<<

. 7
( 9)



>>

government purchases Gf, and the expectation of American government
purchases G 2 .

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


(7)

(8)

Here the endogenous variables are European government purchases Gj and
American government purchases G 2 . Now take the difference between equations
(7) and (8) to reach:


Y1-Y2=A1-A2 (9)

However, this is in direct contradiction to the assumption that Y1? Y2, Ax and A 2
are given independently. As a result, under rational expectations, there is no
equilibrium of fiscal competition between Europe and America. In other words,
under rational expectations, fiscal competition between Europe and America
228


does not lead to full employment. The underlying reason is the large spillover
effect of fiscal policy.




3. Fiscal Competition: Imperfect Capital Mobility



1) The static model. In this section we assume imperfect capital mobility
between Europe and America. As a point of reference, consider the static model.
It can be represented by a system of two equations:


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


According to equation (1), European output is determined by European
government purchases and American government purchases. According to
equation (2), American output is determined by American government purchases
and European government purchases, y and 8 are positive coefficients with
y > 5. The endogenous variables are European output and American output.

2) The dynamic model. This section deals with fiscal competition between
Europe and America. At the beginning there is unemployment in each of the
regions. The target of the European government is full employment in Europe.
The instrument of the European government is European government purchases.
The target of the American government is full employment in America. The
instrument of the American government is American government purchases. We
assume that the European government and the American government decide
simultaneously and independently. The European government sets European
government purchases, forming rational expectations of American government
purchases. And the American government sets American government purchases,
forming rational expectations of European government purchases.
229

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


% (3)
Y2=A2+7G2+5G1e (4)
G?=G1 (5)
G|=G2 (6)

Here is a list of the new symbols:
Yj full-employment output in Europe
Y2 full-employment output in America
Gf the expectation of European government purchases,
as formed by the American government
G2 the expectation of American government purchases,
as formed by the European government
G1 European government purchases,
as set by the European government
G2 American government purchases,
as set by the American government.

According to equation (3), the European government sets European
government purchases, forming an expectation of American government
purchases. According to equation (4), the American government sets American
government purchases, forming an expectation of European government
purchases. According to equation (5), the expectation of European government
purchases is equal to the forecast made by means of the model. According to
equation (6), the expectation of American government purchases is equal to the
forecast made by means of the model. That is to say, the European government
sets European government purchases, predicting American government
purchases with the help of the model. And the American government sets
American government purchases, predicting European government purchases
with the help of the model. The endogenous variables are European government
purchases Gj, American government purchases G 2 , the expectation of European
government purchases Gf, and the expectation of American government
purchases G 2 .
230



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


Y1=A1+yG1+8G2 (7)
Y2=A2+YG2+5G1 (8)


Here the endogenous variables are European government purchases Gj and
American government purchases G 2 . To simplify notation we introduce
Bl = Yx - Al and B 2 = Y2 - A 2 . Then we solve the model for the endogenous
variables:



m

˜2 Y2_52




Equation (9) shows the equilibrium level of European government purchases,
and equation (10) shows the equilibrium level of American government
purchases. There is a solution if and only if y ^ 8. This condition is fulfilled. As
a result, under rational expectations, there is an immediate equilibrium of fiscal
competition between Europe and America. In other words, under rational
expectations, fiscal competition between Europe and America leads to full
employment immediately. It is worth pointing out here that the equilibrium under
rational expectations is identical to the steady state under adaptive expectations,
see Chapter 2 of Part Two.

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


AY 1 =yAG 1 +8AG 2 (11)
AY 2 =yAG 2 +8AG 1 (12)

Here AYj denotes the initial output gap in Europe, AY2 is the initial output gap in
America, AGj is the required increase in European government purchases, and
231


AG2 is the required increase in American government purchases. The
endogenous variables are AGj and AG2. The equilibrium of the system (11) and
(12) is:




AG
^ 14 )
2- 2_g2


3) A numerical example. To illustrate the dynamic model, have a look at a
numerical example. For ease of exposition, without losing generality, assume
Y = 1.5 and 8 = 0.5. On this assumption, the static model can be written as
follows:


Y 1 =A 1 +1.5G 1 +0.5G 2 (15)
Y2=A2+1.5G2+0.5G1 (16)

The endogenous variables are European output and American output. Evidently,
an increase in European government purchases of 100 causes an increase in
European output of 150 and an increase in American output of 50. Further let
full-employment output in Europe be 1000, and let full-employment output in
America be the same.

