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Transitive Preferences in Multi-Member Households

Author

Listed:
  • Bart Smeulders
  • Laurens Cherchye
  • Bram De Rock
  • Frits Spieksma
  • Fabrice Talla Nobibon

Abstract

Abstract The classical result of Rose (Rev Econ Stud, 25:124–125, 1958) shows that, for single-member households, the Weak Axiom of Revealed Preferences (warp) and the Strong Axiom of Revealed Preferences (sarp) are equivalent when there are only two goods. Because sarp extends warp by requiring transitive preferences in addition, this means that transitivity of preferences need not be tested in the case of two goods. We consider the extension of this result towards $$L$$ L -member households, for which we introduce the concepts $$L$$ L -warp and $$L$$ L -sarp. For a general setting, we demonstrate that $$L$$ L -warp and $$L$$ L -sarp are not equivalent if there are at least $$L+1$$ L + 1 goods, which means that transitivity of individual preferences is testable. However, we can also show that $$L$$ L -warp and $$L$$ L -sarp do become equivalent for the restricted “labor supply” setting where we exclusively assign a single good to each different household member, i.e., $$L$$ L (out of $$L+1$$ L + 1 ) goods are exclusive.
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Suggested Citation

  • Bart Smeulders & Laurens Cherchye & Bram De Rock & Frits Spieksma & Fabrice Talla Nobibon, 2014. "Transitive Preferences in Multi-Member Households," Working Papers ECARES ECARES 2014-19, ULB -- Universite Libre de Bruxelles.
  • Handle: RePEc:eca:wpaper:2013/159434
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    References listed on IDEAS

    as
    1. Varian, Hal R, 1982. "The Nonparametric Approach to Demand Analysis," Econometrica, Econometric Society, vol. 50(4), pages 945-973, July.
    2. Cherchye, Laurens & Demuynck, Thomas & De Rock, Bram, 2011. "Testable implications of general equilibrium models: An integer programming approach," Journal of Mathematical Economics, Elsevier, vol. 47(4-5), pages 564-575.
    3. Vermeulen, Frederic, 2002. " Collective Household Models: Principles and Main Results," Journal of Economic Surveys, Wiley Blackwell, vol. 16(4), pages 533-564, September.
    4. Cherchye, Laurens & De Rock, Bram & Vermeulen, Frederic, 2010. "An Afriat Theorem for the collective model of household consumption," Journal of Economic Theory, Elsevier, vol. 145(3), pages 1142-1163, May.
    5. Laurens Cherchye & Bram De Rock & Vincenzo Platino, 2013. "Private versus public consumption within groups: testing the nature of goods from aggregate data," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 54(3), pages 485-500, November.
    6. Brown, Donald J & Matzkin, Rosa L, 1996. "Testable Restrictions on the Equilibrium Manifold," Econometrica, Econometric Society, vol. 64(6), pages 1249-1262, November.
    7. Bram De Rock & Bart Smeulders & Laurens Cherchye & Frits Spieksma, 2013. "Goodness of fit measures for revealed preference tests: Complexity results and algorithms," ULB Institutional Repository 2013/162939, ULB -- Universite Libre de Bruxelles.
    8. Laurens Cherchye & Bram De Rock & Frederic Vermeulen, 2007. "The Collective Model of Household Consumption: A Nonparametric Characterization," Econometrica, Econometric Society, vol. 75(2), pages 553-574, March.
    9. Cherchye, Laurens & Demuynck, Thomas & De Rock, Bram, 2011. "Testable implications of general equilibrium models: An integer programming approach," Journal of Mathematical Economics, Elsevier, vol. 47(4-5), pages 564-575.
    10. Peters Hans & Wakker Peter, 1994. "WARP Does Not Imply SARP for More Than Two Commodities," Journal of Economic Theory, Elsevier, vol. 62(1), pages 152-160, February.
    11. Snyder, Susan K., 2004. "Observable implications of equilibrium behavior on finite data," Journal of Mathematical Economics, Elsevier, vol. 40(1-2), pages 165-176, February.
    12. Cherchye, Laurens & De Rock, Bram & Vermeulen, Frederic, 2012. "Collective Household Consumption Behavior: Revealed Preference Analysis," Foundations and Trends(R) in Econometrics, now publishers, vol. 4(4), pages 225-312, March.
    13. Hugh Rose, 1958. "Consistency of Preference: The Two-Commodity Case," Review of Economic Studies, Oxford University Press, vol. 25(2), pages 124-125.
    14. Chiappori, Pierre-Andre, 1988. "Rational Household Labor Supply," Econometrica, Econometric Society, vol. 56(1), pages 63-90, January.
    15. Laurens Cherchye & Bram De Rock & Frederic Vermeulen, 2011. "The revealed preference approach to collective consumption behavior: nonparametric testing and sharing rule recovery," ULB Institutional Repository 2013/98560, ULB -- Universite Libre de Bruxelles.
    16. Laurens Cherchye & Bram De Rock & Frederic Vermeulen, 2011. "The Revealed Preference Approach to Collective Consumption Behaviour: Testing and Sharing Rule Recovery," Review of Economic Studies, Oxford University Press, vol. 78(1), pages 176-198.
    17. Carvajal, Andres & Ray, Indrajit & Snyder, Susan, 2004. "Equilibrium behavior in markets and games: testable restrictions and identification," Journal of Mathematical Economics, Elsevier, vol. 40(1-2), pages 1-40, February.
    18. Laurens Cherchye & Bram De Rock & Frederic Vermeulen, 2011. "The Revealed Preference Approach to Collective Consumption Behaviour: Testing and Sharing Rule Recovery," Review of Economic Studies, Oxford University Press, vol. 78(1), pages 176-198.
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    Citations

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    Cited by:

    1. Donni, Olivier & Molina, José Alberto, 2018. "Household Collective Models: Three Decades of Theoretical Contributions and Empirical Evidence," IZA Discussion Papers 11915, Institute for the Study of Labor (IZA).
    2. Laurens Cherchye & Sam Cosaert & Bram De Rock & Pieter Jan Kerstens & Frederic Vermeulen, 2017. "Individual Welfare Analysis for Collective Households," Working Papers ECARES ECARES 2017-44, ULB -- Universite Libre de Bruxelles.

    More about this item

    Keywords

    weak axiom of revealed preferences; strong axiom of revealed preferences; multi-member households; transitivity;

    JEL classification:

    • D11 - Microeconomics - - Household Behavior - - - Consumer Economics: Theory
    • D12 - Microeconomics - - Household Behavior - - - Consumer Economics: Empirical Analysis
    • D13 - Microeconomics - - Household Behavior - - - Household Production and Intrahouse Allocation
    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General

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