Optimal Monetary Policy with an Occasionally Binding ZLB and Central Bank Asset Purchases

We derive optimal monetary policy in a New Keynesian model with central bank asset purchases, accounting for an occasionally binding zero lower bound, ZLB, on the policy rate. Potential gains to central bank asset purchases arise with the policy rate away from the ZLB due to a constraint on the financial sector. Optimal central bank balance sheet management eliminates ZLB dampening of "supply" shocks and ZLB amplification of "demand" shocks. In simulations calibrated to match United States data, the average ZLB event length falls by 25%, and the prevalence of ZLB events falls by 75% with optimal monetary policy.