Before revision:  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:  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 imply that the welfare parameters are point identified.