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International Economic Policy Coordination
Michael Carlberg

International Economic
Policy Coordination

With 94 Tables




4y Springer
Professor Dr. Michael Carlberg
Federal University of Hamburg
Department of Economics
Holstenhofweg 85
22043 Hamburg
Germany
carlberg@hsu-hh.de




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Preface


This book studies the international coordination of monetary and fiscal
policies in the world economy. It carefully discusses 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.

The present book is part of a larger research project on European Monetary
Union, see the references at the back of the book. Some parts of this project were
presented at the World Congress of the International Economic Association in
Lisbon. Other parts were presented at the International Institute of Public
Finance, at the Macro Study Group of the German Economic Association, at the
Annual Meeting of the Austrian Economic Association, at the Gottingen
Workshop on International Economics, at the Halle Workshop on Monetary
Economics, at the Research Seminar on Macroeconomics in Freiburg, and at the
Passau Workshop on International Economics.

Over the years, in working on this project, I have benefited from comments
by Iain Begg, Michael Brauninger, Volker Clausen, Valeria de Bonis, Peter
Flaschel, Wilfried Fuhrmann, Michael Funke, Florence Huart, Oliver Landmann,
Jay H. Levin, Alfred MauBner, Jochen Michaelis, Manfred J. M. Neumann,
Klaus Neusser, Franco Reither, Armin Rohde, Sergio Rossi, Gerhard Riibel,
Michael Schmid, Gerhard Schwodiauer, Patrizio Tirelli, Harald Uhlig, Bas van
Aarle, Uwe Vollmer, Jiirgen von Hagen and Helmut Wagner. In addition,
VI


Torsten Bleich and Alkis Otto carefully discussed with me all parts of the
manuscript. Last but not least, Doris Ehrich did the secretarial work as
excellently as ever. I would like to thank all of them.




January 2005 Michael Carlberg
VIII

output, as there are in American output. The European economy oscillates
between unemployment and overemployment, as does the American economy.

4) Fiscal cooperation between Europe and America: perfect capital mobility.
As a result, fiscal cooperation can reduce unemployment in Europe and America
to a certain extent. However, it cannot achieve full employment in Europe and
America. The reason is the large external effect of fiscal policy.

5) Fiscal competition between Europe and America: imperfect capital
mobility. As a result, the process of fiscal competition leads to full employment
in Europe and America. There are damped oscillations in European government
purchases, as there are in American government purchases. There are damped
oscillations in European output, as there are in American output. Fiscal
competition is a slow process. The reason is the positive external effect of fiscal
policy.

6) Fiscal cooperation between Europe and America: imperfect capital
mobility. As a result, fiscal cooperation can achieve full employment in Europe
and America. What is needed is an increase in European and American
government purchases. Fiscal cooperation is a fast process, as compared to fiscal
competition. The reason is that the positive external effect of fiscal policy can be
internalized by cooperation. From this point of view, fiscal cooperation is
superior to fiscal competition.

7) The anticipation of policy spillovers. The focus here is on monetary
competition between Europe and America. The European central bank
anticipates the spillovers from monetary policy in America. And the American
central bank anticipates the spillovers from monetary policy in Europe. As a
result, the anticipation of policy spillovers speeds up the process of monetary
competition. Thus there is no need for monetary cooperation.
Contents in Brief



Introduction l

Part One, The World of Two Monetary Regions:
Basic Models 9
Chapter 1. Monetary Competition between Europe and America 11
Chapter 2. Monetary Cooperation between Europe and America 31
Chapter 3. Fiscal Competition between Europe and America 41
Chapter 4. Fiscal Cooperation between Europe and America 54
Chapter 5. The Anticipation of Policy Spillovers 59


Part Two. The World of Two Monetary Regions:
Intermediate Models 65
Chapter 1. Zero Capital Mobility 67
Chapter 2. Imperfect Capital Mobility 71
Chapter 3. High Capital Mobility 101
Chapter 4. Gradualist Policies 108


Part Three. The World of Two Monetary Regions:
Advanced Models 123
Chapter 1. The Regions Differ in Policy Multipliers 125
Chapter 2. The Regions Differ in Size 133
Chapter 3. Competition between the European Labour Union and
the American Labour Union 141
Chapter 4. Cooperation between the European Labour Union and
the American Labour Union 151
Chapter 5. Inflation in Europe and America 157
X


Part Four. The World of Three Monetary Regions 163
Chapter 1. Monetary Competition between Europe, America and Asia 165
Chapter 2. Monetary Cooperation between Europe, America and Asia 173
Chapter 3. Fiscal Competition: Perfect Capital Mobility 177
Chapter 4. Fiscal Competition: Imperfect Capital Mobility 183
Chapter 5. Fiscal Competition: Gradualist Policies 191
Chapter 6. Fiscal Cooperation: Perfect Capital Mobility 195
Chapter 7. Fiscal Cooperation: Imperfect Capital Mobility 197


Part Five. The World of N Monetary Regions 203
Chapter 1. The World of Four Monetary Regions 205
Chapter 2. The World of Ten Monetary Regions 212
Chapter 3. Synopsis 215


Part Six. Rational Policy Expectations 219
Chapter 1. Rational Policy Expectations in Europe and America 221
Chapter 2. Adaptive Policy Expectations in Europe and America 235
Chapter 3. Adaptive Policy Expectations in Europe,
Rational Policy Expectations in America 239


Synopsis 253
Conclusion 257
Result 285
References 297
Index 309
Contents


Introduction l
1. Subject and Approach 1
2. Basic Models 2
3. Imperfect Capital Mobility 6
4. Gradualist Policies 7



