Identifying the Distribution of Treatment Effects under Support Restrictions

TL;DR

This paper develops a method to partially identify the distribution of treatment effects under support restrictions using optimal transportation, providing bounds and an estimation procedure, with application to smoking's impact on birth weight.

Contribution

It introduces a dual representation approach for bounding the distribution of treatment effects under support restrictions, enhancing identification in economic models.

Findings

Monotone treatment response significantly constrains the DTE.

The proposed bounds are informative in empirical examples.

The estimation procedure is effective in applied analysis.

Abstract

The distribution of treatment effects (DTE) is often of interest in the context of welfare policy evaluation. In this paper, I consider partial identification of the DTE under known marginal distributions and support restrictions on the potential outcomes. Examples of such support restrictions include monotone treatment response, concave treatment response, convex treatment response, and the Roy model of self-selection. To establish informative bounds on the DTE, I formulate the problem as an optimal transportation linear program and develop a new dual representation to characterize the identification region with respect to the known marginal distributions. I use this result to derive informative bounds for concrete economic examples. I also propose an estimation procedure and illustrate the usefulness of my approach in the context of an empirical analysis of the effects of smoking on infant birth weight. The empirical results show that monotone treatment response has a substantial identifying power for the DTE when the marginal distributions of the potential outcomes are given.