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Debiased Inference on Treatment Effect in a High-Dimensional Model

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  • Jingshen Wang
  • Xuming He
  • Gongjun Xu

Abstract

This article concerns the potential bias in statistical inference on treatment effects when a large number of covariates are present in a linear or partially linear model. While the estimation bias in an under-fitted model is well understood, we address a lesser-known bias that arises from an over-fitted model. The over-fitting bias can be eliminated through data splitting at the cost of statistical efficiency, and we show that smoothing over random data splits can be pursued to mitigate the efficiency loss. We also discuss some of the existing methods for debiased inference and provide insights into their intrinsic bias-variance trade-off, which leads to an improvement in bias controls. Under appropriate conditions, we show that the proposed estimators for the treatment effects are asymptotically normal and their variances can be well estimated. We discuss the pros and cons of various methods both theoretically and empirically, and show that the proposed methods are valuable options in post-selection inference. Supplementary materials for this article are available online.

Suggested Citation

  • Jingshen Wang & Xuming He & Gongjun Xu, 2020. "Debiased Inference on Treatment Effect in a High-Dimensional Model," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 115(529), pages 442-454, January.
  • Handle: RePEc:taf:jnlasa:v:115:y:2020:i:529:p:442-454
    DOI: 10.1080/01621459.2018.1558062
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    Cited by:

    1. Maur,Jean-Christophe & Nedeljkovic,Milan & Von Uexkull,Jan Erik, 2022. "FDI and Trade Outcomes at the Industry Level—A Data-Driven Approach," Policy Research Working Paper Series 9901, The World Bank.
    2. Kueck, Jannis & Luo, Ye & Spindler, Martin & Wang, Zigan, 2023. "Estimation and inference of treatment effects with L2-boosting in high-dimensional settings," Journal of Econometrics, Elsevier, vol. 234(2), pages 714-731.
    3. Guo, Xu & Li, Runze & Liu, Jingyuan & Zeng, Mudong, 2023. "Statistical inference for linear mediation models with high-dimensional mediators and application to studying stock reaction to COVID-19 pandemic," Journal of Econometrics, Elsevier, vol. 235(1), pages 166-179.
    4. Shi, Chengchun & Zhang, Shengxing & Lu, Wenbin & Song, Rui, 2022. "Statistical inference of the value function for reinforcement learning in infinite-horizon settings," LSE Research Online Documents on Economics 110882, London School of Economics and Political Science, LSE Library.
    5. Naveen Naidu Narisetty, 2020. "Discussion," International Statistical Review, International Statistical Institute, vol. 88(2), pages 330-334, August.
    6. Chengchun Shi & Sheng Zhang & Wenbin Lu & Rui Song, 2022. "Statistical inference of the value function for reinforcement learning in infinite‐horizon settings," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 84(3), pages 765-793, July.
    7. Agboola, Oluwagbenga David & Yu, Han, 2023. "Neighborhood-based cross fitting approach to treatment effects with high-dimensional data," Computational Statistics & Data Analysis, Elsevier, vol. 186(C).

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