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2. Monetary Competition between Europe and America

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

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

According to equation (1), European output Yx is determined by European
money supply Mj and by some other factors called A^. According to equation
(2), American output Y2 is determined by American money supply M 2 and by
some other factors called A 2 .

In the numerical example, an increase in European money supply of 100
causes an increase in European output of 200 and a decline in American output
of zero. Correspondingly, an increase in American money supply of 100 causes
an increase in American output of 200 and a decline in European output of zero.
Further let full-employment output in Europe be 1000, and let full-employment
output in America be the same. For the model see Carlberg (1999) p. 185.

At the start there is unemployment in both Europe and America. The target of
the European central bank is full employment in Europe. The target of the
American central bank is full employment in America. Let initial output in
Europe be 940, and let initial output in America be 970. Step 1 refers to the
policy response. The output gap in Europe is 60. The monetary policy multiplier
in Europe is 2. So what is needed in Europe is an increase in European money
supply of 30. The output gap in America is 30. The monetary policy multiplier in
America is 2. So what is needed in America is an increase in American money
supply of 15.

Step 2 refers to the output lag. The increase in European money supply of 30
causes an increase in European output of 60. There is no side effect on American
output. The increase in American money supply of 15 causes an increase in
American output of 30. There is no side effect on European output. As a
70

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 applies
to America. Table 2.2 gives an overview.

Table 2.2
Monetary Competition between Europe and America
Zero Capital Mobility

Europe America

Initial Output 940 970
30 15
Change in Money Supply
Output 1000 1000

What are the dynamic characteristics of this process? There is a one-step
increase in European money supply, as there is in American money supply.
There is a one-step increase in European output, as there is in American output.
To sum up, under zero capital mobility, monetary competition leads to full
employment immediately. The underlying reason is that, under zero capital
mobility, there are no spillovers of monetary policy. Coming to an end, compare
zero capital mobility with perfect capital mobility. Under perfect capital
mobility, monetary competition is a slow process. Under zero capital mobility,
however, monetary competition is a fast process.
Chapter 2
Imperfect Capital Mobility
1. Fiscal Competition between Europe and America

1.1. The Dynamic Model

1) The static model. In this chapter we assume imperfect capital mobility
between Europe and America. Under perfect capital mobility, an increase in
European government purchases raises both European output and American
output, to the same extent respectively. Under zero capital mobility, an increase
in European government purchases raises European output to a much larger
degree. On the other hand, it has no effect on American output. Under imperfect
capital mobility, an increase in European government purchases raises both
European output and American output. However, the rise in European output is
relatively large, and the rise in American 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 100 and an increase in American output of
equally 100. So the increase in world output is 200. Under zero capital mobility,
by contrast, an increase in European government purchases of 100 causes an
increase in European output of 200 and an increase in American output of zero.
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 150 and an increase in American output
of 50. 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 and fiscal cooperation? Given imperfect capital mobility, is
fiscal competition a slow process or a fast one?
72

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

Y1=A1+yG1+5G2 (1)
Y2=A2+YG2+5G1 (2)

According to equation (1), European output Y1 is determined by European
government purchases G1? American government purchases G 2 , and some other
factors called A^ According to equation (2), American output Y2 is determined
by American government purchases G 2 , European government purchases G1?
and some other factors called A 2 . Here y and 5 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. At the beginning there is unemployment in both
Europe and America. The target of the European government is full employment
in Europe. The instrument of the European government is European government
purchases. The European government raises European government purchases so
as to close the output gap in Europe:

Here is a list of the new symbols:
Yx European output this period
Yj full-employment output in Europe
Yj - Y1 output gap in Europe this period
Gj^ European government purchases last period
Gj European government purchases this period
1
Gj - Gj" increase in European government purchases.
Here the endogenous variable is European government purchases this period Gj.

The target of the American government is full employment in America. The
instrument of the American government is American government purchases. The
American government raises American government purchases so as to close the
output gap in America:
73

Here is a list of the new symbols:
Y2 American output this period
Y2 full-employment output in America
Y2 - Y 2 output gap in America this period
G2 American government purchases last period
G2 American government purchases this period
G 2 - G2* increase in American government purchases.
Here the endogenous variable is American government purchases this period G 2 .
We assume that the European government and the American government decide
simultaneously and independently.

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

Y1+1=A1+yGi+5G2 (5)

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

Y2+1=A2+yG2+8G1 (6)

Here Y^ 1 denotes American output next period.

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

(7)
74

^ (9)
2

Y 2 + 1 =A 2 +yG 2 +5G 1 (10)

Equation (7) shows the policy response in Europe, (8) shows the policy response
in America, (9) shows the output lag in Europe, and (10) shows the output lag in
America. The endogenous variables are European government purchases this
period G l5 American government purchases this period G 2 , European output
next period Yj , and American output next period Y^ .

