Unemployment risk, liquidity traps, and monetary policy

We study optimal monetary policy in a model with incomplete markets, in the form of uninsurable unemployment risk, and an occasionally binding zero lower bound (ZLB) constraint. The optimal policy consists of keeping the nominal rate at zero longer than implied by current macroeconomic conditions. Such policy improves expected labour market conditions, substantially mitigating the rise in unemployment risk and precautionary savings. As a result, we find that market incompleteness does not significantly amplify contractions in output and inflation at the ZLB. However, when the central bank follows more realistic policy rules instead of the optimal policy, incomplete markets exacerbate the fall in demand, emphasising the importance of unemployment insurance for output stabilisation.