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The influence function of semiparametric two-step estimators with estimated control variables

Author

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  • Hahn, Jinyong
  • Liao, Zhipeng
  • Ridder, Geert
  • Shi, Ruoyao

Abstract

We derive the influence function for two-step estimators with estimated control variables. We adopt a weaker identification assumption than is commonly used in the literature, and as a consequence, an extra term shows up in the influence function.

Suggested Citation

  • Hahn, Jinyong & Liao, Zhipeng & Ridder, Geert & Shi, Ruoyao, 2023. "The influence function of semiparametric two-step estimators with estimated control variables," Economics Letters, Elsevier, vol. 231(C).
    • Handle: RePEc:eee:ecolet:v:231:y:2023:i:c:s0165176523003026
    DOI: 10.1016/j.econlet.2023.111277
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    References listed on IDEAS

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    1. Guido W. Imbens & Whitney K. Newey, 2009. "Identification and Estimation of Triangular Simultaneous Equations Models Without Additivity," Econometrica, Econometric Society, vol. 77(5), pages 1481-1512, September.
    2. Newey, Whitney K, 1994. "The Asymptotic Variance of Semiparametric Estimators," Econometrica, Econometric Society, vol. 62(6), pages 1349-1382, November.
    3. Ida Johnsson & Hyungsik Roger Moon, 2021. "Estimation of Peer Effects in Endogenous Social Networks: Control Function Approach," The Review of Economics and Statistics, MIT Press, vol. 103(2), pages 328-345, May.
    4. Richard W. Blundell & James L. Powell, 2004. "Endogeneity in Semiparametric Binary Response Models," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 71(3), pages 655-679.
    5. Eric Auerbach, 2022. "Identification and Estimation of a Partially Linear Regression Model Using Network Data," Econometrica, Econometric Society, vol. 90(1), pages 347-365, January.
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    More about this item

    Keywords

    Control variable approach; Index restriction; Influence function; Semiparametric two-step estimation;
    All these keywords.

    JEL classification:

    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • C31 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Cross-Sectional Models; Spatial Models; Treatment Effect Models; Quantile Regressions; Social Interaction Models
    • C32 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes; State Space Models

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