Grigory Franguridi, University of Southern California

"Inference in partially identified moment models via regularized optimal transport"

Abstract

Partial identification often arises from incomplete knowledge of the joint distribution of the data, even though the marginal distributions are point-identified. In such cases, bounds on a parameter of interest can be characterized as the solution to an optimal transport problem. To conduct inference on these bounds, we propose the use of entropic regularization, which adds a penalty term to the objective function that penalizes deviations of the joint distribution from the product of input distributions. We derive the $\sqrt{n}$-consistency and asymptotic normality of a general class of plug-in estimators for these bounds. Our theoretical results enable standard statistical inference for partially identified parameters in a wide range of applications, including the estimation of nonlinear treatment effects under unconfoundedness and the estimation of the Euler equation in macro-finance. We illustrate our methodology with Monte Carlo simulations for panel data models with selective attrition under the availability of refreshment samples.

(with Laura Liu)

Contact person: Jesper Riis-Vestergaard Sørensen