A finite sample correction for the variance of linear two-step GMM estimators

Monte Carlo studies have shown that estimated asymptotic standard errors of the efficient two-step generalised method of moments (GMM) estimator can be severely downward biased in small samples. The weight matrix used in the calculation of the efficient two-step GMM estimator is based on initial consistent parameter estimates. In this paper it is shown that the extra variation due to the presence of these estimated parameters in the weight matrix accounts for much of the difference between the finite sample and the asymptotic variance of the two-step GMM estimator that utilises moment conditions that are linear in the parameters. This difference can be estimated, resuling in a finite sample corrected estimate of the variance. In a Monte Carlo study of a panel data model it is shown that the corrected variance estimate approximates the final sample variance well, leading to more accurate inference.