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

Abstract

This paper proposes an identification and estimation method that allows researchers to easily bound continuous functionals of the joint distribution in a completely nonparametric setting without the need to verify sharpness on a case-by-case basis. The focus is on a model where the selection mechanism is left completely unspecified. The method can sharply bound interesting parameters with analytic bounds that may be 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.