Part One. The World of Two Monetary Regions:
Basic Models 9

Chapter 1. Monetary Competition between Europe and America 11
1. The Dynamic Model 11
2. Some Numerical Examples 18
2.1. Unemployment in Europe Equals Unemployment in America 18
2.2. Unemployment in Europe Exceeds Unemployment in America 20
2.3. Unemployment in Europe, Full Employment in America 23
2.4. Unemployment in Europe Exceeds Overemployment in America 25
2.5. Unemployment in Europe Equals Overemployment in America 26
2.6. Inflation in Europe Exceeds Inflation in America 27
2.7. Inflation in Europe Equals Inflation in America 29

Chapter 2. Monetary Cooperation between Europe and America 31
1. The Model 31
2. Some Numerical Examples 33

Chapter 3. Fiscal Competition between Europe and America 41
1. The Dynamic Model 41
2. Some Numerical Examples 45
2.1. Unemployment in Europe Exceeds Unemployment in America 46
2.2. Unemployment in Europe Equals Unemployment in America 48
2.3. Unemployment in Europe Exceeds Overemployment in America 49
2.4. Unemployment in Europe Equals Overemployment in America 51
XII

Chapter 4. Fiscal Cooperation between Europe and America 54
1. The Model 54
2. Some Numerical Examples 55

Chapter 5. The Anticipation of Policy Spillovers 59



Part Two. The World of Two Monetary Regions:
Intermediate Models 65

Chapter 1. Zero Capital Mobility 67
1. Fiscal Competition between Europe and America 67
2. Monetary Competition between Europe and America 69

Chapter 2. Imperfect Capital Mobility 71
1. Fiscal Competition between Europe and America 71
1.1. The Dynamic Model 71
1.2. Some Numerical Examples 78
2. Fiscal Cooperation between Europe and America 84
2.1. The Model 84
2.2. Some Numerical Examples 86
3. Monetary Competition between Europe and America 92
4. Monetary Cooperation between Europe and America 96
5. Monetary and Fiscal Cooperation 98

Chapter 3. High Capital Mobility 101
1. Fiscal Competition between Europe and America 101
2. Fiscal Cooperation between Europe and America 105

Chapter 4. Gradualist Policies 108
1. Fiscal Competition between Europe and America 108
2. Monetary Competition between Europe and America 113
3. Monetary and Fiscal Competition 118
XIII


Part Three. The World of Two Monetary Regions:
Advanced Models 123

Chapter 1. The Regions Differ in Policy Multipliers 125
1. Monetary Competition between Europe and America 125
2. Fiscal Competition between Europe and America 129

Chapter 2. The Regions Differ in Size 133
1. Monetary Competition between Europe and America 133
2. Monetary Cooperation between Europe and America 136
3. Fiscal Competition between Europe and America 137

Chapter 3. Competition between the European Labour Union and
the American Labour Union 141
1. The Dynamic Model 141
2. A Numerical Example 148

Chapter 4. Cooperation between the European Labour Union and
the American Labour Union 151
1. The Model 151
2. Some Numerical Examples 153

Chapter 5. Inflation in Europe and America 157
1. Monetary Competition between Europe and America 157
1.1. The Dynamic Model... 157
1.2. A Numerical Example 158
2. Monetary Cooperation between Europe and America 161



Part Four. The World of Three Monetary Regions 163

Chapter 1. Monetary Competition between Europe, America and Asia ....165
1. The Dynamic Model 165
2. Some Numerical Examples 169
XIV

Chapter 2. Monetary Cooperation between Europe, America and Asia .... 173
1. The Model 173
2. Some Numerical Examples 174

Chapter 3. Fiscal Competition: Perfect Capital Mobility 177
1. The Dynamic Model 177
2. A Numerical Example 181

Chapter 4. Fiscal Competition: Imperfect Capital Mobility 183
1. The Dynamic Model 183
2. Some Numerical Examples 186
2.1. Low Capital Mobility 186
2.2. High Capital Mobility 189

Chapter 5. Fiscal Competition: Gradualist Policies 191

Chapter 6. Fiscal Cooperation: Perfect Capital Mobility 195

Chapter 7. Fiscal Cooperation: Imperfect Capital Mobility 197
1. The Model 197
2. Some Numerical Examples 198



Part Five. The World of N Monetary Regions 203

Chapter 1. The World of Four Monetary Regions 205
1. Monetary Competition between Four Regions 205
2. Fiscal Competition between Four Regions: Perfect Capital Mobility 207
3. Fiscal Competition between Four Regions: Imperfect Capital Mobility 210

Chapter 2. The World of Ten Monetary Regions 212

Chapter 3. Synopsis 215
XV


Part Six. Rational Policy Expectations 219

Chapter 1. Rational Policy Expectations in Europe and America 221
1. Monetary Competition between Europe and America 221
2. Fiscal Competition: Perfect Capital Mobility 225
3. Fiscal Competition: Imperfect Capital Mobility 228
4. Monetary and Fiscal Competition 232

Chapter 2. Adaptive Policy Expectations in Europe and America 235

Chapter 3. Adaptive Policy Expectations in Europe,
Rational Policy Expectations in America 239
1. Monetary Competition between Europe and America 239
2. Fiscal Competition between Europe and America 245



Synopsis 253


Conclusion 257
1. Basic Models 257
1.1. Monetary Competition between Europe and America 257
1.2. Monetary Cooperation between Europe and America 262
1.3. Fiscal Competition between Europe and America 264
1.4 Fiscal Cooperation between Europe and America 267
1.5 The Anticipation of Policy Spillovers 269
2. Imperfect Capital Mobility 271
2.1. Fiscal Competition between Europe and America 271
2.2. Fiscal Cooperation between Europe and America 274
2.3. Monetary Competition between Europe and America 276
2.4. Monetary and Fiscal Cooperation 277
3. Gradualist Policies 278
4. The World of Three Monetary Regions 279
5. Rational Policy Expectations 281
XVI

Result 285
1. Monetary Competition between Europe and America 285
2. Monetary Cooperation between Europe and America 286
3. Fiscal Competition: Perfect Capital Mobility 287
4. Fiscal Cooperation: Perfect Capital Mobility 289
5. Fiscal Competition: Imperfect Capital Mobility 290
6. Fiscal Cooperation: Imperfect Capital Mobility 291
7. The Anticipation of Policy Spillovers 291

Symbols 293

The Current Research Project 295

References 297

Index 309
Introduction
1. Subject and Approach


This book studies the international coordination of monetary and fiscal
policies in the world economy. It carefully discusses the process of policy
competition and the structure of policy cooperation. With respect to policy
competition, the focus is on:
- monetary competition between Europe and America
- fiscal competition between Europe and America.
With respect to policy cooperation, the focus is on:
- monetary cooperation between Europe and America
- fiscal cooperation between Europe and America.

