Quantitative Economics

Journal of the Econometric Society

Edited by: Bernard Salanié • Print ISSN: 1759-7323 • Online ISSN: 1759-7331

Quantitative Economics: Jul, 2025, Volume 16, Issue 3

Estimation of Optimal Dynamic Treatment Assignment Rules under Policy Constraints

https://doi.org/10.3982/QE2288
p. 981-1022

Shosei Sakaguchi

Many policies involve dynamics in their treatment assignments where individuals receive sequential interventions over multiple stages. We study estimation of an optimal dynamic treatment regime that guides the optimal treatment assignment for each individual at each stage based on their history. We propose an empirical welfare maximization approach in this dynamic framework, which estimates the optimal dynamic treatment regime using data from an experimental or quasi‐experimental study while satisfying exogenous constraints on policies. The paper proposes two estimation methods: one solves the treatment assignment problem sequentially through backward induction, and the other solves the entire problem simultaneously across all stages. We establish finite‐sample upper bounds on worst‐case average welfare regrets for these methods and show their optimal n−1/2 convergence rates. We also modify the simultaneous estimation method to accommodate intertemporal budget/capacity constraints.


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Supplemental Material

Supplement to "Estimation of Optimal Dynamic Treatment Assignment Rules under Policy Constraints"

Shosei Sakaguchi

This document contains Appendices C, D, E, F, G, H, and I of the article "Estimation of Optimal Dynamic Treatment Assignment Rules under Policy Constraints."

Supplement to "Estimation of Optimal Dynamic Treatment Assignment Rules under Policy Constraints"

Shosei Sakaguchi

The replication package for this paper is available at https://doi.org/10.5281/zenodo.15042887. The Journal checked the data and codes included in the package for their ability to reproduce the results in the paper and approved online appendices.