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1) The static model. In this chapter we assume imperfect capital mobility
between Europe, America and Asia. Under perfect capital mobility, an increase
in European government purchases raises European output, American output and
Asian output, to the same extent respectively. Under zero capital mobility, an
increase in European government purchases raises European output to a much
larger degree. On the other hand, it has no effect on American output or Asian
output. Under imperfect capital mobility, an increase in European government
purchases raises European output, American output and Asian output. Here the
rise in European output is relatively large, whereas the rise in American output
and Asian output is relatively small.

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 67, an increase in American output of 67, and an
increase in Asian output of equally 67. So the increase in world output is 200.
Under zero capital mobility, an increase in European government purchases of
100 causes an increase in European output of 200, an increase in American
output of zero, and an increase in Asian output of equally zero. So the increase in
world output is 200 again. 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 133, an increase in American output of 33, and an
increase in Asian output of equally 33. So the increase in world output is still
200.

That means, under perfect capital mobility, fiscal spillovers are very large.
Under zero capital mobility, fiscal spillovers are zero. And under imperfect
capital mobility, fiscal spillovers are medium size. What does this imply for
fiscal competition? Given imperfect capital mobility, is fiscal competition a
stable process or an unstable one?
184



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


+5G 2 + SG3 (1)
Y2 = A 2 + yG2 + 8GX + 5G 3 (2)

Y3 = A 3 + yG3 + 8GX + 5G 2 (3)


According to equation (1), European output is determined by European
government purchases, American government purchases, and Asian government
purchases. According to equation (2), American output is determined by
American government purchases, European government purchases, and Asian
government purchases. According to equation (3), Asian output is determined by
Asian government purchases, European government purchases, and American
government purchases. Here y and 8 denote the fiscal policy multipliers. The
internal effect of fiscal policy is positive y > 0. The external effect of fiscal
policy is positive too 8 > 0. And what is more, the internal effect is larger than
the external effect y > 8.

2) The dynamic model. This section deals with fiscal competition between
Europe, America and Asia. At the beginning there is unemployment in each of
the regions. The dynamic model can be characterized by a system of three
equations:


+ 8G 2 1 + 8G 3 1 (4)
Y2 = A 2 + yG2 + SGfl + 8G 3 1 (5)

Y3 = A 3 + yG3 + SGj"1 + 8G 2 ! (6)


According to equation (4), the European government sets European government
purchases so as to reach full employment in Europe, given American government
purchases last period and Asian government purchases last period. According to
equation (5), the American government sets American government purchases so
as to reach full employment in America, given European government purchases
last period and Asian government purchases last period. According to equation
(6), the Asian government sets Asian government purchases so as to reach full
185

employment in Asia, given European government purchases last period and
American government purchases last period.

To summarize, equation (4) shows the policy response in Europe, equation
(5) shows the policy response in America, and equation (6) shows the policy
response in Asia. The endogenous variables are European government purchases
this period, American government purchases this period, and Asian government
purchases this period.

In addition there is an output lag. European output next period is determined
by European government purchases this period, American government purchases
this period, and Asian government purchases this period. Correspondingly,
American output next period is determined by American government purchases
this period, European government purchases this period, and Asian government
purchases this period. By analogy, Asian output next period is determined by
Asian government purchases this period, European government purchases this
period, and American government purchases this period.

3) The steady state. 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), (2) and (3), the model of the steady state can be written as follows:


+ 5AG2 + 8AG3 (7)
AY2 = yAG2 + 5AG2 + 5AG3 (8)
AY3 = yAG3 + 5AG! + 5AG2 (9)


Here AYj is the initial output gap in Europe, AY2 is the initial output gap in
America, and AY3 is the initial output gap in Asia. AGj is the total increase in
European government purchases, AG2 is the total increase in American
government purchases, and AG3 is the total increase in Asian government
purchases. The endogenous variables are AG1? AG2 and AG3.

The solution to the system (7), (8) and (9) is:
186



y2+y8-2S2


(y + 8)AY2 - 8(AY2 + AY3)
Y2+y8-282


(y + 8)AY 3 -8(AY 1 +AY 2 )
A
Y2+Y5-282 (12)
°3=

There is a steady state if and only if y * 8. Owing to the assumption y > 8,
this condition is satisfied. Moreover, the stability condition is y > 28. In other
words, the steady state is stable if and only if the internal effect of fiscal policy y
is larger than the external effect of fiscal policy 28. That means, under low
capital mobility, fiscal competition is a stable process. However, under high
capital mobility, fiscal competition is an unstable process. Put another way,
under low capital mobility, fiscal competition leads to full employment. On the
other hand, under high capital mobility, fiscal competition does not lead to full
employment.




2. Some Numerical Examples



To illustrate the dynamic model, have a look at some numerical examples. It
proves useful to study two distinct cases:
- low capital mobility
- high capital mobility.

1) Low capital mobility. Assume y = 1.33 and 8 = 0.33, for the motivation see
the preceding section. On this assumption the static model can be written as
follows:


Yj = Ax +1.33GJ +0.33G 2 +0.33G 3 (1)
187


Y2 = A 2 +1.33G 2 + 033Gl + 0.33G3 (2)

Y3 = A 3 +1.33G 3 + 0.33G! + 0.33G2 (3)


Obviously, an increase in European government purchases of 100 causes an
increase in European output of 133, an increase in American output of 33, and an
increase in Asian output of equally 33. So the increase in world output is 200.
Further let full-employment output in Europe be 1000, let full-employment
output in America be 1000, and let full-employment output in Asia be equally
1000.

Let initial output in Europe be 940, let initial output in America be 940, and
let initial output in Asia be the same. Step 1 refers to the policy response. The
output gap in Europe is 60. The fiscal policy multiplier in Europe is 1.33. So
what is needed in Europe is an increase in European government purchases of 45.
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. The output gap in Asia is 60. The fiscal policy multiplier in Asia is 1.33.
So what is needed in Asia is an increase in Asian government purchases of 45.

