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endogenous variables are European nominal wages this period W 1 , American
nominal wages this period W 2 , European output next period Yx+1, and American
output next period Y^1.

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

W^Wf1 (11)
W2=W21 (12)

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

Y^^ (13)
Y2 = Y2 (14)
Yx = A 1 - e W 1 +riW2 (15)
Y2 = A 2 - e W 2 + r | W 1 (16)
145

Here the endogenous variables are European output Yl, American output Y 2 ,
European nominal wages W x , and American nominal wages W 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 nominal wages.

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

Yx = A 1 - e W 1 +r|W 2 (17)
Y2 = A 2 - e W 2 + r i W 1 (18)

Here the endogenous variables are European nominal wages and American
nominal wages. To simplify notation we introduce:

B^Ai-Y! (19)
B2=A2-Y2 (20)

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

B1 = eW 1 -riW 2 (21)
B 2 =8W 2 -T 1 W 1 (22)

The endogenous variables are still Wl and W 2 .

Next we solve the model for the endogenous variables:

eB^riEb
8 2 -T| 2

|li (24)
e 2 - r|2
146

Equation (23) shows the steady-state level of European nominal wages, and
equation (24) shows the steady-state level of American nominal wages. As a
result, there is a steady state if and only e ^ r\. Owing to the assumption e > r|,
this condition is fulfilled.

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

AYX = - eAWi + riAW2 (25)
AY2 = - eAW2 + TiAWi (26)

Here AYX is the initial output gap in Europe, AY2 is the initial output gap in
America, AWX is the total change in European nominal wages, and AW2 is the
total change in American nominal wages. The endogenous variables are
and AW2. The solution to the system (25) and (26) is:

82 - rf

ez-r[z

According to equation (27), the total cut in European nominal wages depends on
the initial output gap in Europe, the initial output gap in America, the direct
multiplier 8, and the cross multiplier r\. The larger the initial output gap in
Europe, the larger is the total cut in European nominal wages. Moreover, the
larger the initial output gap in America, the larger is the total cut in European
nominal wages. At first glance this comes as a surprise. According to equation
(28), the total cut in American nominal wages depends on the initial output gap
in America, the initial output gap in Europe, the direct multiplier 8, and the cross
multiplier r|.

4) Stability. Eliminate Yl in equation (7) by means of equation (9) and
rearrange terms Yx = Ax - eW^ + viW^1. By analogy, eliminate Y2 in equation
147

(8) by means of equation (10) to arrive at Y2 = A 2 - eW2 + T|W1 l. On this basis,
the dynamic model can be described by a system of two equations:

Y{ =A 1 -eW 1 +riW 2 - 1 (29)
Y2 = A 2 - eW2 + riWf1 (30)

Here the endogenous variables are European nominal wages W2 and American
nominal wages W 2 . To simplify notation we make use of equations (19) and
(20). With this, the dynamic model can be written as follows:

Bx = eWl - TiWT1 (31)
B 2 = eW2 - riWf1 (32)

The endogenous variables are still Wj and W 2 .

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

^ (33)

Then differentiate equation (33) for Wf2:

-^ =% (34)
dWf2 e2
Finally the stability condition is r\2 I e 2 < 1 or:

e>T! (35)

That means, the steady state is stable if and only if the internal effect of wage
policy is larger than the external effect of wage policy. This condition is satisfied.
As a result, there is a stable steady state of wage policy competition. In other
words, competition between the European labour union and the American labour
union leads to full employment in Europe and America.
148

2. A Numerical Example

To illustrate the dynamic model, have a look at a numerical example. For ease
of exposition, without loss of generality, assume 8 = 3 and r| = l. On this
assumption, the static model can be written as follows:

Y2 = A 1 - 3 W 1 + W 2 (1)
Y2=A2-3W2+W1 (2)

The endogenous variables are European and American output. Obviously, an
increase in European nominal wages of 100 causes a decline in European output
of 300 and an increase in American output of 100. Strictly speaking, what
matters here is the change in European output relative to the change in American
output 300/100 = 3. Compare this with the results given in the preceding section,
where we had 0.75/0.25 = 3. Further, an increase in American nominal wages of
100 causes a decline in American output of 300 and an increase in European
output of 100. Let full-employment output in Europe be 1000, and let full-
employment output in America be the same.

At the beginning there is unemployment in 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 wage policy
multiplier in Europe is - 3 . So what is needed in Europe is a reduction in
European nominal wages of 20. The output gap in America is 60. The wage
policy multiplier in America is - 3 . So what is needed in America is a reduction
in American nominal wages of 20.

Step 2 refers to the output lag. The reduction in European nominal wages of
20 causes an increase in European output of 60. As a side effect, it causes a
decline in American output of 20. The reduction in American nominal wages of
20 causes an increase in American output of 60. As a side effect, it causes a
decline in European output of 20. The net effect is an increase in European
149

output of 40 and an increase in American output of equally 40. As a
consequence, European output goes from 940 to 980, as does American output.

Why does the European labour union not succeed in closing the output gap in
Europe? The underlying reason is the negative external effect of the reduction in
American nominal wages. And why does the American labour union not succeed
in closing the output gap in America? The underlying reason is the negative
external effect of the reduction in European nominal wages.

Step 3 refers to the policy response. The output gap in Europe is 20. The
wage policy multiplier in Europe is - 3 . So what is needed in Europe is a
reduction in European nominal wages of 6.7. The output gap in America is 20.
The wage policy multiplier in America is - 3 . So what is needed in America is a
reduction in American nominal wages of 6.7.

