<<

. 2
( 9)



>>

Output 1010 1020
Change in Money Supply -3.3 -6.7
Output 1006.7 1003.3
Change in Money Supply -2.2 -1.1
1001.1
Output 1002.2
and so on ...




7) Inflation in Europe equals inflation in America. Let initial output in Europe
be 1060, and let initial output in America be the same. Table 1.8 shows the
resulting process of monetary competition. In each round, the inflationary gap
declines by 67 percent. The total reduction in European money supply is 30, and
the same holds for the total reduction in American money supply. The effective
multiplier in Europe is 2, as is the effective multiplier in America.
30


Table 1.8
Monetary Competition between Europe and America
Inflation in Europe Equals Inflation in America

Europe America


Initial Output 1060 1060
Change in Money Supply -20
-20
Output 1020 1020
Change in Money Supply -6.7 -6.7
Output 1006.7 1006.7
and so on
Chapter 2
Monetary Cooperation
between Europe and America
1. The Model


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

Y1=A1+aM1-PM2 (1)
Y2=A2+aM2-PM1 (2)

Here Y_ denotes European output, Y2 is American output, M 1 is European
j
money supply, and M 2 is American money supply. The endogenous variables are
European output and American output. At the beginning there is unemployment
in both Europe and America. The targets of monetary cooperation are full
employment in Europe and full employment in America. The instruments of
monetary cooperation are European money supply and American money supply.
So there are two targets and two instruments.

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


Y1=A1+aM1-(3M2 (3)
Y2=A2+aM2-pM1 (4)

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

To simplify notation, we introduce Bx = Yx - Ax and B 2 = Y2 - A 2 . Then we
solve the model for the endogenous variables:
32




Equation (5) shows the required level of European money supply, and equation
(6) shows the required level of American money supply. There is a solution if
and only if a ^ (3. Due to the assumption a > (3, this condition is met. As a result,
monetary cooperation between Europe and America can achieve full employment
in Europe and America. It is worth pointing out here that the solution to
monetary cooperation is identical to the steady state of monetary 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 money
supply. Taking differences in equations (1) and (2), the policy model can be
written as follows:


AY 1 =aAM 1 -pAM 2 (7)
AY 2 =aAM 2 -(3AM 1 (8)

Here AYj 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 AM2. The solution to the system (7) and (8) is:


(9,


ocAY2+|3AY1
2
a2-(32
"


According to equation (9), the required increase in European money supply
depends on the initial output gap in Europe, the initial output gap in America, the
direct multiplier a, and the cross multiplier (3. The larger the initial output gap in
33


Europe, the larger is the required increase in European money supply. Moreover,
the larger the initial output gap in America, the larger is the required increase in
European money supply. At first glance this comes as a surprise. According to
equation (10), the required increase in American money supply depends on the
initial output gap in America, the initial output gap in Europe, the direct
multiplier a, and the cross multiplier (3.




2. Some Numerical Examples


To illustrate the policy model, have a look at some numerical examples. For
ease of exposition, without losing generality, assume a = 3 and (3 = 1. On this
assumption, the output model can be written as follows:


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

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

It proves useful to consider seven distinct cases:
- unemployment in Europe equals unemployment in America
- unemployment in Europe exceeds unemployment in America
- unemployment in Europe, full employment in America
- unemployment in Europe exceeds overemployment in America
- unemployment in Europe equals overemployment in America
- inflation in Europe exceeds inflation in America
- inflation in Europe equals inflation in America.
34


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 money supply of 30 and an increase in American money supply of
equally 30. The increase in European money supply of 30 raises European output
by 90 and lowers American output by 30. The increase in American money
supply of 30 raises American output by 90 and lowers European output by 30.
The net effect is an increase in European output of 60 and an increase in
American output of equally 60. As a consequence, European output goes from
940 to 1000, as does American output. In Europe there is now full employment,
and the same holds for America. As a result, monetary cooperation can achieve
full employment.

The required increase in European money supply is large, as compared to the
initial output gap in Europe. And the same applies to the required increase in
American money supply, 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 small. And the same
is true of the effective multiplier in America. Table 1.9 presents a synopsis.



Table 1.9
Monetary Cooperation between Europe and America
Unemployment in Europe Equals Unemployment in America

America
Europe


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




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
35

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 money supply of 26.25 and 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, monetary cooperation
can achieve full employment.

The required increase in European money supply is large, as compared to the
initial output gap in Europe. And the required increase in American money
supply is even larger, as compared to the initial output gap in America. The
effective multiplier in Europe is 60/26.25 = 2.3, and the effective multiplier in
America is 30/18.75 = 1.6. That means, the effective multiplier in Europe is
small, and the effective multiplier in America is even smaller. Table 1.10 gives
an overview.



