Inferring Welfare Maximizing Treatment Assignment Under Budget Constraints

71 Pages Posted: 11 Apr 2011

Date Written: April 10, 2011


This paper concerns the problem of allocating a binary treatment among a target population based on observed covariates. The goal is to (i) maximize the mean social welfare arising from an eventual outcome distribution, when a budget constraint limits what fraction of the population can be treated and (ii) to infer the dual value, i.e. the minimum resources needed to attain a specific level of mean welfare via efficient treatment assignment. We consider a treatment allocation procedure based on sample data from randomized treatment assignment and derive asymptotic frequentist confidence interval for the welfare generated from it. The welfare estimate is semiparametrically efficient and its asymptotic distribution informs the choice of conditioning covariates when covariates are financially expensive to measure. The methodology is applied to the efficient provision of anti-malaria bed net subsidies, using data from a randomized experiment conducted in Western Kenya. We find that an allocation rule based on wealth and two discrete covariates can lead to a gain in efficiency of 13 percentage points, compared to an allocation based on the two discrete covariates only. However, if the cost of collecting wealth data is greater than $0.52 per household, means-testing the subsidization of bednets may not be optimal.

Suggested Citation

Bhattacharya, Debopam, Inferring Welfare Maximizing Treatment Assignment Under Budget Constraints (April 10, 2011). Available at SSRN: or

Debopam Bhattacharya (Contact Author)

University of Cambridge ( email )

Sidgwick Site
Austin Robinson Building
Cambridge, CB3 9DD
United Kingdom

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