IDEAS home Printed from https://ideas.repec.org/p/hal/wpaper/hal-03936221.html
   My bibliography  Save this paper

The Unreasonable Effectiveness of Optimal Transport in Economics

Author

Listed:
  • 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," Working Papers hal-03936221, HAL.
    • Handle: RePEc:hal:wpaper:hal-03936221
    Note: View the original document on HAL open archive server: https://sciencespo.hal.science/hal-03936221
    as

    Download full text from publisher

    File URL: https://sciencespo.hal.science/hal-03936221/document
    Download Restriction: no
    ---><---

    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. 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.
    5. 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.
    6. repec:hal:spmain:info:hdl:2441/5rkqqmvrn4tl22s9mc4ao8ocg is not listed on IDEAS
    7. 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.
    8. Alfred Galichon, 2016. "Optimal transport methods in economics," Post-Print hal-03256830, HAL.
    9. repec:hal:spmain:info:hdl:2441/64itsev5509q8aa5mrbhi0g0b6 is not listed on IDEAS
    10. Victor Chernozhukov & Alfred Galichon & Marc Hallin & Marc Henry, 2014. "Monge-Kantorovich Depth, Quantiles, Ranks, and Signs," Papers 1412.8434, arXiv.org, revised Sep 2015.
    11. repec:dau:papers:123456789/2278 is not listed on IDEAS
    12. Alfred Galichon & Ivar Ekeland & Marc Henry, 2009. "Comonotonic measures of multivariates risks," Working Papers hal-00401828, HAL.
    13. Alfred Galichon & Pierre Henri-Labordère & Nizar Touzi, 2013. "A stochastic control approach to No-Arbitrage bounds given marginals, with an application to Lookback options," Sciences Po publications info:hdl:2441/5rkqqmvrn4t, Sciences Po.
    14. 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 [Unobserved Product Differentiation in Discrete-Choice Models: Estimating Price Elasticities and Welfare Effects," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 89(6), pages 3085-3114.
    15. Ning Sun & Zaifu Yang, 2006. "Equilibria and Indivisibilities: Gross Substitutes and Complements," Econometrica, Econometric Society, vol. 74(5), pages 1385-1402, September.
    16. Guillaume Carlier & Victor Chernozhukov & Alfred Galichon, 2015. "Vector quantile regression: an optimal transport approach," CeMMAP working papers 58/15, Institute for Fiscal Studies.
    17. 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.
    18. 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.
    19. repec:dau:papers:123456789/6486 is not listed on IDEAS
    20. repec:hal:wpspec:info:hdl:2441/5rkqqmvrn4tl22s9mc4ao8ocg is not listed on IDEAS
    21. Alfred Galichon, 2016. "Optimal Transport Methods in Economics," Economics Books, Princeton University Press, edition 1, number 10870.
    22. Alfred Galichon & Ivar Ekeland & Marc Henry, 2009. "Comonotonic measures of multivariates risks," Working Papers hal-00401828, HAL.
    23. Alfred Galichon, 2016. "Optimal transport methods in economics," SciencePo Working papers hal-03256830, HAL.
    24. 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.
    25. repec:hal:wpspec:info:hdl:2441/5rkqqmvrn4tl22s9mc4b1h6b4 is not listed on IDEAS
    26. 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.
    27. repec:hal:wpspec:info:hdl:2441/dambferfb7dfprc9m01g1j1k2 is not listed on IDEAS
    28. 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.
    29. 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.
    30. 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).
    31. Alfred Galichon, 2016. "Optimal transport methods in economics," SciencePo Working papers Main hal-03256830, HAL.
    32. 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.
    33. 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.
    34. Galichon, Alfred & Henry, Marc, 2012. "Dual theory of choice with multivariate risks," Journal of Economic Theory, Elsevier, vol. 147(4), pages 1501-1516.
    35. Victor Chernozhukov & Alfred Galichon & Marc Hallin & Marc Henry, 2014. "Monge-Kantorovich Depth, Quantiles, Ranks, and Signs," Papers 1412.8434, arXiv.org, revised Sep 2015.
    36. 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..
    37. 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.
    38. repec:hal:spmain:info:hdl:2441/dambferfb7dfprc9m01g1j1k2 is not listed on IDEAS
    39. 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.
    40. 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.
    41. Koenker, Roger W & Bassett, Gilbert, Jr, 1978. "Regression Quantiles," Econometrica, Econometric Society, vol. 46(1), pages 33-50, January.
