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An Afriat Theorem for the Collective Model of Household Consumption

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  • Cherchye, Laurens

    ()
    (K.U.Leuven)

  • De Rock, Bram

    ()
    (ECARES, Free University of Brussels)

  • Vermeulen, Frederic

    ()
    (Tilburg University)

Abstract

We provide a nonparametric 'revealed preference' characterization of rational household behavior in terms of the collective consumption model, while accounting for general (possibly non-convex) individual preferences. We establish a Collective Axiom of Revealed Preference (CARP), which provides a necessary and sufficient condition for data consistency with collective rationality. Our main result takes the form of a 'collective' version of the Afriat Theorem for rational behavior in terms of the unitary model. This theorem has some interesting implications. With only a finite set of observations, the nature of consumption externalities (positive or negative) in the intra-household allocation process is non-testable. The same non-testability conclusion holds for privateness (with or without externalities) or publicness of consumption. By contrast, concavity of individual utility functions (representing convex preferences) turns out to be testable. In addition, monotonicity is testable for the model that assumes all household consumption is public.

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Bibliographic Info

Paper provided by Institute for the Study of Labor (IZA) in its series IZA Discussion Papers with number 3794.

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Length: 31 pages
Date of creation: Oct 2008
Date of revision:
Publication status: published in: Journal of Economic Theory, 2010, 145(3), 1142-1163.
Handle: RePEc:iza:izadps:dp3794

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Keywords: collective model; consumption; Pareto efficiency; revealed preferences; Afriat theorem; Collective Axiom of Revealed Preferences;

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References

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  1. Chiappori, P.A. & Ekeland, I., 2006. "The micro economics of group behavior: General characterization," Journal of Economic Theory, Elsevier, vol. 130(1), pages 1-26, September.
  2. Mas-Colell, Andreu & Whinston, Michael D. & Green, Jerry R., 1995. "Microeconomic Theory," OUP Catalogue, Oxford University Press, number 9780195102680.
  3. Chiappori, Pierre-Andre, 1988. "Rational Household Labor Supply," Econometrica, Econometric Society, vol. 56(1), pages 63-90, January.
  4. Laurens Cherchye & Bram De Rock & Jeroen Sabbe & Frederic Vermeulen, 2008. "Nonparametric tests of collectively rational consumption behavior: an integer programming procedure," ULB Institutional Repository 2013/131712, ULB -- Universite Libre de Bruxelles.
  5. Laurens Cherchye & Bram De Rock & Frederic Vermeulen, 2007. "The Collective Model of Household Consumption: A nonparametric characterization," ULB Institutional Repository 2013/98559, ULB -- Universite Libre de Bruxelles.
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  16. Fortin, Bernard & Lacroix, Guy, 1997. "A Test of the Unitary and Collective Models of Household Labour Supply," Economic Journal, Royal Economic Society, vol. 107(443), pages 933-55, July.
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  19. Cherchye, Laurens & De Rock, Bram & Vermeulen, Frederic, 2006. "Analyzing Cost Efficient Production Behavior Under Economies of Scope: A Nonparametric Methodology," IZA Discussion Papers 2319, Institute for the Study of Labor (IZA).
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  22. Laurens Cherchye & Ian Crawford & Bram De Rock & Frederic Vermeulen, 2009. "The revealed preference approach to demand," ULB Institutional Repository 2013/132522, ULB -- Universite Libre de Bruxelles.
  23. Forges, Françoise & Minelli, Enrico, 2009. "Afriat's theorem for general budget sets," Journal of Economic Theory, Elsevier, vol. 144(1), pages 135-145, January.
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Citations

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Cited by:
  1. Ennio Bilancini, 2010. "On the rationalizability of observed consumers’ choices when preferences depend on budget sets and (potentially) on anything else," Center for Economic Research (RECent) 052, University of Modena and Reggio E., Dept. of Economics.
  2. Ekeland, Ivar & Galichon, Alfred, 2012. "The housing problem and revealed preference theory: duality and an application," Economics Papers from University Paris Dauphine 123456789/10574, Paris Dauphine University.
  3. Laurens Cherchye & Bram De Rock & Arthur Lewbel & Frederic Vermeulen, 2012. "Sharing Rule Identification for General Collective Consumption Models," Boston College Working Papers in Economics 809, Boston College Department of Economics, revised 01 Jul 2013.
  4. Fabrice Talla Nobibon & Laurens Cherchye & Bram De Rock & Jeroen Sabbe & Frits Spieksma, 2011. "Heuristics for deciding collectively rational consumption behavior," ULB Institutional Repository 2013/131710, ULB -- Universite Libre de Bruxelles.
  5. Laurens Cherchye & Bram De Rock & Vincenzo Platino, 2010. "Private versus public consumption within groups : testing the nature of goods from aggregate data," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-00543999, HAL.
  6. Ennio Bilancini, 2010. "On the Rationalizability of Observed Consumers Choise when Prefeerences else," Department of Economics 0636, University of Modena and Reggio E., Faculty of Economics "Marco Biagi".
  7. Per Hjertstrand & James Swofford, 2012. "Revealed preference tests for consistency with weakly separable indirect utility," Theory and Decision, Springer, vol. 72(2), pages 245-256, February.

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