Efficiency gains by modifying 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 modified GMM (MGMM), exploiting straight-forward modifications of the instruments, can achieve substantial efficiency gains and bias reductions, even under mild heteroskedasticity. Feasible MGMM implementations and their standard error estimates are examined and compared with standard GMM and IV for a range of typical models for cross-section data, both by simulation and by empirical illustration.