To find families for the more than 70,000 children in need of adoptive placements, most United States child welfare agencies have employed a family-driven search approach in which prospective families respond to announcements made by the agency. However, some agencies have switched to a caseworker-driven search approach in which the caseworker directly contacts families recommended for a child. We introduce a novel search-and-matching model that captures the key features of the adoption process and compare family-driven with caseworker-driven search in a game-theoretical framework. Under either approach, the equilibria are generated by threshold strategies and form a lattice structure. Our main theoretical finding then shows that no family-driven equilibrium can Pareto dominate any caseworker-driven outcome, whereas it is possible that each caseworker-driven equilibrium Pareto dominates every equilibrium attainable under family-driven search. We also find that, within our model, when families are sufficiently impatient, caseworker-driven search is better for all children. We numerically illustrate that most agents are better off under caseworker-driven search across a wide range of parameter values. Finally, we present an empirical study of an agency that switched to caseworker-driven search, finding a three-year adoption probability that outperformed a statewide benchmark by 44.9%, along with a statistically significant 54% higher adoption hazard rate.

翻译：为了给超过7万名需要安置的儿童寻找家庭，美国大多数儿童福利机构采用家庭驱动的搜寻方法，即潜在家庭对机构发布的公告进行响应。然而，部分机构已转向案例工作者驱动的搜寻方式，即由案例工作者直接联系被推荐给特定儿童的家庭。我们引入了一种新颖的搜寻与匹配模型，该模型捕捉了收养过程的关键特征，并在博弈论框架下比较了家庭驱动与案例工作者驱动的搜寻方式。在两种方法下，均衡均由阈值策略生成并形成格结构。我们的主要理论发现表明，没有任何家庭驱动均衡能帕累托支配任何案例工作者驱动结果，而每个案例工作者驱动均衡都有可能帕累托支配家庭驱动搜寻下可达到的所有均衡。我们还发现，在我们的模型中，当家庭足够缺乏耐心时，案例工作者驱动搜寻对所有儿童更有利。我们通过数值模拟表明，在广泛的参数范围内，大多数主体在案例工作者驱动搜寻下境况更优。最后，我们对一家转为案例工作者驱动搜寻的机构进行实证研究，发现其三年收养概率比全州基准高出44.9%，并且收养风险率具有统计显著性提高54%。