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

(11)

(12)

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

Y^Yi (13)
Y2 = Y2 (14)
Yx = A 1 +yG 1 +SG 2 (15)
Y2=A2+yG2+5G1 (16)

Here the endogenous variables are European output Y1? American output Y2,
European government purchases G1? and American government purchases G 2 .
According to equation (13) there is full employment in Europe, so European
output is constant. According to equation (14) there is full employment in
America, so American output is constant too. Further, equations (15) and (16)
give the steady state levels of European and American government purchases.
75

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

% = A1+yG1+5G2 (17)
Y2 = A 2 + y G 2 + 5 G 1 (18)

Here the endogenous variables are European government purchases and
American government purchases. To simplify notation we introduce:

B^Yj-Ai (19)
B2 = Y 2 - A 2 (20)

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

B1=yG1+5G2 (21)
B2=yG2+5G1 (22)

The endogenous variables are still Gi and G 2 .

Next we solve the model for the endogenous variables:

Equation (23) shows the steady-state level of European government purchases,
and equation (24) shows the steady-state level of American government
purchases. As a result, there is a steady state if and only if y & 5. Owing to the
assumption y > 8, this condition is fulfilled.
76

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:

AYX =yAG 1 +8AG 2 (25)
AY2 =yAG 2 +5AG 1 (26)

Here AY! is the initial output gap in Europe, AY2 is the initial output gap in
America, AG2 is the total increase in European government purchases, and AG2
is the total increase in American government purchases. The endogenous
variables are AGX and AG2. The solution to the system (25) and (26) is:

1
Y 2 -5 2

Y 2 -8 2

According to equation (27), the total increase in European government purchases
depends on the initial output gap in Europe, the initial output gap in America, the
direct multiplier y, and the cross multiplier 8. The larger the initial output gap in
Europe, the larger is the total increase in European government purchases.
Moreover, the larger the initial output gap in America, the smaller is the total
increase in European government purchases. At first glance this comes as a
surprise. According to equation (28), the total increase in American government
purchases depends on the initial output gap in America, the initial output gap in
Europe, the direct multiplier y, and the cross multiplier 8.

4) Stability. Eliminate Y2 in equation (7) by means of equation (9) and
rearrange terms Y2 = Aj + yG! + 8G2*. By analogy, eliminate Y2 in equation (8)
by means of equation (10) to arrive at Y2 = A 2 + yG2 +8GJ"1. On this basis, the
dynamic model can be described by a system of two equations:

^ (29)
Y2=A2+yG2+8G1-1 (30)
77

Here the endogenous variables are European government purchases this period
Gx and American government purchases this period G 2 . To simplify notation we
make use of equations (19) and (20). With this, the dynamic model can be
written as follows:

(31)
(32)

The endogenous variables are still Gj and G 2 .

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

(33)
Y Y

Then differentiate equation (33) for Gj"2:

(34)
dGf* - Y2

Finally the stability condition is S 2 / y 2 < 1 or:

Y>5 (35)

That means, the steady state is stable if and only if the internal effect of fiscal
policy is larger than the external effect of fiscal policy. This condition is
satisfied. As a result, there is a stable steady state of fiscal competition. In other
words, fiscal competition between Europe and America leads to full employment
in Europe and America.
78

1.2. Some Numerical Examples

To illustrate the dynamic model, have a look at some numerical examples.
For ease of exposition, without loss of generality, assume y = 1.5 and 8 = 0.5. On
this assumption, the static model can be written as follows:

Y{ =A 1 +1.5G 1 +0.5G 2 (1)
Y2 =A 2 +1.5G 2 +0.5G 1 (2)

The endogenous variables are European output and American output. 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.

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

1) Unemployment in Europe equals unemployment in America. At the
beginning there is unemployment in both Europe and America. More precisely,
unemployment in Europe equals unemployment in America. Let initial output in
Europe be 940, and let initial output in America be the same. Step 1 refers to the
policy response. The output gap in Europe is 60. The fiscal policy multiplier in
Europe is 1.5. So what is needed in Europe is an increase in European
government purchases of 40. The output gap in America is 60. The fiscal policy
multiplier in America is 1.5. So what is needed in America is an increase in
American government purchases of 40.

Step 2 refers to the output lag. The increase in European government
purchases of 40 causes an increase in European output of 60. As a side effect, it
79

causes an increase in American output of 20. The increase in American
government purchases of 40 causes an increase in American output of 60. As a
side effect, it causes an increase in European output of 20. The total effect is an
increase in European output of 80 and an increase in American output of equally
80. As a consequence, European output goes from 940 to 1020, as does
American output.

