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Partial Identification in Moment Models with Incomplete Data via Optimal Transport

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  • Yanqin Fan
  • Brendan Pass
  • Xuetao Shi

Abstract

In this paper, we develop a unified approach to study partial identification of a finite-dimensional parameter defined by a moment equality model with incomplete data. We establish a novel characterization of the identified set for 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 through several running examples, including the linear projection model and two algorithmic fairness measures.

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  • Yanqin Fan & Brendan Pass & Xuetao Shi, 2025. "Partial Identification in Moment Models with Incomplete Data via Optimal Transport," Papers 2503.16098, arXiv.org.
    • Handle: RePEc:arx:papers:2503.16098
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    References listed on IDEAS

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    1. Arie Beresteanu & Francesca Molinari, 2008. "Asymptotic Properties for a Class of Partially Identified Models," Econometrica, Econometric Society, vol. 76(4), pages 763-814, July.
    2. Nathan Kallus & Xiaojie Mao & Angela Zhou, 2022. "Assessing Algorithmic Fairness with Unobserved Protected Class Using Data Combination," Management Science, INFORMS, vol. 68(3), pages 1959-1981, March.
    3. Bei, Xinyue, 2024. "Local linearization based subvector inference in moment inequality models," Journal of Econometrics, Elsevier, vol. 238(1).
    4. Yanqin Fan & Carlos A. Manzanares, 2017. "Partial identification of average treatment effects on the treated through difference-in-differences," Econometric Reviews, Taylor & Francis Journals, vol. 36(6-9), pages 1057-1080, October.
    5. Kaido, Hiroaki, 2016. "A dual approach to inference for partially identified econometric models," Journal of Econometrics, Elsevier, vol. 192(1), pages 269-290.
    6. Donald W. K. Andrews & Gustavo Soares, 2010. "Inference for Parameters Defined by Moment Inequalities Using Generalized Moment Selection," Econometrica, Econometric Society, vol. 78(1), pages 119-157, January.
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