Before revision:  In this setting, resource constraints limit preschool slots to only a few eligible children through an assignment mechanism that is not observed in the data, which in turn introduces unobserved heterogeneity in the child's choice set of care settings .
After revision:  In this paper, I develop a framework to show how data on only each individual's treatment assignment status, program participation decision and outcome can be exploited to learn about the average effects of program access .