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Optimally-Transported Generalized Method of Moments

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  • Susanne Schennach
  • Vincent Starck

Abstract

We propose a novel optimal transport-based version of the Generalized Method of Moment (GMM). Instead of handling overidentification by reweighting the data to satisfy the moment conditions (as in Generalized Empirical Likelihood methods), this method proceeds by allowing for errors in the variables of the least mean-square magnitude necessary to simultaneously satisfy all moment conditions. This approach, based on the notions of optimal transport and Wasserstein metric, aims to address the problem of assigning a logical interpretation to GMM results even when overidentification tests reject the null, a situation that cannot always be avoided in applications. We illustrate the method by revisiting Duranton, Morrow and Turner's (2014) study of the relationship between a city's exports and the extent of its transportation infrastructure. Our results corroborate theirs under weaker assumptions and provide insight into the error structure of the variables.

Suggested Citation

  • Susanne Schennach & Vincent Starck, 2025. "Optimally-Transported Generalized Method of Moments," Papers 2511.05712, arXiv.org.
    • Handle: RePEc:arx:papers:2511.05712
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    References listed on IDEAS

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    1. Donald W.K. Andrews & Soonwoo Kwon, 2019. "Inference in Moment Inequality Models That Is Robust to Spurious Precision under Model Misspecification," Cowles Foundation Discussion Papers 2184, Cowles Foundation for Research in Economics, Yale University, revised Oct 2019.
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    10. Alfred Galichon, 2016. "Optimal transport methods in economics," SciencePo Working papers hal-03256830, HAL.
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    13. Susanne M. Schennach, 2016. "Recent Advances in the Measurement Error Literature," Annual Review of Economics, Annual Reviews, vol. 8(1), pages 341-377, October.
    14. Hall, Alastair R. & Inoue, Atsushi, 2007. "Corrigendum to: "The large sample behaviour of the generalized method of moments estimator in misspecified models": [Journal of Econometrics 114 (2003) 361-394]," Journal of Econometrics, Elsevier, vol. 141(2), pages 1417-1418, December.
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    Cited by:

    1. Grigory Franguridi & Laura Liu, 2025. "Inference in partially identified moment models via regularized optimal transport," Papers 2512.18084, arXiv.org, revised Jun 2026.
    2. Rami V. Tabri, 2026. "Distributional Change in Ordinal Data with Missing Observations: Minimal Mobility and Partial Identification," Papers 2604.12611, arXiv.org, revised Apr 2026.

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