This paper examines the small sample properties of the Generalized Method of Moments (GMM) estimator for models of covariance structures, specifically the Optimal Minimum Distance (OMD) estimator. The study presents Monte Carlo experiments based on simulated data and data from Abowd and Card (1987, 1990) to evaluate the performance of OMD and other estimators. The main finding is that OMD is seriously biased in small samples for many distributions and in relatively large samples for poorly behaved distributions. The bias is almost always downward in absolute value and arises because sampling errors in the second moments are correlated with sampling errors in the weighting matrix used by OMD. OMD usually has a larger root mean square error and median absolute error than equally weighted minimum distance (EWMD). An alternative estimator, independently weighted optimal minimum distance (IWOMD), is proposed. IWOMD is a split sample estimator that uses separate groups of observations to estimate the moments and the weights. It has identical large sample properties to the OMD estimator but is unbiased regardless of sample size. However, the Monte Carlo evidence indicates that IWOMD is usually dominated by EWMD. The paper also presents an empirical example based on the data used by Abowd and Card (1987, 1989) to examine the covariance structure of changes in log earnings and changes in log hours. The results show that OMD leads to substantial underestimates of population second moments. The study concludes that EWMD is the best estimator for fitting linear models of the covariance structure of the Panel Study of Income Dynamics (PSID) data. The results suggest that the small sample bias in OMD is a serious problem in applications.This paper examines the small sample properties of the Generalized Method of Moments (GMM) estimator for models of covariance structures, specifically the Optimal Minimum Distance (OMD) estimator. The study presents Monte Carlo experiments based on simulated data and data from Abowd and Card (1987, 1990) to evaluate the performance of OMD and other estimators. The main finding is that OMD is seriously biased in small samples for many distributions and in relatively large samples for poorly behaved distributions. The bias is almost always downward in absolute value and arises because sampling errors in the second moments are correlated with sampling errors in the weighting matrix used by OMD. OMD usually has a larger root mean square error and median absolute error than equally weighted minimum distance (EWMD). An alternative estimator, independently weighted optimal minimum distance (IWOMD), is proposed. IWOMD is a split sample estimator that uses separate groups of observations to estimate the moments and the weights. It has identical large sample properties to the OMD estimator but is unbiased regardless of sample size. However, the Monte Carlo evidence indicates that IWOMD is usually dominated by EWMD. The paper also presents an empirical example based on the data used by Abowd and Card (1987, 1989) to examine the covariance structure of changes in log earnings and changes in log hours. The results show that OMD leads to substantial underestimates of population second moments. The study concludes that EWMD is the best estimator for fitting linear models of the covariance structure of the Panel Study of Income Dynamics (PSID) data. The results suggest that the small sample bias in OMD is a serious problem in applications.