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Matching Multidimensional Types: Theory and Application

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  • Veli Safak

Abstract

Becker (1973) presents a bilateral matching model in which scalar types describe agents. For this framework, he establishes the conditions under which positive sorting between agents' attributes is the unique market outcome. Becker's celebrated sorting result has been applied to address many economic questions. However, recent empirical studies in the fields of health, household, and labor economics suggest that agents have multiple outcome-relevant attributes. In this paper, I study a matching model with multidimensional types. I offer multidimensional generalizations of concordance and supermodularity to construct three multidimensional sorting patterns and two classes of multidimensional complementarities. For each of these sorting patterns, I identify the sufficient conditions which guarantee its optimality. In practice, we observe sorting patterns between observed attributes that are aggregated over unobserved characteristics. To reconcile theory with practice, I establish the link between production complementarities and the aggregated sorting patterns. Finally, I examine the relationship between agents' health status and their spouses' education levels among U.S. households within the framework for multidimensional matching markets. Preliminary analysis reveals a weak positive association between agents' health status and their spouses' education levels. This weak positive association is estimated to be a product of three factors: (a) an attraction between better-educated individuals, (b) an attraction between healthier individuals, and (c) a weak positive association between agents' health status and their education levels. The attraction channel suggests that the insurance risk associated with a two-person family plan is higher than the aggregate risk associated with two individual policies.

