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Optimal Policy Choices Under Uncertainty

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  • Sarah Moon

Abstract

Policymakers often make changes to policies whose benefits and costs are unknown and must be inferred from statistical estimates in empirical studies. The sample estimates are noisier for some policies than for others, which should be adjusted for when comparing policy changes in decision-making. In this paper I consider the problem of a planner who makes changes to upfront spending on a set of policies to maximize social welfare but faces statistical uncertainty about the impact of those changes. I set up an optimization problem that is tractable under statistical uncertainty and solve for the Bayes risk-minimizing decision rule. I propose an empirical Bayes approach to approximating the optimal decision rule when the planner does not know a prior. I show theoretically that the empirical Bayes decision rule can approximate the optimal decision rule well, including in cases where a sample plug-in rule does not.

Suggested Citation

  • Sarah Moon, 2025. "Optimal Policy Choices Under Uncertainty," Papers 2503.03910, arXiv.org.
  • Handle: RePEc:arx:papers:2503.03910
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    References listed on IDEAS

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    1. Magne Mogstad & Joseph P Romano & Azeem M Shaikh & Daniel Wilhelm, 2024. "Inference for Ranks with Applications to Mobility across Neighbourhoods and Academic Achievement across Countries," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 91(1), pages 476-518.
    2. Patrick Kline & Evan K. Rose & Christopher R. Walters, 2024. "A Discrimination Report Card," American Economic Review, American Economic Association, vol. 114(8), pages 2472-2525, August.
    3. Eric Mbakop & Max Tabord‐Meehan, 2021. "Model Selection for Treatment Choice: Penalized Welfare Maximization," Econometrica, Econometric Society, vol. 89(2), pages 825-848, March.
    4. Toru Kitagawa & Aleksey Tetenov, 2018. "Who Should Be Treated? Empirical Welfare Maximization Methods for Treatment Choice," Econometrica, Econometric Society, vol. 86(2), pages 591-616, March.
    5. Amy Finkelstein & Nathaniel Hendren, 2020. "Welfare Analysis Meets Causal Inference," NBER Working Papers 27640, National Bureau of Economic Research, Inc.
    6. Charles F. Manski, 2004. "Statistical Treatment Rules for Heterogeneous Populations," Econometrica, Econometric Society, vol. 72(4), pages 1221-1246, July.
    7. Jiaying Gu & Roger Koenker, 2023. "Reply to: Comments on “Invidious Comparisons: Ranking and Selection as Compound Decisions”," Econometrica, Econometric Society, vol. 91(1), pages 61-66, January.
    8. Susan Athey & Stefan Wager, 2021. "Policy Learning With Observational Data," Econometrica, Econometric Society, vol. 89(1), pages 133-161, January.
    9. Victor Chernozhukov & Sokbae Lee & Adam M. Rosen & Liyang Sun, 2025. "Policy Learning with Confidence," Papers 2502.10653, arXiv.org.
    10. Liyang Sun, 2021. "Empirical Welfare Maximization with Constraints," Papers 2103.15298, arXiv.org, revised Sep 2024.
    11. Roger Koenker & Ivan Mizera, 2014. "Convex Optimization, Shape Constraints, Compound Decisions, and Empirical Bayes Rules," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 109(506), pages 674-685, June.
    12. Jiaying Gu & Roger Koenker, 2023. "Invidious Comparisons: Ranking and Selection as Compound Decisions," Econometrica, Econometric Society, vol. 91(1), pages 1-41, January.
    13. Amy Finkelstein & Nathaniel Hendren, 2020. "Welfare Analysis Meets Causal Inference," Journal of Economic Perspectives, American Economic Association, vol. 34(4), pages 146-167, Fall.
    14. Jiafeng Chen, 2022. "Empirical Bayes When Estimation Precision Predicts Parameters," Papers 2212.14444, arXiv.org, revised Dec 2024.
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