Small Sample Properties of Estimators of Non-Linear
Models of Covariance Structure

Todd E. Clark
March 1995
RWP 95-01
Research Division
Federal Reserve Bank of Kansas City

ABSTRACT

This study examines the small sample properties of GMM and ML estimators of non-linear models of covariance structure. The study focuses on the properties of parameter estimates and the Hansen (1982) and Newey (1985) model specification test. It use Monte Carlo simulations to consider the properties of estimates for some simple factor models, the Hall and Mishkin (1982) model of consumption and income changes, and a simple Bernanke (1986) decomposition model. This analysis establishes and seeks to explain a number of results. Most importantly, optimally weighted GMM estimation yields some biased parameter estimates, and GMM estimation yields a model specification test with size substantially greater than the asymptotic size.

Keywords: GMM, ML, covariance structure, Monte Carlo

Todd E. Clark is an economist at the Federal Reserve Bank of Kansas City. He gratefully acknowledges the helpful comments of Alastair Hall and seminar participants at the Federal Reserve Bank of Kansas City, North Carolina State University, and the University of Kansas. The views expressed herein are solely those of the author and do not necessarily reflect the views of the Federal Reserve Bank of Kansas City or the Federal Reserve System. E-mail address: tclark@frbkc.org.

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