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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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    References listed on IDEAS

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    Cited by:

    1. repec:wly:japmet:v:32:y:2017:i:7:p:1207-1225 is not listed on IDEAS
    2. 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.
    3. 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.
    4. 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.
    5. 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.
    6. repec:eee:econom:v:210:y:2019:i:2:p:379-404 is not listed on IDEAS
    7. Rahul Singh & Liyang Sun, 2019. "De-biased Machine Learning for Compliers," Papers 1909.05244, arXiv.org.
    8. Zhengyuan Zhou & Susan Athey & Stefan Wager, 2018. "Offline Multi-Action Policy Learning: Generalization and Optimization," Papers 1810.04778, arXiv.org, revised Nov 2018.
    9. Khashayar Khosravi & Greg Lewis & Vasilis Syrgkanis, 2019. "Non-Parametric Inference Adaptive to Intrinsic Dimension," Papers 1901.03719, arXiv.org, revised Jun 2019.
    10. 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.
    11. Sant’Anna, Pedro H.C. & Song, Xiaojun, 2019. "Specification tests for the propensity score," Journal of Econometrics, Elsevier, vol. 210(2), pages 379-404.
    12. 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.

    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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