A1672
Title: A dual approach to Wasserstein-robust counterfactuals
Authors: Thomas Russell - Carleton University (Canada) [presenting]
Jiaying Gu - University of Toronto (Canada)
Abstract: The identification of scalar counterfactual parameters is studied in partially identified structural models, paying particular attention to relaxing parametric distributional assumptions on the latent variables. Bounds on scalar counterfactual parameters are shown to be constructed without parametric distributional assumptions by solving two infinite-dimensional optimization problems. Treating these as the primal problems, results from random set theory are used and analysis is convexed to reformulate the problems as finite-dimensional convex optimization problems involving the Aumann expectation of a random set, and then the corresponding Fenchel dual problems are derived. The dual problems can handle outcome variables and covariates with infinite support, and can easily allow a researcher to explore the sensitivity of their results to a baseline parametric distribution for the latent variables using the Wasserstein distance. The approach is compared to another dual approach by a prior study, and an algorithm for estimation and inference is proposed. Finally, the procedure is applied to airline data from another study and bounds on counterfactual market entry probabilities are constructed while exploring the robustness of a parametric distribution for the latent variables.
