Some models to guide monetary policymakers

We consider the nature of optimal cyclical monetary policy in three different stochastic models with various shocks - money demand shocks, productivity shocks, and government consumption shocks. The first is a pure liquidity effect model, the second is a cost of changing prices model, and the third is an optimal seignorage model. We solve for the optimal monetary policy and describe how money growth and interest rates respond to shocks. all of the models have the feature that the Friedman rule of setting the nominal interest rate to zero is not optimal. We find that the optimal response of monetary policy is not always counter-cyclical but depends on the model and the shock.