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

We solve for the optimal time-consistent monetary policy in the New Keynesian model with repeated simultaneous play between the monetary authority, households, and firms. 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 an auxiliary 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 each period. A contribution of our paper is to show how to define the game between the monetary authority, households, and firms with repeated simultaneous play and aggregate resource constraints. We show that the repeated simultaneous play assumption is the proper generalization of the large existing literature on linear-quadratic optimal monetary policy under uncertainty (e.g., Woodford, 2003, Svensson and Woodford, 2003, 2004). We highlight and discuss additional advantages of the repeated simultaneous play assumption. Finally, we derive a closed-form solution for the set of all possible Markov perfect equilibria in the two-period Taylor contracting version of the New Keynesian model with simultaneous play and show that the equilibrium in that model is unique.