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The Unreasonable Effectiveness of Optimal Transport in Economics

Author

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  • Alfred Galichon

    (NYU - NYU System, ECON - Département d'économie (Sciences Po) - Sciences Po - Sciences Po - CNRS - Centre National de la Recherche Scientifique)

Abstract

Optimal transport has become part of the standard quantitative economics toolbox. It is the framework of choice to describe models of matching with transfers, but beyond that, it allows to: extend quantile regression; identify discrete choice models; provide new algorithms for computing the random coefficient logit model; and generalize the gravity model in trade. This paper offer a brief review of the basics of the theory, its applications to economics, and some extensions.

Suggested Citation

  • Alfred Galichon, 2021. "The Unreasonable Effectiveness of Optimal Transport in Economics," SciencePo Working papers Main hal-03936221, HAL.
  • Handle: RePEc:hal:spmain:hal-03936221
    Note: View the original document on HAL open archive server: https://sciencespo.hal.science/hal-03936221
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    References listed on IDEAS

    as
    1. Rust, John, 1987. "Optimal Replacement of GMC Bus Engines: An Empirical Model of Harold Zurcher," Econometrica, Econometric Society, vol. 55(5), pages 999-1033, September.
    2. Head, Keith & Mayer, Thierry, 2014. "Gravity Equations: Workhorse,Toolkit, and Cookbook," Handbook of International Economics, in: Gopinath, G. & Helpman, . & Rogoff, K. (ed.), Handbook of International Economics, edition 1, volume 4, chapter 0, pages 131-195, Elsevier.
    3. Ivar Ekeland & James J. Heckman & Lars Nesheim, 2004. "Identification and Estimation of Hedonic Models," Journal of Political Economy, University of Chicago Press, vol. 112(S1), pages 60-109, February.
    4. Pierre-André Chiappori & Robert McCann & Lars Nesheim, 2010. "Hedonic price equilibria, stable matching, and optimal transport: equivalence, topology, and uniqueness," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 42(2), pages 317-354, February.
    5. repec:hal:spmain:info:hdl:2441/5rkqqmvrn4tl22s9mc4ao8ocg is not listed on IDEAS
    6. Alfred Galichon, 2016. "Optimal transport methods in economics," Post-Print hal-03256830, HAL.
    7. Victor Chernozhukov & Alfred Galichon & Marc Hallin & Marc Henry, 2014. "Monge-Kantorovich Depth, Quantiles, Ranks, and Signs," Papers 1412.8434, arXiv.org, revised Sep 2015.
    8. Odran Bonnet & Alfred Galichon & Yu-Wei Hsieh & Keith O’Hara & Matt Shum, 2022. "Yogurts Choose Consumers? Estimation of Random-Utility Models via Two-Sided Matching," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 89(6), pages 3085-3114.
    9. repec:hal:wpspec:info:hdl:2441/5rkqqmvrn4tl22s9mc4ao8ocg is not listed on IDEAS
    10. Alfred Galichon & Scott Duke Kominers & Simon Weber, 2019. "Costly Concessions: An Empirical Framework for Matching with Imperfectly Transferable Utility," Journal of Political Economy, University of Chicago Press, vol. 127(6), pages 2875-2925.
    11. Alfred Galichon & Ivar Ekeland & Marc Henry, 2009. "Comonotonic measures of multivariates risks," Working Papers hal-00401828, HAL.
    12. Alfred Galichon, 2016. "Optimal transport methods in economics," SciencePo Working papers hal-03256830, HAL.
    13. Guillaume Carlier & Victor Chernozhukov & Alfred Galichon, 2015. "Vector quantile regression: an optimal transport approach," CeMMAP working papers 58/15, Institute for Fiscal Studies.
    14. Alfred Galichon & Pierre Henri-Labordère & Nizar Touzi, 2014. "A stochastic control approach to No-Arbitrage bounds given marginals, with an application to Lookback options," Post-Print hal-03460952, HAL.
    15. Kelso, Alexander S, Jr & Crawford, Vincent P, 1982. "Job Matching, Coalition Formation, and Gross Substitutes," Econometrica, Econometric Society, vol. 50(6), pages 1483-1504, November.
    16. Carlier, Guillaume & Dupuy, Arnaud & Galichon, Alfred & Sun, Yifei, 2021. "SISTA: Learning Optimal Transport Costs under Sparsity Constraints," IZA Discussion Papers 14397, Institute of Labor Economics (IZA).
    17. James E. Anderson & Eric van Wincoop, 2003. "Gravity with Gravitas: A Solution to the Border Puzzle," American Economic Review, American Economic Association, vol. 93(1), pages 170-192, March.
    18. Alfred Galichon & Pierre Henri-Labordère & Nizar Touzi, 2014. "A stochastic control approach to No-Arbitrage bounds given marginals, with an application to Lookback options," SciencePo Working papers Main hal-03460952, HAL.
