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Exact Bias Correction for Linear Adjustment of Randomized Controlled Trials

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  • Haoge Chang
  • Joel A. Middleton
  • P. M. Aronow

Abstract

Freedman (2008a,b) showed that the linear regression estimator is biased for the analysis of randomized controlled trials under the randomization model. Under Freedman's assumptions, we derive exact closed‐form bias corrections for the linear regression estimator. We show that the limiting distribution of the bias corrected estimator is identical to the uncorrected estimator. Taken together with results from Lin (2013), our results show that Freedman's theoretical arguments against the use of regression adjustment can be resolved with minor modifications to practice.

Suggested Citation

  • Haoge Chang & Joel A. Middleton & P. M. Aronow, 2024. "Exact Bias Correction for Linear Adjustment of Randomized Controlled Trials," Econometrica, Econometric Society, vol. 92(5), pages 1503-1519, September.
    • Handle: RePEc:wly:emetrp:v:92:y:2024:i:5:p:1503-1519
    DOI: 10.3982/ECTA20289
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    References listed on IDEAS

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    1. Guido W. Imbens, 2010. "Better LATE Than Nothing: Some Comments on Deaton (2009) and Heckman and Urzua (2009)," Journal of Economic Literature, American Economic Association, vol. 48(2), pages 399-423, June.
    2. Jason Wu & Peng Ding, 2021. "Randomization Tests for Weak Null Hypotheses in Randomized Experiments," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 116(536), pages 1898-1913, October.
    3. Tan, Zhiqiang, 2014. "Second-order asymptotic theory for calibration estimators in sampling and missing-data problems," Journal of Multivariate Analysis, Elsevier, vol. 131(C), pages 240-253.
    4. Imbens,Guido W. & Rubin,Donald B., 2015. "Causal Inference for Statistics, Social, and Biomedical Sciences," Cambridge Books, Cambridge University Press, number 9780521885881, September.
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