We examine the evolution of monetary policy rules in a group of inflation-targeting countries (Australia, Canada, New Zealand, Sweden, and the United Kingdom), applying a moment-based estimator in a time-varying parameter model with endogenous regressors. From this novel flexible framework, our main findings are threefold. First, monetary policy rules change gradually, pointing to the importance of applying a time-varying estimation framework. Second, the interest-rate smoothing parameter is much lower than typically reported by previous time-invariant estimates of policy rules. External factors matter for all countries, although the importance of the exchange rate diminishes after the adoption of inflation targeting. Third, the response of interest rates to inflation is particularly strong during periods when central bankers want to break a record of high inflation, such as in the United Kingdom or Australia at the beginning of the 1980s. Contrary to common perceptions, the response becomes less aggressive after the adoption of inflation targeting, suggesting a positive anchoring effect of this regime on inflation expectations. This result is supported by our finding that inflation persistence typically decreased after the adoption of inflation targeting.