Before revision:  To do so, we develop new discrete choice tools to show how to use data with random allocation of school vouchers to characterize what we can learn about the welfare benefits of providing a voucher of a given amount, as measured by the average willingness to pay for that voucher , and these benefits net of the costs of providing that voucher. A novel feature of our tools is that they allow specifying the relationship of the demand for the various schoolswith respect to pricesto be entirely nonparametric or to be parameterized in a flexible manner, both of which do not necessarily imply that the welfare parameters are point identified.
After revision:  To do so, we develop new discrete choice tools to show how to use data with random allocation of school vouchers to characterize what we can learn about the welfare benefits of providing a voucher of a given amount, as measured by the average willingness to pay for that voucher , and these benefits net of the costs 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 various schoolswith respect to pricesto be entirely nonparametric or to be parameterized in a flexible manner, both of which do not necessarily imply that the welfare parameters are point identified.