Monetary policy strategies in the world economy carlberg_3 potx

Table 3.1 Monetary Interaction between Europe and America A Demand Shock in Europe As a result, given a demand shock in Europe, monetary interaction produces zero inflation and zero un

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central bank is zero inflation in America In case B the targets of the European

central bank are zero inflation and zero unemployment in Europe And the targets

of the American central bank are zero inflation and zero unemployment in

America In case C the European central bank has a single target, that is zero

inflation in Europe By contrast, the American central bank has two conflicting

targets, that is zero inflation and zero unemployment in America This chapter

deals with case A, and the next chapters deal with cases B and C

The target of the European central bank is zero inflation in Europe The

instrument of the European central bank is European money supply By equation

(3), the reaction function of the European central bank is:

Suppose the American central bank lowers American money supply Then, as a

response, the European central bank lowers European money supply

The target of the American central bank is zero inflation in America The

instrument of the American central bank is American money supply By equation

(4), the reaction function of the American central bank is:

Suppose the European central bank lowers European money supply Then, as a

response, the American central bank lowers American money supply

The Nash equilibrium is determined by the reaction functions of the

European central bank and the American central bank The solution to this

Equations (7) and (8) show the Nash equilibrium of European money supply and

American money supply As a result there is a unique Nash equilibrium

According to equations (7) and (8), an increase in B1 causes a decline in both

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European money supply and American money supply A unit increase in B1

causes a decline in European money supply of 1.33 units and a decline in

American money supply of 0.67 units

From equations (1), (7) and (8) follows the equilibrium rate of

As a result, given a shock, monetary interaction produces zero inflation in

Europe and America

Monetary Interaction between Europe and America: Case A

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2 Some Numerical Examples

For easy reference, the basic model is summarized here:

It proves useful to study six distinct cases:

- a demand shock in Europe

- a supply shock in Europe

- a mixed shock in Europe

- another mixed shock in Europe

- a common demand shock

- a common supply shock

1) A demand shock in Europe In each of the regions, let initial

unemployment be zero, and let initial inflation be zero as well Step one refers to

a decline in the demand for European goods In terms of the model there is an

increase in A1 of 3 units and a decline in B1 of equally 3 units Step two refers

to the outside lag Unemployment in Europe goes from zero to 3 percent

Unemployment in America stays at zero percent Inflation in Europe goes from

zero to – 3 percent And inflation in America stays at zero percent

Step three refers to the policy response According to the Nash equilibrium

there is an increase in European money supply of 4 units and an increase in

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American money supply of 2 units Step four refers to the outside lag

Unemployment in Europe goes from 3 to zero percent Unemployment in

America stays at zero percent Inflation in Europe goes from – 3 to zero percent

And inflation in America stays at zero percent Table 3.1 presents a synopsis

Table 3.1

Monetary Interaction between Europe and America

A Demand Shock in Europe

As a result, given a demand shock in Europe, monetary interaction produces

zero inflation and zero unemployment in each of the regions The loss functions

of the European central bank and the American central bank are respectively:

The initial loss of the European central bank is zero, as is the initial loss of the

American central bank The demand shock in Europe causes a loss to the

European central bank of 9 units and a loss to the American central bank of zero

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units Then monetary interaction reduces the loss of the European central bank from 9 to zero units And what is more, monetary interaction keeps the loss of the American central bank at zero units

2) A supply shock in Europe In each of the regions let initial unemployment

be zero, and let initial inflation be zero as well Step one refers to the supply shock in Europe In terms of the model there is an increase in B1 of 3 units and

an increase in A1 of equally 3 units Step two refers to the outside lag Inflation

in Europe goes from zero to 3 percent Inflation in America stays at zero percent Unemployment in Europe goes from zero to 3 percent And unemployment in America stays at zero percent

Step three refers to the policy response According to the Nash equilibrium there is a reduction in European money supply of 4 units and a reduction in American money supply of 2 units Step four refers to the outside lag Inflation in Europe goes from 3 to zero percent Inflation in America stays at zero percent Unemployment in Europe goes from 3 to 6 percent And unemployment in America stays at zero percent Table 3.2 gives an overview