    42. Berry, Steven & Levinsohn, James & Pakes, Ariel, 1995. "Automobile Prices in Market Equilibrium," Econometrica, Econometric Society, vol. 63(4), pages 841-890, July.
    43. repec:hal:spmain:info:hdl:2441/4c5431jp6o888pdrcs0fuirl40 is not listed on IDEAS
    44. Guillaume Carlier & Victor Chernozhukov & Alfred Galichon, 2016. "Vector Quantile Regression: An Optimal Transport Approach," SciencePo Working papers hal-03567920, HAL.
    45. repec:hal:spmain:info:hdl:2441/5rkqqmvrn4tl22s9mc4b1h6b4 is not listed on IDEAS
    46. Arnaud Dupuy & Alfred Galichon & Yifei Sun, 2019. "Estimating Matching Affinity Matrices under Low-Rank Constraints," Post-Print hal-03948102, HAL.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    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.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Alfred Galichon, 2021. "The Unreasonable Effectiveness of Optimal Transport in Economics," SciencePo Working papers Main hal-03936221, HAL.
    2. Alfred Galichon, 2021. "The unreasonable effectiveness of optimal transport in economics," Papers 2107.04700, arXiv.org.
    3. Alfred Galichon & Bernard Salani'e, 2021. "Cupid's Invisible Hand: Social Surplus and Identification in Matching Models," Papers 2106.02371, arXiv.org, revised Jan 2023.
    4. Haiyan Liu & Bin Wang & Ruodu Wang & Sheng Chao Zhuang, 2023. "Distorted optimal transport," Papers 2308.11238, arXiv.org.
    5. Jeremy T. Fox, 2018. "Estimating matching games with transfers," Quantitative Economics, Econometric Society, vol. 9(1), pages 1-38, March.
    6. Tongseok Lim, 2023. "Replication of financial derivatives under extreme market models given marginals," Papers 2307.00807, arXiv.org.
    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. Kuan‐Ming Chen & Yu‐Wei Hsieh & Ming‐Jen Lin, 2023. "Reducing Recommendation Inequality Via Two‐Sided Matching: A Field Experiment Of Online Dating," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 64(3), pages 1201-1221, August.
    9. repec:hal:spmain:info:hdl:2441/3qnaslliat80pbqa8t90240unj is not listed on IDEAS
    10. Michael Greinecker & Christopher Kah, 2021. "Pairwise Stable Matching in Large Economies," Econometrica, Econometric Society, vol. 89(6), pages 2929-2974, November.
    11. Giulio Principi & Peter P. Wakker & Ruodu Wang, 2023. "Antimonotonicity for Preference Axioms: The Natural Counterpart to Comonotonicity," Papers 2307.08542, arXiv.org.
    12. Liang Chen & Eugene Choo & Alfred Galichon & Simon Weber, 2023. "Existence of a Competitive Equilibrium with Substitutes, with Applications to Matching and Discrete Choice Models," Papers 2309.11416, arXiv.org.
    13. repec:hal:spmain:info:hdl:2441/64itsev5509q8aa5mrbhi0g0b6 is not listed on IDEAS
    14. Hongjian Shi & Mathias Drton & Marc Hallin & Fang Han, 2023. "Semiparametrically Efficient Tests of Multivariate Independence Using Center-Outward Quadrant, Spearman, and Kendall Statistics," Working Papers ECARES 2023-03, ULB -- Universite Libre de Bruxelles.
    15. Itai Arieli & Yakov Babichenko & Fedor Sandomirskiy, 2023. "Persuasion as Transportation," Papers 2307.07672, arXiv.org.
    16. Nikhil Agarwal & Eric Budish, 2021. "Market Design," NBER Working Papers 29367, National Bureau of Economic Research, Inc.
    17. Florian Gunsilius, 2018. "Point-identification in multivariate nonseparable triangular models," Papers 1806.09680, arXiv.org.
    18. Anton Kolotilin & Roberto Corrao & Alexander Wolitzky, 2022. "Persuasion with Non-Linear Preferences," Papers 2206.09164, arXiv.org, revised Aug 2022.
    19. Nikhil Agarwal, 2015. "An Empirical Model of the Medical Match," American Economic Review, American Economic Association, vol. 105(7), pages 1939-1978, July.
    20. 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 [Unobserved Product Differentiation in Discrete-Choice Models: Estimating Price Elasticities and Welfare Effects," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 89(6), pages 3085-3114.
    21. Florian Gunsilius & Susanne M. Schennach, 2017. "A nonlinear principal component decomposition," CeMMAP working papers 16/17, Institute for Fiscal Studies.
    22. Salanié, Bernard & Chiappori, Pierre-André, 2021. "Mating Markets," CEPR Discussion Papers 16041, C.E.P.R. Discussion Papers.
      • Pierre-André Chiappori & Bernard Salanié, 2021. "Mating Markets," Working Papers 2021-016, Human Capital and Economic Opportunity Working Group.

    More about this item

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:hal:wpaper:hal-03936221. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: CCSD (email available below). General contact details of provider: https://hal.archives-ouvertes.fr/ .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.