COWLES FOUNDATION FOR RESEARCH IN
ECONOMICS Box 208281
COWLES FOUNDATION DISCUSSION PAPER NO. 1880 Asymptotic Efficiency of Semiparametric Two-step GMM Xiaohong Chen, Jinyong Hahn and Zhipeng Liao October 2012 In this note, we characterize the semiparametric efficiency bound for a
class of semiparametric 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 unconditional 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
nonparametric 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. |
