Efficiency Gains by Modified GMM Estimation in Linear Models under Heteroskedasticity

While coping with nonsphericality of the disturbances, standard GMM suffers from a blind spot for exploiting the most effective instruments when these are obtained directly from unconditional rather than conditional moment assumptions. For instance, standard GMM counteracts that exogenous regressors are used as their own optimal instruments. This is easily seen after transmuting GMM for linear models into IV in terms of transformed variables. It is demonstrated that MGMM, exploiting straight-forward modifications of the instruments, can achieve substantial efficiency gains and bias reductions, even under mild heteroskedasticity. Feasible MGMM implementations for general forms of conditional heteroskedasticity are examined and compared with standard GMM in simulations and empirical illustrations of some typical cross-section and dynamic panel data models.