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Orthogonal Policy Learning Under Ambiguity

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  • Riccardo D'Adamo

Abstract

This paper studies the problem of estimating individualized treatment rules when treatment effects are partially identified, as it is often the case with observational data. By drawing connections between the treatment assignment problem and classical decision theory, we characterize several notions of optimal treatment policies in the presence of partial identification. Our unified framework allows to incorporate user-defined constraints on the set of allowable policies, such as restrictions for transparency or interpretability, while also ensuring computational feasibility. We show how partial identification leads to a new policy learning problem where the objective function is directionally -- but not fully -- differentiable with respect to the nuisance first-stage. We then propose an estimation procedure that ensures Neyman-orthogonality with respect to the nuisance components and we provide statistical guarantees that depend on the amount of concentration around the points of non-differentiability in the data-generating-process. The proposed methods are illustrated using data from the Job Partnership Training Act study.

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  • Riccardo D'Adamo, 2021. "Orthogonal Policy Learning Under Ambiguity," Papers 2111.10904, arXiv.org, revised Dec 2022.
    • Handle: RePEc:arx:papers:2111.10904
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    References listed on IDEAS

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    1. Hidehiko Ichimura & Whitney K. Newey, 2022. "The influence function of semiparametric estimators," Quantitative Economics, Econometric Society, vol. 13(1), pages 29-61, January.
    2. Charles F. Manski, 1997. "Monotone Treatment Response," Econometrica, Econometric Society, vol. 65(6), pages 1311-1334, November.
    3. Keisuke Hirano & Jack R. Porter, 2009. "Asymptotics for Statistical Treatment Rules," Econometrica, Econometric Society, vol. 77(5), pages 1683-1701, September.
    4. Eric Mbakop & Max Tabord‐Meehan, 2021. "Model Selection for Treatment Choice: Penalized Welfare Maximization," Econometrica, Econometric Society, vol. 89(2), pages 825-848, March.
    5. Farrell, Max H., 2015. "Robust inference on average treatment effects with possibly more covariates than observations," Journal of Econometrics, Elsevier, vol. 189(1), pages 1-23.
    6. Victor Chernozhukov & Juan Carlos Escanciano & Hidehiko Ichimura & Whitney K. Newey & James M. Robins, 2022. "Locally Robust Semiparametric Estimation," Econometrica, Econometric Society, vol. 90(4), pages 1501-1535, July.
    7. Chen, Xiaohong, 2007. "Large Sample Sieve Estimation of Semi-Nonparametric Models," Handbook of Econometrics, in: J.J. Heckman & E.E. Leamer (ed.), Handbook of Econometrics, edition 1, volume 6, chapter 76, Elsevier.
    8. Charles F. Manski, 2004. "Statistical Treatment Rules for Heterogeneous Populations," Econometrica, Econometric Society, vol. 72(4), pages 1221-1246, July.
    9. Yifan Cui & Eric Tchetgen Tchetgen, 2021. "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, January.
    10. Charles F. Manski & John V. Pepper, 2000. "Monotone Instrumental Variables, with an Application to the Returns to Schooling," Econometrica, Econometric Society, vol. 68(4), pages 997-1012, July.
    11. Susan Athey & Stefan Wager, 2021. "Policy Learning With Observational Data," Econometrica, Econometric Society, vol. 89(1), pages 133-161, January.
    12. Liyang Sun, 2021. "Empirical Welfare Maximization with Constraints," Papers 2103.15298, arXiv.org, revised Sep 2024.
    13. Charles F. Manski, 2011. "Choosing Treatment Policies Under Ambiguity," Annual Review of Economics, Annual Reviews, vol. 3(1), pages 25-49, September.
    14. Keisuke Hirano & Jack R. Porter, 2012. "Impossibility Results for Nondifferentiable Functionals," Econometrica, Econometric Society, vol. 80(4), pages 1769-1790, July.
    15. David S. Lee, 2009. "Training, Wages, and Sample Selection: Estimating Sharp Bounds on Treatment Effects," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 76(3), pages 1071-1102.
    16. 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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