Monetary and Fiscal Policies in the Euro Area

Monetary and Fiscal Policies in the Euro Area

Michael Carlberg

Monetary and Fiscal Policies in the Euro Area With 59 Tables

12

Professor Dr. Michael Carlberg Helmut Schmidt University Federal University of Hamburg Department of Economics Holstenhofweg 85 22043 Hamburg Germany [email protected]

Cataloging-in-Publication Data Library of Congress Control Number: 2005935478

ISBN-10 3-540-29799-5 Springer Berlin Heidelberg New York ISBN-13 978-3-540-29799-4 Springer Berlin Heidelberg New York This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilm or in any other way, and storage in data banks. Duplication of this publication or parts thereof is permitted only under the provisions of the German Copyright Law of September 9, 1965, in its current version, and permission for use must always be obtained from Springer-Verlag. Violations are liable for prosecution under the German Copyright Law. Springer is a part of Springer Science+Business Media springeronline.com ° Springer Berlin ´ Heidelberg 2006 Printed in Germany The use of general descriptive names, registered names, trademarks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. Hardcover-Design: Erich Kirchner, Heidelberg SPIN 11576563

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Preface

This book studies the interactions between monetary and fiscal poUcies in the euro area. It carefully discusses the process of policy competition and the structure of policy cooperation. As to policy competition, the focus is on competition between the European central bank, the American central bank, the German government, and the French government. As to policy cooperation, the focus is on the same institutions. These are higher-dimensional issues. The pohcy targets are price stability and full employment. The policy makers follow coldturkey or gradualist strategies. The policy decisions are taken sequentially or simultaneously. Monetary and fiscal policies have spillover effects. Special features of this book are numerical simulations of policy competition and numerical solutions to policy cooperation. The present book is part of a larger research project on European Monetary Union, see the references at the back of the book. Some parts of this project were presented at the World Congress of the International Economic Association. Other parts were presented at the International Conference on Macroeconomic Analysis, at the International Institute of Public Finance, at the Macro Study Group of the German Economic Association, at the Annual Meeting of the Austrian Economic Association, at the Gottingen Workshop on International Economics, at the Halle Workshop on Monetary Economics, at the Research Seminar on Macroeconomics in Freiburg, and at the Passau Workshop on International Economics. Over the years, in working on this project, I have benefited from comments by Iain Begg, Michael Brauninger, Volker Clausen, Valeria de Bonis, Peter Flaschel, Wilfried Fuhrmann, Michael Funke, Florence Huart, Oliver Landmann, Jay H. Levin, Alfred MauBner, Jochen Michaelis, Manfred J. M. Neumann, Klaus Neusser, Franco Reither, Armin Rohde, Sergio Rossi, Gerhard RUbel,

VI

Michael Schmid, Gerhard Schwodiauer, Patrizio TirelU, Harald UhUg, Bas van Aarle, Uwe Vollmer, Jtirgen von Hagen and Helmut Wagner. In addition, Torsten Bleich and Alkis Otto carefully discussed with me all parts of the manuscript. Last but not least, Doris Ehrich did the secretarial work as excellently as ever. I would like to thank all of them.

Michael Carlberg

Executive Summary

1) The basic model. The world consists of two monetary regions, say Europe and America. The exchange rate between Europe and America is flexible. Europe in turn consists of two countries, say Germany and France. So Germany and France form a monetary union. There is international trade and capital mobility between Germany, France and America. 2) Monetary competition between Europe and America. As a result, the process of monetary competition leads to full employment in Europe and America. And what is more, it leads to price stability in Europe and America. However, the process of monetary competition does not lead to full employment in Germany and France. And what is more, it does not lead to price stability in Germany and France. 3) Monetary cooperation between Europe and America. As a result, monetary cooperation can achieve full employment in Europe and America. Over and above that, it can achieve price stability in Europe and America. However, monetary cooperation cannot achieve full employment in Germany and France. Over and above that, it cannot achieve price stability in Germany and France. Monetary cooperation is a fast process, as compared to monetary competition. 4) Fiscal competition between Germany and France. As a result, the process of fiscal competition leads to full employment in Germany and France. And what is more, it leads to price stability in Germany and France. However, as a severe side effect, it causes overemployment and inflation in America. Taking the sum over all periods, the total increase in government purchases is very large, as compared to the initial output gap. 5) Fiscal cooperation between Germany and France. As a result, fiscal cooperation can achieve full employment in Germany and France. Over and above that, it can achieve price stability in Germany and France. However, as a severe side effect, it causes overemployment and inflation in America. Fiscal cooperation is a fast process, as compared to fiscal competition.

VIII

6) Competition between the European central bank, the American central bank, the German government, and the French government. As a result, the process of monetary and fiscal competition leads to full employment in Germany, France and America. And what is more, it leads to price stability in Germany, France and America. There are damped oscillations in money supply, government purchases and output. The German economy oscillates between unemployment and overemployment, as does the French economy and the American economy. The total increase in government purchases is small, as compared to the initial output gap. 7) Cooperation between the European central bank, the American central bank, the German government, and the French government. As a result, monetary and fiscal cooperation can achieve full employment in Germany, France and America. Over and above that, it can achieve price stability in Germany, France and America. Policy cooperation is a fast process, as compared to policy competition. The required increase in European government purchases is zero. So policy cooperation seems to be superior to policy competition.

Contents in Brief

Introduction

l

Part One. Basic Models of a Monetary Union

il

Chapter 1. The Small Monetary Union of Two Countries

13

Chapter 2. The World as a Whole

20

Chapter 3. The World of Two Monetary Regions

24

Chapter 4. The Large Monetary Union of Two Countries

33

Part Two. Monetary Interactions between Europe and America

43

Chapter 1. Monetary Competition between Europe and America

45

Chapter 2. Monetary Cooperation between Europe and America

71

Part Three. Fiscal Interactions between Germany and France

83

Chapter 1. Fiscal Competition between Germany and France

85

Chapter 2. Fiscal Cooperation between Germany and France

99

Part Four. Monetary and Fiscal Interactions: Intermediate Models

105

Chapter 1. Competition between European Central Bank, German Government, and French Government

107

Chapter 2. Cooperation between European Central Bank, German Government, and French Government

120

Chapter 3. Competition between European Central Bank, American Central Bank, German Government, and French Government

127

X Chapter 4. Cooperation between European Central Bank, American Central Bank, German Government, and French Government

137

Part Five. Monetary and Fiscal Interactions: Advanced Models

147

Chapter 1. Cold-Turkey Policies: Simultaneous Decisions

149

Chapter 2. Gradualist Policies: Simultaneous Decisions

155

Chapter 3. Fast Monetary Competition and Slow Fiscal Competition

161

Chapter 4. Monetary Cooperation between Europe and America, Fiscal Competition between Germany and France

165

Chapter 5. Monetary Cooperation between Europe and America, Fiscal Cooperation between Germany and France

175

Chapter 6. Policy Cooperation within Europe, Policy Competition between Europe and America

184

Part Six. Rational Policy Expectations

191

Chapter 1. Monetary Competition between Europe and America

193

Chapter 2. Fiscal Competition between Germany and France

198

Chapter 3. Monetary and Fiscal Competition: Sequential Decisions

203

Chapter 4. Monetary and Fiscal Competition: Simultaneous Decisions

212

Chapter 5. Monetary Cooperation between Europe and America, Fiscal Competition between Germany and France

214

Chapter 6. Policy Cooperation within Europe, Policy Competition between Europe and America

Synopsis Conclusion Result References Index

219

227 231 259 275 287

Contents

Introduction

i

1. 2. 3. 4. 5. 6. 7.

1 2 5 5 7 8 9

Subject and Approach Monetary Competition between Europe and America Monetary Cooperation between Europe and America Fiscal Competition between Germany and France Fiscal Cooperation between Germany and France Monetary and Fiscal Competition Monetary and Fiscal Cooperation

Part One. Basic Models of a Monetary Union

ll

Chapter 1. The Small Monetary Union of Two Countries 1. Introduction 2. The Market for German Goods 3. The Market for French Goods 4. The Money Market of the Union 5. The Model 6. The Total Differential 7. Fiscal Policy 8. Monetary Policy

13 13 13 14 ..15 16 16 18 19

Chapter 2. The World as a Whole

20

Chapter 3. The World of Two Monetary Regions 1. Introduction 2. The Market for European Goods 3. The Market for American Goods 4. The European Money Market 5. The American Money Market 6. The Model 7. The Total Differential

24 24 24 25 26 26 27 27

XII 8. Fiscal Policy 9. Monetary Policy

29 31

Chapter 4. The Large Monetary Union of Two Countries 1. Introduction 2. The Market for German Goods 3. The Market for French Goods 4. The Market for American Goods 5. The European Money Market 6. The American Money Market 7. The Model 8. The Total Differential 9. Fiscal Policy

33 33 34 35 36 37 37 37 38 40

Part Two, Monetary Interactions between Europe and America

43

Chapter 1. Monetary Competition between Europe and America 1. The Dynamic Model 2. Some Numerical Examples 2.1. The Case of Unemployment 2.2. Europe and America Differ in Unemployment 2.3. The Case of Inflation 2.4. Unemployment in Europe, Inflation in America 3. Alternative Targets of the European Central Bank 4. The Anticipation of Policy Spillovers

45 45 53 54 57 59 61 64 68

Chapter 2. Monetary Cooperation between Europe and America 1. The Model 2. Some Numerical Examples 3. Altemative Targets of the European Central Bank

71 71 74 79

XIII

Part Three. Fiscal Interactions between Germany and France

83

Chapter 1. Fiscal Competition between Germany and France 1. The Dynamic Model 2. Some Numerical Examples 2.1. Unemployment in Germany and France 2.2. Unemployment in Germany, Overemployment in France

85 85 92 93 96

Chapter 2. Fiscal Cooperation between Germany and France 1. The Model 2. Some Numerical Examples

99 99 101

Fart Four. Monetary and Fiscal Interactions: Intermediate Models

105

Chapter 1. Competition between European Central Bank, German Government, and French Government 1. The Dynamic Model 2. Some Numerical Examples 2.1. Unemployment in Europe, Full Employment in America 2.2. Inflation in Europe, Price Stability in America 2.3. First the Govemments Decide, then the Central Bank Decides

107 107 109 110 113 115

Chapter 2. Cooperation between European Central Bank, German Government, and French Government 1. The Model 2. Some Numerical Examples 2.1. Unemployment in Europe, Full Employment in America 2.2. Inflation in Europe, Price Stability in America 2.3. Alternative Targets of Policy Cooperation

120 120 122 122 124 124

XIV Chapter 3. Competition between European Central Bank, American Central Bank, German Government, and French Government 1. The Dynamic Model 2. Some Numerical Examples 2.1. The Case of Unemployment 2.2. Europe and America Differ in Unemployment

127 127 129 130 133

Chapter 4. Cooperation between European Central Bank, American Central Bank, German Government, and French Government 1. The Model 2. Some Numerical Examples 2.1. The Case of Unemployment 2.2. Europe and America Differ in Unemployment 2.3. The Case of Inflation 2.4. Unemployment in Europe, Inflation in America 2.5. Alternative Targets of Policy Cooperation

137 137 140 140 142 143 144 145

Part Five. Monetary and Fiscal Interactions: Advanced Models

147

Chapter 1. Cold-Turkey Policies: Simultaneous Decisions Chapter 2. Gradualist Policies: Simultaneous Decisions Chapter 3. Fast Monetary Competition and Slow Fiscal Competition Chapter 4. Monetary Cooperation between Europe and America, Fiscal Competition between Germany and France 1. The Model 2. Some Numerical Examples 2.1. The Case of Unemployment 2.2. The Case of Inflation 2.3. Unemployment in Europe, Inflation in America

149 155 161 165 165 166 167 170 172

XV Chapter 5. Monetary Cooperation between Europe and America, Fiscal Cooperation between Germany and France 1. The Model 2. Some Numerical Examples 2.1. The Case of Unemployment 2.2. The Case of Inflation 2.3. Unemployment in Europe, Inflation in America

175 175 177 178 180 182

Chapter 6. Policy Cooperation within Europe, Policy Competition between Europe and America 1. The Model 2. A Numerical Example

184 184 186

Part Six. Rational Policy Expectations

191

Chapter 1. Monetary Competition between Europe and America Chapter 2. Fiscal Competition between Germany and France Chapter 3. Monetary and Fiscal Competition: Sequential Decisions Chapter 4. Monetary and Fiscal Competition: Simultaneous Decisions Chapter 5. Monetary Cooperation between Europe and America, Fiscal Competition between Germany and France Chapter 6. Policy Cooperation within Europe, Policy Competition between Europe and America

193 198 203 212 214 219

Synopsis

227

Conclusion

231

1. 2. 3. 4.

231 236 238 241

Monetary Competition between Europe and America Monetary Cooperation between Europe and America Fiscal Competition between Germany and France Fiscal Cooperation between Germany and France

XVI 5. Monetary and Fiscal Competition: Cold-Turkey Policies 6. Monetary and Fiscal Competition: Gradualist Policies 7. Monetary and Fiscal Cooperation 8. Monetary Cooperation and Fiscal Competition 9. Monetary Cooperation and Fiscal Cooperation 10. Rational Policy Expectations

247 248 250 253 256

Result 1. Monetary Competition between Europe and America 2. Monetary Cooperation between Europe and America 3. Fiscal Competition between Germany and France 4. Fiscal Cooperation between Germany and France 5. Monetary and Fiscal Competition 6. Monetary and Fiscal Cooperation

259 259 261 262 263 264 266

Symbols

267

A Brief Survey of the Literature

269

The Current Research Project

272

References

275

Index

287

243

Introduction 1. Subject and Approach

This book studies the interactions between monetary and fiscal poUcies in the euro area. It carefully discusses the process of policy competition and the structure of policy cooperation. With respect to poUcy competition, the focus is on competition between the European central bank, the American central bank, the German government, and the French government. With respect to policy cooperation, the focus is on cooperation between the European central bank, the American central bank, the German government, and the French government. Further topics are: - cold-turkey policies: sequential decisions - cold-turkey pohcies: simultaneous decisions - gradualist policies: simultaneous decisions - fast monetary competition, slow fiscal competition - monetary cooperation between Europe and America, fiscal competition between Germany and France - monetary cooperation between Europe and America, fiscal cooperation between Germany and France - policy cooperation within Europe, poUcy competition between Europe and America. The targets of the European central bank are price stability and full employment in Europe. The targets of the American central bank are price stability and full employment in America. Monetary policy in one of the regions has a large external effect on the other region. For instance, an increase in European money supply lowers American output. The target of the German government is full employment in Germany. And the target of the French government is full employment in France. Fiscal policy in one of the countries has a large external effect on the other countries. For instance, an increase in German government purchases lowers French output and raises American output.

The key questions are: - Does the process of poUcy competition lead to full employment and price stability? - Can policy cooperation achieve full employment and price stability? - Is policy cooperation superior to policy competition? This book takes new approaches that are firmly grounded on modern macroeconomics. The framework of analysis is as follows. The world consists of two monetary regions, say Europe and America. The exchange rate between Europe and America is flexible. Europe in turn consists of two countries, say Germany and France. So Germany and France form a monetary union. There is international trade and capital mobihty between Germany, France and America. Special features of this book are numerical simulations of policy competition and numerical solutions to policy cooperation. To illustrate all of this there are lots of tables. This book consists of six major parts: - Basic Models of a Monetary Union - Monetary Interactions between Europe and America - Fiscal Interactions between Germany and France - Monetary and Fiscal Interactions: Intermediate Models - Monetary and Fiscal Interactions: Advanced Models - Rational PoUcy Expectations. Now the approach will be presented in greater detail.

2. Monetary Competition between Europe and America

1) The static model. The world consists of two monetary regions, say Europe and America. The exchange rate between Europe and America is flexible. Europe

in turn consists of two countries, say Germany and France. So Germany and France form a monetary union. There is international trade between Germany, France and America. German goods, French goods and American goods are imperfect substitutes for each other. German output is determined by the demand for German goods. French output is determined by the demand for French goods. And American output is determined by the demand for American goods. European money demand equals European money supply. And American money demand equals American money supply. There is perfect capital mobiUty between Germany, France and America. Thus the German interest rate, the French interest rate, and the American interest rate are equalized. The monetary regions are the same size and have the same behavioural functions. The union countries are the same size and have the same behavioural functions. Nominal wages and prices adjust slowly. As a result, an increase in European money supply raises both German output and French output, to the same extent respectively. On the other hand, the increase in European money supply lowers American output. Here the rise in European output exceeds the fall in American output. Correspondingly, an increase in American money supply raises American output. On the other hand, it lowers both German output and French output, to the same extent respectively. Here the rise in American output exceeds the fall in European output. In the numerical example, an increase in European money supply of 100 causes an increase in German output of 150, an increase in French output of equally 150, and a decline in American output of 100. Similarly, an increase in American money supply of 100 causes an increase in American output of 300, a decline in German output of 50, and a decline in French output of equally 50. That is to say, the internal effect of monetary policy is very large, and the external effect of monetary policy is large. Now have a closer look at the process of adjustment. An increase in European money supply causes a depreciation of the euro, an appreciation of the dollar, and a decline in the world interest rate. The depreciation of the euro raises German exports and French exports. The appreciation of the dollar lowers American exports. And the decline in the world interest rate raises German investment, French investment and American investment. The net effect is that German

output and French output go up. However, American output goes down. This model is in the tradition of the Mundell-Fleming model and the Levin model. 2) The dynamic model. At the beginning there is unemployment in Germany, France and America. More precisely, unemployment in Germany exceeds unemployment in France. The primary target of the European central bank is price stability in Europe. The secondary target of the European central bank is high employment in Germany and France. The specific target of the European central bank is that unemployment in Germany equals overemployment in France. In other words, deflation in Germany equals inflation in France. So there is price stability in Europe. In a sense, the specific target of the European central bank is full employment in Europe. The instrument of the European central bank is European money supply. The European central bank raises European money supply so as to close the output gap in Europe. The target of the American central bank is full employment in America. The instrument of the American central bank is American money supply. The American central bank raises American money supply so as to close the output gap in America. We assume that the European central bank and the American central bank decide simultaneously and independently. In addition there is an output lag. German output next period is determined by European money supply this period as well as by American money supply this period. In the same way, French output next period is determined by European money supply this period as well as by American money supply this period. Last but not least, American output next period is determined by American money supply this period as well as by European money supply this period. The key questions are: Is there a steady state of monetary competition? Is the steady state of monetary competition stable? Does monetary competition lead to full employment in Europe and America? Does monetary competition lead to full employment in Germany and France? Besides, what are the dynamic characteristics of this process? Taking the sum over all periods, what is the total increase in European money supply? And what is the total increase in American money supply? How does the total increase in European money supply compare with the initial output gap in Europe? And how does the total increase in American money supply compare with the initial output gap in America?

3. Monetary Cooperation between Europe and America

At the start there is unemployment in Germany, France and America. Let unemployment in Germany exceed unemployment in France. The targets of monetary cooperation are full employment in Europe and full employment in America. The instruments of monetary cooperation are European money supply and American money supply. So there are two targets and two instruments. Here the key questions are: Is there a solution to monetary cooperation? Can monetary cooperation achieve full employment in Europe and America? Can monetary cooperation achieve full employment in Germany and France? What is the required increase in European money supply? And what is the required increase in American money supply? How does the required increase in European money supply compare with the initial output gap in Europe? And how does the required increase in American money supply compare with the initial output gap in America? Moreover, is monetary cooperation superior to monetary competition?

4. Fiscal Competition between Germany and France

1) The static model. An increase in German government purchases raises German output. On the other hand, it lowers French output. And what is more, it raises American output. Here the rise in German output exceeds the fall in French output. And the rise in European output equals the rise in American output. Correspondingly, an increase in French government purchases raises French output. On the other hand, it lowers German output. And what is more, it raises American output. Here the rise in French output exceeds the fall in German output. And the rise in European output equals the rise in American output.

In the numerical example, an increase in German government purchases of 100 causes an increase in German output of 150, a decline in French output of 50, and an increase in American output of 100. Likewise, an increase in French government purchases of 100 causes an increase in French output of 150, a decline in German output of 50, and an increase in American output of 100. Now have a closer look at the process of adjustment. An increase in German government purchases causes an appreciation of the euro, a depreciation of the dollar, and an increase in the world interest rate. The appreciation of the euro lowers German exports and French exports. The depreciation of the dollar raises American exports. And the increase in the world interest rate lowers German investment, French investment and American investment. The net effect is that German output moves up, French output moves down, and American output moves up. This model is in the tradition of the Mundell-Fleming model and the Levin model. 2) The dynamic model. At the beginning there is unemployment in Germany and France. More precisely, unemployment in Germany exceeds unemployment in France. By contrast there is full employment in America. The target of the German government is full employment in Germany. The instrument of the German government is German government purchases. The German government raises German government purchases so as to close the output gap in Germany. The target of the French government is full employment in France. The instrument of the French govemment is French government purchases. The French govemment raises French government purchases so as to close the output gap in France. We assume that the German government and the French govemment decide simultaneously and independently. In addition there is an output lag. German output next period is determined by German government purchases this period as well as by French govemment purchases this period. In the same way, French output next period is determined by French govemment purchases this period as well as by German government purchases this period. Last but not least, American output next period is determined by German government purchases this period as well as by French government purchases this period.

The key questions are: Is there a steady state of fiscal competition? Is the steady state of fiscal competition stable? Does fiscal competition lead to full employment in Germany and France? Does fiscal competition lead to full employment in Europe and America? Besides, what are the dynamic characteristics of this process? Taking the sum over all periods, what is the total increase in German govemment purchases? And what is the total increase in French govemment purchases? How does the total increase in German govemment purchases compare with the initial output gap in Germany? And how does the total increase in French govemment purchases compare with the initial output gap in France?

5. Fiscal Cooperation between Germany and France

At the start there is unemployment in Germany and France. Let unemployment in Germany exceed unemployment in France. By contrast there is full employment in America. The targets of fiscal cooperation are full employment in Germany and full employment in France. The instmments of fiscal cooperation are German govemment purchases and French govemment purchases. So there are two targets and two instmments. Here the key questions are: Is there a solution to fiscal cooperation? Can fiscal cooperation achieve full employment in Germany and France? Can fiscal cooperation achieve full employment in Europe and America? What is the required increase in German govemment purchases? And what is the required increase in French govemment purchases? How does the required increase in German govemment purchases compare with the initial output gap in Germany? And how does the required increase in French govemment purchases compare with the initial output gap in France? Finally, is fiscal cooperation superior to fiscal competition?

6. Monetary and Fiscal Competition

This section deals with competition between the European central bank, the American central bank, the German government, and the French government. At the beginning there is unemployment in Germany, France and America. More precisely, unemployment in Germany exceeds unemployment in France. The primary target of the European central bank is price stability in Europe. The secondary target of the European central bank is high employment in Germany and France. The specific target of the European central bank is that unemployment in Germany equals overemployment in France. In other words, deflation in Germany equals inflation in France. So there is price stability in Europe. In a sense, the specific target of the European central bank is full employment in Europe. The instrument of the European central bank is European money supply. The European central bank raises European money supply so as to close the output gap in Europe. The target of the American central bank is full employment in America. The instrument of the American central bank is American money supply. The American central bank raises American money supply so as to close the output gap in America. The target of the German government is full employment in Germany. The instrument of the German government is German government purchases. The German government raises German government purchases so as to close the output gap in Germany. The target of the French government is full employment in France. The instrument of the French government is French government purchases. The French government raises French government purchases so as to close the output gap in France. We assume that the central banks and the governments decide simultaneously and independently. In step 1, the European central bank, the American central bank, the German government, and the French government decide simultaneously and independently. In step 2 there is an output lag. In step 3, the European central bank, the American central bank, the German government, and the French government decide simultaneously and independently. In step 4 there is an output lag. And so on.

The key questions are: Is there a steady state of monetary and fiscal competition? Is the steady state of monetary and fiscal competition stable? Does the process of monetary and fiscal competition lead to full employment in Germany, France and America? Besides, what are the dynamic characteristics of this process? Taking the sum over all periods, what is the total increase in European money supply? What is the total increase in American money supply? What is the total increase in German government purchases? And what is the total increase in French govemment purchases? How does the total increase in European money supply compare with the initial output gap in Europe? How does the total increase in American money supply compare with the initial output gap in America? How does the total increase in German govemment purchases compare with the initial output gap in Germany? And how does the total increase in French govemment purchases compare with the initial output gap in France? Moreover, is the system of monetary and fiscal competition superior to pure monetary competition? And is the system of monetary and fiscal competition superior to pure fiscal competition?

7. Monetary and Fiscal Cooperation

This section deals with cooperation between the European central bank, the American central bank, the German govemment, and the French govemment. At the start there is unemployment in Germany, France and America. Let unemployment in Germany exceed unemployment in France. The targets of policy cooperation are full employment in Germany, full employment in France, and full employment in America. The instruments of policy cooperation are European money supply, American money supply, German govemment purchases, and French govemment purchases. There are three targets and four instmments, so there is one degree of freedom.

10 Here the key questions are: Is there a solution to monetary and fiscal cooperation? Can monetary and fiscal cooperation achieve full employment in Germany, France and America? What is the required increase in European money supply? What is the required increase in American money supply? What is the required increase in German government purchases? And what is the required increase in French govemment purchases? How does the required increase in European money supply compare with the initial output gap in Europe? How does the required increase in American money supply compare with the initial output gap in America? How does the required increase in German govemment purchases compare with the initial output gap in Germany? And how does the required increase in French govemment purchases compare with the initial output gap in France? Finally, is the system of monetary and fiscal cooperation superior to the system of monetary and fiscal competition?

Part One Basic Models of a Monetary Union

Chapter 1 The Small Monetary Union of Two Countries

1) Introduction. In this chapter we consider a monetary union of two countries, let us say Germany and France. The exchange rate between the monetary union and the rest of the world is flexible. Take for instance an increase in German government purchases. Then what will be the effect on German income, and what on French income? Alternatively, take an increase in union money supply. Again what will be the effect on German income, and what on French income? In doing the analysis we make the following assumptions. German goods and French goods are imperfect substitutes for each other. German output is determined by the demand for German goods. French output is determined by the demand for French goods. And union money demand equals union money supply. The monetary union is a small open economy with perfect capital mobility. For the small union, the world interest rate is given exogenously Yf = const. Under perfect capital mobility, the union interest rate is determined by the world interest rate r = rf. Therefore the union interest rate is constant too. In the short run, nominal wages and prices are rigid. P^ denotes the price of German goods, as measured in euros. And P2 denotes the price of French goods, as measured in euros. To simplify notation let be P^ = P2 = 1. 2) The market for German goods. The behavioural functions underlying the analysis are as follows: Ci=Ci(Yi)

(1)

Ii=Ii(r)

(2)

G^ = const

(3)

Xl2=Xi2(Y2)

(4)

Xi3=Xi3(e)

(5)

Ql=Qi(Yi)

(6)

14

Equation (1) is the consumption function of Germany. It states that German consumption is an increasing function of German income. Here C^ denotes German consumption, and Y^ is German income. Equation (2) is the investment function of Germany. It states that German investment is a decreasing function of the world interest rate. I^ denotes German investment, and r is the world interest rate. According to equation (3), the German government fixes its purchases of goods and services. G^ denotes German government purchases. Equations (4) and (5) are the export functions of Germany. Equation (4) states that German exports to France are an increasing function of French income. X12 denotes German exports to France, and Y2 is French income. Equation (5) states that German exports to non-union countries are an increasing function of the union exchange rate. X13 denotes German exports to non-union countries. And e is the exchange rate between the union and the rest of the world. For example, e is the price of the dollar as measured in euros. The message of equation (5) is that a depreciation of the euro raises German exports to non-union countries. Equation (6) is the import function of Germany. It states that German imports are an increasing function of German income. Q^ denotes German imports from France and from non-union countries. German output is determined by the demand for German goods Yi = Ci + Ii + Gi + X12 + Xi3 - Qi. Taking account of the behavioural functions (1) to (6), we arrive at the goods market equation of Germany: Yi=Ci(Yi) + Ii(r) + Gi+Xi2(Y2) + Xi3(e)-Qi(Yi)

(7)

3) The market for French goods. The behavioural functions are as follows: C2=C2(Y2)

(8)

I2=l2(r)

(9)

G2 = const

(10)

X2i=X2i(Yi)

(11)

X23=X23(e)

(12)

15

Q2=Q2(Y2)

(13)

Equation (8) is the consumption function of France. It states that French consumption is an increasing function of French income. Here C2 denotes French consumption, and Y2 is French income. Equation (9) is the investment function of France. It states that French investment is a decreasing function of the world interest rate. I2 denotes French investment. According to equation (10), the French government fixes its purchases of goods and services. G2 denotes French government purchases. Equations (11) and (12) are the export functions of France. Equation (11) states that French exports to Germany are an increasing function of German income. X21 denotes French exports to Germany. Equation (12) states that French exports to non-union countries are an increasing function of the union exchange rate. X23 denotes French exports to non-union countries. The message of equation (12) is that a depreciation of the euro raises French exports to nonunion countries. Equation (13) is the import function of France. It states that French imports are an increasing function of French income. Q2 denotes French imports from Germany and from non-union countries. French output is determined by the demand for French goods Y2 = C2 +12 + G2 + X21 + X23 - Q2. Upon substituting the behavioural functions (8) to (13), we reach the goods market equation of France: Y2=C2(Y2) + l2(r) + G2+X2i(Yi) + X23(e)-Q2(Y2)

(14)

4) The money market of the union. The behavioural functions are as follows: Li=Li(r,Yi)

(15)

L2=L2(r,Y2)

(16)

M = const

(17)

Equation (15) is the money demand function of Germany. It states that German money demand is a decreasing function of the world interest rate and an increasing function of German income. L^ denotes German money demand.

16 Equation (16) is the money demand function of France. It states that French money demand is a decreasing function of the world interest rate and an increasing function of French income. L2 denotes French money demand. Equation (17) is the money supply function of the union. It states that the union central bank fixes the money supply of the union. M denotes union money supply. The money demand of the union is equal to the money supply of the union L^ +L2 = M. Upon inserting the behavioural functions (15) to (17), we get to the money market equation of the union: Li(r,Yi) + L2(r,Y2) = M

(18)

5) The model. On this foundation, the full model can be represented by a system of three equations: Yi=Ci(Yi) + Ii(r) + Gi+Xi2(Y2) + Xi3(e)-Qi(Yi)

(19)

Y2=C2(Y2) + l2(r) + G2+X2i(Yi) + X23(e)-Q2(Y2)

(20)

M = Li(r,Yi) + L2(r,Y2)

(21)

Equation (19) is the goods market equation of Germany, as measured in German goods. (20) is the goods market equation of France, as measured in French goods. And (21) is the money market equation of the union, as measured in euros. The exogenous variables are union money supply M, German govemment purchases G^, French government purchases G2, and the world interest rate r. The endogenous variables are German income Y^, French income Y2, and the union exchange rate e. This model is in the tradition of the Mundell-Fleming model and the Levin model, see Carlberg (2000, 2001). The goods market equations are well consistent with microfoundations, see Carlberg (2002). 6) The total differential. It is useful to take the total differential of the model: dYi = CidYi + dGi + m2dY2 + h^de - q^dYj

(22)

dY2 = C2dY2 + dG2 + m^dYi + h2de - q2dY2

(23)

dM = kidYi+k2dY2

(24)

17

Here is a list of the new symbols: c^ marginal consumption rate of Germany C2 marginal consumption rate of France hj exchange rate sensitivity of German exports h2 exchange rate sensitivity of French exports kj income sensitivity of German money demand k2 income sensitivity of French money demand m^ marginal import rate of Germany relative to France m2 marginal import rate of France relative to Germany qi marginal import rate of Germany relative to France and non-union countries q2 marginal import rate of France relative to Germany and non-union countries. We assume that the union countries are the same size and have the same behavioural functions. In terms of the model this means: c = Ci = C2

(25)

h = hi = h2

(26)

k = ki = k2

(27)

m = m^ = m2

(28)

q = qi = q2

(29)

These assumptions prove to be particularly fruitful. In addition we make some standard assumptions: 0
(30)

h>0

(31)

k >0

(32)

0<m<1

(33)

0
(34)

18 7) Fiscal policy. Take for instance an increase in German government purchases. Then what will be the effect on German income, and what on French income? The total differential of the model is as follows: dYi = cdYi + dGi + mdY2 + hde - qdYi

(35)

dY2 = cdY2 + mdYi + hde - qdY2

(36)

0 = dYi+dY2

(37)

Subtract equation (36) from equation (35) to verify (1 - c + m + q)(dYi - dY2) = dG^. Further note equation (37) and solve for: dYi dGi dY2 dGi

1 2(1- -c + m +q)

1 2 ( l - c + m + q)

(38)

(39)

As a fundamental result, these are the fiscal policy multipliers. An increase in German government purchases raises German income. On the other hand, it lowers French income. And what is more, the increase in German income is equal in amount to the decline in French income. That is to say, union income does not change. Now have a closer look at the process of adjustment. The increase in German government purchases causes an appreciation of the euro. This in turn reduces both German exports and French exports. The net effect is that German income goes up, while French income goes down. To illustrate this, consider a numerical example with c = 0.72, m = 0.16, and q = 0.24. Let the sensitivity of consumption to net income be 0.9, and let the tax rate be 0.2. Then the sensitivity of consumption to gross income is c = 0.8 * 0.9 = 0.72. The marginal import rate of Germany is q = 0.24. The marginal import rate of Germany relative to France is m = 0.16. And the marginal import rate of Germany relative to non-union countries is q - m = 0.08. Likewise, the marginal import rate of France is q = 0.24. The marginal import rate of France relative to Germany is m = 0.16. And the marginal import rate of France relative to non-union countries is q - m = 0.08. Hence the fiscal policy multipliers are dY^ / dG^ = 0.735 and dY2/dG^ =-0.735. That means, an

19 increase in German government purchases of 100 causes an increase in German income of 74 and a decline in French income of equally 74. In a sense, the internal effect of fiscal policy is very small, while the external effect of fiscal policy is very large. 8) Monetary poUcy. Take for instance an increase in union money supply. Then what will be the effect on German income, and what on French income? The total differential of the model is: dYi = cdYi + mdY2 + hde - qdYi

(40)

dY2 = cdY2 + mdYi + hde - qdY2

(41)

dM = kdYi+kdY2

(42)

Subtract equation (41) from equation (40) to get dYi=dY2. Put this into equation (42) and rearrange terms: dYi dYo 1 ^=-^ = -^=^ = — dM dM 2k

(43)

As a principal result, these are the monetary policy multipliers. An increase in union money supply raises both German income and French income, to the same extent respectively. Moreover have a closer look at the channels of transmission. The increase in union money supply causes a depreciation of the euro. This in turn enhances both German exports and French exports. That is why German income and French income move up. To illustrate this, consider a numerical example with k = 0.25. So the monetary policy multipliers are dYj / dM = dY2 / dM = 2. In other words, an increase in union money supply of 100 causes an increase in German income of 200 and an increase in French income of equally 200.

Chapter 2 The World as a Whole

1) The model. Understanding the world as a whole is helpful in understanding the world of two monetary regions. Take for instance an increase in world government purchases of 100. Then what will be the effect on world income? Alternatively, take a 1 percent increase in world money supply. Again what will be the effect on world income? Of course, the world as a whole is a closed economy. Therefore the model can be represented by a system of two equations: Y = C(Y) + I(r) + G

(1)

M = L(r,Y)

(2)

C(Y) is the consumption function. It states that world consumption is an increasing function of world income. I(r) is the investment function. It states that world investment is a decreasing function of the world interest rate. G denotes world government purchases. Thus equation (1) is the goods market equation of the world as a whole. M denotes world money supply. L(r, Y) is the money demand function. It states that world money demand is a decreasing function of the world interest rate and an increasing function of world income. Hence equation (2) is the money market equation of the world as a whole. The exogenous variables are world government purchases G and world money supply M. The endogenous variables are world income Y and the world interest rate r. Now take the total differential of the model:

dY = cdY-bdrH-dG

(3)

dM = k d Y - j d r

(4)

21 Here c denotes the marginal consumption rate with 0 < c < 1, b is the interest sensitivity of investment with b > 0, k is the income sensitivity of money demand with k > 0, and j is the interest sensitivity of money demand with j > 0. 2) Fiscal policy. To begin with, solve equations (3) and (4) for the fiscal policy multiplier: dY i ^^ = — ^ — dG bk + js

(5)

Here s is shorthand for 1 - c. As a result, an increase in world government purchases raises world income. To illustrate this, have a look at a numerical example with c = 0.72 and k = 0.25. Empirically speaking, however, b and j are not well known. Therefore, as a point of reference, consider the special case that the interest rate is given exogenously. Then the total differential of the goods market equation is dY = cdY + dG. Accordingly, the fiscal policy multiplier is:

^ =i dG

(6)

s

In the numerical example with c = 0.72, the fiscal policy multiplier is 3.5714. That is, an increase in world government purchases of 100 causes an increase in world income of 357. Let us return now to the general case that the interest rate is endogenous. We assume here that the damping effect of the money market on the fiscal policy multiplier is 0.5: dY 1 ^^ =— dG 2s

(7)

In the numerical example with c = 0.72, the fiscal policy multiplier is 1.7857. That is, an increase in world government purchases of 100 causes an increase in world income of 179. Finally, the comparison of equation (5) with equation (7) yields:

22

bk = js

(8)

In the numerical example with c = 0.72 and k = 0.25, we have b/j = 1.12. 3) Monetary policy. To start with, solve equations (3) and (4) for the monetary policy multiplier: ^ =^ dM bk + js

(9)

Obviously, an increase in world money supply raises world income. Further, taking account of equation (8), the monetary policy multiplier simplifies as follows: dY 1 -^=^ = — dM 2k

(10)

In the numerical example with k = 0.25, the monetary policy multiplier is 2. That is, an increase in world money supply of 100 causes an increase in world income of 200. As a point of reference, consider the small open economy with flexible exchange rates and perfect capital mobility. There the monetary policy multiplier is: dY 1 -^^ = ~ dM k

(11)

This is well known, see for instance the small monetary union of two countries. In the numerical example with k = 0.25, the monetary policy multiplier is 4. That is, an increase in domestic money supply of 100 causes an increase in domestic income of 400. Let us return now to the world as a whole. As a finding, the damping effect on the monetary policy multipHer of closing the economy is 0.5. Finally, what does this mean in terms of elasticities? As a starting point, take the monetary policy multiplier dY / dM = 1 / 2k with k = 3L/ 3Y. Assume that

23

the income elasticity of money demand is unity (3L/3Y)(Y/L) = 1. This implies k = L / Y . Due to L = M, we have k = MA". This together with dY/dM = l / 2 k yields: Y=-M 2

(12)

Here the hat denotes the rate of change (e.g. Y = d Y / Y ) . That is, a 1 percent increase in world money supply produces a 0.5 percent increase in world income. 4) Extensions. So far we assumed that the damping effect of the money market on the fiscal multiplier is 0.5. Now, instead, we assume that the damping effect is 0.75 or 0.25. First assume that the damping effect is 0.75. In this case, the fiscal multiplier is dY/dG = 3/4s and the monetary multiplier is dY / dM = 1 / 4k. In the numerical example, an increase in world government purchases of 100 causes an increase in world income of 268. And an increase in world money supply of 100 causes an increase in world income of 100. More generally, a 1 percent increase in world money supply produces a 0.25 percent increase in world income. Second assume that the damping effect is 0.25. In this case, the fiscal multiplier is dY / dG = 1 / 4s and the monetary multiplier is dY / dM = 3 / 4k. In the numerical example, an increase in world government purchases of 100 causes an increase in world income of 89. And an increase in world money supply of 100 causes an increase in world income of 300. More generally, a 1 percent increase in world money supply produces a 0.75 percent increase in world income.

Chapter 3 The World of Two Monetary Regions

1) Introduction. In this section we consider a world of two monetary regions, let us say Europe and America. The exchange rate between Europe and America is flexible. Take for example an increase in European government purchases. Then what will be the effect on European income, and what on American income? Correspondingly, take an increase in European money supply. Then how will European income respond, and how American income? In dealing with these problems we make the following assumptions. European goods and American goods are imperfect substitutes for each other. European output is determined by the demand for European goods. American output is determined by the demand for American goods. European money demand equals European money supply. And American money demand equals American money supply. There is perfect capital mobility between Europe and America, so the European interest rate agrees with the American interest rate. In the short run, nominal wages and prices are rigid. P^ denotes the price of European goods, as measured in euros. And P2 denotes the price of American goods, as measured in dollars. To simplify notation let be P^ = P2 = 1. The letter e denotes the exchange rate between Europe and America. Properly speaking, e is the price of the dollar as measured in euros. Let the initial value of the exchange rate be unity. 2) The market for European goods. The behavioural functions underlying the analysis are as follows: Ci=Ci(Yi)

(1)

Ii=Ii(r)

(2)

Gj = const

(3)

Xi=Xi(e,Y2)

(4)

Qi = Qi(Yi)

(5)

25 Equation (1) is the consumption function of Europe. It states that European consumption is an increasing function of European income. Here C^ denotes European consumption, and Y^ is European income. Equation (2) is the investment function of Europe. It states that European investment is a decreasing function of the world interest rate. I^ denotes European investment, and r is the world interest rate. According to equation (3), the European government fixes its purchases of goods and services. G^ denotes European government purchases. Equation (4) is the export function of Europe. It states that European exports are an increasing function of the exchange rate and an increasing function of American income. X^ denotes European exports to America, and Y2 is American income. The message of equation (4) is that a depreciation of the euro raises European exports. Equation (5) is the import function Europe. It states that European imports are an increasing function of European income. Q^ denotes European imports from America. European output is determined by the demand for European goods Yj = C^ +1^ + G^ + X^ - Q^. Taking account of the behavioural functions (1) to (5), we arrive at the goods market equation of Europe: Yi=Ci(Yi) + Ii(r) + Gi+Xi(e,Y2)-Qi(Yi)

(6)

3) The market for American goods. The behavioural functions are as follows: C2=C2(Y2)

(7)

I2=l2(r)

(8)

G2 = const

(9)

X2=X2(e,Yi)

(10)

Q2=Q2(Y2)

(11)

Equation (7) is the consumption function of America. It states that American consumption is an increasing function of American income. Here C2 denotes American consumption. Equation (8) is the investment function of America. It states that American investment is a decreasing function of the world interest rate. I2 denotes American investment. According to equation (9), the American

26 government fixes its purchases of goods and services. G2 denotes American government purchases. Equation (10) is the export function of America. It states that American exports are a decreasing function of the exchange rate and an increasing function of European income. X2 denotes American exports to Europe. The message of equation (10) is that a depreciation of the dollar raises American exports. Equation (11) is the import function of America. It states that American imports are an increasing function of American income. Q2 denotes American imports from Europe. American output is determined by the demand for American goods Y2 = C2 +12 + G2 + X2 - Q2. Paying attention to the behavioural functions (7) to (11), we reach the goods market equation of America: Y2=C2(Y2) + l2(r) + G2+X2(e,Yi)-Q2(Y2)

(12)

4) The European money market. The behavioural functions are: Li=Li(r,Yi)

(13)

Ml = const

(14)

Equation (13) is the money demand function of Europe. It states that European money demand is a decreasing function of the world interest rate and an increasing function of European income. L^ denotes European money demand. Equation (14) is the money supply function of Europe. It states that the European central bank fixes European money supply. M^ denotes European money supply. European money demand equals European money supply L^ = M^. Upon substituting the behavioural functions (13) and (14), we get to the money market equation of Europe Li(r, Yj) = M^. 5) The American money market. The behavioural functions are: L2=L2(r,Y2)

(15)

M2= const

(16)

27

Equation (15) is the money demand function of America. It states that American money demand is a decreasing function of the world interest rate and an increasing function of American income. L2 denotes American money demand. Equation (16) is the money supply function of America. It states that the American central bank fixes American money supply. M2 denotes American money supply. American money demand equals American money supply L2 = M2. Upon inserting the behavioural functions (15) and (16), we get to the money market equation of America L2(r, Y2) = M2. 6) The model. On this foundation, the full model can be characterized by a system of four equations: Yi=Ci(Yi) + Ii(r) + Gi+Xi(e,Y2)-Qi(Yi)

(17)

Y2=C2(Y2) + l2(r) + G2+X2(e,Yi)-Q2(Y2)

(18)

Mi=Li(r,Yi)

(19)

M2=L2(r,Y2)

(20)

Equation (17) is the goods market equation of Europe, as measured in European goods. (18) is the goods market equation of America, as measured in American goods. (19) is the money market equation of Europe, as measured in euros. And (20) is the money market equation of America, as measured in dollars. The exogenous variables are European money supply M^, American money supply M2, European government purchases G^, and American government purchases G2. The endogenous variables are European income Y^, American income Y2, the exchange rate e, and the world interest rate r. This model is in the tradition of the Mundell-Fleming model, see Carlberg (2000, 2001). The goods market equations are well consistent with microfoundations, see Carlberg (2002). 7) The total differential. It is useful to take the total differential of the model: dYi = CjdYi - bidr + dGj + hide + q2dY2 - qjdY^

(21)

dY2 = C2dY2 - b2dr + dG2 - h2de + q^dY^ - q2dY2

(22)

dMi = kidYi-Jidr

(23)

28 dM2=k2dY2-J2dr

(24)

Here is a list of the new symbols: bj interest sensitivity of European investment b2 interest sensitivity of American investment Cj marginal consumption rate of Europe C2 marginal consumption rate of America hj exchange rate sensitivity of European exports h2 exchange rate sensitivity of American exports ji interest sensitivity of European money demand J2 interest sensitivity of American money demand kj income sensitivity of European money demand k2 income sensitivity of American money demand q^ marginal import rate of Europe q2 marginal import rate of America. We assume that the monetary regions are the same size and have the same behavioural functions. In terms of the model that means: b = bi=b2

(25)

c = Cj = C2

(26)

h = hi = h2

(27)

J = J1=J2

(28)

k = ki=k2

(29)

q = qi = q2

(30)

These assumptions prove to be particularly fruitful. In addition we make some standard assumptions: b>0

(31)

0
(32)

h>0

(33)

j>0

(34)

29

k>0

(35)

0
(36)

8) Fiscal policy. Take for instance an increase in European government purchases. Then what will be the effect on European income, and what on American income? The total differential of the model is as follows: dYi = cdYi - bdr + dGj + hde + qdY2 - qdYj

(37)

dY2 = cdY2 - bdr - hde + qdYi - qdY2

(38)

0 = kdYi-jdr

(39)

0 = kdY2-jdr

(40)

Equations (39) and (40) give immediately: dYi=dY2

(41)

jdr = kdYi

(42)

Now take the sum of equations (37) and (38), observing equation (41), to find out 2dYi = dGj + 2cdYi - 2bdr. Then eliminate dr by means of equation (42), introduce s = 1 - c, and rearrange: dYi-dY2_ j dGi dGi 2bk + 2js

.43.

