Empirical welfare maximization with constraints

Empirical Welfare Maximization (EWM) is a framework that can be used to select welfare program eligibility policies based on data. This paper extends EWM by allowing for uncertainty in estimating the budget needed to implement the selected policy, in addition to its welfare. Due to the additional estimation error, I show there exist no rules that achieve the highest welfare possible while satisfying a budget constraint uniformly over a wide range of DGPs. This differs from the setting without a budget constraint where uniformity is achievable. I propose an alternative trade-off rule and illustrate it with Medicaid expansion, a setting with imperfect take-up and varying program costs.