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Change in Government Purchases 50 -50
Output 1040
960
Change in Government Purchases 33.3 -33.3
Output 973.3 1026.7
and so on

3) Summary. High capital mobility slows down the process of fiscal
competition. And what is more, high capital mobility can increase the total
change in government purchases.
105

2. Fiscal Cooperation between Europe and America

An increase in European government purchases of 100 causes an increase in
European output of 120 and an increase in American output of 80. Likewise, an
increase in American government purchases of 100 causes an increase in
American output of 120 and an increase in European output of 80. It proves
useful to consider two distinct cases:
- unemployment in Europe equals unemployment in America
- unemployment in Europe equals overemployment in America.

1) Unemployment in Europe equals unemployment in America. Let initial
output in Europe be 940, and let initial output in America be the same. The
output gap in Europe is 60, as is the output gap in America. What is needed, then,
is an increase in European government purchases of 30 and an increase in
American government purchases of equally 30. The increase in European
government purchases of 30 raises European output by 36 and American output
by 24. The increase in American government purchases of 30 raises American
output by 36 and European output by 24. The total effect is an increase in
European output of 60 and an increase in American output of equally 60. As a
consequence, European output goes from 940 to 1000, as does American output.
In Europe there is now full employment, and the same holds for America. As a
result, fiscal cooperation can achieve full employment.

The required increase in European government purchases is small, as
compared to the initial output gap in Europe. And the same applies to the
required increase in American government purchases, as compared to the initial
output gap in America. The effective multiplier in Europe is 60 / 30 = 2, as is the
effective multiplier in America. That is to say, the effective multiplier in Europe
in large. And the same is true of the effective multiplier in America. Table 2.18
presents a synopsis.
106

Table 2.18
Fiscal Cooperation between Europe and America
High Capital Mobility

Europe America

Initial Output 940 940
Change in Government Purchases 30 30
Output 1000 1000

2) Unemployment in Europe equals overemployment in America. Let initial
output in Europe be 940, and let initial output in America be 1060. The output
gap in Europe is 60, and the inflationary gap in America is equally 60. What is
needed, then, is an increase in European government purchases of 150 and a
reduction in American government purchases of equally 150. The increase in
European government purchases of 150 raises European output by 180 and
American output by 120. The reduction in American government purchases of
150 lowers American output by 180 and European output by 120. The net effect
is an increase in European output of 60 and a decline in American output of
equally 60. As a consequence, European output goes from 940 to 1000, and
American output goes from 1060 to 1000. In Europe there is now full
employment, and the same holds for America. As a result, fiscal cooperation can
achieve full employment.

However, the required increase in European government purchases is very
large, as compared to the initial output gap in Europe. Correspondingly, the
required cut in American government purchases is very large, as compared to the
initial inflationary gap in America. The effective multiplier in Europe is
60/150 = 0.4. That means, the effective multiplier in Europe is very small. And
the same is true of the effective multiplier in America. This clearly differs from
the conclusions drawn under low capital mobility. What was needed, there, was
an increase in European government purchases of 60 and a reduction in
American government purchases of equally 60. As a result, under high capital
mobility, the required change in government purchases is very large. By contrast,
107

under low capital mobility, the required change in government purchases is just
large. Table 2.19 gives an overview.

Table 2.19
Fiscal Cooperation between Europe and America
High Capital Mobility

America
Europe

Initial Output 940 1060
Change in Government Purchases 150 -150
1000
Output 1000
Chapter 4
1. 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. Besides we
assume imperfect capital mobility between Europe and America. As a point of
reference, consider the static model. It can be represented by a system of two
equations:

Yx =A 1 +1.5G 1 +0.5G 2 (1)
Y2=A2+1.5G2+0.5G1 (2)

Obviously, an increase in European government purchases of 100 causes an
increase in European output of 150 and an increase in American output of 50.
Correspondingly, an increase in American government purchases of 100 causes
an increase in American output of 150 and an increase in European output of 50.
Further let full-employment output in Europe be 1000, and let full-employment
output in America be the same.

At the beginning 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 Xx.
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 X2. We assume that the European government and the American
government decide simultaneously and independently. Under a gradualist
strategy, is fiscal competition a slow process or a fast one? Surprisingly, the
109

It proves useful to study two distinct cases:
- unemployment in Europe equals unemployment in America
- unemployment in Europe equals overemployment in America.

1) Unemployment in Europe equals unemployment in America. We assume
Xi=X2= 0.6. That means, the governments close the output gaps by 60 percent.
Let initial output in Europe be 940, and let initial output in America be the same.
Step 1 refers to the policy response. First consider fiscal policy in Europe. The
output gap in Europe is 60. The specific target of the European government is to
close the output gap in Europe by 60 percent, that is by 36. The fiscal policy
multiplier in Europe is 1.5. So what is needed in Europe is an increase in
European government purchases of 24. Second consider fiscal policy in America.
The output gap in America is 60. The specific target of the American government
is to close the output gap in America by 60 percent, that is by 36. The fiscal
policy multiplier in America is 1.5. So what is needed in America is an increase
in American government purchases of 24.

Step 2 refers to the output lag. The increase in European government
purchases of 24 causes an increase in European output of 36. As a side effect, it
causes an increase in American output of 12. The increase in American
government purchases of 24 causes an increase in American output of 36. As a
side effect, it causes an increase in European output of 12. The total effect is an
increase in European output of 48 and an increase in American output of equally
48. As a consequence, European output goes from 940 to 988, as does American
output.

