Designing the menu of licenses for foster care

In the United States, prospective foster parents must become licensed by a child welfare agency before a foster child can be placed in their care. This paper contributes by developing a theoretical matching model to study the optimal menu of licenses designed to screen foster parents. We construct a two-sided matching model with heterogeneous agents, adverse selection, search frictions, and a designer who coordinates match formation through a menu of contracts. We focus on incentive compatible contracts, examine optimal allocations and transfers, and analyze equilibrium sorting patterns. There are three main results: (i) optimal allocation calls for a segregation of the market, (ii) a simple transfer schedule does the job, (iii) complementarities do not ensure that Positive Assortative Matching (PAM) will arise in equilibrium, thus we provide an additional condition that guarantees it. Our results suggests that the menu of licenses used in practice, exhibits some of the properties of the optimal solution. However, the menu might not be reaching its screening objective.