Small-Sample Bias in GMM Estimation of Covariance Structures

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Abstract
We examine the small-sample properties of the generalized method of moments estimator applied to models of covariance structures, in which case it is commonly known as the optimal minimum distance (OMD) estimator. We find that OMD is almost always biased downward in absolute value. The bias arises because sampling errors in the second moments are correlated with sampling errors in the weighting matrix used by OMD. Furthermore, OMD is usually dominated by equally weighted minimum distance (EWMD). We also propose an alternative estimator that is unbiased and asymptotically equivalent to OMD. The Monte Carlo evidence indicates, however, that it is usually dominated by EWMD.