Let initial output in Europe be 940, and let initial output in America be 970.
That means, the output gap in Europe is 60, and the output gap in America is 30.
What is needed in Europe, according to equation (13), is an increase in European
government purchases of 37.5. And what is needed in America, according to
equation (14), is an increase in American government purchases of 7.5. The
increase in European government purchases of 37.5 raises European output by
56.25 and American output by 18.75. The increase in American government
purchases of 7.5 raises American output by 11.25 and European output by 3.75.
The total effect is an increase in European output of 60 and an increase in
American output of 30. As a consequence, European output goes from 940 to
1000, and American output goes from 970 to 1000. In Europe there is now full
employment, and the same holds for America. As a result, under rational
232


expectations, fiscal competition leads to full employment immediately. Table 6.2
gives an overview.

4) Comparing fiscal competition with monetary competition. Fiscal
competition can cause large changes in government purchases. By contrast,
monetary competition cannot cause any changes in government purchases.
Judging from this point of view, monetary competition seems to be superior to
fiscal competition.



Table 6.2
Fiscal Competition between Europe and America
Rational Policy Expectations

America
Europe


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




4. Monetary and Fiscal Competition



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


- (3M2 + yGi + 5G 2 (1)
233


Y2 = A 2 + a M 2 - PMX + yG2 + bGx (2)

According to equation (1), European output is determined by European money
supply, American money supply, European government purchases, and American
government purchases. According to equation (2), American output is
determined by American money supply, European money supply, American
government purchases, and European government purchases, a, P, y and 8 are
positive coefficients with a > P and y > 5. The endogenous variables are
European output and American output.

2) The dynamic model. At the start there is unemployment in both Europe
and America. The target of the European central bank is full employment in
Europe. The target of the American central bank is full employment in America.
The target of the European government is full employment in Europe. And the
target of the American government is full employment in America. We assume
that the European central bank, the American central bank, the European
government, and the American government decide simultaneously and
independently.

The European central bank sets European money supply, forming rational
expectations of American money supply, European government purchases, and
American government purchases. The American central bank sets American
money supply, forming rational expectations of European money supply,
American government purchases, and European government purchases. The
European government sets European government purchases, forming rational
expectations of American government purchases, European money supply, and
American money supply. The American government sets American government
purchases, forming rational expectations of European government purchases,
American money supply, and European money supply. That is to say, the
European central bank sets European money supply, predicting American money
supply, European government purchases, and American government purchases
by means of the model. The American central bank sets American money supply,
predicting European money supply, American government purchases, and
European government purchases by means of the model. The European
government sets European government purchases, predicting American
government purchases, European money supply, and American money supply by
234


means of the model. The American government sets American government
purchases, predicting European government purchases, American money supply,
and European money supply by means of the model.

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


- (3M2 + YGJ + 5G 2 (3)
Y2 = A 2 + ccM2 - PMj + yG2 + 8GX (4)

Here Yj is full-employment output in Europe, and Y2 is full-employment output
in America. The endogenous variables are European money supply, American
money supply, European government purchases, and American government
purchases. There are two targets and four instruments, so there are two degrees of
freedom. As a result, under rational expectations, there is no unique equilibrium
of monetary and fiscal competition. In other words, under rational expectations,
monetary and fiscal competition does not lead to full employment.
Chapter 2
Adaptive Policy Expectations
in Europe and America


1) The static model. This chapter deals with monetary competition between
Europe and America. As a point of reference, consider the static model. It can be
represented by a system of two equations:


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

According to equation (1), European output is determined by European money
supply and American money supply. According to equation (2), American output
is determined by American money supply and European money supply, a and (3
are positive coefficients with a > ( 3 . The endogenous variables are European
output and American output.

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

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


(3)
236


Y 2 =A 2 +aM 2 -(3Mf (4)
Mf = Mj"1 (5)
M | = M2! (6)


Here is a list of the new symbols:
Yj full-employment output in Europe
Y2 full-employment output in America
Mf the expectation of European money supply,
as formed by the American central bank
M 2 the expectation of American money supply,
as formed by the European central bank
Mj European money supply this period
M 2 American money supply this period
Mj"1 European money supply last period
M2* American money supply last period.

