We analyze the welfare effects of voucher provision in the DC Opportunity Scholarship Program (OSP), a school voucher program in Washington, DC, that randomly allocated a voucher to students. To do so, we develop new discrete choice tools to learn about the average willingness to pay for a voucher of a given amount and its average costs in a nonparametric model of school choice. Our tools exploit the insight that these welfare parameters can be expressed as functions of the underlying demand for the different schools. However, while the random allocation of the voucher reveals the value of demand at two prices, the parameters generally depend on their values beyond these prices. Our tools show how to sharply characterize what we can learn when demand is allowed to remain entirely nonparametric or to be parameterized in a flexible manner, both of which imply that the parameters are not necessarily point identified. Applying our tools to  the OSP, we find that provision of the status-quo as well as a wide range of counterfactual voucher amounts has a positive net average benefit. These positive results arise due to the presence of many low-tuition schools in the program; removing these schools from the program can result in a negative net average benefit.
We develop new robust discrete choice tools to learn about the average willingness to pay and average cost of a school voucher in a program that randomly allocates vouchers. We consider a nonparametric, nonseparable choice model that places no restrictions on the functional form of utilities or the distribution of unobserved heterogeneity. We exploit the insight that the welfare parameters in this model can be expressed as functions of the demand for the different schools. However, while the random allocation of the voucher reveals the value of demand at two prices, the parameters generally depend on its values beyond these prices. We show how to sharply characterize what we can learn when demand is specified to be entirely nonparametric or to be parameterized in a flexible manner, both of which imply that the parameters are not necessarily point identified. We use our tools to analyze the welfare effects of voucher provision in the DC Opportunity Scholarship Program, a school voucher program in Washington, DC. We find that the provision of both the status-quo voucher and a wide range of counterfactual vouchers of different amounts have positive benefits net of costs. In comparison, traditional logit models produce estimates towards the lower end of our bounds, and hence may understate the benefits. We also find that the positive results can be explained by the popularity of low-tuition schools in the program; removing them from the program can result in a negative net benefit.
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