Microfinance for Bankers and Investors_2 doc

The demand shock in Europe causes a loss to the European government of 9 units and a loss to the American government of zero units.. The mixed shock in Europe causes a loss to the Europe

122

2 Some Numerical Examples

For easy reference, the basic model is reproduced 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, 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

Fiscal Interaction between Europe and America

Table 5.1

Fiscal Interaction between Europe and America

A Demand Shock in Europe

124

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

Europe, fiscal interaction lowers unemployment and deflation in Europe On the

other hand, it raises the structural deficit there Second consider the effects on

America As a result, fiscal interaction produces overemployment and inflation in

America And what is more, it produces a structural surplus there The loss

functions of the European government and the American government are

The initial loss of the European government is zero, as is the initial loss of the

American government The demand shock in Europe causes a loss to the

European government of 9 units and a loss to the American government of zero

units Then fiscal interaction reduces the loss of the European government from 9

to 5.12 units On the other hand, fiscal interaction increases the loss of the

American government from zero to 0.32 units

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 an increase in European government purchases of 1.6 units and a

reduction in American government purchases of 0.4 units Step four refers to the

outside lag Unemployment in Europe goes from 3 to 1.6 percent

Unemployment in America goes from zero to – 0.4 percent Inflation in Europe

goes from 3 to 4.4 percent Inflation in America goes from zero to 0.4 percent

The structural deficit in Europe goes from zero to 1.6 percent And the structural

deficit in America goes from zero to – 0.4 percent Table 5.2 gives an overview

Fiscal Interaction between Europe and America

Table 5.2

Fiscal Interaction between Europe and America

A Supply Shock in Europe

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

2 Some Numerical Examples

126

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 an increase in European government purchases of 3.2 units and a reduction in American government purchases of 0.8 units Step four refers to the outside lag Unemployment in Europe goes from 6 to 3.2 percent Unemployment in America goes from zero to – 0.8 percent Inflation in Europe goes from zero to 2.8 percent Inflation in America goes from zero to 0.8 percent The structural deficit in Europe goes from zero to 3.2 percent And the structural deficit in America goes from zero to – 0.8 percent For a synopsis see Table 5.3

Table 5.3

Fiscal Interaction between Europe and America

A Mixed Shock in Europe

First consider the effects on Europe As a result, given a mixed shock in Europe, fiscal interaction lowers unemployment in Europe On the other hand, it raises the structural deficit there And what is more, it raises inflation Second consider the effects on America As a result, fiscal interaction produces overemployment and inflation in America And what is more, it produces a structural surplus there The initial loss of each government is zero The mixed shock in Europe causes a loss to the European government of 36 units and a loss

to the American government of zero units Then fiscal interaction reduces the loss of the European government from 36 to 20.48 units On the other hand, it increases the loss of the American government from zero to 1.28 units

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 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 no change in European government purchases, nor is there in American government purchases Step four refers to the outside lag Inflation in Europe stays at 6 percent Inflation in America stays at zero percent Unemployment in Europe stays at zero percent, as does unemployment in America The structural deficit in Europe stays at zero percent, as does the structural deficit in America For an overview see Table 5.4

As a result, given another mixed shock in Europe, fiscal interaction produces zero unemployment and a zero structural deficit in each of the regions The mixed shock in Europe does not cause any loss to the European government or American government

2 Some Numerical Examples

128

Table 5.4

Fiscal Interaction between Europe and America

Another Mixed Shock in Europe

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 government purchases and American government purchases of 1.2 units each Step four refers to the outside lag Unemployment in Europe goes from 3 to 1.2 percent, as does unemployment in America Inflation in Europe goes from – 3 to – 1.2 percent, as does inflation in

Fiscal Interaction between Europe and America

a loss to the American government of equally 9 units Then fiscal interaction reduces the loss of the European government from 9 to 2.88 units Correspondingly, it reduces the loss of the American government from 9 to 2.88 units

Table 5.5

Fiscal Interaction between Europe and America

A Common Demand Shock

130

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 an increase in European government purchases and American government purchases of 1.2 units each Step four refers to the outside lag Unemployment in Europe goes from 3 to 1.2 percent, as does unemployment in America Inflation in Europe goes from 3 to 4.8 percent, as does inflation in America The structural deficit in Europe goes from zero to 1.2 percent, as does the structural deficit in America Table 5.6 gives an overview

