Optimal Monetary Policy under Commitment with a Zero Bound on Nominal Interest Rates

We compute the optimal nonlinear interest rate policy under commitment for a forward-looking stochastic model with monopolistic competition and sticky prices when nominal interest rates are bounded below by zero. Calibrating the model to the U.S. economy we find that the empirical magnitude of mark-up shocks is too small to entail zero nominal interest rates. While real rate shocks plausibly lead to a binding lower bound under optimal policy, this occurs quite infrequently and generates rather small average welfare losses. The presence of binding real rate shocks, however, requires that policy reduces nominal interest rates more aggressively than suggested by a model without lower bound or without binding shocks. Moreover, binding shocks alter the optimal policy response to non-binding shocks