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  • Veli Safak, 2020. "Matching Multidimensional Types: Theory and Application," Papers 2006.14243, arXiv.org.
    • Handle: RePEc:arx:papers:2006.14243
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    1. Jeremy Greenwood & Nezih Guner & Georgi Kocharkov & Cezar Santos, 2014. "Marry Your Like: Assortative Mating and Income Inequality," American Economic Review, American Economic Association, vol. 104(5), pages 348-353, May.
    2. Kravdal, Øystein, 2008. "A broader perspective on education and mortality: Are we influenced by other people's education?," Social Science & Medicine, Elsevier, vol. 66(3), pages 620-636, February.
    3. Fatih Guvenen & Burhan Kuruscu & Satoshi Tanaka & David Wiczer, 2020. "Multidimensional Skill Mismatch," American Economic Journal: Macroeconomics, American Economic Association, vol. 12(1), pages 210-244, January.
    4. 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.
    5. Aloysius Siow, 2015. "Testing Becker's Theory of Positive Assortative Matching," Journal of Labor Economics, University of Chicago Press, vol. 33(2), pages 409-441.
    6. Xavier Gabaix & Augustin Landier, 2008. "Why has CEO Pay Increased So Much?," The Quarterly Journal of Economics, Oxford University Press, vol. 123(1), pages 49-100.
    7. Arnaud Dupuy & Alfred Galichon, 2014. "Personality Traits and the Marriage Market," Journal of Political Economy, University of Chicago Press, vol. 122(6), pages 1271-1319.
    8. Dustin Brown & Robert Hummer & Mark Hayward, 2014. "The Importance of Spousal Education for the Self-Rated Health of Married Adults in the United States," Population Research and Policy Review, Springer;Southern Demographic Association (SDA), vol. 33(1), pages 127-151, February.
    9. Gunter J. Hitsch & Ali Hortaçsu & Dan Ariely, 2010. "Matching and Sorting in Online Dating," American Economic Review, American Economic Association, vol. 100(1), pages 130-163, March.
    10. Esther Mirjam Girsberger & Miriam Rinawi & Matthias Krapf, 2018. "Wages and employment: The role of occupational skills," Economics of Education Working Paper Series 0153, University of Zurich, Department of Business Administration (IBW).
    11. Margaret Meyer & Bruno Strulovici, 2013. "The Supermodular Stochastic Ordering," Discussion Papers 1563, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
    12. Colangelo, Antonio & Scarsini, Marco & Shaked, Moshe, 2005. "Some notions of multivariate positive dependence," Insurance: Mathematics and Economics, Elsevier, vol. 37(1), pages 13-26, August.
    13. Mackenbach, J.P. & Kunst, A.E. & Groenhof, F. & Borgan, J.-K. & Costa, G. & Faggiano, F. & Józan, P. & Leinsalu, M. & Martikainen, P. & Rychtarikova, J. & Valkonen, T., 1999. "Socioeconomic inequalities in mortality among women and among men: An international study," American Journal of Public Health, American Public Health Association, vol. 89(12), pages 1800-1806.
    14. Hector Chade & Jan Eeckhout & Lones Smith, 2017. "Sorting through Search and Matching Models in Economics," Journal of Economic Literature, American Economic Association, vol. 55(2), pages 493-544, June.
    15. Michael Kremer, 1993. "The O-Ring Theory of Economic Development," The Quarterly Journal of Economics, Oxford University Press, vol. 108(3), pages 551-575.
    16. Manor, Orly & Eisenbach, Zvi & Israeli, Avi & Friedlander, Yechiel, 2000. "Mortality differentials among women: the Israel Longitudinal Mortality Study," Social Science & Medicine, Elsevier, vol. 51(8), pages 1175-1188, October.
    17. Raicho Bojilov & Alfred Galichon, 2016. "Matching in closed-form: equilibrium, identification, and comparative statics," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 61(4), pages 587-609, April.
    18. Pierre-André Chiappori & Sonia Oreffice & Climent Quintana-Domeque, 2012. "Fatter Attraction: Anthropometric and Socioeconomic Matching on the Marriage Market," Journal of Political Economy, University of Chicago Press, vol. 120(4), pages 659-695.
    19. Kunst, A.E. & Mackenbach, J.P., 1994. "The size of mortality differences associated with educational level in nine industrialized countries," American Journal of Public Health, American Public Health Association, vol. 84(6), pages 932-937.
    20. Marco Scarsini, 1984. "On measures of concordance," Post-Print hal-00542380, HAL.
    21. Gretsky, Neil E & Ostroy, Joseph M & Zame, William R, 1992. "The Nonatomic Assignment Model," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 2(1), pages 103-127, January.
    22. Pierre-Andr'e Chiappori & Robert McCann & Brendan Pass, 2016. "Multidimensional matching," Papers 1604.05771, arXiv.org.
    23. Alfred Galichon & Bernard Salanié, 2010. "Matching with Trade-offs: Revealed Preferences over Competiting Characteristics," Working Papers hal-00473173, HAL.
    24. Skalická, Vera & Kunst, Anton E., 2008. "Effects of spouses' socioeconomic characteristics on mortality among men and women in a Norwegian longitudinal study," Social Science & Medicine, Elsevier, vol. 66(9), pages 2035-2047, May.
    25. Fletcher, Jason M. & Padrón, Norma, 2015. "Heterogeneity in Spousal Matching Models," IZA Discussion Papers 8936, Institute of Labor Economics (IZA).
    26. David J. Deming, 2017. "The Growing Importance of Social Skills in the Labor Market," The Quarterly Journal of Economics, Oxford University Press, vol. 132(4), pages 1593-1640.
    27. 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..
    28. Müller, Alfred & Scarsini, Marco, 2012. "Fear of loss, inframodularity, and transfers," Journal of Economic Theory, Elsevier, vol. 147(4), pages 1490-1500.
    29. Margaret Meyer & Bruno Strulovici, 2013. "Beyond Correlation: Measuring Interdependence Through Complementarities," Economics Series Working Papers 655, University of Oxford, Department of Economics.
    30. Steve Laufer & Ahu Gemici, 2009. "Marriage and Cohabitation," 2009 Meeting Papers 1191, Society for Economic Dynamics.
    31. Shaked, Moshe & Shanthikumar, J. George, 1997. "Supermodular Stochastic Orders and Positive Dependence of Random Vectors," Journal of Multivariate Analysis, Elsevier, vol. 61(1), pages 86-101, April.
    32. Ilse Lindenlaub, 2017. "Sorting Multidimensional Types: Theory and Application," Review of Economic Studies, Oxford University Press, vol. 84(2), pages 718-789.
    33. Marco Scarsini, 1984. "Strong measures of concordance and convergence in probability," Post-Print hal-00542387, HAL.
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