Research Publication

Generalized Method of Moments (GMM) refers to a class of estimators which are constructed from exploiting the sample moment counterparts of population moment conditions (sometimes known as orthogonality conditions) of the data generating model. GMM estimators have become widely used, for the following reasons:

• GMM estimators have large sample properties that are easy to characterize in ways that facilitate comparison. A family of such estimators can be studied a priori in ways that make asymptotic efficiency comparisons easy. The method also provides a natural way to construct tests which take account of both sampling and estimation error.
• In practice, researchers find it useful that GMM estimators can be constructed without specifying the full data generating process (which would be required to write down the maximum likelihood estimator.) This characteristic has been exploited in analyzing partially specified economic models, in studying potentially misspecified dynamic mod- els designed to match target moments, and in constructing stochastic discount factor models that link asset pricing to sources of macroeconomic risk.Books with good discussions of GMM estimation with a wide array of applications in- clude: Cochrane (2001), Arellano (2003), Hall (2005), and Singleton (2006). For a theoretical treatment of this method see Hansen (1982) along with the self contained discussions in the books. See also Ogaki (1993) for a general discussion of GMM estimation and applications, and see Hansen (2001) for a complementary entry that, among other things, links GMM estimation to related literatures in statistics. For a collection of recent methodological ad- vances related to GMM estimation see Ghysels and Hall (2002). While some of these other references explore the range of substantive applications, in what follows we focus more on the methodology.