Krugman have described how difﬁcult it is to get an appropriate measure of this variable. At the end they present some values of elasticities of migration with respect to income from different studies. This survey of econometric works provides a good understanding of the questions involved in deﬁning

104

An empirical overview

migration rate or measuring migration, how to calculate return to migration and/or return to education and what problems are involved when one converts an ordinal variable (from a survey questionnaire) to a cardinal variable.

7.1 Migration in European Union (EU) countries One of the important features of the labor market in EU countries is the dominant role of unions and their effects on unemployment. In most of the Western European countries employers and the unions engage in bargaining to decide on the levels of wages and employment. The government later takes care of the unemployment pool from the transfer payment policy. The post-bargained wage is a form of semi-ﬂexible wage and to some extent it is responsible for the unemployment problem in the EU countries. However, in recent years, labor unions have been paying increasing attention to unemployment and the immigrant workers’ problems in setting the wages. It is usually believed that unskilled migrants add to the problem of unemployment in these countries. In Chapter 6, I have allowed these types of labor unions to bargain for both wage and nonwage beneﬁts. I have shown that under some reasonable conditions, unions can reduce unemployment and increase the size of the skilled-labor force by bargaining for a larger increase in the non-wage beneﬁts than that in wage-compensation. One of the conditions under which this proposition will hold is that the skilled and unskilled workers are complements. In fact, an increase in the endowment of the unskilled labor in Europe by 1 percent will augment the return to education by 73 percent and raise the returns to experience by 2.53 percent. Under the circumstances, the unskilled and educated/ experienced workers can be called q-complements (Gang and RiveraBatiz 1994). Following my analysis in Chapter 6, we can develop two hypotheses. 1. 2.

Unemployment has a direct effect on the formation of unions. Training reduces unemployment.

I have used data from a West German socio-economic panel (Soziocikonomisches Panel), which is provided by the Deutsches Institute für Wirtschaftsforschung (DIW) in Berlin. The variables are derived from four Waves (1985, 1989, 1993 and 1998) of the survey sample. I have focused on these four years because the survey was conducted on the same ‘Land’ (Laender) in these years. The data is extracted from ASCII data ﬁles. The variable ‘Land’ represents the German Federal State in which the survey was conducted. Ten ‘Laender’ are included in the survey. The percentage of employed workers who claim to belong to a labor union is pre-

An empirical overview 105 sented by the variable ‘Union’. Those in military or civilian service and those who are unemployed homemakers or retired are excluded from the sample. The variable ‘Foreign’ presents the percentage of employed or unemployed who are not German citizens (those in military service, retired and homemakers, excluded from the sample). ‘Bluecol’ presents the percentage of employed workers who are listed as holding a ‘Bluecollar’ job according to the German socioeconomic panel’s deﬁnition. The percentage of valid respondents claiming to be registered with the government is calculated as ‘Unemployed’. ‘Wage’ is calculated by dividing the gross monthly income in Deutsche Mark (DM) by four times the reported average weekly hours worked. Respondents with monthly incomes of zero DM and respondents with reported weekly hours of one or fewer were excluded. The percentage of all valid respondents claiming to have engaged in ‘ﬁrm-based’ training, continuing education, or retraining is recorded in the ‘Train’ variable. The results of an ordinary least square regression (OLS) is given in Table 7.1. From Table 7.1 we see that unemployment does have a signiﬁcant effect on unionization according to the data set used in this analysis. It is not surprising to see that the proportion of foreign-born workers does not have much effect, because until recently labor unions have not been very inclusive of the foreign-born population. The OLS regression results of ‘Unemp’ on ‘Train’, ‘Wage’ and ‘Blucol’ are shown in Table 7.2. All the variables except ‘Wage’ have signiﬁcant effects. Although Table 7.2 provides support to the second proposition, I must mention that it is very difﬁcult to measure the variable ‘Train’ from the German socioeconomic panel data. Furthermore, the results reported in this chapter are calculated from aggregate-level data. It might produce a Table 7.1 Effect of unemployment on unionization Variables

Co-efﬁcients

t-stat

Signiﬁcance

Constant Foreign Blucol Unemp Wage

0.108 –0.183 0.352 1.535 –0.043

0.967 –1.537 2.093 3.600 –0.290

0.340 0.133 0.044 0.001 0.773

Table 7.2 Effect of training on unemployment Variables

Co-efﬁcients

t-stat

Signiﬁcance

Constant Train Wage Union Blu col

0.097 –0.364 –0.004 0.062 –0.086

3.353 –2.765 –0.23 1.897 –3.002

0.002 0.011 0.605 0.065 0.005

106

An empirical overview

better result if the hypotheses are tested against individual-level data. Also, data from some other EU countries might give some additional insights into the analysis.

7.2 Migration and unemployment created by efﬁciency wages In Chapters 3, 4 and 5, migration to a country or a region that is already suffering from unemployment raises the level of employment. The unemployment in these chapters is created endogenously with an efﬁciency wage. Migration raises employment by relaxing the non-shirking condition in the labor market. In Chapter 3, immigration in the unskilledworkers’ market works to reduce the severity of distortion when production is carried out using a constant returns to scale technology. In Chapter 4, interaction between immigration and unemployment is described in two models when production technology enjoys economies of scale. I have presented the results under both internal and external economies of scale. In Chapter 5, rural–urban migration reduces the problem of unemployment in a developing dual economy in the presence of an efﬁciency-wage distortion. In the case of international migration (i.e. in Chapters 3 and 4), foreign labor, while increasing employment, also increases unemployment. In other words migration may reduce total global employment and output depending on whether the source country is enjoying full employment. In the context of regional migration, i.e. rural–urban migration, in a developing economy, migration may reduce national output even though it increases urban output and employment. It happens because the loss of output in the rural sector is not offset by the gain in output in the urban sector. This is called ‘urban bias’ in the analysis of rural–urban migration (Krichel and Levine 1999). The existence of this urban bias depends on the elasticity of urban wages with respect to unemployment. In their analysis of urban bias, Krichel and Levine (1999) ﬁrst have developed a measure of elasticity (given the values of some parameters), which will be consistent with the urban bias. The elasticity of wage with respect to unemployment is related to the elasticity of employment with respect to migration. It is derived by equating the labor-demand function with the labor-supply function. The semi-ﬂexible wage in Krichel and Levine’s analysis is a post-bargained wage that is a declining function of unemployment. In deriving the elasticity of wages with respect to unemployment, they equated the labor-demand function with the labor-supply at the post-bargained wage. In their model, they have assumed Cobb–Douglas production technology in both the urban and the rural sector. They have also introduced economies of scale in the urban sector and used taxes and subsidies in their analysis.1

An empirical overview 107 The urban output in their model is given by: Yu = ALαu+γ

(7.1)

where Lu denotes urban employment and Yu is the urban output. The rural output Yr is given by: Yr = PBLβr

(7.2)

where Lr denotes rural employment and P the rural/urban terms of trade. The labor resource constraint shows: N = Nu + N r

(7.3)

–– –– where N u, N r denote initial workforce allocations before migration. The labor markets are described by: N u = Lu + U ; N r = Lr

(7.4)

where U is urban unemployment. Labor demand in the respective markets are: αALαu + γ −1 = Wu − Su

(7.5)

βPBLβr−1 = Wr − Sr

(7.6)

The bargained real wage is given by: Wu (1 − T ) = P 1−θ k(U )

(7.7)

Migration equilibrium presents: Wr (1 − T ) = ∏ Wu + (1 − ∏)Wa − C

(7.8)

where Π = Lu /Nu = 1 – U is the probability of employment. The budget constraint that the government needs to satisfy is: T (Yu + Yr ) = G + WaU + Lr Sr + Lu Su

(7.9)

苶a is the direct budgetary cost of unemployment and G is governwhere W ment expenditure. They have started with an initial migration equilibrium resulting in an –– allocation of the total ﬁxed labor force N = Ñu + Ñr between the urban and the rural sectors without any subsidies. They have examined whether this level of migration creates urban bias, i.e. whether this migration is

108

An empirical overview

excessive from a welfare viewpoint, by considering a further migration of MÑr where M is the migration rate. Then: N r = (1 − M ) N˜ r ; N u = N˜ u + MN˜ r give the urban and rural workforce after this further migration. The social welfare functions in their analysis is given by:

[

]

[

]

Z( M ) = Yu + PYr − ( N˜ r − N r )C − Yu Lu ( M ) + Yr N r ( M ) − MN˜ r C

(7.10)

The ﬁrst order condition for a maximum is given by: dZ dM

=

dLu dLu dLu dM

−P

dYr ˜ N r − N˜ r C = 0

dN r

or dYu

dLu dYr = +C dLu d N˜ r M dN r

(

)

(7.11)

The left-hand side of Equation (7.11) is the marginal product of the migrants employed in the urban sector. The right-hand side is the rural marginal product plus the cost of further migration. The demand for labor schedules in Equations (7.5) and (7.6) with no subsidies become: Wu = αALαu+γ −1 ; Wr = βBPLβu−1 Hence, at the laissez-faire equilibrium they get:  γ  dLu = W˜ u  1 +  − (W˜ r + C ) N˜ r dM  α  dM dZ

(7.12)

If ε is the elasticity of urban employment with respect to the migration rate measured at the migration equilibrium, i.e.  dLu  1 ε=   dM  L˜ u the migration would be excessive if dZ/dM < 0 or, from Equation (7.12):  γ  Lu˜ W˜ u  1 +  ε < W˜ γ + C α  N˜ γ 

(7.13)

An empirical overview 109 ε can be derived by equating labor demand with labor supply. Using Equations (7.5) and (7.7): AαLαu + γ −1 =

 U  1 k = 1 − T  Nu  1 − T 1

  Lu k 1 −  ˜ ˜  N u + MN r 

(7.14)

If η = k′/Wu is the elasticity of the wage with respect to unemployment, then implicitly differentiating Equation (7.14) and rearranging terms ε can be expressed as: ε=

1 dLu ηN˜ r L˜ u = ˜ ˜ Lu dM N u [(α + γ − 1) N˜ u + ηL˜ u ]

By using Lu /Nu = 1 − U we can write: η=

(W˜

)

r + C α (1 − α − γ ) ˜ Wu (α + γ )(1 − U˜ ) 2 − (W˜ γ + C )α(1 − U˜ )

(7.15)

~ ~ where µ = 0.33Wr / Wu. ~ ~ Using 苶 C = φ Wr (1 – T); and 苶 Wa = µ Wu (1 – T) from Equation (7.8) we can write: φ=

W˜ u 1 − U˜ (1 − µ) − 1 W˜ r

[

]

Equation 7.15 can now be written as: α(1 − α − γ )[1 + φ(1 − T )] η= ˜ Wu (α + γ )(1 − U˜ ) 2 − α(1 − U˜ )[1 + φ(1 − T )] W˜ r Note that in Krichel and Levine’s (1999) analysis, wage is a declining function of unemployment without any speciﬁcation of the functional form. My model presents an efﬁciency wage that brings in the NSC function on the supply side of the market. I derive an expression for wage elasticity that depends not only on unemployment but also on parametric values of a turnover rate, b, a rate of discount, i, and a probability of getting caught while shirking, q. I then compute the numerical values of this elasticity given the values of b, i and q. In the context of rural and urban migration, after deriving the numerical values of the elasticity of wage with respect to unemployment, Krichel and Levine have used those values to compute urban and rural wage subsidies and corresponding tax increase for a socially optimum level of migration. As I have mentioned before, these types of subsidy policies might not sometimes be politically or economically feasible. By incorporating the

110

An empirical overview

NSC function in the calculation of wage elasticity, I show that the elasticity of wage can be affected by changing the probability of detecting shirking (detection rate) and/or by changing the turnover rate. These do not have many budgetary consequences for the government like the subsidy measures used by many other studies. Employers already spend money by paying above-equilibrium wages (or efﬁciency wages); if they can somehow be encouraged to increase their capability of detecting shirking, and/or to improve the employment condition so that the turnover rate goes down, it will be better for everybody. Also in the context of international migration, the alternatives of choosing b, q or i to control the labor ﬂow are more feasible than migration tax or any such measures. Following Krichel and Levine I use a Cobb–Douglas production function, and thus the demand for labor in the urban sector is presented by: AαLαm−1 where X m = ALαm Xm = manufacturing or urban output Lm = urban employed labor. From Equation 5.5 of Chapter 5 we get the NSC as: wm = e0 +

e0 i q

+

e 0 b  Em    q  Em − Lm 

wm = urban wage e0 = disutility of effort q = probability of getting caught while shirking i = discount rate b = turnover rate Em = total number of people in the urban labor market Lm = number of employed people in the urban sector. Equating labor demand and labor supply:  e 0 i e 0 b  Em   1 AαLα− + m −  e0 +   = 0 q q  Em − Lm    From implicit differentiation of this equilibrium condition we get:

dLm dEm

=

− FEm FLm

e0 b  ( Em − Lm ) − Em    q  ( Em − Lm ) 2  =  e0 b  Em   Aα(α − 1)Lαm−2 − 2 q  ( Em − Lm )  −

An empirical overview 111 e0 b . 1 ε= wm (α − 1)

q U Em − Lm Lm

−

e0 b . 1 q U

ε is the elasticity of employment with respect to migration and U is the unemployment rate. Let’s write the NSC: wm = e0 +

e0 i

wm = e0 +

e0 i

q

+

e 0 b  Em    q  Em − Lm 

+

e0 b  1    q U 

as

dwm dU

=

q

− e0 b qU 2

or η=

dwm . U − e0 b . U = = dU wm qU 2 wm

− e0 b  e0 i e0 b  1   qU e0 + +    q q  U  

After some algebraic manipulation we get: ε= wm (α − 1)

− ηD Em − Lm Lm

+ ηD

where D = e0 +

e0 i q

+

e0 b qU

or ε=

− ηD U wm (α − 1) + ηD 1 −U

112

An empirical overview

Deﬁne the total output of the economy as Z = X m + PX m − CM where Xm = output in the urban sector Xa = output in the rural sector CM = cost of migration P = price level. dZ dEm wm

=

dX m . dLm dX a . dLa dM +P − C dLm dEm dLa dEm dEm

dLm dEm

− Wa − C

since dLa dEm wm ε

= −1, and Lm Em

dM dEm

= 1,

= Wa + C

or wm ε

Lm Em

=

Lm Em

wm

or − ηD Lm Lm = U E Em wm (α − 1) + ηD m 1 −U η=

wm (α − 1) −2 D

U 1 −U

η = wm F where F =

(α − 1)

U

1 −U −2 D

An empirical overview 113 I have used 1991 data for α, and U from India to calibrate the model (see Table 7.3). In the shirking literature the disutility of work effort is assumed to be either 0 or 1 (see Shapiro and Stiglitz 1984. However, in their analysis they have noted that including effort as a continuous variable should not change the results). If workers are feeling uncomfortable about work, their disutility of work effort is high. So I have considered two relatively high values for e0. The history of discount rate in the developing country suggests that the three chosen values are reasonable. There is no guideline for choosing the detection rate. Indeed, according to the shirking models the detection rate could never be observed since no one would ever shirk! I have allowed the detection rate to vary from a relatively small value to a rather large value. The calibrated values show that if q or the detection rate increases, elasticity of wage with respect to unemployment increases. If we start with a Table 7.3 Calibrated values of F α = 0.6, e = 0.5, b = 0.2 U = 0.11

q = 0.1 q = 0.5 q = 0.9

U = 0.12

i = 0.04

i = 0.06

i = 0.08

i = 0.04

i = 0.06

i = 0.08

0.0025247 0.0104823 0.0161318

0.002499 0.010394 0.016016

0.002474 0.010307 0.015901

0.003019 0.012359 0.018833

0.002986 0.012248 0.018689

0.002954 0.012139 0.018458

α = 0.6, e = 1, b = 0.2 U = 0.11

q = 0.1 q = 0.5 q = 0.9

U = 0.12

i = 0.04

i = 0.06

i = 0.08

i = 0.04

i = 0.06

i = 0.08

0.0012623 0.0052411 0.0080659

0.00125 0.005197 0.008008

0.001237 0.005154 0.007951

0.000151 0.00618 0.009416

0.001493 0.006124 0.009345

0.001477 0.00607 0.009274

α = 0.7, e = 0.5, b = 0.2 U = 0.11

q = 0.1 q = 0.5 q = 0.9

U = 0.12

i = 0.04

i = 0.06

i = 0.08

i = 0.04

i = 0.06

i = 0.08

0.0018935 0.0078617 0.0120988

0.001874 0.007796 0.012012

0.001856 0.007731 0.011926

0.002264 0.009269 0.014125

0.00224 0.009186 0.014017

0.002215 0.009104 0.013911

α = 0.7, e = 1, b = 0.2 U = 0.11

q = 0.1 q = 0.5 q = 0.9

U = 0.12

i = 0.04

i = 0.06

i = 0.08

i = 0.04

i = 0.06

i = 0.08

0.0009468 0.0039309 0.0060494

0.000937 0.003898 0.006006

0.000928 0.003865 0.005963

0.001132 0.004635 0.007062

0.00112 0.004593 0.007009

0.00112 0.004593 0.007009

114

An empirical overview

higher unemployment rate, controlling for everything else, we will get a higher value of elasticity. When disutility from work effort is raised, the elasticity value goes down. Another interesting feature that I have noted is that, at a higher unemployment rate, the elasticity value changes by a larger amount as q changes. These have interesting implications for a distortion-ridden developing economy. We know that, if η < wmF, migration will generate an urban bias. Any form of subsidy arrangements to reduce the severity of distortion raises budgetary consequences. In this chapter I show that an increase in q or a decrease in e0 can raise the absolute value of the elasticity and rural–urban migration will produce an equilibrium that will raise the level of employment and national welfare.