Step 2 refers to the output lag. The increase in European government
purchases of 45 causes an increase in European output of 60. As a side effect, it
causes an increase in American output of 15 and an increase in Asian output of
equally 15. 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 15 and an increase in Asian output of equally 15. The
increase in Asian government purchases of 45 causes an increase in Asian output
of 60. As a side effect, it causes an increase in European output of 15 and an
increase in American output of equally 15. The total effect is an increase in
European output of 90, an increase in American output of 90, and an increase in
Asian output of equally 90. As a consequence, European output goes from 940 to
1030, American output goes from 940 to 1030, and Asian output goes from 940
to 1030. And so on. Table 4.6 gives an overview.

What are the dynamic characteristics of this process? There are damped
oscillations in European government purchases, American government
purchases, and Asian government purchases. Correspondingly, there are damped
188

oscillations in European output, American output, and Asian output. In each
round, in absolute values, the output gap declines by 50 percent. As a result, the
process of fiscal competition leads to full employment. Taking the sum over all
periods, the increase in European government purchases is 30, the increase in
American government purchases is 30, and the increase in Asian government
purchases is equally 30, see equations (10), (11) and (12) in the previous section.
The effective multiplier in Europe is 0.5, the effective multiplier in America is
0.5, and the effective multiplier in Asia is equally 0.5.

Coming to an end, compare the world of three regions with the world of two
regions. In the world of two regions, in each round, the output gap declines by 67
percent. By contrast, in the world of three regions, in each round, the output gap
declines by 50 percent. That is to say, in the world of two regions, fiscal
competition is a relatively fast process. And in the world of three regions, fiscal
competition is a relatively slow process. The underlying reason is that, in the
world of two regions, fiscal spillovers are relatively small. And in the world of
three regions, fiscal spillovers are relatively large.



Table 4.6
Fiscal Competition between Europe, America and Asia
Low Capital Mobility

America Asia
Europe


940 940
Initial Output 940
45 45 45
Change in Government Purchases
1030 1030
Output 1030
Change in Government Purchases -22.5
-22.5 -22.5
985
Output 985 985
and so on
189

2) High capital mobility. Assume y = 0.8 and 5 = 0.6. Evidently, an increase
in European government purchases of 100 causes an increase in European output
of 80, an increase in American output of 60, and an increase in Asian output of
equally 60. So the increase in world output is 200.

Let initial output in Europe be 940, let initial output in America be 940, and
let initial output in Asia be the same. Step 1 refers to the policy response. The
output gap in Europe is 60. The fiscal policy multiplier in Europe is 0.8. So what
is needed in Europe is an increase in European government purchases of 75. The
output gap in America is 60. The fiscal policy multiplier in America is 0.8. So
what is needed in America is an increase in American government purchases of
75. The output gap in Asia is 60. The fiscal policy multiplier in Asia is 0.8. So
what is needed in Asia is an increase in Asian government purchases of 75.

Step 2 refers to the output lag. The increase in European government
purchases of 75 causes an increase in European output of 60. As a side effect, it
causes an increase in American output of 45 and an increase in Asian output of
equally 45. The increase in American government purchases of 75 causes an
increase in American output of 60. As a side effect, it causes an increase in
European output of 45 and an increase in Asian output of equally 45. The
increase in Asian government purchases of 75 causes an increase in Asian output
of 60. As a side effect, it causes an increase in European output of 45 and an
increase in American output of equally 45. The total effect is an increase in
European output of 150, an increase in American output of 150, and an increase
in Asian output of equally 150. As a consequence, European output goes from
940 to 1090, American output goes from 940 to 1090, and Asian output goes
from 940 to 1090. And so on. For a synopsis see Table 4.7.

There are explosive oscillations in European government purchases,
American government purchases, and Asian government purchases.
Correspondingly, there are explosive oscillations in European output, American
output, and Asian output. In each round, in absolute values, the output gap grows
by 50 percent. As a result, the process of fiscal competition does not lead to full
employment. After a few periods, the economy will break down.

3) Comparing high capital mobility with low capital mobility. Under low
capital mobility, fiscal competition leads to full employment. However, under
190

high capital mobility, fiscal competition does not lead to full employment. Under
low capital mobility, there are damped oscillations in government purchases and
output. On the other hand, under high capital mobility, there are explosive
oscillations in government purchases and output.



Table 4.7
Fiscal Competition between Europe, America and Asia
High Capital Mobility

Asia
Europe America


Initial Output 940 940 940
75
Change in Government Purchases 75
75
1090
Output 1090 1090
Change in Government Purchases -112.5
-112.5
-112.5
865 865
Output 865
and so on ...
Chapter 5
Fiscal Competition: Gradualist Policies


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, America and Asia. To be
more specific, we assume high capital mobility, see Chapter 4 above. As a point
of reference, consider the static model. It can be represented by a system of three
equations:


Yx = Ax + 0.8G! + 0.6G2 + 0.6G3 (1)
Y2 = A 2 + 0.8G2 + 0.6G! + 0.6G3 (2)
Y3 = A 3 + 0.8G3 + 0.6G! + 0.6G2 (3)


Obviously, an increase in European government purchases of 100 causes an
increase in European output of 80, an increase in American output of 60, and an
increase in Asian output of equally 60. Further let full-employment output in
Europe be 1000, let full-employment output in America be 1000, and let full-
employment output in Asia be the same.

At the start there is unemployment in each of the regions. 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 Xi. 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. The general target of the Asian government is full employment in
Asia. We assume that the Asian government follows a gradualist strategy. The
specific target of the Asian government is to close the output gap in Asia by the
fraction X3. Under a gradualist strategy, does fiscal competition lead to full
employment?
192



We assume Xj = A,2 = X3 = 0.6. That means, the governments close the output
gaps by 60 percent. Let initial output in Europe be 940, let initial output in
America be 940, and let initial output in Asia 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
0.8. So what is needed in Europe is an increase in European government
purchases of 45. 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 0.8. So what is needed in America is an increase in American
government purchases of 45. Third consider fiscal policy in Asia. The output gap
in Asia is 60. The specific target of the Asian government is to close the output
gap in Asia by 60 percent, that is by 36. The fiscal policy multiplier in Asia is
0.8. So what is needed in Asia is an increase in Asian government purchases of
45.