Table 1.10
Monetary Cooperation between Europe and America
Unemployment in Europe Exceeds Unemployment in America

Europe America


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




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
36


increase in European money supply of 22.5 and an increase in American money
supply of 7.5. The increase in European money supply of 22.5 raises European
output by 67.5 and lowers American output by 22.5. The increase in American
money supply of 7.5 raises American output by 22.5 and lowers European output
by 7.5. The net effect is an increase in European output of 60 and an increase in
American output of zero. The effective multiplier in Europe is 2.7, and the
effective multiplier in America is zero. For a synopsis see Table 1.11.



Table 1.11
Monetary Cooperation between Europe and America
Unemployment in Europe, Full Employment in America

Europe America


Initial Output 1000
940
Change in Money Supply 22.5 7.5
Output 1000 1000




4) Unemployment in Europe exceeds overemployment in America. At the
beginning there is unemployment in Europe but overemployment in America.
Thus there is inflation in America. Let initial output in Europe be 940, and let
initial output in America be 1030. The output gap in Europe is 60, and the output
gap in America is -30. What is needed, then, is an increase in European money
supply of 18.75 and a reduction in American money supply of 3.75. The increase
in European money supply of 18.75 raises European output by 56.25 and lowers
American output by 18.75. The reduction in American money supply of 3.75
lowers American output by 11.25 and raises European output by 3.75. The total
effect is an increase in European output of 60 and a decline in American output
of 30. The effective multiplier in Europe is 3.2, and the effective multiplier in
America is 8. For an overview see Table 1.12.
37


Table 1.12
Monetary Cooperation between Europe and America
Unemployment in Europe Exceeds Overemployment in America

Europe America


Initial Output 940 1030
18.75
Change in Money Supply -3.75
1000 1000
Output




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 money supply of 15 and a reduction in American
money supply of equally 15. The increase in European money supply of 15 raises
European output by 45 and lowers American output by 15. The reduction in
American money supply of 15 lowers American output by 45 and raises
European output by 15. The total effect is an increase in European output of 60
and a decline in American output of equally 60.

The required increase in European money supply is small, as compared to the
initial output gap in Europe. Correspondingly, the required cut in American
money supply is small, as compared to the initial inflationary gap in America.
The effective multiplier in Europe is 60/15 = 4, and the effective multiplier in
America is equally 60/15 = 4. That is to say, the effective multiplier in Europe is
large. And the same is true of the effective multiplier in America. Table 1.13
presents a synopsis.
38

Table 1.13
Monetary Cooperation between Europe and America
Unemployment in Europe Equals Overemployment in America

Europe America


Initial Output 940 1060
Change in Money Supply 15 -15
Output 1000 1000




6) Inflation in Europe exceeds inflation in America. At the start there is
overemployment in both Europe and America. For that reason there is inflation in
both Europe and America. Let overemployment in Europe exceed
overemployment in America. Let initial output in Europe be 1060, and let initial
output in America be 1030. The inflationary gap in Europe is 60, and the
inflationary gap in America is 30. The targets of monetary cooperation are price
stability in Europe and price stability in America. What is needed, then, is a
reduction in European money supply of 26.25 and a reduction in American
money supply of 18.75. The reduction in European money supply of 26.25
lowers European output by 78.75 and raises American output by 26.25. The
reduction in American money supply of 18.75 lowers American output by 56.25
and raises European output by 18.75. The net effect is a decline in European
output of 60 and a decline in American output of 30. As a consequence,
European output goes from 1060 to 1000, and American output goes from 1030
to 1000. There is now full employment in both Europe and America. For that
reason there is now price stability in both Europe and America. As a result,
monetary cooperation can achieve full employment and price stability.

The required cut in European money supply is large, as compared to the
initial inflationary gap in Europe. And the required cut in American money
supply is even larger, as compared to the initial inflationary gap in America. The
effective multiplier in Europe is 60/26.25 = 2.3, and the effective multiplier in
America is 30/18.75 = 1.6. That means, the effective multiplier in Europe is
39

small, and the effective multiplier in America is even smaller. Table 1.14 gives
an overview.



Table 1.14
Monetary Cooperation between Europe and America
Inflation in Europe Exceeds Inflation in America

Europe America


Initial Output 1060 1030
Change in Money Supply - 26.25 - 18.75
Output 1000 1000




7) Inflation in Europe equals inflation in America. Let initial output in Europe
be 1060, and let initial output in America be the same. The inflationary gap in
Europe is 60, as is the inflationary gap in America. What is needed, then, is a
reduction in European money supply of 30 and a reduction in American money
supply of equally 30. The reduction in European money supply of 30 lowers
European output by 90 and raises American output by 30. The reduction in
American money supply of 30 lowers American output by 90 and raises
European output by 30. The net effect is a decline in European output of 60 and a
decline in American output of equally 60. The effective multiplier in Europe is 2,
as is the effective multiplier in America. For a synopsis see Table 1.15.

