Foster Care: A Dynamic Matching Approach

This paper studies the two-sided dynamic matching problem that occurs in the US foster care system. In this market, foster parents and foster children can form reversible matches, which may separate, continue in their reversible state, or transition to permanency via adoption. I first present an empirical analysis that yields four new facts. Thereafter, I develop a two-sided search and matching model used to rationalize the empirical facts and carry out predictions regarding match quality. Interestingly, I find that match separation plays a crucial role in adoption by influencing the incentives of foster parents to adopt. Due to the presence of a financial penalty on adoption, parents accept the penalty in exchange for eliminating the likelihood that the child separates from the match in the future. Moreover, I show that the adoption penalty not only exacerbates the intrinsic disadvantage (being less preferred by foster parents) faced by children with a disability, but it also creates incentives for high-quality matches to not transit to adoption.