According to equation (3), the European central bank sets European money
supply, forming an expectation of American money supply. According to
equation (4), the American central bank sets American money supply, forming an
expectation of European money supply. According to equation (5), the
expectation of European money supply is equal to European money supply last
period. According to equation (6), the expectation of American money supply is
equal to American money supply last period. The exogenous variables are Mj"1
and M^ 1 . The endogenous variables are Mf, M 2 , Mx and M 2 .

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


PM^1 (7)
Y2=A2+aM2-(3M1-1 (8)


According to equation (7), the European central bank sets European money
supply, taking American money supply as given. According to equation (8), the
American central bank sets American money supply, taking European money
237


supply as given. The exogenous variables are Mj"1 and M^ 1 . The endogenous
variables are Mx and M 2 .

Strictly speaking, this model is equivalent to the dynamic model developed in
Chapter 1 of Part One. As a result, under adaptive expectations, there is a stable
steady state of monetary competition between Europe and America. In other
words, under adaptive expectations, monetary competition between Europe and
America leads to full employment.

3) A numerical example. To illustrate the dynamic model, have a look at a
numerical example with a = 3 and P = 1. That is, an increase in European money
supply of 100 raises European output by 300 and lowers American output by
100. Let full-employment output in Europe be 1000, and let full-employment
output in America be the same.

Let initial output in Europe be 940, and let initial output in America be 970.
Step 1 refers to the policy response. First consider monetary policy in Europe.
The European central bank sets European money supply, taking American money
supply as given. 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. Second consider monetary policy in America. The American
central bank sets American money supply, taking European money supply as
given. 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.

Step 2 refers to the output lag. The increase in European money supply of 20
causes an increase in European output of 60. As a side effect, it causes a decline
in American output of 20. The increase in American money supply of 10 causes
an increase in American output of 30. As a side effect, it causes a decline in
European output of 10. The net effect is an increase in European output of 50 and
an increase in American output of 10. As a consequence, European output goes
from 940 to 990, and American output goes from 970 to 980.

Step 3 refers to the policy response. First consider monetary policy in Europe.
The European central bank sets European money supply, taking American money
supply as given. The output gap in Europe is 10. The monetary policy multiplier
238


in Europe is 3. So what is needed in Europe is an increase in European money
supply of 3.3. Second consider monetary policy in America. The American
central bank sets American money supply, taking European money supply as
given. The 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.

Step 4 refers to the output lag. The increase in European money supply of 3.3
causes an increase in European output of 10. As a side effect, it causes a decline
in American output of 3.3. The increase in American money supply of 6.7 causes
an increase in American output of 20. As a side effect, it causes a decline in
European output of 6.7. The net effect is an increase in European output of 3.3
and an increase in American output of 16.7. As a consequence, European output
goes from 990 to 993.3, and American output goes from 980 to 996.7. And so on.
Chapter 3
Adaptive Policy Expectations in Europe,
Rational Policy Expectations in America
1. Monetary Competition between Europe and America



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


Y1=A1+aM1-pM2 (1)
Y2=A2+aM2-PM1 (2)

According to equation (1), European output is determined by European money
supply and American money supply. According to equation (2), American output
is determined by American money supply and European money supply, a and (3
are positive coefficients with a > (3. The endogenous variables are European
output and American output.

2) The dynamic model. At the beginning there is unemployment in both
Europe and America. The target of the European central bank is full employment
in Europe. The instrument of the European central bank is European money
supply. The target of the American central bank is full employment in America.
The instrument of the American central bank is American money supply. We
assume that the European central bank and the American central bank decide
simultaneously and independently. The European central bank sets European
money supply, forming adaptive expectations of American money supply. And
the American central bank sets American money supply, forming rational
expectations of European money supply.

On this basis, the dynamic model can be characterized by a system of four
equations:
240




^iPMI (3)
Y 2 =A 2 +aM 2 -PMf (4)
Mf=Mi (5)
M | = M2* (6)


Here is a list of the new symbols:
Yl full-employment output in Europe
Y2 full-employment output in America
Mf the expectation of European money supply,
as formed by the American central bank
M 2 the expectation of American money supply,
as formed by the European central bank
M1 European money supply this period
M 2 American money supply this period
M2* American money supply last period.

According to equation (3), the European central bank sets European money
supply, forming an expectation of American money supply. According to
equation (4), the American central bank sets American money supply, forming an
expectation of European money supply. According to equation (5), the
expectation of European money supply is equal to the forecast made by means of
the model. According to equation (6), the expectation of American money supply
is equal to American money supply last period. The endogenous variables are
M1,M2,Mf andM|.

