251 2.2 Fiscal Cooperation between Europe and America The policy makers are the European government and the American government. The targets of fiscal cooperation are zero unemployment in Europe and America. The instruments of fiscal cooperation are European government purchases and American government purchases. There are two targets and two instruments. We assume that the European government and the American government agree on a common loss function. The amount of loss depends on unemployment in Europe and America. The policy makers set European government purchases and American government purchases so as to minimize the common loss. The cooperative equilibrium is determined by the first-order conditions for a minimum loss. It yields the optimum levels of European government purchases and American government purchases. As a result, the cooperative equilibrium is identical to the corresponding Nash equilibrium. That is to say, fiscal cooperation is equivalent to fiscal interaction. For some numerical examples see Section 2.1. 2. Fiscal Policies in Europe and America: Absence of a Deficit Target 252 3. Fiscal Policies in Europe and America: Presence of a Deficit Target 3.1. Fiscal Interaction between Europe and America 1) The model. An increase in European government purchases lowers European unemployment. 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. In the numerical example, 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. A unit increase in European government purchases lowers American unemployment by 0.5 percentage points and raises American inflation by 0.5 percentage points. However, it has no effect on the American structural deficit. 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 government purchases. Then European unemployment goes from 2 to 1 percent. European inflation goes from 2 to 3 percent. And the European structural deficit goes from 2 to 3 percent as well. 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. Conclusion 253 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. The amount of loss depends on unemployment and the structural deficit in Europe. The European government sets European government purchases so as to minimize its loss. From this follows the reaction function of the European government. Suppose the American government raises American government purchases. Then, as a response, the European government lowers European government purchases. 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. The amount of loss depends on unemployment and the structural deficit in America. The American government sets American government purchases so as to minimize its loss. From this follows the reaction function of the American government. Suppose the European government raises European government purchases. Then, as a response, the American government lowers American government purchases. The Nash equilibrium is determined by the reaction functions of the European government and the American government. It yields the equilibrium levels of European government purchases and American government purchases. As a rule, unemployment in Europe and America is not zero. And the structural deficits in Europe and America are not zero either. 2) A demand shock in Europe. We assume equal weights in each of the loss functions. Let initial unemployment in Europe be 3 percent, and let initial unemployment in America be zero percent. Let initial inflation in Europe be – 3 percent, and let initial inflation in America be zero percent. Let the initial structural deficit in Europe be zero percent, and let the initial structural deficit in America be the same. Step one refers to the policy response. According to the Nash equilibrium there is an increase in European government purchases of 1.6 units and a 3. Fiscal Policies in Europe and America: Presence of a Deficit Target 254 reduction in American government purchases of 0.4 units. Step two 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 – 1.6 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. For a synopsis see Table 9.7. Table 9.7 Fiscal Interaction between Europe and America A Demand Shock in Europe Europe America Unemployment 3 Unemployment 0 Inflation − 3 Inflation 0 Structural Deficit 0 Structural Deficit 0 Change in Govt Purchases 1.6 Change in Govt Purchases − 0.4 Unemployment 1.6 Unemployment − 0.4 Inflation − 1.6 Inflation 0.4 Structural Deficit 1.6 Structural Deficit − 0.4 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. Conclusion 255 3.2. Fiscal Cooperation between Europe and America 1) The model. 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. The amount of loss depends on unemployment and the structural deficit in each of the regions. The policy makers set European government purchases and American government purchases so as to minimize the common loss. The cooperative equilibrium is determined by the first-order conditions for a minimum loss. It yields the optimum levels of European government purchases and American government purchases. 2) A demand shock in Europe. We assume equal weights in the loss function. Let initial unemployment in Europe be 3 percent, and let initial unemployment in America be zero percent. Let initial inflation in Europe be – 3 percent, and let initial inflation in America be zero percent. Let the initial structural deficit in Europe be zero percent, and let the initial structural deficit in America be the same. Step one 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 two 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. For an overview see Table 9.8. 