Small-Sample Properties of Estimators of Nonlinear Models of Covariance Structure

Abstract

This study examines the small-sample properties of generalized method of moments (GMM) and maximum likelihood estimators of nonlinear models of covariance structure. It considers the properties of estimates for a simple factor model, the Hall and Mishkin model of consumption and income, and a simple structural vector autoregression-type error model. This analysis establishes three basic results. First, optimally weighted GMM estimation yields some biased parameter estimates. Second, GMM estimation yields a model-specification test with size substantially greater than the asymptotic size. Third, these problems are mitigated when the number of overidentifying restrictions in a model is reduced.