Monetary and Wage Policies in the Euro Area

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Monetary and Wage Policies in the Euro Area

Michael Carlberg

Monetary and Wage Policies in the Euro Area With 65 Tables

GI - Springer

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

ISBN-10 3-540-36933-3 Springer Berlin Heidelberg New York ISBN-13 978-3-540-36933-2 Springer Berlin Heidelberg New York Cataloging-in-Publi cat ion Data Library of Congress Control Number: 2006931060 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 BerHn • 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 11809838

42/3153-5 4 3 2 1 0 - Printed on acid-free paper

Preface

This book studies the interactions between monetary and wage pohcies 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 labour union, and the French labour union. As to policy cooperation, the focus is on the same institutions. These are higher-dimensional issues. The policy 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 wage 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, at the International Conference on Macroeconomic Analysis, at the International Institute of Public Finance, and at the International Atlantic Economic Conference. Other parts were presented 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 Riibel,

VI Michael Schmid, Gerhard Schwodiauer, Patrizio TirelU, Harald Uhlig, Bas van Aarle, Uwe Vollmer, Jiirgen 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) Competition between the European central bank and the American central bank. As a result, the process of monetary competition leads to fiill 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) Cooperation between the European central bank and the American central bank. 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) Competition between the German labour union and the French labour union. As a result, the process of wage competition leads to fiill employment in Germany and France. However, as an adverse side effect, it causes unemployment in America. There are damped oscillations in nominal wages and output. Taking the sum over all periods, the total reduction in European nominal wages is large, as compared to the initial output gap. 5) Cooperation between the German labour union and the French labour union. As a result, wage cooperation can achieve full employment in Germany and France. However, as an adverse side effect, it causes unemployment in

VIII America. The required cut in European nominal wages is large. Wage cooperation is a fast process, as compared to wage competition. 6) Competition between the European central bank, the American central bank, the German labour union, and the French labour union. As a result, the process of monetary and wage competition leads to full employment in Germany, France and America. There are damped oscillations in output. The German economy oscillates between unemployment and overemployment, as do the French economy and the American economy. Taking the sum over all periods, the total reduction in European nominal wages is small, as compared to the initial output gap. 7) Cooperation between the European central bank, the American central bank, the German labour union, and the French labour union. As a result, monetary and wage cooperation can achieve full employment in Germany, France and America. The required cut in European nominal wages is zero. Policy cooperation is a fast process, as compared to policy competition. So policy cooperation seems to be superior to policy competition.

Contents in Brief

Introduction

1

Part One. Basic Models of a Monetary Union

ll

Chapter 1. The Small Monetary Union of Two Countries Chapter 2. The World as a Whole Chapter 3. The World of Two Monetary Regions

13 27 33

Part Two. Monetary Interactions between Europe and America

49

Chapter 1. Monetary Competition between Europe and America Chapter 2. Monetary Cooperation between Europe and America

51 71

Part Tliree. Wage Interactions between Germany and France

81

Chapter 1. Competition between the German Labour Union and the French Labour Union Chapter 2. Cooperation between the German Labour Union and the French Labour Union

103

Part Four. Monetary and Wage Interactions: Intermediate Models

113

Chapter 1. Competition between European Central Bank, German Labour Union, and French Labour Union Chapter 2. Cooperation between European Central Bank, German Labour Union, and French Labour Union Chapter 3. Competition between European Central Bank, American Central Bank, German Labour Union, and French Labour Union

83

115 130

139

X

Chapter 4. Cooperation between European Central Bank, American Central Bank, German Labour Union, and French Labour Union

150

Part Five. Monetary and Wage Interactions: Advanced Models

163

Chapter 1. Simultaneous Decisions: Cold-Turkey Policies Chapter 2. Simultaneous Decisions: Gradualist Policies Chapter 3. Fast Monetary Competition and Slow Wage Competition Chapter 4. Monetary Cooperation between Europe and America, Wage Competition between Germany and France Chapter 5. Monetary Cooperation between Europe and America, Wage Cooperation between Germany and France Chapter 6. Policy Cooperation within Europe, Policy Competition between Europe and America

165 170 176

202

Part Six. Rational Policy Expectations

209

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

211 217 222, 231

Synopsis Conclusion Result References Index

245 249 277 293 305

180 192

233 238

Contents

Introduction

l

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 Wage Competition between Germany and France Wage Cooperation between Germany and France Monetary and Wage Competition Monetary and Wage Cooperation

Part One. Basic Models of a Monetary Union

ii

Chapter 1. The Small Monetary Union of Two Countries 1. The Model 1.1. Introduction 1.2. The Market for German Goods 1.3. The Market for French Goods 1.4. The Money Market of the Union 1.5. Technology and Price Setting 1.6. The Model 1.7. The Rate-of-Growth Method 2. Monetary Policy 3. Wage Policy

13 13 13 13 15 17 18 19 21 23 25

Chapter 2. The World as a Whole 1. The Model 2. Monetary Policy 3. Wage Policy

27 27 30 31

Chapter 3. The World of Two Monetary Regions 1. The Model 1.1. Introduction

33 33 33

XII 1.2. The Market for European Goods 1.3. The Market for American Goods 1.4. The European Money Market 1.5. The American Money Market 1.6. Technology and Price Setting 1.7. The Model 1.8. The Rate-of-Growth Method 2. Monetary Policy 3. Wage Policy

33 35 36 37 37 39 41 43 45

Part Two. Monetary Interactions between Europe and America

49

Chapter 1. Monetary Competition between Europe and America 1. The Djmamic 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. UnemplojTnent in Europe, Inflation in America

51 51 59 60 64 65 68

Chapter 2. Monetary Cooperation between Europe and America 1. The Model.... ; 2. Some Numerical Examples

71 71 74

Part Three. Wage Interactions between Germany and France

81

Chapter 1. Competition between the German Labour Union and the French Labour Union 1. The Dynamic Model 2. Some Numerical Examples 2.1. Unemployment in Germany Equals Unemployment in France 2.2. Unemployment in Germany Is High, Unemployment in France Is Low

83 83 91 92 95

XIII 2.3. Unemployment in Germany, Full Employment in France 2.4. Unemployment in Germany, Overemployment in France 2.5. Overemployment in Germany and France

97 98 100

Chapter 2. Cooperation between the German Labour Union and the French Labour Union 1. The Model 2. Some Numerical Examples

103 103 105

Part Four. Monetary and Wage Interactions: Intermediate Models

113

Chapter 1. Competition between European Central Banl^, German Labour Union, and French Labour Union 1. The Dynamic Model 2. Some Numerical Examples 2.1. Unemployment in Europe, Full Employment in America 2.2. Another Interpretation 2.3. Overemployment in Europe, Full Employment in America 2.4. First the Labour Unions Decide, then the Central Bank Decides

115 115 117 118 120 122 126

Chapter 2. Cooperation between European Central Bank, German Labour Union, and French Labour Union 1. The Model 2. Some Numerical Examples 2.1. Unemplojonent in Europe, Full Employment in America 2.2. Overemployment in Europe, Full Employment in America 2.3. Alternative Targets of Policy Cooperation

130 130 132 132 134 136

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

139 139 141 142 145

XIV 2.3. The Case of Overemployment

147

Chapter 4. Cooperation between European Central Bank, American Central Bank, German Labour Union, and French Labour Union 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 Overemployment 2.4. Unemployment in Europe, Overemployment in America 2.5. Alternative Targets of Policy Cooperation

150 150 153 153 155 156 158 159

Part Five. Monetary and Wage Interactions: Advanced Models

163

Chapter 1. Simultaneous Decisions: Cold-Turkey Policies Chapter 2. Simultaneous Decisions: Gradualist Policies Chapter 3. Fast Monetary Competition and Slow Wage Competition Chapter 4. Monetary Cooperation between Europe and America, Wage Competition between Germany and France 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 Overemplojmient 2.4. Unemployment in Europe, Overemplojmient in America

165 170 176 180 180 182 182 185 187 189

Chapter 5. Monetary Cooperation between Europe and America, Wage Cooperation between Germany and France 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 Overemployment 2.4. Unemplojonent in Europe, Overemployment in America

192 192 194 195 197 198 200

XV

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

202 202 204

Part Six. Rational Policy Expectations

209

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

211 217 222 231 233 238

Synopsis

245

Conclusion

249

1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11.

249 254 257 260 261 265 267 268 269 272 274

Monetary Competition between Europe and America Monetary Cooperation between Europe and America Wage Competition between Germany and France Wage Cooperation between Germany and France Monetary and Wage Competition Monetary and Wage Cooperation Simultaneous Decisions: Cold-Turkey Policies Simultaneous Decisions: Gradualist Policies Monetary Cooperation and Wage Competition Monetary Cooperation and Wage Cooperation Rational Policy Expectations

XVI

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

277 277 279 280 281 282 284

Symbols

285

A Brief Survey of the Literature

287

The Current Research Project

290

References

293

Index

305

Introduction 1. Subject and Approach

This book studies the interactions between monetary and wage policies in the euro area. It carefully discusses the process of policy competition and the structure of policy cooperation. With respect to policy competition, the focus is on competition between the European central bank, the American central bank, the German labour union, and the French labour union. Similarly, with respect to policy cooperation, the focus is on cooperation between the European central bank, the American central bank, the German labour union, and the French labour union. Further topics are: -

sequential decisions: cold-turkey policies simultaneous decisions: cold-turkey policies simultaneous decisions: gradualist policies fast monetary competition, slow wage competition monetary cooperation between Europe and America, wage competition between Germany and France - monetary cooperation between Europe and America, wage cooperation between Germany and France - policy cooperation within Europe, policy 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 labour union is full employment in Germany. And the target of the French labour union is full employment in France. Wage policy in one of the countries has a large external effect on the other countries. For instance, an increase in German nominal wages lowers French output and raises American output.

The key questions are: - Does the process of policy 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 modem 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 mobility 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 - Wage Interactions between Germany and France - Monetary and Wage Interactions: Intermediate Models - Monetary and Wage Interactions: Advanced Models - Rational Policy 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 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 is larger than 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 is larger than 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. This section deals with competition between the European central bank and the American central bank. At the beginning there is unemplojTnent in Germany, France and America. More precisely, unemployment in Germany is high, and unemployment in France is low. 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 emplojmient 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

This section deals with cooperation between the European central bank and the American central bank. At the start there is unemployment in Germany, France and America. Let unemployment in Germany be high, and let unemployment in France be 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. 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 emplojmient 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. Wage Competition between Germany and France

1) The static model. An increase in German nominal wages lowers German output. And what is more, it lowers French output. On the other hand, it raises American output. Here the fall in German output is larger than the fall in French output. And the fall in European output is larger than the rise in American output. Correspondingly, an increase in French nominal wages lowers French output. And what is more, it lowers German output. On the other hand, it raises American output. Here the fall in French output is larger than the fall in German output. And the fall in European output is larger than the rise in American output.

In the numerical example, an increase in German nominal wages of 100 causes a decline in German output of 120, a decline in French output of 30, and an increase in American output of 50. Likewise, an increase in French nominal wages of 100 causes a decline in French output of 120, a decline in German output of 30, and an increase in American output of 50. Now have a closer look at the process of adjustment. An increase in German nominal wages causes an increase in the price of German goods. This in turn causes an appreciation of the euro, a depreciation of the dollar, and an increase in the world interest rate. The increase in the price of German goods lowers German exports. On the other hand, it raises French exports and American exports. 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 and French output move down. However, American output moves up. This model is in the tradition of the Mundell-Fleming model and the Levin model. 2) The dynamic model. This section deals with competition between the German labour union and the French labour union. At the beginning there is unemployment in Germany and France. More precisely, unemployment in Germany is high, and unemployment in France is low. By contrast there is full employment in America. The target of the German labour union is full employment in Germany. The instrument of the German labour union is German nominal wages. The German labour union lowers German nominal wages so as to close the output gap in Germany. The target of the French labour union is full employment in France. The instrument of the French labour union is French nominal wages. The French labour union lowers French nominal wages so as to close the output gap in France. We assume that the German labour union and the French labour union decide simultaneously and independently. In addition there is an output lag. German output next period is determined by German nominal wages this period as well as by French nominal wages this period. In the same way, French output next period is determined by French nominal wages this period as well as by German nominal wages this period. Last but not least, American output next period is determined by German nominal wages this period as well as by French nominal wages this period.

The key questions are: Is there a steady state of wage competition? Is the steady state of wage competition stable? Does wage competition lead to full employment in Germany and France? Does wage 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 reduction in German nominal wages? And what is the total reduction in French nominal wages? How does the total reduction in German nominal wages compare with the initial output gap in Germany? And how does the total reduction in French nominal wages compare with the initial output gap in France?

5. Wage Cooperation between Germany and France

This section deals with cooperation between the German labour union and the French labour union. At the start there is unemployment in Germany and France. Let unemplojment in Germany be high, and let unemployment in France be low. By contrast there is full employment in America. The targets of wage cooperation are full employment in Germany and full employment in France. The instruments of wage cooperation are German nominal wages and French nominal wages. So there are two targets and two instruments. Here the key questions are: Is there a solution to wage cooperation? Can wage cooperation achieve full employment in Germany and France? Can wage cooperation achieve fiill employment in Europe and America? What is the required cut in German nominal wages? And what is the required cut in French nominal wages? How does the required cut in German nominal wages compare with the initial output gap in Germany? And how does the required cut in French nominal wages compare with the initial output gap in France? Finally, is wage cooperation superior to wage competition?

6. Monetary and Wage Competition

This section deals with competition between the European central bank, the American central bank, the German labour union, and the French labour union. 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 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 unemplojmient in Germany equals overemployment in France. 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 labour union is full employment in Germany. The instrument of the German labour union is German nominal wages. The German labour union lowers German nominal wages so as to close the output gap in Germany. The target of the French labour union is full employment in France. The instrument of the French labour union is French nominal wages. The French labour union lowers French nominal wages so as to close the output gap in France. We assume that the central banks and the labour unions decide sequentially. First the central banks decide, then the labour unions decide. In step 1, the European central bank and the American central bank decide simultaneously and independently. In step 2, the German labour union and the French labour union 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 labour union and the French labour union decide simultaneously and independently. And so on.

The key questions are: Is there a steady state of monetary and wage competition? Is the steady state of monetary and wage competition stable? Does the process of monetary and wage competition lead to full emplojmient 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 reduction in German nominal wages? And what is the total reduction in French nominal wages? 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 reduction in German nominal wages compare with the initial output gap in Germany? And how does the total reduction in French nominal wages compare with the initial output gap in France? Moreover, is the system of monetary and wage competition superior to pure monetary competition? And is the system of monetary and wage competition superior to pure wage competition?

7. Monetary and Wage Cooperation

This section deals with cooperation between the European central bank, the American central bank, the German labour union, and the French labour union. At the start there is unemployment in Germany, France and America. Let unemployment in Germany be high, and let unemployment in France be low. 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 nominal wages, and French nominal wages. There are three targets and four instruments, so there is one degree of freedom. Here the key questions are: Is there a solution to monetary and wage cooperation? Can monetary and wage cooperation achieve full employment in

10 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 cut in German nominal wages? And what is the required cut in French nominal wages? 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 cut in German nominal wages compare with the initial output gap in Germany? And how does the required cut in French nominal wages compare with the initial output gap in France? Finally, is the system of monetary and wage cooperation superior to the system of monetary and wage competition?

Part One Basic Models of a Monetary Union

Chapter 1 The Small Monetary Union of Two Countries 1. The Model

1) Introduction. In this chapter we consider a monetary union of two countries, let us say Germany and France. Take for instance an increase in union money supply. Then what will be the effect on German output, and what on French output? Alternatively take an increase in German nominal wages. Again what will be the effect on German output, and what on French output? The monetary union is a small open economy with perfect capital mobility. For the small open economy, the world interest rate is given exogenously rf = const. Under perfect capital mobility, the union interest rate agrees with the world interest rate r = rf. Therefore the union interest rate is constant, too. The exchange rate between the monetary union and the rest of the world is flexible. German goods and French goods are imperfect substitutes for one another. We assume that the union countries are the same size and have the same behavioural functions. 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). 2) The market for German goods. The behavioural functions underlying the analysis are as follows: Ci = cYi

(1)

Ij = const

(2)

Gi = const

(3)

Xi2 = mP2Y2/Pi

(4)

Xi3=he/Pi

(5)

Ql=qYi

(6)

14 Equation (1) is the consumption function of Germany. Here Cj denotes German consumption, as measured in German goods. Yj is German income, as measured in German goods. And c is the marginal consumption rate of Germany, with 0 < c < 1. Equation (1) states that German consumption is a positive function of German income. According to equation (2), German firms decide on German investment. Here Ij is German investment, as measured in German goods. According to equation (3), the German government sets its purchases of goods and services. Here Gj is German government purchases, as measured in German goods. Equation (4) is the export function of Germany relative to France. Here X12 denotes German exports to France, as measured in German goods. Pj is the price of German goods, as measured in euros. P2 is the price of French goods, as measured in euros. Y2 is French income, as measured in French goods. Then P2Y2 is French income, as measured in euros. And P2Y2 / Pj is French income, as measured in German goods, m is the marginal import rate of France relative to Germany, with m > 0. Equation (4) states that German exports to France are a positive function of French income, a negative fimction of the price of German goods, and a positive function of the price of French goods. A 1 percent increase in French income causes a 1 percent increase in German exports to France. On the other hand, a 1 percent increase in the price of German goods causes a 1 percent decline in German exports to France. And a 1 percent increase in the price of French goods causes a 1 percent increase in German exports to France. Equation (5) is export fimction of Germany relative to non-union countries. Here X13 denotes German exports to non-union countries, as measured in German goods, e is the exchange rate between the monetary union and the rest of the world (e.g. the price of the dollar in terms of the euro). Then Pj / e is the price of German goods, as measured in dollars. And h is the price sensitivity of German exports to non-union countries, with h > 0. Equation (5) states that German exports to non-union countries are a positive function of the exchange rate and a negative function of the price of German goods. A 1 percent depreciation of the euro causes a 1 percent increase in German exports to nonunion countries. The other way round, a 1 percent increase in the price of German goods causes a 1 percent decline in German exports to non-union countries. Equation (6) is the import function of Germany. Here Qi is German imports from France and from non-union countries, as measured in German

15 goods. Yj is German income, as measured in German goods. And q is the marginal import rate of Germany, with q > 0. Equation (6) states that German imports are a positive function of German income. German output is determined by the demand for German goods Yj = Cj + Ij + G^ +Xj2 + Xj3 - Qj. Taking account of the behavioural fiinctions (1) until (6), we arrive at the goods market equation of Germany: Yi = A i + c Y i + m P 2 Y 2 / P i + h e / P i - q Y i

(7)

Here Aj = Ij + G^ is the autonomous part of the demand for German goods. 3) The market for French goods. The underlying behavioural functions are as follows: C2=cY2

(8)

I2 = const

(9)

G2 = const

(10)

X2i = mPiYi/P2

(11)

X23 = he/P2

(12)

Q2=qY2

(13)

Equation (8) is the consumption function of France. Here C2 denotes French consumption, as measured in French goods. Y2 is French income, as measured in French goods. And c is the marginal consumption rate of France, with 0 < c < 1. Equation (8) states that French consumption is a positive function of French income. According to equation (9), French firms decide on French investment. Here I2 is French investment, as measured in French goods. According to equation (10), the French government sets its purchases of goods and services. Here G2 is French government purchases, as measured in French goods. Equation (11) is the export function of France relative to Germany. Here X21 denotes French exports to Germany, as measured in French goods. Yj is German income, as measured in German goods. Then PjYj is German income, as

16 measured in euros. And P^Yj / P2 is German income, as measured in French goods, m is the marginal import rate of Germany relative to France, with m > 0. Equation (11) states that French exports to Germany are a positive function of German income, a negative function of the price of French goods, and a positive function of the price of German goods. A 1 percent increase in German income causes a 1 percent increase in French exports to Germany. On the other hand, a 1 percent increase in the price of French goods causes a 1 percent decline in French exports to Germany. And a 1 percent increase in the price of German goods causes a 1 percent increase in French exports to Germany. Of course, French exports to Germany are identical with German imports from France, as long as both are measured in French goods. Equation (12) is the export function of France relative to non-union countries. Here X23 denotes French exports to non-union countries, as measured in French goods. P2 / e is the price of French goods, as measured in dollars. And h is the price sensitivity of French exports to non-union countries, with h > 0. Equation (12) states that French exports to non-union countries are a positive function of the exchange rate and a negative function of the price of French goods. A 1 percent depreciation of the euro causes a 1 percent increase in French exports to non-union countries. The other way round, a 1 percent increase in the price of French goods causes a 1 percent decline in French exports to non-union countries. Equation (13) is the import function of France. Here Q2 is French imports from Germany and from non-union countries, as measured in French goods. Y2 is French income, as measured in French goods. And q is the marginal import rate of France, with q > 0. Equation (13) states that French imports are a positive function of French income. French output is determined by the demand for French goods ¥2= C2 + I2 + G2 + X21+X23 - Q2 • Upon substituting the behavioural functions (8) until (13), we find out the goods market equation of France: Y2 = A2 + CY2 + mPiYi / P2 + he / P2 - qY2 Here A2 = I2 + G2 is the autonomous part of the demand for French goods.

(14)

17 4) The money market of the union. There is no separate money market in Germany (or, for that matter, in France). On the contrary, there is a single money market in the union. The behavioural functions are as follows:

Li=kPiYi

(15)

L2 = kP2Y2

(16)

M = const

(17)

Equation (15) is the money demand function of Germany. Here L^ symbolizes German money demand, as measured in euros. Yj is German income, as measured in German goods. Pj is the price of German goods, as measured in euros. Then PjYi is German income, as measured in euros. And k is the sensitivity of German money demand to German income, with k > 0. Equation (15) states that German money demand is a positive function of German income and a positive function of the price of German goods. A 1 percent increase in German income causes a 1 percent increase in German money demand. Similarly, a 1 percent increase in the price of German goods causes a 1 percent increase in German money demand. Equation (16) is the money demand fianction of France. Here L2 is French money demand, as measured in euros. Y2 is French income, as measured in French goods. P2 is the price of French goods, as measured in euros. Then P2Y2 is French income, as measured in euros. And k is the sensitivity of French money demand to French income. Equation (16) states that French money demand is a positive function of French income and a positive function of the price of French goods. A 1 percent increase in French income causes a 1 percent increase in French money demand. Likewise, a 1 percent increase in the price of French goods causes a 1 percent increase in French money demand. Equation (17) is the money supply function of the union. Here M is union money supply, as measured in euros. Equation (17) states that the European central bank sets the money supply of the union. Union money demand equals union money supply Lj + L2 = M . Taking account of the behavioural functions (15) until (17), we reach the money market equation of the union:

18 kPiYi + kPjYj = M = const

(18)

5) Technology and price setting. The production function of Germany is characterized by fixed coefficients: Yi-ajNi

(19)

Here Nj designates German labour input, aj is German labour productivity, as measured in German goods. And Yj is German output, as measured in German goods. Accordingly, German labour demand is: Ni = Yi / ai

(20)

That is to say, a 1 percent increase in German output requires a 1 percent increase in German labour demand. Conversely, a 1 percent increase in German productivity allows a 1 percent reduction in German labour demand. German firms set the price of German goods as a markup over unit labour cost in Germany: Pl=gWi/ai

(21)

Here Wj is the nominal wage rate in Germany, as measured in euros. Wj /a^ is unit labour cost in Germany, as measured in euros, g is the markup factor in Germany. And Pj is the price of German goods, as measured in euros. The message of equation (21) is that a 1 percent increase in German nominal wages causes a 1 percent increase in the price of German goods. The other way round, a 1 percent increase in German productivity causes a 1 percent decline in the price of German goods. The production function of France is characterized by fixed coefficients: Y2=a2N2

(22)

Here N2 is French labour input. a2 is French labour productivity, as measured in French goods. And Y2 is French output, as measured in French goods. Accordingly, French labour demand is:

19

Nj-Yj/a,

(23)

That means, a 1 percent increase in French output requires a 1 percent increase in French labour demand. Conversely, a 1 percent increase in French productivity allows a 1 percent reduction in French labour demand. French firms set the price of French goods as a markup over unit labour cost in France: P2=gW2/a2

(24)

Here W2 is the nominal wage rate in France, as measured in euros. W2/a2 is unit labour cost in France, as measured in euros, g is the markup factor in France. And P2 is the price of French goods, as measured in euros. The message of equation (24) is that a 1 percent increase in French nominal wages causes a 1 percent increase in the price of French goods. On the other hand, a 1 percent increase in French productivity causes a 1 percent decline in the price of French goods. 6) The model. On this foundation, the full model can be represented by a system of seven equations: Yi = Ai + cYj + mP2Y2 / Pi + he / Pj - qYj

(25)

Y 2 = A 2 + cY2+mPiYi/P2 + h e / P 2 - q Y 2

(26)

M = kPiYi + kP2Y2

(27)

Pl=gWi/ai

(28)

P2=gW2/a2

(29)

Ni = Yi / ai

(30)

N2=Y2/a2

(31)

Equation (25) is the goods market equation of Germany, as measured in German goods. (26) is the goods market equation of France, as measured in French goods. (27) is the money market equation of the union, as measured in

20 euros. (28) is the price equation of Germany, (29) is the price equation of France, (30) is the labour demand equation of Germany, and (31) is the labour demand equation of France. The exogenous variables are union money supply M, the autonomous demand for German goods A j , the autonomous demand for French goods A2, German nominal wages Wj, French nominal wages Wj, German productivity aj, and French productivity a2. The endogenous variables are German output Yj, French output Y2, the union exchange rate e, the price of German goods P], the price of French goods P2, German labour demand N j , and French labour demand N 2 . Now it proves very useful to rewrite the model as follows: PlYj = PjAj + cPiYj + mPsYj + he - qPiYj

(32)

P2Y2 = P2A2 + CP2Y2 + mPiYi + he - qP2Y2

(33)

M = kPiY, + kP2Y2

(34)

Pl=gWi/ai

(35)

P2=gW2/a2

(36)

Ni=Yi/ai

(37)

N2=Y2/a2

(38)

Equation (32) is the goods market equation of Germany, as measured in euros. Here PjYj is German income, as measured in euros. PjAj is the autonomous demand for German goods, as measured in euros. cPjYi is German consumption, as measured in euros. P2Y2 is French income, as measured in euros. mP2Y2 is French imports from Germany, as measured in euros. Put another way, mP2Y2 is German exports to France, as measured in euros, he is German exports to non-union countries, as measured in euros. And qPiYj is German imports from France and from non-union countries, as measured in euros. Equation (33) is the goods market equation of France, as measured in euros. Here P2Y2 is French income, as measured in euros. P2A2 is the autonomous demand for French goods, as measured in euros. CP2Y2 is French consumption, as measured in euros. PjYj is German income, as measured in euros. mPiYj is

21 German imports from France, as measured in euros. Put differently, mPjYj is French exports to Germany, as measured in euros, he is French exports to nonunion countries, as measured in euros. And qP2Y2 is French imports from Germany and from non-union countries, as measured in euros. As a consequence, qPjYi - mPiYi is German imports from non-union countries, as measured in euros. Similarly, qP2Y2 - mP2Y2 is French imports from non-union countries, as measured in euros. 7) The rate-of-growth method. In the remainder of this section, we make use of the rate-of-growth method. This method, together with suitable initial conditions, proves to be very powerful. For the method see Carlberg (2001) p. 12. Assume that, in the initial state, German income is equal to French income: PlYi = P2Y2

(39)

In this sense, Germany and France are the same size. Moreover assume that, in the initial state, the current account of Germany is balanced: mP2Y2+he = qPiYi

(40)

Then, in the initial state, the current account of France is balanced, too: mPiYi+he = qP2Y2

(41)

Now the goods market equation of Germany (32) together with the initial conditions (39) until (41) yield: ^ t ^ = l-c PlYi mPjYj PlYi

he PiYi

(42)

-= m

(43)

q-- m

(44)

22 Equation (42) has it that the initial share of autonomous demand in German income is 1 - c. Equation (43) has it that the initial share of German exports to France in German income is m. And equation (44) has it that the initial share of German exports to non-union countries in German income is q - m . The goods market equation of France (33) together with the initial conditions (39) until (41) yield:

Ml

=1- c

(45)

P2Y2

mPiY, i =m P2Y2 he

:q- m

(46)

(47)

P2Y2 Equation (45) has it that the initial share of autonomous demand in French income is 1 - c. Equation (46) has it that the initial share of French exports to Germany in French income is m. And equation (47) has it that the initial share of French exports to non-union countries in French income is q - m . The money market equation of the union (34) together with the initial condition (39) yields: kPiYi

= 0.5

(48)

0.5

(49)

M kP2Y2 M

Equation (48) has it that the initial share of German money demand in union money supply is 0.5. And equation (49) has it that the initial share of French money demand in union money supply is 0.5.

23 Taking account of the initial shares (42) until (49), the full model (32) until (38) can be transformed into growth rates as follows: P i + Y i = ( l - c ) ( P i + A i ) + c(Pi+Yi) + m(P2+Y2) + ( q - m ) e - q ( P i + Y i ) (50) P 2 + Y 2 = ( l - c ) ( P 2 + A 2 ) + c(P2+Y2) + m(Pi+Yi) + ( q - m ) e - q ( P 2 + Y 2 ) (51) M = 0.5(Pi+Yi) + 0.5(P2+Y2)

(52)

Pj=Wi-ai

(53)

P2=W2-a2

(54)

Ni=Yi-ai

(55)

N2=Y2-a2

(56)

Here Yj denotes the growth rate of German output, which is defined as Yj = dYj / Yj. Equation (50) is the goods market equation of Germany, (51) is the goods market equation of France, (52) is the money market equation of the union, (53) is the price equation of Germany, (54) is the price equation of France, (55) is the labour demand equation of Germany, and (56) is the labour demand equation of France. The exogenous variables are M, A j , A2, Wj, W2, aj and a2. The endogenous variables are Yj, Y2, e. Pi, P2, Nj and N2 .

2. Monetary Policy

In this section we consider an increase in union money supply. Then what will be the effect on German output, and what on French output? Here the model can be compressed to a system of three equations: Yi = cYi + m Y 2 + ( q - m ) e - q Y i

(1)

24

Y2 = cY2 + mYi + (q - m)e - qY2

(2)

M = 0.5Yi + O.5Y2

(3)

Equation (1) is the goods market equation of Germany, (2) is the goods market equation of France, and (3) is the money market equation of the union. The exogenous variable is union money supply. The endogenous variables are German output, French output, and the union exchange rate. Now rewrite equations (1) and (2) as follows: ( l - c + q)Yi = m Y 2 + ( q - m ) e

(4)

( l - c + q)Y2 = m Y i + ( q - m ) e

(5)

Then take the difference between equations (4) and (5) to get: Yi=Y2

(6)

This together with equation (3) provides: Yi=Y2=M

(7)

That is to say, a 1 percent increase in union money supply causes a 1 percent increase in German output and a 1 percent increase in French output. In addition, substitute equation (7) into equation (4) to obtain: . 1- c+q - m e= M q-m

(8)

That is, an increase in union money supply raises the union exchange rate. Put another way, the euro depreciates. To illustrate this, consider a numerical example with c = 0.72, m = 0.16 and q = 0.24. In other words, 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

25 = 0.16. And the marginal import rate of France relative to non-union countries is q - m = 0.08 . Given these parameter values, the multiplier is 4.5. That means, a 1 percent increase in union money supply causes a 4.5 percent depreciation of the euro. Finally have a brief look at the channels of transmission. An increase in union money supply causes a depreciation of the euro. This in turn raises both German exports and French exports. As a consequence, German output and French output move up.

3. Wage Policy

An increase in German nominal wages causes a proportionate increase in the price of German goods. Then how will German output respond, and how French output? The model can be captured by a system of three equations: Yi = c Y i + m ( Y 2 - P i ) + ( q - m ) ( e - P i ) - q Y i

(1)

Y2 = cY2+m(Pi+Yi) + ( q - m ) e - q Y 2

(2)

0 = Pi+Yi+Y2

(3)

Equation (1) is the goods market equation of Germany, (2) is the goods market equation of France, and (3) is the money market equation of the union. Here the exogenous variable is the price of German goods. The endogenous variables are German output, French output, and the union exchange rate. Now rewrite equations (1) and (2) as follows: ( l - c + q)Yi = m ( Y 2 - P i ) + ( q - m ) ( e - P i )

(4)

( l - c + q)Y2 = m(Pi+Yi) + ( q - m ) e

(5)

26 Then take the difference between equations (4) and (5) to see: ( l - c + m + q)(Yi-Y2) = - ( m + q)Pi

(6)

This together with equation (3) gives:

Yi-

l - c + 2m + 2q ^ 2 ( l - c + m + q) ^

(7)

% =

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

(8)

As an outcome, an increase in the price of German goods lowers German output. And what is more, it lowers French output as well. To better understand this, consider a numerical example with c = 0.72, m = 0.16 and q = 0.24. Then we have Y] = - 0.794Pi and Y2 = - 0.206Pj. That is to say, a 1 percent increase in the price of German goods causes a 0.79 percent decline in German output and a 0.21 percent decline in French output. At last have a closer look at impulse propagation. An increase in German nominal wages causes an increase in the price of German goods and an appreciation of the euro. The increase in the price of German goods lowers German exports but raises French exports. The appreciation of the euro lowers both German exports and French exports. The net effect is that German output and French output move down. Properly speaking, the decline in German output is bigger than the decline in French output. In the numerical example, a 1 percent increase in German nominal wages causes a 1 percent increase in the price of German goods, a 1.75 percent appreciation of the euro, a 0.79 percent decline in German output, and a 0.21 percent decline in French output.