Step 4 refers to the output lag. The reduction in European nominal wages of
6.7 causes an increase in European output of 20. As a side effect, it causes a
decline in American output of 6.7. The reduction in American nominal wages of
6.7 causes an increase in American output of 20. As a side effect, it causes a
decline in European output of 6.7. The net effect is an increase in European
output of 13.3 and an increase in American output of equally 13.3. As a
consequence, European output goes from 980 to 993.3, as does American output.
And so on. Table 3.6 gives an overview.

What are the dynamic characteristics of this process? There are repeated cuts
in European nominal wages, as there are in American nominal wages. There are
repeated increases in European output, as there are in American output. In each
round, the output gap declines by 67 percent. As a result, competition between
the European labour union and the American labour union leads to full
employment in Europe and America.

Taking the sum over all periods, the reduction in European nominal wages is
30, as is the reduction in American nominal wages, see equations (27) and (28) in
the previous section. That means, the total reduction in European nominal wages
is large, as compared to the initial output gap in Europe of 60. And the same
applies to the total reduction in American nominal wages, as compared to the
initial output gap in America of 60. The effective multiplier in Europe is 60/30 =
150

2, as is the effective multiplier in America. In other words, the effective
multiplier in Europe is small. And the same is true of the effective multiplier in
America.

Finally compare wage policy competition with monetary policy competition.
Monetary policy competition leads to full employment. And the same holds for
wage policy competition. Monetary policy competition is a relatively fast
process. By contrast, wage policy competition is a relatively slow process.
Judging from these points of view, monetary policy competition seems to be
superior to wage policy competition.

Table 3.6
Competition between the European Labour Union and
the American Labour Union
Unemployment in Europe and America

America
Europe

Initial Output 940
940
Change in Nominal Wages -20
-20
980
Output 980
Change in Nominal Wages -6.7
-6.7
993.3
Output 993.3
and so on
Chapter 4
Cooperation between
the European Labour Union
and the American Labour Union
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 - e W 1 + r | W 2 (1)
Y2 = A 2 - e W 2 + r i W 1 (2)

Here Yx denotes European output, Y2 is American output, Wj is European
nominal wages, and W2 is American nominal wages. The endogenous variables
are European output and American output. At the beginning there is
unemployment in both Europe and America. The targets of wage policy
cooperation are full employment in Europe and full employment in America. The
instruments of wage policy cooperation are European nominal wages and
American nominal wages. 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-eW1+riW2 (3)
Y2 = A 2 - e W 2 + r i W 1 (4)

Here Yt denotes full-employment output in Europe, and Y2 denotes full-
employment output in America. The endogenous variables are European nominal
wages and American nominal wages.
152

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

_
Â£ 2_ T |2

â€”2 '.-I
= (6)
2 2
e -ri

Equation (5) shows the required level of European nominal wages, and equation
(6) shows the required level of American nominal wages. There is a solution if
and only if e * r\. Due to the assumption e > r|, this condition is met. As a result,
cooperation between the European labour union and the American labour union
can achieve full employment in Europe and America. It is worth pointing out
here that the solution to wage policy cooperation is identical to the steady state of
wage policy 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 change in nominal
wages. Taking differences in equations (1) and (2), the policy model can be
written as follows:

AYt =-8AW1+TIAW2 (7)

AY2 =-eAW 2 +riAW 1 (8)

Here AYX denotes the initial output gap in Europe, AY2 is the initial output gap
in America, AWX is the required change in European nominal wages, and AY2 is
the required change in American nominal wages. The endogenous variables are
and AW2. The solution to the system (7) and (8) is:

8 2 -T| 2

e 2 - r|2
153

According to equation (9), the required cut in European nominal wages depends
on the initial output gap in Europe, the initial output gap in America, the direct
multiplier 8, and the cross multiplier r|. The larger the initial output gap in
Europe, the larger is the required cut in European nominal wages. Moreover, the
larger the initial output gap in America, the larger is the required cut in European
nominal wages. At first glance this comes as a surprise. According to equation
(10), the required cut in American nominal wages depends on the initial output
gap in America, the initial output gap in Europe, the direct multiplier 8, and the
cross multiplier r\.

2. Some Numerical Examples

To illustrate the policy model, have a look at some numerical examples. For
ease of exposition, without losing generality, assume 8 = 3 and r| = l. On this
assumption, the output model can be written as follows:

Yx = A 1 - 3 W 1 + W 2 (1)
Y2=A2-3W2+WX (2)

The endogenous variables are European and American output. Evidently, an
increase in European nominal wages of 100 causes a decline in European output
of 300 and an increase 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 four 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 equals overemployment in America.
154

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 a reduction in
European nominal wages of 30 and a reduction in American nominal wages of
equally 30. The reduction in European nominal wages of 30 raises European
output by 90 and lowers American output by 30. The reduction in American
nominal wages 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, wage policy cooperation can
achieve full employment.

However, the required cut in European nominal wages is large, as compared
to the initial output gap in Europe. And the same applies to the required cut in
American nominal wages, 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 3.7 gives an overview.

Table 3.7
Cooperation between the European Labour Union and
the American Labour Union
Unemployment in Europe and America

Europe America

Initial Output 940
940
Change in Nominal Wages -30
-30
Output 1000
1000
155

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. What is needed, according
to equations (9) and (10) from the previous section, is a reduction in European
nominal wages of 26.25 and a reduction in American nominal wages of 18.75.
The reduction in European nominal wages of 26.25 raises European output by
78.75 and lowers American output by 26.25. The reduction in American nominal
wages 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, wage policy
cooperation can achieve full employment.