7.3 Migration, unemployment created by efﬁciency wages and internal economies of scale In Chapter 4, I have analyzed the implications of migration under unemployment and economies of scale. In doing so, I have discussed whether trade in goods and labor mobility across national borders can be substitutes under unemployment and economies of scale. In that discussion I have brought in both internal and external economies of scale. Trade in goods and labor mobility are considered substitutes in Chapter 4, if they had the same effects on employment and output globally as well as for individual countries. In Section 7.2, I have calibrated a model where labor migration with efﬁciency-wage induced unemployment affects the non-shirking condition and thus the employment level. The process depends on the elasticity of wage with respect to unemployment that is related to elasticity of employment with respect to migration. In deriving that, I have used the constant returns to scale technology in a Cobb–Douglas production function. The calibration of the effect of migration with efﬁciency-wage induced unemployment under external economies of scale will involve adding a scale parameter to the production function. Thus a comparison of the effects of trade in goods with that of labor mobility with unemployment under external economies of scale will involve some extensions and manipulations of the discussion in Section 7.2. Keeping that in mind, I want to focus on the analysis under internal economies of scale. Matusz (1993) has calibrated a model showing the effect of trade on employment when there is efﬁciency-wage induced unemployment in the labor market and the country is enjoying internal economies of scale in its production technology.2 I will follow a similar procedure and compare the results with that of labor mobility under similar conditions. I will ﬁrst show that intra-industry trade increases employment for each country and globally. In Chapter 4, for my analysis with internal economies of scale, each of the two countries has two types of workers (type I and type II) and each is

An empirical overview 115 producing a large number of varieties in each of the two sectors. There is unemployment (efﬁciency-wage distortion) in the type I labor market in each country and type II workers enjoy full employment in both the countries. Consumers in both countries love ‘varieties’, i.e. their utility increases as the number of varieties increases. There is also a symmetry in both production and consumption; consumers distribute their income equally over all the varieties and each ﬁrm produces only one variety with price and output being the same for each ﬁrm. When free trade is allowed, the condition necessary to deter shirking in the type I labor market is given by Equation 4.14, which says: 1−θ  1−θ   w1   w1  * θ  * θ   ln  ( ) ln ( ) n + n + n + n    2 1  2 P1  1   2 P2  2 

= e0 +

e0 i q

+

b  E1    e0 q  E1 − L1 

(7.16)

The main contribution of this equation is that, as trade opens up, n1 + n*1 and n2 + n*2 increase and that raises employment in each country, and, thus global employment also rises. If we assume that all countries of the world are identical, then n1 = λ1(n1 + n*1) and n2 = λ2(n2 + n*2), where λi, i = 1,2 is the home country’s share of world income spent on good i. Substituting these values of n1 and n2 in Equation (7.16) and using ni =

(l − µ)Li li

I get: b 1−θ  1−θ    i+q+   1 − µ1  θ    1 − µ2  θ  µ ln φ1    + ln φ 2   = q   λ1     λ2       where w1  1   L1  φ1 =    2 P  e0   l1 

(7.17)

1−θ

w2  1   L2  φ2 =    2 P2  e0   l 2 

θ

1−θ θ

µ = unemployment rate. Note that unemployed workers ﬁnd employment according to a Poisson process, so that expected duration of a spell of unemployment is 1/a

116

An empirical overview

where a is the probability of ﬁnding a job. If d is the duration, and µ is the unemployment rate, then: d=

µ β(1 – µ )

I use the data from the Economic Reports of the President (1994) for d and µ to get the values of β. The United Nations report provides data on λ. For Equation (7.17) we can insert the values of λ, β and µ. To ﬁnd the value of φ in Equation 7.17, I choose the discount rate (i), elasticity of substitution (θ) and probability of shirking (q). The values of discount rate that I have used in my calculation are 0.05 and 0.10. I choose θ to be 0.7 and 0.9 where I use the fact that elasticity of substitution is related to the markup of price over marginal cost. So for markups of approximately 43 percent and 11 percent, θ would be 0.7 and 0.9. There is, in fact, no guide or published data for detection rate of q. In equilibrium with efﬁciency wage, in fact, there will not be any shirking. However, for my calibration, I follow Matusz (1995) in choosing the values of q. I use q = 0.01, 0.10 and 1 showing a range of very little probability of detection to a very high probability of detection. The purpose of the calibration was to show that trade increases employment. The unemployment rate in Table 7.4 varies from 6.1 to 12.0 when λ = 1, i.e. where there is no trade. The other crucial assumption is that all countries are identical except their sizes. The numbers in Table 7.4 are derived using the data for 1989 with the assumed values of the parameters. The actual unemployment rate for 1989 was 5.3 percent. In addition, to be able to compare the unemployment rate between λ = 1 and λ being any other positive values (showing the effect of trade), it is possible to gain some other insights from Table 7.4. Note that unemployment rate is not at all sensitive to the change in the values of either detection rate, q, or the discount rate, i, at a high value of θ (= 0.9). The high value of θ implies that goods are better substitutes, e.g. θ = 1 implies that goods are perfect substitutes. In that case product differentiation loses its signiﬁcance, and elimination of trade does not have much impact on unemployment. On the other hand, when θ is low, elimination of trade means elimination of varieties and that reduces employment to a large extent. Also, note that, at a given discount rate, the effect of a change in q is very small or at a given q, Table 7.4 Calibrated unemployment with no-trade θ = 0.7

q = 0.01 q = 0.10 q = 1.00

θ = 0.9

i = 0.05

i = 0.10

i = 0.05

i = 0.10

9.63 9.82 11.92

9.70 9.91 12.00

6.10 6.23 6.41

6.11 6.21 6.43

An empirical overview 117 the effect of a change in the discount rate is not big at all. But the effect of a change in q has a larger impact than that in i. However, that may be due to the fact that the assumed changes in q are much bigger for that of i in Table 7.4. The entire exercise for Table 7.4 is designed to show that free trade with internal economies of scale in the absence of labor mobility increases employment. Since this also happens to the trading partners, the global employment and output goes up. In an effort to ﬁnd the effects of labor mobility between these countries when there is no trade, note that Country I or the home country is relatively abundant in type II workers and Country II or the foreign country is relatively abundant in type I workers.3 Also, type I workers in each country face unemployment caused by an efﬁciency-wage distortion, but type II workers in each country enjoy full employment. Krugman (1979) has shown that, for a country producing a variety of goods with internal economies of scale, trade in goods will have the same effect as the inﬂow of workers. This is basically the effect of increasing the size of the market. In my model, when migration is allowed, type I workers will move from Country II to Country I, and type II workers will move in the reverse direction. In the home country, immigration of workers will always increase employment in the type I labor market and labor outﬂow will reduce type I workers’ employment in the foreign country. The effect of labor inﬂow on the employment rate is determined by the elasticity of wage with respect to unemployment that, in turn, depends on elasticity of employment with respect to migration. Only when the elasticity of wage with respect to unemployment in the immigrating country is higher than that in the emigrating country will global employment increase. The calibration technique for ﬁnding the effect of labor ﬂow would resemble the procedure in section 7.4. Thus, free trade and free international labor mobility may not produce similar effects on employment under internal economies of scale and efﬁciency-wage distortion in the labor market.

7.4 Migration, unemployment and minimum-wage countries In Chapter 2, I have discussed the implications for migration in the presence of unemployment created by a minimum-wage law. I have shown that out-migration is a desirable policy for a country with a minimum-wage distortion in its labor market. The minimum-wage country in the model (Chapter 2) is trading with a non-minimum-wage country with full employment and out-migration seems to be an optimal policy when this country exports the capital-intensive good. I have looked at a few minimum-wage countries that have experienced net out-migration with the United States. I have chosen the United States as the immigrating country because it has a relatively very low unemployment rate even though it follows minimum-wage law. I have considered

118

An empirical overview

Canada, Mexico, China, Hong Kong and El Salvador in my sample of other minimum-wage countries. The share of each of these countries export to the United States in their GDP is signiﬁcant. Unfortunately it is not possible to measure the factor content of these exports from any reliable source. Thus it was difﬁcult to test any hypothesis on the basis of the data available. Instead, I will brieﬂy describe the data I have looked at for the minimum-wage countries. Canada’s exports to the United States as a percentage of its GDP increased from 36.87 percent in 1995 to 39.84 percent in 1997. In fact, share of exports in the respective GDPs have increased for all ﬁve countries. Mexico’s export to the United States as a percentage of its GDP has increased from 23.87 percent in 1995 to 26.84 percent in 1996. For China, the numbers are 21.01 percent and 20.89 percent. For both Mexico and Canada, unemployment rates have dropped during the course of three years from 1995–1997. But unemployment rate has gone up in China from 2.90 percent in 1995 to 3 percent in 1996. It is interesting to note that, while unemployment rates were going down in Canada and Mexico, the net out-migration from these two countries to the United States was going up. But unemployment was rising in China even though China’s net outﬂow to the USA was positive. Of course, this is neither a validation nor a negation of the proposition that out-migration is a desirable policy for a country suffering from a labor market distortion due to minimum wages. We also need to remind ourselves that the United States, Mexico and Canada have started enjoying the beneﬁts of the North American Free Trade Agreement during these years. The main conclusion of Chapter 2 is that out-migration reduces the severity of minimum-wage distortion by changing the terms of trade in the country’s favor. I have looked into the export and import prices of all ﬁve countries. As already mentioned, I don’t have any data to check the factor content of the exports from these countries, I have picked up four categories of good (chilled frozen fruits, vegetables, dried fruits and vegetables, and waste of textile fabrics). Interestingly, China has suffered a deterioration in its terms of trade during these years while Canada and Mexico have enjoyed favorable changes in their terms of trade and a favorable employment effect. For Hong Kong also, the terms of trade change are very favorable and the employment scenario is also encouraging. A similar conclusion can also be drawn by looking at El Salvador, although out-migration from this country to the United States is a very low percentage of total US labor inﬂow. But this county also enjoyed an increase in its share of exports to the United States and favorable terms of trade. This description by no means implies that favorable terms of trade are responsible for the reduction in unemployment. This, at the least, makes us aware of the fact that we need to collect more data about the international engagement of countries around the world.

Appendix A

Increasing returns to scale Increasing returns means that the output is increasing at a rate higher than the rate at which inputs or factors of production are increased. These are gains from producing in larger quantities. Alternatively, it is called ‘economies of scale’. Industries that enjoy increasing returns are thus more efﬁcient when they produce a larger scale of output. Table A1 shows that when inputs are increased from four to eight units, output rises from ﬁfteen to thirty-two units and economies of scale are realized These economies of scale can be of two types: (1) external economies of scale and (2) internal economies of scale. If the increase in the industry output is because each ﬁrm in the industry raises its output, then this is called internal economies of scale. However, if the industry output increases without each ﬁrm raising its output, this is called external economies of scale. The ﬁrm that does not increase its output level enjoys the beneﬁt of a larger scale of production in the industry without producing on a larger scale. It is important to understand the distinction between these two types of economies of scale. Under external economies of scale, a large number of ﬁrms can enter the industry to raise the total industrial output originally produced by the existing group. Each ﬁrm behaves like a perfectly competitive ﬁrm and can thus be called a price taker. But when economies of scale are there because the ﬁrm itself increases its scale of production (i.e. it realizes internal economies of scale) the market structure becomes imperfectly competitive. Under an imperfectly competitive market structure, a Table A1 Economies of scale Level of input

Level of ouput

Input per unit of output

Average output

2 3 4 8

5 9 15 32

0.40 0.33 0.27 0.25

2.50 3.00 3.75 4.00

120

Appendix A

very large ﬁrm can behave like a monopolist or a few big ﬁrms can form an oligopoly. Thus models of economies of scale or increasing returns can be classiﬁed into three groups: (1) models that use the perfectly competitive market structure; (2) models where the market faces monopolistic competition; and (3) models of oligopoly behavior. For the purpose of this book, I will focus on the ﬁrst two cases.1 I will start with external economies of scale. The literature on external economies of scale and international trade focuses on patterns of trade, specialization and consequences for income distribution in various types of models. For example, Panagariya (1981) and Ethier (1982) focus on onefactor models, while Markusen and Melvin (1981) bring in two-factor models. Jones (1968), Kemp (1969) and Panagariya (1980) deal with income redistribution effects of external economies of scale, while in the 2 × 2 model, Panagariya analyzes income redistribution effects in the context of a speciﬁc factor model. Kar-yiu Wong (1995) has shown that theorems of international trade in goods cannot be applied to international factor mobility under external economies of scale.2 In this book I use external economies of scale in Chapters 4 and 5. Chapter 4 analyzes the implications of international labor migration in a model where two countries produce two goods with two factors of production. One of the sectors in each country enjoys external economies of scale. In Chapter 5, I discuss implications of sectoral or regional migration in the presence of external economies of scale. In the analysis of trade in the presence of external economies of scale, two issues have dominated the literature: (1) the stability of equilibrium and (2) the implications for established rules of traditional trade theory (with constant returns to scale) such as Stolper–Samuelson theorem and Rybczynski theorem. I begin my analysis with a speciﬁc factor model. There are two sectors. I assume that sector two enjoys external economies of scale. The production function of ﬁrm j in this sector can be written as: X 2j = g( X 2 ) F ( K 2j , L2j ) ≡ g( X 2 )Lj2 f ( k2j )

(A1) j

where F is linear and homogeneous. X2 is the total output of sector 2 and k 2 is the capital–labor ratio of ﬁrm j. The economies of scale are measured by g(X2). Each ﬁrm takes the industry output as given, uses the same technology and pays the same factor prices. So the capital–labor ratio used by each ﬁrm is the same. Summing over the ﬁrms, the industry output can be expressed as: X 2 = g( X 2 ) F ( K 2 , L2 ) ≡ g( X 2 )L2 f ( k2 )

(A2)

To ensure that economies of scale are not strong enough to reduce the total demand for inputs as output increases, it is assumed that elasticity of economies of scale is less than 1, i.e. 0 < ε < 1 or 0 < g′X2/g < 1.

Appendix A 121 Since each ﬁrm takes the industry output level as given, it does not take into account the effect of the change in g(X2) on its marginal product. Thus, each ﬁrm pays its factors according to its own ﬁrm level marginal product (private marginal product). Factor prices are equal to the value of private marginal product. Factor prices are then given by: P2 g( X 2 ) f ′( k2j ) = r2 P2 g( X 2 )[ f ( k2j ) − k2j f ′( k2j )] = w

(A3)

Since the industry-level capital–labor ratio is the same as the ﬁrm-level capital–labor ratio, at the industry level factor prices are given by: P2 g( X 2 ) f ′( k2 ) = r2 P2 g( X 2 )[ f ( k2 ) − k2 f ′( k2 )] = w

(A4)

Because of the presence of external economies of scale, the private marginal product of labor is less than the social marginal product. If V2 represents the value of the private marginal product of labor, then: V2 = P2 g( X 2 )[ f ( k2 ) − k2 f ′( k2j )]

(A5)

and the value of the social marginal product of labor, V 2s , is given by V 2s = V2/(1 − ε). This is derived by differentiating industry-level production function with respect to L2 and multiplying the result by P2 The sectoral labor allocation in this model is decided by V1 and V2 (value of marginal product of labor in sector 1 and sector 2). Since there are constant returns to scale in sector 1, V1 will be a negatively sloped curve. The behavior of V2 can be explained by Figure A1 (Figures A1–A8 have been adapted from graphs used by Bhagwati et al. 1998). As we move from A to B, at constant output level K2/L2 declines. This shows the decline in the marginal product of labor or factor-intensity effect. From B to C, both K2 and L2 rise in the same proportion, but output rises at a higher rate. This is the scale effect. The factor-intensity effect has a negative impact on V2 and the scale effect has a positive impact on V2. dV2 dL2

= factor-intensity effect + scale effect (− )

(+)

(A6)

dV2/dL2 will have a positive slope if the scale effect dominates the factorintensity effect. In this case, it is possible to have an unstable equilibrium. In Figure A2, V2 is positively sloped with respect to the 02 axis and is steeper than V1. The resulting equilibrium E1 is an unstable equilibrium.

