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Generalized Optimal Transport

Andrei Voronin

arXiv 30 Jul 2025 · Econometrics

arXiv:2507.22422 · PDF · Extracted main text

Abstract

Many causal and structural parameters in economics can be identified and estimated by computing the value of an optimization program over all distributions consistent with the model and the data. Existing tools apply when the data is discrete, or when only disjoint marginals of the distribution are identified, which is restrictive in many applications. We develop a general framework that yields sharp bounds on a linear functional of the unknown true distribution under i) an arbitrary collection of identified joint subdistributions and ii) structural conditions, such as (conditional) independence. We encode the identification restrictions as a continuous collection of moments of characteristic kernels, and use duality and approximation theory to rewrite the infinite-dimensional program over Borel measures as a finite-dimensional program that is simple to compute. Our approach yields a consistent estimator that is $\sqrt{n}$-uniformly valid for the sharp bounds. In the special case of empirical optimal transport with Lipschitz cost, where the minimax rate is $n^{2/d}$, our method yields a uniformly consistent estimator with an asymmetric rate, converging at $\sqrt{n}$ uniformly from one side.

Citation extraction

61
references
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in-text mentions
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distinct cited
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self-citations
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Most heavily cited references

The works this paper leans on most, across its whole bibliography — not restricted to papers in our corpus. Ranked by composite intensity, which combines how often a work is mentioned, how many sections mention it, and how much of that falls in the main text rather than the appendix.

ReferenceIntensityMentionsSectionsMain text
1Manole, T. and J. Niles-Weed (2024) Sharp convergence rates for empirical optimal transport with smooth costs1.00064100%
2Athey, S., R. Chetty, and G. Imbens (2020) Combining experimental and observational data to estimate treatment effects on long term outcomes1.00053100%
3Voronin, A (2025) Linear programming approach to partially identified econometric models self1.00053100%
4Ober-Reynolds, D (2023) Estimating functionals of the joint distribution of potential outcomes with optimal transport0.9416383%
5Mogstad, M., A. Santos, and A. Torgovitsky (2018) Using instrumental variables for inference about policy relevant treatment parameters0.87462100%
6Horowitz, J. L (2011) Applied nonparametric instrumental variables estimation0.84333100%
7Balke, A. and J. Pearl (1994) Counterfactual probabilities: Computational methods, bounds and applications, in0.81142100%
8Balke, A. and J. Pearl (1997) Bounds on treatment effects from studies with imperfect compliance0.81142100%
9Galichon, A. and M. Henry (2011) Set Identification in Models with Multiple Equilibria0.81142100%
10Lafférs, L (2019) Bounding average treatment effects using linear programming0.81142100%

Showing the top 10 of 62 scored citations.

Cited by, within the corpus

arXiv econ.EM papers that cite this one, ranked by how heavily they lean on it.

Citing paperIntensityMentionsSections
1Identification of Long-Term Treatment Effects via Temporal Links, Observational, and Experimental Data0.40511
2Inference in partially identified moment models via regularized optimal transport0.40511