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Yogurts Choose Consumers? Estimation of Random-Utility Models via Two-Sided Matching

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  • Odran Bonnet
  • Alfred Galichon
  • Yu-Wei Hsieh
  • Keith O’Hara
  • Matt Shum

Abstract

The problem of demand inversion—a crucial step in the estimation of random utility discrete-choice models—is equivalent to the determination of stable outcomes in two-sided matching models. This equivalence applies to random utility models that are not necessarily additive, smooth, nor even invertible. Based on this equivalence, algorithms for the determination of stable matchings provide effective computational methods for estimating these models. For non-invertible models, the identified set of utility vectors is a lattice, and the matching algorithms recover sharp upper and lower bounds on the utilities. Our matching approach facilitates estimation of models that were previously difficult to estimate, such as the pure characteristics model. An empirical application to voting data from the 1999 European Parliament elections illustrates the good performance of our matching-based demand inversion algorithms in practice.

Suggested Citation

  • 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.
  • Handle: RePEc:oup:restud:v:89:y:2022:i:6:p:3085-3114.
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    as
    1. Jean‐Pierre Dubé & Jeremy T. Fox & Che‐Lin Su, 2012. "Improving the Numerical Performance of Static and Dynamic Aggregate Discrete Choice Random Coefficients Demand Estimation," Econometrica, Econometric Society, vol. 80(5), pages 2231-2267, September.
    2. Daniel A. Ackerberg & Marc Rysman, 2005. "Unobserved Product Differentiation in Discrete-Choice Models: Estimating Price Elasticities and Welfare Effects," RAND Journal of Economics, The RAND Corporation, vol. 36(4), pages 771-788, Winter.
    3. Steven Berry & Amit Gandhi & Philip Haile, 2013. "Connected Substitutes and Invertibility of Demand," Econometrica, Econometric Society, vol. 81(5), pages 2087-2111, September.
    4. Patrick Bajari & C. Lanier Benkard & Jonathan Levin, 2007. "Estimating Dynamic Models of Imperfect Competition," Econometrica, Econometric Society, vol. 75(5), pages 1331-1370, September.
    5. Victor Aguirregabiria & Pedro Mira, 2002. "Swapping the Nested Fixed Point Algorithm: A Class of Estimators for Discrete Markov Decision Models," Econometrica, Econometric Society, vol. 70(4), pages 1519-1543, July.
    6. Thierry Magnac & David Thesmar, 2002. "Identifying Dynamic Discrete Decision Processes," Econometrica, Econometric Society, vol. 70(2), pages 801-816, March.
    7. Steven Berry & Philip Haile, 2016. "Identification in Differentiated Products Markets," Annual Review of Economics, Annual Reviews, vol. 8(1), pages 27-52, October.
    8. Crawford, Vincent P & Knoer, Elsie Marie, 1981. "Job Matching with Heterogeneous Firms and Workers," Econometrica, Econometric Society, vol. 49(2), pages 437-450, March.
    9. V. Joseph Hotz & Robert A. Miller, 1993. "Conditional Choice Probabilities and the Estimation of Dynamic Models," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 60(3), pages 497-529.
    10. Demange, Gabrielle & Gale, David, 1985. "The Strategy Structure of Two-sided Matching Markets," Econometrica, Econometric Society, vol. 53(4), pages 873-888, July.
    11. Antonio Merlo & Áureo de Paula, 2017. "Identification and Estimation of Preference Distributions When Voters Are Ideological," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 84(3), pages 1238-1263.
    12. Simon Hix & Abdul Noury & Gérard Roland, 2006. "Dimensions of Politics in the European Parliament," American Journal of Political Science, John Wiley & Sons, vol. 50(2), pages 494-520, April.
    13. Alfred Galichon, 2016. "Optimal transport methods in economics," Post-Print hal-03256830, HAL.
    14. Steven T. Berry & Philip A. Haile, 2014. "Identification in Differentiated Products Markets Using Market Level Data," Econometrica, Econometric Society, vol. 82, pages 1749-1797, September.
    15. Lee, Jinhyuk & Seo, Kyoungwon, 2016. "Revisiting the nested fixed-point algorithm in BLP random coefficients demand estimation," Economics Letters, Elsevier, vol. 149(C), pages 67-70.
    16. Daniel McFadden & Kenneth Train, 2000. "Mixed MNL models for discrete response," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 15(5), pages 447-470.
    17. 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.
    18. Xiaohong Chen & Timothy M. Christensen & Elie Tamer, 2018. "Monte Carlo Confidence Sets for Identified Sets," Econometrica, Econometric Society, vol. 86(6), pages 1965-2018, November.
    19. Alma Cohen & Liran Einav, 2007. "Estimating Risk Preferences from Deductible Choice," American Economic Review, American Economic Association, vol. 97(3), pages 745-788, June.
    20. Alfred Galichon, 2016. "Optimal Transport Methods in Economics," Economics Books, Princeton University Press, edition 1, number 10870.
    21. Jeremy T. Fox & Patrick Bajari, 2013. "Measuring the Efficiency of an FCC Spectrum Auction," American Economic Journal: Microeconomics, American Economic Association, vol. 5(1), pages 100-146, February.
    22. repec:hal:spmain:info:hdl:2441/5kmb4ke32h9ur9159sab6hvkck is not listed on IDEAS
