Book excerpt: Using stochastic simulations and stability analysis, the paper compares how different monetary rules perform in a moderately nonlinear model with a time-varying nonaccelerating-inflation-rate-of-unemployment (NAIRU). Rules that perform well in linear models but implicitly embody backward-looking measures of real interest rates (such as conventional Taylor rules) or substantial interest rate smoothing perform very poorly in models with moderate nonlinearities, particularly when policymakers tend to make serially correlated errors in estimating the NAIRU. This challenges the practice of evaluating rules within linear models, in which the consequences of responding myopically to significant overheating are extremely unrealistic.