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. Consider for example an increase in world money supply. Then what will be the effect on the world interest rate, and what on world output? Alternatively consider an increase in world nominal wages. Again what will be the effect on the world interest rate, and what on world output? Of course, the world economy is a closed economy. Let us begin with the goods market. The behavioural functions are as follows: C = cY

(1)

I = br""

(2)

Equation (1) is the consumption function. Here C denotes consumption, Y is income, and c is the marginal consumption rate with 0 < c < 1. Equation (1) states that consumption is a positive function of income. Equation (2) is the investment function. Here I symbolizes investment, r is the interest rate, s is the interest elasticity of investment with E > 0, and b is a shift parameter with b > 0. Equation (2) states that investment is a negative function of the interest rate. A 1 percent increase in the interest rate causes an s percent decline in investment. Aggregate supply is determined by aggregate demand Y = C +1. Taking account of the behavioural functions, we arrive at the goods market equation: Y = cY + br"^

(3)

Let us go on to the money market. The behavioural functions look like this: L = kPYr""!

(4)

M = const

(5)

28

Equation (4) is the money demand function. Here L stands for nominal money demand, Y is real income, P is the price level, PY is nominal income, r is the interest rate, r\ is the interest elasticity of money demand with t] > 0, and k is a shift parameter with k > 0. Equation (4) states that money demand is a positive function of real income, a positive function of the price level, and a negative function of the interest rate. Obviously, a 1 percent increase in real income causes a 1 percent increase in money demand. Similarly, a 1 percent increase in the price level causes a 1 percent increase in money demand. And a 1 percent increase in the interest rate causes an r| percent decline in money demand. Equation (5) is the money supply function. It states that the central bank sets the nominal supply of money. Further, the nominal demand for money is equal to the nominal supply of money L = M. Taking account of the behavioural functions, we reach the money market equation: kPYr"^ = M = const

(6)

The production function is characterized by fixed coefficients: Y = aN

(7)

Here N designates labour input, a is labour productivity, and Y is output. Accordingly, labour demand is: N = Y/a

(8)

That is to say, a 1 percent increase in output requires a 1 percent increase in labour demand. Conversely, a 1 percent increase in labour productivity allows a 1 percent reduction in labour demand. Firms set prices as a markup over unit labour cost: P = gW/a

(9)

Here W is the nominal wage rate, W/a is unit labour cost, g is the markup factor, and P is the price level. A 1 percent increase in nominal wages causes a 1 percent increase in the price level. The other way round, a 1 percent increase in labour productivity causes a 1 percent decline in the price level.

29

On this basis, the model can be represented by a system of four equations: Y = cY + br"^

(10)

M = kPYr"^

(11)

P = gW/a

(12)

N = Y/a

(13)

Equation (10) is the goods market equation, (11) is the money market equation, (12) is the price equation, and (13) is the labour demand equation. The exogenous variables are money supply M, the investment parameter b, nominal wages W, and labour productivity a. The endogenous variables are output Y, the interest rate r, the price level P, and labour demand N. The model can be transformed into growth rates as follows: Y = b-si^

(14)

M = P + Y-rif

(15)

P = W-a

(16)

N =Y-a

(17)

Equation (14) is the goods market equation, (15) is the money market equation, (16) is the price equation, and (17) is the labour demand equation. The exogenous variables are M, b , W and a. The endogenous variables are Y, f, P and N.

30

2. Monetary Policy

In this section we consider a 1 percent increase in money supply. Then how will output respond? The model can be compressed to a system of two equations: Y = -Ef

(1)

M = Y-r|f

(2)

Equation (1) is the goods market equation, and (2) is the money market equation. The exogenous variable is money supply. The endogenous variables are output and the interest rate. From equations (1) and (2) it follows that: Y=- ^ M s + r|

(3)

As a result, equation (3) shows the monetary policy multiplier. It is obvious that an increase in money supply raises output. Now consider the important special case s = ri. In this case, equation (3) simplifies as follows: Y =-M 2

(4) ^

As a result, the monetary policy multiplier is 0.5. That means, a 1 percent increase in money supply causes a 0.5 percent increase in output. How does this compare with the conclusions reached for the small open economy with a flexible exchange rate and perfect capital mobility? In Chapter 1, the monetary policy multiplier was shown to be unity: Y=M

(5)

The other way round, the dampening effect on the monetary policy multiplier of closing the economy is 0.5.

31

Coming to an end, have a brief look at the channels of transmission. An increase in money supply cuts down the interest rate. This in turn pushes up investment. Therefore output moves up.

3. Wage Policy

In this section we consider a 1 percent increase in nominal wages. Then what will be the impact on output? Here the model can be characterized by a system of three equations: Y = -sf

(1)

0 = P + Y-r|f

(2)

P=W

(3)

Equation (1) is the goods market equation, (2) is the money market equation, and (3) is the price equation. The exogenous variable is nominal wages. The endogenous variables are output, the interest rate, and the price level. Equation (3) has it that a 1 percent increase in nominal wages causes a 1 percent increase in the price level. Moreover, the general solution to the model is: Y=- ^ ^ W s + ri

(4)

As a result, an increase in nominal wages lowers output. Next consider the special case that s = r|. In this case, equation (4) simplifies as follows:

Y=-iw

(5)

32 That is to say, a 1 percent increase in nominal wages causes a 0.5 percent decline in output. At last have a closer look at the chain of cause and effect. An increase in nominal wages causes a proportionate increase in the price level. This in turn brings down real balances, thereby driving up the interest rate. As a consequence, investment and output come down.

Chapter 3 The World of Two Monetary Regions 1. The Model

1) Introduction. In this chapter we consider a world of two monetary regions, let us say Europe and America. Take for example an increase in European money supply. Then what will be the effect on European output, and what on American output? Alternatively take an increase in European nominal wages. Again what will be the effect on European output, and what on American output? The analysis is conducted within the following framework. There is perfect capital mobility between Europe and America. As a consequence, the European interest rate is equal to the American interest rate. It is worth pointing out here that the world interest rate is endogenous. The exchange rate between Europe and America is' flexible. European goods and American goods are imperfect substitutes for one another. In addition we assume that the monetary regions are the same size and have the same behavioural functions. 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). 2) The market for European goods. The behavioural functions underlying the analysis are as follows: Ci=cYi

(1)

Il=bir-^

(2)

Xi=qeP2Y2/Pi

(3)

Ql=qYi

(4)

Equation (1) is the consumption function of Europe. Here Cj denotes European consumption, as measured in European goods. Yi is European income, as measured in European goods. And c is the marginal consumption rate of Europe, with 0 < c < 1. Equation (1) states that European consumption is a positive

34 function of European income. Equation (2) is the investment function of Europe. Ij symbolizes European investment, as measured in European goods, r is the world interest rate, s is the interest elasticity of European investment, with s > 0. And bj is a shift parameter, with bj > 0. Equation (2) states that European investment is a negative function of the world interest rate. A 1 percent increase in the world interest rate causes an s percent decline in European investment. Equation (3) is the export function of Europe. Xj stands for European exports to America, as measured in European goods. Pj is the price of European goods, as measured in euros. P2 is the price of American goods, as measured in dollars, e is the exchange rate between the dollar and the euro. More exactly, e is the price of the dollar, as measured in euros. Then eP2 is the price of American goods, as measured in euros. Y2 is American income, as measured in American goods. P2Y2 is American income, as measured in dollars. eP2Y2 is American income, as measured in euros. eP2Y2 / Pi is American income, as measured in European goods. And q is the marginal import rate of America, with q > 0. Equation (3) states that European exports are a positive function of American income, a positive function of the exchange rate, a negative function of the price of European goods, and a positive function of the price of American goods. A 1 percent increase in American income causes a 1 percent increase in European exports. Further, a 1 percent depreciation of the euro causes a 1 percent increase in European exports. On the other hand, a 1 percent increase in the price of European goods causes a 1 percent decline in European exports. And a 1 percent increase in the price of American goods causes a 1 percent increase in European exports. Equation (4) is the import function of Europe. Qj designates European imports from America, as measured in European goods. Yj is European income, as measured in European goods. And q is the marginal import rate of Europe, with q > 0. Equation (4) states that European imports are a positive function of European income. European output is determined by the demand for European goods Yj = Cj + Ij + Xj - Qi. Taking account of the behavioural functions (1) until (4), we arrive at the goods market equation of Europe: Yi = cYi + bir-^ + qeP2Y2 / Pj - qYi

(5)

35 3) The market for American goods. The underlying behavioural functions are as follows: C2 = cY2

(6)

I2=b2r"'

(7)

X2=qPiYi/eP2

(8)

Q2=qY2

(9)

Equation (6) is the consumption function of America. Here C2 denotes American consumption, as measured in American goods. Y2 is American income, as measured in American goods. And c is the marginal consumption rate of America, with 0 < c < 1. Equation (6) states that American consumption is a positive function of American income. Equation (7) is the investment function of America. I2 symbolizes American investment, as measured in American goods, r is the world interest rate, s is the interest elasticity of American investment, with s > 0. And b2 is a shift parameter, with b2 > 0. Equation (7) states that American investment is a negative function of the world interest rate. A 1 percent increase in the world interest rate causes an s percent decline in American investment. Equation (8) is the export function of America. X2 stands for American exports to Europe, as measured in American goods. Y^ is European income, as measured in European goods. PiYj is European income, as measured in euros. PjYi / e is European income, as measured in dollars. PjYj / eP2 is European income, as measured in American goods. And q is the marginal import rate of Europe, with q > 0. Equation (8) states that American exports are a positive function of European income, a negative function of the exchange rate, a negative fiinction of the price of American goods, and a positive function of the price of European goods. A 1 percent increase in European income causes a 1 percent increase in American exports. Moreover, a 1 percent depreciation of the dollar causes a 1 percent increase in American exports. The other way round, a 1 percent increase in the price of American goods causes a 1 percent decline in American exports. And a 1 percent increase in the price of European goods causes a 1 percent increase in American exports. Of course, American exports to

36 Europe are identical with European imports from America, as long as both are measured in American goods. Equation (9) is the import function of America. Q2 designates American imports from Europe, as measured in American goods. Y2 is American income, as measured in American goods. And q is the marginal import rate of America, with q > 0. Equation (9) states that American imports are a positive function of American income. American output is determined by the demand for American goods Y2 = C2 +12 + X2 - Q2. Upon substituting the behavioural functions (6) until (9), we reach the goods market equation of America: Y2 = CY2 + b2r-^ + qPiYi / eP2 - qY2

(10)

4) The European money market. The behavioural functions underlying the analysis are as follows. Li=kPiYir-^

(11)

Ml = const

(12)

Equation (11) is the money demand function of Europe. Here Lj denotes European money demand, as measured in euros. Yj is European income, as measured in European goods. Pj is the price of European goods, as measured in euros. PjYj is European income, as measured in euros, r is the world interest rate. r\ is the interest elasticity of European money demand, with T] > 0. And k is a shift parameter, with k > 0. Equation (11) states that European money demand is a positive function of European income, a positive function of the price of European goods, and a negative function of the world interest rate. A 1 percent increase in European income causes a 1 percent increase in European money demand. Similarly, a 1 percent increase in the price of European goods causes a 1 percent increase in European money demand. And a 1 percent increase in the world interest rate causes an T] percent decline in European money demand. Equation (12) is the money supply function of Europe. Mj is European money supply, as measured in euros. Equation (12) states that the European central bank sets the money supply of Europe. European money demand is equal

37

to European money supply L i = M i . Taking account of the behavioural functions (11) and (12), we arrive at the money market equation of Europe: kPiYir""^ = Ml = const

(13)

5) The American money market. The underlying behavioural fixnctions are as follows: L2=kP2Y2r-^

(14)

M2 = const

(15)

Equation (14) is the money demand function of America. L2 symbolizes American money demand, as measured in dollars. Y2 is American income, as measured in American goods. P2 is the price of American goods, as measured in dollars. P2Y2 is American income, as measured in dollars, r is the world interest rate. r| is the interest elasticity of American money demand, with r] > 0. And k is a shift parameter, with k > 0. Equation (14) states that American money demand is a positive function of American income, a positive function of the price of American goods, and a negative fimction of the world interest rate. A 1 percent increase in American income causes a 1 percent increase in American money demand. Likewise, a 1 percent increase in the price of American goods causes a 1 percent increase in American money demand. And a 1 percent increase in the world interest rate causes an r| percent decline in American money demand. Equation (15) is the money supply function of America. M2 is American money supply, as measured in dollars. Equation (15) states that the American central bank sets the money supply of America. American money demand is equal to American money supply L2 = M2. Upon substituting the behavioural functions (14) and (15), we reach the money market equation of America: kP2Y2r~'i = M2 = const

(16)

6) Technology and price setting. The production function of Europe is characterized by fixed coefficients:

38

Yi=aiNi

(17)

Here Nj stands for European labour input, aj is European labour productivity, as measured in European goods. And Yj is European output, as measured in European goods. Accordingly, European labour demand is: Ni=Yi/ai

(18)

That means, a 1 percent increase in European output requires a 1 percent increase in European labour demand. On the other hand, a 1 percent increase in European productivity allows a 1 percent reduction in European labour demand. European firms set the price of European goods as a markup over unit labour cost in Europe: Pl= gW^/ai

(19)

Here Wj is the nominal wage rate in Europe, as measured in euros. Wj/aj is unit labour cost in Europe, as measured in euros, g is the markup factor in Europe. And Pj is the price of European goods, as measured in euros. The message of equation (19) is that a 1 percent increase in European nominal wages causes a 1 percent increase in the price of European goods. Conversely, a 1 percent increase in European productivity causes a 1 percent decline in the price of European goods. The production function of America is characterized by fixed coefficients: Y2 = a2N2

(20)

Here N2 designates American labour input. a2 is American labour productivity, as measured in American goods. And Y2 is American output, as measured in American goods. Accordingly, American labour demand is: N2-Y2/a2

(21)

39

That is to say, a 1 percent increase in American output requires a 1 percent increase in American labour demand. The other way round, a 1 percent increase in American productivity allows a 1 percent reduction in American labour demand. American firms set the price of American goods as a markup over unit labour cost in America: P2=gW2/a2

(22)

Here Wj is the nominal wage rate in America, as measured in dollars. W2/a2 is unit labour cost in America, as measured in dollars, g is the markup factor in America. And P2 is the price of American goods, as measured in dollars. The message of equation (22) is that a 1 percent increase in American nominal wages causes a 1 percent increase in the price of American goods. Conversely, a 1 percent increase in American productivity causes a 1 percent decline in the price of American goods. 7) The model. On this foundation, the full model can be represented by a system of eight equations: Yj = cYj + bjr"^ + qeP2Y2 / Pi - qYj

(23)

Y2 = CY2 + b2r-^ + qPiYi / eP2 - qYj

(24)

Ml = kPiYir""!

(25)

M2 = kP2Y2r-'i

(26)

Pi=gWi/ai

(27)

P2=gW2/a2

(28)

Ni=Yi/ai

(29)

N2=Y2/a2

(30)

Equation (23) is the goods market equation of Europe, as measured in European goods. (24) is the goods market equation of America, as measured in

40 American goods. (25) is the money market equation of Europe, as measured in euros. (26) is the money market equation of America, as measured in dollars. (27) is the price equation of Europe, as measured in euros. (28) is the price equation of America, as measured in dollars. (29) is the labour demand equation of Europe, and (30) is the labour demand equation of America. The exogenous variables are European money supply M j , American money supply M2, the European investment parameter bj, the American investment parameter b2, European nominal wages Wj, American nominal wages W2, European productivity aj, and American productivity a2. The endogenous variables are European output Yj, American output Y2, the exchange rate e, the world interest rate r, the price of European goods Pj, the price of American goods P2, European labour demand N j , and American labour demand N 2 . Now it proves very useful to rewrite the model as follows: PlYi = cPiYi + Pjbir-^ + qeP2Y2 - qPiYi

(31)

P2Y2 = CP2Y2 + P2b2r-^ + qPiYi / e - qP2Y2

(32)

Ml = kPiYir"^

(33)

M2=kP2Y2r-^

(34)

P,=gW,/a,

(35)

P2=gW2/a2

(36)

Ni=Yi/ai

(37)

N2=Y2/a2

(38)

Equation (31) is the goods market equation of Europe, as measured in euros. PjYj is European income, as measured in euros. cP^Yj is European consumption, as measured in euros. Pibir"*^ is European investment, as measured in euros. qeP2Y2 is American imports from Europe, as measured in euros. Put another way, qeP2Y2 is European exports to America, as measured in euros. And qPiYj is European imports from America, as measured in euros. Equation (32) is the goods market equation of America, as measured in dollars. P2Y2 is American income, as measured in dollars. CP2Y2 is American

41 consumption, as measured in dollars. P2b2r~^ is American investment, as measured in dollars. qPiYj / e is European imports from America, as measured in dollars. Put differently, qPiYj / e is American exports to Europe, as measured in dollars. And qP2Y2 is American imports from Europe, as measured in dollars. 8) The rate-of-growth method. In the remainder of this section we make use of the rate-of-growth method. This method, together with suitable initial conditions, proves to be very powerful. Assume that, in the initial state, European income is equal to American income: PiYi=eP2Y2

(39)

In this sense, Europe and America are the same size. Then, in the initial state, the current account of Europe is balanced: qeP2Y2=qPlYi

(40)

For the same reason, in the initial state, the current account of America is balanced too: qPlYi/e = qP2Y2

(41)

Now the goods market equation of Europe (31) together with the initial conditions (39) and (40) yield: -e

= l-c

(42)

PlYi

55^2 PiYi

(43)

Equation (42) has it that the initial share of European investment in European income is 1 - c. And equation (43) has it that the initial share of European exports in European income is q.

42 Similarly, the goods market equation of America (32) together with the initial conditions (39) and (41) yield:

^ ^ ^ P2Y2

= l-c

(44)

^ ^ ^ P2Y2

=^

(45)

Equation (44) has it that the initial share of American investment in American income is 1 - c . And equation (45) has it that the initial share of American exports in American income is q. Taking account of the initial shares (42) until (45), the full model (31) until (38) can be transformed into growth rates as follows: Pl+Yi=c(Pi+Yi) + ( l - c ) ( P i + b i - s r ) + q ( e + P2+Y2)-q(Pi+Yi)

(46)

P2+Y2=c(P2+Y2) + ( l - c ) ( P 2 + b 2 - s f ) + q ( P i + Y i - e ) - q ( P 2 + Y 2 ) ( 4 7 ) Mi=Pi+Yi-rif

(48)

M2-P2+Y2-Tlf

(49)

Pi=Wi-ai

(50)

P2=W2-a2

(51)

Ni=Yi-ai

(52)

N2=Y2-a2

(53)

Equation (46) is the goods market equation of Europe, (47) is the goods market equation of America, (48) is the money market equation of Europe, (49) is the money market equation of America, (50) is the price equation of Europe, (51) is the price equation of America, (52) is the labour demand equation of Europe, and (53) is the labour demand equation of America. The exogenous variables are M j , M2, bj, 62, Wj, W2, aj and §2. The endogenous variables are Yi, Y2> e, f, Pj, P2, Nj and N 2 .

43

2. Monetary Policy

In this section we consider an increase in European money supply. Then what will be the effect on European output, and what on American output? Here the model can be compressed to a system of four equations: Yi = c Y i - ( l - c ) s f + q(e + Y2)-qYi

(1)

Y2 = cY2 - (1 - c)sf + q(Yi - e) - qY2

(2)

Mi=Yi-iif

(3)

0 = Y2-iif

(4)

Equation (1) is the goods market equation of Europe, (2) is the goods market equation of America, (3) is the money market equation of Europe, and (4) is the money market equation of America. The exogenous variable is European money supply. The endogenous variables are European output, American output, the exchange rate, and the world interest rate. Equations (3) and (4) give immediately: rif = Y2

(5)

Mi=Yi-Y2

(6)

Then take the sum of equations (1) and (2) to get: Yi+Y2 = - 2 s f

(7)

This together with equations (5) and (6) yields: 2s + n '^ Y i = f ^ M i 2s + 2ri

(8)

44

Y2=-:r^Mi

(9)

As a result, an increase in European money supply raises European output. On the other hand, it lowers American output. For the remainder of this section, have a look at some further aspects. First consider the world interest rate. Combine equations (5) and (9) to find out:

f=-y4^Mi

(10)

2s + 2r| That is to say, an increase in European money supply lowers the world interest rate. Second consider the exchange rate. Take the difference between equations (1) and (2) to check: ( l - c + 2q)(Yi-Y2) = 2qe

(11)

This together with equation (6) provides: . l - c + 2q e= —^Mi 2q

(12)

Obviously, an increase in European money supply causes a depreciation of the euro and an appreciation of the dollar. To illustrate this, consider a numerical example with c = 0.72 and q = 0.08. So the multiplier is 2.75. That means, a 1 percent increase in European money supply causes a 2.75 percent depreciation of the euro and a 2.75 percent appreciation of the dollar. Third consider the important special case that s = r|. For the motivation of this case see Section 2 of Chapter 2 in Part One. Now insert s = r| into equations (8) and (9) to realize:

YI = | M I

(13)

45

Y2=-^Mi

(14)

That is, a 1 percent increase in European money supply causes a 0.75 percent increase in European output and a 0.25 percent decrease in American output. Fourth consider the channels of transmission. 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, in turn, drives up European exports. The appreciation of the dollar, however, cuts down American exports. And the decline in the world interest rate pushes up both European investment and American investment. The net effect is that European output moves up. Conversely, American output moves down.

3. Wage Policy

An increase in European nominal wages causes a proportionate increase in the price of European goods. Then how will European output respond, and how American output? The model can be captured by a system of four equations: Yi = c Y i - ( l - c ) s f + q(e + Y 2 - P i ) - q Y i

(1)

Y2 = cY2 - ( l - c ) s f + q(Pi + Yi - e ) - q Y 2

(2)

0 = Pi+Yi-Tif

(3)

0 = Y2-iif

(4)

Equation (1) is the goods market equation of Europe, (2) is the goods market equation of America, (3) is the money market equation of Europe, and (4) is the money market equation of America. Here the exogenous variable is the price of European goods. The endogenous variables are European output, American output, the exchange rate, and the world interest rate.

46

From equations (3) and (4) it follows immediately that: P1+Y1-Y2

(5)

Now take the sum of equations (1) and (2) to get: Yi+Y2=-2sf

(6)

This together with equations (4) and (5) furnishes: 2S + T1 ^

Yi=-

Y2 =

2s + 2r| ^

1

(7)

p,

2s + 2r|

(8)

As an outcome, an increase in the price of European goods lowers European output. On the other hand, it raises American output. For the remainder of this section we study some further aspects. First consider the world interest rate. Merge equations (4) and (8) to ascertain:

f=

^- Pi 2s + 2ri

(9)

That is to say, an increase in the price of European goods raises the world interest rate. Second consider the exchange rate. Take the difference between equations (1) and (2), noting equation (5): 1 — c -^ e=-i-^Pi 2q

(10)

47

Obviously, an increase in the price of European goods causes an appreciation of the euro and a depreciation of the dollar. In the numerical example with c = 0.72 and q = 0.08, the multiplier is 1.75. In other words, a 1 percent increase in the price of European goods causes a 1.75 percent appreciation of the euro and a 1.75 percent depreciation of the dollar. Third consider the special case that s = r|. Substitute s = r| into equations (7) and (8) to find out:

Yi = - | P i

(11)

Y2 = ^Pl

(12)

That means, a 1 percent increase in the price of European goods causes a 0.75 percent decline in European output and a 0.25 percent increase in American output. Fourth consider the chain of cause and effect. An increase in European nominal wages pushes up the price of European goods. This in turn causes an appreciation of the euro, a depreciation of the dollar, and an increase in the world interest rate. The increase in the price of European goods lowers European exports and raises American exports. The appreciation of the euro cuts down European exports. Conversely, the depreciation of the dollar drives up American exports. And the increase in the world interest rate brings down both European investment and American investment. The net effect is that European output moves down. On the other hand, American output moves up. In the numerical example, a 1 percent increase in European nominal wages causes a 1 percent increase in the price of European goods, a 1.75 percent appreciation of the euro, a 1.75 percent depreciation of the dollar, a 0.75 percent decline in European output, and a 0.25 percent increase in American output.

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 is larger than 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 is larger than 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

52 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. Compare this with the results obtained in Part One. First consider the small monetary union of two countries. In the basic model, a 1 percent increase in European money supply causes a 1 percent increase in German output and a 1 percent increase in French output. So the ratio of Germany to France is 1/1 = 1. In the current section, an increase in European money supply of 100 causes an increase in German output of 150 and an increase in French output of equally 150. So the ratio of Germany to France is 150/150 = 1. Strictly speaking, what matters here is that the two ratios are identical. Note that by assumption Germany and France are the same size. Second consider the world of two monetary regions. In the basic model, a 1 percent increase in European money supply causes a 0.75 percent increase in European output and a 0.25 percent decline in American output. So the ratio of Europe to America is 0.75/0.25 = 3. In the current section, an increase in European money supply of 100 causes an increase in European output of 300 and a decline in American output of 100. So the ratio of Europe to America is 300/100 = 3. What matters here is that the two ratios are identical. Note that by assumption Europe and America are the same size. 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: Yj = Ai + 0.5aMi2 - O.5PM3

(1)

53

Yj = A2 + 0.5aMi2 - O.SpMj

(2)

Y3=A3+aM3-pMi2

(3)

Of course this is a reduced form. Yj denotes German output, Y2 is French output, Y3 is American output, Mj2 is European money supply, M3 is American money supply, 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 and p 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 fiinction 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. 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 p . Correspondingly, an increase in American money supply of 1 causes an increase in American output of a , a decline in German output of O.Sp, and a decline in French output of equally 0.5p. 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 = Yj + Y2 and A12 = Aj + 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

54 is a positive function of American money supply and a negative function European money supply. An increase in European money supply of 1 causes increase in European output of a and a decline in American output of Similarly, an increase in American money supply of 1 causes an increase American output of a and a decline in European output of P.

of an p. in

2) The dynamic model. This chapter deals with competition between the European central bank and the American central bank. 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 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-Mrj = ^i^"^'2 a

(6)

Here is a list of the new symbols: Yi2 European output this period Yi2 full-employment output in Europe Y[2 - Yi2 output gap in Europe this period M^2 European money supply last period Mi2 European money supply this period Mi2 - M^2 increase in European money supply. Here the endogenous variable is European money supply this period Mi2. 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:

55

M3-M3^=-^^—-^

(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 Mj^ 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 M3. We assume that the European central bank and the American central bank decide simultaneously and independently. In addition there is an output lag: Y+i=Ai2+aMi2-PM3

(8)

Y3+1 = A3 + aM3 - (3Mi2

(9)

According to equation (8), European output next period is determined by European money supply this period as well as by American money supply this period. Here Yj^' denotes European output next period. According to equation (9), American output next period is determined by American money supply this period as well as by European money supply this period. Here Y^ denotes American output next period. On this basis, the dynamic model can be characterized by a system of four equations:

M12 -M^j-

M 3 - -Mg^ =

_ Y12 - Y[2 a

(10)

Y3-Y3 a

Y+1 -= Ai2 + aMj2 - pN

(11)

(12)

56

Y3+1 = A3 + a M j - pMi2

(13)

Equation (10) shows the policy response in Europe, (11) shows the policy 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 Y^^^, and American output next period ¥3^^. 3) The steady state. In the steady state by definition we have: Mi2=Mr]

(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: Y12-Y12

(16)

Y3=Y3

(17)

Yi2=Ai2+cxMi2-pM3

(18)

Y3=A3+aM3-pMi2

(19)

Here the endogenous variables are European output Yj2, American output Y3, European money supply Mj2, and 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 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: Y12 = A12 + aMi2 - PM3

(20)

57

Y3=A3 + a M 3 - p M i 2

(21)

Here the endogenous variables are European money supply and American money supply. To simplify notation we introduce: Bi2=Yi2-Ai2

(22)

B3=Y3-A3

(23)

With this, the model of the steady state can be written as follows: Bi2=aMi2-(5M3

(24)

B3=aM3-pMi2

(25)

The endogenous variables are still M12 and M3. Next we solve the model for the endogenous variables: aBi2+PB3

M>2=^^^S^g^ oB^igi^

(26) (27)

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 > p, this condition is fiilfilled. 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: AY12 = aAMi2 - PAM3

(28)

AY3 = aAM3 - PAM12

(29)

58

Here AY12 is 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:

AM,2=

aAYi2 + PAY3 "^^2'':r ^

aAY3+pAYi2 AM3 = " " ^ 3 ^ " ^ „ , 12

(30)

(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 p. 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 + 0M12 - PM3 . By analogy, eliminate Y3 in equation (11) by means of equation (13) to arrive at Y3 = A3 + aM3 - PMf2 • On this basis, the dynamic model can be described by a system of two equations: Yi2-Ai2+aMi2-PM3i

(32)

Y3 = A3 + aM3 - pMf]

(33)

Here the endogenous variables are European money supply this period M12 and American money supply this period M3. To simplify notation we make use of equations (22) and (23). With this, the dynamic model can be written as follows: B12 = aMi2 - PMji

(34)

B3=aM3-pMf2^

(35)

59

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

cM,=B,.a.B!M a

(36)

a

Then differentiate equation (36) for Mjl dMi2 _ p2 dMfl a2

(37)

Finally the stability condition is p la < 1 or: a >p

(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 emplojmient 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.

2. Some Numerical Examples

To illustrate the djmamic model, have a look at some numerical examples. 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:

60

Yi = Ai+1.5Mi2-0.5M3

(1)

Y 2 = A 2 + 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 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 fiill-emplojanent 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 - 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, unem-

61 ployment 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 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. 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. 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

62 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 decline 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 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.

Table 2.1 Competition between European Central Bank and American Central Bank The Case of Unemployment

Initial Output

Germany

France

America

940

970

1910

30

30

1000

1970

10

10

1010

1990

A Money Supply Output

970

A Money Supply Output

980

3.3

3.3

983.3

1013.3

1996.7

985

1015

2000

A Money Supply Output and so on Steady-State Output

63 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 emplojonent and price stability too. Unemplojmient in Germany equals overemployment in France. And deflation in Germany equals inflation in France. Strictly speaking, unemplojTTient 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 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. 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 multiplier in America. In other words, the effective multiplier in Europe is small. And the same holds for the effective multiplier in America.

64

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 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.

65 Table 2.2 Competition between European Central Bank and American Central Bank Europe and America Differ in Unemployment

Initial Output

Germany

France

America

940

970

1880

30

40

995

1970

A Money Supply Output

965

A Money Supply Output

13.3 980

1986.7

3.3

4.4

982.8

1012.8

1996.7

985

1015

2000

A Money Supply Output

1010

10

and so on 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 overemplojmient 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 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.

66

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 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 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 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 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

67 output goes from 1000 to 990, and American output goes from 2030 to 2010. And so on. Table 2.3 presents a sjTiopsis. 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 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.

Table 2.3 Competition between European Central Bank and American Central Bank The Case of Inflation Germany Initial Output

1060

2090

-30

-30

1000

2030

-10

-10

1020

990

2010

1015

985

2000

1030

A Money Supply Output

America

1030

A Money Supply Output

France

and so on Steady-State Output

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

68 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 decline 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 emplo3Tiient and price stability. In France there is now overemployment and inflation. In Europe there is now 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

69 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 unemplojonent 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.

Table 2.4 Competition between European Central Bank and American Central Bank Unemployment in Europe, Inflation in America

Initial Output

Germany

France

America

940

970

2090

30

-30

1030

1970

-10

10

1010

2010

A Money Supply Output

1000

A Money Supply Output

980

A Money Supply Output

3.3

-3.3

986.7

1016.7

1996.7

985

1015

2000

and so on Steady-State Output

70

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 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. 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 applies to the total reduction in American money supply, as compared to the initial gap in America. The effective multiplier 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.