As a result, given a common supply shock, fiscal interaction lowers unemployment in Europe and America On the other hand, it raises the structural deficits there And what is more, it raises inflation The initial loss of each government is zero The common supply shock causes a loss to the European government of 9 units and a loss to the American government of equally 9 units Then fiscal interaction reduces the loss of the European government from 9 to 2.88 units Correspondingly, it reduces the loss of the American government from 9 to 2.88 units

7) Summary Given a demand shock in Europe, fiscal interaction lowers unemployment and deflation in Europe On the other hand, it raises the structural deficit there Given a supply shock in Europe, fiscal interaction lowers unemployment in Europe On the other hand, it raises the structural deficit there And what is more, as a side effect, it raises inflation Given a certain type of mixed shock in Europe, fiscal interaction produces zero unemployment and a zero structural deficit in each of the regions

Fiscal Interaction between Europe and America

Table 5.6

Fiscal Interaction between Europe and America

A Common Supply Shock

The model of unemployment, inflation, and the structural deficit can be

characterized by a system of six equations:

The policy makers are the European government and the American

government The targets of fiscal cooperation are zero unemployment and a zero

structural deficit in each of the regions The instruments of fiscal cooperation are

European government purchases and American government purchases There are

four targets but only two instruments, so what is needed is a loss function We

assume that the European government and the American government agree on a

common loss function:

L is the loss caused by unemployment and the structural deficit in each of the

regions We assume equal weights in the loss function The specific target of

fiscal cooperation is to minimize the loss, given the unemployment functions and

the structural deficit functions Taking account of equations (1), (2), (5) and (6),

the loss function under fiscal cooperation can be written as follows:

M Carlberg, Monetary and Fiscal Strategies in the World Economy, 132

DOI 10.1007/978-3-642-10476-3_18, © Springer-Verlag Berlin Heidelberg 2010

Equation (9) shows the first-order condition with respect to European

government purchases And equation (10) shows the first-order condition with

respect to American government purchases

The cooperative equilibrium is determined by the first-order conditions for a

minimum loss We assume T T= 1=T2 The solution to this problem is as

Equations (11) and (12) show the cooperative equilibrium of European

government purchases and American government purchases As a result there is

a unique cooperative equilibrium An increase in A1 causes an increase in both

European government purchases and American government purchases A unit

increase in A1 causes an increase in European government purchases of 0.43

units and an increase in American government purchases of 0.03 units

Evidently, the cooperative equilibrium is different from the Nash equilibrium

Put another way, fiscal cooperation is different from fiscal interaction

1 The Model

134

2 Some Numerical Examples

It proves useful to study two distinct cases:

- a demand shock in Europe

- a supply shock in Europe

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 What is needed, according to the

model, is an increase in European government purchases of 1.29 units and an

increase in American government purchases of 0.09 units Step four refers to the

outside lag Unemployment in Europe goes from 3 to 1.66 percent

Unemployment in America goes from zero to – 0.74 percent Inflation in Europe

goes from – 3 to – 1.66 percent Inflation in America goes from zero to 0.74

percent The structural deficit in Europe goes from zero to 1.29 percent And the

structural deficit in America goes from zero to 0.09 percent Table 5.7 presents a

synopsis

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

Europe, fiscal cooperation lowers unemployment and deflation in Europe On the

other hand, it raises the structural deficit there Second consider the effects on

America As a result, fiscal cooperation produces overemployment and inflation

in America And what is more, it produces a structural deficit there The loss

function under fiscal cooperation is:

The initial loss is zero The demand shock in Europe causes a loss of 9 units Then fiscal cooperation brings the loss down to 4.99 units Now compare fiscal cooperation with fiscal interaction The loss under fiscal cooperation is 4.99 units And the loss under fiscal interaction is 5.44 units So, given a demand shock in Europe, fiscal cooperation seems to be superior to fiscal interaction

Table 5.7

Fiscal Cooperation between Europe and America

A Demand Shock in Europe

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

2 Some Numerical Examples

136

Step three refers to the policy response What is needed, according to the model, is an increase in European government purchases of 1.29 units and an increase in American government purchases of 0.09 units Step four refers to the outside lag Unemployment in Europe goes from 3 to 1.66 percent Unemployment in America goes from zero to – 0.74 percent Inflation in Europe goes from 3 to 4.34 percent Inflation in America goes from zero to 0.74 percent The structural deficit in Europe goes from zero to 1.29 percent And the structural deficit in America goes from zero to 0.09 percent Table 5.8 gives an overview

Table 5.8

Fiscal Cooperation between Europe and America

A Supply Shock in Europe