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Bounded, efficient and multiply robust estimation of average treatment effects using instrumental variables

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  • Linbo Wang
  • Eric Tchetgen Tchetgen

Abstract

Instrumental variables are widely used for estimating causal effects in the presence of unmeasured confounding. Under the standard instrumental variable model, however, the average treatment effect is only partially identifiable. To address this, we propose novel assumptions that enable identification of the average treatment effect. Our identification assumptions are clearly separated from model assumptions that are needed for estimation, so researchers are not required to commit to a specific observed data model in establishing identification. We then construct multiple estimators that are consistent under three different observed data models, and multiply robust estimators that are consistent in the union of these observed data models. We pay special attention to the case of binary outcomes, for which we obtain bounded estimators of the average treatment effect that are guaranteed to lie between −1 and 1. Our approaches are illustrated with simulations and a data analysis evaluating the causal effect of education on earnings.

Suggested Citation

  • Linbo Wang & Eric Tchetgen Tchetgen, 2018. "Bounded, efficient and multiply robust estimation of average treatment effects using instrumental variables," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 80(3), pages 531-550, June.
    • Handle: RePEc:bla:jorssb:v:80:y:2018:i:3:p:531-550
    DOI: 10.1111/rssb.12262
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    Cited by:

    1. Linbo Wang & Eric Tchetgen Tchetgen & Torben Martinussen & Stijn Vansteelandt, 2023. "Instrumental variable estimation of the causal hazard ratio," Biometrics, The International Biometric Society, vol. 79(2), pages 539-550, June.
    2. Mao, Lu, 2022. "Identification of the outcome distribution and sensitivity analysis under weak confounder–instrument interaction," Statistics & Probability Letters, Elsevier, vol. 189(C).
    3. Yan Liu, 2022. "Policy Learning under Endogeneity Using Instrumental Variables," Papers 2206.09883, arXiv.org, revised Mar 2024.
    4. Ting Ye & Ashkan Ertefaie & James Flory & Sean Hennessy & Dylan S. Small, 2023. "Instrumented difference‐in‐differences," Biometrics, The International Biometric Society, vol. 79(2), pages 569-581, June.
    5. Martin Emil Jakobsen & Jonas Peters, 2020. "Distributional robustness of K-class estimators and the PULSE," Papers 2005.03353, arXiv.org, revised Mar 2022.
    6. Cui, Yifan & Tchetgen Tchetgen, Eric, 2021. "On a necessary and sufficient identification condition of optimal treatment regimes with an instrumental variable," Statistics & Probability Letters, Elsevier, vol. 178(C).
    7. Shixiao Zhang & Peisong Han & Changbao Wu, 2023. "Calibration Techniques Encompassing Survey Sampling, Missing Data Analysis and Causal Inference," International Statistical Review, International Statistical Institute, vol. 91(2), pages 165-192, August.
    8. Linbo Wang & Eric Tchetgen Tchetgen & Torben Martinussen & Stijn Vansteelandt, 2023. "Rejoinder to discussions on “Instrumental variable estimation of the causal hazard ratio”," Biometrics, The International Biometric Society, vol. 79(2), pages 564-568, June.
    9. Zhichao Jiang & Shu Yang & Peng Ding, 2022. "Multiply robust estimation of causal effects under principal ignorability," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 84(4), pages 1423-1445, September.
    10. Benjamin R. Baer & Robert L. Strawderman & Ashkan Ertefaie, 2023. "Discussion on “Instrumental variable estimation of the causal hazard ratio,” by Linbo Wang, Eric Tchetgen Tchetgen, Torben Martinussen, and Stijn Vansteelandt," Biometrics, The International Biometric Society, vol. 79(2), pages 554-558, June.
    11. Hongming Pu & Bo Zhang, 2021. "Estimating optimal treatment rules with an instrumental variable: A partial identification learning approach," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 83(2), pages 318-345, April.
    12. Choi, Jin-young & Lee, Goeun & Lee, Myoung-jae, 2023. "Endogenous treatment effect for any response conditional on control propensity score," Statistics & Probability Letters, Elsevier, vol. 196(C).
    13. Myoung‐jae Lee, 2021. "Instrument residual estimator for any response variable with endogenous binary treatment," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 83(3), pages 612-635, July.
    14. Shuxiao Chen & Bo Zhang, 2021. "Estimating and Improving Dynamic Treatment Regimes With a Time-Varying Instrumental Variable," Papers 2104.07822, arXiv.org.
    15. Dingke Tang & Dehan Kong & Wenliang Pan & Linbo Wang, 2023. "Ultra‐high dimensional variable selection for doubly robust causal inference," Biometrics, The International Biometric Society, vol. 79(2), pages 903-914, June.
    16. Haoyu Wei & Hengrui Cai & Chengchun Shi & Rui Song, 2024. "On Efficient Inference of Causal Effects with Multiple Mediators," Papers 2401.05517, arXiv.org.

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