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The influence function of semiparametric estimators

Hidehiko Ichimura and Whitney K. Newey ()
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Hidehiko Ichimura: Institute for Fiscal Studies and University of Tokyo
Whitney K. Newey: Institute for Fiscal Studies and MIT

No CWP06/17, CeMMAP working papers from Centre for Microdata Methods and Practice, Institute for Fiscal Studies

Abstract: There are many economic parameters that depend on nonparametric first steps. Examples include games, dynamic discrete choice, average consumer surplus, and treatment effects. Often estimators of these parameters are asymptotically equivalent to a sample average of an object referred to as the influence function. The influence function is useful in formulating regularity conditions for asymptotic normality, for bias reduction, in efficiency comparisons, and for analyzing robustness. We show that the influence function of a semiparametric estimator is the limit of a Gateaux derivative with respect to a smooth deviation as the deviation approaches a point mass. This result generalizes the classic Von Mises (1947) and Hampel (1974) calculation to apply to estimators that depend on smooth nonparametic first steps. We characterize the influence function of M and GMM-estimators.We apply the Gateaux derivative to derive the influence function with a first step nonparametric two stage least squares estimator based on orthogonality conditions. We also use the influence function to analyze high level and primitive regularity conditions for asymptotic normality. We give primitive regularity conditions for linear functionals of series regression that are the weakest known, except for a log term, when the regression function is smooth enough.

Keywords: Influence function; semiparametric estimation; NPIV (search for similar items in EconPapers)
JEL-codes: C13 C14 C20 C26 C36 (search for similar items in EconPapers)
New Economics Papers: this item is included in nep-ecm
Date: 2017-01-26
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