Central Bank and Governments Decide Sequentially

The static model. As a point of reference, consider the static model. It can be represented by a system of six equations:

$${\rm{\pi }}_{\rm{1}} = {\rm{A}}_{\rm{1}} + {\rm{\alpha M + \beta G}}_{\rm{1}}$$

((1))

$${\rm{\pi }}_2 = {\rm{A}}_2 + {\rm{\alpha M + \beta G}}_2$$

((2))

$${\rm{\pi }} = 0.5{\rm{\pi }}_1 + 0.5{\rm{\pi }}_{\rm{2}}$$

((3))

$${\rm{u}}_{\rm{1}} = {\rm{B}}_{\rm{1}} {\rm{ - \gamma M - \delta G}}_{\rm{1}}$$

((4))

$${\rm{u}}_2 = {\rm{B}}_2 {\rm{ - \gamma M - \delta G}}_2$$

((5))

$${\rm{u}} = 0.5{\rm{u}}_1 + 0.5{\rm{u}}_{\rm{2}}$$

((6))

Of course this is a reduced form. π₁ denotes the rate of inflation in Germany, π₂ is the rate of inflation in France, π is the rate of inflation in Europe, u₁ is the rate of unemployment in Germany, u₂ is the rate of unemployment in France, u is the rate of unemployment in Europe, M is European money supply, G₁ is German government purchases, G₂ is French government purchases, α is the monetary policy multiplier with respect to inflation, β is the fiscal policy multiplier with respect to inflation, γ is the monetary policy multiplier with respect to unemployment, δ is the fiscal policy multiplier with respect to unemployment, A₁ is some other factors bearing on the rate of inflation in Germany, A₂ is some other factors bearing on the rate of inflation in France, B₁ is some other factors bearing on the rate of unemployment in Germany, and B₂ is some other factors bearing on the rate of unemployment in France. The endogenous variables are the rates of inflation and the rates of unemployment in Germany, France and Europe.

According to equation (1), the rate of inflation in Germany is a positive function of European money supply and a positive function of German government purchases. According to equation (2), the rate of inflation in France is a positive function of European money supply and a positive function of French government purchases. According to equation (3), the rate of inflation in Europe is the average of the rates of inflation in Germany and France. According to equation (4), the rate of unemployment in Germany is a negative function of European money supply and a negative function of German government purchases. According to equation (5), the rate of unemployment in France is a negative function of European money supply and a negative function of French government purchases. According to equation (6), the rate of unemployment in Europe is the average of the rates of unemployment in Germany and France.