122

Appendix A

Figure A1 Factor intensity effect and scale effect for sector 2.

Figure A2 Value of marginal product curves of two sectors.

In this case, an increase in P2 will shift V2 upwards, and competitive equilibrium will result in a decrease of X2. But even with a positively sloped V2 it is possible to have a stable equilibrium when the V1 curve is steeper than V2, as in Figure A3. In this case, output price response is positive and the proportionate increase in wages is higher than proportionate increases in price. The real wage rises in terms of both the goods. Also, a fall in K2/L2 raises return to capital in sector 2 and causes a fall in return for K1. As I have mentioned before, one of the important issues in the models

Appendix A 123

Figure A3 Effects of a price increase in sector 2.

involving variable returns to scale is the stability of equilibrium. This comes along with the possibility of multiple equilibria, and the pattern of production, specialization and trade vary accordingly. This aspect of variable returns to scale has been discussed neatly by Panagariya (1981) in a speciﬁc factor model. In a two-sector model, he assumes that sector 1 uses labor and capital and enjoys constant returns to scale, and sector 2 employs labor only and is subject to increasing returns to scale. So the production possibility frontier would be concave near Q2 or the vertical axis, and convex near Q1 or the horizontal axis with an inﬂection point in the middle (note that the curvature of the production possibility frontier depends on which sector is assumed to have increasing or decreasing opportunity cost). Since social marginal cost is less than the private marginal cost, and since ﬁrms in each sector pay the factors according to the private marginal product, the price line will intersect the production transformation curve from below, as shown in Figure A4. The slope of the production transformation approaches zero as either Q2 or Q1 approaches zero. Thus, there cannot be complete specialization in Q2 that requires P2 to be ∞. Assuming that P 2I is the price at the inﬂection point, for any ∞ > P2 > P 2I there would be multiple equilibrium – one completely specializing in Q1 and two other points of equilibrium showing incomplete specialization. If the scale effect in sector 2 is strong, it will result in an upward-sloping marginal product curve. Then, in Figure A5 we will have E3 as the stable equilibrium and complete specialization point. Although both E1 and E2 will give incomplete specialization, E2 is the stable equilibrium point with incomplete specialization. The literature

124

Appendix A

Figure A4 Multiple equilibrium points with increasing returns to scale in one of the sectors.

Figure A5 Value of marginal product curves with multiple equilibria.

argues that the actual equilibrium will be determined by the history, i.e. if the country starts somewhere at the left of E1, it will have E2 as its autarky equilibrium, and if it starts somewhere to the right of E1, complete specialization will be obtained at E3. Krugman (1991) argues that the historical position might be dominated if there is no adjustment cost for moving and

Appendix A 125 if workers expect a bigger return from a place other than the place suggested by history. With two such countries that are similar in all categories except size, and with incomplete specialization, the larger country will export the good enjoying increasing returns to scale. The welfare impact for the smaller countries is ambiguous because, although it gains from international exchange, it cannot take advantage of a large scale of production. In this case, subsidization of the sector that is subject to increasing returns to scale might be the optimum policy for the small country. The second issue that has attracted attention in the analysis of trade and increasing returns to scale is whether the traditional theorems of international trade such as the Stolper–Samuelson theorem and Rybczynski theorem hold good. This can be shown by using 2 × 2 models. Let’s assume again, for simplicity, that sector 1 is under constant returns to scale and sector 2 enjoys increasing returns to scale. If the price of good 2 is P2, and given that each ﬁrm in sector 2 produces according to the production function X2 = g(X2)F j (K 2j ,L2j ), it can be said that each ﬁrm in sector 2 sells F j at P2g(X2) or X2 for the entire industry is sold at P2/g(X2). In competitive equilibrium, unit cost for each ﬁrm, c2(w,r), equals P2g(X2). Given an exogenous level of X2, say X 02, and for an exogenously given price for sector 2, P 02, we can draw a negatively sloped function for sector 2 in w–r, (wage–rental) space of Figure A6. Assuming P1 = 1, c1(w,r) can also be drawn in a similar way. The slope at each point of these units cost functions gives the optimal use of the factors at a given r/w by Shepard’s Lemma.3 Now suppose P 02 increases to P 2′ . As a result c2(w,r) moves to the right – wage rises and it rises proportionately more than the increase in P 02. The

Figure A6 Effects of a price change on factor prices.

126

Appendix A

shift of c 2 continues farther because of the scale effect when X 02 becomes X2. The Stolper–Samuelson effect is thus reinforced. This effect can also be shown even when sector 1 is enjoying decreasing returns to scale. Using similar techniques it can be shown that, in the presence of increasing returns to scale, the Rybczynski effect also holds good. Chapter 4 introduces economies of scale in the analysis of migration, together with unemployment. It starts with economies of scale that are internal to the ﬁrm. As noted before, the market is characterized by a few big ﬁrms and there is monopolistic competition. The models that are mostly used in the analysis of international trade with internal economies of scale are developed by Krugman (1979; 1980; 1981), who has introduced Dixit and Stiglitz’s (1977) model for monopolistic competition in the analysis of trade. I will focus mainly on Krugman’s model with a very brief description of two other models (Helpman 1981 and Ethier 1982) that have been used in incorporating internal economies of scale in the analysis of international trade. I will start with Krugman’s (1979) model because, in a very simple way, this model helps to understand how internal economies of scale work in the theory of international trade. The model that I have used in the text is based on this model. There is only one sector in the economy producing a differentiated good with a large number of varieties. Consumers derive their utility from varieties, i.e. the larger the varieties, the larger will be the utility. There is symmetry in consumption. It means that consumers give equal weight to each variety. The utility function of a representative consumer is given by: n

U = ∑ ν( ci ) ν′( ci ) > 0 ν′′( ci ) < 0

(A7)

i =1

Where ci is the individual consumption of good i. Labor is the only factor of production. The cost function of variety i is given by: li = α + βX i

(A8)

α = ﬁxed cost β = marginal cost There is thus symmetry in production too, and each variety enjoys internal economies of scale, i.e. li/Xi or average cost is a decreasing function of output. Since all varieties are perfect substitutes (because of symmetry) in production, and since there is love for varieties in consumption, it does not matter to a ﬁrm which variety it produces. There are L individuals in the economy, each supplying one unit of labor. The market clearing condition for each variety says: X i = ci L. i = 1.....n

(A9)

Appendix A 127 n

The full employment condition is given by

∑l

i

= L.

i =1

The variables that we have to determine from this model are Pi/w, Xi and ni where Pi /w = price of each variety in terms of wage Xi = output of each variety n = actual number of variety. There is symmetry across varieties. So we can replace Pi by P, Xi by X and ci by c. Since each firm is a monopolist, equilibrium output and price for each firm is determined by the equality of marginal cost and marginal revenue. Marginal cost, MC, is given by wβ. Marginal revenue, MR, is related to the price by elasticity. MR = P(1 – 1/ε) where ε is the elasticity of demand. To determine equilibrium output and price we thus have to determine ε. Utility maximization by an individual subject to the budget constraint gives v′(c) = λP, where λ is the marginal utility of income of an individual. From that we get: P=

v ′( X /L) λ

.

(A10)

λ usually depends on all the prices and the income of the individual. Since there is a large number of ﬁrms producing a large number of varieties, pricing decisions of one ﬁrm will not affect this variable and λ can therefore be taken as given. So ε(c), elasticity of demand facing a ﬁrm, is given by: − PdX XdP

=

− v ′( c ) c ⋅ v ′′( c )

.

(A11)

The condition MR = MC gives: P=

ε( c ) ε( c ) − 1

βw

(A12)

Krugman (1979) assumes ε to be a declining function of c. This gives an upward-rising relation between P/w and c. As c rises, elasticity falls and the price, P, rises because the ﬁrm’s monopoly power rises. This upwardrising relation is given by AA in Figure A7. AA is always above β, the marginal cost, so that the loss never exceeds the ﬁxed cost.

128

Appendix A

Figure A7 Equilibrium with internal economies of scale and declining elasticity of demand for goods.

Now to ensure a zero proﬁt condition, there is free entry and free exit. This provides average cost pricing condition given by: α X

+ β = P /w =

α cL

+β

(A13)

According to this equation, we have an inverse relation between c and P/w given by BB in Figure A7. Thus we get equilibrium c苶, or equilibrium X and (P 苶苶/w). Since n苶 = L/(α + βX 苶 ), this also provides the number of ﬁrms or numbers of varieties produced in the economy. Now suppose there is a 1 percent increase in the labor force, L. This will not shift the AA curve but, following the average-cost pricing equation, this will shift the BB curve to the left by 1 percent. c will go down, but not by a full 1 percent. This will mean that X will have to increase to accommodate the rise in L. The average cost would need to go down, which is reﬂected in declining P/w . The number of varieties will go up since X does not increase by 1 percent. Thus, as a result of labor-force growth, each ﬁrm enjoys the economies of scale and consumers enjoy an increase in variety. Introduction of trade in this model will be equivalent to an increase in L. Consider two economies of the type described above. They have similar taste and technology. Thus price, output of each ﬁrm and number of varieties produced by each country are the same. Opening up trade means each ﬁrm will be able to serve a larger market; so X will go up. The number of varieties produced in each country will go down but consumers in each country will enjoy larger numbers of varieties (n + n*, where n* is

Appendix A 129 the varieties produced in the foreign country). The trade here is called intra-industry trade, because each country is exporting and importing the products of the same industry, although of different varieties. Here gains from trade arise from the consumption of the increased varieties and expanded scale of production. Since prices are equalized across varieties, the expenditure on each country’s good is proportional to its labor force. This implies L/(L + L*) is the expenditure on home-produced varieties and L*/L + L* is the expenditure on foreign-produced varieties. So the home country’s import M = WL·L*/(L + L*) = M * = W *L*·L/(L + L*), where W = W * and L = L*. Trade is balanced, but the pattern of trade is indeterminate. Krugman (1980) has also used a speciﬁc form of utility function where v(c) = cθ. This implies that elasticity of demand is constant. Since ε(c) is constant, AA curve is a horizontal line for this model. Consequently, the increase in labor force reduces the consumption exactly by 1 percent (Figure A8). It does not increase the size of output produced by each ﬁrm, X. So there is no scale effect; only the increase in the variety effect is observed. It should be noted that trade with internal economies of scale is intraindustry trade. This is the feature that was observed in post-World War II trade. Krugman’s model explains this intra-industry trade distinct from traditional inter-industry trade. Krugman has also focused on the income redistribution effect of trade. In the traditional factor-endowment model of Heckscher and Ohlin, trade usually hurts the scarce factor (Stolper–Samuelson theorem). With internal economies of scale, Krugman has shown that it is not necessarily true for intra-industry trade. He has retained the assumption of symmetry in consumption as we saw in his 1979

Figure A8 Equilibrium with internal economies of scale and constant elasticity of demand for goods.

130

Appendix A

and 1980 model, although he has used a different form of utility function. The utility function is given by: N1

N2

1=1

j =1

U = ln ( ∑ c1θi )1/θ = ln ( ∑ c 2θ j )1/θ

(A14)

Individual consumers divide their expenditures equally over two types of goods produced in the two sectors, and they further divide their expenditures equally over the varieties of each good (N1 and N2). Although individuals are very identical in their consumption behavior, in the production some (workers) are speciﬁc to sector 1 and others can only be used in sector 2. Thus total labor force size, say 2, is divided between sector 2 (z) and sector 1 (2 – z). The production process in each sector follows the same technique with increasing return to scale. If z = 1 = 2 – z, there will be complete symmetry and prices, wages and output will be equalized across sectors and the number of varieties produced in each sector will be the same. In fact, output of each variety will be invariant with respect to the supply of labor available to produce it. That is, if L1, or the factor speciﬁc to the ﬁrst sector, is a scarce factor, prices and wages will be higher in sector 1, because consumers spend an equal amount on both sectors. The number of varieties will also be less than that of the other sector. We now imagine another country, which is exactly the same as described above (say, our home country), except that its factor endowment ratio is a mirror image of the home country, i.e. L 2 is the scarce factor. Then, in the home country, W1 > W2 and P1 > P2 and in the foreign country, W *1 < W 2* and P *1 < P *2. After trade opens up, all factor and commodity prices will be equalized, but the home country will be a net importer of good 1 and net exporter of good 2. The nature of trade is intra-industry trade. Krugman shows that if z = 1 or close to 1, trade will be intra-industry trade. If countries are dissimilar, the trade will be interindustry trade. When z > 1 or 2 – z < 1, we have noticed that the home country becomes the net importer of good 1 and w1 goes down. It might seem that the scarce factor is hurt as a result of trade but that is not always true. Gains from trade come with increased varieties available for consumption and from a reduction in price of net importable. Krugman has shown that if the elasticity of demand <0.5 and z is close to 1, scarce factor beneﬁts. If z = 1, both the factors enjoy gains from trade (see Krugman 1980 for detailed derivation). The analysis of internal economies of scale has its most important contribution in the area of economic geography. Helpman and Krugman (1985) developed a model where a country is producing a differentiated good and a homogenous good. The production structure of the differentiated good follows Krugman’s (1979) model and the homogeneous

Appendix A 131 good is produced under constant returns to scale. There is only one factor of production: labor. The preferences between these two goods are Cobb–Douglas, and the sub-utility function for the differentiated good is given by: n

ν = ∑ ci i =1

Now suppose we have another country that is similar to the country I have described, but bigger in size. Following the preference pattern, equal amount will be spent on each good. This implies a larger proportion of labor force will be used for the differentiated product in the large country. A larger variety and a larger volume of each variety will be produced and prices of each variety in terms of homogeneous goods will be lower in that country. It is tempting to conclude that this will bring in home-market bias where the smaller country will become a net importer of the differentiated good. However, with internal economies of scale, scale economy does not depend on location. With trade, prices of all varieties and wages will be equalized and production structure becomes indeterminate, so the smaller country might produce a larger variety and become a net exporter of the differentiated good. This is in sharp contrast to the external economies of scale models where the smaller country can compete with the larger country only if it offers lower wages. Later Helpman and Krugman (1985) introduced transportation cost to solve the indeterminacy of the production structure. They have introduced ‘iceberg’ type transportation cost where only a fraction of the commodity arrives in the importing country. For a low transportation cost or for sufﬁciently dissimilar countries, all production of the differentiated goods gets concentrated in the larger country; for larger transportation costs or for sufﬁciently similar countries, production diversiﬁcation is possible and the smaller country will import the differentiated good on a net basis and export the homogeneous good. In a model with two differentiated products, where production technology is the same, not only across varieties but also across sectors, Krugman (1980) shows how home-market bias becomes effective in the presence of transportation costs. Using the interaction between internal economies of scale and transportation cost, Krugman (also) develops an interesting model of economic geography where a country can be divided into an industrialized core and an agricultural ‘periphery’. There are two regions and two factors of production. Individual utility is given by: U = [( ∑ xiα )1/α ]β i

y1−β

(A15)

