FW: Monetary and Fiscal Strategies in the World Economy_5

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2. Some Numerical Examples 155 A second solution is an increase in European money supply of 2 units, an increase in American money supply of 1 unit, a reduction in European government purchases of 2 units, and an increase in American government purchases of 1 unit. As a result, given a supply shock in Europe, monetary and fiscal cooperation is ineffective. The initial loss is zero. The supply shock in Europe causes a loss of 18 units. Then policy cooperation keeps the loss at 18 units. 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. Step three refers to the policy response. According to the model, a first solution is a reduction in European money supply of 4 units, a reduction 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. 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. And unemployment in America stays at zero percent. For a synopsis see Table 6.3. A second solution is no change in European money supply, no change in American money supply, a reduction in European government purchases of 4 units, and an increase in American government purchases of 2 units. A third solution is a reduction in European money supply of 2 units, a reduction in American money supply of 1 unit, a reduction in European government purchases of 2 units, and an increase in American government purchases of 1 unit. First consider the effects on Europe. As a result, given a mixed shock in Europe, monetary and fiscal cooperation lowers inflation in Europe. On the other hand, it raises unemployment there. Second consider the effects on America. As a result, monetary and fiscal cooperation produces zero inflation and zero unemployment in America. The initial loss is zero. The mixed shock in Europe
156 Monetary and Fiscal Cooperation between Europe and America causes a loss of 36 units. Then policy cooperation brings the loss down to 18 units. Table 6.3 Monetary and Fiscal Cooperation between Europe and America A Mixed Shock in Europe Europe America Unemployment 0 Unemployment 0 Inflation 0 Inflation 0 0 Shock in A1 6 Shock in B1 Unemployment 0 Unemployment 0 Inflation 6 Inflation 0 −4 −2 Change in Money Supply Change in Money Supply Change in Govt Purchases 0 Change in Govt Purchases 0 Unemployment 3 Unemployment 0 Inflation 3 Inflation 0 4) Another 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 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 model, a first solution 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
2. Some Numerical Examples 157 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. And inflation in America stays at zero percent. For an overview see Table 6.4. Table 6.4 Monetary and Fiscal Cooperation between Europe and America Another Mixed Shock in Europe Europe America Unemployment 0 Unemployment 0 Inflation 0 Inflation 0 6 Shock in A1 0 Shock in B1 Unemployment 6 Unemployment 0 Inflation 0 Inflation 0 Change in Money Supply 4 Change in Money Supply 2 Change in Govt Purchases 0 Change in Govt Purchases 0 Unemployment 3 Unemployment 0 Inflation 3 Inflation 0 A second solution is no change in European money supply, no change in American money supply, an increase in European government purchases of 4 units, and a reduction in American government purchases of 2 units. A third solution is an increase in European money supply of 2 units, an increase in American money supply of 1 unit, an increase in European government purchases of 2 units, and a reduction in American government purchases of 1 unit.
158 Monetary and Fiscal Cooperation between Europe and America First consider the effects on Europe. As a result, given another mixed shock in Europe, monetary and fiscal cooperation lowers unemployment in Europe. On the other hand, it raises inflation there. Second consider the effects on America. As a result, monetary and fiscal cooperation produces zero inflation and zero unemployment in America. The initial loss is zero. The mixed shock in Europe causes a loss of 36 units. Then policy cooperation brings the loss down to 18 units. 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 A 2 of 3 units, and a decline in B 2 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 model, a first solution is an increase in European money supply of 6 units, an increase in American money supply of 6 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, as does unemployment in America. Inflation in Europe goes from – 3 to zero percent, as does inflation in America. Table 6.5 presents a synopsis. A second solution is no change in European money supply, no change in American money supply, an increase in European government purchases of 2 units, and an increase in American government purchases of 2 units. A third solution is an increase in European money supply of 3 units, an increase in American money supply of 3 units, an increase in European government purchases of 1 unit, and an increase in American government purchases of 1 unit. As a result, given a common demand shock, monetary and fiscal cooperation produces zero inflation and zero unemployment in each of the regions. The initial loss is zero. The common demand shock causes a loss of 36 units. Then policy cooperation brings the loss down to zero again.
