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Unique equilibria and substitution effects in a stochastic model of the marriage market

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  • Decker, Colin
  • Lieb, Elliott H.
  • McCann, Robert J.
  • Stephens, Benjamin K.

Abstract

Choo and Siow (2006) [7] proposed a model for the marriage market which allows for random identically distributed McFadden-type noise in the preferences of each of the participants. In this note we exhibit a strictly convex function whose derivatives vanish precisely at the equilibria of their model. This implies uniqueness of the resulting equilibrium marriage distribution, simplifies the argument for its existence, and gives a representation of it in closed form. We go on to derive smooth dependence of this distribution on exogenous preference and population parameters, and establish sign, symmetry, and size of the various substitution effects. This leads to the testable but unexpected prediction that the percentage change of type i unmarrieds with respect to fluctuations in the total number of type j men or women turns out to form a symmetric positive-definite matrix rij=rji, and thus to satisfy bounds such as |rij|⩽(riirjj)1/2.

Suggested Citation

  • Decker, Colin & Lieb, Elliott H. & McCann, Robert J. & Stephens, Benjamin K., 2013. "Unique equilibria and substitution effects in a stochastic model of the marriage market," Journal of Economic Theory, Elsevier, vol. 148(2), pages 778-792.
  • Handle: RePEc:eee:jetheo:v:148:y:2013:i:2:p:778-792
    DOI: 10.1016/j.jet.2012.12.005
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    References listed on IDEAS

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    1. 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.
    2. Aloysius Siow, 2008. "How does the marriage market clear? An empirical framework," Canadian Journal of Economics/Revue canadienne d'économique, John Wiley & Sons, vol. 41(4), pages 1121-1155, November.
    3. Aloysius Siow, 2008. "How does the marriage market clear? An empirical framework," Canadian Journal of Economics, Canadian Economics Association, vol. 41(4), pages 1121-1155, November.
    4. Dagsvik, John K, 2000. "Aggregation in Matching Markets," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 41(1), pages 27-57, February.
    5. Figalli, Alessio & Kim, Young-Heon & McCann, Robert J., 2011. "When is multidimensional screening a convex program?," Journal of Economic Theory, Elsevier, vol. 146(2), pages 454-478, March.
    6. 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.
    7. 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.
    8. 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..
    9. Loren Brandt & Aloysius Siow & Carl Vogel, 2008. "Large Shocks and Small Changes in the Marriage Market for Famine Born Cohorts in China," Working Papers tecipa-334, University of Toronto, Department of Economics.
    10. 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.
    11. Ivar Ekeland, 2010. "Existence, uniqueness and efficiency of equilibrium in hedonic markets with multidimensional types," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 42(2), pages 275-315, February.
    12. Berry, Steven & Reiss, Peter, 2007. "Empirical Models of Entry and Market Structure," Handbook of Industrial Organization, in: Mark Armstrong & Robert Porter (ed.), Handbook of Industrial Organization, edition 1, volume 3, chapter 29, pages 1845-1886, Elsevier.
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    Citations

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    Cited by:

    1. 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.
    2. Jerez, Belén, 2014. "Competitive equilibrium with search frictions: A general equilibrium approach," Journal of Economic Theory, Elsevier, vol. 153(C), pages 252-286.
    3. Hortaçsu, Ali & Hwang, Sam Il Myoung & Mathur, Divya, 2019. "Monetary incentives on inter-caste marriages in India: Theory and evidence," Journal of Development Economics, Elsevier, vol. 141(C).
    4. Pierre-André Chiappori & Bernard Salanié, 2016. "The Econometrics of Matching Models," Journal of Economic Literature, American Economic Association, vol. 54(3), pages 832-861, September.
    5. 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.
    6. Adda, Jérôme & Pinotti, Paolo & Tura, Giulia, 2020. "There's More to Marriage than Love: The Effect of Legal Status and Cultural Distance on Intermarriages and Separations," CEPR Discussion Papers 14432, C.E.P.R. Discussion Papers.
    7. Alfred Galichon & Bernard Salanié, 2017. "The Econometrics and Some Properties of Separable Matching Models," American Economic Review, American Economic Association, vol. 107(5), pages 251-255, May.
    8. 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.
    9. Lu, Di, 2018. "China’s Selective Two-Child Policy and Its Impact on the Marriage Market," VfS Annual Conference 2018 (Freiburg, Breisgau): Digital Economy 181586, Verein für Socialpolitik / German Economic Association.

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    More about this item

    Keywords

    Choo–Siow; Marriage market; Matching; Random; Unique equilibrium; Comparative statics; Convex analysis;
    All these keywords.

    JEL classification:

    • J12 - Labor and Demographic Economics - - Demographic Economics - - - Marriage; Marital Dissolution; Family Structure
    • C62 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Existence and Stability Conditions of Equilibrium
    • C78 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Bargaining Theory; Matching Theory
    • C81 - Mathematical and Quantitative Methods - - Data Collection and Data Estimation Methodology; Computer Programs - - - Methodology for Collecting, Estimating, and Organizing Microeconomic Data; Data Access
    • D03 - Microeconomics - - General - - - Behavioral Microeconomics: Underlying Principles
    • Z13 - Other Special Topics - - Cultural Economics - - - Economic Sociology; Economic Anthropology; Language; Social and Economic Stratification

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