This paper estimates a New Keynesian model with trend inflation and contrasts Taylor rules featuring fixed versus time-varying inflation target while allowing for passive monetary policy. The estimation is conducted over the Great Inflation and the Great Moderation periods. Time-varying inflation target empirically fits better and active monetary policy prevails in both periods, thereby ruling out sunspots as an explanation of the Great Inflation episode. Counterfactual simulations suggest that the decline in inflation volatility since the mid-1980s is mainly driven by monetary policy, while the reduction in output growth variability is explained by the reduced volatility of technology shocks.