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Regression adjustment in randomized controlled trials with many covariates

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  • Harold D Chiang
  • Yukitoshi Matsushita
  • Taisuke Otsu

Abstract

This paper is concerned with estimation and inference on average treatment effects in randomized controlled trials when researchers observe potentially many covariates. By employing Neyman's (1923) finite population perspective, we propose a bias-corrected regression adjustment estimator using cross-fitting, and show that the proposed estimator has favorable properties over existing alternatives. For inference, we derive the first and second order terms in the stochastic component of the regression adjustment estimators, study higher order properties of the existing inference methods, and propose a bias-corrected version of the HC3 standard error. The proposed methods readily extend to stratified experiments with large strata. Simulation studies show our cross-fitted estimator, combined with the bias-corrected HC3, delivers precise point estimates and robust size controls over a wide range of DGPs. To illustrate, the proposed methods are applied to real dataset on randomized experiments of incentives and services for college achievement following Angrist, Lang, and Oreopoulos (2009).

Suggested Citation

  • Harold D Chiang & Yukitoshi Matsushita & Taisuke Otsu, 2023. "Regression adjustment in randomized controlled trials with many covariates," Papers 2302.00469, arXiv.org, revised Nov 2023.
    • Handle: RePEc:arx:papers:2302.00469
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    File URL: http://arxiv.org/pdf/2302.00469
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    References listed on IDEAS

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    1. Tirthankar Dasgupta & Natesh S. Pillai & Donald B. Rubin, 2015. "Causal inference from 2-super-K factorial designs by using potential outcomes," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 77(4), pages 727-753, September.
    2. Matias D Cattaneo & Michael Jansson & Xinwei Ma, 2019. "Two-Step Estimation and Inference with Possibly Many Included Covariates," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 86(3), pages 1095-1122.
    3. Philip Oreopoulos & Daniel Lang & Joshua Angrist, 2009. "Incentives and Services for College Achievement: Evidence from a Randomized Trial," American Economic Journal: Applied Economics, American Economic Association, vol. 1(1), pages 136-163, January.
    4. Lihua Lei & Peng Ding, 2021. "Regression adjustment in completely randomized experiments with a diverging number of covariates [Covariance adjustments for the analysis of randomized field experiments]," Biometrika, Biometrika Trust, vol. 108(4), pages 815-828.
    5. Jelena Bradic & Stefan Wager & Yinchu Zhu, 2019. "Sparsity Double Robust Inference of Average Treatment Effects," Papers 1905.00744, arXiv.org.
    6. Haoge Chang & Joel Middleton & P. M. Aronow, 2021. "Exact Bias Correction for Linear Adjustment of Randomized Controlled Trials," Papers 2110.08425, arXiv.org, revised Oct 2021.
    7. Xinran Li & Peng Ding, 2020. "Rerandomization and regression adjustment," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 82(1), pages 241-268, February.
    8. Colin B Fogarty, 2018. "Regression-assisted inference for the average treatment effect in paired experiments," Biometrika, Biometrika Trust, vol. 105(4), pages 994-1000.
    9. Imbens,Guido W. & Rubin,Donald B., 2015. "Causal Inference for Statistics, Social, and Biomedical Sciences," Cambridge Books, Cambridge University Press, number 9780521885881.
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    Cited by:

    1. Liang Jiang & Liyao Li & Ke Miao & Yichong Zhang, 2023. "Adjustment with Many Regressors Under Covariate-Adaptive Randomizations," Papers 2304.08184, arXiv.org, revised Feb 2024.

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