Optimal nonlinear policy: signal extraction with a non-normal prior

The literature on optimal monetary policy typically makes three major assumptions: (1) policymakers' preferences are quadratic, (2) the economy is linear, and (3) stochastic shocks and policymakers' prior beliefs about unobserved variables are normally distributed. This paper relaxes the third assumption and explores its implications for optimal policy. The separation principle continues to hold in this framework, allowing for tractability and application to forward-looking models, but policymakers' beliefs are no longer updated in a linear fashion, allowing for plausible nonlinearities in optimal policy. We consider in particular a class of models in which policymakers' priors about the natural rate of unemployment are diffuse in a region around the mean. When this is the case, optimal policy responds cautiously to small surprises in the observed unemployment rate, but becomes increasingly aggressive at the margin. These features match statements by Federal Reserve officials and the behavior of the Fed in the 1990s.