We analyze monetary policy in a model where temporary shocks can permanently scar the economy's productive capacity. Unemployed workers’ skill losses generate multiple steady-state unemployment rates. When monetary policy is constrained by the zero bound, large shocks reduce hiring to a point where the economy recovers slowly at best—at worst, it falls into a permanent unemployment trap. Since monetary policy is powerless to escape such traps ex post, it must avoid them ex ante. The model quantitatively accounts for the slow U.S. recovery following the Great Recession, and suggests that lack of swift monetary accommodation helps explain the European periphery’s stagnation.