IDEAS home Printed from https://ideas.repec.org/a/eee/jetheo/v148y2013i2p778-792.html
   My bibliography  Save this article

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

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0022053112001202
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.jet.2012.12.005?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. 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.
    2. 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.
    3. 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.
    4. 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.
    5. 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.
    6. 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.
    7. 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.
    8. 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.
    9. 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.
    10. 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.
    11. 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.
    12. 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..
    Full references (including those not matched with items on IDEAS)

    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 & Scott Kominers & Simon Weber, 2014. "An Empirical Framework for Matching with Imperfectly Transferable Utility," Working Papers hal-03460155, HAL.
    2. Alfred Galichon & Bernard Salanié, 2022. "Cupid’s Invisible Hand: Social Surplus and Identification in Matching Models," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 89(5), pages 2600-2629.
    3. 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.
    4. Pierre-Andr'e Chiappori & Robert McCann & Brendan Pass, 2016. "Multidimensional matching," Papers 1604.05771, arXiv.org.
    5. Alfred Galichon & Simon Weber, 2024. "Matching under Imperfectly Transferable Utility," Papers 2403.05222, arXiv.org, revised Oct 2024.
    6. Jaerim Choi, 2021. "Two-sided heterogeneity, endogenous sharing, and international matching markets," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 72(2), pages 473-509, September.
    7. Han, Seungjin & Yamaguchi, Shintaro, 2015. "Compensating wage differentials in stable job matching equilibrium," Journal of Economic Behavior & Organization, Elsevier, vol. 114(C), pages 36-45.
    8. repec:hal:spmain:info:hdl:2441/4kovgv3hs883bok2tvdkibejb6 is not listed on IDEAS
    9. Brendan Pass, 2019. "Interpolating between matching and hedonic pricing models," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 67(2), pages 393-419, March.
    10. repec:hal:wpspec:info:hdl:2441/5rkqqmvrn4tl22s9mc0c7apsi is not listed on IDEAS
    11. Jeremy T. Fox & David H. Hsu & Chenyu Yang, 2012. "Unobserved Heterogeneity in Matching Games with an Application to Venture Capital," NBER Working Papers 18168, National Bureau of Economic Research, Inc.
    12. 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.
    13. Brendan Pass, 2017. "Interpolating between matching and hedonic pricing models," Papers 1701.04431, arXiv.org.
    14. McCann, Robert J. & Shi, Xianwen & Siow, Aloysius & Wolthoff, Ronald P., 2012. "Becker Meets Ricardo: Multisector Matching with Social and Cognitive Skills," IZA Discussion Papers 6533, Institute of Labor Economics (IZA).
    15. 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.
    16. Anderson, Gordon & Leo, Teng Wah, 2013. "An empirical examination of matching theories: The one child policy, partner choice and matching intensity in urban China," Journal of Comparative Economics, Elsevier, vol. 41(2), pages 468-489.
    17. repec:spo:wpmain:info:hdl:2441/4kovgv3hs883bok2tvdkibejb6 is not listed on IDEAS
    18. Victor Chernozhukov & Alfred Galichon & Marc Henry & Brendan Pass, 2018. "Single Market Nonparametric Identification of Multi-Attribute Hedonic Equilibrium Models," SciencePo Working papers Main hal-01169655, HAL.
    19. repec:hal:spmain:info:hdl:2441/5kmb4ke32h9ur9159sab6hvkck is not listed on IDEAS
    20. repec:spo:wpecon:info:hdl:2441/5rkqqmvrn4tl22s9mc0c7apsi is not listed on IDEAS
    21. J. Emery & Ana Ferrer, 2009. "Marriage market imbalances and labor force participation of Canadian women," Review of Economics of the Household, Springer, vol. 7(1), pages 43-57, March.
    22. Dizdar, Deniz & Moldovanu, Benny, 2016. "On the importance of uniform sharing rules for efficient matching," Journal of Economic Theory, Elsevier, vol. 165(C), pages 106-123.
    23. Veli Safak, 2020. "Matching Multidimensional Types: Theory and Application," Papers 2006.14243, arXiv.org.
    24. Sinha, Shruti, 2018. "Identification in One-to-One Matching Models with Nonparametric Unobservables," TSE Working Papers 18-897, Toulouse School of Economics (TSE).
    25. Alfred Galichon & Scott Kominers & Simon Weber, 2014. "An Empirical Framework for Matching with Imperfectly Transferable Utility," Working Papers hal-03460155, HAL.

    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

    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:eee:jetheo:v:148:y:2013:i:2:p:778-792. 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: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/inca/622869 .

    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.