17 Generalized method of moments: Econometric applications

Abstract

This chapter explains Hansen's (1982) generalized method of moments (GMM) to applied researchers, and to give practical guidance as to how GMM estimation should be implemented. Many researchers have used GMM to estimate nonlinear rational expectations models with aggregate time series data. Other uses of a GMM program include the implementation of minimum distance estimation, the calculation of standard errors that take into account serially correlated disturbances, and generating inferences that take into account the effects of the first estimation step in sequential (or two-step) estimation. The chapter discusses the statistical properties of GMM estimators and test statistics, the basic GMM framework, the manner in which ordinary least squares and linear and nonlinear instrumental variables estimation are embedded in the GMM framework as special cases, some GMM related statistical procedures that extend the basic GMM framework, important assumptions for GMM, methods for covariance matrix estimation, the optimal choice of instrumental variables, the relation between GMM and semi-parametric estimation, and small sample properties of GMM estimators and test statistics. The chapter also presents some of the recent developments in the GMM procedure that have been used in applications. These include sequential (or two-step) estimation, GMM with deterministic trends, applications for cross sectional and panel data, and some statistics that are used for hypothesis testing.