Allocation of Funds in Bilevel Subsidy Welfare Programs

Most subsidy welfare programs operate in a bilevel hierarchical structure, wherein a funding agency allocates funds to multiple service agencies. These service agencies invest in activities within their areas to generate social impact for beneficiaries by enhancing the quantity and quality of services at local providers. The funds allocation decisions in such programs are complicated by consideration of equity in social impact generated across different areas, information asymmetry between different entities, and intricate relationships among contextual factors in social impact generation. We develop a model to analyze how the funding agency’s funds allocation decisions lead to the most overall social impact in an equitable manner. Considering two scenarios involving restrictions on the use of additional funds that may become available for only one area or one activity, we find that: Under the area-only scenario, the funding agency should allocate more funds to a service agency when either the other service agency may receive more additional funds, it has a relatively balanced mix of subsidy-accepting and non-accepting providers, or outreach activity is more likely to yield a higher investment return and it has fewer non-accepting providers; Under the activity-only scenario, the optimal split of funds between the service agencies could be significantly different when allocating initial versus additional funds. Further, comparison of decisions with and without equity consideration shows that the effect of the contextual factors on the optimal allocation decisions could be directionally opposite. Given the growing impetus to consider equity within their operations, we demonstrate how the funding agencies should adjust their allocation strategies in the presence of such considerations. Further, using a case study based on Massachusetts’ child care subsidy program, we illustrate that the proposed optimal decisions achieve equity while enhancing the overall social impact by approximately 3% versus current allocation decisions