Macroeconomics of Monetary Union

Macroeconomics of Monetary Union

Michael Carlberg

Macroeconomics of Monetary Union With 90 Tables

Spriinger

Professor Dr. Michael Carlberg Helmut Schmidt University Federal University of Hamburg HolstenhofwegSs 22043 Hamburg Germany [email protected]

Library of Congress Control Number: 2007931040

ISBN 978-3-540-73632-5 Springer Berlin Heidelberg New York This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilm or in any other way, and storage in data banks. Duplication of this publication or parts thereof is permitted only under the provisions of the German Copyright Law of September 9,1965, in its current version, and permission for use must always be obtained from Springer. Violations are liable to prosecution under the German Copyright Law. Springer is a part of Springer Science+Business Media springer.com © Springer-Verlag Berlin Heidelberg 2007 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. Production: LE-T^K Jelonek, Schmidt & Vockler GbR, Leipzig Hardcover-Design: WMX Design GmbH, Heidelberg SPIN 12091058

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Preface

This book, unlike other books, provides readers with a practical yet sophisticated grasp of the macroeconomic principles necessary to understand a monetary union. By definition, a monetary union is a group of countries that share a common currency. The most important case in point is the euro area. Policy makers are the central bank, national governments, and national labour unions. Policy targets are price stability and full employment. Policy makers follow cold-turkey or gradualist strategies. Policy decisions are taken sequentially or simultaneously. The countries can differ in size or behaviour. Policy expectations are adaptive or rational. To illustrate all of this there are numerical simulations of monetary policy, fiscal policy, and wage policy. The present book is part of a larger research project on European Monetary Union, see the references given 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, at the Research Seminar on Economics in Kassel, 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, Helmut Frisch, Wilfried Fuhrmann, Franz X. Hof, Florence Huart, Oliver Landmann, Jay H. Levin, Alfred MauBner, Jochen Michaelis, Reinhard Neck, Manfred J. M. Neumann, Klaus Neusser, Franco Reither, Armin Rohde,

VI

Sergio Rossi, Gerhard Riibel, Michael Schmid, Gerhard Schwodiauer, Patrizio TirelH, Harald UhHg, Bas van Aarle, Uwe Vollmer, Jiirgen von Hagen and Helmut Wagner. In addition, Torsten Bleich, Ame Hansen and Mirko Hoppe 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. For ease of exposition we assume that the monetary union consists of two countries, say Germany and France. For ease of exposition we assume that unemployment causes deflation whereas overemployment causes inflation. At the beginning let there be unemployment and hence deflation. 2) Monetary policy in Europe can achieve full employment in Europe on average. And what is more, it can achieve price stability in Europe on average. However, monetary policy in Europe cannot achieve full employment in Germany and France. And what is more, it cannot achieve price stability in Germany and France. 3) Fiscal policies in Germany and France can achieve full employment and price stability in each of the countries. However, this requires a sharp increase in the European budget deficit. 4) Competition between the European central bank, the German government, and the French government leads to full employment and price stability in each of the countries. And what is more, it causes a decline in the European budget deficit. So monetary and fiscal competition is superior to both pure monetary policy and pure fiscal policy. 5) Cooperation between the European central bank, the German government, and the French government can achieve full employment and price stability in each of the countries. Now compare policy cooperation with policy competition. Policy competition is a slow process consisting of four steps. By contrast, policy cooperation is a fast process consisting of only two steps. Policy competition causes some overshooting in output. By contrast, policy cooperation does not cause any overshooting in output. From this point of view, policy cooperation seems to be superior to policy competition.

VIII 6) Wage policies in Germany and France can achieve full employment in each of the countries. However, this requires a deep cut in European nominal wages. 7) Competition between the European central bank, the German labour union, and the French labour union leads to full employment in each of the countries. And what is more, it does not require any cut in European nominal wages. So monetary and wage competition is superior to both pure monetary policy and pure wage policy. 8) Cooperation between the European central bank, the German labour union, and the French labour union can achieve full employment in each of the countries. Now compare policy cooperation with policy competition. Policy competition is a slow process consisting of four steps. By contrast, policy cooperation is a fast process consisting of only two steps. Policy competition causes some overshooting in output. By contrast, policy cooperation does not cause any overshooting in output. From this perspective, policy cooperation seems to be superior to policy competition.

Contents in Brief

Introduction

l

Part One. Monetary and Fiscal Policies: Basic Models

9

Chapter l.Monetary Policy in Europe

11

Chapter 2. Fiscal Policies in Germany and France Chapter 3. Competition between European Central Bank, German Government, and French Government Chapter 4. Cooperation between European Central Bank, German Government, and French Government

23 29 42

Part Two. Monetary and Fiscal Policies: Intermediate Models

53

Chapter 1. Simultaneous Decisions: Cold-Turkey Policies Chapter 2. Simultaneous Decisions: Gradualist Policies Chapter 3. Fiscal Shocks in Germany Chapter 4. The Countries Differ in Size Chapter 5. The Countries Differ in Behaviour Chapter 6. Rational Policy Expectations

55 60 65 69 78 87

Part Three. Monetary and Fiscal Policies: The Case of Three Countries

89

Chapter 1. Monetary Policy in Europe Chapter 2. Fiscal Policies in Germany, France and Italy Chapter 3. Monetary and Fiscal Competition Chapter 4. Monetary and Fiscal Cooperation

91 98 103 110

X

Part Four. Monetary and Wage Policies: Basic Models Chapter 1. Wage Policies in Germany and France Chapter 2. Competition between European Central Bank, German Labour Union, and French Labour Union Chapter 3. Cooperation between European Central Bank, German Labour Union, and French Labour Union

117 119 125 138

Part Five. Monetary and Wage Policies: Intermediate Models

149

Chapter 1. Simultaneous Decisions: Cold-Turkey Policies Chapter 2. Simultaneous Decisions: Gradualist Policies Chapter 3. Wage Shocks in Germany Chapter 4. The Countries Differ in Size Chapter 5. The Countries Differ in Behaviour Chapter 6. Rational Policy Expectations

151 155 160 164 169 176

Part Six. Monetary and Wage Policies: The Case of Three Countries

179

Chapter 1. Wage Policies in Germany, France and Italy Chapter 2. Monetary and Wage Competition Chapter 3. Monetary and Wage Cooperation

181 186 193

Part Seven. Monetary, Fiscal and Wage Policies

199

Synopsis Conclusion Result References Index

221 229 253 269 281

Contents

Introduction

l

1. 2. 3. 4. 5. 6. 7. 8.

1 2 3 4 5 6 7 8

Subject and Approach Monetary Policy in Europe Fiscal Policies in Germany and France Monetary and Fiscal Competition Monetary and Fiscal Cooperation Wage Policies in Germany and France Monetary and Wage Competition Monetary and Wage Cooperation

Part One. Monetary and Fiscal Policies: Basic Models

9

Chapter 1. Monetary Policy in Europe 1. The Model 2. Some Numerical Examples

11 11 14

Chapter 2. Fiscal Policies in Germany and France 1. The Model 2. Some Numerical Examples

23 23 26

Chapter 3. Competition between European Central Bank, German Government, and French Government 1. The Dynamic Model 2. Some Numerical Examples

29 29 32

Chapter 4. Cooperation between European Central Bank, German Government, and French Government 1. The Model 2. Some Numerical Examples

42 42 44

XII

Part Two. Monetary and Fiscal Policies: Intermediate Models

53

Chapter 1. Simultaneous Decisions: Cold-Turkey Policies Chapter 2. Simultaneous Decisions: Gradualist Policies Chapter 3. Fiscal Shocks in Germany Chapter 4. The Countries Differ in Size 1. Monetary Policy in Europe 2. Fiscal Policies in Germany and France 3. Monetary and Fiscal Competition

55 60 65 69 69 73 76

Chapter 5. The Countries Differ in Behaviour 1. Monetary Policy in Europe 2. Fiscal Policies in Germany and France 3. Monetary and Fiscal Competition 4. Monetary and Fiscal Cooperation

78 78 80 83 85

Chapter 6. Rational Policy Expectations

87

Part Three. Monetary and Fiscal Policies: The Case of Three Countries

89

Chapter 1. Monetary Policy in Europe 1. The Model 2. Some Numerical Examples

91 91 94

Chapter 2. Fiscal Policies in Germany, France and Italy 1. Introduction 2. The Policy Model 3. Another Version of the Policy Model 4. A Numerical Example

98 98 98 99 100

XIII Chapter 3. Monetary and Fiscal Competition 1. The Static Model 2. The Dynamic Model 3. A Numerical Example: The Case of Unemployment 4. A Numerical Example: The Case of Inflation

103 103 103 105 108

Chapter 4. Monetary and Fiscal Cooperation 1. Introduction 2. The Policy Model 3. A Numerical Example: The Case of Unemployment 4. A Numerical Example: The Case of Inflation

110 110 110 112 114

Part Four. Monetary and Wage Policies: Basic Models

117

Chapter 1. Wage Policies in Germany and France 1. The Model 2. Some Numerical Examples

119 119 121

Chapter 2. Competition between European Central Bank, German Labour Union, and French Labour Union 1. The Dynamic Model 2. Some Numerical Examples

125 125 128

Chapter 3. Cooperation between European Central Bank, German Labour Union, and French Labour Union 1. The Model 2. Some Numerical Examples

138 138 140

XIV

Part Five. Monetary and Wage Policies: Intermediate Models

149

Chapter 1. Simultaneous Decisions: Cold-Turkey Policies Chapter 2. Simultaneous Decisions: Gradualist Policies Chapter 3. Wage Shocks in Germany Chapter 4. The Countries Differ in Size 1. Wage Policies in Germany and France 2. Monetary and Wage Competition

151 155 160 164 164 167

Chapter 5. The Countries Differ in Behaviour 1. Wage Policies in Germany and France 2. Monetary and Wage Competition 3. Monetary and Wage Cooperation

169 169 171 173

Chapter 6. Rational Policy Expectations

176

Part Six. Monetary and Wage Policies: The Case of Three Countries

179

Chapter 1. Wage Policies in Germany, France and Italy 1. Introduction 2. The Policy Model 3. Another Version of the Policy Model 4. A Numerical Example

181 181 182 182 183

Chapter 2. Monetary and Wage Competition 1. The Static Model 2. The Dynamic Model 3. A Numerical Example: The Case of Unemployment 4. A Numerical Example: The Case of Overemployment

186 186 186 188 191

Chapter 3. Monetary and Wage Cooperation 1. Introduction 2. The Policy Model

193 193 193

XV 3. A Numerical Example: The Case of Unemployment 4. A Numerical Example: The Case of Overemployment

195 197

Part Seven, Monetary, Fiscal and Wage Policies

199

1. The Government Closes the Output Gap by 100 Percent, the Labour Union Closes the Output Gap by 100 Percent 2. The Government Closes the Output Gap by 40 Percent, the Labour Union Closes the Output Gap by 40 Percent 3. The Government Closes the Output Gap by 20 Percent, the Labour Union Closes the Output Gap by 60 Percent 4. The Government Closes the Output Gap by 60 Percent, the Labour Union Closes the Output Gap by 60 Percent 5. The Government Closes the Output Gap by 40 Percent, the Labour Union Closes the Output Gap by 80 Percent

202 206 209 213 216

Synopsis

221

1. Monetary and Fiscal Policies 2. Monetary and Wage Policies

221 225

Conclusion

229

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

Monetary Policy in Europe Fiscal Policies in Germany and France Monetary and Fiscal Competition Monetary and Fiscal Cooperation Wage Policies in Germany and France Monetary and Wage Competition Monetary and Wage Cooperation

229 232 234 238 242 244 249

Result 1. Monetary Policy in Europe 2. Fiscal Policies in Germany and France 3. Monetary and Fiscal Competition 4. Monetary and Fiscal Cooperation

253 253 255 256 258

XVI Symbols

261

A Brief Survey of the Literature

263

Tlie Current Researcli Project

266

References

269

Index

281

Introduction 1. Subject and Approach

This book studies macroeconomic policies in a monetary union. 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 German government, and the French government. With respect to policy cooperation, the focus is on cooperation between the European central bank, the German government, and the French government. Further topics are: - sequential decisions versus simultaneous decisions - cold-turkey policies versus gradualist policies - fiscal shocks in Germany - the countries differ in size - the countries differ in behaviour - rational policy expectations. The targets of the European central bank are price stability and full employment in Europe. The target of the German government is full employment in Germany. And the target of the French government is full employment in France. 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? Special features of this book are numerical simulations of policy competition and numerical solutions to policy cooperation. To illustrate all of this there are a lot of tables. This book consists of seven major parts: - Monetary and Fiscal Policies: Basic Models

- Monetary and Fiscal Policies: Intermediate Models - Monetary and Fiscal Policies: The Case of Three Countries - Monetary and Wage Policies: Basic Models - Monetary and Wage Policies: Intermediate Models - Monetary and Wage Policies: The Case of Three Countries - Monetary, Fiscal and Wage Policies. The approach will now be presented in greater detail.

2. Monetary Policy in Europe

1) Introduction. For ease of exposition we make the following assumptions. The monetary union consists of two countries, say Germany and France. The member 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. In the numerical example, an increase in European money supply of 100 causes an increase in German output of 100 and an increase in French output of equally 100. All of these assumptions will be relaxed below. 2) The policy model. At the beginning there is unemployment in Germany and France. 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 full employment in Europe. For ease of exposition we assume that unemployment causes deflation whereas overemployment causes inflation. The specific target of the European central bank is that unemployment in Germany equals overemployment in France. Accordingly, the specific target of the

European central bank is that deflation in Germany equals inflation in France. In other words, the specific target of the European central bank is full employment in Europe on average. Accordingly, the specific target of the European central bank is price stability in Europe on average. 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 key questions are: Can monetary policy in Europe achieve full employment and price stability in Europe as a whole? And what is more, can monetary policy in Europe achieve fiill employment and price stability in each of the member countries? What is the required increase in European money supply? And what is the effect on the European budget deficit?

3. Fiscal Policies in Germany and France

1) Introduction. An increase in German government purchases raises German output. Correspondingly, an increase in French government purchases raises French output. For ease of exposition we assume that fiscal policy in one of the countries has no effect on output in the other country. In the numerical example, an increase in German government purchases of 100 causes an increase in German output of 100. Correspondingly, an increase in French government purchases of 100 causes an increase in French output of 100. 2) The policy model. At the start there is unemployment in Germany and France. More precisely, unemployment in Germany is high, and unemployment in France is low. The target of the German government is full employment in Germany. The instrument of the German government is German government purchases. The German government raises German government purchases so as to close the output gap in Germany. The target of the French government is full employment in France. The instrument of the French government is French government purchases. The French government raises French government purchases so as to close the output gap in France.

Here the key questions are: Can fiscal policies in Germany and France achieve full employment and price stability in each of the countries? What is the required increase in German government purchases? What is the required increase in French government purchases? And what is the effect on the European budget deficit? Over and above that, how do fiscal policies in Germany and France compare with monetary policy in Europe?

4. Monetary and Fiscal Competition

This section deals with competition between the European central bank, the German government, and the French government. At the beginning there is unemployment in Germany and France. 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 full employment in Europe. For ease of exposition we assume that unemployment causes deflation whereas overemployment causes inflation. The specific target of the European central bank is that unemployment in Germany equals overemployment in France. Accordingly, the specific target of the European central bank is that deflation in Germany equals inflation in France. In other words, the specific target of the European central bank is full employment in Europe on average. Accordingly, the specific target of the European central bank is price stability in Europe on average. 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 government is full employment in Germany. The instrument of the German government is German government purchases. The German government raises German government purchases so as to close the output gap in Germany. The target of the French government is full employment in France. The instrument of the French government is French government

purchases. The French government raises French government purchases so as to close the output gap in France. We assume that the central bank and the governments decide sequentially. First the central bank decides, then the governments decide. Step 1 refers to monetary policy in Europe. Step 2 refers to the output lag. Step 3 refers to fiscal policies in Germany and France. And step 4 refers to the output lag. The key questions are: Does the process of monetary and fiscal competition lead to full employment and price stability in each of the countries? What are the dynamic characteristics of this process? What is the change in European money supply? What is the change in German government purchases? And what is the change in French government purchases? Is the system of monetary and fiscal competition superior to monetary policy in Europe? And is the system of monetary and fiscal competition superior to fiscal policies in Germany and France?

5. Monetary and Fiscal Cooperation

This section deals with cooperation between the European central bank, the German government, and the French government. At the start there is unemployment in Germany and France. Let unemployment in Germany be high, and let unemployment in France be low. The targets of policy cooperation are full employment in Germany and full employment in France. The instruments of policy cooperation are European money supply, German government purchases, and French government purchases. There are two targets and three instruments, so there is one degree of freedom. Here the key questions are: Can monetary and fiscal cooperation achieve full employment and price stability in each of the countries? What is the required change in European money supply? What is the required change in German government purchases? And what is the required change in French government

purchases? Finally, is the system of monetary and fiscal cooperation superior to the system of monetary and fiscal competition?

6. Wage Policies in Germany and France

1) Introduction. An increase in German nominal wages lowers German output. Correspondingly, an increase in French nominal wages lowers French output. For ease of exposition we assume that wage policy in one of the countries has no effect on output in the other country. In the numerical example, an increase in German nominal wages of 100 causes a decline in German output of 100. Correspondingly, an increase in French nominal wages of 100 causes a decline in French output of 100. For ease of exposition we assume that the wage policy multiplier is 1. This assumption is consistent since the wage rate is defined in nominal terms while output is defined in real terms. 2) The policy model. At the beginning there is unemployment in Germany and France. More precisely, unemployment in Germany is high, and unemployment in France is low. 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. The key questions are: Can wage policies in Germany and France achieve full employment in Germany and France? What is the required cut in German nominal wages? What is the required cut in French nominal wages? And what is the effect on the European budget deficit? Over and above that, how do wage policies in Germany and France compare with monetary policy in Europe?

7. Monetary and Wage Competition

This section deals with competition between the European central bank, 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. The primary target of the European central bank is price stability in Europe. The secondary target of the European central bank is full employment in Europe. The specific target of the European central bank is that unemployment in Germany equals overemployment in France. In other words, the specific target of the European central bank is full employment in Europe on average. 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 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 bank and the labour unions decide sequentially. First the central bank decides, then the labour unions decide. Step 1 refers to monetary policy in Europe. Step 2 refers to the output lag. Step 3 refers to wage policies in Germany and France. And step 4 refers to the output lag. The key questions are: Does the process of monetary and wage competition lead to full employment in Germany and France? What are the dynamic characteristics of this process? What is the change in European money supply? What is the change in German nominal wages? And what is the change in French nominal wages? Is the system of monetary and wage competition superior to monetary policy in Europe? And is the system of monetary and wage competition superior to wage policies in Germany and France?

8. Monetary and Wage Cooperation

This section deals with cooperation between the European central bank, the German labour union, and the French labour union. At the start there is unemployment in Germany and France. Let unemployment in Germany be high, and let unemployment in France be low. 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. Here the key questions are: Can monetary and wage cooperation achieve full employment in Germany and France? What is the required change in European money supply? What is the required change in German nominal wages? And what is the required change in French nominal wages? Finally, is the system of monetary and wage cooperation superior to the system of monetary and wage competition?

Part One Monetary and Fiscal Policies Basic Models

Chapter 1 Monetary Policy in Europe 1. The Model

1) Introduction. For ease of exposition we make the following assumptions. The monetary union consists of two countries, say Germany and France. The member 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. In the numerical example, an increase in European money supply of 100 causes an increase in German output of 100 and an increase in French output of equally 100. All of these assumptions will be relaxed in Parts Two and Three. The output model can be represented by a system of two equations: Yj=Ai+aM

(1)

Y2=A2+aM

(2)

Of course this is a reduced form. Y^ denotes German output, Y2 is French output, M is European money supply, a is the monetary policy multiplier, A^ is some other factors bearing on German output, and A2 is some other factors bearing on French output. The endogenous variables are German output and French output. According to equation (1), German output is a positive function of European money supply. And according to equation (2), French output is a positive function of European money supply. An increase in European money supply of 1 causes an increase in German output of a and an increase in French output of equally a . The output model can be compressed to a single equation: Y=A+2aM

(3)

12 Here we have Y= Y^ + Y2 and A= A^ + A2. Y denotes European output, M is European money supply, 2 a is the monetary policy multiplier in Europe, and A is some other factors bearing on European output. The endogenous variable is European output. According to equation (3), European output is a positive function of European money supply. An increase in European money supply of 1 causes an increase in European output of 2 a . 2) The policy model. At the beginning there is unemployment in Germany and France. 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 full employment in Europe. For ease of exposition we assume that unemployment causes deflation whereas overemployment causes inflation. The specific target of the European central bank is that unemployment in Germany equals overemployment in France. Accordingly, the specific target of the European central bank is that deflation in Germany equals inflation in France. In other words, the specific target of the European central bank is full employment in Europe on average. Accordingly, the specific target of the European central bank is price stability in Europe on average. 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. Now have a closer look at the policy model. The specific target of the European central bank is full employment in Europe on average: Y^ + Y^ = %^%

(4)

Here Y^ denotes target output in Germany, Y2 is target output in France, Y^ is full-employment output in Germany, and Y2 is full-employment output in France. According to equation (4), target output in Europe should be equal to full-employment output in Europe. What is the required level of European money supply? To answer this question, eliminate Y^ and Y2 in equation (4) by means of equations (1) and (2) and solve for M:

13 M = ^i + ^2 Ai 2a

A,

Obviously, the required level of European money supply depends on fullemployment output in Europe, the monetary policy multiplier in Europe, and some other factors bearing on European output. Then substitute equation (5) into equations (1) and (2) and rearrange terms: Y,.Y,.A,-A,

^^j

VVVtA,

pj

Equation (6) shows target output in Germany, and equation (7) shows target output in France. As a result, monetary policy in Europe can achieve full employment in Europe on average. And what is more, it can achieve price stability in Europe on average. However, monetary policy in Europe cannot achieve full employment in Germany and France. And what is more, it cannot achieve price stability in Germany and France. 3) Another version of the policy model. As an alternative, the policy model can be stated in terms of the initial output gap and the required increase in money supply. The European central bank raises European money supply so as to close the output gap in Europe: AY+AY, AM = — i ^ 2a

(8)

Here AM denotes the required increase in European money supply, AY^ is the initial output gap in Germany, AY2 is the initial output gap in France, AY^ + AY2 is the initial output gap in Europe, and 2a is the monetary policy multiplier in Europe. Evidently, the required increase in European money supply depends on

14 the initial output gap in Europe and the monetary policy multiplier in Europe. The larger the initial output gap in Europe, the larger is the required increase in European money supply. Here a comment is in place. The output gap is defined as the difference between full-employment output and actual output. For instance, let fullemployment output be 1000, and let actual output be 940. Then the output gap is 60. The other way round, the inflationary gap is defined as the difference between actual output and full-employment output. For instance, let actual output be 1030, and let full-employment output be 1000. Then the inflationary gap is 30.

2. Some Numerical Examples

To illustrate the policy model, have a look at some numerical examples. For ease of exposition, without loss of generality, assume a = 1. On this assumption, the output model can be written as follows: Yi=Ai+M

(1)

Y2=A2+M

(2)

The endogenous variables are German and French output. Obviously, an increase in European money supply of 100 causes an increase in German output of 100 and an increase in French output of equally 100. Further, let full-employment output in Germany be 1000, and let full-employment output in France be the same. The output model can be rewritten as follows: Y = A+2M

(3)

15 The endogenous variable is European output. Evidently, an increase in European money supply of 100 causes an increase in European output of 200. Fullemployment output in Europe is 2000. It proves useful to study six distinct cases: - the case of unemployment - the case of inflation - unemployment in Germany, inflation in France - unemployment in Germany equals unemployment in France - inflation in Germany equals inflation in France - unemployment in Germany equals overemployment in France. 1) The case of unemployment. Let initial output in Germany be 940, and let initial output in France be 970. In each of the countries there is unemployment and hence deflation. Strictly speaking, unemployment in Germany is above its equilibrium level. And the same holds for France. Strictly speaking, inflation in Germany is below 2 percent. And the same holds for France. 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 Europe is 90. In this situation, the specific target of the European central bank is that unemployment in Germany equals overemployment in France. Accordingly, the specific target of the European central bank is that deflation in Germany equals inflation in France. The output gap in Europe is 90. The monetary policy multiplier in Europe is 2. So what is needed in Europe is an increase in European money supply of 45. Step 2 refers to the output lag. The increase in European money supply of 45 causes an increase in German output of 45 and an increase in French output of equally 45. As a consequence, German output goes from 940 to 985, and French output goes from 970 to 1015. Table 1.1 presents a synopsis. In Germany there is still some unemployment and deflation. In France there is now some overemployment and inflation. And in Europe there is now full employment and price stability. Unemployment in Germany equals overemployment in France. And deflation in Germany equals inflation in France.

16 Table 1.1 Monetary Policy in Europe The Case of Unemployment

Initial Output

Germany

France

940

970

Change in Money Supply Output

45 985

1015

Strictly speaking, unemployment in Germany is above its equilibrium level. Unemployment in France is below its equilibrium level. And unemployment in Europe is exactly at its equilibrium level. Strictly speaking, inflation in Germany is below 2 percent. Inflation in France is above 2 percent. And inflation in Europe is at exactly 2 percent. As a result, monetary policy in Europe can achieve full employment in Europe on average. And what is more, it can achieve price stability in Europe on average. However, monetary policy in Europe cannot achieve full employment in Germany and France. And what is more, it cannot achieve price stability in Germany and France. There is an increase in German output, as there is in French output. There is an increase in German tax revenue, as there is in French tax revenue. And there is a decline in the German budget deficit, as there is in the French budget deficit. 2) The case of inflation. Let initial output in Germany be 1060, and let initial output in France be 1030. 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. Strictly speaking, inflation in Germany is above 2 percent. And the same holds for France. Step 1 refers to the policy response. The inflationary gap in Germany is 60, the inflationary gap in France is 30, and the inflationary gap in Europe is 90. In this situation, the specific target of the European central bank is that

17 overemployment in Germany equals unemployment in France. Accordingly, the specific target of the European central bank is that inflation in Germany equals deflation in France. The inflationary gap in Europe is 90. The monetary policy multiplier in Europe is 2. So what is needed in Europe is a reduction in European money supply of 45. Step 2 refers to the output lag. The reduction in European money supply of 45 causes a decline in German output of 45 and a decline in French output of equally 45. As a consequence, German output goes from 1060 to 1015, and French output goes from 1030 to 985. Table 1.2 gives an overview. In Germany there is still some overemployment and inflation. In France there is now some unemployment and deflation. And in Europe there is now full employment and price stability. Overemployment in Germany equals unemployment in France. And inflation in Germany equals deflation in France.

Table 1.2 Monetary Policy in Europe The Case of Inflation

Initial Output

Germany

France

1060

1030

Change in Money Supply Output

-45 1015

985

Strictly speaking, unemployment in Germany is below its equilibrium level. Unemployment in France is above its equilibrium level. And unemployment in Europe is exactly at its equilibrium level. Strictly speaking, inflation in Germany is above 2 percent. Inflation in France is below 2 percent. And inflation in Europe is at exactly 2 percent. As a result, monetary policy in Europe can achieve full employment and price stability in Europe as a whole. However, monetary policy in Europe cannot

18 achieve full employment and price stability in each of the member countries. There is a decline in German output, as there is in French output. There is a decline in German tax revenue, as there is in French tax revenue. And there is an increase in the German budget deficit, as there is in the French budget deficit. 3) Unemployment in Germany, inflation in France. Let initial output in Germany be 940, and let initial output in France be 1030. In Germany there is unemployment and deflation. In France there is overemployment and inflation. And in Europe there is unemployment and deflation. More precisely, unemployment in Germany is high, and overemployment in France is low. Correspondingly, deflation in Germany is high, and inflation in France is low. Step 1 refers to the policy response. The output gap in Germany is 60, the inflationary gap in France is 30, and the output gap in Europe is 30. The monetary policy multiplier in Europe is 2. So what is needed in Europe is an increase in European money supply of 15.

Table 1.3 Monetary Policy in Europe Unemployment in Germany, Inflation in France

Initial Output

Germany

France

940

1030

Change in Money Supply Output

15 955

1045

Step 2 refers to the output lag. The increase in European money supply of 15 raises German output and French output by 15 each. As a consequence, German output goes from 940 to 955, and French output goes from 1030 to 1045. Table 1.3 presents a synopsis. In Germany there is now some less unemployment and deflation. In France there is now some more overemployment and inflation. And in Europe there is now full employment and price stability. Unemployment in Germany equals overemployment in France. And deflation in Germany equals

19 inflation in France. As a result, monetary policy in Europe can achieve fall employment and price stability in Europe as a whole. However, monetary policy in Europe cannot achieve fall employment and price stability in each of the member countries. 4) Unemployment in Germany, inflation in France: another case. Let initial output in Germany be 970, and let initial output in France be 1060. In Germany there is unemployment and deflation. In France there is overemployment and inflation. And in Europe there is overemployment and inflation, too. More precisely, unemployment in Germany is low, and overemployment in France is high. Correspondingly, deflation in Germany is low, and inflation in France is high. Step 1 refers to the policy response. The output gap in Germany is 30, the inflationary gap in France is 60, and the inflationary gap in Europe is 30. The monetary policy multiplier in Europe is 2. So what is needed in Europe is a reduction in European money supply of 15.

Table 1.4 Monetary Policy in Europe Unemployment in Germany, Inflation in France

Initial Output

Germany

France

970

1060

Change in Money Supply Output

-15 955

1045

Step 2 refers to the output lag. The reduction in European money supply of 15 lowers German output and French output by 15 each. As a consequence, German output goes from 970 to 955, and French output goes from 1060 to 1045. Table 1.4 gives an overview. In Germany there is now some more unemployment and deflation. In France there is now some less overemployment and inflation. And in Europe there is now fall employment and price stability. Unemployment in Germany equals overemployment in France. And deflation in Germany equals

20 inflation in France. As a result, monetary policy in Europe can achieve full employment and price stability in Europe as a whole. However, monetary policy in Europe cannot achieve full employment and price stability in each of the member countries. 5) Unemployment in Germany equals unemployment in France. Let initial output in Germany be 970, and let initial output in France be the same. In each of the countries there is unemployment and deflation. Step 1 refers to the policy response. The output gap in Europe is 60. The monetary policy multiplier in Europe is 2. 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 raises German output and French output by 30 each. As a consequence, German output goes from 970 to 1000, as does French output. In each of the countries there is now full employment and price stability. As a result, in this special case, monetary policy in Europe can indeed achieve full employment and price stability in each of the member countries. Table 1.5 presents a synopsis.

Table 1.5 Monetary Policy in Europe Unemployment in Germany Equals Unemployment in France

Initial Output

Germany

France

970

970

Change in Money Supply Output

30 1000

1000

6) Inflation in Germany equals inflation in France. Let initial output in Germany be 1030, and let initial output in France be the same. In each of the countries there is overemployment and inflation. Step 1 refers to the policy response. The inflationary gap in Europe is 60. The monetary policy multiplier in Europe is 2. So what is needed in Europe is a reduction in European money

21 supply of 30. Step 2 refers to the output lag. The reduction in European money supply of 30 lowers German output and French output by 30 each. As a consequence, German output goes from 1030 to 1000, as does French output. In each of the countries there is now full employment and price stability. As a result, in this special case, monetary policy in Europe can indeed achieve full employment and price stability in each of the member countries. Table 1.6 gives an overview.

Table 1.6 Monetary Policy in Europe Inflation in Germany Equals Inflation in France

Initial Output

Germany

France

1030

1030

Change in Money Supply Output

-30 1000

1000

7) Unemployment in Germany equals overemployment in France. Let initial output in Germany be 970, and let initial output in France be 1030. In Germany there is unemployment and deflation. In France there is overemployment and inflation. And in Europe there is full employment and price stability. Step 1 refers to the policy response. The output gap in Europe is zero. So there is no reason for changing European money supply. Step 2 refers to the output lag. As a consequence, German output stays at 970, and French output stays at 1030. In Germany there is still unemployment and deflation. In France there is still overemployment and inflation. And in Europe there is still full employment and price stability. As a result, in this special case, monetary policy in Europe is ineffective. Table 1.7 presents a synopsis.

22

Table 1.7 Monetary Policy in Europe Unemployment in Germany Equals Overemployment in France

Initial Output

Germany

France

970

1030 0

Change in Money Supply Output

970

1030

Chapter 2 Fiscal Policies in Germany and France 1. The Model

1) Introduction. For ease of exposition we assume that the monetary union consists of two countries, say Germany and France. The member countries are the same size and have the same behavioural functions. An increase in German government purchases raises German output. Correspondingly, an increase in French government purchases raises French output. For ease of exposition we assume that fiscal policy in one of the countries has no effect on output in the other country. In the numerical example, an increase in German government purchases of 100 causes an increase in German output of 100. Correspondingly, an increase in French government purchases of 100 causes an increase in French output of 100. All of these assumptions will be relaxed in Parts Two and Three. The output model can be represented by a system of two equations: Yi=Ai+pGi

(1)

Y2=A2+pG2

(2)

Of course this is a reduced form. Yj denotes German output, Yj is French output, G| is German government purchases, G2 is French government purchases, P is the fiscal policy multiplier, A^ is some other factors bearing on German output, and A2 is some other factors bearing on French output. The endogenous variables are German output and French output. According to equation (1), German output is a positive function of German government purchases. And according to equation (2), French output is a positive function of French government purchases. An increase in German government purchases of 1 causes an increase in German output of p . And an increase in French government purchases of 1 causes an increase in French output of p .

24 2) The policy model. At the start there is unemployment in Germany and France. More precisely, unemployment in Germany is high, and unemployment in France is low. The target of the German government is full employment in Germany. The instrument of the German government is German government purchases. The German government raises German government purchases so as to close the output gap in Germany. The target of the French government is full employment in France. The instrument of the French government is French government purchases. The French government raises French government purchases so as to close the output gap in France. The policy model can be characterized by a system of two equations: Yi=Ai+pGi

(3)

Y2=A2+PG2

(4)

Here Yj denotes full-employment output in Germany, Y2 is full-employment output in France, Gj is the required level of German government purchases, and G2 is the required level of French government purchases. The endogenous variables are German government purchases and French government purchases. The solution to the policy model is:

G , = ^ ^

G2 = ^ ,

T

(5)

^

(6)

Equation (5) shows the required level of German government purchases. It depends on full-employment output in Germany, the fiscal policy multiplier in Germany, and some other factors bearing on German output. Equation (6) shows the required level of French government purchases. As a result, fiscal policies in Germany and France can achieve full employment in each of the countries. And what is more, they can achieve price

25 stability there. However, as a severe side effect, fiscal policies in Germany and France cause an increase in the European budget deficit. 3) Another version of the policy model. As an alternative, the policy model can be stated in terms of the initial output gap and the required increase in government purchases. The German government raises German government purchases so as to close the output gap in Germany:

4 0 , = ^ 1

p

(7) V y

Here AG^ denotes the required increase in German government purchases, AY^ is the initial output gap in Germany, and p is the fiscal policy multiplier in Germany. According to equation (7), the required increase in German government purchases depends on the initial output gap in Germany and on the fiscal policy multiplier in Germany. The larger the initial output gap in Germany, the larger is the required increase in German government purchases. Similarly, the French government raises French government purchases so as to close the output gap in France: AY2 AG2=^^

J

(8)

Here AG2 denotes the required increase in French government purchases, AY2 is the initial output gap in France, and P is the fiscal policy multiplier in France. According to equation (8), the required increase in French government purchases depends on the initial output gap in France and on the fiscal policy multiplier in France.

26

2. Some Numerical Examples

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

(1)

Y2=A2+G2

(2)

The endogenous variables are German and French output. Obviously, an increase in German government purchases of 100 causes an increase in German output of 100. Correspondingly, an increase in French government purchases of 100 causes an increase in French output of 100. Further, let full-employment output in Germany be 1000, and let full-employment output in France be the same. It proves useful to consider two distinct cases: - the case of unemployment - unemployment in Germany, overemployment in France. 1) The case of unemployment. Let initial output in Germany be 940, and let initial output in France be 970. In each of the countries there is unemployment and hence deflation. Step 1 refers to the policy response. The output gap in Germany is 60. The fiscal policy multiplier in Germany is 1. So what is needed in Germany is an increase in German government purchases of 60. The output gap in France is 30. The fiscal policy multiplier in France is 1. So what is needed in France is an increase in French government purchases of 30. Step 2 refers to the output lag. The increase in German government purchases of 60 causes an increase in German output of 60. And the increase in French government purchases of 30 causes an increase in French output of 30. As a consequence, German output goes from 940 to 1000, and French output goes from 970 to 1000. In each of the countries there is now full employment and price stability.