The targets of the European central bank are price stability and full
employment in Europe. The targets of the American central bank are price
stability and full employment in America. Monetary policy in one of the regions
has a large external effect on the other region. For instance, an increase in
European money supply lowers American output. The target of the European
government is full employment in Europe. The target of the American
government is full employment in America. Fiscal policy in one of the regions
has a large external effect on the other region. For instance, an increase in
European government purchases raises American output. The key questions are:
- Does the process of policy competition
lead to full employment and price stability?
- Can policy cooperation
achieve full employment and price stability?
- Is policy cooperation superior to policy competition?

This book takes new approaches that are firmly grounded on modern
macroeconomics. The framework of analysis is as follows. The world economy
consists of a certain number of monetary regions. A monetary region is defined
by having a currency of its own. A monetary region is an open economy with
international trade and capital mobility. The exchange rates between the
monetary regions are flexible. Special features of this book are numerical
simulations of policy competition and numerical solutions to policy cooperation.
To illustrate all of this there are lots of tables.

This book consists of six major parts:
- The World of Two Monetary Regions:
Basic Models
- The World of Two Monetary Regions:
Intermediate Models
- The World of Two Monetary Regions:
Advanced Models
- The World of Three Monetary Regions
- The World of N Monetary Regions
- Rational Policy Expectations.
Now the approach will be presented in greater detail.




2. Basic Models


1) Monetary competition between Europe and America. First consider the
static model. The world consists of two monetary regions, say Europe and
America. The exchange rate between Europe and America is flexible. There is
international trade between Europe and America. There is perfect capital
mobility between Europe and America. European goods and American goods are
imperfect substitutes for each other. European output is determined by the
demand for European goods. American output is determined by the demand for
American goods. European money demand equals European money supply. And
American money demand equals American money supply. The monetary regions
are the same size and have the same behavioural functions. Nominal wages and
prices adjust slowly.

As a result, an increase in European money supply raises European output.
On the other hand, it lowers American output. Here the rise in European output
exceeds the fall in American output. Correspondingly, an increase in American
money supply raises American output. On the other hand, it lowers European
output. Here the rise in American output exceeds the fall in European output. In
the numerical example, a 1 percent increase in European money supply causes a
0.75 percent increase in European output and a 0.25 percent decline in American
output. Similarly, a 1 percent increase in American money supply causes a 0.75
percent increase in American output and a 0.25 percent decline in European
output. That is to say, the internal effect of monetary policy is very large, and the
external effect of monetary policy is large. Now have a closer look at the process
of adjustment. An increase in European money supply causes a depreciation of
the euro, an appreciation of the dollar, and a decline in the world interest rate.
The depreciation of the euro raises European exports. The appreciation of the
dollar lowers American exports. And the decline in the world interest rate raises
both European investment and American investment. The net effect is that
European output goes up. However, American output goes down. This model is
in the tradition of the Mundell-Fleming model.

Second consider the dynamic model. At the beginning there is unemployment
in both Europe and America. The target of the European central bank is full
employment in Europe. The instrument of the European central bank is European
money supply. The European central bank raises European money supply so as to
close the output gap in Europe. The target of the American central bank is full
employment in America. The instrument of the American central bank is
American money supply. The American central bank raises American money
supply so as to close the output gap in America. We assume that the European
central bank and the American central bank decide simultaneously and
independently. In addition there is an output lag. European output next period is
determined by European money supply this period as well as by American
money supply this period. In the same way, American output next period is
determined by American money supply this period as well as by European
money supply this period. The key questions are: Is there a steady state of
monetary competition? Is the steady state of monetary competition stable? In
other words, does monetary competition lead to full employment in Europe and
America? Besides, what are the dynamic characteristics of this process? Taking
the sum over all periods, what is the total increase in European money supply, as
compared to the initial output gap in Europe? And what is the total increase in
American money supply, as compared to the initial output gap in America?
2) Monetary cooperation between Europe and America. At the start there is
unemployment in both Europe and America. The targets of monetary cooperation
are full employment in Europe and full employment in America. The instruments
of monetary cooperation are European money supply and American money
supply. So there are two targets and two instruments. Here the key questions are:
Is there a solution to monetary cooperation? Put differently, can monetary
cooperation achieve full employment in Europe and America? What is the
required increase in European money supply, as compared to the initial output
gap in Europe? And what is the required increase in American money supply, as
compared to the initial output gap in America? Moreover, is monetary
cooperation superior to monetary cooperation?

3) Fiscal competition between Europe and America. First consider the static
model. An increase in European government purchases raises both European
output and American output. And what is more, the rise in European output
equals the rise in American output. Correspondingly, an increase in American
government purchases raises both American output and European output. And
what is more, the rise in American output equals the rise in European output. In
the numerical example, an increase in European government purchases of 100
causes an increase in European output of 100 and an increase in American output
of equally 100. Likewise, an increase in American government purchases of 100
causes an increase in American output of 100 and an increase in European output
of equally 100. In a sense, the internal effect of fiscal policy is rather small,
whereas the external effect of fiscal policy is quite large. Now have a closer look
at the process of adjustment. An increase in European government purchases
causes an appreciation of the euro, a depreciation of the dollar, and an increase in
the world interest rate. The appreciation of the euro lowers European exports.
The depreciation of the dollar raises American exports. And the increase in the
world interest rate lowers both European investment and American investment.
The net effect is that European output and American output go up, to the same
extent respectively. This model is in the tradition of the Mundell-Fleming model.