However, the required cut in European nominal wages is large, as compared
to the initial output gap in Europe. And the required cut in American nominal
wages 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.

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 a
reduction in European nominal wages of 22.5 and a reduction in American
nominal wages of 7.5. The reduction in European nominal wages of 22.5 raises
European output by 67.5 and lowers American output by 22.5. The reduction in
American nominal wages 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.

4) 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 a reduction in European nominal wages of 15 and an increase in American
nominal wages of equally 15. The reduction in European nominal wages of 15
156

raises European output by 45 and lowers American output by 15. The increase in
American nominal wages 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 effective multiplier in
Europe is 4, 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.

5) Comparing wage policy cooperation with wage policy competition. Wage
policy competition can achieve full employment. The same applies to wage
policy cooperation. Wage policy competition is a slow process. By contrast,
wage policy cooperation is a fast process. Judging from these points of view,
wage policy cooperation seems to be superior to wage policy competition.

6) Comparing wage policy cooperation with monetary policy cooperation.
Monetary policy cooperation can achieve full employment. The same holds for
wage policy cooperation. Monetary policy cooperation does not require any
changes in nominal wages and prices. On the other hand, wage policy
cooperation can require large changes in nominal wages and prices. Judging from
this perspective, monetary policy cooperation seems to be superior to wage
policy cooperation.
Chapter 5
Inflation in Europe and America
1. Monetary Competition between Europe and America

1.1. The Dynamic Model

1) The model of output and inflation. To begin with, consider a stylized
model of output and inflation:

Yx = A 1 + a M 1 / P 1 - p M 2 / P 2 (1)
Y2 = A 2 + a M 2 / P 2 - ( 3 M 1 / P 1 (2)
Px = M Y i - Y 1 ) / Y 1 (3)
P2=X(Y2-Y2)/Y2 (4)

According to equation (1), European output Yx is determined by European
money supply M1? the price of European goods Pl5 American money supply M 2 ,
the price of American goods P 2 , and some other factors called Ax. According to
equation (2), American output Y2 is determined by American money supply M 2 ,
the price of American goods P 2 , European money supply M l5 the price of
European goods P l5 and some other factors called A 2 . The coefficients a and (3
are positive with a > (3. An increase in European money supply raises European
output but lowers American output. An increase in the price of European goods
lowers European output but raises American output.

In equation (3), Pj is the rate of growth of the price of European goods. The
hat denotes the rate of growth r\ = f\ / P1, and the dot denotes the time derivative
Pl=dPi/dt. In other words, r\ is producer inflation in Europe. Y2 is full-
employment output in Europe. Yx - Y1 is the inflationary gap in Europe.
(Yi - Yj) / Yx is the inflationary gap in Europe, expressed as a percentage of full-
employment output in Europe. And X is the speed of price adjustment.
According to equation (3), producer inflation in Europe is proportional to the
inflationary gap in Europe.
158

In equation (4), P2 is the rate of growth of the price of American goods. In
other words, P2 is producer inflation in America. Y2 is full-employment output in
America. Y 2 - Y 2 is the inflationary gap in America. ( Y 2 - Y 2 ) / Y 2 is the
inflationary gap in America, expressed as a percentage of full-employment
output in America. According to equation (4), producer inflation in America is
proportional to the inflationary gap in America. In equations (1) to (4), the
endogenous variables are European output, American output, producer inflation
in Europe, and producer inflation in America. For the behavioural foundations of
the model see Carlberg (2001, 2002).

2) The policy model. The target of the European central bank is price stability
in Europe. The instrument of the European central bank is European money
supply. The European central bank lowers European money supply so as to close
the inflationary gap in Europe. The target of the American central bank is price
stability in America. The instrument of the American central bank is American
money supply. The American central bank lowers American money supply so as
to close the inflationary gap in America. We assume that the European central
bank and the American central bank decide simultaneously and independently. In
the policy model, the endogenous variables are European money supply,
American money supply, producer inflation in Europe, and producer inflation in
America.

1.2. A Numerical Example

To illustrate the policy model, take a numerical example with a = 3, (3 = 1 and
X = 0.1. Let initial prices be Px = P2 = 1. Then 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. At the beginning there is
overemployment in both Europe and America. For that reason there is inflation in
both Europe and America. More precisely, overemployment in Europe exceeds
overemployment in America. For that reason, inflation in Europe exceeds
159

inflation in America. Let initial output in Europe be 1060, and let initial output in
America be 1030. That means, the inflationary gap in Europe is 60, and the
inflationary gap in America is 30. Then, according to equations (3) and (4),
inflation in Europe is 6 percent, and inflation in America is 3 percent.

Step 1 refers to the policy response. The inflationary gap in Europe is 60. The
monetary policy multiplier in Europe is 3. So what is needed in Europe is a
reduction in European money supply of 20. The inflationary gap in America is
30. The monetary policy multiplier in America is 3. So what is needed in
America is a reduction in American money supply of 10.

Step 2 refers to the output lag. The reduction in European money supply of 20
causes a decline in European output of 60. As a side effect, it causes an increase
in American output of 20. The reduction in American money supply of 10 causes
a decline in American output of 30. As a side effect, it causes an increase in
European output of 10. The net effect is a decline in European output of 50 and a
decline in American output of 10. As a consequence, European output goes from
1060 to 1010, and American output goes from 1030 to 1020. Now the
inflationary gap in Europe is 10, and the inflationary gap in America is 20.
Therefore inflation in Europe is 1 percent, and inflation in America is 2 percent.