2. Some Numerical Examples 159 Table 6.5 Monetary and Fiscal Cooperation between Europe and America A Common Demand Shock Europe America Unemployment 0 Unemployment 0 Inflation 0 Inflation 0 3 3 Shock in A1 Shock in A2 −3 −3 Shock in B1 Shock in B2 Unemployment 3 Unemployment 3 −3 −3 Inflation Inflation Change in Money Supply 6 Change in Money Supply 6 Change in Govt Purchases 0 Change in Govt Purchases 0 Unemployment 0 Unemployment 0 Inflation 0 Inflation 0 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 B 2 of 3 units, as there is in A 2 . 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 model, a first solution is no change in European money supply, no change in American money supply, no change in European government purchases, and no change 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. Table 6.6 gives an overview.
160 Monetary and Fiscal Cooperation between Europe and America A second solution is an increase in European money supply of 2 units, an increase in American money supply of 1 unit, a reduction in European government purchases of 2 units, and an increase in American government purchases of 1 unit. As a result, given a common supply shock, monetary and fiscal cooperation is ineffective. The initial loss is zero. The common supply shock causes a loss of 36 units. Then policy cooperation keeps the loss at 36 units. Table 6.6 Monetary and Fiscal Cooperation between Europe and America A Common Supply Shock Europe America Unemployment 0 Unemployment 0 Inflation 0 Inflation 0 3 3 Shock in A1 Shock in A2 3 3 Shock in B1 Shock in B2 Unemployment 3 Unemployment 3 Inflation 3 Inflation 3 Change in Money Supply 0 Change in Money Supply 0 Change in Govt Purchases 0 Change in Govt Purchases 0 Unemployment 3 Unemployment 3 Inflation 3 Inflation 3 7) A common mixed 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 mixed shock. In terms of the model there is an increase in B1 of 6 units and an increase in B 2 of equally 6 units. Step two refers to the outside lag. Inflation in
2. Some Numerical Examples 161 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 model, a first solution is a reduction in European money supply of 6 units, a reduction in American money supply of 6 units, no change in European government purchases, and no change 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. For a synopsis see Table 6.7. Table 6.7 Monetary and Fiscal Cooperation between Europe and America A Common Mixed Shock Europe America Unemployment 0 Unemployment 0 Inflation 0 Inflation 0 0 0 Shock in A1 Shock in A2 6 6 Shock in B1 Shock in B2 Unemployment 0 Unemployment 0 Inflation 6 Inflation 6 −6 −6 Change in Money Supply Change in Money Supply Change in Govt Purchases 0 Change in Govt Purchases 0 Unemployment 3 Unemployment 3 Inflation 3 Inflation 3 A second solution is no change in European money supply, no change in American money supply, a reduction in European government purchases of 2 units, and a reduction in American government purchases of 2 units. A third
162 Monetary and Fiscal Cooperation between Europe and America solution is a reduction in European money supply of 3 units, a reduction in American money supply of 3 units, a reduction in European government purchases of 1 unit, and a reduction in American government purchases of 1 unit. As a result, given a common mixed shock, monetary and fiscal cooperation lowers inflation in Europe and America. On the other hand, it raises unemployment there. The initial loss is zero. The common mixed shock causes a loss of 72 units. Then policy cooperation brings the loss down to 36 units. 8) Another common mixed 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 mixed shock. In terms of the model there is an increase in A1 of 6 units and an increase in A 2 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 model, a first solution is an increase in European money supply of 6 units, an increase in American money supply of 6 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 6 to 3 percent, as does unemployment in America. Inflation in Europe goes from zero to 3 percent, as does inflation in America. For an overview see Table 6.8. A second solution is no change in European money supply, no change in American money supply, an increase in European government purchases of 2 units, and an increase in American government purchases of 2 units. A third solution is an increase in European money supply of 3 units, an increase in American money supply of 3 units, an increase in European government purchases of 1 unit, and an increase in American government purchases of 1 unit. As a result, given another common mixed shock, monetary and fiscal cooperation lowers unemployment in Europe and America. On the other hand, it raises inflation there. The initial loss is zero. The common mixed shock causes a loss of 72 units. Then policy cooperation brings the loss down to 36 units.
