Identification with Latent Choice Sets

In a common experimental format, individuals are randomly assigned to either a treatment group with access to a program or a control group without access. In such experiments, analyzing the average effects of the treatment of program access may be hindered by the problem that some control individuals do not comply with their assigned status and receive program access from outside the experiment. Available tools to account for such a problem typically require the researcher to observe the receipt of program access for every individual. However, in many experiments, this is not the case as data is not collected on where any individual received access. 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. I propose a nonparametric selection model with latent choice sets to relate where access was received to the treatment assignment status, participation decision and outcome, and a linear programming procedure to compute the identified set for parameters evaluating the average effects of program access in this model. I illustrate the framework by analyzing the average effects of Head Start preschool access using the Head Start Impact Study. I nd that the provision of Head Start access induces parents to enroll their child into Head Start and also positively impacts test scores, and that these effects heterogeneously depend on the availability of access to an alternative preschool.