Optimal Monetary Policy in an Economy with Inflation Persistence

This paper studies optimal monetary policy in a model where inflation is persistent. Two types of price setters are assumed to exist. One acts rationally given Calvo-type constraints on price setting. The other type sets prices according to a rule-of-thumb. This results in a Phillips curve with both a forward-looking term and a backward-looking term. The Phillips curve nests a standard purely forward-looking Phillips curve as well as a standard purely backward-looking Phillips curve as special cases. A cost push supply shock is derived from microfoundations by adding a time varying income tax and by making the elasticity of substitution between goods stochastic. A central bank loss function for this model is derived from a second order Taylor approximation of the welfare. Optimal monetary policy for different relative values of the forwardand backward-looking terms is then analyzed for both the commitment case and the case of discretion.