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

Step 4 refers to the output lag. The reduction in European money supply of
3.3 causes a decline in European output of 10. As a side effect, it causes an
increase in American output of 3.3. The reduction in American money supply of
6.7 causes a decline in American output of 20. As a side effect, it causes an
increase in European output of 6.7. The net effect is a decline in European output
of 3.3 and a decline in American output of 16.7. As a consequence, European
output goes from 1010 to 1006.7, and American output goes from 1020 to
1003.3. Now the inflationary gap in Europe is 6.7, and the inflationary gap in
America is 3.3. Therefore inflation in Europe is 0.67 percent, and inflation in
America is 0.33 percent. And so on. Table 3.8 presents a synopsis.
160

Table 3.8
Monetary Competition between Europe and America
Inflation in Europe and America

Europe America

Initial Output 1060 1030
Inflation 6 3
Change in Money Supply -20 -10
Output 1010 1020
1
Inflation 2
Change in Money Supply -3.3 -6.7
Output 1006.7 1003.3
Inflation 0.7 0.3
and so on

What are the dynamic characteristics of this process? There are repeated cuts
in European money supply, as there are in American money supply. There are
repeated cuts in European output, as there are in American output. There are
repeated cuts in European inflation, as there are in American inflation. As a
result, monetary competition between Europe and America leads to price stability
in Europe and America. By the way, in the numerical example, the feedback
from inflation to output has not been included. This can be defended on the
grounds that monetary policy adjustment is a relatively fast process, as compared
161

2. Monetary Cooperation between Europe and America

At the start there is inflation in Europe and America. More precisely, inflation
in Europe exceeds inflation in America. The targets of monetary cooperation are
price stability in Europe and price stability in America. The instruments of
monetary cooperation are European money supply and American money supply.
So there are two targets and two instruments.

To illustrate this, consider a numerical example with a = 3, (3 = 1 and X = 0.1.
Let initial prices be Pj = P2 = 1. Then an increase in European money supply of
100 causes an increase in European output of 300 and a decline in American
output of 100. Let initial output in Europe be 1060, and let initial output in
America be 1030. That means, the inflationary gap in Europe is 60, and the
inflationary gap in America is 30. According to equations (3) and (4) from
Section 1.1, inflation in Europe is 6 percent, and inflation in America is 3
percent. 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. Now the inflationary gap in
Europe is zero, as is the inflationary gap in America. Therefore, inflation in
Europe is zero, as is inflation in America. As a result, monetary cooperation
between Europe and America can achieve price stability in Europe and America.
Table 3.9 gives an overview.

Finally compare monetary cooperation with monetary competition. Monetary
competition can achieve price stability. And the same holds for 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. However, if policy
162

spillovers are anticipated, then monetary competition is a fast process. Hence, in
this case, there is no need for monetary cooperation.

Table 3.9
Monetary Cooperation between Europe and America
Inflation in Europe and America

Europe America

Initial Output 1060 1030
Inflation 6 3
Change in Money Supply - 26.25 - 18.75
Output 1000 1000
Inflation 0 0
Part Four

The World of
Three Monetary Regions
Chapter 1
Monetary Competition
between Europe, America and Asia
1. The Dynamic Model

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

As a result, an increase in European money supply raises European output.
On the other hand, it lowers both American output and Asian output. Here the
rise in European output exceeds the fall in American output and Asian output
taken together. Correspondingly, an increase in American money supply raises
American output. On the other hand, it lowers both European output and Asian
output. Here the rise in American output exceeds the fall in European output and
Asian output taken together. By analogy, an increase in Asian money supply
raises Asian output. On the other hand, it lowers both European output and
American output. Here the rise in Asian output exceeds the fall in European
output and American output taken together.

In the numerical example, a 1 percent increase in European money supply
causes a 0.83 percent increase in European output, a 0.17 percent decline in
American output, and a 0.17 percent decline in Asian output. Correspondingly, a
166

1 percent increase in American money supply causes a 0.83 percent increase in
American output, 0.17 percent decline in European output, and 0.17 percent
decline in Asian output. By analogy, a 1 percent increase in Asian money supply
causes a 0.83 percent increase in Asian output, a 0.17 percent decline in
European output, and a 0.17 percent decline in American output. That is to say,
the internal effect of monetary policy is very large, and the external effect of
monetary policy is large.

Now have a closer look at the process of adjustment. An increase in European
money supply causes a depreciation of the euro and a decline in the world
interest rate. The depreciation of the euro raises European exports but lowers
American exports and Asian exports. The decline in the world interest rate raises
European investment, American investment, and Asian investment. The net
effect is that European output goes up. However, American output and Asian
output go down. This model is in the tradition of the Mundell-Fleming model,
see Carlberg (2000) p. 205.