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


pMj 1 (7)
Y2=A2+aM2-PM1 (8)


According to equation (7), the European central bank sets European money
supply, taking American money supply as given. And according to equation (8),
the American central bank sets American money supply, predicting European
241

money supply with the help of the model. In a sense, the American central bank
is a Stackelberg leader, and the European central bank is a Stackelberg follower.
The endogenous variables are M1 and M 2 .

3) The steady state. In the steady state by definition we have M 2 = M^1. That
is, American money supply does not change any more. Therefore the steady state
can be captured by a system of two equations:


Y1 = A 1 + a M 1 - ( 3 M 2 (9)
Y2=A2+aM2-(3M1 (10)


The endogenous variables are M1 and M 2 .

To simplify notation we introduce:


B^Yi-Ai (11)
B2 = Y 2 - A 2 (12)


Next we solve the model for the endogenous variables:


„ oB 1+ pB 2



(14)


Equation (13) shows the steady-state level of European money supply, and
equation (14) shows the steady-state level of American money supply. As a
result, there is a steady state if and only if a ^ (3. This condition is fulfilled.

4) Stability. To simplify notation we make use of equations (11) and (12).
With this, the dynamic model (7) and (8) can be written as follows:


(15)
242


B2=aM2˜PM1 (16)


The endogenous variables are M1 and M 2 .

Now eliminate M^1 in equation (15) by means of equation (16) to arrive at:




a a

Then differentiate equation (17) for Mj"1:

B2
dM,
(18)
^ =^

Finally the stability condition is P 2 / a 2 < 1 or:


a>P (19)

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. This
condition is satisfied. As a result, under adaptive-rational expectations, there is a
stable steady state of monetary competition. In other words, under adaptive-
rational expectations, monetary competition leads to full employment.

5) A numerical example. To illustrate the dynamic model, have a look at a
numerical example. For ease of exposition, without loss of generality, assume
a = 3 and P = 1. Obviously, an increase in European money supply of 100 raises
European output by 300 and lowers American output by 100. Further let full-
employment output in Europe be 1000, and let full-employment output in
America be the same.

Let initial output in Europe be 940, and let initial output in America be
equally 940. Step 1 refers to the policy response. First consider monetary policy
in Europe. The European central bank sets European money supply, taking
American money supply as given. The output gap in Europe is 60. The monetary
243


policy multiplier in Europe is 3. So what is needed in Europe is an increase in
European money supply of 20.

Second consider monetary policy in America. The American central bank sets
American money supply, forming rational expectations of European money
supply. The output gap in America is 60. The monetary policy multiplier in
America is 3. So what is needed in America is an increase in American money
supply of 20. Moreover, the expected increase in European money supply is 20.
Hence the expected decline in American output is equally 20. What is needed in
America to counteract this, is another increase in American money supply of 6.7.
Adding up, the total increase in American money supply is 26.7.

Step 2 refers to the output lag. The increase in European money supply of 20
causes an increase in European output of 60. As a side effect, it causes a decline
in American output of 20. The increase in American money supply of 26.7
causes an increase in American output of 80. As a side effect, it causes a decline
in European output of 26.7. The net effect is an increase in European output of
33.3 and an increase in American output of 60. As a consequence, European
output goes from 940 to 973.3, and American output goes from 940 to 1000. In
Europe unemployment comes down, but there is still a lot of unemployment left.
In America there is now full employment.

Step 3 refers to the policy response. First consider monetary policy in Europe.
The European central bank sets European money supply, taking American money
supply as given. The output gap in Europe is 26.7. The monetary policy
multiplier in Europe is 3. So what is needed in Europe is an increase in European
money supply of 8.9.

Second consider monetary policy in America. The American central bank sets
American money supply, forming rational expectations of European money
supply. The output gap in America is zero. From this point of view, there is no
need for a change in American money supply. Moreover, the expected increase
in European money supply is 8.9. Hence the expected decline in American output
is equally 8.9. What is needed in America to counteract this, is an increase in
American money supply of 3.0. Adding up, the total increase in American money
supply is 3.0.
244


Step 4 refers to the output lag. The increase in European money supply of 8.9
causes an increase in European output of 26.7. As a side effect, it causes a
decline in American output of 8.9. The increase in American money supply of
3.0 causes an increase in American output of 8.9. As a side effect, it causes a
decline in European output of 3.0. The net effect is an increase in European
output of 23.7 and an increase in American output of zero. As a consequence,
European output goes from 973.3 to 997.0, while American output stays at 1000.
And so on. Table 6.3 presents a synopsis.



