Imperfect Information and Optimal Monetary Policy

Should the central bank care whether slow adjustment of the price level is due to imperfect information as in Woodford (2002) or due to adjustment costs as in the standard New Keynesian model? To answer this question, we study optimal monetary policy in a model that is an extension of Woodford (2002). Price setters can change prices every period at no cost; price setters have dispersed information about the state of the economy; the central bank has perfect information about the state of the economy; but the central bank cannot communicate its information to price setters because of their limited attention. We show that the optimal monetary policy under commitment equals the optimal monetary policy under discretion. There is no time inconsistency. By contrast, there is time inconsistency in the Calvo model. It follows that the optimal monetary policy in this model cannot be identical to the optimal monetary policy in the Calvo model both under commitment and under discretion. Comparing optimal monetary policy under commitment in the imperfect information model and in the Calvo model, we find that the optimal policy response to TFP shocks is identical in the two models, while the optimal policy response to markup shocks is different in the two models.