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

- (3M2 - (3M3 (1)
Y2 = A 2 + ccM2 - PMX - (3M3 (2)
Y3 = A 3 + a M 3 - PMX - PM 2 (3)

According to equation (1), European output Yl is determined by European
money supply M1? American money supply M 2 , Asian money supply M 3 , and
some other factors called A^ According to equation (2), American output Y2 is
determined by American money supply M 2 , European money supply M^, Asian
money supply M 3 , and some other factors called A 2 . According to equation (3),
Asian output Y3 is determined by Asian money supply M 3 , European money
supply Mi, American money supply M 2 , and some other factors called A 3 . Here
a and P denote the monetary policy multipliers. The internal effect of monetary
policy is positive a > 0 . By contrast, the external effect of monetary policy is
negative P > 0 . In absolute values, the internal effect is larger than the external
effect a > 2P. The endogenous variables are European output, American output,
and Asian output.
167

2) The dynamic model. At the beginning there is unemployment in Europe,
America and Asia. The target of the European central bank is full employment in
Europe. The instrument of the European central bank is European money supply.
The target of the American central bank is full employment in America. The
instrument of the American central bank is American money supply. The target
of the Asian central bank is full employment in Asia. The instrument of the Asian
central bank is Asian money supply. We assume that the European central bank,
the American central bank, and the Asian central bank decide simultaneously and
independently.

The dynamic model can be characterized by a system of three equations:

% = Ax + cxMi - PM2 1 - PM3 l (4)
Y2 = A 2 + ccM2 - (3MJ"1 - PM3 1 (5)

Y3 = A 3 + ocM3 - (3Mfl - (3M21 (6)

Here is a list of the new symbols:
Yl full-employment output in Europe
Y2 full-employment output in America
Y3 full-employment output in Asia
Mj European money supply this period
M2 American money supply this period
M3 Asian money supply this period
Mj"1 European money supply last period
M^ 1 American money supply last period
M 3 1 Asian money supply last period.

According to equation (4), the European central bank sets European money
supply so as to reach full employment in Europe, given American money supply
last period and Asian money supply last period. According to equation (5), the
American central bank sets American money supply so as to reach full
employment in America, given European money supply last period and Asian
money supply last period. According to equation (6), the Asian central bank sets
168

Asian money supply so as to reach full employment in Asia, given European
money supply last period and American money supply last period.

To summarize, equation (4) shows the policy response in Europe, equation
(5) shows the policy response in America, and equation (6) shows the policy
response in Asia. The endogenous variables are European money supply this
period M1? American money supply this period M 2 , and Asian money supply
this period M 3 .

In addition there is an output lag. European output next period is determined
by European money supply this period, American money supply this period, and
Asian money supply this period. American output next period is determined by
American money supply this period, European money supply this period, and
Asian money supply this period. Asian output next period is determined by Asian
money supply this period, European money supply this period, and American
money supply this period.

3) The steady state. The steady state can be represented in terms of the initial
output gap and the total increase in money supply. Taking differences in
equations (1), (2) and (3), the model of the steady state can be written as follows:

i - pAM2 - (3AM3 (7)
AY2 = aAM 2 - PAMj - (3AM3 (8)

AY3 = aAM 3 - PAMj - (3AM2 (9)

Here AYX is the initial output gap in Europe, AY2 is the initial output gap in
America, AY3 is the initial output gap in Asia, AMj_ is the total increase in
European money supply, AM2 is the total increase in American money supply,
and AM3 is the total increase in Asian money supply. The endogenous variables
are AMj, AM2 and AM3.

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

(a-P)AY 1 + P (AY 2 + AY 3 )
AM
1
a 2 -ap-2p 2
169

AM9 = vv˜ K/
" ^ z ' K V "^ i ' " X j ; (11)
â€” r/R â€” 9 R ^
CH^

_ ( g - (3)AY3 + P(AYX + AY 2 )

There is a steady state if and only if a ^2(3. Owing to the assumption
a>2(3, this condition is satisfied. Moreover, the stability condition is a>2(3.
That means, the steady state is stable if and only if the internal effect of monetary
policy is larger than the external effect of monetary policy. By assumption, this
condition is fulfilled. As a result, monetary competition between Europe,
America and Asia leads to full employment in each of the regions.

2. Some Numerical Examples

To illustrate the dynamic model, have a look at some numerical examples.
For ease of exposition, without loss of generality, assume a = 3.33 and (3 = 0.67,
see Carlberg (2000) p. 209. On this assumption, the static model can be written
as follows:

Yx = Aj + 3.33M! - 0.67M2 - 0.67M3 (1)
Y2 = A 2 + 3.33M2 - 0.61Ml - 0.67M3 (2)
Y3 = A 3 + 3.33M3 - 0.61Ml - 0.67M2 (3)

The endogenous variables are European, American and Asian output. Obviously,
an increase in European money supply of 100 causes an increase in European
output of 333. On the other hand, it causes a decline in American output of 67
and a decline in Asian output of equally 67. So the increase in world output is
200. Further let full-employment output in Europe be 1000, let full-employment
170

output in America be 1000, and let full-employment output in Asia be equally
1000.

It proves useful to study two distinct cases:
- the regions have the same unemployment
- the regions differ in unemployment.

1) The regions have the same unemployment. Let initial output in Europe be
940, let initial output in America be 940, and let initial output in Asia be the
same. Step 1 refers to the policy response. The output gap in Europe is 60. The
monetary policy multiplier in Europe is 3.33. So what is needed in Europe is an
increase in European money supply of 18. The output gap in America is 60. The
monetary policy multiplier in America is 3.33. So what is needed in America is
an increase in American money supply of 18. The output gap in Asia is 60. The
monetary policy multiplier in Asia is 3.33. So what is needed in Asia is an
increase in Asian money supply of 18.

