The Influence Function of Semiparametric Two-step Estimators with Estimated Control Variables

Jinyong Hahn, Zhipeng Liao (), Geert Ridder () and Ruoyao Shi ()
Additional contact information
Zhipeng Liao: UCLA
Geert Ridder: USC

No 202107, Working Papers from University of California at Riverside, Department of Economics

Abstract: This paper studies semiparametric two-step estimators with a control variable estimated in a first-step parametric or nonparametric model. We provide the explicit influence function of the two-step estimator under an index restriction which is imposed directly on the unknown control variable. The index restriction is weaker than the commonly used identification conditions in the literature, which are imposed on all exogenous variables. An extra term shows up in the influence function of the semiparametric two-step estimator under the weaker identification condition. We illustrate our influence function formula in a mean regression example, a quantile regression example, and a sample selection example where the control variable approach is applied for identification and consistent estimation of structural parameters.

Keywords: control variable approach; generated regressors; influence function; semiparametric two-step estimation (search for similar items in EconPapers)
JEL-codes: C14 C31 C32 (search for similar items in EconPapers)
Pages: 23 Pages
Date: 2021-05
New Economics Papers: this item is included in nep-ecm and nep-ore
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https://economics.ucr.edu/repec/ucr/wpaper/202107.pdf First version, 2021 (application/pdf)

Related works:
Journal Article: The influence function of semiparametric two-step estimators with estimated control variables (2023)
Working Paper: The Influence Function of Semiparametric Two-step Estimators with Estimated Control Variables (2021)
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Persistent link: https://EconPapers.repec.org/RePEc:ucr:wpaper:202107

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