Estimating a forward-looking monetary policy rule by the Generalized Method of Moments (GMM) has become a popular approach since the influential papers by Clarida, Gali, and Gertler (1998, 2000). We re-examine estimates of the Federal Reserve reaction function using several GMM estimators and a Maximum Likelihood (ML) estimator. First, we show that, over the baseline period 1979-2000, these alternative approaches yield substantially different parameter estimates. Using Monte-Carlo simulations, we show that the finite-sample GMM\ bias can only account for a small part of the discrepancy between estimates. We find that this discrepancy is more plausibly rationalized by the serial correlation of the policy shock, causing mis-specification of GMM estimators through lack of instrument exogeneity. This correlation pattern is related to a shift in the reaction-function parameters in 1987. Re-estimating the reaction function over the 1987-2000 period produces GMM estimates which are very close to the ML estimate.