Jiaying Gu, University of Toronto Mississauga

A Duel Approach to Robust Counterfactuals

Joint with Thomas Russell

Abstract: We study the identification of scalar counterfactual parameters in partially identified structural models, paying particular attention to relaxing parametric distributional assumptions on the latent variables. We begin by studying some recently proposed characterizations of the identified set for scalar counterfactual parameters, which demonstrate how to construct bounds by solving a sequence of optimization problems. Treating these as the primal problems, we use results from random set theory and convex analysis to derive the corresponding Fenchel dual problems. Unlike the primal problems, the dual problems can handle continuous outcome variables and covariates, and can easily allow the researcher to explore sensitivity of their results to a baseline parametric distribution for the latent variables. We then investigate computational issues in detail, and propose an algorithm for estimation and inference. Finally, we apply the procedure to airline data from Ciliberto and Tamer (2009), and investigate the sensitivity of their conclusions to parametric distributional assumptions.