Step 3 refers to the policy response. First consider fiscal policy in Europe.
The output gap in Europe is 12. The specific target of the European government
is to close the output gap in Europe by 60 percent, that is by 7.2. The fiscal
policy multiplier in Europe is 1.5. So what is needed in Europe is an increase in
European government purchases of 4.8. Second consider fiscal policy in
America. The output gap in America is 12. The specific target of the American
government is to close the output gap in America by 60 percent, that is by 7.2.
The fiscal policy multiplier in America is 1.5. So what is needed in America is an
increase in American government purchases of 4.8.
110

Step 4 refers to the output lag. The increase in European government
purchases of 4.8 causes an increase in European output of 7.2. As a side effect, it
causes an increase in American output of 2.4. The increase in American
government purchases of 4.8 causes an increase in American output of 7.2. As a
side effect, it causes an increase in European output of 2.4. The total effect is an
increase in European output of 9.6 and an increase in American output of equally
9.6. As a consequence, European output goes from 988 to 997.6, as does
American output. And so on. Table 2.20 presents a synopsis.

What are the dynamic characteristics of this process? In each round, the
output gap declines by 80 percent. This clearly differs from the conclusions
drawn under a cold-turkey strategy. There, in each round, the output gap declined
by 67 percent. As a result, under a gradualist strategy, fiscal competition is a
relatively fast process. By contrast, under a cold-turkey strategy, fiscal
competition is a relatively slow process. At first glance this comes as a surprise.
Moreover, under a gradualist strategy, there are repeated increases in output. On
the other hand, under a cold-turkey strategy, there are oscillations in output.
Taking the sum over all periods, the increase in European government purchases
is 30, as is the increase in American government purchases. This confirms the
conclusions drawn under a cold-turkey strategy.

Table 2.20
Fiscal Competition between Europe and America

Europe America

Initial Output 940 940
Change in Government Purchases 24 24
Output 988
988
4.8
Change in Government Purchases 4.8
Output 997.6 997.6
and so on
Ill

2) Unemployment in Europe equals overemployment in America. We assume
Xl=X2= 0.5. That is to say, the governments close the output gaps by 50
percent. Let initial output in Europe be 940, and let initial output in America be
1060. Step 1 refers to the policy response. First consider fiscal policy in Europe.
The output gap in Europe is 60. The specific target of the European government
is to close the output gap in Europe by 50 percent, that is by 30. The fiscal policy
multiplier in Europe is 1.5. So what is needed in Europe is an increase in
European government purchases of 20. Second consider fiscal policy in America.
The inflationary gap in America is 60. The specific target of the American
government is to close the inflationary gap in America by 50 percent, that is by
30. The fiscal policy multiplier in America is 1.5. So what is needed in America
is a reduction in American government purchases of 20.

Step 2 refers to the output lag. The increase in European government
purchases of 20 causes an increase in European output of 30. As a side effect, it
causes an increase in American output of 10. The reduction in American
government purchases of 20 causes a decline 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 20 and a decline in American output of equally 20. As a
consequence, European output goes from 940 to 960, and American output goes
from 1060 to 1040.

Step 3 refers to the policy response. First consider fiscal policy in Europe.
The output gap in Europe is 40. The specific target of the European government
is to close the output gap in Europe by 50 percent, that is by 20. The fiscal policy
multiplier in Europe is 1.5. So what is needed in Europe is an increase in
European government purchases of 13.3. Second consider fiscal policy in
America. The inflationary gap in America is 40. The specific target of the
American government is to close the inflationary gap in America by 50 percent,
that is by 20. The fiscal policy multiplier in America is 1.5. So what is needed in
America is a reduction in American government purchases of 13.3.

Step 4 refers to the output lag. The increase in European government
purchases of 13.3 causes an increase in European output of 20. As a side effect, it
causes an increase in American output of 6.7. The reduction in American
government purchases of 13.3 causes a decline in American output of 20. As a
side effect, it causes a decline in European output of 6.7. The net effect is an
112

increase in European output of 13.3 and a decline in American output of equally
13.3. As a consequence, European output goes from 960 to 973.3, and American
output goes from 1040 to 1026.7. And so on. Table 2.21 gives an overview.

What are the dynamic characteristics? In each round, in absolute values, the
output gap declines by 33 percent. This clearly differs from the conclusions
reached under a cold-turkey strategy. There, in each round, the output gap
declined by 67 percent. As a result, under a gradualist strategy, fiscal competition
is a relatively slow process. By contrast, under a cold-turkey strategy, fiscal
competition is a relatively fast process. Under a gradualist strategy, there are
repeated increases in European output, and there are repeated cuts in American
output. Taking the sum over all periods, the increase in European government
purchases is 60, and the reduction in American government purchases is equally
60. This confirms the conclusions reached under a cold-turkey strategy.

3) Summary. A gradualist strategy can speed up or slow down the process of
fiscal competition, depending upon initial conditions. And what is more, a
gradualist strategy can prevent output from oscillating.

Table 2.21
Fiscal Competition between Europe and America

America
Europe

1060
Initial Output 940
Change in Government Purchases 20 -20
1040
Output 960
Change in Government Purchases 13.3 -13.3
Output 973.3 1026.7
and so on
113

2. 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. Besides we
assume perfect capital mobility between Europe and America. As a point of
departure, consider the static model. It can be represented by a system of two
equations:

Yx = A 1 + 3 M 1 - M 2 (1)
Y2 = A 2 + 3 M 2 - M 1 (2)

Evidently, 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.