    19. Alfred Galichon & Marc Henry, 2011. "Set Identification in Models with Multiple Equilibria," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 78(4), pages 1264-1298.
    20. Victor Chernozhukov & Alfred Galichon & Marc Henry & Brendan Pass, 2021. "Identification of Hedonic Equilibrium and Nonseparable Simultaneous Equations," Journal of Political Economy, University of Chicago Press, vol. 129(3), pages 842-870.
    21. Becker, Gary S, 1973. "A Theory of Marriage: Part I," Journal of Political Economy, University of Chicago Press, vol. 81(4), pages 813-846, July-Aug..
    22. Khai Xiang Chiong & Alfred Galichon & Matt Shum, 2016. "Duality in dynamic discrete‐choice models," Quantitative Economics, Econometric Society, vol. 7(1), pages 83-115, March.
    23. Eugene Choo & Aloysius Siow, 2006. "Who Marries Whom and Why," Journal of Political Economy, University of Chicago Press, vol. 114(1), pages 175-201, February.
    24. Koenker, Roger W & Bassett, Gilbert, Jr, 1978. "Regression Quantiles," Econometrica, Econometric Society, vol. 46(1), pages 33-50, January.
    25. Galichon, Alfred & Henry, Marc, 2012. "Dual theory of choice with multivariate risks," Journal of Economic Theory, Elsevier, vol. 147(4), pages 1501-1516.
    26. Berry, Steven & Levinsohn, James & Pakes, Ariel, 1995. "Automobile Prices in Market Equilibrium," Econometrica, Econometric Society, vol. 63(4), pages 841-890, July.
    27. repec:hal:spmain:info:hdl:2441/4c5431jp6o888pdrcs0fuirl40 is not listed on IDEAS
    28. repec:hal:spmain:info:hdl:2441/5rkqqmvrn4tl22s9mc4b1h6b4 is not listed on IDEAS
    29. Arnaud Dupuy & Alfred Galichon & Yifei Sun, 2019. "Estimating Matching Affinity Matrices under Low-Rank Constraints," Post-Print hal-03948102, HAL.
    30. Paulo Guimarães & Pedro Portugal, 2010. "A simple feasible procedure to fit models with high-dimensional fixed effects," Stata Journal, StataCorp LP, vol. 10(4), pages 628-649, December.
    31. repec:hal:spmain:info:hdl:2441/64itsev5509q8aa5mrbhi0g0b6 is not listed on IDEAS
    32. repec:dau:papers:123456789/2278 is not listed on IDEAS
    33. Alfred Galichon & Ivar Ekeland & Marc Henry, 2009. "Comonotonic measures of multivariates risks," Working Papers hal-00401828, HAL.
    34. Ning Sun & Zaifu Yang, 2006. "Equilibria and Indivisibilities: Gross Substitutes and Complements," Econometrica, Econometric Society, vol. 74(5), pages 1385-1402, September.
    35. A. Galichon & P. Henry-Labord`ere & N. Touzi, 2014. "A stochastic control approach to no-arbitrage bounds given marginals, with an application to lookback options," Papers 1401.3921, arXiv.org.
    36. Steven T. Berry, 1994. "Estimating Discrete-Choice Models of Product Differentiation," RAND Journal of Economics, The RAND Corporation, vol. 25(2), pages 242-262, Summer.
    37. repec:dau:papers:123456789/6486 is not listed on IDEAS
    38. Alfred Galichon, 2016. "Optimal Transport Methods in Economics," Economics Books, Princeton University Press, edition 1, number 10870.
    39. repec:hal:wpspec:info:hdl:2441/5rkqqmvrn4tl22s9mc4b1h6b4 is not listed on IDEAS
    40. repec:hal:wpspec:info:hdl:2441/dambferfb7dfprc9m01g1j1k2 is not listed on IDEAS
    41. Alfred Galichon, 2016. "Optimal transport methods in economics," SciencePo Working papers Main hal-03256830, HAL.
    42. Victor Chernozhukov & Alfred Galichon & Marc Hallin & Marc Henry, 2014. "Monge-Kantorovich Depth, Quantiles, Ranks, and Signs," Papers 1412.8434, arXiv.org, revised Sep 2015.
    43. Carlier, Guillaume & Chernozhukov, Victor & Galichon, Alfred, 2017. "Vector quantile regression beyond the specified case," Journal of Multivariate Analysis, Elsevier, vol. 161(C), pages 96-102.
    44. repec:hal:spmain:info:hdl:2441/dambferfb7dfprc9m01g1j1k2 is not listed on IDEAS
    45. Alfred Galichon & Pierre Henri-Labordère & Nizar Touzi, 2014. "A stochastic control approach to No-Arbitrage bounds given marginals, with an application to Lookback options," SciencePo Working papers hal-03460952, HAL.
    46. Guillaume Carlier & Victor Chernozhukov & Alfred Galichon, 2016. "Vector Quantile Regression: An Optimal Transport Approach," SciencePo Working papers hal-03567920, HAL.
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    1. Gunsilius, Florian F., 2023. "A condition for the identification of multivariate models with binary instruments," Journal of Econometrics, Elsevier, vol. 235(1), pages 220-238.

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