8) Comparing monetary cooperation with monetary competition. Monetary
competition can achieve full employment. The same applies to monetary
cooperation. Monetary competition is a slow process. By contrast, monetary
cooperation is a fast process. Judging from these points of view, monetary
cooperation seems to be superior to monetary competition.
40


Table 1.15
Monetary Cooperation between Europe and America
Inflation in Europe Equals Inflation in America

Europe America


Initial Output 1060 1060
Change in Money Supply -30 -30
Output 1000 1000
Chapter 3
Fiscal Competition
between Europe and America
1. The Dynamic Model


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

As a result, an increase in European government purchases raises both
European output and American output. And what is more, the rise in European
output equals the rise in American output. Correspondingly, an increase in
American government purchases raises both American output and European
output. And what is more, the rise in American output equals the rise in
European output. In the numerical example, an increase in European government
purchases of 100 causes an increase in European output of 100 and an increase in
American output of equally 100. Likewise, an increase in American government
purchases of 100 causes an increase in American output of 100 and an increase in
European output of equally 100. In a sense, the internal effect of fiscal policy is
rather small, whereas the external effect of fiscal policy is quite large. Now have
a closer look at the process of adjustment. An increase in European government
purchases causes an appreciation of the euro, a depreciation of the dollar, and an
increase in the world interest rate. The appreciation of the euro lowers European
exports. The depreciation of the dollar raises American exports. And the increase
in the world interest rate lowers both European investment and American
investment. The net effect is that European output and American output go up, to
42


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

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


2 (1)

Y2=A2+YG2+5G1 (2)

According to equation (1), European output Yx 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 a n d 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
and the external effect are the same size y = 5. The endogenous variables are
European output and American output. Along these lines, the static model can be
rewritten as follows:


Y1=A1+yG1+yG2 (3)
Y2=A2+yG2+yG1 (4)

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:
Yj European output this period
Yj full-employment output in Europe
Yx - Yj output gap in Europe this period
Gf European government purchases last period
43


Gj European government purchases this period
Gj - Gf l increase in European government purchases.
Here the endogenous variable is European government purchases this period G x .

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:


(6)


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
G2 - 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:


(7)

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+YG1 (8)

Here Y^1 denotes American output next period.
44


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




”” (10)



Yx+l= Ai+YGi+YGj (11)
1
(12)
Y G !



Equation (9) shows the policy response in Europe, (10) shows the policy
response in America, (11) shows the output lag in Europe, and (12) shows the
output lag in America. The endogenous variables are European government
purchases this period Gx, American government purchases this period G 2 ,
European output next period Y^1, and American output next period Y^ 1 .

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


(13)
(14)

Equation (13) has it that European government purchases do not change any
more. Similarly, equation (14) has it that American government purchases do not
change any more. Therefore the steady state can be captured by a system of four
equations:


Yl=% (15)
Y2 = Y2 (16)


Y2=A2+YG2+yG1 (18)
45


Here the endogenous variables are European output Yl5 American output Y2,
European government purchases Gh and American government purchases G 2 .
According to equation (15) there is full employment in Europe, so European
output is constant. According to equation (16) there is full employment in
America, so American output is constant too. Further, equations (17) and (18)
give the steady state levels of European and American government purchases.

Now subtract equation (18) from equation (17), taking account of equations
(15) and (16), to reach:

Y1-Y2=A1-A2 (19)


However, this is in direct contradiction to the assumption that Y1, Y2, Ax and A 2
are given independently. As a result, there is no steady state of fiscal
competition. In other words, fiscal competition between Europe and America
does not lead to full employment in Europe and America. The underlying reason
is the large external effect of fiscal policy.




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, see Carlberg
(2000) p. 199 and Carlberg (2001) p. 163. On this assumption, the static model
can be written as follows:


Yx = A 1 + G 1 + G 2 (1)
Y2=A2+G2+G1 (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 100 and an increase in American output of equally 100.
46

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

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

1) Unemployment in Europe exceeds unemployment in America. At the
beginning there is unemployment in both Europe and America. More precisely,
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. 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 1. So what is needed in America is an increase in American
government purchases of 30.

Step 2 refers to the output lag. The increase in European government
purchases of 60 causes an increase in European output of 60. As a side effect, it
causes an increase in American output of equally 60. The increase in American
government purchases of 30 causes an increase in American output of 30. As a
side effect, it causes an increase in European output of equally 30. The total
effect is an increase in European output of 90 and an increase in American output
of equally 90. As a consequence, European output goes from 940 to 1030, and
American output goes from 970 to 1060. Put another way, the output gap in
Europe of 60 turns into an inflationary gap of 30. And the output gap in America
of 30 turns into an inflationary gap of 60.

