Optimal Time-Consistent Monetary Policy in the New Keynesian Model with Repeated Simultaneous Play

Abstract

We solve for the optimal time-consistent monetary policy in the New Keynesian model with repeated simultaneous play between the monetary authority, households, and …rms. Recent work on optimal time-consistent monetary policy has emphasized the existence of multiple Markov perfect equilibria in the New Keynesian model (e.g., King and Wolman, 2004). In this paper, we show that this multiplicity is not intrinsic to the New Keynesian model itself, but is instead driven by a special timing assumption by previous authors that play is “repeated Stackelberg” — in which the monetary authority must pre-commit each period to a value for the monetary instrument— as opposed to repeated simultaneous, in which the monetary authority and the private sector determine the economic equilibrium simultaneously and jointly every period. To illlustrate this, we derive a closed-form solution for the set of all possible Markov perfect equilibria in the twoperiod Taylor contracting version of the New Keynesian model under repeated simultaneous play and show that the equilibrium in that model is unique.

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