Before revision:  The latter requires the development of novel tests of linear hypotheses for partially identified parameters . In doing so, we provide new algorithms for the calculation and statistical inference in nonparametric counterfactual analysis for a general partially identified model.
After revision:  The latter requires the development of novel tests of linear hypotheses for partially identified parameters to estimate the proportion of the population who are revealed better off due to a price change in the latter application. This new technique can be used for nonparametric counterfactual analysis for a general partially identified model.