Step 2 refers to the output lag. The increase in European government
purchases of 45 causes an increase in European output of 36. As a side effect, it
causes an increase in American output of 27 and an increase in Asian output of
equally 27. The increase in American government purchases of 45 causes an
increase in American output of 36. As a side effect, it causes an increase in
European output of 27 and an increase in Asian output of equally 27. The
increase in Asian government purchases of 45 causes an increase in Asian output
of 36. As a side effect, it causes an increase in European output of 27 and an
increase in American output of equally 27. The total effect is an increase in
European output of 90, an increase in American output of 90, and an increase in
Asian output of equally 90. As a consequence, European output goes from 940 to
1030, American output goes from 940 to 1030, and Asian output goes from 940
to 1030.

Step 3 refers to the policy response. First consider fiscal policy in Europe.
The inflationary gap in Europe is 30. The specific target of the European
government is to close the inflationary gap in Europe by 60 percent, that is by 18.
The fiscal policy multiplier in Europe is 0.8. So what is needed in Europe is a
reduction in European government purchases of 22.5. Second consider fiscal
193

policy in America. The inflationary gap in America is 30. The specific target of
the American government is to close the inflationary gap in America by 60
percent, that is by 18. The fiscal policy multiplier in America is 0.8. So what is
needed in America is a reduction in American government purchases of 22.5.
Third consider fiscal policy in Asia. The inflationary gap in Asia is 30. The
specific target of the Asian government is to close the inflationary gap in Asia by
60 percent, that is by 18. The fiscal policy multiplier in Asia is 0.8. So what is
needed in Asia is a reduction in Asian government purchases of 22.5.

Step 4 refers to the output lag. The reduction in European government
purchases of 22.5 causes a decline in European output of 18. As a side effect, it
causes a decline in American output of 13.5 and a decline in Asian output of
equally 13.5. The reduction in American government purchases of 22.5 causes a
decline in American output of 18. As a side effect, it causes a decline in
European output of 13.5 and a decline in Asian output of equally 13.5. The
reduction in Asian government purchases of 22.5 causes a decline in Asian
output of 18. As a side effect, it causes a decline in European output of 13.5 and
a decline in American output of equally 13.5. The total effect is a decline in
European output of 45, a decline in American output of 45, and a decline in
Asian output of equally 45. As a consequence, European output goes from 1030
to 985, American output goes from 1030 to 985, and Asian output goes from
1030 to 985. And so on. For an overview see Table 4.8.

What are the dynamic characteristics of this process? There are damped
oscillations in government purchases. Correspondingly, there are damped
oscillations in output. In each round, in absolute values, the output gap declines
by 50 percent. As a result, the process of fiscal competition leads to full
employment.

Coming to an end, compare the gradualist strategy with the cold-turkey
strategy. Under the cold-turkey strategy, in each round, the output gap grows by
50 percent. By contrast, under the gradualist strategy, in each round, the output
gap declines by 50 percent. Under the cold-turkey strategy, fiscal competition is
an unstable process. However, under the gradualist strategy, fiscal competition is
a stable process. That is to say, under the cold-turkey strategy, fiscal competition
does not lead to full employment. On the other hand, under the gradualist
strategy, fiscal competition does lead to full employment. Judging from these
194

points of view, the gradualist strategy seems to be superior to the cold-turkey
strategy.



Table 4.8
Fiscal Competition between Europe, America and Asia
Gradualist Policies

Europe America Asia


Initial Output 940 940 940
Change in Government Purchases 45 45 45
Output 1030 1030 1030
Change in Government Purchases -22.5 -22.5
-22.5
985
Output 985 985
and so on
Chapter 6
Fiscal Cooperation: Perfect Capital Mobility


This chapter deals with fiscal cooperation between Europe, America and
Asia. In this chapter we assume perfect capital mobility. At the beginning there is
unemployment in each of the regions. The targets of fiscal cooperation are full
employment in Europe, full employment in America, and full employment in
Asia. The instruments of fiscal cooperation are European government purchases,
American government purchases, and Asian government purchases. So there are
three targets and three instruments.

The policy model can be represented by a system of three equations:


Y1=A1+YG1+YG2+YG3 (1)

Y2 = A 2 +7G2+7G 1 +7G 3 (2)
Y 3 =A 3 +'yG3+'yG 1 +'yG 2 (3)


Here Yj denotes full-employment output in Europe, Y2 is full-employment
output in America, and Y3 is full-employment output in Asia. Gj denotes the
required level of European government purchases, G 2 is the required level of
American government purchases, and G 3 is the required level of Asian
government purchases.

Now take differences between equations (1), (2) and (3) to reach:


Y1-Y2=A1-A2 (4)
Y1-Y3=A1-A3 (5)
Y2-Y3=A2-A3 (6)


However, this is in direct contradiction to the assumption that Yl, Y2, Y3, Ah
A 2 and A 3 are given independently. As a result, there is no solution to fiscal
196

cooperation. In other words, fiscal cooperation between Europe, America and
Asia cannot achieve full employment in each of the regions. The underlying
reason is the large external effect of fiscal policy.
Chapter 7
Fiscal Cooperation: Imperfect Capital Mobility
1. The Model


This chapter deals with fiscal cooperation between Europe, America and
Asia. In this chapter we assume imperfect capital mobility. At the start there is
unemployment in each of the regions. The targets of fiscal cooperation are full
employment in Europe, full employment in America, and full employment in
Asia. The instruments of fiscal cooperation are European government purchases,
American government purchases, and Asian government purchases. So there are
three targets and three instruments.