Table 6.3
Monetary Competition between Europe and America
Adaptive Policy Expectations in Europe
Rational Policy Expectations in America

Europe America


Initial Output 940 940
Change in Money Supply 20 26.7
Output 973.3 1000
Change in Money Supply 3
8.9
Output 997.0 1000
and so on




What are the dynamic characteristics of this process? There are repeated
increases in European money supply and American money supply. There are
repeated increases in European output. There is a one-time increase in American
output. In Europe unemployment comes down step by step. In America
unemployment comes down immediately. As a result, monetary competition
leads to full employment. Taking the sum over the process as a whole, the
increase in European money supply is 30, and the increase in American money
supply is equally 30.
245


6) Comparison. Coining to an end, compare the three types of expectations:
- adaptive policy expectations in Europe and America
- adaptive policy expectations in Europe,
rational policy expectations in America
- rational policy expectations in Europe and America.
Under adaptive expectations, monetary competition is a slow process. Under
adaptive-rational expectations, monetary competition is a process of intermediate
speed. And under rational expectations, monetary competition is a fast process.
That is to say, rational expectations speed up the process of monetary
competition.




2. Fiscal Competition between Europe and America


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


2 (1)

Y2=A2+yG2+5G1 (2)

According to equation (1), European output is determined by European
government purchases and American government purchases. According to
equation (2), American output is determined by American government purchases
and European government purchases, y and 8 are positive coefficients with
Y > 8. The endogenous variables are European output and American output.

2) The dynamic model. At the beginning there is unemployment in both
Europe and America. The target of the European government is full employment
in Europe. The instrument of the European government is European government
purchases. The target of the American government is full employment in
246

America. The instrument of the American government is American government
purchases. We assume that the European government and the American
government decide simultaneously and independently. The European
government sets European government purchases, forming adaptive expectations
of American government purchases. And the American government sets
American government purchases, forming rational expectations of European
government purchases.

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


^ (3)
Y 2 =A 2 +YG 2 +5G 1 e (4)
Gf=G x (5)
G^G^1 (6)

Here is a list of the new symbols:
Yj full-employment output in Europe
Y2 full-employment output in America
Gf the expectation of European government purchases,
as formed by the American government
G| the expectation of American government purchases,
as formed by the European government
Gj European government purchases this period
G2 American government purchases this period
1
G2 American government purchases last period.

According to equation (3), the European government sets European
government purchases, forming an expectation of American government
purchases. According to equation (4), the American government sets American
government purchases, forming an expectation of European government
purchases. According to equation (5), the expectation of European government
purchases is equal to the forecast made by means of the model. According to
equation (6), the expectation of American government purchases is equal to
247


American government purchases last period. The endogenous variables are Gl,
G 2 ,Gf a n d G | .

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


^ (7)
Y2=A2+YG2+8G1 (8)


According to equation (7), the European government sets European government
purchases, taking American government purchases as given. According to
equation (8), the American government sets American government purchases,
predicting European government purchases with the help of the model. In a
sense, the American government is a Stackelberg leader, and the European
government is a Stackelberg follower. The endogenous variables are Gx and G 2 .

3) The steady state. In the steady state by definition we have G 2 = G 2 1 . That
is, American government purchases do not change any more. Therefore the
steady state can be captured by a system of two equations:


Y1=A1+YG1+5G2 (9)

Y2=A2+yG2+8G1 (10)

The endogenous variables are Gj and G 2 .

To simplify notation we introduce:


B^^-Ai (11)
B2=Y2-A2 (12)


Next we solve the model for the endogenous variables:
248



-5B< /1^
2 2 2
(14)
-5
Y


Equation (13) shows the steady-state level of European government purchases,
and equation (14) shows the steady-state level of American government
purchases. As a result, there is a steady state if and only if y ^ 8. This condition
is fulfilled.

4) Stability. To simplify notation we make use of equations (11) and (12).
With this, the dynamic model (7) and (8) can be written as follows:


(15)



The endogenous variables are G{ and G 2 .

