Inferring Welfare Maximizing Treatment Assignment under Budget Constraints
We consider the problem of efficiently allocating a binary treatment among a target population based on a set of discrete and continuous observed characteristics. The goal is to maximize the population mean of an eventual outcome when a budget constraint limits what fraction of the population can be treated. Using sample data resulting from randomized treatment allocation, the ATE conditional on covariates (CATE) is nonparametrically estimated in a first step. The optimal treatment threshold and resulting value function, which are non-smooth functionals of the CATE, are estimated based on sample realizations of the estimated CATE. We derive large-sample distribution theory for these estimates and for the estimated dual value, i.e. the minimum resources needed to attain a specific average outcome via efficient treatment assignment. These inferential methods are applied to the optimal provision of anti-malaria bed nets, using data from a randomized experiment conducted in western Kenya. We find that a government which can afford to distribute subsidized bed nets 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 can be extended to infer optimal design of eligibility in conditional cash transfer programs.
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