The influence function of semiparametric estimators

• 成果类型: Article
• 署名作者: Ichimura, Hidehiko; Newey, Whitney K.
• 署名单位: University of Arizona; University of Tokyo; Massachusetts Institute of Technology (MIT)
• 刊物名称: QUANTITATIVE ECONOMICS
• ISSN/ISSBN: 1759-7323
• DOI: 10.3982/QE826
• 发表日期: 2022
• 页码: 29-61
• 关键词: Influence function; semiparametric estimation; NPIV; C13; C14; C20; C26; C36

摘要

There 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.