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Optimal Treatment Assignment Rules Under Capacity Constraints

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Listed:
  • Keita Sunada
  • Kohei Izumi

Abstract

We study treatment assignment when treatments are limited in supply, where a planner aims to maximize social welfare by assigning treatments based on observable covariates. Such constraints are common when treatments are scarce and costly, but they complicate the analysis of optimal assignment rules because assignment probabilities must be coordinated across the entire covariate distribution. We develop a new approach that reformulates the planner’s problem as an optimal transport problem, which makes the constraints analytically tractable. Using a limits of experiments framework, we establish local asymptotic optimality results for two canonical decision rules—the plug-in rule and the Bayesian rule. We show that the former rule can dominate the latter rule, with simulations demonstrating sizable risk reductions. An empirical illustration using school voucher program data from Angrist et al. (2006) demonstrates how the two rules differ in practice.

Suggested Citation

  • Keita Sunada & Kohei Izumi, 2026. "Optimal Treatment Assignment Rules Under Capacity Constraints," ISER Discussion Paper 1308, Institute of Social and Economic Research, The University of Osaka.
    • Handle: RePEc:dpr:wpaper:1308
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    References listed on IDEAS

    as
    1. Daido Kido, 2023. "Locally Asymptotically Minimax Statistical Treatment Rules Under Partial Identification," Papers 2311.08958, arXiv.org.
    2. 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.
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