Why does the European government not succeed in closing the output gap in
Europe (or, for that matter, the inflationary gap in Europe)? The underlying
reason is the positive external effect of the increase in American government
purchases. And why does the American government not succeed in closing the
output gap in America (or the inflationary gap in America)? The underlying
47


reason is the positive external effect of the increase in European government
purchases.

Step 3 refers to the policy response. The inflationary gap in Europe is 30. The
fiscal policy multiplier in Europe is 1. So what is needed in Europe is a reduction
in European government purchases of 30. The inflationary gap in America is 60.
The fiscal policy multiplier in America is 1. So what is needed in America is a
reduction in American government purchases of 60.

Step 4 refers to the output lag. The reduction in European government
purchases of 30 causes a decline in European output of 30. As a side effect, it
causes a decline in American output of equally 30. The reduction in American
government purchases of 60 causes a decline in American output of 60. As a side
effect, it causes a decline in European output of equally 60. The total effect is a
decline in European output of 90 and a decline in American output of equally 90.
As a consequence, European output goes from 1030 to 940, and American output
goes from 1060 to 970. With this, European output and American output are back
at their initial levels. That means, this process will repeat itself step by step.
Table 1.16 presents a synopsis.



Table 1.16
Fiscal Competition between Europe and America
Unemployment in Europe Exceeds Unemployment in America

Europe America


Initial Output 940 970
Change in Government Purchases 60 30
Output 1030 1060
Change in Government Purchases -30 -60
Output 940 970
and so on
48


What are the dynamic characteristics of this process? There is an upward
trend in European government purchases. By contrast, there is a downward trend
in American government purchases. There are uniform oscillations in European
output, as there are in American output. The European economy oscillates
between unemployment and overemployment, as does the American economy.
There are repeated appreciations of the euro and repeated depreciations of the
dollar. Accordingly, there are repeated cuts in European exports and repeated
increases in American exports. Moreover, after a certain number of steps,
American government purchases are down to zero. As a result, fiscal competition
between Europe and America does not lead to full employment in Europe and
America.

2) 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. So what is needed in Europe is an increase in European
government purchases of 60. The output gap in America is 60. The fiscal policy
multiplier in America is 1. So what is needed in America is an increase in
American government purchases of 60.

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

Step 3 refers to the policy response. The inflationary gap in Europe is 60. The
fiscal policy multiplier in Europe is 1. So what is needed in Europe is a reduction
in European government purchases of 60. The inflationary gap in America is 60.
The fiscal policy multiplier in America is 1. So what is needed in America is a
reduction in American government purchases of 60.

Step 4 refers to the output lag. The reduction in European government
purchases of 60 causes a decline in European output of 60. As a side effect, it
49

causes a decline in American output of equally 60. The reduction in American
government purchases of 60 causes a decline in American output of 60. As a side
effect, it causes a decline in European output of equally 60. The total effect is a
decline in European output of 120 and a decline in American output of equally
120. As a consequence, European output goes from 1060 to 940, as does
American output.

With this, output is back at its initial level, hence this process will repeat
itself. Table 1.17 gives an overview. There are uniform oscillations in European
government purchases, and the same holds for American government purchases.
There are uniform oscillations in European output, and the same holds for
American output. As a result, the process of fiscal competition does not lead to
full employment.



Table 1.17
Fiscal Competition between Europe and America
Unemployment in Europe Equals Unemployment in America

Europe America


Initial Output 940 940
60 60
Change in Government Purchases
Output 1060 1060
Change in Government Purchases -60
-60
940 940
Output
and so on




3) Unemployment in Europe exceeds overemployment in America. At the
start there is unemployment in Europe but overemployment in America. Thus
there is inflation in America. Let initial output in Europe be 940, and let initial
output in America be 1030. Step 1 refers to the policy response. The output gap
in Europe is 60. The fiscal policy multiplier in Europe is 1. So what is needed in
50

Europe is an increase in European government purchases of 60. The inflationary
gap in America is 30. The fiscal policy multiplier in America is 1. So what is
needed in America is a reduction in American government purchases of 30.

Step 2 refers to the output lag. The increase in European government
purchases of 60 causes an increase in European output of 60. As a side effect, it
causes an increase in American output of equally 60. The reduction in American
government purchases of 30 causes a decline in American output of 30. As a side
effect, it causes a decline in European output of equally 30. The net effect is an
increase in European output of 30 and an increase in American output of equally
30. As a consequence, European output goes from 940 to 970, and American
output goes from 1030 to 1060.

Step 3 refers to the policy response. The output gap in Europe is 30. The
fiscal policy multiplier in Europe is 1. So what is needed in Europe is an increase
in European government purchases of 30. The inflationary gap in America is 60.
The fiscal policy multiplier in America is 1. So what is needed in America is a
reduction in American government purchases of 60.

