This paper concerns the problem of allocating a binary treatment among a target population based on discrete and continuous observed covariates. The goal is to maximize the mean social utility of an eventual outcome when a budget constraint limits what fraction of the population can be treated. We propose a treatment allocation procedure based on sample data from randomized treatment assignment. We examine this procedure in the light of statistical decision theory and derive asymptotic frequentist properties of the allocation rule and the welfare generated from it. The resulting distribution theory is used to conduct inference on the welfare loss resulting from restricted covariate choice and on the dual value, i.e. the minimum resources needed to attain a specific average welfare via efficient treatment assignment. The methodology is applied to the optimal provision of anti-malaria bed net subsidies, using data from a randomized experiment conducted in western Kenya. We find that a government which can afford to distribute bed net subsidies to only 50% of its target population can, with an efficient allocation rule based on multiple covariates, increase bed-net use by 8 percentage points (25 percent) relative to random allocation and by 4 percentage points (11 percent) relative to one based on wealth only. Our methods do not rely on functional form assumptions and can be extended to situations encompassing conditional cash transfers, imperfect treatment take-up and spillover effects on non-eligibles.
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This paper was revised on October 6, 2009
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