Optimal monetary policy under heterogeneous beliefs

We use a New Keynesian model that features rational and non-rational households. Assuming that both the fraction of rational households and the expectations formation process are uncertain from the perspective of the central bank, we derive robust optimal discretionary monetary policy in a simple min-max framework where the central bank plays a zero-sum game versus a fictitious, malevolent evil agent. We show that the central bank is able to improve welfare if it accounts for uncertainty while the model is being distorted. Even if the central bank accounts for the worst possible outcomes while the model is being undistorted, the central bank can still reduce the welfare loss by implementing a more aggressive targeting rule that favorably affects the inflation-output stabilization trade-off.