Second consider the dynamic model. At the beginning there is unemployment
in both Europe and America. The target of the European government is full
employment in Europe. The instrument of the European government is European
government purchases. The European government raises European government
purchases so as to close the output gap in Europe. The target of the American
government is full employment in America. The instrument of the American
government is American government purchases. The American government
raises American government purchases so as to close the output gap in America.
We assume that the European government and the American government decide
simultaneously and independently. In addition there is an output lag. European
output next period is determined by European government purchases this period
as well as by American government purchases this period. In the same way,
American output next period is determined by American government purchases
this period as well as by European government purchases this period. The key
questions are: Is there a steady state of fiscal competition? Is the steady state of
fiscal competition stable? In other words, does fiscal competition lead to full
employment in Europe and America? Besides, what are the dynamic
characteristics of this process? Taking the sum over all periods, what is the total
increase in European government purchases, as compared to the initial output
gap in Europe? And what is the total increase in American government
purchases, as compared to the initial output gap in America? Last but not least, is
monetary competition superior to fiscal competition?

4) Fiscal cooperation between Europe and America. At the start there is
unemployment in Europe and America. The targets of fiscal cooperation are full
employment in Europe and full employment in America. The instruments of
fiscal cooperation are European government purchases and American
government purchases. So there are two targets and two instruments. Here the
key questions are: Is there a solution to fiscal cooperation? Put differently, can
fiscal cooperation achieve full employment in Europe and America? What is the
required increase in European government purchases, as compared to the initial
output gap in Europe? And what is the required increase in American
government purchases, as compared to the initial output gap in America? Finally,
is fiscal cooperation superior to fiscal competition? And is monetary cooperation
superior to fiscal cooperation?
3. Imperfect Capital Mobility



1) Monetary competition and monetary cooperation. To illustrate this,
consider a numerical example. Under perfect capital mobility, an increase in
European money supply of 100 causes an increase in European output of 300 and
a decline in American output of 100. Under zero capital mobility, by contrast, an
increase in European money supply of 100 causes an increase in European output
of 200 and a decline in American output of zero. On this basis we assume that,
under imperfect capital mobility, an increase in European money supply of 100
causes an increase in European output of 250 and a decline in American output
of 50.

That means, under high capital mobility, monetary spillovers are large. On
the other hand, under zero capital mobility, monetary spillovers are zero. And
under low capital mobility, monetary spillovers are small. What does this imply
for monetary competition and monetary cooperation? Given imperfect capital
mobility, is monetary competition a slow process or a fast one? The answer is
that imperfect capital mobility speeds up the process of monetary competition.
The other way round, perfect capital mobility slows down the process of
monetary competition.

2) Fiscal competition and fiscal cooperation. Under perfect capital mobility,
an increase in European government purchases raises both European output and
American output, to the same extent respectively. Under zero capital mobility, an
increase in European government purchases raises European output to a much
larger degree. However, it has no effect on American output. Under imperfect
capital mobility, an increase in European government purchases raises both
European output and American output. Here the rise in European output exceeds
the rise in American output.

To illustrate this, consider a numerical example. Under perfect capital
mobility, an increase in European government purchases of 100 causes an
increase in European output of 100 and an increase in American output of
equally 100. Under zero capital mobility, by contrast, an increase in European
government purchases of 100 causes an increase in European output of 200 and
an increase in American output of zero. On this basis we assume that, under
imperfect capital mobility, an increase in European government purchases of 100
causes an increase in European output of 150 and an increase in American output
of 50.

That means, under high capital mobility, fiscal spillovers are very large. On
the other hand, under zero capital mobility, fiscal spillovers are zero. And under
low capital mobility, fiscal spillovers are medium size. What does this imply for
fiscal competition and fiscal cooperation? Given imperfect capital mobility, is
fiscal competition a slow process or a fast one?




4. Gradualist Policies


1) Monetary competition between Europe and America. So far we have
assumed that the central banks follow a cold-turkey strategy. Now we assume
that the central banks follow a gradualist strategy. At the beginning there is
unemployment in Europe and America. 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 the fraction iij. The general target of
the American central bank is full employment in America. We assume that the
American central bank follows a gradualist strategy. The specific target of the
American central bank is to close the output gap in America by the fraction |Lt2.
Under a gradualist strategy, is monetary competition a slow process or a fast
one? Surprisingly, the answer depends upon initial conditions.

2) Fiscal competition between Europe and America. So far we have assumed
that the governments follow a cold-turkey strategy. Now we assume that the
governments follow a gradualist strategy. At the start there is unemployment in
Europe and America. The general target of the European government is full
employment in Europe. We assume that the European government follows a
gradualist strategy. The specific target of the European government is to close the
output gap in Europe by the fraction A^. The general target of the American
government is full employment in America. We assume that the American
government follows a gradualist strategy. The specific target of the American
government is to close the output gap in America by the fraction X 2 . Under a
gradualist strategy, is fiscal competition a slow process or a fast one?

3) Monetary and fiscal competition. More precisely, we have competition
between the European central bank, the American central bank, the European
government, and the American government. At the beginning there is
unemployment in Europe and America. The specific target of the European
central bank is to close the output gap in Europe by the fraction \il. The specific
target of the American central bank is to close the output gap in America by the
fraction \x2. The specific target of the European government is to close the output
gap in Europe by the fraction Xx. And the specific target of the American
government is to close the output gap in America by the fraction X2. We assume
that the European central bank, the American central bank, the European
government, and the American government decide simultaneously and
independently.

