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Covariate Balancing and the Equivalence of Weighting and Doubly Robust Estimators of Average Treatment Effects

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  • Tymon S{l}oczy'nski
  • S. Derya Uysal
  • Jeffrey M. Wooldridge

Abstract

We show that when the propensity score is estimated using a suitable covariate balancing procedure, the commonly used inverse probability weighting (IPW) estimator, augmented inverse probability weighting (AIPW) with linear conditional mean, and inverse probability weighted regression adjustment (IPWRA) with linear conditional mean are all numerically the same for estimating the average treatment effect (ATE) or the average treatment effect on the treated (ATT). Further, suitably chosen covariate balancing weights are automatically normalized, which means that normalized and unnormalized versions of IPW and AIPW are identical. For estimating the ATE, the weights that achieve the algebraic equivalence of IPW, AIPW, and IPWRA are based on propensity scores estimated using the inverse probability tilting (IPT) method of Graham, Pinto and Egel (2012). For the ATT, the weights are obtained using the covariate balancing propensity score (CBPS) method developed in Imai and Ratkovic (2014). These equivalences also make covariate balancing methods attractive when the treatment is confounded and one is interested in the local average treatment effect.

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  • Tymon S{l}oczy'nski & S. Derya Uysal & Jeffrey M. Wooldridge, 2023. "Covariate Balancing and the Equivalence of Weighting and Doubly Robust Estimators of Average Treatment Effects," Papers 2310.18563, arXiv.org.
    • Handle: RePEc:arx:papers:2310.18563
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    References listed on IDEAS

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    1. Sloczynski, Tymon & Uysal, Derya & Wooldridge, Jeffrey M., 2022. "Doubly Robust Estimation of Local Average Treatment Effects Using Inverse Probability Weighted Regression Adjustment," IZA Discussion Papers 15727, Institute of Labor Economics (IZA).
    2. Słoczyński, Tymon & Wooldridge, Jeffrey M., 2018. "A General Double Robustness Result For Estimating Average Treatment Effects," Econometric Theory, Cambridge University Press, vol. 34(1), pages 112-133, February.
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    Cited by:

    1. Das, Nandini & Gupta, Anubhab & Majumder, Binoy & Das, Mahamitra & Muniappan, Rangaswamy, 2024. "Does Training Farmers on Multiple Technologies Deter Adoption? Evidence from a Farm Management Training Program in Bangladesh," 2024 Annual Meeting, July 28-30, New Orleans, LA 344219, Agricultural and Applied Economics Association.
    2. Michael C. Knaus, 2024. "Treatment Effect Estimators as Weighted Outcomes," Papers 2411.11559, arXiv.org, revised Dec 2024.

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