Step 3 refers to the policy response. The inflationary gap in Europe is 20. The
fiscal policy multiplier in Europe is 1.5. So what is needed in Europe is a
reduction in European government purchases of 13.3. The inflationary gap in
America is 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 reduction in European government
purchases of 13.3 causes a decline in European output of 20. As a side effect, it
causes a decline 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 total effect is a
decline in European output of 26.7 and a decline in American output of equally
26.7. As a consequence, European output goes from 1020 to 993.3, as does
American output. And so on. Table 2.3 presents a synopsis.

What are the dynamic characteristics of this process? There are damped
oscillations in European government purchases, as there are in American
government purchases. There are damped oscillations in European output, as
there are in American output. The European economy oscillates between
unemployment and overemployment, as does the American economy. In each
round, in absolute values, the output gap declines by 67 percent. There are
damped oscillations in the world interest rate. Accordingly, there are damped
oscillations in European investment, as there are in American investment. As a
result, fiscal competition between Europe and America leads to full employment
in Europe and America.

Taking the sum over all periods, the increase in European government
purchases is 30, as is the increase in American government purchases, see
equations (27) and (28) in the preceding section. That means, the total increase in
European government purchases is small, as compared to the initial output gap in
80

Europe of 60. And the same applies to the total increase in American government
purchases, as compared to the initial output gap in America of 60. The effective
multiplier in Europe is 60/30 = 2, as is the effective multiplier in America. In
other words, the effective multiplier in Europe is large. And the same holds for
the effective multiplier in America.

Table 2.3
Fiscal Competition between Europe and America
Imperfect Capital Mobility

Europe America

Initial Output 940 940
Change in Government Purchases 40 40
Output 1020 1020
Change in Government Purchases -13.3 -13.3
Output 993.3 993.3
Change in Government Purchases 4.4 4.4
1002.2 1002.2
Output
and so on

2) Unemployment in Europe exceeds unemployment in America. Let initial
output in Europe be 940, and let initial output in America be 970. Step 1 refers to
the policy response. The output gap in Europe is 60. The fiscal policy multiplier
in Europe is 1.5. So what is needed in Europe is an increase in European
government purchases of 40. The output gap in America is 30. The fiscal policy
multiplier in America is 1.5. So what is needed in America is an increase in
American government purchases of 20.

Step 2 refers to the output lag. The increase in European government
purchases of 40 causes an increase in European output of 60. As a side effect, it
causes an increase in American output of 20. The increase in American
81

government purchases of 20 causes an increase in American output of 30. As a
side effect, it causes an increase in European output of 10. The total effect is an
increase in European output of 70 and an increase in American output of 50. As a
consequence, European output goes from 940 to 1010, and American output goes
from 970 to 1020.

Step 3 refers to the policy response. The inflationary gap in Europe is 10. The
fiscal policy multiplier in Europe is 1.5. So what is needed in Europe is a
reduction in European government purchases of 6.7. The inflationary gap in
America is 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 reduction in European government
purchases of 6.7 causes a decline in European output of 10. As a side effect, it
causes a decline in American output of 3.3. 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 total effect is a
decline in European output of 16.7 and a decline in American output of 23.3. As
a consequence, European output goes from 1010 to 993.3, and American output
goes from 1020 to 996.7. And so on. Table 2.4 gives an overview.

What are the dynamic characteristics of this process? There are damped
oscillations in European government purchases, as there are in American
government purchases. There are damped oscillations in European output, as
there are in American output. 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 37.5, and the increase in American government purchases is 7.5, see
equations (27) and (28) from the previous section. The total increase in European
government purchases is small, as compared to the initial output gap in Europe of
60. And the total increase in American government purchases is even smaller, as
compared to the initial output gap in America of 30. The effective multiplier in
Europe is 60/37.5 = 1.6, and the effective multiplier in America is 30/7.5 = 4.
That is to say, the effective multiplier in Europe is large, and the effective
multiplier in America is even larger.
82

Table 2.4
Fiscal Competition between Europe and America
Imperfect Capital Mobility

Europe America

Initial Output 940 970
20
Change in Government Purchases 40
Output 1010 1020
Change in Government Purchases -6.7 -13.3
993.3 996.7
Output
2.2
4.4
Change in Government Purchases
1002.2
Output 1001.1
and so on

3) Unemployment in Europe equals overemployment in America. Let initial
output in Europe be 940, and let initial output in America be 1060. Step 1 refers
to the policy response. The output gap in Europe is 60. The fiscal policy
multiplier in Europe is 1.5. So what is needed in Europe is an increase in
European government purchases of 40. The inflationary gap in America is 60.
The fiscal policy multiplier in America is 1.5. So what is needed in America is a
reduction in American government purchases of 40.

