By Anton Braun and Tomoyuki Nakajima
This paper considers the properties of an optimal monetary policy when households are subject to countercyclical uninsured income shocks. We develop a tractable incomplete markets model with Calvo price setting. Incomplete markets creates a new distortion and that distortion is large in the sense that the welfare cost of business cycles is large in our model. Nevertheless, the optimal monetary policy is very similar to the optimal policy that emerges in the representative agent framework and calls for nearly complete stabilization of the price-level.
The way incomplete markets is introduced here is through the absence of insurance markets for idiosyncratic labor productivity shocks. While this incompleteness increases considerably the cost of business cycles, it does not change anything to the prescription for monetary policy if firms face a Calvo technology for price changes: very low inflation is best.