Step 4 refers to the output lag. The increase in European government
purchases of 30 causes an increase in European output of 30. As a side effect, it
causes an increase in American output of equally 30. The reduction in American
government purchases of 60 causes a decline in American output of 60. As a side
effect, it causes a decline in European output of equally 60. The net effect is a
decline in European output of 30 and a decline in American output of equally 30.
As a consequence, European output goes from 970 to 940, and American output
goes from 1060 to 1030.

At this point in time, output is back at its initial level. So this process will
repeat itself. For a synopsis see Table 1.18. What are the dynamic
characteristics? There are repeated increases in European government purchases.
On the other hand, there are repeated cuts in American government purchases.
There are uniform oscillations in European output, as there are in American
output. The European economy oscillates between high and low unemployment.
The American economy oscillates between high and low overemployment. As a
result, fiscal competition does not lead to full employment.
51


Table 1.18
Fiscal Competition between Europe and America
Unemployment in Europe Exceeds Overemployment in America

Europe America


1030
Initial Output 940
Change in Government Purchases 60 -30
1060
Output 970
Change in Government Purchases 30 -60
940 1030
Output
and so on




4) 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. So what is needed in Europe is an increase in European
government purchases of 60. The inflationary gap in America is 60. The fiscal
policy multiplier in America is 1. So what is needed in America is a reduction in
American government purchases of 60.

Step 2 refers to the output lag. The increase in European government
purchases of 60 causes an increase in European output of 60. As a side effect, it
causes an increase in American output of equally 60. The reduction in American
government purchases of 60 causes a decline in American output of 60. As a side
effect, it causes a decline in European output of equally 60. The net effect is that
European output does not change, and neither does American output. As a
consequence, European output is still 940, and American output is still 1060.

Step 3 refers to the policy response. The output gap in Europe is 60. The
fiscal policy multiplier in Europe is 1. So what is needed in Europe is an increase
in European government purchases of 60. The inflationary gap in America is 60.
52


The fiscal policy multiplier in America is 1. So what is needed in America is a
reduction in American government purchases of 60.

Step 4 refers to the output lag. The increase in European government
purchases of 60 causes an increase in European output of 60. As a side effect, it
causes an increase in American output of equally 60. The reduction in American
government purchases of 60 causes a decline in American output of 60. As a side
effect, it causes a decline in European output of equally 60. The net effect is that
European output does not change, and neither does American output. As a
consequence, European output is still 940, and American output is still 1060.

That means, European output and American output stay at their initial levels.
This process will repeat itself step by step. For an overview see Table 1.19. There
are repeated increases in European government purchases. By contrast, there are
repeated cuts in American government purchases. However, there is no change in
European output, and the same applies to American output. In Europe there is
unemployment, and in America there is overemployment. As a result, fiscal
competition does not lead to full employment.



Table 1.19
Fiscal Competition between Europe and America
Unemployment in Europe Equals Overemployment in America

Europe America


1060
Initial Output 940
Change in Government Purchases 60 -60
Output 940 1060
Change in Government Purchases 60 -60
Output 940 1060
and so on
53


5) Summary. There is an upward trend in European government purchases.
On the other hand, there is a downward trend in American government
purchases. There are uniform oscillations in European output, and there are
uniform oscillations in American output. As a finding, fiscal competition
between Europe and America does not lead to full employment.

6) Comparing fiscal competition with monetary competition. Monetary
competition can achieve full employment, but fiscal competition cannot do so.
Judging from this point of view, monetary competition is superior to fiscal
competition.
Chapter 4
Fiscal Cooperation
between Europe and America
1. The Model



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


Yj = A 1 + Y G i + Y G 2 (1)
Y2=A2+YG2+yG1 (2)

Here Yx denotes European output, Y2 is American output, Gx 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. More precisely,
unemployment in Europe exceeds unemployment in America. The targets of
fiscal cooperation are full employment in Europe and full employment in
America. The instruments of fiscal cooperation are European government
purchases and American government purchases. So there are two targets and two
instruments.

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


(3)
Y2=A2+YG2+YG1 (4)


Here Yl 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. Now take the
difference between equations (3) and (4) to find out:
55


Y1-Y2=A1-A2 (5)

However, this is in direct contradiction to the assumption that Y±, Y2, AJ and A 2
are given independently. As a result, there is no solution to fiscal cooperation.
That is to say, fiscal cooperation between Europe and America cannot achieve
full employment in Europe and America. The underlying reason is the large
external effect of fiscal policy.




2. Some Numerical Examples



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

Yx = A 1 + G 1 + G 2 (1)
Y2=A2+G2+G1 (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 100 and an increase in American output of equally 100.
Further let full-employment output in Europe be 1000, and let full-employment
output in America be the same.

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

1) Unemployment in Europe exceeds unemployment in America. Let initial
output in Europe be 940, and let initial output in America be 970. In this case, the
specific target of fiscal cooperation is full employment in America. Aiming for
56

full employment in Europe would imply overemployment in America and, hence,
inflation in America. So what is needed is an increase in American output of 30.
What is needed, for instance, is an increase in European government purchases of
15 and an increase in American government purchases of equally 15.

