Please use this identifier to cite or link to this item: https://hdl.handle.net/10419/189692 
Year of Publication: 
2017
Series/Report no.: 
cemmap working paper No. CWP06/17
Publisher: 
Centre for Microdata Methods and Practice (cemmap), London
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.
Subjects: 
Influence function
semiparametric estimation
NPIV
JEL: 
C13
C14
C20
C26
C36
Persistent Identifier of the first edition: 
Document Type: 
Working Paper

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