At the start 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 \il.
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 |i 2 . We assume that the European central bank and the American
central bank decide simultaneously and independently. Under a gradualist
strategy, is monetary competition a slow process or a fast one? Surprisingly, the

It proves useful to study two distinct cases:
- unemployment in Europe equals unemployment in America
- unemployment in Europe equals overemployment in America.
114

1) Unemployment in Europe equals unemployment in America. We assume
Mi M2 = 0.5. That means, the central banks close the output gaps by 50 percent.
=
- -
Let initial output in Europe be 940, and let initial output in America be the same.
Step 1 refers to the policy response. First consider monetary policy in Europe.
The output gap in Europe is 60. The specific target of the European central bank
is to close the output gap in Europe by 50 percent, that is by 30. The monetary
policy multiplier in Europe is 3. So what is needed in Europe is an increase in
European money supply of 10. Second consider monetary policy in America. The
output gap in America is 60. The specific target of the American central bank is
to close the output gap in America by 50 percent, that is by 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 10
causes an increase in European output of 30. As a side effect, it causes a decline
in American output of 10. The increase in American money supply of 10 causes
an increase in American output of 30. As a side effect, it causes a decline in
European output of 10. The net effect is an increase in European output of 20 and
an increase in American output of equally 20. As a consequence, European
output goes from 940 to 960, as does American output.

Step 3 refers to the policy response. First consider monetary policy in Europe.
The output gap in Europe is 40. The specific target of the European central bank
is to close the output gap in Europe by 50 percent, that is by 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. Second consider monetary policy in America.
The output gap in America is 40. The specific target of the American central
bank is to close the output gap in America by 50 percent, that is by 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
115

output goes from 960 to 973.3, as does American output. And so on. For a
synopsis see Table 2.22.

What are the dynamic characteristics of this process? In each round, the
output gap declines by 33 percent. This clearly differs from the conclusions
drawn under a cold-turkey strategy. There, in each round, the output gap declined
by 67 percent. As a result, under a gradualist strategy, monetary competition is a
relatively slow process. By contrast, under a cold-turkey strategy, monetary
competition is a relatively fast process. Taking the sum over all periods, the
increase in European money supply is 30, as is the increase in American money
supply. This confirms the conclusions drawn under a cold-turkey strategy.

Table 2.22
Monetary Competition between Europe and America

Europe America

Initial Output 940 940
Change in Money Supply 10 10
Output 960
960
6.7
Change in Money Supply 6.7
973.3
Output 973.3
and so on

2) Unemployment in Europe equals overemployment in America. We assume
Mi M2 = 0.6- That is to say, the central banks close the output gaps by 60
=
-
percent. Let initial output in Europe be 940, and let initial output in America be
1060. Step 1 refers to the policy response. First consider monetary policy in
Europe. The output gap in Europe is 60. The specific target of the European
central bank is to close the output gap in Europe by 60 percent, that is by 36. The
monetary policy multiplier in Europe is 3. So what is needed in Europe is an
116

increase in European money supply of 12. Second consider monetary policy in
America. The inflationary gap in America is 60. The specific target of the
American central bank is to close the inflationary gap in America by 60 percent,
that is by 36. The monetary policy multiplier in America is 3. So what is needed
in America is a reduction in American money supply of 12.

Step 2 refers to the output lag. The increase in European money supply of 12
causes an increase in European output of 36. As a side effect, it causes a decline
in American output of 12. The reduction in American money supply of 12 causes
a decline in American output of 36. As a side effect, it causes an increase in
European output of 12. The total effect is an increase in European output of 48
and a decline in American output of equally 48. As a consequence, European
output goes from 940 to 988, and American output goes from 1060 to 1012.

Step 3 refers to the policy response. First consider monetary policy in Europe.
The output gap in Europe is 12. The specific target of the European central bank
is to close the output gap in Europe by 60 percent, that is by 7.2. The monetary
policy multiplier in Europe is 3. So what is needed in Europe is an increase in
European money supply of 2.4. Second consider monetary policy in America.
The inflationary gap in America is 12. The specific target of the American
central bank is to close the inflationary gap in America by 60 percent, that is by
7.2. The monetary policy multiplier in America is 3. So what is needed in
America is a reduction in American money supply of 2.4.

Step 4 refers to the output lag. The increase in European money supply of 2.4
causes an increase in European output of 7.2. As a side effect, it causes a decline
in American output of 2.4. The reduction in American money supply of 2.4
causes a decline in American output of 7.2. As a side effect, it causes an increase
in European output of 2.4. The total effect is an increase in European output of
9.6 and a decline in American output of equally 9.6. As a consequence, European
output goes from 988 to 997.6, and American output goes from 1012 to 1002.4.
And so on. For an overview see Table 2.23.

What are the dynamic characteristics? In each round, in absolute values, the
output gap declines by 80 percent. This clearly differs from the conclusions
reached under a cold-turkey strategy. There, in each round, the output gap
declined by 67 percent. As a result, under a gradualist strategy, monetary
117

competition is a relatively fast process. By contrast, under a cold-turkey strategy,
monetary competition is a relatively slow process. At first glance this comes as a
surprise. Moreover, under a gradualist strategy, there are repeated increases in
European output, and there are repeated cuts in American output. On the other
hand, under a cold-turkey strategy, there are oscillations in both European and
American output. Taking the sum over all periods, the increase in European
money supply is 15, and the reduction in American money supply is equally 15.
This confirms the conclusions reached under a cold-turkey strategy.

3) Summary. A gradualist strategy can slow down or speed up the process of
monetary competition, depending upon initial conditions. Further, a gradualist
strategy can prevent output from oscillating.

