Momentary Lapses: Moment Expansions and the Robustness of Minimum Distance Estimation

This paper explores the robustness of minimum distance (GMM) estimators focusing particularly on the effect of intermediate covariance matrix estimation on final estimator performance. Asymptotic expansions to order <italic>O</italic>(<italic>n</italic>^−3/2) are employed to construct <italic>O</italic>(<italic>n</italic>⁻²) expansions for the variance of estimators constructed from preliminary least-squares and general <italic>M</italic>-estimators. In the former case, there is a rather curious robustifying effect due to estimation of the Eicker-White covariance matrix for error distributions with sufficiently large kurtosis.