132

Appendix A

The xi’s are different varieties of manufacturing good and y is the agricultural good. Agriculture uses peasants and manufacturers use workers. Peasants are completely immobile between sectors. Production technology in the manufacturing sector enjoys increasing returns to scale and there is CRS in agriculture. Agricultural products can be transported without any cost but manufacture is subject to iceberg transport costs. Under this scenario, Krugman shows that it is possible that workers will concentrate in one region or equilibrium will be unstable. Suppose, to start with, each region has an equal number of workers. Wages are equal and there is equilibrium. Now we disturb this equilibrium by moving workers from region 2 to region 1. There will be two effects: (1) home-market bias will raise the wage in region 1; (2) and competition among peasants will lower it. If the ﬁrst effect dominates, then equilibrium will be unstable and all workers will move to region 1. Krugman shows that there will be divergence (geographic concentration) with lower transportation cost and geographic diversiﬁcation if transportation costs are high. Later on, Krugman and Venables (1995) used the interactions among internal economies of scale, transportation cost and home bias to show how, for different levels of transportation cost, globalization can have different effects on the production structure of two regions. They started with two regions – North and South. Each produces a variety of manufactured good with internal economies of scale and also a homogeneous good. The production structure and consumption have symmetry between the regions. There is only one factor of production: labor. There is no transportation cost for the manufacturing good. Neither region has comparative advantage in any one of the goods. Initially transportation costs are so high that each region consumes what it produces. Now suppose transportation costs decline and two-way trade in manufacturing and intermediate inputs emerges. If now, for some reason, North acquires a larger manufacturing sector, then in its declining transportation costs, intermediate input production will concentrate in this region. That will reduce production costs of manufacturing in the North and will create an industrialized North and de-industrialized South. If transportation costs decline further, it reduces the need for locating the industry near the place where inputs are concentrated. Producers will rather take advantage of lower wages in the South. The industrialization process will be reversed. Real wages will rise in the South and decline in the North and gradually a convergence of living standards can be achieved. Although Krugman’s models explains the interactions of internal economies of scale and international trade in various forms, and helps to understand the forms of trade since World War II, so far not much empirical testing has been done for these types of models. Davis and Weinstein (1996) have tested the home-market bias effect versus factor endowment effect for OECD countries. It turns out that home-market bias is not

Appendix A 133 always apparent. Helpman’s model of international trade with internal economies of scale has features very similar to Krugman’s model. But Helpman has introduced the variety concept in a different way. He has used two factors of production, and two goods in his model, i.e. manufacturing (m) and food (y) are produced with labor and capital. Food is relatively labor intensive and is a homogeneous good. A continuum of potential variety of the manufactured good is presented by points on the circumference of a circle of radius 1/Π. Each consumer has an ideal variety and the consumers identiﬁed by their ideal variety are distributed uniformly over the circle. So each variety has a constant density of consumers and each consumer has the same income. So there is symmetry on the demand side. The consumer is equally happy with x units of his ideal variety or h(v)x of a variety located at a distance v from the location of the ideal variety. He deﬁnes h(0) = 1, h(v) > 1 for v > 0, h′(0) = 0, h′(v) > 0 for v > 0 and h′′(v) > 0. On the production side, Helpman has shown that the elasticity of demand facing a producer of manufactures depends on px, py, and the number of varieties available. He assumes that the elasticity rises in the number of varieties. In an autarky, equilibrium of the number of varieties and the output of a variety depends on the factor endowments. Given identical technologies, if trade opens up with a country that is similar to the country described, then there will be incomplete specialization and factor prices will be equalized. Helpman’s conclusions about trade are similar in spirit to Krugman’s. If relative factor endowments are similar, there will be more intra-industry models. If they are identical, inter-industry trade will be eliminated completely and trade will be of an intra-industry nature. However, Helpman has shown two additional results that are related to country size. If one country becomes more labor abundant keeping GDP, factor and commodity prices constant, the volume of trade increases. If relative factor endowments are preserved, but countries become more unequal in size, the volume of trade declines. Ethier’s (1982) model of international trade and economies of scale is more complicated in the sense that he has used both internal and external economies of scale in the same model. Like Helpman he has introduced two factors of production. There are two goods, wheat (W) and manufacturing good (M) in his model. W is produced with labor and capital under CRS. M is produced with an intermediate good called ‘components’ (x). There are external economies of scale in the production of M; the externality comes from the number of components used. The component, x, on the other hand, is produced under increasing returns to scale with a factor M. This ‘M’ is just like labor, L, in Krugman’s model. Different components or different varieties are produced with decreasing cost. M is further produced with the labor and capital and W is a relatively laborabundant good.

134

Appendix A

In a two-country world, if the home country is relatively labor abundant, then according to traditional trade theories, M, will be cheaper in the foreign country. But that is not necessarily true. If the home country is bigger in size and the scale effect dominates, the reverse will be true. In spite of this indeterminancy in autarky prices, some general conclusions can be drawn about the trading equilibrium. The ﬁrst point to note is that there will be trade in components and irrespective of relative factor endowments that will lower the cost of production of M(M*). This is called scale economies at the international level. Trade in components would be of an intra-industry nature and trade in ﬁnal products will be of a Heckscher–Ohlin nature, assuming incomplete specialization. In spite of all its new characteristics, the basic feature of trade with internal economies of scale remains the same. If the countries are of similar nature as far as endowments are concerned, there will be more intra-industry trade. At the extreme, if countries are totally dissimilar, there will be complete specialization and trade will be inter-industry. As mentioned before, this book follows Krugman in modeling factor mobility with internal economies of scale. Readers interested in detailed derivations of Helpman and Ethier’s model should look at the references.

Appendix B Unemployment

For a while economic theory mainly dealt with a frictionless, perfect economy without any unemployment. But unemployment does exist and it persists. Any analysis for policy implications becomes relevant when it focuses on real-world issues like unemployment. Even when economic analysis extended itself beyond the Walrasian market clearing mechanism, the analysis of unemployment was based on ad hoc mechanisms. Unemployment was explained by unionism, or rigid wages in one sector that ultimately gives way to market clearing by the other sector. Minimum-wage indexed unemployment covers only a small part of unemployment and it does not even take care of adult involuntary unemployment (minimum-wage induced unemployment is more relevant for young adults or those who are entering the job market). During the last thirty years, we have seen a change in trade. Not only were there approaches totally negative of the Keynesian type of unemployment (rational expectations theory by focus, Sergant and Wallace) but we also saw attempts to provide a micro-foundation for Keynesian-type macro unemployment. In the latter, markets are not clearing, prices/wages are either sluggish to adjust or not adjusting, but the reason for this was based on self-interested price setting or price negotiations. It has helped to explain micro data of price dispersion and, furthermore, these approaches help to explain involuntary unemployment. While rational expectation theory has helped to explain ﬂuctuations in output and employment or, at best, voluntary unemployment, the theory based on search, efﬁciency wage and implicit contract has explained involuntary unemployment. In other words, they have provided a micro-foundation for macroeconomic unemployment. Efﬁciency-wage theory is one of the theories that have been developed in recent decades to provide such foundation. The basis of the efﬁciencywage theory is the assumption that labor productivity depends on the wage rate. The higher the wage rate, the higher will be the productivity. Different types of explanations have been provided in the literature for this relation between wages and productivity. For example, in the context of the developing countries, Leibenstein (1957) has pointed out that better

136

Appendix B

wages provide better nutrition and make workers more able to do their jobs. While this explanation is very appropriate for the malnourished workers of the underdeveloped world, this does not hold good for the developed countries. A number of reasons have been cited in the literature for this positive relation in the context of developed countries. My use of efﬁciency-wage theory relies on one of these explanations. Once this reason or explanation is accepted, it is easy to see why wage rigidity and unemployment need to co-exist. At the current wage, let’s suppose there is unemployment. The unemployed workers are willing to work at a wage less than the current wage. If the ﬁrms allow that then there will be a loss in productivity and thus a reduction in proﬁt. Firms therefore hold onto the higher wage even though there is unemployment. Thus, it is possible to have unemployment that will not drive the wage down to the market-clearing level. This has been described in the literature as unemployment equilibrium. It says that zero unemployment is not consistent with equilibrium. This is why it is observed that involuntary unemployment does not drive down the wages in some labor markets. Firms cannot monitor the workers perfectly, or perfect monitoring is costly. In the absence of perfect monitoring, workers tend to shirk (shirking is a normal behavior because work-effort generates disutility). To avoid this, ﬁrms pay higher wages. Higher wages thus work as a substitute of the cost of perfect monitoring. Thus, imperfect monitoring necessitates unemployment. If a worker is caught shirking and dismissed, then he/she loses the high wage and cannot be rehired immediately if there is unemployment. A high wage and unemployment work together as workers’ discipline devices. If a ﬁrm can avoid shirking by paying high wages, and thus are able to raise productivity and proﬁt, all other ﬁrms in the market will follow through. Then incentive for not shirking could disappear, because the workers will think that they will get this same high wage in other ﬁrms. But when all ﬁrms raise their wages, the demand for workers goes down and a pool of unemployment is created, forcing the shirking worker not to have the option of being hired immediately after losing his/her job if caught shirking. Where there is unemployment, workers will thus have an incentive for not shirking. The idea is similar to Salop’s (1979) idea of paying high wages to save turnover cost. There are a few models (Calvo 1979; Foster and Wan 1984; Miyazaki 1984; Shapiro and Stiglitz 1984) that have worked on this relation between efﬁciency wage and shirking. In this book I use the efﬁciency-wage model posted by Shapiro and Stiglitz. Here all workers are alike, i.e. when they are caught shirking and dismissed, the other ﬁrms treat this dismissed worker and the other unemployed workers alike. The only additional information that other ﬁrms will have at this point is that the ﬁrm that has dismissed this worker must be paying low wages so that this dismissed worker did not have the incentive for not shirking. So the new ﬁrm decides to pay high wages. Thus, for similar workers,

Appendix B 137 there would be wage dispersion. The ﬁrm with a high monitoring cost will pay high wages and ﬁrms with a low monitoring cost will pay low wages. In Stiglitz and Shapiro’s (1984) model, there are N identical individuals who like to consume goods but dislike putting forth effort or derive disutility from working. The price of the consumption good (a composite) is normalized at 1 and consumers don’t borrow or save. The utility function can be written as U(w,e) or, more specifically, U = w – e where w is the wage and e is the effort level. Just for simplicity, they assumed that utility function is separable. If the workers are not shirking, e > 0, otherwise e = 0. Workers can either be employed or unemployed. If the workers are working hard without shirking, then there is a probability, b, that they will lose their job. This ‘b’ is given exogenously as the normal turnover rate decided by the relocation of the firms and/or changes in tastes and preferences. If the workers shirk, then there is an additional probability ‘q’ that they will lose their job if they are caught. The discount rate in the economy is given by ‘r’ and ‘a’ is the probability of getting out of the unemployed pool and it is a decreasing function of the unemployment rate in the economy. w 苶 is the unemployment benefit. Workers maximize the expected present discounted value of utility in choosing their effort. Effort is the only choice the workers make in this model. Let’s define VES as the expected lifetime utility of a worker who is employed and shirking. V ES =

w + ( b + q)V UE + (1 − b − q)V ES 1+ r

.

(B1)

This implies that there is no disutility of effort because he is shirking. He faces a (b + q) chance of being unemployed when his utility will be (b + q)VUE and, (1 – b – q) is the probability of being employed from which his utility gain is (1 – b – q)VES . The expected lifetime utility of a non-shirker is given by: V EN =

w − e + bV UE + (1 − b)V EN 1+ r

(B2)

The difference is that this worker’s disutility has been subtracted from total gain. The only way this worker can lose his job is by normal turnover. This is why the probability of getting caught and dismissed, q, does not appear in this equation. The expected lifetime income of an unemployed worker is given by: V UE =

w − a + bV EN + (1 − a)V UE 1+ r

The worker will not shirk if VEN ≥ VES .

(B3)

138

Appendix B

From Equations (B1) and (B2) we get: V ES = w + ( b + q)V UE /( r + b + q)

(B4)

V EN = (w − e ) + bV UE /( r + b)

(B5)

The NSC, or no-shirking condition, can thus be written as: q(VES − VUE) ≥ e, which, using Equations (B4) and (B5), can be expressed as: w ≥ rV UN + ( r + b + q)e / q

(B6)

This shows that efﬁciency wage cannot exist without unemployment, i.e. if a dismissed worker can ﬁnd a job immediately after being caught shirking, then VUE = VES and the no-shirking condition does not hold good. There are M ﬁrms in the economy, each of which has the production function Qi = f(Li), i = 1. . M leading to an aggregate production Q = F(L). L equals total units of effective labor force, i.e. labor in efﬁciency units. Each worker is assumed to supply one unit of effective labor if he/she does not shirk. The wage package that most ﬁrms offer obeys the non-shirking condition, i.e. it is offered with the constraint that the workers choose not to shirk. Shapiro and Stiglitz (1984) assume that F′(N) > e or full employment is efﬁcient. Monitoring workers is not perfect and it is costly. The only punishment the ﬁrms can make use of is by dismissing the shirking employee, because lowering the wage would induce the worker to shirk again. Each ﬁrm will pay the lowest possible unemployment beneﬁts because a high unemployment beneﬁt, w 苶, will raise the cost both directly and indirectly (by creating more incentive for shirking). Assuming 苶 w = 0, each ﬁrm will pay efﬁciency wage, w = f ′(Li) or w = F(L). Each ﬁrm taking wage and employment offered by other ﬁrms as given, will ﬁnd it optimal to offer the going wage rate. To determine market equilibrium, we look at VUE. From Equation (B3) we get: rV UE = w + a(V EN − V UE )

(B7)

We solve Equations (B5) and (B7) simultaneously to get: rV EN = rV UE =

(w − e )( a + r ) + wb a+b+r (w − e )a + ( b + r )w a+b+r

(B8)

(B9)

Substituting the value of VUE from Equation (B3) in NSC condition (B6) we get:

Appendix B 139 w ≥ w + e + e( a + b + r )/ q

(B10)

In steady-state equilibrium, the ﬂow into unemployment pool is bL where L is the aggregate employment. The ﬂow out of unemployment pool is a(N – L) where N is the total labor supply and bL = a( N − L) bL a= ( N − L) Substituting into Equation (B10) we get: w≥ e+w +

 e  bN + r  q N −L 

(B11)

Again we see that full employment is inconsistent with NSC. If N = L, a = ∞, i.e. the dismissed worker would immediately be rehired and, given that possibility, workers will choose to shirk. The equilibrium for w 苶 = 0, is given by:  e   bN  F ′( L) = e +    + r  q N − L 

(B12)

This is where aggregate demand for labor intersects aggregate NSC. In Figure B1 we measure employment on the horizontal axis and wages on the vertical axis. NSC is a rising function of employment because, as employment rises, the chances of being rehired rises and thus shirking

Figure B1 Labor supply curve with efﬁciency wages.

140

Appendix B

becomes more lucrative. At full employment, shirking is optimal. This is why NSC never intersects the full employment line; rather, it approaches the vertical line N. The shaded area is the no-shirking region and any wage below NSC will result in shirking. Figure B2 incorporates labor demand and shows equilibrium wage and employment in the economy. Firms will be happy because they don’t need to raise wages. Workers are providing full effort and they will not think of lowering wages because that will start shirking. Workers are happy because they know that if they shirk they will lose their jobs and there are plenty of other workers who are willing to work at wage ≤w*. Efﬁciency-wage theory does reveal an information problem, but it is quite different from what is addressed by the search theory. Here both ﬁrms and workers are identical and there is full information about job availability and types of workers available. An information problem arises because ﬁrms think they cannot perfectly monitor the workers, or at least it is too costly for the ﬁrms. By looking at NSC we can see that changes in b, or the turnover rate, changes in the mechanism to catch shirking, changes in the discount rate, and changes in the cost of monitoring will change the NSC around the equilibrium wage. Advocates of efﬁciency-wage theory like to look at it as a discipline device. But it is important to know that there are other discipline devices available. For example, workers can post a bond or give an entrance fee. Critiques of this proposal argue that it will create a moral hazard problem. Employers will ﬁnd it very easy to dismiss the workers to appropriate the bond money or to get their entrance fee. But it is possible to post a bond or to pay an entrance fee that will go directly to the workers’ pension fund. That way, there will not be any incentive for the ﬁrms to dismiss the

Figure B2 Labor market equilibrium with efﬁciency wages.