Step 2 refers to the output lag. The increase in European money supply of 18
causes an increase in European output of 60. As a side effect, it causes a decline
in American output of 12 and a decline in Asian output of equally 12. The
increase in American money supply of 18 causes an increase in American output
of 60. As a side effect, it causes a decline in European output of 12 and a decline
in Asian output of equally 12. The increase in Asian money supply of 18 causes
an increase in Asian output of 60. As a side effect, it causes a decline in
European output of 12 and a decline in American output of equally 12. The net
effect is an increase in European output of 36, an increase in American output of
36, and an increase in Asian output of equally 36. As a consequence, European
output goes from 940 to 976, American output goes from 940 to 976, and Asian
output goes from 940 to 976. And so on. Table 4.1 presents a synopsis.

What are the dynamic characteristics of this process? There are repeated
increases in European money supply, American money supply, and Asian money
supply. Correspondingly, there are repeated increases in European output,
American output, and Asian output. In each round, the output gap declines by 60
percent. Taking the sum over all periods, the increase in European money supply
is 30, the increase in American money supply is 30, and the increase in Asian
money supply is equally 30, see equations (10), (11) and (12) from the preceding
171

section. The effective multiplier in Europe is 2, the effective multiplier in
America is 2, and the effective multiplier in Asia is equally 2.

Coming to an end, compare the world of three regions with the world of two
regions. In the world of two regions, in each round, the output gap declines by 67
percent. By contrast, in the world of three regions, in each round, the output gap
declines by 60 percent. That is to say, in the world of two regions, monetary
competition is a relatively fast process. And in the world of three regions,
monetary competition is a relatively slow process. The underlying reason is that,
in the world of two regions, monetary spillovers are relatively small. And in the
world of three regions, monetary spillovers are relatively large.

Table 4.1
Monetary Competition between Europe, America and Asia

Asia
Europe America

Initial Output 940 940 940
Change in Money Supply 18 18 18
Output 976 976 976
7.2 7.2 7.2
Change in Money Supply
990.4 990.4 990.4
Output
and so on

2) The regions differ in unemployment. Let initial output in Europe be 940,
let initial output in America be 950, and let initial output in Asia be 970. Step 1
refers to the policy response. The output gap in Europe is 60. The monetary
policy multiplier in Europe is 3.33. So what is needed in Europe is an increase in
European money supply of 18. The output gap in America is 50. The monetary
policy multiplier in America is 3.33. So what is needed in America is an increase
in American money supply of 15. The output gap in Asia is 30. The monetary
172

policy multiplier in Asia is 3.33. So what is needed in Asia is an increase in
Asian money supply of 9.

Step 2 refers to the output lag. The increase in European money supply of 18
causes an increase in European output of 60. As a side effect, it causes a decline
in American output of 12 and a decline in Asian output of equally 12. The
increase in American money supply of 15 causes an increase in American output
of 50. As a side effect, it causes a decline in European output of 10 and a decline
in Asian output of equally 10. The increase in Asian money supply of 9 causes an
increase in Asian output of 30. As a side effect, it causes a decline in European
output of 6 and a decline in American output of equally 6. The net effect is an
increase in European output of 44, an increase in American output of 32, and an
increase in Asian output of 8. As a consequence, European output goes from 940
to 984, American output goes from 950 to 982, and Asian output goes from 970
to 978. And so on. Table 4.2 gives an overview.

There are repeated increases in money supply. There are repeated increases
in output. The total increase in European money supply is 26.7, the total increase
in American money supply is 24.2, and the total increase in Asian money supply
is 19.2, see equations (10), (11) and (12) from the previous section. The effective
multiplier in Europe is 2.3, the effective multiplier in America is 2.1, and the
effective multiplier in Asia is 1.6.

Table 4.2
Monetary Competition between Europe, America and Asia

America Asia
Europe

940 970
Initial Output 950
18 9
Change in Money Supply 15
984 982 978
Output
5.4 6.6
Change in Money Supply 4.8
993.2
992.4
Output 992.0
and so on
Chapter 2
Monetary Cooperation
between Europe, America and Asia
1. The Model

At the beginning there is unemployment in Europe, America and Asia. The
targets of monetary cooperation are full employment in Europe, full employment
in America, and full employment in Asia. The instruments of monetary
cooperation are European money supply, American money supply, and Asian
money supply. So there are three targets and three instruments.

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

AYj = ccAMi - PAM2 - (3AM3 (1)
AY2 = ocAM2 - PAMj - (3AM3 (2)

AY3 = aAM 3 - (3AM! - (3AM2 (3)

Here AYX denotes the initial output gap in Europe, AY2 is the initial output gap in
America, and AY3 is the initial output gap in Asia. AM1 denotes the required
increase in European money supply, AM2 is the required increase in American
money supply, and AM3 is the required increase in Asian money supply. The
endogenous variables are AM1? AM2 and AM3.

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

(a-P)AY1+P(AY2 + AY3)
1
a2-ap-2P2

(a-P)AY2+P(AY1 + AY3)
a 2 -a(3-2(3 2
174

There is a solution if and only if a ^2(3. Due to the assumption oc>2|3, this
condition is fulfilled. As a result, monetary cooperation between Europe,
America and Asia can achieve full employment in each of the regions.