3. Fiscal Policies in Europe and America: Presence of a Deficit Target 256 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. Table 9.8 Fiscal Cooperation between Europe and America A Demand Shock in Europe Europe America Unemployment 3 Unemployment 0 Inflation − 3 Inflation 0 Structural Deficit 0 Structural Deficit 0 Change in Govt Purchases 1.29 Change in Govt Purchases 0.09 Unemployment 1.66 Unemployment − 0.74 Inflation − 1.66 Inflation 0.74 Structural Deficit 1.29 Structural Deficit 0.09 3) Comparing fiscal interaction and fiscal cooperation. As a result, the cooperative equilibrium is different from the Nash equilibrium. In the numerical example, fiscal cooperation is superior to fiscal interaction. Conclusion 257 4. Monetary and Fiscal Policies in Europe and America: Absence of a Deficit Target 4.1. Monetary and Fiscal Interaction between Europe and America An increase in European money supply lowers European unemployment. 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 unemploy- ment and lowers European inflation. An increase in European government purchases lowers European unemploy- ment. On the other hand, it raises European inflation. Correspondingly, an increase in American government purchases lowers American unemployment. On the other hand, it raises American inflation. 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. 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. And what is more, a unit increase in European money supply raises American unemployment by 0.5 percentage points and lowers American inflation by 0.5 percentage points. 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, a unit increase in European government purchases lowers American unemployment by 0.5 percentage points and raises American inflation by 0.5 percentage points. 4. Monetary and Fiscal Policies in Europe and America 258 To illustrate this there are two numerical examples. First consider an increase in European money supply. For instance, let European unemployment be 2 percent, and let European inflation be 2 percent as well. Further, let American unemployment be 2 percent, and let American inflation 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 what is more, American unemployment goes from 2 to 2.5 percent, and American inflation goes from 2 to 1.5 percent. Second consider an increase in European government purchases. For instance, let European unemployment be 2 percent, and let European inflation be 2 percent as well. Further, let American unemployment be 2 percent, and let American inflation be 2 percent as well. Now consider a unit 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 what is more, American unemployment goes from 2 to 1.5 percent, and American inflation goes from 2 to 2.5 percent. As to policy targets there are two 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 target of the European government is zero unemployment in Europe. And the target of the American government is zero unemployment 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 target of the European government is zero unemployment in Europe. And the target of the American government is zero unemployment in America. 1) Case A. The target of the European central bank is zero inflation in Europe. The instrument of the European central bank is European money supply. From this follows 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. Suppose 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. Conclusion 259 The target of the American central bank is zero inflation in America. The instrument of the American central bank is American money supply. From this follows the reaction function of the American central bank. The target of the European government is zero unemployment in Europe. The instrument of the European government is European government purchases. From this follows the reaction function of the European government. The target of the American government is zero unemployment in America. The instrument of the American government is American government purchases. From this follows the reaction function of the American government. Suppose the European central bank lowers European money supply. Then, as a response, the European government raises European government purchases, 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. As an important result, in case A, there is no Nash equilibrium. 2) Case B. 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. The amount of loss depends on inflation and unemployment in Europe. The European central bank sets European money supply so as to minimize its loss. From this follows the reaction function of the European central bank. 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. The amount of loss depends on inflation and unemployment in America. The American central bank sets American money supply so as to minimize its loss. From this follows the reaction function of the American central bank. 4. Monetary and Fiscal Policies in Europe and America 260 The target of the European government is zero unemployment in Europe. The instrument of the European government is European government purchases. From this follows the reaction function of the European government. The target of the American government is zero unemployment in America. The instrument of the American government is American government purchases. From this follows the reaction function of the American government. 