Now eliminate G^1 in equation (15) by means of equation (16) to arrive at:




Then differentiate equation (17) for Gj"1:




Finally the stability condition is S 2 / y2 < 1 or:


Y>5 (19)

That means, the steady state is stable if and only if the internal effect of fiscal
policy is larger than the external effect of fiscal policy. This condition is
satisfied. As a result, under adaptive-rational expectations, there is a stable steady
249

state of fiscal competition. In other words, under adaptive-rational expectations,
fiscal competition leads to full employment.

5) A numerical example. To illustrate the dynamic model, have a look at a
numerical example. For ease of exposition, without losing generality, assume
y = 1.2 and 8 = 0.8. Evidently, an increase in European government purchases of
100 raises European output by 120 and American output by 80. Further let full-
employment output in Europe be 1000, and let full-employment output in
America be the same.

Let initial output in Europe be 940, and let initial output in America 1060.
Step 1 refers to the policy response. First consider fiscal policy in Europe. The
European government sets European government purchases, taking American
government purchases as given. The output gap in Europe is 60. The fiscal policy
multiplier in Europe is 1.2. So what is needed in Europe is an increase in
European government purchases of 50.

Second consider fiscal policy in America. The American government sets
American government purchases, forming rational expectations of European
government purchases. The inflationary gap in America is 60. The fiscal policy
multiplier in America is 1.2. So what is needed in America is a reduction in
American government purchases of 50. Moreover, the expected increase in
European government purchases is 50. Hence the expected increase in American
output is 40. What is needed in America to counteract this, is a another reduction
in American government purchases of 33.3. Adding up, the total reduction in
American government purchases is 83.3.

Step 2 refers to the output lag. The increase in European government
purchases of 50 causes an increase in European output of 60. As a side effect, it
causes an increase in American output of 40. The reduction in American
government purchases of 83.3 causes a decline in American output of 100. As a
side effect, it causes a decline in European output of 66.7. The net effect is a
decline in European output of 6.7 and a decline in American output of 60. As a
consequence, European output goes from 940 to 933.3, and American output
goes from 1060 to 1000. In Europe unemployment is even worse. At first glance
this comes as a surprise. In America there is now full employment.
250


Step 3 refers to the policy response. First consider fiscal policy in Europe.
The European government sets European government purchases, taking
American government purchases as given. The output gap in Europe is 66.7. The
fiscal policy multiplier in Europe is 1.2. So what is needed in Europe is an
increase in European government purchases of 55.6.

Second consider fiscal policy in America. The American government sets
American government purchases, forming rational expectations of European
government purchases. The output gap in America is zero. From this point of
view, there is no need for a change in American government purchases.
Moreover, the expected increase in European government purchases is 55.6.
Hence the expected increase in American output is 44.4. What is needed in
America to counteract this, is a reduction in American government purchases of
37.0. Adding up, the total reduction in American government purchases is 37.0.

Step 4 refers to the output lag. The increase in European government
purchases of 55.6 causes an increase in European output of 66.7. As a side effect,
it causes an increase in American output of 44.4. The reduction in American
government purchases of 37.0 causes a decline in American output of 44.4. As a
side effect, it causes a decline in European output of 29.6. The net effect is an
increase in European output of 37.0 and an increase in American output of zero.
As a consequence, European output goes from 933.3 to 970.3, while American
output stays at 1000. In Europe unemployment comes down to a certain extent.
In America there is still full employment. And so on. Table 6.4 gives an
overview.

What are the dynamic characteristics of this process? There are repeated
increases in European government purchases. There are repeated cuts in
American government purchases. There is an initial cut in European output that
is followed by repeated increases in European output. And there is a one-time cut
in American output. In Europe there is unemployment. In America there is full
employment. As a result, fiscal competition leads to full employment. Taking the
sum over the process as a whole, the increase in European government purchases
is 150, and the cut in American government purchases is equally 150.
251

Table 6.4
Fiscal Competition between Europe and America
Adaptive Policy Expectations in Europe
Rational Policy Expectations in America

Europe America


Initial Output 940 1060
Change in Government Purchases 50 -83.3
Output 933.3 1000
Change in Government Purchases 55.6 -37.0
Output 970.3 1000
and so on




