Size Matters: Covariance Matrix Estimation Under the Alternative

The purpose of this paper is to investigate, using Monte Carlo methods, whether or not Hall's (2000) centered test of overidentifying restrictions for parameters estimated by Generalized Method of Moments (GMM) is more powerful, once the test is size-adjusted, than the standard test introduced by Hansen (1982). The Monte Carlo evidence shows that very little size-adjusted power is gained over the standard uncentered calculation. Empirical examples using Epstein and Zin (1991) preferences demonstrate that the centered and uncentered tests sometimes lead to different conclusions about model specification.