As a fundamental result, these are the fiscal policy multipUers. An increase in European government purchases raises both European income and American income, to the same extent respectively. Next have a look at some further aspects. First consider the exchange rate. Take the difference between equations (37) and (38), observe equation (41), and solve for: de

1 =

dGi

(44) 2h

30

Obviously, an increase in European government purchases causes an appreciation of the euro and a depreciation of the dollar. Second consider the world interest rate. Merge equations (42) and (43) to check: '^ dGi

^ 2bk + 2js

(45)

That is, an increase in European government purchases raises the world interest rate. Third consider the process of adjustment. An increase in European government purchases causes an appreciation of the euro and an increase in the world interest rate. The appreciation of the euro lowers European exports but raises American exports. The increase in the world interest rate lowers both European investment and American investment. The net effect is that European income and American income go up, to the same extent respectively. Fourth consider an important special case. Assume that the world fiscal multipher is l/2s. This assumption was discussed in Chapter 2. According to equation (43), the effect on world income is: ^^> dGi bk + js

(46)

Now assume that the world fiscal multiplier is l/2s: '^ dGi

' 2s

(47)

Then the comparison of equations (46) and (47) yields: bk = js

(48)

What does this imply for regional incomes? To answer this question, substitute equation (48) into equation (43):

31 dYi ^ dY2 ^ 1 dGi " dGi " 4s

(49)

As a result, these are the regional fiscal multipliers. To illustrate this, take a numerical example with c = 0.72. Then the multipliers are dYj/dGj =dY2/dGj =0.893. That is, an increase in European government purchases of 100 causes an increase in European income of 89, an increase in American income of equally 89, and an increase in world income of 179. In a sense, the internal effect of fiscal policy is rather small, and the external effect of fiscal policy is quite large. 9) Monetary policy. Consider an increase in European money supply. Then how will European income respond, and how American income? The total differential of the model is as follows: dYi = cdYi - bdr + hde + qdY2 - qdYj

(50)

dY2 = cdY2 - bdr - hde + qdYi - qdY2

(51)

dMi=kdYi-jdr

(52)

0 = kdY2-jdr

(53)

Now take the difference between equations (52) and (53): dY2=dYi-dMi/k

(54)

Then take the sum of equations (50) and (51), observing s = 1 - c: s(dYi+dY2) = -2bdr

(55)

Finally get rid of dY2 and dr in equation (55) with the help of equations (54) and (52): dYi ^ 2bk + js dMi 2k(bk + js)

32

dY2_ dMi

js 2k(bk + js)

(57)

As a principal result, these are the monetary policy multipliers. An increase in European money supply raises European income. On the other hand, it lowers American income. Here the rise in European income exceeds the fall in American income. That means, world income goes up. Besides, have a closer look at the mechanism of transmission. An increase in European money supply causes a depreciation of the euro and a decline in the world interest rate. The depreciation of the euro raises European exports but lowers American exports. The decline in the world interest rate raises both European investment and American investment. The net effect is that European income goes up. However, American income goes down. And what is more, world income goes up. Next consider an important special case. Assume that the world fiscal multiplier is l/2s. Accordingly, insert equation (48) into equations (56) and (57):

^ - A dMi

^ dMi

4k

= --1-

(58) (59)

4k

As a finding, these are the monetary policy multipliers. To illustrate this, consider a numerical example with k = 0.25. Then the multipliers are d Y i / d M i = 3 and dY2/dM^ = ~ 1 . That is to say, an increase in European money supply of 100 causes an increase in European income of 300, a decline in American income 100, and an increase in world income of 200. The internal effect of monetary policy is very large, and the external effect of monetary policy is large.

Chapter 4 The Large Monetary Union of Two Countries

1) Introduction. The world consists of two monetary regions, let us say Europe and America. The exchange rate between Europe and America is flexible. Europe in turn consists of two countries, let us say Germany and France. So Germany and France form a monetary union. Take for example an increase in German government purchases. Then what will be the effect on German income, and what on French income? In doing the analysis, we make the following assumptions. German goods, French goods and American goods are imperfect substitutes for each other. German output is determined by the demand for German goods. French output is determined by the demand for French goods. And American output is determined by the demand for American goods. European money demand equals European money supply. And American money demand equals American money supply. There is perfect capital mobility between Germany, France and America. Thus the German interest rate, the French interest rate, and the American interest rate are equalized. In the short run, nominal wages and prices are rigid. P^ denotes the price of German goods, as measured in euros. P2 is the price of French goods, as measured in euros. And P3 is the price of American goods, as measured in dollars. To simplify notation let be P^ = P2 =P3 = 1 . The letter e denotes the exchange rate between Europe and America. Properly speaking, e is the price of the dollar, as measured in euros. Let the initial value of the exchange rate be unity.

34

2) The market for German goods. The behavioural functions underlying the analysis are as follows: Ci=Ci(Yi)

(1)

Ii=Ii(r)

(2)

Gj = const

(3)

Xi2=Xi2(Y2)

(4)

Xi3=Xi3(e,Y3)

(5)

Qi=Qi(Yi)

(6)

Equation (1) is the consumption function of Germany. It states that German consumption is an increasing function of German income. Here Cj denotes German consumption, and Y^ is German income. Equation (2) is the investment function of Germany. It states that German investment is a decreasing function of the world interest rate. I^ denotes German investment, and r is the world interest rate. According to equation (3), the German government fixes its purchases of goods and services. G^ denotes German government purchases. Equations (4) and (5) are the export functions of Germany. Equation (4) states that German exports to France are an increasing function of French income. X12 denotes German exports to France, and Y2 is French income. Equation (5) states that German exports to America are an increasing function of the exchange rate and an increasing function of American income. X13 denotes German exports to America, and Y3 is American income. The message of equation (5) is that a depreciation of the euro raises German exports to America. Equation (6) is the import function of Germany. It states that German imports are an increasing function of German income. Q^ denotes German imports from France and America. German output is determined by the demand for German goods Y^ = Cj + Ij + Gj + X12 + Xi3 - Qj. Taking account of the behavioural functions (1) to (6), we arrive at the goods market equation of Germany: Yi=Ci(Yi) + Ii(r) + Gi+Xi2(Y2) + Xi3(e,Y3)-Qi(Yi)

(7)

35

3) The market for French goods. The behavioural functions are as follows: C2=C2(Y2)

(8)

I2=l2(r)

(9)

G2 = const

(10)

X2i=X2i(Yi)

(11)

X23=X23(e,Y3)

(12)

Q2=Q2(Y2)

(13)

Equation (8) is the consumption function of France. It states that French consumption is an increasing function of French income. Here C2 denotes French consumption. Equation (9) is the investment function of France. It states that French investment is a decreasing function of the world interest rate. I2 denotes French investment. According to equation (10), the French government fixes its purchases of goods and services. G2 denotes French government purchases. Equations (11) and (12) are the export functions of France. Equation (11) states that French exports to Germany are an increasing function of German income. X21 denotes French exports to Germany. Equation (12) states that French exports to America are an increasing function of the exchange rate and an increasing function of American income. X23 denotes French exports to America. The message of equation (12) is that a depreciation of the euro raises French exports to America. Equation (13) is the import function of France. It states that French imports are an increasing function of French income. Q2 denotes French imports from Germany and America. French output is determined by the demand for French goods Y2 = C2 +12 + G2 + X21 + X23 - Q2. Upon substituting the behavioural functions (8) to (13), we reach the goods market equation of France: Y2=C2(Y2) + l2(r) + G2+X2i(Yi) + X23(e,Y3)-Q2(Y2)

(14)

36 4) The market for American goods. The behavioural functions are as follows: C3=C3(Y3)

(15)

I3=l3«

(16)

G3 = const

(17)

X3i=X3i(e,Yi)

(18)

X32=X32(e,Y2)

(19)

Q3=Q3(Y3)

(20)

Equation (15) is the consumption function of America. It states that American consumption is an increasing function of American income. Here C3 denotes American consumption. Equation (16) is the investment function of America. It states that American investment is a decreasing function of the world interest rate. I3 denotes American investment. According to equation (17), the American government fixes its purchases of goods and services. G3 denotes American government purchases. Equations (18) and (19) are the export functions of America. Equation (18) states that American exports to Germany are a decreasing function of the exchange rate and an increasing function of German income. X^i denotes American exports to Germany. The message of equation (18) is that a depreciation of the dollar raises American exports to Germany. Equation (19) states that American exports to France are a decreasing function of the exchange rate and an increasing function of French income. X32 denotes American exports to France. The message of equation (19) is that a depreciation of the dollar raises American exports to France. Equation (20) is the import function of America. It states that American imports are an increasing function of American income. Q3 denotes American imports from Germany and France. American output is determined by the demand for American goods Y3 = C3 +13 + G3 + X31 + X32 - Q3. Upon inserting the behavioural functions (15) to (20) we get to the goods market equation of America: Y3=C3(Y3) + l3(r) + G3+X3i(e,Yi) + X32(e,Y2)-Q3(Y3)

(21)

37

5) The European money market. The behavioural functions are: Li=Li(r,Yi)

(22)

L2=L2(r,Y2)

(23)

Mi2 = const

(24)

Equation (22) is the money demand function of Germany. It states that German money demand is a decreasing function of the world interest rate and an increasing function of German income. L^ denotes German nioney demand. Equation (23) is the money demand function of France. It states that French money demand is a decreasing function of the world interest rate and an increasing function of French income. L2 denotes French money demand. Equation (24) is the money supply function of Europe. It states that the European central bank fixes European money supply. M12 denotes European money supply. European money demand is equal to European money supply Lj + L2 = M12. Taking account of the behavioural functions (22) to (24), we arrive at the money market equation of Europe L^ (r, Y^) + L2 (r, Y2) = M12. 6) The American money market. The behavioural functions are: L3=L3(r,Y3)

(25)

M3 = const

(26)

Equation (25) is the money demand function of America. It states that American money demand is a decreasing function of the world interest rate and an increasing function of American income. L3 denotes American money demand. Equation (26) is the money supply function of America. It states that the American central bank fixes American money supply. M3 denotes American money supply. American money demand is equal to American money supply L3 = M3. Upon substituting the behavioural functions (25) and (26), we reach the money market equation of America L3(r, Y3) = M3. 7) The model. On this foundation, the full model can be characterized by a system of five equations:

38

Yi=Ci(Yi) + Ii(r) + Gi+Xi2(Y2) + Xi3(e,Y3)-Qi(Yi)

(27)

Y2=C2(Y2) + l2(r) + G2+X2i(Yi) + X23(e,Y3)-Q2(Y2)

(28)

Y3 =C3(Y3) + l3(r) + G3+X3i(e,Yi) + X32(e,Y2)-Q3(Y3)

(29)

Mi2=Li(r,Yi) + L2(r,Y2)

(30)

M3=L3(r,Y3)

(31)

Equation (27) is the goods market equation of Germany, as measured in German goods. (28) is the goods market equation of France, as measured in French goods. (29) is the goods market equation of America, as measured in American goods. (30) is the money market equation of Europe, as measured in euros. And (31) is the money market equation of America, as measured in dollars. It is worth pointing out here that the goods market equations are well consistent with microfoundations, see Carlberg (2002). The exogenous variables are European money supply M125 American money supply M3, German govemment purchases G^, French govemment purchases G2, and American govemment purchases G3. The endogenous variables are German income Y^, French income Y2, American income Y3, the exchange rate between Europe and America e, and the world interest rate r. 8) The total differential. It is useful to take the total differential of the model. In doing this, we assume that the monetary regions are the same size and have the same behavioural functions. Moreover, we assume that the union countries are the same size and have the same behavioural functions. These assumptions prove to be particularly fruitful: dYi = cdYi - 0.5bdr + dGj + 0.5hde + mdY2 + 0.5qdY3 - (m + q)dYi

(32)

dY2 = cdY2 - 0.5bdr + dG2 + 0.5hde + mdYj + 0.5qdY3 - (m + q)dY2

(33)

dY3 = cdY3 - bdr + dG3 - hde 4- qdYj + qdY2 - qdY3

(34)

dMi2 = kdYi - 0.5jdr + kdY2 - 0.5jdr

(35)

dM3 = kdY3-jdr

(36)

Here is a list of the new symbols:

39 b 0.5b c h 0.5h j 0.5j k m q 0.5q

interest sensitivity of European investment, interest sensitivity of American investment interest sensitivity of German investment, interest sensitivity of French investment marginal consumption rate exchange rate sensitivity of European exports, exchange rate sensitivity of American exports exchange rate sensitivity of German exports, exchange rate sensitivity of French exports interest sensitivity of European money demand, interest sensitivity of American money demand interest sensitivity of German money demand, interest sensitivity of French money demand income sensitivity of money demand marginal import rate of Germany relative to France, marginal import rate of France relative to Germany marginal import rate of Europe relative to America, marginal import rate of America relative to Europe marginal import rate of America relative to Germany, marginal import rate of America relative to France.

Now take the sum of equations (32) and (33). Then define dYi2 = dY^ + dY2 as well as dGi2 =dGi+dG2, where Y12 denotes European income and G12 denotes European government purchases. Hence the total differential of the model can be rewritten as follows: dYi2 = cdYi2 - bdr + dGi2 + hde + qdY3 - qdYi2

(37)

dY3 = cdY3 - bdr + dG3 - hde + qdYi2 ~ qdY3

(38)

dMi2=kdYi2-"jdr

(39)

dM3 = kdY3-jdr

(40)

Equation (37) is the goods market equation of Europe, (38) is the goods market equation of America, (39) is the money market equation of Europe, and (40) is the money market equation of America. The exogenous variables are (the change in) European money supply dMi2, American money supply dM3,

40 European government purchases dGi2, and American government purchases dG3. The endogenous variables are European income dYi2, American income dY3, the exchange rate de, and the world interest rate dr. As a result, this model is equivalent to that derived for the world of two monetary regions, cf. Chapter 3. Thus we can make use of the multipliers obtained there. 9) Fiscal policy. Consider for example an increase in German government purchases. Then what will be the effect on German income, French income, and American income? To solve this problem, we start with equation (32) and eliminate de, dr, dY2 as well as dY3. This can be done in several steps. We assume that the world fiscal multiplier is l/2s. Then the fiscal multipliers for the world of two monetary regions are as follows: dYi2 _ dY3 _ 1 dGi2 dGi2 4s de dGi2

1 2h

dr _ 1 dGi2 4b

(41)

(42)

(43)

In equation (43) we have used the important finding bk = js. Next observe dGi2 = dGj and dYi2 = dY^ + dY2 to get to: de = - ( l / 2 h ) d G i

(44)

dr = (l/4b)dGi

(45)

dY3=(l/4s)dGi

(46)

dY2=(l/4s)dGi-dYi

(47)

Then, in equation (32), eUminate de, dr, dY2 and dY3 by means of equations (44) to (47), noting s = 1 - c: d Y i ^ 2m + q + 5s dGj 8s(2m + q + s)

41

As a fundamental result, this is the fiscal multiplier in Germany. An increase in German government purchases raises German income. To illustrate this, take a numerical example with c = 0.72, m = 0.08, and q = 0.08. So the multipUers are d Y i / d G i = 1.408, dY2/dGj =-0.515, and dY3/dGj = 0.893. That is, an increase in German government purchases of 100 causes an increase in German income of 141. On the other hand, it causes a decline in French income of 52. And what is more, it causes an increase in European income of 89 and an increase in American income of equally 89. Finally consider the process of adjustment. An increase in German government purchases causes an appreciation of the euro and an increase in the world interest rate. The appreciation of the euro lowers German exports and French exports but raises American exports. The increase in the world interest rate lowers German investment, French investment, and American investment. The net effect is that German income moves up. However, French income moves down. And American income moves up.

Part Two Monetary Interactions between Europe and America

Chapter 1 Monetary Competition between Europe and America 1. The Dynamic Model

1) The static model. The world consists of two monetary regions, say Europe and America. The exchange rate between Europe and America is flexible. Europe in turn consists of two countries, say Germany and France. So Germany and France form a monetary union. There is international trade between Germany, France and America. German goods, French goods and American goods are imperfect substitutes for each other. German output is determined by the demand for German goods. French output is determined by the demand for French goods. And American output is determined by the demand for American goods. European money demand equals European money supply. And American money demand equals American money supply. There is perfect capital mobility between Germany, France and America. Thus the German interest rate, the French interest rate, and the American interest rate are equalized. The monetary regions are the same size and have the same behavioural functions. The union countries are the same size and have the same behavioural functions. Nominal wages and prices adjust slowly. As a result, an increase in European money supply raises both German output and French output, to the same extent respectively. On the other hand, the increase in European money supply lowers American output. Here the rise in European output exceeds the fall in American output. Correspondingly, an increase in American money supply raises American output. On the other hand, it lowers both German output and French output, to the same extent respectively. Here the rise in American output exceeds the fall in European output. In the numerical example, an increase in European money supply of 100 causes an increase in German output of 150, an increase in French output of equally 150, and a decline in American output of 100. Similarly, an increase in American money supply of 100 causes an increase in American output of 300, a

46 decline in German output of 50, and a decline in French output of equally 50. That is to say, the internal effect of monetary policy is very large, and the external effect of monetary policy is large. Now have a closer look at the process of adjustment. An increase in European money supply causes a depreciation of the euro, an appreciation of the dollar, and a decline in the world interest rate. The depreciation of the euro raises German exports and French exports. The appreciation of the dollar lowers American exports. And the decline in the world interest rate raises German investment, French investment and American investment. The net effect is that German output and French output go up. However, American output goes down. This model is in the tradition of the Mundell-Fleming model and the Levin model, see Part One. The static model can be represented by a system of three equations: Yi = Ai + 0.5aMi2 - O.5PM3

(1)

Y2 = A2 + 0.5aMi2 - O.5PM3

(2)

Y3=A3+aM3-|3Mi2

(3)

Of course this is a reduced form. Yj denotes German output, Y2 is French output, Y3 is American output, M12 is European money supply, M3 is American money supply, A^ is some other factors bearing on German output, A2 is some other factors bearing on French output, and A3 is some other factors bearing on American output, a and (3 denote the monetary policy multipliers. The internal effect of monetary policy is positive a > 0 . By contrast, the external effect of monetary policy is negative p > 0. In absolute values, the internal effect is larger than the external effect a > p . The endogenous variables are German output, French output, and American output. According to equation (1), German output is a positive function of European money supply and a negative function of American money supply. According to equation (2), French output is a positive function of European money supply and a negative function of American money supply. According to equation (3), American output is a positive function of American money supply and a negative function of European money supply.

47

The static model can be compressed to a system of two equations: Yi2=Ai2+aMi2-PM3

(4)

Y3=A3+aM3-pMi2

(5)

Here we have Y12 = ^ 1 + ^ 2 and A12 = A^ + A2. Y12 denotes European output and A12 is some other factors bearing on European output. The endogenous variables are European output and American output. According to equation (4), European output is a positive function of European money supply and a negative function of American money supply. According to equation (5), American output is a positive function of American money supply and a negative function of European money supply. 2) The dynamic model. At the beginning there is unemployment in Germany, France and America. More precisely, unemployment in Germany exceeds unemployment in France. The primary target of the European central bank is price stability in Europe. The secondary target of the European central bank is high employment in Germany and France. The specific target of the European central bank is that unemployment in Germany equals overemployment in France. In other words, deflation in Germany equals inflation in France. So there is price stability in Europe. In a sense, the specific target of the European central bank is full employment in Europe. The instrument of the European central bank is European money supply. The European central bank raises European money supply so as to close the output gap in Europe: Mi2-Mri=^i^^

Here is a list of the new symbols: Y12

European output this period

Y22

full-employment output in Europe

Y12 - Y22

output gap in Europe this period

Mj"2

European money supply last period

M12

European money supply this period

M12 - Mj"2 increase in European money supply.

(6)

48

Here the endogenous variable is European money supply this period M12. The target of the American central bank is full employment in America. The instrument of the American central bank is American money supply. The American central bank raises American money supply so as to close the output gap in America:

M3-M7^ = ^ ^ ^ ^ ^ a

(7)

Here is a list of the new symbols: Y3

American output this period

Y3

full-employment output in America

Y3 "- Y3

output gap in America this period

M3 ^

American money supply last period

M3

American money supply this period

M3 - M3 ^ increase in American money supply. Here the endogenous variable is American money supply this period M 3 . We assume that the European central bank and the American central bank decide simultaneously and independently. In addition there is an output lag. European output next period is determined by European money supply this period as well as by American money supply this period: Yi^2^=Ai2+aMi2-pM3 Here Y^i

(8)

denotes European output next period. In the same way, American

output next period is determined by American money supply this period as well as by European money supply this period: Y3+i=A3+aM3-pMi2

(9)

Here Y3'^ denotes American output next period. On this basis, the dynamic model can be characterized by a system of four equations:

49

Mi2 - Mj-2^ = ^^^

^^^

(10)

Ma-MT^=^^-^ a

(11)

Yi^2^=Ai2+aMi2-|3M3

(12)

Y3+i=A3+aM3-PMi2

(13)

Equation (10) shows the pohcy response in Europe, (11) shows the poUcy response in America, (12) shows the output lag in Europe, and (13) shows the output lag in America. The endogenous variables are European money supply this period M12, American money supply this period M3, European output next period ¥^"2^ and American output next period Y^^. 3) The steady state. In the steady state by definition we have: Mi2=M^2^

(14)

M3=M3i

(15)

Equation (14) has it that European money supply does not change any more. Similarly, equation (15) has it that American money supply does not change any more. Therefore the steady state can be captured by a system of four equations: Yi2=Yi2

(16)

Y3=Y3

(17)

Yi2=Ai2+aMi2"PM3

(18)

Y3=A3+aM3-PMi2

(19)

Here the endogenous variables are European output Y22, American output Y3, European money supply M^2' ^^^ American money supply M3. According to equation (16) there is full employment in Europe, so European output is constant. According to equation (17) there is full employment in America, so American

50 output is constant too. Further, equations (18) and (19) give the steady-state levels of European and American money supply. The model of the steady state can be compressed to a system of only two equations: %2 = Ai2 + aMi2 - PM3

(20)

Y3=A3+aM3-PMi2

(21)

Here the endogenous variables are European money supply and American money supply. To simplify notation we introduce:

B3 = Y3-A3

(23)

With this, the model of the steady state can be written as follows: Bi2=aMi2-PM3

(24)

B3=aM3-PMi2

(25)

The endogenous variables are still M12 and M3. Next we solve the model for the endogenous variables: _aBi2+PB3

Mi2=^^^FS^

(26)

_0^3+PBi2 M3=^^^^^

(27)

a2-p^

Equation (26) shows the steady-state level of European money supply, and equation (27) shows the steady-state level of American money supply. As a result, there is a steady state if and only if a ;^ p. Owing to the assumption a > (3, this condition is fulfilled.

51 As an alternative, the steady state can be represented in terms of the initial output gap and the total increase in money supply. Taking differences in equations (4) and (5), the model of the steady state can be written as follows: AYi2 = aAMi2 ~ PAM3

(28)

AY3=aAM3-pAMi2

(29)

Here AY12 ^^ the initial output gap in Europe, AY3 is the initial output gap in America, AM12 is the total increase in European money supply, and AM3 is the total increase in American money supply. The endogenous variables are AM12 and AM3. The solution to the system (28) and (29) is: aAY,.pAY3

^3„,

... aAY3+PAYi2 AM3= \ "^ ^^

,^., (31)

According to equation (30), the total increase in European money supply depends on the initial output gap in Europe, the initial output gap in America, the direct multiplier a , and the cross multiplier (3. The larger the initial output gap in Europe, the larger is the total increase in European money supply. Moreover, the larger the initial output gap in America, the larger is the total increase in European money supply. At first glance this comes as a surprise. According to equation (31), the total increase in American money supply depends on the initial output gap in America, the initial output gap in Europe, the direct multiplier a, and the cross multiplier p. 4) Stability. Eliminate Y12 in equation (10) by means of equation (12) and rearrange terms Y12 = A12 +OCM12 - P M 3 ^ By analogy, eliminate Y3 in equation (11) by means of equation (13) to arrive at Y3 = A3 + aM3 - pMj"2. On this basis, the dynamic model can be described by a system of two equations: Yi2=Ai2+aMi2-PM3i

(32)

Y3=A3+aM3~pMr]

(33)

52

Here the endogenous variables are European money supply this period M12 and American money supply this period M3. To simpUfy notation we make use of equations (22) and (23). With this, the dynamic model can be written as follows: Bi2=ocMi2-|3M3i

(34)

B3=aM3~pMf]

(35)

The endogenous variables are still M12 and M3. Now substitute equation (35) into equation (34) and solve for:

c^., = B,,^fi5i^P!Mii ^^

^^

a

(36)

a

Then differentiate equation (36) for Mj"!:

Finally the stability condition is P / a a>P

< 1 or: (38)

That means, the steady state is stable if and only if the internal effect of monetary policy is larger than the external effect of monetary policy. This condition is satisfied. As a result, there is a stable steady state of monetary competition. In other words, the process of monetary competition leads to full employment in Europe and America. And what is more, it leads to price stability in Europe and America. However, the process of monetary competition does not lead to full employment in Germany and France. And what is more, it does not lead to price stability in Germany and France.

53

2. Some Numerical Examples

To illustrate the dynamic model, have a look at some numerical examples. For ease of exposition, without loss of generaUty, assume a = 3 and P = 1, see Part One. On this assumption, the static model can be written as follows: Yi=Ai+1.5Mi2-0.5M3

(1)

Y2=A2+1.5Mi2-0.5M3

(2)

Y3=A3+3M3-Mi2

(3)

The endogenous variables are German output, French output, and American output. Obviously, an increase in European money supply of 100 causes an increase in German output of 150, an increase in French output of equally 150, and a decline in American output of 100. Similarly, an increase in American money supply of 100 causes an increase in American output of 300, a decUne in German output of 50, and a decline in French output of equally 50. Further let full-employment output in Germany be 1000, let full-employment output in France be equally 1000, and let full-employment output in America be 2000. The static model can be rewritten as follows: Yi2=Ai2+3Mi2-M3

(4)

Y3=A3+3M3-Mi2

(5)

The endogenous variables are European output and American output. Obviously, an increase in European money supply of 100 causes an increase in European output of 300 and a decline in American output of 100. Correspondingly, an increase in American money supply of 100 causes an increase in American output of 300 and a decline in European output of 100. Full-employment output in Europe is 2000, and full-employment output in America is equally 2000. It proves useful to study four distinct cases: - the case of unemployment

54 - Europe and America differ in unemployment - the case of inflation - unemployment in Europe, inflation in America. 1) The case of unemployment. Let initial output in Germany be 940, let initial output in France be 970, and let initial output in America be 1910. In each of the countries there is unemployment and hence deflation. Strictly speaking, unemployment in Germany is above its equilibrium level. And the same holds for France and America. Strictly speaking, inflation in Germany is below 2 percent. And the same holds for France and America. Step 1 refers to the policy response. First consider monetary policy in Europe. The output gap in Germany is 60, the output gap in France is 30, and the output gap in Europe is 90. In this situation, the specific target of the European central bank is that unemployment in Germany equals overemployment in France. In other words, deflation in Germany equals inflation in France. Thus there is price stability in Europe. The output gap in Europe is 90. The monetary policy multiplier in Europe is 3. So what is needed in Europe is an increase in European money supply of 30. Second consider monetary policy in America. The specific target of the American central bank is full employment in America. The output gap in America is 90. The monetary policy multiplier in America is 3. So what is needed in America is an increase in American money supply of 30. Step 2 refers to the output lag. The increase in European money supply of 30 causes an increase in German output of 45 and an increase in French output of equally 45. As a side effect, it causes a decline in American output of 30. The increase in American money supply of 30 causes an increase in American output of 90. As a side effect, it causes a decline in German output of 15 and a decUne in French output of equally 15. The net effect is an increase in German output of 30, an increase in French output of equally 30, and an increase in American output of 60. As a consequence, German output goes from 940 to 970, French output goes from 970 to 1000, and American output goes from 1910 to 1970. In Germany there is still some unemployment and deflation. In France there is now full employment and price stabiUty. In Europe there is still some unemployment and deflation. And the same is true of America.

55 Why does the European central bank not succeed in closing the output gap in Europe? The underlying reason is the negative external effect of the increase in American money supply. And why does the American central bank not succeed in closing the output gap in America? The underlying reason is the negative external effect of the increase in European money supply. Step 3 refers to the policy response. The output gap in Europe is 30. The monetary policy multiplier in Europe is 3. So what is needed in Europe is an increase in European money supply of 10. The output gap in America is 30. The monetary policy multiplier in America is 3. So what is needed in America is an increase in American money supply of 10. Step 4 refers to the output lag. The increase in European money supply of 10 causes an increase in German output of 15 and an increase in French output of equally 15. As a side effect, it causes a decUne in American output of 10. The increase in American money supply of 10 causes an increase in American output of 30. As a side effect, it causes a decUne in German output of 5 and a dechne in French output of equally 5. The net effect is an increase in German output of 10, an increase in French output of equally 10, and an increase in American output of 20. As a consequence, German output goes from 970 to 980, French output goes from 1000 to 1010, and American output goes from 1970 to 1990. In Germany there is still some unemployment and deflation. In France there is now overemployment and inflation. In Europe there is still some unemployment and deflation. And the same is true of America. This process repeats itself round by round. Table 2.1 presents a synopsis. In the steady state, German output is 985, French output is 1015, and American output is 2000. In Germany there is unemployment and deflation. In France there is overemployment and inflation. In Europe there is full employment and price stability. And in America there is full employment and price stability too. Unemployment in Germany equals overemployment in France. And deflation in Germany equals inflation in France. Strictly speaking, unemployment in Germany is above its equilibrium level. Unemployment in France is below its equilibrium level. Unemployment in Europe is at its equilibrium level. And unemployment in America is at its equilibrium level too. Strictly speaking, inflation in Germany is below 2 percent. Inflation in France is

56 above 2 percent. Inflation in Europe is at 2 percent. And inflation in America is equally at 2 percent. As a result, the process of monetary competition leads to full employment in Europe and America. And what is more, it leads to price stability in Europe and America. However, the process of monetary competition does not lead to full employment in Germany and France. And what is more, it does not lead to price stability in Germany and France. What are the dynamic characteristics of this process? There are repeated increases in European money supply, as there are in American money supply. There are repeated increases in German output, as there are in French output and American output. The exchange rate between Europe and America is constant. There are repeated cuts in the world interest rate. There are repeated increases in German investment, as there are in French investment and American investment. There are repeated cuts in the German budget deficit, as there are in the French budget deficit and the American budget deficit.

Table 2.1 Monetary Competition between Europe and America The Case of Unemployment

Initial Output

Germany

France

America

940

970

1910

30

30

1000

1970

10

10

1010

1990

A Money Supply 1 Output

970

A Money Supply Output

980

A Money Supply 1 Output

3.3

3.3

983.3

1013.3

1996.7

985

1015

2000

1 1 1

and so on \ Steady-State Output

1

57 Taking the sum over all periods, the total increase in European money supply is 45, as is the total increase in American money supply, see equations (30) and (31) in the preceding section. That means, the total increase in European money supply is large, as compared to the initial output gap in Europe of 90. And the same applies to the total increase in American money supply, as compared to the initial output gap in America of 90. The effective multiplier in Europe is 90/ 45 = 2, as is the effective multipHer in America. In other words, the effective multiplier in Europe is small. And the same holds for the effective multiplier in America. 2) Europe and America differ in unemployment. Let initial output in Germany be 940, let initial output in France be 970, and let initial output in America be 1880. Unemployment in America exceeds unemployment in Europe. Step 1 refers to the policy response. The output gap in Europe is 90. The monetary policy multiplier in Europe is 3. So what is needed in Europe is an increase in European money supply of 30. The output gap in America is 120. The monetary policy multiplier in America is 3. So what is needed in America is an increase in American money supply of 40. Step 2 refers to the output lag. The increase in European money supply of 30 causes an increase in German output of 45 and an increase in French output of equally 45. As a side effect, it causes a decline in American output of 30. The increase in American money supply of 40 causes an increase in American output of 120. As a side effect, it causes a decline in German output of 20 and a decline in French output of equally 20. The net effect is an increase in German output of 25, an increase in French output of equally 25, and an increase in American output of 90. As a consequence, German output goes from 940 to 965, French output goes from 970 to 995, and American output goes from 1880 to 1970. Step 3 refers to the policy response. The output gap in Europe is 40. The monetary policy multiplier in Europe is 3. So what is needed in Europe is an increase in European money supply of 13.3. The output gap in America is 30. The monetary policy multiplier in America is 3. So what is needed in America is an increase in American money supply of 10. Step 4 refers to the output lag. The increase in European money supply of 13.3 causes an increase in German output of 20 and an increase in French output

58 of equally 20. As a side effect, it causes a decline in American output of 13.3. The increase in American money supply of 10 causes an increase in American output of 30. As a side effect, it causes a decline in German output of 5 and a decline in French output of equally 5. The net effect is an increase in German output of 15, an increase in French output of equally 15, and an increase in American output of 16.7. As a consequence, German output goes from 965 to 980, French output goes from 995 to 1010, and American output goes from 1970 to 1986.7. And so on. Table 2.2 gives an overview.

Table 2.2 Monetary Competition between Europe and America Europe and America Differ in Unemployment

Initial Output

Germany

France

America

940

970

1880

30

40

995

1970

A Money Supply 1 Output

965

A Money Supply 1 Output

13.3 980

A Money Supply 1 Output

1010

1 1

10 1986.7

1

3.3

4.4

982.8

1012.8

1996.7

1

985

1015

2000

1

and so on 1 Steady-State Output

In the steady state, German output is 985, French output is 1015, and American output is 2000. In Germany there is unemployment and deflation. In France there is overemployment and inflation. In Europe there is full employment and price stability. And in America there is full employment and price stability too. What are the dynamic characteristics of this process? There are repeated increases in European money supply, as there are in American money supply. There are repeated increases in German output, as there are in

59 French output and American output. Taking the sum over all periods, the total increase in European money supply is 48.8, and the total increase in American money supply is 56.3, see equations (30) and (31) in the previous section. 3) The case of inflation. Let initial output in Germany be 1060, let initial output in France be 1030, and let initial output in America be 2090. In each of the countries there is overemployment and hence inflation. Strictly speaking, unemployment in Germany is below its equilibrium level. And the same holds for France and America. Strictly speaking, inflation in Germany is above 2 percent. And the same holds for France and America. Step 1 refers to the policy response. First consider monetary policy in Europe. The specific target of the European central bank is price stability in Europe. The inflationary gap in Europe is 90. The monetary poUcy multiplier in Europe is 3. So what is needed in Europe is a reduction in European money supply of 30. Second consider monetary poUcy in America. The specific target of the American central bank is price stability in America. The inflationary gap in America is 90. The monetary policy multiplier in America is 3. So what is needed in America is a reduction in American money supply of 30. Step 2 refers to the output lag. The reduction in European money supply of 30 causes a decline in German output of 45 and a decline in French output of equally 45. As a side effect, it causes an increase in American output of 30. The reduction in American money supply of 30 causes a decline in American output of 90. As a side effect, it causes an increase in German output of 15 and an increase in French output of equally 15. The net effect is a decline in German output of 30, a decline in French output of equally 30, and a decline in American output of 60. As a consequence, German output goes from 1060 to 1030, French output goes from 1030 to 1000, and American output goes from 2090 to 2030. In Germany there is still some overemployment and inflation. In France there is now full employment and price stability. In Europe there is still some overemployment and inflation. And the same is true of America. Step 3 refers to the policy response. The inflationary gap in Europe is 30. The monetary policy multiplier in Europe is 3. So what is needed in Europe is a reduction in European money supply of 10. The inflationary gap in America is

60 30. The monetary policy multiplier in America is 3. So what is needed in America is a reduction in American money supply of 10. Step 4 refers to the output lag. The reduction in European money supply of 10 causes a decline in German output of 15 and a decUne in French output of equally 15. As a side effect, it causes an increase in American output of 10. The reduction in American money supply of 10 causes a decline in American output of 30. As a side effect, it causes an increase in German output of 5 and an increase in French output of equally 5. The net effect is a decline in German output of 10, a decline in French output of equally 10, and a decline in American output of 20. As a consequence, German output goes from 1030 to 1020, French output goes from 1000 to 990, and American output goes from 2030 to 2010. And so on. Table 2.3 presents a synopsis.

Table 2.3 Monetary Competition between Europe and America The Case of Inflation Germany Initial Output

2090

1

-30

-30

1

1000

2030

1

-10

-10

1

1020

990

2010

1

1015

985

2000

1

1030

A Money Supply Output

America

1030

1060

A Money Supply Output

France

and so on Steady-State Output

In the steady state, German output is 1015, French output is 985, and American output is 2000. In Germany there is overemployment and inflation. In France there is unemployment and deflation. In Europe there is full employment and price stability. And in America there is full employment and price stability too. As a result, the process of monetary competition leads to full employment in

61 Europe and America. And what is more, it leads to price stability in Europe and America. However, the process of monetary competition does not lead to full employment in Germany and France. And what is more, it does not lead to price stability in Germany and France. What are the dynamic characteristics? There are repeated cuts in European money supply, as there are in American money supply. There are repeated cuts in German output, as there are in French output and American output. There are repeated increases in the world interest rate. There are repeated cuts in German investment, as there are in French investment and American investment. The exchange rate between Europe and America is constant. Taking the sum over all periods, the total reduction in European money supply is 45, as is the total reduction in American money supply, see equations (30) and (31) in the preceding section. 4) Unemployment in Europe, inflation in America. Let initial output in Germany be 940, let initial output in France be 970, and let initial output in America be 2090. In Germany there is unemployment and deflation. In France there is unemployment and deflation too. But in America there is overemployment and inflation. Step 1 refers to the policy response. The output gap in Europe is 90. The monetary policy multiplier in Europe is 3. So what is needed in Europe is an increase in European money supply of 30. The inflationary gap in America is 90. The monetary policy multiplier in America is 3. So what is needed in America is a reduction in American money supply of 30. Step 2 refers to the output lag. The increase in European money supply of 30 causes an increase in German output of 45 and an increase in French output of equally 45. As a side effect, it causes a dechne in American output of 30. The reduction in American money supply of 30 causes a decline in American output of 90. As a side effect, it causes an increase in German output of 15 and an increase in French output of equally 15. The net effect is an increase in German output of 60, an increase in French output of equally 60, and a decline in American output of 120. As a consequence, German output goes from 940 to 1000, French output goes from 970 to 1030, and American output goes from 2090 to 1970. In Germany there is now full employment and price stabihty. In France there is now overemployment and inflation. In Europe there is now

62 overemployment and inflation. And in America there is now unemployment and deflation. Step 3 refers to the policy response. The inflationary gap in Europe is 30. The monetary policy multiplier in Europe is 3. So what is needed in Europe is a reduction in European money supply of 10. The output gap in America is 30. The monetary policy multiplier in America is 3. So what is needed in America is an increase in American money supply of 10. Step 4 refers to the output lag. The reduction in European money supply of 10 causes a decline in German output of 15 and a decline in French output of equally 15. As a side effect, it causes an increase in American output of 10. The increase in American money supply of 10 causes an increase in American output of 30. As a side effect, it causes a decline in German output of 5 and a decline in French output of equally 5. The net effect is a decline in German output of 20, a decline in French output of equally 20, and an increase in American output of 40. As a consequence, German output goes from 1000 to 980, French output goes from 1030 to 1010, and American output goes from 1970 to 2010. In Germany there is now unemployment and deflation. In France there is still some overemployment and inflation. In Europe there is now unemployment and deflation. And in America there is now overemployment and inflation. This process repeats itself round by round. Table 2.4 gives an overview. In the steady state, German output is 985, French output is 1015, and American output is 2000. In Germany there is unemployment and deflation. In France there is overemployment and inflation. In Europe there is full employment and price stability. And in America there is full employment and price stability too. What are the dynamic characteristics of this process? There is an upward trend in European money supply and a downward trend in American money supply. There is an upward trend in German output, as there is in French output. There is a downward trend in American output. There is a downward trend in the euro and an upward trend in the dollar. There is an upward trend in German exports, as there is in French exports. There is a downward trend in American exports. In addition, there are damped oscillations in European money supply, as there are in American money supply. There are damped oscillations in German

63 output, as there are in French output and American output. The German economy oscillates between high and low unemployment. The French economy oscillates between high and low overemployment. And the American economy oscillates between unemployment and overemployment.

Table 2.4 Monetary Competition between Europe and America Unemployment in Europe, Inflation in America

Initial Output

Germany

France

America

940

970

2090

1

30

-30

1

1030

1970

1

-10

10

1010

2010

A Money Supply 1 Output

1000

A Money Supply Output

980

3.3

-3.3

1

986.7

1016.7

1996.7

1

985

1015

2000

1

A Money Supply 1 Output

1

and so on 1 Steady-State Output

Taking the sum over all periods, the total increase in European money supply is 22.5, and the total reduction in American money supply is equally 22.5. That means, the total increase in European money supply is small, as compared to the initial gap in Europe. And the same apphes to the total reduction in American money supply, as compared to the initial gap in America. The effective multipher in Europe is 90/22.5 = 4, as is the effective multiplier in America. In other words, the effective multiplier in Europe is large. And the same holds for the effective multiplier in America.

