Monetary and Fiscal Strategies in the World Economy by Michael Carlberg_6 pdf

Taking account of equations 1 and 5, the loss function of the European government can be written as follows: Then the first-order condition for a minimum loss gives the reaction function

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

The targets of the European government are zero unemployment and a zero

structural deficit in Europe The instrument of the European government is

European government purchases There are two targets but only one instrument,

so what is needed is a loss function We assume that the European government

has a quadratic loss function:

2 2

1

LG is the loss to the European government caused by unemployment and the

structural deficit in Europe We assume equal weights in the loss function The

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

unemployment function and the structural deficit function Taking account of

equations (1) and (5), the loss function of the European government can be

written as follows:

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

the European government:

The targets of the American government are zero unemployment and a zero

structural deficit in America The instrument of the American government is

American government purchases There are two targets but only one instrument,

so what is needed is a loss function We assume that the American government

has a quadratic loss function:

2 2

2

LG is the loss to the American government caused by unemployment and the

structural deficit in America We assume equal weights in the loss function The

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

unemployment function and the structural deficit function Taking account of

equations (2) and (6), the loss function of the American government can be

written as follows:

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

the American government:

Suppose the European government raises European government purchases Then,

as a response, the European central bank lowers European money supply, the

American central bank lowers American money supply, and the American

government lowers American government purchases

The Nash equilibrium is determined by the reaction functions of the

European central bank, the American central bank, the European government,

and the American government We assume T T= 1=T2 The solution to this

Equations (19) to (22) show the Nash equilibrium of European money supply,

American money supply, European government purchases, and American

government purchases As a result there is a unique Nash equilibrium An

increase in A1 causes a decline in European money supply, a decline in

American money supply, an increase in European government purchases, and no

change in American government purchases A unit increase in A1 causes a

decline in European money supply of 0.17 units, a decline in American money

supply of 0.33 units, and an increase in European government purchases of 0.5

units

2 Some Numerical Examples

For easy reference, the basic model is reproduced here:

It proves useful to study eight 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

- a common mixed shock

- another common mixed shock

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

unemployment be zero, let initial inflation be zero, and let the initial structural

deficit 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

1

B 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 Inflation in America

stays at zero percent The structural deficit in Europe stays at zero percent, as

does the structural deficit in America

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

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

American money supply of 2 units, no change in European government

purchases, and no change in American government purchases 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 Inflation in America stays at zero percent The structural

deficit in Europe stays at zero percent, as does the structural deficit in America

For a synopsis see Table 7.7

As a result, given a demand shock in Europe, monetary and fiscal interaction

produces zero inflation, zero unemployment, and a zero structural deficit in each

of the regions

The loss functions of the European central bank, the American central bank,

the European government, and the American government are respectively:

2 2

The initial loss of each policy maker is zero The demand shock in Europe causes

a loss to the European central bank of 18 units, a loss to the European

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

the American government of zero Then policy interaction reduces the loss of the

European central bank from 18 to zero units Correspondingly, it reduces the loss

of the European government from 9 to zero units Policy interaction keeps the

loss of the American central bank at zero Similarly, it keeps the loss of the

American government at zero

Table 7.7

Monetary and Fiscal Interaction between Europe and America

A Demand Shock in Europe

Change in Money Supply 4 Change in Money Supply 2

Change in Govt Purchases 0 Change in Govt Purchases 0

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

be zero, let initial inflation be zero, and let the initial structural deficit 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 5 units, a reduction in American money supply of 4 units, an increase in European government purchases of 3 units, and no change in American government purchases Step four refers to the outside lag Inflation in Europe stays at 3 percent Inflation in America stays at zero percent Unemployment in Europe stays at 3 percent Unemployment in America stays at zero percent The structural deficit in Europe goes from zero to 3 percent And the structural deficit in America stays at zero percent For an overview see Table 7.8

First consider the effects on Europe As a result, given a supply shock in Europe, monetary and fiscal interaction has no effects on inflation and unemployment in Europe And what is more, it causes a structural deficit there Second consider the effects on America As a result, monetary and fiscal interaction produces zero inflation, zero unemployment, and a zero structural deficit in America

The initial loss of each policy maker is zero The supply shock in Europe causes a loss to the European central bank of 18 units, a loss to the European government of 9 units, a loss to the American central bank of zero, and a loss to the American government of equally zero Then policy interaction keeps the loss

of the European central bank at 18 units And what is more, it increases the loss

of the European government from 9 to 18 units On the other hand, policy interaction keeps the loss of the American central bank at zero Correspondingly,

it keeps the loss of the American government at zero That is to say, in this case, the Nash equilibrium is not Pareto efficient

