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 three equations:

$$ \begin{array}{*{20}l} {{\rm{\pi }}_1 = }& {\rm{A}}_1 {{\rm{ + \alpha M + \beta G}}_1 } & {\left( {\rm{1}} \right)} \\ {{\rm{\pi }}_2 = } & {\rm{A}}_2 {{\rm{ + \alpha M + \beta G}}_2 } & {\left( 2 \right)} \\ {{\rm{\pi }} = } & 0.5{\rm{\pi }}_1 { + 0.5{\rm{\pi }}_2 } & {\left( 3 \right)} \\ \end{array} $$

Of course this is a reduced form. π

1

denotes producer inflation in Germany, π

2

is producer inflation in France, π is producer inflation in Europe, M is European money supply, G

1

is German government purchases, G

2

is French government purchases, α is the monetary policy multiplier, β is the fiscal policy multiplier, A

1

is some other factors bearing on producer inflation in Germany, and A

2

is some other factors bearing on producer inflation in France.

The endogenous variables are producer inflation in Germany, producer inflation in France, and producer inflation in Europe. According to equation (1), producer inflation in Germany is a positive function of European money supply and a positive function of German government purchases. According to equation (2), producer inflation in France is a positive function of European money supply and a positive function of French government purchases. According to equation (3), producer inflation in Europe is the average of producer inflation in Germany and France.