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

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  • Toru Kitagawa
  • Aleksey Tetenov

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.

Suggested Citation

  • Toru Kitagawa & Aleksey Tetenov, 2015. "Who should be Treated? Empirical Welfare Maximization Methods for Treatment Choice," Carlo Alberto Notebooks 402, Collegio Carlo Alberto.
    • Handle: RePEc:cca:wpaper:402
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    References listed on IDEAS

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    More about this item

    Keywords

    randomized experiments; statistical treatment rules; minimax rate optimality; VC-dimension.;
    All these keywords.

    JEL classification:

    • C21 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Cross-Sectional Models; Spatial Models; Treatment Effect Models
    • C44 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - Operations Research; Statistical Decision Theory
    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General

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