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

1) Introduction. This chapter deals with cooperation between the European central bank and the American central bank. As a point of departure, take the output model. It can be represented by a system of three equations: Yi=Ai+0.5aMi2-0.5pM3

(1)

Y2 = A2 + 0.5aMi2 - O.5PM3

(2)

Y3=A3+aM3-|3Mi2

(3)

Here Yj 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 = Yj + Y2 and A12 = Aj + 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 is high, and unemployment in France is low. 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.

72

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 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 - Y12 - A12 and B3 = Y3 - A3 . Then we solve the model for the endogenous variables:

Mn-"^¥^ M3-

aB3+pBt2

V'V'

(8) (9)

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 ;^ 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 pohcy 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 - PAM3

(10)

AY3 = aAMj - PAM12

(11)

Here AYi2 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 AIVI3 is the required increase in American money supply. The endogenous variables are AMj2 and AM3. The solution to the system (10) and (11) is: _ aAYi2 + (3AY3 AMi2= ^2 ^2

(12)

_aAY3+pAYi2 AM3= \ >;, 12

(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 p.

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 (3 = 1. 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 + 3 M 3 - M i 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. 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 fuU-emplojonent output in America be 2000. It proves useftil 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 2.5 Cooperation between European Central Bank and American Central Bank The Case of Unemployment

Initial Output

Germany

France

America

940

970

1910

45

45

1015

2000

A Money Supply Output

985

In Germany there is still some unemplojmient 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 fiiU 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 2.5 presents a synopsis. 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 fi:om 970 to 1015, and American output goes from 1880 to 2000.

Table 2.6 Cooperation between European Central Bank and American Central Bank 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 overemplojTnent 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 Ml employment in Europe and America. However, it cannot achieve full employment in Germany and France. Table 2.6 gives an overview. 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 2.7 presents a synopsis.

Table 2.7 Cooperation between European Central Bank and American Central Bank The Case of Inflation

Initial Output

Germany

France

America

1060

1030

2090

-45

-45

985

2000

A Money Supply Output

1015

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 2.8 Cooperation between European Central Bank and American Central Bank Unemployment in Europe, Inflation in America

Initial Output

Germany

France

America

940

970

2090

A Money Supply Output

22.5 985

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 multiplier in Europe is large. And the same is true of the effective multiplier in America. Table 2.8 gives an overview. 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.

Part Three Wage Interactions between Germany and France

Chapter 1 Competition between the German Labour Union and the French Labour Union 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 countries in the monetary union are the same size and have the same behavioural fiinctions. As a result, an increase in German nominal wages lowers German output. And what is more, it lowers French output. On the other hand, it raises American output. Here the fall in German output is larger than the fall in French output. And the fall in European output is larger than the rise in American output. Correspondingly, an increase in French nominal wages lowers French output. And what is more, it lowers German output. On the other hand, it raises American output. Here the fall in French output is larger than the fall in German output. And the fall in European output is larger than the rise in American output. In the numerical example, an increase in German nominal wages of 100 causes a decline in German output of 120, a decline in French output of 30, and an increase in American output of 50. Likewise, an increase in French nominal

84

wages of 100 causes a decline in French output of 120, a decline in German output of 30, and an increase in American output of 50. Compare this with the results obtained in Part One. First consider the small monetary union of two countries. In the basic model, a 1 percent increase in German nominal wages causes a 0.8 percent decline in German output and a 0.2 percent decline in French output. So the ratio of Germany to France is 0.8/0.2 = 4. In the current section, an increase in German nominal wages of 100 causes a decline in German output of 120 and a decline in French output of 30. So the ratio of Germany to France is 120/30 = 4. Strictly speaking, what matters here is that the two ratios are identical. Note that by assumption Germany and France are the same size. Second consider the world of two monetary regions. In the basic model, a 1 percent increase in European nominal wages causes a 0.75 percent decline in European output and a 0.25 percent increase in American output. So the ratio of Europe to America is 0.75/0.25 = 3. In the current section, an increase in European nominal wages of 100 causes a decline in European output of 300 and an increase in American output of 100. So the ratio of Europe to America is 300/100 = 3. What matters here is that the two ratios are identical. Note that by assumption Europe and America are the same size. Now have a closer look at the process of adjustment. An increase in German nominal wages causes an increase in the price of German goods. This in turn causes an appreciation of the euro, a depreciation of the dollar, and an increase in the world interest rate. The increase in the price of German goods lowers German exports. On the other hand, it raises French exports and American exports. 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 and French output move down. However, 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 system of three equations:

85

Yj=Aj-XWj-nW2

(1)

Y2=A2-XW2-nWi

(2)

Y3=A3+vWi+vW2

(3)

Of course this is a reduced form. Yj denotes German output, Y2 is French output, Yj is American output, Wj is German nominal wages, W2 is French nominal wages, 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. X, [i and v denote the wage policy multipliers. X, |x and v are positive coefficients with 'k> \i and X> v. The endogenous variables are German output, French output, and American output. According to equation (1), German output is a negative function of German nominal wages and a negative function of French nominal wages. According to equation (2), French output is a negative function of French nominal wages and a negative function of German nominal wages. According to equation (3), American output is a positive function of German nominal wages and a positive function of French nominal wages. An increase in German nominal wages of 1 causes a decline in German output of X, a decline in French output of p,, and an increase in American output of v . Similarly, an increase in French nominal wages of 1 causes a decline in French output of X,, a decline in German output of |x, and an increase in American output of v . 2) The dynamic model. This chapter deals with competition between the German labour union and the French labour union. At the beginning there is unemployment in Germany and France. More precisely, unemployment in Germany is high, and unemployment in France is low. By contrast there is full employment in America. The target of the German labour union is full employment in Germany. The instrument of the German labour union is German nominal wages. The German labour union lowers German nominal wages so as to close the output gap in Germany: W j - W r i = -^^LZZL

Here is a list of the new symbols:

(4)

86 Yj German output this period Yj full-employment output in Germany Yj - Yj output gap in Germany this period Wf German nominal wages last period Wj German nominal wages this period Wj - Wf change in German nominal wages. Here the endogenous variable is German nominal wages this period Wj. The target of the French labour union is full employment in France. The instrument of the French labour union is French nominal wages. The French labour union lowers French nominal wages so as to close the output gap in France:

W2-W2-^ = - ^ ^ ^ ^

(5)

Here is a list of the new symbols: Y2 French output this period Y2 fiiU-emplojmient output in France Y2 - Y2 output gap in France this period W^ French nominal wages last period W2 French nominal wages this period W2 - W^ change in French nominal wages. Here the endogenous variable is French nominal wages this period W2. We assume that the German labour union and the French labour union decide simultaneously and independently. In addition there is an output lag: y^

= A i --A,Wj- -^W2

(6)

n'

(7)

Y3^^ = A3 + vWi + VW2

(8)

= A2 - ^ 2 -HWj

According to equation (6), German output next period is determined by German nominal wages this period as well as by French nominal wages this period. Here Yj"^^ denotes German output next period. According to equation (7), French

87 output next period is determined by French nominal wages this period as well as by German nominal wages this period. According to equation (8), American output next period is determined by German nominal wages this period as well as by French nominal wages this period. On this basis, the dynamic model can be characterized by a system four equations:

Wi-Wfi = - ^ ^ ^

(9)

A.

W2-W2"^ = - ^

^

(10)

Yi+^ = A i - ; i W i - ^ W 2

(11)

Y2+i = A 2 - X W 2 - ^ W i

(12)

Y3+^-A3 + vWi+vW2

(13)

Equation (9) shows the wage response by the German labour union, (10) shows the wage response by the French labour union, (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 nominal wages this period Wj, French nominal wages this period W2, German output next period Y^ , French output next period Y^ , and American output next period Y3' . 3) The steady state. In the steady state by definition we have: Wi = Wf ^

(14)

W2=W2->

(15)

Equation (14) has it that German nominal wages do not move any more. Likewise, equation (15) has it that French nominal wages do not move any more. Therefore the steady state can be captured by a system of four equations: Yi = Yi

(16)

88

Y2 = Y2

(17)

Yi = A i - X W i - | i W 2

(18)

Y2=A2-m2-^iWi

(19)

Y3 =A3 + vWi + vW2

(20)

Here the endogenous variables are German output Yj, French output Y2, American output Y3 , German nominal wages W^, and French nominal wages W2. 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 nominal wages, French nominal wages, and American output. The model of the steady state can be compressed to a system of only two equations: Yi = A i - X W i - n W 2

(21)

Y2=A2-XW2-^Wi

(22)

Here the endogenous variables are German nominal wages and French nominal wages. To simplify notation we introduce: Bi=Ai-Yi

(23)

B2=A2-Y2

(24)

With this, the model of the steady state can be written as follows: Bi = XWi + i^Wj

(25)

B2 = A,W2+|aWi

(26)

The endogenous variables are still Wj and W2. Next we solve the model for the endogenous variables:

Wi =

w„ •

XBi- -[^^2

(27)

y}- -^' XBj - ^ B i

(28)

X^- - ^ ^

Equation (27) shows the steady-state level of German nominal wages, and equation (28) shows the steady-state level of French nominal wages. As a result, there is a steady state if and only if X^[i. Owing to the assumption A, > [i, this condition is fulfilled. The steady-state levels of Wj and W2 are positive if f4,/>-
(29)

AY2 = - XAW2 - i^AWj

(30)

Here AYj is the initial output gap in Germany, AY2 is the initial output gap in France, AWj is the total change in German nominal wages, and AW2 is the total change in French nominal wages. The endogenous variables are AWj and AW2. The solution to the system (29) and (30) is: AWi^-^^^r^f^

(31)

V

A.2-

AW2 =

XAY2-- ^ A Y i

J

"

X^- -^'

'

(32)

According to equation (31), the total reduction in German nominal wages depends on the initial output gap in Germany, the initial output gap in France, the direct multiplier X, and the cross multiplier |A . The larger the initial output gap in Germany, the larger is the total reduction in German nominal wages. On the other hand, the larger the initial output gap in France, the smaller is the total

90 reduction in German nominal wages. At first glance this comes as a surprise. According to equation (32), the total reduction in French nominal wages depends on the initial output gap in France, the initial output gap in Germany, the direct multiplier A,, and the cross multiplier \i. 4) Stability. Eliminate Yj in equation (9) by means of equation (11) and rearrange terms Yj = Aj - XW^ - 11W2 . By analogy, eliminate Y2 in equation (10) by means of equation (12) to arrive at Y2 = A2 - A-W2 - |xWf . On this basis, the dynamic model can be described by a system of two equations: Yi ^ A i - ^ W j - i ^ W j " ^

(33)

Y2 = A2 - XW2 - |iWf ^

(34)

Here the endogenous variables are German nominal wages this period Wj and French nominal wages this period W2. To simplify notation we make use of equations (23) and (24). With this, the dynamic model can be written as follows: Bj = XWi + |aW2"^

(35)

B2 = XW2 + nWf ^

(36)

The endogenous variables are still Wj and W2. Now substitute equation (36) into equation (35) and solve for:

Then differentiate equation (37) for Wj :

"*• - " '

dWf^

(38)

la^ 9

Finally the stability condition is ^ X>ii

9

or: (39)

91 That means, the steady state is stable if and only if the internal effect of wage policy is larger than the external effect of wage policy. This condition is satisfied. As a result, there is a stable steady state of wage competition. In other words, competition between the German labour union and the French labour union leads to full employment in Germany and France. However, as an adverse side effect, it causes unemployment 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 A, = 1.2, ^ === 0.3 and V = 0.5 . On this assumption, the static model can be written as follows: Yj = A i - 1 . 2 W i - 0 . 3 W 2

(1)

Y2 = A 2 - 1 . 2 W 2 - 0 . 3 W i

(2)

Y3 = A3 + 0.5Wi + O.5W2

(3)

The endogenous variables are German output, French output, and American output. Obviously, an increase in German nominal wages of 100 causes a decline in German output of 120, a decline in French output of 30, and an increase in American output of 50. Correspondingly, an increase in French nominal wages of 100 causes a decline in French output of 120, a decline in German output of 30, and an increase in American output of 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 useftil to study five distinct cases: - unemployment in Germany equals unemployment in France - unemployment in Germany is high, unemployment in France is low - unemployment in Germany, fiill employment in France - unemployment in Germany, overemployment in France

92 - overemployment in Germany and France. 1) Unemployment in Germany equals unemployment in France. Let initial output in Germany be 940, let initial output in France be equally 940 and let initial output in America be 2000. In Germany and France there is unemployment, but in America there is full employment. Step 1 refers to the policy response. The output gap in Germany is 60. The wage policy multiplier in Germany is - 1 . 2 . So what is needed in Germany is a reduction in German nominal wages of 50. The output gap in France is 60. The wage policy multiplier in France is - 1.2. So what is needed in France is a reduction in French nominal wages of 50. Step 2 refers to the output lag. The reduction in German nominal wages of 50 causes an increase in German output of 60. As a side effect, it causes an increase in French output of 15 and a decline in American output of 25. The reduction in French nominal wages of 50 causes an increase in French output of 60. As a side effect, it causes an increase in German output of 15 and a decline in American output of 25. The total effect is an increase in German output of 75, an increase in French output of equally 75, and a decline in American output of 50. As a consequence, German output goes from 940 to 1015, French output equally goes from 940 to 1015, and American output goes from 2000 to 1950. Why does the German labour union not succeed in closing the output gap in Germany (or, for that matter, the inflationary gap in Germany)? The underlying reason is the external effect of the reduction in French nominal wages. Why does the French labour union not succeed in closing the output gap in France (or the inflationary gap in France)? The underlying reason is the external effect of the reduction in German nominal wages. And why is there now unemployment in America? The underlying reason is the external effect of the reduction in German and French nominal wages. Step 3 refers to the policy response. The inflationary gap in Germany is 15. The wage policy multiplier in Germany is -1.2. So what is needed in Germany is an increase in German nominal wages of 12.5. The inflationary gap in France is 15. The wage policy multiplier in France is -1.2. So what is needed in France is an increase in French nominal wages of 12.5.

93 Step 4 refers to the output lag. The increase in German nominal wages of 12.5 causes a decline in German output of 15. As a side effect, it causes a decline in French output of 3.8 and an increase in American output of 6.3 The increase in French nominal wages of 12.5 causes a decline in French output of 15. As a side effect, it causes a decline in German output of 3.8 and an increase in American output of 6.3. The total effect is a decline in German output of 18.8, a decline in French output of equally 18.8, and an increase in American output of 12.5. As a consequence, German output goes from 1015 to 996.3, French output equally goes from 1015 to 996.3, and American output goes from 1950 to 1962.5. Step 5 refers to the policy response. The output gap in Germany is 3.8. The wage policy multiplier in Germany is -1.2. So what is needed in Germany is a reduction in German nominal wages of 3.1. The output gap in France is 3.8. The wage policy multiplier in France is -1.2. So what is needed in France is a reduction in French nominal wages of 3.1. Step 6 refers to the output lag. The total effect is an increase in German output of 4.7, an increase in French output of equally 4.7, and a decline in American output of 3.1. As a consequence, German output goes to 1000.9, French output equally goes to 1000.9, and American output goes to 1959.4. 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 1960. In Germany and France there is full employment. But in America there is unemployment. As a result, competition between the German labour union and the French labour union leads to full employment in Germany and France. However, as an adverse side effect, it causes unemployment in America. What are the dynamic characteristics of this process? There is a downward trend in German nominal wages, as there is in French nominal wages. There is an upward trend in German output, as there is in French output. There is a downward trend in American output. There are damped oscillations in German nominal wages, as there are in French nominal wages. There are damped oscillations in German output, as there are in French output and American output. The German economy oscillates between unemployment and overemployment, as does the French economy. The American economy oscillates between high and low unemployment. In each round, the output gap in Europe (the inflationary gap in Europe) declines by 75 percent.

94 Table 3.1 Competition between German Labour Union and Frencli Labour Union Unemployment in Germany Equals Unemployment in France Germany

France

America

940

940

2000

A Nominal Wages

-50

-50

Output

1015

1015

Initial Output

A Nominal Wages

1950

12.5

12.5

Output

996.3

996.3

A Nominal Wages

-3.1

-3.1

1000.9

1000.9

1959.4

1000

1000

1960

Output

1962.5

and so on Steady-State Output

There is a decline in the price of German goods, as there is in the price of French goods. There is a depreciation of the euro and an appreciation of the dollar. There is an increase in European exports and a decline in American exports. There is an increase in the European current account surplus and an increase in the American current account deficit. There is a decline in the European budget deficit and an increase in the American budget deficit. Taking the sum over all periods, the total reduction in German nominal wages is 40, as is the total reduction in French nominal wages, see equations (31) and (32) in the preceding section. That means, the total reduction in German nominal wages is small, as compared to the initial output gap in Germany of 60. And the total reduction in French nominal wages is small, as compared to the initial output gap in France of 60. The effective multiplier in Germany is 60/40 = 1.5, 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.

95 2) Unemployment in Germany is high, unemployment in France is low. Let initial output in Germany be 940, let initial output in France be 970, and let initial output in America be 2000. Step 1 refers to the policy response. The output gap in Germany is 60. The wage policy multiplier in Germany is -1.2. So what is needed in Germany is a reduction German nominal wages of 50. The output gap in France is 30. The wage policy multiplier in France is -1.2. So what is needed in France is a reduction in French nominal wages of 25. Step 2 refers to the output lag. The reduction in German nominal wages of 50 causes an increase in German output of 60. As a side effect, it causes an increase in French output of 15 and a decline in American output of 25. The reduction in French nominal wages of 25 causes an increase in French output of 30. As a side effect, it causes an increase in German output of 7.5 and a decline in American output of 12.5. The total effect is an increase in German output of 67.5, an increase in French output of 45, and a decline in American output of 37.5. As a consequence, German output goes from 940 to 1007.5, French output goes from 970 to 1015, and American output goes from 2000 to 1962.5. Step 3 refers to the policy response. The inflationary gap in Germany is 7.5. The wage policy multiplier in Germany is -1.2. So what is needed in Germany is an increase in German nominal wages of 6.3. The inflationary gap in France is 15. The wage policy multiplier in France is -1.2. So what is needed in France is an increase in French nominal wages of 12.5. Step 4 refers to the output lag. The increase in German nominal wages of 6.3 causes a decline in German output of 7.5. As a side effect, it causes a decline in French output of 1.9 and an increase in American output of 3.1. The increase in French nominal wages of 12.5 causes a decline in French output of 15. As a side effect, it causes a decline in German output of 3.8 and an increase in American output of 6.3. The total effect is a decline in German output of 11.3, a decline in French output of 16.9, and an increase in American output of 9.4. As a consequence, German output goes from 1007.5 to 996.3, French output goes from 1015 to 998.1, and American output goes from 1962.5 to 1971.9. And so on. Table 3.2 gives an overview. In the steady state, German output is 1000, French output is equally 1000, and American output is 1970. In Germany and France there is fiill employment. But

96 in America there is unemplojTnent. What are the djmamic characteristics of this process? There is a downward trend in German nominal wages, as there is in French nominal wages. There is an upward trend in German output, as there is in French output. There is a downward trend in American output. There are damped oscillations in German nominal wages, as there are in French nominal wages. There are damped oscillations in German output, as there are in French output and American output. Taking the sum over all periods, the total reduction in German nominal wages is 46.7, and the total reduction in French nominal wages is 13.3, see equations (31) and (32) in the previous section. That means, the total reduction in German nominal wages is medium size, as compared to the initial output gap in Germany of 60. And the total reduction in French nominal wages is very small, as compared to the initial output gap in France of 30. The effective multiplier in Germany is 60/46.7 = 1.3, and the effective multiplier in France is 30/13.3 = 2.3. In other words, the effective multiplier in Germany is medium size, and the effective multiplier in France is very large.

Table 3.2 Competition between German Labour Union and Frencli Labour Union Unemployment in Germany Is High, Unemployment in France Is Low Germany

France

America

940

970

2000

A Nominal Wages

-50

-25

Output

1007.5

1015

Initial Output

A Nominal Wages

1962.5

6.3

12.5

Output

996.3

998.1

A Nominal Wages

-3.1

-1.6

1000.5

1000.9

1969.5

1000

1000

1970

Output

1971.9

and so on Steady-State Output

97 3) Unemplojmient in Germany, full employment in France. Let initial output in Germany be 940, let initial output in France be 1000, and let initial output in America be 2000. Step 1 refers to the policy response. The output gap in Germany is 60. The wage policy multiplier in Germany is -1.2. So what is needed in Germany is a reduction in German nominal wages of 50. The output gap in France is zero. So there is no need for a change in French nominal wages. Step 2 refers to the output lag. The reduction in German nominal wages of 50 causes an increase in German output of 60. As a side effect, it causes an increase in French output of 15 and a decline in American output of 25. As a consequence, German output goes to 1000, French output goes to 1015, and American output goes to 1975. Step 3 refers to the policy response. The output gap in Germany is zero. So there is no need for a change in German nominal wages. The inflationary gap in France is 15. The wage policy multiplier in France is -1.2. So what is needed in France is an increase in French nominal wages of 12.5. Step 4 refers to the output lag. The increase in French nominal wages of 12.5 causes a decline in French output of 15. As a side effect, it causes a decline in German output of 3.8 and an increase in American output of 6.3. As a consequence, French output goes to 1000, German output goes to 996.3, and American output goes to 1981.3. And so on. Table 3.3 presents a synopsis. In the steady state, German output is 1000, French output is equally 1000, and American output is 1980. In Germany and France there is full employment. But in America there is unemployment. German nominal wages have a downward trend, French nominal wages have an upward trend, and European nominal wages have a downward trend. German output has an upward trend, French output has a zero trend, European output has an upward trend, and American output has a downward trend. German output shows damped oscillations, as do French output and American output. Taking the sum over all periods, the total reduction in German nominal wages is 53.3, and the total increase in French nominal wages is 13.3. That means, the total reduction in German nominal wages is medium size, as compared to the initial output gap in Germany of 60. And the total increase in French nominal wages is extremely large, as compared to the initial output gap in France of zero. The effective multiplier in Germany is 60/53.3 = 1.1, and the effective multiplier

98 in France is 0/13.3 = 0. In other words, the effective muhipHer in Germany is medium size, and the effective multiplier in France is zero.

Table 3.3 Competition between German Labour Union and French Labour Union Unemployment in Germany, Full Unemployment in France Germany

France

940

1000

A Nominal Wages

-50

0

Output

1000

1015

Initial Output

A Nominal Wages Output

0 996.3

America

2000

1975

12.5 1000

1981.3

1000

1980

and so on Steady-State Output

1000

4) Unemployment in Germany, overemployment in France. Let initial output in Germany be 940, let initial output in France be 1060, and let initial output in America be 2000. Step 1 refers to the policy response. The output gap in Germany is 60. The wage policy multiplier in Germany is -1.2. So what is needed in Germany is a reduction in German nominal wages of 50. The inflationary gap in France is 60. The wage policy multiplier in France is -1.2. So what is needed in France is an increase in French nominal wages of 50. Step 2 refers to the output lag. The net effect is an increase in German output of 45, a decline in French output of equally 45, and a change in American output of zero. As a consequence, German output goes to 985, French output goes to 1015, and American output stays at 2000. Step 3 refers to the policy response. The output gap in Germany is 15. The wage policy multiplier in Germany is -1.2. So what is needed in Germany is a reduction in German nominal wages of 12.5. The inflationary gap in France is 15. The wage policy multiplier in France is -1.2. So what is needed in France is

99 an increase in French nominal wages of 12.5. Step 4 refers to the output gap. The net effect is an increase in German output of 11.3, a decline in French output of equally 11.3, and a change in American output of zero. As a consequence, German output goes to 996.3, French output goes to 1003.8, and American output stays at 2000. And so on. Table 3.4 gives an overview.

Table 3.4 Competition between German Labour Union and French Labour Union Unemployment in Germany, Overemployment in France Germany

Initial Output A Nominal Wages Output A Nominal Wages Output

France

940

1060

-50

50

985

1015

America

2000

2000

-12.5

12.5

996.3

1003.8

2000

1000

2000

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. In this special case, wage competition between Germany and France has no effect on employment in America. There are repeated cuts in German nominal wages, while there are repeated increases in French nominal wages. There are no changes in European nominal wages. There are repeated increases in German output, while there are repeated cuts in French output. There are no changes in European or American output. There are repeated cuts in the price of German goods, while there are repeated increases in the price of French goods. There are no changes in the price of European goods. The exchange rate between Europe and America is constant. There are no changes in European or American exports. There are no changes in

100 the European current account surplus, nor are there in the American current account deficit. There are no changes in the European budget deficit, nor are there in the American budget deficit. Taking the sum over all periods, the total reduction in German nominal wages is 66.7, and the total increase in French nominal wages is equally 66.7. That means, the total reduction in German nominal wages is large, as compared to the initial output gap in Germany of 60. And the total increase in French nominal wages is large, as compared to the initial inflationary gap in France of 60. The effective multiplier in Germany is 60/66.7 = 0.9, as is the effective multiplier in France. In other words, the effective multiplier in Germany is small, and the same holds for the effective multiplier in France. 5) Overemployment in Germany and France. Let initial output in Germany be 1060, let initial output in France be equally 1060, and let initial output in America be 2000. Step 1 refers to the policy response. The inflationary gap in Germany is 60. The wage policy multiplier in Germany is -1.2. So what is needed in Germany is an increase in German nominal wages of 50. The inflationary gap in France is; 60. The wage policy multiplier in France is -1.2. So what is needed in France is an increase in French nominal wages of 50. Step 2 refers to the output lag. The total effect is a decline in German output of 75, a decline in French output of equally 75, and an increase in American output of 50. As a consequence, German output goes to 985, French output equally goes to 985, and American output goes to 2050. Step 3 refers to the policy response. The output gap in Germany is 15. The wage policy multiplier in Germany is -1.2. So what is needed in Germany is a reduction in German nominal wages of 12.5. The output gap in France is 15. The wage policy multiplier in France is -1.2. So what is needed in France is a reduction in French nominal wages of 12.5. Step 4 refers to the output lag. The total effect is an increase in German output of 18.8, an increase in French output of equally 18.8, and a decline in American output of 12.5. As a consequence, German output goes to 1003.8, French output equally goes to 1003.8, and American output goes to 2037.5. And so on. Table 3.5 presents a synopsis. In the steady state, German output is 1000, French output is equally 1000, and American output is 2040. In Germany and France there is full employment. But

101 in America there is overemployment. As a result, competition between the German labour union and the French labour union leads to full employment in Germany and France. However, as an adverse side effect, it causes overemployment in America.

Table 3.5 Competition between German Labour Union and French Labour Union Overemployment in Germany and France Germany

France

America

1060

1060

2000

50

50

985

985

A Nominal Wages

-12.5

-12.5

Output

1003.8

1003.8

2037.5

1000

1000

2040

Initial Output A Nominal Wages Output

2050

and so on Steady-State Output

What are the djmamic characteristics of this process? There is an upward trend in German nominal wages, as there is in French nominal wages. There is a downward trend in German output, as there is in French output. And there is an upward trend in American output. There are damped oscillations in German nominal wages, as there are in French nominal wages. There are damped oscillations in German output, as there are in French output and American output. The German economy oscillates between overemployment and unemployment, as does the French economy. The American economy oscillates between high and low overemployment. In each round, the inflationary gap in Europe (the output gap in Europe) declines by 75 percent. There is an increase in the price of German goods, as there is in the price of French goods. There is an appreciation of the euro and a depreciation of the dollar. There is a decline in European exports and an increase in American

102 exports. There is a decline in the European current account surplus and a decline in the American current account deficit. There is an increase in the European budget deficit and a decline in the American budget deficit. Taking the sum over all periods, the total increase in German nominal wages is 40, as is the total increase in French nominal wages. That means, the total increase in German nominal wages is small, as compared to the initial inflationary gap in Germany of 60. And the total increase in French nominal wages is small, as compared to the initial inflationary gap in France of 60. The effective multiplier in Germany is 60/40 = 1.5, 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.

Chapter 2 Cooperation between the German Labour Union and the French Labour Union 1. The Model

1) Introduction. As a starting point, take the output model. It can be represented by a system of three equations: Yj = A i - X W i - n W 2

(1)

Y2=A2-m2-^Wi

(2)

Y3 = A 3 + v W i + v W 2

(3)

Here Yj denotes German output, Y2 is French output, Y3 is American output, Wi is German nominal wages, and W2 is French nominal wages. 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 is high, and unemployment in France is low. By contrast there is full employment in America. The targets of wage cooperation are full employment in Germany and full emplojonent in France. The instruments of wage cooperation are German nominal wages and French nominal wages. 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: Yj = A i - X W i - ^ W 2

(4)

Y2=A2-XW2-^Wi

(5)

Here Yj denotes full-emplojmient output in Germany, and Y2 denotes fullemployment output in France. The endogenous variables are German nominal wages and French nominal wages.

104 To simplify notation, we introduce Bj = Aj - Yj and B2 = A2 - Y2. Then we solve the model for the endogenous variables:

Wi =

W2 =

1

^2

(6)

X^-lx' XB2-|aBi X2-^2

(V)

Equation (6) shows the required level of German nominal wages, and equation (7) shows the required level of French nominal wages. There is a solution if and only if A, ?i |a,. Due to the assumption X, > |J,, this condition is met. The solution is positive if ix/X < B]^/B2 < ^/fx. As a result, cooperation between the German labour union and the French labour union can achieve full employment in Germany and France. However, as an adverse side effect, it causes unemployment in America. It is worth pointing out here that the solution to wage cooperation is identical to the steady state of wage 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 change in nominal wages. Taking differences in equations (1) and (2), the policy model can be written as follows: AYj = - MWj - 11AW2

(8)

AY2 = - >.AW2 - ^lAWj

(9)

Here AYj denotes the initial output gap in Germany, AY2 is the initial output gap in France, AWj is the required change in German nominal wages, and AW2 is the required change in French nominal wages. The endogenous variables are AWj and AW2. The solution to the system (8) and (9) is as follows:

Aw.^-^^^r^^f^

(10)

105

Aw,=-^^^r^f^

(11)

According to equation (10), the required cut in German nominal wages depends on the initial output gap in Germany, the initial output gap in France, the direct multiplier X, and the cross multiplier | i . The larger the initial output gap in Germany, the larger is the required cut in German nominal wages. On the other hand, the larger the initial output gap in France, the smaller is the required cut in German nominal wages. At first glance this comes as a surprise. According to equation (11), the required cut in French nominal wages depends on the initial output gap in France, the initial output gap in Germany, the direct multiplier X, and the cross multiplier \i.

2. Some Numerical Examples

To illustrate the policy model, have a look at some numerical examples. For ease of exposition, without losing generality, assume ?i = 1.2, |j, = 0.3 and V = 0.5. On this assumption, the output model can be written as follows: Yj = A i - 1 . 2 W i - 0 . 3 W 2

(1)

Y2=A2-1.2W2-0.3Wi

(2)

Y3 =A3+0.5Wi+0.5W2

(3)

The endogenous variables are German output, French output, and American output. Evidently, an increase in German nominal wages of 100 causes a decline in German output of 120, a decline in French output of 30, and an increase in American output of 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 consider five distinct cases:

106 - unemployment in Germany equals unemployment in France - unemployment in Germany is high, unemployment in France is low - unemployment in Germany, full employment in France - unemployment in Germany, overemployment in France - overemployment in Germany and France. 1) Unemployment in Germany equals unemployment in France. Let initial output in Germany be 940, let initial output in France be equally 940 and let initial output in America be 2000. In Germany and France there is unemployment, but in America there is full employment. Step 1 refers to the policy response. The output gap in Germany is 60, as is the output gap in France. So what is needed, according to equations (10) and (11) from the preceding section, is a reduction in German nominal wages of 40 and a reduction in French nominal wages of equally 40. Step 2 refers to the output lag. The reduction in German nominal wages of 40 raises German output by 48 and French output by 12. As a side effect, it lowers American output by 20. The reduction in French nominal wages of 40 raises French output by 48 and German output by 12. As a side effect, it lowers American output by 20. The total effect is an increase in German output of 60, an increase in French output of equally 60, and a decline in American output of 40. As a consequence, German output goes from 940 to 1000, French output equally goes from 940 to 1000, and American output goes from 2000 to 1960. In Germany and France there is now full employment. But in America there is now unemployment. As a result, cooperation between the German labour union and the French labour union can achieve full employment in Germany and France. However, as an adverse side effect, it causes unemployment in America. There is a reduction in German nominal wages, as there is in French nominal wages. There is an increase in German output, as there is in French output. There is a decline in American output. There is a decline in the price of German goods, as there is in the price of French goods. There is a depreciation of the euro and an appreciation of the dollar. There is an increase in European exports and a decline in American exports. There is an increase in the European current account surplus and an increase in the American current account deficit. There is a

107 decline in the European budget deficit and an increase in the American budget deficit. The required cut in German nominal wages is small, as compared to the initial output gap in Germany. And the required cut in French nominal wages is small, as compared to the initial output gap in France. The effective multiplier in Germany is 60/40 = 1.5, as is the effective multiplier in France. That is to say, the effective multiplier in Germany is large. And the same is true of the effective multiplier in France. Table 3.6 gives an overview.