Table 7.8

Monetary and Fiscal Interaction between Europe and America

A Supply Shock in Europe

Change in Money Supply − 5 Change in Money Supply − 4

Change in Govt Purchases 3 Change in Govt Purchases 0

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

be zero, let initial inflation be zero, and let the initial structural deficit 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

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

there is a reduction in European money supply of 9 units, a reduction in

American money supply of 6 units, an increase in European government

purchases of 3 units, and no change in American government purchases Step

four refers to the outside lag Inflation in Europe goes from 6 to 3 percent

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

zero to 3 percent Unemployment in America stays at zero percent The structural

deficit in Europe goes from zero to 3 percent And the structural deficit in

America stays at zero percent Table 7.9 presents a synopsis

Table 7.9

Monetary and Fiscal Interaction between Europe and America

A Mixed Shock in Europe

Change in Money Supply − 9 Change in Money Supply − 6

Change in Govt Purchases 3 Change in Govt Purchases 0

As a result, given a mixed shock in Europe, monetary and fiscal interaction

lowers inflation in Europe On the other hand, it raises unemployment and the

structural deficit there

The initial loss of each policy maker is zero The mixed shock in Europe

causes a loss to the European central bank of 36 units, a loss to the European

government of zero, a loss to the American central bank of zero, and a loss to the

American government of zero Then policy interaction reduces the loss of the European central bank from 36 to 18 units On the other hand, it increases the loss of the European government from zero to 18 units Policy interaction keeps the loss of the American central bank at zero Correspondingly, it keeps the loss

of the American government at zero The total loss in Europe stays at 36 units And the total loss in America stays at zero

4) Another mixed shock in Europe In each of the regions, let initial unemployment be zero, let initial inflation be zero, and let the initial structural deficit be zero as well Step one refers to 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

Step three refers to the policy response According to the Nash equilibrium there is a reduction in European money supply of 1 unit, a reduction in American money supply of 2 units, an increase in European government purchases of 3 units, and no change in American government purchases Step four refers to the outside lag Unemployment in Europe goes from 6 to 3 percent Unemployment

in America stays at zero percent Inflation in Europe goes from zero to 3 percent Inflation in America stays at zero percent The structural deficit in Europe goes from zero to 3 percent And the structural deficit in America stays at zero percent Table 7.10 gives an overview

As a result, given another mixed shock in Europe, monetary and fiscal interaction lowers unemployment in Europe On the other hand, it raises inflation and the structural deficit there

The initial loss of each policy maker is zero The mixed shock in Europe causes a loss to the European central bank of 36 units, a loss to the European government of 36 units, a loss to the American central bank of zero, and a loss to the American government of zero Then policy interaction reduces the loss of the European central bank from 36 to 18 units Correspondingly, it reduces the loss

of the European government from 36 to 18 units Policy interaction keeps the loss of the American central bank at zero Similarly, it keeps the loss of the American government at zero

Table 7.10

Monetary and Fiscal Interaction between Europe and America

Another Mixed Shock in Europe

Change in Money Supply − 1 Change in Money Supply − 2

Change in Govt Purchases 3 Change in Govt Purchases 0

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

be zero, let initial inflation be zero, and let the initial structural deficit 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, 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

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

there is an increase in European money supply of 6 units, as there is in American

money supply There is no change in European government purchases, nor is

there in American government purchases 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 And the structural deficit in Europe stays at zero percent, as does the

structural deficit in America For a synopsis see Table 7.11

Table 7.11

Monetary and Fiscal Interaction between Europe and America

A Common Demand Shock

Change in Money Supply 6 Change in Money Supply 6

Change in Govt Purchases 0 Change in Govt Purchases 0

As a result, given a common demand shock, monetary and fiscal interaction

produces zero inflation, zero unemployment, and a zero structural deficit in each

of the regions

The initial loss of each policy maker is zero The common demand shock

causes a loss to the European central bank of 18 units, a loss to the American

central bank of 18 units, a loss to the European government of 9 units, and a loss

to the American government of 9 units Then policy interaction reduces the loss

of the European central bank from 18 to zero units Correspondingly, it reduces the loss of the American central bank from 18 to zero units Policy interaction reduces the loss of the European government from 9 to zero units Similarly, it reduces the loss of the American government from 9 to zero units

