Optimal price-level drift under commitment in the canonical New Keynesian model

In both the canonical and many extended versions of the New Keynesian model, optimal monetary policy under commitment implies price-level stationarity as long as expectations are rational. We show that this is no longer the case if the central bank and private agents make decisions before observing current shocks. The optimal amount of price-level drift in response to unexpected innovations to inflation is quantitatively important. This result has important implications for monetary policy, including the design of the optimal loss function for the central bank if it cannot commit to its future policies.