The semiparametric efficiency bound for models of sequential moment restrictions containing unknown functions |
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Authors: | Chunrong Ai Xiaohong Chen |
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Institution: | 1. Department of Economics, University of Florida, Gainesville, FL 32611, USA;2. Shanghai University of Finance and Economics, China;3. Cowles Foundation for Research in Economics, Yale University, Box 208281, New Haven, CT 06520, USA |
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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 restrictions 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 results are applicable to semiparametric panel data models and two stage plug-in problems. As an important example, we compute the efficiency bound for a weighted average derivative of a nonparametric instrumental variables regression (NPIV), and find that simple plug-in NPIV estimators are not efficient. We present an optimally weighted, orthogonalized, sieve minimum distance estimator that achieves the semiparametric efficiency bound. |
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