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Who should be Treated? Empirical Welfare Maximization Methods for Treatment Choice

Kitagawa, T; Tetenov, A; (2017) Who should be Treated? Empirical Welfare Maximization Methods for Treatment Choice. (CEMMAP Working Paper CWP24/17). Centre for Microdata Methods and Practice (CEMMAP), Institute for Fiscal Studies: London, UK. Green open access

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Abstract

One of the main objectives of empirical analysis of experiments and quasi-experiments is to inform policy decisions that determine the allocation of treatments to individuals with different observable covariates. We propose the Empirical Welfare Maximization (EWM) method, which estimates a treatment assignment policy by maximizing the sample analog of average social welfare over a class of candidate treatment policies. The EWM approach is attractive in terms of both statistical performance and practical implementation in realistic settings of policy design. Common features of these settings include: (i) feasible treatment assignment rules are constrained exogenously for ethical, legislative, or political reasons, (ii) a policy maker wants a simple treatment assignment rule based on one or more eligibility scores in order to reduce the dimensionality of individual observable characteristics, and/or (iii) the proportion of individuals who can receive the treatment is a priori limited due to a budget or a capacity constraint. We show that when the propensity score is known, the average social welfare attained by EWM rules converges at least at n^(-1/2) rate to the maximum obtainable welfare uniformly over a minimally constrained class of data distributions, and this uniform convergence rate is minimax optimal. In comparison with this benchmark rate, we examine how the uniform convergence rate of the average welfare improves or deteriorates depending on the richness of the class of candidate decision rules, the distribution of conditional treatment effects, and the lack of knowledge of the propensity score. We provide an asymptotically valid inference procedure for the population welfare gain obtained by exercising the EWM rule. We offer easily implementable algorithms for computing the EWM rule and an application using experimental data from the National JTPA Study.

Type: Working / discussion paper
Title: Who should be Treated? Empirical Welfare Maximization Methods for Treatment Choice
Open access status: An open access version is available from UCL Discovery
DOI: 10.1920/wp.cem.2015.1015
Publisher version: http://dx.medra.org/10.1920/wp.cem.2017.2417
Language: English
Additional information: This is the published version of record. For information on re-use, please refer to the publisher’s terms and conditions.
UCL classification: UCL
UCL > Provost and Vice Provost Offices
UCL > Provost and Vice Provost Offices > UCL SLASH
UCL > Provost and Vice Provost Offices > UCL SLASH > Faculty of S&HS
UCL > Provost and Vice Provost Offices > UCL SLASH > Faculty of S&HS > Dept of Economics
URI: https://discovery.ucl.ac.uk/id/eprint/1522145
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