Step 2 refers to the output lag. The increase in European government
purchases of 40 causes an increase in European output of 60. As a side effect, it
causes an increase in American output of 20. The reduction in American
government purchases of 40 causes a decline in American output of 60. As a side
effect, it causes a decline in European output of 20. The net effect is an increase
in European output of 40 and a decline in American output of equally 40. As a
consequence, European output goes from 940 to 980, and American output goes
from 1060 to 1020.
83

Step 3 refers to the policy response. The output gap in Europe is 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. The inflationary gap in
America is 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
increase in European output of 13.3 and decline in American output of equally
13.3. As a consequence, European output goes from 980 to 993.3, and American
output goes from 1020 to 1006.7. And so on. For a synopsis see Table 2.5.

What are the dynamic characteristics? There are repeated increases in
European government purchases. There are repeated cuts in American
government purchases. There are repeated increases in European output. There
are repeated cuts in American output. In each round, in absolute values, the gap
declines by 67 percent.

Taking the sum over all periods, the increase in European government
purchases is 60, and the reduction in American government purchases is equally
60. The total increase in European government purchases is large, as compared to
the initial output gap in Europe of 60. Correspondingly, the total reduction in
American government purchases is large, as compared to the initial inflationary
gap in America of 60. The effective multiplier in Europe is 60/60 = 1, and the
effective multiplier in America is equally 60/60 = 1. That means, the effective
multiplier in Europe is small. And the same is true of the effective multiplier in
America.

4) Comparing imperfect capital mobility with perfect capital mobility. Under
perfect capital mobility, fiscal competition does not lead to full employment.
Under imperfect capital mobility, by contrast, fiscal competition does lead to full
employment.
84

Table 2.5
Fiscal Competition between Europe and America
Imperfect Capital Mobility

Europe America

Initial Output 1060
940
Change in Government Purchases 40 -40
1020
Output 980
13.3
Change in Government Purchases -13.3
Output 993.3 1006.7
and so on

2. Fiscal Cooperation between Europe and America

2.1. The Model

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

Yx = A 1 + y G 1 + 8 G 2 (1)
Y2 = A 2 + Y G 2 + 5 G 1 (2)

Here Yl denotes European output, Y2 is American output, G2 is European
government purchases, and G 2 is American government purchases. The
endogenous variables are European output and American output. At the
beginning there is unemployment in both Europe and America. The targets of
fiscal cooperation are full employment in Europe and full employment in
85

America. The instruments of fiscal cooperation are European government
purchases and American government purchases. So there are two targets and two
instruments.

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

% =A1+yG1+6G2 (3)
Y2 = A 2 + y G 2 + 8 G 1 (4)

Here Y1 denotes full-employment output in Europe, and Y2 denotes full-
employment output in America. The endogenous variables are European
government purchases and American government purchases.

To simplify notation, we introduce Bj = Y1 - A 1 and B 2 = Y2 - A 2 . Then we
solve the model for the endogenous variables:

YBx-5B 2
Gl (5)
=^2-5^

Â°2 = ^Ff L (6)
Equation (5) shows the required level of European government purchases, and
equation (6) shows the required level of American government purchases. There
is a solution if and only if y ^ 8. Due to the assumption y > 8, this condition is
met. As a result, fiscal cooperation between Europe and America can achieve full
employment in Europe and America. It is worth pointing out here that the
solution to fiscal cooperation is identical to the steady state of fiscal competition.

3) Another version of the policy model. As an alternative, the policy model
can be stated in terms of the initial output gap and the required increase in
government purchases. Taking differences in equations (1) and (2), the policy
model can be written as follows:
86

AYX = yAG 1 +5AG 2 (7)
AY2 =yAG 2 +5AG 1 (8)

Here AYX denotes the initial output gap in Europe, AY2 is the initial output gap
in America, AGX is the required increase in European government purchases, and
AG2 is the required increase in American government purchases. The
endogenous variables are AGX and AG 2 . The solution to the system (7) and (8)
is:

yz - S 2

_yAY 2 -SAY 1
2
y2-52
"

According to equation (9), the required increase in European government
purchases depends on the initial output gap in Europe, the initial output gap in
America, 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, the smaller is
the required increase in European government purchases. At first glance this
comes as a surprise. According to equation (10), the required increase in
American government purchases depends on the initial output gap in America,
the initial output gap in Europe, the direct multiplier y, and the cross multiplier
8.

2.2. Some Numerical Examples

To illustrate the policy model, have a look at some numerical examples. For
ease of exposition, without losing generality, assume y = 1.5 and 5 = 0.5. On this
assumption, the output model can be written as follows:
87

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

The endogenous variables are European output and American output. Evidently,
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.

It proves useful to consider five distinct cases:
- unemployment in Europe equals unemployment in America
- unemployment in Europe exceeds unemployment in America
- unemployment in Europe, full employment in America
- unemployment in Europe exceeds overemployment in America
- unemployment in Europe equals overemployment in America.