Table 3.6 Cooperation between German Labour Union and French Labour Union Unemployment in Germany Equals Unemployment in France Germany

Initial Output

France

940

940

A Nominal Wages

-40

-40

Output

1000

1000

America

2000

1960

2) Unemployment in Germany is high, unemployment in France is low. Let initial output in Germany be 940, let initial output in France be 970, and let initial output in America be 2000. 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 (10) and (11) from the previous section, is a reduction in German nominal wages of 46.7 and a reduction in French nominal wages of 13.3. Step 2 refers to the output lag. The reduction in German nominal wages of 46.7 raises German output by 56 and French output by 14. As a side effect, it lowers American output by 23.3. The reduction in French nominal wages of 13.3 raises French output by 16 and German output by 4. As a side effect, it lowers American output by 6.7. 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 equally

108 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 and France there is now full employment. But in America there is now unemployment. The required cut in German nominal wages is medium size, as compared to the initial output gap in Germany. And the required cut in French nominal wages is very small, as compared to the initial output gap in France. The effective multiplier in Germany is 60/46.7 = 1.3, and the effective multiplier in France is 30/13.3 = 2.3. That is to say, the effective multipUer in Germany is medium size, and the effective multiplier in France is very large. Table 3.7 presents a sjmopsis.

Table 3.7 Cooperation between German Labour Union and French Labour Union Unemployment in Germany Is High, Unemployment in France Is Low Germany

France

America

940

970

2000

A Nominal Wages

-46.7

-13.3

Output

1000

1000

Initial Output

1970

3) Unemployment in Germany, full employment in France. Let initial output in Germany be 940, let initial output in France be 1000, and let initial output in America be 2000. Step 1 refers to the policy response. The output gap in Germany is 60, and the output gap in France is zero. So what is needed, according to equations (10) and (11) from the preceding section, is a reduction in German nominal wages of 53.3 and an increase in French nominal wages of 13.3. Step 2 refers to the output lag. The reduction in German nominal wages of 53.3 raises German output by 64 and French output by 16. As a side effect, it lowers American output by 26.7. The increase in French nominal wages of 13.3 lowers French output by 16 and German output by 4. As a side effect, it raises

109 American output by 6.7. The net effect is an increase in German output of 60, a change in French output of zero, and a decline in American output of 20. As a consequence, German output goes from 940 to 1000, French output stays at 1000, and American output goes from 2000 to 1980. In Germany and France there is now frill employment. But in America there is now unemployment. There is a reduction in German nominal wages, an increase in French nominal wages, and a reduction in European nominal wages. There is an increase in German output, no change in French output, an increase in European output, and a decline in American output. The required cut in German nominal wages is medium size, as compared to the initial output gap in Germany. And the required increase in French nominal wages is extremely large, as compared to the initial output gap in France. The effective multiplier in Germany is 60/53.3 = 1.1, and the effective multiplier in France is 0/13.3 = 0. That is to say, the effective multiplier in Germany is medium size, and the effective multiplier in France is zero. Table 3.8 gives an overview.

Table 3.8 Cooperation between German Labour Union and Frencli Labour Union Unemployment in Germany, Full Employment in France

Germany Initial Output

940

A Nominal Wages

-53.3

Output

1000

France 1000

America 2000

13.3 1000

1980

4) Unemployment in Germany, overemployment in France. Let initial output in Germany be 940, let initial output in France be 1060, and let initial output in America be 2000. Step 1 refers to the policy response. The output gap in Germany is 60, and the inflationary gap in France is equally 60. So what is

110 needed, according to equations (10) and (11) from the previous section, is a reduction in German nominal wages of 66.7 and an increase in French nominal wages of equally 66.7. Step 2 refers to the output lag. The reduction in German nominal wages of 66.7 raises German output by 80 and French output by 20. As a side effect, it lowers American output by 33.3. The increase in French nominal wages of 66.7 lowers French output by 80 and German output by 20. As a side effect, it raises American output by 33.3. The net effect is an increase in German output of 60, a decline in French output of equally 60, and a change in American output of zero. As a consequence, German output goes from 940 to 1000, French output goes from 1060 to 1000, and American output stays at 2000. In each of the countries there is now full employment. In this special case, wage cooperation between Germany and France has no effect on employment in America. There is a reduction in German nominal wages, while there is an increase in French nominal wages. There is no change in European nominal wages. There is an increase in German output, while there is a decline in French output. There is no change in European or American output. There is a decline in the price of German goods, while there is an increase in the price of French goods. There is no change in the price of European goods. The exchange rate between Europe and America is constant. There is no change in European or American exports. There is no change in the European current account surplus, nor is there in the American current account deficit. There is no change in the European budget deficit, nor is there in the American budget deficit. The required cut in German nominal wages is large, as compared to the initial output gap in Germany. And the required increase in French nominal wages is large, as compared to the initial inflationary gap in France. The effective multiplier in Germany is 60/66.7 = 0.9, as is the effective multiplier in France. That is to say, the effective multiplier in Germany is small, and the same is true of the effective multiplier in France. Table 3.9 presents a sjoiopsis.

Ill Table 3.9 Cooperation between German Labour Union and Frencli Labour Union Unemployment in Germany, Overemployment in France Germany Initial Output

940

A Nominal Wages

-66.7

Output

1000

France

America

1060

2000

66.7 1000

2000

5) Overemployment in Germany and France. Let initial output in Germany be 1060, let initial output in France be equally 1060, and let initial output in America be 2000. Step 1 refers to the policy response. The inflationary gap in Germany is 60, as is the inflationary gap in France. So what is needed, according to equations (10) and (11) from the preceding section, is an increase in German nominal wages of 40 and an increase in French nominal wages of equally 40. Step 2 refers to the output lag. The increase in German nominal wages of 40 lowers German output by 48 and French output by 12. As a side effect, it raises American output by 20. The increase in French nominal wages of 40 lowers French output by 48 and German output by 12. As a side effect, it raises American output by 20. The total effect is a decline in German output of 60, a decline in French output of equally 60, and an increase in American output of 40. As a consequence, German output goes from 1060 to 1000, French output equally goes from 1060 to 1000, and American output goes from 2000 to 2040. In Germany and France there is now full employment. But in America there is now overemployment. As a result, cooperation between the German labour union and the French labour union can achieve full employment in Germany and France. However, as an adverse side effect, it causes overemployment in America. There is an increase in German nominal wages, as there is in French nominal wages. There is a decline in German output, as there is in French output. There is

112 an increase in American output. There is an increase in the price of German goods, as there is in the price of French goods. There is an appreciation of the euro and a depreciation of the dollar. There is a decline in European exports and an increase in American exports. There is a decline in the European current account surplus and a decline in the American current account deficit. There is an increase in the European budget deficit and a decline in the American budget deficit. The required increase in German nominal wages is small, as compared to the initial inflationary gap in Germany. And the required increase in French nominal wages is small, as compared to the initial inflationary gap in France. The effective multiplier in Germany is 60/40 = 1.5, 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. Table 3.10 gives an overview.

Table 3.10 Cooperation between German Labour Union and Frencli Labour Union Overemployment in Germany and France

Initial Output A Nominal Wages Output

Germany

France

America

1060

1060

2000

40

40

1000

1000

2040

6) Comparing wage cooperation with wage competition. Wage competition can achieve full employment. And the same applies to wage cooperation. Wage competition is a slow process. By contrast, wage cooperation is a fast process. Wage competition can cause oscillations in nominal wages and output. By contrast, wage cooperation cannot cause oscillations in nominal wages and output. Judging from these points of view, wage cooperation seems to be superior to wage competition.

Part Four Monetary and Wage Interactions Intermediate Models

Chapter 1 Competition between European Central Bank, German Labour Union, and French Labour Union 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 = Aj + 0.5aMi2 - ?^Wj - ^Wj

(1)

Y2 = A2 + 0.5aMi2 - XW2 - ^iWj

(2)

Y3 = A3 - pMi2 + vWj + vWj

(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, Mj2 is European money supply, Wj is German nominal wages, W2 is French nominal wages, 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, X, \i and v are positive coefficients with a > p , 'k> 11 and A, > v. 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 German nominal wages, and a negative function of French nominal wages. According to equation (2), French output is a positive function of European money supply, a negative function of French nominal wages, and a negative function of German nominal wages. According to equation (3), American output is a negative function of European money supply, a positive function of German nominal wages, and a positive function of French nominal wages.

116 An increase in European money supply raises German output and French output but lowers American output. An increase in German nominal wages lowers German output. And what is more, it lowers French output. On the other hand, it raises American output. Correspondingly, an increase in French nominal wages lowers French output. And what is more, it lowers German output. On the other hand, 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 P. An increase in German nominal wages of 1 causes a decline in German output of >^, a decline in French output of |4., and an increase in American output of v. Similarly, an increase in French nominal wages of 1 causes a decline in French output of >u, a decline in German output of \i, and an increase in American output of v . 2) The dynamic model. At the beginning there is unemployment in Germany and France. More precisely, unemployment in Germany is high, and unemployment in France is low. 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 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 German labour union is full emplojmient in Germany. The instrument of the German labour union is German nominal wages. The German labour union lowers German nominal wages so as to close the output gap in Germany. The target of the French labour union is fiiU employment in France. The instrument of the French labour union is French nominal wages. The French labour union lowers French nominal wages so as to close the output gap in France. We assume that the central bank and the labour unions decide sequentially. First the central bank decides, then the labour unions decide. In step 1, the

117 European central bank decides. In step 2, the German labour union and the French labour union decide simultaneously and independently. In step 3, the European central bank decides. In step 4, the German labour union and the French labour union decide simultaneously and independently. And so on. For a mathematical presentation of the djoiamic model see Chapter 1 of Part Three.

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, A, = 1.2, |j, = 0.3 and v = 0.5. On this assumption, the static model can be written as follows:

Yi=Ai+1.5Mi2-1.2Wi-0.3W2

(1)

Y2 = A2 +1.5Mi2 -1.2W2 -0.3Wj

(2)

Y3 = A3 - M12 + 0.5Wi + O.5W2

(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 nominal wages of 100 causes a decline in German output of 120, a decline in French output of 30, and an increase in American output of 50. Correspondingly, an increase in French nominal wages of 100 causes a decline in French output of 120, a decline in German output of 30, and an increase in American output of 50. Further let full-employment output in Germany be 1000, let fiill-employment output in France be equally 1000, and let full-employment output in America be 2000. It proves useful to study four distinct cases: - unemployment in Europe, full employment in America - another interpretation

118 - overemployment in Europe, fUll employment in America - first the labour unions decide, then the central bank decides. 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 and France there is unemployment, but in America there is full employment. 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. In France there is now some overemployment. Strictly speaking, unemployment in Germany equals overemployment in France. In Europe there is now full emplojonent. And in America there is now some unemployment. Step 3 refers to wage policy in Germany and France. The output gap in Germany is 15. The wage policy multiplier in Germany is -1.2. So what is needed in Germany is a reduction in German nominal wages of 12.5. The inflationary gap in France is 15. The wage policy multiplier in France is -1.2. So what is needed in France is an increase in French nominal wages of 12.5. Step 4 refers to the output lag. The reduction in German nominal wages of 12.5 causes an increase in German output of 15. As a side effect, it causes an increase in French output of 3.8 and a decline in American output of 6.3. The increase in French nominal wages of 12.5 causes a decline in French output of 15. As a side effect, it causes a decline in German output of 3.8 and an increase in American output of 6.3. The net effect is an increase in German output of 11.3, a decline in French output of equally 11.3, and a change in American output of zero. As a consequence, German output goes from 985 to 996.3, French output goes from 1015 to 1003.8, and American output stays at 1970.

119 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 996.3, French output stays at 1003.8, and American output stays at 1970. Step 7 refers to wage policy in Germany and France. The output gap in Germany is 3.8. The wage policy multiplier in Germany is -1.2. So what is needed in Germany is a reduction in German nominal wages of 3.1. The inflationary gap in France is 3.8. The wage policy multiplier in France is -1.2. So what is needed in France is an increase in French nominal wages of 3.1. Step 8 refers to the output lag. The net effect is an increase in German output of 2.8, a decline in French output of equally 2.8, and a change in American output of zero. As a consequence, German output goes to 999.1, French output goes to 1000.9, 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 and France there is full employment. But in America there is unemployment. As a result, competition between the European central bank, the German labour union, and the French labour union leads to full employment in Germany and France. However, as an adverse side effect, it causes unemployment in America. What are the dynamic characteristics of this process? There is a one-time increase in European money supply. There are repeated cuts in German nominal wages, while there are repeated increases in French nominal wages. There are no changes in European nominal wages. There are repeated increases in German output. There is an initial increase in French output that is followed by repeated cuts. There is a one-time increase in European output, while there is a one-time cut in American output. There are repeated cuts in the price of German goods, while there are repeated increases in the price of French goods. There are no changes in the price level of European goods. There is a depreciation of the euro and an appreciation of the dollar. There is an increase in European exports and a decline in American exports. There is an increase in the European current account surplus and an increase in the American

120 current account deficit. There is a decline in the world interest rate. There is an increase in European investment, as there is an American investment. There is a decline 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 reduction in German nominal wages is 16.7, and the total increase in French nominal wages is equally 16.7. The total change in European nominal wages is zero.

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

Initial Output

Germany

France

America

940

970

2000

A Money Supply Output A Nominal Wages Output

30 985

1015

-12.5

12.5

996.3

1003.8

A Money Supply

1970

1970

0

Output

996.3

1003.8

1970

A Nominal Wages

-3.1

3.1

Output

999.1

1000.9

1970

1000

1970

and so on Steady-State Output

1000

2) Another interpretation. Let initial output in Germany be 940, let initial output in France be 970, and let initial output in America be 2000. 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.

121 Step 2 refers to wage policy in Germany and France. The German labour union and the French labour union anticipate the effect of the increase in European money supply. The German labour union expects that, due to the increase in European money supply of 30, German output will rise to 985. The French labour union expects that, due to the increase in European money supply of 30, French output will rise to 1015. The expected output gap in Germany is 15. The wage policy multiplier in Germany is -1.2. So what is needed in Germany is a reduction in German nominal wages of 12.5. The expected inflationary gap in France is 15. The wage policy multiplier in France is -1.2. So what is needed in France is an increase in French nominal wages of 12.5. Step 3 refers to the output lag. The increase in European money supply of 30 causes an increase in German output of 45, an increase in French output of equally 45, and a decline in American output of 30. The reduction in German nominal wages of 12.5 causes an increase in German output of 15, an increase in French output of 3.8, and a decline in American output of 6.3. The increase in French nominal wages of 12.5 causes a decline in French output of 15, a decline in German output of 3.8, and an increase in American output of 6.3. The net effect is an increase in German output of 56.3, an increase in French output of 33.8, and a decline in American output of 30. As a consequence, German output goes from 940 to 996.3, French output goes from 970 to 1003.8, and American output goes from 2000 to 1970. Step 4 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 5 refers to wage policy in Germany and France. The German labour union expects that, due to the constancy of European money supply, German output will stay at 996.3. The French labour union expects that, due to the constancy of European money supply, French output will stay at 1003.8. The expected output gap in Germany is 3.8. The wage policy multiplier in Germany is -1.2. So what is needed in Germany is a reduction in German nominal wages of 3.1. The expected inflationary gap in France is 3.8. The wage policy multiplier in France is -1.2. So what is needed in France is an increase in French nominal wages of 3.1. Step 6 refers to the output lag. The reduction in German nominal wages of 3.1 causes an increase in German output of 3.8, an increase in French output of 0.9, and a decline in American output of 1.6. The increase in French nominal wages

122 of 3.1 causes a decline in French output of 3.8, a decline in German output of 0.9, and an increase in American output of 1.6. The net effect is an increase in German output of 2.8, a decline in French output of equally 2.8, and a change in American output of zero. As a consequence, German output goes from 996.3 to 999.1, French output goes from 1003.8 to 1000.9, and American output stays at 1970. And so on. Table 4.2 gives an overview.

Table 4.2 Competition between the European Central Bank, the German Labour Union, and the French Labour Union Another Interpretation

Initial Output

Germany

France

America

940

970

2000

30

A Money Supply A Nominal Wages Output

-12.5

12.5

996.3

1003.8 0

A Money Supply A Nominal Wages

-3.1

3.1

Output

999.1

1000.9

and so on Steady-State Output

1970

1970 ...

1000

1000

1970

3) Overemployment in Europe, full employment 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 and France there is overemployment, but in America there is full employment. 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.

123 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. In France there is now some unemployment. Strictly speaking, overemployment in Germany equals unemployment in France. In Europe there is now full employment. And in America there is now some overemployment. Step 3 refers to wage policy in Germany and France. The inflationary gap in Germany is 15. The wage policy multiplier in Germany is -1.2. So what is needed in Germany is an increase in German nominal wages of 12.5. The output gap in France is 15. The wage policy multiplier in France is -1.2. So what is needed in France is a reduction in French nominal wages of 12.5. Step 4 refers to the output lag. The increase in German nominal wages of 12.5 causes a decline in German output of 15. As a side effect, it causes a decline in French output of 3.8 and an increase in American output of 6.3. The reduction in French nominal wages of 12.5 causes an increase in French output of 15. As a side effect, it causes an increase in German output of 3.8 and a decline in American output of 6.3. The net effect is a decline in German output of 11.3, an increase in French output of equally 11.3, and a change in American output of zero. As a consequence, German output goes from 1015 to 1003.8, French output goes from 985 to 996.3, and American output stays at 2030. Step 5 refers to wage policy in Germany and France. The inflationary gap in Germany is 3.8. The wage policy multiplier in Germany is -1.2. So what is needed in Germany is an increase in German nominal wages of 3.1. The output gap in France is 3.8. The wage policy multiplier in France is -1.2. So what is needed in France is a reduction in French nominal wages of 3.1. Step 6 refers to the output lag. The net effect is a decline in German output of 2.8, an increase in French output of equally 2.8, and a change in American output of zero. As a consequence, German output goes to 1000.9, French output goes to 999.1, and American output stays at 2030. And so on. Table 4.3 presents a synopsis.

124 Table 4.3 Competition between the European Central Bank, the German Labour Union, and the French Labour Union Overemployment in Europe, Full Employment in America

Initial Output

Germany

France

America

1060

1030

2000

A Money Supply Output A Nominal Wages Output A Nominal Wages Output

-30 1015

985

12.5

-12.5

1003.8

996.3

3.1

-3.1

1000.9

999.1

2030 2030 2030

and so on Steady-State Output

1000

1000

2030

In the steady state, German output is 1000, French output is equally 1000, and American output is 2030. In Germany and France there is full employment. But in America there is overemployment. As a result, competition between the European central bank, the German labour union, and the French labour union leads to full employment in Germany and France. However, as an adverse side effect, it causes overemplojTnent in America. What are the dynamic characteristics of this process? There is a one-time cut in European money supply. There are repeated increases in German nominal wages, while there are repeated cuts in French nominal wages. There are no changes in European nominal wages. There are repeated cuts in German output. There is an initial cut in French output that is followed by repeated increases. There is a one-time cut in European output, while there is a one-time increase in American output. There are repeated increases in the price of German goods, while there are repeated cuts in the price of French goods. There are no changes in the price level of European goods.

125

There is an appreciation of the euro and a depreciation of the dollar. There is a decline in European exports and an increase in American exports. There is a decline in the European current account surplus and a decline in the American current account deficit. There is an increase in the world interest rate. There is a decline in European investment, as there is in American investment. There is an increase in the European budget deficit and a decline in the American budget deficit. Taking the sum over all periods, the total reduction in European money supply is 30, the total increase in German nominal wages is 16.7, and the total reduction in French nominal wages is equally 16.7. The total change in European nominal wages is zero. 4) Comparing monetary and wage competition with pure wage competition. First consider the case of unemployment in Europe. Pure wage competition is a slow process. By contrast, monetary and wage competition is a process of intermediate speed. Pure wage competition causes a large reduction in German nominal wages, a large reduction in French nominal wages, and a large reduction in European nominal wages. By contrast, monetary and wage competition causes a small reduction in German nominal wages, a small increase in French nominal wages, and no change in European nominal wages. Pure wage competition causes a large reduction in the price of European goods. By contrast, monetary and wage competition causes a zero reduction in the price of European goods. Judging from these point of view, monetary and wage competition seems to be superior to pure wage competition. Second consider the case of overemployment in Europe. Pure wage competition is a slow process. By contrast, monetary and wage competition is a process of intermediate speed. Pure wage competition causes a large increase in German nominal wages, a large increase in French nominal wages, and a large increase in European nominal wages. By contrast, monetary and wage competition causes a small increase in German nominal wages, a small reduction in French nominal wages, and no change in European nominal wages. Pure wage competition causes a large increase in the price of European goods. By contrast, monetary and wage competition causes a zero increase in the price of European goods. Judging from this perspective, monetary and wage competition seems to be superior to pure wage competition.

126 5) First the labour unions decide, then the central bank decides. So far we have assumed that the central bank decides first. Now we assume that the labour unions 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 and France there is unemployment, but in America there is full employment. Step 1 refers to wage policy in Germany and France. The output gap in Germany is 60. The wage policy multiplier in Germany is -1.2. So what is needed in Germany is a reduction in German nominal wages of 50. The output gap in France is 30. The wage policy multiplier in France is -1.2. So what is needed in France is a reduction in French nominal wages of 25. Step 2 refers to the output lag. The reduction in German nominal wages of 50 causes an increase in German output of 60. As a side effect, it causes an increase in French output of 15 and a decline in American output of 25. The reduction in French nominal wages of 25 causes an increase in French output of 30. As a side effect, it causes an increase in German output of 7.5 and a decline in American output of 12.5. The net effect is an increase in German output of 67.5, an increase in French output 45, and a decline in American output of 37.5. As a consequence, German output goes from 940 to 1007.5, French output goes from 970 to 1015, and American output goes from 2000 to 1962.5. In Germany and France there is now some overemployment. And in America there is now some unemployment. Step 3 refers to monetary policy in Europe. The inflationary gap in Europe is 22.5. The monetary policy multiplier in Europe is 3. So what is needed in Europe is a reduction in European money supply of 7.5. Step 4 refers to the output lag. The reduction in European money supply of 7.5 causes a decline in German output of 11.3 and a decline in French output of equally 11.3. As a side effect, it causes an increase in American output of 7.5. As a consequence, German output goes from 1007.5 to 996.3, French output goes from 1015 to 1003.8, and American output goes from 1962.5 to 1970. In Germany there is now some unemployment. In France there is still some overemployment. Strictly speaking, unemployment in Germany equals overemployment in France. In Europe there is now full employment. And in America there is still some unemployment. Step 5 refers to wage policy in Germany and France. The output gap in Germany is 3.8. The wage policy multiplier in Germany is -1.2. So what is

127 needed in Germany is a reduction in German nominal wages of 3.1. The inflationary gap in France is 3.8. The wage policy multiplier in France is -1.2. So what is needed in France is an increase in French nominal wages of 3.1. Step 6 refers to the output lag. The net effect is an increase in German output of 2.8, a decline in French output of equally 2.8, and a change in American output of zero. As a consequence, German output goes to 999.1, French output goes to 1000.9, and American output stays at 1970. Step 7 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 8 refers to the output lag. As a consequence, German output stays at 999.1, French output stays at 1000.9, and American output stays at 1970. And so on. Table 4.4 gives an overview.

Table 4.4 Competition between tlie European Central Bank, the German Labour Union, and the French Labour Union First the Labour Unions Decide, then the Central Bank Decides Germany

France

America

Initial Output

940

970

2000

A Nominal Wages

-50

-25

Output

1007.5

1015

A Money Supply

-7.5

Output

996.3

1003.8

A Nominal Wages

-3.1

3.1

Output

999.1

1000.9

A Money Supply Output

1962.5

1970

1970

0 999.1

1000.9

1970

1000

1970

and so on Steady-State Output

1000

128 In the steady state, German output is 1000, French output is equally 1000, and American output is 1970. In Germany and France there is full employment. But in America there is unemployment. As a result, competition between the German labour union, the French labour union, and the European central bank leads to full employment in Germany and France. However, as an adverse side effect, it causes unemplojonent in America. Taking the sum over all periods, the total reduction in European money supply is 7.5, the total reduction in German nominal wages is 54.2, and the total reduction in French nominal wages is 20.8. The total reduction in European nominal wages is 75/2 = 37.5. 6) Comparing - first the central bank decides, then the labour unions decide - first the labour unions 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 reduction in German nominal wages is 16.7, the increase in French nominal wages is equally 16.7, the change in European nominal wages is zero, and the decline in American output is 30. Case number 2: The labour unions decide first. Taking the sum over all periods, the reduction in European money supply is 7.5, the reduction in German nominal wages is 54.2, the reduction in French nominal wages is 20.8, the reduction in European nominal wages is 37.5, and the decline in American output is 30. Table 4.5 presents a synopsis. As a result, if the central bank decides first, there will be a large increase in European money supply and a zero reduction in European nominal wages. The other way round, if the labour unions decide first, there will be large reduction in European nominal wages and a small reduction in European money supply. Judging fi-om these points of view, it seems that the central bank should decide first.

129 Table 4.5 Who Should Decide First, the Central Bank or the Labour Unions? The Central Bank Decides First

The Labour Unions Decide First

European Money Supply

30

-7.5

German Nominal Wages

-16.7

-54.2

16.7

-20.8

0

-37.5

Total Change in

French Nominal Wages European Nominal Wages American Output

-30

-30

Chapter 2 Cooperation between European Central Bank, German Labour Union, and Frencli Labour Union 1. The Model

1) Introduction. As a starting point, take the output model. It can be represented by a system of three equations:

Yj=Ai+0.5aMi2->^Wi-nW2

(1)

Y2 = A2 + 0.5aMi2 - >.W2 - |xWj

(2)

Y3 = A3 - pMi2 + vWi + VW2

(3)

Here Yj denotes German output, Y2 is French output, Y3 is American output, M12 is European money supply, Wj is German nominal wages, and W2 is French nominal wages. 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 is high, and unemployment in France is low. By contrast there is full employment in America. The policy makers are the European central bank, the German labour union, and the French labour union. 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 nominal wages, and French nominal wages. 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 labour union, and the French labour union can achieve full employment in Germany and France.

131 2) The policy model. On this basis, the policy model can be characterized by a system of three equations:

AYj = 0.5aAMj2 - XAWj - [lAV^^

(4)

AY2 = 0.5aAMi2 - MW2 - nAWj

(5)

AY3 = - PAM12 + vAWi + VAW2

(6)

Here AYj denotes the initial output gap in Germany, AY2 is the initial output gap in France, AY^ is the change in American output, AMjj is the required change in European money supply, AWj is the required change in German nominal wages, and AWj is the required change in French nominal wages. The endogenous variables are AMj2, AWj, AW2 and AY3 . We now introduce a third target. We assume that the reduction in German nominal wages should be equal in size to the increase in French nominal wages AWJ + AW2 = 0. Put another way, we assume that the price level of European goods should be constant. Add up equations (4) and (5), taking account of AWJ + AW2 = 0, to find out: AY, + AY, AMi2=—J ^ a

(7)

Then subtract equation (5) from equation (4), taking account of AWj + AW2 = 0, and solve for: AY,-AYo L—2. 2(^-^)

(8)

AY - AY, AW, = — i 2.

(9)

AW 1

According to equation (7), the required change in European money supply depends on the initial output gap in Europe and the direct multiplier a . According to equation (8), the required change in German nominal wages depends on the initial output gap in Germany, the initial output gap in France, the

132 direct multiplier X, and the cross multiplier \i. According to equation (9), the required change in French nominal wages depends on the initial output gap in France, the initial output gap in Germany, the direct multiplier X, and the cross multiplier p..

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, p = 1, X = 1.2, |x= 0.3 and v = 0.5. 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 decline in American output of 100. An increase in German nominal wages of 100 causes a decline in German output of 120, a decline in French output of 30, and an increase in American output of 50. 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. It proves useful to consider three distinct cases: - unemployment in Europe, full employment in America - overemployment in Europe, full employment 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 and France there is unemployment, but in America there is full employment. 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, a reduction in German nominal wages of 16.7, and an increase in French nominal wages of equally 16.7.

133

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 American output by 30. The reduction in German nominal wages of 16.7 raises German output by 20 and French output by 5. As a side effect, it lowers American output by 8.3. The increase in French nominal wages of 16.7 lowers French output by 20 and German output by 5. As a side effect, it raises American output by 8.3. 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 equally 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. Table 4.6 gives an overview.

Table 4.6 Cooperation between the European Central Bank, the German Labour Union, and the French Labour Union Unemployment in Europe, Full Emplojmient in America

Initial Output

Germany

France

America

940

970

2000

A Money Supply

30

A Nominal Wages

-16.7

Output

1000

16.7 1000

1970

In Germany and France there is now full employment. But in America there is now unemployment. As a result, cooperation between the European central bank, the German labour union, and the French labour union can achieve full employment in Germany and France. However, as an adverse side effect, it causes unemployment in America. There is an increase in European money supply. There is a reduction in German nominal wages and an increase in French nominal wages. There is no change in European nominal wages. There is an increase in German output, as

134 there is in French output. There is a decHne in American output. There is a decline in the price of German goods and an increase in the price of French goods. There is no change in the price level of European goods. There is a depreciation of the euro and an appreciation of the dollar. There is an increase in European exports and a decline in American exports. There is an increase in the European current account surplus and an increase in the American current account deficit. There is a decline in the world interest rate. There is an increase in European investment, as there is an American investment. There is a decline in the European budget deficit and an increase in the American budget deficit. 2) Comparing policy cooperation with policy competition. Policy competition can achieve full employment in Germany and France. And the same applies to policy cooperation. Under policy competition, the total increase in European money supply is 30, the total reduction in German nominal wages is 16.7, and the total increase in French nominal wages is equally 16.7 (assuming that the central bank decides first). Hence the solution to policy cooperation is identical to the steady state of policy competition. Policy competition is a slow process. By contrast, policy cooperation is a fast process. Policy competition causes oscillations in output. By contrast, policy cooperation does not cause oscillations in output. Judging from these points of view, policy cooperation seems to be superior to policy competition. 3) Overemployment in Europe, full employment 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 and France there is overemployment, but in America there is full emplojonent. 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 section, is a reduction in European money supply of 30, an increase in German nominal wages of 16.7, and a reduction in French nominal wages of equally 16.7. Step 2 refers to the output lag. The reduction in European money supply of 30 lowers German output and French output by 45 each. As a side effect, it raises American output by 30. The increase in German nominal wages of 16.7 lowers German output by 20 and French output by 5. As a side effect, it raises American output by 8.3. The reduction in French nominal wages of 16.7 raises French output by 20 and German output by 5. As a side effect, it lowers American output

135 by 8.3. The net effect is a decline in German output of 60, a decline in French output of 30, and an increase in American output of equally 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. Table 4.7 presents a synopsis.

Table 4.7 Cooperation between the European Central Bank, the German Labour Union, and the French Labour Union Overemployment in Europe, Full Employment in America

Initial Output

Germany

France

America

1060

1030

2000

A Money Supply A Nominal Wages Output

-30 16.7 1000

-16.7 1000

2030

In Germany and France there is now full employment. But in America there is now overemployment. As a result, cooperation between the European central bank, the German labour union, and the French labour union can achieve full employment in Germany and France. However, as an adverse side effect, it causes overemployment in America. There is a reduction in European money supply. There is an increase in German nominal wages and a reduction in French nominal wages. There is no change in European nominal wages. There is a decline in German output, as there is in French output. There is an increase in American output. There is an increase in the price of German goods and a decline in the price of French goods. There is no change in the price level of European goods. There is an appreciation of the euro and a depreciation of the dollar. There is a decline in European exports and an increase in American exports. There is a decline in the European current account surplus and a decline in the American current account deficit. There is an

136 increase in the world interest rate. There is a decline in European investment, as there is in American investment. There is an increase in the European budget deficit and a decline in the American budget deficit. 4) Comparing monetary and wage cooperation with pure wage cooperation. First consider the case of unemployment in Europe. Pure wage cooperation causes a large reduction in European nominal wages and a large reduction in the price of European goods. By contrast, monetary and wage cooperation causes no change in European nominal wages and no change in the price of European goods. Judging from this perspective, monetary and wage cooperation seems to be superior to pure wage cooperation. Second consider the case of overemployment in Europe. Pure wage cooperation causes a large increase in European nominal wages and large increase in the price of European goods. By contrast, monetary and wage cooperation causes no change in European nominal wages and no change in the price of European goods. Judging from this perspective, monetary and wage cooperation seems to be superior to pure wage cooperation. 5) Alternative targets of policy cooperation: no reduction in German nominal wages. Let initial output in Germany be 940, let initial output in France be 970, and let initial output in America be 2000. In Germany and France there is unemployment, but in America there is full employment. 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 European money supply of 46.7, a reduction in German nominal wages of zero, and an increase in French nominal wages of 33.3. Step 2 refers to the output lag. The increase in European money supply of 46.7 raises German output and French output by 70 each. As a side effect, it lowers American output by 46.7. The increase in French nominal wages of 33.3 lowers French output by 40 and German output by 10. As a side effect, it raises American output by 16.7. 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 equally 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. Table 4.8 gives an overview.