The policy model can be stated in terms of the initial output gap and the
required increase in government purchases:


+ 5AG2 + 5AG3 (1)
AY2 = yAG2 + 5AGX + 5AG3 (2)
AY3 = yAG3 + SAGj + 5AG2 (3)


Here AY1 denotes the initial output gap in Europe, AY2 is the initial output gap in
America, and AY3 is the initial output gap in Asia. AGi denotes the required
increase in European government purchases, AG2 is the required increase in
American government purchases, and AG3 is the required increase in Asian
government purchases. The endogenous variables are AGl5 AG2 and AG3.

The solution to the system (1), (2) and (3) is:


^(Y+5)AY1-5(AY2+AY3)
AG
1
252
198

(Y+S)AY 2 -S(AY 1 +AY 3 )
˜ 9 e T^O
2 2
Y +y5-28


2 2
Y +§25


There is a solution if and only if y ^ 8 . Owing to the assumption y > 5 , this
condition is fulfilled. As a result, fiscal cooperation between Europe, America
and Asia can achieve full employment in each of the regions.

According to equation (4), the required increase in European government
purchases depends on the initial output gap in Europe, the initial output gap in
America, the initial output gap in Asia, the direct multiplier y, and the cross
multiplier 8. The larger the initial output gap in Europe, the larger is the required
increase in European government purchases. Moreover, the larger the initial
output gap in America or Asia, the smaller is the required increase in European
government purchases. According to equation (5), the required increase in
American government purchases depends on the initial output gap in America,
the initial output gap in Europe, the initial output gap in Asia, the direct
multiplier, and the cross multiplier. According to equation (6), the required
increase in Asian government purchases depends on the initial output gap in
Asia, the initial output gap in Europe, the initial output gap in America, the direct
multiplier, and the cross multiplier.

Finally compare fiscal cooperation with fiscal competition. Fiscal competition
can achieve full employment, provided capital mobility is sufficiently low. By
contrast, fiscal cooperation can achieve full employment in any case.




2. Some Numerical Examples


To illustrate the policy model, have a look at some numerical examples. It
proves useful to consider three distinct cases:
199


- low capital mobility: the regions have the same unemployment
- low capital mobility: the regions differ in unemployment
- high capital mobility.

1) Low capital mobility: The regions have the same unemployment. For ease
of exposition, without losing generality, assume y = 1.33 and 8 = 0.33. Let initial
output in Europe be 940, let initial output in America be 940, and let initial
output in Asia be the same. In other words, the output gap in Europe is 60, the
output gap in America is 60, and the output gap in Asia is the same. What is
needed, according to equations (4), (5) and (6) from the preceding section, is an
increase in European government purchases of 30, an increase in American
government purchases of 30, and an increase in Asian government purchases of
equally 30.

The increase in European government purchases of 30 raises European output
by 40. In addition, it raises American output and Asian output by 10 each. The
increase in American government purchases of 30 raises American output by 40.
In addition, it raises European output and Asian output by 10 each. The increase
in Asian government purchases of 30 raises Asian output by 40. In addition, it
raises European output and American output by 10 each. The total effect is an
increase in European output of 60, an increase in American output of 60, and an
increase in Asian output of equally 60. As a consequence, European output goes
from 940 to 1000, American output goes from 940 to 1000, and Asian output
goes from 940 to 1000. As a result, fiscal cooperation can achieve full
employment. Table 4.9 presents a synopsis.

Table 4.9
Fiscal Cooperation between Europe, America and Asia
Low Capital Mobility

Europe America Asia


940
Initial Output 940 940
Change in Government Purchases 30 30 30
Output 1000 1000 1000
200


2) Low capital mobility: The regions differ in unemployment. Let initial
output in Europe be 940, let initial output in America be 950, and let initial
output in Asia be 970. In other words, the output gap in Europe is 60, the output
gap in America is 50, and the output gap in Asia is 30. What is needed, according
to equations (4), (5) and (6) from the previous section, is an increase in European
government purchases of 36.7, an increase in American government purchases of
26.7, and an increase in Asian government purchases of 6.7

The increase in European government purchases of 36.7 raises European
output by 48.9. In addition, it raises American output and Asian output by 12.2
each. The increase in American government purchases of 26.7 raises American
output by 35.6. In addition, it raises European output and Asian output by 8.9
each. The increase in Asian government purchases of 6.7 raises Asian output by
8.9. In addition, it raises European output and American output by 2.2 each. The
total effect is an increase in European output of 60, an increase in American
output of 50, and an increase in Asian output of 30. As a consequence, European
output goes from 940 to 1000, American output goes from 950 to 1000, and
Asian output goes from 970 to 1000.



Table 4.10
Fiscal Cooperation between Europe, America and Asia
Low Capital Mobility

Europe America Asia


Initial Output 940 950 970
Change in Government Purchases 6.7
36.7 26.7
Output 1000 1000 1000




As a result, fiscal cooperation can achieve full employment. The required
increase in government purchases is small, as compared to the initial output gap.
The effective multiplier in Europe is 1.6, the effective multiplier in America is
1.9, and the effective multiplier in Asia is 4.5. Table 4.10 gives an overview.
201



3) High capital mobility. Assume y = 0.8 and 5 = 0.6. That means, the
internal effect of fiscal policy y is smaller than the external effect of fiscal policy
25. Let initial output in Europe be 940, let initial output in America be 950, and
let initial output in Asia be 970. In other words, the output gap in Europe is 60,
the output gap in America is 50, and the output gap in Asia is 30. What is
needed, according to equations (4), (5) and (6) from the preceding section, is an
increase in European government purchases of 90, an increase in American
government purchases of 40, and a reduction in Asian government purchases of
60.

The increase in European government purchases of 90 raises European output
by 72. In addition, it raises American output and Asian output by 54 each. The
increase in American government purchases of 40 raises American output by 32.
In addition, it raises European output and Asian output by 24 each. The reduction
in Asian government purchases of 60 lowers Asian output by 48. In addition, it
lowers European output and American output by 36 each. The net effect is an
increase in European output of 60, an increase in American output of 50, and an
increase in Asian output of 30. As a consequence, European output goes from
940 to 1000, American output goes from 950 to 1000, and Asian output goes
from 970 to 1000.

