Andrei Voronin
arXiv 30 Jul 2025 · Econometrics
arXiv:2507.22422 · PDF · Extracted main text
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.
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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.
| Reference | Intensity | Mentions | Sections | Main text | |
|---|---|---|---|---|---|
| 1 | Manole, T. and J. Niles-Weed (2024) Sharp convergence rates for empirical optimal transport with smooth costs | 1.000 | 6 | 4 | 100% |
| 2 | Athey, S., R. Chetty, and G. Imbens (2020) Combining experimental and observational data to estimate treatment effects on long term outcomes | 1.000 | 5 | 3 | 100% |
| 3 | Voronin, A (2025) Linear programming approach to partially identified econometric models self | 1.000 | 5 | 3 | 100% |
| 4 | Ober-Reynolds, D (2023) Estimating functionals of the joint distribution of potential outcomes with optimal transport | 0.941 | 6 | 3 | 83% |
| 5 | Mogstad, M., A. Santos, and A. Torgovitsky (2018) Using instrumental variables for inference about policy relevant treatment parameters | 0.874 | 6 | 2 | 100% |
| 6 | Horowitz, J. L (2011) Applied nonparametric instrumental variables estimation | 0.843 | 3 | 3 | 100% |
| 7 | Balke, A. and J. Pearl (1994) Counterfactual probabilities: Computational methods, bounds and applications, in | 0.811 | 4 | 2 | 100% |
| 8 | Balke, A. and J. Pearl (1997) Bounds on treatment effects from studies with imperfect compliance | 0.811 | 4 | 2 | 100% |
| 9 | Galichon, A. and M. Henry (2011) Set Identification in Models with Multiple Equilibria | 0.811 | 4 | 2 | 100% |
| 10 | Lafférs, L (2019) Bounding average treatment effects using linear programming | 0.811 | 4 | 2 | 100% |
Showing the top 10 of 62 scored citations.
arXiv econ.EM papers that cite this one, ranked by how heavily they lean on it.
| Citing paper | Intensity | Mentions | Sections | |
|---|---|---|---|---|
| 1 | Identification of Long-Term Treatment Effects via Temporal Links, Observational, and Experimental Data | 0.405 | 1 | 1 |
| 2 | Inference in partially identified moment models via regularized optimal transport | 0.405 | 1 | 1 |