2. Some Numerical Examples 163 Table 6.8 Monetary and Fiscal Cooperation between Europe and America Another Common Mixed Shock Europe America Unemployment 0 Unemployment 0 Inflation 0 Inflation 0 6 6 Shock in A1 Shock in A2 0 0 Shock in B1 Shock in B2 Unemployment 6 Unemployment 6 Inflation 0 Inflation 0 Change in Money Supply 6 Change in Money Supply 6 Change in Govt Purchases 0 Change in Govt Purchases 0 Unemployment 3 Unemployment 3 Inflation 3 Inflation 3 9) Summary. Given a demand shock in Europe, policy cooperation achieves zero inflation and zero unemployment in each of the regions. Given a supply shock in Europe, policy cooperation is ineffective. Given a mixed shock in Europe, policy cooperation lowers inflation in Europe. On the other hand, it raises unemployment there. Given another mixed shock in Europe, policy cooperation lowers unemployment in Europe. On the other hand, it raises inflation there. Given a common demand shock, policy cooperation achieves zero inflation and zero unemployment in each of the regions. Given a common supply shock, policy cooperation is ineffective. Given a common mixed shock, policy cooperation lowers inflation. On the other hand, it raises unemployment. Given another common mixed shock, policy cooperation lowers unemployment. On the other hand, it raises inflation.
164 Monetary and Fiscal Cooperation between Europe and America 10) Comparing policy interaction and policy cooperation. Under policy interaction there is no Nash equilibrium. By contrast, under policy cooperation, the loss can be brought down. That is to say, policy cooperation seems to be superior to policy interaction.
Part Seven Monetary and Fiscal Policies in Europe and America Presence of a Deficit Target
167 Chapter 1 Monetary and Fiscal Interaction between Europe and America: Case A 1. The Model The world economy consists of two monetary regions, say Europe and America. The monetary regions are the same size and have the same behavioural functions. An increase in European money supply lowers European unemploy- ment. On the other hand, it raises European inflation. Correspondingly, an increase in American money supply lowers American unemployment. On the other hand, it raises American inflation. An essential point is that monetary policy in Europe has spillover effects on America and vice versa. An increase in European money supply raises American unemployment and lowers American inflation. Similarly, an increase in American money supply raises European unemployment and lowers European inflation. An increase in European government purchases lowers European unemploy- ment. On the other hand, it raises European inflation. And what is more, it raises the European structural deficit. Correspondingly, an increase in American government purchases lowers American unemployment. On the other hand, it raises American inflation. And what is more, it raises the American structural deficit. An essential point is that fiscal policy in Europe has spillover effects on America and vice versa. An increase in European government purchases lowers American unemployment and raises American inflation. Similarly, an increase in American government purchases lowers European unemployment and raises European inflation. The model of unemployment, inflation, and the structural deficit can be represented by a system of six equations: u1 = A1 − M1 + 0.5M 2 − G1 − 0.5G 2 (1) u 2 = A 2 − M 2 + 0.5M1 − G 2 − 0.5G1 (2) M. Carlberg, Monetary and Fiscal Strategies in the World Economy, 167 DOI 10.1007/978-3-642-10476-3_21, © Springer-Verlag Berlin Heidelberg 2010
168 Monetary and Fiscal Interaction between Europe and America: Case A π1 = B1 + M1 − 0.5M 2 + G1 + 0.5G 2 (3) π2 = B2 + M 2 − 0.5M1 + G 2 + 0.5G1 (4) s1 = G1 − T1 (5) s 2 = G 2 − T2 (6) Here u1 denotes the rate of unemployment in Europe, u 2 is the rate of unemployment in America, π1 is the rate of inflation in Europe, π2 is the rate of inflation in America, s1 is the structural deficit ratio in Europe, s 2 is the structural deficit ratio in America, M1 is European money supply, M 2 is American money supply, G1 is European government purchases, G 2 is American government purchases, T1 is European tax revenue at full-employment output, T2 is American tax revenue at full-employment output, G1 – T1 is the European structural deficit, and G 2 – T2 is the American structural deficit. A1 is some other factors bearing