    23. Bresnahan, Timothy F., 1981. "Departures from marginal-cost pricing in the American automobile industry : Estimates for 1977-1978," Journal of Econometrics, Elsevier, vol. 17(2), pages 201-227, November.
    24. Train,Kenneth E., 2009. "Discrete Choice Methods with Simulation," Cambridge Books, Cambridge University Press, number 9780521766555, September.
    25. Susanna Esteban & Matthew Shum, 2007. "Durable-goods oligopoly with secondary markets: the case of automobiles," RAND Journal of Economics, RAND Corporation, vol. 38(2), pages 332-354, June.
    26. John William Hatfield & Paul R. Milgrom, 2005. "Matching with Contracts," American Economic Review, American Economic Association, vol. 95(4), pages 913-935, September.
    27. Roth, Alvin E, 1984. "The Evolution of the Labor Market for Medical Interns and Residents: A Case Study in Game Theory," Journal of Political Economy, University of Chicago Press, vol. 92(6), pages 991-1016, December.
    28. Jose Apesteguia & Miguel A. Ballester, 2014. "Discrete choice estimation of risk aversion," Economics Working Papers 1443, Department of Economics and Business, Universitat Pompeu Fabra.
    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. Echenique, Federico & Oviedo, Jorge, 2004. "Core many-to-one matchings by fixed-point methods," Journal of Economic Theory, Elsevier, vol. 115(2), pages 358-376, April.
    31. Andriy Norets & Satoru Takahashi, 2013. "On the surjectivity of the mapping between utilities and choice probabilities," Quantitative Economics, Econometric Society, vol. 4(1), pages 149-155, March.
    32. Jong-Shi Pang & Che-Lin Su & Yu-Ching Lee, 2015. "A Constructive Approach to Estimating Pure Characteristics Demand Models with Pricing," Operations Research, INFORMS, vol. 63(3), pages 639-659, June.
    33. Shakeeb Khan & Fu Ouyang & Elie Tamer, 2019. "Inference on Semiparametric Multinomial Response Models," Boston College Working Papers in Economics 980, Boston College Department of Economics.
    34. Edward C. Prescott & Michael Visscher, 1977. "Sequential Location among Firms with Foresight," Bell Journal of Economics, The RAND Corporation, vol. 8(2), pages 378-393, Autumn.
    35. Anthony Downs, 1957. "An Economic Theory of Political Action in a Democracy," Journal of Political Economy, University of Chicago Press, vol. 65(2), pages 135-135.
    36. Victor Chernozhukov & Alfred Galichon & Marc Henry & Brendan Pass, 2018. "Single Market Nonparametric Identification of Multi-Attribute Hedonic Equilibrium Models," Working Papers hal-01169655, HAL.
    37. Peter Arcidiacono & Robert A. Miller, 2011. "Conditional Choice Probability Estimation of Dynamic Discrete Choice Models With Unobserved Heterogeneity," Econometrica, Econometric Society, vol. 79(6), pages 1823-1867, November.
    38. Adachi, Hiroyuki, 2000. "On a characterization of stable matchings," Economics Letters, Elsevier, vol. 68(1), pages 43-49, July.
    39. Tamás Fleiner, 2003. "A Fixed-Point Approach to Stable Matchings and Some Applications," Mathematics of Operations Research, INFORMS, vol. 28(1), pages 103-126, February.
    40. Erdem, Tulin & Keane, Michael P. & Sun, Baohong, 1998. "Missing price and coupon availability data in scanner panels: Correcting for the self-selection bias in choice model parameters," Journal of Econometrics, Elsevier, vol. 89(1-2), pages 177-196, November.
    41. Berry, Steven & Levinsohn, James & Pakes, Ariel, 1995. "Automobile Prices in Market Equilibrium," Econometrica, Econometric Society, vol. 63(4), pages 841-890, July.
    42. Igal Hendel, 1999. "Estimating Multiple-Discrete Choice Models: An Application to Computerization Returns," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 66(2), pages 423-446.
    43. Panle Jia, 2008. "What Happens When Wal-Mart Comes to Town: An Empirical Analysis of the Discount Retailing Industry," Econometrica, Econometric Society, vol. 76(6), pages 1263-1316, November.
    44. Steven Berry & Ariel Pakes, 2007. "The Pure Characteristics Demand Model," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 48(4), pages 1193-1225, November.
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    3. Zhaonan Qu & Alfred Galichon & Johan Ugander, 2023. "On Sinkhorn's Algorithm and Choice Modeling," Papers 2310.00260, arXiv.org.
    4. Takeshi Fukasawa, 2024. "Fast and simple inner-loop algorithms of static / dynamic BLP estimations," Papers 2404.04494, arXiv.org, revised Oct 2024.
    5. Allen, Roy, 2022. "Injectivity and the law of demand," Economics Letters, Elsevier, vol. 215(C).
    6. Alfred Galichon, 2021. "The Unreasonable Effectiveness of Optimal Transport in Economics," Working Papers hal-03936221, HAL.
    7. Alfred Galichon, 2021. "The unreasonable effectiveness of optimal transport in economics," Papers 2107.04700, arXiv.org.
    8. Alfred Galichon & Yu-Wei Hsieh & Maxime Sylvestre, 2023. "Monotone comparative statics for submodular functions, with an application to aggregated deferred acceptance," Papers 2304.12171, arXiv.org, revised Aug 2024.
    9. Yao (Alex) Yao & Sha Yang & K. Sudhir, 2021. "Two-Sided Matching Between Fashion Firms and Publishers: When Firms Strategically Target Consumers for Brand Image," Working Papers 21-07, NET Institute.

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