27 As a result, fiscal policies in Germany and France can achieve full employment and price stability in each of the countries. There is an increase in European government purchases, an increase in European output, and an increase in the European budget deficit. There is an increase in the interest rate and a decline in European investment. There is an appreciation of the euro, a decline in European exports, and a decline in the European current account surplus. Table 1.8 gives an overview.

Table 1.8 Fiscal Policies in Germany and France The Case of Unemployment

Initial Output Change in Government Purchases Output

Germany

France

940

970

60

30

1000

1000

2) Comparing fiscal policies with monetary policy. Monetary policy in Europe can achieve full employment and price stability in Europe as a whole. However, monetary policy in Europe cannot achieve full employment and price stability in each of the member countries. By contrast, fiscal policies in Germany and France can indeed achieve full employment and price stability in each of the member countries. However, as a severe side effect, fiscal policies in Germany and France cause an increase in the European budget deficit. 3) Unemployment in Germany, overemployment in France. Let initial output in Germany be 970, and let initial output in France be 1030. In Germany there is unemployment and deflation. In France there is overemployment and inflation. And in Europe there is full employment and price stability. Step 1 refers to the policy response. The output gap in Germany is 30. The fiscal policy multiplier in Germany is 1. So what is needed in Germany is an increase in German government purchases of 30. The inflationary gap in France is 30. The fiscal

28 policy multiplier in France is 1. So what is needed in France is a reduction in French government purchases of 30. Step 2 refers to the output lag. The increase in German government purchases of 30 raises German output by 30. And the reduction in French government purchases of 30 lowers French output by 30. As a consequence, German output goes from 970 to 1000, and French output goes from 1030 to 1000. In each of the countries there is now full employment and price stability. As a result, fiscal policies in Germany and France can achieve full employment and price stability in each of the countries. There is no change in European government purchases, no change in European output, and no change in the European budget deficit. There is no change in the interest rate and no change in European investment. There is no change in the price of the euro, no change in European exports, and no change in the European current account surplus. Table 1.9 presents a synopsis.

Table 1.9 Fiscal Policies in Germany and France Unemployment in Germany, Overemployment in France

Initial Output Change in Government Purchases Output

Germany

France

970

1030

30

-30

1000

1000

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

1) The static model. As a point of reference, consider the static model. It can be represented by a system of two equations: Y i = A i + a M + pGi

(1)

Y 2 = A 2 + a M + pG2

(2)

Of course this is a reduced form. Yj denotes German output, Y2 is French output, M is European money supply, Gj is German government purchases, G2 is French government purchases, A^ is some other factors bearing on German output, A2 is some other factors bearing on French output, a is the monetary policy multiplier, and P is the fiscal policy multiplier. The endogenous variables are German output and French output. According to equation (1), German output is a positive function of European money supply and a positive function of German government purchases. According to equation (2), French output is a positive function of European money supply and a positive function of French government purchases. An increase in European money supply raises both German output and French output. An increase in German government purchases raises German output. And an increase in French government purchases raises French output. An increase in European money supply of 1 causes an increase in German output of a and an increase in French output of equally a . An increase in German government purchases of 1 causes an increase in German output of P. And an increase in French government purchases of 1 causes an increase in French output of P. 2) The dynamic model. At the beginning there is unemployment in Germany and France. More precisely, unemployment in Germany is high, and un-

30 employment 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 full employment in Europe. For ease of exposition we assume that unemployment causes deflation whereas overemployment causes inflation. The specific target of the European central bank is that unemployment in Germany equals overemployment in France. Accordingly, the specific target of the European central bank is that deflation in Germany equals inflation in France. In other words, the specific target of the European central bank is full employment in Europe on average. Accordingly, the specific target of the European central bank is price stability in Europe on average. 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 government is full employment in Germany. The instrument of the German government is German government purchases. The German government raises German government purchases so as to close the output gap in Germany. The target of the French government is full employment in France. The instrument of the French government is French government purchases. The French government raises French government purchases so as to close the output gap in France. We assume that the central bank and the governments decide sequentially. First the central bank decides, then the governments decide. Step 1 refers to monetary policy in Europe. Step 2 refers to the output lag. Step 3 refers to fiscal policies in Germany and France. And step 4 refers to the output lag. Now have a closer look at the dynamic model. Step 1 refers to monetary policy in Europe. The European central bank raises European money supply so as to close the output gap in Europe:

AM = —^

^

(3)

2a Here AM denotes the required increase in European money supply, AY^ is the initial output gap in Germany, AY2 is the initial output gap in France, AY^+AY2 is the initial output gap in Europe, and 2a is the monetary policy multiplier in

31 Europe. According to equation (3), the required increase in European money supply depends on the initial output gap in Europe and on the monetary policy multiplier in Europe. The larger the initial output gap in Europe, the larger is the required increase in European money supply. Step 2 refers to the output lag. Step 3 refers to fiscal policies in Germany and France. The German government raises German government purchases so as to close the output gap in Germany:

1

p

V y

Here AGj denotes the required increase in German government purchases, AY^ is the initial output gap in Germany, and p is the fiscal policy multiplier in Germany. According to equation (4), the required increase in German government purchases depends on the initial output gap in Germany and on the fiscal policy multiplier in Germany. The larger the initial output gap in Germany, the larger is the required increase in German government purchases. Similarly, the French government raises French government purchases so as to close the output gap in France:

AG,=^^^

(5)

Here AG2 denotes the required increase in French government purchases, AY2 is the initial output gap in France, and P is the fiscal policy multiplier in France. According to equation (5), the required increase in French government purchases depends on the initial output gap in France and on the fiscal policy multiplier in France. Step 4 refers to the output lag. As a result, the process of competition between the European central bank, the German government, and the French government leads to full employment in Germany and France.

32

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 and P = 1. On this assumption, the static model can be written as follows: Y i = A i + M + Gi

(1)

Y2=A2+M4-G2

(2)

The endogenous variables are German and French output. Obviously, an increase in European money supply of 100 causes an increase in German output of 100 and an increase in French output of equally 100. An increase in German government purchases of 100 causes an increase in German output of 100. Correspondingly, an increase in French government purchases of 100 causes an increase in French output of 100. Further, let full-employment output in Germany be 1000, and let full-employment output in France be the same. It proves useful to study four distinct cases: - the case of unemployment - the case of inflation - unemployment in Germany, inflation in France - first the governments decide, then the central bank decides. 1) The case of unemployment. Let initial output in Germany be 940, and let initial output in France be 970. In each of the countries there is unemployment and deflation. Step 1 refers to monetary policy in Europe. The output gap in Europe is 90. The monetary policy multiplier in Europe is 2. So what is needed in Europe is an increase in European money supply of 45. Step 2 refers to the output lag. The increase in European money supply of 45 causes an increase in German output of 45 and an increase in French output of equally 45. As a consequence, German output goes from 940 to 985, and French output goes from 970 to 1015. In Germany there is still some unemployment and deflation. In France there is now some overemployment and inflation. And in

33 Europe there is now full employment and price stability. Unemployment in Germany equals overemployment in France. And deflation in Germany equals inflation in France. Step 3 refers to fiscal policies in Germany and France. The output gap in Germany is 15. The fiscal policy multiplier in Germany is 1. So what is needed in Germany is an increase in German government purchases of 15. The inflationary gap in France is 15. The fiscal policy multiplier in France is 1. So what is needed in France is a reduction in French government purchases of 15. Step 4 refers to the output lag. The increase in German government purchases of 15 causes an increase in German output of 15. And the reduction in French government purchases of 15 causes a decline in French output of 15. As a consequence, German output goes from 985 to 1000, and French output goes from 1015 to 1000. In each of the countries there is now full employment and price stability. Table 1.10 gives an overview.

Table 1.10 Competition between the European Central Bank, the German Government, and the French Government The Case of Unemployment

Initial Output

Germany

France

940

970

Change in Money Supply

1 Output Change in Government Purchases Output

45 985

1015

15

-15

1000

1000

34 As a result, the process of competition between the European central bank, the German government, and the French government leads to full employment and price stability in each of the countries. There is an increase in European money supply. There is an increase in German government purchases, a reduction in French government purchases, and no change in European government purchases. There is an increase in German output, as there is in French output. In steps 1 and 2 there is some overshooting in French output. There is an increase in European output, an increase in European tax revenue, and a decline in the European budget deficit. There is a decline in the interest rate and an increase in European investment.There is a depreciation of the euro, an increase in European exports, and an increase in the European current account surplus. 2) Comparing monetary and fiscal competition with pure monetary policy. Pure monetary policy can achieve full employment and price stability in Europe as a whole. However, it cannot achieve full employment and price stability in each of the member countries. By contrast, monetary and fiscal competition can indeed achieve full employment and price stability in each of the member countries. Judging from this point of view, monetary and fiscal competition seems to be superior to pure monetary policy. 3) Comparing monetary and fiscal competition with pure fiscal policies. Pure fiscal policies can achieve full employment and price stability in each of the member countries. And the same holds for monetary and fiscal competition. Pure fiscal policies cause an increase in the European budget deficit. By contrast, monetary and fiscal competition causes a decline in the European budget deficit. Judging from this perspective, monetary and fiscal competition seems to be superior to pure fiscal policies. 4) The case of inflation. Let initial output in Germany be 1060, and let initial output in France be 1030. In each of the countries there is overemployment and inflation. Step 1 refers to monetary policy in Europe. The inflationary gap in Europe is 90. The monetary policy multiplier in Europe is 2. So what is needed in Europe is a reduction in European money supply of 45.

35 Step 2 refers to the output lag. The reduction in European money supply of 45 causes a decline in German output of 45 and a decline in French output of equally 45. As a consequence, German output goes from 1060 to 1015, and French output goes from 1030 to 985. In Germany there is still some overemployment and inflation. In France there is now some unemployment and deflation. And in Europe there is now fall employment and price stability. Overemployment in Germany equals unemployment in France. And inflation in Germany equals deflation in France. Step 3 refers to fiscal policies in Germany and France. The inflationary gap in Germany is 15. The fiscal policy multiplier in Germany is 1. So what is needed in Germany is a reduction in German government purchases of 15. The output gap in France is 15. The fiscal policy multiplier in France is 1. So what is needed in France is an increase in French government purchases of 15. Step 4 refers to the output lag. The reduction in German government purchases of 15 causes a decline in German output of 15. And the increase in French government purchases of 15 causes an increase in French output of 15. As a consequence, German output goes from 1015 to 1000, and French output goes from 985 to 1000. In each of the countries there is now fall employment and price stability. Table 1.11 presents a synopsis. As a result, the process of monetary and fiscal competition leads to fall employment and price stability in each of the countries. There is a reduction in European money supply. There is a reduction in German government purchases, an increase in French government purchases, and no change in European government purchases. There is a decline in German output, as there is in French output. In steps 1 and 2 there is some overshooting in French output. There is a decline in European output, a decline in European tax revenue, and an increase in the European budget deficit. There is an increase in the interest rate and a decline in European investment. There is an appreciation of the euro, a decline in European exports, and a decline in the European current account surplus.

36 Table 1.11 Competition between the European Central Bank, the German Government, and the French Government The Case of Inflation

Initial Output

Germany

France

1060

1030

Change in Money Supply

-45

Output

1015

985

Change in Government Purchases

-15

15

Output

1000

1000

5) Unemployment in Germany, inflation in France. Let initial output in Germany be 940, and let initial output in France be 1030. In Germany there is unemployment and deflation. In France there is overemployment and inflation. And in Europe there is unemployment and deflation. Step 1 refers to monetary policy in Europe. The output gap in Europe is 30. The monetary policy multiplier in Europe is 2. So what is needed in Europe is an increase in European money supply of 15. Step 2 refers to the output lag. The increase in European money supply of 15 raises German output and French output by 15 each. As a consequence, German output goes from 940 to 955, and French output goes from 1030 to 1045. In Germany there is now some less unemployment and deflation. In France there is now some more overemployment and inflation. And in Europe there is now full employment and price stability. Unemployment in Germany equals overemployment in France. And deflation in Germany equals inflation in France. Step 3 refers to fiscal policies in Germany and France. The output gap in Germany is 45. The fiscal policy multiplier in Germany is 1. So what is needed in Germany is an increase in German government purchases of 45. The

37 inflationary gap in France is 45. The fiscal policy multiplier in France is 1. So what is needed in France is a reduction in French government purchases of 45. Step 4 refers to the output lag. The increase in German government purchases of 45 raises German output by 45. And the reduction in French government purchases of 45 lowers French output by 45. As a consequence, German output goes from 955 to 1000, and French output goes from 1045 to 1000. In each of the countries there is now full employment and price stability. Table 1.12 gives an overview.

Table 1.12 Competition between tlie European Central Bank, the German Government, and the French Government Unemployment in Germany, Inflation in France

Initial Output

Germany

France

940

1030

Change in Money Supply Output Change in Government Purchases Output

15 955

1045

45

-45

1000

1000

6) Unemployment in Germany, inflation in France: another case. Let initial output in Germany be 970, and let initial output in France be 1060. In Germany there is unemployment and deflation. In France there is overemployment and inflation. And in Europe there is overemployment and inflation, too. Step 1 refers to monetary policy in Europe. The inflationary gap in Europe is 30. The monetary policy multiplier in Europe is 2. So what is needed in Europe is a reduction in European money supply of 15.

38 Step 2 refers to the output lag. The reduction in European money supply of 15 lowers German output and French output by 15 each. As a consequence, German output goes from 970 to 955, and French output goes from 1060 to 1045. In Germany there is now some more unemployment and deflation. In France there is now some less overemployment and inflation. And in Europe there is now full employment and price stability. Unemployment in Germany equals overemployment in France. And deflation in Germany equals inflation in France. Step 3 refers to fiscal policies in Germany and France. The output gap in Germany is 45. The fiscal policy multiplier in Germany is 1. So what is needed in Germany is an increase in German government purchases of 45. The infiationary gap in France is 45. The fiscal policy multiplier in France is 1. So what is needed in France is a reduction in French government purchases of 45. Step 4 refers to the output lag. The increase in German government purchases of 45 raises German output by 45. And the reduction in French government purchases of 45 lowers French output by 45. As a consequence, German output goes from 955 to 1000, and French output goes from 1045 to 1000. In each of the countries there is now fiill employment and price stability. Table 1.13 presents a synopsis.

Table 1.13 Competition between the European Central Bank, the German Government, and the French Government Unemployment in Germany, Inflation in France

Initial Output

Germany

France

970

1060

Change in Money Supply Output Change in Government Purchases Output

-15 955

1045

45

-45

1000

1000

39 7) First the governments decide, then the central bank decides. So far we have assumed that the central bank decides first. Now we assume that the governments decide first. Let initial output in Germany be 940, and let initial output in France be 970. In each of the countries there is unemployment and deflation. Step 1 refers to fiscal policies in Germany and France. The output gap in Germany is 60. The fiscal policy multiplier in Germany is 1. So what is needed in Germany is an increase in German government purchases of 60. The output gap in France is 30. The fiscal policy multiplier in France is 1. So what is needed in France is an increase in French government purchases of 30. Step 2 refers to the output lag. The increase in German government purchases of 60 raises German output by 60. And the increase in French government purchases of 30 raises French output by 30. As a consequence, German output goes from 940 to 1000, and French output goes from 970 to 1000. In each of the countries there is now full employment and price stability. Step 3 refers to monetary policy in Europe. The output gap in Europe is zero. So there is no reason for changing European money supply. Step 4 refers to the output lag. As a consequence, German output stays at 1000, as does French output. In each of the countries there is still full employment and price stability. Table 1.14 gives an overview. As a result, the process of competition between the German government, the French government, and the European central bank leads to full employment and price stability in each of the countries.

40 Table 1.14 Competition between the European Central Bank, the German Government, and the French Government First the Governments Decide, then the Central Bank Decides

Initial Output Change in Government Purchases Output

Germany

France

940

970

60

30

1000

1000

Change in Money Supply Output

0 1000

1000

8) Comparing - first the central bank decides, then the governments decide - first the governments decide, then the central bank decides. Let initial output in Germany be 940, and let initial output in France be 970. Case number 1: The central bank decides first. The increase in European money supply is 45, the increase in German government purchases is 15, the reduction in French government purchases is equally 15, and the change in European government purchases is zero. Case number 2: The governments decide first. The increase in European money supply is zero, the increase in German government purchases is 60, the increase in French government purchases is 30, and the increase in European government purchases is 90. Table 1.15 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 increase in European government purchases. The other way round, if the governments decide first, there will be a zero increase in European money supply and a large increase in European government

41 purchases. Judging from this point of view, it seems that the central bank should decide first.

Table 1.15 Who Should Decide First, the Central Bank or the Governments?

Increase in

The Central Bank The Governments Decide First Decides First

European Money Supply

45

0

German Government Purchases

15

60

-15

30

0

90

French Government Purchases European Government Purchases

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

1) Introduction. As a starting point, take the output model. It can be represented by a system of two equations: Y i = A i + a M + pGi

(1)

Y 2 = A 2 + a M + pG2

(2)

Here Yj denotes German output, Y2 is French output, M is European money supply, Gj is German government purchases, G2 is French government purchases, a is the monetary policy multiplier, and P is the fiscal policy multiplier. The endogenous variables are German output and French output. 2) The policy model. At the beginning there is unemployment in Germany and France. More precisely, unemployment in Germany is high, and unemployment in France is low. The policy makers are the European central bank, the German government, and the French government. The targets of policy cooperation are full employment in Germany and full employment in France. The instruments of policy cooperation are European money supply, German government purchases, and French government purchases. There are two targets and three instruments, so there is one degree of freedom. As a result, there is an infinite number of solutions. In other words, cooperation between the European central bank, the German government, and the French government can achieve full employment in Germany and France. Of course there are many more potential targets of policy cooperation: - balancing the budget in Germany and France - balancing the current account in Germany and France - high investment in Germany and France

43 - 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. Taking differences in equations (1) and (2), the policy model can be written as follows: AYj=aAM + pAGj

(3)

AY2=aAM + pAG2

(4)

Here AYj denotes the initial output gap in Germany, AYj is the initial output gap in France, AM is the required increase in European money supply, AGj is the required increase in German government purchases, and AG2 is the required increase in French government purchases. The endogenous variables are AM, AGiandAG2. We now introduce a third target. We assume that the increase in German government purchases should be equal in size to the reduction in French government purchases AG^ + AG2 = 0. Put another way, we assume that the sum total of European government purchases should be constant. Add up equations (3) and (4), taking account of AG^ + AG2 = 0, to find out:

AM = ^ S ± ^

(5,

2a Here AY^ + AY2 is the initial output gap in Europe. Then subtract equation (4) from equation (3), taking account of AG^ + AG2 = 0, and solve for:

44 According to equation (5), the required increase in European money supply depends on the initial output gap in Europe and on the monetary policy multiplier in Europe. According to equation (6), the required increase in German government purchases depends on the initial output gap in Germany, the initial output gap in France, and the fiscal policy multiplier. The larger the initial output gap in Germany, the larger is the required increase in German government purchases. Moreover, the larger the initial output gap in France, the smaller is the required increase in German government purchases. At first glance this comes as a surprise. According to equation (7), the required increase in French government purchases depends on the initial output gap in France, the initial output gap in Germany, and the fiscal policy multiplier.

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 = 1 and P = 1. That is, an increase in European money supply of 100 causes an increase in German output of 100 and an increase in French output of equally 100. An increase in German government purchases of 100 causes an increase in German output of 100. Correspondingly, an increase in French government purchases of 100 causes an increase in French output of 100. Further, let full-employment output in Germany be 1000, and let full-employment output in France be the same. It proves useful to consider four distinct cases: - the case of unemployment - the case of inflation - unemployment in Germany, inflation in France - alternative targets of policy cooperation. 1) The case of unemployment. Let initial output in Germany be 940, and let initial output in France be 970. In each of the countries there is unemployment and deflation. Step 1 refers to the policy response. The output gap in Germany is

45 60, the output gap in France is 30, and the output gap in Europe is 90. So what is needed, according to equations (5), (6) and (7) from the preceding section, is an increase in European money supply of 45, an increase in German government purchases of 15, and a reduction in French government purchases of equally 15. Step 2 refers to the output lag. The increase in European money supply of 45 causes an increase in German output of 45 and an increase in French output of equally 45. The increase in German government purchases of 15 causes an increase in German output of 15. And the reduction in French government purchases of 15 causes a decline in French output of 15. The net effect is an increase in German output of 60 and an increase in French output of 30. As a consequence, German output goes from 940 to 1000, and French output goes from 970 to 1000. In each of the countries there is now full employment and price stability. Table 1.16 gives an overview.

Table 1.16 Cooperation between the European Central Bank, the German Government, and the French Government The Case of Unemployment

Initial Output

Germany

France

940

970

Change in Money Supply Change in Government Purchases Output

45 15

-15

1000

1000

As a result, cooperation between the European central bank, the German government, and the French government can achieve full employment and price stability in each of the countries. There is an increase in European money supply. There is an increase in German government purchases, a reduction in French government purchases, and

46 no change in European government purchases. There is an increase in German output, as there is in French output. There is an increase in European output, an increase in European tax revenue, and a decline in the European budget deficit. There is a decHne in the interest rate and an increase in European investment. There is a depreciation of the euro, an increase in European exports, and an increase in the European current account surplus. 2) Comparing policy cooperation with policy competition. Policy competition can achieve full employment and price stability in each of the countries. And the same applies to policy cooperation. Under policy competition, the increase in European money supply is 45, the increase in German government purchases is 15, and the reduction in French government purchases is equally 15 (assuming that the central bank decides first). Hence the solution to policy cooperation is identical with the solution to policy competition. Policy competition is a slow process consisting of four steps. By contrast, policy cooperation is a fast process consisting of only two steps. Policy competition causes some overshooting in output. By contrast, policy cooperation does not cause any overshooting in output. Judging from this point of view, policy cooperation seems to be superior to policy competition. 3) The case of inflation. Let initial output in Germany be 1060, and let initial output in France be 1030. In each of the countries there is overemployment and inflation. Step 1 refers to the policy response. The inflationary gap in Germany is 60, the inflationary gap in France is 30, and the inflationary gap in Europe is 90. So what is needed, according to equations (5), (6) and (7) from the previous section, is a reduction in European money supply of 45, a reduction in German government purchases of 15, and an increase in French government purchases of equally 15. Step 2 refers to the output lag. The reduction in European money supply of 45 causes a decline in German output of 45 and a decline in French output of equally 45. The reduction in German government purchases of 15 causes a decline in German output of 15. And the increase in French government purchases of 15 causes an increase in French output of 15. The net effect is a decline in German output of 60 and a decline in French output of 30. As a consequence, German output goes from 1060 to 1000, and French output goes

47 from 1030 to 1000. In each of the countries there is now full employment and price stability. Table 1.17 presents a synopsis.

Table 1.17 Cooperation between the European Central Bank, the German Government, and the French Government The Case of Inflation

Initial Output

Germany

France

1060

1030

Change in Money Supply

-45

Change in Government Purchases

-15

15

Output

1000

1000

As a result, monetary and fiscal cooperation can achieve full employment and price stability in each of the countries. There is a reduction in European money supply. There is a reduction in German government purchases, an increase in French government purchases, and no change in European government purchases. There is a decline in German output, as there is in French output. There is a decline in European output, a decline in European tax revenue, and an increase in the European budget deficit. There is an increase in the interest rate and a decline in European investment. There is an appreciation of the euro, a decline in European exports, and a decline in the European current account surplus. 4) Unemployment in Germany, inflation in France. Let initial output in Germany be 940, and let initial output in France be 1030. In Germany there is unemployment and deflation. In France there is overemployment and inflation. And in Europe there is unemployment and deflation. Step 1 refers to the policy response. The output gap in Germany is 60, the inflationary gap in France is 30, and the output gap in Europe is 30. So what is needed is an increase in European

48 money supply of 15, an increase in German government purchases of 45, and a reduction in French government purchases of equally 45. Step 2 refers to the output lag. The increase in European money supply of 15 raises German output and French output by 15 each. The increase in German government purchases of 45 raises German output by 45. And the reduction in French government purchases of 45 lowers French output by 45. The net effect is an increase in German output of 60 and a decline in French output of 30. As a consequence, German output goes from 940 to 1000, and French output goes from 1030 to 1000. In each of the countries there is now full employment and price stability. Table 1.18 gives an overview.

Table 1.18 Cooperation between the European Central Bank, the German Government, and the French Government Unemployment in Germany, Inflation in France

Initial Output

Germany

France

940

1030

Change in Money Supply Change in Government Purchases Output

1

15 45

-45

1000

1000

5) Unemployment in Germany, inflation in France: another case. Let initial output in Germany be 970, and let initial output in France be 1060. In Germany there is unemployment and deflation. In France there is overemployment and inflation. And in Europe there is overemployment and inflation, too. Step 1 refers to the policy response. The output gap in Germany is 30, the inflationary gap in France is 60, and the inflationary gap in Europe is 30. So what is needed is a reduction in European money supply of 15, an increase in German government purchases of 45, and a reduction in French government purchases of equally 45.

49 Step 2 refers to the output lag. The reduction in European money supply of 15 lowers German output and French output by 15 each. The increase in German government purchases of 45 raises German output by 45. And the reduction in French government purchases of 45 lowers French output by 45. The net effect is an increase in German output of 30 and a decline in French output of 60. As a consequence, German output goes from 970 to 1000, and French output goes from 1060 to 1000. In each of the countries there is now full employment and price stability. Table 1.19 presents a synopsis.

Table 1.19 Cooperation between the European Central Bank, the German Government, and the French Government Unemployment in Germany, Inflation in France

Initial Output

Germany

France

970

1060

Change in Money Supply Change in Government Purchases Output

-15 45

-45

1000

1000

6) Alternative targets of policy cooperation: no increase in national government purchases. Let initial output in Germany be 940, and let initial output in France be 970. In each of the countries there is unemployment and deflation. 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 60, an increase in German government purchases of zero, and a reduction in French government purchases of 30. Step 2 refers to the output lag. The increase in European money supply of 60 raises German output and French output by 60 each. And the reduction in French government purchases of 30 lowers French output by 30. The net effect is an increase in German output of 60 and an increase in French output of 30. As a

50 consequence, German output goes from 940 to 1000, and French output goes from 970 to 1000. In each of the countries there is now full employment and price stability. Table 1.20 gives an overview.

Table 1.20 Cooperation between the European Central Bank, the German Government, and the French Government No Increase in National Government Purchases

Initial Output

Germany

France

940

970 60

Change in Money Supply Change in Government Purchases Output

0

-30

1000

1000

As a result, monetary and fiscal cooperation can achieve full employment and price stability in each of the countries. There is a large increase in European money supply. There is no change in German government purchases, a reduction in French government purchases, and a reduction in European government purchases. 7) Alternative targets of policy cooperation: no reduction in national government purchases. Let initial output in Germany be 940, and let initial output in France be 970. In each of the countries there is unemployment and deflation. 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 30, an increase in German government purchases of equally 30, and a reduction in French government purchases of zero. Step 2 refers to the output lag. The increase in European money supply of 30 raises German output and French output by 30 each. And the increase in German government purchases of 30 raises German output by 30. The total effect is an

51 increase in German output of 60 and an increase in French output of 30. As a consequence, German output goes from 940 to 1000, and French output goes from 970 to 1000. Table 1.21 presents a synopsis.

Table 1.21 Cooperation between the European Central Bank, the German Government, and the French Government No Reduction in National Government Purchases

Initial Output

Germany

France

940

970 30

Change in Money Supply Change in Government Purchases Output

1

30

0

1000

1000

As a result, monetary and fiscal cooperation can achieve full employment and price stability in each of the countries. There is a small increase in European money supply. There is an increase in German government purchases, no change in French government purchases, and an increase in European government purchases.

Part Two Monetary and Fiscal Policies Intermediate Models

Chapter 1 Simultaneous Decisions: Cold-Turkey Policies

This chapter deals with competition between the European central bank, the German government, and the French government. So far we have assumed that the central bank and the governments decide sequentially. First the central bank decides, then the governments decide. Now we assume that the central bank and the governments decide simultaneously and independently. As a point of reference, consider the static model. It can be represented by a system of two equations: Y j = A i + M + Gi

(1)

Y 2 = A 2 + M + G2

(2)

The endogenous variables are German output and French output. An increase in European money supply of 100 causes an increase in German output of 100 and an increase in French output of equally 100. An increase in German government purchases of 100 causes an increase in German output of 100. Correspondingly, an increase in French government purchases of 100 causes an increase in French output of 100. Further, let full-employment output in Germany be 1000, and let full-employment output in France be the same. At the beginning there is unemployment in Germany and France. 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 full employment in Europe. The specific target of the European central bank is that unemployment in Germany equals overemployment in France. Accordingly, the specific target of the European central bank is that deflation in Germany equals inflation in France. In other words, the specific target of the European central bank is full employment in Europe on average. Accordingly, the specific target of the European central bank is price stability in Europe on average. The instrument of

56 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 government is full employment in Germany. The instrument of the German government is German government purchases. The German government raises German government purchases so as to close the output gap in Germany. The target of the French government is full employment in France. The instrument of the French government is French government purchases. The French government raises French government purchases so as to close the output gap in France. We assume that the central bank and the governments decide simultaneously and independently. In step 1 the European central bank, the German government, and the French government decide simultaneously and independently. In step 2 there is an output lag. In step 3 the European central bank, the German government, and the French government decide simultaneously and independently. In step 4 there is an output lag. And so on. Let initial output in Germany be 940, and let initial output in France be 970. In each of the countries there is unemployment and deflation. Step 1 refers to the policy response. First consider monetary policy in Europe. The output gap in Europe is 90. The monetary policy multiplier in Europe is 2. So what is needed in Europe is an increase in European money supply of 45. Second consider fiscal policy in Germany. The output gap in Germany is 60. The fiscal policy multiplier in Germany is 1. So what is needed in Germany is an increase in German government purchases of 60. Third consider fiscal policy in France. The output gap in France is 30. The fiscal policy multiplier in France is 1. So what is needed in France is an increase in French government purchases of 30. Step 2 refers to the output lag. The increase in European money supply of 45 causes an increase in German output of 45 and an increase in French output of equally 45. The increase in German government purchases of 60 causes an increase in German output of 60. And the increase in French government purchases of 30 causes an increase in French output of 30. The total effect is an increase in German output of 105 and an increase in French output of 75. As a consequence, German output goes from 940 to 1045, and French output goes

57 from 970 to 1045. In each of the countries there is now overemployment and inflation. Step 3 refers to the policy response. First consider monetary policy in Europe. The inflationary gap in Europe is 90. The monetary policy multiplier in Europe is 2. So what is needed in Europe is a reduction in European money supply of 45. Second consider fiscal policy in Germany. The inflationary gap in Germany is 45. The fiscal policy multiplier in Germany is 1. So what is needed in Germany is a reduction in German government purchases of 45. Third consider fiscal policy in France. The inflationary gap in France is 45. The fiscal policy multipHer in France is 1. So what is needed in France is a reduction in French government purchases of 45. Step 4 refers to the output lag. The reduction in European money supply of 45 causes a decline in German output of 45 and a decline in French output of equally 45. The reduction in German government purchases of 45 causes a decline in German output of 45. And the reduction in French government purchases of 45 causes a decline in French output of 45. The total effect is a decline in German output of 90 and a decline in French output of equally 90. As a consequence, German output goes from 1045 to 955, as does French output. In each of the countries there is now unemployment and deflation. Step 5 refers to the policy response. First consider monetary policy in Europe. The output gap in Europe is 90. The monetary policy multiplier in Europe is 2. So what is needed in Europe is an increase in European money supply of 45. Second consider fiscal policy in Germany. The output gap in Germany is 45. The fiscal policy multiplier in Germany is 1. So what is needed in Germany is an increase in German government purchases of 45. Third consider fiscal policy in France. The output gap in France is 45. The fiscal policy multiplier in France is 1. So what is needed in France is an increase in French government purchases of 45. Step 6 refers to the output lag. The increase in European money supply of 45 causes an increase in German output of 45 and an increase in French output of equally 45. The increase in German government purchases of 45 causes an increase in German output of 45. And the increase in French government purchases of 45 causes an increase in French output of 45. The total effect is an

58 increase in German output of 90 and an increase in French output of equally 90. As a consequence, German output goes from 955 to 1045, as does French output. In each of the countries there is now overemployment and inflation. This process will repeat itself round by round. Table 2.1 presents a synopsis.

Table 2.1 Simultaneous Decisions: Cold-Turkey Policies France

Germany Initial Output Change in Money Supply Change in Government Purchases Output

45 60

30

1045

1045

Change in Money Supply Change in Government Purchases Output

-45 -45

-45

955

955

Change in Money Supply Change in Government Purchases Output

970

940

45 45

45

1045

1045

and so on

As a result, the simultaneous process of monetary and fiscal competition does not lead to full employment and price stability in any of the countries. Instead, there are uniform oscillations in money supply, government purchases, and output. The German economy oscillates between unemployment and overemployment, as does the French economy. And what is more, the German economy oscillates between deflation and inflation, as does the French economy. Last but not least, compare simultaneous decisions with sequential decisions, see Chapter 3 of Part One. The sequential process of monetary and fiscal

59 competition leads to foil employment and price stability in each of the countries. By contrast, the simultaneous process of monetary and fiscal competition does not lead to foil employment and price stability in any of the countries. Judging from this perspective, sequential decisions seem to be superior to simultaneous decisions.

Chapter 2 Simultaneous Decisions: Gradualist Policies

This chapter deals with competition between the European central bank, the German government, and the French government. So far we have assumed that the central bank and the governments follow a cold-turkey strategy. Now we assume that the central bank and the governments follow a gradualist strategy. In addition, we assume that the central bank and the governments decide simultaneously and independently. In the numerical example, an increase in European money supply of 100 causes an increase in German output of 100 and an increase in French output of equally 100. An increase in German government purchases of 100 causes an increase in German output of 100. Correspondingly, an increase in French government purchases of 100 causes an increase in French output of 100. Further, let full-employment output in Germany be 1000, and let fullemployment output in France be the same. At the start there is unemployment in Germany and France. 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 German government is full employment in Germany. We assume that the German government follows a gradualist strategy. The specific target of the German government is to close the output gap in Germany by 60 percent. The general target of the French government is full employment in France. We assume that the French government follows a gradualist strategy. The specific target of the French government is to close the output gap in France by 60 percent. We assume that the central bank and the governments decide simultaneously and independently. In step 1 the European central bank, the German government, and the French government decide simultaneously and independently. In step 2

61 there is an output lag. In step 3 the European central bank, the German government, and the French government decide simultaneously and independently. In step 4 there is an output lag. And so on. For a mathematical presentation of the model see Carlberg (2004) p. 154. Let initial output in Germany be 940, and let initial output in France be 970. In each of the countries there is unemployment and deflation. Step 1 refers to the policy response. First consider monetary policy in Europe. The output gap in Europe is 90. The specific target of the European central bank is to close the output gap in Europe by 80 percent, that is by 72. The monetary policy multiplier in Europe is 2. So what is needed in Europe is an increase in European money supply of 36. Second consider fiscal policy in Germany. The output gap in Germany is 60. The specific target of the German government is to close the output gap in Germany by 60 percent, that is by 36. The fiscal policy multiplier in Germany is 1. So what is needed in Germany is an increase in German government purchases of 36. Third consider fiscal policy in France. The output gap in France is 30. The specific target of the French government is to close the output gap in France by 60 percent, that is by 18. The fiscal policy multiplier in France is 1. So what is needed in France is an increase in French government purchases of 18. Step 2 refers to the output lag. The increase in European money supply of 36 causes an increase in German output of 36 and an increase in French output of equally 36. The increase in German government purchases of 36 causes an increase in German output of 36. And the increase in French government purchases of 18 causes an increase in French output of 18. The total effect is an increase in German output of 72 and an increase in French output of 54. As a consequence, German output goes from 940 to 1012, and French output goes from 970 to 1024. In each of the countries there is now overemployment and inflation. Step 3 refers to the policy response. First consider monetary policy in Europe. The inflationary gap in Europe is 36. The specific target of the European central bank is to close the inflationary gap in Europe by 80 percent, that is by 28.8. The monetary policy multiplier in Europe is 2. So what is needed in Europe is a reduction in European money supply of 14.4. Second consider fiscal policy in

62 Germany. The inflationary gap in Germany is 12. The specific target of the German government is to close the inflationary gap in Germany by 60 percent, that is by 7.2. The fiscal policy multiplier in Germany is 1. So what is needed in Germany is a reduction in German government purchases of 7.2. Third consider fiscal policy in France. The inflationary gap in France is 24. The specific target of the French government is to close the inflationary gap in France by 60 percent, that is by 14.4. The fiscal policy multiplier in France is 1. So what is needed in France is a reduction in French government purchases of 14.4. Step 4 refers to the output lag. The reduction in European money supply of 14.4 causes a decline in German output of 14.4 and a decline in French output of equally 14.4. The reduction in German government purchases of 7.2 causes a decline in German output of 7.2. And the reduction in French government purchases of 14.4 causes a decline in French output of 14.4. The total effect is a decline in German output of 21.6 and a decline in French output of 28.8. As a consequence, German output goes from 1012 to 990.4, and French output goes from 1024 to 995.2. In each of the countries there is now unemployment and deflation. Step 5 refers to the policy response. First consider monetary policy in Europe. The output gap in Europe is 14.4. The specific target of the European central bank is to close the output gap in Europe by 80 percent, that is by 11.5. The monetary policy multiplier in Europe is 2. So what is needed in Europe is an increase in European money supply of 5.8. Second consider fiscal policy in Germany. The output gap in Germany is 9.6. The specific target of the German government is to close the output gap in Germany by 60 percent, that is by 5.8. The fiscal policy multiplier in Germany is 1. So what is needed in Germany is an increase in German government purchases of 5.8. Third consider fiscal policy in France. The output gap in France is 4.8. The specific target of the French government is to close the output gap in France by 60 percent, that is by 2.9. The fiscal policy multiplier in France is 1. So what is needed in France is an increase in French government purchases of 2.9. Step 6 refers to the output lag. The increase in European money supply of 5.8 causes an increase in German output of 5.8 and an increase in French output of equally 5.8. The increase in German government purchases of 5.8 causes an increase in German output of 5.8. And the increase in French government

63 purchases of 2.9 causes an increase in French output of 2.9. The total effect is an increase in German output of 11.5 and an increase in French output of 8.6. As a consequence, German output goes from 990.4 to 1001.9, and French output goes from 995.2 to 1003.8. In each of the countries there is now overemployment and inflation. And so on. Table 2.2 gives an overview.

