AffiliationDepartment of Economics, University of Arizona
MetadataShow full item record
PublisherJohn Wiley and Sons Ltd
CitationIchimura, H., & Newey, W. K. (2022). The influence function of semiparametric estimators. Quantitative Economics.
RightsCopyright © 2022 The Authors. Licensed under the Creative Commons Attribution-NonCommercial License 4.0.
Collection InformationThis item from the UA Faculty Publications collection is made available by the University of Arizona with support from the University of Arizona Libraries. If you have questions, please contact us at email@example.com.
AbstractThere are many economic parameters that depend on nonparametric first steps. Examples include games, dynamic discrete choice, average exact 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 local policy analysis, in evaluating local sensitivity of estimators, and constructing debiased machine learning estimators. We show that the influence function is a Gateaux derivative with respect to a smooth deviation evaluated at a point mass. This result generalizes the classic Von Mises (1947) and Hampel (1974) calculation to estimators that depend on smooth nonparametric first steps. We give explicit influence functions for first steps that satisfy exogenous or endogenous orthogonality conditions. We use these results to generalize the omitted variable bias formula for regression to policy analysis for and sensitivity to structural changes. We apply this analysis and find no sensitivity to endogeneity of average equivalent variation estimates in a gasoline demand application. Copyright © 2022 The Authors.
NoteOpen access journal
VersionFinal published version
Except where otherwise noted, this item's license is described as Copyright © 2022 The Authors. Licensed under the Creative Commons Attribution-NonCommercial License 4.0.