64

3. Alternative Targets of the European Central Bank

At the start there is unemployment in Germany, France and America. To be more expUcit, unemployment in Germany is high, and unemployment in France is low. In the last section, the target of the European central bank was assumed to be full employment in Europe. In the present section we consider two alternative cases: - the target of the European central bank is full employment in Germany - the target of the European central bank is full employment in France. Then what will be the impUcations? 1) The target of the European central bank is full employment in Germany. To illustrate this, have a look at a numerical example. Let initial output in Germany be 940, let initial output in France be 970, and let initial output in America be 1910. In each of the countries there is unemployment and deflation. Step 1 refers to the policy response. The output gap in Germany is 60. The monetary policy multiplier in Germany is 1.5. So what is needed in Europe is an increase in European money supply of 40. The output gap in America is 90. The monetary policy multiplier in America is 3. So what is needed in America is an increase in American money supply of 30. Step 2 refers to the output lag. The increase in European money supply of 40 causes an increase in German output of 60 and an increase in French output of equally 60. As a side effect, it causes a decline in American output of 40. The increase in American money supply of 30 causes an increase in American output of 90. As a side effect, it causes a decline in German output of 15 and a decline in French output of equally 15. The net effect is an increase in German output of 45, an increase in French output of equally 45, and an increase in American output of 50. As a consequence, German output goes from 940 to 985, French output goes from 970 to 1015, and American output goes from 1910 to 1960. In Germany there is still some unemployment and deflation. In France there is now some overemployment and inflation. In Europe there is now full employment and price stability. And in America there is still some unemployment and deflation.

65 Step 3 refers to the policy response. The output gap in Germany is 15. The monetary policy multiplier in Germany is 1.5. So what is needed in Europe is an increase in European money supply of 10. The output gap in America is 40. The monetary policy multiplier in America is 3. So what is needed in America is an increase in American money supply of 13.3. Step 4 refers to the output lag. The increase in European money supply of 10 causes an increase in German output of 15 and an increase in French output of equally 15. As a side effect, it causes a decline in American output of 10. The increase in American money supply of 13.3 causes an increase in American output of 40. As a side effect, it causes a decline in German output of 6.7 and a decline in French output of equally 6.7. The net effect is an increase in German output of 8.3, an increase in French output of equally 8.3, and an increase in American output of 30. As a consequence, German output goes from 985 to 993.3, French output goes from 1015 to 1023.3, and American output goes from 1960 to 1990. And so on. Table 2.5 presents a synopsis.

Table 2.5 Monetary Competition between Europe and America The Target of the ECB is Full Employment in Germany

Initial Output

Germany

France

America

940

970

1910

40

30

1015

1960

A Money Supply Output

985

A Money Supply 1 Output

10 993.3

A Money Supply 1 Output

998.3

1023.3

1 1

13.3 1990

1

4.4

3.3

1028.3

1995.6

1

1030

2000

1

and so on 1 Steady-State Output

1000

66 In the steady state, German output is 1000, French output is 1030, and American output is 2000. In Germany there is full employment and price stabiUty. In France there is overemployment and inflation. In Europe there is overemployment and inflation too. And in America there is full employment and price stability. As a result, the process of monetary competition leads to full employment in Germany and America. And what is more, it leads to price stability in Germany and America. However, the process of monetary competition does not lead to full employment in France and Europe. And what is more, it does not lead to price stability in France and Europe. Taking the sum over all periods, the total increase in European money supply is 56.3, and the total increase in American money supply is 48.8. 2) The target of the European central bank is full employment in France. Let initial output in Germany be 940, let initial output in France be 970, and let initial output in America be 1910. In each of the countries there is unemployment and deflation. Step 1 refers to the policy response. The output gap in France is 30. The monetary poUcy multiplier in France is 1.5. So what is needed in Europe is an increase in European money supply of 20. The output gap in America is 90. The monetary policy multiplier in America is 3. So what is needed in America is an increase in American money supply of 30. Step 2 refers to the output lag. The increase in European money supply of 20 causes an increase in German output of 30 and an increase in French output of equally 30. As a side effect, it causes a decUne in American output of 20. The increase in American money supply of 30 causes an increase in American output of 90. As a side effect, it causes a decline in German output of 15 and a dechne in French output of equally 15. The net effect is an increase in German output of 15, an increase in French output of equally 15, and an increase in American output of 70. As a consequence, German output goes from 940 to 955, French output goes from 970 to 985, and American output goes from 1910 to 1980. Step 3 refers to the policy response. The output gap in France is 15. The monetary policy multiplier in France is 1.5. So what is needed in Europe is an increase in European money supply of 10. The output gap in America is 20. The

67 monetary policy multiplier in America is 3. So what is needed in America is an increase in American money supply of 6.7. Step 4 refers to the output lag. The increase in European money supply of 10 causes an increase in German output of 15 and an increase in French output of equally 15. As a side effect, it causes a dechne in American output of 10. The increase in American money supply of 6.7 causes an increase in American output of 20. As a side effect, it causes a decHne in German output of 3.3 and a decUne in French output of equally 3.3. The net effect is an increase in German output of 11.7, an increase in French output of equally 11.7, and an increase in American output of 10. As a consequence, German output goes from 955 to 966.7, French output goes from 985 to 996.7, and American output goes from 1980 to 1990. And so on. Table 2.6 gives an overview.

Table 2.6 Monetary Competition between Europe and America The Target of the ECB is Full Employment in France

Initial Output

Germany

France

America

940

970

1910

20

30

985

1980

A Money Supply 1 Output

955

A Money Supply 1 Output

10 966.7

A Money Supply 1 Output

968.3

996.7

1

6.7 1990

2.2

3.3

998.3

1997.8

1

2000

1

and so on \ Steady-State Output

970

1000

In the steady state, German output is 970, French output is 1000, and American output is 2000. In Germany there is unemployment and deflation. In

68 France there is full employment and price stability. In Europe there is unemployment and deflation. And in America there is full employment and price stability. As a result, the process of monetary competition leads to full employment in France and America. And what is more, it leads to price stability in France and America. However, the process of monetary competition does not lead to full employment in Germany and Europe. And what is more, it does not lead to price stability in Germany and Europe. Taking the sum over all periods, the total increase in European money supply is 33.8, and the total increase in American money supply is 41.3.

4. The Anticipation of Policy Spillovers

The European central bank closely observes the measures taken by the American central bank. And what is more, the European central bank can respond immediately to the measures taken by the American central bank. The other way round, the American central bank closely observes the measures taken by the European central bank. And what is more, the American central bank can respond immediately to the measures taken by the European central bank. From this point of view, the inside lag of monetary policy is short. On the other hand, the outside lag of monetary poHcy is long and variable, as is well known. In the current section we assume that the European central bank anticipates the spillovers from monetary policy in America. Likewise we assume that the American central bank anticipates the spillovers from monetary policy in Europe. To illustrate this, have a look at a numerical example. Let initial output in Germany be 940, let initial output in France be 970, and let initial output in America be 1910. In each of the countries there is unemployment and deflation. Steps 1, 2 and 3 refer to a series of policy responses. Then step 4 refers to the output lag. Let us begin with step 1. The target of the European central bank is full employment in Europe. The output gap in Europe is 90. The monetary policy

69 multiplier in Europe is 3. So what is needed in Europe is an increase in European money supply of 30. The output gap in America is 90. The monetary policy multiplier in America is 3. So what is needed in America is an increase in American money supply of 30. In step 2, the European central bank anticipates the effect of the increase in American money supply. And the American central bank anticipates the effect of the increase in European money supply. The European central bank expects that, due to the increase in American money supply of 30, German output will only rise to 970, and French output will only rise to 1000. The American central bank expects that, due to the increase in European money supply of 30, American output will only rise to 1970. The expected output gap in Europe is 30. The monetary policy multiplier in Europe is 3. So what is needed in Europe is an increase in European money supply of 10. The expected output gap in America is 30. The monetary policy multiplier in America is 3. So what is needed in America is an increase in American money supply of 10. We now come to step 3. The European central bank expects that, due to the increase in American money supply of 10, German output will only rise to 980, and French output will only rise to 1010. The American central bank expects that, due to the increase in European money supply of 10, American output will only rise to 1990. The expected output gap in Europe is 10. The monetary policy multipUer in Europe is 3. So what is needed in Europe is an increase in European money supply of 3.3. The expected output gap in America is 10. The monetary policy multiplier in America is 3. So what is needed in America is an increase in American money supply of 3.3. Step 4 refers to the output lag. The accumulated increase in European money supply of 43.3 causes an increase in German output of 65 and an increase in French output of equally 65. As a side effect, it causes a decline in American output of 43.3. The accumulated increase in American money supply of 43.3 causes an increase in American output of 130. As a side effect, it causes a decline in German output of 21.7 and a decline in French output of equally 21.7. The net effect is an increase in German output of 43.3, an increase in French output of 43.3, and an increase in American output of 86.7. As a consequence, German output goes from 940 to 983.3, French output goes from 970 to 1013.3, and American output goes from 1910 to 1996.7. In Germany there is unemployment

70

and deflation. In France there is overemployment and inflation. In Europe there is nearly full employment and price stability. And in America there is nearly full employment and price stability too. Table 2.7 presents a synopsis.

Table 2.7 Monetary Competition between Europe and America The Anticipation of Policy Spillovers Germany

France

America

940

970

1910

A Money Supply

30

30

A Money Supply

10

10

Initial Output

A Money Supply

1 Output

3.3

3.3

983.3

1013.3

1996.7

985

1015

2000

and so on \ Steady-State Output

As a result, the process of monetary competition leads to full employment in Europe and America. And what is more, it leads to price stability in Europe and America. However, the process of monetary competition does not lead to full employment in Germany and France. And what is more, it does not lead to price stabiUty in Germany and France. In summary, the anticipation of policy spillovers speeds up the process of monetary competition.

Chapter 2 Monetary Cooperation between Europe and America 1. The Model

1) Introduction. As a point of departure, take the output model. It can be represented by a system of three equations: Yi = Ai + 0.5aMi2 - O.5PM3

(1)

Y2 = A2 + 0.5aMi2 - O.5PM3

(2)

Y3=A3+aM3-PMi2

(3)

Here Y^ denotes German output, Y2 is French output, Y3 is American output, M12 is European money supply, and M3 is American money supply. The endogenous variables are German output, French output, and American output. The output model can be compressed to a system of two equations: Yi2=Ai2+aMi2-PM3

(4)

Y3=A3+aM3-PMi2

(5)

Here we have Y12 = Y^ + Y2 and A12 = A^ + A2. The endogenous variables are European output Y12 and American output Y3. At the beginning there is unemployment in Germany, France and America. More precisely, unemployment in Germany exceeds unemployment in France. The primary target of the European central bank is price stability in Europe. The secondary target of the European central bank is high employment in Germany and France. The specific target of the European central bank is that unemployment in Germany equals overemployment in France. In other words, deflation in Germany equals inflation in France. So there is price stability in

72

Europe. In a sense, the specific target of the European central bank is full employment in Europe. The targets of monetary cooperation are full employment in Europe and full employment in America. The instruments of monetary cooperation are European money supply and American money supply. So there are two targets and two instruments. 2) The policy model. On this basis, the policy model can be characterized by a system of two equations: Yi2=Ai2+aMi2-PM3

(6)

Y3=A3+aM3-PMi2

(7)

Here Y12 denotes full-employment output in Europe, and Y3 denotes fullemployment output in America. The endogenous variables are European money supply and American money supply. To simplify notation, we introduce B12 = ^^u " ^u ^^^ ^3 = Y3 - A3. Then we solve the model for the endogenous variables:

Equation (8) shows the required level of European money supply, and equation (9) shows the required level of American money supply. There is a solution if and only if a 9^ p. Due to the assumption a > P, this condition is met. As a result, monetary cooperation can achieve full employment in Europe and America. And what is more, it can achieve price stability in Europe and America. However, monetary cooperation cannot achieve full employment in Germany and France. And what is more, it cannot achieve price stability in Germany and France. It is worth pointing out here that the solution to monetary cooperation is identical to the steady state of monetary competition.

73

3) Another version of the poUcy model. As an alternative, the policy model can be stated in terms of the initial output gap and the required increase in money supply. Taking differences in equations (4) and (5), the policy model can be written as follows: AYi2 = aAMi2 - PAMj

(10)

AY3=aAM3-pAMi2

(11)

Here AY12 denotes the initial output gap in Europe, AY3 is the initial output gap in America, AM12 is the required increase in European money supply, and AM3 is the required increase in American money supply. The endogenous variables are AM12 and AM3. The solution to the system (10) and (11) is: _ocAYi2+PAY3 ^Ml2= aJ 2 - p.2 2 '

(12)

_aAY3+PAYi2 ^^3 = aA2 - pa2 2 ''

(13)

According to equation (12), the required increase in European money supply depends on the initial output gap in Europe, the initial output gap in America, the direct multiplier a , and the cross multiplier p. The larger the initial output gap in Europe, the larger is the required increase in European money supply. Moreover, the larger the initial output gap in America, the larger is the required increase in European money supply. At first glance this comes as a surprise. According to equation (13), the required increase in American money supply depends on the initial output gap in America, the initial output gap in Europe, the direct multiplier a, and the cross multiplier (3.

74

2. Some Numerical Examples

To illustrate the policy model, have a look at some numerical examples. For ease of exposition, without losing generality, assume a = 3 and P = l. On this assumption, the output model can be written as follows: Yi=Ai+1.5Mi2-0.5M3

(1)

Y2 = A2 +1.5Mi2 - O.5M3

(2)

Y3=A3+3M3-Mi2

(3)

The endogenous variables are German output, French output, and American output. Obviously, an increase in European money supply of 100 causes an increase in German output of 150, an increase in French output of equally 150, and a decline in American output of 100. Similarly, an increase in American money supply of 100 causes an increase in American output of 300, a decline in German output of 50, and a decUne in French output of equally 50. Further let full-employment output in Germany be 1000, let full-employment output in France be equally 1000, and let full-employment output in America be 2000. It proves useful to study four distinct cases: - the case of unemployment - Europe and America differ in unemployment - the case of inflation - unemployment in Europe, inflation in America. 1) The case of unemployment. Let initial output in Germany be 940, let initial output in France be 970, and let initial output in America be 1910. In each of the countries there is unemployment and deflation. Step 1 refers to the policy response. The output gap in Europe is 90, as is the output gap in America. So what is needed, according to equations (12) and (13) from the preceding section, is an increase in European money supply of 45 and an increase in American money supply of equally 45.

75 Step 2 refers to the output lag. The increase in European money supply of 45 raises German output and French output by 67.5 each. On the other hand, it lowers American output by 45. The increase in American money supply of 45 raises American output by 135. On the other hand, it lowers German output and French output by 22.5 each. The net effect is an increase in German output of 45, an increase in French output of equally 45, and an increase in American output of 90. As a consequence, German output goes from 940 to 985, French output goes from 970 to 1015, and American output goes from 1910 to 2000.

Table 2.8 Monetary Cooperation between Europe and America The Case of Unemployment

Initial Output

Germany

France

America

940

970

1910

45

45

1015

2000

A Money Supply Output

985

1

In Germany there is still some unemployment and deflation. In France there is now some overemployment and inflation. In Europe there is now full employment and price stability. And the same holds for America. Unemployment in Germany equals overemployment in France. And deflation in Germany equals inflation in France. As a result, monetary cooperation can achieve full employment in Europe and America. And what is more, it can achieve price stability in Europe and America. However, monetary cooperation cannot achieve full employment in Germany and France. And what is more, it cannot achieve price stability in Germany and France. The required increase in European money supply is large, as compared to the initial output gap in Europe. And the same applies to the required increase in American money supply, as compared to the initial output gap in America. The effective multiplier in Europe is 90/45 = 2, as is the effective multiplier in

76 America. That is to say, the effective multipHer in Europe is small. And the same is true of the effective multiplier in America. Table 2.8 gives an overview. 2) Europe and America differ in unemployment. Let initial output in Germany be 940, let initial output in France be 970, and let initial output in America be 1880. Unemployment in America exceeds unemployment in Europe. Step 1 refers to the policy response. The output gap in Europe is 90, and the output gap in America is 120. So what is needed, according to equations (12) and (13) from the previous section, is an increase in European money supply of 48.8 and an increase in American money supply of 56.3 Step 2 refers to the output lag. The increase in European money supply of 48.8 raises German output and French output by 73.1 each. On the other hand, it lowers American output by 48.8. The increase in American money supply of 56.3 raises American output by 168.8. On the other hand, it lowers German output and French output by 28.1 each. The net effect is an increase in German output of 45, an increase in French output of equally 45, and an increase in American output of 120. As a consequence, German output goes from 940 to 985, French output goes from 970 to 1015, and American output goes from 1880 to 2000.

Table 2.9 Monetary Cooperation between Europe and America Europe and America Differ in Unemployment

Initial Output

Germany

France

America

940

970

1880

A Money Supply Output

48.8 985

1015

56.3 2000

In Germany there is still some unemployment and deflation. In France there is now some overemployment and inflation. In Europe there is now full employment and price stability. And the same holds for America. As a result.

77

monetary cooperation can achieve full employment in Europe and America. However, it cannot achieve full employment in Germany and France. Table 2.9 presents a synopsis. 3) The case of inflation. Let initial output in Germany be 1060, let initial output in France be 1030, and let initial output in America be 2090. In each of the countries there is overemployment and inflation. Step 1 refers to the policy response. The inflationary gap in Europe is 90, as is the inflationary gap in America. The targets of monetary cooperation are price stability in Europe and price stability in America. So what is needed, according to equations (12) and (13) from the preceding section, is a reduction in European money supply of 45 and a reduction in American money supply of equally 45. Step 2 refers to the output lag. The reduction in European money supply of 45 lowers German output and French output by 67.5 each. On the other hand, it raises American output by 45. The reduction in American money supply of 45 lowers American output by 135. On the other hand, it raises German output and French output by 22.5 each. The net effect is a decline in German output of 45, a decline in French output of equally 45, and a decline in American output of 90. As a consequence, German output goes from 1060 to 1015, French output goes from 1030 to 985, and American output goes from 2090 to 2000. In Germany there is still some overemployment and inflation. In France there is now some unemployment and deflation. In Europe there is now full employment and price stability. And the same is true of America. Table 2.10 gives an overview.

Table 2.10 Monetary Cooperation between Europe and America The Case of Inflation

Initial Output

Germany

France

1060

1030

2090

-45

-45

985

2000

A Money Supply Output

1015

America

1

78 4) Unemployment in Europe, inflation in America. Let initial output in Germany be 940, let initial output in France be 970, and let initial output in America be 2090. In Germany there is unemployment and deflation. In France there is unemployment and deflation too. But in America there is overemployment and inflation. Step 1 refers to the policy response. The output gap in Europe is 90, and the inflationary gap in America is equally 90. So what is needed, according to equations (12) and (13) from the previous section, is an increase in European money supply of 22.5 and a reduction in American money supply of equally 22.5. Step 2 refers to the output lag. The increase in European money supply of 22.5 raises German output and French output by 33.8 each. On the other hand, it lowers American output by 22.5. The reduction in American money supply of 22.5 lowers American output by 67.5. On the other hand, it raises German output and French output by 11.3 each. The total effect is an increase in German output of 45, an increase in French output of equally 45, and a decline in American output of 90. As a consequence, German output goes from 940 to 985, French output goes from 970 to 1015, and American output goes from 2090 to 2000.

Table 2.11 Monetary Cooperation between Europe and America Unemployment in Europe, Inflation in America

Initial Output

Germany

France

America

940

970

2090

22.5

A Money Supply Output

985

1015

- 22.5 2000

In Germany there is still some unemployment and deflation. In France there is now some overemployment and inflation. In Europe there is now full employment and price stability. And the same holds for America. The required increase in European money supply is small, as compared to the initial output

79 gap in Europe. Correspondingly, the required cut in American money supply is small, as compared to the initial inflationary gap in America. The effective multiplier in Europe is 90/22.5 = 4, and the effective multiplier in America is equally 90/22.5 = 4. That is to say, the effective multipHer in Europe is large. And the same is true of the effective multipHer in America. Table 2.11 presents a synopsis. 5) Comparing monetary cooperation with monetary competition. Monetary competition can achieve full employment and price stability. The same applies to monetary cooperation. Monetary competition is a slow process. By contrast, monetary cooperation is a fast process. Judging from these points of view, monetary cooperation seems to be superior to monetary competition.

3. Alternative Targets of the European Central Bank

At the start there is unemployment in Germany, France and America. To be more explicit, unemployment in Germany is high, and unemployment in France is low. In the last section, the target of the European central bank was assumed to be full employment in Europe. In the present section we consider two alternative cases: - the target of the European central bank is full employment in Germany - the target of the European central bank is full employment in France. Then what will be the implications? 1) The target of the European central bank is full employment in Germany. The targets of monetary cooperation are full employment in Germany and full employment in America. The instruments of monetary cooperation are European money supply and American money supply. To illustrate this, have a look at a numerical example. Let initial output in Germany be 940, let initial output in France be 970, and let initial output in America be 1910. In each of the countries there is unemployment and deflation. Step 1 refers to the policy response. The output gap in Germany is 60, the output gap in Europe is 120, and the output gap

80 in America is 90. So what is needed, according to equations (12) and (13) from Section 1, is an increase in European money supply of 56.3 and an increase in American money supply of 48.8. Step 2 refers to the output lag. The increase in European money supply of 56.3 raises German output and French output by 84.4 each. On the other hand, it lowers American output by 56.3. The increase in American money supply of 48.8 raises American output by 146.3. On the other hand, it lowers German output and French output by 24.4. The net effect is an increase in German output of 60, an increase in French output of equally 60, and an increase in American output of 90. As a consequence, German output goes from 940 to 1000, French output goes from 970 to 1030, and American output goes from 1910 to 2000. In Germany there is now full employment and price stability. In France there is now some overemployment and inflation. In Europe there is now some overemployment and inflation too. And in America there is now full employment and price stability. As a result, monetary cooperation can achieve full employment in Germany and America. And what is more, it can achieve price stability there. However, monetary cooperation cannot achieve full employment in France and Europe. And what is more, it cannot achieve price stability there. Table 2.12 gives an overview.

Table 2.12 Monetary Cooperation between Europe and America The Target of the ECB is Full Employment in Germany

Initial Output

Germany

France

America

940

970

1910

A Money Supply Output

56.3 1000

1030

48.8 2000

1

81 2) The target of the European central bank is full employment in France. The targets of monetary cooperation are full employment in France and full employment in America. The instruments of monetary cooperation are European money supply and American money supply. Let initial output in Germany be 940, let initial output in France be 970, and let initial output in America be 1910. In each of the countries there is unemployment and deflation. Step 1 refers to the policy response. The output gap in France is 30, the output gap in Europe is 60, and the output gap in America is 90. What is needed, then, is an increase in European money supply of 33.8 and an increase in American money supply of 41.3. Step 2 refers to the output lag. The increase in European money supply of 33.8 raises German output and French output by 50.6 each. On the other hand, it lowers American output by 33.8. The increase in American money supply of 41.3 raises American output by 123.8. On the other hand, it lowers German output and French output by 20.6 each. The net effect is an increase in German output of 30, an increase in French output of equally 30, and an increase in American output of 90. As a consequence, German output goes from 940 to 970, French output goes from 970 to 1000, and American output goes from 1910 to 2000.

Table 2.13 Monetary Cooperation between Europe and America The Target of the ECB is Full Employment in France

Initial Output

Germany

France

America

940

970

1910

33.8

A Money Supply Output

970

1000

1

41.3 2000

In Germany there is still some unemployment and deflation. In France there is now full employment and price stability. In Europe there is still some unemployment und deflation. And in America there is now full employment and

82 price stability. As a result, monetary cooperation can achieve full employment in France and America. And what is more, it can achieve price stability there. However, monetary cooperation cannot achieve full employment in Germany and Europe. And what is more, it cannot achieve price stability there. Table 2.13 presents a synopsis.

Part Three Fiscal Interactions between Germany and France

Chapter 1 Fiscal Competition between Germany and France 1. The Dynamic Model

1) The static model. The world consists of two monetary regions, say Europe and America. The exchange rate between Europe and America is flexible. Europe in turn consists of two countries, say Germany and France. So Germany and France form a monetary union. There is international trade between Germany, France and America. German goods, French goods and American goods are imperfect substitutes for each other. German output is determined by the demand for German goods. French output is determined by the demand for French goods. And American output is determined by the demand for American goods. European money demand equals European money supply. And American money demand equals American money supply. There is perfect capital mobility between Germany, France and America. Thus the German interest rate, the French interest rate, and the American interest rate are equalized. The monetary regions are the same size and have the same behavioural functions. The union countries are the same size and have the same behavioural functions. Nominal wages and prices adjust slowly. As a result, an increase in German government purchases raises German output. On the other hand, it lowers French output. And what is more, it raises American output. Here the rise in German output exceeds the fall in French output. And the rise in European output equals the rise in American output. Correspondingly, an increase in French government purchases raises French output. On the other hand, it lowers German output. And what is more, it raises American output. Here the rise in French output exceeds the fall in German output. And the rise in European output equals the rise in American output. In the numerical example, an increase in German government purchases of 100 causes an increase in German output of 150, a decline in French output of 50, and an increase in American output of 100. Likewise, an increase in French

86 government purchases of 100 causes an increase in French output of 150, a decline in German output of 50, and an increase in American output of 100. Now have a closer look at the process of adjustment. An increase in German government purchases causes an appreciation of the euro, a depreciation of the dollar, and an increase in the world interest rate. The appreciation of the euro lowers German exports and French exports. The depreciation of the dollar raises American exports. And the increase in the world interest rate lowers German investment, French investment and American investment. The net effect is that German output moves up, French output moves down, and American output moves up. This model is in the tradition of the Mundell-Fleming model and the Levin model, see Part One. The static model can be represented by a system of three equations: YI=AI+YGI-5G2

(1)

Y2=A2+YG2-5GI

(2)

Y3 = A3 + 8G1 + 8G2

(3)

Of course this is a reduced form. Y^ denotes German output, Y2 is French output, Y3 is American output, G^ is German government purchases, G2 is French government purchases, A^ is some other factors bearing on German output, A2 is some other factors bearing on French output, and A3 is some other factors bearing on American output, y, 5 and 8 denote the fiscal poHcy multipUers. Strictly speaking, y, 5 and 8 are positive coefficients with y >5 and 8 = y ~ 5 . Obviously, an increase in German government purchases causes an increase in German output, a decline in French output, and an increase in American output. The endogenous variables are German output, French output, and American output. According to equation (1), German output is a positive function of German government purchases and a negative function of French government purchases. According to equation (2), French output is a positive function of French government purchases and a negative function of German government purchases. According to equation (3), American output is a positive function of German government purchases and a positive function of French government purchases.

87

2) The dynamic model. At the beginning there is unemployment in both Germany and France. More precisely, unemployment in Germany exceeds unemployment in France. By contrast there is full employment in America. The target of the German government is full employment in Germany. The instrument of the German government is German government purchases. The German government raises German government purchases so as to close the output gap in Germany: G,-GT'=^^^^

(4)

Here is a list of the new symbols: Yj German output this period full-employment output in Germany Yi Y i - •Yi output gap in Germany this period German government purchases last period Gr^ German government purchases this period Gi G i - •Gr^ increase in German government purchases. Here the endogenous variable is German government purchases this period G^. The target of the French government is full employment in France. The instrument of the French govemment is French government purchases. The French government raises French govemment purchases so as to close the output gap in France: G2-G2^=^^^

Here is a list of the new symbols: Y2 French output this period Y2 full-employment output in France Y2 - Y2 output gap in France this period G2 French government purchases last period G2 French government purchases this period G2 - G2 increase in French government purchases.

(5)

Here the endogenous variable is French government purchases this period G2. We assume that the German government and the French government decide simultaneously and independently. In addition there is an output lag: YI^I=AI+YGI-5G2

(6)

Y+I=A2+YG2-5GI

(7)

Y3+i=A3+8Gi+8G2

(8)

According to equation (6), German output next period is determined by German government purchases this period as well as by French government purchases this period. Here Y^^ denotes German output next period. According to equation (7), French output next period is determined by French government purchases this period as well as by German government purchases this period. According to equation (8), American output next period is determined by German government purchases this period as well as by French government purchases this period. On this basis, the dynamic model can be characterized by a system of five equations: Gi-Gr^=^^^

(9)

G2-G2^=^^^^

(10)

YI+I=AI+YGI-6G2

(11)

Y2+I=A2+YG2-6GI

(12)

Y3+i=A3+eGi + eG2

(13)

Equation (9) shows the poUcy response in Germany, (10) shows the policy response in France, (11) shows the output lag in Germany, (12) shows the output lag in France, and (13) shows the output lag in America. The endogenous variables are German government purchases this period Gj, French government

89 purchases this period G2, German output next period Y^ , French output next period ¥2^ , and American output next period Y^^. 3) The steady state. In the steady state by definition we have: Gi=Gr^

(14)

62=02'

(15)

Equation (14) has it that German government purchases do not change any more. Similarly, equation (15) has it that French government purchases do not change any more. Therefore the steady state can be captured by a system of five equations: Yi = Yi

(16)

Y2 = Y2

(17)

Yi = A I + Y G I - 5 G 2

(18)

Y2=A2+YG2-5GI

(19)

Y3 =A3 + eGi+8G2

(20)

Here the endogenous variables are German output Y^, French output Y2, American output Y3, German government purchases Gj, and French government purchases G2. According to equation (16) there is full employment in Germany, so German output is constant. According to equation (17) there is full employment in France, so French output is constant too. Further, equations (18), (19) and (20) give the steady-state levels of German government purchases, French government purchases, and American output. The model of the steady state can be compressed to a system of only two equations:

%

=AI+YGI-5G2

(21)

Y2=A2+YG2-5GI

(22)

90 Here the endogenous variables are German government purchases and French government purchases. To simpUfy notation we introduce: Bi=Yi-Ai

(23)

B2 = Y2-A2

(24)

With this, the model of the steady state can be written as follows:

BI=YGI-6G2

(25)

B2=YG2-5GI

(26)

The endogenous variables are still G^ and G2. Next we solve the model for the endogenous variables:

Equation (27) shows the steady-state level of German government purchases, and equation (28) shows the steady-state level of French government purchases. As a result, there is a steady state if and only if y ^ §. Owing to the assumption y > S, this condition is fulfilled. As an alternative, the steady state can be represented in terms of the initial output gap and the total increase in government purchases. Taking differences in equations (1) and (2), the model of the steady state can be written as follows:

AYi = Y A G I - 5 A G 2

(29)

AY2=YAG2-5AGI

(30)

Here AY^ is the initial output gap in Germany, AY2 is the initial output gap in France, AG^ is the total increase in German government purchases, and AG2 is

91 the total increase in French government purchases. The endogenous variables are AGj and AG2. The solution to the system (29) and (30) is: -I^XL±5^ Y2. -52

1 ~

.YAY2-+8AY1 ^2 -

(31)

(32)

Y2.-52

According to equation (31), the total increase in German government purchases depends on the initial output gap in Germany, the initial output gap in France, the direct multiplier y, and the cross multiplier 5. The larger the initial output gap in Germany, the larger is the total increase in German government purchases. Moreover, the larger the initial output gap in France, the larger is the total increase in German government purchases. At first glance this comes as a surprise. According to equation (32), the total increase in French government purchases depends on the initial output gap in France, the initial output gap in Germany, the direct multiplier y, and the cross multiplier 5. 4) Stability. Eliminate Y^ in equation (9) by means of equation (11) and rearrange terms Y^ = A I + Y G I - 6 G 2 ^ By analogy, eliminate Y2 in equation (10) by means of equation (12) to arrive at Y2 = A2 + 7^2 - 5Gj" . On this basis, the dynamic model can be described by a system of two equations:

%

=AI+YGI-5G2^

(33)

Y2=A2+YG2-5Gr^

(34)

Here the endogenous variables are German government purchases this period G^ and French government purchases this period G2. To simplify notation we make use of equations (23) and (24). With this, the dynamic model can be written as follows:

BI=YGI-5G2'

(35)

B2=YG2--5Gr^

(36)

92 The endogenous variables are still G^ and G2. Now substitute equation (36) into equation (35) and solve for: YGi=Bi + ^

+ Y

^

^

(37)

Y

Then differentiate equation (37) for Gj"^:

^ - ' dOj"^ Y^

(38)

Finally the stability condition is 5 / y < 1 or: Y>5

(39)

That means, the steady state is stable if and only if the internal effect of fiscal pohcy is larger than the external effect of fiscal poHcy. This condition is satisfied. As a result, there is a stable steady state of fiscal competition. In other words, fiscal competition between Germany and France leads to full employment in Germany and France. And what is more, it leads to price stability in Germany and France. However, as a severe side effect, it causes overemployment and inflation in America.

2. Some Numerical Examples

To illustrate the dynamic model, have a look at some numerical examples. For ease of exposition, without loss of generality, assume y = 1-5, 5 = 0.5 and 8 = 1, see Part One. On this assumption, the static model can be written as follows:

93

Yi =Ai+1.5Gi-0.5G2

(1)

Y2=A2+1.5G2-0.5Gi

(2)

Y3 = A 3 + G i + G 2

(3)

The endogenous variables are German output, French output, and American output. Obviously, an increase in German government purchases of 100 causes an increase in German output of 150, a decline in French output of 50, and an increase in American output of 100. Correspondingly, an increase in French government purchases of 100 causes an increase in French output of 150, a decline in German output of 50, and an increase in American output of 100. Further let full-employment output in Germany be 1000, let full-employment output in France be equally 1000, and let full-employment output in America be 2000. It proves useful to study two distinct cases: - unemployment in Germany and France - unemployment in Germany, overemployment in France. 1) Unemployment in Germany and France. Let initial output in Germany be 940, let initial output in France be 970, and let initial output in America be 2000. In Germany there is unemployment and deflation. In France there is unemployment and deflation too. But in America there is full employment and price stability. Step 1 refers to the policy response. The output gap in Germany is 60. The fiscal policy multiplier in Germany is 1.5. So what is needed in Germany is an increase in German government purchases of 40. The output gap in France is 30. The fiscal policy multiplier in France is 1.5. So what is needed in France is an increase in French government purchases of 20. Step 2 refers to the output lag. The increase in German government purchases of 40 causes an increase in German output of 60. As a side effect, it causes a decline in French output of 20 and an increase in American output of 40. The increase in French government purchases of 20 causes an increase in French output of 30. As a side effect, it causes a decline in German output of 10 and an increase in American output of 20. The net effect is an increase in German output of 50, an increase in French output of 10, and an increase in American output of

94 60. As a consequence, German output goes from 940 to 990, French output goes from 970 to 980, and American output goes from 2000 to 2060. Why does the German govemment not succeed in closing the output gap in Germany? The underlying reason is the negative external effect of the increase in French govemment purchases. Why does the French government not succeed in closing the output gap in France? The underlying reason is the negative extemal effect of the increase in German government purchases. And why is there now overemployment in America? The underlying reason is the positive external effect of the increase in German and French government purchases. Step 3 refers to the policy response. The output gap in Germany is 10. The fiscal policy multiplier in Germany is 1.5. So what is needed in Germany is an increase in German government purchases of 6.7. The output gap in France is 20. The fiscal policy multiplier in France is 1.5. So what is needed in France is an increase in French government purchases of 13.3. Step 4 refers to the output lag. The increase in German govemment purchases of 6.7 causes an increase in German output of 10. As a side effect, it causes a decline in French output of 3.3 and an increase in American output of 6.7. The increase in French government purchases of 13.3 causes an increase in French output of 20. As a side effect, it causes a decHne in German output of 6.7 and an increase in American output of 13.3. The net effect is an increase in German output of 3.3, an increase in French output of 16.7, and an increase in American output of 20. As a consequence, German output goes from 990 to 993.3, French output goes from 980 to 996.7, and American output goes from 2060 to 2080. And so on. Table 3.1 presents a synopsis. In the steady state, German output is 1000, French output is equally 1000, and American output is 2090. In Germany there is full employment and price stability. In France there is full employment and price stability too. But in America there is overemployment and inflation. As a result, fiscal competition between Germany and France leads to full employment in Germany and France. And what is more, it leads to price stability in Germany and France. However, as a severe side effect, it causes overemployment and inflation in America.

95 What are the dynamic characteristics of this process? There are repeated increases in German government purchases, as there are in French government purchases. There are repeated increases in German output, as there are in French output and American output. There are repeated increases in the European budget deficit, while there are repeated cuts in the American budget deficit. There are repeated appreciations of the euro, and there are repeated depreciations of the dollar. There are repeated cuts in European exports, and there are repeated increases in American exports. There are repeated increases in the European current account deficit, and there are repeated increases in the American current account surplus.

Table 3.1 Fiscal Competition between Germany and France Unemployment in Germany and France

Initial Output A Government Purchases Output A Government Purchases Output A Government Purchases Output

Germany

France

America

940

970

2000

1

40

20

990

980

2060

1

2080

1

2086.7

1

2090

1

6.7

13.3

993.3

996.7

4.4

2.2

998.9

997.8

and so on 1 Steady-State Output

1000

1000

Taking the sum over all periods, the total increase in German government purchases is 52.5, and the total increase in French government purchases is 37.5, see equations (31) and (32) in the preceding section. That means, the total increase in German government purchases is very large, as compared to the initial output gap in Germany of 60. And the total increase in French government

96 purchases is even larger, as compared to the initial output gap in France of 30. The effective multiplier in Germany is only 60/52.5 = 1.1, and the effective multiplier in France is only 30/37.5 = 0.8. In other words, the effective multiplier in Germany is very small, and the effective multiplier in France is even smaller. 2) Unemployment in Germany, overemployment in France. Let initial output in Germany be 970, let initial output in France be 1030, and let initial output in America be 2000. In Germany there is unemployment and deflation. In France there is overemployment and inflation. And in America there is full employment and price stabiUty. Step 1 refers to the policy response. The output gap in Germany is 30. The fiscal policy multiplier in Germany is 1.5. So what is needed in Germany is an increase in German government purchases of 20. The inflationary gap in France is 30. The fiscal policy multiplier in France is 1.5. So what is needed in France is a reduction in French government purchases of 20. Step 2 refers to the output lag. The increase in German government purchases of 20 causes an increase in German output of 30. As a side effect, it causes a decline in French output of 10 and an increase in American output of 20. The reduction in French government purchases of 20 causes a decline in French output of 30. As a side effect, it causes an increase in German output of 10 and a decline in American output of 20. The net effect is an increase in German output of 40, a decline in French output of equally 40, and a change in American output of zero. As a consequence, German output goes from 970 to 1010, French output goes from 1030 to 990, and American output stays at 2000. In Germany there is now overemployment and inflation. In France there is now unemployment and deflation. And in America there is still full employment and price stability. Step 3 refers to the policy response. The inflationary gap in Germany is 10. The fiscal policy multiplier in Germany is 1.5. So what is needed in Germany is a reduction in German government purchases of 6.7. The output gap in France is 10. The fiscal policy multipUer in France is 1.5. So what is needed in France is an increase in French government purchases of 6.7. Step 4 refers to the output lag. The reduction in German government purchases of 6.7 causes a decline in German output of 10. As a side effect, it causes an increase in French output of 3.3 and a decline in American output of 6.7. The increase in French government purchases of 6.7 causes an increase in

97 French output of 10. As a side effect, it causes a decline in German output of 3.3 and an increase in American output of 6.7. The net effect is a decUne in German output of 13.3, an increase in French output of equally 13.3, and a change in American output of zero. As a consequence, German output goes from 1010 to 996.7, French output goes from 990 to 1003.3, and American output stays at 2000. In Germany there is now unemployment and deflation. In France there is now overemployment and inflation. And in America there is still full employment and price stability. This process repeats itself round by round. Table 3.2 gives an overview.

Table 3.2 Fiscal Competition between Germany and France Unemployment in Germany, Overemployment in France

Initial Output A Government Purchases 1 Output A Government Purchases 1 Output A Government Purchases 1 Output

Germany

France

America

970

1030

2000

1

20

-20

1010

990

2000

1

2000

1

2000

1

2000

1

-6.7

6.7

996.7

1003.3

2.2

-2.2

1001.1

998.9

and so on \ Steady-State Output

1000

1000

In the steady state, German output is 1000, French output is equally 1000, and American output is 2000. In each of the countries there is full employment and price stability. As a result, fiscal competition between Germany and France leads to full employment in Germany and France. And what is more, it leads to price stability in Germany and France. Fiscal competition between Germany and

98 France does not cause overemployment and inflation in America. And neither does it cause unemployment and deflation in America. What are the dynamic characteristics of this process? There is an upward trend in German government purchases. There is a downward trend in French government purchases. There is an upward trend in German output. There is a downward trend in French output. And there is no change in American output. There are damped oscillations in German government purchases, as there are in French government purchases. There are damped oscillations in German output, as there are in French output. There is no change in European government purchases, so there is no change in European output. There is no change in the European budget deficit, and neither is there a change in the American budget deficit. Taking the sum over all periods, the total increase in German government purchases is 15, and the total reduction in French government purchases is equally 15, see equations (31) and (32) in the previous section. The total increase in German government purchases is small, as compared to the initial output gap in Germany of 30. And the total reduction in French government purchases is small, as compared to the initial inflationary gap in France of 30. The effective multiplier in Germany is 30/15 = 2, as is the effective multiplier in France. That is to say, the effective multiplier in Germany is large. And the same holds for the effective multiplier in France.

Chapter 2 Fiscal Cooperation between Germany and France 1. The Model

1) Introduction. As a starting point, take the output model. It can be represented by a system of three equations: Yi =Ai+yGi--6G2

(1)

Y2=A2+yG2-5Gi

(2)

Y3 = A 3 + s G i + s G 2

(3)

Here Y^ denotes German output, Y2 is French output, Y3 is American output, Gj is German govemment purchases, and G2 is French govemment purchases. The endogenous variables are German output, French output, and American output. At the beginning there is unemployment in both Germany and France. More precisely, unemployment in Germany exceeds unemployment in France. By contrast there is full employment in America. The targets of fiscal cooperation are full employment in Germany and full employment in France. The instruments of fiscal cooperation are German govemment purchases and French govemment purchases. So there are two targets and two instruments. 2) The policy model. On this basis, the policy model can be characterized by a system of two equations: Yi = A i + y G i - 5 G 2

(4)

Y2 = A 2 + Y G 2 - 5 G I

(5)

Here Y| denotes full-employment output in Germany, and Y2 denotes fullemployment output in France. The endogenous variables are German govemment purchases and French govemment purchases.

100 To simplify notation, we introduce B^ = Y^ - A^ and B2 = Y2 - A2. Then we solve the model for the endogenous variables: _YBI+SB2 ^ 1 - Y2_52

G2=^^

T^

(6)

(7)

Equation (6) shows the required level of German government purchases, and equation (7) shows the required level of French government purchases. There is a solution if and only if Y ^ 5. Due to the assumption Y > S, this condition is met. As a result, fiscal cooperation between Germany and France can achieve full employment in Germany and France. And what is more, it can achieve price stability in Germany and France. However, as a severe side effect, it causes overemployment and inflation in America. It is worth pointing out here that the solution to fiscal cooperation is identical to the steady state of fiscal competition. 3) Another version of the policy model. As an alternative, the policy model can be stated in terms of the initial output gap and the required increase in government purchases. Taking differences in equations (1) and (2), the poUcy model can be written as follows:

AYj = Y A G I - 5 A G 2

(8)

AY2=YAG2-5AGI

(9)

Here AY^ denotes the initial output gap in Germany, AY2 is the initial output gap in France, AG^ is the required increase in German government purchases, and AG2 is the required increase in French government purchases. The endogenous variables are AG^ and AG2. The solution to the system (8) and (9) is:

AG,=I^J1|^

101 . G . ^ V A V ^

(„)

According to equation (10), the required increase in German government purchases depends on the initial output gap in Germany, the initial output gap in France, the direct multiplier y, and the cross multiplier 5. The larger the initial output gap in Germany, the larger is the required increase in German government purchases. Moreover, the larger the initial output gap in France, the larger is the required increase in German government purchases. At first glance this comes as a surprise. According to equation (11), the required increase in French govemment purchases depends on the initial output gap in France, the initial output gap in Germany, the direct multiplier y, and the cross multiplier 5.