Table 2.2 Simultaneous Decisions: Gradualist Policies Germany Initial Output

940

Change in Money Supply Change in Government Purchases Output

France 970 36

36

18

1012

1024

Change in Money Supply

-14.4

Change in Government Purchases

-7.2

- 14.4

Output

990.4

995.2 5.8

Change in Money Supply Change in Government Purchases

1 Output

5.8

2.9

1001.9

1003.8

1000

1000

and so on Steady-State Output

In the steady state, German output is 1000, as is French output. In each of the countries there is now full employment and price stability. As a result, the gradualist process of monetary and fiscal competition leads to full employment and price stability in each of the countries. There are damped oscillations in money supply, government purchases, and output. The German economy oscillates between unemployment and overemployment, as does the French

64 economy. And what is more, the German economy oscillates between deflation and inflation, as does the French economy. Taking the sum over all periods, the total increase in European money supply is 25.7, the total increase in German government purchases is 34.3, and the total increase in French government purchases is 4.3. Generally speaking, the total increase in European money supply depends on: - the initial output gap in Germany - the initial output gap in France - the monetary policy multiplier in Europe - the fiscal policy multiplier in Germany - the fiscal policy multiplier in France - the speed of adjustment in European money supply - the speed of adjustment in German government purchases - the speed of adjustment in French government purchases. And the same holds for the total increase in German government purchases and the total increase in French government purchases. Finally compare gradualist policies with cold-turkey policies, given simultaneous decisions, see Chapter 1 of Part Two. Under cold-turkey policies there are uniform oscillations in money supply, government purchases, and output. By contrast, under gradualist policies there are damped oscillations in money supply, government purchases, and output. Under cold-turkey policies, monetary and fiscal competition does not lead to full employment and price stability. By contrast, under gradualist policies, monetary and fiscal competition leads to full employment and price stability. Judging from this point of view, gradualist policies seem to be superior to cold-turkey policies.

Chapter 3 Fiscal Shocks in Germany

This chapter is concerned with competition between the European central bank, the German government, and the French government. We assume that the central bank and the governments decide sequentially. First the central bank decides, then the governments decide. In addition, we assume that the central bank and the governments follow a cold-turkey strategy. In the numerical example, an increase in European money supply of 100 raises German output and French output by 100 each. An increase in German government purchases of 100 raises German output by 100. Correspondingly, an increase in French government purchases of 100 raises French output by 100. Let foil-employment output in Germany be 1000, and let foil-employment output in France be the same. It proves usefol to study two distinct cases: - the German government aims for overemployment - the German government aims for budget balance. 1) The German government aims for overemployment. The target of the European central bank is foil employment and price stability in Europe. More precisely, the target of the European central bank is that European output equals 2000. The target of the German government is overemployment in Germany. More precisely, the target of the German government is that German output equals 1060. The target of the French government is foil employment in France. More precisely, the target of the French government is that French output equals 1000. Let initial output in Germany be 1000, and let initial output in France be also 1000. In each of the countries there is foil employment and price stability. Step 1 refers to the fiscal shock in Germany. The target of the German government is that German output equals 1060. In a sense, the output gap in Germany is 60.

66 The fiscal policy multiplier in Germany is 1. So what is needed in Germany is an increase in German government purchases of 60. Step 2 refers to the output lag. The increase in German government purchases of 60 raises German output by 60. As a consequence, German output goes from 1000 to 1060 while French output stays at 1000. In Germany there is now some overemployment and inflation. In France there is still full employment and price stability. And in Europe there is now some overemployment and inflation. Step 3 refers to monetary policy in Europe. The target of the European central bank is that European output equals 2000. The inflationary gap in Europe is 60. The monetary policy multiplier in Europe is 2. So what is needed in Europe is a reduction in European money supply of 30. Step 4 refers to the output lag. The reduction in European money supply of 30 lowers German output and French output by 30 each. As a consequence, German output goes from 1060 to 1030, and French output goes from 1000 to 970. In Germany there is still some overemployment and inflation. In France there is now some unemployment and deflation. And in Europe there is now full employment and price stability.

Table 2.3 Fiscal Shock in Germany The German Government Aims for Overemployment

Initial Output Change in Government Purchases Output

Germany

France

1000

1000

60

Change in Money Supply Output

1000

1060 -30 1030

970

1

67 As a result, the fiscal shock in Germany causes overemployment in Germany. On the other hand, it causes unemployment in France. Table 2.3 presents a synopsis. 2) The German government aims for budget balance. Let initial output in Germany be 1000, and let initial output in France be the same. In each of the countries there is full employment and price stability. Now we assume that, in the initial state, the German budget is in deficit and the French budget is balanced. Step 1 refers to the fiscal shock in Germany. The German government reduces German government purchases in order to balance the German budget. To be more specific, we assume that German government purchases are reduced by 60. Step 2 refers to the output lag. The reduction in German government purchases of 60 lowers German output by 60. As a consequence, German output goes from 1000 to 940 while French output stays at 1000. In Germany there is now some unemployment and deflation. In France there is still full employment and price stability. And in Europe there is now some unemployment and deflation. Step 3 refers to monetary policy in Europe. The target of the European central bank is that European output equals 2000. The output gap in Europe is 60. The monetary policy multiplier in Europe is 2. So what is needed in Europe is an increase in European money supply of 30. Step 4 refers to the output lag. The increase in European money supply of 30 raises German output and French output by 30 each. As a consequence, German output goes from 940 to 970, and French output goes from 1000 to 1030. In Germany there is still some unemployment and deflation. In France there is now some overemployment and inflation. And in Europe there is now full employment and price stability. Step 5 refers to fiscal policies in Germany and France. The output gap in Germany is 30. The fiscal policy multiplier in Germany is 1. So what is needed in Germany is an increase in German government purchases of 30. The inflationary gap in France is 30. The fiscal policy multiplier in France is 1. So what is needed in France is a reduction in French government purchases of 30.

68 Step 6 refers to the output lag. The increase in German government purchases of 30 raises German output by 30. And the reduction in French government purchases of 30 lowers French output by 30. As a consequence, German output goes from 970 to 1000, and French output goes from 1030 to 1000. In each of the countries there is now full employment and price stability. As a result, there is a decline in the German budget deficit. As an adverse side effect, there is a decline in French government purchases and an increase in the French budget surplus. Table 2.4 gives an overview.

Table 2.4 Fiscal Shock in Germany The German Government Aims for Budget Balance Germany

France

Initial Output

1000

1000

Change in Government Purchases

-60

1 Output Change in Money Supply 1 Output Change in Government Purchases Output

1000

940 30 970

1030

30

-30

1000

1000

Chapter 4 The Countries Differ in Size 1. Monetary Policy in Europe

1) Introduction. We assume that the countries only differ in size. To be more specific, we assume that the German economy is large and the French economy is small. More precisely, we assume that full-employment output in Germany is large and full-employment output in France is small. As a result, an increase in European money supply raises both German output and French output. Here the increase in German output is large, and the increase in French output is small. In the numerical example, an increase in European money supply of 100 causes an increase in German output of 200 and an increase in French output of 100. The output model can be represented by a system of two equations: Yi=Ai+aiM

(1)

Y2=A2+a2M

(2)

Here Yj denotes German output, Y2 is French output, M is European money supply, ttj is the monetary policy multiplier in Germany, and a2 is the monetary policy multiplier in France. We assume a^ > a2. The endogenous variables are German output and French output. An increase in European money supply of 1 causes an increase in German output of a^ and an increase in French output of

2) The policy model. At the beginning there is unemployment in Germany and France. 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 full employment in Europe. For ease of exposition we assume that unemployment causes deflation whereas overemployment causes inflation. The specific target of the European central bank is that unemployment in Germany equals overemployment in France. Accordingly, the specific target of the

70 European central bank is that the weighted average of deflation in Germany and inflation in France is zero. In other words, the specific target of the European central bank is full employment in Europe on average. Accordingly, the specific target of the European central bank is price stability in Europe on average. 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. Now have a closer look at the policy model. The specific target of the European central bank is full employment in Europe on average: Yi + Y2 = Yi + Y2

(3)

Here Y^ denotes target output in Germany, Y2 is target output in France, Y^ is full-employment output in Germany, and Y2 is full-employment output in France. According to equation (3), target output in Europe should be equal to full-employment output in Europe. What is the required level of European money supply? To answer this question, eliminate Y^ and Y2 in equation (3) by means of equations (1) and (2) and solve for M:

M ^ ^ i + ^2 Ai A2

^4^

Obviously, the required level of European money supply depends on fullemployment output in Europe, some other factors bearing on European output, and the monetary policy multiplier in Europe. As a result, monetary policy in Europe can achieve full employment in Europe on average. And what is more, it can achieve price stability in Europe on average. However, monetary policy in Europe cannot achieve full employment in Germany and France. And what is more, it cannot achieve price stability in Germany and France.

71 3) Another version of the poUcy model. As an alternative, the policy model can be stated in terms of the initial output gap and the required increase in money supply. The European central bank raises European money supply so as to close the output gap in Europe: AY,+AYo AM = —^ 2.

(5)

Here AM denotes the required increase in European money supply, AYj is the initial output gap in Germany, AY2 is the initial output gap in France, AY^+AY2 is the initial output gap in Europe, and a^ + a2 is the monetary policy multiplier in Europe. Evidently, the required increase in European money supply depends on the initial output gap in Europe and on the monetary policy multiplier in Europe. 4) A numerical example. We assume that the German economy is twice as large as the French economy. More precisely, we assume that full-employment output in Germany is twice as large as full-employment output in France. For ease of exposition, without loss of generality, we assume a^ = 2 and (X2 = 1. On this assumption, the output model can be written as follows: Yi=Ai+2M

(6)

Y2 = A2 + M

(7)

Obviously, an increase in European money supply of 100 causes an increase in German output of 200 and an increase in French output of 100. The policy multipliers are from the case of three countries, see Chapter 1 of Part Three below. In the large country, the monetary policy multiplier is large. And in the small country, the monetary policy multiplier is small. Further, let fullemployment output in Germany be 2000, and let full-employment output in France be 1000. Let initial output in Germany be 1880, and let initial output in France be 970. In each of the countries there is unemployment and deflation. Step 1 refers to the policy response. The output gap in Germany is 120, the output gap in France is

72 30, and the output gap in Europe is 150. The monetary poHcy multipHer in Europe is 3. So what is needed in Europe is an increase in European money supply of 50. Step 2 refers to the output lag. The increase in European money supply of 50 causes an increase in German output of 100 and an increase in French output of 50. As a consequence, German output goes from 1880 to 1980, and French output goes from 970 to 1020. Table 2.5 presents a synopsis. In Germany there is still some unemployment and deflation. In France there is now some overemployment and inflation. And in Europe there is now full employment and price stability. As a result, monetary policy in Europe can achieve full employment and price stability in Europe as a whole. However, monetary policy in Europe cannot achieve full employment and price stability in each of the member countries.

Table 2.5 Monetary Policy in Europe The Countries Differ in Size

Initial Output

Germany

France

1880

970 50

Change in Money Supply Output

1980

1020

Now have a closer look at the final output gap. The final output gap in Germany is 20, and the final output gap in France is -20. That means, the final output gap in Germany is equal in size to the final output gap in France. The second point refers to the relative output gap. The final output gap in Germany is 1 percent of full-employment output in Germany (20/2000 = 0.01). The final output gap in France is - 2 percent of full-employment output in France (20/1000 = 0.02). And the final output gap in Europe is zero percent of full-employment output in Europe (0/3000 = 0). It is worth pointing out here that the relative

73 output gap in Germany differs in size from the relative output gap in France (1 percent versus - 2 percent). The third point refers to the final rate of unemployment. Let final unemployment in Germany be 1 percent, and let final unemployment in France be - 2 percent. Then final unemployment in Europe is zero percent (the weights are 2/3 and 1/3). That is to say, the final rate of unemployment in Germany differs in size from the final rate of unemployment in France (1 percent versus - 2 percent). The fourth point refers to the final rate of inflation. Let final inflation in Germany be - 1 percent, and let final inflation in France be 2 percent. Then final inflation in Europe is zero percent (the weights are 2/3 and 1/3). That means, the final rate of inflation in Germany differs in size from the final rate of inflation in France (-1 percent versus 2 percent).

2. Fiscal Policies in Germany and France

1) Introduction. We assume that the countries only differ in size. To be more specific, we assume that the German economy is large and the French economy is small. More precisely, we assume that full-employment output in Germany is large and full-employment output in France is small. As a result, the size of the fiscal policy multiplier does not depend on the size of the country. In the numerical example, an increase in German government purchases of 100 causes an increase in German output of 100. Correspondingly, an increase in French government purchases of 100 causes an increase in French output of 100. The output model can be characterized by a system of two equations: Y, = Ai + pGi

(1)

Y2=A2 + pG2

(2)

74 Here Y^ denotes German output, Y2 is French output, G^ is German government purchases, G2 is French government purchases, A^ is some other factors bearing on German output, A2 is some other factors bearing on French output, and P is the fiscal poUcy multipHer. The endogenous variables are German output and French output. 2) The policy model. At the start there is unemployment in Germany and France. More precisely, unemployment in Germany is high, and unemployment in France is low. The German government raises German government purchases so as to close the output gap in Germany:

1

p

V 7

Here AG^ denotes the required increase in German government purchases, AY^ is the initial output gap in Germany, and P is the fiscal policy multiplier in Germany. Similarly, the French government raises French government purchases so as to close the output gap in France:

^ ^ 2 = ^ -

(4)

Here AG2 denotes the required increase in French government purchases, AY2 is the initial output gap in France, and P is the fiscal policy multiplier in France. 3) A numerical example. We assume that the German economy is twice as large as the French economy. More exactly, we assume that full-employment output in Germany is twice as large as full-employment output in France. For ease of exposition, without losing generality, we assume P = 1. On this assumption, the output model can be written as follows: Yi=Ai+Gi

(5)

Y2=A2+G2

(6)

75 Obviously, an increase in German government purchases of 100 causes an increase in German output of 100. Correspondingly, an increase in French government purchases of 100 causes an increase in French output of 100. The policy multipliers are from the case of three countries, see Chapter 2 of Part Three below. Further, let full-employment output in Germany be 2000, and let full-employment output in France be 1000. Let initial output in Germany be 1880, and let initial output in France be 970. In each of the countries there is unemployment and deflation. Step 1 refers to the policy response. The output gap in Germany is 120. The fiscal policy multiplier in Germany is 1. So what is needed in Germany is an increase in German government purchases of 120. The output gap in France is 30. The fiscal policy multiplier in France is 1. So what is needed in France is an increase in French government purchases of 30. Step 2 refers to the output lag. The increase in German government purchases of 120 causes in increase in German output of 120. And the increase in French government purchases of 30 causes an increase in French output of 30. As a consequence, German output goes from 1880 to 2000, and French output goes from 970 to 1000. In each of the countries there is now full employment and price stability. As a result, fiscal policies in Germany and France can achieve full employment and price stability in each of the countries. Table 2.6 gives an overview.

Table 2.6 Fiscal Policies in Germany and France The Countries Differ in Size

Initial Output Change in Government Purchases Output

Germany

France

1880

970

120

30

2000

1000

76

3. Monetary and Fiscal Competition

This section deals with competition between the European central bank, the German government, and the French government. We assume that the central bank and the governments decide sequentially. First the central bank decides, then the governments decide. In addition, we assume that the central bank and the governments follow a cold-turkey strategy. The output model can be represented by a system of two equations: Yi=Aj+aiM+pGi

(1)

Y2= A2+a2M+pG2

(2)

We assume that the German economy is twice as large as the French economy. More precisely, we assume that full-employment output in Germany is twice as large as full-employment output in France. In the numerical example we assume that a^ = 2, a2 = 1 and P = 1. On this assumption, the output model can be written as follows: Yi=Ai+2M+Gi

(3)

Y2=A2+M+G2

(4)

Evidently, an increase in European money supply of 100 causes an increase in German output of 200 and an increase in French output of 100. An increase in German government purchases of 100 causes an increase in German output of 100. Correspondingly, an increase in French government purchases of 100 causes an increase in French output of 100. Further, let full-employment output in Germany be 2000, and let full-employment output in France be 1000. Let initial output in Germany be 1880, and let initial output in France be 970. In each of the countries there is unemployment and deflation. Step 1 refers to monetary policy in Europe. The output gap in Europe is 150. The monetary policy multiplier in Europe is 3. So what is needed in Europe is an increase in

77 European money supply of 50. Step 2 refers to the output lag. The increase in European money supply of 50 causes an increase in German output of 100 and an increase in French output of 50. As a consequence, German output goes from 1880 to 1980, and French output goes from 970 to 1020. Step 3 refers to fiscal policies Germany and France. The output gap in Germany is 20. The fiscal policy multiplier in Germany is 1. So what is needed in Germany is an increase in German government purchases of 20. The inflationary gap in France is 20. The fiscal policy multiplier in France is 1. So what is needed in France is a reduction in French government purchases of 20. Step 4 refers to the output lag. The increase in German government purchases of 20 causes an increase in German output of 20. And the reduction in French government purchases of 20 causes a decline in French output of 20. As a consequence, German output goes from 1980 to 2000, and French output goes from 1020 to 1000. In each of the countries there is now full employment and price stability. As a result, the process of monetary and fiscal competition leads to full employment and price stability in each of the countries. Table 2.7 presents a synopsis.

Table 2.7 Monetary and Fiscal Competition The Countries Differ in Size

Initial Output

Germany

France

1880

970

1

1980

1020

1

20

-20

1

2000

1000

Change in Money Supply

1 Output Change in Government Purchases Output

50

Chapter 5 The Countries Differ in Behaviour 1. Monetary Policy in Europe

1) Introduction. We assume that the countries only differ in behavioural functions. To be more specific, we assume that the countries differ in monetary policy multipliers. In the numerical example, an increase in European money supply of 100 causes an increase in German output of 200 and an increase in French output of 100. The output model can be represented by a system of two equations: Yj = A j + a i M

(1)

Y2=A2+a2M

(2)

Here Y^ denotes German output, Y2 is French output, M is European money supply, ttj is the monetary policy multiplier in Germany, and a2 is the monetary policy multiplier in France. 2) The policy model. At the beginning there is unemployment in Germany and France. 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 full employment in Europe. The specific target of the European central bank is that unemployment in Germany equals overemployment in France. Accordingly, the specific target of the European central bank is that deflation in Germany equals inflation in France. In other words, the specific target of the European central bank is full employment in Europe on average. Accordingly, the specific target of the European central bank is price stability in Europe on average. The European central bank raises European money supply so as to close the output gap in Europe:

79

AM = —^

2.

(3)

Here AM denotes the required increase in European money supply, AY^ is the initial output gap in Germany, AY2 is the initial output gap in France, AY^+AY2 is the initial output gap in Europe, and a^ + a2 is the monetary policy multiplier in Europe. Evidently, the required increase in European money supply depends on the initial output gap in Europe and on the monetary policy multiplier in Europe. 3) A numerical example. For ease of exposition we assume a^ = 2 and a2 = 1. On this assumption, the output model can be written as follows: Yj=Ai+2M

(4)

Y2=A24-M

(5)

Obviously, an increase in European money supply of 100 causes an increase in German output of 200 and an increase in French output of 100. Further, let fullemployment output in Germany be 1000, and let full-employment output in France be the same. Let initial output in Germany be 880, and let initial output in France be 970. In each of the countries there is unemployment and deflation. Step 1 refers to the policy response. The output gap in Germany is 120, the output gap in France is 30, and the output gap in Europe is 150. The monetary policy multiplier in Europe is 3. So what is needed in Europe is an increase in European money supply of 50. Step 2 refers to the output lag. The increase in European money supply of 50 causes an increase in German output of 100 and an increase in French output of 50. As a consequence, German output goes from 880 to 980, and French output goes from 970 to 1020. Table 2.8 gives an overview. In Germany there is still some unemployment and deflation. In France there is now some overemployment and inflation. And in Europe there is now full employment and price stability. As

80 a result, monetary policy in Europe can achieve full employment and price stability in Europe as a whole. However, monetary policy in Europe cannot achieve full employment and price stability in each of the member countries.

Table 2.8 Monetary Policy in Europe The Countries Differ in Behaviour

Initial Output

Germany

France

880

970

Change in Money Supply Output

50 980

1020

2. Fiscal Policies in Germany and France

1) Introduction. We assume that the countries only differ in behavioural functions. To be more specific, we assume that the countries differ in fiscal policy multipliers. The output model can be represented by a system of two equations: Yi = A, + p,Gi

(1)

Y2=A2 + P2G2

(2)

Here Y^ denotes German output, Y2 is French output, Gj is German government purchases, G2 is French government purchases, P^ is the fiscal policy multiplier in Germany, and P2 is the fiscal policy multiplier in France. The endogenous variables are German output and French output. An increase in German

81 government purchases of 1 causes an increase in German output of Pj. And an increase in French government purchases of 1 causes an increase in French output of P2. 2) The poHcy model. At the start there is unemployment in Germany and France. More precisely, unemployment in Germany is high, and unemployment in France is low. The German government raises German government purchases so as to close the output gap in Germany:

AG. = ^ ^ ' Pi

(3)

Here AG^ denotes the required increase in German government purchases, AY^ is the initial output gap in Germany, and Pj is the fiscal policy multiplier in Germany. According to equation (3), the required increase in German government purchases depends on the initial output gap in Germany and on the fiscal policy multiplier in Germany. Similarly, the French government raises French government purchases so as to close the output gap in France: AY, AG2=^7^

T2

(4)

Here AG2 denotes the required increase in French government purchases, AY2 is the initial output gap in France, and P2 is the fiscal policy multiplier in France. According to equation (4), the required increase in French government purchases depends on the initial output gap in France and on the fiscal policy multiplier in France. 3) A numerical example. For ease of exposition we assume that P^ = 2 and P2 = 1. On this assumption, the output model can be written as follows: Y, = A,+ 2Gi

(5)

Y2=A2+G2

(6)

82

Obviously, an increase in German government purchases of 100 causes an increase in German output of 200. And an increase in French government purchases of 100 causes an increase in French output of 100. Further, let fullemployment output in Germany be 1000, and let full-employment output in France be the same. Let initial output in Germany be 880, and let initial output in France be 970. In each of the countries there is unemployment and deflation. Step 1 refers to the policy response. The output gap in Germany is 120. The fiscal policy multiplier in Germany is 2. So what is needed in Germany is an increase in German government purchases of 60. The output gap in France is 30. The fiscal policy multiplier in France is 1. So what is needed in France is an increase in French government purchases of 30. Step 2 refers to the output lag. The increase in German government purchases of 60 causes an increase in German output of 120. And the increase in French government purchases of 30 causes an increase in French output of 30. As a consequence, German output goes from 880 to 1000, and French output goes from 970 to 1000. In each of the countries there is now full employment and price stability. As a result, fiscal policies in Germany and France can achieve full employment and price stability in each of the countries. Table 2.9 presents a synopsis.

Table 2.9 Fiscal Policies in Germany and France The Countries Differ in Behaviour

Initial Output Change in Government Purchases Output

Germany

France

880

970

60

30

1000

1000

83

3. Monetary and Fiscal Competition

This section deals with competition between the European central bank, the German government, and the French government. We assume that the central bank and the governments decide sequentially. First the central bank decides, then the governments decide. In addition, we assume that the central bank and the governments follow a cold-turkey strategy. The output model can be represented by a system of two equations: Yi=Ai+aiM+piGi

(1)

Y2= A2+a2M+p2G2

(2)

In the numerical example we assume that a^ = 2, a2 = 1, Pj = 2 and P2 = 1. On this assumption, the output model can be written as follows: Yi = A i + 2 M + 2 G i

(3)

Y2=A2+M+G2

(4)

Evidently, an increase in European money supply of 100 causes an increase in German output of 200 and an increase in French output of 100. An increase in German government purchases of 100 causes an increase in German output of 200. And an increase in French government purchases of 100 causes an increase in French output of 100. Further, let full-employment output in Germany be 1000, and let full-employment output in France be the same. Let initial output in Germany be 880, and let initial output in France be 970. In each of the countries there is unemployment and deflation. Step 1 refers to monetary policy in Europe. The output gap in Europe is 150. The monetary policy multiplier in Europe is 3. So what is needed in Europe is an increase in European money supply of 50. Step 2 refers to the output lag. The increase in European money supply of 50 causes an increase in German output of 100 and an increase French output of 50. As a consequence, German output goes from 880 to 980, and French output goes from 970 to 1020.

84

Step 3 refers to fiscal policies in Germany and France. The output gap in Germany is 20. The fiscal policy multiplier in Germany is 2. So what is needed in Germany is an increase in German government purchases of 10. The inflationary gap in France is 20. The fiscal policy multiplier in France is 1. So what is needed in France is a reduction in French government purchases of 20. Step 4 refers to the output lag. The increase in German government purchases of 10 causes an increase in German output of 20. And the reduction in French government purchases of 20 causes a decline in French output of 20. As a consequence, German output goes from 980 to 1000, and French output goes from 1020 to 1000. In each of the countries there is now full employment and price stability. As a result, the process of monetary and fiscal competition leads to full employment and price stability in each of the countries. The increase in German government purchases is smaller than the reduction in French government purchases. Table 2.10 gives an overview.

Table 2.10 Monetary and Fiscal Competition The Countries Differ in Behaviour

Initial Output

Germany

France

880

970

Change in Money Supply

1 Output Change in Government Purchases Output

50 980

1020

10

-20

1000

1000

85

4. Monetary and Fiscal Cooperation

This section deals with cooperation between the European central bank, the German government, and the French government. At the beginning there is unemployment in Germany and France. More precisely, unemployment in Germany is high, and unemployment in France is low. The targets of policy cooperation are full employment in Germany and full employment in France. The instruments of policy cooperation are European money supply, German government purchases, and French government purchases. There are two targets and three instruments, so there is one degree of freedom. We now introduce a third target. We assume that the increase in German government purchases should be equal in size to the reduction in French government purchases. Let initial output in Germany be 880, and let initial output in France be 970. Step 1 refers to the policy response. What is needed, then, is an increase in European money supply of 45, an increase in German government purchases of 15, and a reduction in French government purchases of equally 15. Step 2 refers to the output lag. The increase in European money supply of 45 causes an increase in German output of 90 and an increase in French output of 45. The increase in German government purchases of 15 causes an increase in German output of 30. And the reduction in French government purchases of 15 causes a decline in French output of 15. The net effect is an increase in German output of 120 and an increase in French output of 30. As a consequence, German output goes from 880 to 1000, and French output goes from 970 to 1000. In each of the countries there is now full employment and price stability. Table 2.11 presents a synopsis. As a result, monetary and fiscal cooperation can achieve full employment and price stability in each of the countries. The increase in German government purchases is equal in size to the reduction in French government purchases. There is no change in European government purchases. Judging from this point of view, policy cooperation seems to be superior to policy competition.

86 Table 2.11 Monetary and Fiscal Cooperation The Countries Differ in Behaviour

Initial Output

Germany

France

880

970

Change in Money Supply Change in Government Purchases Output

45 15

-15

1000

1000

Chapter 6 Rational Policy Expectations

1) The output model. This chapter deals with competition between the European central bank, the German government, and the French government. The member countries are the same size and have the same behavioural functions. As a point of departure, take the output model. It can be represented by a system of two equations: Yj =Aj + aM + pGj

(1)

Y2=A2+aM + pG2

(2)

Here Yj denotes German output, Y2 is French output, M is European money supply, Gj is German government purchases, and G2 is French government purchases. The endogenous variables are German output and French output. 2) The policy model. At the start there is unemployment in Germany and France. 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 German government is full employment in Germany. And the target of the French government is full employment in France. We assume that the European central bank, the German government, and the French government decide simultaneously and independently. The European central bank sets European money supply, forming rational expectations of German government purchases and French government purchases. The German government sets German government purchases, forming rational expectations of European money supply and French government purchases. And the French government sets French government purchases, forming rational expectations of European money supply and German government purchases.

That is to say, the European central bank sets European money supply, predicting German government purchases and French government purchases with the help of the model. The German government sets German government purchases, predicting European money supply and French government purchases with the help of the model. And the French government sets French government purchases, predicting European money supply and German government purchases with the help of the model. On this basis, the policy model can be characterized by a system of two equations: % =Aj + aM + pGi

(3)

Y2=A2+aM + pG2

(4)

Here Yj denotes full-employment output in Germany and Y2 is full-employment output in France. The endogenous variables are European money supply, German government purchases, and French government purchases. There are two targets and three instruments, so there is one degree of freedom. There seems to be no simple way of how to make use of this degree of freedom. As a result, under rational expectations, there is no unique equilibrium of monetary and fiscal competition. Put another way, under rational expectations, the simultaneous process of monetary and fiscal competition does not lead to full employment in each of the countries.

Part Three Monetary and Fiscal Policies The Case of Three Countries

Chapter 1 Monetary Policy in Europe 1. The Model

1) Introduction. For ease of exposition we make the following assumptions. The monetary union consists of three countries, say Germany, France and Italy. The member countries are the same size and have the same behavioural functions. An increase in European money supply raises German output, French output, and Italian output, to the same extent respectively. In the numerical example, an increase in European money supply of 100 raises German output, French output, and Italian output by 100 each. The output model can be represented by a system of three equations: Yi=Ai+aM

(1)

Y2=A2+a]V[

(2)

Y3=A3+aM

(3)

Yj denotes German output, Y2 is French output, Y3 is Italian output, M is European money supply, A^ is some other factors bearing on German output, A2 is some other factors bearing on French output, A3 is some other factors bearing on Italian output, and a is the monetary policy multiplier. The endogenous variables are German output, French output, and Italian output. An increase in European money supply of 1 causes an increase in German output of a, an increase in French output of a, and an increase in Italian output of a. The output model can be compressed to a single equation: Y = A+3aM

(4)

92 Here we have Y=Yj + Y2 + Y3 and A = A j + A2 + A3. Y denotes European output, M is European money supply, A is some other factors bearing on European output, and 3a is the monetary poUcy multipUer in Europe. The endogenous variable is European output. An increase in European money supply of 1 causes an increase in European output of 3a. 2) The policy model. At the beginning there is unemployment in Germany, France and Italy. More precisely, unemployment in Germany is high, unemployment in France is medium size, and unemployment in Italy is low. The primary target of the European central bank is price stability in Europe. The secondary target of the European central bank is full employment in Europe. For ease of exposition we assume that unemployment causes deflation whereas overemployment causes inflation. The specific target of the European central bank is that unemployment in Germany, France and Italy add up to zero. Accordingly, the specific target of the European central bank is that inflation in Germany, France and Italy add up to zero. In other words, the specific target of the European central bank is full employment in Europe on average. Accordingly, the specific target of the European central bank is price stability in Europe on average. 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. Now have a closer look at the policy model. The specific target of the European central bank is full employment in Europe on average: Yi + Y2+Y3 = Yi + Y2 + Y3

(5)

Here Y^ denotes target output in Germany, Y2 is target output in France, Y3 is target output in Italy, Yj is full-employment output in Germany, Y2 is fullemployment output in France, and Y3 is full-employment output in Italy. According to equation (5), target output in Europe should be equal to fullemployment output in Europe. What is the required level of European money supply? To answer this question, eliminate Y^, Y2 and Y3 in equation (5) by means of equations (1), (2) and (3) and solve for M:

93

M = ^^

^

^

i

2^

^

(6)

3a Obviously, the required level of European money supply depends on fullemployment output in Europe, some other factors bearing on European output, and the monetary policy multiplier in Europe. As a result, monetary policy in Europe can achieve full employment in Europe on average. And what is more, it can achieve price stability in Europe on average. However, monetary policy in Europe cannot achieve full employment in Germany, France and Italy. And what is more, it cannot achieve price stability in Germany, France and Italy. 3) Another version of the policy model. As an alternative, the policy model can be stated in terms of the initial output gap and the required increase in money supply. The European central bank raises European money supply so as to close the output gap in Europe: AY. + AY, + AY, AM = —^^ ^ 3a

(7)

Here AM denotes the required increase in European money supply, AY^ is the initial output gap in Germany, AY2 is the initial output gap in France, AY3 is the initial output gap in Italy, AYJ + AY2 + AY3 is the initial output gap in Europe, and 3a is the monetary policy multiplier in Europe. Evidently, the required increase in European money supply depends on the initial output gap in Europe and on the monetary policy multiplier in Europe. The larger the initial output gap in Europe, the larger is the required increase in European money supply.

94

2. Some Numerical Examples

To illustrate the policy model, have a look at some numerical examples. For ease of exposition, without loss of generality, assume a = 1. On this assumption, the output model can be written as follows: Yi=Ai+M

(1)

Y2=A2+M

(2)

Y3=A3+M

(3)

The endogenous variables are German, French and Italian output. Obviously, an increase in European money supply of 100 causes an increase in German output of 100, an increase in French output of 100, and an increase in Italian output of equally 100. Further, let full-employment output in Germany be 1000, let fullemployment output in France be 1000, and let full-employment output in Italy be the same. It proves useful to study three distinct cases: - the case of unemployment - the case of inflation - unemployment in Germany and France, inflation in Italy. 1) The case of unemployment. Let initial output in Germany be 940, let initial output in France be 950, and let initial output in Italy be 990. In each of the countries there is unemployment and deflation. Step 1 refers to the policy response. The output gap in Germany is 60, the output gap in France is 50, the output gap in Italy is 10, and the output gap in Europe is 120. The monetary policy multiplier in Europe is 3. So what is needed in Europe is an increase in European money supply of 40. Step 2 refers to the output lag. The increase in European money supply of 40 causes an increase in German output of 40, an increase in French output of 40, and an increase in Italian output of equally 40. As a consequence, German output

95 goes from 940 to 980, French output goes from 950 to 990, and Italian output goes from 990 to 1030. In Germany there is still some unemployment and deflation. In France there is still some unemployment and deflation, too. In Italy there is now some overemployment and inflation. And in Europe there is now full employment and price stability. Unemployment in Germany, France and Italy add up to zero. Accordingly, inflation in Germany, France and Italy add up to zero. Table 3.1 presents a synopsis. As a result, monetary policy in Europe can achieve full employment in Europe on average. And what is more, it can achieve price stability in Europe on average. However, monetary policy in Europe cannot achieve full employment in Germany, France and Italy. And what is more, it cannot achieve price stability in Germany, France and Italy. There is an increase in German output, as there is in French output and Italian output. There is an increase in German tax revenue, as there is in French tax revenue and Italian tax revenue. There is a decline in the German budget deficit, as there is in the French budget deficit and the Italian budget deficit.