As a result, fiscal cooperation can achieve full employment. The required
increase in European government purchases is very large, as compared to the
initial output gap in Europe. The required increase in American government
purchases is large, as compared to the initial output gap in America. And the
required cut in Asian government purchases has the wrong sign, as compared to
the initial output gap in Asia. The effective multiplier in Europe is 0.67, the
effective multiplier in America is 1.25, and the effective multiplier in Asia is
-0.5. For a synopsis see Table 4.11.
202


Table 4.11
Fiscal Cooperation between Europe, America and Asia
High Capital Mobility

Europe America Asia


Initial Output 970
940 950
Change in Government Purchases 40
90 -60
1000
Output 1000 1000
Part Five


The World of
N Monetary Regions
Chapter 1
The World of Four Monetary Regions
1. Monetary Competition between Four Regions



The world consists of four monetary regions, say Europe, America, Asia and
Africa. We assume that the monetary regions are the same size and have the
same behavioural functions. Here the focus is on monetary competition between
Europe, America, Asia and Africa. Besides we assume perfect capital mobility.
As a point of departure, take the static model. It can be represented by a system
of four equations:


Yx = Ax +3.5M! -0.5(M 2 + M 3 + M 4 ) (1)
Y2 = A 2 + 3.5M2 -0.5(M! + M 3 + M 4 ) (2)
Y3 = A 3 +3.5M 3 -0.5(M! + M 2 + M 4 ) (3)
Y4 = A 4 + 3.5M4 -0.5(M! + M 2 +M 3 ) (4)


Subscript 1 denotes Europe, subscript 2 denotes America, subscript 3 denotes
Asia, and subscript 4 denotes Africa. According to equation (1), European output
Yj is determined by European money supply M1? American money supply M 2 ,
Asian money supply M 3 , and African money supply M 4 . An increase in
European money supply of 100 raises European output by 350. On the other
hand, it lowers American output, Asian output, and African output by 50 each.
Adding up, it raises world output by 200. Further let full-employment output in
each of the regions be 1000. This model is in the tradition of the Mundell-
Fleming model, see Carlberg (2000) p. 213.

At the beginning there is unemployment in each of the regions. The target of
the European central bank is full employment in Europe. The target of the
American central bank is full employment in America. The target of the Asian
central bank is full employment in Asia. And the target of the African central
206

bank is full employment in Africa. We assume that the central banks decide
simultaneously and independently.

Let initial output in each of the regions be 940. Step 1 refers to the policy
response. The output gap in Europe is 60. The monetary policy multiplier in
Europe is 3.5. So what is needed in Europe is an increase in European money
supply of 17.1. The output gap in America is 60. The monetary policy multiplier
in America is 3.5. So what is needed in America is an increase in American
money supply of 17.1. And so on.

Step 2 refers to the output lag. The increase in European money supply of
17.1 causes an increase in European output of 60. As a side effect, it causes a
decline in American output of 8.6, a decline in Asian output of 8.6, and a decline
in African output of equally 8.6. The increase in American money supply of 17.1
causes an increase in American output of 60. As a side effect, it causes a decline
in European output of 8.6, a decline in Asian output of 8.6, and a decline in
African output of equally 8.6. And so on. The net effect is an increase in
European output of 34.3, an increase in American output of 34.3, an increase in
Asian output of 34.3, and an increase in African output of 34.3. As a
consequence, European output goes from 940 to 974.3, American output goes
from 940 to 974.3, Asian output goes from 940 to 974.3, and African output goes
from 940 to 974.3.

Step 3 refers to the policy response. The output gap in Europe is 25.7. The
monetary policy multiplier in Europe is 3.5. So what is needed in Europe is an
increase in European money supply of 7.3. Step 4 refers to the output lag. The
increase in European money supply of 7.3 causes an increase in European output
of 25.7. As a side effect, it causes a decline in American output of 3.7, a decline
in Asian output of 3.7, and a decline in African output of equally 3.7. The net
effect is an increase in European output of 14.7. As a consequence, European
output goes from 974.3 to 989.0. And so on. Table 5.1 presents a synopsis. There
are repeated increases in money supply and output. In each round, the output gap
declines by 57 percent.
207


Table 5.1
Monetary Competition between Four Regions

Africa
America Asia
Europe


Initial Output 940 940
940 940
A Money Supply 17.1 17.1 17.1
17.1
974.3 974.3
Output 974.3 974.3
A Money Supply 7.3 7.3
7.3 7.3
989.0 989.0
Output 989.0
989.0
and so on




2. Fiscal Competition between Four Regions:
Perfect Capital Mobility



The world consists of four monetary regions, say Europe, America, Asia and
Africa. We assume that the monetary regions are the same size and have the
same behavioural functions. Here the focus is on fiscal competition between
Europe, America, Asia and Africa. Besides we assume perfect capital mobility.
As a point of departure, take the static model. It can be represented by a system
of four equations:


Yx = Ax + 0.5(0! + G 2 + G 3 + G 4 ) (1)
Y2 = A 2 + 0.5(G! + G 2 + G 3 + G 4 ) (2)
Y3 = A 3 + 0.5(Gi + G 2 + G 3 + G 4 ) (3)
Y4 = A 4 + 0.5(G! + G 2 + G 3 + G 4 ) (4)
208

According to equation (1), European output Yx is determined by European
government purchases G l5 American government purchases G 2 , Asian
government purchases G 3 , and African government purchases G 4 . An increase
in European government purchases of 100 raises European output, American
output, Asian output, and African output by 50 each. Adding up, it raises world
output by 200. Further let full-employment output in each of the regions be 1000.
This model is in the tradition of the Mundell-Fleming model, see Carlberg (2000)
p. 213.

At the beginning there is unemployment in each of the regions. The target of
the European government is full employment in Europe. The target of the
American government is full employment in America. The target of the Asian
government is full employment in Asia. And the target of the African
government is full employment in Africa. We assume that the governments
decide simultaneously and independently.