Appendix B 141 workers and fellow workers will co-operate with each other to provide a full effort level to the ﬁrms. It still leaves the question of whether this mechanism will work in an economy where the capital market is not fully developed because, in that case, it will be hard for the workers to come up with the money for bonds or for entrance fees (see Davidson 1990). Efﬁciency-wage theory has gathered lots of support from various authors. A large number of economists, most notably, Akerlof and Yellen (1986), argue that efﬁciency-wage theory is better able to explain a number of stylized facts in the labor market than any other theories. It provides a good explanation for both equilibrium unemployment as involuntary, or why quit rates should fall with unemployment. It explains why the unemployment rate is lower for the skilled-labor market than it is in the unskilled-labor market. According to this, skilled workers do not need monitoring. They gather skill because they are eager to perform at their peak performance level. The working conditions and related things are boring, monotonous and tiring for unskilled workers, who ﬁnd it difﬁcult to put their full energy or effort into their jobs. Since monitoring costs for unskilled workers becomes high, we should see higher rates of unemployment in the market for unskilled workers. Bulow and Summers (1986) support efﬁciency wage theory in the context of a dual labor market. The primary sector is difﬁcult to monitor and thus has a higher wage and unemployment. The secondary sector does not have any monitoring problem and thus has a market-clearing wage. The unemployed in the primary sector do not move to the secondary sector, because even after considering the probability of being unemployed, the primary sector’s wage is tempting. This also helps to explain dispersion among sectors or ﬁrms that cannot be explained by other theories, i.e. compensating differentials, differences in union coverage and labor quality difference. Efﬁciency-wage theory has several important implications for policy purposes. If the government increases unemployment beneﬁt or any other types of transfer payment to the unemployed, this would make workers less fearful about being unemployed. So non-shirking wages will have to be higher or the NSC will move upward. On the other hand, an increase in unemployment insurance (UI) means employer’s share in this beneﬁt program goes up. So, the cost of hiring a worker rises and that moves the labor-demand curve downward. As a result wages and unemployment rise. In a multi-sector economy, an increase in UI moves resources to the high-wage/high-unemployment sector, because workers tend to risk unemployment for the sake of high wages. Transfer payments, either in the form of wage or employment subsidy or job bonus programs, raise employment. If it is paid to the workers, they value the state of being employed and the NSC curve moves down. If it is paid to the ﬁrms, the value of a ﬁlled vacancy becomes relatively higher

142

Appendix B

than the value of an unﬁlled vacancy. So the labor-demand curve shifts rightward and employment increases. If we use NSC with a minimum wage, to have an impact the minimum wage would have to be higher than the equilibrium wage. In this case, wages and unemployment rise. The low-wage sectors are also highemployment sectors, the program of minimum wage shifts resources toward the high-wage sector. Finally, according to Bulow and Summers (1986) if, in a dual economy, trade reduces the price of primary sector’s good, then there would be a welfare-reducing impact, because a high wage will be explained by a low wage/low productivity job, and this economy’s welfare will go down. The implication is that the government should try to subsidize or somehow protect these high wage productive sectors. In this book I use efﬁciency wage as the reason for an endogenous wage distortion. While using it in the context of a developing dual economy, I have found that implications of this distortion stand in sharp contrast with these of exogenous wage distortion. Furthermore, I brought in increasing returns to scale. The effect of factor accumulation or effects of changes in terms of trade are quite different from the effects under exogenous distortion. In the context of the developing countries, I omitted the use of unemployment insurance because it is not present here.

Appendix C

In this appendix I will provide proofs of some of the results I have discussed in the text by using the standard techniques of international trade theory. I will show how, at constant terms of trade, the remaining residents’ income and thereby welfare increases as they receive the migrants’ gift of capital resource. In order to be able to compare the pre-migration and the postmigration situation for the non-migrants, I separate the production equilibrium reached by the non-migrants alone from the equilibrium of the entire economy in the pre-migration situation. The non-traded good produced by the non-migrants is denoted as xn and the trade good produced by the non-migrants is denoted as x1. K2 and L2 are two inputs for the nonmigrants, and Cij is the amount of input i used in the production of j when i = K2,L2 and j = 1,n. Denoting w and r as wage and rental rates respectively, P1 and Pn as output prices and using a full-employment condition, and competitive proﬁt condition, we get: CL2n xn + CL2 1 x1 = L2 ,

(C1)

CK 2n xn + CK 2 1 x1 = K 2 ,

(C2)

where xn and x1 denote the output produced by the non-migrants alone, xn is a capital intensive good relative to x1, wCL2n + rCK 2n = Pn ,

(C3)

wCL2 1 + rCK 2 1 = P1 .

(C4)

and

Further, Cijs are functions of the wage–rental ratio, Cij = Cij (w / r )

(C5)

144

Appendix C

At constant terms of trade, if K2 goes up, the output of xn goes up and that of x1 goes down. Furthermore, following the magniﬁcation effect (Jones 1965) xˆ n > xˆ 1 . Since Y2 = Pn xn + P1 x1 ,

(C6)

at constant terms of trade

(

)

(

)

dY2 = P ∂x1 / ∂K dK + ∂xn / ∂K dk where P = P1 / Pn ,

(C7)

dY2 = ( Pxˆ 1 x1 + xˆ n xn )dK > 0

(C8)

or

using the magniﬁcation effect. Consequently, non-migrants’ income and welfare would go up.

Appendix D

Here it is shown that, as a result of migration, the terms of trade move favorably for the source country. Laborers move out of the source country while leaving behind some or all of their capital resources. The source country produces two goods, Xn and X1, where X1 is the labor-intensive commodity. Following the Rybczynski theorem, production of X1 falls and ˆ | > |Kˆ |, |Xˆ | > |X ˆ | due to the magniﬁcation effect that of Xn rises. Since |L 1 n (Jones 1965) where ‘ ˆ ’ over a variable denotes the rate of change. Income of this country is given by Y = P1X1 + Pn Xn. At constant terms of trade: dY = P1dX 1 + Pn dX n ,

(D1)

where P1 = price of X 1 and Pn = price of X n Therefore, there would be a loss in income in the source country. At unchanged terms of trade, if X1 is a numeraire, i.e. P1 is constant, Pn is the only price that can vary and the market-clearing condition for the nontradables at home can be written: DX n ( Pn , Y ) = X n ( Pn , k ), where DXn = demand for non-traded good, Xn = supply of non-traded good, k = K /L

(D2)

146

Appendix D

Differentiating Equation (D2) we get:

()

Enn Pˆn + (1/ DX n ) ⋅ ( ∂DX n / ∂Y )dY = enn Pˆn + e(nk ) kˆ ,

(D3)

where E nn = own-substitution elasticity in demand (negative) e nn = own-substitution elasticity in production (positive) n ekˆ = elasticity of production with respect to the change in the factor endowment ratio. Solving for Pˆ n, Pˆn = −

{[(m P dY )/[P DX (−E n

1

n

n

+ enn

n n

)]] + e (kˆ )} n kˆ

(D4)

( Pn / P1 ) ⋅ ( ∂DX n / ∂Y ) = mn is the marginal propensity to consume the non-traded good. Similarly, Pˆn* =

{( m P dY ) / [P DX (−E * n 1

*

* n

* n

n* n

+ enn *

)]} − e (kˆ ) n* (k )

(D5)

The world’s excess demand for the source country’s importable commodity is given by (DX2 – X2). At given terms of trade, each change in demand depends on the change in Pn and Y, and production changes (along the production surface) depend only upon the price of non-tradables. Thus, the value of the change in world excess demand for commodity 2 is given by:

(P DX E Pˆ − mdY ) − P X e 2

2

n 2

n

Pˆ

n* * 2 2 n

2

(D6)

Substituting the solution for Pˆ n and Pˆ *n : − P2 DX 2 E2n − P2 X 2 e 2n *

{[( m ) / [P DX (−E n

n

n

{[(m ) / [P DX (−E * n

* n

* n

n* n

n n

)]]P dY + e (kˆ )} − mdY )]]P dY − e (kˆ )}

+ enn

+ enn *

n (k )

1

1

*

n* (k )

(D7)

For substitution effects in consumption, ΣPj dDj = 0, which implies that Σj θj Enj = 0, where θ j is the share of income spent on commodity j(j = X1 or X2 or Xn). Along the transformation surface Σj Pj dxj = 0 so that Σj αj e nj = 0 as well, where α j is the share of income represented by the production of commodity j. Therefore, if all goods are substitutes:

Appendix D 147

{

)[ (

{(

)

( )]}P m }

P2 d ( DX 2 − X 2 ) = dY − m − θx 2 + E2n / θx n − Enn + a x n e nn

{{[α

( − e )] / [θ ( − E ) + α ( e )]}m P dY − P DX E e − P X ( − e ) e ( kˆ ) +

2

n* 2

n2

2

n n 2 ( kˆ )

n n

xn

2

2

n* 2

xn

n* kˆ

n n

* n 1

*

}

1

n

(D8)

where E nj = substitution elasticity in demand of a change in the price of nontradables on consumption of the jth good e nj = substitution elasticity in production of a change in the price of non-tradables on production of the jth good αj = fraction of national income represented by production of good j. The direct-income effect (reﬂecting the shift in demand) via m is deﬁnitely improving the terms of trade. The income effect via the non-traded goods markets in both the countries will affect the terms of trade favorably if the demand elasticities are stronger than the supply elasticities, when dYmn = dY *m n*. As far as the capital-enrichment effect is concerned, its effect via the non-traded good markets in both countries would also be favorable when the demand elasticities are stronger than the supply elasticities.

Appendix E

Since three price ratios – P1/Pn,P2/Pn and P2/P1 – are related because of the interconnection of the markets in this model, following a change in P2/P1 or the terms of trade, the domestic production price ratio P1/Pn, and the domestic consumption price ratio P2/Pn will change. The interrelations of these prices, which come directly from Jones (1974), are shown below. The change in a country’s real income, dy, can be deﬁned as the priceweighted sum of consumption changes: dy = ( P2 / Pn )dDX 2 + dDX n .

(E1)

The budget constraint is given by: ( P2 / Pn ) DX 2 + DXn = ( P1 / Pn ) X 1 + X n .

(E2)

Since, for output movements along the transformation curve, ( P1 / Pn )dX 1 + dXn = 0,

(E3)

by differentiating the budget constraint, we get another expression for, i.e.

)(

(

)

dy = − P2 M / Pn Pˆ2 − Pˆ1 ,

(E4)

where M = import. The equilibrium in the non-traded good market is given by: DX n ( P2 / Pn , Y ) = X n ( P1 / Pn ).

(E5)

If

[(

)

][

(

E = − P2 / Pn / DX 2 ⋅ ∂DX 2 / ∂ P2 / P2

(

)(

m = P1 / Pn ∂DX 2 / dy

)

)]

Appendix E 149 and

(

)

(

e = P1 / Pn / X 1 • dX 1 / d P1 / Pn

)

then, by setting Equation (E1) equal to zero,

) (

)

(E6)

dX n = −( P2 / Pn )e Pˆ1 − Pˆn .

(E7)

(

dDX n − P2 / Pn E Pˆ2 − Pˆn + (1 − m)dy, and

(

)

Therefore, by equating dDXn and dXn, we get:

(

)

(

E Pˆ2 − Pˆn + ( Pn − P2 M )(1 − m)dy = e Pˆn − Pˆ1

)

(E8)

Since,

(Pˆ − Pˆ ) = (Pˆ − Pˆ ) − (Pˆ − Pˆ ), 2

n

2

1

n

(E9)

1

or

(Pˆ − Pˆ ) = [E /(E + e)](Pˆ − Pˆ ) + {[P (1 − m)] / [P M(E + e)]}dy,

(E10)

(Pˆ − Pˆ ) = [(E + m − 1) / (E + e)](Pˆ − Pˆ )

(E11)

n

n

1

1

2

1

n

2

2

1

Appendix F

To trace the effect of migration from Country I to Country II on the world’s terms of trade, it is necessary to look at the changes in the global demand and supply of the goods. In this appendix, I have shown how the relative world supply of X and Y is affected by this labor outﬂow. Migraˆ * > 0 (where a ‘ ˆ ’ over a tion from Country I to Country II implies that L variable denotes the rate of change of that variable). From Equations (2.1), (2.2), (2.3) and (2.4) we get (see Jones 1965):

(Yˆ

*

1 ˆ * ˆ * δ *L + δ *K − Xˆ * = L −K + wˆ − rˆ * λ* λ*

)

(

)

(

)

(F1)

* * − θ Lx , λ*ij = fraction of factor i in industry j. where λ* = λ*Ly − λ*Ky , θ * = θ Ly

θij = distributive share of factor i in industry j. * δ *L = λ*Ly θ Ky σ *y + λ*Lx θ *Kx σ *x * * δ *K = λ*Ky θ Ly σ *y + λ*Kx θ Lx σ *x

σ *x = σ *y =

(

* * aˆ Kx − aˆ Lx wˆ * − rˆ * * * aˆ Ky − aˆ Ly

wˆ * − rˆ * 1 ˆ wˆ * − rˆ * = PYw − Pˆxw θ*

(Yˆ

(

)

*

)

(

) ) (

1 ˆ* ˆ * − Xˆ * = L − K + δ *s PˆYw − Pˆ X w λ*

)

Appendix F 151 δ *s =

1 λ θ* *

(δ

* L

+ δ K*

)

(F2)

For Country I:

(Yˆ − Xˆ ) = λ1 (Eˆ − Kˆ ) − δ (Pˆ * s

Yw

)

− Pˆ X w eE

(F3)

where |λ| and σs, are deﬁned in a similar fashion and eE is the elasticity of ˆ shows the change in employment with respect to product prices. E employment at a given price. But, for a given minimum wage, E also changes with the change in the price and this is shown by the second term ˆ and K ˆ are zero, on the right-hand side. Since both E

(Yˆ − Xˆ ) = −δ (Pˆ s

Yw

)

w − Pˆ X w eE

(F4)

The relative rate of change in the world supply of goods Y and X can be shown as:

(Yˆ

w

) (

)

(

)

Y */ X * Y/X − Xˆ w = Yˆ * − Xˆ * + Yˆ − Xˆ Yw / X w Yw / X w

(

)

 ˆ* ˆ * Y* − X*  L − K * * ˆ ˆ Y −X + δ *x Pyw − Pˆ X w =  Yw / X w λ*  ˆ * Since K = 0,

(

)

(Yˆ

*

(

(F5) 

)  YY // XX 

*

w

  w  *

 Y */ X *  Y * / X * Lˆ * Y * / X * − Xˆ * = + δ *x Pˆyw − Pˆxw   * Yw / X w λ Yw / X w  Yw / X w 

)

(

)

(F6)

(F7)

For Country I

(Yˆ − Xˆ ) YY//XX = [− e δ (Pˆ E

w

w

s

yw

− Pˆ X w

)] YY//XX w

(F8)

w

So,

(Yˆ

w

)

− Xˆ w =

  Y */ X *  Y/X  ˆ + δ *s  + ( − eE δ s )  Pyw − Pˆxw  Yw / X w  λ* Yw / X w   Yw / X w 

Lˆ * Y * / X *

(

) (F9)

The change in the commodity–price ratio is then derived by the mutual interaction of demand and supply.

Appendix G

Using Shapiro and Stiglitz’s (1984) model, I will show that, if skilled workers are fully committed to work and there is no desire for shirking, then equilibrium will be consistent with full employment. If any worker ever shirks and is dismissed for shirking in this market, the worker can ﬁnd another employment. The normal turnover of workers and the workers dismissed for shirking create a pool of unemployed workers for a short period of time. Although absence of any distortion naturally results in full employment, I will use Shapiro and Stiglitz (1984) to show that, if there is no disutility from work and workers are fully committed, then the market will operate at full employment level. For a non-shirker in this market:

[

(

rV N1 = W1 + b V U1 − V N1

)] / P

(G1)

where VN1 is the expected lifetime utility of a non-shirker in the skilledworkers’ market, W1 is the current wage in the skilled-workers’ market, b is the exogenously given turnover rate, and VU1 is the expected lifetime utility of an unemployed worker in this market. For a shirker in the skilled-workers’ market (if anybody ever wants to shirk in this market):

(

)

rV S1 = W1 + ( b + q) V U1 − V S1 − e

(G2)

where VS1 is the expected lifetime utility of a shirker in the skilled-workers’ market, e苶 is the disutility of not being able to do the job an individual is trained for and q is the probability of being caught if shirking. b and q are assumed to be the same in both markets. The introduction of a different turnover rate and a different q in the skilled workers’ market would not change the conclusions. For an unemployed worker in this market:

(

)

rV U1 = W + a′ V N1 − V U1 − e

(G3)

where W 苶 is the unemployment beneﬁt in this market and a′ is the probability of getting a job when unemployed in this market. Since the short-run

Appendix G 153 pool of unemployed workers in this market results from the regular turnover of workers and the workers who are dismissed for shirking, the unemployment pool would be made of (b + q)L1. So a′(E1 – L1) = (b + q)L1 where E1 is the total number of skilled workers and L1 is the number of employed skilled workers. In the steady-state equilibrium when ﬂow out of the existing unemployment pool equals ﬂow into this pool, a′ = 1. Using Equations (G1) and (G2) we can write: V N1 =

W1 + bV U1 P ( r + b)

(G4)

and V S1 =

W1 − e + ( b + q)V U1 P ( r + b + q)

(G5)

Workers would not shirk if: V N1 ≥ V1S By manipulating Equations (G4) and (G5) we get: e W1 ≥ − ( r + b) + rV U1 q

(G6)

as the NSC. Using Equations (G3) and (G4) we get: V1U =

W ( r + b) + a′W1 − e ( r + b) r ( a′ + b + r )

(G7)

Substituting Equation (G6) into Equation (G7) we get:  a′ + b + r  W1 ≥ W − e  + 1 q   as the NSC and the equilibrium in the skilled-labor market is attained when f ′(L1) = W1.