The increase in European government purchases of 15 raises European output
and American output by 15 each. Similarly, the increase in American
government purchases of 15 raises American output and European output by 15
each. The total effect is an increase in European output of 30 and an increase in
American output of equally 30. As a consequence, European output goes from
940 to 970, and American output goes from 970 to 1000. In Europe
unemployment comes down, but there is still some unemployment left. In
America there is now full employment. As a result, in this case, fiscal
cooperation can reduce unemployment in Europe and America to a certain
extent. On the other hand, fiscal cooperation cannot achieve full employment in
both Europe and America. Table 1.20 presents a synopsis.



Table 1.20
Fiscal Cooperation between Europe and America
Unemployment in Europe Exceeds Unemployment in America

Europe America


970
Initial Output 940
15
Change in Government Purchases 15
1000
Output 970




2) Unemployment in Europe equals unemployment in America. Let initial
output in Europe be 940, and let initial output in America be the same. In this
case, the specific targets of fiscal cooperation are full employment in Europe and
full employment in America. What is needed, then, is an increase in European
output of 60 and an increase in American output of equally 60. What is needed,
for instance, is an increase in European government purchases of 30 and an
57


increase in American government purchases of equally 30. The total effect is to
raise European output and American output by 60 each. As a consequence,
European output goes from 940 to 1000, as does American output. In this special
case, fiscal cooperation can in fact achieve full employment in both Europe and
America. Table 1.21 gives an overview.



Table 1.21
Fiscal Cooperation between Europe and America
Unemployment in Europe Equals Unemployment in America

Europe America


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




3) Unemployment in Europe, overemployment in America. At the start there
is unemployment in Europe but overemployment in America. Thus there is
inflation in America. Let initial output in Europe be 940, and let initial output in
America be 1030. First consider an increase in European government purchases
of 60. This policy action raises European output and American output by 60
each. As a consequence, European output goes from 940 to 1000, and American
output goes from 1030 to 1090. In Europe, unemployment comes down. In
America, however, inflation goes up. So this cannot be a solution to fiscal
cooperation.

Second consider a reduction in American government purchases of 30. This
policy action lowers American output and European output by 30 each. As a
consequence, American output goes from 1030 to 1000, and European output
goes from 940 to 910. In America, inflation comes down. In Europe, however,
unemployment goes up. So this cannot be a solution to fiscal cooperation either.
For a synopsis see Table 1.22. The general point is that fiscal cooperation cannot
58


raise European output and lower American output at the same time. As a result,
in this case, there is no solution to fiscal cooperation.



Table 1.22
Fiscal Cooperation between Europe and America
Unemployment in Europe, Overemployment in America

Europe America


Initial Output 940 1030
Change in Government Purchases 0 -30
Output 910 1000




4) Summary. Fiscal cooperation between Europe and America generally
cannot achieve full employment in Europe and America. On the other hand, it
can reduce unemployment in Europe and America to a certain extent.

5) Comparing fiscal cooperation with fiscal competition. Fiscal competition
cannot achieve full employment. The same is true of fiscal cooperation. Fiscal
competition cannot reduce unemployment. Fiscal cooperation can reduce
unemployment to a certain extent. Under fiscal competition there is a tendency
for government purchases to explode. And there is a tendency for output to
oscillate uniformly. Under fiscal cooperation there are no such tendencies.
Judging from these points of view, fiscal cooperation seems to be superior to
fiscal competition.

6) Comparing fiscal cooperation with monetary cooperation. Monetary
cooperation can achieve full employment. By contrast, fiscal cooperation cannot
achieve full employment. From this perspective, monetary cooperation is
superior to fiscal cooperation.
Chapter 5
The Anticipation of Policy Spillovers


The focus here is on monetary competition between Europe and America. 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. That
means, the inside lag of monetary policy is short. On the other hand, the outside
lag of monetary policy is long and variable.

In the current chapter we assume that the European central bank anticipates
the spillovers from monetary policy in America. Likewise we assume that the
American central bank anticipates the spillovers from monetary policy in Europe.
To illustrate this, have a look at some numerical examples. An increase in
European money supply of 100 causes an increase in European output of 300 and
a decline in American output of 100. Similarly, an increase in American money
supply of 100 causes an increase in American output of 300 and a decline in
European output of 100. Further let full-employment output in Europe be 1000,
and let full-employment output in America be the same.

