Sharp Bounds on Functionals of the Joint Distribution in the Analysis of Treatment Effects

This article proposes an identification and estimation method that allows researchers to bound continuous functionals of the joint distribution of potential outcomes from the literature on treatment effects. The focus is on a model where no restrictions are imposed on treatment selection. The method can sharply bound interesting parameters when analytical bounds are difficult to derive, can be used in settings in which instruments are available, and can easily accommodate additional model constraints. However, computational considerations for the method are found to be important and are discussed in detail. Supplementary materials for this article are available online.