2. Some Numerical Examples

To illustrate the policy model, have a look at some numerical examples. For ease of exposition, without losing generality, assume y = 1.5, 5 = 0.5 and s = 1. On this assumption, the output model can be written as follows: Yi =Ai+1.5Gi-0.5G2

(1)

Y2=A2+1.5G2-0.5Gi

(2)

Y3=A3+Gi+G2

(3)

The endogenous variables are German output, French output, and American output. Evidently, an increase in German govemment purchases of 100 causes an increase in German output of 150, a decline in French output of 50, and an increase in American output of 100. Further let full-employment output in Germany be 1000, let full-employment output in France be equally 1000, and let full-employment output in America be 2000. It proves useful to consider two distinct cases:

102 - unemployment in Gemiany and France - unemployment in Germany, overemployment in France. 1) Unemployment in Germany and France. Let initial output in Germany be 940, let initial output in France be 970, and let initial output in America be 2000. In Germany there is unemployment and deflation. In France there is unemployment and deflation too. But in America there is full employment and price stabiUty. Step 1 refers to the poUcy response. The output gap in Germany is 60, and the output gap in France is 30. So what is needed, according to equations (10) and (11) from the preceding section, is an increase in German government purchases of 52.5 and an increase in French government purchases of 37.5. Step 2 refers to the output lag. The increase in German government purchases of 52.5 raises German output by 78.8 and lowers French output by 26.3. As a side effect, it raises American output by 52.5. The increase in French government purchases of 37.5 raises French output by 56.3 and lowers German output by 18.8. As a side effect, it raises American output by 37.5. The net effect is an increase in German output of 60, an increase in French output of 30, and an increase in American output of 90. As a consequence, German output goes from 940 to 1000, French output goes from 970 to 1000, and American output goes from 2000 to 2090. In Germany there is now full employment and price stability. In France there is now full employment and price stability too. But in America there is now overemployment and inflation. As a result, fiscal cooperation between Germany and France can achieve full employment in Germany and France. And what is more, it can achieve price stability in Germany and France. However, as a severe side effect, it causes overemployment and inflation in America. The required increase in German government purchases is very large, as compared to the initial output gap in Germany. And the required increase in French government purchases is even larger, as compared to the initial output gap in France. The effective multiplier in Germany is only 60/52.5 = 1.1, and the effective multipUer in France is only 30/37.5 = 0.8. That is to say, the effective multiplier in Germany is very small, and the effective multiplier in France is even smaller. Table 3.3 presents a synopsis.

103 Table 3.3 Fiscal Cooperation between Germany and France Unemployment in Germany and France Germany Initial Output A Government Purchases Output

940 52.5 1000

France

America

970

2000

1

37.5 1000

2090

2) Unemployment in Germany, overemployment in France. Let initial output in Germany be 970, let initial output in France be 1030, and let initial output in America be 2000. In Germany there is unemployment and deflation. In France there is overemployment and inflation. And in America there is full employment and price stability. Step 1 refers to the policy response. The output gap in Germany is 30, and the inflationary gap in France is equally 30. So what is needed, according to equations (10) and (11) from the previous section, is an increase in German government purchases of 15 and a reduction in French government purchases of equally 15. Step 2 refers to the output lag. The increase in German government purchases of 15 raises German output by 22.5 and lowers French output by 7.5. As a side effect, it raises American output by 15. The reduction in French government purchases of 15 lowers French output by 22.5 and raises German output by 7.5. As a side effect, it lowers American output by 15. The net effect is an increase in German output of 30, a decline in French output of equally 30, and a change in American output of zero. As a consequence, German output goes from 970 to 1000, French output goes from 1030 to 1000, and American output stays at 2000. In each of the countries there is now full employment and price stability. As a result, fiscal cooperation between Germany and France can achieve full employment in Germany and France. And what is more, it can achieve price stability in Germany and France. Fiscal cooperation between Germany and

104 France does not cause overemployment and inflation in America. And neither does is cause unemployment and deflation in America. The required increase in German government purchases is small, as compared to the initial output gap in Germany. And the required cut in French government purchases is small, as compared to the initial inflationary gap in France. The effective multiplier in Germany is 30/15 = 2, as is the effective multiplier in France. In other words, the effective multiplier in Germany is large. And the same holds for the effective multiplier in France. Table 3.4 gives an overview.

Table 3.4 Fiscal Cooperation between Germany and France Unemployment in Germany, Overemployment in France Germany Initial Output A Government Purchases Output

France

America

970

1030

2000

15

-15

1000

1000

1

2000

3) Comparing fiscal cooperation with fiscal competition. Fiscal competition can achieve full employment and price stability. The same applies to fiscal cooperation. Fiscal competition is a slow process. By contrast, fiscal cooperation is a fast process. Judging from these points of view, fiscal cooperation seems to be superior to fiscal competition.

Part Four Monetary and Fiscal Interactions Intermediate Models

Chapter 1 Competition between European Central Bank^ German Government^ and French Government 1. The Dynamic Model

1) The static model. As a point of reference, consider the static model. It can be represented by a system of three equations: Yi = Ai + 0.5aMi2 + yGi - 5G2

(1)

Y2 = A2 + 0.5aMi2 + YG2 ~ 5Gi

(2)

Y3 = A3 - pMi2 + eGi + 8G2

(3)

This is a reduced form of the basic model, see Part One. Y^ denotes German output, Y2 is French output, Y3 is American output, M12 is European money supply, Gj is German government purchases, G2 is French government purchases, A^ is some other factors bearing on German output, A2 is some other factors bearing on French output, and A3 is some other factors bearing on American output, a, P, y, 5 and 8 are positive coefficients with a > P, y > S and e = Y - 5. The endogenous variables are German output, French output, and American output. According to equation (1), German output is a positive function of European money supply, a positive function of German government purchases, and a negative function of French government purchases. According to equation (2), French output is a positive function of European money supply, a positive function of French government purchases, and a negative function of German government purchases. According to equation (3), American output is a negative function of European money supply, a positive function of German government purchases, and a positive function of French government purchases.

108 An increase in European money supply raises German output and French output but lowers American output. An increase in German government purchases raises German output. On the other hand, it lowers French output. And what is more, it raises American output. Correspondingly, an increase in French government purchases raises French output. On the other hand, it lowers German output. And what is more, it raises American output. An increase in European money supply of 1 causes an increase in German output of 0.5a, an increase in French output of equally 0.5a, and a decline in American output of (3. An increase in German government purchases of 1 causes an increase in German output of y. ^ decline in French output of 5, and an increase in American output of e. Similarly, an increase in French government purchases of 1 causes an increase in French output of y. a decline in German output of 5, and an increase in American output of e. 2) The dynamic model. At the beginning there is unemployment in Germany and France. More precisely, unemployment in Germany exceeds unemployment in France. By contrast there is full employment in America. The primary target of the European central bank is price stability in Europe. The secondary target of the European central bank is high employment in Germany and France. The specific target of the European central bank is that unemployment in Germany equals overemployment in France. In other words, deflation in Germany equals inflation in France. So there is price stability in Europe. In a sense, the specific target of the European central bank is full employment in Europe. The instrument of the European central bank is European money supply. The target of the German government is full employment in Germany. The instrument of the German government is German government purchases. The target of the French government is full employment in France. The instrument of the French government is French government purchases. We assume that the central bank and the governments decide sequentially. First the central bank decides, then the governments decide. In step 1, the European central bank decides. In step 2, the German government and the French government decide simultaneously and independently. In step 3, the European central bank decides. In step 4, the German government and the French government decide simultaneously and independently. And so on. The reasons for this stepwise procedure are: First, the inside lag of monetary policy is short.

109 whereas the inside lag of fiscal policy is long. And second, the internal effect of monetary policy is large, whereas the internal effect of fiscal policy is small. Indeed, the effective multiplier of fiscal policy is very small. For a mathematical presentation of the dynamic model see Carlberg (2004) p. 132.

2. Some Numerical Examples

To illustrate the dynamic model, have a look at some numerical examples. For ease of exposition, without loss of generality, assume a = 3, (3 = 1, Y = l-5, 5 = 0.5 and 8 = 1. On this assumption, the static model can be written as follows: Yi =Ai+1.5Mi2+1.5Gi-0.5G2

(1)

Y2 = A2 +1.5Mi2 +1.5G2 ~ 0.5Gi

(2)

Y3=A3-Mi2+Gi+G2

(3)

The endogenous variables are German output, French output, and American output. Obviously, an increase in European money supply of 100 causes an increase in German output of 150, an increase in French output of equally 150, and a decline in American output of 100. An increase in German government purchases of 100 causes an increase in German output of 150, a decline in French output of 50, and an increase in American output of 100. Correspondingly, an increase in French government purchases of 100 causes an increase in French output of 150, a decline in German output of 50, and an increase in American output of 100. Further let full-employment output in Germany be 1000, let fullemployment output in France be equally 1000, and let full-employment output in America be 2000. It proves useful to study three distinct cases: - unemployment in Europe, full employment in America - inflation in Europe, price stability in America - first the governments decide, then the central bank decides.

110

1) Unemployment in Europe, full employment in America. Let initial output in Germany be 940, let initial output in France be 970, and let initial output in America be 2000. In Germany there is unemployment and deflation. In France there is unemployment and deflation too. But in America there is full employment and price stability. Step 1 refers to monetary policy in Europe. The output gap in Europe is 90. The monetary policy multiplier in Europe is 3. So what is needed in Europe is an increase in European money supply of 30. Step 2 refers to the output lag. The increase in European money supply of 30 causes an increase in German output of 45 and an increase in French output of equally 45. As a side effect, it causes a decline in American output of 30. As a consequence, German output goes from 940 to 985, French output goes from 970 to 1015, and American output goes from 2000 to 1970. In Germany there is still some unemployment and deflation. In France there is now some overemployment and inflation. In Europe there is now full employment and price stability. And in America there is now some unemployment and deflation. Unemployment in Germany equals overemployment in France. And deflation in Germany equals inflation in France. Step 3 refers to fiscal policy in Germany and France. The output gap in Germany is 15. The fiscal policy multipUer in Germany is 1.5. So what is needed in Germany is an increase in German government purchases of 10. The inflationary gap in France is 15. The fiscal poUcy multiplier in France is 1.5. So what is needed in France is a reduction in French government purchases of 10. Step 4 refers to the output lag. The increase in German government purchases of 10 causes an increase in German output of 15. As a side effect, it causes a decline in French output of 5 and an increase in American output of 10. The reduction in French government purchases of 10 causes a decline in French output of 15. As a side effect, it causes an increase in German output of 5 and a decline in American output of 10. The net effect is an increase in German output of 20, a decline in French output of equally 20, and a change in American output of zero. As a consequence, German output goes from 985 to 1005, French output goes from 1015 to 995, and American output stays at 1970. In Germany there is now some overemployment and inflation. In France there is now some unemployment and deflation. In Europe there is still full employment and price

Ill

stability. And in America there is still some unemployment and deflation. Overemployment in Germany equals unemployment in France. And inflation in Germany equals deflation in France. Step 5 refers to monetary policy in Europe. The output gap in Europe is zero. So there is no need for a change in European money supply. Step 6 refers to the output lag. As a consequence, German output stays at 1005, French output stays at 995, and American output stays at 1970. Step 7 refers to fiscal policy in Germany and France. The inflationary gap in Germany is 5. The fiscal policy multiplier in Germany is 1.5. So what is needed in Germany is a reduction in German government purchases of 3.3. The output gap in France is 5. The fiscal policy multiplier in France is 1.5. So what is needed in France is an increase in French government purchases of 3.3. Step 8 refers to the output lag. The reduction in German government purchases of 3.3 causes a dechne in German output of 5. As a side effect, it causes an increase in French output of 1.7 and a decline in American output of 3.3. The increase in French government purchases of 3.3 causes an increase in French output of 5. As a side effect, it causes a decline in German output of 1.7 and an increase in American output of 3.3. The net effect is a decline in German output of 6.7, an increase in French output of equally 6.7, and a change in American output of zero. As a consequence, German output goes from 1005 to 998.3, French output goes from 995 to 1001.7, and American output stays at 1970. And so on. Table 4.1 presents a synopsis. In the steady state, German output is 1000, French output is equally 1000, and American output is 1970. In Germany there is full employment and price stability. In France there is full employment and price stability too. But in America there is unemployment and deflation. As a result, competition between the European central bank, the German government, and the French government leads to full employment in Germany and France. And what is more, it leads to price stability in Germany and France. However, as an adverse side effect, it causes unemployment and deflation in America. What are the dynamic characteristics of this process? There is a one-time increase in European money supply. There are damped oscillations in German

112 government purchases, as there are in French government purchases. There are damped oscillations in German output, as there are in French output. And there is a one-time reduction in American output. The German economy oscillates between unemployment and overemployment, as does the French economy. There is a depreciation of the euro and an appreciation of the dollar. There is an increase in European exports and a cut in American exports. There is a cut in the world interest rate. There is an increase in European and American investment. There is a cut in the European budget deficit and an increase in the American budget deficit. Taking the sum over all periods, the total increase in European money supply is 30, the total increase in German government purchases is 7.5, and the total reduction in French government purchases is equally 7.5. The total change in European government purchases is zero.

Table 4.1 Competition between the European Central Bank, the German Government, and the French Government Unemployment in Europe, Full Employment in America

Initial Output

Germany

France

America

940

970

2000

1

1970

1

1970

1

1970

1 1

A Money Supply 1 Output A Government Purchases 1 Output

30 985

1015

10

-10

1005

995

A Money Supply Output A Government Purchases 1 Output

0 1005

995

-3.3

3.3

998.3

1001.7

1970

1000

1970

and so on Steady-State Output

1000

113 2) Inflation in Europe, price stability in America. Let initial output in Germany be 1060, let initial output in France be 1030, and let initial output in America be 2000. In Germany there is overemployment and inflation. In France there is overemployment and inflation too. But in America there is full employment and price stability. Step 1 refers to monetary policy in Europe. The inflationary gap in Europe is 90. The monetary policy multiplier in Europe is 3. So what is needed in Europe is a reduction in European money supply of 30. Step 2 refers to the output lag. The reduction in European money supply of 30 causes a decline in German output of 45 and a decline in French output of equally 45. As a side effect, it causes an increase in American output of 30. As a consequence, German output goes from 1060 to 1015, French output goes from 1030 to 985, and American output goes from 2000 to 2030. In Germany there is still some overemployment and inflation. In France there is now some unemployment and deflation. In Europe there is now full employment and price stability. And in America there is now some overemployment and inflation. Step 3 refers to fiscal policy in Germany and France. The inflationary gap in Germany is 15. The fiscal policy multiplier in Germany is 1.5. So what is needed in Germany is a reduction in German government purchases of 10. The output gap in France is 15. The fiscal poUcy multiplier in France is 1.5. So what is needed in France is an increase in French government purchases of 10. Step 4 refers to the output lag. The reduction in German government purchases of 10 causes a decline in German output of 15. As a side effect, it causes an increase in French output of 5 and a decline in American output of 10. The increase in French government purchases of 10 causes an increase in French output of 15. As a side effect, it causes a decline in German output of 5 and an increase in American output of 10. The net effect is a decUne in German output of 20, an increase in French output of equally 20, and a change in American output of zero. As a consequence, German output goes from 1015 to 995, French output goes from 985 to 1005, and American output stays at 2030. In Germany there is now some unemployment and deflation. In France there is now some overemployment and inflation. In Europe there is still full employment and price stability. And in America there is still some overemployment and inflation. This process repeats itself round by round. Table 4.2 gives an overview.

114 Table 4.2 Competition between the European Central Bank, the German Government, and the French Government Inflation in Europe, Price Stability in America Germany Initial Output

1060

A Money Supply

France 1030

1015

985

A Government Purchases

-10

10

995

1005

A Government Purchases Output

2000

1

-30

Output

1 Output

America

3.3

-3.3

1001.7

998.3

2030

2030

1

2030

1

2030

1

and so on \ Steady-State Output

1000

1000

In the steady state, German output is 1000, French output is equally 1000, and American output is 2030. In Germany there is full employment and price stability. In France there is full employment and price stability too. But in America there is overemployment and inflation. As a result, competition between the European central bank, the German government, and the French government leads to full employment in Germany and France. And what is more, it leads to price stability in Germany and France. However, as an adverse side effect, it causes overemployment and inflation in America. What are the dynamic characteristics of this process? There is a one-time cut in European money supply. There are damped oscillations in German government purchases, as there are in French government purchases. There are damped oscillations in German output, as there are in French output. And there is a one-time increase in American output. Taking the sum over all periods, the total reduction in German government purchases is 7.5, the total increase in

115 French government purchases is equally 7.5, and the total change in European government purchases is zero. 3) Comparing monetary and fiscal competition with pure fiscal competition. Fiscal competition is a slow process. By contrast, monetary and fiscal competition is a process of intermediate speed. Fiscal competition causes a large increase in European govemment purchases. Monetary and fiscal competition causes a zero increase in European govemment purchases. Judging from these points of view, monetary and fiscal competition seems to be superior to fiscal competition. 4) First the govemments decide, then the central bank decides. So far we have assumed that the central bank decides first. Now we assume that the govemments decide first. Let initial output in Germany be 940, let initial output in France be 970, and let initial output in America be 2000. In Germany there is unemployment and deflation. In France there is unemployment and deflation too. But in America there is full employment and price stability. Step 1 refers to fiscal policy in Germany and France. The output gap in Germany is 60. The fiscal policy multiplier in Germany is 1.5. So what is needed in Germany is an increase in German govemment purchases of 40. The output gap in France is 30. The fiscal policy multiplier in France is 1.5. So what is needed in France is an increase in French govemment purchases of 20. Step 2 refers to the output lag. The increase in German govemment purchases of 40 causes an increase in German output of 60. As a side effect, it causes a decline in French output of 20 and an increase in American output of 40. The increase in French govemment purchases of 20 causes an increase in French output of 30. As a side effect, it causes a decline in German output of 10 and an increase in American output of 20. The net effect is an increase in German output of 50, an increase in French output of 10, and an increase in American output of 60. As a consequence, German output goes from 940 to 990, French output goes from 970 to 980, and American output goes from 2000 to 2060. Step 3 refers to monetary policy in Europe. The output gap in Europe is 30. The monetary policy multiplier in Europe is 3. So what is needed in Europe is an increase in European money supply of 10. Step 4 refers to the output lag. The increase in European money supply of 10 causes an increase in German output of

116 15 and an increase in French output of equally 15. As a side effect, it causes a decline in American output of 10. As a consequence, German output goes from 990 to 1005, French output goes from 980 to 995, and American output goes from 2060 to 2050. Step 5 refers to fiscal policy in Germany and France. The inflationary gap in Germany is 5. The fiscal policy multiplier in Germany is 1.5. So what is needed in Germany is a reduction in German government purchases of 3.3. The output gap in France is 5. The fiscal policy multipher in France is 1.5. So what is needed in France is an increase in French government purchases of 3.3. Step 6 refers to the output lag. The reduction in German government purchases of 3.3 causes a decUne in German output of 5. As a side effect, it causes an increase in French output of 1.7 and a decline in American output of 3.3. The increase in French government purchases of 3.3 causes an increase in French output of 5. As a side effect, it causes a decline in German output of 1.7 and an increase in American output of 3.3. The net effect is a decline in German output of 6.7, an increase in French output of equally 6.7, and a change in American output of zero. As a consequence, German output goes from 1005 to 998.3, French output goes from 995 to 1001.7, and American output stays at 2050. Step 7 refers to fiscal policy in Germany and France. The output gap in Germany is 1.7. The fiscal policy multiplier in Germany is 1.5. So what is needed in Germany is an increase in German government purchases of 1.1. The inflationary gap in France is 1.7. The fiscal policy multiplier in France is 1.5. So what is needed in France is a reduction in French government purchases of 1.1. Step 8 refers to the output lag. The net effect is an increase in German output of 2.2, a decline in French output of equally 2.2, and a change in American output of zero. As a consequence, German output goes from 998.3 to 1000.6, French output goes from 1001.7 to 999.4, and American output stays at 2050. And so on. Table 4.3 presents a synopsis. In the steady state, German output is 1000, French output is equally 1000, and American output is 2050. In Germany there is full employment and price stability. In France there is full employment and price stability too. But in America there is overemployment and inflation. As a result, competition between

117 the German government, the French government, and the European central bank leads to full employment in Germany and France. And what is more, it leads to price stability in Germany and France. However, as a severe side effect, it causes overemployment and inflation in America. What are the dynamic characteristics of this process? There is a one-time increase in German government purchases, as there is in French government purchases. There is a one-time increase in European money supply. This in turn is followed by damped oscillations in German and French government purchases. Taking the sum over all periods, the total increase in German government purchases is 37.5, the total increase in French government purchases is 22.5, the total increase in European government purchases is 60, and the total increase in European money supply is 10. Besides, the total increase in American output is 50.

Table 4.3 Competition between the European Central Bank, the German Government, and the French Government First the Governments Decide, then the Central Bank Decides

Initial Output A Government Purchases 1 Output

Germany

France

America

940

970

2000

1

40

20

990

980

2060

1

2050

1

2050

1

2050

1

2050

1

10

A Money Supply 1 Output A Government Purchases 1 Output A Government Purchases 1 Output

1005

995

-3.3

3.3

998.3

1001.7

1.1

-1.1

1000.6

999.4

and so on Steady-State Output

1000

1000

118 5) Comparing - first the central bank decides, then the governments decide - first the governments decide, then the central bank decides. Let initial output in Germany be 940, let initial output in France be 970, and let initial output in America be 2000. Case number 1: The central bank decides first. Taking the sum over all periods, the increase in European money supply is 30, the increase in German government purchases is 7.5, the reduction in French government is equally 7.5, the change in European government purchases is zero, and the decline in American output is 30. Case number 2: The governments decide first. Taking the sum over all periods, the increase in European money supply is 10, the increase in German government purchases is 37.5, the increase in French government purchases is 22.5, the increase in European government purchases is 60, and the increase in American output is 50. Table 4.4 gives an overview.

Table 4.4 Who Should Decide First, the Central Bank or the Governments?

Total Increase in

European Money Supply German Government Purchases French Government Purchases European Government Purchases American Output

The Central Bank The Governments Decides First Decide First

30

10

7.5

37.5

-7.5

22.5

0

60

-30

50

As a result, if the central bank decides first, the increase in European money supply is large and the increase in European government purchases is zero. The

119 other way round, if the governments decide first, the increase in European money supply is small and the increase in European government purchases is large. Judging from this point of view, it seems that the central bank should decide first.

Chapter 2 Cooperation between European Central Bank, German Government, and French Government 1. The Model

1) Introduction. As a starting point, take the output model. It can be represented by a system of three equations: Yi = Ai + 0.5aMi2 + YGI ~ 6G2

(1)

Y2 = A2 + 0.5aMi2 + YG2 - SGi

(2)

Y3 = A3 - PM12 + eGi + 8G2

(3)

Here Y^ denotes German output, Y2 is French output, Y3 is American output, M12 is European money supply, G^ is German government purchases, and G2 is French government purchases. The endogenous variables are German output, French output, and American output. At the beginning there is unemployment in Germany and France. More precisely, unemployment in Germany exceeds unemployment in France. By contrast there is full employment in America. The policy makers are the European central bank, the German government, and the French government. The targets of policy cooperation are full employment in Germany and full employment in France. The instruments of policy cooperation are European money supply, German government purchases, and French government purchases. There are two targets and three instruments, so there is one degree of freedom. As a result, there is an infinite number of solutions. In other words, cooperation between the European central bank, the German government, and the French government can achieve full employment in Germany and France. 2) The policy model. On this basis, the policy model can be characterized by a system of three equations:

121

AYi = 0.5aAMi2 + yAGi - 5AG2

(4)

AY2 = 0.5aAMi2 + YAG2 - 6AG1

(5)

AY3 = - PAM12 + BAGI + 8AG2

(6)

Here AY^ denotes the initial output gap in Germany, AY2 is the initial output gap in France, AY3 is the change in American output, AM12 is the required increase in European money supply, AG^ is the required increase in German government purchases, and AG2 is the required increase in French government purchases. The endogenous variables are AM12, AGp AG2 and AY3. We now introduce a third target. We assume that the increase in German government purchases should be equal in size to the reduction in French government purchases AG^ + AG2 = 0. Put another way, we assume that the sum total of European government purchases should be constant. Add up equations (4) and (5), taking account of AG^ + AG2 = 0, to find out:

AM.,=^^il^ a

(7)

Then subtract equation (5) from equation (4), taking account of AG^ + AG2 = 0, and solve for:

^ ° . = ^ ^

(8)

2(Y + 5) A:)^-AY, '2-^,—?r2(Y + 5)

(9)

According to equation (7), the required increase in European money supply depends on the initial output gap in Europe and the direct multiplier a . According to equation (8), the required increase in German government purchases depends on the initial output gap in Germany, the initial output gap in France, the direct multiplier y, and the cross multiplier 5. According to equation (9), the required increase in French government purchases depends on the initial

122 output gap in France, the initial output gap in Germany, the direct multiplier y, and the cross multiplier 5.

2. Some Numerical Examples

To illustrate the policy model, have a look at some numerical examples. For ease of exposition, without losing generality, assume a = 3, y = 1.5, 6 = 0.5 and 8 = 1. That is, an increase in European money supply of 100 causes an increase in German output of 150, an increase in French output of equally 150, and a decUne in American output of 100. An increase in German government purchases of 100 causes an increase in German output of 150, a decline in French output of 50, and an increase in American output of 100. Further let full-employment output in Germany be 1000, let full-employment output in France be equally 1000, and let full-employment output in America be 2000. It proves useful to consider three distinct cases: - unemployment in Europe, full employment in America - inflation in Europe, price stability in America - alternative targets of policy cooperation. 1) Unemployment in Europe, full employment in America. Let initial output in Germany be 940, let initial output in France be 970, and let initial output in America be 2000. In Germany there is unemployment and deflation. In France there is unemployment and deflation too. But in America there is full employment and price stability. Step 1 refers to the policy response. The output gap in Germany is 60, and the output gap in France is 30. So what is needed, according to equations (7), (8) and (9) from the preceding section, is an increase in European money supply of 30, an increase in German government purchases of 7.5, and a reduction in French government purchases of equally 7.5. Step 2 refers to the output lag. The increase in European money supply of 30 raises German output and French output by 45 each. As a side effect, it lowers

123 American output by 30. The increase in German government purchases of 7.5 raises German output by 11.3 and lowers French output by 3.8. As a side effect, it raises American output by 7.5. The reduction in French government purchases of 7.5 lowers French output by 11.3 and raises German output by 3.8. As a side effect, it lowers American output by 7.5. The total effect is an increase in German output of 60, an increase in French output of 30, and a decline in American output of 30. As a consequence, German output goes from 940 to 1000, French output goes from 970 to 1000, and American output goes from 2000 to 1970. In Germany there is now full employment and price stability. In France there is now full employment and price stability too. But in America there is now unemployment and deflation. As a result, cooperation between the European central bank, the German government, and the French government can achieve full employment in Germany and France. And what is more, it can achieve price stability in Germany and France. However, as an adverse side effect, it causes unemployment and deflation in America. Table 4.5 presents a synopsis.

Table 4.5 Cooperation between the European Central Bank, the German Government, and the French Government Unemployment in Europe, Full Employment in America

Initial Output

Germany

France

America

940

970

2000

A Money Supply A Government Purchases Output

1

30 7.5 1000

-7.5 1000

1970

Finally compare monetary and fiscal cooperation with monetary and fiscal competition. Under monetary and fiscal competition, the total increase in European money supply is 30, the total increase in German government

124 purchases is 7.5, and the total reduction in French government purchases is equally 7.5. That means, the solution to monetary and fiscal cooperation is identical to the steady state of monetary and fiscal competition. 2) Inflation in Europe, price stability in America. Let initial output in Germany be 1060, let initial output in France be 1030, and let initial output in America be 2000. In Germany there is overemployment and inflation. In France there is overemployment and inflation too. But in America there is full employment and price stability. Step 1 refers to the policy response. The inflationary gap in Germany is 60, and the inflationary gap in France is 30. So what is needed, according to equations (7), (8) and (9) from the previous sections, is a reduction in European money supply of 30, a reduction in German govemment purchases of 7.5, and an increase in French govemment purchases of equally 7.5. Step 2 refers to the output lag. The total effect is a decline in German output of 60, a decline in French output of 30, and an increase in American output of 30. As a consequence, German output goes from 1060 to 1000, French output goes from 1030 to 1000, and American output goes from 2000 to 2030. In Germany there is now full employment and price stability. In France there is now full employment and price stability too. But in America there is now overemployment and inflation. As a result, cooperation between the European central bank, the German govemment, and the French govemment can achieve full employment in Germany and France. And what is more, it can achieve price stability in Germany and France. However, as an adverse side effect, it causes overemployment and inflation in America. Table 4.6 gives an overview. 3) Altemative targets of policy cooperation. In Table 4.7 we assume that the third target of policy cooperation is no increase in national govemment purchases. What is needed, then, is an increase in European money supply of 35, a change in German govemment purchases of zero, and a reduction in French govemment purchases of 15. As an adverse side effect, American output goes from 2000 to 1950. In Table 4.8 we assume that the third target of policy cooperation is no reduction in national govemment purchases. What is needed, then, is an increase in European money supply of 25, an increase in German govemment purchases of 15, and a change in French govemment purchases of zero. As a side effect, American output goes from 2000 to 1990.

125 Table 4.6 Cooperation between the European Central Bank, the German Government, and the French Government Inflation in Europe, Price Stability in America

Initial Output

Germany

France

America

1060

1030

2000

A Money Supply A Government Purchases Output

1

-30 7.5

-7.5 1000

1000

2030

Table 4.7 Cooperation between the European Central Bank, the German Government, and the French Government No Increase in Government Purchases

Initial Output

Germany

France

America

940

970

2000

A Money Supply A Government Purchases Output

1

35 0

-15

1000

1000

1950

4) Comparing policy cooperation with policy competition. Policy competition can achieve full employment in Germany and France. The same applies to policy cooperation. Policy competition is a slow process. By contrast, policy cooperation is a fast process. Judging from these points of view, policy cooperation seems to be superior to policy competition.

126 Table 4.8 Cooperation between the European Central Bank, the German Government, and the French Government No Reduction in Government Purchases

Initial Output

Germany

France

America

940

970

2000

A Money Supply A Government Purchases Output

25 15

0

1000

1000

1990

1

Chapter 3 Competition between European Central Bank^ American Central Bank^ German Government^ and French Government 1. The Dynamic Model

1) The static model. As a point of reference, consider the static model. It can be represented by a system of three equations: Yj = Ai + 0.5aMi2 - O.5PM3 + yGi - 5G2

(1)

Y2 = A2 + 0.5aMi2 - O.5PM3 + YG2 - 5Gi

(2)

Y3 = A3 + aM3 - PM12 + BGI + 8G2

(3)

This is a reduced form of the basic model, see Part One. Y^ denotes German output, Y2 is French output, Y3 is American output, M12 is European money supply, M3 is American money supply, G^ is German government purchases, G2 is French government purchases, Aj is some other factors bearing on German output, A2 is some other factors bearing on French output, and A3 is some other factors bearing on American output, a, P, y, 5 and 8 are positive coefficients with a > P, Y > 5 and e = y -d. The endogenous variables are German output, French output, and American output. According to equation (1), German output is a positive function of European money supply, a negative function of American money supply, a positive function of German government purchases, and a negative function of French government purchases. According to equation (2), French output is a positive function of European money supply, a negative function of American money supply, a positive function of French government purchases, and a negative function of German government purchases. According to equation (3), American output is a positive function of American money supply, a negative function of

128 European money supply, a positive function of German government purchases, and a positive function of French government purchases. An increase in European money supply raises German output and French output but lowers American output. An increase in American money supply raises American output but lowers German output and French output. An increase in German government purchases raises German output. On the other hand, it lowers French output. And what is more, it raises American output. Correspondingly, an increase in French government purchases raises French output. On the other hand, it lowers German output. And what is more, it raises American output. An increase in European money supply of 1 causes an increase in German output of 0.5a, an increase in French output of equally 0.5a, and a dechne in American output of p. An increase in American money supply of 1 causes an increase in American output of a, a decline in German output of 0.5P, and a decline in French output of equally 0.5(3. An increase in German government purchases of 1 causes an increase in German output of y. a decline in French output of 5, and an increase in American output of 8. Similarly, an increase in French government purchases of 1 causes an increase in French output of y, a decline in German output of 5, and an increase in American output of e. 2) The dynamic model. At the beginning there is unemployment in Germany, France and America. More precisely, unemployment in Germany exceeds unemployment in France. The primary target of the European central bank is price stability in Europe. The secondary target of the European central bank is high employment in Germany and France. The specific target of the European central bank is that unemployment in Germany equals overemployment in France. In other words, deflation in Germany equals inflation in France. So there is price stability in Europe. In a sense, the specific target of the European central bank is full employment in Europe. The instrument of the European central bank is European money supply. The target of the American central bank is full employment in America. The instrument of the American central bank is American money supply. The target of the German government is full employment in Germany. The instrument of the German government is German government purchases. The target of the

129 French government is full employment in France. The instrument of the French government is French government purchases. We assume that the central banks and the governments decide sequentially. First the central banks decide, then the governments decide. In step 1, the European central bank and the American central bank decide simultaneously and independently. In step 2, the German government and the French government decide simultaneously and independently. In step 3, the European central bank and the American central bank decide simultaneously and independently. In step 4, the German government and the French government decide simultaneously and independently. And so on. For a small-scale model see Carlberg (2004) p. 132.

2. Some Numerical Examples

To illustrate the dynamic model, have a look at some numerical examples. For ease of exposition, without loss of generality, assume a = 3, P = l, Y = l-5, 5 = 0.5 and 8 = 1. On this assumption, the static model can be written as follows: Yi =Ai+1.5Mi2-0.5M3+1.5Gi-0.5G2

(1)

Y2 = A2 +1.5Mi2 - O.5M3 +1.5G2 - 0.5Gi

(2)

Y3 = A 3 + 3 M 3 - M i 2 + G i + G 2

(3)

The endogenous variables are German output, French output, and American output. Obviously, an increase in European money supply of 100 causes an increase in German output of 150, an increase in French output of equally 150, and a decline in American output of 100. An increase in American money supply of 100 causes an increase in American output of 300, a decline in German output of 50, and a decline in French output of equally 50. An increase in German government purchases of 100 causes an increase in German output of 150, a decline in French output of 50, and an increase in American output of 100.

130 Correspondingly, an increase in French government purchases of 100 causes increase in French output of 150, a decline in German output of 50, and increase in American output of 100. Further let full-employment output Germany be 1000, let full-employment output in France be equally 1000, and full-employment output in America be 2000.

an an in let

It proves useful to study two distinct cases: - the case of unemployment - Europe and America differ in unemployment. 1) The case of unemployment. Let initial output in Germany be 940, let initial output in France be 970, and let initial output in America be 1910. In each of the countries there is unemployment and deflation. Step 1 refers to monetary poHcy in Europe and America. The output gap in Europe is 90. The monetary policy multiplier in Europe is 3. So what is needed in Europe is an increase in European money supply of 30. The output gap in America is 90. The monetary pohcy multiplier in America is 3. So what is needed in America is an increase in American money supply of 30. Step 2 refers to the output lag. The increase in European money supply of 30 causes an increase in German output of 45 and an increase in French output of equally 45. As a side effect, it causes a decline in American output of 30. The increase in American money supply of 30 causes an increase in American output of 90. As a side effect, it causes a decline in German output of 15 and a decUne in French output of equally 15. The net effect is an increase in German output of 30, an increase in French output of equally 30, and an increase in American output of 60. As a consequence, German output goes from 940 to 970, French output goes from 970 to 1000, and American output goes from 1910 to 1970. In Germany there is still some unemployment and deflation. In France there is now full employment and price stability. In Europe there is still some unemployment and deflation. And the same is true of America. Step 3 refers to fiscal policy in Germany and France. The output gap in Germany is 30. The fiscal poUcy multipUer in Germany is 1.5. So what is needed in Germany is an increase in German government purchases of 20. The output gap in France is zero. So there is no need for a change in French government purchases.

131

Step 4 refers to the output lag. The increase in German government purchases of 20 causes an increase in German output of 30. As a side effect, it causes a decline in French output of 10 and an increase in American output of 20. As a consequence, German output goes from 970 to 1000, French output goes from 1000 to 990, and American output goes from 1970 to 1990. In Germany there is now full employment and price stability. In France there is now unemployment and deflation. In Europe there is still some unemployment and deflation. And the same is true of America. Step 5 refers to monetary policy in Europe and America. The output gap in Europe is 10. The monetary policy multiplier in Europe is 3. So what is needed in Europe is an increase in European money supply of 3.3. The output gap in America is 10. The monetary policy multiplier in America is 3. So what is needed in America is an increase in American money supply of 3.3. Step 6 refers to the output lag. The increase in European money supply of 3.3 causes an increase in German output of 5 and an increase in French output of equally 5. As a side effect, it causes a decline in American output of 3.3. The increase in American money supply of 3.3 causes an increase in American output of 10. As a side effect, it causes a decUne in German output of 1.7 and a decUne in French output of equally 1.7. The net effect is an increase in German output of 3.3, an increase in French output of equally 3.3, and an increase in American output of 6.7. As a consequence, German output goes from 1000 to 1003.3, French output goes from 990 to 993.3, and American output goes from 1990 to 1996.7. In Germany there is now some overemployment and inflation. In France there is still some unemployment and deflation. In Europe there is still some unemployment and deflation. And the same is true of America. Step 7 refers to fiscal policy in Germany and France. The inflationary gap in Germany is 3.3. The fiscal pohcy multiplier in Germany is 1.5. So what is needed in Germany is a reduction in German government purchases of 2.2. The output gap in France is 6.7. The fiscal policy multiplier in France is 1.5. So what is needed in France is an increase in French government purchases of 4.4. Step 8 refers to the output lag. The reduction in German government purchases of 2.2 causes a decline in German output of 3.3. As a side effect, it

132 causes an increase in French output of 1.1 and a decline in American output of 2.2. The increase in French government purchases of 4.4 causes an increase in French output of 6.7. As a side effect, it causes a decline in German output of 2.2 and an increase in American output of 4.4. The net effect is a decline in German output of 5.6, an increase in French output of equally 7.8, and an increase in American output of 2.2. As a consequence, German output goes from 1003.3 to 997.8, French output goes from 993.3 to 1001.1, and American output goes from 1996.7 to 1998.9. This process repeats itself round by round. Table 4.9 presents a synopsis.

Table 4.9 Competition between European Central Bank, American Central Bank, German Government, and French Government The Case of Unemployment

Initial Output

Germany

France

America

940

970

1910

30

30

970

1000

1970

1

20

0

1000

990

1990

1

A Money Supply 1 Output A Government Purchases 1 Output

3.3

3.3

1003.3

993.3

1996.7

A Government Purchases

-2.2

4.4

Output

997.8

1001.1

1998.9

1000

2000

A Money Supply 1 Output

1

1

and so on 1 Steady-State Output

1000

In the steady state, German output is 1000, French output is equally 1000, and American output is 2000. In each of the countries there is full employment and price stability. As a result, competition between the European central bank, the

133 American central bank, the German government, and the French government leads to full employment in Germany, France and America. And what is more, it leads to price stability in Germany, France and America. What are the dynamic characteristics of this process? There are repeated increases in European money supply, as there are in American money supply. There is an upward trend in German government purchases, as there is in French government purchases. There is an upward trend in German output, as there is in French output and American output. Taking the sum over all periods, the total increase in European money supply is 33.8, the total increase in American money supply is equally 33.8, the total increase in German government purchases is 18.8, and the total increase in French government purchases is 3.8. 2) Europe and America differ in unemployment. Let initial output in Germany be 940, let initial output in France be 970, and let initial output in America be 1880. In each of the countries there is unemployment and deflation. Step 1 refers to monetary policy in Europe and America. The output gap in Europe is 90. The monetary policy multiplier in Europe is 3. So what is needed in Europe is an increase in European money supply of 30. The output gap in America is 120. The monetary policy multipUer in America is 3. So what is needed in America is an increase in American money supply of 40. Step 2 refers to the output lag. The increase in European money supply of 30 causes an increase in German output of 45 and an increase in French output of equally 45. As a side effect, it causes a decUne in American output of 30. The increase in American money supply of 40 causes an increase in American output of 120. As a side effect, it causes a decline in German output of 20 and a decline in French output of equally 20. The net effect is an increase in German output of 25, an increase in French output of equally 25, and an increase in American output of 90. As a consequence, German output goes from 940 to 965, French output goes from 970 to 995, and American output goes from 1880 to 1970. Step 3 refers to fiscal policy in Germany and France. The output gap in Germany is 35. The fiscal pohcy multiplier in Germany is 1.5. So what is needed in Germany is an increase in German government purchases of 23.3. The output gap in France is 5. The fiscal policy multiplier in France is 1.5. So what is needed in France is an increase in French government purchases of 3.3.

134

Step 4 refers to the output lag. The increase in German government purchases of 23.3 causes an increase in German output of 35. As a side effect, it causes a decUne in French output of 11.7 and an increase in American output of 23.3. The increase in French government purchases of 3.3 causes an increase in French output of 5. As a side effect, it causes a decline in German output of 1.7 and an increase in American output of 3.3. The net effect is an increase in German output of 33.3, a decline in French output of 6.7, and an increase in American output of 26.7. As a consequence, German output goes from 965 to 998.3, French output goes from 995 to 988.3, and American output goes from 1970 to 1996.7. Step 5 refers to monetary policy in Europe and America. The output gap in Europe is 13.3. The monetary poHcy multiplier in Europe is 3. So what is needed in Europe is an increase in European money supply of 4.4. The output gap in America is 3.3. The monetary policy multipHer in America is 3. So what is needed in America is an increase in American money supply of 1.1. Step 6 refers to the output lag. The increase in European money supply of 4.4 causes an increase in German output of 6.7 and an increase in French output of equally 6.7. As a side effect, it causes a decline in American output of 4.4. The increase in American money supply of 1.1 causes an increase in American output of 3.3. As a side effect, it causes a decline in German output of 0.6 and a decline in French output of equally 0.6. The net effect is an increase in German output of 6.1, an increase in French output of equally 6.1, and a decline in American output of 1.1. As a consequence, German output goes from 998.3 to 1004.4, French output goes from 988.3 to 994.4, and American output goes from 1996.7 to 1995.6. Step 7 refers to fiscal policy in Germany and France. The inflationary gap in Germany is 4.4. The fiscal policy multiplier in Germany is 1.5. So what is needed in Germany is a reduction in German government purchases of 3.0. The output gap in France is 5.6. The fiscal policy multiplier in France is 1.5. So what is needed in France is an increase in French government purchases of 3.7. Step 8 refers to the output lag. The reduction in German government purchases of 3.0 causes a decline in German output of 4.4. As a side effect, it causes an increase in French output of 1.5 and a decline in American output of

135 3.0. The increase in French government purchases of 3.7 causes an increase in French output of 5.5. As a side effect, it causes a decHne in German output of 1.9 and an increase in American output of 3.7. The net effect is a decline in German output of 6.3, an increase in French output of 7.0, and an increase in American output of 0.7. As a consequence, German output goes from 1004.4 to 998.1, French output goes from 994.4 to 1001.4, and American output goes from 1995.6 to 1996.3. And so on. Table 4.10 gives an overview. In the steady state, German output is 1000, French output is equally 1000, and American output is 2000. In each of the countries there is full employment and price stability. As a result, monetary and fiscal competition leads to full employment in Germany, France and America. And what is more, it leads to price stability in Germany, France and America.