Is there a stable steady state of monetary and fiscal competition? In other
words, does the process of monetary and fiscal competition lead to full
employment? Taking the sum over all periods, does the increase in European
money supply, American money supply, European government purchases, and
American government purchases depend on the relative speed of adjustment?
Part One


The World of
Two Monetary Regions


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



1) The static model. As a point of reference, consider the static model. The
world consists of two monetary regions, say Europe and America. The exchange
rate between Europe and America is flexible. There is international trade between
Europe and America. There is perfect capital mobility between Europe and
America. European goods and American goods are imperfect substitutes for each
other. European output is determined by the demand for European goods.
American output is determined by the demand for American goods. European
money demand equals European money supply. And American money demand
equals American money supply. The monetary regions are the same size and
have the same behavioural functions. Nominal wages and prices adjust slowly.

As a result, an increase in European money supply raises European output.
On the other hand, it lowers American output. Here the rise in European output
exceeds the fall in American output. Correspondingly, an increase in American
money supply raises American output. On the other hand, it lowers European
output. Here the rise in American output exceeds the fall in European output. In
the numerical example, a 1 percent increase in European money supply causes a
0.75 percent increase in European output and a 0.25 percent decline in American
output. Similarly, a 1 percent increase in American money supply causes a 0.75
percent increase in American output and a 0.25 percent decline in European
output. That is to say, the internal effect of monetary policy is very large, and the
external effect of monetary policy is large. Now have a closer look at the process
of adjustment. An increase in European money supply causes a depreciation of
the euro, an appreciation of the dollar, and a decline in the world interest rate.
The depreciation of the euro raises European exports. The appreciation of the
dollar lowers American exports. And the decline in the world interest rate raises
both European investment and American investment. The net effect is that
European output goes up. However, American output goes down. This model is
12

in the tradition of the Mundell-Fleming model, see Carlberg (2000) p. 189 and
Carlberg (2001) p. 147.


The static model can be represented by a system of two equations:


Y1=A1+aM1-PM2 (1)
Y2=A2+aM2-(3M1 (2)


According to equation (1), European output Yx is determined by European
money supply M l5 American money supply M 2 , and some other factors called
A^ According to equation (2), American output Y2 is determined by American
money supply M 2 , European money supply Mj, and some other factors called
A 2 . Here a and (3 denote the monetary policy multipliers. The internal effect of
monetary policy is positive a > 0 . By contrast, the external effect of monetary
policy is negative (3 > 0. In absolute values, the internal effect is larger than the
external effect a > ( 3 . The endogenous variables are European output and
American output.

2) The dynamic model. At the beginning there is unemployment in both
Europe and America. The target of the European central bank is full employment
in Europe. The instrument of the European central bank is European money
supply. The European central bank raises European money supply so as to close
the output gap in Europe:


I
cx

Here is a list of the new symbols:
Yj European output this period
Yj full-employment output in Europe
Yx - Yj output gap in Europe this period
Mj˜ European money supply last period
M1 European money supply this period
M 1 - MJ" increase in European money supply.
Here the endogenous variable is European money supply this period
13

The target of the American central bank is full employment in America. The
instrument of the American central bank is American money supply. The
American central bank raises American money supply so as to close the output
gap in America:


(4)
(JC



Here is a list of the new symbols:
Y2 American output this period
Y2 full-employment output in America
Y2 - Y 2 output gap in America this period
M2X American money supply last period
M2 American money supply this period
1
M2 - M2 increase in American money supply.
Here the endogenous variable is American money supply this period M 2 . We
assume that the European central bank and the American central bank decide
simultaneously and independently.


In addition there is an output lag. European output next period is determined
by European money supply this period as well as by American money supply this
period:


Y1+1=A1+aM1-PM2 (5)


Here Y^ 1 denotes European output next period. In the same way, American
output next period is determined by American money supply this period as well
as by European money supply this period:


-(3M 1 (6)


Here Y^ 1 denotes American output next period.


On this basis, the dynamic model can be characterized by a system of four
equations:
14


Yl
(7)




Y1+1=A1+aM1-PM2 (9)
Y2+1=A2+aM2-PM1 (10)

Equation (7) shows the policy response in Europe, (8) shows the policy response
in America, (9) shows the output lag in Europe, and (10) shows the output lag in
America. The endogenous variables are European money supply this period M 1 ,
American money supply this period M 2 , European output next period Yf1, and
American output next period Y2l.

3) The steady state. In the steady state by definition we have:


M^Mr1 (ID
M 2 = M^ 1 (12)

Equation (11) has it that European money supply does not change any more.
Similarly, equation (12) has it that American money supply does not change any
more. Therefore the steady state can be captured by a system of four equations:


Y! = Y! (13)
Y2=Y2 (14)
Y1=A1+aM1-(3M2 (15)
Y2=A2+aM2-(3M1 (16)


Here the endogenous variables are European output Y x , American output Y 2 ,
European money supply M1? and American money supply M 2 . According to
equation (13) there is full employment in Europe, so European output is constant.
According to equation (14) there is full employment in America, so American
15

output is constant too. Further, equations (15) and (16) give the steady-state
levels of European and American money supply.

The model of the steady state can be compressed to a system of only two
equations:

Y1=A1+aM1-(3M2 (17)
Y2=A2+aM2-pM1 (18)

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


B^Yi-A! (19)
B2=Y2-A2 (20)

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


PM 2 (21)
B2=aM2-PM1 (22)

The endogenous variables are still Mx and M 2 .