According to equation (4), the required increase in European money supply
depends on the initial output gap in Europe, the initial output gap in America, the
initial output gap in Asia, the direct multiplier a, and the cross multiplier (3. The
larger the initial output gap in Europe, the larger is the required increase in
European money supply. Moreover, the larger the initial output gap in America
or Asia, the larger is the required increase in European money supply. According
to equation (5), the required increase in American money supply depends on the
initial output gap in America, the initial output gap in Europe, the initial output
gap in Asia, the direct multiplier, and the cross multiplier. According to equation
(6), the required increase in Asian money supply depends on the initial output
gap in Asia, the initial output gap in Europe, the initial output gap in America,
the direct multiplier, and the cross multiplier.

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 = 3.33 and (3 = 0.67. It
proves useful to consider two distinct cases:
- the regions have the same unemployment
- the regions differ in unemployment.

1) The regions have the same unemployment. Let initial output in Europe be
940, let initial output in America be 940, and let initial output in Asia be the
same. In other words, the output gap in Europe is 60, the output gap in America
175

is 60, and the output gap in Asia is the same. What is needed, according to
equations (4), (5) and (6) from the preceding section, is an increase in European
money supply of 30, an increase in American money supply of 30, and an
increase in Asian money supply of equally 30.

The increase in European money supply of 30 raises European output by 100.
On the other hand, it lowers American output and Asian output by 20 each. The
increase in American money supply of 30 raises American output by 100. On the
other hand, it lowers European output and Asian output by 20 each. The increase
in Asian money supply of 30 raises Asian output by 100. On the other hand, it
lowers European output and American output by 20 each. The net effect is an
increase in European output of 60, an increase in American output of 60, and an
increase in Asian output of equally 60. As a consequence, European output goes
from 940 to 1000, American output goes from 940 to 1000, and Asian output
goes from 940 to 1000. As a result, monetary cooperation can achieve full
employment. For a synopsis see Table 4.3.

Table 4.3
Monetary Cooperation between Europe, America and Asia

America Asia
Europe

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

2) The regions differ in unemployment. Let initial output in Europe be 940,
let initial output in America be 950, and let initial output in Asia be 970. In other
words, the output gap in Europe is 60, the output gap in America is 50, and the
output gap in Asia is 30. What is needed, according to equations (4), (5) and (6)
from the previous section, is an increase in European money supply of 26.7, an
increase in American money supply of 24.2, and an increase in Asian money
supply of 19.2.
176

The increase in European money supply of 26.7 raises European output by
88.9. On the other hand, it lowers American output and Asian output by 17.8
each. The increase in American money supply of 24.2 raises American output by
80.6. On the other hand, it lowers European output and Asian output by 16.1
each. The increase in Asian money supply of 19.2 raises Asian output by 63.9.
On the other hand, it lowers European output and American output by 12.8 each.
The net effect is an increase in European output of 60, an increase in American
output of 50, and an increase in Asian output of 30. As a consequence, European
output goes from 940 to 1000, American output goes from 950 to 1000, and
Asian output goes from 970 to 1000. As a result, monetary cooperation can
achieve full employment. For an overview see Table 4.4.

Table 4.4
Monetary Cooperation between Europe, America and Asia

America Asia
Europe

Initial Output 940 950 970
24.2 19.2
Change in Money Supply 26.7
Output 1000 1000
1000
Chapter 3
Fiscal Competition: Perfect Capital Mobility
1. The Dynamic Model

1) The static model. As a point of reference, consider the static model. The
world consists of three monetary regions, say Europe, America and Asia. The
exchange rates between Europe, America and Asia are flexible. There is
international trade between Europe, America and Asia. There is perfect capital
mobility between Europe, America and Asia. European goods, American goods,
and Asian 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. And Asian output is determined by the
demand for Asian goods. European money demand equals European money
supply. American money demand equals American money supply. And Asian
money demand equals Asian 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 European
output, American output and Asian output, to the same extent respectively.
Correspondingly, an increase in American government purchases raises
American output, European output and Asian output, to the same extent
respectively. By analogy, an increase in Asian government purchases raises
Asian output, European output and American output, to the same extent
respectively.

In the numerical example, an increase in European government purchases of
100 causes an increase in European output of 67, an increase in American output
of 67, and an increase in Asian output of equally 67. Correspondingly, an
increase in American government purchases of 100 causes an increase in
American output of 67, an increase in European output of 67, and an increase in
Asian output of equally 67. By analogy, an increase in Asian government
purchases of 100 causes an increase in Asian output of 67, an increase in
178

European output of 67, and an increase in American output of equally 67. That
means, the internal effect of fiscal policy is very small, whereas the external
effect of fiscal policy is very large.

Now have a closer look at the process of adjustment. An increase in European
government purchases causes an appreciation of the euro and an increase in the
world interest rate. The appreciation of the euro lowers European exports but
raises American exports and Asian exports. The increase in the world interest
rate lowers European investment, American investment, and Asian investment.
The net effect is that European output, American output, and Asian output go up.
This model is in the tradition of the Mundell-Fleming model, see Carlberg (2000)
p. 205.

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

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

(2)
(3)

According to equation (1), European output Y1 is determined by European
government purchases G1? American government purchases G 2 , Asian
government purchases G 3 , and some other factors called A^ According to
equation (2), American output is determined by American government purchases,
European government purchases, Asian government purchases, and some other
factors. According to equation (3), Asian output is determined by Asian
government purchases, European government purchases, American government
purchases, and some other factors. Here y is the fiscal policy multiplier. The
internal effect of fiscal policy is positive y > 0. The external effect of fiscal
policy is positive too y > 0. In a sense, the internal effect is smaller than the
external effect y < 2y. The endogenous variables are European output, American
output, and Asian output.