Table 4.10 Competition between European Central Bank, American Central Bank, German Government, and French Government Europe and America Differ in Unemployment

Initial Output

Germany

France

America

940

970

1880

30

40

995

1970

1

1

A Money Supply 1 Output

965 23.3

3.3

998.3

988.3

1996.7

4.4

1.1

1004.4

994.4

1995.6

A Government Purchases

-3.0

3.7

Output

998.1

1001.5

1996.3

1000

2000

A Government Purchases 1 Output A Money Supply Output

and so on 1 Steady-State Output

1000

1

136 What are the dynamic characteristics of this process? There are repeated increases in European money supply, as there are in American money supply. There is an upward trend in German govemment purchases, as there is in French government purchases. There is an upward trend in German output, as there is in French output and American output. Taking the sum over all periods, the total increase in European money supply is 34.7, the total increase in American money supply is 42.2, the total increase in German govemment purchases is 21.6, and the total increase in French govemment purchases is 6.6. Generally speaking, the total increase in European money supply depends on: - the initial output gap in Germany - the initial output gap in France - the initial output gap in America - the direct policy multipliers a and y - the cross policy multipliers p and 5. And the same holds for the total increase in American money supply, the total increase in German govemment purchases, and the total increase in French govemment purchases.

Chapter 4 Cooperation between European Central Bank, American Central Bank, German Government, and French Government 1. The Model

1) Introduction. As a starting point, take the output model. It can be represented by a system of three equations: Yi = Ai + 0.5aMi2 - O.5PM3 + yGi - 862

(1)

Y2 = A2 + 0.5aMi2 - O.5PM3 + YG2 - 5Gi

(2)

Y3 = A3 + aM3 - PM12 + eGi + 8G2

(3)

Here Yj denotes German output, Y2 is French output, Y3 is American output, M12 is European money supply, M3 is American money supply, G^ is German government purchases, and G2 is French government purchases. The endogenous variables are German output, French output, and American output. At the beginning there is unemployment in Germany, France and America. More precisely, unemployment in Germany exceeds unemployment in France. The policy makers are the European central bank, the American central bank, the German government, and the French government. The targets of policy cooperation are full employment in Germany, full employment in France, and full employment in America. The instruments of policy cooperation are European money supply, American money supply, German government purchases, and French government purchases. There are three targets and four instruments, so there is one degree of freedom. As a result, there is an infinite number of solutions. In other words, cooperation between the European central bank, the American central bank, the German government, and the French government can achieve full employment in Germany, France and America.

138 Of course there are many more potential targets of policy cooperation: - balancing the budget in Germany, France and America - balancing the current account in Germany, France and America - high investment in Germany, France and America - preventing foreign exchange bubbles - preventing stock market bubbles - and so on. To sum up, in a sense, policy instruments are abundant. And in another sense, policy instruments are scarce. 2) The policy model. On this basis, the policy model can be characterized by a system of three equations: AYj = 0.5aAMi2 - O.5PAM3 + yAGj - 6AG2

(4)

AY2 = 0.5aAMi2 - O.5PAM3 + YAG2 - 5AGi

(5)

AY3 = aAM3 - PAM12 + eAGi + 8AG2

(6)

Here AY^ denotes the initial output gap in Germany, AY2 is the initial output gap in France, AY3 is the initial output gap in America, AM12 is the required increase in European money supply, AM3 is the required increase in American money supply, AG^ is the required increase in German government purchases, and AG2 is the required increase in French government purchases. The endogenous variables are AM12, AM3, AG^ and AG2. We now introduce a fourth target. We assume that the increase in German government purchases should be equal in size to the reduction in French government purchases: AGi+AG2=0

(7)

Put another way, we assume that the sum total of European government purchases should be constant. Add up equations (4) and (5), taking account of equation (7), to find out: AYi + AY2 = aAMi2 - PAM3

(8)

139

To simplify notation we introduce AY12 = ^^i + ^ ^ 2 , where AY12 is the initial output gap in Europe. This yields: AYi2=aAMi2-PAM3

(9)

Taking account of equation (7), equation (6) can be written as follows: AY3=aAM3-|3AMi2

(10)

Then solve equations (9) and (10) for: ocAY,,+6AYo

^^3 =

aAY3+pAYi2 i .2 ''

(12)

Further subtract equation (5) from equation (4) to find out: AYi - AY2 = (Y + 5)(AGi - AG2)

(13)

Then solve equations (7) and (13) for:

AG.=

2

AY,-^ 2(Y + 5)

(14)

AYo - AY, ^ ^

(15)

2(Y + 5)

According to equation (11), the required increase in European money supply depends on the initial output gap in Europe, the initial output gap in America, the direct multiplier a , and the cross multipUer (3. According to equation (12), the required increase in American money supply depends on the initial output gap in America, the initial output gap in Europe, the direct multiplier a , and the cross

140 multiplier p. According to equation (14), the required increase in German govemment purchases depends on the initial output gap in Germany, the initial output gap in France, the direct multiplier y, and the cross multiplier 6. According to equation (15), the required increase in French govemment purchases depends on the initial output gap in France, the initial output gap in Germany, the direct multiplier y, and the cross multiplier 5.

2. Some Numerical Examples

To illustrate the policy model, have a look at some numerical examples. For ease of exposition, without losing generality, assume a = 3, (3 = 1, y = 1.5, 5 = 0.5 and 8 = 1. An increase in European money supply of 100 causes an increase in German output of 150, an increase in French output of equally 150, and a decline in American output of 100. Similarly, an increase in American money supply of 100 causes an increase in American output of 300, a decline in German output of 50, and a decline in French output of equally 50. An increase in French govemment purchases of 100 causes an increase in French output of 150, a decline in German output of 50, and an increase in American output of 100. Further let full-employment output in Germany be 1000, let full-employment output in France be equally 1000, and let full-employment output in America be 2000. It proves useful to study five distinct cases: - the case of unemployment - Europe and America differ in unemployment - the case of inflation - unemployment in Europe, inflation in America - altemative targets of policy cooperation. 1) The case of unemployment. Let initial output in Germany be 940, let initial output in France be 970, and let initial output in America be 1910. In each of the countries there is unemployment and deflation. Step 1 refers to the policy

141 response. The output gap in Germany is 60, the output gap in France is 30, the output gap in Europe is 90, and the output gap in America is equally 90. So what is needed, according to equations (11), (12), (14) and (15) from the preceding section, is an increase in European money supply of 45, an increase in American money supply of equally 45, an increase in German government purchases of 7.5, and a reduction in French government purchases of equally 7.5. Step 2 refers to the output lag. The increase in European money supply of 45 raises German output and French output by 67.5 each. On the other hand, it lowers American output by 45. The increase in American money supply of 45 raises American output by 135. On the other hand, it lowers German output and French output by 22.5 each. The increase in German government purchases of 7.5 raises German output by 11.3. On the other hand, it lowers French output by 3.8. And what is more, it raises American output by 7.5. The reduction in French government purchases of 7.5 lowers French output by 11.3. On the other hand, it raises German output by 3.8. And what is more, it lowers American output by 7.5. The net effect is an increase in German output of 60, an increase in French output of 30, and an increase in American output of 90. As a consequence, German output goes from 940 to 1000, French output goes from 970 to 1000, and American output goes from 1910 to 2000. In each of the countries there is now full employment and price stability. As a result, cooperation between the European central bank, the American central bank, the German government, and the French government can achieve full employment in Germany, France and America. Over and above that, it can achieve price stability in Germany, France and America. Table 4.11 presents a synopsis. Finally compare policy cooperation with policy competition. Under pohcy competition, the total increase in European money supply is 33.8, the total increase in American money supply is equally 33.8, the total increase in German government purchases is 18.8, the total increase in French government purchases is 3.8, and the total increase in European government purchases is 22.5. That means, the solution to policy cooperation is different from the steady state of policy competition. Under policy competition, there is a small increase in money supply and a large increase in government purchases. Under policy cooperation, however, there is a large increase in money supply and a zero increase in

142 government purchases. Judging from this perspective, poUcy cooperation seems to be superior to poUcy competition.

Table 4.11 Cooperation between European Central Bank, American Central Bank, German Government, and French Government The Case of Unemployment

Initial Output

Germany

France

America

940

970

1910

45

45

A Money Supply A Government Purchases Output

7.5 1000

-7.5 1000

2000

2) Europe and America differ in unemployment. Let initial output in Germany be 940, let initial output in France be 970, and let initial output in America be 1880. In each of the countries there is unemployment and deflation. Step 1 refers to the policy response. The output gap in Germany is 60, the output gap in France is 30, the output gap in Europe is 90, and the output gap in America is 120. So what is needed, according to equations (11), (12), (14) and (15) from the previous section, is an increase in European money supply of 48.8, an increase in American money supply of 56.3, an increase in German government purchases of 7.5, and a reduction in French government purchases of equally 7.5. Step 2 refers to the output lag. The net effect is an increase in German output of 60, an increase in French output of 30, and an increase in American output of 120. As a consequence, German output goes to 1000, French output goes to 1000 too, and American output goes to 2000. In each of the countries there is now full employment and price stability. Table 4.12 gives an overview.

143 Table 4.12 Cooperation between European Central Bank, American Central Bank, German Government, and French Government Europe and America Differ in Unemployment

Initial Output

Germany

France

America

940

970

1880

A Money Supply A Government Purchases Output

48.8 7.5 1000

1

56.3

-7.5 1000

2000

3) The case of inflation. Let initial output in Germany be 1060, let initial output in France be 1030, and let initial output in America be 2120. In each of the countries there is overemployment and inflation. Step 1 refers to the policy response. The inflationary gap in Germany is 60, the inflationary gap in France is 30, the inflationary gap in Europe is 90, and the inflationary gap in America is 120. What is needed, then, is a reduction in European money supply of 48.8, a reduction in American money supply of 56.3, a reduction in German government purchases of 7.5, and an increase in French government purchases of equally 7.5. Step 2 refers to the output lag. The net effect is a decline in German output of 60, a decUne in French output of 30, and a decUne in American output of 120. As a consequence, German output goes to 1000, French output also goes to 1000, and American output goes to 2000. In each of the countries there is now full employment and price stability. Table 4.13 presents a synopsis.

144 Table 4.13 Cooperation between European Central Bank, American Central Bank, German Government, and French Government The Case of Inflation

Initial Output

Germany

France

America

1060

1030

2120

1

-48.8

- 56.3

1

A Money Supply A Government Purchases Output

-7.5 1000

7.5 1000

2000

4) Unemployment in Europe, inflation in America. Let initial output in Germany be 940, let initial output in France be 970, and let initial output in America be 2120. In Germany there is unemployment and deflation. In France there is unemployment and deflation as well. But in America there is overemployment and inflation. Step 1 refers to the policy response. The output gap in Germany is 60, the output gap in France is 30, the output gap in Europe is 90, and the output gap in America is -120. What is needed, then, is an increase in European money supply of 18.8, a reduction in American money supply of 33.8, an increase in German government purchases of 7.5, and a reduction in French government purchases of equally 7.5. Step 2 refers to the output lag. The net effect is an increase in German output of 60, an increase in French output of 30, and a decline in American output of 120. As a consequence, German output goes to 1000, French output goes to 1000 too, and American output goes to 2000. In each of the countries there is now full employment and price stability. Table 4.14 gives an overview. 5) Comparing policy cooperation with poUcy competition. Policy competition can achieve full employment in Germany, France and America. The same applies to policy cooperation. Policy competition is a slow process. By contrast, policy cooperation is a fast process. PoUcy competition causes some change in European government purchases. By contrast, policy cooperation does not cause

145 any change in European government purchases. Judging from these points of view, pohcy cooperation seems to be superior to poHcy competition. It is worth pointing out here that the solution to policy cooperation is different from the steady state of policy competition.

Table 4.14 Cooperation between European Central Bank, American Central Bank, German Government, and French Government Unemployment in Europe, Inflation in America

Initial Output

Germany

France

America

940

970

2120

1

-33.8

1

18.8

A Money Supply A Government Purchases Output

7.5 1000

-7.5 1000

2000

6) Alternative targets of policy cooperation. We assume here that the fourth target of poUcy cooperation is no increase in national government purchases. Let initial output in Germany be 940, let initial output in France be 970, and let initial output in America be 1880. In each of the countries there is unemployment and deflation. Step 1 refers to the policy response. The output gap in Germany is 60, the output gap in France is 30, and the output gap in America is 120. What is needed, then, is an increase in European money supply of 56.3, an increase in American money supply of 63.8, a change in German government purchases of zero, and a reduction in French government purchases of 15. Step 2 refers to the output lag. The net effect is an increase in German output of 60, an increase in French output of 30, and an increase in American output of 120. As a consequence, German output goes to 1000, French output also goes to 1000, and American output goes to 2000. In each of the countries there is now full employment and price stability. Table 4.15 presents a synopsis.

146 Table 4.15 Cooperation between European Central Bank, American Central Bank, German Government, and French Government No Increase in Government Purchases

Initial Output

Germany

France

America

940

970

1880

A Money Supply A Government Purchases Output

56.3 0

-15

1000

1000

63.8 2000

1

Part Five Monetary and Fiscal Interactions Advanced Models

Chapter 1 Cold-Turkey Policies: Simultaneous Decisions

This chapter deals with competition between the European central bank, the American central bank, the German government, and the French government. So far we have assumed that the central banks and the governments decide sequentially. First the central banks decide, then the governments decide. Now we assume that the central banks and the governments decide simultaneously and independently. As a point of reference, consider the static model. It can be represented by a system of three equations: Yi =Ai+1.5Mi2-0.5M3+1.5Gi-0.5G2

(1)

Y2 = A2 +1.5Mi2 - O.5M3 +1.5G2 - 0.5Gi

(2)

Y3 =A3+3M3~Mi2H-Gi+G2

(3)

The endogenous variables are German output, French output, and American output. Obviously, an increase in European money supply of 100 causes an increase in German output of 150, an increase in French output of equally 150, and a decline in American output of 100. An increase in American money supply of 100 causes an increase in American output of 300, a decline in German output of 50, and a decline in French output of equally 50. An increase in German government purchases of 100 causes an increase in German output of 150, a decline in French output of 50, and an increase in American output of 100. Correspondingly, an increase in French government purchases of 100 causes an increase in French output of 150, a decline in German output of 50, and an increase in American output of 100. Further let full-employment output in Germany be 1000, let full-employment output in France be equally 1000, and let full-employment output in America be 2000. At the beginning there is unemployment in Germany, France and America. More precisely, unemployment in Germany exceeds unemployment in France.

150 The primary target of the European central bank is price stability in Europe. The secondary target of the European central bank is high employment in Germany and France. The specific target of the European central bank is that unemployment in Germany equals overemployment in France. In other words, deflation in Germany equals inflation in France. So there is price stability in Europe. In a sense, the specific target of the European central bank is full employment in Europe. The target of the American central bank is full employment in America. The target of the German govemment is full employment in Germany. And the target of the French govemment is full employment in France. We assume that the central banks and the govemments decide simultaneously and independently. In step 1, the European central bank, the American central bank, the German govemment, and the French govemment decide simultaneously and independently. In step 2, the European central bank, the American central bank, the German govemment, and the French govemment decide simultaneously and independently. And so on. For a small-scale model see Carlberg (2004) p. 137. Let initial output in Germany be 940, let initial output in France be 970, and let initial output in America be 1910. In each of the countries there is unemployment and deflation. Step 1 refers to the policy response. First consider monetary policy in Europe. The output gap in Europe is 90. The monetary policy multiplier in Europe is 3. So what is needed in Europe is an increase in European money supply of 30. Second consider monetary policy in America. The output gap in America is 90. The monetary policy multiplier in America is 3. So what is needed in America is an increase in American money supply of 30. Third consider fiscal policy in Germany. The output gap in Germany is 60. The fiscal policy multiplier in Germany is 1.5. So what is needed in Germany is an increase in German govemment purchases of 40. Fourth consider fiscal policy in France. The output gap in France is 30. The fiscal policy multiplier in France is 1.5. So what is needed in France is an increase in French govemment purchases of 20. Step 2 refers to the output lag. The increase in European money supply of 30 causes an increase in German output of 45 and an increase in French output of equally 45. As a side effect, it causes a decline in American output of 30. The increase in American money supply of 30 causes an increase in American output

151 of 90. As a side effect, it causes a decline in German output of 15 and a decline in French output of equally 15. The increase in German government purchases of 40 causes an increase in German output of 60. As a side effect, it causes a decUne in French output of 20 and an increase in American output of 40. The increase in French government purchases of 20 causes an increase in French output of 30. As a side effect, it causes a decUne in German output of 10 and an increase in American output of 20. The net effect is an increase in German output of 80, an increase in French output of 40, and an increase in American output of 120. As a consequence, German output goes from 940 to 1020, French output goes from 970 to 1010, and American output goes from 1910 to 2030. Step 3 refers to the policy response. First consider monetary policy in Europe. The inflationary gap in Europe is 30. The monetary policy multiplier in Europe is 3. So what is needed in Europe is a reduction in European money supply of 10. Second consider monetary policy in America. The inflationary gap in America is 30. The monetary policy multipUer in America is 3. So what is needed in America is a reduction in American money supply of 10. Third consider fiscal policy in Germany. The inflationary gap in Germany is 20. The fiscal policy multiplier in Germany is 1.5. So what is needed in Germany is a reduction in German government purchases of 13.3. Fourth consider fiscal policy in France. The inflationary gap in France is 10. The fiscal policy multiplier in France is 1.5. So what is needed in France is a reduction in French government purchases of 6.7. Step 4 refers to the output lag. The reduction in European money supply of 10 causes a decline in German output of 15 and a decline in French output of equally 15. As a side effect, it causes an increase in American output of 10. The reduction in American money supply of 10 causes a decline in American output of 30. As a side effect, it causes an increase in German output of 5 and an increase in French output of equally 5. The reduction in German government purchases of 13.3 causes a decline in German output of 20. As a side effect, it causes an increase in French output of 6.7 and a decline in American output of 13.3. The reduction in French government purchases of 6.7 causes a dechne in French output of 10. As a side effect, it causes an increase in German output of 3.3 and a decline in American output of 6.7. The net effect is a decline in German output of 26.7, a decline in French output of 13.3, and a decline in American

152 output of 40. As a consequence, German output goes from 1020 to 993.3, French output goes from 1010 to 996.7, and American output goes from 2030 to 1990. Step 5 refers to the poUcy response. The output gap in Europe is 10. So what is needed in Europe is an increase in European money supply of 3.3. The output gap in America is 10. So what is needed in America is an increase in American money supply of 3.3. The output gap in Germany is 6.7. So what is needed in Germany is an increase in German government purchases of 4.4. The output gap in France is 3.3. So what is needed in France is an increase in French government purchases of 2.2. Step 6 refers to the output lag. The net effect is an increase in German output of 8.9, an increase in French output of 4.4, and an increase in American output of 13.3. As a consequence, German output goes from 993.3 to 1002.2, French output goes from 996.7 to 1001.1, and American output goes from 1990 to 2003.3. And so on. Table 5.1 presents a synopsis. In the steady state, German output is 1000, French output is equally 1000, and American output is 2000. In each of the countries there is full employment and price stability. As a result, the simultaneous process of monetary and fiscal competition leads to full employment in Germany, France and America. And what is more, it leads to price stability in Germany, France and America. What are the dynamic characteristics of this process? There are damped oscillations in money supply, government purchases and output. The German economy oscillates between unemployment and overemployment, as does the French economy and the American economy. Taking the sum over all periods, the total increase in European money supply is 22.5, the total increase in American money supply is equally 22.5, the total increase in German govemment purchases is 30, and the total increase in French government purchases is 15. Now compare simultaneous decisions with sequential decisions, see Chapter 3 of Part Four. Under sequential decisions, the total increase in European money supply is 33.8, the total increase in American money supply is equally 33.8, the total increase in German government purchases is 18.8, and the total increase in French govemment purchases is 3.8. That means, the steady state under

153 simultaneous decisions is different from the steady state under sequential decisions. Under sequential decisions there is a large increase in money supply and a small increase in government purchases. Under simultaneous decisions, however, there is a small increase in money supply and a large increase in government purchases. Judging from this perspective, sequential decisions seem to be superior to simultaneous decisions.

Table 5J Cold-Turkey Policies: Simultaneous Decisions

Initial Output

Germany

France

America

940

970

1910

30

30

A Money Supply A Government Purchases Output

40

20

1020

1010

2030

1

-10

-10

1

1990

1

A Money Supply A Government Purchases

-13.3

-6.7

Output

993.3

996.7 3.3

A Money Supply A Government Purchases

1 Output

3.3

4.4

2.2

1002.2

1001.1

2003.3

1000

1000

2000

and so on Steady-State Output

1

1

154

Generally speaking, the total increase in European money supply depends on: - the initial output gap in Germany - the initial output gap in France - the initial output gap in America - the direct policy multipliers a and y - the cross poUcy multipliers p and 5 - the type of coordination mechanism (ie cold-turkey policies, simultaneous decisions). And the same holds for the total increase in American money supply, the total increase in German government purchases, and the total increase in French government purchases.

Chapter 2 Gradualist Policies: Simultaneous Decisions

This chapter is concerned with competition between the European central bank, the American central bank, the German government, and the French government. So far we have assumed that the central banks and the governments follow a cold-turkey strategy. Now we assume that the central banks and the governments follow a gradualist strategy. In addition, we assume that the central banks and the governments decide simultaneously and independently. In the numerical example, an increase in European money supply of 100 causes an increase in German output of 150, an increase in French output of equally 150, and a decline in American output of 100. An increase in American money supply of 100 causes an increase in American output of 300, a dechne in German output of 50, and a decHne in French output of equally 50. An increase in German government purchases of 100 causes an increase in German output of 150, a decline in French output of 50, and an increase in American output of 100. Correspondingly, an increase in French government purchases of 100 causes an increase in French output of 150, a decline in German output of 50, and an increase in American output of 100. Further let full-employment output in Germany be 1000, let full-employment output in France be equally 1000, and let full-employment output in America be 2000. At the start there is unemployment in Germany, France and America. More precisely, unemployment in Germany exceeds unemployment in France. The general target of the European central bank is full employment in Europe. We assume that the European central bank follows a gradualist strategy. The specific target of the European central bank is to close the output gap in Europe by 80 percent. The general target of the American central bank is full employment in America. We assume that the American central bank follows a graduaUst strategy. The specific target of the American central bank is to close the output gap in America by 80 percent. The general target of the German government is full employment in Germany. We assume that the German government follows a gradualist strategy. The specific target of the German government is to close the

156 output gap government govemment govemment

in Germany by 20 percent. The general target of the French is full employment in France. We assume that the French follows a gradualist strategy. The specific target of the French is to close the output gap in France by 20 percent.

We assume that the central banks and the govemments decide simultaneously and independently. In step 1, the European central bank, the American central bank, the German govemment, and the French govemment decide simultaneously and independently. In step 2, the European central bank, the American central bank, the German govemment, and the French govemment decide simultaneously and independently. And so on. For a small-scale model see Carlberg (2004) p. 154. Let initial output in Germany be 940, let initial output in France be 970, and let initial output in America be 1910. In each of the countries there is unemployment and deflation. Step 1 refers to the policy response. First consider monetary policy in Europe. The output gap in Europe is 90. The specific target of the European central bank is to close the output gap in Europe by 80 percent, that is by 72. The monetary policy multiplier in Europe is 3. So what is needed in Europe is an increase in European money supply of 24. Second consider monetary policy in America. The output gap in America is 90. The specific target of the American central bank is to close the output gap in America by 80 percent, that is by 72. The monetary policy multiplier in America is 3. So what is needed in America is an increase in American money supply of 24. Third consider fiscal policy in Germany. The output gap in Germany is 60. The specific target of the German govemment is to close the output gap in Germany by 20 percent, that is by 12. The fiscal policy multiplier in Germany is 1.5. So what is needed in Germany is an increase in German govemment purchases of 8. Fourth consider fiscal policy in France. The output gap in France is 30. The specific target of the French govemment is to close the output gap in France by 20 percent, that is by 6. The fiscal policy multiplier in France is 1.5. So what is needed in France is an increase in French govemment purchases of 4. Step 2 refers to the output lag. The increase in European money supply of 24 causes an increase in German output of 36 and an increase in French output of equally 36. As a side effect, it causes a decline in American output of 24. The

157 increase in American money supply of 24 causes an increase in American output of 72. As a side effect, it causes a decline in German output of 12 and a decline in French output of equally 12. The increase in German government purchases of 8 causes an increase in German output of 12. As a side effect, it causes a decline in French output of 4 and an increase in American output of 8. The increase in French government purchases of 4 causes an increase in French output of 6. As a side effect, it causes a decline in German output of 2 and an increase in American output of 4. The net effect is an increase in German output of 34, an increase in French output of 26, and an increase in American output of 60. As a consequence, German output goes from 940 to 974, French output goes from 970 to 996, and American output goes from 1910 to 1970. Step 3 refers the policy response. First consider monetary policy in Europe. The output gap in Europe is 30. The specific target of the European central bank is to close the output gap in Europe by 80 percent, that is by 24. The monetary policy multiplier in Europe is 3. So what is needed in Europe is an increase in European money supply of 8. Second consider monetary policy in America. The output gap in America is 30. The specific target of the American central bank is to close the output gap in America by 80 percent, that is by 24. The monetary policy multiplier in America is 3. So what is needed in America is an increase in American money supply of 8. Third consider fiscal poHcy in Germany. The output gap in Germany is 26. The specific target of the German government is to close the output gap in Germany by 20 percent, that is by 5.2. The fiscal policy multiplier in Germany is 1.5. So what is needed in Germany is an increase in German government purchases of 3.5. Fourth consider fiscal policy in France. The output gap in France is 4. The specific target of the French government is to close the output gap in France by 20 percent, that is by 0.8. The fiscal policy multiplier in France is 1.5. So what is needed in France is an increase in French government purchases of 0.5. Step 4 refers to the output lag. The increase in European money supply of 8 causes an increase in German output of 12 and an increase in French output of equally 12. As a side effect, it causes a decline in American output of 8. The increase in American money supply of 8 causes an increase in American output of 24. As a side effect, it causes a decline in German output of 4 and a decHne in

158 French output of equally 4. The increase in German government purchases of 3.5 causes an increase in German output of 5.2. As a side effect, it causes a decUne in French output of 1.7 and an increase in American output of 3.5. The increase in French government purchases of 0.5 causes an increase in French output of 0.8. As a side effect, it causes a decUne in German output of 0.3 and an increase in American output of 0.5. The net effect is an increase in German output of 12.9, an increase in French output of 7.1, and an increase in American output of 20.0. As a consequence, German output goes from 974 to 986.9, French output goes from 996 to 1003.1, and American output goes from 1970 to 1990.0. Step 5 refers to the policy response. The output gap in Europe is 10. So what is needed in Europe is an increase in European money supply of 2.7. The output gap in America is 10. So what is needed in America is an increase in American money supply of 2.7. The output gap in Germany is 13.1. So what is needed in Germany is an increase in German government purchases of 1.8. The inflationary gap in France is 3.1. So what is needed in France is a reduction in French govemment purchases of 0.4. Step 6 refers to the output lag. The net effect is an increase in German output of 5.5, an increase in French output of 1.2, and an increase in American output of 6.7. As a consequence, German output goes from 986.9 to 992.4, French output goes from 1003.1 to 1004.3, and American output goes from 1990.0 to 1996.7. And so on. Table 5.2 gives an overview. In the steady state, German output is 1000, French output is equally 1000, and American output is 2000. In each of the countries there is full employment and price stability. As a result, the gradualist process of monetary and fiscal competition leads to full employment in Germany, France and America. And what is more, it leads to price stability in Germany, France and America. What are the dynamic characteristics of this process? There are repeated increases in European money supply, as there are in American money supply. There is an upward trend in German government purchases, as there is in French govemment purchases. There is an upward trend in German output, as there is in French output and American output. There is some overshooting in French government purchases and French output. Taking the sum over all periods, the total increase in European money supply is 36, the total increase in American

159 money supply is equally 36, the total increase in German government purchases is 16.5, and the total increase in French government purchases is 1.5.

Table 5.2 Gradualist Policies: Simultaneous Decisions

Initial Output

Germany

France

America

940

970

1910

24

24

A Money Supply A Government Purchases Output

8

4

974

996

1970

8

8

A Money Supply A Government Purchases Output

3.5

0.5

986.9

1003.1

1990.0

2.7

2.7

A Money Supply A Government Purchases Output

1.8

-0.4

992.4

1004.3

1996.7

1000

2000

1

1

1

and so on Steady-State Output

1000

Now compare graduaUst poUcies with cold-turkey policies, given simultaneous decisions, see Chapter 1 of Part Five. Under cold-turkey poHcies, the total increase in European money supply is 22.5, the total increase in American money supply is equally 22.5, the total increase in German government purchases is 30, and the total increase in French government purchases is 15. That means, under cold-turkey policies there is a small increase in money supply and a large increase in government purchases. Under gradualist policies, conversely, there is a large increase in money supply and a small increase in government purchases. Of course, this depends on the relative speed

160 of adjustment in money supply and government purchases. Judging from this point of view, gradualist policies seem to be superior to cold-turkey policies. Generally speaking, the total increase in European money supply depends on: - the initial output gap in Germany - the initial output gap in France - the initial output gap in America - the direct policy multipliers a and y - the cross policy multipliers (3 and 5 - the speed of adjustment in European money supply - the speed of adjustment in American money supply - the speed of adjustment in German government purchases - the speed of adjustment in French government purchases. And the same holds for the total increase in American money supply, the total increase in German government purchases, and the total increase in French govemment purchases.

Chapter 3 Fast Monetary Competition and Slow Fiscal Competition

This chapter deals with competition between the European central bank, the American central bank, the German government, and the French government. We assume that the central banks and the governments decide sequentially. First the central banks decide, then the governments decide. In steps 1, 2 and 3 the central banks decide. Then in steps 4 and 5 the governments decide. We assume that the central banks and the governments follow a cold-turkey strategy. And we assume that the policy spillovers are anticipated. In the numerical example, an increase in European money supply of 100 causes an increase in German output of 150, an increase in French output of equally 150, and a decline in American output of 100. An increase in American money supply of 100 causes an increase in American output of 300, a decline in German output of 50, and a decline in French output of equally 50. An increase in German government purchases of 100 causes an increase in German output of 150, a decline in French output of 50, and an increase in American output of 100. Correspondingly, an increase in French government purchases of 100 causes an increase in French output of 150, a decUne in German output of 50, and an increase in American output of 100. Further let full-employment output in Germany be 1000, let full-employment output in France be equally 1000, and let full-employment output in America be 2000. Let initial output in Germany be 940, let initial output in France be 970, and let initial output in America be 1910. In each of the countries there is unemployment and deflation. Now steps 1, 2 and 3 refer to monetary competition between Europe and America. Then steps 4 and 5 refer to fiscal competition between Germany and France. Finally step 6 refers to the output lag. Step 1 refers to monetary policy in Europe and America. The output gap in Europe is 90. The monetary poUcy multipUer in Europe is 3. So what is needed in Europe is an increase in European money supply of 30. The output gap in

162 America is 90. The monetary policy multiplier in America is 3. So what is needed in America is an increase in American money supply of 30. In step 2, the European central bank anticipates the effect of the increase in American money supply. And the American central bank anticipates the effect of the increase in European money supply. The European central bank expects that, due to the increase in American money supply of 30, German output will only rise to 970, and French output will only rise to 1000. The American central bank expects that, due to the increase in European money supply of 30, American output will only rise to 1970. The expected output gap in Europe is 30. The monetary policy multipher in Europe is 3. So what is needed in Europe is an increase in European money supply of 10. The expected output gap in America is 30. The monetary policy multiplier in America is 3. So what is needed in America is an increase in American money supply of 10. We now come to step 3. The European central bank expects that, due to the increase in American money supply of 10, German output will only rise to 980, and French output will only rise to 1010. The American central bank expects that, due to the increase in European money supply of 10, American output will only rise to 1990. The expected output gap in Europe is 10. The monetary policy multiplier in Europe is 3. So what is needed in Europe is an increase in European money supply of 3.3. The expected output gap in America is 10. The monetary policy multiplier in America is 3. So what is needed in America is an increase in American money supply of 3.3. Step 4 refers to fiscal policy in Germany and France. The German government anticipates the effect of the accumulated increase in European money supply and American money supply. And the same applies to the French government. The accumulated increase in European money supply is 43.3, and the accumulated increase in American money supply is equally 43.3. So the expected increase in European output is 86.7, and the expected increase in American output is equally 86.7. That is to say, the expected increase in German output is 43.3, and the expected increase in French output is equally 43.3. In other words, the German government expects that German output will only rise to 983.3. And the French government expects that French output will only rise to 1013.3. The expected output gap in Germany is 16.7. The fiscal poUcy multipher in Germany is 1.5. So what is needed in Germany is an increase in German

163 government purchases of 11.1. The expected inflationary gap in France is 13.3. The fiscal policy multiplier in France is 1.5. So what is needed in France is a reduction in French government purchases of 8.9. We now come to step 5. The German government expects that, due to the reduction in French government purchases of 8.9, German output will even rise to 1004.4. The French government expects that, due to the increase in German government purchases of 11.1, French output will only rise to 994.4. The expected inflationary gap in Germany is 4.4. The fiscal policy multipHer in Germany is 1.5. So what is needed in Germany is a reduction in German government purchases of 3.0. The expected output gap in France is 5.6. The fiscal policy multiplier in France is 1.5. So what is needed in France is an increase in French government purchases of 3.7. Step 6 refers to the output lag. The accumulated increase in European money supply of 43.3 raises German output and French output by 65 each. On the other hand, it lowers American output by 43.3. The accumulated increase in American money supply of 43.3 raises American output by 130. On the other hand, it lowers German output and French output by 21.7 each. The accumulated increase in German government purchases of 8.1 raises German output by 12.2. On the other hand, it lowers French output by 4.1. And what is more, it raises American output by 8.1. The accumulated reduction in French government purchases of 5.2 lowers French output by 7.8. On the other hand, it raises German output by 2.6. And what is more, it lowers American output by 5.2. The net effect is an increase in German output of 58.1, an increase in French output of 31.4, and an increase in American output of 89.6. As a consequence, German output goes from 940 to 998.1, French output goes from 970 to 1001.4, and American output goes from 1910 to 1999.6. In each of the countries there is nearly full employment and price stabiUty. As a result, the process of fast monetary competition and slow fiscal competition leads to full employment in Germany, France and America. Over and above that, it leads to price stability in Germany, France and America. Table 5.3 presents a synopsis. The total increase in Europe money supply is 43.3, the total increase in American money supply is equally 43.3, the total increase in German government purchases is 8.1, and the total reduction in French government

164 purchases is 5.2. That means, there is a large increase in money supply and a small increase in government purchases. Generally speaking, the total increase in European money supply depends upon the initial output gap in Germany, the initial output gap in France, the initial output gap in America, the policy multipliers (a,P,Y,§), and the type of coordination mechanism (ie fast monetary competition and slow fiscal competition). And the same holds for the total increase in American money supply, the total increase in German government purchases, and the total increase in French government purchases.

Table 5.3 Fast Monetary Competition, Slow Fiscal Competition Germany

France

America

940

970

1910

A Money Supply

30

30

A Money Supply

10

10

Initial Output

A Money Supply

3.3

A Government Purchases

11.1

-8.9

A Government Purchases

-3.0

3.7

998.1

1001.4

1 Output and so on Steady-State Output

1

3.3

1999.6

1

... 1000

1000

2000

1

Chapter 4 Monetary Cooperation between Europe and America, Fiscal Competition between Germany and France 1. The Model

1) The Static model. As a point of departure, consider the static model. It can be represented by a system of three equations: Yi = Ai + 0.5aMi2 ~ O.5PM3 + yGi - 862

(1)

Y2 = A2 + 0.5aMi2 - O.5PM3 + YG2 - 5Gi

(2)

Y3 = A3 + aM3 - PM12 + eGi + eG2

(3)

This is a reduced form of the basic model, see Part One. Y^ denotes German output, Y2 is French output, Y3 is American output, M12 is European money supply, M3 is American money supply, G^ is German government purchases, and G2 is French government purchases. The endogenous variables are German output, French output, and American output. Note that e = y -d. 2) The dynamic model. At the beginning there is unemployment in Germany, France and America. More precisely, unemployment in Germany is high, and unemployment in France is low. The targets of monetary cooperation are full employment in Europe and full employment in America. The instruments of monetary cooperation are European money supply and American money supply. Under monetary cooperation, there are two targets and two instruments, so there is no degree of freedom. The target of the German government is full employment in Germany. The instrument of the German government is German government purchases. The target of the French government is full employment in France. The instrument of the French government is French government purchases.

166 We assume that the central banks and the governments decide sequentially. First the central banks decide, then the governments decide. In step 1, the European central bank and the American central bank decide cooperatively. In step 2, the German government and the French government decide simultaneously and independently. In step 3, the European central bank and the American central bank decide cooperatively. In step 4, the German govemment and the French govemment decide simultaneously and independently. And so on. Now have a closer look at step 1. It refers to monetary cooperation between Europe and America. Taking differences in equations (1), (2) and (3), the model of monetary cooperation can be written as follows: AYi2=aAMi2-pAM3

(4)

AY3=aAM3-pA]V[i2

(5)

Here AY12 denotes the initial output gap in Europe, AY3 is the initial output gap in America, AM12 is the required increase in European money supply, and AM3 is the required increase in American money supply. The endogenous variables are AM12 and AM3. The solution to the system (4) and (5) is: aAYi2+PAY3

2. Some Numerical Examples

To illustrate the dynamic model, have a look at some numerical examples. For ease of exposition, without loss of generality, assume a = 3, p = l, y = 1.5, 5 = 0.5 and s = l. An increase in European money supply of 100 causes an

167 increase in German output of 150, an increase in French output of equally 150, and a decline in American output of 100. An increase in American money supply of 100 causes an increase in American output of 300, a decline in German output of 50, and a decline in French output of equally 50. An increase in German government purchases of 100 causes an increase in German output of 150, a decHne in French output of 50, and an increase in American output of 100. Further let full-employment output in Germany be 1000, let full-employment output in France be equally 1000, and let full-employment output in America be 2000. It proves useful to study three distinct cases: - the case of unemployment - the case of inflation - unemployment in Europe, inflation in America. 1) The case of unemployment. Let initial output in Germany be 940, let initial output in France be 970, and let initial output in America be 1880. In each of the countries there is unemployment and deflation. Step 1 refers to monetary cooperation between Europe and America. The output gap in Europe is 90, and the output gap in America is 120. So what is needed, according to equations (6) and (7) from the preceding section, is an increase in European money supply of 48.8 and an increase in American money supply of 56.3. Step 2 refers to the output lag. The increase in European money supply of 48.8 raises German output and French output by 73.1 each. On the other hand, it lowers American output by 48.8. The increase in American money supply of 56.3 raises American output by 168.8. On the other hand, it lowers German output and French output by 28.1 each. The net effect is an increase in German output of 45, an increase in French output of equally 45, and an increase in American output of 120. As a consequence, German output goes from 940 to 985, French output goes from 970 to 1015, and American output goes from 1880 to 2000. In Germany there is still some unemployment and deflation. In France there is now some overemployment and inflation. In Europe there is now full employment and price stability. And the same is true of America. Step 3 refers to fiscal competition between Germany and France. The output gap in Germany is 15. The fiscal poUcy multipUer in Germany is 1.5. So what is

168 needed in Germany is an increase in German government purchases of 10. The inflationary gap in France is 15. The fiscal poUcy multiplier in France is 1.5. So what is needed in France is a reduction in French government purchases of 10. Step 4 refers to the output lag. The increase in German government purchases of 10 causes an increase in German output of 15. As a side effect, it causes a decline in French output of 5 and an increase in American output of 10. The reduction in French government purchases of 10 causes a decline in French output of 15. As a side effect, it causes an increase in German output of 5 and a decUne in American output of 10. The net effect is an increase in German output of 20, a decline in French output of equally 20, and a change in American output of zero. As a consequence, German output goes from 985 to 1005, French output goes from 1015 to 995, and American output stays at 2000. In Germany there is now some overemployment and inflation. In France there is now some unemployment and deflation. In Europe there is still full employment and price stability. And the same is true of America. Step 5 refers to monetary cooperation between Europe and America. The output gap in Europe is zero, as is the output gap in America. So there is no need for a change in European money supply or American money supply. Step 6 refers to the output lag. As a consequence, German output stays at 1005, French output stays at 995, and American output stays at 2000. Step 7 refers to fiscal competition between Germany and France. The inflationary gap in Germany is 5. The fiscal policy multipUer in Germany is 1.5. So what is needed in Germany is a reduction in German government purchases of 3.3. The output gap in France is 5. The fiscal poUcy multipHer in France is 1.5. So what is needed in France is an increase in French government purchases of 3.3. Step 8 refers to the output lag. The reduction in German government purchases of 3.3 causes a decline in German output of 5. As a side effect, it causes an increase in French output of 1.7 and a decline in American output of 3.3. The increase in French government purchases of 3.3 causes an increase in French output of 5. As a side effect, it causes a decline in German output of 1.7 and an increase in American output of 3.3. The net effect is a decline in German output of 6.7, an increase in French output of equally 6.7, and a change in

169 American output of zero. As a consequence, German output goes from 1005 to 998.3, French output goes from 995 to 1001.7, and American output stays at 2000. In Germany there is now some unemployment and deflation. In France there is now some overemployment and inflation. In Europe there is still full employment and price stability. And the same is true of America. This process repeats itself round by round. Table 5.4 gives an overview.

Table 5.4 Monetary Cooperation between Europe and America, Fiscal Competition between Germany and France The Case of Unemployment Germany Initial Output

940

A Money Supply 1 Output A Government Purchases Output

A Government Purchases 1 Output

America

970

1880

48.8

56.3

1

995

2000

1

0

0

995

2000

1

1015

10

-10

1005

1005

1

2000

985

A Money Supply 1 Output

France

-3.3

3.3

998.3

1001.7

2000

1

1000

2000

1

and so on Steady-State Output

1000

In the steady state, German output is 1000, French output is equally 1000, and American output is 2000. In each of the countries there is full employment and price stability. As a result, the alternating process of monetary cooperation and fiscal competition leads to full employment in Germany, France and America. And what is more, it leads to price stability in Germany, France and America.