Table 2.23
Monetary Competition between Europe and America

America
Europe

Initial Output 940 1060
Change in Money Supply 12 -12
1012
Output 988
Change in Money Supply 2.4 -2.4
1002.4
Output 997.6
and so on
118

3. Monetary and Fiscal Competition

1) The static model. This section deals with competition between the
European central bank, the American central bank, the European government,
and the American government. We assume imperfect capital mobility between
Europe and America. As a point of reference, consider the static model. It can be
represented by a system of two equations:

Yx = A 1 +2.5M 1 -0.5M 2 +1.5G 1 +0.5G 2 (1)
Y2 = A 2 + 2.5M2 - 0.5M! +1.5G 2 + 0 ^ (2)

Obviously, an increase in European money supply of 100 causes an increase in
European output of 250 and a decline in American output of 50. An increase in
European government purchases of 100 causes an increase in European output of
150 and an increase in American output of 50. Further let full-employment
output in Europe be 1000, and let full-employment output in America be the
same.

2) The dynamic model. At the beginning there is unemployment in Europe
and America. The general target of the European central bank is full employment
in Europe. The specific target of the European central bank is to close the output
gap in Europe by the fraction [iv The general target of the American central bank
is full employment in America. The specific target of the American central bank
is to close the output gap in America by the fraction \x2. The general target of the
European government is full employment in Europe. The specific target of the
European government is to close the output gap in Europe by the fraction A,1# The
general target of the American government is full employment in America. 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.

As a result, there is a stability condition. The steady state of monetary and
fiscal competition is stable if the speed of adjustment in European money supply,
119

American money supply, European government purchases, and American
government purchases is sufficiently low. Taking the sum over all periods, the
increase in European money supply, American money supply, European
government purchases, and American government purchases depends upon the
relative speed of adjustment in European money supply, American money
supply, European government purchases, and American government purchases.
For the method see Carlberg (2004) p. 154.

3) A numerical example. To illustrate the dynamic model, have a look at a
numerical example with \i^ = 0.8, \i2 = 0.6, A^ = 0.2, and X2 = 0.4. That means,
the specific target of the European central bank is to close the output gap in
Europe by 80 percent. The specific target of the American central bank is to close
the output gap in America by 60 percent. The specific target of the European
government is to close the output gap in Europe by 20 percent. And the specific
target of the American government is to close the output gap in America by 40
percent.

Let initial output in Europe be 940, and let initial output in America be the
same. Step 1 refers to the policy response. First consider monetary policy in
Europe. The output gap in Europe is 60. The specific target of the European
central bank is to close the output gap in Europe by 80 percent, that is by 48. The
monetary policy multiplier in Europe is 2.5. So what is needed in Europe is an
increase in European money supply of 19.2. Second consider monetary policy in
America. The output gap in America is 60. The specific target of the American
central bank is to close the output gap in America by 60 percent, that is by 36.
The monetary policy multiplier in America is 2.5. So what is needed in America
is an increase in American money supply of 14.4.

Third consider fiscal policy in Europe. The output gap in Europe is 60. The
specific target of the European government is to close the output gap in Europe
by 20 percent, that is by 12. The fiscal policy multiplier in Europe is 1.5. So what
is needed in Europe is an increase in European government purchases of 8.
Fourth consider fiscal policy in America. The output gap in America is 60. The
specific target of the American government is to close the output gap in America
by 40 percent, that is by 24. The fiscal policy multiplier in America is 1.5. So
what is needed in America is an increase in American government purchases of
16.
120

Step 2 refers to the output lag. The increase in European money supply of
19.2 causes an increase in European output of 48. As a side effect, it causes a
decline in American output of 9.6. The increase in American money supply of
14.4 causes an increase in American output of 36. As a side effect, it causes a
decline in European output of 7.2. The increase in European government
purchases of 8 causes an increase in European output of 12. As a side effect, it
causes an increase in American output of 4. The increase in American
government purchases of 16 causes an increase in American output of 24. As a
side effect, it causes an increase in European output of 8. The net effect is an
increase in European output of 60.8 and an increase in American output of 54.4.
As a consequence, European output goes from 940 to 1000.8, and American
output goes from 940 to 994.4.

Step 3 refers to the policy response. First consider monetary policy in Europe.
The inflationary gap in Europe is 0.8. The specific target of the European central
bank is to close the inflationary gap in Europe by 80 percent, that is by 0.64. The
monetary policy multiplier in Europe is 2.5. So what is needed in Europe is a
reduction in European money supply of 0.26. Second consider monetary policy
in America. The output gap in America is 5.6. The specific target of the
American central bank is to close the output gap in America by 60 percent, that is
by 3.36. The monetary policy multiplier in America is 2.5. So what is needed in
America is an increase in American money supply of 1.34.

Third consider fiscal policy in Europe. The inflationary gap in Europe is 0.8.
The specific target of the European government is to close the inflationary gap in
Europe by 20 percent, that is by 0.16. The fiscal policy multiplier in Europe is
1.5. So what is needed in Europe is a reduction in European government
purchases of 0.11. Fourth consider fiscal policy in America. The output gap in
America is 5.6. The specific target of the American government is to close the
output gap in America by 40 percent, that is by 2.24. The fiscal policy multiplier
in America is 1.5. So what is needed in America is an increase in American
government purchases of 1.49.

Step 4 refers to the output lag. The reduction in European money supply of
0.26 causes a decline in European output of 0.64. As a side effect, it causes an
increase in American output of 0.13. The increase in American money supply of
121

1.34 causes an increase in American output of 3.36. As a side effect, it causes a
decline in European output of 0.67. The reduction in European government
purchases of 0.11 causes a decline in European output of 0.16. As a side effect, it
causes a decline in American output of 0.05. The increase in American
government purchases of 1.49 causes an increase in American output of 2.24. As
a side effect, it causes an increase in European output of 0.75. The net effect is a
decline in European output of 0.72 and an increase in American output of 5.68.
As a consequence, European output goes from 1000.8 to 1000.1, and American
output goes from 994.4 to 1000.1. And so on. Table 2.24 presents a synopsis.

