Asymptotic efficiency of semiparametric two-step GMM - Xiaohong Chen; Jinyong Hahn; Zhipeng Liao (Centre for Microdata Methods and Practice (cemmap), 2012)
In this note, we characterize the semiparametric efficiency bound for a class of semi- parametric models in which the unknown nuisance functions are identified via nonparametric conditional moment restrictions with possibly non-nested or over-lapping conditioning sets, and the finite dimensional parameters are potentially over-identified via uncondi tional moment restrictions involving the nuisance functions. We discover a surprising result that semiparametric two-step optimally weighted GMM estimators achieve the efficiency bound, where the nuisance functions could be estimated via any consistent non- parametric procedures in the first 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.
Keywords: C14; C31; C32; 330; Overlapping Information Sets; Semiparametric Efficiency; Two-Step GMM