[Paper Review] Empirical Welfare Maximization with Constraints

Liyang Sun|arXiv (Cornell University)|Mar 29, 2021

Healthcare Policy and Management18 references4 citations

TL;DR

This paper extends Empirical Welfare Maximization to settings with uncertain program costs by proposing two new econometric rules: a mistake-controlling rule that ensures budget feasibility with high probability, and a trade-off rule that optimally balances benefit gains against cost overruns. The key contribution is enabling optimal eligibility criterion selection under realistic budget uncertainty due to imperfect take-up and heterogeneous costs.

ABSTRACT

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.

Motivation & Objective

• To address the gap in existing Empirical Welfare Maximization (EWM) methods that assume known program costs, which is unrealistic due to imperfect take-up and heterogeneous individual needs.
• To develop statistical rules that select optimal eligibility criteria when the budget required for implementation is unknown and must be estimated from experimental data.
• To ensure that the selected eligibility rules are both asymptotically feasible (satisfy the budget constraint with high probability) and asymptotically optimal (maximize expected welfare).
• To provide policymakers with two distinct decision rules aligned with different risk preferences: one conservative (mistake-controlling), one more aggressive (trade-off).
• To empirically demonstrate the methods using data from the Oregon Health Insurance Experiment (OHIE), deriving a budget-constrained Medicaid expansion policy.

Proposed method

• Proposes the mistake-controlling rule, which selects an eligibility criterion that maximizes expected benefit while constraining the probability of budget violation to be below a pre-specified level α.
• Develops the trade-off rule, which incorporates a penalty for budget violations proportional to the marginal benefit gain, allowing selection of infeasible criteria only if the benefit gain justifies the cost of exceeding the budget.
• Uses a uniform asymptotic framework to establish theoretical properties across a broad class of data distributions, ensuring robustness to model misspecification.
• Employs a Gaussian approximation to the joint distribution of benefit and cost estimates to compute critical values for the mistake-controlling rule, relying on uniform consistency of the covariance estimator.
• Applies the methods to the OHIE dataset, using self-reported health as a proxy for benefit and estimating costs via experimental data.
• Calibrates the trade-off parameter λ using a conservative estimate of the value of a statistical life year (VSLY), setting λ = 1/(0.6 × 100,000) based on QALY gains from improved health status.

Experimental results

Research questions

• RQ1 How can we select an optimal eligibility criterion for a welfare program when the cost of implementation is unknown and must be estimated from experimental data?
• RQ2 What statistical rules can ensure that the selected eligibility criterion satisfies a budget constraint with high probability, even when costs are uncertain?
• RQ3 How can we optimally trade off the expected benefit of expanding eligibility against the cost of violating the budget constraint?
• RQ4 Under what conditions do the proposed rules achieve uniform asymptotic feasibility and uniform asymptotic optimality?
• RQ5 How do the proposed rules compare to the standard EWM approach in terms of feasibility and welfare performance under cost uncertainty?

Key findings

• The mistake-controlling rule ensures uniform asymptotic feasibility, meaning it selects only feasible eligibility criteria with high probability as the sample size grows.
• The trade-off rule achieves uniform asymptotic optimality, meaning it selects eligibility criteria that maximize expected welfare even when some violate the budget constraint.
• The standard EWM approach, which assumes known costs, fails to satisfy either uniform asymptotic feasibility or optimality under cost uncertainty.
• In the empirical application to the OHIE, the simulation study suggests that budget violations under the trade-off rule are not prohibitively costly, supporting its practical viability.
• The choice between the two rules should align with policymakers’ risk preferences: the mistake-controlling rule is suitable for financially conservative policymakers, while the trade-off rule is better for those seeking broader coverage.