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...

This paper describes a method for carrying out non-asymptotic inference on partially identifi ed parameters that are solutions to a class of optimization problems. The optimization problems arise in applications in which grouped data are used for estimation of a model's structural parameters....