As a result, the process of monetary and fiscal competition leads to full
employment in Europe and America. And what is more, monetary and fiscal
competition is a fast process. Taking the sum over all periods, the increase in
European money supply is 18.9, the increase in American money supply is 15.7,
the increase in European government purchases in 7.9, and the increase in
American government purchases is 17.5.

Table 2.24
Monetary and Fiscal Competition

America
Europe

940 940
Initial Output
19.2 19.2
Change in Money Supply
8 8
Change in Government Purchases
1000.8 1000.8
Output
Change in Money Supply -0.3 -0.3
Change in Government Purchases -0.1 -0.1
Output 1000.1 1000.1
and so on
122

Generally speaking, the total increase in European government purchases
depends on:
- the initial output gap in Europe
- the initial output gap in America
- the direct policy multipliers a and y
- the cross policy multipliers (3 and 8
- the speed of adjustment in European money supply jo^
- the speed of adjustment in American money supply \i2
- the speed of adjustment in European government purchases Xx
- the speed of adjustment in American government purchases X2.
Part Three

The World of
Two Monetary Regions

Chapter 1
The Regions Differ in Policy Multipliers
1. Monetary Competition between Europe and America

1) The static model. In this section we assume that the regions differ in
monetary policy multipliers. Besides we assume that the central banks follow a
cold-turkey strategy. As a point of reference, consider the static model. It can be
represented by a system of two equations:

Y1=A1+a1M1-p2M2 (1)
Y2=A2+a2M2-P1M1 (2)

According to equation (1), European output Y{ is determined by European
money supply Mx and American money supply M 2 . According to equation (2),
American output Y2 is determined by American money supply M 2 and European
money supply M^ Here cq, oc2, fii and (32 denote the monetary policy
multipliers. The direct effects of monetary policy are positive oq > 0 and a 2 > 0.
By contrast, the cross effects of monetary policy are negative Pi > 0 and P 2 > 0.

An increase in European money supply raises European output but lowers
American output. An increase in American money supply raises American output
but lowers European output. An increase in European money supply of 1 causes
an increase in European output of o^ and a decline in American output of P^ An
increase in American money supply of 1 causes an increase in American output
of oc2 and a decline in European output of P 2 .

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. And the target of the American central bank is full employment in
America. The dynamic model can be characterized by a system of two equations:

(3)
126

Y2=A2+a2MJ1-p1M1 (4)

Here is a list of the new symbols:
Yj full-employment output in Europe
Y2 full-employment output in America
Mj European money supply this period
M 2 American money supply this period
M+1 European money supply next period
M2* American money supply next period.
Here the endogenous variables are M+1 and MJ 1 .

According to equation (3), the European central bank raises European money
supply so as to close the output gap in Europe. According to equation (4), 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.

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

Mi (5)
J M2 (6)

Equation (5) has it that European money supply does not change any more.
Similarly, equation (6) has it that American money supply does not change any
more. Therefore the steady state of the dynamic model can be described by a
system of two equations:

Y1=A1+a1M1-(32M2 (7)
Y2=A2+a2M2-(31M1 (8)

Here the endogenous variables are European money supply and American money
supply.
127

To simplify notation, we introduce Bx = Yx - A{ and B 2 = Y2 - A 2 . Then we
solve the model for the endogenous variables:

(10)
- PlP 2

Equation (9) shows the steady-state level of European money supply, and
equation (10) shows the steady-state level of American money supply. As a
result, there is a steady state if and only if a ^ 2 ^ PiP2- That means, there is a
steady state if and only if the mathematical product of the direct multipliers is
unequal to the mathematical product of the cross multipliers.

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 =a 1 AM 1 -p 2 AM 2 (11)
AY2 = a 2 AM 2 - PiAMi (12)

Here AY! denotes 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 AMj
and AM2. The solution to the system (11) and (12) is:

(13)

CAY^AY,
aaPP
According to equation (13), the total increase in European money supply depends
on the initial output gap in Europe, the initial output gap in America, the direct
multipliers, and the cross multipliers. The larger the initial output gap in Europe,
128

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.

4) Stability. As a point of departure, take the dynamic model. Equation (3)
yields dMj^1 / dM 2 = P 2 / ah and equation (4) yields dM 2 / dMj"1 = Pi / a 2 . This
implies:

Hence the stability condition is (31(32/a1a2 < 1 or:

a 1 a 2 >P 1 P 2 (16)

As a result, the steady state is stable if and only if the mathematical product of
the direct multipliers is larger than the mathematical product of the cross
multipliers. If a x a 2 =PiP 2 , there is no steady state. If a x a 2 >PiP 2 , there is a
stable steady state. And if a x a 2 < PiP 2 , there is a steady state, but it is unstable.
To illustrate this, have a look at a numerical example. Let be 0 ^ = 1 , oc2 = 1 ,
Px = 1.2, and P 2 = 0.8. From this follows a x a 2 > PiP 2 . In other words, there is a
stable steady state. For simulations see Chapter 2 below.

5) Summary. The process of monetary competition is stable if and only if the
product of the direct multipliers is larger than the product of the cross multipliers.
129

2. Fiscal Competition between Europe and America

1) The static model. In this section we assume that the regions differ in fiscal
policy multipliers. Besides we assume that the governments follow a cold-turkey
strategy. As a point of reference, consider the static model. It can be represented
by a system of two equations:

CD
AS^
Y2=A2+Y2G2+51G1 (2)

According to equation (1), European output Yl is determined by European
government purchases Gx and American government purchases G 2 . According
to equation (2), American output Y2 is determined by American government
purchases G 2 and European government purchases G2. Here YiÂ» Y2Â» ^i and 5 2
denote the fiscal policy multipliers. The direct effects of fiscal policy are positive
Yi > 0 and y2 > Â®- The cross effects of fiscal policy are positive too 8X > 0 and
52>0.

