Working Paper

Asymptotic efficiency of semiparametric two-step GMM


Xiaohong Chen, Jinyong Hahn

Published Date

15 October 2012


Working Paper (CWP31/12)

In this note, we characterise 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 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.

Latest version

Asymptotic efficiency of semiparametric two-step GMM
Daniel Ackerberg, Xiaohong Chen, Jinyong Hahn