This article uses a DSGE framework to evaluate the role of monetary policy in determining the likelihood of encountering the zero lower bound. We find that the probability of experiencing episodes of being at zero lower bound depends almost exclusively on the monetary policy rule. A policy rule, such as the one proposed by Taylor (1993) which is based on the dual mandate is highly likely to lead to episodes of zero short-term interest rates if the central bank is not committed to its inflation target. Our results on nominal interest rate and inflation dynamics do not depend on the particular mechanism that makes monetary policy have real effects. The key and necessary assumption is that expectations are forward looking. The bottom line in models in which monetary policy can influence the real economy is that a central bank must be committed to a long-run average-inflation objective if it wishes to achieve a dual mandate while avoiding the zero lower bound.