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Partial Identification of the Average Treatment Effect Using Instrumental Variables: Review of Methods for Binary Instruments, Treatments, and Outcomes

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  • Sonja A. Swanson
  • Miguel A. Hernán
  • Matthew Miller
  • James M. Robins
  • Thomas S. Richardson

Abstract

Several methods have been proposed for partially or point identifying the average treatment effect (ATE) using instrumental variable (IV) type assumptions. The descriptions of these methods are widespread across the statistical, economic, epidemiologic, and computer science literature, and the connections between the methods have not been readily apparent. In the setting of a binary instrument, treatment, and outcome, we review proposed methods for partial and point identification of the ATE under IV assumptions, express the identification results in a common notation and terminology, and propose a taxonomy that is based on sets of identifying assumptions. We further demonstrate and provide software for the application of these methods to estimate bounds. Supplementary materials for this article are available online.

Suggested Citation

  • Sonja A. Swanson & Miguel A. Hernán & Matthew Miller & James M. Robins & Thomas S. Richardson, 2018. "Partial Identification of the Average Treatment Effect Using Instrumental Variables: Review of Methods for Binary Instruments, Treatments, and Outcomes," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 113(522), pages 933-947, April.
    • Handle: RePEc:taf:jnlasa:v:113:y:2018:i:522:p:933-947
    DOI: 10.1080/01621459.2018.1434530
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    Citations

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    Cited by:

    1. Tommasi, Denni & Zhang, Lina, 2024. "Bounding program benefits when participation is misreported," Journal of Econometrics, Elsevier, vol. 238(1).
    2. Didier Nibbering & Matthijs Oosterveen, 2023. "Instrument-based estimation of full treatment effects with movers," Papers 2306.07018, arXiv.org.
    3. Lina Zhang & David T. Frazier & Don S. Poskitt & Xueyan Zhao, 2020. "Decomposing Identification Gains and Evaluating Instrument Identification Power for Partially Identified Average Treatment Effects," Monash Econometrics and Business Statistics Working Papers 34/20, Monash University, Department of Econometrics and Business Statistics.
    4. Jaffer M. Zaidi & Tyler J. VanderWeele, 2021. "On the identification of individual level pleiotropic, pure direct, and principal stratum direct effects without cross world assumptions," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 48(3), pages 881-907, September.
    5. Jad Beyhum & Jean-Pierre Florens & Ingrid Keilegom, 2023. "A nonparametric instrumental approach to confounding in competing risks models," Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, Springer, vol. 29(4), pages 709-734, October.
    6. Donald S. Poskitt & Xueyan Zhao, 2023. "Bootstrap Hausdorff Confidence Regions for Average Treatment Effect Identified Sets," Monash Econometrics and Business Statistics Working Papers 9/23, Monash University, Department of Econometrics and Business Statistics.
    7. 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.
    8. Ting Ye & Luke Keele & Raiden Hasegawa & Dylan S. Small, 2020. "A Negative Correlation Strategy for Bracketing in Difference-in-Differences," Papers 2006.02423, arXiv.org, revised Jun 2022.
    9. Shuxiao Chen & Bo Zhang, 2021. "Estimating and Improving Dynamic Treatment Regimes With a Time-Varying Instrumental Variable," Papers 2104.07822, arXiv.org.
    10. Zhonghua Liu & Ting Ye & Baoluo Sun & Mary Schooling & Eric Tchetgen Tchetgen, 2023. "Mendelian randomization mixed‐scale treatment effect robust identification and estimation for causal inference," Biometrics, The International Biometric Society, vol. 79(3), pages 2208-2219, September.
    11. Kitagawa, Toru, 2021. "The identification region of the potential outcome distributions under instrument independence," Journal of Econometrics, Elsevier, vol. 225(2), pages 231-253.
    12. Matthew A. Masten & Alexandre Poirier, 2021. "Salvaging Falsified Instrumental Variable Models," Econometrica, Econometric Society, vol. 89(3), pages 1449-1469, May.

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