Let initial output in each of the regions be 970. Step 1 refers to the policy
response. The output gap in Europe is 30. The fiscal policy multiplier in Europe
is 0.5. So what is needed in Europe is an increase in European government
purchases of 60. The output gap in America is 30. The fiscal policy multiplier in
America is 0.5. So what is needed in America is an increase in American
government purchases of 60. And so on.

Step 2 refers to the output lag. The increase in European government
purchases of 60 causes an increase in European output of 30. As a side effect, it
causes an increase in American output of 30, an increase in Asian output of 30,
and an increase in African output of equally 30. The increase in American
government purchases of 60 causes an increase in American output of 30. As a
side effect, it causes an increase in European output of 30, an increase in Asian
output of 30, and an increase in African output of equally 30. And so on. The
total effect is an increase in European output of 120, an increase in American
output of 120, an increase in Asian output of 120, and an increase in African
output of equally 120. As a consequence, European output goes from 970 to
1090, American output goes from 970 to 1090, Asian output goes from 970 to
1090, and African output goes from 970 to 1090.
209

Step 3 refers to the policy response. The inflationary gap in Europe is 90. The
fiscal policy multiplier in Europe is 0.5. So what is needed in Europe is a
reduction in European government purchases of 180. Step 4 refers to the output
lag. The reduction in European government purchases of 180 causes a decline in
European output of 90. As a side effect, it causes a decline in American output of
90, a decline in Asian output of 90, and a decline in African output of equally 90.
The total effect is a decline in European output of 360. As a consequence,
European output goes from 1090 to 730. And so on. Table 5.2 gives an overview.
There are explosive oscillations in government purchases and output. In each
round, in absolute values, the output gap grows by a factor of 3.



Table 5.2
Fiscal Competition between Four Regions
Perfect Capital Mobility

Africa
Europe America Asia


Initial Output 970 970 970 970
A Government Purchases 60 60
60 60
Output 1090 1090 1090
1090
A Government Purchases -180 -180 -180 -180
730 730 730 730
Output
and so on
210

3. Fiscal Competition between Four Regions:
Imperfect Capital Mobility



Under perfect capital mobility, an increase in European government
purchases of 100 raises European output, American output, Asian output, and
African output by 50 each. Under zero capital mobility, an increase in European
government purchases of 100 raises European output by 200. On the other hand,
it has no effect on American output, Asian output, and African output. On this
basis we assume that, under imperfect capital mobility, an increase in European
government purchases of 100 raises European output by 125. In addition, it raises
American output, Asian output, and African output by 25 each.

The static model can be written in the following way:


+0.25(G 2 +G 3 + G 4 ) (1)
Y2 = A 2 +1.25G 2 + 0.25(G! + G 3 + G 4 ) (2)
Y3 = A 3 +1.25G 3 + 0.25(Gi + G 2 + G 4 ) (3)
Y4 = A 4 +1.25G 4 + 0.25(G! + G 2 + G 3 ) (4)


Let initial output in each of the regions be 940. Step 1 refers to the policy
response. The output gap in Europe is 60. The fiscal policy multiplier in Europe
is 1.25. So what is needed in Europe is an increase in European government
purchases of 48. The output gap in America is 60. The fiscal policy multiplier in
America is 1.25. So what is needed in America is an increase in American
government purchases of 48. And so on.

Step 2 refers to the output lag. The increase in European government
purchases of 48 causes an increase in European output of 60. As a side effect, it
causes an increase in American output of 12, an increase in Asian output of 12,
and an increase in African output of equally 12. The increase in American
government purchases of 48 causes an increase in American output of 60. As a
side effect, it causes an increase in European output of 12, an increase in Asian
output of 12, and an increase in African output of equally 12. And so on. The
211

total effect is an increase in European output of 96, an increase in American
output of 96, an increase in Asian output of 96, and an increase in African output
of equally 96. As a consequence, European output goes from 940 to 1036,
American output goes from 940 to 1036, Asian output goes from 940 to 1036,
and African output goes from 940 to 1036.

Step 3 refers to the policy response. The inflationary gap in Europe is 36. The
fiscal policy multiplier in Europe is 1.25. So what is needed in Europe is a
reduction in European government purchases of 28.8. Step 4 refers to the output
lag. The reduction in European government purchases of 28.8 causes a decline in
European output of 36. As a side effect, it causes a decline in American output of
7.2, a decline in Asian output of 7.2, and a decline in African output of equally
7.2. The total effect is a decline in European output of 57.6. As a consequence,
European output goes from 1036 to 978.4. And so on. For a synopsis see Table
5.3. There are damped oscillations in government purchases and output. In each
round, in absolute values, the output gap declines by 40 percent.



Table 5.3
Fiscal Competition between Four Regions
Imperfect Capital Mobility

Africa
Europe America Asia


Initial Output 940 940 940
940
A Government Purchases 48 48 48 48
Output 1036 1036 1036
1036
A Government Purchases -28.8 -28.8 -28.8
-28.8
978.4 978.4 978.4
Output 978.4
and so on
Chapter 2
The World of Ten Monetary Regions


1) Monetary competition between ten regions. We assume that the regions are
the same size and have the same behavioural functions. Besides we assume
perfect capital mobility. Now consider one of the regions, let us say Japan. As a
result, an increase in Japanese money supply of 100 causes an increase in
Japanese output of 380. On the other hand, it causes a decline in rest-of-the-
world output of 180. So the increase in world output is 200. For the model see
Carlberg (2000) p. 217. Further let full-employment output in each of the regions
be 1000.

Let initial output in each of the regions be 940. Step 1 refers to the policy
response. The output gap in Japan is 60. The monetary policy multiplier in Japan
is 3.8. So what is needed in Japan is an increase in Japanese money supply of
15.8. Step 2 refers to the output lag. The increase in Japanese money supply of
15.8 causes an increase in Japanese output of 60. As a side effect, it causes a
decline in rest-of-the-world output of 28.4. The net effect is an increase in
Japanese output of 31.6. As a consequence, Japanese output goes from 940 to
971.6. And so on. Table 5.4 presents a synopsis. In each round, the output gap
declines by 53 percent.