An increase in European government purchases raises both European output
and American output. An increase in American government purchases raises both
American output and European output. An increase in European government
purchases of 1 causes an increase in European output of Yi and an increase in
American output of 5^ An increase in American government purchases of 1
causes an increase in American output of y2 and an increase in European output
of 8 2 .

2) 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. And the target of the American government is full employment in
America. The dynamic model can be characterized by a system of two equations:

^asGa (3)
Y 2 =A 2 +Y 2 GJ 1 +5 1 G 1 (4)
130

Here is a list of the new symbols:
Yx full-employment output in Europe
Y2 full-employment output in America
G! European government purchases this period
G2 American government purchases this period
European government purchases next period
American government purchases next period.
Here the endogenous variables are Gj^1 and GJ 1 .

According to equation (3), the European government raises European
government purchases so as to close the output gap in Europe. According to
equation (4), 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.

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

(5)
(6)

Equation (5) has it that European government purchases do not change any more.
Similarly, equation (6) has it that American government purchases do not change
any more. Therefore the steady state of the dynamic model can be described by a
system of two equations:

Y1=A1+YiG1+52G2 (7)
Y2=A2+Y2G2+51G1 (8)

Here the endogenous variables are European government purchases and
American government purchases.

To simplify notation we introduce Bj = Y1 - A1 and B 2 = Y2 - A 2 . Then we
solve the model for the endogenous variables:
131

(9)

Equation (9) shows the steady-state level of European government purchases,
and equation (10) shows the steady-state level of American government
purchases. As a result, there is a steady state if and only if Y1Y2 ^ S 1 5 2 . That
means, there is a steady state if and only if the mathematical product of the direct
multipliers is unequal to the mathematical product of the cross multipliers.

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

AY 1 =YiAG 1 +5 2 AG 2 (11)
AY2 =Y 2 AG 2 +8 1 AG 1 (12)

Here AYX denotes the initial output gap in Europe, AY2 is the initial output gap in
America, AG! is the total increase in European government purchases, and AG2
is the total increase in American government purchases. The endogenous
variables are AG! and AG2. The solution to the system (11) and (12) is:

According to equation (13), the total increase in European government purchases
depends on the initial output gap in Europe, the initial output gap in America, the
direct multipliers, and the cross multipliers. The larger the initial output gap in
Europe, the larger is the total increase in European government purchases.
132

Moreover, the larger the initial output gap in America, the smaller is the total
increase in European government purchases.

4) Stability. As a point of departure, take the dynamic model. Equation (3)
yields dGj^1 / d G 2 = - 5 2 /Yi> a n ( i equation (4) yields dG 2 /dGf 1 = - 5X / y 2 .
This implies:

(15)
dGr 1 Y1Y2

Hence the stability condition is 8^2 / Y1Y2 < 1 o r :

YlY2> 8 l 8 2

As a result, the steady state is stable if and only if the mathematical product of
the direct multipliers is larger than the mathematical product of the cross
multipliers. If Y1Y2 = 8 i 8 2> t n e r e *s n o steady state. If Y1Y2 > 8 i 5 2 , there is a
stable steady state. If Y1Y2 < 8 i S 2 , there is a steady state, but it is unstable. To
illustrate this, have a look at a numerical example. Let be Yi = 1, Y2 = 1, Sj = 1.2
and 8 2 =0.8. From this follows Y1Y2 > 8 i 8 2 - ^n other words, there is a stable
steady state. For simulations see Chapter 2 below.

5) Summary. The process of fiscal competition is stable if and only if the
product of the direct multipliers is larger than the product of the cross multipliers.
Chapter 2
The Regions Differ in Size
1. Monetary Competition between Europe and America

In this chapter we assume that the regions only differ in size. To be more
specific, we assume that the European economy is half as large as the American
economy. More precisely, full-employment output in Europe is half as large as
full-employment output in America. There is perfect capital mobility between
Europe and America. The central banks follow a cold-turkey strategy.

As a point of reference, consider the static model. It can be represented by a
system of two equations:

Yx = Ax + 3.33M1 - 0.67M2 (1)
Y2 = A 2 + 2.67M2 -1.33Mi (2)

According to equation (1), European output Yl is determined by European
money supply Ml and American money supply M 2 . According to equation (2),
American output Y2 is determined by American money supply M 2 and European
money supply M x .

An increase in European money supply of 100 causes an increase in European
output of 333 and a decline in American output of 133. So the increase in world
output is 200. An increase in American money supply of 100 causes an increase
in American output of 267 and a decline in European output of 67. So the
increase in world output is 200 again. The monetary policy multipliers are from
the world of three regions, see Part Four below. Obviously, in the small region,
the monetary policy multiplier is large. And in the large region, the monetary
policy multiplier is small. Further let full-employment output in Europe be 1000,
and let full-employment output in America be 2000. The target of the European
central bank is full employment in Europe, and the target of the American central
bank is full employment in America.
134

At the beginning there is unemployment in both Europe and America. Let the
rate of unemployment in Europe be equal to the rate of unemployment in
America. For instance, let initial output in Europe be 940, and let initial output in
America be 1880. Step 1 refers to the policy response. The output gap in Europe
is 60. The monetary policy multiplier in Europe is 3.33. So what is needed in
Europe is an increase in European money supply of 18. The output gap in
America is 120. The monetary policy multiplier in America is 2.67. So what is
needed in America is an increase in American money supply of 45.

