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Doubly robust estimation of the local average treatment effect curve

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  • Elizabeth L. Ogburn
  • Andrea Rotnitzky
  • James M. Robins

Abstract

type="main" xml:id="rssb12078-abs-0001"> We consider estimation of the causal effect of a binary treatment on an outcome, conditionally on covariates, from observational studies or natural experiments in which there is a binary instrument for treatment. We describe a doubly robust, locally efficient estimator of the parameters indexing a model for the local average treatment effect conditionally on covariates V when randomization of the instrument is only true conditionally on a high dimensional vector of covariates X , possibly bigger than V . We discuss the surprising result that inference is identical to inference for the parameters of a model for an additive treatment effect on the treated conditionally on V that assumes no treatment–instrument interaction. We illustrate our methods with the estimation of the local average effect of participating in 401(k) retirement programmes on savings by using data from the US Census Bureau's 1991 Survey of Income and Program Participation.

Suggested Citation

  • Elizabeth L. Ogburn & Andrea Rotnitzky & James M. Robins, 2015. "Doubly robust estimation of the local average treatment effect curve," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 77(2), pages 373-396, March.
    • Handle: RePEc:bla:jorssb:v:77:y:2015:i:2:p:373-396
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    File URL: http://hdl.handle.net/10.1111/rssb.2015.77.issue-2
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    Citations

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    Cited by:

    1. Sokbae Lee & Ryo Okui & Yoon†Jae Whang, 2017. "Doubly robust uniform confidence band for the conditional average treatment effect function," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 32(7), pages 1207-1225, November.
    2. A. Belloni & V. Chernozhukov & I. Fernández‐Val & C. Hansen, 2017. "Program Evaluation and Causal Inference With High‐Dimensional Data," Econometrica, Econometric Society, vol. 85, pages 233-298, January.
    3. Alexandre Belloni & Victor Chernozhukov & Ivan Fernandez-Val & Christian Hansen, 2013. "Program evaluation with high-dimensional data," CeMMAP working papers CWP77/13, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    4. 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.
    5. Kazuhiko Shinoda & Takahiro Hoshino, 2022. "Orthogonal Series Estimation for the Ratio of Conditional Expectation Functions," Papers 2212.13145, arXiv.org.
    6. Kara E. Rudolph & Iván Díaz, 2022. "When the ends do not justify the means: Learning who is predicted to have harmful indirect effects," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 185(S2), pages 573-589, December.
    7. Chunrong Ai & Lukang Huang & Zheng Zhang, 2018. "A Simple and Efficient Estimation of the Average Treatment Effect in the Presence of Unmeasured Confounders," Papers 1807.05678, arXiv.org.
    8. Tymon Sloczynski & S. Derya Uysal & Jeffrey M. Wooldridge & Derya Uysal, 2022. "Doubly Robust Estimation of Local Average Treatment Effects Using Inverse Probability Weighted Regression Adjustment," CESifo Working Paper Series 10105, CESifo.
    9. 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.
    10. Jierui Du & Gao Wen & Xin Liang, 2024. "Estimating the Complier Average Causal Effect with Non-Ignorable Missing Outcomes Using Likelihood Analysis," Mathematics, MDPI, vol. 12(9), pages 1-16, April.
    11. Yu, Haiyan & Yang, Ching-Chi & Yu, Ping, 2023. "Constrained optimization for stratified treatment rules in reducing hospital readmission rates of diabetic patients," European Journal of Operational Research, Elsevier, vol. 308(3), pages 1355-1364.
    12. Andreas Nordland & Torben Martinussen, 2024. "Estimation of treatment effect among treatment responders with a time‐to‐event endpoint," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 51(3), pages 1161-1180, September.
    13. Rahul Singh & Liyang Sun, 2024. "Double robustness for complier parameters and a semi-parametric test for complier characteristics," The Econometrics Journal, Royal Economic Society, vol. 27(1), pages 1-20.
    14. 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.
    15. Yumou Qiu & Jing Tao & Xiao‐Hua Zhou, 2021. "Inference of heterogeneous treatment effects using observational data with high‐dimensional covariates," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 83(5), pages 1016-1043, November.
    16. 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.
    17. Wei, Bo & Tan, Kean Ming & He, Xuming, 2024. "Estimation of complier expected shortfall treatment effects with a binary instrumental variable," Journal of Econometrics, Elsevier, vol. 238(2).
    18. Maria Cuellar & Edward H. Kennedy, 2020. "A non‐parametric projection‐based estimator for the probability of causation, with application to water sanitation in Kenya," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 183(4), pages 1793-1818, October.
    19. 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).
    20. Shengfang Tang & Zongwu Cai & Ying Fang & Ming Lin, 2019. "Testing Unconfoundedness Assumption Using Auxiliary Variables," WORKING PAPERS SERIES IN THEORETICAL AND APPLIED ECONOMICS 201905, University of Kansas, Department of Economics, revised Mar 2019.
    21. Sung Jae Jun & Sokbae Lee, 2022. "Average Adjusted Association: Efficient Estimation with High Dimensional Confounders," Papers 2205.14048, arXiv.org, revised Apr 2023.
    22. Pan Zhao & Yifan Cui, 2023. "A Semiparametric Instrumented Difference-in-Differences Approach to Policy Learning," Papers 2310.09545, arXiv.org.
    23. Zongwu Cai & Ying Fang & Ming Lin & Shengfang Tang, 2020. "Testing Unconfoundedness Assumption Using Auxiliary Variables," WORKING PAPERS SERIES IN THEORETICAL AND APPLIED ECONOMICS 202004, University of Kansas, Department of Economics, revised Feb 2020.
    24. 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.
    25. Yang Ning & Sida Peng & Jing Tao, 2020. "Doubly Robust Semiparametric Difference-in-Differences Estimators with High-Dimensional Data," Papers 2009.03151, arXiv.org.

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