Semiparametric Efficiency Bound for Models of Sequential Moment Restrictions Containing Unknown Functions

Chunrong Ai and Xiaohong Chen ()
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Chunrong Ai: Dept. of Economics, University of Florida
Xiaohong Chen: Cowles Foundation, Yale University, http://cowles.econ.yale.edu/faculty/chen.htm

No 1731, Cowles Foundation Discussion Papers from Cowles Foundation, Yale University

Abstract: 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.

Keywords: Sequential moment models; Semiparametric efficiency bounds; Optimally weighted orthogonalized sieve minimum distance; Nonparametric IV regression; Weighted average derivatives; Partially linear quantile IV (search for similar items in EconPapers)
JEL-codes: C14 C22 (search for similar items in EconPapers)
New Economics Papers: this item is included in nep-ecm and nep-mic
Date: 2009-10
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