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On the Revealed Preference Analysis of Stable Aggregate Matchings

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  • Thomas Demuynck
  • Umutcan Salman

Abstract

We extend the analysis of (Echenique, Lee, Shum, and Yenmez, 2013) by looking at the testable revealed preference restrictions for stable aggregate matchings with non-transferable utility. We rephrase their revealed preference test in terms of a bipartite graph. From this, we obtain an simple condition that verifies whether a given matching is rationalisable. Next, for a matching that is not rationalisable, we show how to find the minimal number of matches that needs to be removed in order to restore rationalisability. This produces a goodness-of-fit measure that indicates how close a matching is to being rationalisable. We also show that the related problem of finding the minimal number of types that we need to remove in order to obtain rationalisability is NP-hard. We provide two illustrations to demonstrate the usefulness of our results.
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Suggested Citation

  • Thomas Demuynck & Umutcan Salman, 2022. "On the Revealed Preference Analysis of Stable Aggregate Matchings," ULB Institutional Repository 2013/359108, ULB -- Universite Libre de Bruxelles.
    • Handle: RePEc:ulb:ulbeco:2013/359108
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    References listed on IDEAS

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    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. Laurens Cherchye & Thomas Demuynck & Bram De Rock & Frederic Vermeulen, 2017. "Household Consumption When the Marriage Is Stable," American Economic Review, American Economic Association, vol. 107(6), pages 1507-1534, June.
    3. Federico Echenique & Sangmok Lee & Matthew Shum, 2011. "The Money Pump as a Measure of Revealed Preference Violations," Journal of Political Economy, University of Chicago Press, vol. 119(6), pages 1201-1223.
    4. Alan Agresti & Dennis Wackerly & James Boyett, 1979. "Exact conditional tests for cross-classifications: Approximation of attained significance levels," Psychometrika, Springer;The Psychometric Society, vol. 44(1), pages 75-83, March.
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    6. Federico Echenique, 2008. "What Matchings Can Be Stable? The Testable Implications of Matching Theory," Mathematics of Operations Research, INFORMS, vol. 33(3), pages 757-768, August.
    7. Jose Apesteguia & Miguel A. Ballester, 2015. "A Measure of Rationality and Welfare," Journal of Political Economy, University of Chicago Press, vol. 123(6), pages 1278-1310.
    8. Mark Dean & Daniel Martin, 2016. "Measuring Rationality with the Minimum Cost of Revealed Preference Violations," The Review of Economics and Statistics, MIT Press, vol. 98(3), pages 524-534, July.
    9. Demuynck, Thomas & Salman, Umutcan, 2022. "On the revealed preference analysis of stable aggregate matchings," Theoretical Economics, Econometric Society, vol. 17(4), November.
    10. Varian, Hal R., 1990. "Goodness-of-fit in optimizing models," Journal of Econometrics, Elsevier, vol. 46(1-2), pages 125-140.
    11. Fortunato Pesarin & Luigi Salmaso, 2010. "The permutation testing approach: a review," Statistica, Department of Statistics, University of Bologna, vol. 70(4), pages 481-509.
    12. Hu, Gaoji & Li, Jiangtao & Tang, Rui, 2020. "The revealed preference theory of stable matchings with one-sided preferences," Games and Economic Behavior, Elsevier, vol. 124(C), pages 305-318.
    13. Arnaud Dupuy & Alfred Galichon, 2014. "Personality traits and the marriage market," SciencePo Working papers hal-03470458, HAL.
    14. Federico Echenique & Sangmok Lee & Matthew Shum & M. Bumin Yenmez, 2013. "The Revealed Preference Theory of Stable and Extremal Stable Matchings," Econometrica, Econometric Society, vol. 81(1), pages 153-171, January.
    15. Arnaud Dupuy & Alfred Galichon, 2014. "Personality traits and the marriage market," Post-Print hal-03470458, HAL.
    16. Laurens Cherchye & Thomas Demuynck & Bram De Rock & Joshua Lanier, 2020. "Are Consumers Rational ?Shifting the Burden of Proof," Working Papers ECARES 2020-19, ULB -- Universite Libre de Bruxelles.
    17. Arnaud Dupuy & Alfred Galichon, 2014. "Personality traits and the marriage market," SciencePo Working papers Main hal-03470458, HAL.
    18. repec:hal:spmain:info:hdl:2441/361levbcs399s9oa154em6h9jl is not listed on IDEAS
    19. Varian, Hal R., 1985. "Non-parametric analysis of optimizing behavior with measurement error," Journal of Econometrics, Elsevier, vol. 30(1-2), pages 445-458.
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    Cited by:

    1. Federico Echenique & SangMok Lee & Matthew Shum & M. Bumin Yenmez, 2021. "Stability and Median Rationalizability for Aggregate Matchings," Games, MDPI, vol. 12(2), pages 1-15, April.
    2. Demuynck, Thomas & Salman, Umutcan, 2022. "On the revealed preference analysis of stable aggregate matchings," Theoretical Economics, Econometric Society, vol. 17(4), November.

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    More about this item

    JEL classification:

    • C78 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Bargaining Theory; Matching Theory
    • D11 - Microeconomics - - Household Behavior - - - Consumer Economics: Theory

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