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. So what is needed,
according to equations (9) and (10) from the preceding section, 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 45 and American output by 15. The increase in
American government purchases of 30 raises American output by 45 and
European output by 15. 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
is large. And the same is true of the effective multiplier in America. Table 2.6
presents a synopsis.

2) Unemployment in Europe exceeds unemployment in America. Let initial
output in Europe be 940, and let initial output in America be 970. The output gap
in Europe is 60, and the output gap in America is 30. So what is needed,
according to equations (9) and (10) from the previous section, is an increase in
European government purchases of 37.5 and an increase in American
government purchases of 7.5. The increase in European government purchases of
37.5 raises European output by 56.25 and American output by 18.75. The
increase in American government purchases of 7.5 raises American output by
11.25 and European output by 3.75. The total 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, 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 required increase in
American government purchases is even smaller, as compared to the initial
output gap in America. The effective multiplier in Europe is 60/37.5 = 1.6, and
the effective multiplier in America is 30/7.5 = 4. That means, the effective
multiplier in Europe is large, and the effective multiplier in America is even
larger. Table 2.7 gives an overview.

3) Unemployment in Europe, full employment in America. Let initial output
in Europe be 940, and let initial output in America be 1000. The output gap in
Europe is 60, and the output gap in America is zero. What is needed, then, is an
increase in European government purchases of 45 and a reduction in American
government purchases of 15. The increase in European government purchases of
45 raises European output by 67.5 and American output by 22.5. The reduction
in American government purchases of 15 lowers American output by 22.5 and
European output by 7.5. The net effect is an increase in European output of 60
and a decline in American output of zero. The effective multiplier in Europe is
1.3, and the effective multiplier in America is zero. For a synopsis see Table 2.8.
89

Table 2.6
Fiscal Cooperation between Europe and America
Imperfect Capital Mobility

America
Europe

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

Table 2.7
Fiscal Cooperation between Europe and America
Imperfect Capital Mobility

Europe America

Initial Output 940 970
Change in Government Purchases 7.5
37.5
Output 1000 1000

Table 2.8
Fiscal Cooperation between Europe and America
Imperfect Capital Mobility

America
Europe

940
Initial Output 1000
Change in Government Purchases 45 -15
Output 1000 1000
90

4) Unemployment in Europe exceeds overemployment in America. Let initial
output in Europe be 940, and let initial output in America be 1030. The output
gap in Europe is 60, and the output gap in America is -30. What is needed, then,
is an increase in European government purchases of 52.5 and a reduction in
American government purchases of 37.5. The increase in European government
purchases of 52.5 raises European output by 78.75 and American output by
26.25. The reduction in American government purchases of 37.5 lowers
American output by 56.25 and European output by 18.75. The net effect is an
increase in European output of 60 and a decline in American output of 30. As a
result, fiscal cooperation can achieve full employment.

However, the required increase in European government purchases is large, as
compared to the initial output gap in Europe. And the required cut in American
government purchases is even larger, as compared to the initial inflationary gap
in America. The effective multiplier in Europe is 1.1, and the effective multiplier
in America is 0.8. That is to say, the effective multiplier in Europe is small, and
the effective multiplier in America is even smaller. For an overview see Table
2.9.

5) 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 output gap in America is -60. What is needed, then,
is an increase in European government purchases of 60 and a reduction in
American government purchases of equally 60. The increase in European
government purchases of 60 raises European output by 90 and American output
by 30. The reduction in American government purchases of 60 lowers American
output by 90 and European output by 30. The net effect is an increase in
European output of 60 and a decline in American output of equally 60. As a
result, fiscal cooperation can achieve full employment.

However, the required increase in European government purchases is large, as
compared to the initial output gap in Europe. Correspondingly, the required cut
in American government purchases is large, as compared to the initial
inflationary gap in America. The effective multiplier in Europe is 60/60 = 1, and
the effective multiplier in America is equally 60/60 = 1. That means, the effective
multiplier in Europe is small. And the same is true of the effective multiplier in
America. Table 2.10 presents a synopsis.
91

6) Comparing imperfect capital mobility with perfect capital mobility. Under
perfect capital mobility, fiscal cooperation cannot achieve full employment.
Under imperfect capital mobility, by contrast, fiscal cooperation can indeed
achieve full employment.

7) Comparing fiscal cooperation with fiscal competition, given imperfect
capital mobility. Fiscal competition can achieve full employment. The same
applies to fiscal cooperation. Fiscal competition is a slow process. On the other
hand, fiscal cooperation is a fast process. Judging from these points of view,
fiscal cooperation seems to be superior to fiscal competition.

