Optimal Monetary Policy with Dispersed Information and Policy-Contingent Phillips Curve

I study optimal monetary policy in a neo-Keynesian model with heterogeneous information, à la Mankiw and Reis (2010). The role of monetary policy is to correct market inefficiency generated by economic uncertainty. In doing so, the standard Lucas critique applies: monetary policy itself would affect firms’ responsiveness to the policy and other shocks. The question then is how the central bank should modify the monetary policy to take such structural dependence into account. I find that if the central bank (naively) assumes that the responsiveness of the aggregate output to the productivity shock does not depend on the monetary policy, it minimizes the output gap volatility. In this situation, the price dispersion is not taken into account and the central bank underestimates the magnitude of the optimal monetary shock. When the central bank has perfect information about aggregate variables, it should fully accommodate the productivity shocks. Such a policy reduces both the output gap volatility and price dispersion to their minimum. However, when the central bank acts under information constraints, it faces a trade-off between price and output stability. This justifies the use of the Taylor rule, which optimizes their weighted sum.