122 2. Some Numerical Examples For easy reference, the basic model is reproduced here: 111 2 uAG0.5G=−− (1) 222 1 uAG0.5G=−− (2) 111 2 BG0.5Gπ= + + (3) 222 1 BG0.5Gπ= + + (4) 111 sGT=− (5) 222 sGT=− (6) And the Nash equilibrium can be described by two equations: 11 2 15G 8A 2A 6T=− + (7) 221 15G 8A 2A 6T=−+ (8) 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 1 A 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 123 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 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 – 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. Table 5.1 presents a synopsis. Table 5.1 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 Shock in A 1 3 Shock in B 1 − 3 Unemployment 3 Unemployment 0 Inflation − 3 Inflation 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 2. Some Numerical Examples 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 respectively: 22 111 Lus=+ (9) 22 222 Lus=+ (10) 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 1 B of 3 units and an increase in 1 A 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 125 Table 5.2 Fiscal Interaction between Europe and America A Supply Shock in Europe Europe America Unemployment 0 Unemployment 0 Inflation 0 Inflation 0 Structural Deficit 0 Structural Deficit 0 Shock in A 1 3 Shock in B 1 3 Unemployment 3 Unemployment 0 Inflation 3 Inflation 0 Change in Govt Purchases 1.6 Change in Govt Purchases − 0.4 Unemployment 1.6 Unemployment − 0.4 Inflation 4.4 Inflation 0.4 Structural Deficit 1.6 Structural Deficit − 0.4 First consider the effects on Europe. As a result, 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. 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 supply 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, it increases the loss of the American government from zero to 0.32 units. 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 1 A 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 Europe America Unemployment 0 Unemployment 0 Inflation 0 Inflation 0 Structural Deficit 0 Structural Deficit 0 Shock in A 1 6 Shock in B 1 0 Unemployment 6 Unemployment 0 Inflation 0 Inflation 0 Change in Govt Purchases 3.2 Change in Govt Purchases − 0.8 Unemployment 3.2 Unemployment − 0.8 Inflation 2.8 Inflation 0.8 Structural Deficit 3.2 Structural Deficit − 0.8 Fiscal Interaction between Europe and America 127 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 1 B 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 Europe America Unemployment 0 Unemployment 0 Inflation 0 Inflation 0 Structural Deficit 0 Structural Deficit 0 Shock in A 1 0 Shock in B 1 6 Unemployment 0 Unemployment 0 Inflation 6 Inflation 0 Change in Govt Purchases 0 Change in Govt Purchases 0 Unemployment 0 Unemployment 0 Inflation 6 Inflation 0 Structural Deficit 0 Structural Deficit 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 1 A of 3 units, a decline in 1 B of 3 units, an increase in 2 A of 3 units, and a decline in 2 B 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 129 America. The structural deficit in Europe goes from zero to 1.2 percent, as does the structural deficit in America. Table 5.5 presents a synopsis. As a result, given a common demand shock, fiscal interaction lowers unemployment and deflation in each of the regions. On the other hand, it raises the structural deficit there. The initial loss of each government is zero. The common demand 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. Table 5.5 Fiscal Interaction between Europe and America A Common Demand Shock Europe America Unemployment 0 Unemployment 0 Inflation 0 Inflation 0 Structural Deficit 0 Structural Deficit 0 Shock in A 1 3 Shock in A 2 3 Shock in B 1 − 3 Shock in B 2 − 3 Unemployment 3 Unemployment 3 Inflation − 3 Inflation − 3 Change in Govt Purchases 1.2 Change in Govt Purchases 1.2 Unemployment 1.2 Unemployment 1.2 Inflation − 1.2 Inflation − 1.2 Structural Deficit 1.2 Structural Deficit 1.2 2. Some Numerical Examples 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 1 B of 3 units, as there is in 1 A . And there is an increase in 2 B of 3 units, as there is in 2 A . 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 131 Table 5.6 Fiscal Interaction between Europe and America A Common Supply Shock Europe America Unemployment 0 Unemployment 0 Inflation 0 Inflation 0 Structural Deficit 0 Structural Deficit 0 Shock in A 1 3 Shock in A 2 3 Shock in B 1 3 Shock in B 2 3 Unemployment 3 Unemployment 3 Inflation 3 Inflation 3 Change in Govt Purchases 1.2 Change in Govt Purchases 1.2 Unemployment 1.2 Unemployment 1.2 Inflation 4.8 Inflation 4.8 Structural Deficit 1.2 Structural Deficit 1.2 2. Some Numerical Examples [...]... unemployment in Europe On the other hand, it raises the structural deficit there Given a demand shock in Europe, fiscal cooperation is superior to fiscal interaction And the same applies to a supply shock in Europe Part Six Monetary and Fiscal Policies in Europe and America Absence of a Deficit Target 141 Chapter 1 Monetary and Fiscal Interaction between Europe and America The world economy consists of two monetary. .. 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, and the rate of inflation in America According to equation (1), 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 According to the model, a unit increase in European government purchases lowers European unemployment by 1 percentage point On the other hand,... case C the target of the European central bank is zero inflation 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 144 Monetary and Fiscal Interaction between Europe and America 1) Case A The target of the European... demand shock in Europe, monetary and fiscal cooperation produces zero inflation and zero unemployment in each of the regions The loss function under policy cooperation is: 2 2 2 L = π1 + π2 + u1 + u 2 2 (1) The initial loss is zero The demand shock in Europe causes a loss of 18 units Then policy cooperation brings the loss down to zero again Table 6.1 Monetary and Fiscal Cooperation between Europe and. .. zero, and let initial inflation be zero as well Step one refers to the supply 154 Monetary and Fiscal Cooperation between Europe and America 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... 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 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... 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 supply shock in Europe, fiscal cooperation seems to be superior to fiscal interaction 3) Summary Given a demand shock in Europe, fiscal. .. raises European Monetary and Fiscal Interaction between Europe and America 143 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 To illustrate this there are two numerical examples First consider an increase in European money supply For instance, let... 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 In case . − + + (4) M. Carlberg, Monetary and Fiscal Strategies in the World Economy, 141 DOI 10.1007/978-3- 642 -1 047 6-3_19, © Springer-Verlag Berlin Heidelberg 2010 142 Here 1 u denotes the rate. In terms of the model there is an increase in 1 B of 3 units, as there is in 1 A . And there is an increase in 2 B of 3 units, as there is in 2 A . Step two refers to the outside lag. Inflation. 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.