Identifying the Distribution of Treatment Effects under Support Restrictions Ju Hyun Kim ∗ August 27, 2018 The distribution of treatment effects (DTE) is often of interest in the context of welfare policy eval- uation. 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 mono- tone 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. In this paper, I study partial identification of the distribution of treatment effects (DTE) under a broad class of restrictions on potential outcomes. The DTE is defined as follows: for any fixed δ ∈$_{R}$ , $^{∗}$University of North Carolina at Chapel Hill, juhkim@email.unc.edu. I am greatly indebted to my advisor Bernard Salani´e for numerous discussions and his support throughout this project. I am also grateful to Jushan Bai, Pierre-Andr´e Chiappori, Serena Ng, and Christoph Rothe for their encouragement and helpful comments. This paper has benefited from discussions with Andrew Chesher, Xavier D’Haultfoeuille, Alfred Galichon, Kyle Jurado, Shakeeb Khan, Toru Kitagawa, Dennis Kristensen, Seunghoon Na, Salvador Navarro, Byoung Park, and Charles Zheng. While writing this paper, I was generously supported by a Wueller pre-dissertation award fellowship from the Economics Department at Columbia University. All errors are mine. 1 F$_{Δ}$ ( δ ) = Pr (Δ ≤ δ ) , arXiv:1410.5885v1 [stat.ME] 21 Oct 2014 1 Introduction Abstract