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Identifying the Effects of a Program Offer with an Application to Head Start

Vishal Kamat

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Abstract: I develop tools to learn about the average effects of providing an offer to participate in a program given data from an experiment that randomizes offers. I allow for the complication that individuals may not comply with their assigned status in the sense that those who are not provided an offer may receive one from outside the experiment, and that the data may provide only partial information on the receipt of an offer across individuals. To do so, I propose a new nonparametric selection model with unobserved choice sets that provides a conceptual framework to define a range of parameters evaluating the effects of an offer, exploit the partial information available on offer receipt, and also consider an array of identifying assumptions. I illustrate how a computational procedure can be used to sharply learn about the parameters under the various assumptions. Using these tools, I analyze the effects of a policy that provides an offer to participate in the Head Start preschool program given data from the Head Start Impact Study. I find that such a policy affects a large number of children who take up the offer, and that they subsequently have positive effects on test scores. These effects primarily arise from children who do not have any preschool as an outside option. Performing a cost-benefit analysis, I find that the earning benefits associated with the test score gains can outweigh the net costs associated with the take up of the offer.

Date: 2017-11, Revised 2021-07
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