First consider the effects on Europe As a result, given a supply shock in Europe, monetary interaction produces zero inflation in Europe However, as a side effect, it raises unemployment there Second consider the effects on America As a result, monetary interaction produces zero inflation and zero unemployment in America The initial loss of each central bank is zero The supply shock in Europe causes a loss to the European central bank of 9 units and

a loss to the American central bank of zero units Then monetary interaction reduces the loss of the European central bank from 9 to zero units And what is more, it keeps the loss of the American central bank at zero units

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Table 3.2

A Supply Shock in Europe

3) A mixed shock in Europe In each of the regions, let initial unemployment

be zero, and let initial inflation be zero as well Step one refers to the mixed

shock in Europe In terms of the model there is an increase in B1 of 6 units Step

two refers to the outside lag Inflation in Europe goes from zero to 6 percent

Inflation in America stays at zero percent Unemployment in Europe stays at zero

percent, as does unemployment in America

there is a reduction in European money supply of 8 units and a reduction in

American money supply of 4 units Step four refers to the outside lag Inflation in

Europe goes from 6 to zero percent Inflation in America stays at zero percent

Unemployment in Europe goes from zero to 6 percent And unemployment in

America stays at zero percent For a synopsis see Table 3.3

First consider the effects on Europe As a result, given a mixed shock in

Europe, monetary interaction produces zero inflation in Europe However, as a

side effect, it produces unemployment there Second consider the effects on

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America As a result, monetary interaction produces zero inflation and zero

unemployment in America The initial loss of each central bank is zero The

mixed shock in Europe causes a loss to the European central bank of 36 units and

a loss to the American central bank of zero units Then monetary interaction

reduces the loss of the European central bank from 36 to zero units And what is

more, it keeps the loss of the American central bank at zero units

Table 3.3

A Mixed Shock in Europe

4) Another mixed shock in Europe In each of the regions, let initial

the mixed shock in Europe In terms of the model there is an increase in A1 of 6

units Step two refers to the outside lag Unemployment in Europe goes from

zero to 6 percent Unemployment in America stays at zero percent Inflation in

Europe stays at zero percent, as does inflation in America

there is no change in European money supply, nor is there in American money

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supply Step four refers to the outside lag Unemployment in Europe stays at 6

percent Unemployment in America stays at zero percent Inflation in Europe

stays at zero percent, as does inflation in America For an overview see Table

3.4

First consider the effects on Europe As a result, given another mixed shock

in Europe, monetary interaction produces zero inflation in Europe However, as a

side effect, it produces unemployment there Second consider the effects on

America As a result, monetary interaction produces zero inflation and zero

unemployment in America The mixed shock in Europe causes no loss to the

European central bank or American central bank

Table 3.4

Another Mixed Shock in Europe

5) A common demand shock In each of the regions, let initial unemployment

be zero, and let initial inflation be zero as well Step one refers to a decline in the

demand for European and American goods In terms of the model there is an

increase in A1 of 3 units, a decline in B1 of 3 units, an increase in A2 of 3 units,

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and a decline in B2 of 3 units Step two refers to the outside lag Unemployment

in Europe goes from zero to 3 percent, as does unemployment in America

Inflation in Europe goes from zero to – 3 percent, as does inflation in America

there is an increase in European money supply and American money supply of 6

units each Step four refers to the outside lag Unemployment in Europe goes

from 3 to zero percent, as does unemployment in America Inflation in Europe

goes from – 3 to zero percent, as does inflation in America Table 3.5 presents a

synopsis

Table 3.5

A Common Demand Shock

As a result, given a common demand shock, monetary interaction produces

zero inflation and zero unemployment in each of the regions The initial loss of

each central bank is zero The common demand shock causes a loss to the

European central bank of 9 units and a loss to the American central bank of

equally 9 units Then monetary interaction reduces the loss of the European

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central bank from 9 to zero units Correspondingly, it reduces the loss of the American central bank from 9 to zero units

