Woodford's Approach to Robust Policy Analysis in a Linear-Quadratic Framework

This paper extends Woodford's (2010) approach to the robustly monetary policy to a general linear quadratic framwork. We provide algorithms to solve for a time-invariant linear robustly optimal policy from a timeless perspective and for a time-invariant linear Markov perfect equilibrium under discretation. We apply our methods to two New Keynesian models of monetary policy: (i) a model with persistent cost-push shocks and (ii) a model with inflation persistence. We find that the robustly optimal commitment inflation is less responsive to a cost-push shock when the shock is more persistent and that the robustly optimal discretionary policy is more responsive to lagged inflation in the presence inflation inertia.