In the first chapter, I study the two-sided, dynamic matching problem that occurs in the United States (US) foster care system. In this market, foster parents and foster children can form reversible foster matches, which may disrupt, continue in a reversible state, or transition into permanency via adoption. I first present an empirical analysis that yields four new stylized facts related to match transitions of children in foster care and their exit through adoption. Thereafter, I develop a two-sided dynamic matching model with five key features: (a) children are heterogeneous (with and without a disability), (b) children must be foster matched before being adopted, (c) children search for parents while foster matched to another parent, (d) parents receive a smaller per-period payoff when adopting than fostering (capturing the presence of a financial penalty on adoption), and (e) matches differ in their quality. I use the model to derive conditions for the stylized facts to arise in equilibrium and carry out predictions regarding match quality. The main insight is that the intrinsic disadvantage (being less preferred by foster parents) faced by children with a disability exacerbates due to the penalty. Moreover, I show that foster parents in high-quality matches (relative to foster parents in low-quality matches) might have fewer incentives to adopt.
In the second chapter, I study the Minnesota's 2015 Northstar Care Program which eliminated the adoption penalty (i.e., the decrease in fostering-based financial transfers associated with adoption) for children aged six and older, while maintaining it for children under age six. Using a differences-in-differences estimation strategy that controls for a rich set of covariates, I find that parents were responsive to the change in direct financial payments; the annual adoption rate of older foster children (aged six to eleven) increased by approximately 8 percentage points (24% at the mean) as a result of the program. I additionally find evidence of strategic adoption behavior as the adoption rate of younger children temporarily increased by 9 percentage points (23% at the mean) while the adoption rate of the oldest children (aged fifteen) temporarily decreased by 9 percentage points (65% at the mean) in the year prior to the program's implementation.