Table 2.9
Fiscal Cooperation between Europe and America
Imperfect Capital Mobility

Europe America

Initial Output 1030
940
Change in Government Purchases 52.5 -37.5
Output 1000 1000

Table 2.10
Fiscal Cooperation between Europe and America
Imperfect Capital Mobility

Europe America

1060
Initial Output 940
Change in Government Purchases 60 -60
Output 1000 1000
92

3. Monetary Competition between Europe and America

1) The static model. To illustrate this, consider a numerical example. Under
perfect capital mobility, an increase in European money supply of 100 causes an
increase in European output of 300 and a decline in American output of 100. So
the increase in world output is 200. Under zero capital mobility, by contrast, an
increase in European money supply of 100 causes an increase in European output
of 200 and a decline in American output of zero. So the increase in world output
is 200 again. On this basis we assume that, under imperfect capital mobility, an
increase in European money supply of 100 causes an increase in European output
of 250 and a decline in American output of 50. So the increase in world output is
still 200.

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

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

Yx = A 1 + 2 . 5 M 1 - 0 . 5 M 2 (1)
Y2 = A 2 + 2 . 5 M 2 - 0 . 5 M 1 (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.
Correspondingly, an increase in American money supply of 100 causes an
increase in American output of 250 and a decline in European 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 both
Europe and America. The target of the European central bank is full employment
in Europe. The European central bank raises European money supply so as to
93

close the output gap in Europe. The target of the American central bank is full
employment in America. 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. For the details see Chapter 1 of Part One. As a result, there is a
stable steady state of monetary competition. In other words, monetary
competition between Europe and America leads to full employment in Europe
and America.

3) Some numerical examples. It proves useful to study two distinct cases:
- unemployment in Europe equals unemployment in America
- unemployment in Europe equals overemployment in America.

First consider the case that unemployment in Europe equals unemployment in
America. Let initial output in Europe be 940, and let initial output in America be
the same. Step 1 refers to the policy response. The output gap in Europe is 60.
The monetary policy multiplier in Europe is 2.5. So what is needed in Europe is
an increase in European money supply of 24. The output gap in America is 60.
The monetary policy multiplier in America is 2.5. So what is needed in America
is an increase in American money supply of 24.

Step 2 refers to the output lag. The increase in European money supply of 24
causes an increase in European output of 60. As a side effect, it causes a decline
in American output of 12. The increase in American money supply of 24 causes
an increase in American output of 60. As a side effect, it causes a decline in
European output of 12. The net 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. And so on.

Table 2.11 shows the process of monetary competition between Europe and
America. In each round, the output gap declines by 80 percent. This clearly
differs from the conclusions drawn under perfect capital mobility. There, in each
round, the output gap declined by 67 percent. As a result, under low capital
mobility, monetary competition is a fast process. By contrast, under high capital
mobility, monetary competition is a slow process. Taking the sum over all
periods, the increase in European money supply is 30, as is the increase in
94

American money supply. This confirms the conclusions drawn under perfect
capital mobility.

Table 2.11
Monetary Competition between Europe and America
Imperfect Capital Mobility

America
Europe

Initial Output 940 940
24
Change in Money Supply 24
988
Output 988
4.8
Change in Money Supply 4.8
997.6 997.6
Output
and so on

Second consider the case that unemployment in Europe equals
overemployment in America. Let initial output in Europe be 940, and let initial
output in America be 1060. Step 1 refers to the policy response. The output gap
in Europe is 60. The monetary policy multiplier in Europe is 2.5. So what is
needed in Europe is an increase in European money supply of 24. The
inflationary gap in America is 60. The monetary policy multiplier in America is
2.5. So what is needed in America is a reduction in American money supply of
24.

Step 2 refers to the output lag. The increase in European money supply of 24
causes an increase in European output of 60. As a side effect, it causes a decline
in American output of 12. The reduction in American money supply of 24 causes
a decline in American output of 60. As a side effect, it causes an increase in
European output of 12. The total effect is an increase in European output of 72
and a decline in American output of equally 72. As a consequence, European
95

output goes from 940 to 1012, and American output goes from 1060 to 988. And
so on.

Table 2.12 shows the process of monetary competition. In each round, in
absolute values, the output gap declines by 80 percent. This clearly differs from
the conclusions drawn under perfect capital mobility. There, in each round, the
output gap declined by 67 percent. As a result, under low capital mobility,
monetary competition is a fast process. By contrast, under high capital mobility,
monetary competition is a slow process. Taking the sum over all periods, the
increase in European money supply is 20, and the reduction in American money
supply is equally 20. Again, this clearly differs from the conclusions drawn under
perfect capital mobility. There the total increase in European money supply was
15, and the total reduction in American money supply was equally 15.

