Thomas Russell from Carleton University will present "Wasserstein-Robust Counterfactuals"

Abstract:

We study the identification of scalar counterfactual parameters in partially-identified structural models. We focus on relaxing parametric distributional assumptions on the latent variables and propose a method that allows a researcher to investigate the sensitivity of their results to deviations from a parametric distribution using the Wasserstein distance. We show that bounds on scalar counterfactual parameters can be constructed without parametric distributional assumptions by solving two infinite-dimensional optimization problems. Treating these as the primal problems, we use results from random set theory and convex analysis to reformulate the problems as finite-dimensional convex optimization problems involving the Aumann expectation of a random set, and then we derive the corresponding Fenchel dual problems. We then propose an algorithm for estimation, prove the consistency of our estimator, and derive its rate of convergence, which is nonstandard in our setting. Finally, we illustrate the method by revisiting the airline entry data from Ciliberto and Tamer (2009).