2) Fiscal competition between ten regions: perfect capital mobility. An
increase in Japanese government purchases of 100 causes an increase in Japanese
output of 20. In addition, it causes an increase in rest-of-the-world output of 180.
So the increase in world output is 200.

Let initial output in each of the regions be 970. Step 1 refers to the policy
response. The output gap in Japan is 30. The fiscal policy multiplier in Japan is
0.2. So what is needed in Japan is an increase in Japanese government purchases
of 150. Step 2 refers to the output lag. The increase in Japanese government
purchases of 150 causes an increase in Japanese output of 30. As a side effect, it
causes an increase in rest-of-the-world output of 270. The total effect is an
increase in Japanese output of 300. As a consequence, Japanese output goes from
213

970 to 1270. And so on. Table 5.5 gives an overview. In each round, in absolute
values, the output gap grows by a factor of 9.



Table 5.4
Monetary Competition between Ten Regions

Region 1 Region 2


Initial Output 940 940
Change in Money Supply 15.8 15.8
Output 971.6 971.6
Change in Money Supply 7.5 7.5
Output 986.5 986.5
and so on ... ...




Table 5.5
Fiscal Competition between Ten Regions
Perfect Capital Mobility

Region 1 Region 2


Initial Output 970 970
Change in Government Purchases 150 150
Output 1270
1270
Change in Government Purchases -1350
-1350
Output 0 0
and so on
214

3) Fiscal competition between ten regions: imperfect capital mobility. Under
perfect capital mobility, an increase in Japanese government purchases of 100
causes an increase in Japanese output of 20. In addition, it causes an increase in
rest-of-the-world output of 180. Under zero capital mobility, an increase in
Japanese government purchases of 100 causes an increase in Japanese output of
200. On the other hand, it has no effect on output in the rest of the world. On this
basis we assume that, under imperfect capital mobility, an increase in Japanese
government purchases of 100 causes an increase in Japanese output of 110. In
addition, it causes an increase in rest-of-the-world output of 90.

Let initial output in each of the regions be 940. Step 1 refers to the policy
response. The output gap in Japan is 60. The fiscal policy multiplier in Japan is
1.1. So what is needed in Japan is an increase in Japanese government purchases
of 54.5. Step 2 refers to the output lag. The increase in Japanese government
purchases of 54.5 causes an increase in Japanese output of 60. As a side effect, it
causes an increase in rest-of-the-world output of 49.1. The total effect is an
increase in Japanese output of 109.1. As a consequence, Japanese output goes
from 940 to 1049.1. And so on. For a synopsis see Table 5.6. In each round, in
absolute values, the output gap declines by 18 percent.



Table 5.6
Fiscal Competition between Ten Regions
Imperfect Capital Mobility

Region 2
Region 1


940
Initial Output 940
54.5
Change in Government Purchases 54.5
1049.1
Output 1049.1
Change in Government Purchases -44.6
-44.6
959.8
Output 959.8
and so on
Chapter 3
Synopsis


1) Monetary competition. Table 5.7 gives an overview. In a world of a few
large regions, monetary competition is a relatively fast process. On the other
hand, in a world of many small regions, monetary competition is a relatively
slow process. The reason for this is that in a world of a few large regions,
monetary spillovers are relatively small. On the other hand, in a world of many
small regions, monetary spillovers are relatively large. As a consequence, in a
world of a few large regions, unemployment (or for that matter inflation) will be
relatively low. On the other hand, in a world of many small regions,
unemployment will be relatively high.



Table 5.7
Monetary Competition: A Synopsis


In Each Round,
the Gap Declines by



World of 2 Regions 67%
World of 3 Regions 60%
World of 4 Regions 57%
World of 10 Regions 53%
World of °° Regions 50%
216

2) Fiscal competition: perfect capital mobility. Table 5.8 presents a synopsis.
In a world of two large regions, fiscal competition causes uniform oscillations in
output. However, in a world of many small regions, fiscal competition causes
explosive oscillations in output. The reason for this is that in a world of two large
regions, fiscal spillovers are very large. However, in a world of many small
regions, fiscal spillovers are extremely large.



Table 5.8
Fiscal Competition: Perfect Capital Mobility


In Each Round,
the Gap Grows
by a Factor of


World of 2 Regions 1
World of 3 Regions 2
World of 4 Regions 3
World of 10 Regions 9
217

3) Fiscal competition: imperfect capital mobility. Table 5.9 gives an
overview. Under imperfect capital mobility, fiscal competition causes damped
oscillations in output. In a world of a few large regions, fiscal competition is a
relatively fast process. On the other hand, in a world of many small regions,
fiscal competition is a relatively slow process. The reason for this is that in a
world of a few large regions, fiscal spillovers are relatively small. On the other
hand, in a world of many small regions, fiscal spillovers are relatively large.



Table 5.9
Fiscal Competition: Imperfect Capital Mobility


In Each Round,
the Gap Declines by



World of 2 Regions 67 %
World of 3 Regions 50 %
World of 4 Regions 40 %
World of 10 Regions 18%
Part Six


Rational
Policy Expectations
Chapter 1
Rational Policy Expectations
in Europe and America
1. Monetary Competition between Europe and America


1) The static model. The world consists of two monetary regions, say Europe
and America. We assume that the monetary regions are the same size and have
the same behavioural functions. As a point of reference, consider the static
model. It can be represented by a system of two equations:


Y1=A1+aM1-(3M2 (1)
Y2=A2+aM2-|3M1 (2)

According to equation (1), European output is determined by European money
supply and American money supply. According to equation (2), American output
is determined by American money supply and European money supply, a and (3
are positive coefficients with 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 target of the American central bank is full employment in America.
The instrument of the American central bank is American money supply. We
assume that the European central bank and the American central bank decide
simultaneously and independently. The European central bank sets European
money supply, forming rational expectations of American money supply. And
the American central bank sets American money supply, forming rational
expectations of European money supply.