Table 3.1 Monetary Policy in Europe The Case of Unemployment

Initial Output

Germany

France

Italy

940

950

990

Change in Money Supply Output

40 980

990

1030

2) The case of inflation. Let initial output in Germany be 1060, let initial output in France be 1050, and let initial output in Italy be 1010. In each of the countries there is overemployment and inflation. Step 1 refers to the policy response. The inflationary gap in Germany is 60, the inflationary gap in France is 50, the inflationary gap in Italy is 10, and the inflationary gap in Europe is 120.

96 The monetary policy multiplier in Europe is 3. So what is needed in Europe is a reduction in European money supply of 40. Step 2 refers to the output lag. The reduction in European money supply of 40 causes a decline in German output of 40, a decline in French output of 40, and a decline in Italian output of equally 40. As a consequence, German output goes from 1060 to 1020, French output goes from 1050 to 1010, and Italian output goes from 1010 to 970. In Germany there is still some overemployment and inflation. In France there is still some overemployment and inflation, too. In Italy there is now some unemployment and deflation. And in Europe there is now full employment and price stability. Unemployment in Germany, France and Italy add up to zero. Accordingly, inflation in Germany, France and Italy add up to zero. Table 3.2 gives an overview. As a result, monetary policy in Europe can achieve full employment and price stability in Europe as a whole. However, monetary policy in Europe cannot achieve full employment and price stability in each of the member countries. There is a decline in German output, as there is in French output and Italian output. There is a decline in German tax revenue, as there is in French tax revenue and Italian tax revenue. There is an increase in the German budget deficit, as there is in the French budget deficit and the Italian budget deficit.

Table 3.2 Monetary Policy in Europe The Case of Inflation

Initial Output

Germany

France

Italy

1060

1050

1010

Change in Money Supply Output

-40 1020

1010

970

97 3) Unemployment in Germany and France, inflation in Italy. Let initial output in Germany be 940, let initial output in France be 970, and let initial output in Italy be 1030. In Germany there is unemployment and deflation. In France there is unemployment and deflation, too. In Italy there is overemployment and inflation. And in Europe there is unemployment and deflation. Step 1 refers to the policy response. The output gap in Germany is 60, the output gap in France is 30, the inflationary gap in Italy is 30, and the output gap in Europe is 60. The monetary policy multiplier in Europe is 3. So what is needed in Europe is an increase in European money supply of 20. Step 2 refers to the output lag. The increase in European money supply of 20 raises German output, French output, and Italian output by 20 each. As a consequence, German output goes from 940 to 960, French output goes from 970 to 990, and Italian output goes from 1030 to 1050. In Germany there is now some less unemployment and deflation. In France there is now some less unemployment and deflation, too. In Italy there is now some more overemployment and inflation. And in Europe there is now full employment and price stability. Unemployment in Germany, France and Italy add up to zero. Accordingly, inflation in Germany, France and Italy add up to zero. Table 3.3 presents a synopsis. As a result, monetary policy in Europe can achieve full employment and price stability in Europe as a whole. However, monetary policy in Europe cannot achieve full employment and price stability in each of the member countries.

Table 3.3 Monetary Policy in Europe Unemployment in Germany and France, Inflation in Italy

Initial Output

Germany

France

Italy

940

970

1030

Change in Money Supply Output

20 960

990

1050

Chapter 2 Fiscal Policies in Germany, France and Italy

1) Introduction. For ease of exposition we assume that the monetary union consists of three countries, say Germany, France and Italy. The member countries are the same size and have the same behavioural functions. An increase in German government purchases raises German output. Correspondingly, an increase in French government purchases raises French output. And an increase in Italian government purchases raises Italian output. For ease of exposition we assume that fiscal policy in one of the countries has no effect on output in the other countries. In the numerical example, an increase in German government purchases of 100 causes an increase in German output of 100. Correspondingly, an increase in French government purchases of 100 causes an increase in French output of 100. And an increase in Italian government purchases of 100 causes an increase in Italian output of 100. The output model can be represented by a system of three equations: Yi=Ai + pGi

(1)

Y2=A2 + |3G2

(2)

Y3=A3 + PG3

(3)

Yj denotes German output, Y2 is French output, Y3 is Italian output, Gj is German government purchases, Gj is French government purchases, G3 is Italian government purchases, and P is the fiscal policy multiplier. The endogenous variables are German output, French output, and Italian output. An increase in German government purchases of 1 causes an increase in German output of p . Correspondingly, an increase in French government purchases of 1 causes an increase in French output of p . And an increase in Italian government purchases of 1 causes an increase in Italian output of P. 2) The policy model. At the start there is unemployment in Germany, France and Italy. More precisely, unemployment in Germany is high, unemployment in

99 France is medium size, and unemployment in Italy is low. The target of the German government is full employment in Germany. The instrument of the German government is German government purchases. The target of the French government is full employment in France. The instrument of the French government is French government purchases. The target of the Italian government is full employment in Italy. The instrument of the Italian government is Italian government purchases. The policy model can be characterized by a system of three equations: Yi=Ai+pGi

(4)

Y2=A2+pG2

(5)

Y3=A3+pG3

(6)

Here Y^ denotes full-employment output in Germany, Y2 is full-employment output in France, Y3 is full-employment output in Italy, Gj is the required level of German government purchases, G2 is the required level of French government purchases, and G3 is the required level of Italian government purchases. The endogenous variables are German government purchases, French government purchases, and Italian government purchases. As a result, fiscal policies in Germany, France and Italy can achieve full employment and price stability in each of the countries. However, as a severe side effect, fiscal policies in Germany, France and Italy cause an increase in the European budget deficit. 3) Another version of the policy model. As an alternative, the policy model can be stated in terms of the initial output gap and the required increase in government purchases. The German government raises German government purchases so as to close the output gap in Germany:

A0, = ^

(7)

Here AG^ denotes the required increase in German government purchases, AYj is the initial output gap in Germany, and P is the fiscal policy multiplier in Germany. According to equation (7), the required increase in German

100 government purchases depends on the initial output gap in Germany and on the fiscal policy multiplier in Germany. Similarly, the French government raises French government purchases so as to close the output gap in France: AY2 AG2=-^

T

(8)

Here AG2 denotes the required increase in French government purchases, AY2 is the initial output gap in France, and P is the fiscal policy multiplier in France. According to equation (8), the required increase in French government purchases depends on the initial output gap in France and on the fiscal policy multiplier in France. And the Italian government raises Italian government purchases so as to close the output gap in Italy: AY3 ^^3=^;^

T

(9)

Here AG3 denotes the required increase in Italian government purchases, AY3 is the initial output gap in Italy, and p is the fiscal policy multiplier in Italy. According to equation (9), the required increase in Italian government purchases depends on the initial output gap in Italy and on the fiscal policy multiplier in Italy. 4) A numerical example. To illustrate the policy model, have a look at a numerical example. For ease of exposition, without losing generality, assume that P = 1. On this assumption, the output model can be written as follows: Yi = A i + G i

(10)

Y2=A2+G2

(11)

Y3=A3+G3

(12)

101 The endogenous variables are German, French and Italian output. Obviously, an increase in German government purchases of 100 causes an increase in German output of 100. Correspondingly, an increase in French government purchases of 100 causes an increase in French output of 100. And an increase in Italian government purchases of 100 causes an increase in Italian output of 100. Further, let full-employment output in Germany be 1000, let full-employment output in France be 1000, and let full-employment output in Italy be the same. Let initial output in Germany be 940, let initial output in France be 950, and let initial output in Italy be 990. In each of the countries there is unemployment and deflation. Step 1 refers to the policy response. The output gap in Germany is 60. The fiscal policy multiplier in Germany is 1. So what is needed in Germany is an increase in German government purchases of 60. The output gap in France is 50. The fiscal policy multiplier in France is 1. So what is needed in France is an increase in French government purchases of 50. The output gap in Italy is 10. The fiscal policy multiplier in Italy is 1. So what is needed in Italy is an increase in Italian government purchases of 10. Step 2 refers to the output lag. The increase in German government purchases of 60 raises German output by 60. The increase in French government purchases of 50 raises French output by 50. And the increase in Italian government purchases of 10 raises Italian output by 10. As a consequence, German output goes from 940 to 1000, French output goes from 950 to 1000, and Italian output goes from 990 to 1000. In each of the countries there is now full employment and price stability. As a result, fiscal policies in Germany, France and Italy can achieve full employment and price stability in each of the countries. There is an increase in European government purchases, an increase in European output, and an increase in the European budget deficit. There is an increase in the interest rate and a decline in European investment. There is an appreciation of the euro, a decline in European exports, and a decline in the European current account surplus. Table 3.4 gives an overview.

102 Table 3.4 Fiscal Policies in Germany, France and Italy The Case of Unemployment

Initial Output Change in Government Purchases Output

Germany

France

Italy

940

950

990

60

50

10

1000

1000

1000

Chapter 3 Monetary and Fiscal Competition

1) The static model. This chapter deals with competition between the European central bank, the German government, the French government, and the Italian government. As a point of reference, consider the static model. It can be represented by a system of three equations: Y i = A i + a M + pGi

(1)

Y 2 = A 2 + a M + pG2

(2)

Y 3 = A 3 + a M + pG3

(3)

Yj denotes German output, Y2 is French output, Y3 is Italian output, M is European money supply, G^ is German government purchases, G2 is French government purchases, G3 is Italian government purchases, a is the monetary policy multiplier, and p is the fiscal policy multiplier. The endogenous variables are German output, French output, and Italian output. An increase in European money supply of 1 causes an increase in German output of a , an increase in French output of a , and an increase in Italian output of a . An increase in German government purchases of 1 causes an increase in German output of p . Correspondingly, an increase in French government purchases of 1 causes an increase in French output of p . And an increase in Italian government purchases of 1 causes an increase in Italian output of p . 2) The dynamic model. At the beginning there is unemployment in Germany, France and Italy. More precisely, unemployment in Germany is high, unemployment in France is medium size, and unemployment in Italy is low. The primary target of the European central bank is price stability in Europe. The secondary target of the European central bank is foil employment in Europe. The specific target of the European central bank is full employment in Europe on average. The instrument of the European central bank is European money supply.

104

The target of the German government is full employment in Germany. The instrument of the German government is German government purchases. The target of the French government is full employment in France. The instrument of the French government is French government purchases. The target of the Italian government is full employment in Italy. And the instrument of the Italian government is Italian government purchases. We assume that the central bank and the governments decide sequentially. First the central bank decides, then the governments decide. Step 1 refers to monetary policy in Europe. Step 2 refers to the output lag. Step 3 refers to fiscal policies in Germany, France and Italy. And step 4 refers to the output lag. Now have a closer look at the dynamic model. Step 1 refers to monetary policy in Europe. The European central bank raises European money supply so as to close the output gap in Europe: AY. + AY, + AY, AM = —^ ^ ^ 3a

(4)

Here AM denotes the required increase in European money supply, AYj is the initial output gap in Germany, AY2 is the initial output gap in France, AY3 is the initial output gap in Italy, AYJ + AY2 + AY3 is the initial output gap in Europe, and 3a is the monetary policy multiplier in Europe. According to equation (4), the required increase in European money supply depends on the initial output gap in Europe and on the monetary policy multiplier in Europe. Step 2 refers to the output lag. Step 3 refers to fiscal policies in Germany, France and Italy. The German government raises German government purchases so as to close the output gap in Germany:

AGi=^^ 1 p

(5) V /

105 Here AGj denotes the required increase in German government purchases, AY^ is the initial output gap in Germany, and p is the fiscal policy multiplier in Germany. According to equation (5), the required increase in German government purchases depends on the initial output gap in Germany and on the fiscal policy multiplier in Germany. Similarly, the French government raises French government purchases so as to close the output gap in France: A^ AG2=—^

P

(6)

Here AG2 denotes the required increase in French government purchases, AY2 is the initial output gap in France, and P is the fiscal policy multiplier in France. According to equation (6), the required increase in French government purchases depends on the initial output gap in France and on the fiscal policy multiplier in France. And the Italian government raises Italian government purchases so as to close the output gap in Italy: AY, AG, = — ^ 3

p

(7) V 7

Here AG3 denotes the required increase in Italian government purchases, AY3 is the initial output gap in Italy, and P is the fiscal policy multiplier in Italy. According to equation (7), the required increase in Italian government purchases depends on the initial output gap in Italy and on the fiscal policy multiplier in Italy. Step 4 refers to the output lag. As a result, the process of monetary and fiscal competition leads to full employment in Germany, France and Italy. 3) A numerical example: the case of unemployment. To illustrate the dynamic model, have a look at a numerical example. For ease of exposition, without loss of generality, assume that a = 1 and P = 1. On this assumption, the static model can be written as follows:

106

Y i = A i + M + Gi

(8)

Y 2 = A 2 + M + G2

(9)

Y3=A3+M + G3

(10)

The endogenous variables are German, French and Italian output. Obviously, an increase in European money supply of 100 causes an increase in German output of 100, an increase in French output of 100, and an increase in Italian output of equally 100. An increase in German government purchases of 100 causes an increase in German output of 100. Correspondingly, an increase in French government purchases of 100 causes an increase in French output of 100. And an increase in Italian government purchases of 100 causes an increase in Italian output of 100. Further, let full-employment output in Germany be 1000, let foil-employment output in France be 1000, and let foil-employment output in Italy be the same. Let initial output in Germany be 940, let initial output in France be 950, and let initial output in Italy be 990. In each of the countries there is unemployment and deflation. Step 1 refers to monetary policy in Europe. The output gap in Europe is 120. The monetary policy multiplier in Europe is 3. So what is needed in Europe is an increase in European money supply of 40. Step 2 refers to the output lag. The increase in European money supply of 40 causes an increase in German output of 40, an increase in French output of 40, and an increase in Italian output of equally 40. As a consequence, German output goes from 940 to 980, French output goes from 950 to 990, and Italian output goes from 990 to 1030. In Germany there is still some unemployment and deflation. In France there is still some unemployment and deflation, too. In Italy there is now some overemployment and inflation. And in Europe there is now foil employment and price stability. Step 3 refers to fiscal policies in Germany, France and Italy. The output gap in Germany is 20. The fiscal policy multiplier in Germany is 1. So what is needed in Germany is an increase in German government purchases of 20. The output gap in France is 10. The fiscal policy multiplier in France is 1. So what is needed in France is an increase in French government purchases of 10. The

107 inflationary gap in Italy is 30. The fiscal policy multiplier in Italy is 1. So what is needed in Italy is a reduction in Italian government purchases of 30. Step 4 refers to the output lag. The increase in German government purchases of 20 raises German output by 20. The increase in French government purchases of 10 raises French output by 10. And the reduction in Italian government purchases of 30 lowers Italian output by 30. As a consequence, German output goes from 980 to 1000, French output goes from 990 to 1000, and Italian output goes from 1030 to 1000. In each of the countries there is now full employment and price stability. Table 3.5 presents a synopsis.

Table 3.5 Competition between the European Central Bank, the German Government, the French Government, and the Italian Government The Case of Unemployment

Initial Output

Germany

France

Italy

940

950

990

Change in Money Supply

1 Output Change in Government Purchases Output

1

40 980

990

1030

20

10

-30

1000

1000

1000

As a result, the process of monetary and fiscal competition leads to full employment and price stability in each of the countries. There is an increase in European money supply. There is an increase in German government purchases, an increase in French government purchases, a reduction in Italian government purchases, and no change in European government purchases. There is an increase in German output, as there is in French output and Italian output. In steps 1 and 2 there is some overshooting in Italian output.

108

4) A numerical example: the case of inflation. Let initial output in Germany be 1060, let initial output in France be 1050, and let initial output in Italy be 1010. In each of the countries there is overemployment and inflation. Step 1 refers to monetary policy in Europe. The inflationary gap in Europe is 120. The monetary policy multiplier in Europe is 3. So what is needed in Europe is a reduction in European money supply of 40. Step 2 refers to the output lag. The reduction in European money supply of 40 causes a decline in German output of 40, a decline in French output of 40, and a decline in Italian output of equally 40. As a consequence, German output goes from 1060 to 1020, French output goes from 1050 to 1010, and Italian output goes from 1010 to 970. In Germany there is still some overemployment and inflation. In France there is still some overemployment and inflation, too. In Italy there is now some unemployment and deflation. And in Europe there is now fall employment and price stability. Step 3 refers to fiscal policies in Germany, France and Italy. The inflationary gap in Germany is 20. The fiscal policy multiplier in Germany is 1. So what is needed in Germany is a reduction in German government purchases of 20. The inflationary gap in France is 10. The fiscal policy multiplier in France is 1. So what is needed in France is a reduction in French government purchases of 10. The output gap in Italy is 30. The fiscal policy multiplier in Italy is 1. So what is needed in Italy is an increase in Italian government purchases of 30. Step 4 refers to the output lag. The reduction in German government purchases of 20 lowers German output by 20. The reduction in French government purchases of 10 lowers French output by 10. And the increase in Italian government purchases of 30 raises Italian output by 30. As a consequence, German output goes from 1020 to 1000, French output goes from 1010 to 1000, and Italian output goes from 970 to 1000. In each of the countries there is now fall employment and price stability. As a result, the process of monetary and fiscal competition leads to fall employment and price stability in each of the countries. Table 3.6 gives an overview.

109 Table 3.6 Competition between the European Central Bank, the German Government, the French Government, and the Italian Government The Case of Inflation

Initial Output

Germany

France

Italy

1060

1050

1010

Change in Money Supply

1 Output

-40 1020

1010

970

Change in Government Purchases

-20

-10

30

Output

1000

1000

1000

Chapter 4 Monetary and Fiscal Cooperation

1) Introduction. This chapter deals with cooperation between the European central bank, the German government, the French government, and the Italian government. As a starting point, take the output model. It can be represented by a system of three equations: Yi=AiH-a]V[ + pGi

(1)

Y 2 = A 2 + a M + pG2

(2)

Y3=A3+a]V[ + pG3

(3)

Here Y^ denotes German output, Y2 is French output, Y3 is Italian output, M is European money supply, G^ is German government purchases, G2 is French government purchases, G3 is Italian government purchases, a is the monetary policy multiplier, and P is the fiscal policy multiplier. The endogenous variables are German output, French output, and Italian output. 2) The policy model. At the beginning there is unemployment in Germany, France and Italy. More precisely, unemployment in Germany is high, unemployment in France is medium size, and unemployment in Italy is low. The policy makers are the European central bank, the German government, the French government, and the Italian government. The targets of policy cooperation are full employment in Germany, full employment in France, and full employment in Italy. The instruments of policy cooperation are European money supply, German government purchases, French government purchases, and Italian government purchases. There are three targets and four instruments, so there is one degree of freedom. As a result, there is an infinite number of solutions. In other words, monetary and fiscal cooperation can achieve full employment in Germany, France and Italy. Taking differences in equations (1), (2) and (3), the policy model can be written as follows:

Ill

AYj=aAM + pAGi

(4)

AY2=aAM + pAG2

(5)

AY3=aAM + pAG3

(6)

Here AYj denotes the initial output gap in Germany, AY2 is the initial output gap in France, AY^ is the initial output gap in Italy, AM is the required increase in European money supply, AG^ is the required increase in German government purchases, AG2 is the required increase in French government purchases, and AG3 is the required increase in Italian government purchases. The endogenous variables are AM, AG^, AG2 and AG3. We now introduce a fourth target. We assume that the sum total of European government purchases should be constant: AGi + AG2+AG3=0

(7)

Add up equations (4), (5) and (6), taking account of equation (7), to find out: AY+AY^+AY. AM = —^ 2 ^ 3a

(8)

Here AY^ + AY2 + AY3 is the initial output gap in Europe, and 3a is the monetary policy multiplier in Europe. Then subtract equation (5) from equation (4): AYj - AY2 = pAGj - PAG2

(9)

Similarly, subtract equation (6) from equation (4): AYj - AY3 = pAGj -pAGj Moreover, add up equations (9) and (10):

(10)

112

2AYj - AY2 - AY3 = 2 pAGj - pAGj - PAG3

(11)

Then eliminate AGj and AG3 in equation (11) by means of equation (7) and solve for:

•

2AY,-AY,-AY3 3p

In the same way it can be derived that: 2AY,-AY,-AY, 2

3p

2AY3-AY,-AY,

According to equation (8), the required increase in European money supply depends on the initial output gap in Europe and on the monetary policy multiplier in Europe. According to equation (12), the required increase in German government purchases depends on the initial output gap in Germany, the initial output gap in France, the initial output gap in Italy, and the fiscal policy multiplier. According to equation (13), the required increase in French government purchases depends on the initial output gap in France, the initial output gap in Germany, the initial output gap in Italy, and the fiscal policy multiplier. And so on. 3) A numerical example: the case of unemployment. To illustrate the policy model, have a look at a numerical example. For ease of exposition, without losing generality, assume a = 1 and P = 1. That is, an increase in European money supply of 100 causes an increase in German output of 100, an increase in French output of 100, and an increase in Italian output of equally 100. An increase in German government purchases of 100 causes an increase in German output of 100. Correspondingly, an increase in French government purchases of 100 causes

113 an increase in French output of 100. And an increase in Italian government purchases of 100 causes an increase in Italian output of 100. Further, let fullemployment output in Germany be 1000, let full-employment output in France be 1000, and let full-employment output in Italy be the same. Let initial output in Germany be 940, let initial output in France be 950, and let initial output in Italy be 990. In each of the countries there is unemployment and deflation. Step 1 refers to the policy response. The output gap in Germany is 60, the output gap in France is 50, the output gap in Italy is 10, and the output gap in Europe is 120. So what is needed, according to equations (8), (12), (13) and (14), is an increase in European money supply of 40, an increase in German government purchases of 20, an increase in French government purchases of 10, and a reduction in Italian government purchases of 30. Step 2 refers to the output lag. The increase in European money supply of 40 causes an increase in German output of 40, an increase in French output of 40, and an increase in Italian output of equally 40. The increase in German government purchases of 20 raises German output by 20. The increase in French government purchases of 10 raises French output by 10. And the reduction in Italian government purchases of 30 lowers Italian output by 30. The net effect is an increase in German output of 60, an increase in French output of 50, and an increase in Italian output of 10. As a consequence, German output goes from 940 to 1000, French output goes from 950 to 1000, and Italian output goes from 990 to 1000. In each of the countries there is now full employment and price stability. Table 3.7 presents a synopsis. As a result, monetary and fiscal cooperation can achieve full employment and price stability in each of the countries. There is an increase in European money supply. There is an increase in German government purchases, an increase in French government purchases, a reduction in Italian government purchases, and no change in European government purchases. There is an increase in German output, as there is in French output and Italian output.

114 Table 3.7 Cooperation between the European Central Bank, the German Government, the French Government, and the Italian Government The Case of Unemployment

Initial Output

Germany

France

Italy

940

950

990

40

Change in Money Supply Change in Government Purchases Output

20

10

-30

1000

1000

1000

4) A numerical example: the case of inflation. Let initial output in Germany be 1060, let initial output in France be 1050, and let initial output in Italy be 1010. In each of the countries there is overemployment and inflation. Step 1 refers to the policy response. The inflationary gap in Germany is 60, the inflationary gap in France is 50, the inflationary gap in Italy is 10, and the inflationary gap in Europe is 120. So what is needed, according to equations (8), (12), (13) and (14), is a reduction in European money supply of 40, a reduction in German government purchases of 20, a reduction in French government purchases of 10, and an increase in Italian government purchases of 30. Step 2 refers to the output lag. The reduction in European money supply of 40 causes a decline in German output of 40, a decline in French output of 40, and a decline in Italian output of equally 40. The reduction in German government purchases of 20 lowers German output by 20. The reduction in French government purchases of 10 lowers French output by 10. And the increase in Italian government purchases of 30 raises Italian output by 30. The net effect is a decline in German output of 60, a decline in French output of 50, and a decline in Italian output of 10. As a consequence, German output goes from 1060 to 1000, French output goes from 1050 to 1000, and Italian output goes from 1010 to 1000. In each of the countries there is now full employment and price stability.

115 As a result, monetary and fiscal cooperation can achieve full employment and price stability in each of the countries. Table 3.8 gives an overview.

Table 3.8 Cooperation between the European Central Bank, the German Government, the French Government, and the Italian Government The Case of Inflation

Initial Output

Germany

France

Italy

1060

1050

1010

Change in Money Supply

-40

Change in Government Purchases

-20

-10

30

Output

1000

1000

1000

1

Part Four Monetary and Wage Policies Basic Models

Chapter 1 Wage Policies in Germany and France 1. The Model

1) Introduction. For ease of exposition we assume that the monetary union consists of two countries, say Germany and France. The member countries are the same size and have the same behavioural functions. An increase in German nominal wages lowers German output. Correspondingly, an increase in French nominal wages lowers French output. For ease of exposition we assume that wage policy in one of the countries has no effect on output in the other country. In the numerical example, an increase in German nominal wages of 100 causes a decline in German output of 100. Correspondingly, an increase in French nominal wages of 100 causes a decline in French output of 100. For ease of exposition we assume that the wage policy multiplier is 1. This assumption is consistent since the wage rate is defined in nominal terms while output is defined in real terms. The output model can be represented by a system of two equations: Yi=Ai-yWi

(1)

Y2=A2-yW2

(2)

Of course this is a reduced form. Y^ denotes German output, Y2 is French output, Wj is the nominal wage rate in Germany, W2 ^^ ^^^ nominal wage rate in France, Aj is some other factors bearing on German output, A2 is some other factors bearing on French output, and y is the wage policy multiplier. The endogenous variables are German output and French output. According to equation (1), German output is a negative function of German nominal wages. And according to equation (2), French output is a negative function of French nominal wages. An increase in German nominal wages of 1 causes a decline in German output of y. And an increase in French nominal wages of 1 causes a decline in French output of y.

120

2) The policy model. At the beginning there is unemployment in Germany and France. More precisely, unemployment in Germany is high, and unemployment in France is low. 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. The policy model can be characterized by a system of two equations: Yi=Ai-yWi

(3)

Y2=A2-yW2

(4)

Here Yj denotes full-employment output in Germany, Y2 is full-employment output in France, Wj is the required level of German nominal wages, and W2 is the required level of French nominal wages. The endogenous variables are German nominal wages and French nominal wages. The solution to the policy model is:

W , = ^ i ^

(5)

W2=^^^^

(6)

Equation (5) shows the required level of German nominal wages. It depends on full-employment output in Germany and on some other factors bearing on German output. Equation (6) shows the required level of French nominal wages. As a result, wage policies in Germany and France can achieve full employment in each of the countries.

121 3) Another version of the policy model. As an alternative, the poHcy model can be stated in terms of the initial output gap and the required change in nominal wages. The German labour union lowers German nominal wages so as to close the output gap in Germany:

AWi = - ^ Y

(7)

Here AW^ denotes the required change in German nominal wages, AY^ is the initial output gap in Germany, and y is the wage policy multiplier in Germany. According to equation (7), the required cut in German nominal wages depends on the initial output gap in Germany and on the wage policy multiplier in Germany. The larger the initial output gap in Germany, the larger is the required cut in German nominal wages. Similarly, the French labour union lowers French nominal wages so as to close the output gap in France:

AW2 =

AYo ^

(8)

Here AW2 denotes the required change in French nominal wages, AY2 is the initial output gap in France, and y is the wage policy multiplier in France. According to equation (8), the required cut in French nominal wages depends on the initial output gap in France and on the wage policy multiplier in France.

2. Some Numerical Examples

To illustrate the policy model, have a look at some numerical examples. For ease of exposition, without losing generality, assume y= 1. On this assumption, the output model can be written as follows:

122

Yi = A i - W i

(1)

Y2 = A 2 - W 2

(2)

The endogenous variables are German and French output. Obviously, an increase in German nominal wages of 100 causes a decline in German output of 100. Correspondingly, an increase in French nominal wages of 100 causes a decline in French output of 100. Further, let full-employment output in Germany be 1000, and let full-employment output in France be the same. It proves useful to consider two distinct cases: - the case of unemployment - unemployment in Germany, overemployment in France. 1) The case of unemployment. Let initial output in Germany be 940, and let initial output in France be 970. In each of the countries there is unemployment. Step 1 refers to the policy response. The output gap in Germany is 60. The wage policy multiplier in Germany is 1. So what is needed in Germany is a reduction in German nominal wages of 60. The output gap in France is 30. The wage policy multiplier in France is 1. So what is needed in France is a reduction in French nominal wages of 30. Step 2 refers to the output lag. The reduction in German nominal wages of 60 causes an increase in German output of 60. And the reduction in French nominal wages of 30 causes an increase in French output of 30. As a consequence, German output goes from 940 to 1000, and French output goes from 970 to 1000. In each of the countries there is now full employment. As a result, wage policies in Germany and France can achieve full employment in each of the countries. There is a reduction in European nominal wages, a decline the price of European goods, a depreciation of the euro, an increase in European exports, and an increase in European output. There is an increase in the European current account surplus and a decline in the European budget deficit. Table 4.1 presents a synopsis.

123 Table 4.1 Wage Policies in Germany and France The Case of Unemployment Germany

France

940

970

Change in Nominal Wages

-60

-30

Output

1000

1000

Initial Output

1

2) Comparing wage policies with monetary policy. Monetary policy in Europe can achieve full employment in Europe as a whole. However, monetary policy in Europe cannot achieve full employment in each of the member countries. By contrast, wage policies in Germany and France can indeed achieve full employment in each of the member countries. However, wage policies in Germany and France require a deep cut in European nominal wages. 3) Comparing wage policies with fiscal policies. Fiscal policies in Germany and France can achieve full employment in each of the countries. However, as a severe side effect, fiscal policies in Germany and France cause an increase in the European budget deficit. Wage policies in Germany and France can achieve full employment in each of the countries, too. However, wage policies in Germany and France require a deep cut in European nominal wages. 4) Unemployment in Germany, overemployment in France. Let initial output in Germany be 970, and let initial output in France be 1030. In Germany there is unemployment, in France there is overemployment, and in Europe there is full employment. Step 1 refers to the policy response. The output gap in Germany is 30. The wage policy multiplier in Germany is 1. So what is needed in Germany is a reduction in German nominal wages of 30. The inflationary gap in France is 30. The wage policy multiplier in France is 1. So what is needed in France is an increase in French nominal wages of 30.

124 Step 2 refers to the output lag. The reduction in German nominal wages of 30 causes an increase in German output of 30. And the increase in French nominal wages of 30 causes a decline in French output of 30. As a consequence, German output goes from 970 to 1000, and French output goes from 1030 to 1000. In each of the countries there is now full employment. As a result, wage policies in Germany and France can achieve full employment in each of the countries. There is no change in European nominal wages, no change in the price of European goods, no change in the exchange rate, no change in European exports, and no change in European output. There is no change in the European current account surplus and no change in the European budget deficit. Table 4.2 gives an overview.

Table 4.2 Wage Policies in Germany and France Unemployment in Germany, Overemployment in France Germany

France

970

1030

Change in Nominal Wages

-30

30

Output

1000

1000

Initial Output

1

Chapter 2 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 two equations: Yi=Ai+aM-yWi

(1)

Y2=A2+aM-yW2

(2)

Of course this is a reduced form. Y^ denotes German output, Y2 is French output, M is European money supply, W^ 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, a is the monetary policy multiplier, and y is the wage policy multiplier. The endogenous variables are German output and French output. According to equation (1), German output is a positive function of European money supply and a negative function of German nominal wages. According to equation (2), French output is a positive function of European money supply and a negative function of French nominal wages. An increase in European money supply raises both German output and French output. An increase in German nominal wages lowers German output. And an increase in French nominal wages lowers French output. An increase in European money supply of 1 causes an increase in German output of a and an increase in French output of equally a . An increase in German nominal wages of 1 causes a decline in German output of y. And an increase in French nominal wages of 1 causes a decline in French output of y.

126 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. The primary target of the European central bank is price stability in Europe. The secondary target of the European central bank is full employment in Europe. The specific target of the European central bank is that unemployment in Germany equals overemployment in France. In other words, the specific target of the European central bank is full employment in Europe on average. 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 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 bank and the labour unions decide sequentially. First the central bank decides, then the labour unions decide. Step 1 refers to monetary policy in Europe. Step 2 refers to the output lag. Step 3 refers to wage policies in Germany and France. And step 4 refers to the output lag. Now have a closer look at the dynamic model. Step 1 refers to monetary policy in Europe. The European central bank raises European money supply so as to close the output gap in Europe:

AM = —^

^

(3)

2a Here AM denotes the required increase in European money supply, AYj is the initial output gap in Germany, AY2 is the initial output gap in France, AY^+AY2 is the initial output gap in Europe, and 2a is the monetary policy multiplier in Europe. According to equation (3), the required increase in European money supply depends on the initial output gap in Europe and on the monetary policy

127 multiplier in Europe. The larger the initial output gap in Europe, the larger is the required increase in European money supply. Step 2 refers to the output lag. Step 3 refers to wage policies in Germany and France. The German labour union lowers German nominal wages so as to close the output gap in Germany:

AWj = - ^

(4)

Here AWj denotes the required change in German nominal wages, AYj is the initial output gap in Germany, and y is the wage policy multiplier in Germany. According to equation (4), the required cut in German nominal wages depends on the initial output gap in Germany and on the wage policy multiplier in Germany. The larger the initial output gap in Germany, the larger is the required cut in German nominal wages. Similarly, the French labour union lowers French nominal wages so as to close the output gap in France:

AW2 =

AY, ^

(5)

Here AW2 denotes the required change in French nominal wages, AY2 is the initial output gap in France, and y is the wage policy multiplier in France. According to equation (5), the required cut in French nominal wages depends on the initial output gap in France and on the wage policy multiplier in France. Step 4 refers to the output lag. As a result, the process of competition between the European central bank, the German labour union, and the French labour union leads to full employment in Germany and France.

128

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 and y = 1. On this assumption, the static model can be written as follows: Yi=Ai+M-Wi

(1)

Y2=A2+M-W2

(2)

The endogenous variables are German and French output. Obviously, an increase in European money supply of 100 causes an increase in German output of 100 and an increase in French output of equally 100. An increase in German nominal wages of 100 causes a decline in German output of 100. Correspondingly, an increase in French nominal wages of 100 causes a decline in French output of 100. Further, let full-employment output in Germany be 1000, and let fallemployment output in France be the same. It proves usefal to study four distinct cases: - the case of unemployment - the case of overemployment - unemployment in Germany, overemployment in France - first the labour unions decide, then the central bank decides. 1) The case of unemployment. Let initial output in Germany be 940, and let initial output in France be 970. In each of the countries there is unemployment. Step 1 refers to monetary policy in Europe. The output gap in Europe is 90. The monetary policy multiplier in Europe is 2. So what is needed in Europe is an increase in European money supply of 45. Step 2 refers to the output lag. The increase in European money supply of 45 causes an increase in German output of 45 and an increase in French output of equally 45. As a consequence, German output goes from 940 to 985, and French output goes from 970 to 1015. In Germany there is still some unemployment. In

129 France there is now some overemployment. And in Europe there is now full employment. Unemployment in Germany equals overemployment in France. Step 3 refers to wage policies in Germany and France. The output gap in Germany is 15. The wage policy multiplier in Germany is 1. So what is needed in Germany is a reduction in German nominal wages of 15. The inflationary gap in France is 15. The wage policy multiplier in France is 1. So what is needed in France is an increase in French nominal wages of 15. Step 4 refers to the output lag. The reduction in German nominal wages of 15 causes an increase in German output of 15. And the increase in French nominal wages of 15 causes a decline in French output of 15. As a consequence, German output goes from 985 to 1000, and French output goes from 1015 to 1000. In each of the countries there is now full employment. Table 4.3 presents a synopsis. As a result, the process of competition between the European central bank, the German labour union, and the French labour union leads to full employment in each of the countries.