170 What are the dynamic characteristics of this process? There is a one-time increase in European money supply, as there is in American money supply. There are damped oscillations in German government purchases, as there are in French government purchases. There are damped oscillations in German output, as there are in French output. There is a one-time increase in American output. The German economy oscillates between unemployment and overemployment, as does the French economy. There is an appreciation of the euro and a depreciation of the dollar. There is a cut in European exports and an increase in American exports. There is a cut in the world interest rate. There is an increase in European investment, as there is in American investment. There is a cut in the European budget deficit, as there is in the American budget deficit. Taking the sum over all periods, the total increase in European money supply is 48.8, the total increase in American money supply is 56.3, the total increase in German government purchases is 7.5, and the total reduction in French government purchases is equally 7.5. Generally speaking, the total increase in European money supply depends on the type of coordination mechanism (ie monetary cooperation between Europe and America, fiscal competition between Germany and France). And the same holds for the total increase in American money supply, the total increase in German government purchases, and the total increase in French government purchases. Finally compare the system of monetary cooperation and fiscal competition with the system of monetary and fiscal competition, see Chapter 3 of Part Four. Under monetary and fiscal competition, the total increase in European money supply is 34.7, the total increase in American money supply is 42.2, the total increase in German government purchases is 21.6, and the total increase in French government purchases is 6.6. That is to say, under monetary and fiscal competition, we have a small increase in money supply and a large increase in government purchases. Under monetary cooperation and fiscal competition, however, we have a large increase in money supply and a small increase in government purchases. Judging from this perspective, the system of monetary cooperation and fiscal competition seems to be superior to the system of monetary and fiscal competition. 2) The case of inflation. Let initial output in Germany be 1060, let initial output in France be 1030, and let initial output in America be 2120. In each of

171 the countries there is overemployment and inflation. Step 1 refers to monetary cooperation between Europe and America. The inflationary gap in Europe is 90, and the inflationary gap in America is 120. What is needed, then, is a reduction in European money supply of 48.8 and a reduction in American money supply of 56.3. Step 2 refers to the output lag. The net effect is a decline in German output of 45, a decline in French output of equally 45, and a decline in American output of 120. As a consequence, German output goes from 1060 to 1015, French output goes from 1030 to 985, and American output goes from 2120 to 2000. In Germany there is still some overemployment and inflation. In France there is now some unemployment and deflation. In Europe there is now full employment and price stability. And the same holds for America. Step 3 refers to fiscal competition between Germany and France. The inflationary gap in Germany is 15. The fiscal policy multiplier in Germany is 1.5. So what is needed in Germany is a reduction in German government purchases of 10. The output gap in France is 15. The fiscal policy multiplier in France is 1.5. So what is needed in France is an increase in French government purchases of 10. Step 4 refers to the output lag. The net effect is a decline in German output of 20, an increase in French output of equally 20, and a change in American output of zero. As a consequence, German output goes from 1015 to 995, French output goes from 985 to 1005, and American output stays at 2000. Step 5 refers to fiscal competition between Germany and France. The output gap in Germany is 5. The fiscal policy multiplier in Germany is 1.5. So what is needed in Germany is an increase in German government purchases of 3.3. The inflationary gap in France is 5. The fiscal policy multiplier in France is 1.5. So what is needed in France is a reduction in French government purchases of 3.3. Step 6 refers to the output lag. The net effect is an increase in German output of 6.7, a decline in French output of equally 6.7, and a change in American output of zero. As a consequence, German output goes from 995 to 1001.7, French output goes from 1005 to 998.3, and American output stays at 2000. And so on. Table 5.5 presents a synopsis.

172

In the steady state, German output is 1000, French output is equally 1000, and American output is 2000. In each of the countries there is full employment and price stability. What are the dynamic characteristics of this process? There is a one-time cut in European money supply, as there is in American money supply. There are damped oscillations in German government purchases, as there are in French government purchases. There are damped oscillations in German output, as there are in French output. And there is a one-time cut in American output. Taking the sum over all periods, the total reduction in European money supply is 48.8, the total reduction in American money supply is 56.3, the total reduction in German government purchases is 7.5, and the total increase in French government purchases is equally 7.5.

Table 5.5 Monetary Cooperation between Europe and America, Fiscal Competition between Germany and France The Case of Inflation

Germany Initial Output

1060

A Money Supply 1 Output A Government Purchases 1 Output A Government Purchases 1 Output

France

America

1030

2120

1

-48.8

- 56.3 2000

1 1

2000

1

2000

1

2000

1

1015

985

-10

10

995

1005

3.3

-3.3

1001.7

998.3

and so on 1 Steady-State Output

1000

1000

3) Unemployment in Europe, inflation in America. Let initial output in Germany be 940, let initial output in France be 970, and let initial output in

173 America be 2120. In Germany there is unemployment and deflation. In France there is unemployment and deflation too. But in America there is overemployment and inflation. Step 1 refers to monetary cooperation between Europe and America. The output gap in Europe is 90, and the inflationary gap in America is 120. What is needed, then, is an increase in European money supply of 18.8 and a reduction in American money supply of 33.8. Step 2 refers to the output lag. The net effect is an increase in German output of 45, an increase in French output of equally 45, and a decline in American output of 120. As a consequence, German output goes from 940 to 985, French output goes from 970 to 1015, and American output goes from 2120 to 2000. Step 3 refers to fiscal competition between Germany and France. The output gap in Germany is 15. The fiscal policy multiplier in Germany is 1.5. So what is needed in Germany is an increase in German government purchases of 10. The inflationary gap in France is 15. The fiscal policy multiplier in France is 1.5. So what is needed in France is a reduction in French government purchases of 10. Step 4 refers to the output lag. The net effect is an increase in German output of 20, a decline in French output of equally 20, and a change in American output of zero. As a consequence, German output goes from 985 to 1005, French output goes from 1015 to 995, and American output stays at 2000. This process repeats itself round by round. Table 5.6 gives an overview. In the steady state, German output is 1000, French output is equally 1000, and American output is 2000. In each of the countries there is full employment and price stability. What are the dynamic characteristics of this process? There is a one-time increase in European money supply. There is a one-time cut in American money supply. There are damped oscillations in German government purchases, as there are in French government purchases. There are damped oscillations in German output, as there are in French output. And there is a onetime cut in American output. Taking the sum over all periods, the total increase in European money supply is 18.8, the total reduction in American money supply is 33.8, the total increase in German government purchases is 7.5, and the total reduction in French government purchases is equally 7.5.

174 Table 5.6 Monetary Cooperation between Europe and America, Fiscal Competition between Germany and France Unemployment in Europe, Inflation in America Germany Initial Output

940

A Money Supply 1 Output A Government Purchases 1 Output A Government Purchases 1 Output

France

America

970

2120

1

- 33.8 2000

1 1

2000

1

18.8 985

1015

10

-10

1005

995

-3.3

3.3

998.3

1001.7

2000

1

1000

2000

1

and so on Steady-State Output

1000

4) Comparison. Finally compare the system of monetary cooperation and fiscal competition with the system of monetary and fiscal competition, see Chapter 3 of Part Four. Monetary and fiscal competition is a relatively slow process. Monetary cooperation and fiscal competition, by contrast, is a relatively fast process. Monetary and fiscal competition causes some change in European government purchases. Monetary cooperation and fiscal competition does not cause any change in European government purchases. Judging from these points of view, the system of monetary cooperation and fiscal competition seems to be superior to the system of monetary and fiscal competition.

Chapter 5 Monetary Cooperation between Europe and America, Fiscal Cooperation between Germany and France 1. The Model

1) The Static model. As a point of reference, consider the static model. It can be characterized by a system of three equations: Yi = Ai + 0.5aMi2 - O.5PM3 + yGi - 862

(1)

Y2 = A2 + 0.5aMi2 " O.5PM3 + YG2 - 6G1

(2)

Y3 = A3 + aM3 - pMi2 + eOi + 8G2

(3)

This is a reduced form of the basic model, see Part One. Yj denotes German output, Y2 is French output, Y3 is American output, M12 is European money supply, M3 is American money supply, G^ is German government purchases, and G2 is French government purchases. The endogenous variables are German output, French output, and American output. Note that 8 = y ~ 5. 2) The dynamic model. At the beginning there is unemployment in Germany, France and America. More precisely, unemployment in Germany is high, and unemployment in France is low. The targets of monetary cooperation are full employment in Europe and full employment in America. The instruments of monetary cooperation are European money supply and American money supply. Under monetary cooperation, there are two targets and two instruments, so there is no degree of freedom. The targets of fiscal cooperation are full employment in Germany and full employment in France. The instruments of fiscal cooperation are German government purchases and French government purchases. Under fiscal cooperation, there are two targets and two instruments, so there is no degree of freedom.

176 We assume that the central banks and the governments decide sequentially. First the central banks decide, then the governments decide. In step 1, the European central bank and the American central bank decide cooperatively. In step 2, the German government and the French government decide cooperatively. In step 3, the European central bank and the American central bank decide cooperatively. In step 4, the German government and the French government decide cooperatively. And so on. Now have a closer look at step 1. It refers to monetary cooperation between Europe and America. Taking differences in equations (1), (2) and (3), the model of monetary cooperation can be written as follows: AYi2=aAMi2-PAM3

(4)

AY3=aAM3-PAMi2

(5)

Here AY12 denotes the initial output gap in Europe, AY3 is the initial output gap in America, AM12 is the required increase in European money supply, and AM3 is the required increase in American money supply. The endogenous variables are AM12 and AM3. The solution to the system (4) and (5) is:

Step 2 refers to the output lag. Next have a closer look at step 3. It refers to fiscal cooperation between Germany and France. Taking differences in equations (1) and (2), the model of fiscal cooperation can be written as follows:

AYi = Y A G I - 5 A G 2

(8)

AY2=YAG2-5AGI

(9)

177 Here AY^ denotes the initial output gap in Germany, AY2 is the initial output gap in France, AG^ is the required increase in German government purchases, and AG2 is the required increase in French government purchases. The endogenous variables are AGj and AG2. The solution to the system (8) and (9) is: _YAYI+5AY2

AGi=^

\ . ^ Y^-5^

(10)

.o,=I^^» Step 4 refers to the output lag.

2. Some Numerical Examples

To illustrate the dynamic model, have a look at some numerical examples. For ease of exposition, without losing generality, assume a = 3, P = l, Y = l-5, 5 = 0.5 and 8 = 1. An increase in European money supply of 100 causes an increase in German output of 150, an increase in French output of equally 150, and a decline in American output of 100. An increase in American money supply of 100 causes an increase in American output of 300, a decline in German output of 50, and a decline in French output of equally 50. An increase in French government purchases of 100 causes an increase in French output of 150, a decline in German output of 50, and an increase in American output of 100. Further let full-employment output in Germany be 1000, let full-employment output in France be equally 1000, and let full-employment output in America be 2000. It proves useful to study three distinct cases: - the case of unemployment - the case of inflation

178 - unemployment in Europe, inflation in America. 1) The case of unemployment. Let initial output in Germany be 940, let initial output in France be 970, and let initial output in America be 1880. In each of the countries there is unemployment and deflation. Step 1 refers to monetary cooperation between Europe and America. The output gap in Europe is 90, and the output gap in America is 120. So what is needed, according to equations (6) and (7) from the preceding section, is an increase in European money supply of 48.8 and an increase in American money supply of 56.3. Step 2 refers to the output lag. The increase in European money supply of 48.8 raises German output and French output by 73.1 each. On the other hand, it lowers American output by 48.8. The increase in American money supply of 56.3 raises American output by 168.8. On the other hand, it lowers German output and French output by 28.1 each. The net effect is an increase in German output of 45, an increase in French output of equally 45, and an increase in American output of 120. As a consequence, German output goes from 940 to 985, French output goes from 970 to 1015, and American output goes from 1880 to 2000. In Germany there is still some unemployment and deflation. In France there is now some overemployment and inflation. In Europe there is now full employment and price stability. And the same is true of America. Step 3 refers to fiscal cooperation between Germany and France. The output gap in Germany is 15, and the inflationary gap in France is equally 15. So what is needed, according to equations (10) and (11), is an increase in German government purchases of 7.5 and a reduction in French government purchases of equally 7.5. Step 4 refers to the output lag. The increase in German government purchases of 7.5 raises German output by 11.3. On the other hand, it lowers French output by 3.8. And what is more, it raises American output by 7.5. The reduction in French government purchases of 7.5 lowers French output by 11.3. On the other hand, it raises German output by 3.8. And what is more, it lowers American output by 7.5. The net effect is an increase in German output of 15, a decline in French output of equally 15, and a change in American output of zero. As a consequence, German output goes from 985 to 1000, French output goes from

179 1015 to 1000, and American output stays at 2000. In each of the countries there is now full employment and price stability. Table 5.7 presents a synopsis. As a result, the sequential process of monetary cooperation and fiscal cooperation leads to full employment in Germany, France and America. Over and above that, it leads to price stability in Germany, France and America. What are the dynamic characteristics of this process? There is an increase in European money supply, as there is in American money supply. There is an increase in German government purchases and a reduction in French government purchases. There is no change in European government purchases. There is an appreciation of the euro and a depreciation of the dollar. There is a cut in European exports and an increase in American exports. There is a cut in the world interest rate. There is an increase in European investment, as there is in American investment. There is a cut in the European budget deficit, as there is in the American budget deficit.

Table 5.7 Monetary Cooperation between Europe and America, Fiscal Cooperation between Germany and France The Case of Unemployment

Initial Output

Germany

France

America

940

970

1880

48.8

A Money Supply Output A Government Purchases Output

985 7.5 1000

1015

1

56.3

2000

1

2000

1

-7.5 1000

Taking the sum over all periods, the total increase in European money supply is 48.8, the total increase in American money supply is 56.3, the total increase in German government purchases is 7.5, and the total reduction in French

180 government purchases is equally 7.5. Generally speaking, the total increase in European money supply depends on the type of coordination mechanism (i.e. monetary cooperation between Europe and America, fiscal cooperation between Germany and France). Now compare the sequential process of monetary cooperation and fiscal cooperation with the simultaneous process of monetary and fiscal cooperation, see Chapter 4 of Part Four. Under monetary and fiscal cooperation, the total increase in European money supply is 48.8, the total increase in American money supply is 56.3, the total increase in German govemment purchases is 7.5, and the total reduction in French govemment purchases is equally 7.5. That means, under monetary and fiscal cooperation, we have a large increase in money supply and a zero increase in govemment purchases. And the same applies to monetary cooperation and fiscal cooperation. Monetary and fiscal cooperation is a fast process. And much the same applies to monetary cooperation and fiscal cooperation. Judging from this perspective, the sequential process of monetary cooperation and fiscal cooperation seems to be equivalent to the simultaneous process of monetary and fiscal cooperation. In other words, there seems to be no need for full cooperation between the European central bank, the American central bank, the German govemment, and the French govemment. Next compare the sequential process of monetary cooperation and fiscal cooperation with the sequential process of monetary cooperation and fiscal competition, see Chapter 4 of Part Five. Under monetary cooperation and fiscal competition, we have a large increase in money supply and a zero increase in govemment purchases. And the same holds for monetary cooperation and fiscal cooperation. Monetary cooperation and fiscal competition is a process of intermediate speed. Monetary cooperation and fiscal cooperation, however, is a fast process. Judging from these points of view, the sequential process of monetary cooperation and fiscal cooperation seems to be superior to the sequential process of monetary cooperation and fiscal competition. 2) The case of inflation. Let initial output in Germany be 1060, let initial output in France be 1030, and let initial output in America be 2120. In each of the countries there is overemployment and inflation. Step 1 refers to monetary cooperation between Europe and America. The inflationary gap in Europe is 90, and the inflationary gap in America is 120. What is needed, then, is a reduction

181 in European money supply of 48.8 and a reduction in American money supply of 56.3. Step 2 refers to the output lag. The net effect is a decline in German output of 45, a decline in French output of equally 45, and a decHne in American output of 120. As a consequence, German output goes from 1060 to 1015, French output goes from 1030 to 985, and American output goes from 2120 to 2000. In Germany there is still some overemployment and inflation. In France there is now some unemployment and deflation. In Europe there is now full employment and price stability. And the same holds for America. Step 3 refers to fiscal cooperation between Germany and France. The inflationary gap in Germany is 15, and the output gap in France is equally 15. What is needed, then, is a reduction in German government purchases of 7.5 and an increase in French government purchases of equally 7.5. Step 4 refers to the output lag. The net effect is a decline in German output of 15, an increase in French output of equally 15, and a change in American output of zero. As a consequence, German output goes from 1015 to 1000, French output goes from 985 to 1000, and American output stays at 2000. In each of the countries there is now full employment and price stability. Table 5.8 gives an overview. There is a cut in European money supply, as there is in American money supply. There is a cut in German government purchases and an increase in French government purchases. There is no change in European government purchases.

182 Table 5.8 Monetary Cooperation between Europe and America, Fiscal Cooperation between Germany and France The Case of Inflation Germany Initial Output

1060

A Money Supply

1 Output A Government Purchases Output

France 1030 -48.8

1015 -7.5 1000

985

America

2120 - 56.3 2000

1 1 1

2000

1

7.5 1000

3) Unemployment in Europe, inflation in America. Let initial output in Germany be 940, let initial output in France be 970, and let initial output in America be 2120. In Germany there is unemployment and deflation. In France there is unemployment and deflation too. But in America there is overemployment and inflation. Step 1 refers to monetary cooperation between Europe and America. The output gap in Europe is 90, and the inflationary gap in America is 120. What is needed, then, is an increase in European money supply of 18.8 and a reduction in American money supply of 33.8. Step 2 refers to the output lag. The net effect is an increase in German output of 45, an increase in French output of equally 45, and a decline in American output of 120. As a consequence, German output goes from 940 to 985, French output goes from 970 to 1015, and American output goes from 2120 to 2000. Step 3 refers to fiscal cooperation between Germany and France. The output gap in Germany is 15, and the inflationary gap in France is equally 15. What is needed, then, is an increase in German government purchases of 7.5 and a reduction in French government purchases of equally 7.5. Step 4 refers to the output lag. The net effect is an increase in German output of 15, a decline in French output of equally 15, and a change in American output

183 of zero. As a consequence, German output goes from 985 to 1000, French output goes from 1015 to 1000, and American output stays at 2000. In each of the countries there is now full employment and price stability. Table 5.9 presents a synopsis. There is an increase in European money supply and a cut in American money supply. There is an increase in German government purchases and a cut in French government purchases. There is no change in European government purchases.

Table 5.9 Monetary Cooperation between Europe and America, Fiscal Cooperation between Germany and France Unemployment in Europe, Inflation in America

Initial Output

Germany

France

America

940

970

2120

18.8

A Money Supply

1 Output A Government Purchases Output

985 7.5 1000

1015

1

- 33.8

2000

1

2000

1

-7.5 1000

Chapter 6 Policy Cooperation within Europe, PoUcy Competition between Europe and America 1. The Model

1) The Static model. As a point of departure, consider the static model. It can be represented by a system of three equations: Yj = Ai + 0.5aMi2 - O.5PM3 + yGi - 862

(1)

Y2 = A2 + 0.5aMi2 - O.5PM3 + YG2 - 5Gi

(2)

Y3 = A3 + aM3 - PM12 + £Gi + 8G2

(3)

This is a reduced form of the basic model, see Part One. Y^ denotes German output, Y2 is French output, Y3 is American output, M12 is European money supply, M3 is American money supply, G^ is German government purchases, and G2 is French government purchases. The endogenous variables are German output, French output, and American output. Note that 8 = 7 - 8 . 2) The dynamic model. At the beginning there is unemployment in Germany, France and America. More precisely, unemployment in Germany is high, and unemployment in France is low. The policy makers are the European central bank, the American central bank, the German government, and the French government. There is cooperation between the European central bank, the German government, and the French government. There is competition between the European coalition and the American central bank. Here the term European coalition refers to cooperation between the European central bank, the German government, and the French government. The targets of policy cooperation within Europe are full employment in Germany and full employment in France. The third target is that the increase in German government purchases should be equal in size to the reduction in French

185 government purchases. Put another way, the sum total of European govemment purchases should be constant. The instruments of policy cooperation within Europe are European money supply, German govemment purchases, and French govemment purchases. Under policy cooperation within Europe, there are three targets and three instmments, so there is no degree of freedom. The target of the American central bank is full employment in America. And the instrument of the American central bank is American money supply. We assume that the European coalition and the American central bank decide simultaneously and independently. In step 1, the European coalition and the American central bank decide simultaneously and independently. In step 2, again, the European coalition and the American central bank decide simultaneously and independently. And so on. Now have a closer look at cooperation between the European central bank, the German govemment, and the French govemment. Taking differences in equations (1) and (2), the model of policy cooperation within Europe can be written as follows: AYi = 0.5aAMi2 + yAGi - 6AG2

(4)

AY2 = 0.5aAMi2 + yAG2 - 5AGi

(5)

Here AYj denotes the initial output gap in Germany, AY2 is the initial output gap in France, AM12 is the required increase in European money supply, AGj is the required increase in German govemment purchases, and AG2 is the required increase in French govemment purchases. The endogenous variables are AM12, AGj and AG2. Add up equations (4) and (5), taking account of AGj + AG2 = 0, to find out: ..^ AY1+AY2 AM12 = — a

... (6)

Then subtract equation (5) from equation (4), taking account of AGj + AG2 = 0, and solve for:

186

^

A](,-AY, 2(Y + 5)

2. A Numerical Example

To illustrate the dynamic model, have a look at a numerical example. For ease of exposition, without loss of generaUty, assume a = 3, P = l, Y = l-5, S = 0.5 and 8 = 1. An increase in European money supply of 100 causes an increase in German output of 150, an increase in French output of equally 150, and a decUne in American output of 100. An increase in American money supply of 100 causes an increase in American output of 300, a decline in German output of 50, and a decline in French output of equally 50. An increase in German government purchases of 100 causes an increase in German output of 150, a decline in French output of 50, and an increase in American output of 100. Further let fullemployment output in Germany be 1000, let full-employment output in France be equally 1000, and let full-employment output in America be 2000. Let initial output in Germany be 940, let initial output in France be 970, and let initial output in America be 1880. In each of the countries there is unemployment and deflation. Step 1 refers to the policy response. First consider cooperation between the European central bank, the German government, and the French government. The output gap in Germany is 60, and the output gap in France is 30. So what is needed, according to equations (6), (7) and (8) from the preceding section, is an increase in European money supply of 30, an increase in German government purchases of 7.5, and a reduction in French government purchases of equally 7.5. Second consider the policy of the American central bank. The output gap in America is 120. The monetary pohcy multiplier in America is 3. So what is needed in America is an increase in American money supply of 40.

187

Step 2 refers to the output lag. The increase in European money supply of 30 causes an increase in German output of 45 and an increase in French output of equally 45. As a side effect, it causes a decUne in American output of 30. The increase in German government purchases of 7.5 causes an increase in German output of 11.3 and a decline in French output of 3.8. As a side effect, it causes an increase in American output of 7.5. The reduction in French government purchases of 7.5 causes a decline in French output of 11.3 and an increase in German output of 3.8. As a side effect, it causes a decline in American output of 7.5. The increase in American money supply of 40 causes an increase in American output of 120. As a side effect, it causes a decline in German output of 20 and a decline in French output of equally 20. The net effect is an increase in German output of 40, an increase in French output of 10, and an increase in American output of 90. As a consequence, German output goes from 940 to 980, French output goes from 970 to 980, and American output goes from 1880 to 1970. In each of the countries there is still some unemployment and deflation. Strictly speaking, unemployment in Germany equals unemployment in France. Step 3 refers to the policy response. First consider cooperation between the European central bank, the German government, and the French government. The output gap in Germany is 20, and the output gap in France is equally 20. So what is needed, according to equations (6), (7) and (8) from the previous section, is an increase in European money supply of 13.3, a change in German government purchases of zero, and a change in French government purchases of equally zero. Second consider the poUcy of the American central bank. The output gap in America is 30. The monetary policy multiplier in America is 3. So what is needed in America is an increase in American money supply of 10. Step 4 refers to the output lag. The increase in European money supply of 13.3 causes an increase in German output of 20 and an increase in French output of equally 20. As a side effect, it causes a decline in American output of 13.3. The increase in American money supply of 10 causes an increase in American output of 30. As a side effect, it causes a decline in German output of 5 and a decline in French output of equally 5. The net effect is an increase in German output of 15, an increase in French output of equally 15, and an increase in

188 American output of 16.7. As a consequence, German output goes from 980 to 995, French output equally goes from 980 to 995, and American output goes from 1970 to 1986.7. Step 5 refers to the policy response. The output gap in Europe is 10. The monetary policy multiplier in Europe is 3. So what is needed in Europe is an increase in European money supply of 3.3. The output gap in America is 13.3. The monetary policy multiplier in America is 3. So what is needed in America is an increase in American money supply of 4.4. Step 6 refers to the output lag. The net effect is an increase in German output of 2.8, an increase in French output of equally 2.8, and an increase in American output of 10. As a consequence, German output goes from 995 to 997.8, French output equally goes from 995 to 997.8, and American output goes from 1986.7 to 1996.7. This process repeats itself round by round. Table 5.10 gives an overview. In the steady state, German output is 1000, French output is equally 1000, and American output is 2000. In each of the countries there is full employment and price stability. As a result, the process of policy competition between Europe and America leads to full employment in Germany, France and America. And what is more, it leads to price stability in Germany, France and America. What are the dynamic characteristics of this process? There are repeated increases in European money supply, as there are in American money supply. There is a one-time increase in German government purchases and a one-time reduction in French government purchases. There are repeated increases in German output, as there are in French output and American output. Taking the sum over all periods, the total increase in European money supply is 48.8, the total increase in American money supply is 56.3, the total increase in German government purchases is 7.5, and the total reduction in French government purchases is equally 7.5. Broadly speaking, the total increase in European money supply depends on the type of coordination mechanism (ie policy cooperation within Europe, policy competition between Europe and America). Coming to an end, compare the following two systems: - monetary cooperation between Europe and America, fiscal competition between Germany and France

189 (see Chapter 4 of Part Five) - policy cooperation within Europe, policy competition between Europe and America. Monetary cooperation and fiscal competition is a relatively fast process. On the other hand, policy competition between Europe and America is a relatively slow process. Judging from this perspective, the system of monetary cooperation and fiscal competition seems to be superior to the system of poUcy competition between Europe and America.

Table 5.10 Policy Cooperation within Europe, Policy Competition between Europe and America

Initial Output

Germany

France

America

940

970

1880

30

40

A Money Supply A Government Purchases Output

7.5 980

A Money Supply A Government Purchases 1 Output

A Government Purchases 1 Output

-7.5 980 13.3

0

0

995

995

A Money Supply

3.3 0

0

997.8

997.8

1970

1000

1000

1

10

1986.7

1

4.4 1 1996.7

and so on Steady-State Output

1

2000

1

Part Six Rational Policy Expectations

Chapter 1 Monetary Competition between Europe and America

1) The static model. As a point of reference, consider the static model. It can be represented by a system of three equations: Yi = Ai + 0.5aMi2 - O.5PM3

(1)

Y2 = A2 + 0.5aMi2 - O.5PM3

(2)

Y3=A3+aM3-PMi2

(3)

This is a reduced form of the basic model, see Part One. a and P are positive coefficients with a > (3. According to equation (1), German output is a positive function of European money supply and a negative function of American money supply. According to equation (2), French output is a positive function of European money supply and a negative function of American money supply. According to equation (3), American output is a positive function of American money supply and a negative function of European money supply. The static model can be compressed to a system of two equations: Yi2=Ai2+aMi2-PM3

(4)

Y3=A3+aM3-|3Mi2

(5)

According to equation (4), European output is a positive function of European money supply and a negative function of American money supply. According to equation (5), American output is a positive function of American money supply and a negative function of European money supply. 2) The dynamic model. At the beginning there is unemployment in both Europe and America. The target of the European central bank is full employment in Europe. The instrument of the European central bank is European money

194 supply. The target of the American central bank is full employment in America. The instrument of the American central bank is American money supply. We assume that the European central bank and the American central bank decide simultaneously and independently. The European central bank sets European money supply, forming rational expectations of American money supply. And the American central bank sets American money supply, forming rational expectations of European money supply. On this basis, the dynamic model can be characterized by a system of four equations: Yi2=Ai2+aMi2-PM^

(6)

Y3=A3+aM3-PMf2

(7)

Mf2=Mi2

(8)

M^ = M3

(9)

Here is a list of the new symbols: Y12 full-employment output in Europe Y3 full-employment output in America Mf2 the expectation of European money supply, as formed by the American central bank M3 the expectation of American money supply, as formed by the European central bank Mj2 European money supply, as set by the European central bank M3 American money supply, as set by the American central bank. According to equation (6), the European central bank sets European money supply, forming an expectation of American money supply. According to equation (7), the American central bank sets American money supply, forming an expectation of European money supply. According to equation (8), the expectation of European money supply is equal to the forecast made by means of the model. According to equation (9), the expectation of American money supply is equal to the forecast made by means of the model. That is to say, the European

195 central bank sets European money supply, predicting American money supply with the help of the model. And the American central bank sets American money supply, predicting European money supply with the help of the model. The endogenous variables are European money supply M12, American money supply M3, the expectation of European money supply Mf2, and the expectation of American money supply M3. The dynamic model can be condensed to a system of two equations: Yi2=Ai2+aMi2-PM3

(10)

Y3=A3+aM3-pMi2

(11)

Here the endogenous variables are European money supply M12 and American money supply M3. To simplify notation we introduce 6^2 = ^u ~ A12 and B3 = Y3 - A3. Then we solve the model for the endogenous variables:

O B ^

(12)

Equation (12) shows the equilibrium level of European money supply, and equation (13) shows the equilibrium level of American money supply. There is a solution if and only if a 5^ (3. This condition is fulfilled. As a result, under rational expectations, there is an immediate equilibrium of monetary competition between Europe and America. In other words, under rational expectations, monetary competition leads immediately to full employment in Europe and America. However, it does not lead to full employment in Germany and France. It is worth pointing out here that the equilibrium under rational expectations is identical to the steady state under adaptive expectations, see Chapter 1 of Part Two. As an alternative, the dynamic model can be stated in terms of the initial output gap and the required increase in money supply:

196 AYi2 = aAMi2 - PAM3

(14)

AY3=aAM3-pAMi2

(15)

Here AY12 denotes the initial output gap in Europe, AY3 is the initial output gap in America, AM12 is the required increase in European money supply, and AM3 is the required increase in American money supply. The endogenous variables are AM12 and AM3. The equilibrium of the system (14) and (15) is: ...

aAYi2+|3AY3

^Mi2=

^^^

2

02

_aAY3+PAYi2 .

.... (1^)

^j^^

3) A numerical example. To illustrate the dynamic model, have a look at a numerical example. For ease of exposition, without loss of generality, assume a = 3 and p = 1. On this assumption, the static model can be written as follows: Yi=Ai+1.5Mi2-0.5M3

(18)

Y2 = A2 +1.5Mi2 -O.5M3

(19)

Y3=A3+3M3-Mi2

(20)

The endogenous variables are German output, French output, and American output. Obviously, an increase in European money supply of 100 causes an increase in German output of 150, an increase in French output of equally 150, and a decline in American output of 100. Similarly, an increase in American money supply of 100 causes an increase in American output of 300, a decline in German output of 50, and a decline in French output of equally 50. Further let full-employment output in Germany be 1000, let full-employment output in France be equally 1000, and let full-employment output in America be 2000. Let initial output in Germany be 940, let initial output in France be 970, and let initial output in America be 1880. In each of the countries there is unemployment and deflation. Step 1 refers to the policy response. The output gap in Europe is 90, and the output gap in America is 120. So what is needed in

197 Europe, according to equation (16), is an increase in European money supply of 48.8. And what is needed in America, according to equation (17), is an increase in American money supply of 56.3. Step 2 refers to the output lag. The net effect is an increase in German output of 45, an increase in French output of equally 45, and an increase in American output of 120. As a consequence, German output goes from 940 to 985, French output goes from 970 to 1015, and American output goes from 1880 to 2000. In Germany there is still some unemployment and deflation. In France there is now some overemployment and inflation. In Europe there is now full employment and price stability. And the same is true of America. As a result, under rational expectations, monetary competition leads immediately to full employment and price stability. Table 6.1 presents a synopsis. 4) A comment. The European central bank closely observes the measures taken by the American central bank. And what is more, the European central bank can respond immediately to the measures taken by the American central bank. The other way round, the American central bank closely observes the measures taken by the European central bank. And what is more, the American central bank can respond immediately to the measures taken by the European central bank. Therefore rational policy expectations do not seem to be very important.

Table 6.1 Monetary Competition between Europe and America Rational Policy Expectations

Initial Output

Germany

France

America

940

970

1880

A Money Supply Output

48.8 985

1015

56.3 2000

1

Chapter 2 Fiscal Competition between Germany and France

1) The static model. As a point of departure, take the static model. It can be represented by a system of three equations: YI=AI+YGI-5G2

(1)

Y2=A2+YG2-5GI

(2)

Y3=A3+8Gi+8G2

(3)

This is a reduced form of the basic model, see Part One. y, 5 and 8 are positive coefficients with y > 5 and 8 = 7 - 8 . According to equation (1), German output is a positive function of German government purchases and a negative function of French government purchases. According to equation (2), French output is a positive function of French government purchases and a negative function of German government purchases. According to equation (3), American output is a positive function of German government purchases and a positive function of French government purchases. 2) The dynamic model. At the beginning there is unemployment in both Germany and France. More precisely, unemployment in Germany exceeds unemployment in France. By contrast there is full employment in America. The target of the German government is full employment in Germany. The instrument of the German government is German government purchases. The target of the French government is full employment in France. The instrument of the French government is French government purchases. We assume that the German government and the French government decide simultaneously and independently. The German government sets German government purchases, forming rational expectations of French government purchases. And the French government sets French government purchases, forming rational expectations of German government purchases.

199 On this basis, the dynamic model can be characterized by a system of four equations:

Yi = A I + Y G I - 6 G |

(4)

Y2=A2+YG2-5Gf

(5)

Gf=Gi

(6)

G|=G2

(7)

Here is a list of the new symbols: Y^ full-employment output in Germany Y2 full-employment output in France Gf the expectation of German government purchases, as formed by the French government G2 the expectation of French government purchases, as formed by the German government G^ German government purchases, as set by the German govemment G2 French government purchases, as set by the French government. According to equation (4), the German government sets German government purchases, forming an expectation of French government purchases. According to equation (5), the French govemment sets French government purchases, forming an expectation of German government purchases. According to equation (6), the expectation of German government purchases is equal to the forecast made by means of the model. According to equation (7), the expectation of French government purchases is equal to the forecast made by means of the model. That is to say, the German government sets German government purchases, predicting French government purchases with the help of the model. And the French government sets French government purchases, predicting German government purchases with the help of the model. The endogenous variables are German government purchases G^, French government purchases G2, the expectation of German government purchases Gf, and the expectation of French government purchases G2.

200

The dynamic model can be compressed to a system of two equations: Yi = A i + y G i - 5 G 2

(8)

Y2=A2+yG2-5Gi

(9)

Here the endogenous variables are German government purchases G| and French government purchases G2. To simplify notation we introduce Bj = Yj - Aj and B2 = Y2 - A2. Then we solve the model for the endogenous variables: G i = ' y2_52 ^ , /

G. = y2_§2 ^5|±|?.

(10)

(H)

Equation (10) shows the equiHbrium level of German government purchases, and equation (11) shows the equilibrium level of French government purchases. There is a solution if and only if y 7^ 6. This condition is fulfilled. As a result, under rational expectations, there is an immediate equilibrium of fiscal competition between Germany and France. In other words, under rational expectations, fiscal competition leads immediately to full employment in Germany and France. However, as a severe side effect, it causes overemplo)mient and inflation in America. It is worth pointing out here that the equilibrium under rational expectations is identical to the steady state under adaptive expectations, see Chapter 1 of Part Three. As an altemative, the dynamic model can be stated in terms of the initial output gap and the required increase in government purchases: AYi =yAGi-6AG2

(12)

AY2 =yAG2-5AGi

(13)

Here AYj denotes the initial output gap in Germany, AY2 is the initial output gap in France, AG| is the required increase in German govemment purchases, and AG2 is the required increase in French govemment purchases. The endogenous variables are AG^ and AG2. The equilibrium of the system (12) and (13) is:

201

VA^ilM^

(.4)

_YAY2+5AYI

A G 2 = ^ Y" 2^ _r §r 2r ^

(15)

3) A numerical example. To illustrate the dynamic model, have a look at a numerical example. For ease of exposition, without losing generality, assume Y = 1.5, 5 = 0.5 and 8 = 1. On this assumption, the static model can be written as follows: Yi =Ai+1.5Gi-0.5G2

(16)

Y2=A2+1.5G2-0.5Gi

(17)

Y3 =A3 + Gi+G2

(18)

The endogenous variables are German output, French output, and American output. Evidently, an increase in German government purchases of 100 causes an increase in German output of 150, a decline in French output of 50, and an increase in American output of 100. Further let full-employment output in Germany be 1000, let full-employment output in France be equally 1000, and let full-employment output in America be 2000. Let initial output in Germany be 940, let initial output in France be 970, and let initial output in America be 2000. In Germany there is unemployment and deflation. In France there is unemployment and deflation too. But in America there is full employment and price stability. Step 1 refers to the policy response. The output gap in Germany is 60, and the output gap in France is 30. So what is needed in Germany, according to equation (14), is an increase in German government purchases of 52.5. And what is needed in France, according to equation (15), is an increase in French government purchases of 37.5. Step 2 refers to the output lag. The net effect is an increase in German output of 60, an increase in French output of 30, and an increase in American output of 90. As a consequence, German output goes from 940 to 1000, French output goes from 970 to 1000, and American output goes from 2000 to 2090. In Germany

202

there is now full employment and price stability. And the same is true of France. But in America there is now overemployment and inflation. As a result, under rational expectations, fiscal competition leads immediately to full employment and price stability. However, the required increase in German government purchases is very large, as compared to the initial output gap in Germany. And the required increase in French government purchases is even larger, as compared to the initial output gap in France. The effective multipUer in Germany is only 1.1, and the effective multipUer in France is only 0.8. Table 6.2 gives an overview.

Table 6.2 Fiscal Competition between Germany and France Rational Policy Expectations Germany Initial Output A Government Purchases Output

940 52.5 1000

France

America

970

2000

37.5 1000

2090

1

Chapter 3 Monetary and Fiscal Competition: Sequential Decisions

1) The static model. This chapter deals with competition between the European central bank, the American central bank, the German government, and the French government. As a point of reference, consider the static model. It can be represented by a system of three equations: Yj = Ai + 0.5aMi2 - O.5PM3 + yGi - 862

(1)

Y2 = A2 + 0.5aMi2 - O.5PM3 + YG2 - 5Gi

(2)

Y3 = A3 + aM3 - PM12 + eGi + 6G2

(3)

This is a reduced form of the basic model, see Part One. a, (3, y, 5 and e are positive coefficients with a > (3, y > 5 and 8 = 7 - 8 . According to equation (1), German output is a positive function of European money supply, a negative function of American money supply, a positive function of German government purchases, and a negative function of French government purchases. According to equation (2), French output is a positive function of European money supply, a negative function of American money supply, a positive function of French government purchases, and a negative function of German government purchases. According to equation (3), American output is a positive function of American money supply, a negative function of European money supply, a positive function of German government purchases, and a positive function of French government purchases. The static model can be compressed to a system of two equations: Y12 = A12 + aMi2 - PM3 + eGi + 8G2

(4)

Y3 = A3 + aM3 ~ PM12 + eGi + 8G2

(5)

204

According to equation (4), European output is a positive function of European money supply, a negative function of American money supply, a positive function of German government purchases, and a positive function of French government purchases. 2) The dynamic model. At the beginning there is unemployment in Germany, France and America. More precisely, unemployment in Germany exceeds unemployment in France. The target of the European central bank is full employment in Europe. The instrument of the European central bank is European money supply. The target of the American central bank is full employment in America. The instrument of the American central bank is American money supply. The target of the German government is full employment in Germany. The instrument of the German government is German government purchases. The target of the French government is full employment in France. The instrument of the French government is French government purchases. We assume that the central banks and the governments decide sequentially. First the central banks decide, then the governments decide. In step 1, the European central bank and the American central bank decide simultaneously and independently. In step 2, the German government and the French government decide simultaneously and independently. In step 3, the European central bank and the American central bank decide simultaneously and independently. In step 4, the German government and the French govemment decide simultaneously and independently. And so on. Now have a closer look at step 1. The European central bank and the American central bank decide simultaneously and independently. The European central bank sets European money supply, forming rational expectations of American money supply. And the American central bank sets American money supply, forming rational expectations of European money supply. On this basis, the dynamic model can be characterized by a system of four equations: %2 = Ai2 + 0LMI2 - PM^ + 8Gi + 8G2

(6)

Y3 = A3 + aM3 - |3Mf2 + eGi + 8G2

(7)

Mf2=Mi2

(8)

205

M^ = M3

(9)

Here is a list of the new symbols: Y12 full-employment output in Europe Y3 full-employment output in America Mf2 the expectation of European money supply, as formed by the American central bank M3 the expectation of American money supply, as formed by the European central bank M^2 European money supply, as set by the European central bank M3 American money supply, as set by the American central bank. According to equation (6), the European central bank sets European money supply, forming an expectation of American money supply. According to equation (7), the American central bank sets American money supply, forming an expectation of European money supply. According to equation (8), the expectation of European money supply is equal to the forecast made by means of the model. According to equation (9), the expectation of American money supply is equal to the forecast made by means of the model. That is to say, the European central bank sets European money supply, predicting American money supply with the help of the model. And the American central bank sets American money supply, predicting European money supply with the help of the model. The endogenous variables are European money supply M12, American money supply M3, the expectation of European money supply Mf2, and the expectation of American money supply M3. The dynamic model can be condensed to a system of two equations: Y12 = A12 + aMi2 - PM^ + 8G1 + 8G2

(10)

Y3 = A3 + aM3 - PMf2 + eGi + 8G2

(11)

Here the endogenous variables are European money supply M12 and American money supply M3. To simplify notation we introduce:

206

Bi2=Yi2-Ai2-eGi-8G2

(12)

B3 = Y 3 - A 3 - e G i - e G 2

(13)

Then we solve the model for the endogenous variables: -.

aBi2+pB3

_aB3+pBi2 ^^3=^^^^^

....