Next we solve the model for the endogenous variables:




ocBo+PB,
”7 „•> (24)



Equation (23) shows the steady-state level of European money supply, and
equation (24) shows the steady-state level of American money supply. As a
result, there is a steady state if and only if a ^ (3. Owing to the assumption a > (3,
this condition is fulfilled.
16


As an alternative, the steady state can be represented in terms of the initial
output gap and the total increase in money supply. Taking differences in
equations (1) and (2), the model of the steady state can be written as follows:

AY 1 =aAM 1 -PAM 2 (25)
AY2=aAM2-pAM! (26)

Here AYj is the initial output gap in Europe, AY2 is the initial output gap in
America, AMj is the total increase in European money supply, and AM2 is the
total increase in American money supply. The endogenous variables are
and AM2. The solution to the system (25) and (26) is:

aAY



aAY2
a 2 -p 2
According to equation (27), the total increase in European money supply depends
on the initial output gap in Europe, the initial output gap in America, the direct
multiplier a, and the cross multiplier p. The larger the initial output gap in
Europe, the larger is the total increase in European money supply. Moreover, the
larger the initial output gap in America, the larger is the total increase in
European money supply. At first glance this comes as a surprise. According to
equation (28), the total increase in American money supply depends on the initial
output gap in America, the initial output gap in Europe, the direct multiplier a,
and the cross multiplier p.

4) Stability. Eliminate Yl in equation (7) by means of equation (9) and
rearrange terms Y^ = Aj_ + a M 1 ˜PM 2 . By analogy, eliminate Y2 in equation (8)
by means of equation (10) to arrive at Y2 = A 2 + ocM2 - PMj" . On this basis, the
dynamic model can be described by a system of two equations:

PM^1 (29)
Y2=A2+aM2-PMJ'1 (30)
17

Here the endogenous variables are European money supply this period Mj^ and
American money supply this period M 2 . To simplify notation we make use of
equations (19) and (20). With this, the dynamic model can be written as follows:


pM^1 (31)
B 2 =aM 2 -(3Mf 1 (32)

The endogenous variables are still Mx and M 2 .

Now substitute equation (32) into equation (31) and solve for:



1 1
a a

Then differentiate equation (33) for Mf2:


^V = 4 (34)
2 2
dMJ" a

Finally the stability condition is (32 / a2 < 1 or:

oc>(3 (35)

That means, the steady state is stable if and only if the internal effect of monetary
policy is larger than the external effect of monetary policy. This condition is
satisfied. As a result, there is a stable steady state of monetary competition. In
other words, monetary competition between Europe and America leads to full
employment in Europe and America.
18


2. Some Numerical Examples


To illustrate the dynamic model, have a look at some numerical examples.
For ease of exposition, without loss of generality, assume a = 3 and (3 = 1, see
Carlberg (2000) p. 201 and Carlberg (2001) p. 161. On this assumption, the static
model can be written as follows:


Y1=A1+3M1-M2 (1)
Y2=A2+3M2-M1 (2)

The endogenous variables are European output and American output. Obviously,
an increase in European money supply of 100 causes an increase in European
output of 300 and a decline in American output of 100. Correspondingly, an
increase in American money supply of 100 causes an increase in American
output of 300 and a decline in European output of 100. Further let full-
employment output in Europe be 1000, and let full-employment output in
America be the same.

It proves useful to study seven distinct cases:
- unemployment in Europe equals unemployment in America
- unemployment in Europe exceeds unemployment in America
- unemployment in Europe, full employment in America
- unemployment in Europe exceeds overemployment in America
- unemployment in Europe equals overemployment in America
- inflation in Europe exceeds inflation in America
- inflation in Europe equals inflation in America.

1) Unemployment in Europe equals unemployment in America. At the
beginning there is unemployment in both Europe and America. More precisely,
unemployment in Europe equals unemployment in America. Let initial output in
Europe be 940, and let initial output in America be the same. Step 1 refers to the
policy response. 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. The output gap in America is 60. The monetary policy multiplier in
19

America is 3. So what is needed in America is an increase in American money
supply of 20.

Step 2 refers to the output lag. The increase in European money supply of 20
causes an increase in European output of 60. As a side effect, it causes a decline
in American output of 20. The increase in American money supply of 20 causes
an increase in American output of 60. As a side effect, it causes a decline in
European output of 20. The net effect is an increase in European output of 40 and
an increase in American output of equally 40. As a consequence, European
output goes from 940 to 980, as does American output. Put another way, the
output gap in Europe narrows from 60 to 20, as does the output gap in America.

Why does the European central bank not succeed in closing the output gap in
Europe? The underlying reason is the negative external effect of the increase in
American money supply. And why does the American central bank not succeed
in closing the output gap in America? The underlying reason is the negative
external effect of the increase in European money supply.

Step 3 refers to the policy response. The output gap in Europe is 20. The
monetary policy multiplier in Europe is 3. So what is needed in Europe is an
increase in European money supply of 6.7. The output gap in America is 20. The
monetary policy multiplier in America is 3. So what is needed in America is an
increase in American money supply of 6.7.

Step 4 refers to the output lag. The increase in European money supply of 6.7
causes an increase in European output of 20. As a side effect, it causes a decline
in American output of 6.7. The increase in American money supply of 6.7 causes
an increase in American output of 20. As a side effect, it causes a decline in
European output of 6.7. The net effect is an increase in European output of 13.3
and an increase in American output of equally 13.3. As a consequence, European
output goes from 980 to 993.3, as does American output. And so on. Table 1.1
presents a synopsis.
20


Table 1.1
Monetary Competition between Europe and America
Unemployment in Europe Equals Unemployment in America

Europe America


Initial Output 940 940
20 20
Change in Money Supply
980
Output 980
6.7
Change in Money Supply 6.7
993.3 993.3
Output
and so on




What are the dynamic characteristics of this process? There are repeated
increases in European money supply, as there are in American money supply.
There are repeated increases in European output, as there are in American output.
In each round, the output gap declines by 67 percent. There are repeated cuts in
the world interest rate. There are repeated increases in European investment, as
there are in American investment. There are repeated cuts in budget deficits and
public debts. As a result, monetary competition between Europe and America
leads to full employment in Europe and America.

Taking the sum over all periods, the increase in European money supply is
30, as is the increase in American money supply, see equations (27) and (28) in
the preceding section. That means, the total increase in European money supply
is large, as compared to the initial output gap in Europe of 60. And the same
applies to the total increase in American money supply, as compared to the initial
output gap in America of 60. The effective multiplier in Europe is 60 / 30 = 2, as
is the effective multiplier in America. In other words, the effective multiplier in
Europe is small. And the same holds for the effective multiplier in America.

