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Locally robust semiparametric estimation

Author

Listed:
  • Victor Chernozhukov

    () (Institute for Fiscal Studies and MIT)

  • Juan Carlos Escanciano

    (Institute for Fiscal Studies and Universidad Carlos III de Madrid)

  • Hidehiko Ichimura

    () (Institute for Fiscal Studies and University of Tokyo)

  • Whitney K. Newey

    () (Institute for Fiscal Studies and MIT)

  • James M. Robins

    (Institute for Fiscal Studies)

Abstract

We give a general construction of debiased/locally robust/orthogonal (LR) moment functions for GMM, where the derivative with respect to first step nonparametric estimation is zero and equivalently first step estimation has no effect on the influence function. This construction consists of adding an estimator of the influence function adjustment term for first step nonparametric estimation to identifying or original moment conditions. We also give numerical methods for estimating LR moment functions that do not require an explicit formula for the adjustment term. LR moment conditions have reduced bias and so are important when the first step is machine learning. We derive LR moment conditions for dynamic discrete choice based on first step machine learning estimators of conditional choice probabilities. We provide simple and general asymptotic theory for LR estimators based on sample splitting. This theory uses the additive decomposition of LR moment conditions into an identifying condition and a first step influence adjustment. Our conditions require only mean square consistency and a few (generally either one or two) readily interpretable rate conditions. LR moment functions have the advantage of being less sensitive to first step estimation. Some LR moment functions are also doubly robust meaning they hold if one first step is incorrect. We give novel classes of doubly robust moment functions and characterize double robustness. For doubly robust estimators our asymptotic theory only requires one rate condition.

Suggested Citation

  • Victor Chernozhukov & Juan Carlos Escanciano & Hidehiko Ichimura & Whitney K. Newey & James M. Robins, 2018. "Locally robust semiparametric estimation," CeMMAP working papers CWP30/18, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
  • Handle: RePEc:ifs:cemmap:30/18
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    Cited by:

    1. Sokbae Lee & Ryo Okui & Yoon†Jae Whang, 2017. "Doubly robust uniform confidence band for the conditional average treatment effect function," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 32(7), pages 1207-1225, November.
    2. Kyle Colangelo & Ying-Ying Lee, 2020. "Double Debiased Machine Learning Nonparametric Inference with Continuous Treatments," Papers 2004.03036, arXiv.org, revised Oct 2020.
    3. Matias D Cattaneo & Michael Jansson & Xinwei Ma, 2019. "Two-Step Estimation and Inference with Possibly Many Included Covariates," Review of Economic Studies, Oxford University Press, vol. 86(3), pages 1095-1122.
    4. Victor Chernozhukov & Denis Chetverikov & Mert Demirer & Esther Duflo & Christian Hansen & Whitney Newey & James Robins, 2018. "Double/debiased machine learning for treatment and structural parameters," Econometrics Journal, Royal Economic Society, vol. 21(1), pages 1-68, February.
    5. Santiago Pereda Fernández, 2019. "Identification and estimation of triangular models with a binary treatment," Temi di discussione (Economic working papers) 1210, Bank of Italy, Economic Research and International Relations Area.
    6. Victor Chernozhukov & Denis Chetverikov & Mert Demirer & Esther Duflo & Christian Hansen & Whitney Newey & James Robins, 2016. "Double/Debiased Machine Learning for Treatment and Causal Parameters," Papers 1608.00060, arXiv.org, revised Dec 2017.
    7. Sant’Anna, Pedro H.C. & Song, Xiaojun, 2019. "Specification tests for the propensity score," Journal of Econometrics, Elsevier, vol. 210(2), pages 379-404.
    8. Rahul Singh & Liyang Sun, 2019. "De-biased Machine Learning in Instrumental Variable Models for Treatment Effects," Papers 1909.05244, arXiv.org, revised Dec 2020.
    9. Zhengyuan Zhou & Susan Athey & Stefan Wager, 2018. "Offline Multi-Action Policy Learning: Generalization and Optimization," Papers 1810.04778, arXiv.org, revised Nov 2018.
    10. Khashayar Khosravi & Greg Lewis & Vasilis Syrgkanis, 2019. "Non-Parametric Inference Adaptive to Intrinsic Dimension," Papers 1901.03719, arXiv.org, revised Jun 2019.
    11. Kyle Colangelo & Ying-Ying Lee, 2019. "Double debiased machine learning nonparametric inference with continuous treatments," CeMMAP working papers CWP54/19, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    12. Greg Lewis & Vasilis Syrgkanis, 2020. "Double/Debiased Machine Learning for Dynamic Treatment Effects," Papers 2002.07285, arXiv.org, revised Jun 2020.
    13. Victor Chernozhukov & Whitney K. Newey & James Robins, 2018. "Double/de-biased machine learning using regularized Riesz representers," CeMMAP working papers CWP15/18, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    14. Victor Chernozhukov & Vira Semenova, 2018. "Simultaneous inference for Best Linear Predictor of the Conditional Average Treatment Effect and other structural functions," CeMMAP working papers CWP40/18, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    15. Arthur Lewbel & Jin-Young Choi & Zhuzhu Zhou, 2019. "General Doubly Robust Identification and Estimation," Boston College Working Papers in Economics 1003, Boston College Department of Economics.
    16. Rahul Singh, 2020. "Kernel Methods for Unobserved Confounding: Negative Controls, Proxies, and Instruments," Papers 2012.10315, arXiv.org.
    17. Max H. Farrell & Tengyuan Liang & Sanjog Misra, 2018. "Deep Neural Networks for Estimation and Inference," Papers 1809.09953, arXiv.org, revised Sep 2019.
    18. Vira Semenova, 2020. "Better Lee Bounds," Papers 2008.12720, arXiv.org.
    19. Yusuke Narita & Shota Yasui & Kohei Yata, 2020. "Off-policy Bandit and Reinforcement Learning," Papers 2002.08536, arXiv.org, revised Jun 2020.
    20. Rahul Singh & Liyuan Xu & Arthur Gretton, 2020. "Kernel Methods for Policy Evaluation: Treatment Effects, Mediation Analysis, and Off-Policy Planning," Papers 2010.04855, arXiv.org, revised Oct 2020.
    21. Xinwei Ma & Jingshen Wang, 2018. "Robust Inference Using Inverse Probability Weighting," Papers 1810.11397, arXiv.org, revised May 2019.
    22. Whitney K. Newey & James M. Robins, 2017. "Cross-fitting and fast remainder rates for semiparametric estimation," CeMMAP working papers CWP41/17, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    23. Yang Ning & Sida Peng & Jing Tao, 2020. "Doubly Robust Semiparametric Difference-in-Differences Estimators with High-Dimensional Data," Papers 2009.03151, arXiv.org.
    24. Bertille Antoine & Xiaolin Sun, 2020. "Partially Linear Models with Endogeneity: a conditional moment based approach," Discussion Papers dp20-06, Department of Economics, Simon Fraser University.

    More about this item

    Keywords

    Local robustness; orthogonal moments; double robustness; semiparametric estimation; bias; GMM;

    JEL classification:

    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • C21 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Cross-Sectional Models; Spatial Models; Treatment Effect Models
    • D24 - Microeconomics - - Production and Organizations - - - Production; Cost; Capital; Capital, Total Factor, and Multifactor Productivity; Capacity

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