Partial Identification in Moment Models withIncomplete Data—A Conditional Optimal Transport Approach∗

Abstract:
In this paper, we develop a unified approach to study partial identification
of a finite-dimensional parameter defined by a general moment model with in complete data. We establish a novel characterization of the identified set for the true parameter in terms of a continuum of inequalities defined by conditional optimal transport. For the special case of an affine moment model, we show that the identified set is convex and that its support function can be easily computed by solving a conditional optimal transport problem. For parameters that may not satisfy the moment model, we propose a two-step procedure to construct its identified set. Finally, we demonstrate the generality and effectiveness of our approach through several running examples.

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