on the rate of unemployment in Europe, A 2 is some other factors bearing on the rate of unemployment in America, B1 is some other factors bearing on the rate of inflation in Europe, and B2 is some other factors bearing on the rate of inflation in America. The endogenous variables are the rate of unemployment in Europe, the rate of unemployment in America, the rate of inflation in Europe, the rate of inflation in America, the structural deficit ratio in Europe, and the structural deficit ratio in America. According to equation (1), European unemployment is a positive function of A1 , a negative function of European money supply, a positive function of American money supply, a negative function of European government purchases, and a negative function of American government purchases. According to equation (2), American unemployment is a positive function of A 2 , a negative function of American money supply, a positive function of European money supply, a negative function of American government purchases, and a negative function of European government purchases. According to equation (3), European inflation is a positive function of B1 , a positive function of European money supply, a negative function of American money supply, a positive function of European government purchases, and a positive function of American government purchases. According to equation (4),
1. The Model 169 American inflation is a positive function of B2 , a positive function of American money supply, a negative function of European money supply, a positive function of American government purchases, and a positive function of European government purchases. According to equation (5), the structural deficit in Europe is a positive function of European government purchases. According to equation (6), the structural deficit in America is a positive function of American government purchases. According to the model, a unit increase in European money supply lowers European unemployment by 1 percentage point. On the other hand, it raises European inflation by 1 percentage point. Correspondingly, a unit increase in European government purchases lowers European unemployment by 1 percentage point. On the other hand, it raises European inflation by 1 percentage point. And what is more, it raises the European structural deficit by 1 percentage point. As to the spillover effects, a unit increase in European money supply raises American unemployment by 0.5 percentage points and lowers American inflation by 0.5 percentage points. Conversely, a unit increase in European government purchases lowers American unemployment by 0.5 percentage points and raises American inflation by 0.5 percentage points. To illustrate this there are two numerical examples. First consider an increase in European money supply. For instance, let European unemployment be 2 percent, let European inflation be 2 percent, and let the European structural deficit be 2 percent as well. Further, let American unemployment be 2 percent, let American inflation be 2 percent, and let the American structural deficit be 2 percent as well. Now consider a unit increase in European money supply. Then European unemployment goes from 2 to 1 percent. On the other hand, European inflation goes from 2 to 3 percent. And the European structural deficit stays at 2 percent. What is more, American unemployment goes from 2 to 2.5 percent. American inflation goes from 2 to 1.5 percent. And the American structural deficit stays at 2 percent. Second consider an increase in European government purchases. For instance, let European unemployment be 2 percent, let European inflation be 2 percent, and let the European structural deficit be 2 percent as well. Further, let American unemployment be 2 percent, let American inflation be 2 percent, and let the American structural deficit be 2 percent as well. Now consider a unit
