Assessing GMM Estimates of the Federal Reserve Reaction Function

Abstract

Estimating a forward-looking monetary policy rule by the Generalized Method of Moments (GMM) has become a popular approach since the influential paper by Clarida, Gali, and Gertler (1998). However, an abundant econometric literature underlines to the unappealing small-samples properties of GMM estimators. Focusing on the Federal Reserve reaction function, we assess GMM estimates in the context of monetary policy rules. First, we show that three usual alternative GMM estimators yield substantially different results. Then, we compare the GMM estimates with two Maximum-Likelihood (ML) estimates, obtained using a small model of the economy. We use Monte-Carlo simulations to investigate the empirical results. We find that the GMM are biased in small sample, inducing an overestimate of the inflation parameter. The two-step GMM estimates are found to be rather close to the ML estimates. By contrast, iterative and continuous-updating GMM procedures produce more biased and more dispersed estimators.

Keywords: Forward-looking model, monetary policy reaction function, GMM estimator, FIML estimator, small-sample properties of an estimator

JEL Classification: E52, E58, F41