Appendix H Derivation of the non-shirking condition and a subsequent comparative static analysis

According to the efﬁciency-wage theory posited by Shapiro and Stiglitz (1984), workers’ asset utility varies depending on whether the worker is employed and shirking, or employed but not shirking or unemployed. Given an exogenous turnover rate, b, a probability of being caught if shirking, q, a discount rate, i and a job acquisition rate, a, the asset-value equation of a worker who shirks is given by: iVmS = ( b + q)(V mU − V mS ) + wm

(H1)

Here iVmS (interest rate times asset value) equals ﬂow beneﬁts (wm = Wm/P) plus expected loss (which includes unemployment resulting either from normal turn over or from being dismissed after caught shirking). The similar equation for a worker who is employed but not shirking is given by: iVmN = wm − e0 + b(V mU − V mN )

(H2)

Note that disutility from work, e0, is taken into consideration. For an unemployed worker, the asset-value equation is given by: iV Um = a (V mN − V Um )

(H3)

Workers stop shirking if, and only if, VNm ≥ VmS (utility from non-shirking ≥ utility from shirking). Using Equations (H1) and (H2), the no-shirking condition (NSC) is written as: wm ≥ iV Um + (i + b + q)e0 / q

(H4)

Using Equations (H2) and (H3), we can write: iV mN = (wm − e0 )( a + i ) / ( a + b + i )

(H5)

iVUm = (wm − e0) a /( a + b + i )

(H6)

Appendix H 155 Substituting the expression for VUm in Equation (H4), we get the NSC: wm > e0 + e0 ( a + b + i )/ q

(H7)

Since in steady state equilibrium a = bLm /(Em – Lm), Equation (H7) can be written as: wm > e0 + ( e0i / q)( e0 bEm ) / ( qEm − Lm )

(H8)

From Equation (H8) we can write: Lm = Em ( A − e0 b) / A where A = wmq – e0q – e0i Em = total labor supply in the urban sector. Lm = employed labor in the urban sector. Thus, 0 < ( ∂Lm / ∂Em ) < 1 or ( ∂U m / ∂Em ) = 1 − ( ∂Lm / ∂Em ) > 0 This implies that any increase in the size of the urban labor market will increase the number of both employed and unemployed workers. Thus, when the rural migrants join the pool of existing unemployed workers they raise both employment and unemployment levels in the economy. The unemployment rate, however, may go down if the elasticity of wage with respect to unemployment is high.

Effects of changes in factor supply Totally differentiating Equation (5.1) and using Equation (5.2) we obtain: (1 − ε )dX m = h ( FKm dKm + FLm dLm )

(H9)

where FKm and FLm denote the partial derivative of Fm with respect to capital and labor respectively. Using Equations (5.3) and (H9) again we get: (1 − ε ) Xˆ m = θ Lm Lˆ m + θ Km Kˆ m

(H10)

156

Appendix H

The corresponding equation for the rural sector is: Xˆ a = θ La Lˆ a + θ Ka Kˆ a

(H11)

We get Equation (H11) by using Equations (5.6) and (5.7). The circumﬂex ‘ˆ’ denotes the rate of change in a variable, e.g.: Xˆ m = dX m / X m and θ ij (i = L, K

j = 1, 2)

is the share of the ith factor in the total value of the jth commodity. The external economies of scale implies average cost pricing in manufactures. Thus, writing rm = ra = r, we have: Wi Li + rKi = Pi X i Differentiating that, and utilizing Equations (H10) and (H11), we get: θ Lm Wˆ m + θ Km rˆ = εXˆ m θ LaWˆ a + θ Ka rˆ = 0

(H12)

Deﬁne elasticity of factor substitution of the ith sector as: δ i = ( Kˆ i − Lˆ i ) / (Wˆ i − rˆi )

(H13)

where δi > 0. Substitution of Equations (H10) and (H11) into Equation (H13) for each sector yields: Lˆ m = (1 − ε ) Xˆ m − θ Km δ m (Wˆ m − rˆ) Kˆ m = (1 − ε ) Xˆ m + θ Lm δ m (Wˆ m − rˆ)

(H14)

Lˆ a = Xˆ a − θ Ka δ a (Wˆ a − rˆ) Kˆ a = Xˆ a + θ La δ a (Wˆ a − rˆ)

(H15)

From Equation (5.9): Wˆ m − Wˆ a + Lˆ m = Eˆ m αˆ + Lˆ m = Eˆ m

(H16)

ˆ . ˆm – W where αˆ = W a Differentiating Equation (5.10) we get: λ km Kˆ m + λ ka Kˆ a = Kˆ αλ Lm Lˆ m + λ La Lˆ a + αλ Lm αˆ = Lˆ

(H17)

Appendix H 157 Where λij (i = L, K j = 1,2) is the proportion of the ith factor employed in the jth industries and Vm. Substitute Equations (H14) and (H15) into Equation (H17). This yields: λ Km (1 − ε ) Xˆ m + λ Ka Xˆ a = − λ Km θ Lm δ m (Wˆ m − rˆ) − λ Ka θ La δ a (Wˆ a − rˆ) + Kˆ

(H18)

αλ Lm (1 − ε ) Xˆ m + λ La Xˆ a = αλ Lm θ Km δ m (Wˆ m − rˆ) + λ La θKa δ a (Wˆ a − rˆ) − λ Lm ααˆ + Lˆ

(H19)

As we know from Equation (5.9): Wa α = Wm Wˆ a + αˆ = Wˆ m substituting this into Equation (H12): θ Lm Wˆ m + θ Km rˆ = εXˆ m θ LaWˆ m + θ Ka rˆ − θ La αˆ = 0

(H20)

With some algebraic manipulation we get: (Wˆ m − rˆ) = ( εXˆ m − θ La αˆ ) / (θ Lm − θ La )

(H21)

(Wˆ a − rˆ) = ( εXˆ m − θ Lm αˆ ) / (θ Lm − θ La )

(H22)

Now substitute Equations (H21) and (H22) into Equations (H18) and (H19):

[

λ Km (1 − ε ) Xˆ m + λ Ka Xˆ a = − λ Km θKm δ m ( εXˆ m − θLa αˆ ) / θLm − θLa

[

]

]

− λ Ka θLa δ a ( εXˆ m − θLm αˆ ) / θLm − θLa + Kˆ

(H23)

[

αλ Lm (1 − ε ) Xˆ m + λ La Xˆ a = αλ Lm θKm δ m ( εXˆ m − θ La αˆ ) / θ Lm − θ La

[

]

+ λ La θ Ka δ a ( εXˆ m − θ Lm αˆ ) / θ Lm − θ La ) − λ Lm ααˆ + Lˆ

] (H24)

ˆ m in Equation (H16) we get: Substituting the value of L

[(

)

]

αˆ θ Lm − θ La + θ Km δ m θ La / θ Lm − θ La + Xˆ m

[(1 − ε)(θ

Lm

) (

)(

− θ La − θ Km δ m ε / θ Lm − θ La

)] = Eˆ

m

(H25)

158

Appendix H

From Equations (H23), (H24) and (H25):  Π11   Π 21  Π 31 

Π12 Π 22 Π 32

Π13   Π 23  Π 33 

 Kˆ   Xˆ m   ˆ   ˆ   Xa  =  L   Eˆ m   αˆ     

Where ∏11 = λ Km (1 − ε ) + [ λ Km θ Km δ m ε / (θ Lm − θ Ls )] + [ λ Ka θ La δ a ε / (θ Lm − θ La )] ∏12 = λ Ka ∏13 = − [ λ Km θ Km δ m θ La / (θ Lm − θ La )] − [ λ Ka θ La δ a θ Lm /(θ Lm − θ La )] ∏ 21 = [αλ Lm (1 − ε ) − αλ Lm θ Km δ m ε / (θ Lm − θ La )] − [ λ La θ Ka δ a ε / (θ Lm − θ La )] ∏ 22 = λ La ∏ 23 = [αλ Lm θ Km δ m θ La / (θ Lm − θ La )] + [ λ La θ Ka δ a θ Lm / (θ Lm − θ La )] + λ Lm α ∏ 31 = [(1 − ε )(θ Lm − θ La ) − θ Km δ m ε ] / (θ Lm − θ La ) ∏ 32 = 0 ∏ 33 = [(θ Lm − θ La + θ Km δ m θ La ) / (θ Lm − θ La )] X m = [ Kˆ ( Π 22 Π 33 − Π 23 Π 32) − Lˆ ( Π12 Π 33 − Π13 Π 33) + Eˆ m ( Π12 Π 23 − Π13 Π 22)] / ∏

( Π 22 Π 33 − Π 23 Π 32) > 0, thus

Xˆ m >0 Kˆ

( Π12 Π 33 − Π13 Π 32) > 0, thus

Xˆ m >0 Lˆ

( Π12 Π 23 − Π13 Π 22) > 0, thus

Xˆ m >0 Eˆ m

Xˆ a = [ − Kˆ ( Π 21Π 33 − Π 23 Π 31) + Lˆ ( Π11Π 33 − Π13 Π 31) − Eˆ m ( Π11Π 23 − Π13 Π 21)] / ∏ Xˆ a Xˆ a Xˆ < 0, > 0, and a < 0 Kˆ a Lˆ a Eˆ m

Appendix H 159 αˆ = [ Kˆ ( Π 21Π 32 − Π 22 Π 31) − Lˆ ( Π11Π 32 − Π12 Π 31) + Eˆ m ( Π11Π 22 − Π12 Π 21)] / Π αˆ αˆ αˆ > 0, < 0, and >0 Kˆ Lˆ Eˆ m I will now show the effects of changes in factor supply on factor returns. ˆ m from Equation Using Equations (H23) to (H25), and the value of X (H12), we get:    1− ε λ Ka X mT ′ θ Lm + λ Km θ Km δ m Wˆ m +  λ Km   θ Lm + ε Xa  ε       1− ε  λ KaT ′X m θ Km  θ Km +  λ Km   θ Km +  ( λ Km θ Km δ m + λ Ka θ La δ a ) rˆ ε Xa  ε   (θ Lm − θ La )    +

θ La θ Lm − θ La

[ λ Lm θ Km δ m − λ Ka θ Lm δ a ]Wˆ a = Kˆ

(H26)

   1− ε λ LaT ′X m θ Lm − αλ Lm θ Km δ m + λ Lm α Wˆ m + αλ Lm   θ Lm + ε Xa  ε       1− ε λ LaT ′X m θ Km θ Km + (αλ Lm θ Km δ m + λ La θ Ka δ a ) rˆ + αλ Lm   θ Km + ε θ Lm − θ La Xa  ε      1 (H27) (αλ Lm θ Km δ m θ La + λ La θ Ka δ a θ lm ) − λ Lm α Wˆ a = Lˆ −  θ Lm − θ La    (θ Lm − θ La + θ Km δ m θ La )   [(1 − e)(θ Lm − θ La ) − θ Km δ M e ]  θ Lm  θ Km Wˆ m +   + θ Lm − θ La (θ Lm − θ La ) ε      ε   [(1 − ε )(θ Lm − θ La ) − θ Km δ m ε ]   (θ Lm − θ La + θ Km δ m θ La )   rˆ +  Wˆ a = Eˆ m (H28) (θ Lm − θ La ) − θ θ  Lm La     A11   A21  A31 

A12 A22 A32

A13   A23  A33 

 Kˆ  Wˆ m   ˆ     rˆ  =  L   Eˆ m   Wˆ a     

Wˆ m  ( A22 A33 − A23 A32)  = >0   Kˆ A  

160

Appendix H A A −A A  rˆ 21 33 23 31  >0 = −   Kˆ A Wˆ a  ( A21 A32 − A22 A31)  = <0   Kˆ A   Wˆ m ( A12 A33 − A13 A31) =− Lˆ A rˆ ( A11 A33 − A13 A31) = Lˆ A Wˆ a ( A11 A33 − A12 A31) = Lˆ A Wˆ m  ( A12 A23 − A13 A22)  = <0  Eˆ m  A  ( A A − A A )  rˆ 11 33 13 21  = − <0   Eˆ m A   ( A A − A A )  ˆa W 11 22 12 21  = >0 ˆm   E A  

where  1−ε λ KaT ′X m θLm A11 = λ Km  + λ Km θKm δ m  θLm + Xaε  ε   1− ε λ KaT ′X m θ Km θ Km A12 = λ Km  + ( λ Km θ Lm δ m + λ Ka θ La δ a )  θ Km + Xa ε θ Lm − θ La  ε  A13 =

θLa θLm − θLa

( λ Lm θKm δ m − λ Ka θLa δ a )

 1−ε λ LaT ′X m θLm A21 = αλ Lm  − αλ Lm θKm δ m + λ Lm α  θLm + ε Xa ε    1−ε λ LaT ′X m θKm θKm A22 = αλ Lm  + (αλ Lm θKm δ m + λ La θKa δ a )  θKm + Xa ε θLm − θLa  ε    1 A23 =  − (αλ Lm θKm δ m θLa + λ La θKa δ a θLm ) − λ Lm α   θLm − θLa 

Appendix H 161 A31 = A32 =

(θLm − θLa + θKm δ m θLa ) (θLm − θLa )

 [(1 − e )(θLm − θLa ) − θKm δ m ε ]  θLm +  (θLm − θLa )   ε

θKm  [(1 − ε )(θLm − θLa ) − θKm δ m ε ]     ε  (θLm − θLa )

 (θLm − θLa + θKm δ m θLa )  A33 =   θLm − θLa  

Effects of changes in commodity prices Wm Lm + rKm = Pm X m

(H29)

Totally differentiating this equation and using Equation (H10) we get: θLm Wˆ m + θKm rˆ − eXˆ m = Pˆm

(H30)

Similarly, totally differentiating Wa La + rKa = Pa X a and using Equation (H10) we get: θLaWˆ a + θKm rˆ = Pˆa

(H31)

ˆ m from Equation (H14) in the ﬁrst equation of Substituting the value of L ˆ ˆ a, we get: (H16) and using αˆ = Wm – W Wˆ m (1 − θKm δ m ) − Wˆ a + (1 − ε ) Xˆ m + θKm δ M rˆ = Eˆ m

(H32)

and from Equation (H14) we get: Wˆ m ( −θKm δ m ) + (1 − ε ) Xˆ m + θKm δ m rˆ = Lˆ m Using Equations (H30) to (H32) we write:  A11   A21   A31 A  41 A >0

A12 A22 A32 A42

A13 A23 A33 A43

A14   A24   A34  A44 

Wˆ m   Pˆm       rˆ   Pˆa   ˆ  = ˆ  Xm   Em   ˆ  ˆ   Wa   Lm 

(H33)

162

Appendix H Wˆ M =

Pˆm A1 − Pˆa A2 + Eˆ M A3 − Lˆ M A4 A

[

]

[

]

[

Pˆm θKm (1 − ε ) − Pˆa θKm (1 − ε ) + θKm δ m ε + Eˆ m −θKm θLa (1 − ε ) − θKm δ m εθLa    − Lˆ m θKm θLa (1 − ε ) + εθKa + θKm δ m εθLa Wˆ m =  A

[

]

Thus: Wˆ m Wˆ m Wˆ m Wˆ m > 0, < 0, < 0 and Pˆm Pˆa Eˆ m Lˆ m Using this calculation, we also ﬁnd: rˆ Wˆ a > 0, and < 0. Pˆm Pˆm

<0 Eˆ m = 0

] 

