We provide novel bounds on average treatment effects (on the treated) that are valid under an unconfoundedness assumption. Our bounds are designed to be robust in challenging situations, for example, when the conditioning variables take on a large number of different values in the observed...

This paper explores methods for inferring the causal effects of treatments on choices by combining data on real choices with hypothetical evaluations. We propose a class of estimators, identify conditions under which they yield consistent estimates, and derive their asymptotic distributions. The...