170 Monetary and Fiscal Interaction between Europe and America: Case A increase in European government purchases. Then European unemployment goes from 2 to 1 percent. On the other hand, European inflation goes from 2 to 3 percent. And the European structural deficit goes from 2 to 3 percent as well. What is more, American unemployment goes from 2 to 1.5 percent. American inflation goes from 2 to 2.5 percent. And the American structural deficit stays at 2 percent. As to policy targets there are three distinct cases. In case A the target of the European central bank is zero inflation in Europe. The target of the American central bank is zero inflation in America. The targets of the European government are zero unemployment and a zero structural deficit in Europe. And the targets of the American government are zero unemployment and a zero structural deficit in America. In case B the targets of the European central bank are zero inflation and zero unemployment in Europe. The targets of the American central bank are zero inflation and zero unemployment in America. The targets of the European government are zero unemployment and a zero structural deficit in Europe. And the targets of the American government are zero unemployment and a zero structural deficit 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. The targets of the European government are zero unemployment and a zero structural deficit in Europe. And the targets of the American government are zero unemployment and a zero structural deficit 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: 2M1 = − 2B1 − 2G1 − G 2 + M 2 (7) Suppose the American central bank lowers American money supply. Then, as a response, the European central bank lowers European money supply. Suppose
1. The Model 171 the European government raises European government purchases. Then, as a response, the European central bank lowers European money supply. Suppose the American government raises American government purchases. 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: 2M 2 = − 2B2 − 2G 2 − G1 + M1 (8) 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 LG1 = u1 + s1 (9) LG1 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: LG1 = (A1 − M1 + 0.5M 2 − G1 − 0.5G 2 )2 + (G1 − T1 )2 (10) Then the first-order condition for a minimum loss gives the reaction function of the European government: 4G1 = 2A1 + 2T1 − 2M1 + M 2 − G 2 (11) 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,
172 Monetary and Fiscal Interaction between Europe and America: Case A so what is needed is a loss function. We assume that the American government has a quadratic loss function: LG 2 = u 2 + s 2 2 (12) 2 LG 2 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: LG 2 = (A 2 − M 2 + 0.5M1 − G 2 − 0.5G1 )2 + (G 2 − T2 ) 2 (13) Then the first-order condition for a minimum loss gives the reaction function of the American government: 4G 2 = 2A 2 + 2T2 − 2M 2 + M1 − G1 (14) 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 = T1 = T2 . The solution to this problem is as follows: 3M1 = − 5A1 − 4A 2 − 9B1 − 6B2 − 9T (15) 3M 2 = − 5A 2 − 4A1 − 9B2 − 6B1 − 9T (16) G1 = A1 + B1 + T (17) G 2 = A 2 + B2 + T (18)
2. Some Numerical Examples 173 Equations (15) to (18) 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 1.67 units, a decline in American money supply of 1.33 units, and an increase in European government purchases of 1 unit. 2. Some Numerical Examples For easy reference, the basic model is summarized here: u1 = A1 − M1 + 0.5M 2 − G1 − 0.5G 2 (1) u 2 = A 2 − M 2 + 0.5M1 − G 2 − 0.5G1 (2) π1 = B1 + M1 − 0.5M 2 + G1 + 0.5G 2 (3) π2 = B2 + M 2 − 0.5M1 + G 2 + 0.5G1 (4) s1 = G1 − T1 (5) s 2 = G 2 − T2 (6) And the Nash equilibrium can be described by four equations: 3M1 = − 5A1 − 4A 2 − 9B1 − 6B2 − 9T (7) 3M 2 = − 5A 2 − 4A1 − 9B2 − 6B1 − 9T (8) G1 = A1 + B1 + T (9) G 2 = A 2 + B2 + T (10)
174 Monetary and Fiscal Interaction between Europe and America: Case A 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 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. 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. Table 7.1 presents a synopsis. 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 LM1 = π1 (11)
2. Some Numerical Examples 175 LM 2 = π2 (12) 2 2 2 LG1 = u1 + s1 (13) LG 2 = u 2 + s 2 (14) 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 9 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 9 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 7.1 Monetary and Fiscal Interaction between Europe and America A Demand Shock in Europe Europe America Unemployment 0 Unemployment 0 Inflation 0 Inflation 0 Structural Deficit 0 Structural Deficit 0 3 Shock in A1 −3 Shock in B1 Unemployment 3 Unemployment 0 −3 Inflation Inflation 0 Change in Money Supply 4 Change in Money Supply 2 Change in Govt Purchases 0 Change in Govt Purchases 0 Unemployment 0 Unemployment 0 Inflation 0 Inflation 0 Structural Deficit 0 Structural Deficit 0