This paper computes the semiparametric eﬀiciency bound for ﬁnite dimensional parameters identiﬁed by models of sequential moment restrictions containing unknown functions. Our results extend those of Chamberlain (1992b) and Ai and Chen (2003) for semiparametric conditional moment restriction models with identical information sets to the case of nested information sets, and those of Chamberlain (1992a) and Brown and Newey (1998) for models of sequential moment restrictions without unknown functions to cases with unknown functions of possibly endogenous variables. Our bound results are applicable to semiparametric panel data models and semiparametric two stage plug-in problems. As an example, we compute the eﬀiciency bound for a weighted average derivative of a nonparametric instrumental variables (IV) regression, and ﬁnd that the simple plug-in estimator is not eﬀicient. Finally, we present an optimally weighted, orthogonalized, sieve minimum distance estimator that achieves the semiparametric eﬀiciency bound.
Ai, Chunrong and Chen, Xiaohong, "Semiparametric Efficiency Bound for Models of Sequential Moment Restrictions Containing Unknown Functions" (2009). Cowles Foundation Discussion Papers. 2055.