2) Unemployment in Europe exceeds unemployment in America. Let initial
output in Europe be 940, and let initial output in America be 970. Step 1 refers to
21

the policy response. 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. The output gap in America is 30. The monetary policy
multiplier in America is 3. So what is needed in America is an increase in
American money supply of 10.

Step 2 refers to the output lag. The increase in European money supply of 20
causes an increase in European output of 60. As a side effect, it causes a decline
in American output of 20. The increase in American money supply of 10 causes
an increase in American output of 30. As a side effect, it causes a decline in
European output of 10. The net effect is an increase in European output of 50 and
an increase in American output of 10. As a consequence, European output goes
from 940 to 990, and American output goes from 970 to 980.

Step 3 refers to the policy response. The output gap in Europe is 10. The
monetary policy multiplier in Europe is 3. So what is needed in Europe is an
increase in European money supply of 3.3. The output gap in America is 20. The
monetary policy multiplier in America is 3. So what is needed in America is an
increase in American money supply of 6.7.

Step 4 refers to the output lag. The increase in European money supply of 3.3
causes an increase in European output of 10. As a side effect, it causes a decline
in American output of 3.3. The increase in American money supply of 6.7 causes
an increase in American output of 20. As a side effect, it causes a decline in
European output of 6.7. The net effect is an increase in European output of 3.3
and an increase in American output of 16.7. As a consequence, European output
goes from 990 to 993.3, and American output goes from 980 to 996.7. And so on.
Table 1.2 gives an overview.

What are the dynamic characteristics of this process? There are repeated
increases in European money supply, as there are in American money supply.
There are repeated increases in European output, as there are in American output.
As a result, the process of monetary competition leads to full employment.
22


Table 1.2
Monetary Competition between Europe and America
Unemployment in Europe Exceeds Unemployment in America

Europe America


940
Initial Output 970
Change in Money Supply 20 10
990 980
Output
Change in Money Supply 3.3 6.7
Output 993.3 996.7
2.2 1.1
Change in Money Supply
997.8
998.9
Output
and so on




Taking the sum over all periods, the increase in European money supply is
26.25, and the increase in American money supply is 18.75, see equations (27)
and (28) from the previous section. The total increase in European money supply
is large, as compared to the initial output gap in Europe of 60. And the total
increase in American money supply is even larger, as compared to the initial
output gap in America of 30. The effective multiplier in Europe is
60/ 26.25 = 2.3, and the effective multiplier in America is 30/18.75 = 1.6. That
is to say, the effective multiplier in Europe is small, and the effective multiplier
in America is even smaller.

Table 1.3 differs in initial conditions. Initial output in Europe is 940, and
initial output in America is 990. Table 1.3 shows the resulting process of
monetary competition. There are repeated increases in European money supply,
as there are in American money supply. There are damped oscillations in
European output, as there are in American output. The European economy
oscillates between high and low unemployment, as does the American economy.
As a result, monetary competition leads to full employment. The total increase in
European money supply is 23.75, and the total increase in American money
23


supply is 11.25. The effective multiplier in Europe is 2.5, and the effective
multiplier in America in 0.9.



Table 1.3
Monetary Competition between Europe and America
Unemployment in Europe Exceeds Unemployment in America

America
Europe


990
Initial Output 940
Change in Money Supply 20 3.3
996.7 980
Output
Change in Money Supply 1.1 6.7
998.9
Output 993.3
2.2 0.4
Change in Money Supply
997.8
Output 999.6
and so on




3) Unemployment in Europe, full employment in America. Let initial output
in Europe be 940, and let initial output in America be 1000. Step 1 refers to the
policy response. 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. The output gap in America is zero. So there is no need for a change
in American money supply. Step 2 refers to the output lag. The increase in
European money supply of 20 causes an increase in European output of 60. As a
side effect, it causes a decline in American output of 20. As a consequence,
European output goes from 940 to 1000, and American output goes from 1000 to
980.

Step 3 refers to the policy response. The output gap in Europe is zero. So
there is no need for a change in European money supply. The output gap in
America is 20. The monetary policy multiplier in America is 3. So what is
24


needed in America is an increase in American money supply of 6.7. Step 4 refers
to the output lag. The increase in American money supply of 6.7 causes an
increase in American output of 20. As a side effect, it causes a decline in
European output of 6.7. As a consequence, American output goes from 980 to
1000, and European output goes from 1000 to 993.3. And so on. Table 1.4
presents a synopsis.

What are the dynamic characteristics? There are repeated increases in
European money supply, as there are in American money supply. There are
damped oscillations in European output, as there are in American output. The
European economy oscillates between unemployment and full employment, as
does the American economy. The total increase in European money supply is
22.5, and the total increase in American money supply is 7.5. The effective
multiplier in Europe is 2.7, and the effective multiplier in America is zero.



Table 1.4
Monetary Competition between Europe and America
Unemployment in Europe, Full Employment in America

America
Europe


1000
Initial Output 940
Change in Money Supply 0
20
Output 980
1000
Change in Money Supply 0 6.7
1000
993.3
Output
2.2
Change in Money Supply 0
997.8
Output 1000
and so on
25


4) Unemployment in Europe exceeds overemployment in America. At the
beginning there is unemployment in Europe but overemployment in America.
Thus there is inflation in America. Let initial output in Europe be 940, and let
initial output in America be 1030. Step 1 refers to the policy response. The
output gap in Europe is 60. The target of the European central bank is full
employment in Europe. The monetary policy multiplier in Europe is 3. So what is
needed in Europe is an increase in European money supply of 20. The
inflationary gap in America is 30. The target of the American central bank is
price stability in America. The monetary policy multiplier in America is 3. So
what is needed in America is a reduction in American money supply of 10.

