Foster Care: A Dynamic Matching Approach (Job Market Paper) [Last Updated: November 14, 2019]

Abstract. 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 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. An interesting 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.

Abstract. Aimed at increasing the adoption rate of older children, Minnesota's 2015 Northstar Care Program 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 difference-in-differences estimation strategy that controls for a rich set of covariates, we find that parents were responsive to this 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. We additionally find evidence of strategic adoption behavior as the adoption rate of younger children temporarily increased by 9 percentage points (22% at the mean) in the year prior to the program's implementation.

Assortative Matching with On-the-Match Search with Hector Chade, in progress

Abstract. We analyze two-sided matching markets with heterogeneous agents who search for partners while unmatched or matched. We contribute by finding conditions on the match payoff function such that every equilibrium exhibits Positive Assortative Matching (PAM) when on-the match search is allowed, and utility is strictly non-transferable. Since match-status and match-partners may vary over time, we say that an equilibrium exhibits PAM if the conditional cumulative distribution function over matches is increasing in the agents' attributes. The reversibility on matches adds a trade-off absent in models where matches are irreversible: agents not only care about the payoff received from the match but also the likelihood that the partner leaves, and they become unmatched. In our environment, the probability that a match disrupts is an endogenous object determined in equilibrium and can potentially vary across agents' attributes. We find that, in equilibrium, partners who produce higher payoffs are not always preferred since there is a higher probability that they leave to form a new match. Preliminary results suggest that, if the match payoff function is strictly increasing in the partner's attribute, then the equilibrium sorting exhibits PAM. Currently, we are generalizing the analysis in several directions, including allowing for transfers.