137 Table 4.8 Cooperation between the European Central Bank, the German Labour Union, and the French Labour Union No Reduction in Nominal Wages

Initial Output

Germany

France

America

940

970

2000

A Money Supply A Nominal Wages Output

46.7 0 1000

33.3 1000

1970

In Germany and France there is now full employment. But in America there is now unemployment. There is a large increase in European money supply. There is no change in German nominal wages and an increase in French nominal wages. There is an increase in European nominal wages. There is no change in the price of German goods and an increase in the price of French goods. There is an increase in the price level of European goods. 6) Alternative targets of policy cooperation: no increase in French nominal wages. Let initial output in Germany be 940, let initial output in France be 970, and let initial output in America be 2000. In Germany and France there is unemployment, but in America there is full employment. 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 European money supply of 13.3, a reduction in German nominal wages of 33.3, and an increase in French nominal wages of zero. Step 2 refers to the output lag. The increase in European money supply of 13.3 raises German output and French output by 20 each. As a side effect, it lowers American output by 13.3. The reduction in German nominal wages of 33.3 raises German output by 40 and French output by 10. As a side effect, it lowers American output by 16.7. 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

138 equally 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. Table 4.9 presents a synopsis.

Table 4.9 Cooperation between the European Central Bank, the German Labour Union, and the French Labour Union No Increase in Nominal Wages

Initial Output

Germany

France

America

940

970

2000

A Money Supply

13.3

A Nominal Wages

-33.3

Output

1000

0 1000

1970

In Germany and France there is now full employment. But in America there is now unemployment. There is a small increase in European money supply. There is a reduction in German nominal wages and no change in French nominal wages. There is a reduction in European nominal wages. There is a reduction in the price of German goods and no change in the price of French goods. There is a reduction in the price level of European goods.

Chapter 3 Competition between European Central Bank, American Central Bank, German Labour Union, and French Labour Union 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+0.5aMj2-0.5pM3-XWi-nW2

(1)

Y 2 - A 2 + 0.5aMj2-0.5pM3-XW2-^Wi

(2)

Y3 = A3 + aM3 - I3Mi2 + vWi + vWj

(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, Wj is German nominal wages, W2 is French nominal wages, 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, X, fi and v are positive coefficients with a > p , %> n and X> v. 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 negative function of German nominal wages, and a negative function of French nominal wages. According to equation (2), French output is a positive function of European money supply, a negative function of American money supply, a negative function of French nominal wages, and a negative function of German nominal wages. According to equation (3), American output is a positive function of American money supply, a negative function of European money

140 supply, a positive function of German nominal wages, and a positive function of French nominal wages. 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 nominal wages lowers German output. And what is more, it lowers French output. On the other hand, it raises American output. Correspondingly, an increase in French nominal wages lowers French output. And what is more, it lowers German output. On the other hand, 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 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 O.Sp . An increase in German nominal wages of 1 causes a decline in German output of X., a decline in French output of |J, , and an increase in American output of v. Similarly, an increase in French nominal wages of 1 causes a decline in French output of X,, a decline in German output of |j,, and an increase in American output of v. 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 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 unemplojmient in Germany equals overemployment in France. 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 labour union is full employment in

141 Germany. The instrument of the German labour union is German nominal wages. The German labour union lowers German nominal wages so as to close the output gap in Germany. The target of the French labour union is full employment in France. The instrument of the French labour union is French nominal wages. The French labour union lowers French nominal wages so as to close the output gap in France. We assume that the central banks and the labour unions decide sequentially. First the central banks decide, then the labour unions decide. In step 1, the European central bank and the American central bank decide simultaneously and independently. In step 2, the German labour union and the French labour union 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 labour union and the French labour union 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, A, = 1.2, |j, = 0.3 and v = 0.5. On this assumption, the static model can be written as follows:

Yj = Aj +1.5Mi2 -O.5M3 -1.2Wi -O.3W2

(1)

Y2 = A2 +I.5M12 -O.5M3 -I.2W2 -0.3Wi

(2)

Y3=A3 + 3 M 3 - M i 2 + 0.5Wi + 0.5W2

(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,

142 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 nominal wages of 100 causes a decline in German output of 120, a decline in French output of 30, and an increase in American output of 50. Correspondingly, an increase in French nominal wages of 100 causes a decline in French output of 120, a decline in German output of 30, and an increase in American output of 50. Further let full-employment output in Germany be 1000, let fuU-emplojonent 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 - Europe and America differ in unemployment - the case of overemployment. 1) The case of unemplojmient. 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. 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 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. In Germany there is still some unemployment. In France there is now full employment. In Europe there is still some unemployment. And the same is true of America.

143 Step 3 refers to wage policy in Germany and France. The output gap in Germany is 30. The wage policy multiplier in Germany is -1.2. So what is needed in Germany is a reduction in German nominal wages of 25. The output gap in France is zero. So there is no need for a change in French nominal wages. Step 4 refers to the output lag. The reduction in German nominal wages of 25 causes an increase in German output of 30. As a side effect, it causes an increase in French output of 7.5 and a decline in American output of 12.5. As a consequence, German output goes from 970 to 1000, French output goes from 1000 to 1007.5, and American output goes from 1970 to 1957.5. In Germany there is now full employment. In France there is now some overemplojonent. And the same is true of Europe. In America there is still some unemployment. Step 5 refers to monetary policy in Europe and America. The inflationary gap in Europe in 7.5. The monetary policy multiplier in Europe is 3. So what is needed in Europe is a reduction in European money supply of 2.5. The output gap in America is 42.5. The monetary policy multiplier in America is 3. So what is needed in America is an increase in American money supply of 14.2. Step 6 refers to the output lag. The net effect is a decline in German output of 10.8, a decline in French output of equally 10.8, and an increase in American output of 45. As a consequence, German output goes from 1000 to 989.2, French output goes from 1007.5 to 996.7, and American output goes from 1957.5 to 2002.5. In Germany and France there is now some unemployment. In America there is now some overemployment. Step 7 refers to wage policy in Germany and France. The output gap in Germany is 10.8. The wage policy multiplier in Germany is -1.2. So what is needed in Germany is a reduction in German nominal wages of 9.0. The output gap in France is 3.3. The wage policy multiplier in France is -1.2. So what is needed in France is a reduction in French nominal wages of 2.8. Step 8 refers to the output lag. The net effect is an increase in German output of 11.7, an increase in French output of 6.0, and a decline in American output of 5.9. As a consequence, German output goes from 989.2 to 1000.8, French output goes from 996.7 to 1002.7, and American output goes from 2002.5 to 1996.6. In

144 Germany and France there is now some overemployment. In America there is now some unemployment. And so on. Table 4.10 gives an overview.

Table 4.10 Competition between European Central Bank, American Central Bank, German Labour Union, and French Labour Union The Case of Unemployment Germany

France

America

940

970

1910

30

30

970

1000

1970

A Nominal Wages

-25

0

Output

1000

Initial Output A Money Supply Output

A Money Supply

1007.5

1957.5

-2.5

14.2 2002.5

Output

989.2

996.7

A Nominal Wages

-9.0

-2.8

1000.8

1002.7

1996.6

1000

1000

2000

Output and so on Steady-State Output

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. As a result, competition between the European central bank, the American central bank, the German labour union, and the French labour union leads to full employment in Germany, France and America. Taking the sum over all periods, the total increase in European money supply is 26.3, the total increase in American money supply is 45, the total reduction in German nominal wages is 35.4, and the total reduction in French nominal wages is 2.1.

145 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. 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 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 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 to 965, French output goes to 995, and American output goes to 1970. Step 3 refers to wage policy in Germany and France. The output gap in Germany is 35. The wage policy multiplier in Germany is -1.2. So what is needed in Germany is a reduction in German nominal wages of 29.2. The output gap in France is 5. The wage policy multiplier in France is -1.2. So what is needed in France is a reduction in French nominal wages of 4.2. Step 4 refers to the output lag. The net effect is an increase in German output of 36.3, an increase in French output of 13.8, and a decline in American output of 16.7. As a consequence, German output goes to 1001.3, French output goes to 1008.8, and American output goes to 1953.3. Step 5 refers to monetary policy in Europe and America. The inflationary gap in Europe is 10. The monetary policy multiplier in Europe is 3. So what is needed in Europe is a reduction in European money supply of 3.3. The output gap in America is 46.7. The monetary policy multiplier in America is 3. So what is needed in America is an increase in American money supply is 15.6. Step 6 refers to the output lag. The net effect is a decline in German output of 12.8, a decline in French output of equally 12.8, and an increase in American output of 50. As a consequence, German output goes to 988.5, French output goes to 996.0, and American output goes to 2003.3. Step 7 refers to wage policy in Germany and France. The output gap in Germany is 11.5. The wage policy multiplier in Germany is -1.2. So what is needed in Germany is a reduction in German nominal wages of 9.6. The output gap in France is 4.0. The wage policy multiplier in France is -1.2. So what is

146 needed in France is a reduction in French nominal wages of 3.4. Step 8 refers to the output lag. The net effect is an increase in German output of 12.5, an increase in French output of 6.9, and a decline in American output of 6.5. As a consequence, German output goes to 1001.0, French output goes to 1002.9, and American output goes to 1996.9. And so on. Table 4.11 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. Taking the sum over all periods, the total increase in European money supply is 25.3, the total increase in American money supply is 56.3, the total reduction in German nominal wages is 40.1, and the total reduction in French nominal wages is 6.8.

Table 4.11 Competition between European Central Bank, American Central Banli, German Labour Union, and Frencli Labour Union Europe and America Differ in Unemployment

Initial Output

Germany

France

America

940

970

1880

30

40

995

1970

A Money Supply Output

965

A Nominal Wages

-29.2

-4.2

Output

1001.3

1008.8

1953.3

-3.3

15.6 2003.3

A Money Supply Output

988.5

996.0

A Nominal Wages

-9.6

-3.4

1001.0

1002.9

1996.9

1000

1000

2000

Output and so on Steady-State Output

147 3) The case of overemployment. 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. Step 1 refers to monetary policy in Europe and America. 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. 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 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 to 1030, French output goes to 1000, and American output goes to 2030. Step 3 refers to wage policy in Germany and France. The inflationary gap in Germany is 30. The wage policy multiplier in Germany is -1.2. So what is needed in Germany is an increase in German nominal wages of 25. The inflationary gap in France is zero. So there is no need for a change in French nominal wages. Step 4 refers to the output lag. The increase in German nominal wages of 25 causes a decline in German output of 30, a decline in French output of 7.5, and an increase in American output of 12.5. As a consequence, German output goes to 1000, French output goes to 992.5, and American output goes to 2042.5. Step 5 refers to monetary policy in Europe and America. The output gap in Europe is 7.5. The monetary policy multiplier in Europe is 3. So what is needed in Europe is an increase in European money supply of 2.5. The inflationary gap in America is 42.5. The monetary policy multiplier in America is 3. So what is needed in America is a reduction in American money supply of 14.2. Step 6 refers to the output lag. The net effect is an increase in German output of 10.8, an increase in French output of equally 10.8, and a decline in American output of 45. As a consequence, German output goes to 1010.8, French output goes to 1003.3, and American output goes to 1997.5. Step 7 refers to wage policy in Germany and France. The inflationary gap in Germany is 10.8. The wage policy multiplier in Germany is -1.2. So what is needed in Germany is an increase in German nominal wages of 9.0. The inflationary gap in France is 3.3. The wage policy multiplier in France is -1.2. So

148 what is needed in France is an increase in French nominal wages of 2.8. Step 8 refers to the output lag. The net effect is a decline in German output of 11.7, a decline in French output of 6.0, and an increase in American output of 5.9. As a consequence, German output goes to 999.2, French output goes to 997.3, and American output goes to 2003.4. And so on. Table 4.12 gives an overview.

Table 4.12 Competition between European Central Banlc, American Central Banl^, German Labour Union, and Frencli Labour Union The Case of Overemployment Germany

Initial Output

1060

A Nominal Wages Output

2090

-30

-30

1030

1000

2030

25

0

1000

992.5

2042.5

2.5

-14.2

1010.8

1003.3

1997.5

9.0

2.8

999.2

997.3

A Money Supply Output A Nominal Wages Output

America

1030

A Money Supply Output

France

2003.4

and so on Steady-State Output

1000

1000

2000

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. Taking the sum over all periods, the total reduction in European money supply is 26.3, the total reduction in American money supply is 45, the total increase in German nominal wages is 35.4, and the total increase in French nominal wages is 2.1.

149 Generally speaking, the total change 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 A, - the cross policy multipliers P and |j,. And the same holds for the total change in American money supply, the total change in German nominal wages, and the total change in French nominal wages.

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

1) Introduction. As a starting point, take the output model. It can be represented by a system of three equations: Yj=Ai+0.5aMj2-0.5pM3-?.Wi-)aW2

(1)

Y2=A2+0.5aMl2-0.5pM3-XW2-^Wl

(2)

Y3 = A3 + aM3 - pMi2 + vWj + vWj

(3)

Here Yj denotes German output, Y2 is French output, Y3 is American output, Mj2 is European money supply, M3 is American money supply, Wj is German nominal wages, and W2 is French nominal wages. 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 is high, and unemployment in France is low. The policy makers are the European central bank, the American central bank, the German labour union, and the French labour union. 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 nominal wages, and French nominal wages. 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 labour union, and the French labour union can achieve full employment in Germany, France and America.

151 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: AY^ = 0.5aAMj2 - O.SpAMg - XAW^ - nAW^

(4)

AY2 = 0.5aAMi2 - O.SpAMj - XAWj - liAWj

(5)

AY3 = aAMj - PAM12 + vAWj + VAW2

(6)

Here AYj 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 change in European money supply, AM3 is the required change in American money supply, AWj is the required change in German nominal wages, and AW2 is the required change in French nominal wages. The endogenous variables are AM12, AM3, AWi and AW2. We now introduce a fourth target. We assume that the reduction in German nominal wages should be equal in size to the increase in French nominal wages: AWj+AW2=0

(7)

Put another way, we assume that the price level of European goods should be constant. Add up equations (4) and (5), taking account of equation (7), to find out: AYj + AYj = aAMi2 - PAM3

(8)

152 To simplify notation we introduce AY12 = AYj + AY2, where AY12 is the initial output gap in Europe. This yields:

AY12 = aAMi2 - (3AM3

(9)

Taking account of equation (7), equation (6) can be written as follows:

AY3 = aAMj - PAM12

(10)

Then solve equations (9) and (10) for:

AMi2=

aAYi2 + pAYg / 2 a2

aAYg + |3AYj2

AM3= " aY2 -^p r2 ^ '

(11)

(12)

Further subtract equation (5) from equation (4) to find out: AYi - AY2 = -(X - ^)(AWi - AW2)

(13)

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

AW,=-^^i^^

(14)

AW^.fLzAI,

(,5)

2(A

- |j,)

According to equation (11), the required change 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. According to equation (12), the required change 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 . According to equation (14), the required change in German

153 nominal wages depends on the initial output gap in Germany, the initial output gap in France, the direct multiplier X, and the cross multiplier |j,. According to equation (15), the required change in French nominal wages depends on the initial output gap in France, the initial output gap in Germany, the direct multiplier A,, and the cross multiplier fi.

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, P = l, X = 1.2, ^J,= 0.3 and v = 0.5. 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 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 German nominal wages of 100 causes a decline in German output of 120, a decline in French output of 30, and an increase in American output of 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 five distinct cases: - the case of unemployment - Europe and America differ in unemployment - the case of overemployment - unemployment in Europe, overemployment in America - alternative 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. 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. So what is needed, according to

154 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, a reduction in German nominal wages of 16.7, and an increase in French nominal wages of equally 16.7. 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 reduction in German nominal wages of 16.7 raises German output by 20 and French output by 5. On the other hand, it lowers American output by 8.3. The increase in French nominal wages of 16.7 lowers French output by 20 and German output by 5. On the other hand, it raises American output by 8.3. 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. Table 4.13 presents a synopsis.

Table 4.13 Cooperation between European Central Bank, American Central Bank, German Labour Union, and French Labour Union The Case of Unemployment

Initial Output

Germany

France

America

940

970

1910

45

45

A Money Supply A Nominal Wages

-16.7

Output

1000

16.7 1000

2000

In each of the countries there is now full employment. As a result, cooperation between the European cenfral bank, the American central bank, the

155 German labour union, and the French labour union can achieve full employment in Germany, France and America. There is an increase in European money supply, as there is in American money supply. There is a reduction in German nominal wages and an increase in French nominal wages. There is no change in European nominal wages. There is an increase in German output, as there is in French output and American output. There is a decline in the price of German goods and an increase in the price of French goods. There is no change in the price level of European goods. The exchange rate between Europe and America is constant. There is a decline in the world interest rate. There is a decline in the European budget deficit, as there is in the American budget deficit. Finally compare policy cooperation with policy competition. Policy competition can achieve full emplojonent in Germany, France and America. And the same applies to policy cooperation. Policy competition is a process of intermediate speed. By contrast, policy cooperation is a fast process. Policy competition causes oscillations in output. By contrast, policy cooperation does not cause oscillations in output. Under policy competition, the total increase in European money supply is 26.3, the total increase in American money supply is 45, the total reduction in German nominal wages is 35.4, and the total reduction in French nominal wages is 2.1. That means, the solution to policy cooperation is different from the steady state of policy competition. Policy competition causes a small increase in European money supply, a large reduction in European nominal wages, and a large reduction in the price of European goods. By contrast, policy cooperation causes a large increase in European money supply, no change in European nominal wages, and no change in the price of European goods. Judging from these points of view, policy cooperation seems to be superior to policy competition. 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. 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 56.3, a reduction

156 in German nominal wages of 16.7, and an increase in French nominal wages of equally 16.7. 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. Table 4.14 gives an overview. Finally compare policy cooperation with policy competition. Under policy competition, the total increase in European money supply is 25.3, the total increase in American money supply is 56.3, the total reduction in German nominal wages is 40.1, and the total reduction in French nominal wages is 6.8.

Table 4.14 Cooperation between European Central Bank, American Central Bank, German Labour Union, and French Labour Union Europe and America Differ in Unemployment

Initial Output

Germany

France

America

940

970

1880

A Money Supply

48.8

A Nominal Wages

-16.7

Output

1000

56.3

16.7 1000

2000

3) The case of overemployment. 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. 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 equally 90. What is needed, then, is a reduction in European money supply of 45, a reduction in American money supply of equally 45, an increase in German nominal wages of 16.7, and a reduction in French nominal wages of equally 16.7.

157

Step 2 refers to the output lag. The net effect is a decline in German output of 60, a decline in French output of 30, and a decline in American output of 90. 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. Table 4.15 presents a synopsis.

Table 4.15 Cooperation between European Central Bank, American Central Bank, German Labour Union, and French Labour Union The Case of Overemployment

Initial Output

Germany

France

America

1060

1030

2090

-45

-45

A Money Supply A Nominal Wages Output

16.7 1000

-16.7 1000

2000

There is a reduction in European money supply, as there is in American money supply. There is an increase in German nominal wages and a reduction in French nominal wages. There is no change in European nominal wages. There is a decline in German output, as there is in French output and American output. There is an increase in the price of German goods and a decline in the price of French goods. There is no change in the price level of European goods. The exchange rate between Europe and America is constant. There is an increase in the world interest rate. There is an increase in the European budget deficit, as there is in the American budget deficit. Finally compare policy cooperation with policy competition. Under policy competition, the total reduction in European money supply is 26.3, the total reduction in American money supply is 45, the total increase in German nominal wages is 35.4, and the total increase in French nominal wages is 2.1. That means.

158 the solution to policy cooperation is different from the steady state of policy competition. Policy competition causes a small reduction in European money supply, a large increase in European nominal wages, and a large increase in the price of European goods. By contrast, policy cooperation causes a large reduction in European money supply, no change in European nominal wages, and no change in the price of European goods. Judging from this perspective, policy cooperation seems to be superior to policy competition. 4) Unemployment in Europe, overemployment 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 and France there is unemployment, but in America there is overemployment. 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 -90. What is needed, then, is an increase in European money supply of 22.5, a reduction in American money supply of equally 22.5, a reduction in German nominal wages of 16.7, and an increase in French nominal wages of equally 16.7. 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 90. 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. Table 4.16 gives an overview. There is an increase in European money supply and a reduction in American money supply. There is a reduction in German nominal wages and an increase in French nominal wages. There is no change in European nominal wages. There is an increase in German output, as there is in French output. There is a decline in American output. There is a decline in the price of German goods and an increase in the price of French goods. There is no change in the price level of European goods. There is a depreciation of the euro and an appreciation of the dollar. There is no change in the world interest rate. There is a decline in the European budget deficit and an increase in the American budget deficit.

159 Table 4.16 Cooperation between European Central Bank, American Central Bank, German Labour Union, and French Labour Union Unemployment in Europe, Overemployment in America

Initial Output

Germany

France

America

940

970

2090

A Money Supply

22.5

A Nominal Wages

-16.7

Output

1000

-22.5

16.7 1000

2000

5) Comparing policy cooperation with policy competition. Policy competition can achieve full employment in Germany, France and America. The same applies to policy cooperation. Policy competition is a process of intermediate speed. By contrast, policy cooperation is a fast process. Policy competition causes some change in European nominal wages. By contrast, policy cooperation does not cause any change in European nominal wages. Judging from these points of view, policy cooperation seems to be superior to policy competition. It is worth pointing out here that the solution to policy cooperation is different from the steady state of policy competition. 6) Alternative targets of policy cooperation: no reduction in German nominal wages. 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. 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 90. What is needed, then, is an increase in European money supply of 61.7, an increase in American money supply of 45, a reduction in German nominal wages of zero, and an increase in French nominal wages of 33.3. 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 90. As a consequence, German output goes to 1000, French output also goes to

160 1000, and American output goes to 2000. In each of the countries there is now full employment. Table 4.17 presents a sjmopsis. There is a large increase in European money supply and a medium-size increase in American money supply. There is no change in German nominal wages and an increase in French nominal wages. There is an increase in European nominal wages. There is no change in the price of German goods and an increase in the price of French goods. There is an increase in the price level of European goods.

Table 4.17 Cooperation between European Central Bank, American Central Bank, German Labour Union, and French Labour Union No Reduction in Nominal Wages

Initial Output

Germany

France

America

940

970

1910

61.7

A Money Supply A Nominal Wages Output

0 1000

45

33.3 1000

2000

7) Alternative targets of policy cooperation: no increase in French nominal wages. 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. 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 90. What is needed, then, is an increase in European money supply of 28.3, an increase in American money supply of 45, a reduction in German nominal wages of 33.3, and an increase in French nominal wages of zero. 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

161 90. As a consequence, Gennan 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. Table 4.18 gives an overview. There is a small increase in European money supply and a medium-size increase in American money supply. There is a reduction in German nominal wages and no change in French nominal wages. There is a reduction in European nominal wages. There is a reduction in the price of German goods and no change in the price of French goods. There is a reduction in the price level of European goods.

Table 4.18 Cooperation between European Central Bank, American Central Bank, German Labour Union, and French Labour Union No Increase in Nominal Wages

Initial Output

Germany

France

America

940

970

1910

A Money Supply

28.3

A Nominal Wages

-33.3

Output

1000

45

0 1000

2000

Part Five Monetary and Wage Interactions Advanced Models

Chapter 1 Simultaneous Decisions: Cold-Turkey Policies

This chapter deals with competition between the European central bank, the American central bank, the German labour union, and the French labour union. So far we have assumed that the central banks and the labour unions decide sequentially. First the central banks decide, then the labour unions decide. Now we assume that the central banks and the labour unions decide simultaneously and independently. As a point of reference, consider the static model. It can be represented by a system of three equations:

Yj = Aj +1.5Mi2 -O.5M3 -l.2W1-O.3W2

(1)

Y2 = A2 +I.5M12 -O.5M3 -I.2W2 -O.SWj

(2)

Y3 = A3 + 3M3 - M12 + 0.5Wi + O.5W2

(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, Wj is German nominal wages, and W2 is French nominal wages. 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 nominal wages of 100 causes a decline in German output of 120, a decline in French output of 30, and an increase in American output of 50. Correspondingly, an increase in French nominal wages of 100 causes a decline in French output of 120, a decline in German output of 30, and an increase in American output of 50. Further let full-employment output in Germany be 1000, let full-employment

166 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 is high, and unemployment in France is low. 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 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 fiill 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 labour union is full emplojonent in Germany. The instrument of the German labour union is German nominal wages. The German labour union lowers German nominal wages so as to close the output gap in Germany. The target of the French labour union is full employment in France. The instrument of the French labour union is French nominal wages. The French labour union lowers French nominal wages so as to close the output gap in France. We assume that the central banks and the labour unions decide simultaneously and independently. In step 1 the European central bank, the American central bank, the German labour union, and the French labour union 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 labour union, and the French labour union decide simultaneously and independently. In step 4 there is an output lag. 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. Step 1 refers to the policy response. First consider monetary

167 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 wage policy in Germany. The output gap in Germany is 60. The wage policy multiplier in Germany is -1.2. So what is needed in Germany is a reduction in German nominal wages of 50. Fourth consider wage policy in France. The output gap in France is 30. The wage policy multiplier in France is -1.2. So what is needed in France is a reduction in French nominal wages of 25. 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 reduction in German nominal wages of 50 causes an increase in German output of 60. As a side effect, it causes an increase in French output of 15 and a decline in American output of 25. The reduction in French nominal wages of 25 causes an increase in French output of 30. As a side effect, it causes an increase in German output of 7.5 and a decline in American output of 12.5. The net effect is an increase in German output of 97.5, an increase in French output of 75, and an increase in American output of 22.5. As a consequence, German output goes from 940 to 1037.5, French output goes from 970 to 1045, and American output goes from 1910 to 1932.5. Step 3 refers to the policy response. First consider monetary policy in Europe. The inflationary gap in Europe is 82.5. The monetary policy multiplier in Europe is 3. So what is needed in Europe is a reduction in European money supply of 27.5. Second consider monetary policy in America. The output gap in America is 67.5. The monetary policy multiplier in America is 3. So what is needed in America is an increase in American money supply of 22.5. Third consider wage policy in Germany. The inflationary gap in Germany is 37.5. The wage policy multiplier in Germany is -1.2. So what is needed in Germany is an increase in German nominal wages of 31.3. Fourth consider wage policy in France. The inflationary gap in France is 45. The wage policy multiplier in France is -1.2. So what is needed in France is an increase in French nominal wages of 37.5.

168

Step 4 refers to the output lag. The reduction in European money supply of 27.5 causes a decline in German output of 41.3 and a decline in French output of equally 41.3. As a side effect, it causes an increase in American output of 27.5. The increase in American money supply of 22.5 causes an increase in American output of 67.5. As a side effect, it causes a decline in German output of 11.3 and a decline in French output of equally 11.3. The increase in German nominal wages of 31.3 causes a decline in German output of 37.5. As a side effect, it causes a decline in French output of 9.4 and an increase in American output of 15.6. The increase in French nominal wages of 37.5 causes a decline in French output of 45. As a side effect, it causes a decline in German output of 11.3 and an increase in American output of 18.8. The net effect is a decline in German output of 101.3, a decline in French output of 106.9, and an increase in American output of 129.4. As a consequence, German output goes from 1037.5 to 936.3, French output goes from 1045 to 938.1, and American output goes from 1932.5 to 2061.9. Step 5 refers to the policy response. The output gap in Europe is 125.6. So what is needed in Europe is an increase in European money supply of 41.9. The inflationary gap in America is 61.9. So what is needed in America is a reduction in American money supply of 20.6. The output gap in Germany is 63.8. So what is needed in Germany is a reduction in German nominal wages of 53.1. And the output gap in France is 61.9. So what is needed in France is a reduction in French nominal wages of 51.6. Step 6 refers to the output lag. The net effect is an increase in German output of 152.3, an increase in French output of 150.9, and a decline in American output of 156.1. As a consequence, German output goes to 1088.6, French output goes to 1089.1, and American output goes to 1905.8. And so on. Table 5.1 presents a synopsis. As a result, there is no steady state. In other words, the simultaneous process of monetary and wage competition does not lead to full employment in Germany, France and America. What are the dynamic characteristics of this process? There are explosive oscillations in money supply, nominal wages, and output. The German economy oscillates between unemployment and overemployment, as do

169 the French economy and the American economy. After a certain number of periods, the national economies will collapse. Finally compare simultaneous decisions with sequential decisions, see Chapter 3 of Part Four. Under sequential decisions there are damped oscillations in output. Under simultaneous decisions, however, there are explosive oscillations in output. Under sequential decisions, monetary and wage competition leads to full employment. Under simultaneous decisions, however, monetary and wage competition does not lead to full employment. Judging from these points of view, sequential decisions seem to be superior to simultaneous decisions.

Table 5.1 Simultaneous Decisions: Cold-Turkey Policies

Initial Output

Germany

France

America

940

970

1910

30

30

A Money Supply A Nominal Wages

-50

-25

Output

1037.5

1045

A Money Supply A Nominal Wages Output

-27.5

22.5

31.3

37.5

936.3

938.1

2061.9

41.9

-20.6

A Money Supply A Nominal Wages

-53.1

-51.6

Output

1088.6

1089.1

and so on

1932.5

1905.8

Chapter 2 Simultaneous Decisions: Gradualist Policies

This chapter is concerned with competition between the European central bank, the American central bank, the German labour union, and the French labour union. So far we have assumed that the central banks and the labour unions follow a cold-turkey strategy. Now we assume that the central banks and the labour unions follow a gradualist strategy. We still assume that the central banks and the labour unions 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 decline in German output of 50, and a decline in French output of equally 50. An increase in German nominal wages of 100 causes a decline in German output of 120, a decline in French output of 30, and an increase in American output of 50. Correspondingly, an increase in French nominal wages of 100 causes a decline in French output of 120, a decline in German output of 30, and an increase in American output of 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. At the start there is unemployment in Germany, France and America. More precisely, unemployment in Germany is high, and unemployment in France is low. 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 fiill 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 labour union is full employment in Germany. We assume that the German labour union follows a gradualist strategy. The specific target of the German labour

171 union is to close the output gap in Germany by 20 percent. The general target of the French labour union is full employment in France. We assume that the French labour union follows a gradualist strategy. The specific target of the French labour union is to close the output gap in France by 20 percent. We assume that the central banks and the labour unions decide simultaneously and independently. In step 1 the European central bank, the American central bank, the German labour union, and the French labour union 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 labour union, and the French labour union decide simultaneously and independently. In step 4 there is an output lag. 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. 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 wage policy in Germany. The output gap in Germany is 60. The specific target of the German labour union is to close the output gap in Germany by 20 percent, that is by 12. The wage policy multiplier in Germany is -1.2. So what is needed in Germany is a reduction in German nominal wages of 10. Fourth consider wage policy in France. The output gap in France is 30. The specific target of the French labour union is to close the output gap in France by 20 percent, that is by 6. The wage policy multiplier in France is -1.2. So what is needed in France is a reduction in French nominal wages of 5. 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

172 equally 36. As a side effect, it causes a decline in American output of 24. The 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 reduction in German nominal wages of 10 causes an increase in German output of 12. As a side effect, it causes an increase in French output of 3 and a decline in American output of 5. The reduction in French nominal wages of 5 causes an increase in French output of 6. As a side effect, it causes an increase in German output of 1.5 and a decline in American output of 2.5. The net effect is an increase in German output of 37.5, an increase in French output of 33, and an increase in American output of 40.5. As a consequence, German output goes from 940 to 977.5, French output goes from 970 to 1003, and American output goes from 1910 to 1950.5. Step 3 refers to the policy response. First consider monetary policy in Europe. The output gap in Europe is 19.5. The specific target of the European central bank is to close the output gap in Europe by 80 percent, that is by 15.6. The monetary policy multiplier in Europe is 3. So what is needed in Europe is an increase in European money supply of 5.2. Second consider monetary policy in America. The output gap in America is 49.5. The specific target of the American central bank is to close the output gap in America by 80 percent, that is by 39.6. The monetary policy multiplier in America is 3. So what is needed in America is an increase in American money supply of 13.2. Third consider wage policy in Germany. The output gap in Germany is 22.5. The specific target of the German labour union is to close the output gap in Germany by 20 percent, that is by 4.5. The wage policy multiplier in Germany is -1.2. So what is needed in Germany is a reduction in German nominal wages of 3.8. Fourth consider wage policy in France. The inflationary gap in France is 3. The specific target of the French labour union is to close the output gap in France by 20 percent, that is by 0.6. The wage policy multiplier in France is -1.2. So what is needed in France is an increase in French nominal wages of 0.5. Step 4 refers to the output lag. The increase in European money supply of 5.2 causes an increase in German output of 7.8 and an increase in French output of equally 7.8. As a side effect, it causes a decline in American output of 5.2. The increase in American money supply of 13.2 causes an increase in American output of 39.6. As a side effect, it causes a decline in German output of 6.6 and a

173 decline in French output of equally 6.6. The reduction in German nominal wages of 3.8 causes an increase in German output of 4.5. As a side effect, it causes an increase in French output of 1.1 and a decline in American output of 1.9. The increase in French nominal wages of 0.5 causes a decline in French output of 0.6. As a side effect, it causes a decline in German output of 0.2 and an increase in American output of 0.3. The net effect is an increase in German output of 5.6, an increase in French output of 1.7, and an increase in American output of 32.8. As a consequence, German output goes from 977.5 to 983.1, French output goes from 1003 to 1004.7, and American output goes from 1950.5 to 1983.3. Step 5 refers to the policy response. The output gap in Europe is 12.2. So what is needed in Europe is an increase in European money supply of 3.3. The output gap in America is 16.7. So what is needed in America is an increase in American money supply of 4.5. The output gap in Germany is 17.0. So what is needed in Germany is a reduction in German nominal wages of 2.8. And the inflationary gap in France is 4.7. So what is needed in France is an increase in French nominal wages of 0.8. Step 6 refers to the output lag. The net effect is an increase in German output of 5.8, an increase in French output of 2.6, and an increase in American output of 9.1. As a consequence, German output goes to 988.9, French output goes to 1007.3, and American output goes to 1992.4. 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. As a result, the gradualist process of monetary and wage competition leads to full employment 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 are repeated cuts in German nominal wages. There is an initial cut in French nominal wages that is followed by repeated increases. There are repeated increases in German output. There is an upward trend in French output. And there are repeated increases in American output. Taking the sum over all periods, the total increase in European money supply is 34.3, the total increase in

174 American money supply is 45, the total reduction in German nominal wages is 27.4, and the total increase in French nominal wages is 5.9.