Step 2 refers to the output lag. The increase in European money supply of 20
causes an increase in European output of 60. As a side effect, it causes a decline
in American output of 20. The reduction in American money supply of 10 causes
a decline in American output of 30. As a side effect, it causes an increase in
European output of 10. The total effect is an increase in European output of 70
and a decline in American output of 50. As a consequence, European output goes
from 940 to 1010, and American output goes from 1030 to 980.

Step 3 refers to the policy response. The inflationary gap in Europe is 10. The
monetary policy multiplier in Europe is 3. So what is needed in Europe is a
reduction in European money supply of 3.3. The output gap in America is 20.
The monetary policy multiplier in America is 3. So what is needed in America is
an increase in American money supply of 6.7.

Step 4 refers to the output lag. The reduction in European money supply of
3.3 causes a decline in European output of 10. As a side effect, it causes an
increase in American output of 3.3. The increase in American money supply of
6.7 causes an increase in American output of 20. As a side effect, it causes a
decline in European output of 6.7. The total effect is a decline in European output
of 16.7 and an increase in American output of 23.3. As a consequence, European
output goes from 1010 to 993.3, and American output goes from 980 to 1003.3.
And so on. For an overview see Table 1.5.

What are the dynamic characteristics of this process? There are damped
oscillations in European money supply, as there are in American money supply.
There are damped oscillations in European output, as there are in American
26

output. The European economy oscillates between unemployment and
overemployment, and the same holds for the American economy. As a result, the
process of monetary competition leads to both price stability and full
employment. The total increase in European money supply is 18.75, and the total
reduction in American money supply is 3.75. The effective multiplier in Europe
is 3.2, and the effective multiplier in America is 8.



Table 1.5
Monetary Competition between Europe and America
Unemployment in Europe Exceeds Overemployment in America

Europe America


Initial Output 940 1030
Change in Money Supply 20 -10
Output 1010 980
Change in Money Supply 6.7
-3.3
Output 993.3 1003.3
2.2
Change in Money Supply -1.1
Output 1001.1 997.8
and so on




5) Unemployment in Europe equals overemployment in America. Let initial
output in Europe be 940, and let initial output in America be 1060. Table 1.6
shows the resulting process of monetary competition. In each round, in absolute
values, the output gap declines by 67 percent. Taking the sum over all periods,
the increase in European money supply is 15, and the reduction in American
money supply is equally 15. The total increase in European money supply is
small, as compared to the initial output gap in Europe of 60. Correspondingly,
the total reduction in American money supply is small, as compared to the initial
inflationary gap in America of 60. The effective multiplier in Europe is
60/15 = 4, and the effective multiplier in America is equally 60/15 = 4. That
27


means, the effective multiplier in Europe is large. And the same is true of the
effective multiplier in America.



Table 1.6
Monetary Competition between Europe and America
Unemployment in Europe Equals Overemployment in America

Europe America


Initial Output 940 1060
20
Change in Money Supply -20
Output 1020 980
Change in Money Supply 6.7
-6.7
Output 993.3 1006.7
Change in Money Supply 2.2 -2.2
1002.2 997.8
Output
and so on




6) Inflation in Europe exceeds inflation in America. At the start there is
overemployment in both Europe and America. For that reason there is inflation in
both Europe and America. Let overemployment in Europe exceed
overemployment in America. Let initial output in Europe be 1060, and let initial
output in America be 1030. Step 1 refers to the policy response. The inflationary
gap in Europe is 60. The target of the European central bank is price stability in
Europe. The monetary policy multiplier in Europe is 3. So what is needed in
Europe is a reduction in European money supply of 20. The inflationary gap in
America is 30. The target of the American central bank is price stability in
America. The monetary policy multiplier in America is 3. So what is needed in
America is a reduction in American money supply of 10.

Step 2 refers to the output lag. The reduction in European money supply of 20
causes a decline in European output of 60. As a side effect, it causes an increase
28


in American output of 20. The reduction in American money supply of 10 causes
a decline in American output of 30. As a side effect, it causes an increase in
European output of 10. The net effect is a decline in European output of 50 and a
decline in American output of 10. As a consequence, European output goes from
1060 to 1010, and American output goes from 1030 to 1020.

Step 3 refers to the policy response. The inflationary gap in Europe is 10. The
monetary policy multiplier in Europe is 3. So what is needed in Europe is a
reduction in European money supply of 3.3. The inflationary gap in America is
20. The monetary policy multiplier in America is 3. So what is needed in
America is a reduction in American money supply of 6.7.

Step 4 refers to the output lag. The reduction in European money supply of
3.3 causes a decline in European output of 10. As a side effect, it causes an
increase in American output of 3.3. The reduction in American money supply of
6.7 causes a decline in American output of 20. As a side effect, it causes an
increase in European output of 6.7. The net effect is a decline in European output
of 3.3 and a decline in American output of 16.7. As a consequence, European
output goes from 1010 to 1006.7, and American output goes from 1020 to
1003.3. And so on. For a synopsis see Table 1.7.

What are the dynamic characteristics of this process? There are repeated cuts
in European money supply, as there are in American money supply. There are
repeated cuts in European output, as there are in American output. As a result,
the process of monetary competition leads to both price stability and full
employment.

Taking the sum over all periods, the reduction in European money supply is
26.25, and the reduction in American money supply is 18.75. The total reduction
in European money supply is large, as compared to the initial inflationary gap in
Europe of 60. And the total reduction in American money supply is even larger,
as compared to the initial inflationary gap in America of 30. The effective
multiplier in Europe is 2.3, and the effective multiplier in America is 1.6. That is
to say, the effective multiplier in Europe is small, and the effective multiplier in
America is even smaller.
29

Table 1.7
Monetary Competition between Europe and America
Inflation in Europe Exceeds Inflation in America

Europe America


Initial Output 1060 1030
Change in Money Supply -20 -10

. 1
( 9)



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