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. As an important result, in case B, there is no Nash equilibrium. 4.2. Monetary and Fiscal Cooperation between Europe and America 1) The model. The policy makers are the European central bank, the American central bank, the European government, and the American government. The targets of policy cooperation are zero inflation in Europe, zero inflation in America, zero unemployment in Europe, and zero unemployment in America. The instruments of policy cooperation are European money supply, American money supply, European government purchases, and American government purchases. There are four targets and four instruments. We assume that the policy makers agree on a common loss function. The amount of loss depends on inflation and unemployment in each of the regions. The policy makers set European money supply, American money supply, European government purchases, and American government purchases so as to minimize the common loss. The cooperative equilibrium is determined by the first-order conditions for a minimum loss. It yields the optimum levels of European money supply, American money supply, European government purchases, and American Conclusion [...]... shock in Europe, monetary and fiscal interaction produces zero inflation in Europe On the 5 Monetary and Fiscal Policies in Europe and America 269 other hand, it raises unemployment and the 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 Table 9.12 Monetary and. .. Europe In case A, policy interaction achieves zero inflation in Europe On the other hand, it raises unemployment and the structural deficit there In case B, policy interaction has no effect on inflation and unemployment in Europe And what is more, it causes a structural deficit there 6) Comparing pure monetary interaction and monetary- fiscal interaction As a result, in case B, the system of pure monetary. .. in Europe, monetary interaction lowers inflation in Europe On the other hand, it raises unemployment there 279 280 Result Given another mixed shock in Europe, monetary interaction lowers unemployment in Europe On the other hand, it raises inflation there 1.2 Monetary Cooperation between Europe and America The policy makers are the European central bank and the American central bank The targets of monetary. ..4 Monetary and Fiscal Policies in Europe and America 261 government purchases As a result there is an infinite number of solutions Put another way, monetary and fiscal cooperation can reduce the loss caused by inflation and unemployment 2) A demand shock in Europe We assume equal weights in the loss function Let initial unemployment in Europe be 3 percent, and let initial unemployment in America... Comparing the system of monetary and fiscal cooperation with other regimes First, monetary and fiscal cooperation is equivalent to pure monetary cooperation of type B Second, monetary and fiscal cooperation is equivalent to pure monetary interaction of type B Third, monetary and fiscal cooperation is superior to monetary and fiscal interaction of type B 279 Result 1 Monetary Policies in Europe and America... Comparing pure monetary interaction and monetary- fiscal interaction As a result, in case A, the system of pure monetary interaction is superior to the system of monetary and fiscal interaction, see Part Three 270 Conclusion 5.2 Monetary and Fiscal Interaction between Europe and America: Case B 1) The model This section deals with case B The targets of the European central bank are zero inflation and zero... structural deficit there Given a mixed shock in Europe, policy interaction lowers inflation in Europe On the other hand, it raises unemployment and the structural deficit there Given another type of mixed shock in Europe, policy interaction lowers unemployment in Europe On the other hand, it raises inflation and the structural deficit there As an important result, the system of pure monetary interaction seems... unemployment in America be zero percent Let initial inflation in Europe be – 3 percent, and let initial inflation in America be zero percent Let the initial structural deficit in Europe be zero percent, and let the initial structural deficit in America be the same Step one refers to the policy response According to the Nash equilibrium there is an increase in European money supply of 4 units, an increase in. .. demand shock in Europe We assume equal weights in each of the loss functions Let initial unemployment in Europe be 3 percent, and let initial unemployment in America be zero percent Let initial inflation in Europe be – 3 percent, and let initial inflation in America be zero percent Let the initial structural deficit in Europe be zero percent, and let the initial structural deficit in America be the. .. 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 5) Comparing policy interaction and policy cooperation Under policy interaction there is no Nash equilibrium By contrast, under . Comparing pure monetary interaction and monetary- fiscal interaction. As a result, in case A, the system of pure monetary interaction is superior to the system of monetary and fiscal interaction,. unemployment, and a zero structural deficit in each of the regions. 5. Monetary and Fiscal Policies in Europe and America 2 68 Table 9.11 Monetary and Fiscal Interaction between Europe and America. 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