Who should be treated? Empirical welfare maximization methods for treatment choice

Toru Kitagawa () and Aleksey Tetenov ()
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Toru Kitagawa: Institute for Fiscal Studies and University College London

No CWP10/15, CeMMAP working papers from Centre for Microdata Methods and Practice, Institute for Fiscal Studies

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

Keywords: Randomized experiments; statistical treatment rules; minimax rate optimality; VC-dimension (search for similar items in EconPapers)
JEL-codes: C14 C21 C44 (search for similar items in EconPapers)
Date: 2015-03-10
New Economics Papers: this item is included in nep-exp
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Citations: View citations in EconPapers (16)

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Related works:
Journal Article: Who Should Be Treated? Empirical Welfare Maximization Methods for Treatment Choice (2018)
Working Paper: Who should be treated? Empirical welfare maximization methods for treatment choice (2017)
Working Paper: Who should be Treated? Empirical Welfare Maximization Methods for Treatment Choice (2015)
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