Step 2 refers to the output lag. The increase in European money supply of 18
causes an increase in European output of 60. As a side effect, it causes a decline
in American output of 24. The increase in American money supply of 45 causes
an increase in American output of 120. As a side effect, it causes a decline in
European output of 30. The net effect is an increase in European output of 30 and
an increase in American output of 96. As a consequence, European output goes
from 940 to 970, and American output goes from 1880 to 1976. And so on. Table
3.1 presents a synopsis.

Table 3.1
Monetary Competition between Europe and America
The Regions Differ in Size

Europe America

Initial Output 1880
940
Change in Money Supply 18 45
Output 970 1976
Change in Money Supply 9
9
Output 994 1988
Change in Money Supply 1.8 4.5
Output 997 1997.6
and so on
135

As a result, the process of monetary competition leads to full employment in
Europe and America. According to Chapter 1, the total increase in European
money supply is 30, and the total increase in American money supply is 60. The
effective monetary multiplier in Europe is 2, as is the effective monetary
multiplier in America.

Next have a closer look at the output gap as a percentage of full-employment
output. At the start, the output gap in Europe relative to full-employment output
in Europe is 6 percent. And the output gap in America relative to full-
employment output in America is equally 6 percent. In step 2, the output gap in
Europe is 3 percent, and the output gap in America is 1.2 percent. In step 4, the
output gap in Europe is 0.6 percent, and the output gap in America is equally 0.6
percent. In step 6, the output gap in Europe is 0.3 percent, and the output gap in
America is 0.12 percent. And so on. Table 3.2 gives an overview. Evidently, the
relative output gap in Europe is larger than the relative output gap in America.
The underlying reason is that, in the small region, monetary competition is a
relatively slow process. And in the large region, monetary competition is a
relatively fast process.

Table 3.2
Monetary Competition between Europe and America
The Regions Differ in Size

Output Gap in Europe Output Gap in America
in Percent in Percent

6 6
3 1.2
0.6 0.6
0.3 0.12
and so on
136

2. Monetary Cooperation between Europe and America

At the beginning there is unemployment in both Europe and America. More
precisely, the output gap in Europe equals the output gap in America. Let initial
output in Europe be 940, and let initial output in America be 1940. The output
gap in Europe is 60, as is the output gap in America. So what is needed,
according to Chapter 1, is an increase in European money supply of 25 and an
increase in American money supply of 35. The increase in European money
supply of 25 raises European output by 83.3 and lowers American output by
33.3. The increase in American money supply of 35 raises American output by
93.3 and lowers European output by 23.3. The net effect is an increase in
European output of 60 and an increase in American output of equally 60. As a
consequence, European output goes from 940 to 1000, and American output goes
from 1940 to 2000. As a result, monetary cooperation can achieve full
employment.

It is worth pointing out here that the required increase in European money
supply differs from the required increase in American money supply, even
though the initial output gap in Europe equals the initial output gap in America.
The reason is that Europe and America differ in size. For a synopsis see Table
3.3.

Table 3.3
Monetary Cooperation between Europe and America
The Regions Differ in Size

America
Europe

1940
Initial Output 940
35
Change in Money Supply 25
2000
Output 1000
137

3. Fiscal Competition between Europe and America

We assume perfect capital mobility between Europe and America. Besides,
we assume that the governments follow a cold-turkey strategy. As a point of
departure, take the static model. It can be represented by a system of two
equations:

+ 0.67G2 (1)
Y 2 =A 2 +1.33G 2 +1.33G 1 (2)

According to equation (1), European output Yx is determined by European
government purchases G^ and American government purchases G 2 . According
to equation (2), American output is determined by American government
purchases and European government purchases.

An increase in European government purchases of 100 causes an increase in
European output of 67 and an increase in American output of 133. So the
increase in world output is 200. An increase in American government purchases
of 100 causes an increase in American output of 133 and an increase in European
output of 67. So the increase in world output is 200 again. The fiscal policy
multipliers are from the world of three regions, see Part Four below. Obviously,
in the small region, the fiscal policy multiplier is small. And in the large region,
the fiscal policy multiplier is large. Further let full-employment output in Europe
be 1000, and let full-employment output in America be 2000. The target of the
European government is full employment in Europe, and the target of the
American government is full employment in America.

It proves useful to study two distinct cases:
- the rate of unemployment in Europe equals
the rate of unemployment in America
- the output gap in Europe equals the output gap in America.

1) The rate of unemployment in Europe equals the rate of unemployment in
America. At the beginning there is unemployment in Europe and America. Let
138

initial output in Europe be 940, and let initial output in America be 1880. Step 1
refers to the policy response. The output gap in Europe is 60. The fiscal policy
multiplier in Europe is 0.67. So what is needed in Europe is an increase in
European government purchases of 90. The output gap in America is 120. The
fiscal policy multiplier in America is 1.33. So what is needed in America is an
increase in American government purchases of 90.

Step 2 refers to the output lag. The increase in European government
purchases of 90 causes an increase in European output of 60. As a side effect, it
causes an increase in American output of 120. The increase in American
government purchases of 90 causes an increase in American output of 120. As a
side effect, it causes an increase in European output of 60. The total effect is an
increase in European output of 120 and an increase in American output of 240.
As a consequence, European output goes from 940 to 1060, and American output
goes from 1880 to 2120.

In step 3, European government purchases are lowered by 90, and the same
holds for American government purchases. In step 4, European output goes from
1060 to 940, and American output goes from 2120 to 1880. With this, European
output and American output are back at their initial levels. That means, this
process will repeat itself step by step. Table 3.4 presents a synopsis. As a result,
the process of fiscal competition does not lead to full employment in Europe and
America.