6) Comparison. Coming to an end, compare the three types of expectations:
- adaptive policy expectations in Europe and America
- adaptive policy expectations in Europe,
rational policy expectations in America
- rational policy expectations in Europe and America.
Under adaptive expectations, fiscal competition is a slow process. Under
adaptive-rational expectations, fiscal competition is a process of intermediate
speed. And under rational expectations, fiscal competition is a fast process. That
is to say, rational expectations speed up the process of fiscal competition.
Synopsis

Table 7.1
The World of Two Monetary Regions


Monetary Competition
between Europe and America Stable

Fiscal Competition
between Europe and America:
Perfect Capital Mobility Unstable

Fiscal Competition
between Europe and America:
Imperfect Capital Mobility Stable

Monetary and Fiscal Competition: Stability
Gradualist Policies Condition


Monetary Cooperation
Solution
between Europe and America

Fiscal Cooperation
between Europe and America:
Perfect Capital Mobility No Solution

Fiscal Cooperation
between Europe and America:
Imperfect Capital Mobility Solution

Monetary and Fiscal Cooperation:
Solution
Imperfect Capital Mobility
254


Table 7.2
The World of Three Monetary Regions


Monetary Competition
Stable
between Europe, America and Asia

Fiscal Competition
between Europe, America and Asia:
Perfect Capital Mobility Unstable

Fiscal Competition
between Europe, America and Asia:
Low Capital Mobility Stable

Fiscal Competition
between Europe, America and Asia:
Unstable
High Capital Mobility

Fiscal Competition
Stability
between Europe, America and Asia:
Condition
Gradualist Policies


Monetary Cooperation
between Europe, America and Asia Solution

Fiscal Cooperation
between Europe, America and Asia:
No Solution
Perfect Capital Mobility

Fiscal Cooperation
between Europe, America and Asia:
Solution
Imperfect Capital Mobility
255


Table 7.3
Rational Policy Expectations


Monetary Competition Unique
between Europe and America Equilibrium

Fiscal Competition
between Europe and America: No
Equilibrium
Perfect Capital Mobility

Fiscal Competition
between Europe and America: Unique
Imperfect Capital Mobility Equilibrium

Monetary and Fiscal Competition: No Unique
Equilibrium
Imperfect Capital Mobility
Conclusion
1. Basic Models

1.1. Monetary Competition between Europe and America



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 money supply raises European output.
On the other hand, it lowers American output. Here the rise in European output
exceeds the fall in American output. Correspondingly, an increase in American
money supply raises American output. On the other hand, it lowers European
output. Here the rise in American output exceeds the fall in European output.
That is to say, the internal effect of monetary policy is positive. By contrast, the
external effect of monetary policy is negative. In absolute values, the internal
effect is larger than the external effect.

Now have a closer look at the process of adjustment. An increase in European
money supply causes a depreciation of the euro, an appreciation of the dollar, and
a decline in the world interest rate. The depreciation of the euro raises European
exports. The appreciation of the dollar lowers American exports. And the decline
in the world interest rate raises both European investment and American
investment. The net effect is that European output goes up. However, American
output goes down. This model is in the tradition of the Mundell-Fleming model.
258


2) The dynamic model. At the beginning there is unemployment in both
Europe and America. The target of the European central bank is full employment
in Europe. The instrument of the European central bank is European money
supply. The European central bank raises European money supply so as to close
the output gap in Europe. The target of the American central bank is full
employment in America. The instrument of the American central bank is
American money supply. The American central bank raises American money
supply so as to close the output gap in America. We assume that the European
central bank and the American central bank decide simultaneously and
independently. In addition there is an output lag. As a result, there is a stable
steady state of monetary competition. In other words, monetary competition
leads to full employment in Europe and America.

3) 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 two distinct cases:
- unemployment in Europe and America
- inflation in Europe and America.

First consider unemployment in Europe and America. Let initial output in
Europe be 940, and let initial output in America be 970. Step 1 refers to the
policy response. The output gap in Europe is 60. The monetary policy multiplier
in Europe is 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.

Step 2 refers to the output lag. The increase in European money supply of 20
causes an increase in European output of 60. As a side effect, it causes a decline
in American output of 20. The increase in American money supply of 10 causes
an increase in American output of 30. As a side effect, it causes a decline in
European output of 10. The net effect is an increase in European output of 50 and
an increase in American output of 10. As a consequence, European output goes
from 940 to 990, and American output goes from 970 to 980.
259

Why does the European central bank not succeed in closing the output gap in
Europe? The underlying reason is the negative external effect of the increase in
American money supply. And why does the American central bank not succeed
in closing the output gap in America? The underlying reason is the negative
external effect of the increase in European money supply.

