Estimating Welfare Effects in a Nonparametric Choice Model: The Case of School Vouchers

We develop new robust discrete choice tools to learn about the average willingness to pay for a price subsidy and its effects on demand given exogenous, discrete variation in prices. Our starting point is a nonparametric, nonseparable model of choice. We exploit the insight that our welfare parameters in this model can be expressed as functions of demand for the different alternatives. However, while the variation in the data reveals the value of demand at the observed 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 price subsidies provided by school vouchers in the DC Opportunity Scholarship Program. We robustly find that the provision of the status quo voucher and a wide range of counterfactual vouchers of different amounts have positive benefits net of costs. This positive effect 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. Relative to our bounds, we also find that comparable logit estimates potentially understate the benefits for certain voucher amounts, and provide a misleading sense of robustness for alternative amounts.