2) The dynamic model. This section deals with fiscal competition between
Europe, America and Asia. At the beginning there is unemployment in each of
the regions. The target of the European government is full employment in
179

Europe. The instrument of the European government is European government
purchases. The target of the American government is full employment in
America. The instrument of the American government is American government
purchases. The target of the Asian government is full employment in Asia. The
instrument of the Asian government is Asian government purchases. We assume
that the European government, the American government, and the Asian
government decide simultaneously and independently.

The dynamic model can be characterized by a system of three equations:

^ s (4)
Y2=A2+ YG2+70^+703! (5)
1 1
(6)

Here is a list of the new symbols:
Yj full-employment output in Europe
Y2 full-employment output in America
Y3 full-employment output in Asia
Gx European government purchases this period
G2 American government purchases this period
G3 Asian government purchases this period
Gj"1 European government purchases last period
G2* American government purchases last period
G3l Asian government purchases last period.

According to equation (4), the European government sets European
government purchases so as to reach full employment in Europe, given American
government purchases last period and Asian government purchases last period.
According to equation (5), the American government sets American government
purchases so as to reach full employment in America, given European
government purchases last period and Asian government purchases last period.
According to equation (6), the Asian government sets Asian government
purchases so as to reach full employment in Asia, given European government
purchases last period and American government purchases last period.
180

To summarize, equation (4) shows the policy response in Europe, equation
(5) shows the policy response in America, and equation (6) shows the policy
response in Asia. The endogenous variables are European government purchases
this period Gh American government purchases this period G 2 , and Asian
government purchases this period G 3 .

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

3) The steady state. The model of the steady state can be written as follows:

Y1=A1+YG1+YG2+YG3 (7)

Y2=A2+YG2+YG1+YG3 (8)

Y3=A3+YG3+YG1+YG2 (9)

The endogenous variables are G1? G 2 and G 3 . Now take differences between
equations (7), (8) and (9) to reach:

Y1-Y2=A1-A2 (10)
Y1-Y3=A1-A3 (11)
Y2-Y3=A2-A3 (12)

However, this is in direct contradiction to the assumption that Yl5 Y2, Y3, A1?
A 2 and A 3 are given independently. As a result, there is no steady state of fiscal
competition. In other words, fiscal competition between Europe, America and
Asia does not lead to full employment in each of the regions. The underlying
reason is the large external effect of fiscal policy.
2. A Numerical Example

To illustrate the dynamic model, have a look at a numerical example. For ease
of exposition, without loss of generality, assume y = 0.67, see Carlberg (2000) p.
207. On this assumption, the static model can be written as follows:

Yj = Aj + 0.67Gx + 0.67G2 + 0.67G3 (1)
Y2 = A 2 + 0.67G2 + 0.67G! + 0.67G3 (2)

Y3 = A 3 + 0.67G3 + 0.67Gx + 0.67G2 (3)

The endogenous variables are European, American and Asian output. Evidently,
an increase in European government purchases of 100 causes an increase in
European output of 67, an increase in American output of 67, and an increase in
Asian output of equally 67. So the increase in world output is 200. Further let
full-employment output in Europe be 1000, let full-employment output in
America be 1000, and let full-employment output in Asia be equally 1000.

Let initial output in Europe be 970, let initial output in America be 970, and
let initial output in Asia be the same. Step 1 refers to the policy response. The
output gap in Europe is 30. The fiscal policy multiplier in Europe is 0.67. So
what is needed in Europe is an increase in European government purchases of 45.
The output gap in America is 30. The fiscal policy multiplier in America is 0.67.
So what is needed in America is an increase in American government purchases
of 45. The output gap in Asia is 30. The fiscal policy multiplier in Asia is 0.67.
So what is needed in Asia is an increase in Asian government purchases of 45.

Step 2 refers to the output lag. The increase in European government
purchases of 45 causes an increase in European output of 30. As a side effect, it
causes an increase in American output of 30 and an increase in Asian output of
equally 30. The increase in American government purchases of 45 causes an
increase in American output of 30. As a side effect, it causes an increase in
European output of 30 and an increase in Asian output of equally 30. The
increase in Asian government purchases of 45 causes an increase in Asian output
182

of 30. As a side effect, it causes an increase in European output of 30 and an
increase in American output of equally 30. The total effect is an increase in
European output of 90, an increase in American output of 90, and an increase in
Asian output of equally 90. As a consequence, European output goes form 970 to
1060, American output goes from 970 to 1060, and Asian output goes from 970
to 1060. And so on. Table 4.5 presents a synopsis.

What are the dynamic characteristics of this process? There are explosive
oscillations in European government purchases, American government
purchases, and Asian government purchases. Correspondingly, there are
explosive oscillations in European output, American output, and Asian output. In
each round, in absolute values, the output gap doubles. After a few periods, the
economy will collapse.

Coining to an end, compare the world of three regions with the world of two
regions. In the world of two regions, fiscal competition causes uniform
oscillations in government purchases and output. By contrast, in the world of
three regions, fiscal competition causes explosive oscillations in government
purchases and output.

Table 4.5
Fiscal Competition between Europe, America and Asia
Perfect Capital Mobility

Europe America Asia

Initial Output 970 970 970
Change in Government Purchases 45 45 45
Output 1060 1060
1060
Change in Government Purchases -90 -90
-90
Output 880 880 880
and so on
Chapter 4
Fiscal Competition: Imperfect Capital Mobility
1. The Dynamic Model

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