Optimal Monetary Policy Under Uncertainty: A Markov Jump-Linear-Quadratic Approach

We study the design of optimal monetary policy under uncertainty using a Markov jumplinear-quadratic (MJLQ) approach. We approximating the uncertainty that policymakers face by different discrete modes in a Markov chain, and by taking mode-dependent linear-quadratic approximations of the underlying model. This allows us to apply a powerful methodology with convenient solution algorithms that we have developed. We apply our methods to analyze the effects of uncertainty and potential gains from experimentation for two sources of uncertainty in the New Keynesian Phillips curve. Our examples highlight that learning may have sizeable effects on losses, and while it is generally beneficial it need not always be so. The experimentation component typically has little effect, and in some cases it can lead to attenuation of policy. JEL Classification: E42, E52, E58