Partial Identification in Moment Models with Incomplete Data via Optimal Transport

Author: Yanqin Fan, Brendan Pass, and Xuetao Shi

In this talk, we present a unified approach to study partial identification of a finite-dimensional parameter defined by a moment equality model with incomplete data. We establish a characterization of the identified set of the true parameter in terms of a continuum of inequalities defined by optimal transport costs. For a special class of moment functions, we show that the identified set is convex and its support function can be easily computed by solving an optimal transport problem. We demonstrate the generality and effectiveness of our approach via several running examples including the linear projection model and algorithmic fairness measures in Kallus et al. (2022). Our results for the algorithmic fairness measures extend those for two protected classes in Kallus et al. (2022) to any finite number of protected classes and any finite number of measures. We also provide a detailed numerical illustration of our identified sets in the linear projection model and for the demographic disparity measure.