This paper examines the small sample properties of the Generalized Method of Moments (GMM) estimator, specifically the optimal minimum distance (OMD) estimator, for models of covariance structures. The authors present Monte Carlo experiments based on simulated data and real data used by Abowd and Card (1987, 1990) to investigate the covariance structure of hours and earnings changes. The main findings are that OMD is seriously biased in small samples for many distributions and in relatively large samples for poorly behaved distributions, with the bias being almost always 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. OMD typically has a larger root mean square error and median absolute error than equally weighted minimum distance (EWMD). The authors also propose an alternative estimator called independently weighted optimal minimum distance (IWOMD), which is a split sample estimator using separate groups of observations to estimate the moments and weights. IWOMD has identical large sample properties to OMD but is unbiased regardless of sample size. However, Monte Carlo evidence indicates that IWOMD is usually dominated by EWMD. The paper discusses the theoretical basis for the bias in OMD and provides a broader assessment of the performance of EWMD, OMD, and IWOMD, including their behavior in models with correlated moments.This paper examines the small sample properties of the Generalized Method of Moments (GMM) estimator, specifically the optimal minimum distance (OMD) estimator, for models of covariance structures. The authors present Monte Carlo experiments based on simulated data and real data used by Abowd and Card (1987, 1990) to investigate the covariance structure of hours and earnings changes. The main findings are that OMD is seriously biased in small samples for many distributions and in relatively large samples for poorly behaved distributions, with the bias being almost always 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. OMD typically has a larger root mean square error and median absolute error than equally weighted minimum distance (EWMD). The authors also propose an alternative estimator called independently weighted optimal minimum distance (IWOMD), which is a split sample estimator using separate groups of observations to estimate the moments and weights. IWOMD has identical large sample properties to OMD but is unbiased regardless of sample size. However, Monte Carlo evidence indicates that IWOMD is usually dominated by EWMD. The paper discusses the theoretical basis for the bias in OMD and provides a broader assessment of the performance of EWMD, OMD, and IWOMD, including their behavior in models with correlated moments.