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Policy Learning under Endogeneity Using Instrumental Variables

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  • Yan Liu

Abstract

This paper studies the identification and estimation of individualized intervention policies in observational data settings characterized by endogenous treatment selection and the availability of instrumental variables. We introduce encouragement rules that manipulate an instrument. Incorporating the marginal treatment effects (MTE) as policy invariant structural parameters, we establish the identification of the social welfare criterion for the optimal encouragement rule. Focusing on binary encouragement rules, we propose to estimate the optimal policy via the Empirical Welfare Maximization (EWM) method and derive convergence rates of the regret (welfare loss). We consider extensions to accommodate multiple instruments and budget constraints. Using data from the Indonesian Family Life Survey, we apply the EWM encouragement rule to advise on the optimal tuition subsidy assignment. Our framework offers interpretability regarding why a certain subpopulation is targeted.

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  • Yan Liu, 2022. "Policy Learning under Endogeneity Using Instrumental Variables," Papers 2206.09883, arXiv.org, revised Mar 2024.
    • Handle: RePEc:arx:papers:2206.09883
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    References listed on IDEAS

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    1. Yingqi Zhao & Donglin Zeng & A. John Rush & Michael R. Kosorok, 2012. "Estimating Individualized Treatment Rules Using Outcome Weighted Learning," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 107(499), pages 1106-1118, September.
    2. Pedro Carneiro & James J. Heckman & Edward Vytlacil, 2010. "Evaluating Marginal Policy Changes and the Average Effect of Treatment for Individuals at the Margin," Econometrica, Econometric Society, vol. 78(1), pages 377-394, January.
    3. Keisuke Hirano & Jack R. Porter, 2009. "Asymptotics for Statistical Treatment Rules," Econometrica, Econometric Society, vol. 77(5), pages 1683-1701, September.
    4. Cornelissen, Thomas & Dustmann, Christian & Raute, Anna & Schönberg, Uta, 2016. "From LATE to MTE: Alternative methods for the evaluation of policy interventions," Labour Economics, Elsevier, vol. 41(C), pages 47-60.
    5. Yuya Sasaki & Takuya Ura, 2020. "Welfare Analysis via Marginal Treatment Effects," Papers 2012.07624, arXiv.org.
    6. Pedro Carneiro & James J. Heckman & Edward J. Vytlacil, 2011. "Estimating Marginal Returns to Education," American Economic Review, American Economic Association, vol. 101(6), pages 2754-2781, October.
    7. Maximilian Kasy, 2016. "Partial Identification, Distributional Preferences, and the Welfare Ranking of Policies," The Review of Economics and Statistics, MIT Press, vol. 98(1), pages 111-131, March.
    8. Yifan Cui & Eric Tchetgen Tchetgen, 2020. "A Semiparametric Instrumental Variable Approach to Optimal Treatment Regimes Under Endogeneity," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 116(533), pages 162-173, December.
    9. Bhattacharya, Debopam & Dupas, Pascaline, 2012. "Inferring welfare maximizing treatment assignment under budget constraints," Journal of Econometrics, Elsevier, vol. 167(1), pages 168-196.
    10. James Heckman & Justin L. Tobias & Edward Vytlacil, 2001. "Four Parameters of Interest in the Evaluation of Social Programs," Southern Economic Journal, John Wiley & Sons, vol. 68(2), pages 210-223, October.
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    12. Chen, Xiaohong & Christensen, Timothy M., 2015. "Optimal uniform convergence rates and asymptotic normality for series estimators under weak dependence and weak conditions," Journal of Econometrics, Elsevier, vol. 188(2), pages 447-465.
    13. Carneiro, Pedro & Lee, Sokbae, 2009. "Estimating distributions of potential outcomes using local instrumental variables with an application to changes in college enrollment and wage inequality," Journal of Econometrics, Elsevier, vol. 149(2), pages 191-208, April.
    14. James Heckman & Justin L. Tobias & Edward Vytlacil, 2001. "Four Parameters of Interest in the Evaluation of Social Programs," Southern Economic Journal, John Wiley & Sons, vol. 68(2), pages 210-223, October.
    15. Susan Athey & Stefan Wager, 2021. "Policy Learning With Observational Data," Econometrica, Econometric Society, vol. 89(1), pages 133-161, January.
    16. Magne Mogstad & Andres Santos & Alexander Torgovitsky, 2018. "Using Instrumental Variables for Inference About Policy Relevant Treatment Parameters," Econometrica, Econometric Society, vol. 86(5), pages 1589-1619, September.
    17. Edward Vytlacil & James J. Heckman, 2001. "Policy-Relevant Treatment Effects," American Economic Review, American Economic Association, vol. 91(2), pages 107-111, May.
    18. Liyang Sun, 2021. "Empirical Welfare Maximization with Constraints," Papers 2103.15298, arXiv.org, revised Sep 2024.
    19. 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.
    20. Rebecca L. Thornton, 2008. "The Demand for, and Impact of, Learning HIV Status," American Economic Review, American Economic Association, vol. 98(5), pages 1829-1863, December.
    21. 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.
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    Cited by:

    1. Toru Kitagawa & Hugo Lopez & Jeff Rowley, 2022. "Stochastic Treatment Choice with Empirical Welfare Updating," Papers 2211.01537, arXiv.org, revised Feb 2023.

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