Uninsured Unemployment Risk and Optimal Monetary Policy in a Zero-Liquidity Economy

I study optimal monetary policy in a sticky-price economy wherein households precautionary-save against uninsured, endogenous unemployment risk. In this economy greater unemployment risk raises desired savings, causing aggregate demand to fall and feed back to greater unemployment risk. This deflationary spiral is constrained inefficient and calls for an accommodative monetary policy response: after a contractionary aggregate shock the policy rate should be kept significantly lower and for longer than in the perfect-insurance benchmark. For example, the usual prescription obtained under perfect insurance of a hike in the policy rate in the face of a bad supply (i.e., productivity or cost-push) shock is easily overturned. The optimal policy breaks the deflationary spiral and takes the dynamics of the imperfect-insurance economy close to that of the perfect-insurance benchmark. These results are derived in an economy with zero asset supply (zero liquidity) and are thus independent of any redistributive effect of monetary policy on household wealth.