Table 4.3 Competition between the European Central Bank, the German Labour Union, and the French Labour Union The Case of Unemployment

Initial Output

Germany

France

940

970

Change in Money Supply

1 Output

45 985

1015

Change in Nominal Wages

-15

15

Output

1000

1000

1

130

There is an increase in European money supply. There is a reduction in German nominal wages, an increase in French nominal wages, and no change in European nominal wages. There is a decline in the price of German goods, an increase in the price of French goods, and no change in the price of European goods. There is an increase in German output, as there is in French output. In steps 1 and 2 there is some overshooting in French output. There is an increase in European output, an increase in European tax revenue, and a decline in the European budget deficit. There is a decline in the interest rate and an increase in European investment. There is a depreciation of the euro, an increase in European exports, and an increase in the European current account surplus. 2) The case of overemployment. Let initial output in Germany be 1060, and let initial output in France be 1030. In each of the countries there is overemployment. Step 1 refers to monetary policy in Europe. The inflationary gap in Europe is 90. The monetary policy multiplier in Europe is 2. So what is needed in Europe is a reduction in European money supply of 45. Step 2 refers to the output lag. The reduction in European money supply of 45 causes a decline in German output of 45 and a decline in French output of equally 45. As a consequence, German output goes from 1060 to 1015, and French output goes from 1030 to 985. In Germany there is still some overemployment. In France there is now some unemployment. And in Europe there is now full employment. Overemployment in Germany equals unemployment in France. Step 3 refers to wage policies in Germany and France. The inflationary gap in Germany is 15. The wage policy multiplier in Germany is 1. So what is needed in Germany is an increase in German nominal wages of 15. The output gap in France is 15. The wage policy multiplier in France is 1. So what is needed in France is a reduction in French nominal wages of 15. Step 4 refers to the output lag. The increase in German nominal wages of 15 causes a decline in German output of 15. And the reduction in French nominal wages of 15 causes an increase in French output of 15. As a consequence, German output goes from 1015 to 1000, and French output goes from 985 to

131 1000. In each of the countries there is now full employment. Table 4.4 gives an overview.

Table 4.4 Competition between the European Central Bank, The German Labour Union, and the French Labour Union The Case of Overemployment

Initial Output

Germany

France

1060

1030

Change in Money Supply Output Change in Nominal Wages Output

-45 1015

985

15

-15

1000

1000

As a result, the process of monetary and wage competition leads to full employment in Germany and France. There is a reduction in European money supply. There is an increase in German nominal wages, a reduction in French nominal wages, and no change in European nominal wages. There is an increase in the price of German goods, a decline in the price of French goods, and no change in the price of European goods. There is a decline in German output, as there is in French output. In steps 1 and 2 there is some overshooting in French output. There is a decline in European output, a decline in European tax revenue, and an increase in the European budget deficit. There is an increase in the interest rate and a decline in European investment. There is an appreciation of the euro, a decline in European exports, and a decline in the European current account surplus. 3) Unemployment in Germany, overemployment in France. Let initial output in Germany be 940, and let initial output in France be 1030. In Germany there is unemployment, in France there is overemployment, and in Europe there is

132 unemployment. Step 1 refers to monetary policy in Europe. The output gap in Europe is 30. The monetary policy multiplier in Europe is 2. So what is needed in Europe is an increase in European money supply of 15. Step 2 refers to the output lag. The increase in European money supply of 15 raises German output and French output by 15 each. As a consequence, German output goes from 940 to 955, and French output goes from 1030 to 1045. In Germany there is now some less unemployment. In France there is now some more overemployment. And in Europe there is now full employment. Unemployment in Germany equals overemployment in France. Step 3 refers to wage policies in Germany and France. The output gap in Germany is 45. The wage policy multiplier in Germany is 1. So what is needed in Germany is a reduction in German nominal wages of 45. The inflationary gap in France is 45. The wage policy multiplier in France is 1. So what is needed in France is an increase in French nominal wages of 45.

Table 4.5 Competition between the European Central Bank, the German Labour Union, and the French Labour Union Unemployment in Germany, Overemployment in France Germany

France

940

1030

1

955

1045

1

Change in Nominal Wages

-45

45

1

Output

1000

1000

Initial Output

15

Change in Money Supply Output

Step 4 refers to the output lag. The reduction in German nominal wages of 45 raises German output by 45. And the increase in French nominal wages of 45

133 lowers French output by 45. As a consequence, German output goes from 955 to 1000, and French output goes from 1045 to 1000. In each of the countries there is now full employment. Table 4.5 presents a synopsis. 4) Unemployment in Germany, overemployment in France: another case. Let initial output in Germany be 970, and let initial output in France be 1060. Step 1 refers to monetary policy in Europe. The inflationary gap in Europe is 30. The monetary policy multiplier in Europe is 2. So what is needed in Europe is a reduction in European money supply of 15. Step 2 refers to the output lag. The reduction in European money supply of 15 lowers German output and French output by 15 each. As a consequence, German output goes from 970 to 955, and French output goes from 1060 to 1045. In Germany there is now some more unemployment. In France there is now some less overemployment. And in Europe there is now full employment. Unemployment in Germany equals overemployment in France. Step 3 refers to wage policies in Germany and France. The output gap in Germany is 45. The wage policy multiplier in Germany is 1. So what is needed in Germany is a reduction in German nominal wages of 45. The inflationary gap in France is 45. The wage policy multiplier in France is 1. So what is needed in France is an increase in French nominal wages of 45. Step 4 refers to the output lag. The reduction in German nominal wages of 45 raises German output by 45. And the increase in French nominal wages of 45 lowers French output by 45. As a consequence, German output goes from 955 to 1000, and French output goes from 1045 to 1000. In each of the countries there is now full employment. Table 4.6 gives an overview. 5) Comparing monetary and wage competition with pure monetary policy. Pure monetary policy can achieve full employment in Europe as a whole. However, it cannot achieve full employment in each of the member countries. By contrast, monetary and wage competition can indeed achieve full employment in each of the member countries. Judging from this point of view, monetary and wage competition seems to be superior to pure monetary policy.

134 Table 4.6 Competition between the European Central Bank, the German Labour Union, and the French Labour Union Unemployment in Germany, Overemployment in France Germany

France

970

1060

1

955

1045

1

Change in Nominal Wages

-45

45

Output

1000

1000

Initial Output Change in Money Supply Output

-15

6) Comparing monetary and wage competition with pure wage policies. First consider the case of unemployment. Pure wage policies can achieve full employment in each of the member countries. And the same holds for monetary and wage competition. Pure wage policies cause 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 policies cause a large decline in the price of German goods, a large decline in the price of French goods, and a large decline in the price of European goods. By contrast, monetary and wage competition causes a small decline in the price of German goods, a small increase in the price of French goods, and no change in the price of European goods. Judging from this perspective, monetary and wage competition seems to be superior to pure wage policies. Second consider the case of overemployment. Pure wage policies can achieve full employment in each of the member countries. And the same holds for monetary and wage competition. Pure wage policies cause 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 compe-

135 tition causes a small increase in German nominal wages, a small reduction in French nominal wages, and no change in European nominal wages. Pure wage policies cause a large increase in the price of German goods, a large increase in the price of French goods, and a large increase in the price of European goods. By contrast, monetary and wage competition causes a small increase in the price of German goods, a small decline in the price of French goods, and no change in the price of European goods. Judging from this perspective, monetary and wage competition seems to be superior to pure wage policies. 7) 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, and let initial output in France be 970. In each of the countries there is unemployment. Step 1 refers to wage policies in Germany and France. The output gap in Germany is 60. The wage policy multiplier in Germany is 1. So what is needed in Germany is a reduction in German nominal wages of 60. The output gap in France is 30. The wage policy multiplier in France is 1. So what is needed in France is a reduction in French nominal wages of 30. Step 2 refers to the output lag. The reduction in German nominal wages of 60 raises German output by 60. And the reduction in French nominal wages of 30 raises French output by 30. As a consequence, German output goes from 940 to 1000, and French output goes from 970 to 1000. In each of the countries there is now full employment. Step 3 refers to monetary policy in Europe. The output gap in Europe is zero. So there is no reason for changing European money supply. Step 4 refers to the output lag. As a consequence, German output stays at 1000, as does French output. In each of the countries there is still full employment. Table 4.7 presents a synopsis. As a result, the process of competition between the German labour union, the French labour union, and the European central bank leads to full employment in each of the countries.

136 Table 4.7 Competition between the European Central Bank, the German Labour Union, and the French Labour Union First the Labour Unions Decide, then the Central Bank Decides Germany

France

940

970

Change in Nominal Wages

-60

-30

Output

1000

1000

Initial Output

Change in Money Supply Output

1

0 1000

1000

8) 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, and let initial output in France be 970. Case number 1: The central bank decides first. The increase in European money supply is 45, the reduction in German nominal wages is 15, the increase in French nominal wages is equally 15, and the change in European nominal wages is zero. Case number 2: The labour unions decide first. The increase in European money supply is zero, the reduction in German nominal wages is 60, the reduction in French nominal wages is 30, and the reduction in European nominal wages is 45. Table 4.8 gives an overview. 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 a zero increase in European money supply and a large reduction in European nominal wages. Judging from this point of view, it seems that the central bank should decide first.

137 Table 4.8 Who Should Decide First, the Central Bank or the Labour Unions?

Increase in

The Central Bank The Labour Unions Decides First Decide First

European Money Supply

45

0

German Nominal Wages

-15

-60

15

-30

0

-45

French Nominal Wages European Nominal Wages

Chapter 3 Cooperation between European 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 two equations: Yi=Ai+aM-yWj

(1)

Y2=A2+aM-yW2

(2)

Here Y^ denotes German output, Y2 is French output, M is European money supply, Wi is German nominal wages, W2 is French nominal wages, a is the monetary policy multiplier, and y is the wage policy multiplier. The endogenous variables are German output and French output. 2) The policy model. At the beginning there is unemployment in Germany and France. More precisely, unemployment in Germany is high, and unemployment in France is low. 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. Of course there are many more potential targets of policy cooperation: - balancing the budget in Germany and France - balancing the current account in Germany and France

139 - high investment in Germany and France - 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. Taking differences in equations (1) and (2), the policy model can be written as follows: AYi=aAM-YAWj

(3)

AY2=aAM-yAW2

(4)

Here AYj denotes the initial output gap in Germany, AY2 is the initial output gap in France, AM is the required change in European money supply, AW^ is the required change in German nominal wages, and AW2 is the required change in French nominal wages. The endogenous variables are AM, AW^ and AW2. 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 (3) and (4), taking account of AWj + AW2 = 0, to find out:

AM = ^ i l ^

(5)

2a Here AYj + AY2 is the initial output gap in Europe. Then subtract equation (4) from equation (3), taking account of AWj + AWj = 0, and solve for:

AW, = 1

AY,-AY, ! 2. 2y

_ AY,-AYo AW, ^ '2 = ^^-^ 2Y

(6)

(7)

140

According to equation (5), the required change in European money supply depends on the initial output gap in Europe and on the monetary policy multiplier in Europe. According to equation (6), the required change in German nominal wages depends on the initial output gap in Germany, the initial output gap in France, and the wage policy multiplier. The larger the initial output gap in Germany, the larger is the required cut in German nominal wages. Moreover, 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 (7), the required change in French nominal wages depends on the initial output gap in France, the initial output gap in Germany, and the wage policy multiplier.

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 = 1 and y = 1. That is, an increase in European money supply of 100 causes an increase in German output of 100 and an increase in French output of equally 100. An increase in German nominal wages of 100 causes a decline in German output of 100. Correspondingly, an increase in French nominal wages of 100 causes a decline in French output of 100. Further, let full-employment output in Germany be 1000, and let full-employment output in France be the same. It proves useful to consider four distinct cases: - the case of unemployment - the case of overemployment - unemployment in Germany, overemployment in France - alternative targets of policy cooperation. 1) The case of unemployment. Let initial output in Germany be 940, and let initial output in France be 970. In each of the countries there is unemployment.

141 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 Europe is 90. So what is needed, according to equations (5), (6) and (7) from the preceding section, is an increase in European money supply of 45, a reduction in German nominal wages of 15, and an increase in French nominal wages of equally 15. Step 2 refers to the output lag. The increase in European money supply of 45 causes an increase in German output of 45 and an increase in French output of equally 45. The reduction in German nominal wages of 15 causes an increase in German output of 15. And the increase in French nominal wages of 15 causes a decline in French output of 15. The net effect is an increase in German output of 60 and an increase in French output of 30. As a consequence, German output goes from 940 to 1000, and French output goes from 970 to 1000. In each of the countries there is now full employment. Table 4.9 presents a synopsis.

Table 4.9 Cooperation between the European Central Bank, the German Labour Union, and the French Labour Union The Case of Unemployment

Initial Output

Germany

France

940

970

Change in Money Supply

45

Change in Nominal Wages

-15

15

Output

1000

1000

As a result, cooperation between the European central bank, the German labour union, and the French labour union can achieve full employment in each of the countries. There is an increase in European money supply. There is a reduction in German nominal wages, an increase in French nominal wages, and no change in

142 European nominal wages. There is a decline in the price of German goods, an increase in the price of French goods, and no change in the price of European goods. There is an increase in German output, as there is French output. There is an increase in European output, an increase in European tax revenue, and a decline in the European budget deficit. There is a decline in the interest rate and an increase in European investment. There is a depreciation of the euro, an increase in European exports, and an increase in the European current account surplus. 2) Comparing policy cooperation with policy competition. Policy competition can achieve full employment in each of the countries. And the same applies to policy cooperation. Under policy competition, the increase in European money supply is 45, the reduction in German nominal wages is 15, and the increase in French nominal wages is equally 15 (assuming that the central bank decides first). Hence the solution to policy cooperation is identical with the solution to policy competition. Policy competition is a slow process consisting of four steps. By contrast, policy cooperation is a fast process consisting of only two steps. Policy competition causes some overshooting in output. By contrast, policy cooperation does not cause any overshooting in output. Judging from this point of view, policy cooperation seems to be superior to policy competition. 3) The case of overemployment. Let initial output in Germany be 1060, and let initial output in France be 1030. 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, and the inflationary gap in Europe is 90. So what is needed, according to equations (5), (6) and (7) from the previous section, is a reduction in European money supply of 45, an increase in German nominal wages of 15, and a reduction in French nominal wages of equally 15. Step 2 refers to the output lag. The reduction in European money supply of 45 causes a decline in German output of 45 and a decline in French output of equally 45. The increase in German nominal wages of 15 causes a decline in German output of 15. And the reduction in French nominal wages of 15 causes an increase in French output of 15. The net effect is a decline in German output of 60 and a decline in French output of 30. As a consequence, German output

143 goes from 1060 to 1000, and French output goes from 1030 to 1000. In each of the countries there is now full employment. Table 4.10 gives an overview.

Table 4.10 Cooperation between the European Central Bank, the German Labour Union, and the French Labour Union The Case of Overemployment

Initial Output

Germany

France

1060

1030

Change in Money Supply Change in Nominal Wages Output

-45 15

-15

1000

1000

As a result, monetary and wage cooperation can achieve full employment in Germany and France. There is a reduction in European money supply. There is an increase in German nominal wages, a reduction in French nominal wages, and no change in European nominal wages. There is an increase in the price of German goods, a decline in the price of French goods, and no change in the price of European goods. There is a decline in German output, as there is in French output. There is a decline European output, a decline in European tax revenue, and an increase in the European budget deficit. There is an increase in the interest rate and a decline in European investment. There is an appreciation of the euro, a decline in European exports, and a decline in the European current account surplus. 4) Unemployment in Germany, overemployment in France. Let initial output in Germany be 940, and let initial output in France be 1030. In Germany there is unemployment, in France there is overemployment, and in Europe there is unemployment. Step 1 refers to the policy response. The output gap in Germany is 60, the inflationary gap in France is 30, and the output gap in Europe is 30. So what is needed is an increase in European money supply of 15, a reduction in

144 German nominal wages of 45, and an increase in French nominal wages of equally 45. Step 2 refers to the output lag. The increase in European money supply of 15 raises German output and French output by 15 each. The reduction in German nominal wages of 45 raises German output by 45. And the increase in French nominal wages of 45 lowers French output by 45. The net effect is an increase in German output of 60 and a decline in French output of 30. As a consequence, German output goes from 940 to 1000, and French output goes from 1030 to 1000. In each of the countries there is now full employment. Table 4.11 presents a synopsis.

Table 4.11 Cooperation between the European Central Bank, the German Labour Union, and the French Labour Union Unemployment in Germany, Overemployment in France

Initial Output

Germany

France

940

1030

Change in Money Supply

15

Change in Nominal Wages

-45

45

Output

1000

1000

5) Unemployment in Germany, overemployment in France: another case. Let initial output in Germany be 970, and let initial output in France be 1060. In Germany there is unemployment, in France there is overemployment, and in Europe there is overemployment, too. Step 1 refers to the policy response. The output gap in Germany is 30, the inflationary gap in France is 60, and the inflationary gap in Europe is 30. So what is needed is a reduction in European money supply of 15, a reduction in German nominal wages of 45, and an increase in French nominal wages of equally 45.

145 Step 2 refers to the output lag. The reduction in European money supply of 15 lowers German output and French output by 15 each. The reduction in German nominal wages of 45 raises German output by 45. And the increase in French nominal wages of 45 lowers French output by 45. The net effect is an increase in German output of 30 and a decline in French output of 60. As a consequence, German output goes from 970 to 1000, and French output goes from 1060 to 1000. In each of the countries there is now full employment. Table 4.12 gives an overview.

Table 4.12 Cooperation between the European Central Bank, the German Labour Union, and the French Labour Union Unemployment in Germany, Overemployment in France

Initial Output

Germany

France

970

1060

Change in Money Supply

-15

Change in Nominal Wages

-45

45

Output

1000

1000

6) Alternative targets of policy cooperation: no reduction in national nominal wages. Let initial output in Germany be 940, and let initial output in France be 970. In each of the countries there is unemployment. 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 60, a reduction in German nominal wages of zero, and an increase in French nominal wages of 30. Step 2 refers to the output lag. The increase in European money supply of 60 raises German output and French output by 60 each. And the increase in French nominal wages of 30 lowers French output by 30. The net effect is an increase in German output of 60 and an increase in French output of 30. As a consequence.

146 German output goes from 940 to 1000, and French output goes from 970 to 1000. In each of the countries there is now full employment. Table 4.13 presents a synopsis.

Table 4.13 Cooperation between the European Central Bank, the German Labour Union, and the French Labour Union No Reduction in National Nominal Wages

Initial Output

Germany

France

940

970 60

Change in Money Supply Change in Nominal Wages Output

0

30

1000

1000

There is a large increase in European money supply. There is no change in German nominal wages, an increase in French nominal wages, and an increase in European nominal wages. There is no change in the price of German goods, an increase in the price of French goods, and an increase in the price of European goods. 7) Alternative targets of policy cooperation: no increase in national nominal wages. Let initial output in Germany be 940, and let initial output in France be 970. In each of the countries there is unemployment. 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 30, a reduction in German nominal wages of 30, and an increase in French nominal wages of zero. Step 2 refers to the output lag. The increase in European money supply of 30 raises German output and French output by 30 each. And the reduction in German nominal wages of 30 raises German output by 30. The total effect is an

147 increase in German output of 60 and an increase in French output of 30. As a consequence, German output goes from 940 to 1000, and French output goes from 970 to 1000. In each of the countries there is now full employment. Table 4.14 gives an overview.

Table 4.14 Cooperation between the European Central Bank, the German Labour Union, and the French Labour Union No Increase in National Nominal Wages

Initial Output

Germany

France

940

970

Change in Money Supply

30

Change in Nominal Wages

-30

0

Output

1000

1000

There is a small increase in European money supply. There is a reduction in German nominal wages, no change in French nominal wages, and a reduction in European nominal wages. There is a reduction in the price of German goods, no change in the price of French goods, and a reduction in the price of European goods.

Part Five Monetary and Wage Policies Intermediate Models

Chapter 1 Simultaneous Decisions: Cold-Turkey Policies

This chapter deals with competition between the European central bank, the German labour union, and the French labour union. So far we have assumed that the central bank and the labour unions decide sequentially. First the central bank decides, then the labour unions decide. Now we assume that the central bank 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 two equations: Yi=Ai+M-Wi

(1)

Y2=A2+M-W2

(2)

The endogenous variables are German output and French output. An increase in European money supply of 100 causes an increase in German output of 100 and an increase in French output of equally 100. An increase in German nominal wages of 100 causes a decline in German output of 100. Correspondingly, an increase in French nominal wages of 100 causes a decline in French output of 100. Further, let full-employment output in Germany be 1000, and let foilemployment output in France be the same. At the beginning there is unemployment in Germany and France. 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 foil employment in Europe. The specific target of the European central bank is that unemployment in Germany equals overemployment in France. In other words, the specific target of the European central bank is foil employment in Europe on average. 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.

152 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 bank and the labour unions decide simultaneously and independently. In step 1 the European 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 German labour union, and the French labour union decide simultaneously and independently. In step 4 there is an output lag. And so on. Let initial output in Germany be 940, and let initial output in France be 970. 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 monetary policy multiplier in Europe is 2. So what is needed in Europe is an increase in European money supply of 45. Second consider wage policy in Germany. The output gap in Germany is 60. The wage policy multiplier in Germany is 1. So what is needed in Germany is a reduction in German nominal wages of 60. Third consider wage policy in France. The output gap in France is 30. The wage policy multiplier in France is 1. So what is needed in France is a reduction in French nominal wages of 30. Step 2 refers to the output lag. The increase in European money supply of 45 causes an increase in German output of 45 and an increase in French output of equally 45. The reduction in German nominal wages of 60 causes an increase in German output of 60. And the reduction in French nominal wages of 30 causes an increase in French output of 30. The total effect is an increase in German output of 105 and an increase in French output of 75. As a consequence, German output goes from 940 to 1045, and French output goes from 970 to 1045. In each of the countries there is now overemployment. Step 3 refers to the policy response. First consider monetary policy in Europe. The inflationary gap in Europe is 90. The monetary policy multiplier in Europe is

153 2. So what is needed in Europe is a reduction in European money supply of 45. Second consider wage policy in Germany. The inflationary gap in Germany is 45. The wage policy multiplier in Germany is 1. So what is needed in Germany is an increase in German nominal wages of 45. Third consider wage policy in France. The inflationary gap in France is 45. The wage policy multiplier in France is 1. So what is needed in France is an increase in French nominal wages of 45. Step 4 refers to the output lag. The reduction in European money supply of 45 causes a decline in German output of 45 and a decline in French output of equally 45. The increase in German nominal wages of 45 causes a decline in German output of 45. And the increase in French nominal wages of 45 causes a decline in French output of 45. The total effect is a decline in German output of 90 and a decline in French output of equally 90. As a consequence, German output goes from 1045 to 955, as does French output. In each of the countries there is now unemployment. Step 5 refers to the policy response. First consider monetary policy in Europe. The output gap in Europe is 90. The monetary policy multiplier in Europe is 2. So what is needed in Europe is an increase in European money supply of 45. Second consider wage policy in Germany. The output gap in Germany is 45. The wage policy multiplier in Germany is 1. So what is needed in Germany is a reduction in German nominal wages of 45. Third consider wage policy in France. The output gap in France is 45. The wage policy multiplier in France is 1. So what is needed in France is a reduction in French nominal wages of 45. Step 6 refers to the output lag. The increase in European money supply of 45 causes an increase in German output of 45 and an increase in French output of equally 45. The reduction in German nominal wages of 45 causes an increase in German output of 45. And the reduction in French nominal wages of 45 causes an increase in French output of 45. The total effect is an increase in German output of 90 and an increase in French output of equally 90. As a consequence, German output goes from 955 to 1045, as does French output. In each of the countries there is now overemployment. This process will repeat itself round by round. Table 5.1 presents a synopsis.

154 Table 5.1 Simultaneous Decisions: Cold-Turkey Policies Germany Initial Output

France

970

940

Change in Money Supply

45

Change in Nominal Wages

-60

-30

Output

1045

1045

Change in Money Supply Change in Nominal Wages Output

1 Output

1

-45 45

45

955

955

Change in Money Supply Change in Nominal Wages

1

1

45 -45

-45

1045

1045

and so on

As a result, the simultaneous process of monetary and wage competition does not lead to full employment in any of the countries. Instead, there are uniform oscillations in money supply, nominal wages, and output. The German economy oscillates between unemployment and overemployment, as does the French economy. Last but not least, compare simultaneous decisions with sequential decisions, see Chapter 2 of Part Four. The sequential process of monetary and wage competition leads to full employment in each of the countries. By contrast, the simultaneous process of monetary and wage competition does not lead to full employment in any of the countries. Judging from this perspective, sequential decisions seem to be superior to simultaneous decisions.

Chapter 2 Simultaneous Decisions: Gradualist Policies

This chapter deals with competition between the European central bank, the German labour union, and the French labour union. So far we have assumed that the central bank and the labour unions follow a cold-turkey strategy. Now we assume that the central bank and the labour unions follow a gradualist strategy. In addition, we assume that the central bank 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 100 and an increase in French output of equally 100. An increase in German nominal wages of 100 causes a decline in German output of 100. Correspondingly, an increase in French nominal wages of 100 causes a decline in French output of 100. Further, let full-employment output in Germany be 1000, and let full-employment output in France be the same. At the start there is unemployment in Germany and France. 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 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 union is to close the output gap in Germany by 60 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 60 percent. We assume that the central bank and the labour unions decide simultaneously and independently. In step 1 the European 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 German

156 labour union, and the French labour union decide simultaneously and independently. In step 4 there is an output lag. And so on. Let initial output in Germany be 940, and let initial output in France be 970. 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 2. So what is needed in Europe is an increase in European money supply of 36. Second 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 60 percent, that is by 36. The wage policy multiplier in Germany is 1. So what is needed in Germany is a reduction in German nominal wages of 36. Third 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 60 percent, that is by 18. The wage policy multiplier in France is 1. So what is needed in France is a reduction in French nominal wages of 18. Step 2 refers to the output lag. The increase in European money supply of 36 causes an increase in German output of 36 and an increase in French output of equally 36. The reduction in German nominal wages of 36 causes an increase in German output of 36. And the reduction in French nominal wages of 18 causes an increase in French output of 18. The total effect is an increase in German output of 72 and an increase in French output of 54. As a consequence, German output goes from 940 to 1012, and French output goes from 970 to 1024. In each of the countries there is now overemployment. Step 3 refers to the policy response. First consider monetary policy in Europe. The inflationary gap in Europe is 36. The specific target of the European central bank is to close the inflationary gap in Europe by 80 percent, that is by 28.8. The monetary policy multiplier in Europe is 2. So what is needed in Europe is a reduction in European money supply of 14.4. Second consider wage policy in Germany. The inflationary gap in Germany is 12. The specific target of the German labour union is to close the inflationary gap in Germany by 60 percent, that is by 7.2. The wage policy multiplier in Germany is 1. So what is needed in Germany is an increase in German nominal wages of 7.2. Third consider wage

157 policy in France. The inflationary gap in France is 24. The specific target of the French labour union is to close the inflationary gap in France by 60 percent, that is by 14.4. The wage policy multiplier in France is 1. So what is needed in France is an increase in French nominal wages of 14.4. Step 4 refers to the output lag. The reduction in European money supply of 14.4 causes a decline in German output of 14.4 and a decline in French output of equally 14.4. The increase in German nominal wages of 7.2 causes a decline in German output of 7.2. And the increase in French nominal wages of 14.4 causes a decline in French output of 14.4. The total effect is a decline in German output of 21.6 and a decline in French output of 28.8. As a consequence, German output goes from 1012 to 990.4, and French output goes from 1024 to 995.2. In each of the countries there is now unemployment. Step 5 refers to the policy response. First consider monetary policy in Europe. The output gap in Europe is 14.4. The specific target of the European central bank is to close the output gap in Europe by 80 percent, that is by 11.5. The monetary policy multiplier in Europe is 2. So what is needed in Europe is an increase in European money supply of 5.8. Second consider wage policy in Germany. The output gap in Germany is 9.6. The specific target of the German labour union is to close the output gap in Germany by 60 percent, that is by 5.8. The wage policy multiplier in Germany is 1. So what is needed in Germany is a reduction in German nominal wages of 5.8. Third consider wage policy in France. The output gap in France is 4.8. The specific target of the French labour union is to close the output gap in France by 60 percent, that is by 2.9. The wage policy multiplier in France is 1. So what is needed in France is a reduction in French nominal wages of 2.9. Step 6 refers to the output lag. The increase in European money supply of 5.8 causes an increase in German output of 5.8 and an increase in French output of equally 5.8. The reduction in German nominal wages of 5.8 causes an increase in German output of 5.8. And the reduction in French nominal wages of 2.9 causes an increase in French output of 2.9. The total effect is an increase in German output of 11.5 and an increase in French output of 8.6. As a consequence, German output goes from 990.4 to 1001.9, and French output goes from 995.2 to 1003.8. In each of the countries there is now overemployment. And so on. Table 5.2 gives an overview.

158 Table 5.2 Simultaneous Decisions: Gradualist Policies Germany Initial Output

1 Output

1 Output

-36

-18

1012

1024 -14.4

7.2

14.4

990.4

995.2

Change in Money Supply Change in Nominal Wages Output

1

36

Change in Money Supply Change in Nominal Wages

970

940

Change in Money Supply Change in Nominal Wages

France

5.8 -5.8

-2.9

1001.9

1003.8

1000

1000

and so on Steady-State Output

In the steady state, German output is 1000, as is French output. In each of the countries there is now full employment. As a result, the gradualist process of monetary and wage competition leads to full employment in each of the countries. There are damped oscillations in money supply, nominal wages, and output. The German economy oscillates between unemployment and overemployment, as does the French economy. Taking the sum over all periods, the total increase in European money supply is 25.7, the total reduction in German nominal wages is 34.3, and the total reduction in French nominal wages is 4.3. Generally speaking, the total increase in European money supply depends on: - the initial output gap in Germany - the initial output gap in France

159 - the monetary policy multiplier in Europe - the wage policy multiplier in Germany - the wage policy multiplier in France - the speed of adjustment in European money supply - the speed of adjustment in German nominal wages - the speed of adjustment in French nominal wages. And the same holds for the total reduction in German nominal wages and the total reduction 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 there are uniform oscillations in money supply, nominal wages, and output. By contrast, under gradualist policies there are damped oscillations in money supply, nominal wages, and output. Under cold-turkey policies, monetary and wage competition does not lead to full employment. By contrast, under gradualist policies, monetary and wage competition leads to full employment. Judging from this point of view, gradualist policies seem to be superior to cold-turkey policies.

Chapter 3 Wage Shocks in Germany

This chapter is concerned with competition between the European central bank, the German labour union, and the French labour union. We assume that the central bank and the labour unions decide sequentially. First the central bank decides, then the labour unions decide. In addition, we assume that the central bank and the labour unions follow a cold-turkey strategy. Now suppose there is an increase in German nominal wages. Then, as a response, the European central bank can raise European money supply, lower European money supply, or do nothing. Accordingly, we study three distinct cases: - increase in German nominal wages, increase in European money supply - increase in German nominal wages, reduction in European money supply - increase in German nominal wages, no change in European money supply. 1) Increase in German nominal wages, increase in European money supply. In the numerical example, an increase in European money supply of 100 raises German output and French output by 100 each. An increase in German nominal wages of 100 lowers German output by 100. Correspondingly, an increase in French nominal wages of 100 lowers French output by 100. Further, let fullemployment output in Germany be 1000, and let full-employment output in France be the same. Let initial output in Germany be 1000, and let initial output in France be 1000 as well. In each of the countries there is full employment. Step 1 refers to the wage shock in Germany. Suppose there is an increase in German nominal wages of 60. Step 2 refers to the output lag. The increase in German nominal wages of 60 lowers German output by 60. As a consequence, German output goes from 1000 to 940 while French output stays at 1000. In Germany there is now some

161 unemployment. In France there is still full employment. And in Europe there is now some unemployment. Step 3 refers to monetary policy in Europe. We assume that the target of the European central bank is full employment in Europe. The output gap in Europe is 60. The monetary policy multiplier in Europe is 2. So what is needed in Europe is an increase in European money supply of 30. Step 4 refers to the output lag. The increase in European money supply of 30 raises German output and French output by 30 each. As a consequence, German output goes from 940 to 970, and French output goes from 1000 to 1030. In Germany there is still some unemployment. In France there is now some overemployment. And in Europe there is now full employment. As a result, the wage shock in Germany causes unemployment in Germany. On the other hand, it causes overemployment in France. Table 5.3 presents a synopsis.

Table 5.3 Wage Shock in Germany Increase in German Nominal Wages, Increase in European Money Supply

Initial Output Change in Nominal Wages Output

Germany

France

1000

1000

60 940

Change in Money Supply Output

1000 30

970

1030

2) Increase in German nominal wages, reduction in European money supply. Let initial output in Germany be 1000, and let initial output in France be the same. In each of the countries there is full employment. Step 1 refers to the wage

162 shock in Germany. Suppose there is an increase in German nominal wages of 60. Step 2 refers to the output lag. The increase in German nominal wages of 60 lowers German output by 60. As a consequence, German output goes from 1000 to 940 while French output stays at 1000. In Germany there is now some unemployment. In France there is still full employment. And in Europe there is now some unemployment. Step 3 refers to monetary policy in Europe. We assume that the target of the European central bank is price stability in Europe. So the European central bank punishes the German labour union with a reduction in European money supply of 30. Step 4 refers to the output lag. The reduction in European money supply of 30 lowers German output and French output by 30 each. As a consequence, German output goes from 940 to 910, and French output goes from 1000 to 970. In Germany there is now some more unemployment. In France there is now some unemployment, too. And in Europe there is now some more unemployment. As a result, the wage shock in Germany causes a lot of unemployment in Germany. And what is more, it causes some unemployment in France, too. Table 5.4 gives an overview.

Table 5.4 Wage Shock in Germany Increase in German Nominal Wages, Reduction in European Money Supply

Initial Output Change in Nominal Wages Output

Germany

France

1000

1000

60 940

Change in Money Supply Output

1000 -30

910

970

1

163 3) Increase in German nominal wages, no change in European money supply. Let initial output in Germany be 1000, and let initial output in France be the same. In each of the countries there is full employment. Step 1 refers to the wage shock in Germany. Suppose there is an increase in German nominal wages of 60. Step 2 refers to the output lag. The increase in German nominal wages of 60 lowers German output by 60. As a consequence, German output goes from 1000 to 940 while French output stays at 1000. In Germany there is now some unemployment. In France there is still full employment. And in Europe there is now some unemployment. Step 3 refers to monetary policy in Europe. We assume that the targets of the European central bank are price stability in Europe and full employment in Europe. So the European central bank does not respond to the wage shock in Germany. Table 5.5 presents a synopsis.

Table 5.5 Wage Shock in Germany Increase in German Nominal Wages, No Change in European Money Supply

Initial Output Change in Nominal Wages Output

Germany

France

1000

1000

60 940

Change in Money Supply Output

1000 0

940

1000

Chapter 4 The Countries Differ in Size 1. Wage Policies in Germany and France

1) Introduction. In this chapter we assume that the countries only differ in size. To be more specific, we assume that the German economy is large and the French economy is small. More precisely, we assume that full-employment output in Germany is large and full-employment output in France is small. As a result, the size of the wage policy multiplier depends on the size of the country. In the numerical example, an increase in German nominal wages of 100 causes a decline in German output of 200. And an increase in French nominal wages of 100 causes a decline in French output of 100. The output model can be characterized by a system of two equations: Yi=Ai-YiW,

(1)

Y2=A2-Y2W2

(2)

Here Y| denotes German output, Y2 is French output, W^ is the nominal wage rate in Germany, W2 is the nominal wage rate in France, y^ is the wage policy multiplier in Germany, and 72 is the wage policy multiplier in France. We assume Yj > 72 • The endogenous variables are German output and French output. An increase in German nominal wages of 1 causes a decline in German output of Yj. And an increase in French nominal wages of 1 causes a decline in French output of Y2 • 2) The policy model. At the start there is unemployment in Germany and France. More precisely, unemployment in Germany is high, and unemployment in France is low. The German labour union lowers German nominal wages so as to close the output gap in Germany:

165

AWi=-^^ Tl

(3)

Here AWj denotes the required change in German nominal wages, AY^ is the initial output gap in Germany, and y^ is the wage policy multiplier in Germany. According to equation (3), the required cut in German nominal wages depends on the initial output gap in Germany and on the wage policy multiplier in Germany. Similarly, the French labour union lowers French nominal wages so as to close the output gap in France:

AW2=

AY, 2_

(4)

Here AW2 denotes the required change in French nominal wages, AY2 is the initial output gap in France, and 72 is the wage policy multiplier in France. According to equation (4), the required cut in French nominal wages depends on the initial output gap in France and on the wage poUcy multiplier in France. 3) A numerical example. We assume that the German economy is twice as large as the French economy. More exactly, we assume that full-employment output in Germany is twice as large as full-employment output in France. For ease of exposition, without losing generality, we assume y^ = 2 and y2 = 1. On this assumption, the output model can be written as follows: Yi=Ai-2W,

(5)

Y2=A2-W2

(6)

Obviously, an increase in German nominal wages of 100 causes a decline in German output of 200. And an increase in French nominal wages of 100 causes a decline in French output of 100. The policy multipliers are from the case of three countries, see Chapter 1 of Part Six below. In the large country, the wage policy multiplier is large. And in the small country, the wage policy multiplier is small. Further, let full-employment output in Germany be 2000, and let fullemployment output in France be 1000.

