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Properties Of Doubly Robust Estimators When Nuisance Functions Are Estimated Nonparametrically

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  • Rothe, Christoph
  • Firpo, Sergio

Abstract

An estimator of a finite-dimensional parameter is said to be doubly robust (DR) if it imposes parametric specifications on two unknown nuisance functions, but only requires that one of these two specifications is correct in order for the estimator to be consistent for the object of interest. In this article, we study versions of such estimators that use local polynomial smoothing for estimating the nuisance functions. We show that such semiparametric two-step (STS) versions of DR estimators have favorable theoretical and practical properties relative to other commonly used STS estimators. We also show that these gains are not generated by the DR property alone. Instead, it needs to be combined with an orthogonality condition on the estimation residuals from the nonparametric first stage, which we show to be satisfied in a wide range of models.

Suggested Citation

  • Rothe, Christoph & Firpo, Sergio, 2019. "Properties Of Doubly Robust Estimators When Nuisance Functions Are Estimated Nonparametrically," Econometric Theory, Cambridge University Press, vol. 35(5), pages 1048-1087, October.
    • Handle: RePEc:cup:etheor:v:35:y:2019:i:05:p:1048-1087_00
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    Cited by:

    1. Kyle Colangelo & Ying-Ying Lee, 2020. "Double Debiased Machine Learning Nonparametric Inference with Continuous Treatments," Papers 2004.03036, arXiv.org, revised Sep 2023.
    2. Tang, Shengfang & Huang, Zhilin, 2022. "Empirical likelihood confidence interval for difference-in-differences estimator with panel data," Economics Letters, Elsevier, vol. 216(C).
    3. Yuya Sasaki & Takuya Ura & Yichong Zhang, 2022. "Unconditional quantile regression with high‐dimensional data," Quantitative Economics, Econometric Society, vol. 13(3), pages 955-978, July.
    4. Liang Jiang & Oliver B. Linton & Haihan Tang & Yichong Zhang, 2022. "Improving Estimation Efficiency via Regression-Adjustment in Covariate-Adaptive Randomizations with Imperfect Compliance," Papers 2201.13004, arXiv.org, revised Jun 2023.
    5. Atı̇la Abdulkadı̇roğlu & Joshua D. Angrist & Yusuke Narita & Parag Pathak, 2022. "Breaking Ties: Regression Discontinuity Design Meets Market Design," Econometrica, Econometric Society, vol. 90(1), pages 117-151, January.
    6. Ahnaf Rafi, 2023. "Efficient Semiparametric Estimation of Average Treatment Effects Under Covariate Adaptive Randomization," Papers 2305.08340, arXiv.org.
    7. Pedro H. C. Sant'Anna & Qi Xu, 2023. "Difference-in-Differences with Compositional Changes," Papers 2304.13925, arXiv.org, revised Jan 2025.
    8. Mengshan Xu & Taisuke Otsu, 2022. "Isotonic propensity score matching," Papers 2207.08868, arXiv.org, revised Jan 2025.
    9. Ganesh Karapakula, 2023. "Stable Probability Weighting: Large-Sample and Finite-Sample Estimation and Inference Methods for Heterogeneous Causal Effects of Multivalued Treatments Under Limited Overlap," Papers 2301.05703, arXiv.org, revised Jan 2023.
    10. Sasaki, Yuya & Ura, Takuya, 2023. "Estimation and inference for policy relevant treatment effects," Journal of Econometrics, Elsevier, vol. 234(2), pages 394-450.
    11. Taisuke Otsu & Mengshan Xu, 2022. "Isotonic propensity score matching," STICERD - Econometrics Paper Series 623, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE.
    12. Laura Liu & Alexandre Poirier & Ji-Liang Shiu, 2021. "Identification and Estimation of Partial Effects in Nonlinear Semiparametric Panel Models," Papers 2105.12891, arXiv.org, revised Jul 2024.
    13. Amilcar Velez, 2024. "On the Asymptotic Properties of Debiased Machine Learning Estimators," Papers 2411.01864, arXiv.org.

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