(15)

Equation (14) shows the equiUbrium level of European money supply, and equation (15) shows the equilibrium level of American money supply. There is a solution if and only if a 9^ p. This condition is fulfilled. As a result, under rational expectations, there is an immediate equilibrium of monetary competition between Europe and America. In other words, under rational expectations, monetary competition leads immediately to full employment in Europe and America. However, it does not lead to full employment in Germany and France. As an alternative, the dynamic model can be stated in terms of the initial output gap and the required increase in money supply: AY12 = aAMi2 - PAM3

(16)

AY3=aAM3~|3AMi2

(17)

Here AY12 denotes the initial output gap in Europe, AY3 is the initial output gap in America, AM12 is the required increase in European money supply, and AM3 is the required increase in American money supply. The endogenous variables are AM12 and AM3. The equilibrium of the system (16) and (17) is:

'^n=:r:r ^aAYi2+PAY3

c^)

207

_aAY3+pAYi2

(«)

^M, = -yz''

Step 2 refers to the output lag. Next have a closer look at step 3. The German government and the French govemment decide simultaneously and independently. The German government sets German govemment purchases, forming rational expectations of French govemment purchases. And the French govemment sets French govemment purchases, forming rational expectations of German govemment purchases. On this basis, the dynamic model can be characterized by a system of four equations: % = Ai + 0.5aMi2 - O.5PM3 + yGi - 5G^

(20)

Y2 = A2 + 0.5aMi2 - O.5PM3 + yG2 - 5Gf

(21)

Gf=Gi

(22)

G|=G2

(23)

Here is a list of the new symbols: Y| full-employment output in Germany Y2 full-employment output in France Gf the expectation of German govemment purchases, as formed by the French govemment G2 the expectation of French govemment purchases, as formed by the German govemment Gj German govemment purchases, as set by the German govemment G2 French govemment purchases, as set by the French govemment. According to equation (20), the German govemment sets German govemment purchases, forming an expectation of French govemment purchases. According to equation (21), the French govemment sets French govemment purchases, forming an expectation of German govemment purchases. According to equation (22), the expectation of German govemment purchases is equal to the forecast made by means of the model. According to equation (23), the

208

expectation of French government purchases is equal to the forecast made by means of the model. That is to say, the German government sets German government purchases, predicting French government purchases with the help of the model. And the French government sets French government purchases, predicting German government purchases with the help of the model. The endogenous variables are German government purchases G^, French government purchases G2, the expectation of German government purchases Gf, and the expectation of French government purchases G^. The dynamic model can be compressed to a system of two equations: % = Ai + 0.5aMi2 " O.5PM3 + YGI - 5G2

(24)

Y2 = A2 + 0.5aMi2 - O.5PM3 + YG2 - 5Gi

(25)

Here the endogenous variables are German government purchases G^ and French government purchases G2. To simplify notation we introduce: Fi = Yi - Aj - 0.5aMi2 + O.5PM3

(26)

F2 = Y2 ~ A2 - 0.5aMi2 + O.5PM3

(27)

Then we solve the model for the endogenous variables:

° r - ^ ^ _YF2+SFI

G2 = 'Y ^2 _ §J2

(28) (29)

Equation (28) shows the equilibrium level of German government purchases, and equation (29) shows the equilibrium level of French government purchases. There is a solution if and only if y =5^ 5. This condition is fulfilled. As a result, under rational expectations, there is an immediate equilibrium of fiscal competition between Germany and France. In other words, under rational expectations, fiscal competition leads immediately to full employment in Germany and France. It is worth pointing out here that the equilibrium under

209 rational expectations is different from the steady state under adaptive expectations, see Chapter 3 of Part Four. As an alternative, the dynamic model can be stated in terms of the initial output gap and the required increase in government purchases:

AYi = Y A G I ~ 5 A G 2

(30)

AY2=YAG2-5AGI

(31)

Here AY^ denotes the initial output gap in Germany, AY2 is the initial output gap in France, AG^ is the required increase in German government purchases, and AG2 is the required increase in French government purchases. The endogenous variables are AG^ and AG2. The equilibrium of the system (30) and (31) is:

Step 4 refers to the output lag. 3) A numerical example. To illustrate the dynamic model, have a look at a numerical example. For ease of exposition, without loss of generality, assume a = 3, P = l, Y^l-^j 5 = 0.5 and 8 = 1. On this assumption, the static model can be written as follows: Yi = Ai +1.5Mi2 - O.5M3 +1.5Gi - O.5G2

(34)

Y2 = A2 +1.5Mi2 - O.5M3 +1.5G2 - 0.5Gi

(35)

Y3 = A3 + 3M3 - M12 + Gi + G2

(36)

The endogenous variables are German output, French output, and American output. Obviously, an increase in European money supply of 100 causes an increase in German output of 150, an increase in French output of equally 150, and a decline in American output of 100. An increase in American money supply

210 of 100 causes an increase in American output of 300, a decline in German output of 50, and a decline in French output of equally 50. An increase in French government purchases of 100 causes an increase in French output of 150, a decline in German output of 50, and an increase in American output of 100. Further let full-employment output in Germany be 1000, let full-employment output in France be equally 1000, and let full-employment output in America be 2000. Let initial output in Germany be 940, let initial output in France be 970, and let initial output in America be 1880. In each of the countries there is unemployment and deflation. Step 1 refers to monetary competition between Europe and America. The output gap in Europe is 90, and the output gap in America is 120. So what is needed in Europe, according to equation (18), is an increase in European money supply of 48.8. And what is needed in America, according to equation (19), is an increase in American money supply of 56.3. Step 2 refers to the output lag. The net effect is an increase in German output of 45, an increase in French output of equally 45, and an increase in American output of 120. As a consequence, German output goes from 940 to 985, French output goes from 970 to 1015, and American output goes from 1880 to 2000. In Germany there is still some unemployment and deflation. In France there is now some overemployment and inflation. And in America there is now full employment and price stability. Step 3 refers to fiscal competition between Germany and France. The output gap in Germany is 15, and the inflationary gap in France is equally 15. So what is needed in Germany, according to equation (32), is an increase in German govemment purchases of 7.5. And what is needed in France, according to equation (33), is a reduction in French govemment purchases of equally 7.5. Step 4 refers to the output lag. The net effect is an increase in German output of 15, a decline in French output of equally 15, and a change in American output of zero. As a consequence, German output goes from 985 to 1000, French output goes from 1015 to 1000, and American output stays at 2000. In each of the countries there is now full employment and price stability. As a result, under rational expectations, the sequential process of monetary and fiscal competition

211 leads immediately to full employment and price stability. Table 6.3 presents a synopsis.

Table 6.3 Monetary and Fiscal Competition: Sequential Decisions Rational Policy Expectations

Initial Output

Germany

France

America

940

970

1880

48.8

A Money Supply Output A Government Purchases 1 Output

985 7.5 1000

1015

1

56.3

2000

1

2000

1

-7.5 1000

Chapter 4 Monetary and Fiscal Competition: Simultaneous Decisions

1) The static model. This chapter deals with competition between the European central bank, the American central bank, the German government, and the French government. As a point of departure, take the static model. It can be represented by a system of three equations: Yj = Ai + 0.5aMi2 - O.SpMj + yGi - 862

(1)

Y2 = A2 + 0.5aMi2 - O.5PM3 + YG2 - 5Gi

(2)

Y3 = A3 + aM3 - pMi2 + BGI + 8G2

(3)

Here Y^ denotes German output, Y2 is French output, Y3 is American output, M12 is European money supply, M3 is American money supply, G^ is German government purchases, and G2 is French government purchases. The endogenous variables are German output, French output, and American output. 2) The dynamic model. At the start there is unemployment in Germany, France and America. To be more specific, unemployment in Germany is high, and unemployment in France is low. The target of the European central bank is full employment in Europe. The target of the American central bank is full employment in America. The target of the German government is full employment in Germany. And the target of the French government is full employment in France. We assume that the European central bank, the American central bank, the German government, and the French government decide simultaneously and independently. The European central bank sets European money supply, forming rational expectations of American money supply, German government purchases, and French government purchases. The American central bank sets American money supply, forming rational expectations of European money supply, German

213 government purchases, and French government purchases. The German government sets German govemment purchases, forming rational expectations of European money supply, American money supply, and French govemment purchases. And the French govemment sets French govemment purchases, forming rational expectations of European money supply, American money supply, and German govemment purchases. That is to say, the European central bank sets European money supply, predicting American money supply, German govemment purchases, and French govemment purchases with the help of the model. The American central bank sets American money supply, predicting European money supply, German govemment purchases, and French govemment purchases with the help of the model. The German govemment sets German govemment purchases, predicting European money supply, American money supply, and French govemment purchases with the help of the model. And the French govemment sets French govemment purchases, predicting European money supply, American money supply, and German govemment purchases with the help of the model. On this basis, the dynamic model can be characterized by a system of three equations: Yj = Ai + 0.5aMi2 - O.5PM3 + yGj - 6G2

(4)

Y2 = A2 + 0.5aMi2 - O.5PM3 + YG2 - 5Gi

(5)

Y3 = A3 + aM3 - pMi2 + sGi + SG2

(6)

Here Yj denotes full-employment output in Germany, Y2 is full-employment output in France, and Y3 is full-employment output in America. The endogenous variables are European money supply, American money supply, German govemment purchases, and French govemment purchases. Under simultaneous decisions there are three targets and four instmments, so there is one degree of freedom. As a result, under rational expectations, there is no unique equilibrium of monetary and fiscal competition. Put another way, under rational expectations, the simultaneous process of monetary and fiscal competition does not lead to full employment and price stability.

Chapter 5 Monetary Cooperation between Europe and America^ Fiscal Competition between Germany and France

1) The static model. As a point of reference, consider the static model. It can be represented by a system of three equations: Yj = Ai + 0.5aMi2 - O.5PM3 + yGj - 862

(1)

Y2 = A2 + 0.5aMi2 - O.5PM3 + yG2 - 5Gi

(2)

Y3 = A3 + aM3 ~ PM12 + sGi + SG2

(3)

The endogenous variables are German output, French output, and American output. 2) The dynamic model. At the beginning there is unemployment in Germany, France and America. More precisely, unemployment in Germany is high, and unemployment in France is low. The targets of monetary cooperation are full employment in Europe and full employment in America. The instruments of monetary cooperation are European money supply and American money supply. Under monetary cooperation, there are two targets and two instruments, so there is no degree of freedom. The target of the German govemment is full employment in Germany. The instrument of the German govemment is German govemment purchases. The target of the French govemment is full employment in France. The instrument of the French govemment is French govemment purchases. We assume that the central banks and the governments decide sequentially. First the central banks decide, then the governments decide. In step 1, the European central bank and the American central bank decide cooperatively. In step 2, the German govemment and the French govemment decide simultaneously and independently. In step 3, the European central bank and the

215 American central bank decide cooperatively. In step 4, the German government and the French government decide simultaneously and independently. And so on. Now have a closer look at step 1. It refers to monetary cooperation between Europe and America. Taking differences in equations (1), (2) and (3), the model of monetary cooperation can be written as follows: AYi2=aAMi2-pAM3

(4)

AY3=aAM3-pAMi2

(5)

Here AY12 denotes the initial output gap in Europe, AY3 is the initial output gap in America, AM12 is the required increase in European money supply, and AM3 is the required increase in American money supply. The endogenous variables are AM12 and AM3. The solution to the system (4) and (5) is: _aAYi2+PAY3

^^12=

li.al

_aAY3+|3AY^2 AM3= i ^2 ^'

'

(6)

(7)

As a result, there is a solution to monetary cooperation between Europe and America. In other words, monetary cooperation can achieve full employment in Europe and America. Step 2 refers to the output lag. Next have a closer look at step 3. It refers to fiscal competition between Germany and France. The German government sets German government purchases, forming rational expectations of French government purchases. And the French government sets French government purchases, forming rational expectations of German government purchases. That means, the German government sets German government purchases, predicting French government purchases with the help of model. And the French government sets French government purchases, predicting German government purchases with the help of the model. Taking differences in equations (1) and (2), the model of fiscal competition can be written as follows:

216

AYi = Y A G I - 5 A G 2

(8)

AY2=YAG2-5AGI

(9)

Here AY^ denotes the initial output gap in Germany, AY2 is the initial output gap in France, AG^ is the required increase in German government purchases, and AG2 is the required increase in French government purchases. The endogenous variables are AG^ and AG2. The equilibrium of the system (8) and (9) is: AG,=V^^lfi VA]i±|AY,

(.0) ^„,

As a result, under rational expectations, there is an immediate equilibrium of fiscal competition between Germany and France. That is to say, under rational expectations, fiscal competition leads immediately to full employment in Germany and France. Step 4 refers to the output lag. 3) A numerical example. To illustrate the dynamic model, have a look at a numerical example. For ease of exposition, without losing generality, assume a = 3, P = l, Y = l-5, 5 = 0.5 and 8 = 1. An increase in European money supply of 100 causes an increase in German output of 150, an increase in French output of equally 150, and a decline in American output of 100. An increase in American money supply of 100 causes an increase in American output of 300, a decline in German output of 50, and a decline in French output of equally 50. An increase in German government purchases of 100 causes an increase in German output of 150, a decline in French output of 50, and an increase in American output of 100. Further let full-employment output in Germany be 1000, let fullemployment output in France be equally 1000, and let full-employment output in America be 2000. Let initial output in Germany be 940, let initial output in France be 970, and let initial output in America be 1880. In each of the countries there is unemployment and deflation. Step 1 refers to monetary cooperation between Europe and America. The output gap in Europe is 90, and the output gap in

217 America is 120. So what is needed, according to equations (6) and (7), is an increase in European money supply of 48.8 and an increase in American money supply of 56.3. Step 2 refers to the output lag. The net effect is an increase in German output of 45, an increase in French output of equally 45, and an increase in American output of 120. As a consequence, German output goes from 940 to 985, French output goes from 970 to 1015, and American output goes from 1880 to 2000. In Germany there is still some unemployment and deflation. In France there is now some overemployment and inflation. And in America there is now full employment and price stability. Step 3 refers to fiscal competition between Germany and France. The output gap in Germany is 15, and the inflationary gap in France is equally 15. So what is needed in Germany, according to equation (10), is an increase in German govemment purchases of 7.5. And what is needed in France, according to equation (11), is a reduction in French govemment purchases of equally 7.5. Step 4 refers to the output lag. The net effect is an increase in German output of 15, a decline in French output of equally 15, and a change in American output of zero. As a consequence, German output goes from 985 to 1000, French output goes from 1015 to 1000, and American output stays at 2000. In each of the countries there is now full employment and price stability. As a result, under rational expectations, the sequential process of monetary cooperation and fiscal competition leads immediately to full employment and price stability. Table 6.4 gives an overview.

218 Table 6.4 Monetary Cooperation between Europe and America, Fiscal Competition between Germany and France Rational Policy Expectations

Initial Output

Germany

France

America

940

970

1880

A Money Supply Output A Government Purchases Output

48.8 985 7.5 1000

1015

56.3 2000

-7.5 1000

2000

1

Chapter 6 Policy Cooperation within Europe^ Policy Competition between Europe and America

1) The static model. As a point of departure, take the static model. It can be represented by a system of three equations: Yi = Ai + 0.5aMi2 - O.5PM3 + yG^ - 862

(1)

Y2 = A2 + 0.5aMi2 - O.5PM3 + YG2 - 6G1

(2)

Y3 = A3 + aM3 - PM12 + eGi + 8G2

(3)

The endogenous variables are German output, French output, and American output. 2) The dynamic model. At the start there is unemployment in Germany, France and America. Unemployment in Germany is high, and unemployment in France is low. First consider policy cooperation within Europe. The policy makers are the European central bank, the German government, and the French government. They form the European coalition. The targets of policy cooperation within Europe are full employment in Germany and full employment in France. The third target is that the increase in German government purchases should be equal in size to the reduction in French government purchases. The instruments of policy cooperation within Europe are European money supply, German government purchases, and French government purchases. Under policy cooperation within Europe, there are three targets and three instruments, so there is no degree of freedom. Second consider monetary policy in America. The pohcy maker is the American central bank. The target of the American central bank is full employment in America. And the instrument of the American central bank is American money supply. We assume that the European coalition and the American central bank decide simultaneously and independently. In step 1, the European coalition and the

220

American central bank decide simultaneously and independently. In step 2, again, the European coalition and the American central bank decide simultaneously and independently. And so on. The European coalition sets European money supply, German government purchases, and French government purchases, forming rational expectations of American money supply. And the American central bank sets American money supply, forming rational expectations of European money supply, German government purchases, and French government purchases. On this basis, the dynamic model can be characterized by a system of eight equations: Yi = Ai + 0.5aMi2 - O.SPM^ + yGj - 5G2

(4)

%=k2+

(5)

0.5aMi2 - 0.5pM^ + YG2 - 5Gi

Y3 = A3 + aM3 - pMf2 + eGf + 8G|

(6)

G1+G2 = const

(7)

Mf2=Mi2

(8)

M^ = M3

(9)

Gf=Gi

(10)

G|=G2

(11)

Here is a list of the new symbols: Yj full-employment output in Germany Y2 full-employment output in France Y3 full-employment output in America Mf2 the expectation of European money supply, as formed by the American central bank G\ the expectation of German government purchases, as formed by the American central bank G2 the expectation of French government purchases, as formed by the American central bank M3 the expectation of American money supply, as formed by the European coalition

221 Mj2 Gj G2 M3

European money supply, as set by the European coalition German govemment purchases, as set by the European coalition French govemment purchases, as set by the European coalition American money supply, as set by the American central bank.

According to equations (4), (5) and (7), the European coalition sets European money supply, German govemment purchases, and French govemment purchases, forming an expectation of American money supply. According to equation (6), the American central bank sets American money supply, forming an expectation of European money supply, German govemment purchases, and French govemment purchases. According to equation (7), the sum total of German and French govemment purchases is constant. According to equation (8), the expectation of European money supply is equal to the forecast made by means of the model. According to equation (9), the expectation of American money supply is equal to the forecast made by means of the model. According to equation (10), the expectation of German govemment purchases is equal to the forecast made by means of the model. And according to equation (11), the expectation of French govemment purchases is equal to the forecast made by means of the model. That is to say, the European coalition sets European money supply, German govemment purchases, and French govemment purchases, predicting American money supply with the help of the model. And the American central bank sets American money supply, predicting European money supply, German govemment purchases, and French govemment purchases with the help of the model. The endogenous variables are European money supply M12, American money supply M3, German govemment purchases G^, French govemment purchases G2, the expectation of European money supply M|2, the expectation of American money supply M3, the expectation of German govemment purchases Gf, and the expectation of French govemment purchases G2. The dynamic model can be compressed to a system of four equations:

222

% = Ai + 0.5aMi2 - O.5PM3 + YGI - 862

(12)

Y2 =A2+0.5aMi2-0.5PM3+YG2~5Gi

(13)

Y3 = A3 + aM3 - PM12 + eGi + 8G2

(14)

G i + G 2 = const

(15)

Here the endogenous variables are European money supply Mj2' American money supply M3, German government purchases G^, and French government purchases G2. As an alternative, the dynamic model can be stated in terms of the initial output gap, the required increase in money supply, and the required increase in government purchases. Taking differences in equations (12), (13), (14) and (15), the dynamic model can be written as follows: AYj = 0.5aAMi2 - O.5PAM3 + yAGi - 5AG2

(16)

AY2 = 0.5aAMi2 - O.5PAM3 + YAG2 - 5AGi

(17)

AY3 =aAM3 - PAM12 + sAGi + 8AG2

(18)

AGi+AG2=0

(19)

Here AY^ denotes the initial output gap in Germany, AY2 is the initial output gap in France, AY3 is the initial output gap in America, AM12 is the required increase in European money supply, AM3 is the required increase in American money supply, AG^ is the required increase in German government purchases, and AG2 is the required increase in French government purchases. The endogenous variables are AM12, AM3, AGj and AG2. Add up equations (16) and (17), taking account of equation (19), to find out: AYi + AY2 = aAMi2 - PAM3

(20)

To simphfy notation we introduce AY12 = AY^ + AY2, where AY12 is the initial output gap in Europe. This yields:

223

AYi2 = aAMi2 - PAM3

(21)

Taking account of equation (19), equation (18) can be written as follows: AY3 = aAMj - PAM12

(22)

Then solve equations (21) and (22) for: _aAYi2+P^Y3 ^Mi2= 'i :2 '

-^^3 =

aAY3+|3AYi2 i " ''

(23)

(24)

Further subtract equation (17) from equation (16) to find out: AYi ~ AY2 = (Y +5)(AGi - AG2)

(25)

Then solve equations (19) and (25) for:

'

A Y ^ 2(Y + 5)

2

AY2ZAY, 2(Y + 5)

(27)

As a result, under rational expectations, there is an immediate equilibrium of policy competition between Europe and America. In other words, under rational expectations, policy competition between Europe and America leads immediately to full employment in Germany, France and America. 3) A numerical example. To illustrate the dynamic model, have a look at a numerical example. For ease of exposition, without loss of generality, assume a = 3, P = l, Y = l-5, 5 = 0.5 and e = 1. Full-employment output in Germany is 1000, full-employment output in France is equally 1000, and full-employment

224

output in America is 2000. Let initial output in Germany be 940, let initial output in France be 970, and let initial output in America be 1880. In each of the countries there is unemployment and deflation. Step 1 refers to the policy response. First consider policy cooperation within Europe. The output gap in Germany is 60, the output gap in France is 30, and the output gap in America is 120. So what is needed in Europe, according to equations (23), (26) and (27), is an increase in European money supply of 48.8, an increase in German government purchases of 7.5, and a decline in French government purchases of equally 7.5. Second consider monetary policy in America. The output gap in America is 120, and the output gap in Europe is 90. So what is needed in America, according to equation (24), is an increase in American money supply of 56.3. Step 2 refers to the output lag. The net effect is an increase in German output of 60, an increase in French output of 30, and an increase in American output of 120. As a consequence, German output goes from 940 to 1000, French output goes from 970 to 1000, and American output goes from 1880 to 2000. In each of the countries there is now full employment and price stability. As a result, under rational expectations, the process of policy competition between Europe and America leads immediately to full employment and price stability. Table 6.5 presents a synopsis.

225 Table 6.5 Policy Cooperation within Europe, Policy Competition between Europe and America Rational Policy Expectations

Initial Output

Germany

France

America

940

970

1880

A Money Supply A Government Purchases Output

48.8 7.5 1000

56.3

-7.5 1000

2000

1

Synopsis

The synopsis refers to the interactions between - the European central bank, - the American central bank, - the German government, and - the French government. The synopsis is based on a numerical example. The initial output gap in Germany is 60, the initial output gap in France is 30, and the initial output gap in America is 90. As a result, taking the sum over all periods. Table 7.1 shows: - the total increase in European money supply, - the total increase in American money supply, - the total increase in German government purchases, - the total increase in French government purchases, and - the total increase in European government purchases. Obviously, the result depends on the type of coordination mechanism. In addition. Table 7.2 shows the total increase in European government purchases, as a percentage of the initial output gap in Europe. Again, the result depends on the type of coordination mechanism.

228

Table 7.1 Total Increase in Money Supply and Government Purchases According to Type of Coordination Mechanism Monetary and Fiscal Competition Cold-Turkey Policies: Sequential Decisions Total Increase in European Money Supply

33.8

Total Increase in American Money Supply

33.8

Total Increase in German Government Purchases

18.8

Total Increase in French Government Purchases

3.8

Total Increase in European Government Purchases

22.5

Monetary and Fiscal Competition Cold-Turkey Policies: Simultaneous Decisions Total Increase in European Money Supply

22.5

Total Increase in American Money Supply

22.5

Total Increase in German Government Purchases

30

Total Increase in French Government Purchases

15

Total Increase in European Government Purchases

45

Monetary and Fiscal Competition Gradualist Policies: Simultaneous Decisions Total Increase in European Money Supply

36

Total Increase in American Money Supply

36

Total Increase in German Government Purchases

16.5

Total Increase in French Government Purchases

1.5

Total Increase in European Government Purchases

18

Monetary and Fiscal Cooperation Required Increase in European Money Supply

45

Required Increase in American Money Supply

45

Required Increase in German Government Purchases Required Increase in French Government Purchases Required Increase in European Government Purchases

7.5 -7.5 0

1

229

Fast Monetary Competition, Slow Fiscal Competition Total Increase in European Money Supply

43.3

Total Increase in American Money Supply

43.3

Total Increase in German Government Purchases Total Increase in French Government Purchases Total Increase in European Government Purchases

8.1 -5.2

2.9

Monetary Cooperation between Europe and America, Fiscal Competition between Germany and France Total Increase in European Money Supply

45

Total Increase in American Money Supply

45

Total Increase in German Government Purchases Total Increase in French Government Purchases Total Increase in European Government Purchases

7.5 -7.5 0

Monetary Cooperation between Europe and America, Fiscal Cooperation between Germany and France Total Increase in European Money Supply

45

Total Increase in American Money Supply

45

Total Increase in German Government Purchases Total Increase in French Government Purchases Total Increase in European Government Purchases

7.5 -7.5 0

Policy Cooperation within Europe, Policy Competition between Europe and America Total Increase in European Money Supply

45

Total Increase in American Money Supply

45

Total Increase in German Government Purchases Total Increase in French Government Purchases Total Increase in European Government Purchases

7.5 -7.5 0

1

230

Table 7.2 Total Increase in European Government Purchases Relative to Initial Output Gap in Europe According to Type of Coordination Mechanism Cold-Turkey Policies: Sequential Decisions

25%

Cold-Turkey Policies: Simultaneous Decisions

50%

Gradualist Policies: Simultaneous Decisions

20%

Monetary and Fiscal Cooperation

0%

Fast Monetary Competition, Slow Fiscal Competition

3%

Monetary Cooperation and Fiscal Competition

0%

Monetary Cooperation and Fiscal Cooperation

0%

Policy Cooperation within Europe

0%

1

Conclusion 1. Monetary Competition between Europe and America

1) The static model. The world consists of two monetary regions, say Europe and America. The exchange rate between Europe and America is flexible. Europe in turn consists of two countries, say Germany and France. So Germany and France form a monetary union. There is international trade between Germany, France and America. German goods, French goods and American goods are imperfect substitutes for each other. German output is determined by the demand for German goods. French output is determined by the demand for French goods. And American output is determined by the demand for American goods. European money demand equals European money supply. And American money demand equals American money supply. There is perfect capital mobility between Germany, France and America. Thus the German interest rate, the French interest rate, and the American interest rate are equalized. The monetary regions are the same size and have the same behavioural functions. The union countries are the same size and have the same behavioural functions. Nominal wages and prices adjust slowly. As a result, an increase in European money supply raises both German output and French output, to the same extent respectively. On the other hand, the increase in European money supply lowers American output. Here the rise in European output exceeds the fall in American output. Correspondingly, an increase in American money supply raises American output. On the other hand, it lowers both German output and French output, to the same extent respectively. Here the rise in American output exceeds the fall in European output. In the numerical example, an increase in European money supply of 100 causes an increase in German output of 150, an increase in French output of equally 150, and a decline in American output of 100. Similarly, an increase in American money supply of 100 causes an increase in American output of 300, a decline in German output of 50, and a decHne in French output of equally 50. That is to say, the internal effect of monetary policy is very large, and the external effect of monetary policy is large.

232

Now have a closer look at the process of adjustment. An increase in European money supply causes a depreciation of the euro, an appreciation of the dollar, and a decline in the world interest rate. The depreciation of the euro raises German exports and French exports. The appreciation of the dollar lowers American exports. And the decline in the world interest rate raises German investment, French investment and American investment. The net effect is that German output and French output go up. However, American output goes down. This model is in the tradition of the Mundell-Fleming model and the Levin model. 2) The dynamic model. At the beginning there is unemployment in Germany, France and America. More precisely, unemployment in Germany exceeds unemployment in France. The primary target of the European central bank is price stability in Europe. The secondary target of the European central bank is high employment in Germany and France. The specific target of the European central bank is that unemployment in Germany equals overemployment in France. In other words, deflation in Germany equals inflation in France. So there is price stability in Europe. In a sense, the specific target of the European central bank is full employment in Europe. The instrument of the European central bank is European money supply. The European central bank raises European money supply so as to close the output gap in Europe. The target of the American central bank is full employment in America. The instrument of the American central bank is American money supply. The American central bank raises American money supply so as to close the output gap in America. We assume that the European central bank and the American central bank decide simultaneously and independently. In addition there is an output lag. European output next period is determined by European money supply this period as well as by American money supply this period. In the same way, American output next period is determined by American money supply this period as well as by European money supply this period. As a result, there is a stable steady state of monetary competition. 3) A numerical example: The case of unemployment. Full-employment output in Germany is 1000, full-employment output in France is equally 1000, and full-employment output in America is 2000. Let initial output in Germany be

233

940, let initial output in France be 970, and let initial output in America be 1910. In each of the countries there is unemployment and hence deflation. Step 1 refers to the policy response. First consider monetary policy in Europe. The specific target of the European central bank is full employment in Europe. The output gap in Europe is 90. The monetary poUcy multiplier in Europe is 3. So what is needed in Europe is an increase in European money supply of 30. Second consider monetary poUcy in America. The specific target of the American central bank is full employment in America. The output gap in America is 90. The monetary policy multiplier in America is 3. So what is needed in America is an increase in American money supply of 30. Step 2 refers to the output lag. The increase in European money supply of 30 causes an increase in German output of 45 and an increase in French output of equally 45. As a side effect, it causes a decline in American output of 30. The increase in American money supply of 30 causes an increase in American output of 90. As a side effect, it causes a decline in German output of 15 and a decline in French output of equally 15. The net effect is an increase in German output of 30, an increase in French output of equally 30, and an increase in American output of 60. As a consequence, German output goes from 940 to 970, French output goes from 970 to 1000, and American output goes from 1910 to 1970. Step 3 refers to the poUcy response. The output gap in Europe is 30. The monetary policy multiplier in Europe is 3. So what is needed in Europe is an increase in European money supply of 10. The output gap in America is 30. The monetary policy multiplier in America is 3. So what is needed in America is an increase in American money supply of 10. Step 4 refers to the output lag. The net effect is an increase in German output of 10, an increase in French output of equally 10, and an increase in American output of 20. As a consequence, German output goes from 970 to 980, French output goes from 1000 to 1010, and American output goes from 1970 to 1990. This process repeats itself round by round. Table 8.1 presents a synopsis. In the steady state, German output is 985, French output is 1015, and American output is 2000. In Germany there is unemployment and deflation. In France there is overemployment and inflation. In Europe there is full employment and price stability. And in America there is full employment and

234

price stability too. As a result, the process of monetary competition leads to full employment in Europe and America. And what is more, it leads to price stabiUty in Europe and America. However, the process of monetary competition does not lead to full employment in Germany and France. And what is more, it does not lead to price stability in Germany and France.

Table 8.1 Monetary Competition between Europe and America The Case of Unemployment

Initial Output

Germany

France

America

940

970

1910

30

30

1000

1970

10

10

980

1010

1990

1

985

1015

2000

1

A Money Supply Output

970

A Money Supply

1 Output

1 1

and so on Steady-State Output

4) A numerical example: The case of inflation. Let initial output in Germany be 1060, let initial output in France be 1030, and let initial output in America be 2090. In each of the countries there is overemployment and hence inflation. Step 1 refers to the policy response. First consider monetary policy in Europe. The specific target of the European central bank is price stability in Europe. The inflationary gap in Europe is 90. The monetary policy multiplier in Europe is 3. So what is needed in Europe is a reduction in European money supply of 30. Second consider monetary policy in America. The specific target of the American central bank is price stability in America. The inflationary gap in America is 90. The monetary poUcy multipUer in America is 3. So what is needed in America is a reduction in American money supply of 30.

235 Step 2 refers to the output lag. The reduction in European money supply of 30 causes a decline in German output of 45 and a decline in French output of equally 45. As a side effect, it causes an increase in American output of 30. The reduction in American money supply of 30 causes a decline in American output of 90. As a side effect, it causes an increase in German output of 15 and an increase in French output of equally 15. The net effect is a decline in German output of 30, a decline in French output of equally 30, and a decline in American output of 60. As a consequence, German output goes from 1060 to 1030, French output goes from 1030 to 1000, and American output goes from 2090 to 2030. Step 3 refers to the policy response. The inflationary gap in Europe is 30. The monetary policy multiplier in Europe is 3. So what is needed in Europe is a reduction in European money supply of 10. The inflationary gap in America is 30. The monetary policy multiplier in America is 3. So what is needed in America is a reduction in American money supply of 10. Step 4 refers to the output lag. The net effect is a decline in German output of 10, a decline in French output of equally 10, and a decline in American output of 20. As a consequence, German output goes from 1030 to 1020, French output goes from 1000 to 990, and American output goes from 2030 to 2010. And so on. Table 8.2 gives an overview.

Table 8.2 Monetary Competition between Europe and America The Case of Inflation Germany Initial Output

2090

1

-30

-30

1

1000

2030

1

-10

-10

1

1020

990

2010

1

1015

985

2000

1

1030

A Money Supply

1 Output

America

1030

1060

A Money Supply Output

France

and so on Steady-State Output

236 In the steady state, German output is 1015, French output is 985, and American output is 2000. In Germany there is overemployment and inflation. In France there is unemployment and deflation. In Europe there is full employment and price stability. And in America there is full employment and price stability too.

2. Monetary Cooperation between Europe and America

1) The model. At the beginning there is unemployment in Germany, France and America. More precisely, unemployment in Germany exceeds unemployment in France. The targets of monetary cooperation are full employment in Europe and full employment in America. The instruments of monetary cooperation are European money supply and American money supply. So there are two targets and two instruments. As a result, there is a solution to monetary cooperation. 2) A numerical example: The case of unemployment. Let initial output in Germany be 940, let initial output in France be 970, and let initial output in America be 1910. In each of the countries there is unemployment and deflation. Step 1 refers to the policy response. The output gap in Europe is 90, as is the output gap in America. What is needed, then, is an increase in European money supply of 45 and an increase in American money supply of equally 45. Step 2 refers to the output lag. The increase in European money supply of 45 raises German output and French output by 67.5 each. On the other hand, it lowers American output by 45. The increase in American money supply of 45 raises American output by 135. On the other hand, it lowers German output and French output by 22.5 each. The net effect is an increase in German output of 45, an increase in French output of equally 45, and an increase in American output of 90. As a consequence, German output goes from 940 to 985, French output goes from 970 to 1015, and American output goes from 1910 to 2000.

237

In Germany there is still some unemployment and deflation. In France there is now some overemployment and inflation. In Europe there is now full employment and price stability. And the same holds for America. As a result, monetary cooperation can achieve full employment in Europe and America. And what is more, it can achieve price stability in Europe and America. However, monetary cooperation cannot achieve full employment in Germany and France. And what is more, it cannot achieve price stability in Germany and France. Table 8.3 presents a synopsis.

Table 8.3 Monetary Cooperation between Europe and America The Case of Unemployment

Initial Output

Germany

France

America

940

970

1910

45

45

1015

2000

A Money Supply Output

985

3) A numerical example: the case of inflation. Let initial output in Germany be 1060, let initial output in France be 1030, and let initial output in America be 2090. In each of the countries there is overemployment and inflation. Step 1 refers to the policy response. The inflationary gap in Europe is 90, as is the inflationary gap in America. The targets of monetary cooperation are price stability in Europe and price stability in America. What is needed, then, is a reduction in European money supply of 45 and a reduction in American money supply of equally 45. Step 2 refers to the output lag. The reduction in European money supply of 45 lowers German output and French output by 67.5 each. On the other hand, it raises American output by 45. The reduction in American money supply of 45 lowers American output by 135. On the other hand, it raises German output and French output by 22.5 each. The net effect is decline in German output of 45, a

238

decline in French output of equally 45, and a decline in American output of 90. As a consequence, German output goes from 1060 to 1015, French output goes from 1030 to 985, and American output goes from 2090 to 2000. In Germany there is still some overemployment and inflation. In France there is now some unemployment and deflation. In Europe there is now full employment and price stabiUty. And the same is true of America. Table 8.4 gives an overview. 4) Comparing monetary cooperation with monetary competition. Monetary competition can achieve full employment and price stability. The same applies to monetary cooperation. Monetary competition is a slow process. By contrast, monetary cooperation is a fast process. Judging from these points of view, monetary cooperation seems to be superior to monetary competition.

Table 8,4 Monetary Cooperation between Europe and America The Case of Inflation

Initial Output

Germany

France

America

1060

1030

2090

1015

-45 985

-45 2000

A Money Supply Output

1

3. Fiscal Competition between Germany and France

1) The static model. An increase in German government purchases raises German output. On the other hand, it lowers French output. And what is more, it raises American output. Here the rise in German output exceeds the fall in French output. And the rise in European output equals the rise in American

239 output. Correspondingly, an increase in French government purchases raises French output. On the other hand, it lowers German output. And what is more, it raises American output. Here the rise in French output exceeds the fall in German output. And the rise in European output equals the rise in American output. In the numerical example, an increase in German government purchases of 100 causes an increase in German output of 150, a decline in French output of 50, and an increase in American output of 100. Likewise, an increase in French government purchases of 100 causes an increase in French output of 150, a decline in German output of 50, and an increase in American output of 100. Now have a closer look at the process of adjustment. An increase in German government purchases causes an appreciation of the euro, a depreciation of the dollar, and an increase in the world interest rate. The appreciation of the euro lowers German exports and French exports. The depreciation of the dollar raises American exports. And the increase in the world interest rate lowers German investment, French investment and American investment. The net effect is that German output moves up, French output moves down, and American output moves up. This model is in the tradition of the Mundell-Fleming model and the Levin model. 2) The dynamic model. At the beginning there is unemployment in both Germany and France. More precisely, unemployment in Germany exceeds unemployment in France. By contrast there is full employment in America. The target of the German government is full employment in Germany. The instrument of the German government is German government purchases. The German government raises German government purchases so as to close the output gap in Germany. The target of the French government is full employment in France. The instrument of the French government is French government purchases. The French government raises French government purchases so as to close the output gap in France. We assume that the German government and the French government decide simultaneously and independently. In addition there is an output lag. German output next period is determined by German government purchases this period as well as by French government purchases this period. French output next period is determined by French

240

government purchases this period as well as by German government purchases this period. And American output next period is determined by German government purchases this period as well as by French government purchases this period. As a result, there is a stable steady state of fiscal competition. 3) A numerical example. Full-employment output in Germany is 1000, fullemployment output in France is equally 1000, and full-employment output in America is 2000. Let initial output in Germany be 940, let initial output in France be 970, and let initial output in America be 2000. In Germany there is unemployment and deflation. In France there is unemployment and deflation too. But in America there is full employment and price stability. Step 1 refers to the policy response. The output gap in Germany is 60. The fiscal policy multipUer in Germany is 1.5. So what is needed in Germany is an increase in German government purchases of 40. The output gap in France is 30. The fiscal policy multiplier in France is 1.5. So what is needed in France is an increase in French government purchases of 20. Step 2 refers to the output lag. The increase in German government purchases of 40 causes an increase in German output of 60. As a side effect, it causes a decline in French output of 20 and an increase in American output of 40. The increase in French government purchases of 20 causes an increase in French output of 30. As a side effect, it causes a decline in German output of 10 and an increase in American output of 20. The net effect is an increase in German output of 50, an increase in French output of 10, and an increase in American output of 60. As a consequence, German output goes from 940 to 990, French output goes from 970 to 980, and American output goes from 2000 to 2060. Step 3 refers to the poUcy response. The output gap in Germany is 10. The fiscal policy multiplier in Germany is 1.5. So what is needed in Germany is an increase in German government purchases of 6.7. The output gap in France is 20. The fiscal policy multiplier in France is 1.5. So what is needed in France is an increase in French government purchases of 13.3. Step 4 refers to the output lag. The net effect is an increase in German output of 3.3, an increase in French output of 16.7, and an increase in American output of 20. As a consequence, German output goes from 990 to 993.3, French output goes from 980 to 996.7, and American output goes from 2060 to 2080. And so on. Table 8.5 presents a synopsis.

241

In the steady state, German output is 1000, French output is equally 1000, and American output is 2090. In Germany there is full employment and price stability. In France there is full employment and price stability too. But in America there is overemployment and inflation. As a result, fiscal competition between Germany and France leads to full employment in Germany and France. And what is more, it leads to price stability in Germany and France. However, as a severe side effect, it causes overemployment and inflation in America.

Table 8.5 Fiscal Competition between Germany and France

Initial Output A Government Purchases 1 Output A Government Purchases 1 Output

Germany

France

America

940

970

2000

1

40

20

990

980

2060

1

2080

1

2090

1

6.7

13.3

993.3

996.7

and so on 1 Steady-State Output

1000

1000

4. Fiscal Cooperation between Germany and France

1) The model. At the beginning there is unemployment in both Germany and France. More precisely, unemployment in Germany exceeds unemployment in France. By contrast there is full employment in America. The targets of fiscal cooperation are full employment in Germany and full employment in France. The instruments of fiscal cooperation are German government purchases and

242

French government purchases. So there are two targets and two instruments. As a result, there is a solution to fiscal cooperation. 2) A numerical example. Let initial output in Germany be 940, let initial output in France be 970, and let initial output in America be 2000. In Germany there is unemployment and deflation. In France there is unemployment and deflation too. But in America there is full employment and price stability. Step 1 refers to the policy response. The output gap in Germany is 60, and the output gap in France is 30. What is needed, then, is an increase in German government purchases of 52.5 and an increase in French government purchases of 37.5. Step 2 refers to the output lag. The increase in German government purchases of 52.5 raises German output by 78.8 and lowers French output by 26.3. As a side effect, it raises American output by 52.5. The increase in French government purchases of 37.5 raises French output by 56.3 and lowers German output by 18.8. As a side effect, it raises American output by 37.5. The net effect is an increase in German output of 60, an increase in French output of 30, and an increase in American output of 90. As a consequence, German output goes from 940 to 1000, French output goes from 970 to 1000, and American output goes from 2000 to 2090. In Germany there is now full employment and price stability. In France there is now full employment and price stability too. But in America there is now overemployment and inflation. As a result, fiscal cooperation between Germany and France can achieve full employment in Germany and France. And what is more, it can achieve price stability in Germany and France. However, as a severe side effect, it causes overemployment and inflation in America. Table 8.6 gives an overview. 3) Comparing fiscal cooperation with fiscal competition. Fiscal competition can achieve full employment and price stabiUty. The same applies to fiscal cooperation. Fiscal competition is a slow process. By contrast, fiscal cooperation is a fast process. Judging from these points of view, fiscal cooperation seems to be superior to fiscal competition.

243

Table 8.6 Fiscal Cooperation between Germany and France Germany Initial Output A Government Purchases Output

940 52.5 1000

France

America

970

2000

1

37.5 1000

2090

5. Monetary and Fiscal Competition: Cold-Turkey Policies

1) The model. This section deals with competition between the European central bank, the American central bank, the German government, and the French government. At the beginning there is unemployment in Germany, France and America. More precisely, unemployment in Germany exceeds unemployment in France. The primary target of the European central bank is price stability in Europe. The secondary target of the European central bank is high employment in Germany and France. The specific target of the European central bank is that unemployment in Germany equals overemployment in France. In other words, deflation in Germany equals inflation in France. So there is price stability in Europe. In a sense, the specific target of the European central bank is full employment in Europe. The instrument of the European central bank is European money supply. The target of the American central bank is full employment in America. The instrument of the American central bank is American money supply. The target of the German government is full employment in Germany. The instrument of the German government is German government purchases. The target of the

244

French government is full employment in France. The instrument of the French govemment is French govemment purchases. We assume that the central banks and the govemments decide simultaneously and independently. In step 1, the European central bank, the American central bank, the German govemment, and the French govemment decide simultaneously and independently. In step 2, the European central bank, the American central bank, the German govemment, and the French govemment decide simultaneously and independently. And so on. 2) A numerical example. An increase in European money supply of 100 causes an increase in German output of 150, an increase in French output of equally 150, and a decline in American output of 100. An increase in American money supply of 100 causes an increase in American output of 300, a decline in German output of 50, and a decline in French output of equally 50. An increase in German govemment purchases of 100 causes an increase in German output of 150, a decline in French output of 50, and an increase in American output of 100. Correspondingly, an increase in French govemment purchases of 100 causes an increase in French output of 150, a decline in German output of 50, and an increase in American output of 100. Further, full-employment output in Germany is 1000, full-employment output in France is equally 1000, and full-employment output in America is 2000. Let initial output in Germany be 940, let initial output in France be 970, and let initial output in America be 1910. In each of the countries there is unemployment and deflation. Step 1 refers to the policy response. First consider monetary policy in Europe. The output gap in Europe is 90. The monetary policy multiplier in Europe is 3. So what is needed in Europe is an increase in European money supply of 30. Second consider monetary policy in America. The output gap in America is 90. The monetary policy multiplier in America is 3. So what is needed in America is an increase in American money supply of 30. Third consider fiscal policy in Germany. The output gap in Germany is 60. The fiscal policy multiplier in Germany is 1.5. So what is needed in Germany is an increase in German govemment purchases of 40. Fourth consider fiscal policy in France. The output gap in France is 30. The fiscal policy multiplier in France is 1.5. So what is needed in France is an increase in French govemment purchases of 20.

245 Step 2 refers to the output lag. The increase in European money supply of 30 causes an increase in German output of 45 and an increase in French output of equally 45. As a side effect, it causes a decline in American output of 30. The increase in American money supply of 30 causes an increase in American output of 90. As a side effect, it causes a decline in German output of 15 and a decline in French output of equally 15. The increase in German government purchases of 40 causes an increase in German output of 60. As a side effect, it causes a decUne in French output of 20 and an increase in American output of 40. The increase in French government purchases of 20 causes an increase in French output of 30. As a side effect, it causes a decline in German output of 10 and an increase in American output of 20. The net effect is an increase in German output of 80, an increase in French output of 40, and an increase in American output of 120. As a consequence, German output goes from 940 to 1020, French output goes from 970 to 1010, and American output goes from 1910 to 2030. Step 3 refers to the policy response. First consider monetary policy in Europe. The inflationary gap in Europe is 30. The monetary policy multiplier in Europe is 3. So what is needed in Europe is a reduction in European money supply of 10. Second consider monetary policy in America. The inflationary gap in America is 30. The monetary policy multiplier in America is 3. So what is needed in America is a reduction in American money supply of 10. Third consider fiscal poUcy in Germany. The inflationary gap in Germany is 20. The fiscal pohcy multipUer in Germany is 1.5. So what is needed in Germany is a reduction in German government purchases of 13.3. Fourth consider fiscal poUcy in France. The inflationary gap in France is 10. The fiscal policy multiplier in France is 1.5. So what is needed in France is a reduction in French government purchases of 6.7. Step 4 refers to the output lag. The net effect is a decline in German output of 26.7, a decline in French output of 13.3, and a decline in American output of 40. As a consequence, German output goes from 1020 to 993.3, French output goes from 1010 to 996.7, and American output goes from 2030 to 1990. And so on. Table 8.7 presents a synopsis. In the steady state, German output is 1000, French output is equally 1000, and American output is 2000. In each of the countries there is full employment and price stability. As a result, the process of monetary and fiscal competition leads

246 to full employment in Germany, France and America. And what is more, it leads to price stability in Germany, France and America. What are the dynamic characteristics of this process? There are damped oscillations in money supply, government purchases and output. The German economy oscillates between unemployment and overemployment, as does the French economy and the American economy. Taking the sum over all periods, the total increase in European money supply is 22.5, the total increase in American money supply is equally 22.5, the total increase in German government purchases is 30, and the total increase in French government purchases is 15.