166

Let initial output in Germany be 1880, and let initial output in France be 970. In each of the countries there is unemployment. Step 1 refers to the policy response. The output gap in Germany is 120. The wage policy multiplier in Germany is 2. So what is needed in Germany is a reduction in German nominal wages of 120. The output gap in France is 30. The wage policy multiplier in France is 1. So what is needed in France is a reduction in French nominal wage of 30. Step 2 refers to the output lag. The reduction in German nominal wages of 60 causes in increase in German output of 120. And the reduction in French nominal wages of 30 causes an increase in French output of 30. As a consequence, German output goes from 1880 to 2000, and French output goes from 970 to 1000. In each of the countries there is now full employment. As a result, wage policies in Germany and France can achieve full employment in each of the countries. Table 5.6 gives an overview.

Table 5.6 Wage Policies in Germany and France The Countries Differ in Size Germany

France

Initial Output

1880

970

Change in Nominal Wages

-60

-30

Output

2000

1000

167

2. Monetary and Wage Competition

This section deals with competition between the European central bank, the German labour union, and the French labour union. We assume that the central bank and the labour unions decide sequentially. First the central bank decides, then the labour unions decide. In addition, we assume that the central bank and the labour unions follow a cold-turkey strategy. The output model can be represented by a system of two equations: Yi=Ai+aiM-yiWi

(1)

Y2=A2+a2M-y2W2

(2)

Here M denotes European money supply, a^ is the monetary policy multiplier in Germany, and a2 is the monetary policy multiplier in France. We assume that the German economy is twice as large as the French economy. More precisely, we assume that full-employment output in Germany is twice as large as fullemployment output in France. In the numerical example we assume that a^ = 2, a2 = 1, y^ = 2 and y2 = 1 • On this assumption, the output model can be written as follows: Yi = A i + 2 M - 2 W i

(3)

Y2=A2+M-W2

(4)

Evidently, an increase in European money supply of 100 causes an increase in German output of 200 and an increase in French output of 100. An increase in German nominal wages of 100 causes a decline in German output of 200. And an increase in French nominal wages of 100 causes a decline in French output of 100. Further, let full-employment output in Germany be 2000, and let fullemployment output in France be 1000. Let initial output in Germany be 1880, and let initial output in France be 970. In each of the countries there is unemployment. Step 1 refers to monetary policy

168 in Europe. The output gap in Europe is 150. The monetary policy multiplier in Europe is 3. So what is needed in Europe is an increase in European money supply of 50. Step 2 refers to the output lag. The increase in European money supply of 50 causes an increase in German output of 100 and an increase in French output of 50. As a consequence, German output goes from 1880 to 1980, and French output goes from 970 to 1020. Step 3 refers to wage policies Germany and France. The output gap in Germany is 20. The wage policy multiplier in Germany is 2. So what is needed in Germany is a reduction in German nominal wages of 10. The inflationary gap in France is 20. The wage policy multiplier in France is 1. So what is needed in France is an increase in French nominal wages of 20. Step 4 refers to the output lag. The reduction in German nominal wages of 10 causes an increase in German output of 20. And the increase in French nominal wages of 20 causes a decline in French output of 20. As a consequence, German output goes from 1980 to 2000, and French output goes from 1020 to 1000. In each of the countries there is now full employment. As a result, the process of monetary and wage competition leads to full employment in each of the countries. There is no change in European nominal wages and no change in the price level of European goods. Table 5.7 presents a synopsis.

Table 5.7 Monetary and Wage Competition The Countries Differ in Size

Initial Output

Germany

France

1880

970

Change in Money Supply

50

Output

1980

1020

Change in Nominal Wages

-10

20

Output

2000

1000

Chapter 5 The Countries Differ in Behaviour 1. Wage Policies in Germany and France

1) Introduction. We assume that the countries only differ in behavioural functions. To be more specific, we assume that the countries differ in wage policy multipliers. In the numerical example, an increase in German nominal wages of 100 causes a decline in German output of 200. And an increase in French nominal wages of 100 causes a decline in French output of 100. The output model can be represented by a system of two equations: Yi = Ai-Y,Wi

(1)

Y2=A2-T2W2

(2)

Here Y^ denotes German output, Y2 is French output, Wj is the nominal wage rate in Germany, W2 is the nominal wage rate in France, y^ is the wage policy multiplier in Germany, and 72 is the wage policy multiplier in France. The endogenous variables are German output and French output. An increase in German nominal wages of 1 causes a decline in German output of y^. And an increase in French nominal wages of 1 causes a decline in French output of y2. 2) The policy model. At the start there is unemployment in Germany and France. More precisely, unemployment in Germany is high, and unemployment in France is low. The German labour union lowers German nominal wages so as to close the output gap in Germany:

AWi=

L

(3)

Here AW^ denotes the required change in German nominal wages, AYj^ is the initial output gap in Germany, and y^ is the wage policy multiplier in Germany.

170 According to equation (3), the required change in German nominal wages depends on the initial output gap in Germany and on the wage policy multiplier in Germany. Similarly, the French labour union lowers French nominal wages so as to close the output gap in France: _ AYo AW2 = - ^ = ^ ^

(4)

Here AW2 denotes the required change in French nominal wages, AY2 is the initial output gap in France, and 72 is the wage policy multiplier in France. According to equation (4), the required change in French nominal wages depends on the initial output gap in France and on the wage policy multiplier in France. 3) A numerical example. For ease of exposition we assume that y^ = 2 and 72 = 1. On this assumption, the output model can be written as follows: Yi=Ai-2Wi

(5)

Y2=A2-W2

(6)

Obviously, an increase in German nominal wages of 100 causes a decline in German output of 200. And an increase in French nominal wages of 100 causes a decline in French output of 100. Further, let full-employment output in Germany be 1000, and let full-employment output in France be the same. Let initial output in Germany be 940, and let initial output in France be 970. In each of the countries there is unemployment. Step 1 refers to the policy response. The output gap in Germany is 60. The wage policy multiplier in Germany is 2. So what is needed in Germany is a reduction in German nominal wages of 30. The output gap in France is 30. The wage policy multiplier in France is 1. So what is needed in France is a reduction in French nominal wages of 30. Step 2 refers to the output lag. The reduction in German nominal wages of 30 causes an increase in German output of 60. And the reduction in French nominal

171 wages of 30 causes an increase in French output of 30. As a consequence, German output goes from 940 to 1000, and French output goes from 970 to 1000. In each of the countries there is now full employment. As a result, wage policies in Germany and France can achieve full employment in each of the countries. Table 5.8 gives an overview.

Table 5.8 Wage Policies in Germany and France The Countries Differ in Behaviour Germany

France

940

970

Change in Nominal Wages

-30

-30

Output

1000

1000

Initial Output

2. Monetary and Wage Competition

This section deals with competition between the European central bank, the German labour union, and the French labour union. We assume that the central bank and the labour unions decide sequentially. First the central bank decides, then the labour unions decide. In addition, we assume that the central bank and the labour unions follow a cold-turkey strategy. The output model can be represented by a system of two equations: Yi = Ai + aiM-YiWi

(1)

Y2 = A2 + a2M-Y2W2

(2)

172

Here M denotes European money supply, a^ is the monetary policy multiplier in Germany, and a2 is the monetary policy multiplier in France. In the numerical example we assume that a^ = 1, 0^2 = 1, y^ = 2 and 72 = 1. On this assumption, the output model can be written as follows: Yi=Ai+M-2Wi

(3)

Y2=A2+M-W2

(4)

Evidently, an increase in European money supply of 100 causes an increase in German output of 100 and an increase in French output of equally 100. An increase in German nominal wages of 100 causes a decline in German output of 200. And an increase in French nominal wages of 100 causes a decline in French output of 100. Further, let full-employment output in Germany be 1000, and let full-employment output in France be the same. Let initial output in Germany be 940, and let initial output in France be 970. In each of the countries there is unemployment. Step 1 refers to monetary policy in Europe. The output gap in Europe is 90. The monetary policy multiplier in Europe is 2. So what is needed in Europe is an increase in European money supply of 45. Step 2 refers to the output lag. The increase in European money supply of 45 causes an increase in German output of 45 and an increase in French output of equally 45. As a consequence, German output goes from 940 to 985, and French output goes from 970 to 1015. Step 3 refers to wage policies in Germany and France. The output gap in Germany is 15. The wage policy multiplier in Germany is 2. So what is needed in Germany is a reduction in German nominal wages of 7.5. The inflationary gap in France is 15. The wage policy multiplier in France is 1. So what is needed in France is an increase in French nominal wages of 15. Step 4 refers to the output lag. The reduction in German nominal wages of 7.5 causes an increase in German output of 15. And the increase in French nominal wages of 15 causes a decline in French output of 15. As a consequence, German output goes from 985 to 1000, and French output goes from 1015 to

173 1000. In each of the countries there is now full employment. Table 5.9 presents a synopsis. As a result, the process of monetary and wage competition leads to full employment in Germany and France. The reduction in German nominal wages is smaller than the increase in French nominal wages. So there is an increase in European nominal wages and, hence, an increase in the price level of European goods. Can monetary and wage cooperation do better in this respect?

Table 5.9 Monetary and Wage Competition The Countries Differ in Behaviour

Initial Output

Germany

France

940

970

Change in Money Supply

1 Output Change in Nominal Wages Output

45 985 -7.5 1000

1015 15 1000

3. Monetary and Wage Cooperation

This section deals with cooperation between the European central bank, 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. The targets of policy cooperation are full employment in Germany and full employment in France.

174 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. 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. Let initial output in Germany be 940, and let initial output in France be 970. Step 1 refers to the policy response. What is needed, then, is an increase in European money supply of 40, a reduction in German nominal wages of 10, and an increase in French nominal wages of equally 10. Step 2 refers to the output lag. The increase in European money supply of 40 causes an increase in German output of 40 and an increase in French output of equally 40. The reduction in German nominal wages of 10 causes an increase in German output of 20. And the increase in French nominal wages of 10 causes a decline in French output of 10. The net effect is an increase in German output of 60 and an increase in French output of 30. As a consequence, German output goes from 940 to 1000, and French output goes from 970 to 1000. In each of the countries there is now full employment. Table 5.10 gives an overview.

Table 5.10 Monetary and Wage Cooperation The Countries Differ in Behaviour

Initial Output

Germany

France

940

970

Change in Money Supply

40

Change in Nominal Wages

-10

10

Output

1000

1000

As a result, monetary and wage cooperation can achieve full employment in Germany and France. The reduction in German nominal wages is equal in size to

175 the increase in French nominal wages. There is no change in European nominal wages. And there is no change in the price level of European goods. Judging from this point of view, policy cooperation seems to be superior to policy competition.

Chapter 6 Rational Policy Expectations

1) The output model. This chapter deals with competition between the European central bank, the German labour union, and the French labour union. The member countries are the same size and have the same behavioural functions. As a point of departure, take the output model. It can be represented by a system of two equations: Yj=Aj+aM-yWi

(1)

Y2=A2+aM-yW2

(2)

Here Y^ denotes German output, Y2 is French output, M is European money supply, Wj is German nominal wages, and W2 is French nominal wages. The endogenous variables are German output and French output. 2) The policy model. At the start there is unemployment in Germany and France. 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 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 German labour union, and the French labour union decide simultaneously and independently. The European central bank sets European money supply, forming rational expectations of German nominal wages and French nominal wages. The German labour union sets German nominal wages, forming rational expectations of European money supply and French nominal wages. And the French labour union sets French nominal wages, forming rational expectations of European money supply and German nominal wages. That is to say, the European central bank sets European money supply, predicting German nominal wages and French nominal wages with the help of

177 the model. The German labour union sets German nominal wages, predicting European 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 and German nominal wages with the help of the model. On this basis, the policy model can be characterized by a system of two equations: Yj=Aj+aM-yWi

(3)

Y2=A2+aM-yW2

(4)

Here Y^ denotes full-employment output in Germany and Y2 is full-employment output in France. The endogenous variables 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. There seems to be no simple way of how to make use of this 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 each of the countries.

Part Six Monetary and Wage Policies The Case of Three Countries

Chapter 1 Wage Policies in Germany, France and Italy

1) Introduction. For ease of exposition we assume that the monetary union consists of three countries, say Germany, France and Italy. The member countries are the same size and have the same behavioural functions. An increase in German nominal wages lowers German output. Correspondingly, an increase in French nominal wages lowers French output. And an increase in Italian nominal wages lowers Italian output. For ease of exposition we assume that wage policy in one of the countries has no effect on output in the other countries. In the numerical example, an increase in German nominal wages of 100 causes a decline in German output of 100. Correspondingly, an increase in French nominal wages of 100 causes a decline in French output of 100. And an increase in Italian nominal wages of 100 causes a decline in Italian output of 100. For ease of exposition we assume that the wage policy multiplier is 1. This assumption is consistent since the wage rate is defined in nominal terms while output is defined in real terms. The output model can be represented by a system of three equations:

YI=AI-YWI

(1)

Y2=A2-YW2

(2)

Y3=A3-YW3

(3)

Yj denotes German output, Y2 is French output, Y3 is Italian output, W^ is the nominal wage rate in Germany, W2 is the nominal wage rate in France, W3 is the nominal wage rate in Italy, and y is the wage policy multiplier. The endogenous variables are German output, French output, and Italian output. An increase in German nominal wages of 1 causes a decline in German output of y. Correspondingly, an increase in French nominal wages of 1 causes a decline in French output of y. And an increase in Italian nominal wages of 1 causes a decline in Italian output of y.

182

2) The policy model. At the start there is unemployment in Germany, France and Italy. More precisely, unemployment in Germany is high, unemployment in France is medium size, and unemployment in Italy is low. 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. The target of the Italian labour union is full employment in Italy. The instrument of the Italian labour union is Italian nominal wages. The policy model can be characterized by a system of three equations: Yi = A i - y W i

(4)

Y2 = A2-yW2

(5)

Y3=A3-yW3

(6)

Here Y^ denotes full-employment output in Germany, Y2 is full-employment output in France, Y3 is full-employment output in Italy, Wj is the required level of German nominal wages, W2 is the required level of French nominal wages, and W3 is the required level of Italian nominal wages. The endogenous variables are German nominal wages, French nominal wages, and Italian nominal wages. As a result, wage policies in Germany, France and Italy can achieve full employment in each of the countries. 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. The German labour union lowers German nominal wages so as to close the output gap in Germany:

AWi = - ^ y

(7)

Here AWj denotes the required change in German nominal wages, AYj is the initial output gap in Germany, and y is the wage policy multiplier in Germany.

183 According to equation (7), the required cut in German nominal wages depends on the initial output gap in Germany and on the wage policy multiplier in Germany. Similarly, the French labour union lowers French nominal wages so as to close the output gap in France:

AW2 =

AY, 2.

(8)

Here AW2 denotes the required change in French nominal wages, AY2 is the initial output gap in France, and y is the wage policy multiplier in France. According to equation (8), the required cut in French nominal wages depends on the initial output gap in France and on the wage policy multiplier in France. And the Italian labour union lowers Italian nominal wages so as to close the output gap in Italy:

AW3=

AY. ^

(9)

Here AW3 denotes the required change in Italian nominal wages, AY3 is the initial output gap in Italy, and y is the wage policy multiplier in Italy. According to equation (9), the required cut in Italian nominal wages depends on the initial output gap in Italy and on the wage policy multiplier in Italy. 4) A numerical example. To illustrate the policy model, have a look at a numerical example. For ease of exposition, without losing generality, assume that y = 1. On this assumption, the output model can be written as follows: Yi=Ai-Wi

(10)

Y2=A2-W2

(11)

Y3=A3-W3

(12)

The endogenous variables are German, French and Italian output. Obviously, an increase in German nominal wages of 100 causes a decline in German output of

184 100. Correspondingly, an increase in French nominal wages of 100 causes a decline in French output of 100. And an increase in Italian nominal wages of 100 causes a decline in Italian output of 100. Further, let full-employment output in Germany be 1000, let full-employment output in France be 1000, and let fullemployment output in Italy be the same. Let initial output in Germany be 940, let initial output in France be 950, and let initial output in Italy be 990. In each of the countries there is unemployment. Step 1 refers to the policy response. The output gap in Germany is 60. The wage policy multiplier in Germany is 1. So what is needed in Germany is a reduction in German nominal wages of 60. The output gap in France is 50. The wage policy multiplier in France is 1. So what is needed in France is a reduction in French nominal wages of 50. The output gap in Italy is 10. The wage policy multiplier in Italy is 1. So what is needed in Italy is a reduction in Italian nominal wages of 10. Step 2 refers to the output lag. The reduction in German nominal wages of 60 raises German output by 60. The reduction in French nominal wages of 50 raises French output by 50. And the reduction in Italian nominal wages of 10 raises Italian output by 10. As a consequence, German output goes from 940 to 1000, French output goes from 950 to 1000, and Italian output goes from 990 to 1000. In each of the countries there is now full employment. As a result, wage policies in Germany, France and Italy can achieve full employment in each of the countries. There is a reduction in European nominal wages, a decline the price of European goods, a depreciation of the euro, an increase in European exports, and an increase in European output. There is an increase in the European current account surplus and a decline in the European budget deficit. Table 6.1 presents a synopsis.

185 Table 6.1 Wage Policies in Germany, France and Italy The Case of Unemployment Germany

France

Italy

940

950

990

Change in Nominal Wages

-60

-50

-10

Output

1000

1000

1000

Initial Output

Chapter 2 Monetary and Wage Competition

1) The static model. This chapter deals with competition between the European central bank, the German labour union, the French labour union, and the Italian labour union. As a point of reference, consider the static model. It can be represented by a system of three equations: Yi = A i + a M - y W i

(1)

Y2=A2+aM-yW2

(2)

Y3=A3+aM-yW3

(3)

Yj denotes German output, Y2 is French output, Y3 is Italian output, M is European money supply, W^ is German nominal wages, W2 is French nominal wages, W3 is Italian nominal wages, a is the monetary policy multiplier, and y is the wage policy multiplier. The endogenous variables are German output, French output, and Italian output. An increase in European money supply of 1 causes an increase in German output of a , an increase in French output of a , and an increase in Italian output of a . An increase in German nominal wages of 1 causes a decline in German output of y. Correspondingly, an increase in French nominal wages of 1 causes a decline in French output of y. And an increase in Italian nominal wages of 1 causes a decline in Italian output of y. 2) The dynamic model. At the beginning there is unemployment in Germany, France and Italy. More precisely, unemployment in Germany is high, unemployment in France is medium size, and unemployment in Italy is low. The primary target of the European central bank is price stability in Europe. The secondary target of the European central bank is full employment in Europe. The specific target of the European central bank is that unemployment in Germany, France and Italy add up to zero. In other words, the specific target of the

187 European central bank is full employment in Europe on average. The instrument of the European central bank is European 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. The target of the Italian labour union is full employment in Italy. And the instrument of the Italian labour union is Italian nominal wages. We assume that the central bank and the labour unions decide sequentially. First the central bank decides, then the labour unions decide. Step 1 refers to monetary policy in Europe. Step 2 refers to the output lag. Step 3 refers to wage policies in Germany, France and Italy. And step 4 refers to the output lag. Now have a closer look at the dynamic model. Step 1 refers to monetary policy in Europe. The European central bank raises European money supply so as to close the output gap in Europe: AY+AY^+AY. AbA = —^ ^ ^ 3a

(4)

Here AM denotes the required increase in European money supply, AY^ is the initial output gap in Germany, AY2 is the initial output gap in France, AY3 is the initial output gap in Italy, AYJ + AY2 + AY3 is the initial output gap in Europe, and 3a is the monetary policy multiplier in Europe. According to equation (4), the required increase in European money supply depends on the initial output gap in Europe and on the monetary policy multiplier in Europe. Step 2 refers to the output lag. Step 3 refers to wage policies in Germany, France and Italy. The German labour union lowers German nominal wages so as to close the output gap in Germany:

AWi = - ^

(5)

188

Here AWj denotes the required change in German nominal wages, AYj is the initial output gap in Germany, and y is the wage policy multiplier in Germany. According to equation (5), the required cut in German nominal wages depends on the initial output gap in Germany and on the wage policy multiplier in Germany. Similarly, the French labour union lowers French nominal wages so as to close the output gap in France:

AW2 =

AY, ^

(6)

Here AW2 denotes the required change in French nominal wages, AY2 is the initial output gap in France, and y is the wage policy multiplier in France. According to equation (6), the required cut in French nominal wages depends on the initial output gap in France and on the wage policy multiplier in France. And the Italian labour union lowers Italian nominal wages so as to close the output gap in Italy:

AW3 =

AY, '-

(7)

Here AW3 denotes the required change in Italian nominal wages, AY3 is the initial output gap in Italy, and y is the wage policy multiplier in Italy. According to equation (7), the required cut in Italian nominal wages depends on the initial output gap in Italy and on the wage policy multiplier in Italy. Step 4 refers to the output lag. As a result, the process of monetary and wage competition leads to full employment in Germany, France and Italy. 3) A numerical example: the case of unemployment. To illustrate the dynamic model, have a look at a numerical example. For ease of exposition, without loss of generality, assume that a = 1 and y = 1. On this assumption, the static model can be written as follows:

189 Yi=Ai+M-Wi

(8)

Y2=A2+M-W2

(9)

Y3=A3+M-W3

(10)

The endogenous variables are German, French and Italian output. Obviously, an increase in European money supply of 100 causes an increase in German output of 100, an increase in French output of 100, and an increase in Italian output of equally 100. An increase in German nominal wages of 100 causes a decline in German output of 100. Correspondingly, an increase in French nominal wages of 100 causes a decline in French output of 100. And an increase in Italian nominal wages of 100 causes a decline in Italian output of 100. Further, let full-employment output in Germany be 1000, let full-employment output in France be 1000, and let full-employment output in Italy be the same. Let initial output in Germany be 940, let initial output in France be 950, and let initial output in Italy be 990. In each of the countries there is unemployment. Step 1 refers to monetary policy in Europe. The output gap in Europe is 120. The monetary policy multiplier in Europe is 3. So what is needed in Europe is an increase in European money supply of 40. Step 2 refers to the output lag. The increase in European money supply of 40 causes an increase in German output of 40, an increase in French output of 40, and an increase in Italian output of equally 40. As a consequence, German output goes from 940 to 980, French output goes from 950 to 990, and Italian output goes from 990 to 1030. In Germany there is still some unemployment. In France there is still some unemployment, too. In Italy there is now some overemployment. And in Europe there is now full employment. Step 3 refers to wage policies in Germany, France and Italy. The output gap in Germany is 20. The wage policy multiplier in Germany is 1. So what is needed in Germany is a reduction in German nominal wages of 20. The output gap in France is 10. The wage policy multiplier in France is 1. So what is needed in France is a reduction in French nominal wages of 10. The inflationary gap in Italy is 30. The wage policy multiplier in Italy is 1. So what is needed in Italy is an increase in Italian nominal wages of 30.

190 Step 4 refers to the output lag. The reduction in German nominal wages of 20 raises German output by 20. The reduction in French nominal wages of 10 raises French output by 10. And the increase in Italian nominal wages of 30 lowers Italian output by 30. As a consequence, German output goes from 980 to 1000, French output goes from 990 to 1000, and Italian output goes from 1030 to 1000. In each of the countries there is now full employment. Table 6.2 gives an overview.

Table 6.2 Competition between the European Central Bank, the German Labour Union, the French Labour Union, and the Italian Labour Union The Case of Unemployment

Initial Output

Germany

France

Italy

940

950

990

Change in Money Supply Output

40 980

990

1030

Change in Nominal Wages

-20

-10

30

Output

1000

1000

1000

As a result, the process of monetary and wage competition leads to full employment in Germany, France and Italy. There is an increase in European money supply. There is a reduction in German nominal wages, a reduction in French nominal wages, an increase in Italian nominal wages, and no change in European nominal wages. There is a decline in the price of German goods, a decline in the price of French goods, an increase in the price of Italian goods, and no change in the price level of European goods. There is an increase in German output, as there is in French output and Italian output. In steps 1 and 2 there is some overshooting in Italian output.

191 4) A numerical example: the case of overemployment. Let initial output in Germany be 1060, let initial output in France be 1050, and let initial output in Italy be 1010. In each of the countries there is overemployment. Step 1 refers to monetary policy in Europe. The inflationary gap in Europe is 120. The monetary policy multiplier in Europe is 3. So what is needed in Europe is a reduction in European money supply of 40. Step 2 refers to the output lag. The reduction in European money supply of 40 causes a decline in German output of 40, a decline in French output of 40, and a decline in Italian output of equally 40. As a consequence, German output goes from 1060 to 1020, French output goes from 1050 to 1010, and Italian output goes from 1010 to 970. In Germany there is still some overemployment. In France there is still some overemployment, too. In Italy there is now some unemployment. And in Europe there is now full employment. Step 3 refers to wage policies in Germany, France and Italy. The inflationary gap in Germany is 20. The wage policy multiplier in Germany is 1. So what is needed in Germany is an increase in German nominal wages of 20. The inflationary gap in France is 10. The wage policy multiplier in France is 1. So what is needed in France is an increase in French nominal wages of 10. The output gap in Italy is 30. The wage policy multiplier in Italy is 1. So what is needed in Italy is a reduction in Italian nominal wages of 30. Step 4 refers to the output lag. The increase in German nominal wages of 20 lowers German output by 20. The increase in French nominal wages of 10 lowers French output by 10. And the reduction in Italian nominal wages of 30 raises Italian output by 30. As a consequence, German output goes from 1020 to 1000, French output goes from 1010 to 1000, and Italian output goes from 970 to 1000. In each of the countries there is now full employment. As a result, the process of monetary and wage competition leads to full employment in Germany, France and Italy. Table 6.3 presents a synopsis.

192 Table 6.3 Competition between the European Central Bank, the German Labour Union, the French Labour Union, and the Italian Labour Union The Case of Overemployment

Initial Output

Germany

France

Italy

1060

1050

1010

Change in Money Supply

1 Output Change in Nominal Wages Output

-40 1020

1010

970

20

10

-30

1000

1000

1000

1

Chapter 3 Monetary and Wage Cooperation

1) Introduction. This chapter deals with cooperation between the European central bank, the German labour union, the French labour union, and the Italian labour union. As a starting point, take the output model. It can be represented by a system of three equations: Yi=Ai+aM-yWi

(1)

Y2=A2+aM-yW2

(2)

Y3=A3+aM-yW3

(3)

Here Yj denotes German output, Y2 is French output, Y3 is Italian output, M is European money supply, W^ is German nominal wages, W2 is French nominal wages, W3 is Italian nominal wages, a is the monetary policy multiplier, and y is the wage policy multiplier. The endogenous variables are German output, French output, and Italian output. 2) The policy model. At the beginning there is unemployment in Germany, France and Italy. More precisely, unemployment in Germany is high, unemployment in France is medium size, and unemployment in Italy is low. The policy makers are the European central bank, the German labour union, the French labour union, and the Italian labour union. The targets of policy cooperation are full employment in Germany, full employment in France, and full employment in Italy. The instruments of policy cooperation are European money supply, German nominal wages, French nominal wages, and Italian 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 Italy. Taking differences in equations (1), (2) and (3), the policy model can be written as follows:

194

AYj=aAM-yAWi

(4)

AY2=aAM-yAW2

(5)

AY3=aAM-yAW3

(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 Italy, AM is the required change in European money supply, AW^ is the required change in German nominal wages, AW2 is the required change in French nominal wages, and AW3 is the required change in Italian nominal wages. The endogenous variables are AM, AWj, AW2 and AW3. We now introduce a fourth target. We assume that the level of European nominal wages should be constant: AWj+AW2+AW3=0

(7)

Accordingly, the price level of European goods should be constant, too. Add up equations (4), (5) and (6), taking account of equation (7), to find out: AY+AY^+AY. AM = —^2 ^ 3a

(8)

Here AY^ + AY2 + AY3 is the initial output gap in Europe, and 3a is the monetary policy multiplier in Europe. Then subtract equation (5) from equation (4): AY, - AY2 = YAW2 - YAW,

(9)

Similarly, subtract equation (6) from equation (4): AYj - AYj = yAWj -yAWj

(10)

195 Moreover, add up equations (9) and (10): 2AYi-AY2-AY3= yAW2+YAW3-2YAWj

(11)

Then eliminate AWj and AWj in equation (11) by means of equation (7) and solve for:

AWj =

2AY,-AY,-AY, ^ 3Y ? ^

, ^ (12)

In the same way it can be derived that: 2AY,-AY,-AY, ^^' 2 "--r:l-2 \ 1

(13)

2AY,-AY,-AY-, AW, ^ ^ ' 3 ~= - ^^^^-^

(14)

3Y

3Y

According to equation (8), the required change in European money supply depends on the initial output gap in Europe and on the monetary policy multiplier in Europe. According to equation (12), the required change in German nominal wages depends on the initial output gap in Germany, the initial output gap in France, the initial output gap in Italy, and the wage policy multiplier. According to equation (13), the required change in French nominal wages depends on the initial output gap in France, the initial output gap in Germany, the initial output gap in Italy, and the wage policy multiplier. And so on. 3) A numerical example: the case of unemployment. To illustrate the policy model, have a look at a numerical example. For ease of exposition, without losing generality, assume a = 1 and y = 1. That is, an increase in European money supply of 100 causes an increase in German output of 100, an increase in French output of 100, and an increase in Italian output of equally 100. An increase in German nominal wages of 100 causes a decline in German output of 100. Correspondingly, an increase in French nominal wages of 100 causes a decline in

196 French output of 100. And an increase in Italian nominal wages of 100 causes a decline in Italian output of 100. Further, let full-employment output in Germany be 1000, let full-employment output in France be 1000, and let full-employment output in Italy be the same. Let initial output in Germany be 940, let initial output in France be 950, and let initial output in Italy be 990. 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 50, the output gap in Italy is 10, and the output gap in Europe is 120. So what is needed, according to equations (8), (12), (13) and (14), is an increase in European money supply of 40, a reduction in German nominal wages of 20, a reduction in French nominal wages of 10, and an increase in Italian nominal wages of 30. Step 2 refers to the output lag. The increase in European money supply of 40 causes an increase in German output of 40, an increase in French output of 40, and an increase in Italian output of equally 40. The reduction in German nominal wages of 20 raises German output by 20. The reduction in French nominal wages of 10 raises French output by 10. And the increase in Italian nominal wages of 30 lowers Italian output by 30. The net effect is an increase in German output of 60, an increase in French output of 50, and an increase in Italian output of 10. As a consequence, German output goes from 940 to 1000, French output goes from 950 to 1000, and ItaHan output goes from 990 to 1000. In each of the countries there is now full employment. Table 6.4 gives an overview. As a result, monetary and wage cooperation can achieve full employment in Germany, France and Italy. There is an increase in European money supply. There is a reduction in German nominal wages, a reduction in French nominal wages, an increase in Italian nominal wages, and no change in European nominal wages. There is an increase in German output, as there is in French output and Italian output. There is a decline in the price of German goods, a decline in the price of French goods, an increase in the price of Italian goods, and no change in the price level of European goods.

197 Table 6.4 Cooperation between the European Central Bank, the German Labour Union, the French Labour Union, and the Italian Labour Union The Case of Unemployment

Initial Output

Germany

France

Italy

940

950

990

Change in Money Supply

40

Change in Nominal Wages

-20

-10

30

Output

1000

1000

1000

4) A numerical example: the case of overemployment. Let initial output in Germany be 1060, let initial output in France be 1050, and let initial output in Italy be 1010. 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 50, the inflationary gap in Italy is 10, and the inflationary gap in Europe is 120. So what is needed, according to equations (8), (12), (13) and (14), is a reduction in European money supply of 40, an increase in German nominal wages of 20, an increase in French nominal wages of 10, and a reduction in Italian nominal wages of 30. Step 2 refers to the output lag. The reduction in European money supply of 40 causes a decline in German output of 40, a decline in French output of 40, and a decline in Italian output of equally 40. The increase in German nominal wages of 20 lowers German output by 20. The increase in French nominal wages of 10 lowers French output by 10. And the reduction in Italian nominal wages of 30 raises Italian output by 30. The net effect is a decline in German output of 60, a decline in French output of 50, and a decline in Italian output of 10. As a consequence, German output goes from 1060 to 1000, French output goes from 1050 to 1000, and ItaHan output goes from 1010 to 1000. In each of the countries there is now full employment.

198 As a result, monetary and wage cooperation can achieve full employment in Germany, France and Italy. Table 6.5 presents a synopsis.

Table 6.5 Cooperation between the European Central Bank, the German Labour Union, the French Labour Union, and the Italian Labour Union The Case of Overemployment

Initial Output

Germany

France

Italy

1060

1050

1010

Change in Money Supply Change in Nominal Wages Output

-40 20

10

-30

1000

1000

1000

Part Seven Monetary, Fiscal and Wage Policies

201 For ease of exposition we assume that the euro area consists of two countries, say Germany and France. The member countries are the same size and have the same behavioural functions. This part deals with competition between the European central bank, the German government, the French government, 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 two equations: Y j = A i + a M + pGi-yWi

(1)

Y2 = A2 + aM + PG2 -yW2

(2)

Yj denotes German output, Y2 is French output, M is European money supply, Gj is German government purchases, G2 is French government purchases, W^ is German nominal wages, W2 is French nominal wages, a is the monetary policy multiplier, p is the fiscal policy multiplier, and y is the wage policy multiplier. The endogenous variables are German output and French output. According to equation (1), German output is a positive function of European money supply, a positive function of German government purchases, and a negative function of German nominal wages. According to equation (2), French output is a positive function of European money supply, a positive function of French government purchases, and a negative function of French nominal wages. In the numerical example we assume that a = 1, p = 1 and y = 1. Evidently, an increase in European money supply of 100 raises German output and French output by 100 each. An increase in German government purchases of 100 raises German output by 100. An increase in French government purchases of 100 raises French output by 100. An increase in German nominal wages of 100 lowers German output by 100. And an increase in French nominal wages of 100 lowers French output by 100. Further, let full-employment output in Germany be 1000, and let full-employment output in France be the same. At the beginning there is unemployment in Germany and France. 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 full employment in Europe. The specific target of the European central bank is that unemployment in

202 Germany equals overemployment in France. In other words, the specific target of the European central bank is full employment in Europe on average. The general target of the German government is full employment in Germany. The general target of the French government is full employment in France. The general target of the German labour union is full employment in Germany. And the general target of the French labour union is full employment in France. We assume that the central bank, the governments, and the labour unions decide sequentially. First the central bank decides, then the governments and the labour unions decide. In step 1, the central bank decides. In step 2, the German government, the French government, the German labour union, and the French labour union decide simultaneously and independently. In step 3, the central bank decides. In step 4, the German government, the French government, the German labour union, and the French labour union decide simultaneously and independently. And so on. Moreover, we assume that the central bank follows a cold-turkey strategy. The governments and the labour unions can follow either a cold-turkey strategy or a gradualist strategy. It proves useful to consider five distinct cases: - the government closes the output gap by 100 percent, the labour union closes the output gap by 100 percent - the government closes the output gap by 40 percent, the labour union closes the output gap by 40 percent - the government closes the output gap by 20 percent, the labour union closes the output gap by 60 percent - the government closes the output gap by 60 percent, the labour union closes the output gap by 60 percent - the government closes the output gap by 40 percent, the labour union closes the output gap by 80 percent. 1) The government closes the output gap by 100 percent, the labour union closes the output gap by 100 percent. We assume that the governments and the labour unions follow a cold-turkey strategy. The specific target of the German government is to close the output gap in Germany by 100 percent. The specific target of the French government is to close the output gap in France by 100 percent. The specific target of the German labour union is to close the output gap

203 in Germany by 100 percent. And the specific target of the French labour union is to close the output gap in France by 100 percent. Let initial output in Germany be 940, and let initial output in France be 970. Step 1 refers to monetary policy in Europe. The output gap in Europe is 90. The target of the European central bank is to close the output gap in Europe by 100 percent, that is by 90. The monetary policy multiplier in Europe is 2. So what is needed in Europe is an increase in European money supply of 45. Step 2 refers to the output lag. The increase in European money supply of 45 causes an increase in German output of 45 and an increase in French output of equally 45. As a consequence, German output goes from 940 to 985, and French output goes from 970 to 1015. Step 3 refers to fiscal and wage policies. First consider fiscal policy in Germany. The output gap in Germany is 15. The target of the German government is to close the output gap in Germany by 100 percent, that is by 15. The fiscal policy multiplier in Germany is 1. So what is needed in Germany is an increase in German government purchases of 15. Second consider fiscal policy in France. The inflationary gap in France is 15. The target of the French government is to close the inflationary gap in France by 100 percent, that is by 15. The fiscal policy multiplier in France is 1. So what is needed in France is a reduction in French government purchases of 15. Third consider wage policy in Germany. The output gap in Germany is 15. The target of the German labour union is to close the output gap in Germany by 100 percent, that is by 15. The wage policy multiplier in Germany is 1. So what is needed in Germany is a reduction in German nominal wages of 15. Fourth consider wage policy in France. The inflationary gap in France is 15. The target of the French labour union is to close the inflationary gap in France by 100 percent, that is by 15. The wage policy multiplier in France is 1. So what is needed in France is an increase in French nominal wages of 15. Step 4 refers to the output lag. The increase in German government purchases of 15 causes an increase in German output of 15. The reduction in French government purchases of 15 causes a decline in French output of 15. The reduction in German nominal wages of 15 causes an increase in German output of 15. And the increase in French nominal wages of 15 causes a decline in

204 French output of 15. The total effect is an increase in German output of 30 and a decline in French output of equally 30. As a consequence, German output goes from 985 to 1015, and French output goes from 1015 to 985. 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 1015, and French output stays at 985. Step 7 refers to fiscal and wage policies. First consider fiscal policy in Germany. The inflationary gap in Germany is 15. The target of the German government is to close the inflationary gap in Germany by 100 percent, that is by 15. The fiscal policy multiplier in Germany is 1. So what is needed in Germany is a reduction in German government purchases of 15. Second consider fiscal policy in France. The output gap in France is 15. The target of the French government is to close the output gap in France by 100 percent, that is by 15. The fiscal policy multiplier in France is 1. So what is needed in France is an increase in French government purchases of 15. Third consider wage policy in Germany. The inflationary gap in Germany is 15. The target of the German labour union is to close the inflationary gap in Germany by 100 percent, that is by 15. The wage policy multiplier in Germany is 1. So what is needed in Germany is an increase in German nominal wages of 15. Fourth consider wage policy in France. The output gap in France is 15. The target of the French labour union is to close the output gap in France by 100 percent, that is by 15. The wage policy multiplier in France is 1. So what is needed in France is a reduction in French nominal wages of 15. Step 8 refers to the output lag. The reduction in German government purchases of 15 causes a decline in German output of 15. The increase in French government purchases of 15 causes an increase in French output of 15. The increase in German nominal wages of 15 causes a decline in German output of 15. And the reduction in French nominal wages of 15 causes an increase in French output of 15. The total effect is a decline in German output of 30 and an increase in French output of equally 30. As a consequence, German output goes from 1015 to 985, and French output goes from 985 to 1015. With this, output is

205 back at its initial level. This process will repeat itself step by step. Table 7.1 presents a synopsis. As a result, the process of monetary, fiscal and wage competition does not lead to full employment in Germany and France. What are the dynamic characteristics of this process? There is a one-time increase in European money supply. There are uniform oscillations in German government purchases, German nominal wages, and German output. Similarly, there are uniform oscillations in French government purchases, French nominal wages, and French output. The German economy oscillates between unemployment and overemployment, as does the French economy.