Table 5.2 Simultaneous Decisions: Gradualist Policies

Initial Output

Germany

France

America

940

970

1910

24

24

A Money Supply A Nominal Wages

-10

Output

977.5

A Money Supply

-5 1003 5.2

1950.5 13.2

A Nominal Wages

-3.8

0.5

Output

983.1

1004.7

1983.3

3.3

4.5

A Money Supply A Nominal Wages

-2.8

0.8

Output

988.9

1007.3

1992.4

1000

2000

and so on Steady-State Output

1000

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 A, - the cross policy multipliers (3 and |j, - the speed of adjustment in European money supply - the speed of adjustment in American money supply - the speed of adjustment in German nominal wages

175 - the speed of adjustment in French nominal wages - the type of coordination mechanism (i.e. simultaneous decisions, gradualist policies). And the same holds for the total increase in American money supply, the total increase in German nominal wages, and the total increase in French nominal wages. Finally compare gradualist policies with cold-turkey policies, given simultaneous decisions, see Chapter 1 of Part Five. Under cold-turkey policies, the process of monetary and wage competition in unstable. Under gradualist policies, however, the process of monetary and wage competition is stable. Under coldturkey policies, monetary and wage competition does not lead to fiiU emplojTnent. Under gradualist policies, however, monetary and wage competition leads to fiill employment. Of course, this depends on the speed of adjustment in money supply and nominal wages. Moreover, it depends on initial conditions. Judging from these points of view, gradualist policies seem to be superior to cold-turkey policies.

Chapter 3 Fast Monetary Competition and Slow Wage Competition

This chapter deals with competition between the European central bank, the American central bank, the German labour union, and the French labour union. We assume that the central banks and the labour unions decide sequentially. First the central banks decide, then the labour unions decide. In steps 1, 2 and 3 the central banks decide. Then in steps 4 and 5 the labour unions decide. We assume that the central banks and the labour unions 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 nominal wages of 100 causes a decline in German output of 120, a decline in French output of 30, and an increase in American output of 50. Correspondingly, an increase in French nominal wages of 100 causes a decline in French output of 120, a decline in German output of 30, and an increase in American output of 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 let initial output in America be 1910. In each of the countries unemployment. Now steps 1, 2 and 3 refer to monetary competition Europe and America. Then steps 4 and 5 refer to wage competition Germany and France. Finally step 6 refers to the output lag.

970, and there is between between

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 European money

177 supply is raised by 30. The output gap in America is 90. The monetary policy multiplier in America is 3. So American money supply is raised by 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 European money supply is raised by 10. The expected output gap in America is 30. The monetary policy multiplier in America is 3. So American money supply is raised by 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 European money supply is raised by 3.3. The expected output gap in America is 10. The monetary policy multiplier in America is 3. So American money supply is raised by 3.3. Step 4 refers to wage policy in Germany and France. The German labour union anticipates the effect of the accumulated increase in European money supply and American money supply. And the same applies to the French labour union. 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 labour union expects that German output will only rise to 983.3. And the French labour union expects that French output will only rise to 1013.3. The expected output gap in Germany is 16.7. The wage policy multiplier in Germany is -1.2. So German nominal wages are lowered by 13.9. The expected inflationary gap in France is 13.3. The wage policy multiplier in France is -1.2. So French nominal wages are raised by 11.1.

178 We now come to step 5. The German labour union expects that, due to the increase in French nominal wages of 11.1, German output will only rise to 996.7. The French labour union expects that, due to the reduction in German nominal wages of 13.9, French output will even rise to 1004.2. The expected output gap in Germany is 3.3. The wage policy multiplier in Germany is -1.2. So German nominal wages are lowered by 2.8. The expected inflationary gap in France is 4.2. The wage policy multiplier in France is -1.2. So French nominal wages are raised by 3.5. Step 6 refers to the output lag. The accumulated increase in European money supply of 43.3 causes an increase in German output of 65, an increase in French output of equally 65, and 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, a decline in German output of 21.7, and a decline in French output of equally 21.7. The accumulated reduction in German nominal wages of 16.7 causes an increase in German output of 20, an increase in French output of 5, and a decline in American output of 8.3. The accumulated increase in French nominal wages of 14.6 causes a decline in French output of 17.5, a decline in German output of 4.4, and an increase in American output of 7.3. The net effect is an increase in German output of 59.0, an increase in French output of 30.8, and an increase in American output of 85.6. As a consequence, German output goes from 940 to 999.0, French output goes from 970 to 1000.8, and American output goes from 1910 to 1995.6. In each of the countries there is nearly full emplojmient. As a result, the process of fast monetary competition and slow wage competition leads to frill employment in Germany, France and America. Table 5.3 presents a synopsis. The total increase in European money supply is 43.3, the total increase in American money supply is equally 43.3, the total reduction in German nominal wages is 16.7, and the total increase in French nominal wages is 14.6. That means, there is a large increase in money supply and a small reduction in nominal wages. 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

179 - the direct policy multipliers a and X - the cross policy multipliers |3 and |J. - the type of coordination mechanism (i.e. fast monetary competition and slow wage competition). And the same holds for the total increase in American money supply, the total increase in German nominal wages, and the total increase in French nominal wages.

Table 5.3 Fast Monetary Competition, Slow Wage Competition Germany

France

America

940

970

1910

A Money Supply

30

30

A Money Supply

10

10

Initial Output

3.3

A Money Supply

3.3

A Nominal Wages

-13.9

11.1

A Nominal Wages

-2.8

3.5

Output

999.0

1000.8

1995.6

1000

2000

and so on Steady-State-Output

...

1000

Chapter 4 Monetary Cooperation between Europe and America, Wage 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: Yj=Aj + 0.5aMi2-0.5pM3-XWj-|xW2

(1)

Y2 = A2 + 0.5aMi2 - O.5PM3 -XW2 - ixWj

(2)

Y3 = A3 + aM3 - PM12 + vWj + VW2

(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, Wj is German nominal wages, and W2 is French nominal wages. 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 labour union is full employment in Germany. The instrument of the German labour union is German nominal wages. The target of the French labour union is full employment in France. The instrument of the French labour union is French nominal wages.

181 We assume that the central banks and the labour unions decide sequentially. First the central banks decide, then the labour unions decide. In step 1, the European central bank and the American central bank decide cooperatively. In step 2, the German labour union and the French labour union decide simultaneously and independently. In step 3, the European central bank and the American central bank decide cooperatively. In step 4, the German labour union and the French labour union 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 = aAMj - PAM12

(5)

Here AY12 denotes the initial output gap in Europe, AY3 is the initial output gap in America, AMj2 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: ^

^ ^ X A Y ^ ^

(6)

aAY3+pAYi2 a2-p2

(7)

AM3=^^^i^P^J^

182

2. Some Numerical Examples

To illustrate the djTiamic model, have a look at some numerical examples. For ease of exposition, without loss of generality, assume a = 3, P = l, X = 1.2, |a, = 0.3 and v = 0.5. 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 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 nominal wages of 100 causes a decline in German output of 120, a decline in French output of 30, and an increase in American output of 50. Further let fuU-emplojnnent 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 overemplojonent - unemployment in Europe, overemployment 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. Step 1 refers to monetary cooperation between Europe and America. The output gap in Europe is 90, as is the output gap in America. So what is needed, according to equations (6) and (7) from the preceding section, 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

183 from 970 to 1015, and American output goes from 1910 to 2000. In Germany there is still some unemployment. In France there is now some overemployment. In Europe there is now full employment. And the same holds for America. Step 3 refers to wage competition between Germany and France. The output gap in Germany is 15. The wage policy multiplier in Germany is -1.2. So what is needed in Germany is a reduction in German nominal wages of 12.5. The inflationary gap in France is 15. The wage policy multiplier in France is -1.2. So what is needed in France is an increase in French nominal wages of 12.5. Step 4 refers to the output lag. The reduction in German nominal wages of 12.5 causes an increase in German output of 15. As a side effect, it causes an increase in French output of 3.8 and a decline in American output of 6.3. The increase in French nominal wages of 12.5 causes a decline in French output of 15. As a side effect, it causes a decline in German output of 3.8 and an increase in American output of 6.3. The net effect is an increase in German output of 11.3, a decline in French output of equally 11.3, and a change in American output of zero. As a consequence, German output goes from 985 to 996.3, French output goes from 1015 to 1003.8, 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 996.3, French output stays at 1003.8, and American output stays at 2000. Step 7 refers to wage competition between Germany and France. The output gap in Germany is 3.8. The wage policy multiplier in Germany is -1.2. So what is needed in Germany is a reduction in German nominal wages of 3.1. The inflationary gap in France is 3.8. The wage policy multiplier in France is -1.2. So what is needed in France is an increase in French nominal wages of 3.1. Step 8 refers to the output lag. The reduction in German nominal wages of 3.1 causes an increase in German output of 3.8. As a side effect, it causes an increase in French output of 0.9 and a decline in American output of 1.6. The increase in French nominal wages of 3.1 causes a decline in French output of 3.8. As a side effect, it causes a decline in German output of 0.9 and an increase in American

184 output of 1.6. The net effect is an increase in German output of 2.8, a decline in French output of equally 2.8, and a change in American output of zero. As a consequence, German output goes from 996.3 to 999.1, French output goes from 1003.8 to 1000.9, and American output stays at 2000. And so on. Table 5.4 gives an overview.

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

Initial Output

940

A Money Supply Output

985

France

America

970

1910

45

45

1015

2000

A Nominal Wages

-12.5

12.5

Output

996.3

1003.8 0

A Money Supply

2000 0

Output

996.3

1003.8

2000

A Nominal Wages

-3.1

3.1

Output

999.1

1000.9

2000

1000

2000

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. As a result, the alternating process of monetary cooperation and wage competition leads to full employment in Germany, France and America. 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.

185 There are repeated cuts in German nominal wages, while there are repeated increases in French nominal wages. There are no changes in European nominal wages. There are repeated increases in German output. There is an initial increase in French output that is followed by repeated cuts. There is a one-time increase in European output, as there is in American output. There are repeated cuts in the price of German goods, while there are repeated increases in the price of French goods. There are no changes in the price level of European goods. The exchange rate between Europe and America is constant. There is a decline in the world interest rate. There is a decline 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 45, the total increase in American money supply is equally 45, the total reduction in German nominal wages is 16.7, and the total increase in French nominal wages is equally 16.7. Generally speaking, the total increase in European money supply depends on the type of coordination mechanism (i.e. monetary cooperation between Europe and America, wage competition between Germany and France). And the same holds for the total increase in American money supply, the total reduction in German nominal wages, and the total increase in French nominal wages. Finally compare the system of monetary cooperation and wage competition with the system of monetary and wage competition, see Chapter 3 of Part Four. Under monetary and wage competition, the total increase in European money supply is 26.3, the total increase in American money supply is 45, the total reduction in German nominal wages is 35.4, and the total reduction in French nominal wages is 2.1. That is to say, under monetary and wage competition, we have a small increase in European money supply, a large reduction in European nominal wages, and a large reduction in the price of European goods. Under monetary cooperation and wage competition, however, we have a large increase in European money supply, no change in European nominal wages, and no change in the price of European goods. Judging from this perspective, the system of monetary cooperation and wage competition seems to be superior to the system of monetary and wage competition. 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

186 America be 1880. In each of the countries there is unemployment. 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 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 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. Step 3 refers to wage competition between Germany and France. The output gap in Germany is 15. The wage policy multiplier in Germany is -1.2. So what is needed in Germany is a reduction in German nominal wages of 12.5. The inflationary gap in France is 15. The wage policy multiplier in France is -1.2. So what is needed in France is an increase in French nominal wages of 12.5. Step 4 refers to the output lag. The net effect is an increase in German output of 11.3, a decline in French output of equally 11.3, and a change in American output of zero. As a consequence, German output goes from 985 to 996.3, French output goes from 1015 to 1003.8, and American output stays at 2000. And so on. Table 5.5 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. 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 reduction in German nominal wages is 16.7, and the total increase in French nominal wages is equally 16.7.

187 Table 5.5 Monetary Cooperation between Europe and America, Wage Competition between Germany and France Europe and America Differ in Unemployment Germany

Initial Output

940

A Money Supply Output

France

America

970

1880

48.8 985

1015

56.3 2000

A Nominal Wages

-12.5

12.5

Output

996.3

1003.8

A Nominal Wages

-3.1

3.1

Output

999.1

1000.9

2000

1000

2000

2000

and so on Steady-State Output

1000

3) The case of overemployment. 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 overemplo3mient. Step 1 refers to monetary cooperation between Europe and America. The inflationary gap in Europe is 90, as is the inflationary gap 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 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. In France there is now some unemployment. In Europe there is now fiill employment. And the same holds for America.

188 Step 3 refers to wage competition between Germany and France. The inflationary gap in Germany is 15. The wage policy multiplier in Germany is -1.2. So what is needed in Germany is an increase in German nominal wages of 12.5. The output gap in France is 15. The wage policy multiplier in France is -1.2. So what is needed in France is a reduction in French nominal wages of 12.5. Step 4 refers to the output lag. The net effect is a decline in German output of 11.3, an increase in French output of equally 11.3, and a change in American output of zero. As a consequence, German output goes from 1015 to 1003.8, French output goes from 985 to 996.3, and American output stays at 2000. Step 5 refers to wage competition between Germany and France. The inflationary gap in Germany is 3.8. The wage policy multiplier in Germany is -1.2. So what is needed in Germany is an increase in German nominal wages of 3.1. The output gap in France is 3.8. The wage policy multiplier in France is -1.2. So what is needed in France is a reduction in French nominal wages of 3.1. Step 6 refers to the output lag. The net effect is a decline in German output of 2.8, an increase in French output of equally 2.8, and a change in American output of zero. As a consequence, German output goes from 1003.8 to 1000.9, French output goes from 996.3 to 999.1, and American output stays at 2000. And so on. 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. 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 repeated increases in German nominal wages, while there are repeated cuts in French nominal wages. There are no changes in European nominal wages. There are repeated cuts in German output. There is an initial cut in French output that is followed by repeated increases. There is a one-time cut in European output, as there is in American output. There are repeated increases in the price of German goods, while there are repeated cuts in the price of French goods. There are no changes in the price level of European goods. The exchange rate between Europe and America is constant. There is an increase in the world interest rate. There is

189 an increase in the European budget deficit, as there is in the American budget deficit. Taking the sum over all periods, the total reduction in European money supply is 45, the total reduction in American money supply is equally 45, the total increase in German nominal wages is 16.7, and the total reduction in French nominal wages is equally 16.7.

Table 5.6 Monetary Cooperation between Europe and America, Wage Competition between Germany and France The Case of Overemployment Germany

Initial Output

1060

A Money Supply Output A Nominal Wages Output A Nominal Wages Output

1015

France

America

1030

2090

-45

-45

985

2000

12.5

-12.5

1003.8

996.3

3.1

-3.1

1000.9

999.1

2000

2000

and so on Steady-State Output

1000

1000

2000

4) Unemployment in Europe, overemployment 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 and France there is unemployment, but in America there is overemployment. Step 1 refers to monetary cooperation between Europe and America. The output gap in Europe is 90, and the inflationary gap in America is equally 90. What is needed, then, is an increase in

190 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 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 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. Step 3 refers to wage competition between Germany and France. The output gap in Germany is 15. The wage policy multiplier in Germany is -1.2. So what is needed in Germany is a reduction in German nominal wages of 12.5. The inflationary gap in France is 15. The wage policy multiplier in France is -1.2. So what is needed in France is an increase in French nominal wages of 12.5. Step 4 refers to the output lag. The net effect is an increase in German output of 11.3, a decline in French output of equally 11.3, and a change in American output of zero. As a consequence, German output goes from 985 to 996.3, French output goes from 1015 to 1003.8, and American output stays at 2000. And so on. Table 5.7 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. What are the dynamic characteristics of this process? There is a one-time increase in European money supply, while there is a one-time cut in American money supply. There are repeated cuts in German nominal wages, while there are repeated increases in French nominal wages. There are no changes in European nominal wages. There are repeated increases in German output. There is an initial increase in French output that is followed by repeated cuts. There is a onetime increase in European output, while there is a one-time cut in American output. There are repeated cuts in the price of German goods, while there are repeated increases in the price of French goods. There are no changes in the price level of European goods. There is a depreciation of the euro and an appreciation of the dollar. There is no change in the world interest rate. There is a decline in the European budget deficit, while there is an increase in the American budget deficit.

191 Taking the sum over all periods, the total increase in European money supply is 22.5, the total reduction in American money supply is equally 22.5, the total reduction in German nominal wages is 16.7, and the total increase in French nominal wages is equally 16.7.

Table 5.7 Monetary Cooperation between Europe and America, Wage Competition between Germany and France Unemployment in Europe, Overemployment in America Germany

Initial Output

940

A Money Supply Output A Nominal Wages

France

America

970

2090

22.5 985

1015

-22.5 2000

-12.5

12.5

Output

996.3

1003.8

A Nominal Wages

-3.1

3.1

Output

999.1

1000.9

2000

1000

2000

2000

and so on Steady-State Output

1000

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

Chapter 5 Monetary Cooperation between Europe and America, Wage Cooperation between Germany and France 1. The 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+0.5aMi2-0.5pM3-XWi-|xW2

(1)

Y2 = Aj + 0.5aMi2 -O.5PM3 -XW2 -^Wj

(2)

Y3 = A3 + aM3 - pMi2 + vWj + VW2

(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, Wj is German nominal wages, and W2 is French nominal wages. 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 emplojmient 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 wage cooperation are full employment in Germany and full employment in France. The instruments of wage cooperation are German nominal wages and French nominal wages. Under wage cooperation there are two targets and two instruments, so there is no degree of freedom.

193 We assume that the central banks and the labour unions decide sequentially. First the central banks decide, then the labour unions decide. In step 1, the European central bank and the American central bank decide cooperatively. In step 2, the German labour union and the French labour union decide cooperatively. In step 3, the European central bank and the American central bank decide cooperatively. In step 4, the German labour union and the French labour union 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 = aAMg - PAM12

(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: O A Y ^ ^

,,, ^^3=

(6)

aAY3+|3AY,2 2

.2

(^)

Step 2 refers to the output lag. Next have a closer look at step 3. It refers to wage cooperation between Germany and France. Taking differences in equations (1) and (2), the model of wage cooperation can be written as follows: AYj - - >.AW^ - ^AW2

(8)

AY2 = - XAW2 - l^AWj

(9)

194 Here AYj denotes the initial output gap in Germany, AY2 is the initial output gap in France, AWj is the required change in German nominal wages, and AW2 is the required change in French nominal wages. The endogenous variables are AWj and AW2. The solution to the system (8) and (9) is as follows:

AW, = - M ^ ^ ^ 4 ^ X^- -^'

AW2 =

XAY2-- ^ A Y i

- j - ^ ^

X^-- ^ ^

(10)

(11)

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, A, = 1.2, |x = 0.3 and v = 0.5 . 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 nominal wages of 100 causes a decline in French output of 120, a decline in German output of 30, and an increase in American output of 50. Further let fullemployment output in Germany be 1000, let full-emplojonent 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 overemployment - unemployment in Europe, overemployment in America.

195 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. Step 1 refers to monetary cooperation between Europe and America. The output gap in Europe is 90, as is the output gap in America. So what is needed, according to equations (6) and (7) from the preceding section, 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. In Germany there is still some unemployment. In France there is now some overemployment. In Europe there is now full employment. And the same holds for America. Step 3 refers to wage 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 a reduction in German nominal wages of 16.7 and an increase in French nominal wages of equally 16.7. Step 4 refers to the output lag. The reduction in German nominal wages of 16.7 raises German output by 20 and French output by 5. As a side effect, it lowers American output by 8.3. The increase in French nominal wages of 16.7 lowers French output by 20 and German output by 5. As a side effect, it raises American output by 8.3. 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 fiall employment. Table 5.8 gives an overview. As a result, the sequential process of monetary cooperation and wage cooperation leads to full employment in Germany, France and America. What are the dynamic characteristics of this process? There is an increase in European

196 money supply, as there is in American money supply. There is a reduction in German nominal wages and an increase in French nominal wages. There is no change in European nominal wages. There is a two-step increase in German output. There is a two-step change in French output. And there is a one-step increase in American output. There is a decline in the price of German goods and an increase in the price of French goods. There is no change in the price level of European goods. The exchange rate between Europe and America is constant. There is a decline in the world interest rate. There is a decline 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 45, the total increase in American money supply is equally 45, the total reduction in German nominal wages is 16.7, and the total increase in French nominal wages is equally 16.7. Generally speaking, the total increase in European money supply depends on the type of coordination mechanism (i.e. monetary cooperation between Europe and America, wage cooperation between Germany and France).

Table 5.8 Monetary Cooperation between Europe and America, Wage Cooperation between Germany and France The Case of Unemployment

Initial Output

Germany

France

America

940

970

1910

45

45

1015

2000

A Money Supply Output

985

A Nominal Wages

-16.7

Output

1000

16.7 1000

2000

Now compare the sequential process of monetary cooperation and wage )peration with the simultaneous process of monetary and wage cooperation.

197 see Chapter 4 of Part Four. Under monetary and wage cooperation, the total increase in European money supply is 45, the total increase in American money supply is equally 45, the total reduction in German nominal wages is 16.7, and the total increase in French nominal wages is equally 16.7. That means, under monetary and wage cooperation, we have a large increase in European money supply, no change in European nominal wages, and no change in the price of European goods. And the same applies to monetary cooperation and wage cooperation. Monetary and wage cooperation is a fast process. And much the same applies to monetary cooperation and wage cooperation. Judging from this perspective, the sequential process of monetary cooperation and wage cooperation seems to be equivalent to the simultaneous process of monetary and wage cooperation. In other words, there seems to be no need for full cooperation between the European central bank, the American central bank, the German labour union, and the French labour union. Next compare the sequential process of monetary cooperation and wage cooperation with the sequential process of monetary cooperation and wage competition, see Chapter 4 of Part Five. Under monetary cooperation and wage competition, we have a large increase in European money supply, no change in European nominal wages, and no change in the price of European goods. And the same holds for monetary cooperation and wage cooperation. Monetary cooperation and wage competition is a process of intermediate speed. Monetary cooperation and wage cooperation, however, is a fast process. Judging from these points of view, the sequential process of monetary cooperation and wage cooperation seems to be superior to the sequential process of monetary cooperation and wage competition. 2) Europe and America differ in unemplojonent. 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. 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 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 net effect is an increase in German output of 45, an increase in French output of equally 45, and an increase in American

198 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. Step 3 refers to wage 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 a reduction in German nominal wages of 16.7 and an increase in French nominal wages of equally 16.7. 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. Table 5.9 presents a synopsis.

Table 5.9 Monetary Cooperation between Europe and America, Wage Cooperation between Germany and France Europe and America Differ in Unemployment

Initial Output

Germany

France

America

940

970

1880

48.8

A Money Supply Output

985

A Nominal Wages

-16.7

Output

1000

1015

56.3 2000

16.7 1000

2000

3) The case of overemployment. 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. Step 1 refers to monetary cooperation between Europe and America. The inflationary gap in Europe is 90, as is the inflationary gap in America. What is needed, then, is a reduction in

199 European money supply of 45 and a reduction in American money supply of equally 45. 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 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. In France there is now some unemployment. In Europe there is now full employment. And the same holds for America. Step 3 refers to wage 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 an increase in German nominal wages of 16.7 and a reduction in French nominal wages of equally 16.7. 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. Table 5.10 gives an overview.

Table 5.10 Monetary Cooperation between Europe and America, Wage Cooperation between Germany and France The Case of Overemployment Germany Initial Output

1060

A Money Supply Output A Nominal Wages Output

1015 16.7 1000

France

America

1030

2090

-45

-45

985

2000

-16.7 1000

2000

200 What are the dynamic characteristics of this process? There is a reduction in European money supply, as there is in American money supply. There is an increase in German nominal wages and a reduction in French nominal wages. There is no change in European nominal wages. There is a two-step decline in German output. There is a two-step change in French output. And there is a onestep decline in American output. There is an increase in the price of German goods and a decline in the price of French goods. There is no change in the price level of European goods. The exchange rate between Europe and America is constant. There is an increase in the world interest rate. There is an increase in the European budget deficit, as there is in the American budget deficit. 4) Unemployment in Europe, overemployment 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 and France there is unemployment, but in America there is overemployment. Step 1 refers to monetary cooperation between Europe and America. The output gap in Europe is 90, and the inflationary gap in America is equally 90. What is needed, then, 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 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 90. As a consequence, German output goes fi-om 940 to 985, French output goes from 970 to 1015, and American output goes from 2090 to 2000. In Germany there is still some unemployment. In France there is now some overemplojmient. In Europe there is now full employment. And the same holds for America. Step 3 refers to wage 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 a reduction in German nominal wages of 16.7 and an increase in French nominal wages of equally 16.7. 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

201 goes from 1015 to 1000, and American output stays at 2000. In each of the countries there is now full employment. Table 5.11 presents a synopsis. What are the dynamic characteristics of this process? There is an increase in European money supply and a reduction in American money supply. There is a reduction in German nominal wages and an increase in French nominal wages. There is no change in European nominal wages. There is a two-step increase in German output. There is a two-step change in French output. And there is a onestep decline in American output. There is a reduction in the price of German goods and an increase in the price of French goods. There is no change in the price level of European goods. There is a depreciation of the euro and an appreciation of the dollar. There is no change in the world interest rate. There is a decline in the European budget deficit and an increase in the American budget deficit.

Table 5.11 Monetary Cooperation between Europe and America, Wage Cooperation between Germany and France Unemployment in Europe, Overemployment in America

Initial Output

Germany

France

America

940

970

2090

A Money Supply Output

22.5 985

A Nominal Wages

-16.7

Output

1000

1015

-22.5 2000

16.7 1000

2000

Chapter 6 Policy Cooperation withiin Europe, Policy 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+0.5aMj2-0.5|3M3-XWj-|xW2

(1)

Yj = A2 +0.5aMj2 -O.5PM3 -XW2 -^Wj

(2)

Y3 = A3 + aM3 - PM12 + vWi + VW2

(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, Wj is German nominal wages, and W2 is French nominal wages. 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 policy makers are the European central bank, the American central bank, the German labour union, and the French labour union. There is cooperation between the European central bank, the German labour union, and the French labour union. 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 labour union, and the French labour union. The targets of policy cooperation within Europe are full employment in Germany and fiill employment in France. The third target is that the reduction in German nominal wages should be equal in size to the increase in French nominal wages. Put another way, the price level of European goods should be constant.

203 The instruments of policy cooperation within Europe are European money supply, German nominal wages, and French nominal wages. Under policy cooperation within Europe there are three targets and three instruments, 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 labour union, and the French labour union. Taking differences in equations (1) and (2), the model of policy cooperation within Europe can be written as follows:

AYj = 0.5aAMi2 - ?^AWj - ^AW2

(4)

AY2 = 0.5aAMi2 -XAW2 - ^AW^

(5)

Here AYj denotes the initial output gap in Germany, AY2 is the initial output gap in France, AMj2 is the required change in European money supply, AWj is the required change in German nominal wages, and AW2 is the required change in French nominal wages. The endogenous variables are AMj2, AWj and AW2. Add up equations (4) and (5), taking account of AWj + AW2 = 0, to find out: AY + AY, AM,2=^ ^ a

(6)

Then subtract equation (5) from equation (4), taking account of AW^ + AW2 = 0, and solve for:

AW, =

AY,-AY, ! 2.

(7)

204 AYj-AY^ AW2 = ^^ ^

(8)

2. 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, A, = 1.2, fi, = 0.3 and V = 0.5 . 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 nominal wages of 100 causes a decline in German output of 120, a decline in French output of 30, and an increase in American output of 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 1910. In each of the countries there is unemployment. Step 1 refers to the policy response. First consider cooperation between the European central bank, the German labour union, and the French labour union. 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, a reduction in German nominal wages of 16.7, and an increase in French nominal wages of equally 16.7. Second consider the policy of the American central bank. 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 raises German output and French output by 45 each. As a side effect, it lowers American output by 30. The reduction in German nominal wages of 16.7 raises

205 German output by 20 and French output by 5. As a side effect, it lowers American output by 8.3. The increase in French nominal wages of 16.7 lowers French output by 20 and German output by 5. As a side effect, it raises American output by 8.3. The increase in American money supply of 30 raises American output by 90. As a side effect, it lowers German output and French output by 15 each. The net effect is an increase in German output of 45, an increase in French output of 15, and an increase in American output of 60. As a consequence, German output goes from 940 to 985, French output goes from 970 to 985, and American output goes from 1910 to 1970. In each of the countries there is still some unemployment. 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 labour union, and the French labour union. The output gap in Germany is 15, and the output gap in France is equally 15. So what is needed, according to equations (6), (7) and (8) from the previous section, is an increase in European money supply of 10, a change in German nominal wages of zero, and a change in French nominal wages of equally zero. Second consider the policy 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 10 raises German output and French output by 15 each. As a side effect, it lowers American output by 10. The increase in American money supply of 10 raises American output by 30. As a side effect, it lowers German output and French output by 5 each. 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 985 to 995, French output equally goes from 985 to 995, and American output goes from 1970 to 1990. 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 10. The

206 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 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 995 to 998.3, French output equally goes from 995 to 998.3, and American output goes from 1990 to 1996.7. This process repeats itself round by round. Table 5.12 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 emplojmient. As a result, the process of policy competition between Europe and America leads to full employment 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 cut in German nominal wages and a one-time increase in French nominal wages. There is no change in European nominal wages. There are repeated increases in German output, as there are in French output and American output. There is a one-time cut in the price of German goods and a one-time increase in the price of French goods. There is no change in the price level of European goods. The exchange rate between Europe and America is constant. There is a decline in the world interest rate. There is a decline 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 45, the total increase in American money supply is equally 45, the total reduction in German nominal wages is 16.7, and the total increase in French nominal wages is equally 16.7. Broadly speaking, the total increase in European money supply depends on the type of coordination mechanism (i.e. policy cooperation within Europe, policy competition between Europe and America).

207 Table 5.12 Policy Cooperation within Europe, Policy Competition between Europe and America

Initial Output

Gennany

France

America

940

970

1910

30

30

A Money Supply A Nominal Wages Output

-16.7 985

A Money Supply A Nominal Wages Output

Output

985

1970

10

10

0

0

995

995 3.3

A Money Supply A Nominal Wages

16.7

0

0

998.3

998.3

1990 3.3

1996.7

and so on Steady-State Output

1000

1000

2000

Part Six Rational Policy Expectations

Chapter 1 Monetary Competition between Europe and America

1) The static model. This chapter deals with competition between the European central bank and the American central bank. 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

(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. Y^ denotes German output, Y2 is French output, Y3 is American output, M^^ i^ European money supply, and M3 is American money supply, a and P are positive coefficients with a > P. 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 fianction of European money supply. The static model can be compressed to a system of two equations: Yi2=Ai2+aMi2-PM3

(4)

Y3=A3+aM3-pMi2

(5)

Here Yj2 denotes European output. According to equation (4), European output is a positive function of European money supply and a negative function of American money supply.

