Asymptotic efficiency of semiparametric two-step GMM

Many structural economics models are semiparametric ones in which the unknown nuisance functions are identifiÂ…ed via nonparametric conditional moment restrictions with possibly non-nested or overlapping conditioning sets, and the Â…finite dimensional parameters of interest are over-identiÂ…fied via unconditional moment restrictions involving the nuisance functions. In this paper we characterize the semiparametric efficiency bound for this class of models. We show that semiparametric two-step optimally weighted GMM estimators achieve the efficiency bound, where the nuisance functions could be estimated via any consistent nonparametric methods in the fiÂ…rst step. Regardless of whether the efficiency bound has a closed form expression or not, we provide easy-to-compute sieve based optimal weight matrices that lead to asymptotically efficient two-step GMM estimators.