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 find 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  .
Many experiments randomly assign individuals to either a treatment group with access to a program or a control group without such access. I study what we can learn about the average effects of providing access to the program given data from such experiments when individuals do not comply with their assigned status and when the data may only provide partial information on the receipt of program access across individuals. I propose a new nonparametric multiple treatment selection model that provides a general setup to define a range of parameters evaluating the effects of program access and to exploit the partial information the data may provide on where access was received . I illustrate how a computational procedure can be used to learn about these parameters in this model. Using the developed framework, I analyze the effects of providing access to the Head Start preschool program given data from the Head Start Impact Study. I find that providing access to Head Start can have positive effects on test scores and that these effects can negatively depend on whether access to an alternative preschool was available. In addition, I find that the earning benefits associated with the test score gains can outweigh the net costs for various policies providing access to Head Start .
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the treatment of program access may be hindered by the problem that some control
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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
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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
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the provision of Head Start access induces parents to enroll their child into Head Start and also positively impacts test scores ,
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was available. In addition, I find that the earning benefits associated with the test score gains can outweigh the net costs for various policies providing access to Head Start