Imperfect Information and Optimal Monetary Policy

Should the central bank care whether slow adjustment of the price level is due to adjustment costs as in the standard New Keynesian model or due to imperfect infor-mation? To answer this question, we study optimal monetary policy in an extension of the Woodford (2002) imperfect information model. 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; and the central bank cannot communicate its information to price setters because of their limited attention. We show that the optimal policy under commitment in the imperfect information model is time consistent, whereas the optimal policy under commitment in the Calvo model is not time consistent. Hence, the optimal policy in the imperfect information model cannot equal the optimal policy in the Calvo model both under com-mitment 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 can be quite different in the two models. In addition, we study optimal monetary policy in a rational inattention model