Notes

1 International labor mobility with full employment 1 See Bordo et al. (1999), according to whom, ‘our world is different: commercial and ﬁnancial integration before World War I was more limited’. 2 Net migration accounted for between 32 percent and 43 percent of the total increase in the white population during 1880–1910. The only comparable intercontinental migration was the black slaves from Africa to the Americas and the Caribbean (Hatton and Williamson 1998). 3 In fact, wages the emigrants expect to receive are usually higher than W1 – the home country’s wage in the post-migration period. In this case, the argument for the home country’s or source country’s gain becomes stronger. 4 This conclusion seems to be especially relevant for Third-World countries because a large fraction of the migrants from these countries are professionals or semi-skilled workers in service-sector occupations that typically belong to the non-traded goods sector. See Grubel and Scott (1966) and McMillan (1982). 5 This assumption implies that each country has no demand for the commodity it exports (e.g. some types of medicines and pesticides exported by the USA and some types of leather goods exported by India) and that neither country can produce the commodity similar to the one it imports (e.g. import of some types of medicines, pesticides and some machineries by the developing countries, import of coffee by the USA). See Jones (1974; 1979). 6 See Goldlust and Richmond (1974) and Richmond (1981) for a detailed analysis of immigration adaptation process. 7 Due to the pattern of production specialization and the nature of consumption, domestic production–price ratio is different from the domestic consumption– price ratio in this model. 8 Most potential migrants that move to developed-countries usually own capital assets directly related to their profession or business. Although the human capital they own is usually moved in its entirety to the host country after migration, it may not be possible for the migrants to move all of the capital stock they own out of the source country. Some of the capital stock may be in terms of nontraded goods and hence not movable to other countries. Or, the migrant may own some capital stock jointly with other members of his/her family or with other people in a partnership business. The migrants do not sell the capital stock they own because they do not rule out the possibility of return migration. After migration, they may transfer ownership of part of this capital stock to the nonmigrants. See also Basu and Bhattacharyya (1991) and Rivera-Batiz (1982) for a discussion of this effect in the context of a model with non-traded goods. 9 Capital enrichment would have a direct income effect and another effect via change in the terms of trade, both of which would favorably affect the welfare of

164

Notes

non-migrants. Since this chapter analyzes all factors affecting the terms of trade separately, only analysis of how the gift of capital can raise the remaining residents’ welfare through the direct-income effect is provided. 2 International labor mobility with exogenously created unemployment 1 In Brecher and Choudhri’s (1987) analysis, if the law regarding the unemployment beneﬁt package is equally applicable to migrants as well as to domestic residents, then immigrants only add to the existing number of unemployed workers. The national and global unemployment rates go up. The employment rate of domestic workers remains unchanged. In this chapter’s model, immigrants not only join the existing pool of unemployed workers, but by changing the terms of trade they also reduce the employment rate of domestic workers. The host country therefore suffers more severely. 2 For example, if we consider trade and labor migration between the USA and Mexico, the analysis in this chapter suggests that, to provide a guaranteed minimum compensation for its workers, it would be better for the USA to pursue a policy of unemployment beneﬁt packages than to use the minimumwage law. This model can also be used to analyze trade and factor movements within the block of developing countries. A relatively capital abundant developing country with a binding minimum-wage law can trade with another developing country and use a free-migration policy to reduce its unemployment or the severity resulting from its domestic factor market distortion (see also note 10). 3 Although the logistics of the model follows Brecher (1974a), it uses the seminal work of Jones (1965) in laying down the production structure of these two countries. 4 Since a binding minimum wage, i.e. a minimum wage higher than the full employment wage, always creates unemployment, the focus of this chapter is on the unemployment equilibrium. The cases of full-employment equilibrium are not discussed here. 5 The conclusions do not change if the wage is ﬁxed in terms of the other good (see Brecher 1974a). 6 The diagrammatic exposition of these linear segments of the PPF and the offer curve is given in Brecher (1974a). To avoid unnecessary repetition, it is not presented here. The mathematical proof may be obtained from the author upon request. 7 In this complete specialization zone, when X is the only good produced, real wage has to be expressed in terms of X. If, in this zone, the price of X, Px, goes up, then  Py  P =   Px  苶y goes down and the real wage Wx /P goes up, i.e. Wx /P becomes higher then W (the constrained wage Wy = Wx /P before any price change). Since  Wx  E = f= = Wy   Px  this provides the opportunity to hire more workers until these additional workers, via their impact on marginal products, bring down Wx /P to W 苶y (minimum wage).

Notes

165

8 The expected wage is deﬁned as the actual wage multiplied by the probability of employment. Harris and Todaro used this term for the ﬁrst time in their 1970 article (Migration, unemployment and development: a two sector analysis), where they deﬁne the probability of employment as the ratio of the number of people employed to the total number of workers. 9 In the present model, the dynamics of the migration process and the resulting adjustment in the expected wages are taken into consideration to separate out long-run equilibrium from all other equilibrium situations. In Brecher and Choudhri’s (1987) model this adjustment process is not explicitly taken into consideration. Migrants in their model never consider the possibility of being unemployed. 10 This type of migration policy would be relevant for the factor movements within a group of less-developed countries (LDCs). The unemployment implication of a minimum-wage law is serious for these labor-abundant countries. A large number of these countries are now experiencing the consequences of minimum-wage laws resulting from union pressures. If a minimum wage results in a high level of unemployment, then workers might be eager to move to a neighboring country where the expected wage is higher. Depending on the pattern of production or the nature of specialization, this labor outﬂow will then work favorably for this country to reduce the severity of the effects of domestic factor market distortion. 11 Since the trading Zones 2 and 3 represent equilibrium where terms of trade cannot be changed, the formal proof of changing employment or welfare by terms of trade changes is not necessary. Unemployment is reduced because a part of the unemployment pool goes out of the country. The terms of trade might change at equilibrium Zone 1 but, as shown in Figure 2.1 it does not affect employment. So out-migration just results in reduction of unemployment in Country I and increases in Country II’s employment or global employment. 12 The conclusion does not change if the demand pattern is different in the two countries, but the equation showing the effect of migration becomes more cumbersome. 13 The price of the labor-intensive good does not rise so much as to enable Country I to change its specialization because that would result in a no-trade situation. 14 The level of unemployment at this point could be higher than that of a no-trade situation if the new equilibrium happened to be in Zone 4, i.e. on a PPF, which is lower than a no-trade PPF. 15 Introduction of any trade policy to reduce distortion would not only involve either consumption distortion or production distortion, or both, but it might also impose a ﬁnancial burden (for trade subsidy) on the economy. Free migration does not introduce any additional distortion and/or any ﬁnancial burden. 3 International labor mobility with endogenously created unemployment 1 Akerlof and Yellen referred to this aspect of efﬁciency wage hypotheses in their survey of efﬁciency wage models (1986: 16). 2 Hazari’s model focuses on an issue relevant to developing countries where a large number of skilled workers emigrate from the urban non-traded goods (service) sector. Since urban traded goods in these countries are usually capital intensive, according to Hazari’s model, emigration of skilled workers will create more unemployment for the unskilled workers and wages of the skilled workers will go up. This might also have some not-so-desirable ‘Dutch Disease’ type of effects on structural changes involving dual sectors of these countries, which are so important for this development process. While analyzing employment and wage effect of immigration, Djajic’s model, on the other hand, shows that the

166

3

4 5 6 7

8 9

10

11 12

13

Notes

skill composition of the native labor force will change as a result of labor inﬂow, which compares very well with the similar analysis of this chapter. Capital in this broad sense is not a collection of tangible assets to be used directly in the production process. Capital is something (some form of ‘stock of waiting’) that makes other available resource(s) in the economy usable for the production process. These other resources must be improved by acts of investment before they can contribute to current production. The individual holding of this capital depends on the distribution rule for K in the economy. This should not be confused with ability. This is an asset that is marketable and is used for increasing skill or ability. The marginal product of capital here should not be confused with the rate of interest, since it is only the rental of a capital good. The price of a unit of capital, if it lasts forever, will of course be equal to the rental divided by the rate of interest. K is not large enough to transform the entire labor force into skilled workers. To avoid unnecessary repetition, the analysis has been shortened. For more information, see Shapiro and Stiglitz (1984). If e were a continuous variable, it would not change the result. The assumption of a ﬁxed turnover rate is introduced to avoid explicit modeling of job turnover and it is a standard assumption in the literature covering efﬁciency wages. See Bulow and Summers (1986), Jones (1987) and Shapiro and Stiglitz (1984). See Shapiro and Stiglitz (1984) for detailed derivation of this condition. This derivation involves the maximization of the expected present discounted value of utility. The same format is also used to explain the skill requiring decision. The derivations in this section also follow within the expected utility format. In this section, V′1 presents the expected lifetime utility for a worker in the skilledlabor market and V′2 presents the expected lifetime utility for a worker in the unskilled-workers’ market. In the previous section, V 2s , V N2 and V u2 presented expected lifetime utility for a shirker, non-shirker and an unemployed person respectively in the unskilled market. Note that the expected loss from unemployment depends on b(V′u – V′2) where b is the turnover rate. But in a steady state of equilibrium a(E2 – L2) = bL2 where a is the probability of getting a job. So (1 – a) is the probability of being unemployed in steady-state equilibrium which, in terms of b, becomes 1 – bL2 / U2 or (1 – bL2 (·))/(E2 – L2). And thus (1 – a)(V′u – V′2) becomes the expected loss if unemployed in steady state. Note that a difference in φi does not contribute to the wage differences. It determines whether a worker should belong to the skilled- or the unskilledlabor workforce by inﬂuencing rV′1 and rV′2 given W1 and W2. From Equation (3.11) it is obvious that, given N, a change in f(φ) (which is similar to a density function giving the proportion of population enjoying φ1, a value for capital assets) would change L1. A change in f(φ) can only result from a change in the distribution rule. ∫f(φ)dφ is an anti-derivative of F(φ) with respect to φ within the interval zero and φ. Pˆx − Pˆy Wˆ 1 − Wˆ 2 = . θ

ˆ i denotes We use ‘ ˆ ’ to denote the relative change. On the left-hand side, W dWi /Wi where i = 1, 2 and |θ| = θx1θy2 – θx2θy1 where θji = Wi aji /Pj is the share of the ith factor in the cost of good j = X,Y and |θ| > 0 if, and only if, industry X is relatively intensive in L1·Px and Py are the prices of these two goods. So an increase in Px and Py will raise the real return to the skilled labor, which is being used intensively in the production of good X (see Jones 1965).

Notes

167

14 A change in relative commodity prices will change the relative factor supply. Using simpler notation, we can say that, given everything else, L1/L2 = h(We1/We2), where Wei, i = 1,2 is the expected wage deﬁned as the actual wage multiplied by the probability of employment. Totally differentiating L1/L2 = h(We1/We2), we get ˆ –L ˆ = E (W ˆ e –W ˆ e ) where E is the elasticity of h with respect to We/We . L 1 2 hw hw 1 2 1 2. Using Pˆx − Pˆy ˆ e ˆ e L1 + L2 + U = N , Wˆ 1 − Wˆ 2 = , W 1 − W 2 = Wˆ 1 − Wˆ 2 + dˆ θ

(

)

where dˆ is the probability of employment.  Pˆ − Pˆ  N U L2 x y  Lˆ 1 = λ 2 Ehw  + λ 2 Ehw dˆ + Nˆ − Uˆ where λ 2 =  θ  L L L L L + + 1 2 1 2 1 + L2   By differentiating the full employment condition and using these relations, we can express output changes as: Pˆx − Pˆy λ y 2 δ 1 + λ 2 Ehw + λ y1 δ 2 + λ 1Ehw + λ y 2 λ 2 Ehw dˆ + λ y1λ 1Ehw dˆ Xˆ = θλ

[ (

+ Nˆ

N L2 + L2

− Uˆ

)

(

)]

U L1 + L2

Pˆx − Pˆy Xˆ = λ x 2 δ 1 + λ 2 Ehw + λ x 2 λ 2 Ehw dˆ + λ x 1 δ 2 + λ 1Ehw + λ 12 λ 2 Ehw dˆ θλ

[ (

+ Nˆ

N L2 + L2

− Uˆ

)

(

)]

U L1 + L2

where λij is the fraction of labor of type I in sector j. δ 1 = λ x 1θ y 1 δ x + λ y 2 θ y 2 δ y δ 1 = λ x 1θ y 2 δ x + λ y 1 θ y 1 δ y , and δj is elasticity of substitution along an isoquant in sector I. Since |λ||θ| > 0 output effects have a standard sign, but are somewhat stronger than in a standard two-sector model because of the added effect of the changes in L1/L2 reﬂected in λ1Ehw. It must be noted that this price output response has been calculated with the assumption of perfect intersectoral mobility of two types of workers. The question of factor mobility in this chapter is related to mobility across national borders. Because an alternative would complicate the analysis considerably, and take away attention from this main issue, I have assumed perfect intersectional mobility of factors. 15 Since each of the two goods produced in the economy needs both skilled and unskilled workers, the economy will have to maintain a positive supply level for each type of worker. A very high price for skilled labor-intensive goods will encourage all workers to participate in the skilled-workers’ market, which the existing production structure cannot operate with. 16 Just for simplicity, it makes more sense for the model to consider the individual share of the special input φi rather than Ki, because if, for some reason, the total supply of this input changes (maybe by borrowing from a foreign country or if migrants bring additional supply of K), the derivation of the effects

168

17

18

19 20 21

22

Notes

becomes direct. The equilibrium share of the special input, Ki /K, changes, i.e. ~ ~ ∂ φ/∂K = – φ/K and that consequently affects the distribution of skilled and unskilled labor. Any changes in the economy are bound to affect the shirking decision for individuals (i.e. e = 0 or e > 0) and thus would affect the total effort level or total supply of labor in the economy. As migrant unskilled workers join the pool of the existing unemployed workers, NSC suggests that the effective labor supply curve moves downward and total supply of effort goes up. Consequently, employment goes up and, since ∂L2 /∂E2 < 1, unemployment levels rise too. The total number of newly created jobs are equally divided between the unemployed residents and unemployed migrants. If we distribute the new jobs according to the share of each type (residents or migrants) of workers in the labor force, the conclusion will become more favorable. It should be noted that the rise in the employment rate in the unskilled-labor market does not cause any return movement from the skilled-labor market because cs(φ) is a sunk cost, i.e. once skilled, the worker will not be willing to work in the unskilledlabor market. Following the convention in migration literature, we would look into the effects of labor ﬂow on domestic residents, migrants and the world economy separately. Even if E′2 is made up of previously employed unskilled workers or of both previously employed and unemployed unskilled workers, the domestic income goes up. No special consideration is given to foreign unskilled workers’ participation decision about the two markets, because unskilled migrants would enter as unskilled workers and would ﬁrst join the pool of unskilled and unemployed resident workers. If unskilled workers move in with capital but there is no migration tax then all of them or a part of them will join the skilled labor market. In the ﬁrst case dI = 0 but in the second case dI > 0 following the logic of the ﬁrst scenario. The assumption of a small country helps us to stay away from the complications resulting from terms of trade changes. However, this also presents a realistic picture in terms of those countries whose share in the world market is small, and where skilled workers emigrate to developed nations such as the USA, the UK, etc., and unskilled labor comes in from poorer countries.