Table 8.7 Monetary and Fiscal Competition Cold-Turkey Policies

Initial Output

Germany

France

America

940

970

1910

30

30

A Money Supply A Government Purchases Output

40

20

1020

1010

2030

1

-10

-10

1

1990

1

A Money Supply A Government Purchases

1 Output

1

-13.3

-6.7

993.3

996.7

and so on Steady-State Output

1000

1000

2000

Generally speaking, the total increase in European money supply depends on: - the initial output gap in Germany - the initial output gap in France

247

- the initial output gap in America - the direct poHcy multiphers - the cross poHcy multiphers. And the same holds for the total increase in American money supply, the total increase in German govemment purchases, and the total increase in French govemment purchases.

6. Monetary and Fiscal Competition: Gradualist Policies

At the start there is unemployment in Germany, France and America. More precisely, unemployment in Germany exceeds unemployment in France. The general target of the European central bank is full employment in Europe. We assume that the European central bank follows a gradualist strategy. The specific target of the European central bank is to close the output gap in Europe by 80 percent. The general target of the American central bank is full employment in America. We assume that the American central bank follows a gradualist strategy. The specific target of the American central bank is to close the output gap in America by 80 percent. The general target of the German govemment is full employment in Germany. We assume that the German govemment follows a gradualist strategy. The specific target of the German govemment is to close the output gap in Germany by 20 percent. The general target of the French govemment is full employment in France. We assume that the French govemment follows a gradualist strategy. The specific target of the French govemment is to close the output gap in France by 20 percent. We assume that the central banks and the governments decide simultaneously and independently. In step 1, the European central bank, the American central bank, the German govemment, and the French govemment decide simultaneously and independently. In step 2, the European central bank, the American

248 central bank, the German government, and the French govemment decide simultaneously and independently. And so on. As a result, the process of monetary and fiscal competition leads to full employment in Germany, France and America. And what is more, it leads to price stability in Germany, France and America. Let initial output in Germany be 940, let initial output in France be 970, and let initial output in America be 1910. Then, taking the sum over all periods, the total increase in European money supply is 36, the total increase in American money supply is equally 36, the total increase in German govemment purchases is 16.5, and the total increase in French govemment purchases is 1.5. Now compare gradualist policies with cold-turkey policies. Under cold-turkey policies, there is a small increase in money supply and a large increase in govemment purchases. Under gradualist policies, conversely, there is a large increase in money supply and a small increase in govemment purchases. Of course, this depends on the relative speed of adjustment in money supply and govemment purchases. Judging from this point of view, gradualist policies seem to be superior to cold-turkey policies.

7. Monetary and Fiscal Cooperation

1) The model. This section deals with cooperation between the European central bank, the American central bank, the German govemment, and the French govemment. At the beginning there is unemployment in Germany, France and America. More precisely, unemployment in Germany exceeds unemployment in France. The targets of policy cooperation are full employment in Germany, full employment in France, and full employment in America. The instmments of policy cooperation are European money supply, American money supply, German govemment purchases, and French govemment purchases. There are three targets and four instmments, so there is one degree of freedom. As a result.

249 there is an infinite number of solutions. In other words, monetary and fiscal cooperation can achieve full employment in Germany, France and America. 2) A numerical example. We now introduce a fourth target. We assume that the increase in German government purchases should be equal in size to the reduction in French government purchases. Put another way, we assume that the sum total of European government purchases should be constant. Let initial output in Germany be 940, let initial output in France be 970, and let initial output in America be 1910. In each of the countries there is unemployment and deflation. Step 1 refers to the policy response. The output gap in Germany is 60, the output gap in France is 30, the output gap in Europe is 90, and the output gap in America is equally 90. What is needed, then, is an increase in European money supply of 45, an increase in American money supply of equally 45, an increase in German government purchases of 7.5, and a reduction in French government purchases of equally 7.5. Step 2 refers to the output lag. The increase in European money supply of 45 raises German output and French output by 67.5 each. On the other hand, it lowers American output by 45. The increase in American money supply of 45 raises American output by 135. On the other hand, it lowers German output and French output by 22.5 each. The increase in German government purchases of 7.5 raises German output by 11.3. On the other hand, it lowers French output by 3.8. And what is more, it raises American output by 7.5. The reduction in French government purchases of 7.5 lowers French output by 11.3. On the other hand, it raises German output by 3.8. And what is more, it lowers American output by 7.5. The net effect is an increase in German output of 60, an increase in French output of 30, and an increase in American output of 90. As a consequence, German output goes from 940 to 1000, French output goes from 970 to 1000, and American output goes from 1910 to 2000. In each of the countries there is now full employment and price stability. As a result, monetary and fiscal cooperation can achieve full employment in Germany, France and America. Over and above that, it can achieve price stability in Germany, France and America. Table 8.8 gives an overview. Finally compare policy cooperation with policy competition. Under policy competition (cold-turkey pohcies), the total increase in European money supply

250 is 22.5, the total increase in American money supply is equally 22.5, the total increase in German government purchases is 30, the total increase in French government purchases is 15, and the total increase in European govemment purchases is 45. That means, the solution to policy cooperation is different from the steady state of policy competition. Under policy competition, there is a small increase in money supply and a large increase in govemment purchases. Under policy cooperation, however, there is a large increase in money supply and a zero increase in govemment purchases. Judging from this perspective, policy cooperation seems to be superior to policy competition.

Table 8.8 Monetary and Fiscal Cooperation

Initial Output

Germany

France

America

940

970

1910

45

45

A Money Supply A Govemment Purchases Output

7.5 1000

-7.5 1000

2000

8. Monetary Cooperation and Fiscal Competition

1) The model. At the beginning there is unemployment in Gemiany, France and America. More precisely, unemployment in Germany is high, and unemployment in France is low. The targets of monetary cooperation are full employment in Europe and full employment in America. The instruments of monetary cooperation are European money supply and American money supply. Under monetary cooperation, there are two targets and two instruments, so there is no degree of freedom. The target of the German govemment is full em-

251 ployment in Germany. The instrument of the German govemment is German government purchases. The target of the French govemment is full employment in France. The instrument of the French govemment is French govemment purchases. We assume that the central banks and the govemments decide sequentially. First the central banks decide, then the govemments decide. In step 1, the European central bank and the American central bank decide cooperatively. In step 2, the German govemment and the French govemment decide simultaneously and independently. In step 3, the European central bank and the American central bank decide cooperatively. In step 4, the German govemment and the French govemment decide simultaneously and independently. And so on. 2) A numerical example. Let initial output in Germany be 940, let initial output in France be 970, and let initial output in America be 1910. In each of the countries there is unemployment and deflation. Step 1 refers to monetary cooperation between Europe and America. The output gap in Europe is 90, as is the output gap in America. What is needed, then, is an increase in European money supply of 45 and an increase in American money supply of equally 45. Step 2 refers to the output lag. The increase in European money supply of 45 raises German output and French output by 67.5 each. On the other hand, it lowers American output by 45. The increase in American money supply of 45 raises American output by 135. On the other hand, it lowers German output and French output by 22.5 each. The net effect is an increase in German output of 45, an increase in French output of equally 45, and an increase in American output of 90. As a consequence, German output goes from 940 to 985, French output goes from 970 to 1015, and American output goes from 1910 to 2000. Step 3 refers to fiscal competition between Germany and France. The output gap in Germany is 15. The fiscal policy multiplier in Germany is 1.5. So what is needed in Germany is an increase in German govemment purchases of 10. The inflationary gap in France is 15. The fiscal policy multiplier in France is 1.5. So what is needed in France is a reduction in French govemment purchases of 10. Step 4 refers to the output lag. The increase in German govemment purchases of 10 causes an increase in German output of 15. As a side effect, it causes a

252 decline in French output of 5 and an increase in American output of 10. The reduction in French government purchases of 10 causes a decline in French output of 15. As a side effect, it causes an increase in German output of 5 and a decline in American output of 10. The net effect is an increase in German output of 20, a decline in French output of equally 20, and a change in American output of zero. As a consequence, German output goes from 985 to 1005, French output goes from 1015 to 995, and American output stays at 2000. Step 5 refers to monetary cooperation between Europe and America. The output gap in Europe is zero, as is the output gap in America. So there is no need for a change in European money supply or American money supply. Step 6 refers to the output lag. As a consequence, German output stays at 1005, French output stays at 995, and American output stays at 2000. Step 7 refers to fiscal competition between Germany and France. The inflationary gap in Germany is 5. The fiscal pohcy multiplier in Germany is 1.5. So what is needed in Germany is a reduction in German government purchases of 3.3. The output gap in France is 5. The fiscal pohcy multipUer in France is 1.5. So what is needed in France is an increase in French government purchases of 3.3. Step 8 refers to the output lag. The net effect is a decline in German output of 6.7, an increase in French output of equally 6.7, and a change in American output of zero. As a consequence, German output goes from 1005 to 998.3, French output goes from 995 to 1001.7, and American output stays at 2000. This process repeats itself round by round. Table 8.9 presents a synopsis. In the steady state, German output is 1000, French output is equally 1000, and American output is 2000. In each of the countries there is full employment and price stability. As a result, the alternating process of monetary cooperation and fiscal competition leads to full employment in Germany, France and America. And what is more, it leads to price stability in Germany, France and America. Taking the sum over all periods, the total increase in European money supply is 45, as is the total increase in American money supply. The total increase in German government purchases is 7.5, and the total reduction in French government purchases is equally 7.5.

253 Table 8.9 Monetary Cooperation and Fiscal Competition Germany Initial Output

France

America

970

1910

45

45

985

1015

2000

1

10

-10

1005

995

2000

1

940

A Money Supply 1 Output A Government Purchases Output A Government Purchases 1 Output

-3.3

3.3

998.3

1001.7

2000

1000

2000

1

and so on Steady-State Output

1000

9. Monetary Cooperation and Fiscal Cooperation

1) The model. At the beginning there is unemployment in Germany, France and America. More precisely, unemployment in Germany is high, and unemployment in France is low. The targets of monetary cooperation are full employment in Europe and full employment in America. The instruments of monetary cooperation are European money supply and American money supply. Under monetary cooperation, there are two targets and two instruments, so there is no degree of freedom. The targets of fiscal cooperation are full employment in Germany and full employment in France. The instruments of fiscal cooperation are German government purchases and French government purchases. Under fiscal cooperation, there are two targets and two instruments, so there is no degree of freedom.

254

We assume that the central banks and the governments decide sequentially. First the central banks decide, then the governments decide. In step 1, the European central bank and the American central bank decide cooperatively. In step 2, the German government and the French government decide cooperatively. In step 3, the European central bank and the American central bank decide cooperatively. In step 4, the German government and the French government decide cooperatively. And so on. 2) A numerical example. Let initial output in Germany be 940, let initial output in France be 970, and let initial output in America be 1910. In each of the countries there is unemployment and deflation. Step 1 refers to monetary cooperation between Europe and America. The output gap in Europe is 90, as is the output gap in America. What is needed, then, is an increase in European money supply of 45 and an increase in American money supply of equally 45. Step 2 refers to the output lag. The increase in European money supply of 45 raises German output and French output by 67.5 each. On the other hand, it lowers American output by 45. The increase in American money supply of 45 raises American output by 135. On the other hand, it lowers German output and French output by 22.5 each. The net effect is an increase in German output of 45, an increase in French output of equally 45, and an increase in American output of 90. As a consequence, German output goes from 940 to 985, French output goes from 970 to 1015, and American output goes from 1910 to 2000. Step 3 refers to fiscal cooperation between Germany and France. The output gap in Germany is 15, and the inflationary gap in France is equally 15. What is needed, then, is an increase in German government purchases of 7.5 and a reduction in French govemment purchases of equally 7.5. Step 4 refers to the output lag. The increase in German government purchases of 7.5 raises German output by 11.3. On the other hand, it lowers French output by 3.8. And what is more, it raises American output by 7.5. The reduction in French government purchases of 7.5 lowers French output by 11.3. On the other hand, it raises German output by 3.8. And what is more, it lowers American output by 7.5. The net effect is an increase in German output of 15, a decUne in French output of equally 15, and a change in American output of zero. As a consequence, German output goes from 985 to 1000, French output goes from

255 1015 to 1000, and American output stays at 2000. In each of the countries there is now full employment and price stabiUty. Table 8.10 gives an overview. As a result, the sequential process of monetary cooperation and fiscal cooperation leads to full employment in Germany, France and America. Over and above that, it leads to price stability in Germany, France and America. Now compare the sequential process of monetary cooperation and fiscal cooperation with the simultaneous process of monetary and fiscal cooperation, see Section 7. Monetary and fiscal cooperation is a fast process. And much the same applies to monetary cooperation and fiscal cooperation. Judging from this perspective, there seems to be no need for full cooperation between the European central bank, the American central bank, the German government, and the French government.

Table 8.10 Monetary Cooperation and Fiscal Cooperation

Initial Output

Germany

France

America

940

970

1910

45

45

1015

2000

1

2000

1

A Money Supply

1 Output A Government Purchases Output

985 7.5 1000

1

-7.5 1000

256

10. Rational Policy Expectations

1) Monetary and fiscal competition: sequential decisions. At the beginning there is unemployment in Germany, France and America. More precisely, unemployment in Germany exceeds unemployment in France. The target of the European central bank is full employment in Europe. The instrument of the European central bank is European money supply. The target of the American central bank is full employment in America. The instrument of the American central bank is American money supply. The target of the German government is full employment in Germany. The instrument of the German government is German government purchases. The target of the French government is full employment in France. The instrument of the French government is French government purchases. We assume that the central banks and the governments decide sequentially. First the central banks decide, then the governments decide. In step 1, the European central bank and the American central bank decide simultaneously and independently. In step 2, the German government and the French govemment decide simultaneously and independently. In step 3, the European central bank and the American central bank decide simultaneously and independently. In step 4, the German government and the French govemment decide simultaneously and independently. And so on. Now have a closer look at step 1. The European central bank and the American central bank decide simultaneously and independently. The European central bank sets European money supply, forming rational expectations of American money supply. And the American central bank sets American money supply, forming rational expectations of European money supply. That is to say, the European central bank sets European money supply, predicting American money supply with the help of the model. And the American central bank sets American money supply, predicting European money supply with the help of the model. As a result, there is an immediate equilibrium of monetary competition between Europe and America. In other words, monetary competition leads immediately to full employment in Europe and America. However, it does not lead to full employment in Germany and France.

257

Next have a closer look at step 2. The German government and the French government decide simultaneously and independently. The German government sets German government purchases, forming rational expectations of French government purchases. And the French government sets French government purchases, forming rational expectations of German government purchases. That is to say, the German government sets German government purchases, predicting French government purchases with the help of the model. And the French government sets French government purchases, predicting German government purchases with the help of the model. As a result, there is an immediate equilibrium of fiscal competition between Germany and France. In other words, fiscal competition leads immediately to full employment in Germany and France. It is worth pointing out here that the equilibrium under rational expectations is different from the steady state under adaptive expectations. 2) Monetary and fiscal competition: simultaneous decisions. At the start there is unemployment in Germany, France and America. To be more specific, unemployment in Germany is high, and unemployment in France is low. The target of the European central bank is full employment in Europe. The target of the American central bank is full employment in America. The target of the German government is full employment in Germany. And the target of the French government is full employment in France. We assume that the European central bank, the American central bank, the German government, and the French government decide simultaneously and independently. The European central bank sets European money supply, forming rational expectations of American money supply, German government purchases, and French government purchases. The American central bank sets American money supply, forming rational expectations of European money supply, German government purchases, and French government purchases. The German government sets German government purchases, forming rational expectations of European money supply, American money supply, and French government purchases. And the French government sets French government purchases, forming rational expectations of European money supply, American money supply, and German government purchases.

258 That is to say, the European central bank sets European money supply, predicting American money supply, German government purchases, and French govemment purchases with the help of the model. The American central bank sets American money supply, predicting European money supply, German govemment purchases, and French govemment purchases with the help of the model. The German govemment sets German govemment purchases, predicting European money supply, American money supply, and French govemment purchases with the help of the model. And the French govemment sets French govemment purchases, predicting European money supply, American money supply, and German govemment purchases with the help of the model. As a result, there is no unique equilibrium of monetary and fiscal competition. Put another way, the simultaneous process of monetary and fiscal competition does not lead to full employment and price stability.

Result 1. Monetary Competition between Europe and America

1) The static model. The world consists of two monetary regions, say Europe and America. The exchange rate between Europe and America is flexible. Europe in turn consists of two countries, say Germany and France. So Germany and France form a monetary union. The monetary regions are the same size and have the same behavioural functions. The union countries are the same size and have the same behavioural functions. An increase in European money supply raises both German output and French output, to the same extent respectively. On the other hand, the increase in European money supply lowers American output. Here the rise in European output exceeds the fall in American output. Correspondingly, an increase in American money supply raises American output. On the other hand, it lowers both German output and French output, to the same extent respectively. Here the rise in American output exceeds the fall in European output. In the numerical example, an increase in European money supply of 100 causes an increase in German output of 150, an increase in French output of equally 150, and a decline in American output of 100. Similarly, an increase in American money supply of 100 causes an increase in American output of 300, a decline in German output of 50, and a decline in French output of equally 50. That is to say, the internal effect of monetary policy is very large, and the external effect of monetary policy is large. 2) The dynamic model. At the beginning there is unemployment in Germany, France and America. More precisely, unemployment in Germany exceeds unemployment in France. The target of the European central bank is full employment in Europe. The instrument of the European central bank is European money supply. The European central bank raises European money supply so as to close the output gap in Europe. The target of the American central bank is full employment in America. The instrument of the American central bank is American money supply. The American central bank raises American money

260 supply so as to close the output gap in America. We assume that the European central bank and the American central bank decide simultaneously and independently. In addition there is an output lag. As a result, the process of monetary competition is stable. 3) A numerical example. Full-employment output in Germany is 1000, fullemployment output in France is equally 1000, and full-employment output in America is 2000. Let initial output in Germany be 940, let initial output in France be 970, and let initial output in America be 1910. In each of the countries there is unemployment and hence deflation. Step 1 refers to the policy response. What is needed in Europe is an increase in European money supply of 30. And what is needed in America is an increase in American money supply of equally 30. Step 2 refers to the output lag. The net effect is an increase in German output of 30, an increase in French output of equally 30, and an increase in American output of 60. As a consequence, German output goes to 970, French output goes to 1000, and American output goes to 1970. In step 3, European money supply is raised by 10, as is American money supply. In step 4, German output goes to 980, French output goes to 1010, and American output goes to 1990. And so on. In the steady state, German output is 985, French output is 1015, and American output is 2000. In Germany there is unemployment and deflation. In France there is overemployment and inflation. In Europe there is full employment and price stability. And in America there is full employment and price stability too. As a result, the process of monetary competition leads to full employment in Europe and America. And what is more, it leads to price stability in Europe and America. However, the process of monetary competition does not lead to full employment in Germany and France. And what is more, it does not lead to price stability in Germany and France.

261

2. Monetary Cooperation between Europe and America

1) The model. At the beginning there is unemployment in Germany, France and America. More precisely, unemployment in Germany exceeds unemployment in France. The targets of monetary cooperation are full employment in Europe and full employment in America. The instruments of monetary cooperation are European money supply and American money supply. So there are two targets and two instruments. As a result, there is a solution to monetary cooperation. 2) A numerical example. Let initial output in Germany be 940, let initial output in France be 970, and let initial output in America be 1910. In each of the countries there is unemployment and deflation. What is needed is an increase in European money supply of 45 and an increase in American money supply of equally 45. The net effect is an increase in German output of 45, an increase in French output of equally 45, and an increase in American output of 90. As a consequence, German output goes to 985, French output goes to 1015, and American output goes to 2000. In Germany there is still some unemployment and deflation. In France there is now some overemployment and inflation. In Europe there is now full employment and price stability. And the same holds for America. As a result, monetary cooperation can achieve full employment in Europe and America. And what is more, it can achieve price stability in Europe and America. However, monetary cooperation cannot achieve full employment in Germany and France. And what is more, it cannot achieve price stability in Germany and France. 3) Comparing monetary cooperation with monetary competition. Monetary competition is a slow process. By contrast, monetary cooperation is a fast process. Judging from this point of view, monetary cooperation seems to be superior to monetary competition.

262

3. Fiscal Competition between Germany and France

1) The static model. An increase in German government purchases raises German output. On the other hand, it lowers French output. And what is more, it raises American output. Here the rise in German output exceeds the fall in French output. And the rise in European output equals the rise in American output. Correspondingly, an increase in French government purchases raises French output. On the other hand, it lowers German output. And what is more, it raises American output. Here the rise in French output exceeds the fall in German output. And the rise in European output equals the rise in American output. In the numerical example, an increase in German government purchases of 100 causes an increase in German output of 150, a decline in French output of 50, and an increase in American output of 100. Likewise, an increase in French govemment purchases of 100 causes an increase in French output of 150, a decUne in German output of 50, and an increase in American output of 100. 2) The dynamic model. At the beginning there is unemployment in both Germany and France. More precisely, unemployment in Germany exceeds unemployment in France. By contrast there is full employment in America. The target of the German government is full employment in Germany. The instrument of the German govemment is German government purchases. The German government raises German government purchases so as to close the output gap in Germany. The target of the French government is full employment in France. The instrument of the French government is French government purchases. The French government raises French government purchases so as to close the output gap in France. We assume that the German government and the French government decide simultaneously and independently. In addition there is an output lag. As a result, the process of fiscal competition is stable. 3) A numerical example. Full-employment output in Germany is 1000, fullemployment output in France is equally 1000, and full-employment output in America is 2000. Let initial output in Germany be 940, let initial output in France be 970, and let initial output in America be 2000. In Germany there is

263 unemployment and deflation. In France there is unemployment and deflation too. But in America there is full employment and price stability. Step 1 refers to the policy response. What is needed in Germany is an increase in German government purchases of 40. And what is needed in France is an increase in French government purchases of 20. Step 2 refers to the output lag. The net effect is an increase in German output of 50, an increase in French output of 10, and an increase in American output of 60. As a consequence, German output goes to 990, French output goes to 980, and American output goes to 2060. In step 3, German government purchases are raised by 6.7, and French govemment purchases are raised by 13.3. In step 4, German output goes to 993.3, French output goes to 996.7, and American output goes to 2080. And so on. In the steady state, German output is 1000, French output is equally 1000, and American output is 2090. In Germany there is full employment and price stability. In France there is full employment and price stability too. But in America there is overemployment and inflation. As a result, the process of fiscal competition leads to full employment in Germany and France. And what is more, it leads to price stability in Germany and France. However, as a severe side effect, it causes overemployment and inflation in America.

4. Fiscal Cooperation between Germany and France

1) The model. At the beginning there is unemployment in both Germany and France. More precisely, unemployment in Germany exceeds unemployment in France. By contrast there is full employment in America. The targets of fiscal cooperation are full employment in Germany and full employment in France. The instruments of fiscal cooperation are German government purchases and French government purchases. So there are two targets and two instruments. As a result, there is a solution to fiscal cooperation.

264 2) A numerical example. Let initial output in Germany be 940, let initial output in France be 970, and let initial output in America be 2000. In Germany there is unemployment and deflation. In France there is unemployment and deflation too. But in America there is full employment and price stability. What is needed is an increase in German government purchases of 52.5 and an increase in French government purchases of 37.5. The net effect is an increase in German output of 60, an increase in French output of 30, and an increase in American output of 90. As a consequence, German output goes to 1000, French output goes to 1000, and American output goes to 2090. In Germany there is now full employment and price stability. In France there is now full employment and price stability too. But in America there is now overemployment and inflation. As a result, fiscal cooperation can achieve full employment in Germany and France. And what is more, it can achieve price stability in Germany and France. However, as a severe side effect, it causes overemployment and inflation in America. 3) Comparing fiscal cooperation with fiscal competition. Fiscal competition is a slow process. By contrast, fiscal cooperation is a fast process. Judging from this perspective, fiscal cooperation seems to be superior to fiscal competition.

5. Monetary and Fiscal Competition

1) The model. This section deals with competition between the European central bank, the American central bank, the German government, and the French government. At the beginning there is unemployment in Germany, France and America. More precisely, unemployment in Germany exceeds unemployment in France. The target of the European central bank is full employment in Europe. The instrument of the European central bank is European money supply. The target of the American central bank is full employment in America. The instrument of the American central bank is American money supply. The target of the German government is full employment in Germany. The instrument of

265 the German government is German government purchases. The target of the French government is full employment in France. The instrument of the French government is French government purchases. We assume that the central banks and the governments decide simultaneously and independently. 2) A numerical example. Let initial output in Germany be 940, let initial output in France be 970, and let initial output in America be 1910. In each of the countries there is unemployment and deflation. Step 1 refers to the policy response. What is needed in Europe is an increase in European money supply of 30. What is needed in America is an increase in American money supply of equally 30. What is needed in Germany is an increase in German government purchases of 40. And what is needed in France is an increase in French government purchases of 20. Step 2 refers to the output lag. The net effect is an increase in German output of 80, an increase in French output of 40, and an increase in American output of 120. As a consequence, German output goes to 1020, French output goes to 1010, and American output goes to 2030. In step 3, European money supply is lowered by 10, as is American money supply. German government purchases are lowered by 13.3, and French government purchases are lowered by 6.7. In step 4, German output goes to 993.3, French output goes to 996.7, and American output goes to 1990. And so on. In the steady state, German output is 1000, French output is equally 1000, and American output is 2000. In each of the countries there is full employment and price stability. As a result, the process of monetary and fiscal competition leads to full employment in Germany, France and America. And what is more, it leads to price stability in Germany, France and America.

266

7. Monetary and Fiscal Cooperation

1) The model. This section deals with cooperation between the European central bank, the American central bank, the German government, and the French government. At the beginning there is unemployment in Germany, France and America. More precisely, unemployment in Germany exceeds unemployment in France. The targets of policy cooperation are full employment in Germany, full employment in France, and full employment in America. The instruments of policy cooperation are European money supply, American money supply, German government purchases, and French government purchases. There are three targets and four instruments, so there is one degree of freedom. As a result, there is an infinite number of solutions. 2) A numerical example. Let initial output in Germany be 940, let initial output in France be 970, and let initial output in America be 1910. In each of the countries there is unemployment and deflation. What is needed, for instance, is an increase in European money supply of 45, an increase in American money supply of equally 45, an increase in German government purchases of 7.5, and a reduction in French government purchases of equally 7.5. The net effect is an increase in German output of 60, an increase in French output of 30, and an increase in American output of 90. As a consequence, German output goes to 1000, French output goes to 1000, and American output goes to 2000. In each of the countries there is now full employment and price stability. As a result, monetary and fiscal cooperation can achieve full employment in Germany, France and America. Over and above that, it can achieve price stability in Germany, France and America. 3) Comparing policy cooperation with policy competition. Policy competition is a slow process. By contrast, policy cooperation is a fast process. PoHcy competition causes a large increase in European government purchases. By contrast, policy cooperation causes a zero increase in European government purchases. Judging from these points of view, policy cooperation seems to be superior to policy competition.

Symbols

A B C F G I L M P Q X Y Y

b c d e h

J k m q r s t

a

P Y

autonomous term autonomous temi (private) consumption autonomous term government purchases of goods and services (private) investment money demand money supply price level imports exports output, income full-employment output

interest sensitivity of investment marginal consumption rate differential exchange rate exchange rate sensitivity of exports interest sensitivity of money demand income sensitivity of money demand marginal import rate marginal import rate interest rate 1-c time

monetary policy multiplier (direct effect) monetary policy multiplier (cross effect) fiscal policy multiplier (direct effect)

268 5 e

fiscal policy multiplier (cross effect) y-d

A Brief Survey of the Literature

The focus of this survey is on the macroeconomics of monetary union. It is based on that given in Carlberg (2004). As a starting point take the classic papers by Fleming (1962) and Mundell (1963, 1964, 1968). They discuss monetary and fiscal policy in an open economy characterized by perfect capital mobility. The exchange rate can either be flexible or fixed. They consider both the small open economy and the world economy made up of two large countries. The seminal papers by Levin (1983) as well as by Rose and Sauemheimer (1983) are natural extensions of the papers by Fleming and Mundell. They deal with stabilization policy in a jointly floating currency area. It turns out, however, that the joint float produces results for the individual countries within the currency area and for the area as a whole that in some cases differ sharply from those in the Fleming and Mundell papers. The currency area is a small open economy with perfect capital mobility. For the small currency area, the world interest rate is given exogenously. Under perfect capital mobility, the interest rate of the currency area coincides with the world interest rate. Therefore the interest rate of the currency area is constant, too. The currency area consists of two countries. The exchange rate within the currency area is pegged. The exchange rate between the currency area and the rest of the world is floating. Country 1 manufactures good 1, and country 2 manufactures good 2. These goods are imperfect substitutes. The authors examine monetary and fiscal policy by one of the countries in the currency area, paying special attention to the effects on the domestic country and the partner country. Moreover they study demand switches within the currency area as well as a realignment of the exchange rate within the currency area. The most surprising finding is that a fiscal expansion by one of the countries in the currency area produces a contraction of economic activity in the other country. This beggar-my-neighbour effect can be so strong as to cause a dechne in economic activity within the area as a whole. Conversely, a monetary expansion by one of the countries in the currency area produces an expansion of economic activity in the other country as well. Levin concludes his paper with a

270

practical observation. Since the cross effects of fiscal expansion in one currency area country may well be negative because of the joint float, it is crucial for econometric model builders concerned with linkages within a currency area to incorporate the induced exchange rate movements into their models. Sauernheimer (1984) argues that a depreciation brings up consumer prices. To prevent a loss of purchasing power, trade unions call for higher money wages. On that account, producer prices go up as well. He sums up that the results obtained in the 1983 papers are very robust. Moutos and Scarth (1988) further investigate the supply side and the part played by real wage rigidity. Under markup pricing, there is no beggar-my-neighbour effect of fiscal policy. Under marginal cost pricing, on the other hand, the beggar-my-neighbour effect is a serious possibility. Feuerstein and Siebke (1990) also model the supply side. In addition, they introduce exchange rate expectations. The monograph by Feuerstein (1992) contains a thorough analysis of the supply side. Beyond that the author looks into wage indexation and the role of a lead currency. Over and above that, she develops a portfoHo model of a small currency area. The books by Hansen, Heinrich and Nielsen (1992) as well as by Hansen and Nielsen (1997) are devoted to the economics of the European Community. As far as the macroeconomics of monetary union is concerned, the main topics are policy coordination, exchange rate expectations, and slow prices. In the paper by Wohltmann (1993), prices are a slow variable. Both inflation expectations and exchange rate expectations are rational. He contemplates an economy with or without wage indexation. The paper by Jarchow (1993) has a world economy that consists of three large countries. Two of them share one money. Prices are flexible, and real wages are fixed. A fiscal expansion in union country 1 enhances union income. Unfortunately, it can depress the income of union country 2. It can inflate prices in each of the union countries. A depreciation of the union currency is possible. Finally have a look at a list of some recent books: ALESINA, A., BLANCHARD, O., GALI, J., GIAVAZZI, F., UHLIG, H., Defining a Macroeconomic Framework for the Euro Area, London 2001 ALLSOPP, C , VINES, D., eds., Macroeconomic PoHcy after EMU, Oxford 1998 BEETSMA, R., et al., eds.. Monetary Policy, Fiscal Policies and Labour Markets, Cambridge 2004

271 BEGG, D., CANOVA, F., DE GRAUWE, P., FATAS, A., LANE, P., Surviving the Slowdown, London 2002 BEGG, L, ed., Europe: Government and Money: Running EMU: The Challenges of Policy Coordination, London 2002 BRUNILA, A., BUTI, M., FRANCO, D., eds., The Stability and Growth Pact, Houndmills 2001 BUTI, M., ed.. Monetary and Fiscal Policies in the EMU: Interactions and Coordination, Cambridge 2003 BUTI, M., FRANCO, D., Fiscal Policy in EMU, Cheltenham 2005 BUTI, M., SAPIR, A., eds.. Economic Policy in EMU, Oxford 1998 BUTI, M., SAPIR, A., eds., EMU and Economic Policy in Europe: The Challenge of the Early Years, Cheltenham 2002 CALMFORS, L., et al, EMU - A Swedish Perspective, Dordrecht 1997 CLAUSEN, v.. Asymmetric Monetary Transmission in Europe, Berlin 2000 DE GRAUWE, P., Economics of Monetary Union, Oxford 2005 EICHENGREEN, B., European Monetary Unification, Cambridge 1997 EIJFFINGER, S., DE HAAN, J., European Monetary and Fiscal Policy, Oxford 2000 GROS, D,, ed., Macroeconomic Policy under the Euro, Cheltenham 2004 HUGHES HALLET, A., HUTCHISON, M. M., JENSEN, S. H., eds.. Fiscal Aspects of European Monetary Integration, Cambridge 1999 HUGHES HALLET, A., MOOSLECHNER, P., SCHUERZ, M., eds.. Challenges for Economic Policy Coordination within European Monetary Union, Dordrecht 2001 ISSING, O., CASPAR, V., ANGELONI, I., TRISTANI, O., Monetary PoUcy in the Euro Area, Cambridge 2001 MASSON, P. R., KRUEGER, T.H., TURTELBOOM, B. G., eds., EMU and the International Monetary System, Washington 1997 MUNDELL, R. A., ZAK, P. J., SCHAEFFER, D., eds.. International Monetary Policy after the Euro, Cheltenham 2005 SMETS, J., DOMBRECHT, M., eds.. How to Promote Economic Growth in the Euro Area, Cheltenham 2001

The Current Research Project

The present book is part of a larger research project on monetary union, see Carlberg (1999, 2000, 2001, 2002, 2003, 2004, 2005). Volume two (2000) deals with the scope and limits of macroeconomic policy in a monetary union. The leading protagonists are the union central bank, national governments, and national trade unions. Special emphasis is put on wage shocks and wage restraint. This book develops a series of basic, intermediate and more advanced models. A striking feature is the numerical estimation of policy multipliers. A lot of diagrams serve to illustrate the subject in hand. The monetary union is an open economy with high capital mobility. The exchange rate between the monetary union and the rest of the world is flexible. The world interest rate can be exogenous or endogenous. The union countries may differ in money demand, consumption, imports, openness, or size. Volume three (2001) explores the new economics of monetary union. It discusses the effects of shocks and policies on output and prices. Shocks and policies are country-specific or common. They occur on the demand or supply side. Countries can differ in behavioural functions. Wages can be fixed, flexible, or slow. In addition, fixed wages and flexible wages can coexist. Take for instance fixed wages in Germany and flexible wages in France. Or take fixed wages in Europe and flexible wages in America. Throughout this book makes use of the rate-of-growth method. This method, together with suitable initial conditions, proves to be very powerful. Further topics are inflation and disinflation. Take for instance inflation in Germany and price stability in France. Then what policy is needed for disinflation in the union? And what will be the dynamic effects on Germany and France? Volume four (2002) deals with the causes and cures of inflation in a monetary union. It studies the effects of money growth and output growth on inflation. The focus is on producer inflation, currency depreciation and consumer inflation. For instance, what determines the rate of consumer inflation in Europe, and what in America? Moreover, what determines the rate of consumer inflation in Germany, and what in France? Further issues are real depreciation, nominal and real interest rates, the growth of nominal wages, the growth of producer real

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wages, and the growth of consumer real wages. Here productivity growth and labour growth play significant roles. Another issue is target inflation and required money growth. A prominent feature of this book is microfoundations for a monetary union. Volume five (2003) deals with the international coordination of economic policy in a monetary union. It discusses the process of policy competition and the structure of policy cooperation. As to policy competition, the focus is on competition between the union central bank, the German government, and the French government. Similarly, as to policy cooperation, the focus is on cooperation between the union central bank, the German government, and the French government. The key questions are: Does the process of pohcy competition lead to price stability and full employment? Can these targets be achieved through policy cooperation? And is policy cooperation superior to policy competition? Volume six (2004) studies the interactions between monetary and fiscal policies in the euro area. The policy makers are the union central bank, the German government, the French government, and other governments. The policy targets are price stability in the union, full employment in Germany, full employment in France, etc. The policy instruments are union money supply, German government purchases, French government purchases, etc. As a rule, the spillovers of fiscal policy are negative. The policy makers follow either coldturkey or gradualist strategies. The policy decisions are taken sequentially or simultaneously. Policy expectations are adaptive or rational. This book carefully discusses the case for central bank independence and fiscal cooperation. Volume seven (2005) deals with the international coordination of monetary and fiscal policies in the world economy. It examines the process of pohcy competition and the structure of policy cooperation. As to policy competition, the focus is on monetary and fiscal competition between Europe and America. Similarly, as to policy cooperation, the focus is on monetary and fiscal cooperation between Europe and America. The spillover effects of monetary pohcy are negative while the spillover effects of fiscal policy are positive. The policy targets are price stability and full employment. The policy makers follow either cold-turkey or gradualist strategies. Policy expectations are adaptive or rational. The world economy consists of two, three or more regions.

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Further information about these books is given on the web-page: http://[email protected]

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Index

Adaptive policy expectations, 195, 200, 209 American money market, 26, 37 Anticipation, 68, 161 Appreciation, 46, 62, 86, 95, 112,170, 179 Budget deficit, 56, 95, 112,170, 179 Cold-turkey policies, 127,149 Comparing fiscal cooperation with fiscal competition, 104 Comparing gradualist policies with cold-turkey policies, 159 Comparing monetary and fiscal competition with pure fiscal competition, 115 Comparing monetary and fiscal cooperation with monetary and fiscal competition, 125, 144 Comparing monetary cooperation with monetary competition, 79 Comparing simultaneous decisions with sequential decisions, 152 Comparing the sequential process of monetary cooperation and fiscal cooperation with the sequential process of monetary cooperation and fiscal competition, 180 Comparing the sequential process of monetary cooperation and fiscal cooperation with the simultaneous process of monetary and fiscal cooperation, 180 Comparing the system of monetary cooperation and fiscal competition with the system of monetary and fiscal competition, 174 Competition between European central bank, American central bank, German government, and French government, 127, 149, 155, 161, 203, 212 Competition between European central bank, German government, and French government, 107 Cooperation between European central bank, American central bank, German government, and French government, 137 Cooperation between European central bank, German government, and French government, 120 Coordination mechanism, type of, 154, 160, 164, 170, 180, 188 Current account deficit, 95

288 Current account surplus, 95 Deflation in America, 111, 123 Deflation in France, 60, 77 Deflation in Germany, 47, 55, 75 Degrees of freedom, 120, 137, 165, 175, 213 Depreciation, 46, 62, 86, 95, 112, 170, 179 Dynamic characteristics, 56, 62, 95, 111, 133, 152, 158, 163, 170, 179, 188 Dynamic model, 45, 85, 107, 127, 149, 155, 161, 165, 175, 184, 191 Effective multiplier, 57, 63, 75, 79, 96, 98 European money market, 26, 37 Expectations, adaptive, 195, 200, 209 Expectations, rational, 194-195, 198-199, 204-205, 207-208, 212-213, 215-216, 220-221 External effect of fiscal policy, 85, 86, 92-94, 131 External effect of monetary policy, 46, 52, 54, 55, 130 Fast monetary competition, slow fiscal competition, 161 First the governments decide, then the central bank decides, 115 Fiscal competition between Germany and France, 85, 198 Fiscal cooperation between Germany and France, 99 Fiscal interactions between Germany and France, 83 Fiscal policy, 18,29,40 Full employment in America, 48, 52, 55, 72, 75, 133, 141 Full employment in Europe, 47, 55, 72, 75 Full employment in France, 68, 87, 94, 123, 133, 141 Full employment in Germany, 66, 87, 94, 123, 133, 141 Goods market, 13, 14, 24, 25, 34, 35 Gradualist policies, 155 High employment in Germany and France, 47, 108, 128 Inflation, 59, 77, 143, 170, 180 Inflationary gap, 59, 96 Inflation in America, 92, 94, 100, 102, 114

289 Inflation in Europe, 66 Inflation in Europe and America, 59, 77, 143, 170, 180 Inflation in Europe, price stability in America, 113, 124 Inflation in France, 47, 55, 75 Inflation in Germany, 60, 77 Internal effect of fiscal policy, 85, 86, 92, 93 Internal effect of monetary policy, 46, 52, 54 Large monetary union of two countries, 33 Market for American goods, 25, 36 Market for European goods, 24 Market for French goods, 14, 35 Market for German goods, 13, 34 Model, 16, 27, 37, 71, 99, 120, 137, 165, 175, 184 Models, basic, 13, 20, 24, 33 Monetary and fiscal interactions, 105, 147 Monetary competition between Europe and America, 45, 193 Monetary cooperation between Europe and America, 71 Monetary cooperation between Europe and America, fiscal competition between Germany and France, 165, 214 Monetary cooperation between Europe and America, fiscal cooperation between Germany and France, 175 Monetary interactions between Europe and America, 43 Monetary policy, 19, 31 Money market, 15, 26, 37 Money market of the union, 15 Numerical example, 53, 74, 92, 101, 109, 122, 129, 140, 166, 177, 186 Oscillations, 62, 98, 112, 152, 170 Output gap, 47, 54, 93 Output lag, 48, 54, 88, 93 Output model, 71, 99, 120, 137 Overemployment in America, 92, 94, 100, 102, 114 Overemployment in Europe, 66 Overemployment in France, 47, 55, 75

290 Overemployment in Germany, 60, 77 Policy cooperation within Europe, policy competition between Europe and America, 184,219 Policy model, 72, 99, 120, 138 Price stability in America, 48, 52, 55, 59, 72, 75, 133, 141 Price stability in Europe, 47, 52, 55, 59, 72, 75 Price stability in France, 68, 94, 123, 133, 141 Price stability in Germany, 66, 94, 123, 133, 141 Rational policy expectations, 191 Sequential decisions, 107, 127, 161, 165, 175, 203, 214 Simultaneous decisions, 149, 155, 212 Small monetary union of two countries, 13 Speed of adjustment in money supply and government purchases, 160 Speed of fiscal competition, 104 Speed of monetary and fiscal competition, 125, 144 Speed of monetary competition, 70 Spillovers, see External effects Stability, 51, 91 Static model, 45, 85, 107, 127, 165 Steady state, 49, 89, 111, 132,152,158, 169, 188 Synopsis, 227 Target of American central bank, 48, 128 Target of European central bank, 47, 64, 79, 108, 128 Target of French government, 87,128 Target of German government, 87, 128 Targets of fiscal cooperation, 99,175 Targets of monetary and fiscal cooperation, 120, 124, 137, 138, 145 Targets of monetary cooperation, 72, 165, 175 Unemployment, 54, 74, 130, 140, 149, 155, 161, 167, 178, 186 Unemployment in America, 111,123 Unemployment in Europe and America, 54, 74, 130, 140, 149, 155, 161, 167, 178, 186

291 Unemployment in Europe, full employment in America, 110, 122 Unemployment in Europe, inflation in America, 61, 78, 144, 172, 182 Unemployment in France, 60, 77 Unemployment in Germany, 47, 55, 75 Unemployment in Germany and France, 93, 102, 110, 122, 130, 140, 144, 149, 155, 161, 167, 178, 184, 191 Unemployment in Germany, overemployment in France, 96, 103 World as a whole, 20 World of two monetary regions, 24