Optimal treatment assignment rules under capacity constraints

TL;DR

This paper develops a novel approach to optimize treatment assignment under capacity constraints by reformulating the problem as an optimal transport problem, enabling effective solutions and demonstrating local asymptotic optimality.

Contribution

It introduces a new method that transforms constrained treatment assignment into an optimal transport problem, providing theoretical and practical insights.

Findings

Reformulation as an optimal transport problem simplifies capacity-constrained assignment.

Establishment of local asymptotic optimality of assignment rules.

Application to a voucher assignment case study with real data.

Abstract

We study treatment assignment problems under capacity constraints, where a planner aims to maximize social welfare by assigning treatments based on observable covariates. Such constraints, common when treatments are costly or limited in supply, introduce nontrivial challenges for deriving optimal statistical assignment rules because the planner needs to coordinate treatment assignment probabilities across the entire covariate distribution. To address these challenges, we reformulate the planner's constrained maximization problem as an optimal transport problem, which makes the problem effectively unconstrained. We then establish local asymptotic optimality results of assignment rules using a limits of experiments framework. Finally, we illustrate our method with a voucher assignment problem for private secondary school attendance using data from Angrist et al. (2006)