What are the dynamic characteristics of this process? There are uniform
oscillations in European government purchases, as there are in American
government purchases. There are uniform oscillations in European output, as
there are in American output. The European economy oscillates between
unemployment and overemployment, as does the American economy. It is worth
pointing out here that the change in European government purchases equals the
change in American government purchases, even though the initial output gap in
Europe is half as large as the initial output gap in America. The reason is that
Europe and America differ in size.
139

Table 3.4
Fiscal Competition between Europe and America
The Regions Differ in Size

Europe America

1880
Initial Output 940
Change in Government Purchases 90 90
Output 1060 2120
Change in Government Purchases -90 -90
Output 940 1880
and so on

2) The output gap in Europe equals the output gap in America. Let initial
output in Europe be 940, and let initial output in America be 1940. Step 1 refers
to the policy response. The output gap in Europe is 60. The fiscal policy
multiplier in Europe is 0.67. So what is needed in Europe is an increase in
European government purchases of 90. The output gap in America is 60. The
fiscal policy multiplier in America is 1.33. So what is needed in America is an
increase in American government purchases of 45.

Step 2 refers to the output lag. The increase in European government
purchases of 90 causes an increase in European output of 60. As a side effect, it
causes an increase in American output of 120. The increase in American
government purchases of 45 causes an increase in American output of 60. As a
side effect, it causes an increase in European output of 30. The total effect is an
increase in European output of 90 and an increase in American output of 180. As
a consequence, European output goes from 940 to 1030, and American output
goes from 1940 to 2120.

In step 3, European government purchases are reduced by 45, and American
government purchases are reduced by 90. In step 4, European output goes from
1030 to 940, and American output goes from 2120 to 1940. With this, output is
140

back at its initial level, hence this process will repeat itself. Table 3.5 gives an
overview. As a result, fiscal competition does not lead to full employment. There
is an upward trend in European government purchases. By contrast, there is a
downward trend in American government purchases. There are uniform
oscillations in European output, as there are in American output. Moreover, after
a certain number of steps, American government purchases are down to zero.

Table 3.5
Fiscal Competition between Europe and America
The Regions Differ in Size

America
Europe

Initial Output 940 1940
Change in Government Purchases 90 45
Output 1030 2120
Change in Government Purchases -45 -90
Output 940 1940
and so on
Chapter 3
Competition between
the European Labour Union
and the American Labour Union
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.

As a result, an increase in European nominal wages lowers European output.
On the other hand, it raises American output. Here the fall in European output
exceeds the rise in American output. Correspondingly, an increase in American
nominal wages lowers American output. On the other hand, it raises European
output. Here the fall in American output exceeds the rise in European output. In
the numerical example, a 1 percent increase in European nominal wages causes a
0.75 percent decline in European output and a 0.25 percent increase in American
output. Similarly, a 1 percent increase in American nominal wages causes a 0.75
percent decline in American output and a 0.25 percent increase in European
output. That is to say, the internal effect of wage policy is very large, and the
external effect of wage policy is large. Now have a closer look at the process of
adjustment. An increase in European nominal wages causes an increase in the
price of European goods. This in turn causes an appreciation of the euro, a
depreciation of the dollar, and an increase in the world interest rate. The increase
in the price of European goods lowers European exports and raises American
142

exports. 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 goes down. However, American output goes up. This model is
in the tradition of the Mundell-Fleming model, see Carlberg (2001) p. 164 and
Carlberg (2002) p. 181.

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

Y 1 =A 1 -8W 1 +T 1 W 2 (1)
Y2=A2-eW2+TiW1 (2)

According to equation (1), European output Yx is determined by European
nominal wages W^ American nominal wages W 2 , and some other factors called
Aj. According to equation (2), American output Y2 is determined by American
nominal wages W 2 , European nominal wages Wl5 and some other factors called
A 2 . Here 8 and r\ denote the wage policy multipliers. The internal effect of wage
policy is negative e > 0. By contrast, the external effect of wage policy is
positive r\ > 0. In absolute values, the internal effect is larger than the external
effect 8 > r|. 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 labour union is full employment
in Europe. The instrument of the European labour union is European nominal
wages. The European labour union lowers European nominal wages so as to
close the output gap in Europe:

Yl
˜Yl
Wi-Wf^- (3)

Here is a list of the new symbols:
Yx European output this period
Yx full-employment output in Europe
Yx - Yi output gap in Europe this period
1
Wf European nominal wages last period
143

Wj European nominal wages this period
Wj - Wj" 1 change in European nominal wages.
Here the endogenous variable is European nominal wages this period W x .

The target of the American labour union is full employment in America. The
instrument of the American labour union is American nominal wages. The
American labour union lowers American nominal wages so as to close the output
gap in America:

(4)

Here is a list of the new symbols:
Y2 American output this period
Y2 full-employment output in America
Y2 - Y2 output gap in America this period
1
W^" American nominal wages last period
W2 American nominal wages this period
W 2 - W^"1 change in American nominal wages.
Here the endogenous variable is American nominal wages this period W 2 . We
assume that the European labour union and the American labour union decide
simultaneously and independently.

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

Yi^Ai-eWi+TIW2 (5)

Here Yf1 denotes European output next period. In the same way, American
output next period is determined by American nominal wages this period as well
as by European nominal wages this period:

Y+ 1 = A 2 - eW 2 + TjWi (6)

Here Y^ 1 denotes American output next period.
144

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

Yl
˜Yl (7)

W 2 -W 2 ˜ 1 = - Y2
˜Y2 (8)

(9)
Y2+1=A2-eW2+r|W1 (10)

Equation (7) shows the wage response by the European labour union, equation
(8) shows the wage response by the American labour union, equation (9) shows
the output lag in Europe, and equation (10) shows the output lag in America. The
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