Table 7.1 Monetary, Fiscal and Wage Competition The Government Closes the Output Gap by 100 Percent The Labour Union Closes the Output Gap by 100 Percent Germany Initial Output

France

940

970 45

Change in Money Supply 985

1015

15

-15

Change in Nominal Wages

-15

15

Output

1015

985

Change in Government Purchases

-15

15

15

-15

985

1015

...

...

Output Change in Government Purchases

Change in Nominal Wages Output and so on

206 2) The government closes the output gap by 40 percent, the labour union closes the output gap by 40 percent. So far we have assumed that the governments and the labour unions follow a cold-turkey strategy. Now we assume that the governments and the labour unions follow a gradualist strategy. The specific target of the German government is to close the output gap in Germany by 40 percent. The specific target of the French government is to close the output gap in France by 40 percent. The specific target of the German labour union is to close the output gap in Germany by 40 percent. And the specific target of the French labour union is to close the output gap in France by 40 percent. Let initial output in Germany be 940, and let initial output in France be 970. Step 1 refers to monetary policy in Europe. The output gap in Europe is 90. The target of the European central bank is to close the output gap in Europe by 100 percent, that is by 90. The monetary policy multiplier in Europe is 2. So what is needed in Europe is an increase in European money supply of 45. Step 2 refers to the output lag. The increase in European money supply of 45 causes an increase in German output of 45 and an increase in French output of equally 45. As a consequence, German output goes from 940 to 985, and French output goes from 970 to 1015. Step 3 refers to fiscal and wage policies. First consider fiscal policy in Germany. The output gap in Germany is 15. The target of the German government is to close the output gap in Germany by 40 percent, that is by 6. The fiscal policy multiplier in Germany is 1. So what is needed in Germany is an increase in German government purchases of 6. Second consider fiscal policy in France. The inflationary gap in France is 15. The target of the French government is to close the inflationary gap in France by 40 percent, that is by 6. The fiscal policy multiplier in France is 1. So what is needed in France is a reduction in French government purchases of 6. Third consider wage policy in Germany. The output gap in Germany is 15. The target of the German labour union is to close the output gap in Germany by 40 percent, that is by 6. The wage policy multiplier in Germany is 1. So what is needed in Germany is a reduction in German nominal wages of 6. Fourth consider wage policy in France. The inflationary gap in France is 15. The target of the French labour union is to close the inflationary gap in France by 40

207 percent, that is by 6. The wage poHcy multiplier in France is 1. So what is needed in France is an increase in French nominal wages of 6. Step 4 refers to the output lag. The increase in German government purchases of 6 causes an increase in German output of 6. The reduction in French government purchases of 6 causes a decline in French output of 6. The reduction in German nominal wages of 6 causes an increase in German output of 6. And the increase in French nominal wages of 6 causes a decline in French output of 6. The total effect is an increase in German output of 12 and a decline in French output of equally 12. As a consequence, German output goes from 985 to 997, and French output goes from 1015 to 1003. 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 997, and French output stays at 1003. Step 7 refers to fiscal and wage policies. First consider fiscal policy in Germany. The output gap in Germany is 3. The target of the German government is to close the output gap in Germany by 40 percent, that is by 1.2. The fiscal policy multiplier in Germany is 1. So what is needed in Germany is an increase in German government purchases of 1.2. Second consider fiscal policy in France. The inflationary gap in France is 3. The target of the French government is to close the inflationary gap in France by 40 percent, that is by 1.2. The fiscal policy multiplier in France is 1. So what is needed in France is a reduction in French government purchases of 1.2. Third consider wage policy in Germany. The output gap in Germany is 3. The target of the German labour union is to close the output gap in Germany by 40 percent, that is by 1.2. The wage policy multiplier in Germany is 1. So what is needed in Germany is a reduction in German nominal wages of 1.2. Fourth consider wage policy in France. The inflationary gap in France is 3. The target of the French labour union is to close the inflationary gap in France by 40 percent, that is by 1.2. The wage policy multiplier in France is 1. So what is needed in France is an increase in French nominal wages of 1.2.

208 Step 8 refers to the output lag. The increase in German government purchases of 1.2 causes an increase in German output of 1.2. The reduction in French government purchases of 1.2 causes a decline in French output of 1.2. The reduction in German nominal wages of 1.2 causes an increase in German output of 1.2. And the increase in French nominal wages of 1.2 causes a decline in French output of 1.2. The total effect is an increase in German output of 2.4 and a decline in French output of equally 2.4. As a consequence, German output goes from 997 to 999.4, and French output goes from 1003 to 1000.6. And so on. Table 7.2 gives an overview. In the steady state, German output is 1000, and French output is equally 1000. In each of the countries there is now full employment. As a result, the process of monetary, fiscal and wage competition leads to full employment in Germany and France. What are the dynamic characteristics of this process? There is a one-time increase in European money supply. There are repeated increases in German government purchases, there are repeated cuts in German nominal wages, and there are repeated increases in German output. There are repeated cuts in French government purchases, there are repeated increases in French nominal wages, and there are repeated cuts in French output. It is worth pointing out here that there are no oscillations. Taking the sum over all periods, the increase in European money supply is 45, the increase in German government purchases is 7.5, and the reduction in German nominal wages is 7.5 as well. Evidently, the total increase in German government purchases and the total reduction in German nominal wages depend on the relative speed of adjustment of German government purchases and German nominal wages (0.4/0.4 = 1). Besides, the total reduction in French government purchases is 7.5, and the total increase in French nominal wages is 7.5 as well.

209 Table 7.2 Monetary, Fiscal and Wage Competition The Government Closes the Output Gap by 40 Percent The Labour Union Closes the Output Gap by 40 Percent Germany Initial Output

940

Change in Government Purchases Change in Nominal Wages 1 Output Change in Government Purchases Change in Nominal Wages 1 Output and so on

970 45

Change in Money Supply 1 Output

France

985

1015

6

-6

-6

6

997

1003

1.2

-1.2

-1.2

1.2

999.4

1000.6

...

...

3) The government closes the output gap by 20 percent, the labour union closes the output gap by 60 percent. The target of the German government is to close the output gap in Germany by 20 percent. The target of the French government is to close the output gap in France by 20 percent. The target of the German labour union is to close the output gap in Germany by 60 percent. And the target of the French labour union is to close the output gap in France by 60 percent. Let initial output in Germany be 940, and let initial output in France be 970. Step 1 refers to monetary policy in Europe. The output gap in Europe is 90. The target of the European central bank is to close the output gap in Europe by 100 percent, that is by 90. The monetary policy multiplier in Europe is 2. So what is needed in Europe is an increase in European money supply of 45. Step 2 refers to the output lag. The increase in European money supply of 45 causes an increase

210 in German output of 45 and an increase in French output of equally 45. As a consequence, German output goes from 940 to 985, and French output goes from 970 to 1015. Step 3 refers to fiscal and wage poUcies. First consider fiscal policy in Germany. The output gap in Germany is 15. The target of the German government is to close the output gap in Germany by 20 percent, that is by 3. The fiscal policy multiplier in Germany is 1. So what is needed in Germany is an increase in German government purchases of 3. Second consider fiscal policy in France. The inflationary gap in France is 15. The target of the French government is to close the inflationary gap in France by 20 percent, that is by 3. The fiscal policy multiplier in France is 1. So what is needed in France is a reduction in French government purchases of 3. Third consider wage policy in Germany. The output gap in Germany is 15. The target of the German labour union is to close the output gap in Germany by 60 percent, that is by 9. The wage policy multiplier in Germany is 1. So what is needed in Germany is a reduction in German nominal wages of 9. Fourth consider wage policy in France. The inflationary gap in France is 15. The target of the French labour union is to close the inflationary gap in France by 60 percent, that is by 9. The wage policy multiplier in France is 1. So what is needed in France is an increase in French nominal wages of 9. Step 4 refers to the output lag. The increase in German government purchases of 3 causes an increase in German output of 3. The reduction in French government purchases of 3 causes a decline in French output of 3. The reduction in German nominal wages of 9 causes an increase in German output of 9. And the increase in French nominal wages of 9 causes a decline in French output of 9. The total effect is an increase in German output of 12 and a decline in French output of equally 12. As a consequence, German output goes from 985 to 997, and French output goes from 1015 to 1003. 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 997, and French output stays at 1003.

211 Step 7 refers to fiscal and wage policies. First consider fiscal policy in Germany. The output gap in Germany is 3. The target of the German government is to close the output gap in Germany by 20 percent, that is by 0.6. The fiscal policy multiplier in Germany is 1. So what is needed in Germany is an increase in German government purchases of 0.6. Second consider fiscal policy in France. The inflationary gap in France is 3. The target of the French government is to close the inflationary gap in France by 20 percent, that is by 0.6. The fiscal policy multiplier in France is 1. So what is needed in France is a reduction in French government purchases of 0.6. Third consider wage policy in Germany. The output gap in Germany is 3. The target of the German labour union is to close the output gap in Germany by 60 percent, that is by 1.8. The wage policy multiplier in Germany is 1. So what is needed in Germany is a reduction in German nominal wages of 1.8. Fourth consider wage policy in France. The inflationary gap in France is 3. The target of the French labour union is to close the inflationary gap in France by 60 percent, that is by 1.8. The wage policy multiplier in France is 1. So what is needed in France is an increase in French nominal wages of 1.8. Step 8 refers to the output lag. The increase in German government purchases of 0.6 causes an increase in German output of 0.6. The reduction in French government purchases of 0.6 causes a decline in French output of 0.6. The reduction in German nominal wages of 1.8 causes an increase in German output of 1.8. And the increase in French nominal wages of 1.8 causes a decline in French output of 1.8. The total effect is an increase in German output of 2.4 and a decline in French output of equally 2.4. As a consequence, German output goes from 997 to 999.4, and French output goes from 1003 to 1000.6. And so on. Table 7.3 presents a synopsis. In the steady state, German output is 1000, and the same holds for French output. In each of the countries there is now full employment. As a result, the process of monetary, fiscal and wage competition leads to full employment in Germany and France. What are the dynamic characteristics of this process? There is a one-time increase in European money supply. There are repeated increases in German government purchases, there are repeated cuts in German nominal wages, and

212 there are repeated increases in German output. There are repeated cuts in French government purchases, there are repeated increases in French nominal wages, and there are repeated cuts in French output. It is worth pointing out here that there are no oscillations. Taking the sum over all periods, the increase in European money supply is 45, the increase in German government purchases is 3.75, and the reduction in German nominal wages is 11.25. Obviously, the total increase in German government purchases and the total reduction in German nominal wages depend on the relative speed of adjustment of German government purchases and German nominal wages (0.2/0.6 = 1/3). Moreover, the total reduction in French government purchases is 3.75, and the total increase in French nominal wages is 11.25.

Table 7.3 Monetary, Fiscal and Wage Competition The Government Closes the Output Gap by 20 Percent The Labour Union Closes the Output Gap by 60 Percent Germany Initial Output

940

Change in Money Supply Output

France 970 45

985

1015

3

-3

Change in Nominal Wages

-9

9

Output

997

1003

Change in Government Purchases

0.6

-0.6

Change in Nominal Wages

-1.8

1.8

Output

999.4

1000.6

...

...

Change in Government Purchases

and so on

213 4) The government closes the output gap by 60 percent, the labour union closes the output gap by 60 percent. The target of the German government is to close the output gap in Germany by 60 percent. The target of the French government is to close the output gap in France by 60 percent. The target of the German labour union is to close the output gap in Germany by 60 percent. And the target of the French labour union is to close the output gap in France by 60 percent. Let initial output in Germany be 940, and let initial output in France be 970. Step 1 refers to monetary policy in Europe. The output gap in Europe is 90. The target of the European central bank is to close the output gap in Europe by 100 percent, that is by 90. The monetary policy multiplier in Europe is 2. So what is needed in Europe is an increase in European money supply of 45. Step 2 refers to the output lag. The increase in European money supply of 45 causes an increase in German output of 45 and an increase in French output of equally 45. As a consequence, German output goes from 940 to 985, and French output goes from 970 to 1015. Step 3 refers to fiscal and wage policies. First consider fiscal policy in Germany. The output gap in Germany is 15. The target of the German government is to close the output gap in Germany by 60 percent, that is by 9. The fiscal policy multiplier in Germany is 1. So what is needed in Germany is an increase in German government purchases of 9. Second consider fiscal policy in France. The inflationary gap in France is 15. The target of the French government is to close the inflationary gap in France by 60 percent, that is by 9. The fiscal policy multiplier in France is 1. So what is needed in France is a reduction in French government purchases of 9. Third consider wage policy in Germany. The output gap in Germany is 15. The target of the German labour union is to close the output gap in Germany by 60 percent, that is by 9. The wage policy multiplier in Germany is 1. So what is needed in Germany is a reduction in German nominal wages of 9. Fourth consider wage policy in France. The inflationary gap in France is 15. The target of the French labour union is to close the inflationary gap in France by 60 percent, that is by 9. The wage policy multiplier in France is 1. So what is needed in France is an increase in French nominal wages of 9.

214 Step 4 refers to the output lag. The increase in German government purchases of 9 causes an increase in German output of 9. The reduction in French government purchases of 9 causes a decline in French output of 9. The reduction in German nominal wages of 9 causes an increase in German output of 9. And the increase in French nominal wages of 9 causes a decline in French output of 9. The total effect is an increase in German output of 18 and a decline in French output of equally 18. As a consequence, German output goes from 985 to 1003, and French output goes from 1015 to 997. 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 1003, and French output stays at 997. Step 7 refers to fiscal and wage policies. First consider fiscal policy in Germany. The inflationary gap in Germany is 3. The target of the German government is to close the inflationary gap in Germany by 60 percent, that is by 1.8. The fiscal policy multiplier in Germany is 1. So what is needed in Germany is a reduction in German government purchases of 1.8. Second consider fiscal policy in France. The output gap in France is 3. The target of the French government is to close the output gap in France by 60 percent, that is by 1.8. The fiscal policy multiplier in France is 1. So what is needed in France is an increase in French government purchases of 1.8. Third consider wage policy in Germany. The inflationary gap in Germany is 3. The target of the German labour union is to close the inflationary gap in Germany by 60 percent, that is by 1.8. The wage policy multiplier in Germany is 1. So what is needed in Germany is an increase in German nominal wages of 1.8. Fourth consider wage policy in France. The output gap in France is 3. The target of the French labour union is to close the output gap in France by 60 percent, that is by 1.8. The wage policy multiplier in France is 1. So what is needed in France is a reduction in French nominal wages of 1.8. Step 8 refers to the output lag. The reduction in German government purchases of 1.8 causes a decline in German output of 1.8. The increase in French government purchases of 1.8 causes an increase in French output of 1.8. The increase in German nominal wages of 1.8 causes a decline in German output

215 of 1.8. And the reduction in French nominal wages of 1.8 causes an increase in French output of 1.8. The total effect is a decline in German output of 3.6 and an increase in French output of equally 3.6. As a consequence, German output goes from 1003 to 999.4, and French output goes from 997 to 1000.6. And so on. Table 7.4 gives an overview.

Table 7.4 Monetary, Fiscal and Wage Competition The Government Closes the Output Gap by 60 Percent The Labour Union Closes the Output Gap by 60 Percent Germany Initial Output

940

Change in Money Supply 1 Output

France 970 45

985

1015

9

-9

-9

9

Output

1003

997

Change in Government Purchases

-1.8

1.8

1.8

-1.8

999.4

1000.6

...

...

Change in Government Purchases Change in Nominal Wages

Change in Nominal Wages 1 Output and soon

In the steady state, German output is 1000, and French output is equally 1000. In each of the countries there is now full employment. As a result, the process of monetary, fiscal and wage competition leads to full employment in Germany and France. What are the dynamic characteristics of this process? There is a one-time increase in European money supply. There are damped oscillations in German

216 government purchases, German nominal wages, and German output. Likewise, there are damped oscillations in French government purchases, French nominal wages, and French output. The German economy oscillates between unemployment and overemployment, as does the French economy. Taking the sum over all periods, the increase in European money supply is 45, the increase in German government purchases is 7.5, and the reduction in German nominal wages is 7.5 as well. Evidently, the total increase in German government purchases and the total reduction in German nominal wages depend on the relative speed of adjustment of German government purchases and German nominal wages (0.6/0.6 = 1). Besides, the total reduction in French government purchases is 7.5, and the total increase in French nominal wages is 7.5 as well. 5) The government closes the output gap by 40 percent, the labour union closes the output gap by 80 percent. The target of the German government is to close the output gap in Germany by 40 percent. The target of the French government is to close the output gap in France by 40 percent. The target of the German labour union is to close the output gap in Germany by 80 percent. And the target of the French labour union is to close the output gap in France by 80 percent. Let initial output in Germany be 940, and let initial output in France be 970. Step 1 refers to monetary policy in Europe. The output gap in Europe is 90. The target of the European central bank is to close the output gap in Europe by 100 percent, that is by 90. The monetary policy multiplier in Europe is 2. So what is needed in Europe is an increase in European money supply of 45. Step 2 refers to the output lag. The increase in European money supply of 45 causes an increase in German output of 45 and an increase in French output of equally 45. As a consequence, German output goes from 940 to 985, and French output goes from 970 to 1015. Step 3 refers to fiscal and wage policies. First consider fiscal policy in Germany. The output gap in Germany is 15. The target of the German government is to close the output gap in Germany by 40 percent, that is by 6. The fiscal policy multiplier in Germany is 1. So what is needed in Germany is an increase in German government purchases of 6. Second consider fiscal policy in

217 France. The inflationary gap in France is 15. The target of the French government is to close the inflationary gap in France by 40 percent, that is by 6. The fiscal policy multiplier in France is 1. So what is needed in France is a reduction in French government purchases of 6. Third consider wage policy in Germany. The output gap in Germany is 15. The target of the German labour union is to close the output gap in Germany by 80 percent, that is by 12. The wage policy multiplier in Germany is 1. So what is needed in Germany is a reduction in German nominal wages of 12. Fourth consider wage policy in France. The inflationary gap in France is 15. The target of the French labour union is to close the inflationary gap in France by 80 percent, that is by 12. The wage policy multiplier in France is 1. So what is needed in France is an increase in French nominal wages of 12. Step 4 refers to the output lag. The increase in German government purchases of 6 causes an increase in German output of 6. The reduction in French government purchases of 6 causes a decline in French output of 6. The reduction in German nominal wages of 12 causes an increase in German output of 12. And the increase in French nominal wages of 12 causes a decline in French output of 12. The total effect is an increase in German output of 18 and a decline in French output of equally 18. As a consequence, German output goes from 985 to 1003, and French output goes from 1015 to 997. 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 1003, and French output stays at 997. Step 7 refers to fiscal and wage policies. First consider fiscal policy in Germany. The inflationary gap in Germany is 3. The target of the German government is to close the inflationary gap in Germany by 40 percent, that is by 1.2. The fiscal policy multiplier in Germany is 1. So what is needed in Germany is a reduction in German government purchases of 1.2. Second consider fiscal policy in France. The output gap in France is 3. The target of the French government is to close the output gap in France by 40 percent, that is by 1.2. The fiscal policy multiplier in France is 1. So what is needed in France is an increase in French government purchases of 1.2.

218

Third consider wage policy in Germany. The inflationary gap in Germany is 3. The target of the German labour union is to close the inflationary gap in Germany by 80 percent, that is by 2.4. The wage policy multiplier in Germany is 1. So what is needed in Germany is an increase in German nominal wages of 2.4. Fourth consider wage policy in France. The output gap in France is 3. The target of the French labour union is to close the output gap in France by 80 percent, that is by 2.4. The wage policy multiplier in France is 1. So what is needed in France is a reduction in French nominal wages of 2.4. Step 8 refers to the output lag. The reduction in German government purchases of 1.2 causes a decline in German output of 1.2. The increase in French government purchases of 1.2 causes an increase in French output of 1.2. The increase in German nominal wages of 2.4 causes a decline in German output of 2.4. And the reduction in French nominal wages of 2.4 causes an increase in French output of 2.4. The total effect is a decline in German output of 3.6 and an increase in French output of equally 3.6. As a consequence, German output goes from 1003 to 999.4, and French output goes from 997 to 1000.6. And so on. For a synopsis see Table 7.5. In the steady state, German output is 1000, and the same applies to French output. In each of the countries there is now full employment. As a result, the process of monetary, fiscal and wage competition leads to full employment in Germany and France. What are the dynamic characteristics of this process? There is a one-time increase in European money supply. There are damped oscillations in German government purchases, German nominal wages, and German output. Likewise, there are damped oscillations in French government purchases, French nominal wages, and French output. The German economy oscillates between unemployment and overemployment, as does the French economy. Taking the sum over all periods, the increase in European money supply is 45, the increase in German government purchases is 5, and the reduction in German nominal wages is 10. Evidently, the total increase in German government purchases and the total reduction in German nominal wages depend on the relative speed of adjustment of German government purchases and

219 German nominal wages (0.4/0.8 = 1/2). Besides, the total reduction in French government purchases is 5, and the total increase in French nominal wages is 10.

Table 7.5 Monetary, Fiscal and Wage Competition The Government Closes the Output Gap by 40 Percent The Labour Union Closes the Output Gap by 80 Percent

France

Germany Initial Output

45

Change in Money Supply Output Change in Government Purchases Change in Nominal Wages 1 Output Change in Government Purchases Change in Nominal Wages 1 Output and so on

970

940 985

1015

6

-6

-12

12

1003

997

-1.2

1.2

2.4

-2.4

999.4

1000.6

...

...

Synopsis 1. Monetary and Fiscal Policies

The synopsis refers to the interactions between - the European central bank, - the German government, and - the French government. The synopsis is based on a numerical example. The initial output gap in Germany is 60, and the initial output gap in France is 30. As a result, taking the sum over all periods, Table 8.1 shows: - the total increase in European money supply, - the total increase in German government purchases, - the total increase in French government purchases, and - the total increase in European government purchases. Obviously, the result depends on the type of policy system. In addition. Table 8.2 shows the total increase in European government purchases, as a percentage of the initial output gap in Europe. Again, the result depends on the type of policy system.

222

Table 8.1 Increase in Money Supply and Government Purchases According to Type of Policy System Monetary Policy in Europe Increase in European Money Supply

45

Increase in German Government Purchases

0

Increase in French Government Purchases

0

Increase in European Government Purchases

0

Fiscal Policies in Germany and France Increase in European Money Supply Increase in German Government Purchases

60

Increase in French Government Purchases

30

Increase in European Government Purchases

90

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

45

Increase in German Government Purchases

15

Increase in French Government Purchases Increase in European Government Purchases

1

0

Monetary and Fiscal Competition Sequential Decisions: Cold-Turkey Policies The process of monetary and fiscal competition does not lead to full employment in Germany and France. There are uniform oscillations in money supply, government purchases, and output.

-15 0

223

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

25.7

Increase in German Government Purchases

34.3

Increase in French Government Purchases

4.3

Increase in European Government Purchases

38.7

Monetary and Fiscal Cooperation Increase in European Money Supply

45

Increase in German Government Purchases

15

Increase in French Government Purchases Increase in European Government Purchases

-15 0

Table 8.2 Increase in European Government Purchases Relative to Initial Output Gap in Europe According to Type of Policy System Monetary Policy in Europe Fiscal Policies in Germany and France Sequential Decisions: Cold-Turkey Policies Simultaneous Decisions: Cold-Turkey Policies Simultaneous Decisions: Gradualist Policies Monetary and Fiscal Cooperation

0% 100 % 0% unstable 43 %

0%

1

2. Monetary and Wage Policies

The synopsis refers to the interactions between - the European central bank, - the German labour union, and - the French labour union. The synopsis is based on a numerical example. The initial output gap in Germany is 60, and the initial output gap in France is 30. As a result, taking the sum over all periods, Table 8.3 shows: - the total change in European money supply, - the total change in German nominal wages, - the total change in French nominal wages, and - the total change in European nominal wages. Obviously, the result depends on the type of policy system. In addition. Table 8.4 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 policy system.

226 Table 8.3 Change in Money Supply and Nominal Wages According to Type of Policy System Monetary Policy in Europe Change in European Money Supply

45

Change in German Nominal Wages

0

Change in French Nominal Wages

0

Change in European Nominal Wages

0

Wage Policies in Germany and France Change in European Money Supply

0

Change in German Nominal Wages

-60

Change in French Nominal Wages

-30

Change in European Nominal Wages

-45

Monetary and Wage Competition Sequential Decisions: Cold-Turkey Policies Change in European Money Supply Change in German Nominal Wages Change in French Nominal Wages Change in European Nominal Wages Monetary and Wage Competition Sequential Decisions: Cold-Turkey Policies The process of monetary and wage competition does not lead to full employment in Germany and France. There are uniform oscillations in money supply, nominal wages, and output.

45 -15 15 0

227

Monetary and Wage Competition Simultaneous Decisions: Gradualist Policies Change in European Money Supply

25.7

Change in German Nominal Wages

- 34.3

Change in French Nominal Wages

-4.3

Change in European Nominal Wages

- 19.3

Monetary and Wage Cooperation Change in European Money Supply

45

Change in German Nominal Wages

-15

Change in French Nominal Wages Change in European Nominal Wages

15 0

Table 8.4 Reduction in European Nominal Wages Relative to Initial Output Gap in Europe According to Type of Policy System Monetary Policy in Europe Wage Policies in Germany and France Sequential Decisions: Cold-Turkey Policies Simultaneous Decisions: Cold-Turkey Policies Simultaneous Decisions: Gradualist Policies Monetary and Wage Cooperation

0%

1

50 % 0% unstable 21 %

0%

1

Conclusion 1. Monetary Policy in Europe

1) Introduction. For ease of exposition we make the following assumptions. The monetary union consists of two countries, say Germany and France. The member 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. In the numerical example, an increase in European money supply of 100 causes an increase in German output of 100 and an increase in French output of equally 100. 2) The policy model. At the beginning there is unemployment in Germany and France. 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 full employment in Europe. For ease of exposition we assume that unemployment causes deflation whereas overemployment causes inflation. The specific target of the European central bank is that unemployment in Germany equals overemployment in France. Accordingly, the specific target of the European central bank is that deflation in Germany equals inflation in France. In other words, the specific target of the European central bank is full employment in Europe on average. Accordingly, the specific target of the European central bank is price stability in Europe on average. 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. 3) A numerical example: the case of unemployment. Full-employment output in Germany is 1000, and full-employment output in France is the same. Let initial output in Germany be 940, and let initial output in France be 970. In each of the countries there is unemployment and hence deflation. Step 1 refers to the policy response. The output gap in Europe is 90. The monetary policy multiplier in Europe is 2. So what is needed in Europe is an increase in European money supply of 45.

230

Step 2 refers to the output lag. The increase in European money supply of 45 causes an increase in German output of 45 and an increase in French output of equally 45. As a consequence, German output goes from 940 to 985, and French output goes from 970 to 1015. Table 9.1 presents a synopsis. In Germany there is still some unemployment and deflation. In France there is now some overemployment and inflation. And in Europe there is now full employment and price stability. Unemployment in Germany equals overemployment in France. And deflation in Germany equals inflation in France. As a result, monetary policy in Europe can achieve full employment in Europe on average. And what is more, it can achieve price stability in Europe on average. However, monetary policy in Europe cannot achieve full employment in Germany and France. And what is more, it cannot achieve price stability in Germany and France. There is an increase in German output, as there is in French output. There is an increase in German tax revenue, as there is in French tax revenue. And there is a decline in the German budget deficit, as there is in the French budget deficit.

Table 9.1 Monetary Policy in Europe The Case of Unemployment

Initial Output

Germany

France

940

970

Change in Money Supply Output

45 985

1015

4) A numerical example: the case of inflation. Let initial output in Germany be 1060, and let initial output in France be 1030. In each of the countries there is overemployment and hence inflation. Step 1 refers to the policy response. The

231 inflationary gap in Europe is 90. The monetary policy multiplier in Europe is 2. So what is needed in Europe is a reduction in European money supply of 45. Step 2 refers to the output lag. The reduction in European money supply of 45 causes a decline in German output of 45 and a decline in French output of equally 45. As a consequence, German output goes from 1060 to 1015, and French output goes from 1030 to 985. Table 9.2 gives an overview. In Germany there is still some overemployment and inflation. In France there is now some unemployment and deflation. And in Europe there is now full employment and price stability. Overemployment in Germany equals unemployment in France. And inflation in Germany equals deflation in France. As a result, monetary policy in Europe can achieve full employment and price stability in Europe as a whole. However, monetary policy in Europe cannot achieve full employment and price stability in each of the member countries. There is a decline in German output, as there is in French output. There is a decline in German tax revenue, as there is in French tax revenue. And there is an increase in the German budget deficit, as there is in the French budget deficit.

Table 9.2 Monetary Policy in Europe The Case of Inflation

Initial Output

Germany

France

1060

1030

Change in Money Supply Output

-45 1015

985

232

2. Fiscal Policies in Germany and France

1) Introduction. An increase in German government purchases raises German output. Correspondingly, an increase in French government purchases raises French output. For ease of exposition we assume that fiscal policy in one of the countries has no effect on output in the other country. In the numerical example, an increase in German government purchases of 100 causes an increase in German output of 100. Correspondingly, an increase in French government purchases of 100 causes an increase in French output of 100. 2) The policy model. At the start there is unemployment in Germany and France. More precisely, unemployment in Germany is high, and unemployment in France is low. The target of the German government is full employment in Germany. The instrument of the German government is German government purchases. The German government raises German government purchases so as to close the output gap in Germany. The target of the French government is full employment in France. The instrument of the French government is French government purchases. The French government raises French government purchases so as to close the output gap in France. 3) A numerical example. Full-employment output in Germany is 1000, and full-employment output in France is the same. Let initial output in Germany be 940, and let initial output in France be 970. In each of the countries there is unemployment and hence deflation. Step 1 refers to the policy response. The output gap in Germany is 60. The fiscal policy multiplier in Germany is 1. So what is needed in Germany is an increase in German government purchases of 60. The output gap in France is 30. The fiscal policy multiplier in France is 1. So what is needed in France is an increase in French government purchases of 30. Step 2 refers to the output lag. The increase in German government purchases of 60 causes an increase in German output of 60. And the increase in French government purchases of 30 causes an increase in French output of 30. As a consequence, German output goes from 940 to 1000, and French output goes from 970 to 1000. In each of the countries there is now full employment and price stability.

233

As a result, fiscal policies in Germany and France can achieve foil employment and price stability in each of the countries. There is an increase in European government purchases, an increase in European output, and an increase in the European budget deficit. There is an increase in the interest rate and a decline in European investment. There is an appreciation of the euro, a decline in European exports, and a decline in the European current account surplus. For a synopsis see Table 9.3.

Table 9.3 Fiscal Policies in Germany and France The Case of Unemployment

Initial Output Change in Government Purchases Output

Germany

France

940

970

60

30

1000

1000

4) Comparing fiscal policies with monetary policy. Monetary policy in Europe can achieve foil employment and price stability in Europe as a whole. However, monetary policy in Europe cannot achieve foil employment and price stability in each of the member countries. By contrast, fiscal policies in Germany and France can indeed achieve foil employment and price stability in each of the member countries. However, as a severe side effect, fiscal policies in Germany and France cause an increase in the European budget deficit.

234

3. Monetary and Fiscal Competition

1) The model. This section deals with competition between the European central bank, the German government, and the French government. At the beginning there is unemployment in Germany and France. 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 full employment in Europe. For ease of exposition we assume that unemployment causes deflation whereas overemployment causes inflation. The specific target of the European central bank is that unemployment in Germany equals overemployment in France. Accordingly, the specific target of the European central bank is that deflation in Germany equals inflation in France. In other words, the specific target of the European central bank is fiill employment in Europe on average. Accordingly, the specific target of the European central bank is price stability in Europe on average. 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 government is full employment in Germany. The instrument of the German government is German government purchases. The German government raises German government purchases so as to close the output gap in Germany. The target of the French government is full employment in France. The instrument of the French government is French government purchases. The French government raises French government purchases so as to close the output gap in France. We assume that the central bank and the governments decide sequentially. First the central bank decides, then the governments decide. Step 1 refers to monetary policy in Europe. Step 2 refers to the output lag. Step 3 refers to fiscal policies in Germany and France. And step 4 refers to the output lag. 2) A numerical example: the case of unemplo)mient. An increase in European money supply of 100 causes an increase in German output of 100 and an increase in French output of equally 100. An increase in German government purchases of

235 100 causes an increase in German output of 100. Correspondingly, an increase in French government purchases of 100 causes an increase in French output of 100. Full-employment output in Germany is 1000, and full-employment output in France is the same. Let initial output in Germany be 940, and let initial output in France be 970. In each of the countries there is unemployment and deflation. Step 1 refers to monetary policy in Europe. The output gap in Europe is 90. The monetary policy multiplier in Europe is 2. So what is needed in Europe is an increase in European money supply of 45. Step 2 refers to the output lag. The increase in European money supply of 45 causes an increase in German output of 45 and an increase in French output of equally 45. As a consequence, German output goes from 940 to 985, and French output goes from 970 to 1015. In Germany there is still some unemployment and deflation. In France there is now some overemployment and inflation. And in Europe there is now full employment and price stability. Step 3 refers to fiscal policies in Germany and France. The output gap in Germany is 15. The fiscal policy multiplier in Germany is 1. So what is needed in Germany is an increase in German government purchases of 15. The inflationary gap in France is 15. The fiscal policy multiplier in France is 1. So what is needed in France is a reduction in French government purchases of 15. Step 4 refers to the output lag. The increase in German government purchases of 15 causes an increase in German output of 15. And the reduction in French government purchases of 15 causes a decline in French output of 15. As a consequence, German output goes from 985 to 1000, and French output goes from 1015 to 1000. In each of the countries there is now full employment and price stability. For an overview see Table 9.4. As a result, the process of monetary and fiscal competition leads to full employment and price stability in each of the countries. There is an increase in European money supply. There is an increase in German government purchases, a reduction in French government purchases, and no change in European government purchases. There is an increase in German output, as there is in French output. In steps 1 and 2 there is some overshooting in French output.