It proves useful to study 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. Let initial
output in Europe be 940, and let initial output in America be the same. Steps 1, 2
and 3 refer to a series of policy responses. Then step 4 refers to the output lag.
Let us begin with step 1. The output gap in Europe is 60. The monetary policy
multiplier in Europe is 3. So what is needed in Europe is an increase in European
money supply of 20. The output gap in America is 60. The monetary policy
60


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

In step 2, the European central bank anticipates the effect of the increase in
American money supply. And the American central bank anticipates the effect of
the increase in European money supply. The European central bank expects that,
due to the increase in American money supply of 20, European output will only
rise to 980. And the American central bank expects that, due to the increase in
European money supply of 20, American output will only rise to 980. The
expected output gap in Europe is 20. The monetary policy multiplier in Europe is
3. So what is needed in Europe is an increase in European money supply of 6.7.
The expected output gap in America is 20. The monetary policy multiplier in
America is 3. So what is needed in America is an increase in American money
supply of 6.7.

We now come to step 3. The European central bank expects that, due to the
increase in American money supply of 6.7, European output will only rise to
993.3. And the American central bank expects that, due to the increase in
European money supply of 6.7, American output will only rise to 993.3. The
expected output gap in Europe is 6.7. The monetary policy multiplier in Europe
is 3. So what is needed in Europe is an increase in European money supply of
2.2. The expected output gap in America is 6.7. The monetary policy multiplier
in America is 3. So what is needed in America is an increase in American money
supply of 2.2.

Step 4 refers to the output lag. The accumulated increase in European money
supply of 28.9 causes an increase in European output of 86.7. As a side effect, it
causes a decline in American output of 28.9. The accumulated increase in
American money supply of 28.9 causes an increase in American output of 86.7.
As a side effect, it causes a decline in European output of 28.9. The net effect is
an increase in European output of 57.8 and an increase in American output of
equally 57.8. As a consequence, European output goes from 940 to 997.8, as
does American output. Table 1.23 presents a synopsis. As a result, the
anticipation of policy spillovers speeds up the process of monetary competition.
61

Table 1.23
Monetary Competition between Europe and America
The Anticipation of Policy Spillovers

Europe America


940 940
Initial Output
20
Change in Money Supply 20
6.7
Change in Money Supply 6.7
2.2
Change in Money Supply 2.2
997.8
Output 997.8




2) Unemployment in Europe exceeds unemployment in America. Let initial
output in Europe be 940, and let initial output in America be 970. Steps 1, 2 and
3 refer to a series of policy responses. Then step 4 refers to the output lag. Let us
begin with step 1. The output gap in Europe is 60. The monetary policy
multiplier in Europe is 3. So what is needed in Europe is an increase in European
money supply of 20. The output gap in America is 30. The monetary policy
multiplier in America is 3. So what is needed in America is an increase in
American money supply of 10.

In step 2, the European central bank anticipates the effect of the increase in
American money supply. And the American central bank anticipates the effect of
the increase in European money supply. The European central bank expects that,
due to the increase in American money supply of 10, European output will only
rise to 990. And the American central bank expects that, due to the increase in
European money supply of 20, American output will only rise to 980. The
expected output gap in Europe is 10. The monetary policy multiplier in Europe is
3. So what is needed in Europe is an increase in European money supply of 3.3.
The expected output gap in America is 20. The monetary policy multiplier in
America is 3. So what is needed in America is an increase in American money
supply of 6.7.
62

We now come to step 3. The European central bank expects that, due to the
increase in American money supply of 6.7, European output will only rise to
993.3. And the American central bank expects that, due to the increase in
European money supply of 3.3, American output will only rise to 996.7. The
expected output gap in Europe is 6.7. The monetary policy multiplier in Europe
is 3. So what is needed in Europe is an increase in European money supply of
2.2. The expected output gap in America is 3.3. The monetary policy multiplier
in America is 3. So what is needed in America is an increase in American money
supply of 1.1.

Step 4 refers to the output lag. The accumulated increase in European money
supply of 25.6 causes an increase in European output of 76.7. As a side effect, it
causes a decline in American output of 25.6. The accumulated increase in
American money supply of 17.8 causes an increase in American output of 53.3.
As a side effect, it causes a decline in European output of 17.8. The net effect is
an increase in European output of 58.9 and an increase in American output of
27.8. As a consequence, European output goes from 940 to 998.9, and American
output goes from 970 to 997.8. Table 1.24 gives an overview.



Table 1.24
Monetary Competition between Europe and America
The Anticipation of Policy Spillovers

Europe America


Initial Output 940 970
Change in Money Supply 20 10
Change in Money Supply 3.3 6.7
Change in Money Supply 2.2 1.1
Output 998.9 997.8
63

3) Unemployment in Europe equals overemployment in America. Let initial
output in Europe be 940, and let initial output in America be 1060. Steps 1, 2 and
3 refer to a series of policy responses. Then step 4 refers to the output lag. Let us
begin with step 1. The output gap in Europe is 60. The monetary policy
multiplier in Europe is 3. So what is needed in Europe is an increase in European
money supply of 20. The inflationary gap in America is 60. The monetary policy
multiplier in America is 3. So what is needed in America is a reduction in
American money supply of 20.

