Allocation of Funds in Bilevel Subsidy Welfare Programs

Problem definition: Most subsidy welfare programs operate in a bilevel hierarchical structure, wherein a funding agency allocates funds to multiple service organizations. These service organizations invest in activities within their areas to generate societal impact for beneficiaries by enhancing the quantity and quality of services at local providers. The funds allocation decisions in such programs are complicated by the funding agency’s equity consideration, intricate relationships among contextual factors in societal impact generation, and information asymmetry between different entities about availability of additional funds for an agency. Methodology/results: We propose a model to analyze how the funding agency should allocate funds to generate the most societal impact equitably across areas. We show that the funding agency should direct more funds toward an area with a relatively balanced mix of subsidy-accepting and nonaccepting providers, or with fewer nonaccepting providers, and outreach activity is more likely to yield a higher investment return. Further, comparing the inequity levels and total societal impact under the proposed equity-ensuring method with those under other methods, we find that an efficiency-focused method enhances total societal impact, but can result in greater inequity, especially when there is a large across-area disparity in the size of beneficiaries. A simple formula-based method could achieve greater total societal impact, while not severely sacrificing equity in certain situations. Conversely, the equity-ensuring method always eliminates inequity by not severely sacrificing the total societal impact under a wide range of parameter values. Managerial implications: Given the growing impetus to consider equity within their operations, our equity-ensuring method helps the funding agencies adjust their allocation strategies to generate the greatest equitable impact. Finally, using a case study based on Massachusetts’ child care subsidy program, we illustrate that the proposed method achieves equity while enhancing the overall societal impact by approximately 3% versus the current formula-based method. Supplemental Material: The online appendix is available at https://doi.org/10.1287/msom.2022.0474 .