Partial Identification of Policy-Relevant Treatment Effects with Instrumental Variables via Optimal Transport

2026-04-14

AI Summary

When instrumental variables provide only limited support for treatment propensity, the policy-relevant treatment effect (PRTE) is generally not point-identified. This work formulates the partial identification of PRTE as a constrained conditional optimal transport (CCOT) problem and, through analytical dimension reduction, transforms it into a separable one-dimensional optimal transport problem, yielding closed-form sharp bounds without requiring high-dimensional optimization. The approach accommodates both discrete and continuous instruments as well as high-dimensional covariates, and integrates double machine learning with Neyman-orthogonal scores to achieve asymptotically normal estimation at the √n rate. Simulations and an empirical application on bed net subsidies demonstrate that the resulting bounds are substantially tighter than those from existing moment relaxation methods.

Technology Category

• Reasoning under Uncertainty: Stochastic Optimization
• Constraint Satisfaction and Optimization: Mixed Discrete/Continuous Optimization
• Search and Optimization: Mixed Discrete/Continuous Search

Application Category

• Security and Privacy: Privacy-enhancing technologies
• Responsible Web: Data and user privacy-enhancing technologies for the Web
• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems

Abstract

Policy-Relevant Treatment Effects (PRTEs) are generally not point-identified under standard instrumental variable (IV) assumptions when the instrument generates limited support in treatment propensity. Existing approaches typically optimize over marginal treatment response functions subject to moment restrictions and can discard identifying distributional information. We show that PRTE partial identification in the generalized Roy model can instead be formulated as a Constrained Conditional Optimal Transport (CCOT) problem. The resulting multidimensional CCOT problem reduces analytically to separable one-dimensional OT problems with product costs, yielding sharp closed-form bounds and avoiding direct solution of the original high-dimensional CCOT problem. We also develop estimation and inference procedures for these bounds: for discrete instruments, a Double Machine Learning (DML) approach based on Neyman-orthogonal scores that accommodates high-dimensional covariates while achieving the parametric $\sqrt{n}$ rate and asymptotic normality; for continuous instruments, we explicitly characterize the corresponding nonparametric convergence rates. The framework accommodates covariates, discrete and continuous instruments, and extensions to general treatment settings. In simulations and a bed-net subsidy application, the resulting bounds are substantially tighter than existing moment-relaxation methods.

Problem

• Partial Identification
• Policy-Relevant Treatment Effects
• Instrumental Variables
• Optimal Transport

Innovation

• Optimal Transport
• Partial Identification
• Instrumental Variables
• Double Machine Learning
• Policy-Relevant Treatment Effects