Search and Matching for Adoption from Foster Care

More than 100,000 children in the US foster care system are currently waiting for an adoptive placement. Adoption agencies differ significantly in what systems they use to identify matches between families and children. We consider two prominent alternatives: (1) family-driven search, where families respond to announcements made by the caseworker responsible for a child, and (2) caseworker-driven search, where caseworkers utilize a software tool to perform a targeted search for families. In this work, we compare these two systems via a game-theoretic analysis. We introduce a dynamic search-and-matching model that captures the heterogeneous preferences of families and children. This allows us to study their incentives during the search process, and we can compare the resulting welfare of the two systems in equilibrium. We first show that, in general, no system dominates the other, neither in terms of family welfare nor in terms of child welfare. This result maybe surprising, given that the caseworker-driven approach employs a less wasteful search process. However, we do identify various advantages of the caseworker-driven approach. Our main theoretical result establishes that the equilibrium outcomes in caseworker-driven search can Pareto-dominate the outcomes in family-driven search, but not the other way around. We illustrate our results numerically to demonstrate the effect different model parameters (e.g., search costs and discount factors) have on welfare.