212 2) The dynamic model. At the beginning there is unemployment in both Europe and America. The target of the European central bank is full emplojonent 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. 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: Yl2^= A i 2 + a M ] 2 - P M |

-mh

(6)

Y 3 - • A3 + a M 3 -

(7)

Mf2 - M 1 2

(8)

M ^ = M3

(9)

Here Yi2 Y3 Mj2

is a list of the new symbols: full-employment output in Europe full-employment output in America 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

213 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 Mj2, American money supply M3, the expectation of European money supply M^2' ^^'^ 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 + a M 3 - p M i 2

(11)

Here the endogenous variables are European money supply M12 and American money supply M3. To simplify notation we introduce B12 = Y12 - Aj2 and B3 = Y3 - A3 . Then we solve the model for the endogenous variables:

o

B

^

oB^iSl

(12)

(13)

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 aji^^. 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.

214 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

(14)

AY3 = aAMj - |3AMi2

(15)

Here AY12 denotes the initial output gap in Europe, AY3 is the initial output gap in America, AM] 2 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+pAY3

,,,

,_.

aAY3+|5AYi2

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+1.5Mi2-0.5M3

(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.

215 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. 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 in Europe, according to equation (16), is an increase in European money supply of 45. And what is needed in America, according to equation (17), is an increase in American money supply of equally 45. 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 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. In Germany there is still some unemployment. In France there is now some overemployment. In Europe there is now full employment. And the same is true of America. As a result, under rational expectations, monetary competition leads immediately to full emplojTiient in Europe and America. However, it does not lead to full employment in Germany and France. Table 6.1 presents a synopsis.

Table 6.1 Competition between European Central Bank and American Central Bank Rational Policy Expectations

Initial Output

Germany

France

America

940

970

1910

45

45

1015

2000

A Money Supply Output

985

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

216 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.

Chapter 2 Wage Competition between Germany and France

1) The static model. This chapter deals with competition between the German labour union and the French labour union. As a point of departure, take the static model. It can be represented by a system of three equations: Yi=Ai-XWi-^W2

(1)

Y2=A2-m2-^Wi

(2)

Y3=A3+vWi + vW2

(3)

This is a reduced form of the basic model, see Part One. Yj denotes German output, Yj is French output, Y3 is American output, Wj is German nominal wages, and W2 is French nominal wages. X, \i and v denote the wage policy multipliers. X, \i. and v are positive coefficients with X> |J, and X> v. According to equation (1), German output is a negative function of German nominal wages and a negative function of French nominal wages. According to equation (2), French output is a negative fimction of French nominal wages and a negative function of German nominal wages. According to equation (3), American output is a positive function of German nominal wages and a positive function of French nominal wages. 2) The dynamic model. At the beginning there is unemployment in Germany and France. More precisely, unemployment in Germany is high, and unemployment in France is low. By contrast there is full employment in America. The target of the German labour union is fiall employment in Germany. The instrument of the German labour union is German nominal wages. The target of the French labour union is full employment in France. The instrument of the French labour union is French nominal wages. We assume that the German labour union and the French labour union decide simultaneously and independently. The German labour union sets German nominal wages, forming

218 rational expectations of French nominal wages. And the French labour union sets French nominal wages, forming rational expectations of German nominal wages. On this basis, the dynamic model can be characterized by a system of four equations: Yi = A i - ^ W i - -^iWl

(4)

Y2 =: A 2 - •XW2 -^iWf

(5)

Wf

= Wi

(6)

w| = W2

(7)

Here is a list of the new symbols: Yj full-employment output in Germany Yj fiiU-employment output in France W® the expectation of German nominal wages, as formed by the French labour union W | the expectation of French nominal wages, as formed by the German labour union Wj German nominal wages, as set by the German labour union W2 French nominal wages, as set by the French labour union. According to equation (4), the German labour union sets German nominal wages, forming an expectation of French nominal wages. According to equation (5), the French labour union sets French nominal wages, forming an expectation of German nominal wages. According to equation (6), the expectation of German nominal wages is equal to the forecast made by means of the model. According to equation (7), the expectation of French nominal wages is equal to the forecast made by means of the model. That is to say, the German labour union sets German nominal wages, predicting French nominal wages with the help of the model. And the French labour union sets French nominal wages, predicting German nominal wages with the help of the model. The endogenous variables are German nominal wages Wj, French nominal wages W j , the expectation of German nominal wages W^, and the expectation of French nominal wages W|.

219

The dynamic model can be compressed to a system of two equations:

Yi=Ai-mi-^W2

(8)

Y2=A2-m2-[iW^

(9)

The endogenous variables are German nominal wages Wj and French nominal wages Wj . To simplify notation, we introduce Bj = Aj - Y^ and B2 = A2 - Y2. Then we solve the model for the endogenous variables: XBj- -^B^

Wr

W2:

(10)

l'- -^^ XB2 - ^ B i X^-- ^ ^

(11)

Equation (10) shows the equilibrium level of German nominal wages, and equation (11) shows the equilibrium level of French nominal wages. There is a solution if and only if X^[i. This condition is fulfilled. As a result, under rational expectations, there is an immediate equilibrium of wage competition between Germany and France. In other words, under rational expectations, wage competition leads immediately to full employment in Germany and France. However, as an adverse side effect, it causes unemplojTnent 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 alternative, the dynamic model can be stated in terms of the initial output gap and the required change in nominal wages: AYj = - XAWj - IXAW2

(12)

AY2 = - XAW2 - [xAWj

(13)

220 Here AYj denotes the initial output gap in Germany, AY2 is the initial output gap in France, AWj is the required change in German nominal wages, and AW2 is the required change in French nominal wages. The endogenous variables are AWj and AW2. The equilibrium of the system (12) and (13) is:

AWi^-M^^i^ X^-

AW2 = -

V

XAYj--^lAYi .," % ^ -k^-- ^ ^

(14)

(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 X = 1.2, |J, = 0.3 and v = 0.5 . On this assumption, the static model can be written as follows: Yi = A i - 1 . 2 W i - 0 . 3 W 2

(16)

Y2 = A 2 - 1 . 2 W 2 - 0 . 3 W i

(17)

Y3 =A3+0.5Wi+0.5W2

(18)

The endogenous variables are German output, French output, and American output. Evidently, an increase in German nominal wages of 100 causes a decline in German output of 120, a decline in French output of 30, and an increase in American output of 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 2000. In Germany and France there is unemplojonent, but in America there is full employment. 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 a reduction in German nominal wages of 46.7. And what is needed in France, according to equation (15), is a reduction in French nominal wages of 13.3.

221 Step 2 refers to the output lag. 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 equally 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 and France there is now full employment. But in America there is now unemployment. As a result, under rational expectations, wage competition leads immediately to full emplojonent in Germany and France. However, as an adverse side effect, it causes unemployment in America. Table 6.2 gives an overview.

Table 6.2 Competition between German Labour Union and French Labour Union Rational Policy Expectations Germany

Initial Output

France

940

970

A Nominal Wages

-46.7

-13.3

Output

1000

1000

America

2000

1970

Chapter 3 Monetary and Wage Competition: Sequential Decisions

1) The static model. This chapter deals with competition between the European central bank, the American central bank, the German labour union, and the French labour union. As a point of reference, consider the static model. It can be represented by a system of three equations:

Y i = A j + 0.5aMj2-0.5pM3-?.Wj-nW2

(1)

Y2 = A2 + 0.5aMj2 -O.5PM3 -XW2 -|iWj

(2)

Y3=A3 + aM3-pMi2 + vWi + vW2

(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, Mj2 is European money supply, M3 is American money supply, Wj is German nominal wages, and W2 is French nominal wages, a, P, X, \i and v are positive coefficients with a > P, k> \i and X> V. According to equation (1), German output is a positive function of European money supply, a negative function of American money supply, a negative function of German nominal wages, and a negative function of French nominal wages. According to equation (2), French output is a positive function of European money supply, a negative function of American money supply, a negative function of French nominal wages, and a negative function of German nominal wages. 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 nominal wages, and a positive function of French nominal wages. The static model can be compressed to a system of two equations:

223

Yi2 = Ai2 + aMi2 - PM3 - (^i + )a)Wi - (X + ^)W2

(4)

Y3 = A3 + aM3 - PM12 + vWi + VW2

(5)

Here Y12 denotes European output. According to equation (4), European output is a positive function of European money supply, a negative function of American money supply, a negative function of German nominal wages, and a negative function of French nominal wages. 2) The dynamic model. At the beginning there is unemployment in Germany, France and America. More precisely, unemployment in Germany is high, and unemplojTnent in France is low. 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 labour union is full employment in Germany. The instrument of the German labour union is German nominal wages. The target of the French labour union is full employment in France. The instrument of the French labour union is French nominal wages. We assume that the central banks and the labour unions decide sequentially. First the central banks decide, then the labour unions decide. In step 1, the European central bank and the American central bank decide simultaneously and independently. In step 2, the German labour union and the French labour union 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 labour union and the French labour union 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: Y12 = A12 + aMi2 - P M | -(X+^)Wi - ( } . + ^i)W2

(6)

224

Yg = A3 + aMj - pMf2 + vWi + VW2

(7)

Mf2=Mi2

(8)

M^ = M3

(9)

Here Yj2 Y3 Mj2

is a list of the new symbols: full-employment output in Europe full-employment output in America 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, M3

as set by the European central bank 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 Mj2, and the expectation of American money supply M3. The dynamic model can be condensed to a system of two equations:

Y12 = A12 + aMi2 - ml

- a + P^Wi - a + ^i)W2

Y3=A3+aM3-pMi^2+^Wi + vW2

(10) (11)

225

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

B12 = Y12 - A12+ (k + ^)Wi +{% + liWi B3=Y3-A3-vWi-vW2

(12) (13)

Then we solve the model for the endogenous variables:

M12:

M3 =

aBi2 + (3B3 a2 -P2 aB3 + PB12 a 2 - -32

(14)

(15)

Equation (14) shows the equilibrium 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^^. 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 - PAM12

(17)

Here AYj2 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 AIVI12 and AIVI3. The equilibrium of the system (16) and (17) is:

226 O A Y ^ ^

(18)

aAY3+pAYi2 AM3 = ^ ^ ^ 3 ^ ' ' ; , ^ i ^

(19)

Step 2 refers to the output lag. Next have a closer look at step 3. The German labour union and the French labour union decide simultaneously and independently. The German labour union sets German nominal wages, forming rational expectations of French nominal wages. And the French labour union sets French nominal wages, forming rational expectations of German nominal wages. On this basis, the dynamic model can be characterized by a system of four equations:

Yj = Aj + 0.5aM,2 - O.513M3 -XWj - ^ W |

(20)

Y2 = A2 + 0.5aMj2 - O.5PM3 - IW2 - |iWf

(21)

Wf = Wi

(22)

W | = W2

(23)

Here Yj Y2 Wj^

is a list of the new symbols: full-emplo3Tnent output in Germany full-employment output in France the expectation of German nominal wages, as formed by the French labour union W| the expectation of French nominal wages, as formed by the German labour union Wj German nominal wages, as set by the German labour union W2 French nominal wages, as set by the French labour union.

According to equation (20), the German labour union sets German nominal wages, forming an expectation of French nominal wages. According to equation (21), the French labour union sets French nominal wages, forming an expectation

227 of German nominal wages. According to equation (22), the expectation of German nominal wages is equal to the forecast made by means of the model. According to equation (23), the expectation of French nominal wages is equal to the forecast made by means of the model. That is to say, the German labour union sets German nominal wages, predicting French nominal wages with the help of the model. And the French labour union sets French nominal wages, predicting German nominal wages with the help of the model. The endogenous variables are German nominal wages Wj, French nominal wages Wj, the expectation of German nominal wages Wj^, and the expectation of French nominal wages W|. The dynamic model can be compressed to a system of two equations: Yj = Aj +0.5aMi2-O.5PM3 -XW^-iiW^

(24)

Y2 = A2 + 0.5aMi2 -O.5PM3 -XW2 -^Wj

(25)

Here the endogenous variables are German nominal wages Wj and French nominal wages W j . To simplify notation we introduce: F i = A i - Y i + 0.5aMj2-0.5pM3

(26)

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

(27)

Then we solve the model for the endogenous variables: ?LFJ-

Wi =

w, W2 -

5.2-

-^^2

V

?iF2 - f i F i

X2.-l^'

(28)

(29)

Equation (28) shows the equilibrium level of German nominal wages, and equation (29) shows the equilibrium level of French nominal wages. There is a solution if and only if X^yi. This condition is fulfilled. As a result, under rational expectations, there is an immediate equilibrium of wage competition between Germany and France. In other words, under rational expectations, wage

228 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, 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 change in nominal wages: AYj = - XAW^ - ^AWj

(30)

AYj = - XAW2 - ^AWj

(31)

Here AYj denotes the initial output gap in Germany, AY2 is the initial output gap in France, AWj is the required change in German nominal wages, and AW2 is the required change in French nominal wages. The endogenous variables are AWj and AW2 • The equilibrium of the system (30) and (31) is: AW, = - M ^ Z i i ^

X^-

V

XAY2--HAYi

AW2 = - ' " ," " " '

X^--^'

(32)

(33)

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 = 1, X, = 1.2, )J. = 0.3 and v = 0.5. On this assumption, the static model can be written as follows: Yj = A, +1.5Mj2 -O.5M3 -l.2W1-O.3W2

(34)

Y2 = A2 +I.5M12 -O.5M3 -I.2W2 -0.3Wi

(35)

Y3=A3 + 3 M 3 - M i 2 + 0.5Wi + 0.5W2

(36)

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

229 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 nominal wages of 100 causes a decline in French output of 120, a decline in German output of 30, and an increase in American output of 50. 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 1910. In each of the countries there is unemplojmient. Step 1 refers to monetary competition between Europe and America. The output gap in Europe is 90, as is the output gap in America. So what is needed in Europe, according to equation (18), is an increase in European money supply of 45. And what is needed in America, according to equation (19), is an increase in American money supply of equally 45. 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 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. In Germany there is still some unemployment. In France there is now some overemployment. And in America there is now full employment. Step 3 refers to wage 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 a reduction in German nominal wages of 16.7. And what is needed in France, according to equation (33), is an increase in French nominal wages of equally 16.7. 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. As a result, under rational expectations, the sequential process of monetary and wage competition leads immediately to full emplojTnent in Germany, France and America. Table 6.3 presents a synopsis.

230

Table 6.3 Competition between European Central Bank, American Central Bank, German Labour Union, and French Labour Union Rational Policy Expectations

Initial Output

Germany

France

America

940

970

1910

45

45

1015

2000

A Money Supply Output

985

A Nominal Wages

-16.7

Output

1000

16.7 1000

2000

Chapter 4 Monetary and Wage Competition: Simultaneous Decisions

1) The static model. This chapter deals with competition between the European central bank, the American central bank, the German labour union, and the French labour union. As a point of departure, take the static model. It can be represented by a system of three equations:

Yj=Ai+0.5aM^2-0.5pM3-XWi-^W2

(1)

Y2 = A2 + 0.5aMi2 -O.5PM3 -XW^ -^iWj

(2)

Y3 = A3 + aM3 - pMi2 + vWi + VW2

(3)

Here Yj denotes German output, Y2 is French output, Y3 is American output, M12 is European money supply, M3 is American money supply, Wj is German nominal wages, and W2 is French nominal wages. 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 labour union is full employment in Germany. And the target of the French labour union is full employment in France. We assume that the European central bank, the American central bank, the German labour union, and the French labour union decide simultaneously and independently. The European central bank sets European money supply, forming rational expectations of American money supply, German nominal wages, and French nominal wages. The American central bank sets American money supply, forming rational expectations of European money supply, German nominal wages, and French nominal wages. The German labour union sets German

232 nominal wages, forming rational expectations of European money supply, American money supply, and French nominal wages. And the French labour union sets French nominal wages, forming rational expectations of European money supply, American money supply, and German nominal wages. That is to say, the European central bank sets European money supply, predicting American money supply, German nominal wages, and French nominal wages with the help of the model. The American central bank sets American money supply, predicting European money supply, German nominal wages, and French nominal wages with the help of the model. The German labour union sets German nominal wages, predicting European money supply, American money supply, and French nominal wages with the help of the model. And the French labour union sets French nominal wages, predicting European money supply, American money supply, and German nominal wages with the help of the model. On this basis, the dynamic model can be characterized by a system of three equations:

Yj=Aj + 0.5aMj2-0.5pM3-XWi-|xW2

(4)

Y2=A2+0.5aMi2-0.5|3M3-?iW2-nWi

(5)

Y3 = A3 + aMj - pMj 2 + VWi + VW2

(6)

Here Yj denotes full-employment output in Germany, Yj 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 nominal wages, and French nominal wages. Under simultaneous decisions there are three targets and four instruments, so there is one degree of freedom. As a result, under rational expectations, there is no unique equilibrium of monetary and wage competition. Put another way, under rational expectations, the simultaneous process of monetary and wage competition does not lead to full employment in Germany, France and America.

Chapter 5 Monetary Cooperation between Europe and America, Wage 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: Yi=Ai+0.5aMi2-0.5pM3->iWi-|xW2

(1)

Y2 = A2 + 0.5aM^2 -O-SPMj -XW^ -\iW^

(2)

Y3 = A3 + aM3 - pMi2 + vWi + VW2

(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. To be more specific, 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 labour union is full employment in Germany. The instrument of the German labour union is German nominal wages. The target of the French labour union is full employment in France. The instrument of the French labour union is French nominal wages. We assume that the central banks and the labour unions decide sequentially. First the central banks decide, then the labour unions decide. In step 1, the European central bank and the American central bank decide cooperatively. In step 2, the German labour union and the French labour union decide simultaneously and independently. In step 3, the European central bank and the American central bank decide cooperatively. In step 4, the German labour union

234 and the French labour union 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 = aAMj - PAM12

(5)

Here AYj2 denotes the initial output gap in Europe, AY3 is the initial output gap in America, AIVI12 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:

AMi2=

aAYi2 + (3AY3 .^2 ^9

aAYg + PAY12

AM,= -YT2''

(6)

0)

As a result, there is a solution to monetary cooperation between Europe and America. In other words, monetary cooperation can achieve fiiU employment in Europe and America. Step 2 refers to the output lag. Next have a closer look at step 3. It refers to wage competition between Germany and France. The German labour union sets German nominal wages, forming rational expectations of French nominal wages. And the French labour union sets French nominal wages, forming rational expectations of German nominal wages. That means, the German labour union sets German nominal wages, predicting French nominal wages with the help of model. And the French labour union sets French nominal wages, predicting German nominal wages with the help of the model. Taking differences in equations (1) and (2), the model of wage competition can be written as follows (see Chapter 3): AYj = - XAWj - IXAW2

(8)

235 AYj = - IAW2 - nAWj

(9)

Here AY^ denotes the initial output gap in Germany, AY2 is the initial output gap in France, AWj is the required change in German nominal wages, and AW2 is the required change in French nominal wages. The endogenous variables are AWj and AW2. The equilibrium of the system (8) and (9) is:

^W, = - M ^ Z i ^

(10)

XA^-MAY.

As a result, under rational expectations, there is an immediate equilibrium of wage competition between Germany and France. That is to say, under rational expectations, wage competition leads immediately to fiill emplojmient 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 loss of generality, assume a = 3, p = l, A, = 1.2, [x = 0.3 and v = 0.5. 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 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 nominal wages of 100 causes a decline in German output of 120, a decline in French output of 30, and an increase in American output of 50. Further let fiill-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. Step 1 refers to monetary cooperation between Europe and America. The output gap in Europe is 90, as is the output gap in America. So

236 what is needed, according to equations (6) and (7), 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 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. In Germany there is still some unemplojmient. In France there is now some overemployment. And in America there is now full employment. Step 3 refers to wage 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 a reduction in German nominal wages of 16.7. And what is needed in France, according to equation (11), is an increase in French nominal wages of equally 16.7. 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 emplojmient. As a result, under rational expectations, the sequential process of monetary cooperation and wage competition leads immediately to fiiU employment in Germany, France and America. Table 6.4 gives an overview.

237

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

Initial Output

Germany

France

America

940

970

1910

45

45

1015

2000

A Money Supply Output

985

A Nominal Wages

-16.7

Output

1000

16.7 1000

2000

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:

Yj=Ai + 0.5aMi2-0.5pM3->.Wj-|iW2

(1)

Y2 = A2 + 0.5aMi2 - O.5PM3 -XW2 - ^Wj

(2)

Y3=A3 + a M 3 - p M i 2 + vWi + vW2

(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 labour union, and the French labour union. 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 reduction in German nominal wages should be equal in size to the increase in French nominal wages. The instruments of policy cooperation within Europe are European money supply, German nominal wages, and French nominal wages. 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 policy 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 American central bank decide simultaneously and independently. In step 2,

239 again, the European coalition and the American central bank decide simultaneously and independently. And so on. The European coalition sets European money supply, German nominal wages, and French nominal wages, forming rational expectations of American money supply. And the American central bank sets American money supply, forming rational expectations of European money supply, German nominal wages, and French nominal wages. On this basis, the dynamic model can be characterized by a system of eight equations:

Yi=Ai+0.5aMj2-0.5pM^->.Wi-^W2

(4)

Y2=A2+0.5aMi2-0.5pM^-).W2-|iW^

(5)

Y3 = A3 + aMj - pMf2 + vWf + T/W|

(6)

Wj + W2 = const

(7)

Mf2-Mi2

(8)

M^ = M3

(9)

Wf = Wi

(10)

W| = W2

(11)

Here Yj Yj Y3 Mj2

is a list of the new symbols: fiill-employment output in Germany fiill-employment output in France full-employment output in America the expectation of European money supply, as formed by the American central bank W® the expectation of German nominal wages, as formed by the American central bank W| the expectation of French nominal wages, as formed by the American central bank M3 the expectation of American money supply, Mj2

as formed by the European coalition European money supply, as set by the European coalition

240 Wj W2 M3

German nominal wages, as set by the European coalition French nominal wages, 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 nominal wages, and French nominal wages, 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 nominal wages, and French nominal wages. According to equation (7), the sum total of German and French nominal wages 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 nominal wages is equal to the forecast made by means of the model. And according to equation (11), the expectation of French nominal wages is equal to the forecast made by means of the model. That is to say, the European coalition sets European money supply, German nominal wages, and French nominal wages, predicting American money supply with the help of the model. And the American central bank sets American money supply, predicting European money supply, German nominal wages, and French nominal wages with the help of the model. The endogenous variables are European money supply M12, American money supply M3, German nominal wages Wj, French nominal wages Wj, the expectation of European money supply Mf2, the expectation of American money supply M3, the expectation of German nominal wages W®, and the expectation of French nominal wages W | . The dynamic model can be compressed to a system of four equations: Yj = Aj +0.5aMi2 -O.5PM3 -IW^-iiW^

(12)

Y2 = A2 + 0.5aMi2 -O.5PM3 -XW2 -^Wl

(13)

Y3 = A3 + aM3 - pMi2 + vWj + VW2

(14)

241 Wi+W2 = const

(15)

Here the endogenous variables are European money supply M|2, American money supply M3, German nominal wages Wj, and French nominal wages Wj. As an alternative, the dynamic model can be stated in terms of the initial output gap, the required change in money supply, and the required change in nominal wages. Taking differences in equations (12), (13), (14) and (15), the dynamic model can be written as follows: AYj = 0.5aAMj2 - O.SpAMj - XAW^ - nAW2

(16)

AY2 = 0.5aAMi2 - O.5PAM3 - XAW2 - nAWi

(17)

AY3 = aAM3 - PAM12 + vAWi + VAW2

(18)

AWi+AW2=0

(19)

Here AYj 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 change in European money supply, AM3 is the required change in American money supply, AWi is the required change in German nominal wages, and AW2 is the required change in French nominal wages. The endogenous variables are AM12, AM3, AWj and AW2. Add up equations (16) and (17), taking account of equation (19), to find out:

AYi + AY2 = aAMi2 - PAM3

(20)

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

AY12 = aAMi2 - PAM3

(21)

Taking account of equation (19), equation (18) can be written as follows: AY3 = aAM3 - PAM12

(22)

242

Then solve equations (21) and (22) for: O A Y ^ ^

,^^

(23)

aAY3+pAY,2

Further subtract equation (17) from equation (16) to find out: AYi - AY2 = - (X - |^)(AWi - AW2)

(25)

Then solve equations (19) and (25) for: AW.^-fLZ^ 2(A, - p.)

(26)

2(X-rt 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, (3 = 1, A, = 1.2, 10. = 0.3 and v = 0.5. 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. 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

243

output gap in America is 90. So what is needed in Europe, according to equations (23), (26) and (27), is an increase in European money supply of 45, a reduction in German nominal wages of 16.7, and an increase in French nominal wages of equally 16.7. Second consider monetary policy in America. The output gap in America is 90, as is the output gap in Europe. So what is needed in America, according to equation (24), is an increase in American money supply of 45. 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 1910 to 2000. In each of the countries there is now full employment. As a result, under rational expectations, the process of policy competition between Europe and America leads immediately to full employment in Germany, France and America. Table 6.5 presents a sjoiopsis.

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

Initial Output

Germany

France

America

940

970

1910

45

45

A Money Supply A Nominal Wages

-16.7

Output

1000

16.7 1000

2000

Synopsis

The synopsis refers to the interactions between - the European central bank, - the American central bank, - the German labour union, and - the French labour union. The sjTiopsis 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 change - the total change - the total change - the total change - the total change Obviously, the result

in European money supply, in American money supply, in German nominal wages, in French nominal wages, and in European nominal wages. depends on the type of coordination mechanism.

In addition. Table 7.2 shows the total change in European nominal wages, as a percentage of the initial output gap in Europe. Again, the result depends on the type of coordination mechanism.

246 Table 7.1 Total Change in Money Supply and Nominal Wages According to Type of Coordination Mechanism Monetary and Wage Competition Sequential Decisions: Cold-Turkey Policies Total Change in European Money Supply

26.3

Total Change in American Money Supply

45

Total Change in German Nominal Wages

-35.4

Total Change in French Nominal Wages

-2.1

Total Change in European Nominal Wages

-18.8

Monetary and Wage Competition Simultaneous Decisions: Cold-Turkey Policies Monetary and wage competition does not lead to full employment in Germany, France and America. There are explosive oscillations in money supply, nominal wages, and output. Monetary and Wage Competition Simultaneous Decisions: Gradualist Policies Total Change in European Money Supply

34.3

Total Change in American Money Supply

45

Total Change in German Nominal Wages

-27.4

Total Change in French Nominal Wages Total Change in European Nominal Wages

5.9 -10.8

Monetary and Wage Cooperation Required Change in European Money Supply

45

Required Change in American Money Supply

45

Required Change in German Nominal Wages

-16.7

Required Change in French Nominal Wages Required Change in European Nominal Wages

16.7 0

247 Fast Monetary Competition, Slow Wage Competition Total Change in European Money Supply

43.3

Total Change in American Money Supply

43.3

Total Change in German Nominal Wages

-16.7

Total Change in French Nominal Wages Total Change in European Nominal Wages

14.6 -1.1

Monetary Cooperation between Europe and America, Wage Competition between Germany and France Total Change in European Money Supply

45

Total Change in American Money Supply

45

Total Change in German Nominal Wages

-16.7

Total Change in French Nominal Wages Total Change in European Nominal Wages

16.7 0

Monetary Cooperation between Europe and America, Wage Cooperation between Germany and France Total Change in European Money Supply

45

Total Change in American Money Supply

45

Total Change in German Nominal Wages

-16.7

Total Change in French Nominal Wages Total Change in European Nominal Wages

16.7 0

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

45

Total Change in American Money Supply

45

Total Change in German Nominal Wages

-16.7

Total Change in French Nominal Wages Total Change in European Nominal Wages

16.7 0

248

Table 7.2 Total Reduction in European Nominal Wages Relative to Initial Output Gap in Europe According to Type of Coordination Mechanism Sequential Decisions: Cold-Turkey Policies

21%

Simultaneous Decisions: Cold-Turkey Policies

unstable

Simultaneous Decisions: Gradualist Policies

12%

Monetary and Wage Cooperation

0%

Fast Monetary Competition, Slow Wage Competition

1%

Monetary Cooperation and Wage Competition

0%

Monetary Cooperation and Wage Cooperation

0%

Policy Cooperation within Europe

0%

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 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.

250

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. This section deals with competition between the European central bank and the American central bank. 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 primary target of the European central bank is price stability in Europe. The secondary target of the European central bank is high emplojonent in Germany and France. The specific target of the European central bank is that unemployment in Germany equals overemployment in France. In a sense, the specific target of the European central bank is full emplojmient 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 fuU-emplojonent output in America is 2000. Let initial output in Germany be

251 940, 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 emplojonent 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 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 fi-om 940 to 970, French output goes from 970 to 1000, and American output goes from 1910 to 1970. 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 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 overemplojonent and inflation. In Europe there is full employment and price stability. And in America there is full employment and price

252 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.

Table 8.1 Competition between European Central Bank and American Central Bank The Case of Unemployment

Initial Output

Germany

France

America

940

970

1910

30

30

1000

1970

10

10

980

1010

1990

985

1015

2000

A Money Supply Output

970

A Money Supply Output 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 overemplo3mient 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 policy multiplier in America is 3. So what is needed in America is a reduction in American money supply of 30.

253 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 Competition between European Central Bank and American Central Bank The Case of Inflation

Germany Initial Output

1060

2090

-30

-30

1000

2030

-10

-10

1020

990

2010

1015

985

2000

1030

A Money Supply Output

America

1030

A Money Supply Output

France

and so on Steady-State Output

254 In the steady state, German output is 1015, French output is 985, and American output is 2000. In Germany there is overemplo5Tnent 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. This section deals with cooperation between the European central bank and the American central bank. At the start 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. 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.

255

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 Cooperation between European Central Bank and American Central Bank 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

256 French output by 22.5 each. The net effect is 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 fiill emploj^ment and price stability. 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 Cooperation between European Central Bank and American Central Banic The Case of Inflation

Initial Output

Germany

France

America

1060

1030

2090

-45

-45

985

2000

A Money Supply Output

1015

257

3. Wage Competition between Germany and France

1) The static model. An increase in German nominal wages lowers German output. And what is more, it lowers French output. On the other hand, it raises American output. Here the fall in German output is larger than the fall in French output. And the fall in European output is larger than the rise in American output. Correspondingly, an increase in French nominal wages lowers French output. And what is more, it lowers German output. On the other hand, it raises American output. Here the fall in French output is larger than the fall in German output. And the fall in European output is larger than the rise in American output. In the numerical example, an increase in German nominal wages of 100 causes a decline in German output of 120, a decline in French output of 30, and an increase in American output of 50. Likewise, an increase in French nominal wages of 100 causes a decline in French output of 120, a decline in German output of 30, and an increase in American output of 50. Now have a closer look at the process of adjustment. An increase in German nominal wages causes an increase in the price of German goods. This in turn causes an appreciation of the euro, a depreciation of the dollar, and an increase in the world interest rate. The increase in the price of German goods lowers German exports. On the other hand, it raises French exports and American exports. 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 and French output move down. However, American output moves up. This model is in the tradition of the Mundell-Fleming model and the Levin model. 2) The dynamic model. This section deals with competition between the German labour union and the French labour union. At the beginning there is unemployment in Germany and France. More precisely, unemployment in Germany is high, and unemployment in France is low. By contrast there is full employment in America. The target of the German labour union is fiiU employment in Germany. The instrument of the German labour union is German

258 nominal wages. The German labour union lowers German nominal wages so as to close the output gap in Germany. The target of the French labour union is full employment in France. The instrument of the French labour union is French nominal wages. The French labour union lowers French nominal wages so as to close the output gap in France. We assume that the German labour union and the French labour union decide simultaneously and independently. In addition there is an output lag. German output next period is determined by German nominal wages this period as well as by French nominal wages this period. In the same way, French output next period is determined by French nominal wages this period as well as by German nominal wages this period. Last but not least, American output next period is determined by German nominal wages this period as well as by French nominal wages this period. As a result, there is a stable steady state of wage 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 and France there is unemployment, but in America there is full employment. Step 1 refers to the policy response. The output gap in Germany is 60. The wage policy multiplier in Germany is -1.2. So what is needed in Germany is a reduction German nominal wages of 50. The output gap in France is 30. The wage policy multiplier in France is -1.2. So what is needed in France is a reduction in French nominal wages of 25. Step 2 refers to the output lag. The reduction in German nominal wages of 50 causes an increase in German output of 60. As a side effect, it causes an increase in French output of 15 and a decline in American output of 25. The reduction in French nominal wages of 25 causes an increase in French output of 30. As a side effect, it causes an increase in German output of 7.5 and a decline in American output of 12.5. The total effect is an increase in German output of 67.5, an increase in French output of 45, and a decline in American output of 37.5. As a consequence, German output goes from 940 to 1007.5, French output goes from 970 to 1015, and American output goes from 2000 to 1962.5.

