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

We compute the optimal non-linear 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. When the lower bound binds, the optimal policy is to reduce the real rate by generating inflation expectations. This is achieved by committing to increase future interest rates by less than what purely forward-looking policy would suggest. As a result, there is a ‘commitment bias’, i.e., average output and inflation turn out to be higher than their target values. Calibrating the model to the US economy we find that the quantitative importance of the average effects on output and inflation are negligible. Moreover, the empirical magnitude of US mark-up shocks is too small to entail zero nominal interest rates. Real rate shocks, however, plausibly lead to a binding lower bound under optimal policy, albeit relatively infrequently. Interestingly, the presence of binding real rate shocks alters the optimal policy response to (non-binding) mark-up shocks.