Conclusion

This monograph presents a comprehensive treatment of the conditional moment approach to GMM estimation of nonlinear equation systems. Particular attention is paid to the analysis of the large sample efficiency properties of GMM estimators. The semiparametric efficiency bounds for given orthogonality conditions and given conditional moment restrictions are derived and feasible GMM estimators attaining these bounds are presented. Conditions for asymptotic efficiency gains through the use of additional moment functions providing over-identifying restrictions are derived and different strategies are proposed for obtaining these additional moment functions in applied work. While most of the large sample properties of the GMM estimators are well understood there remain some open questions. For example, a procedure for obtaining the optimal instruments under the assumption that admissible instruments for one equation are correlated with an other equation’s residual is still missing.