Optimal monetary policy with imperfect unemployment insurance

We consider an efficiency-wage model with the Calvo-type sticky prices and analyze optimal monetary policy when unemployment insurance is not perfect. With imperfect risk sharing, strict zero-inflation policy is no longer optimal even if the zero-inflation steady-state equilibrium is assumed to be (conditionally) efficient. Quantitative result depends on how idiosyncratic earning losses, measured by the (inverse of the) relative income of the unemployed to the employed, vary over business cycles. If idiosyncratic income losses are acyclical, optimal policy differs very little from the zero-inflation policy. However, if they vary countercyclically, as evidence suggests, the deviation of optimal policy from complete price stabilization becomes quantitatively significant. Furthermore, optimal policy in such a case involves stabilization of output to a much larger extent