In step 2, the European central bank anticipates the effect of the reduction in
American money supply. And the American central bank anticipates the effect of
the increase in European money supply. The European central bank expects that,
due to the reduction in American money supply of 20, European output will go to
1020. And the American central bank expects that, due to the increase in
European money supply of 20, American output will go to 980. The expected
inflationary gap in Europe is 20. The monetary policy multiplier in Europe is 3.
So what is needed in Europe is a reduction in European money supply of 6.7. The
expected output gap in America is 20. The monetary policy multiplier in America
is 3. So what is needed in America is an increase in American money supply of
6.7.

We now come to step 3. The European central bank expects that, due to the
increase in American money supply of 6.7, European output will go to 993.3.
And the American central bank expects that, due to the reduction in European
money supply of 6.7, American output will go to 1006.7. The expected output
gap in Europe is 6.7. The monetary policy multiplier in Europe is 3. So what is
needed in Europe is an increase in European money supply of 2.2. The expected
inflationary gap in America is 6.7. The monetary policy multiplier in America is
3. So what is needed in America is a reduction in American money supply of 2.2.

Step 4 refers to the output lag. The accumulated increase in European money
supply of 15.6 causes an increase in European output of 46.7. As a side effect, it
causes a decline in American output of 15.6. The accumulated reduction in
American money supply of 15.6 causes a decline in American output of 46.7. As
a side effect, it causes an increase in European output of 15.6. The total effect is
an increase in European output of 62.2 and a decline in American output of
equally 62.2. As a consequence, European output goes from 940 to 1002.2, and
64

American output goes from 1060 to 997.8. For a synopsis see Table 1.25. As a
result, the anticipation of policy spillovers speeds up the process of monetary
competition. In a sense, it prevents output from oscillating.



Table 1.25
Monetary Competition between Europe and America
The Anticipation of Policy Spillovers

Europe America


Initial Output 940 1060
Change in Money Supply 20 -20
-6.7
Change in Money Supply 6.7
2.2
Change in Money Supply -2.2
1002.2 997.8
Output




4) Comparing anticipation and non-anticipation. Without anticipation,
monetary competition is a slow process. With anticipation, by contrast, monetary
competition is a fast process. Without anticipation, there can be damped
oscillations in output. With anticipation, there cannot be damped oscillations in
output. Judging from these points of view, anticipation is superior to non-
anticipation.

5) Comparing monetary competition and monetary cooperation, given
anticipation. Monetary competition can achieve full employment. The same is
true of monetary cooperation. Monetary competition is a fast process. Again, the
same is true of monetary cooperation. From these perspectives, there seems to be
no need for monetary cooperation.
Part Two


The World of
Two Monetary Regions


Intermediate Models
Chapter 1
Zero Capital Mobility
1. Fiscal Competition between Europe and America


In the preceding chapters we assumed perfect capital mobility between
Europe and America. In the current chapter, instead, we assume zero capital
mobility between Europe and America. As a point of reference, consider the
static model. It can be represented by a system of two equations:


(1)
Y2=A2+2G2 (2)


According to equation (1), European output Yx is determined by European
government purchases Gi and by some other factors called A1# According to
equation (2), American output Y2 is determined by American government
purchases G 2 and by some other factors called A 2 .

In the numerical example, an increase in European government purchases of
100 causes an increase in European output of 200 and an increase in American
output of zero. Correspondingly, an increase in American government purchases
of 100 causes an increase in American output of 200 and an increase 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 beginning there is unemployment in both Europe and America. The
target of the European government is full employment in Europe. The target of
the American government 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 fiscal policy multiplier in
Europe is 2. So what is needed in Europe is an increase in European government
purchases of 30. The output gap in America is 30. The fiscal policy multiplier in
68


America is 2. So what is needed in America is an increase in American
government purchases of 15.

Step 2 refers to the output lag. The increase in European government
purchases of 30 causes an increase in European output of 60. There is no side
effect on American output. The increase in American government purchases of
15 causes an increase in American output of 30. There is no side effect on
European output. 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. Table 2.1 presents a synopsis.



Table 2.1
Fiscal Competition between Europe and America
Zero Capital Mobility

Europe America


Initial Output 940 970
Change in Government Purchases 15
30
Output 1000 1000




What are the dynamic characteristics of this process? There is a one-step
increase in European government purchases, as there is in American government
purchases. There is a one-step increase in European output, as there is in
American output. To sum up, under zero capital mobility, fiscal competition
leads to full employment immediately. The underlying reason is that, under zero
capital mobility, there are no spillovers of fiscal policy. Finally compare zero
capital mobility with perfect capital mobility. Under perfect capital mobility,
fiscal competition does not lead to full employment at all. Under zero capital
mobility, however, fiscal competition leads to full employment immediately.
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