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Efficient covariate balancing for the average treatment effect with missing outcome

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  • Tang, Shengfang
  • Zhan, Mingfeng
  • Jiang, Qingshan
  • Zhang, Tong

Abstract

This paper develops an empirical balancing approach for the estimation of treatment effects under the framework of outcomes being suffered from missing. We first represent the parameter of interest as a weighted expectation of the observed outcome by introducing two auxiliary binary variables and then estimate the weighting functions using covariate balancing methods. By tailoring the loss function for the weighting functions, the resulting treatment effect estimates are automatically weight-normalized and exhibit both low bias and reduced variance in finite samples when compared to conventional inverse probability weighting methods. Under some regularity conditions, we show that the proposed estimator is consistent, asymptotically normally distributed with the asymptotic variance achieving the semiparametric efficiency bound. Finite-sample performance of the proposed method is evaluated via Monte Carlo simulations.

Suggested Citation

  • Tang, Shengfang & Zhan, Mingfeng & Jiang, Qingshan & Zhang, Tong, 2024. "Efficient covariate balancing for the average treatment effect with missing outcome," Economics Letters, Elsevier, vol. 244(C).
    • Handle: RePEc:eee:ecolet:v:244:y:2024:i:c:s0165176524004452
    DOI: 10.1016/j.econlet.2024.111961
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    References listed on IDEAS

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    1. Sergio Firpo, 2007. "Efficient Semiparametric Estimation of Quantile Treatment Effects," Econometrica, Econometric Society, vol. 75(1), pages 259-276, January.
    2. Stephen G. Donald & Yu-Chin Hsu & Robert P. Lieli, 2014. "Testing the Unconfoundedness Assumption via Inverse Probability Weighted Estimators of (L)ATT," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 32(3), pages 395-415, July.
    3. Alberto Abadie & Guido W. Imbens, 2016. "Matching on the Estimated Propensity Score," Econometrica, Econometric Society, vol. 84, pages 781-807, March.
    4. Keisuke Hirano & Guido W. Imbens & Geert Ridder, 2003. "Efficient Estimation of Average Treatment Effects Using the Estimated Propensity Score," Econometrica, Econometric Society, vol. 71(4), pages 1161-1189, July.
    5. Donald, Stephen G. & Hsu, Yu-Chin, 2014. "Estimation and inference for distribution functions and quantile functions in treatment effect models," Journal of Econometrics, Elsevier, vol. 178(P3), pages 383-397.
    6. Kosuke Imai & Marc Ratkovic, 2014. "Covariate balancing propensity score," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 76(1), pages 243-263, January.
    7. Kwun Chuen Gary Chan & Sheung Chi Phillip Yam & Zheng Zhang, 2016. "Globally efficient non-parametric inference of average treatment effects by empirical balancing calibration weighting," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 78(3), pages 673-700, June.
    8. 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.
    9. Phillip Heiler, 2022. "Efficient Covariate Balancing for the Local Average Treatment Effect," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 40(4), pages 1569-1582, October.
    10. Wei, Kecheng & Qin, Guoyou & Zhang, Jiajia & Sui, Xuemei, 2022. "Doubly robust estimation in causal inference with missing outcomes: With an application to the Aerobics Center Longitudinal Study," Computational Statistics & Data Analysis, Elsevier, vol. 168(C).
    11. Alberto Abadie & Guido W. Imbens, 2006. "Large Sample Properties of Matching Estimators for Average Treatment Effects," Econometrica, Econometric Society, vol. 74(1), pages 235-267, January.
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