  When designing eligibility criteria for welfare programs, policymakers
naturally want to target the individuals who will benefit the most. This paper
proposes two new econometric approaches to selecting an optimal eligibility
criterion when individuals' costs to the program are unknown and need to be
estimated. One is designed to achieve the highest benefit possible while
satisfying a budget constraint with high probability. The other is designed to
optimally trade off the benefit and the cost from violating the budget
constraint. The setting I consider extends the previous literature on Empirical
Welfare Maximization by allowing for uncertainty in estimating the budget
needed to implement the criterion, in addition to its benefit. Consequently, my
approaches improve the existing approach as they can be applied to settings
with imperfect take-up or varying program needs. I illustrate my approaches
empirically by deriving an optimal budget-constrained Medicaid expansion in the
US.
