Central Bank and Governments Cooperate

As a starting point, take the model of unemployment. It can be represented by a system of three equations:

$$ \begin{array}{*{20}l} {{\rm{u}}_1 {\rm{ = }}} & {{\rm{B}}_1 {\rm{ - \gamma M - \delta G}}_1 } & {\left( {\rm{1}} \right)} \\ {{\rm{u}}_2 {\rm{ = }}} & {{\rm{B}}_2 {\rm{ - \gamma M - \delta G}}_2 } & {\left( 2 \right)} \\ {{\rm{u = }}} & {0.5{\rm{u}}_1 + 0.5{\rm{u}}_2 } & {\left( 3 \right)} \\ \end{array} $$

Here u

1

denotes the rate of unemployment in Germany, u

2

is the rate of unemployment in France, u is the rate of unemployment in Europe, M is European money supply, G

1

is German government purchases, and G

2

is French government purchases. The endogenous variables are the rates of unemployment in Germany, France and Europe.

2) The policy model. At the beginning there is unemployment in Germany and France. More precisely, unemployment in Germany is high, and unemployment in France is low. The policy makers are the European central bank, the German government, and the French government. The targets of policy cooperation are zero unemployment in Germany and zero unemployment in France. The instruments of policy cooperation are European money supply, German government purchases, and French government purchases. There are two targets and three instruments, so there is one degree of freedom. As a result, there is an infinite number of solutions. In other words, monetary and fiscal cooperation can achieve zero unemployment in Germany and France.