236 There is an increase in European output, an increase in European tax revenue, and a decline in the European budget deficit. There is a decline in the interest rate and an increase in European investment. There is a depreciation of the euro, an increase in European exports, and an increase in the European current account surplus.

Table 9.4 Monetary and Fiscal Competition The Case of Unemployment

Initial Output

Germany

France

940

970

Change in Money Supply Output Change in Government Purchases Output

1

45 985

1015

15

-15

1000

1000

3) Comparing monetary and fiscal competition with pure monetary policy. Pure monetary policy can achieve full employment and price stability in Europe as a whole. However, it cannot achieve full employment and price stability in each of the member countries. By contrast, monetary and fiscal competition can indeed achieve full employment and price stability in each of the member countries. Judging from this point of view, monetary and fiscal competition seems to be superior to pure monetary policy. 4) Comparing monetary and fiscal competition with pure fiscal policies. Pure fiscal policies can achieve full employment and price stability in each of the member countries. And the same holds for monetary and fiscal competition. Pure fiscal policies cause an increase in the European budget deficit. By contrast, monetary and fiscal competition causes a decline in the European budget deficit.

237 Judging from this perspective, monetary and fiscal competition seems to be superior to pure fiscal policies. 5) A numerical example: the case of inflation. Let initial output in Germany be 1060, and let initial output in France be 1030. In each of the countries there is overemployment and inflation. Step 1 refers to monetary policy in Europe. The inflationary gap in Europe is 90. The monetary policy multiplier in Europe is 2. So what is needed in Europe is a reduction in European money supply of 45. Step 2 refers to the output lag. The reduction in European money supply of 45 causes a decline in German output of 45 and a decline in French output of equally 45. As a consequence, German output goes from 1060 to 1015, and French output goes from 1030 to 985. In Germany there is still some overemployment and inflation. In France there is now some unemployment and deflation. And in Europe there is now full employment and price stability. Step 3 refers to fiscal poUcies in Germany and France. The inflationary gap in Germany is 15. The fiscal policy multiplier in Germany is 1. So what is needed in Germany is a reduction in German government purchases of 15. The output gap in France is 15. The fiscal policy multiplier in France is 1. So what is needed in France is an increase in French government purchases of 15. Step 4 refers to the output lag. The reduction in German government purchases of 15 causes a decline in German output of 15. And the increase in French government purchases of 15 causes an increase in French output of 15. As a consequence, German output goes from 1015 to 1000, and French output goes from 985 to 1000. In each of the countries there is now full employment and price stability. Table 9.5 presents a synopsis. As a result, the process of monetary and fiscal competition leads to full employment and price stability in each of the countries. There is a reduction in European money supply. There is a reduction in German government purchases, an increase in French government purchases, and no change in European government purchases. There is a decline in German output, as there is in French output. In steps 1 and 2 there is some overshooting in French output. There is a decline in European output, a decline in European tax revenue, and an increase in the European budget deficit. There is an increase in the interest rate and a decline

238 in European investment. There is an appreciation of the euro, a decHne in European exports, and a decHne in the European current account surplus.

Table 9.5 Monetary and Fiscal Competition The Case of Inflation

Initial Output

Germany

France

1060

1030

Change in Money Supply

-45

Output

1015

985

Change in Government Purchases

-15

15

Output

1000

1000

4. Monetary and Fiscal Cooperation

1) The model. This section deals with cooperation between the European central bank, the German government, and the French government. At the start there is unemployment in Germany and France. Let unemployment in Germany be high, and let unemployment in France be low. The targets of policy cooperation are full employment in Germany and full employment in France. The instruments of policy cooperation are European money supply, German government purchases, and French government purchases. There are two targets and three instruments, so there is one degree of freedom. As a result, there is an infinite number of solutions. In other words, monetary and fiscal cooperation can achieve full employment in Germany and France.

239 2) A numerical example: the case of unemployment. We now introduce a third target. We assume that the increase in German government purchases should be equal in size to the reduction in French government purchases. Put another way, we assume that the sum total of European government purchases should be constant. Let initial output in Germany be 940, and let initial output in France be 970. In each of the countries there is unemployment and deflation. Step 1 refers to the policy response. The output gap in Germany is 60, the output gap in France is 30, and the output gap in Europe is 90. What is needed, then, is an increase in European money supply of 45, an increase in German government purchases of 15, and a reduction in French government purchases of equally 15. Step 2 refers to the output lag. The increase in European money supply of 45 causes an increase in German output of 45 and an increase in French output of equally 45. The increase in German government purchases of 15 causes an increase in German output of 15. And the reduction in French government purchases of 15 causes a decline in French output of 15. The net effect is an increase in German output of 60 and an increase in French output of 30. As a consequence, German output goes from 940 to 1000, and French output goes from 970 to 1000. In each of the countries there is now full employment and price stability. Table 9.6 gives an overview.

Table 9.6 Monetary and Fiscal Cooperation The Case of Unemployment

Initial Output

Germany

France

940

970

Change in Money Supply Change in Government Purchases Output

45 15

-15

1000

1000

240 As a result, monetary and fiscal cooperation can achieve full employment and price stability in each of the countries. There is an increase in European money supply. There is an increase in German government purchases, a reduction in French government purchases, and no change in European government purchases. There is an increase in German output, as there is in French output. There is an increase in European output, an increase in European tax revenue, and a decline in the European budget deficit. There is a decline in the interest rate and an increase in European investment. There is a depreciation of the euro, an increase in European exports, and an increase in the European current account surplus. 3) Comparing policy cooperation with policy competition. Policy competition can achieve full employment and price stability in each of the countries. And the same applies to policy cooperation. Under policy competition, the increase in European money supply is 45, the increase in German government purchases is 15, and the reduction in French government purchases is equally 15. Hence the solution to policy cooperation is identical with the solution to policy competition. Policy competition is a slow process consisting of four steps. By contrast, policy cooperation is a fast process consisting of only two steps. Policy competition causes some overshooting in output. By contrast, policy cooperation does not cause any overshooting in output. Judging from this point of view, policy cooperation seems to be superior to policy competition. 4) A numerical example: the case of inflation. Let initial output in Germany be 1060, and let initial output in France be 1030. In each of the countries there is overemployment and inflation. Step 1 refers to the policy response. The inflationary gap in Germany is 60, the inflationary gap in France is 30, and the inflationary gap in Europe is 90. What is needed, then, is a reduction in European money supply of 45, a reduction in German government purchases of 15, and an increase in French government purchases of equally 15. Step 2 refers to the output lag. The reduction in European money supply of 45 causes a decline in German output of 45 and a decline in French output of equally 45. The reduction in German government purchases of 15 causes a decline in German output of 15. And the increase in French government purchases of 15 causes an increase in French output of 15. The net effect is a decline in German output of 60 and a decline in French output of 30. As a

241 consequence, German output goes from 1060 to 1000, and French output goes from 1030 to 1000. In each of the countries there is now full employment and price stability. For a synopsis see Table 9.7. As a result, monetary and fiscal cooperation can achieve full employment and price stability in each of the countries. There is a reduction in European money supply. There is a reduction in German government purchases, an increase in French government purchases, and no change in European government purchases. There is a decline in German output, as there is in French output. There is a decline in European output, a decline in European tax revenue, and an increase in the European budget deficit. There is an increase in the interest rate and a decline in European investment. There is an appreciation of the euro, a decline in European exports, and a decline in the European current account surplus.

Table 9.7 Monetary and Fiscal Cooperation The Case of Inflation

Initial Output

Germany

France

1060

1030

Change in Money Supply

-45

Change in Government Purchases

-15

15

Output

1000

1000

242

5. Wage Policies in Germany and France

1) Introduction. An increase in German nominal wages lowers German output. Correspondingly, an increase in French nominal wages lowers French output. For ease of exposition we assume that wage policy in one of the countries has no effect on output in the other country. In the numerical example, an increase in German nominal wages of 100 causes a decline in German output of 100. Correspondingly, an increase in French nominal wages of 100 causes a decline in French output of 100. For ease of exposition we assume that the wage policy multiplier is 1. This assumption is consistent since the wage rate is defined in nominal terms while output is defined in real terms. 2) The policy model. At the beginning there is unemployment in Germany and France. More precisely, unemployment in Germany is high, and unemployment in France is low. 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. 3) A numerical example. Full-employment output in Germany is 1000, and full-employment output in France is the same. Let initial output in Germany be 940, and let initial output in France be 970. In each of the countries there is unemployment. Step 1 refers to the policy response. The output gap in Germany is 60. The wage policy multiplier in Germany is 1. So what is needed in Germany is a reduction in German nominal wages of 60. The output gap in France is 30. The wage policy multiplier in France is 1. So what is needed in France is a reduction in French nominal wages of 30. Step 2 refers to the output lag. The reduction in German nominal wages of 60 causes an increase in German output of 60. And the reduction in French nominal wages of 30 causes an increase in French output of 30. As a consequence.

243 German output goes from 940 to 1000, and French output goes from 970 to 1000. In each of the countries there is now full employment. As a result, wage policies in Germany and France can achieve full employment in each of the countries. There is a reduction in European nominal wages, a decline the price of European goods, a depreciation of the euro, an increase in European exports, and an increase in European output. There is an increase in the European current account surplus and a decline in the European budget deficit. For an overview see Table 9.8.

Table 9.8 Wage Policies in Germany and France The Case of Unemployment Germany

France

940

970

Change in Nominal Wages

-60

-30

Output

1000

1000

Initial Output

4) Comparing wage policies with monetary policy. Monetary policy in Europe can achieve full employment in Europe as a whole. However, monetary policy in Europe cannot achieve full employment in each of the member countries. By contrast, wage policies in Germany and France can indeed achieve full employment in each of the member countries. However, wage policies in Germany and France require a deep cut in European nominal wages. 5) Comparing wage policies with fiscal policies. Fiscal policies in Germany and France can achieve full employment in each of the countries. However, as a severe side effect, fiscal policies in Germany and France cause an increase in the European budget deficit. Wage policies in Germany and France can achieve full employment in each of the countries, too. However, wage policies in Germany and France require a deep cut in European nominal wages.

244

6. Monetary and Wage Competition

1) The model. This section deals with competition between the European central bank, 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. The primary target of the European central bank is price stability in Europe. The secondary target of the European central bank is full employment in Europe. The specific target of the European central bank is that unemployment in Germany equals overemployment in France. In other words, the specific target of the European central bank is full employment in Europe on average. 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 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 bank and the labour unions decide sequentially. First the central bank decides, then the labour unions decide. Step 1 refers to monetary policy in Europe. Step 2 refers to the output lag. Step 3 refers to wage policies in Germany and France. And step 4 refers to the output lag. 2) A numerical example: the case of unemployment. An increase in European money supply of 100 causes an increase in German output of 100 and an increase in French output of equally 100. An increase in German nominal wages of 100 causes a decline in German output of 100. Correspondingly, an increase in French nominal wages of 100 causes a decline in French output of 100. Fullemployment output in Germany is 1000, and full-employment output in France is the same.

245 Let initial output in Germany be 940, and let initial output in France be 970. In each of the countries there is unemployment. Step 1 refers to monetary policy in Europe. The output gap in Europe is 90. The monetary policy multiplier in Europe is 2. So what is needed in Europe is an increase in European money supply of 45. Step 2 refers to the output lag. The increase in European money supply of 45 causes an increase in German output of 45 and an increase in French output of equally 45. As a consequence, German output goes from 940 to 985, and French output goes from 970 to 1015. In Germany there is still some unemployment. In France there is now some overemployment. And in Europe there is now full employment. Step 3 refers to wage policies in Germany and France. The output gap in Germany is 15. The wage policy multiplier in Germany is 1. So what is needed in Germany is a reduction in German nominal wages of 15. The inflationary gap in France is 15. The wage policy multiplier in France is 1. So what is needed in France is an increase in French nominal wages of 15. Step 4 refers to the output lag. The reduction in German nominal wages of 15 causes an increase in German output of 15. And the increase in French nominal wages of 15 causes a decline in French output of 15. As a consequence, German output goes from 985 to 1000, and French output goes from 1015 to 1000. In each of the countries there is now full employment. Table 9.9 presents a synopsis. As a result, the process of monetary and wage competition leads to full employment in each of the countries. There is an increase in European money supply. There is a reduction in German nominal wages, an increase in French nominal wages, and no change in European nominal wages. There is a decline in the price of German goods, an increase in the price of French goods, and no change in the price of European goods. There is an increase in German output, as there is in French output. In steps 1 and 2 there is some overshooting in French output. There is an increase in European output, an increase in European tax revenue, and a decline in the European budget deficit. There is a decline in the interest rate and an increase in European investment. There is a depreciation of

246 the euro, an increase in European exports, and an increase in the European current account surplus.

Table 9.9 Monetary and Wage Competition The Case of Unemployment

Initial Output

Germany

France

940

970

Change in Money Supply Output

45 985

1015

Change in Nominal Wages

-15

15

Output

1000

1000

3) A numerical example: the case of overemployment. Let initial output in Germany be 1060, and let initial output in France be 1030. In each of the countries there is overemployment. Step 1 refers to monetary policy in Europe. The inflationary gap in Europe is 90. The monetary policy multiplier in Europe is 2. So what is needed in Europe is a reduction in European money supply of 45. Step 2 refers to the output lag. The reduction in European money supply of 45 causes a decline in German output of 45 and a decline in French output of equally 45. As a consequence, German output goes from 1060 to 1015, and French output goes from 1030 to 985. In Germany there is still some overemployment. In France there is now some unemployment. And in Europe there is now full employment. Step 3 refers to wage policies in Germany and France. The inflationary gap in Germany is 15. The wage policy multiplier in Germany is 1. So what is needed in Germany is an increase in German nominal wages of 15. The output gap in

247 France is 15. The wage policy multiplier in France is 1. So what is needed in France is a reduction in French nominal wages of 15. Step 4 refers to the output lag. The increase in German nominal wages of 15 causes a decline in German output of 15. And the reduction in French nominal wages of 15 causes an increase in French output of 15. As a consequence, German output goes from 1015 to 1000, and French output goes from 985 to 1000. In each of the countries there is now full employment. Table 9.10 gives an overview.

Table 9.10 Monetary and Wage Competition The Case of Overemployment

Initial Output

Germany

France

1060

1030

Change in Money Supply

1 Output Change in Nominal Wages Output

-45 1015

985

15

-15

1000

1000

As a result, the process of monetary and wage competition leads to full employment in Germany and France. There is a reduction in European money supply. There is an increase in German nominal wages, a reduction in French nominal wages, and no change in European nominal wages. There is an increase in the price of German goods, a decline in the price of French goods, and no change in the price of European goods. There is a decline in German output, as there is in French output. In steps 1 and 2 there is some overshooting in French output. There is a decline in European output, a decline in European tax revenue, and an increase in the European budget deficit. There is an increase in the interest rate and a decline in European investment. There is an appreciation of the euro, a

248 decline in European exports, and a decline in the European current account surplus. 4) Comparing monetary and wage competition with pure monetary policy. Pure monetary policy can achieve full employment in Europe as a whole. However, it cannot achieve full employment in each of the member countries. By contrast, monetary and wage competition can indeed achieve full employment in each of the member countries. Judging from this point of view, monetary and wage competition seems to be superior to pure monetary policy. 5) Comparing monetary and wage competition with pure wage policies. First consider the case of unemployment. Pure wage policies can achieve full employment in each of the member countries. And the same holds for monetary and wage competition. Pure wage policies cause a large reduction in European nominal wages and a large reduction in the price of European goods. By contrast, monetary and wage competition causes a zero reduction in European nominal wages and a zero reduction in the price of European goods. Judging from this perspective, monetary and wage competition seems to be superior to pure wage policies. Second consider the case of overemployment. Pure wage policies can achieve full employment in each of the member countries. And the same holds for monetary and wage competition. Pure wage policies cause a large increase in European nominal wages and a large increase in the price of European goods. By contrast, monetary and wage competition causes a zero increase in European nominal wages and a zero increase in the price of European goods. Judging from this perspective, monetary and wage competition seems to be superior to pure wage policies.

249

7. Monetary and Wage Cooperation

1) The model. This section deals with cooperation between the European central bank, the German labour union, and the French labour union. At the start there is unemployment in Germany and France. Let unemployment in Germany be high, and let unemployment in France be low. 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, monetary and wage cooperation can achieve full employment in Germany and France. 2) A numerical example: the case of unemployment. 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. Put another way, we assume that the price level of European goods should be constant. Let initial output in Germany be 940, and let initial output in France be 970. 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 Europe is 90. What is needed, then, is an increase in European money supply of 45, a reduction in German nominal wages of 15, and an increase in French nominal wages of equally 15. Step 2 refers to the output lag. The increase in European money supply of 45 causes an increase in German output of 45 and an increase in French output of equally 45. The reduction in German nominal wages of 15 causes an increase in German output of 15. And the increase in French nominal wages of 15 causes a decline in French output of 15. The net effect is an increase in German output of 60 and an increase in French output of 30. As a consequence, German output goes from 940 to 1000, and French output goes from 970 to 1000. In each of the countries there is now full employment. For a synopsis see Table 9.11. As a result, monetary and wage cooperation can achieve full employment in each of the countries. There is an increase in European money supply. There is a

250 reduction in German nominal wages, an increase in French nominal wages, and no change in European nominal wages. There is a decline in the price of German goods, an increase in the price of French goods, and no change in the price of European goods. There is an increase in German output, as there is French output. There is an increase in European output, an increase in European tax revenue, and a decline in the European budget deficit. There is a decline in the interest rate and an increase in European investment. There is a depreciation of the euro, an increase in European exports, and an increase in the European current account surplus.

Table 9.11 Monetary and Wage Cooperation The Case of Unemployment

Initial Output

Germany

France

940

970

Change in Money Supply

45

Change in Nominal Wages

-15

15

Output

1000

1000

3) Comparing policy cooperation with policy competition. Policy competition can achieve full employment in each of the countries. And the same applies to policy cooperation. Under policy competition, the increase in European money supply is 45, the reduction in German nominal wages is 15, and the increase in French nominal wages is equally 15. Hence the solution to policy cooperation is identical with the solution to policy competition. Policy competition is a slow process consisting of four steps. By contrast, policy cooperation is a fast process consisting of only two steps. Policy competition causes some overshooting in output. By contrast, policy cooperation does not cause any overshooting in output. Judging from this point of view, policy cooperation seems to be superior to policy competition.

251 4) A numerical example: the case of overemployment. Let initial output in Germany be 1060, and let initial output in France be 1030. 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, and the inflationary gap in Europe is 90. What is needed, then, is a reduction in European money supply of 45, an increase in German nominal wages of 15, and a reduction in French nominal wages of equally 15. Step 2 refers to the output lag. The reduction in European money supply of 45 causes a decline in German output of 45 and a decline in French output of equally 45. The increase in German nominal wages of 15 causes a decline in German output of 15. And the reduction in French nominal wages of 15 causes an increase in French output of 15. The net effect is a decline in German output of 60 and a decline in French output of 30. As a consequence, German output goes from 1060 to 1000, and French output goes from 1030 to 1000. In each of the countries there is now full employment. For an overview see Table 9.12.

Table 9.12 Monetary and Wage Cooperation The Case of Overemployment

Initial Output

Germany

France

1060

1030

Change in Money Supply Change in Nominal Wages Output

-45 15

-15

1000

1000

As a result, monetary and wage cooperation can achieve full employment in Germany and France. There is a reduction in European money supply. There is an increase in German nominal wages, a reduction in French nominal wages, and no change in European nominal wages. There is an increase in the price of German goods, a decline in the price of French goods, and no change in the price

252 of European goods. There is a decline in German output, as there is in French output. There is a decline European output, a decline in European tax revenue, and an increase in the European budget deficit. There is an increase in the interest rate and a decline in European investment. There is an appreciation of the euro, a decline in European exports, and a decline in the European current account surplus.

Result 1. Monetary Policy in Europe

1) Introduction. For ease of exposition we make the following assumptions. The monetary union consists of two countries, say Germany and France The member 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. In the numerical example, an increase in European money supply of 100 causes an increase in German output of 100 and an increase in French output of equally 100. 2) The policy model. At the beginning there is unemployment in Germany and France. 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 full employment in Europe. For ease of exposition we assume that unemployment causes deflation whereas overemployment causes inflation. The specific target of the European central bank is that unemployment in Germany equals overemployment in France. Accordingly, the specific target of the European central bank is that deflation in Germany equals inflation in France. In other words, the specific target of the European central bank is full employment in Europe on average. Accordingly, the specific target of the European central bank is price stability in Europe on average. 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. 3) A numerical example: the case of unemployment. Full-employment output in Germany is 1000, and full-employment output in France is the same. Let initial output in Germany be 940, and let initial output in France be 970. In each of the countries there is unemployment and hence deflation. Step 1 refers to the policy response. The output gap in Europe is 90. The monetary policy multiplier in Europe is 2. So what is needed in Europe is an increase in European money supply of 45.

254

Step 2 refers to the output lag. The increase in European money supply of 45 causes an increase in German output of 45 and an increase in French output of equally 45. As a consequence, German output goes from 940 to 985, and French output goes from 970 to 1015. In Germany there is still some unemployment and deflation. In France there is now some overemployment and inflation. And in Europe there is now full employment and price stability. Unemployment in Germany equals overemployment in France. And deflation in Germany equals inflation in France. As a result, monetary policy in Europe can achieve full employment in Europe on average. And what is more, it can achieve price stability in Europe on average. However, monetary policy in Europe cannot achieve full employment in Germany and France. And what is more, it cannot achieve price stability in Germany and France. 4) A numerical example: the case of inflation. Let initial output in Germany be 1060, and let initial output in France be 1030. In each of the countries there is overemployment and hence inflation. Step 1 refers to the policy response. The inflationary gap in Europe is 90. The monetary policy multiplier in Europe is 2. So what is needed in Europe is a reduction in European money supply of 45. Step 2 refers to the output lag. The reduction in European money supply of 45 causes a decline in German output of 45 and a decline in French output of equally 45. As a consequence, German output goes from 1060 to 1015, and French output goes from 1030 to 985. In Germany there is still some overemployment and inflation. In France there is now some unemployment and deflation. And in Europe there is now full employment and price stability. As a result, monetary policy in Europe can achieve full employment and price stability in Europe as a whole. However, monetary policy in Europe cannot achieve full employment and price stability in each of the member countries.

255

2. Fiscal Policies in Germany and France

1) Introduction. An increase in German government purchases raises German output. Correspondingly, an increase in French government purchases raises French output. For ease of exposition we assume that fiscal policy in one of the countries has no effect on output in the other country. In the numerical example, an increase in German government purchases of 100 causes an increase in German output of 100. Correspondingly, an increase in French government purchases of 100 causes an increase in French output of 100. 2) The policy model. At the start there is unemployment in Germany and France. More precisely, unemployment in Germany is high, and unemployment in France is low. The target of the German government is full employment in Germany. The instrument of the German government is German government purchases. The German government raises German government purchases so as to close the output gap in Germany. The target of the French government is full employment in France. The instrument of the French government is French government purchases. The French government raises French government purchases so as to close the output gap in France. 3) A numerical example. Full-employment output in Germany is 1000, and full-employment output in France is the same. Let initial output in Germany be 940, and let initial output in France be 970. In each of the countries there is unemployment and hence deflation. Step 1 refers to the policy response. The output gap in Germany is 60. The fiscal policy multiplier in Germany is 1. So what is needed in Germany is an increase in German government purchases of 60. The output gap in France is 30. The fiscal policy multiplier in France is 1. So what is needed in France is an increase in French government purchases of 30. Step 2 refers to the output lag. The increase in German government purchases of 60 causes an increase in German output of 60. And the increase in French government purchases of 30 causes an increase in French output of 30. As a consequence, German output goes from 940 to 1000, and French output goes from 970 to 1000. In each of the countries there is now full employment and

256 price stability. As a result, fiscal policies in Germany and France can achieve full employment and price stability in each of the countries. 4) Comparing fiscal policies with monetary policy. Monetary policy in Europe can achieve full employment and price stability in Europe as a whole. However, monetary policy in Europe cannot achieve full employment and price stability in each of the member countries. By contrast, fiscal policies in Germany and France can indeed achieve full employment and price stability in each of the member countries. However, as a severe side effect, fiscal policies in Germany and France cause an increase in the European budget deficit.

3. Monetary and Fiscal Competition

1) The model. This section deals with competition between the European central bank, the German government, and the French government. At the beginning there is unemployment in Germany and France. 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 German government is full employment in Germany. The instrument of the German government is German government purchases. The German government raises German government purchases so as to close the output gap in Germany. The target of the French government is full employment in France. The instrument of the French government is French government purchases. The French government raises French government purchases so as to close the output gap in France. We assume that the central bank and the governments decide sequentially. First the central bank decides, then the governments decide.

257 2) A numerical example. An increase in European money supply of 100 causes an increase in German output of 100 and an increase in French output of equally 100. An increase in German government purchases of 100 causes an increase in German output of 100. Correspondingly, an increase in French government purchases of 100 causes an increase in French output of 100. Fullemployment output in Germany is 1000, and full-employment output in France is the same. Let initial output in Germany be 940, and let initial output in France be 970. In each of the countries there is unemployment and deflation. Step 1 refers to monetary policy in Europe. The output gap in Europe is 90. The monetary policy multiplier in Europe is 2. So what is needed in Europe is an increase in European money supply of 45. Step 2 refers to the output lag. The increase in European money supply of 45 causes an increase in German output of 45 and an increase in French output of equally 45. As a consequence, German output goes from 940 to 985, and French output goes from 970 to 1015. In Germany there is still some unemployment and deflation. In France there is now some overemployment and inflation. And in Europe there is now full employment and price stability. Step 3 refers to fiscal policies in Germany and France. The output gap in Germany is 15. The fiscal policy multiplier in Germany is 1. So what is needed in Germany is an increase in German government purchases of 15. The inflationary gap in France is 15. The fiscal policy multiplier in France is 1. So what is needed in France is a reduction in French government purchases of 15. Step 4 refers to the output lag. The increase in German government purchases of 15 causes an increase in German output of 15. And the reduction in French government purchases of 15 causes a decline in French output of 15. As a consequence, German output goes from 985 to 1000, and French output goes from 1015 to 1000. In each of the countries there is now full employment and price stability. As a result, the process of monetary and fiscal competition leads to full employment and price stability in each of the countries. 3) Comparing monetary and fiscal competition with pure monetary policy. Pure monetary policy can achieve full employment and price stability in Europe

258 as a whole. However, it cannot achieve full employment and price stability in each of the member countries. By contrast, monetary and fiscal competition can indeed achieve full employment and price stability in each of the member countries. Judging from this point of view, monetary and fiscal competition seems to be superior to pure monetary policy. 4) Comparing monetary and fiscal competition with pure fiscal policies. Pure fiscal policies can achieve full employment and price stability in each of the member countries. And the same holds for monetary and fiscal competition. Pure fiscal policies cause an increase in the European budget deficit. By contrast, monetary and fiscal competition causes a decline in the European budget deficit. Judging from this perspective, monetary and fiscal competition seems to be superior to pure fiscal policies.

4. Monetary and Fiscal Cooperation

1) The model. This section deals with cooperation between the European central bank, the German government, and the French government. At the start there is unemployment in Germany and France. Let unemployment in Germany be high, and let unemployment in France be low. The targets of policy cooperation are full employment in Germany and full employment in France. The instruments of policy cooperation are European money supply, German government purchases, and French government purchases. There are two targets and three instruments, so there is one degree of freedom. As a result, there is an infinite number of solutions. In other words, monetary and fiscal cooperation can achieve full employment in Germany and France. 2) A numerical example. We now introduce a third target. We assume that the increase in German government purchases should be equal in size to the reduction in French government purchases. Put another way, we assume that the sum total of European government purchases should be constant. Let initial output in Germany be 940, and let initial output in France be 970. In each of the

259 countries there is unemployment and deflation. Step 1 refers to the policy response. What is needed, then, is an increase in European money supply of 45, an increase in German government purchases of 15, and a reduction in French government purchases of equally 15. Step 2 refers to the output lag. The increase in European money supply of 45 causes an increase in German output of 45 and an increase in French output of equally 45. The increase in German government purchases of 15 causes an increase in German output of 15. And the reduction in French government purchases of 15 causes a decline in French output of 15. The net effect is an increase in German output of 60 and an increase in French output of 30. As a consequence, German output goes from 940 to 1000, and French output goes from 970 to 1000. In each of the countries there is now full employment and price stability. As a result, monetary and fiscal cooperation can achieve full employment and price stability in each of the countries. 3) Comparing policy cooperation with policy competition. Policy competition can achieve full employment and price stability in each of the countries. And the same applies to policy cooperation. Policy competition is a slow process consisting of four steps. By contrast, policy cooperation is a fast process consisting of only two steps. Policy competition causes some overshooting in output. By contrast, policy cooperation does not cause any overshooting in output. Judging from this point of view, policy cooperation seems to be superior to policy competition.

Symbols

Aj A2 A3 Gj G2 G3 M Wj W2 W3 Yj Y2 Y3 Yj Y2 Y3

autonomous term for Germany autonomous term for France autonomous term for Italy German government purchases French government purchases Itahan government purchases European money supply nominal wage rate in Germany nominal wage rate in France nominal wage rate in Italy German output, German income French output, French income Italian output, Italian income full-employment output in Germany full-employment output in France full-employment output in Italy

AGj AG2 AG3 AM AWj AW2 AW3 AYj AY2 AY3

required increase in German government purchases required increase in French government purchases required increase in Italian government purchases required increase in European money supply required change in German nominal wages required change in French nominal wages required change in Italian nominal wages initial output gap in Germany initial output gap in France initial output gap in Italy

a ttj a2 P

monetary policy multiplier monetary policy multiplier in Germany monetary policy multiplier in France fiscal policy multiplier

262 Pi

h J Yi T2

fiscal policy multiplier in Germany fiscal policy multiplier in France wage policy multiplier wage policy multiplier in Germany wage policy multiplier in France

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 w^orld 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

264 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

265 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, L, 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 PoHcy in EMU, Cheltenham 2005 BUTI, M., SAPIR, A., eds.. Economic PoHcy 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 PoHcy 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, 2006a, 2006b). Volume two (2000) deals with the scope and limits of macroeconomic policy in a monetary union. The leading protagonists are the union central bank, national governments, and national trade unions. Special emphasis is put on wage shocks and wage restraint. This book develops a series of basic, intermediate and more advanced models. A striking feature is the numerical estimation of policy multipliers. A lot of diagrams serve to illustrate the subject in hand. The monetary union is an open economy with high capital mobility. The exchange rate between the monetary union and the rest of the world is flexible. The world interest rate can be exogenous or endogenous. The union countries may differ in money demand, consumption, imports, openness, or size. Volume three (2001) explores the new economics of monetary union. It discusses the effects of shocks and policies on output and prices. Shocks and policies are country-specific or common. They occur on the demand or supply side. Countries can differ in behavioural functions. Wages can be fixed, flexible, or slow. In addition, fixed wages and flexible wages can coexist. Take for instance fixed wages in Germany and flexible wages in France. Or take fixed wages in Europe and flexible wages in America. Throughout this book makes use of the rate-of-growth method. This method, together with suitable initial conditions, proves to be very powerfiil. 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

267 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 carefully discusses the case for central bank independence and fiscal cooperation. Volume seven (2005) deals with the international coordination of monetary and fiscal policies in the world economy. It examines the process of 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 full employment. The policy makers follow either cold-turkey or gradualist strategies. Policy expectations are adaptive or rational. The world economy consists of two, three or more regions.

268 Volume eight (2006a) 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. Volume nine (2006b) deals with the interactions between monetary and wage policies in the euro area. It examines 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.

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

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Index

Alternative targets of policy cooperation, 49, 145 Basic models, 9, 117 Behaviour of a country, 78, 169 Cold-turkey policies, 55, 151, 199 Comparing fiscal policies with monetary policy, 27 Comparing gradualist policies with cold-turkey policies, 64,159 Comparing monetary and fiscal competition with pure fiscal policies, 34 Comparing monetary and fiscal competition with pure monetary policy, 34 Comparing monetary and wage competition with pure monetary policy, 133 Comparing monetary and wage competition with pure wage policies, 134 Comparing policy cooperation with policy competition, 46, 142 Comparing simultaneous decisions with sequential decisions, 58, 154 Comparing wage policies with fiscal policies, 123 Comparing wage policies with monetary policy, 123 Competition between European central bank, German government, and French government, 29 Competition between European central bank, German labour union, and French labour union, 125 Cooperation between European central bank, German government, and French government, 42 Cooperation between European central bank, German labour union, and French labour union, 138 Deflation in France, 17 Deflation in Germany, 12, 15 Degrees of freedom, 42, 88, 138, 177 Dynamic model, 29, 103, 125, 186 First the governments decide, then the central bank decides, 39 First the labour unions decide, then the central bank decides, 135

282 Fiscal policies in Germany and France, 23, 73, 80, 232, 255 Fiscal policies in Germany, France and Italy, 98 Fiscal shocks in Germany, 65 Full employment in Europe, 12, 15, 17 Full employment in France, 24, 27, 34, 42, 45, 120, 122 Full employment in Germany, 24, 27, 34, 42, 45, 120, 122 Gradualist policies, 60, 155, 199 Inflation, 16,34,46 Inflationary gap, 14, 16 Inflation in France, 12, 15 Inflation in Germany, 17 Inflation in Germany equals inflation in France, 20 Inflation rate, 73 Intermediate models, 53, 149 Model, 11,23,42,91, 119, 138 Monetary and fiscal competition, 29, 55, 60, 65, 76, 83, 103, 234, 256 Monetary and fiscal cooperation, 42, 85, 110, 238, 258 Monetary and wage competition, 125, 151, 155, 167, 171, 186, 244 Monetary and wage cooperation, 138, 173, 193, 249 Monetary, fiscal and wage policies, 199 Monetary policy in Europe, 11, 69, 78, 91, 229, 253 Monetary union of three countries, 89, 179 Monetary union of two countries, 9, 53, 117, 149, 199 Oscillations, 58, 63, 154, 158, 205 Oscillations, damped, 63, 158 Oscillations, uniform, 58, 154, 205 Output gap, 14, 15,72 Output model, 11, 23, 42, 119, 138 Overemployment, 130, 142 Overemployment in France, 12, 15 Overemployment in Germany, 17 Overshooting, 34, 46, 130, 142

283 Policy model, 12, 13, 24, 25,42, 120, 121, 138 Policy system, 221, 225 Price stability in Europe, 12, 15, 17 Price stability in France, 34, 45 Price stability in Germany, 34, 45 Rational policy expectations, 87, 176 Sequential decisions, 29, 76, 83, 103, 125, 167, 171, 186, 199 Simultaneous decisions, 55, 60, 151, 155 Size of a country, 69,164 Speed of adjustment in government purchases, 64 Speed of adjustment in money supply, 64, 159 Speed of adjustment in nominal wages, 159 Speed of policy competition, 46, 142 Speed of policy cooperation, 46, 142 Static model, 103, 186 Synopsis, 221 Target of European central bank, 12, 30, 92, 126 Target of French government, 24, 30 Target of French labour union, 120, 126 Target of German government, 24, 30 Target of German labour union, 120, 126 Targets of monetary and fiscal cooperation, 42, 110 Targets of monetary and wage cooperation, 138 Unemployment, 15, 26, 32, 44, 122, 128, 140 Unemployment in France, 17 Unemployment in Germany, 12, 15 Unemployment in Germany equals overemployment in France, 21 Unemployment in Germany equals unemployment in France, 20 Unemployment in Germany, inflation in France, 18, 36, 47 Unemployment in Germany, overemployment in France, 123, 131, 143 Unemployment rate, 73 Wage policies in Germany and France, 119, 164, 169, 242

284 Wage policies in Germany, France and Italy, 181 Wage shocks in Germany, 160