6) A common supply shock In each of the regions, let initial unemployment

be zero, and let initial inflation be zero as well Step one refers to the common supply shock In terms of the model there is an increase in B1 of 3 units, as there

is in A1 And there is an increase in B2 of 3 units, as there is in A2 Step two refers to the outside lag Inflation in Europe goes from zero to 3 percent, as does inflation in America Unemployment in Europe goes from zero to 3 percent, as does unemployment in America

Step three refers to the policy response According to the Nash equilibrium there is a reduction in European money supply and American money supply of 6 units each Step four refers to the outside lag Inflation in Europe goes from 3 to zero percent, as does inflation in America Unemployment in Europe goes from 3

to 6 percent, as does unemployment in America Table 3.6 gives an overview

As a result, given a common supply shock, monetary interaction produces zero inflation in Europe and America However, as a side effect, it raises unemployment there The initial loss of each central bank is zero The common supply shock causes a loss to the European central bank of 9 units and a loss to the American central bank of equally 9 units Then monetary interaction reduces the loss of the European central bank from 9 to zero units Correspondingly, it reduces the loss of the American central bank from 9 to zero units

7) Summary Given a demand shock in Europe, monetary interaction produces zero inflation and zero unemployment in each of the regions Given a supply shock in Europe, monetary interaction produces zero inflation in Europe However, as a side effect, it raises unemployment there Given a mixed shock in Europe, monetary interaction produces zero inflation in Europe However, as a side effect, it causes unemployment there Given a common demand shock, monetary interaction produces zero inflation and zero unemployment in each of the regions Given a common supply shock, monetary interaction produces zero inflation in Europe and America However, as a side effect, it raises unemployment there

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Table 3.6

A Common Supply Shock

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This chapter deals with case B The targets of the European central bank are

zero inflation and zero unemployment in Europe Correspondingly, the targets of

the American central bank are zero inflation and zero unemployment in America

The model of unemployment and inflation can be characterized by a system of

The targets of the European central bank are zero inflation and zero

unemployment in Europe The instrument of the European central bank is

European money supply There are two targets but only one instrument, so what

is needed is a loss function We assume that the European central bank has a

quadratic loss function:

1

L is the loss to the European central bank caused by inflation and

unemployment in Europe We assume equal weights in the loss function The

specific target of the European central bank is to minimize its loss, given the

inflation function and the unemployment function Taking account of equations

(1) and (3), the loss function of the European central bank can be written as

follows:

M Carlberg, Monetary and Fiscal Strategies in the World Economy, 68

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2 2

Then the first-order condition for a minimum loss gives the reaction function of

the European central bank:

Suppose the American central bank lowers American money supply Then, as a

response, the European central bank lowers European money supply

The targets of the American central bank are zero inflation and zero

unemployment in America The instrument of the American central bank is

American money supply There are two targets but only one instrument, so what

is needed is a loss function We assume that the American central bank has a

quadratic loss function:

2

L is the loss to the American central bank caused by inflation and

unemployment in America We assume equal weights in the loss function The

specific target of the American central bank is to minimize its loss, given the

inflation function and the unemployment function Taking account of equations

(2) and (4), the loss function of the American central bank can be written as

follows:

Then the first-order condition for a minimum loss gives the reaction function of

the American central bank:

Suppose the European central bank lowers European money supply Then, as a

response, the American central bank lowers American money supply

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70

The Nash equilibrium is determined by the reaction functions of the

European central bank and the American central bank The solution to this

Equations (11) and (12) show the Nash equilibrium of European money supply

and American money supply As a result there is a unique Nash equilibrium

According to equations (11) and (12), an increase in A1 causes an increase in

both European money supply and American money supply A unit increase in A1

causes an increase in European money supply of 0.67 units and an increase in

American money supply of 0.33 units

From equations (1), (11) and (12) follows the equilibrium rate of

As a rule, unemployment in Europe and America is not zero And inflation in

Europe and America is not zero either

Monetary Interaction between Europe and America: Case B

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