Before revision:  Our methods are computationally simple to implement, with the nuisance distribution effectively profiled out via a low-dimensional convex program . Our procedure delivers sharp bounds for the identified set of counterfactuals (i.e. without parametric assumptions about the distribution of unobservables) as the neighborhoods become large .
After revision:  Our procedure replaces the infinite-dimensional optimization with respect to the distribution by a finite-dimensional convex program and is therefore computationally simple to implement. We develop a novel MPEC implementation of our procedure to further simplify computation in models featuring endogenous parameters defined by equilibrium constraints. Our procedure recovers sharp bounds on the nonparametrically identified set of counterfactuals (i.e. without parametric assumptions about the distribution of unobservables) as the neighborhoods become large .