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

be zero, let initial inflation be zero, and let the initial structural deficit 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 of 9 units, as there is in American money supply There is an increase in European government purchases of 3 units, as there is in American government purchases Step four refers to the outside lag Inflation in Europe stays at 3 percent, as does inflation in America Unemployment in Europe stays at 3 percent, as does unemployment in America And the structural deficit in Europe goes from zero to 3 percent, as does the structural deficit in America For an overview see Table 7.12

As a result, given a common supply shock, monetary and fiscal interaction has no effect on inflation and unemployment Over and above that, it raises the structural deficits

The initial loss of each policy maker is zero The common supply shock causes a loss to the European central bank of 18 units, a loss to the American central bank of 18 units, a loss to the European government of 9 units, and a loss

to the American government of 9 units Then policy interaction keeps the loss of the European central bank at 18 units Correspondingly, it keeps the loss of the American central bank at 18 units And what is more, policy interaction increases the loss of the European government from 9 to 18 units Similarly, it increases the loss of the American government from 9 to 18 units That is to say, in this case, the Nash equilibrium is not Pareto efficient

Table 7.12

Monetary and Fiscal Interaction between Europe and America

A Common Supply Shock

Change in Money Supply − 9 Change in Money Supply − 9

Change in Govt Purchases 3 Change in Govt Purchases 3

7) A common mixed shock In each of the regions, let initial unemployment

be zero, let initial inflation be zero, and let the initial structural deficit be zero as

well Step one refers to the common mixed shock In terms of the model there is

an increase in B1 of 6 units and an increase in B2 of equally 6 units Step two

refers to the outside lag Inflation in Europe goes from zero to 6 percent, as does

inflation in America Unemployment in Europe stays at zero 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 of 15 units, as there is in

American money supply There is an increase in European government purchases

of 3 units, as there is in American government purchases Step four refers to the

outside lag Inflation in Europe goes from 6 to 3 percent, as does inflation in

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

unemployment in America And the structural deficit in Europe goes from zero to

3 percent, as does the structural deficit in America Table 7.13 presents a

synopsis

Table 7.13

Monetary and Fiscal Interaction between Europe and America

A Common Mixed Shock

Change in Money Supply − 15 Change in Money Supply − 15

Change in Govt Purchases 3 Change in Govt Purchases 3

As a result, given a common mixed shock, monetary and fiscal interaction

lowers inflation On the other hand, it raises unemployment and the structural

deficits

The initial loss of each policy maker is zero The common mixed shock

causes a loss to the European central bank of 36 units, a loss to the American

central bank of 36 units, a loss to the European government of zero, and a loss to

the American government of zero Then policy interaction reduces the loss of the European central bank from 36 to 18 units Correspondingly, it reduces the loss

of the American central bank from 36 to 18 units On the other hand, policy interaction increases the loss of the European government from zero to 18 units Similarly, it increases the loss of the American government from zero to 18 units The total loss in Europe stays at 36 units And the same applies to the total loss in America

8) Another common mixed shock In each of the regions, let initial unemployment be zero, let initial inflation be zero, and let the initial structural deficit be zero as well Step one refers to the common mixed shock In terms of the model there is an increase in A1 of 6 units and an increase in A2 of equally

6 units Step two refers to the outside lag Unemployment in Europe goes from zero to 6 percent, as does unemployment in America Inflation in Europe stays at zero percent, as does inflation in America

Step three refers to the policy response According to the Nash equilibrium there is a reduction in European money supply of 3 units, as there is in American money supply There is an increase in European government purchases of 3 units, as there is in American government purchases Step four refers to the outside lag Unemployment in Europe goes from 6 to 3 percent, as does unemployment in America Inflation in Europe goes from zero to 3 percent, as does inflation in America And the structural deficit in Europe goes from zero to

3 percent, as does the structural deficit in America Table 7.14 gives an overview

As a result, given another common mixed shock, monetary and fiscal interaction lowers unemployment On the other hand, it causes inflation and structural deficits

The initial loss of each policy maker is zero The common mixed shock causes a loss to the European central bank of 36 units, a loss to the American central bank of 36 units, a loss to the European government of 36 units, and a loss to the American government of equally 36 units Then policy interaction reduces the loss of the European central bank from 36 to 18 units Correspondingly, it reduces the loss of the American central bank from 36 to 18 units Policy interaction reduces the loss of the European government from 36 to

18 units Similarly, it reduces the loss of the American government from 36 to 18