This paper employs stochastic simulations of a small structural rational expectations model to investigate the consequences of the zero bound constraint on nominal interest rates. We find that if the economy is subject to stochastic shocks similar in magnitude to those experienced in the U.S. over the 1980s and 1990s, the consequences of the zero bound are negligible for target inflation rates as low as 2 percent. However, the effects of the constraint are very non-linear with respect to the inflation target and produce a quantitatively significant deterioration of the performance of the economy with targets between 0 and 1 percent. The variability of output increases significantly and that of inflation also rises somewhat. The stationary distribution of output is distorted, with recessions becoming somewhat more frequent and longer lasting. Our model also uncovers the fact the asymmetry of the policy ineffectiveness induced by the zero bound constraint generates a non-vertical long run Phillips curve. Output falls increasingly short of potential, with lower inflation targets. At zero average inflation, the output loss is on the order of 0.1 percentage points. We also investigate the consequences of the constraint on the analysis of optimal policy based on the inflation-output variability frontier. We demonstrate that in the presence of the zero bound, the variability frontier is distorted as the inflation target approaches zero. As a result, comparisons of alternative policy rules that ignore the zero bound can be seriously misleading.
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