On this basis, the dynamic model can be characterized by a system of four
equations:
222




^M^ (3)
Y2=A2+aM2-(3Mf (4)
Mf=Mi (5)
M | = M2 (6)


Here is a list of the new symbols:
Yt full-employment output in Europe
Y2 full-employment output in America
Mf the expectation of European money supply,
as formed by the American central bank
M 2 the expectation of American money supply,
as formed by the European central bank
M1 European money supply,
as set by the European central bank
M 2 American money supply,
as set by the American central bank.

According to equation (3), the European central bank sets European money
supply, forming an expectation of American money supply. According to
equation (4), the American central bank sets American money supply, forming an
expectation of European money supply. According to equation (5), the
expectation of European money supply is equal to the forecast made by means of
the model. According to equation (6), the expectation of American money supply
is equal to the forecast made by means of the model. That is to say, the European
central bank sets European money supply, predicting American money supply
with the help of the model. And the American central bank sets American money
supply, predicting European money supply with the help of the model. The
endogenous variables are European money supply Mj, American money supply
M 2 , the expectation of European money supply Mf, and the expectation of
American money supply M | .

The dynamic model can be compressed to a system of two equations:
223


Y1=A1+aM1˜PM2 (7)
Y2=A2+aM2-(3M1 (8)

Here the endogenous variables are European money supply M^ and American
money supply M 2 . To simplify notation we introduce B ^ Y J - A J and
B 2 = Y2 - A 2 . Then we solve the model for the endogenous variables:




Equation (9) shows the equilibrium level of European money supply, and
equation (10) shows the equilibrium level of American money supply. There is a
solution if and only if a ^ p . This condition is fulfilled. As a result, under
rational expectations, there is an immediate equilibrium of monetary competition
between Europe and America. In other words, under rational expectations,
monetary competition between Europe and America leads to full employment
immediately. It is worth pointing out here that the equilibrium under rational
expectations is identical to the steady state under adaptive expectations, see
Chapter 1 of Part One.

As an alternative, the dynamic model can be stated in terms of the initial
output gap and the required increase in money supply:


AY 1 =aAM 1 -pAM 2 (11)
AY 2 =aAM 2 -PAM 1 (12)

Here AY^ denotes the initial output gap in Europe, AY2 is the initial output gap in
America, AMj is the required increase in European money supply, and AM2 is
the required increase in American money supply. The endogenous variables are
and AM 2 . The equilibrium of the system (11) and (12) is:
224


ccAYi + (3AY2
a2 2
-P
aAY;; +PA Yl
a2-(

3) A numerical example. To illustrate the dynamic model, have a look at a
numerical example. For ease of exposition, without loss of generality, assume
a = 3 and (3 = 1. On this assumption, the static model can be written as follows:


Y1=A1+3M1-M2 (15)
Y2=A2+3M2-M1 (16)

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. Further let full-
employment output in Europe be 1000, and let full-employment output in
America be the same.

Let initial output in Europe be 940, and let initial output in America be 970.
That means, the output gap in Europe is 60, and the output gap in America is 30.
What is needed in Europe, according to equation (13), is an increase in European
money supply of 26.25. And what is needed in America, according to equation
(14), is an increase in American money supply of 18.75. The increase in
European money supply of 26.25 raises European output by 78.75 and lowers
American output by 26.25. The increase in American money supply of 18.75
raises American output by 56.25 and lowers European output by 18.75. The net
effect is an increase in European output of 60 and an increase in American output
of 30. As a consequence, European output goes from 940 to 1000, and American
output goes from 970 to 1000. In Europe there is now full employment, and the
same holds for America. As a result, under rational expectations, monetary
competition leads to full employment immediately. Table 6.1 presents a synopsis.
225


Table 6.1
Monetary Competition between Europe and America
Rational Policy Expectations

Europe America


970
Initial Output 940
Change in Money Supply 26.25 18.75
1000 1000
Output




4) A comment. The European central bank closely observes the measures
taken by the American central bank. And what is more, the European central
bank can respond immediately to the measures taken by the American central
bank. The other way round, the American central bank closely observes the
measures taken by the European central bank. And what is more, the American
central bank can respond immediately to the measures taken by the European
central bank. Therefore rational policy expectations seem not to be very
important.




2. Fiscal Competition: Perfect Capital Mobility



1) The static model. The world consists of two monetary regions, say Europe
and America. We assume that the monetary regions are the same size and have
the same behavioural functions. 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:


(1)
226


Y2=A2+YG2+YG1 (2)

According to equation (1), European output is determined by European
government purchases and American government purchases. According to
equation (2), American output is determined by American government purchases
and European government purchases, y is a positive coefficient. The endogenous
variables are European output and American output.

2) The dynamic model. This section deals with fiscal competition between
Europe and America. At the beginning there is unemployment in each of the
regions. The target of the European government is full employment in Europe.
The instrument of the European government is European government purchases.
The target of the American government is full employment in America. The
instrument of the American government is American government purchases. We
assume that the European government and the American government decide
simultaneously and independently. The European government sets European
government purchases, forming rational expectations of American government
purchases. And the American government sets American government purchases,
forming rational expectations of European government purchases.

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


yGf (3)
Y 2 =A 2 + Y G 2 +YGf (4)
Gf = G! (5)
G|=G2 (6)

Here is a list of the new symbols:
Yj full-employment output in Europe
Y2 full-employment output in America
Gf the expectation of European government purchases,
as formed by the American government
G2 the expectation of American government purchases,
as formed by the European government
227


Gj European government purchases,
as set by the European government
G2 American government purchases,
as set by the American government.

According to equation (3), the European government sets European
government purchases, forming an expectation of American government
purchases. According to equation (4), the American government sets American
government purchases, forming an expectation of European government
purchases. According to equation (5), the expectation of European government
purchases is equal to the forecast made by means of the model. According to
equation (6), the expectation of American government purchases is equal to the
forecast made by means of the model. That is to say, the European government
sets European government purchases, predicting American government
purchases with the help of the model. And the American government sets
American government purchases, predicting European government purchases
with the help of the model. The endogenous variables are European government
purchases G^, American government purchases G 2 , the expectation of European

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