Step 3 refers to the policy response. The 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 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.

Step 4 refers to the output lag. The increase in European money supply of 3.3
causes an increase in European output of 10. As a side effect, it causes a decline
in American output of 3.3. The increase in American money supply of 6.7 causes
an increase in American output of 20. As a side effect, it causes a decline in
European output of 6.7. The net effect is an increase in European output of 3.3
and an increase in American output of 16.7. As a consequence, European output
goes from 990 to 993.3, and American output goes from 980 to 996.7. And so on.
Table 8.1 presents a synopsis.



Table 8.1
Monetary Competition between Europe and America
Unemployment in Europe and America

America
Europe


970
Initial Output 940
10
Change in Money Supply 20
980
Output 990
6.7
Change in Money Supply 3.3
996.7
993.3
Output
and so on
260


What are the dynamic characteristics of this process? There are repeated
increases in European money supply, as there are in American money supply.
There are repeated increases in European output, as there are in American output.
There are repeated cuts in the world interest rate. There are repeated increases in
European investment, as there are in American investment. There are repeated
cuts in budget deficits and public debts. As a result, monetary competition leads
to full employment.

Taking the sum over all periods, the increase in European money supply is
26.25, and the increase in American money supply is 18.75. The total increase in
European money supply is large, as compared to the initial output gap in Europe
of 60. And the total increase in American money supply is even larger, as
compared to the initial output gap in America of 30. The effective multiplier in
Europe is 60/26.25 = 2.3, and the effective multiplier in America is
30 /18.75 = 1.6. That is to say, the effective multiplier in Europe is small, and the
effective multiplier in America is even smaller.

Second consider inflation in Europe and America. At the start there is
overemployment in both Europe and America. For that reason there is inflation in
both Europe and America. Let initial output in Europe be 1060, and let initial
output in America be 1030. Step 1 refers to the policy response. The inflationary
gap in Europe is 60. The target of the European central bank is price stability in
Europe. 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 target of the American central bank is price stability in
America. 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.
261

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. And so on. Table 8.2 gives an overview.

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. As a result,
the process of monetary competition leads to both price stability and full
employment.



Table 8.2
Monetary Competition between Europe and America
Inflation in Europe and America

America
Europe


Initial Output 1060 1030
Change in Money Supply -10
-20
Output 1020
1010
Change in Money Supply -6.7
-3.3
1003.3
Output 1006.7
and so on
262


1.2. Monetary Cooperation between Europe and America



1) The model. 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. As a result, there is a solution to monetary cooperation. In
other words, monetary cooperation can achieve full employment in Europe and
America. The required increase in European money supply depends on the initial
output gap in Europe, the initial output gap in America, the direct multiplier, and
the cross multiplier. 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, the larger is the required increase in European money
supply. At first glance this comes as a surprise. The required increase in
American money supply depends on the initial output gap in America, the initial
output gap in Europe, the direct multiplier, and the cross multiplier. It is worth
pointing out here that the solution to monetary cooperation is identical to the
steady state of monetary competition.


2) Some numerical examples. It proves useful to study two distinct cases.
First consider unemployment in Europe and 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, then, 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. The required increase in money
supply is large, as compared to the initial output gap. For a synopsis see Table
8.3.
263

Table 8.3
Monetary Cooperation between Europe and America
Unemployment in Europe and America

Europe America


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




Second consider inflation in Europe and 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. 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. For an overview see Table 8.4.

3) 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.
264

Table 8.4
Monetary Cooperation between Europe and America
Inflation in Europe and America

Europe America


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




1.3. Fiscal Competition between Europe and America


1) The static model. 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. That is to say, the internal effect of fiscal policy is positive.
The external effect of fiscal policy is positive too. And what is more, the internal
effect and the external effect are the same size.

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 the same extent respectively. This model is in the tradition of the
Mundell-Fleming model.
265

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. 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. We assume that
the European government and the American government decide simultaneously
and independently. In addition there is an output lag. As a result, there is no
steady state of fiscal competition. In other words, fiscal competition does not
lead to full employment in Europe and America. The underlying reason is the
large external effect of fiscal policy.

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

At the start there is unemployment in both Europe and 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
266

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
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

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