Table 2.12
Monetary Competition between Europe and America
Imperfect Capital Mobility

America
Europe

Initial Output 940 1060
24
Change in Money Supply -24
1012 988
Output
4.8
Change in Money Supply -4.8
1002.4
Output 997.6
and so on

4) Summary. Imperfect capital mobility speeds up the process of monetary
competition. On the other hand, imperfect capital mobility can increase the total
change in money supply.
96

5) Comparing monetary competition with fiscal competition. Monetary
competition leads to full employment. The same is true of fiscal competition.
Monetary competition is a relatively fast process. By contrast, fiscal competition
is a relatively slow process. Judging from this perspective, monetary competition
seems to be superior to fiscal competition.

4. Monetary Cooperation between Europe and America

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. What is
needed, then, is an increase in European money supply of 30 and an increase in
American money supply of equally 30. This confirms the conclusions reached
under perfect capital mobility. Table 2.13 presents a synopsis.

2) Unemployment in Europe equals overemployment in America. Let initial
output in Europe be 940, and let initial output in America be 1060. What is
needed, then, is an increase in European money supply of 20 and a reduction in
American money supply of equally 20. This clearly differs from the conclusions
reached under perfect capital mobility. What was needed, there, was an increase
in European money supply of 15 and a reduction in American money supply of
equally 15. As a result, what is needed under low capital mobility, is a large
change in money supply. By contrast, what is needed under high capital mobility,
is a small change in money supply. Table 2.14 gives an overview.

3) Comparing monetary cooperation with fiscal cooperation. Fiscal
cooperation can achieve full employment. The same is true of monetary
cooperation. Fiscal cooperation is a fast process. The same is true of monetary
cooperation. Fiscal cooperation can require large changes in government
97

purchases. On the other hand, monetary cooperation cannot require any changes
in government purchases. Judging from these points of view, monetary
cooperation seems to be superior to fiscal cooperation.

Table 2.13
Monetary Cooperation between Europe and America
Imperfect Capital Mobility

Europe America

940
Initial Output 940
Change in Money Supply 30
30
Output 1000
1000

Table 2.14
Monetary Cooperation between Europe and America
Imperfect Capital Mobility

America
Europe

Initial Output 940 1060
Change in Money Supply 20 -20
Output 1000 1000
98

5. Monetary and Fiscal Cooperation

1) The model. This section deals with cooperation between the European
central bank, the American central bank, the European government, and the
American government. As a starting point, take the output model. It can be
represented by a system of two equations:

Yx = A 1 + a M 1 - p M 2 + Y G 1 + 5 G 2 (1)
Y2 = A 2 + a M 2 - PMX + yG2 + SGX (2)

According to equation (1), European output is determined by European money
supply, American money supply, European government purchases, and American
government purchases. According to equation (2), American output is
determined by American money supply, European money supply, American
government purchases, and European government purchases. Here a, P, y and 8
are positive coefficients with a > P and y > 5 . An increase in European money
supply raises European output but lowers American output. An increase in
European government purchases raises both European output and American
output.

At the beginning there is unemployment in Europe as well as America. The
targets of policy cooperation are full employment in Europe and full employment
in America. The instruments of policy cooperation are European money supply,
American money supply, European government purchases, and American
government purchases. There are two targets and four instruments, so there are
two degrees of freedom. As a result, there is an infinite number of solutions. In
other words, monetary and fiscal cooperation can achieve full employment in
Europe and America.

On this basis, the policy model can be characterized by a system of two
equations:

Yx = A 1 + a M 1 - P M 2 + ' y G 1 + 8 G 2 (3)
99

Y2 = A 2 + ocM2 - PMX + Y^2 + 5 G i (4)

Here Yx denotes full-employment output in Europe, and Y2 denotes full-
employment output in America. The endogenous variables are European money
supply, American money supply, European government purchases, and American
government purchases.

Of course there are many more potential targets of policy cooperation:
- balancing the budget in Europe
- balancing the budget in America
- balancing the current account in Europe and America
- high investment in Europe
- high investment in America
- preventing foreign exchange bubbles
- preventing stock market bubbles
- and so on.
To sum up, in a sense, policy instruments are abundant. And in another sense,
policy instruments are scarce.

2) A numerical example. For ease of exposition, without losing generality,
assume a = 2.5, P = 0.5, y = l-5 and 8 = 0.5. On this assumption, the output
model can be written as follows:

Yx = Ax + 2.5M! - 0.5M2 +1.5GX + 0.5G2 (5)
Y2 = A 2 + 2.5M2 - 0.5M! +1.5G 2 + 0.5Gx (6)

Evidently, 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.

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, for instance, is an increase in European money supply of 20, an increase
100

in American money supply of equally 20, an increase in European government
purchases of 10, and an increase in American government purchases of equally
10. The increase in European money supply of 20 raises European output by 50
and lowers American output by 10. Correspondingly, the increase in American
money supply of 20 raises American output by 50 and lowers European output
by 10. The increase in European government purchases of 10 raises European
output by 15 and American output by 5. Correspondingly, the increase in
American government purchases of 10 raises American output by 15 and
European output by 5.

