IDEAS home Printed from https://ideas.repec.org/p/arx/papers/2310.18563.html
   My bibliography  Save this paper

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

Author

Listed:
  • 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.

Suggested Citation

  • 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
    as

    Download full text from publisher

    File URL: http://arxiv.org/pdf/2310.18563
    File Function: Latest version
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    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.
    3. Tymon S{l}oczy'nski & S. Derya Uysal & Jeffrey M. Wooldridge, 2022. "Doubly Robust Estimation of Local Average Treatment Effects Using Inverse Probability Weighted Regression Adjustment," Papers 2208.01300, arXiv.org, revised Nov 2022.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Sant’Anna, Pedro H.C. & Zhao, Jun, 2020. "Doubly robust difference-in-differences estimators," Journal of Econometrics, Elsevier, vol. 219(1), pages 101-122.
    2. Pedro H. C. Sant'Anna & Xiaojun Song & Qi Xu, 2022. "Covariate distribution balance via propensity scores," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 37(6), pages 1093-1120, September.
    3. Chunrong Ai & Oliver Linton & Kaiji Motegi & Zheng Zhang, 2021. "A unified framework for efficient estimation of general treatment models," Quantitative Economics, Econometric Society, vol. 12(3), pages 779-816, July.
    4. Jörg Kalbfuß & Reto Odermatt & Alois Stutzer, 2018. "Medical marijuana laws and mental health in the United States," CEP Discussion Papers dp1546, Centre for Economic Performance, LSE.
    5. Tymon Sloczynski & S. Derya Uysal & Jeffrey M. Wooldridge & Derya Uysal, 2022. "Abadie's Kappa and Weighting Estimators of the Local Average Treatment Effect," CESifo Working Paper Series 9715, CESifo.
    6. Yukun Ma & Pedro H. C. Sant'Anna & Yuya Sasaki & Takuya Ura, 2023. "Doubly Robust Estimators with Weak Overlap," Papers 2304.08974, arXiv.org, revised Apr 2023.
    7. Jiaqi Chen & Song Xu & Jing Gao, 2020. "The Mixed Effect of China’s New Health Care Reform on Health Insurance Coverage and the Efficiency of Health Service Utilisation: A Longitudinal Approach," IJERPH, MDPI, vol. 17(5), pages 1-13, March.
    8. Lewbel, Arthur & Choi, Jin Young & Zhou, Zhuzhu, 2023. "Over-identified Doubly Robust identification and estimation," Journal of Econometrics, Elsevier, vol. 235(1), pages 25-42.
    9. Difang Huang & Jiti Gao & Tatsushi Oka, 2022. "Semiparametric Single-Index Estimation for Average Treatment Effects," Papers 2206.08503, arXiv.org, revised Oct 2022.
    10. Antonio Filippin & Marco Mantovani, 2024. "Moral Preferences over Health-Wealth Trade-offs," Working Papers 531, University of Milano-Bicocca, Department of Economics.
    11. Yang Ning & Sida Peng & Jing Tao, 2020. "Doubly Robust Semiparametric Difference-in-Differences Estimators with High-Dimensional Data," Papers 2009.03151, arXiv.org.
    12. Jun Hyung Kim & Yu Kyung Koh & Jinseong Park, 2023. "Mental Health Consequences of Working from Home during the Pandemic," Global Economic Review, Taylor & Francis Journals, vol. 52(1), pages 18-50, January.
    13. Arun Advani & Toru Kitagawa & Tymon Słoczyński, 2019. "Mostly harmless simulations? Using Monte Carlo studies for estimator selection," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 34(6), pages 893-910, September.
    14. Nikolic, Jelena & Rubil, Ivica & Tomić, Iva, 2017. "Pre-crisis reforms, austerity measures and the public-private wage gap in two emerging economies," Economic Systems, Elsevier, vol. 41(2), pages 248-265.
    15. Hartley, Robert Paul & Lamarche, Carlos, 2018. "Behavioral responses and welfare reform: Evidence from a randomized experiment," Labour Economics, Elsevier, vol. 54(C), pages 135-151.
    16. Georgios Nalbantis & Tim Pawlowski & Dominik Schreyer, 2023. "Substitution Effects and the Transnational Demand for European Soccer Telecasts," Journal of Sports Economics, , vol. 24(4), pages 407-442, May.
    17. Sasaki, Yuya & Ura, Takuya, 2023. "Estimation and inference for policy relevant treatment effects," Journal of Econometrics, Elsevier, vol. 234(2), pages 394-450.
    18. Böckerman, Petri & Bryson, Alex & Ilmakunnas, Ilari & Ilmakunnas, Pekka, 2024. "Does High Involvement Management Make You Work Longer? Insights from Linked Survey and Register Data," IZA Discussion Papers 16827, Institute of Labor Economics (IZA).
    19. Liang Jiang & Oliver B. Linton & Haihan Tang & Yichong Zhang, 2022. "Improving Estimation Efficiency via Regression-Adjustment in Covariate-Adaptive Randomizations with Imperfect Compliance," Papers 2201.13004, arXiv.org, revised Jun 2023.
    20. Navjot Sangwan & Luca Tasciotti, 2023. "Losing the Plot: The Impact of Urban Agriculture on Household Food Expenditure and Dietary Diversity in Sub-Saharan African Countries," Agriculture, MDPI, vol. 13(2), pages 1-20, January.

    More about this item

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:arx:papers:2310.18563. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: arXiv administrators (email available below). General contact details of provider: http://arxiv.org/ .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.