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Partial Identification in Moment Models with Incomplete Data--A Conditional Optimal Transport Approach

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  • Yanqin Fan
  • Hyeonseok Park
  • 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 general moment 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 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.

Suggested Citation

  • Yanqin Fan & Hyeonseok Park & Brendan Pass & Xuetao Shi, 2025. "Partial Identification in Moment Models with Incomplete Data--A Conditional Optimal Transport Approach," Papers 2503.16098, arXiv.org, revised Oct 2025.
    • 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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    Cited by:

    1. Ertian Chen, 2025. "Robust Structural Estimation under Misspecified Latent-State Dynamics," Papers 2510.22347, arXiv.org, revised Nov 2025.
    2. Romuald Meango & Marc Henry & Ismael Mourifie, 2025. "Combining stated and revealed preferences," Papers 2507.13552, arXiv.org, revised Nov 2025.
    3. D'Haultfoeuille, Xavier & Gaillac, Christophe & Maurel, Arnaud, 2025. "Linear Regressions with Combined Data," IZA Discussion Papers 18276, Institute of Labor Economics (IZA).

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