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, monetary and fiscal cooperation can
achieve full employment. Table 2.15 presents a synopsis.

Table 2.15
Monetary and Fiscal Cooperation
Imperfect Capital Mobility

America
Europe

940
Initial Output 940
20
Change in Money Supply 20
10
Change in Government Purchases 10
1000
Output 1000
Chapter 3
High Capital Mobility
1. Fiscal Competition between Europe and America

To illustrate high capital mobility, have a look at some numerical examples.
For ease of exposition, without loss of generality, assume y = 1.2 and 8 = 0.8.
On this assumption, the static model can be written as follows:

Yj =A 1 +1.2G 1 +0.8G 2 (1)
Y2 =A 2 +1.2G 2 +0.8G 1 (2)

Obviously, an increase in European government purchases of 100 causes an
increase in European output of 120 and an increase in American output of 80. In
the same way, an increase in American government purchases of 100 causes an
increase in American output of 120 and an increase in European output of 80.
That means, under high capital mobility, fiscal spillovers are large. Further let
full-employment output in Europe be 1000, and let full-employment output in
America be the same.

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. Let initial
output in Europe be 940, and let initial output in America be the same. Step 1
refers to the policy response. The output gap in Europe is 60. The fiscal policy
multiplier in Europe is 1.2. So what is needed in Europe is an increase in
European government purchases of 50. The output gap in America is 60. The
fiscal policy multiplier in America is 1.2. So what is needed in America is an
increase in American government purchases of 50.
102

Step 2 refers to the output lag. The increase in European government
purchases of 50 causes an increase in European output of 60. As a side effect, it
causes an increase in American output of 40. The increase in American
government purchases of 50 causes an increase in American output of 60. As a
side effect, it causes an increase in European output of 40. The total effect is an
increase in European output of 100 and an increase in American output of
equally 100. As a consequence, European output goes from 940 to 1040, as does
American output. And so on.

Table 2.16 shows the process of fiscal competition between Europe and
America. In each round, the output gap declines by 33 percent. This clearly
differs from the conclusions drawn under low capital mobility. There, in each
round, the output gap declined by 67 percent. As a result, under high capital
mobility, fiscal competition is a relatively slow process. By contrast, under low
capital mobility, fiscal competition is a relatively fast process.

Table 2.16
Fiscal Competition between Europe and America
High Capital Mobility

America
Europe

940 940
Initial Output
50 50
Change in Government Purchases
Output 1040 1040
Change in Government Purchases -33.3 -33.3
973.3 973.3
Output
and so on ...

Taking the sum over all periods, the increase in European government
purchases is 30, as is the increase in American government purchases. That is to
say, the total increase in European government purchases is small, as compared
103

to the initial output gap in Europe of 60. And the same applies to the total
increase in American government purchases, as compared to the initial output
gap in America of 60. The effective multiplier in Europe is 60/ 30 = 2, as is the
effective multiplier in America. In other words, the effective multiplier in Europe
is large. And the same holds for the effective multiplier in America. This
confirms the conclusions drawn under low capital mobility.

2) Unemployment in Europe equals overemployment in America. Let initial
output in Europe be 940, and let initial output in America be 1060. Step 1 refers
to the policy response. The output gap in Europe is 60. The fiscal policy
multiplier in Europe is 1.2. So what is needed in Europe is an increase in
European government purchases of 50. The inflationary gap in America is 60.
The fiscal policy multiplier in America is 1.2. So what is needed in America is a
reduction in American government purchases of 50.

Step 2 refers to the output lag. The increase in European government
purchases of 50 causes an increase in European output of 60. As a side effect, it
causes an increase in American output of 40. The reduction in American
government purchases of 50 causes a decline in American output of 60. As a side
effect, it causes a decline in European output of 40. 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. And so on.

Table 2.17 shows the process of fiscal competition. In each round, in
absolute values, the output gap declines by 33 percent. This clearly differs from
the conclusions drawn under low capital mobility. There, in each round, the
output gap declined by 67 percent. As a result, under high capital mobility, fiscal
competition is a relatively slow process. By contrast, under low capital mobility,
fiscal competition is a relatively fast process.

Taking the sum over all periods, the increase in European government
purchases is 150, and the reduction in American government purchases is equally
150. The total increase in European government purchases is very large, as
compared to the initial output gap in Europe of 60. Correspondingly, the total
reduction in American government purchases is very large, as compared to the
initial inflationary gap in America of 60. The effective multiplier in Europe is
104

60 /150 = 0.4, and the effective multiplier in America is equally 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. Again, this clearly differs from the
conclusions drawn under low capital mobility. There the total increase in
European government purchases was 60, and the total reduction in American
government purchases was equally 60.

Table 2.17
Fiscal Competition between Europe and America
High Capital Mobility

Europe America

Initial Output 940 1060
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