4 Free trade versus free-labor mobility with increasing returns and unemployment 1 Samuelson (1948) and Mundell (1957) have established the equivalence between the above ﬂows from a world (global) perspective. Bhagwati (1973), Brecher and Diaz-Alejandro (1977), Markusen and Melvin (1979) and Bhagwati and Brecher (1980) have examined the issue from the point of view of maximizing the welfare of a country. Meade (1955) and Purvis (1972) have examined each one of them as a tool to maximize efﬁciency in world production. In the 1980s Markusen (1983), Svensson (1984), Markusen and Svensson (1985) and Wong (1986b:) have considered a comparison of commodity and factor ﬂows from a quantitative point of view, i.e. whether factor trade augments or reduces commodity trade or vice versa. 2 Only Wong (1995) has focused on the issue in the presence of external economies of scale. 3 The use of the model of monopolistic competition has now become a standard

Notes

169

tool in the analysis of internal economies of scale, and trade theorists have also started paying attention to the implications of an efﬁciency wage for an open economy. 4 Maximizing Equation (4.1) subject to a budget constraint, we get n1    Ciθ−1 /∑ Ciθ  = λPi i =1  

where Pi is the price of the good and λ is the shadow price on the budget constraint. Since all individuals are alike, this can be used to show that the demand curve for the ith good facing the ﬁrm is  ni  Pi = Ciθ−1 / λ  ∑ Ciθ ) .  i =1  From that we derive the elasticity of demand as 1/(1 – θ). Equating βwi (marginal cost) with P(1 – 1 + θ) (marginal revenue), we get Equation (4). 5 If e is a continuous variable, it would not change the result. 6 The assumption of a ﬁxed turnover rate is introduced to avoid explicit modeling of job turnover and it is a standard assumption in the literature covering efﬁciency wages. See Shapiro and Stiglitz (1984), Bulow and Summers (1986), Jones (1987). 7 Denote   w1  1−θ    w1  1−θ  Z = ln    n1 θ  + ln    n2 θ    2 P1     2 P2   so: V 1s = ( Z + ( b + q)V 1u ) / ( r + b + q)

(a)

V 1n = (( Z − e0 ) + bV 1u ) / r + b

(b)

For no shirking we need Vn1 ≥ V1s . From Equations (a) and (b) we get: Z ≥ rV 1u + ( r + b + q)e0 /q

(c)

rV 1u = a(V 1n − V 1u )

(d)

We can now solve Equations (b) and (d) simultaneously to get: rVn1 = (Z – e0)(a + r)/(a + b + r) rVu1 = (Z – e0) a/a(a + b + r) Substituting the expression for Vu1 in Equation (c) we get: Z ≥ e0 + e0 (a + b + r)/q or Equation (4.11) of the text. 8 In the type I labor market, elasticity of wage with respect to employment is higher than that in the type II labor market. It happens because the equilibrium non-shirking wage is affected by the level of unemployment (NSC). 9 Note that there could be a large number of ﬁrms within each industry, but unlike the previous section, each ﬁrm will produce the same good. The advantage of

170

Notes

having a large variety of goods does not exist here because economies of scale are external to each ﬁrm. 10 This is a deviation from the previous section. But even if we allow IRS in the X2 sector the conclusions hold good. 11 In this section there is no ‘love of variety effect’. Thus, although the labor market faces the same distortion as in the previous section, it is better to describe the labor market distortion separately for ‘external economies of scale’. 5 Labor mobility and a dual economy: a case of external economies of scale and unemployment 1 Employment in the economy will increase when the wage elasticity of unemployment is favorable. 6 Labor migration in European Union countries 1 In Germany labor unions engage in bargaining with the employers to ﬁx the wage and the responding employment level along the industry line. All these industry unions belong to a single umbrella organization, called ‘Deutscher Gewerkschaftsbund’. 2 Germany does not have an ofﬁcial immigration policy but, by paying to encourage return migration, de facto it is trying to restrict immigration. 3 Capital in this broad sense is not a collection of tangible assets to be used directly in the production process. Capital is something (some form of ‘stock of waiting’) that makes other available resources(s) in the economy usable for the production process. These other resources must be improved by acts of investments before this can contribute to current production. The individual holding of this capital depends on the distribution rule for K in the economy. This should not be confused with ability. This is an asset that is marketable and is used for increasing skill or ability. The marginal product of capital here should not be confused with the rate of interest, since it is only the rental of a capital good. The price of a unit of capita, if it lasts forever, would of course be equal to the rental divided by the rate of interest. 4 K is not large enough to transform the entire labor force into skilled workers. It is also assumed that no skilled workers would work as unskilled workers. 5 Non-wage beneﬁts usually include a host of things. But to simplify, I am focusing on payment for training. 6 In OECD countries ﬁrms are reluctant to provide training because of their fear of poaching (i.e. turnover after training). In that case, on-the-job, or investment on training can be made feasible by some forms of institutional arrangements such as strong unions and employers’ organizations (Houseman 1990; Buechtemann, 1993). 7 Since unskilled workers do not become eligible for β until they start taking training; αi is the amount of special resource each unskilled worker would own. 8 For workers, αi – c(βi) may be zero or positive or negative depending on the size of αi. 9 As Table 6.1 suggests the majority of migrants to EU countries are from the developing countries of Africa and Asia. Historically, these migrants do not own much in terms of capital assets to start with. Furthermore, due to institutional and cultural barriers, and their concern about family members who are left behind, the migrants also prefer to leave their capital assets behind. 10 This is not an unrealistic assumption considering that a large percentage of migrants are unskilled workers and the problem of unemployment mainly manifests itself in the unskilled-workers’ market.

Notes

171

11 At a high level of consumption, consumers will not be responsive to price changes. This assumption helps to bring out an economies of scale effect. In a special case of CES utility function ε is constant and scale effect does not show. See Krugman (1979). 7 An empirical overview 1 Note that, in analyzing the effect of migration in a labor market with an efﬁciency wage distortion, I have not used economies of scale in Chapters 3 and 5, but I incorporated external economies of scale in Chapter 4. 2 Most of the values came from Shukla and Stark (1990) and Krichel and Levine (1999). I have expressed η in terms of wm because it was difﬁcult to get an average manufacturing wage for India for 1991. 3 The difference in relative factor endowment is assumed in analyzing labor mobility in Chapter 4 which does not change the results of free trade in goods. Appendix A 1 A survey of increasing returns and oligopoly behavior can be found in Bhagwati et al. (1998). 2 Readers interested in a survey of earlier works on external economies of scale in relation to international trade should look at Caves (1960) and Chipman (1965). 3 Once an objective function is optimized, the optimized value of the function can be expressed as a function of the parameter(s) in the objective function. This function is called the ‘envelope function’. Differentiation of this envelope function with respect to the parameter(s) tells how the value of the objective function at the optimum will change if there is any change in the parameters.

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Index

Tables and ﬁgures are indicated by italic. African countries 85 age distribution 86 Akerlof, G.A. 37, 141 Altonji, J.G. 39 America see United States of America Asian countries 85 bargaining strategy 88–91; workers’ unions 86, 98–9, 104–18 beneﬁt: unemployment 141–2 beneﬁt packages 22, 28, 34 Berry, Albert R. 9 Bhagwati, J.N. 9, 16, 34, 69, 103 binding minimum wage 22, 34–5 brain drain 103–4 Brecher, R.A. 16, 21–3, 26, 28, 36, 39, 49 Brecher and Choudhri’s model 21–3, 28, 33–4 Bulow, J.I. 53, 141, 142 Burda, M. 87 Calvo, G.A. 87, 136 Canada 118 capital: movements of xv capital-enrichment effects 14–17 capital ﬂow xv capital inﬂow: without labor migration 52–3 Card, D. 39 China xvi, 118 Choi, Jai-Young 82 Choudhri, Eshan U. 21–3, 39, 49 commodity markets 64–5 commodity prices 44–5 control mechanisms 72 Copeland, Brian R. 36, 53 Corden, W.M. 71, 72, 76

countries: African 85; Asian 85; European 84–101; OECD 4, 5 CPPP assumption xv, xvi Das, Satya P. 36 Davidson, C. 141 Davis, D.R. 132 Denmark: inﬂow structures 88 discipline devices 72, 140–1 Dixit, A.K. 55, 96 Dixit and Stiglitz’s model 126 Djajic, S. 39, 50 dual economy 71–83; labor allocation 77, 78 dual labor market 141 dual labor market models 37, 44, 52–3 economic incentive 9 economies of scale 119–34; external 67, 69; internal 55–6 efﬁciency-wage hypothesis 36–7, 74 efﬁciency-wage model 136–40 efﬁciency wages 36–7, 62, 67, 72; and migration 55–7, 69 efﬁciency-wage theory 135–6, 140–2, 154–62 effort decision: workers’ 40–2 El Salvador 118 employment 92 see also unemployment; equilibrium 59–60; full 5–6, 49, 53, 54–5 employment rates 89 endogenous wage distortion: and rural–urban migration 71–83 Ethier, W.J. 126 Ethier’s model 132, 133 EU (European Union) 2 European Central Bank 2

Index 179 European countries (EU): employment rates 89; immigration 85; intraindustry trade 99–100 European Union (EU) 2 exogenously determined unemployment 49 expected wage 93 external economies of scale 67; and migration 69 factor endowment changes: effects of 80 factor ﬂow: policy induced 52–3 factor mobility 102, 103; free 46–51, 54–70; and trade in goods 11–13; and trade mobility 66–70 factor price equalization theorem 103 factors: free-ﬂow 61–4; international movements of xv–xvii factor supply 45 Findlay, R. 40, 71, 72, 76, 88 ﬂow of factors 52–3 Foster, J. 136 France: immigration policy 87; inﬂow structures 88; population distribution by age 86 free-factor mobility 46–51, 54–70 free-ﬂow factors 61–4 free-labor ﬂows 49–50 free-labor mobility: with increasing returns 54–70 free trade 11, 23, 29 free trade mobility: with increasing returns 54–70 full employment equilibrium 59–60 Funke, M. 87 gains: from migration 11 Gang, I.N. 104 Germany: immigration policy 87; labor market decisions 84; population distribution by age 86 global demand 150–1 globalization 1 Goldstein, G.S. 72 government policies 100–1; on migration 86–8 guest workers xvi, 2 Harberger triangle 9 Harris, J. 71 Harris–Torado model 71, 76, 78 Haus, L. 87 Hazari, B. 39, 50, 53 Heckscher–Ohlin–Samuelson model 23

Helpman, E. 2, 126 Helpman and Krugman’s model 130–1 Helpman’s model: international trade 133 home-market bias 131–3 Hong Kong 118 H–O production structure: with unemployment 39–40 IMF (International Monetary Fund) 2 immigration rates 4; in EU countries 85 incentive: economic 9 increasing returns to scale (IRS) 119–34; urban sector 72 inﬂow structures 88 integration 87; of immigrants 86; unions 87–8 international migration: effects of 2–5 International Monetary Fund (IMF) 2 intra-industry trade 129; EU countries 99–100 IRS (increasing returns to scale): urban sector 72 job bonus programmes 141–2 Jones, R.W. 10, 22, 23, 33, 148, 150 Jones, S.R.G. 53 Katz, Lawrence 36 Kenen, P.B. 40, 88 Kierzkowski, H. 40, 88 Krichel, L. 106, 109 Krugman, P. 63, 96, 103, 124, 126 Krugman’s model 126–30; of economic geography 131–2 labor allocation: dual economy 77, 78 labor force: size 64 labor immigration: restrictions on 2 labor inﬂows 21, 22; effects of 31–2 labor markets 65–6; equilibrium 67 labor migration: with capital movement 50–1; in European Union (EU) countries 84–101; international xvi–xvii; without capital movement 46–50 labor mobility: dual economy 71–83; with endogenously created unemployment 36–53; with exogenously created unemployment 21–35 labor unions see unions Leibenstein, H. 135 Levine, P. 106, 109

180

Index

losses: from migration 10 Markusen, J.R. 13 Matusz, S. 114, 116 Mexico 118 migrant stock: by region 3 migration: control of 82; economies of scale 113–17; efﬁciency wages 106–17; in European Union (EU) countries 84–101, 104–6; expected wage 93–101; external economies of scale 69; minimum-wage countries 117–18; non-traded goods 13–20; non-zero effect 9–11; two-goods, two-factor model 93–101; and unemployment 21–35; zero effect 6–8 migration efﬁciency wages 47 migration equilibrium 76–80, 82 migration policy xviii migration tax 50 minimum-wage countries 117–18 minimum-wage law 34, 71 minimum wages 21, 26, 28, 142; binding 22, 34–5 Miyazaki, H. 136 mobility: with endogenously created unemployment 36–53; with exogenously created unemployment 21–35 models: Brecher and Choudhri’s 21–3, 28, 33–4; Dixit and Stiglitz’s 126; dual labor market 37, 44, 52–3; efﬁciencywage 55–7, 136–40; Ethier’s 132; Harris–Torado 71, 76, 78; Heckscher–Ohlin–Samuelson 23; Helpman and Krugman’s 130–1; Helpman’s international trade 132; Krugman’s 126–30; migration in EU countries 88–93; monopolistic competition 55–7; Rivera-Batiz 13–14; rural–urban migration 71–83; Schmidt, Stilz and Zimmermann’s (SSZ) 93; Shapiro and Stiglitz 136–40, 152–3; two-goods, two-factors 9–11, 95–101 monitoring 136, 138, 141 monopolistic competition model 55–7 Moses, L.N. 72 movements of capital xv movements of factors: international xv–xvii Mundell, Robert A. 11, 102, 103 Neary, J.P. 76

non-EU immigrants 85 non-migrants: welfare 14, 20 non-shirking condition 154–62 non-shirking equilibrium 57–60 non-traded goods 13–20 non-wage beneﬁts 90 non-zero effect: of migration 9–11 North American Free Trade Agreement xv–xvi, 118 OECD countries: foreign-born population 4; unemployment 5 Panagariya, A. 69, 80, 82 participation decision: workers’ 42–4 PKT (Professionals, Trained and Kindred) see brain drain policies: government 100–1; on migration 86–8 population distribution by age 86 post-bargained wages 86 price ratios 148–9 prices: commodity 44–5 production possibility frontiers 25, 26 Professionals, Trained and Kindred (PKT) see brain drain Purvis, D.D. 13 Quibria, M.G. 9 Ramaswami, V.K. 34 remittances: workers’ 7 returns to scale 54–5 Rivera-Batiz, F.L. 10, 16, 104 Rivera-Batiz model 13–14 Rodriguez, E. 9 rural sector 74–5 rural–urban migration 106–9; model 71–83 Rybczynski theorem 125–6, 145–7 Salop, S.C. 136 Samuelson, P.A. 103 Schmidt, C.M. 87, 92 Schmidt, Stilz and Zimmermann’s model 92 search theory 140 Shapiro, C. 36, 40, 57, 65, 113, 136, 154 Shapiro and Stiglitz’s model 136–40, 152–3 shirking 36–7, 40–2, 57–60, 65–6, 72, 113, 136–40, 152–3 skilled labor 37, 88–93; see also unskilled labor

Index 181 skilled labor market 141 Soligo, R. 9 specialization: of production 28 Srinivasan, T.N. 69 Stiglitz, J.E. 36, 40, 55, 57, 65, 96, 113, 126, 136, 154 Stolper–Samuelson theorem 125–6 subsidies 141–2 Succar, P. 80, 82 Summers, L.H. 53, 141, 142 Svensson, L.E.O. 13 Sweden: inﬂow structures 88 Switzerland: inﬂow structures 88 tariffs 33 terms of trade 35, 145–7 terms-of-trade effects 14–16, 17–20 theorems of international trade 125–30 Tobin, J. 9 Todaro, M.P. 71 trade: intra-industry in EU countries 99–100 trade in factors 61–4, 69 trade in goods xv, 60–1, 62, 67, 102, 103; and factor mobility 11–13 trade mobility: and factor mobility 66–70 trade offer curves 26 trade-related investment measures (TRIMs) xvi trade theoretic approach xviii training: effect on unemployment 105 training beneﬁts 90 transfer payments 141–2 transportation costs: economies of scale 130–1 TRIMs (trade-related investment measures) xvi two-goods, two-factors: model 9–11, 95–101 UK (United Kingdom): inﬂow structures 88; population distribution by age 86 unemployment xviii, 28, 104–18, 135–42; see also employment; created by economies of scale 113–17; created by efﬁciency wages 113–17; desirable 72; discipline device 37; endogenously created 36–53, 106;

exogenously determined 21–35, 49; and external economies of scale 71–83; and international factor movements 36–53; and migration policies 21–35; in minimum-wage countries 117–18; in OECD countries 5 unemployment beneﬁt 141–2 unemployment equilibrium 82, 136 unemployment rates 116 unions 84, 86; bargaining strategy 88–91, 98–9, 104–18; integration 87–8; migration policy 87; wage beneﬁts 98–9 United Kingdom (UK) see UK (United Kingdom) United States of America 117–18 unskilled labor 88–93; see also skilled labor urban bias 106 urban employment 78 urban labor market equilibrium 75 urban sector 73–4, 78; increasing returns to scale (IRS) 72 Venables, A.J. 132 wage beneﬁts 98–9 wage levels 87 wage rigidity 136 wages 29; binding minimum 22; efﬁciency 36–7; post-bargained 86 wages distortion: union-bargained 84 Wan, H. 136 Weinstein, D.E. 132 welfare 31, 35 Wong, Kar-yiu 9, 11, 13, 103 workers’ effort decision 40–2 workers’ participation decision 42–4 workers’ remittances 7 workers’ unions see unions World Bank 1–2 world organizations 1–2 World Trade Organization (WTO) xvi, 2 Yellen, Janet L. 36, 37, 141 zero effect: of migration 6–8 Zimmermann, K.F. 86

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