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Regression adjustment in randomized controlled trials with many covariates

Author

Listed:
  • 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 em- ploying 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 er- ror. 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 illus- trate, 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," STICERD - Econometrics Paper Series 627, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE.
    • Handle: RePEc:cep:stiecm:627
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    File URL: http://sticerd.lse.ac.uk/dps/em/em627.pdf
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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. Jelena Bradic & Stefan Wager & Yinchu Zhu, 2019. "Sparsity Double Robust Inference of Average Treatment Effects," Papers 1905.00744, arXiv.org.
    3. 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.
    4. 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.
    5. 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.
    6. Colin B Fogarty, 2018. "Regression-assisted inference for the average treatment effect in paired experiments," Biometrika, Biometrika Trust, vol. 105(4), pages 994-1000.
    7. Imbens,Guido W. & Rubin,Donald B., 2015. "Causal Inference for Statistics, Social, and Biomedical Sciences," Cambridge Books, Cambridge University Press, number 9780521885881, October.
    8. 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.
    9. 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.
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    Citations

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    Cited by:

    1. Undral Byambadalai & Tatsushi Oka & Shota Yasui, 2024. "Estimating Distributional Treatment Effects in Randomized Experiments: Machine Learning for Variance Reduction," Papers 2407.16037, arXiv.org.
    2. Yuehao Bai & Azeem M. Shaikh & Max Tabord-Meehan, 2024. "A Primer on the Analysis of Randomized Experiments and a Survey of some Recent Advances," Papers 2405.03910, arXiv.org.
    3. 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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    More about this item

    Keywords

    Randomized controlled trials; regression adjustment; many covariates;
    All these keywords.

    JEL classification:

    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General

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