259 Step 3 refers to the policy response. The inflationary gap in Germany is 7.5. The wage policy multiplier in Germany is -1.2. So what is needed in Germany is an increase in German nominal wages of 6.3. The inflationary gap in France is 15. The wage pohcy multiplier in France is -1.2. So what is needed in France is an increase in French nominal wages of 12.5. Step 4 refers to the output lag. The total effect is a decline in German output of 11.3, a decline in French output of 16.9, and an increase in American output of 9.4. As a consequence, German output goes from 1007.5 to 996.3, French output goes from 1015 to 998.1, and American output goes from 1962.5 to 1971.9. And so on. Table 8.5 presents a synopsis.

Table 8.5 Competition between German Labour Union and French Labour Union Germany

France

America

940

970

2000

A Nominal Wages

-50

-25

Output

1007.5

1015

Initial Output

A Nominal Wages Output

6.3

12.5

996.3

998.1

1962.5

1971.9

and so on Steady-State Output

1000

1000

1970

In the steady state, German output is 1000, French output is equally 1000, and American output is 1970. In Germany and France there is full employment. But in America there is unemployment. As a result, competition between the German labour union and the French labour union leads to full employment in Germany and France. However, as an adverse side effect, it causes unemplo3anent in America.

260

4. Wage Cooperation between Germany and France

1) The model. This section deals with cooperation between the German labour union and the French labour union. At the beginning there is unemployment in Germany and France. More precisely, unemployment in Germany is high, and unemplo5anent in France is low. By contrast there is full employment in America. The targets of wage cooperation are full employment in Germany and full employment in France. The instruments of wage cooperation are German nominal wages and French nominal wages. So there are two targets and two instruments. As a result, there is a solution to wage 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 and France there is unemployment, but in America there is full employment. 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 a reduction in German nominal wages of 46.7 and a reduction in French nominal wages of 13.3. Step 2 refers to the output lag. The reduction in German nominal wages of 46.7 raises German output by 56 and French output by 14. As a side effect, it lowers American output by 23.3. The reduction in French nominal wages of 13.3 raises French output by 16 and German output by 4. As a side effect, it lowers American output by 6.7. 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 equally 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 and France there is now full emplojonent. But in America there is now unemployment. As a result, cooperation between the German labour union and the French labour union can achieve full employment in Germany and France. However, as an adverse side effect, it causes unemploj'ment in America. Table 8.6 gives an overview. 3) Comparing wage cooperation with wage competition. Wage competition is a slow process. By contrast, wage cooperation is a fast process. Wage com-

261 petition can cause oscillations in nominal wages and output. By contrast, wage cooperation cannot cause oscillations in nominal wages and output. Judging from these points of view, wage cooperation seems to be superior to wage competition.

Table 8.6 Cooperation between German Labour Union and French Labour Union Germany

Initial Output

France

940

970

A Nominal Wages

-46.7

-13.3

Output

1000

1000

America

2000

1970

5. Monetary and Wage Competition

1) The dynamic model. This section deals with competition between the European central bank, the American central bank, the German labour union, and the French labour union. At the beginning there is unemploj^nent in Germany, France and America. More precisely, unemployment in Germany is high, and unemployment in France is low. The primary target of the European central bank is price stability in Europe. The secondary target of the European central bank is high emplo3aiient in Germany and France. The specific target of the European central bank is that unemployment in Germany equals overemployment in France. 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.

262 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 labour union is full employment in Germany. The instrument of the German labour union is German nominal wages. The German labour union lowers German nominal wages so as to close the output gap in Germany. The target of the French labour union is full employment in France. The instrument of the French labour union is French nominal wages. The French labour union lowers French nominal wages so as to close the output gap in France. We assume that the central banks and the labour unions decide sequentially. First the central banks decide, then the labour unions decide. In step 1, the European central bank and the American central bank decide simultaneously and independently. In step 2, the German labour union and the French labour union 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 labour union and the French labour union 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 nominal wages of 100 causes a decline in German output of 120, a decline in French output of 30, and an increase in American output of 50. Correspondingly, an increase in French nominal wages of 100 causes a decline in French output of 120, a decline in German output of 30, and an increase in American output of 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 1910. In each of the countries there is unemployment. 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

263 what is needed in Europe is an increase in European money supply of 30. The output gap in America is 90. The monetary poUcy multipUer 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 wage policy in Germany and France. The output gap in Germany is 30. The wage policy multiplier in Germany is -1.2. So what is needed in Germany is a reduction in German nominal wages of 25. The output gap in France is zero. So there is no need for a change in French nominal wages. Step 4 refers to the output lag. The reduction in German nominal wages of 25 causes an increase in German output of 30. As a side effect, it causes an increase in French output of 7.5 and a decline in American output of 12.5. As a consequence, German output goes from 970 to 1000, French output goes from 1000 to 1007.5, and American output goes from 1970 to 1957.5. Step 5 refers to monetary policy in Europe and America. The inflationary gap in Europe in 7.5. The monetary policy multiplier in Europe is 3. So what is needed in Europe is a reduction in European money supply of 2.5. The output gap in America is 42.5. The monetary policy multiplier in America is 3. So what is needed in America is an increase in American money supply of 14.2. Step 6 refers to the output lag. The net effect is a decline in German output of 10.8, a decline in French output of equally 10.8, and an increase in American output of 45. As a consequence, German output goes from 1000 to 989.2, French output goes from 1007.5 to 996.7, and American output goes from 1957.5 to 2002.5. Step 7 refers to wage policy in Germany and France. The output gap in Germany is 10.8. The wage policy multiplier in Germany is -1.2. So what is needed in Germany is a reduction in German nominal wages of 9.0. The output

264 gap in France is 3.3. The wage policy multiplier in France is -1.2. So what is needed in France is a reduction in French nominal wages of 2.8. Step 8 refers to the output lag. The net effect is an increase in German output of 11.7, an increase in French output of 6.0, and a decline in American output of 5.9. As a consequence, German output goes from 989.2 to 1000.8, French output goes from 996.7 to 1002.7, and American output goes from 2002.5 to 1996.6. And so on. Table 8.7 presents a synopsis.

Table 8.7 Competition between European Central Bank, American Central Bank, German Labour Union, and French Labour Union

Initial Output

Germany

France

America

940

970

1910

30

30 1970

A Money Supply Output

970

1000

A Nominal Wages

-25

0

Output

1000

A Money Supply

1007.5

1957.5

-2.5

14.2 2002.5

Output

989.2

996.7

A Nominal Wages

-9.0

-2.8

1000.8

1002.7

1996.6

1000

1000

2000

Output and so on Steady-State Output

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 fixll employment. As a result, the sequential process of monetary and wage competition leads to fiill employment in Germany, France and America. Taking the sum over all periods, the total increase in European money supply is 26.3, the total increase in

265 American money supply is 45, the total reduction in German nominal wages is 35.4, and the total reduction in French nominal wages is 2.1. Generally speaking, the total change 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 X - the cross policy multipliers p and \i. And the same holds for the total change in American money supply, the total change in German nominal wages, and the total change in French nominal wages.

6. Monetary and Wage Cooperation

1) The model. This section deals with cooperation between the European central bank, the American central bank, the German labour union, and the French labour union. At the start there is unemplojmient in Germany, France and America. Let unemployment in Germany be high, and let unemployment in France be low. 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 nominal wages, and French nominal wages. 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, monetary and wage cooperation can achieve full employment in Germany, France and America. 2) A numerical example. We now introduce a fourth target. We assume that the reduction in German nominal wages should be equal in size to the increase in French nominal wages. Put another way, we assume that the price level of European goods 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

266 of the countries there is unemployment. Step 1 refers to the poUcy response. The output gap in Germany is 60, the output gap in France is 30, and the output gap in America is 90. What is needed, then, is an increase in European money supply of 45, an increase in American money supply of equally 45, a reduction in German nominal wages of 16.7, and an increase in French nominal wages of equally 16.7. 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 reduction in German nominal wages of 16.7 raises German output by 20 and French output by 5. On the other hand, it lowers American output by 8.3. The increase in French nominal wages of 16.7 lowers French output by 20 and German output by 5. On the other hand, it raises American output by 8.3. 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 fiill employment. As a result, monetary and wage cooperation can achieve full employment in Germany, France and America. Table 8.8 gives an overview. Finally compare policy cooperation with policy competition. Policy competition is a process of intermediate speed. By contrast, policy cooperation is a fast process. Policy competition causes oscillations in output. By contrast, policy cooperation does not cause oscillations in output. Under policy competition, the total increase in European money supply is 26.3, the total increase in American money supply is 45, the total reduction in German nominal wages is 35.4, and the total reduction in French nominal wages is 2.1. That means, the solution to policy cooperation is different from the steady state of policy competition. Policy competition causes a small increase in European money supply and a large reduction in European nominal wages. By contrast, policy cooperation causes a large increase in European money supply and no change in European nominal wages. Judging from these points of view, policy cooperation seems to be superior to policy competition.

267 Table 8.8 Cooperation between European Central Bank, American Central Bank, German Labour Union, and French Labour Union

Initial Output

Germany

France

America

940

970

1910

45

45

A Money Supply A Nominal Wages

-16.7

Output

1000

16.7 1000

2000

7. Simultaneous Decisions: Cold-Turkey Policies

This section deals with competition between the European central bank, the American central bank, the German labour union, and the French labour union. We assume that the central banks and the labour unions decide simultaneously and independently. In step 1 the European central bank, the American central bank, the German labour union, and the French labour union 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 labour union, and the French labour union decide simultaneously and independently. In step 4 there is an output lag. And so on. As a result, the simultaneous process of monetary and wage competition does not lead to full employment in Germany, France and America. Instead there are explosive oscillations in money supply, nominal wages, and output.

268

8. Simultaneous Decisions: Gradualist Policies

This section is concerned with competition between the European central bank, the American central bank, the German labour union, and the French labour union. At the beginning there is unemployment in Germany, France and America. Unemployment in Germany is high, and unemployment in France is low. 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 labour union is fiill employment in Germany. We assume that the German labour union follows a gradualist strategy. The specific target of the German labour union is to close the output gap in Germany by 20 percent. The general target of the French labour union is full employment in France. We assume that the French labour union follows a gradualist strategy. The specific target of the French labour union is to close the output gap in France by 20 percent. We assume that the central banks and the labour unions decide simultaneously and independently. In step 1 the European central bank, the American central bank, the German labour union, and the French labour union 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 labour union, and the French labour union decide simultaneously and independently. In step 4 there is an output lag. And so on. As a result, the gradualist process of monetary and wage competition leads to full employment in Germany, France and America. Now 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 34.3, the total increase in American money supply is

269 45, the total reduction in German nominal wages is 27.4, and the total increase in French nominal wages is 5.9.

9. Monetary Cooperation and Wage Competition

1) The model. At the start there is unemployment in Germany, France and America. Unemployment in Germany is high, and unemplojTnent 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 labour union is full employment in Germany. The instrument of the German labour union is German nominal wages. The target of the French labour union is full emplojonent in France. The instrument of the French labour union is French nominal wages. We assume that the central banks and the labour unions decide sequentially. First the central banks decide, then the labour unions decide. In step 1, the European central bank and the American central bank decide cooperatively. In step 2, the German labour union and the French labour union decide simultaneously and independently. In step 3, the European central bank and the American central bank decide cooperatively. In step 4, the German labour union and the French labour union 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. 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.

270 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 wage competition between Germany and France. The output gap in Germany is 15. The wage policy multiplier in Germany is -1.2. So what is needed in Germany is a reduction in German nominal wages of 12.5. The inflationary gap in France is 15. The wage policy multiplier in France is -1.2. So what is needed in France is an increase in French nominal wages of 12.5. Step 4 refers to the output lag. The reduction in German nominal wages of 12.5 causes an increase in German output of 15. As a side effect, it causes an increase in French output of 3.8 and a decline in American output of 6.3. The increase in French nominal wages of 12.5 causes a decline in French output of 15. As a side effect, it causes a decline in German output of 3.8 and an increase in American output of 6.3. The net effect is an increase in German output of 11.3, a decline in French output of equally 11.3, and a change in American output of zero. As a consequence, German output goes from 985 to 996.3, French output goes from 1015 to 1003.8, 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 996.3, French output stays at 1003.8, and American output stays at 2000. Step 7 refers to wage competition between Germany and France. The output gap in Germany is 3.8. The wage policy multiplier in Germany is -1.2. So what is needed in Germany is a reduction in German nominal wages of 3.1. The inflationary gap in France is 3.8. The wage policy multiplier in France is -1.2. So what is needed in France is an increase in French nominal wages of 3.1.

271 Step 8 refers to the output lag. The net effect is an increase in German output of 2.8, a decline in French output of equally 2.8, and a change in American output of zero. As a consequence, German output goes from 996.3 to 999.1, French output goes from 1003.8 to 1000.9, and American output stays at 2000. And so on. Table 8.9 presents a synopsis.

Table 8.9 Monetary Cooperation between Europe and America, Wage Competition between Germany and France Germany

Initial Output

940

A Money Supply Output

985

France

America

970

1910

45

45

1015

2000

A Nominal Wages

-12.5

12.5

Output

996.3

1003.8

A Nominal Wages

-3.1

3.1

Output

999.1

1000.9

2000

1000

2000

2000

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. As a result, the alternating process of monetary cooperation and wage competition leads to full employment in Germany, France and America. Taking the sum over all periods, the total increase in European money supply is 45, the total increase in American money supply is equally 45, the total reduction in German nominal wages is 16.7, and the total increase in French nominal wages is equally 16.7.

272

10. Monetary Cooperation and Wage Cooperation

1) The model. At the beginning there is unemployment in Germany, France and America. 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 wage cooperation are full employment in Germany and full employment in France. The instruments of wage cooperation are German nominal wages and French nominal wages. Under wage cooperation there are two targets and two instruments, so there is no degree of freedom. We assume that the central banks and the labour unions decide sequentially. First the central banks decide, then the labour unions decide. In step 1, the European central bank and the American central bank decide cooperatively. In step 2, the German labour union and the French labour union decide cooperatively. In step 3, the European central bank and the American central bank decide cooperatively. In step 4, the German labour union and the French labour union 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. 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

273

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 wage 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 a reduction in German nominal wages of 16.7 and an increase in French nominal wages of equally 16.7. Step 4 refers to the output lag. The reduction in German nominal wages of 16.7 raises German output by 20 and French output by 5. As a side effect, it lowers American output by 8.3. The increase in French nominal wages of 16.7 lowers French output by 20 and German output by 5. As a side effect, it raises American output by 8.3. 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. Table 8.10 gives an overview.

Table 8.10 Monetary Cooperation between Europe and America, Wage Cooperation between Germany and France

Initial Output

Germany

France

America

940

970

1910

45

45

1015

2000

A Money Supply Output

985

A Nominal Wages

-16.7

Output

1000

16.7 1000

2000

As a result, the sequential process of monetary cooperation and wage cooperation leads to frill employment in Germany, France and America. Now compare the sequential process of monetary cooperation and wage cooperation

274 with the simultaneous process of monetary and wage cooperation, see Section 6. Monetary and wage cooperation is a fast process. And much the same applies to monetary cooperation and wage cooperation. Judging from this perspective, there seems to be no need for fiiU cooperation between the European central bank, the American central bank, the German labour union, and the French labour union.

11. Rational Policy Expectations

1) Monetary and wage competition: sequential decisions. At the start there is unemployment in Germany, France and America. More precisely, unemployment in Germany is high, and unemployment in France is low. 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 labour union is full employment in Germany. The instrument of the German labour union is German nominal wages. The target of the French labour union is full employment in France. The instrument of the French labour union is French nominal wages. We assume that the central banks and the labour unions decide sequentially. First the central banks decide, then the labour unions decide. In step 1, the European central bank and the American central bank decide simultaneously and independently. In step 2, the German labour union and the French labour union 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 labour union and the French labour union 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

275 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 emplojonent in Europe and America. However, it does not lead to full employment in Germany and France. Next have a closer look at step 2. The German labour union and the French labour union decide simultaneously and independently. The German labour union sets German nominal wages, forming rational expectations of French nominal wages. And the French labour union sets French nominal wages, forming rational expectations of German nominal wages. That is to say, the German labour union sets German nominal wages, predicting French nominal wages with the help of the model. And the French labour union sets French nominal wages, predicting German nominal wages with the help of the model. As a result, there is an immediate equilibrium of wage competition between Germany and France. In other words, wage 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 wage competition: simultaneous decisions. At the beginning 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 labour union is full employment in Germany. And the target of the French labour union is full employment in France. We assume that the European central bank, the American central bank, the German labour union, and the French labour union decide simultaneously and independently. The European central bank sets European money supply, forming rational expectations of American money supply, German nominal wages, and French nominal wages. The American central bank sets American money supply.

276 forming rational expectations of European money supply, German nominal wages, and French nominal wages. The German labour union sets German nominal wages, forming rational expectations of European money supply, American money supply, and French nominal wages. And the French labour union sets French nominal wages, forming rational expectations of European money supply, American money supply, and German nominal wages. That is to say, the European central bank sets European money supply, predicting American money supply, German nominal wages, and French nominal wages with the help of the model. The American central bank sets American money supply, predicting European money supply, German nominal wages, and French nominal wages with the help of the model. The German labour union sets German nominal wages, predicting European money supply, American money supply, and French nominal wages with the help of the model. And the French labour union sets French nominal wages, predicting European money supply, American money supply, and German nominal wages with the help of the model. As a result, there is no unique equilibrium of monetary and wage competition. Put another way, the simultaneous process of monetary and wage competition does not lead to full employment in Germany, France and America.

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. This section deals with competition between the European central bank and the American central bank. 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 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

278 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. 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-emplo5TTient 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 unemploj^ment 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 fiill 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 fiill employment in Germany and France. And what is more, it does not lead to price stability in Germany and France.

279

2. Monetary Cooperation between Europe and America

1) The model. This section deals with cooperation between the European central bank and the American central bank. At the beginning there is unemployment in Germany, France and America. To be more specific, 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. 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 unemplo5mient 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 unemplojmient 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.

280

3. Wage Competition between Germany and France

1) The static model. An increase in German nominal wages lowers German output. And what is more, it lowers French output. On the other hand, it raises American output. Here the fall in German output is larger than the fall in French output. And the fall in European output is larger than the rise in American output. Correspondingly, an increase in French nominal wages lowers French output. And what is more, it lowers German output. On the other hand, it raises American output. Here the fall in French output is larger than the fall in German output. And the fall in European output is larger than the rise in American output. In the numerical example, an increase in German nominal wages of 100 causes a decline in German output of 120, a decline in French output of 30, and an increase in American output of 50. Likewise, an increase in French nominal wages of 100 causes a decline in French output of 120, a decline in German output of 30, and an increase in American output of 50. 2) The dynamic model. This section deals with competition between the German labour union and the French labour union. At the beginning there is unemployment in Germany and France. More precisely, unemployment in Germany is high, and unemployment in France is low. By contrast there is full employment in America. The target of the German labour union is full employment in Germany. The instrument of the German labour union is German nominal wages. The German labour union lowers German nominal wages so as to close the output gap in Germany. The target of the French labour union is full emplojmient in France. The instrument of the French labour union is French nominal wages. The French labour union lowers French nominal wages so as to close the output gap in France. We assume that the German labour union and the French labour union decide simultaneously and independently. In addition there is an output lag. As a result, the process of wage 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

281 be 970, and let initial output in America be 2000. In Germany and France there is unemployment, but in America there is full employment. Step 1 refers to the policy response. What is needed in Germany is a reduction German nominal wages of 50. And what is needed in France is a reduction in French nominal wages of 25. Step 2 refers to the output lag. The total effect is an increase in German output of 67.5, an increase in French output of 45, and a decline in American output of 37.5. As a consequence, German output goes to 1007.5, French output goes to 1015, and American output goes to 1962.5. In step 3, German nominal wages are raised by 6.3, and French nominal wages are raised by 12.5. In step 4, German output goes to 996.3, French output goes to 998.1, and American output goes to 1971.9. And so on. In the steady state, German output is 1000, French output is equally 1000, and American output is 1970. In Germany and France there is full employment. But in America there is unemployment. As a result, competition between the German labour union and the French labour union leads to full employment in Germany and France. However, as an adverse side effect, it causes unemployment in America.

4. Wage Cooperation between Germany and France

1) The model. This section deals with cooperation between the German labour union and the French labour union. At the beginning there is unemployment in Germany and France. To be more specific, unemployment in Germany is high, and unemployment in France is low. By contrast there is full employment in America. The targets of wage cooperation are full employment in Germany and full employment in France. The instruments of wage cooperation are German nominal wages and French nominal wages. So there are two targets and two instruments. As a result, there is a solution the wage cooperation.

282

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 and France there is unemployment, but in America there is full employment. What is needed is a reduction in German nominal wages of 46.7 and a reduction in French nominal wages of 13.3. 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 equally 30. As a consequence, German output goes to 1000, French output goes to 1000, and American output goes to 1970. In Germany and France there is now full employment. But in America there is now unemployment. As a result, cooperation between the German labour union and the French labour union can achieve full employment in Germany and France. However, as an adverse side effect, it causes unemplojonent in America. 3) Comparing wage cooperation with wage competition. Wage competition is a slow process. By contrast, wage cooperation is a fast process. Wage competition can cause oscillations in nominal wages and output. By contrast, wage cooperation cannot cause oscillations in nominal wages and output. Judging from this perspective, wage cooperation seems to be superior to wage competition.

5. Monetary and Wage Competition

1) The model. This section deals with competition between the European central bank, the American central bank, the German labour union, and the French labour union. 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 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 labour union is full employment in Germany. The instrument of the German labour union is German nominal wages. The target

283

of the French labour union is full emplojmient in France. The instrument of the French labour union is French nominal wages. We assume that the central banks and the labour unions decide sequentially. First the central banks decide, then the labour unions decide. In step 1, the European central bank and the American central bank decide simultaneously and independently. In step 2, the German labour union and the French labour union 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 labour union and the French labour union 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. Step 1 refers to monetary policy in Europe and America. 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. Step 3 refers to wage policy in Germany and France. What is needed in Germany is a reduction in German nominal wages of 25. And what is needed in France is no change in French nominal wages. Step 4 refers to the output lag. There is an increase in German output of 30, an increase in French output of 7.5, and a decline in American output of 12.5. As a consequence, German output goes to 1000, French output goes to 1007.5, and American output goes to 1957.5. In step 5, European money supply is lowered by 2.5, and American money supply is raised by 14.2. In step 6, German output goes to 989.2, French output goes to 996.7, and American output goes to 2002.5. In step 7, German nominal wages are lowered by 9.0, and French nominal wages are lowered by 2.8. In step 8, German output goes to 1000.8, French output goes to 1002.7, and American output goes to 1996.6. 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

284 countries there is full employment. As a result, the process of monetary and wage competition leads to full employment in Germany, France and America.

6. Monetary and Wage Cooperation

1) The model. This section deals with cooperation between the European central bank, the American central bank, the German labour union, and the French labour union. At the beginning there is unemplo5anent in Germany, France and America. The targets of policy cooperation are fiill employment in Germany, full emplo)Tnent in France, and full employment in America. The instruments of policy cooperation are European money supply, American money supply, German nominal wages, and French nominal wages. 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. What is needed, for instance, is an increase in European money supply of 45, an increase in American money supply of equally 45, a reduction in German nominal wages of 16.7, and an increase in French nominal wages of equally 16.7. 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. As a result, monetary and wage cooperation can achieve full employment in Germany, France and America. 3) Comparing policy cooperation with policy competition. Policy competition is a process of intermediate speed. By contrast, policy cooperation is a fast process. Policy competition causes a reduction in European nominal wages. By contrast, policy cooperation causes no change in European nominal wages. Therefore, policy cooperation seems to be superior to policy competition.

Symbols

A B C F G I L M N P Q

w X Y Y

a b c d e g h k m q r t X

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

labour productivity parameter of investment function (marginal) consumption rate differential exchange rate markup factor price sensitivity of exports parameter of money demand function (marginal) import rate (marginal) import rate interest rate time initial share of exports in output

286 a (3 e ri X 1^ V

monetary policy multiplier (direct effect) monetary policy multiplier (cross effect) interest elasticity of investment interest elasticity of money demand wage policy multiplier (direct effect) wage policy multiplier (cross effect) wage policy multiplier (cross effect)

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 (2006). 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 decline 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

288 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. Sauemheimer (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 portfolio 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, ARTIS, M., eds., EMU, Four Years On, in: Oxford Review of Economic Policy 19:1, 2003

289 BEETSMA, R., et al., eds., Monetary Policy, Fiscal Policies and Labour Markets, Cambridge 2004 BEGG, D., CANOVA, F., DE GRAUWE, P., FATAS, A., LANE, P., Surviving the Slowdown, London 2002 BEGG, I., ed., Europe: Government and Money: Running EMU: The Challenges of Policy Coordination, London 2002 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 Policy 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 NECK, R., ed.. The Macroeconomics of EMU, in: Open Economies Review 13:4, 2002 POSEN, A. S., ed.. The Euro at Five: Ready for a Global Role?, Washington 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, 2006). 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 fimctions. 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 powerfial. 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

291 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 policy 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 carefiilly 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 policy 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 policy are negative while the spillover effects of fiscal policy are positive. The policy targets are price stability and fiiU 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.

292 Volume eight (2006) further studies the interactions between monetary and fiscal policies in the euro area. It 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 policy 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. Further information about these books is given on the web-page: http://[email protected]

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Index

Adaptive policy expectations, 213, 219, 228 American money market, 37 American money supply, 57-58, 63, 72-76, 144, 152-155, 174, 178, 184-185, 196 Anticipation, 121, 176 Appreciation, 52, 70, 84, 94, 106, 119, 155, 185, 196, 206 Budget deficit, 63, 94, 100, 107, 120, 134, 155, 185, 196, 206 Cold-turkey policies, 139, 165 Comparing gradualist policies with cold-turkey policies, 175 Comparing monetary and wage competition with pure wage competition, 125 Comparing monetary and wage cooperation with monetary and wage competition, 134, 155, 159 Comparing monetary and wage cooperation with pure wage cooperation, 136 Comparing monetary cooperation with monetary competition, 79 Comparing simultaneous decisions with sequential decisions, 169 Comparing the sequential process of monetary cooperation and wage cooperation with the sequential process of monetary cooperation and wage competition, 197 Comparing the sequential process of monetary cooperation and wage cooperation with the simultaneous process of monetary and wage cooperation, 196 Comparing the system of monetary cooperation and wage competition with the system of monetary and wage competition, 185, 191 Comparing wage cooperation with wage competition, 112 Competition between European central bank, American central bank, German labour union, and French labour union, 139, 165, 170, 176, 222, 231 Competition between European central bank, German labour union, and French labour union, 115 Competition between German labour union and French labour union, 83, 217 Cooperation between European central bank, American central bank, German labour union, and French labour union, 150

306 Cooperation between European central bank, German labour union, and French labour union, 130 Cooperation between German labour union and French labour union, 103 Coordination mechanism, type of, 175, 179, 185, 196, 206 Current account deficit, 94, 100, 106, 119, 134 Current account surplus, 94, 100, 106, 119, 134 Deflation in France, 67, 77 Deflation in Germany, 54, 63, 72, 75 Degrees of freedom, 130, 150, 180, 192 Depreciation, 52, 70, 84, 94, 106, 119, 155, 185, 196, 206 Dynamic characteristics, 63, 93, 119, 168, 173, 184, 195, 206 Dynamic model, 51,83, 115, 139, 165, 170, 176, 180, 192,202,211 Effective multipher, 63, 70, 94, 100 European money market, 36 European money supply, 57-58, 63, 72-76, 119-120, 131-134, 144, 152-155, 173, 178, 184-185, 195-196 European nominal wages, 99, 119-220, 133, 155, 185, 196 Expectations, adaptive, 213, 219, 228 Expectations, rational, 209 External effect of monetary policy, 52, 53, 59, 61 External effect of wage policy, 91, 92 Fast monetary competition, slow wage competition, 176 First the central bank decides, then the labour unions decide, 116, 141, 176 First the labour unions decide, then the central bank decides, 126 French nominal wages, 89-90, 93-94, 104-107, 119-120, 131-133, 152-155, 174, 178, 185, 196 Full employment in America, 54, 59, 72, 75, 144 Full employment in Europe, 54, 59, 72, 75 Full employment in France, 86, 91, 103, 104, 130 Full employment in Germany, 85, 91, 103, 104, 130 German nominal wages, 89-90, 93-94, 104-107, 119-120, 131-133, 152-155, 174, 178, 185, 196 Goods market, 13, 15, 33, 35

307 Gradualist policies, 170 High employment in Germany and France, 54, 116, 140 Inflation, 65, 77 Inflationary gap, 66, 100 Inflation in Europe and America, 65, 77 Inflation in France, 54, 63, 72, 75 Inflation in Germany, 67, 77 Instability, 168 Internal effect of monetary policy, 52, 53, 59, 61 Internal effect of wage policy, 91, 92 Market for American goods, 35 Market for European goods, 33 Market for French goods, 15 Market for German goods, 13 Model, 19, 39, 71, 103, 130, 150, 180, 192, 202 Model, basic, 13,27,33 Monetary and wage interactions, 113, 163 Monetary competition between Europe and America, 51,211 Monetary cooperation between Europe and America, 71 Monetary cooperation between Europe and America, wage competition between Germany and France, 180, 233 Monetary cooperation between Europe and America, wage cooperation between Germany and France, 192 Monetary interactions between Europe and America, 49 Monetary policy, 23, 43 Money market, 17, 36, 37 Money market of the union, 17 Money supply, see American money supply, European money supply Nominal wages, see French nominal wages, German nominal wages Numerical example, 59, 74, 91, 105, 117, 132, 141, 153, 182, 194, 204 Oscillations, 70, 93, 168 Outputgap, 54, 61,85, 92

308 Outputlag, 55, 61,86, 92 Output model, 71, 103, 130, 150 Overemployment, 147, 156, 187, 198 Overemployment in America, 124, 135 Overemployment in Europe, full employment in America, 122, 134 Overemployment in France, 54, 63, 71, 75 Overemployment in Germany, 67, 77 Overemployment in Germany and France, 100, 111 Policy cooperation within Europe, policy competition between Europe and America, 202, 238 Policy model, 72, 103, 131, 151 Price of European goods, 99, 119, 134, 155, 185, 196 Price ofFrench goods, 94,99, 119, 134, 155, 185 196 Price ofGerman goods, 95,99, 119, 134, 155, 185, 196 Price setting, 18, 37 Price stability in America, 59, 63, 72, 75 Price stability in Europe, 54, 59, 63, 72, 75 Rate-of-growth method, 21, 41 Rational policy expectations, 209 Sequential decisions, 116, 141, 176, 181, 193 Simultaneous decisions, 165, 170, 231 Small monetary union of two countries, 13 Speed of adjustment in money supply and wages, 174 Speed of monetary competition, 79 Speed of monetary and wage competition, 125, 134, 159 Speed of wage competition, 112, 125 Spillovers, see External effects Stability, 58, 90, 119, 144, 168, 173, 184, 195, 206 Static model, 51, 83, 115, 139, 180 Steady state, 56, 87, 119, 144, 168, 173, 184, 195, 206 Synopsis, 245 Target of American central bank, 54, 140 Target of European central bank, 54, 71, 116, 140

309 Target of French labour union, 86, 116, 141 Target of German labour union, 85, 116, 140 Targets of monetary and wage cooperation, 130, 136, 137, 150, 151, 159, 160 Targets of monetary cooperation, 72, 180, 192 Targets of wage cooperation, 103, 192 Technology, 18, 37 Unemployment, 60, 142, 153, 182, 195 Unemployment in America, 91, 93, 104, 106, 119 Unemployment in Europe and America, 64, 145, 155, 185, 197 Unemployment in Europe, full employment in America, 118, 132 Unemplojonent in Europe, inflation in America, 68, 78 Unemployment in Europe, overemployment in America, 158, 189, 200 Unemployment in France, 67, 77 Unemployment in Germany, 54, 63, 71, 75 Unemployment in Germany and France, 92, 95, 106, 107 UnemplojTnent in Germany, full employment in France, 97, 108 Unemployment in Germany, overemployment in France, 98, 109 Wage competition between Germany and France, 83, 217 Wage interactions between Germany and France, 81 Wage policy, 25, 45 Wage rate, see French nominal wages, German nominal wages World as a whole, 27 World of two monetary regions, 33

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