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An Afriat theorem for the collective model of household consumption

  • Laurens Cherchye
  • Bram De Rock
  • Frederic Vermeulen

We provide a nonparametric 'revealed preference' characterization of rational household behavior in terms of the collective consumption model, while accounting for general individual preferences that can be non-convex. Our main result is the Collective Afriat Theorem, which parallels the well-known Afriat Theorem for the unitary model. First, it provides a characterization of collectively rational consumption behavior in terms of collective Afriat inequalities. Next, it implies the Collective Axiom of Revealed Preference (CARP) as a testable necessary and sufficient condition for data consistency with collective rationality. Finally, the theorem has some interesting testability 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. © 2009 Elsevier Inc.

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Paper provided by ULB -- Universite Libre de Bruxelles in its series ULB Institutional Repository with number 2013/131711.

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Date of creation: 2010
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Publication status: Published in: Journal of economic theory (2010) v.145 n° 3,p.1142–1163
Handle: RePEc:ulb:ulbeco:2013/131711
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  1. Laurens Cherchye & Frederic Vermeulen, 2003. "Nonparametric Analysis of Household Labour Supply: Goodness-of-Fit and Power of the Unitary and the Collective Model," Public Economics Working Paper Series ces0302, Katholieke Universiteit Leuven, Centrum voor Economische Studiën, Working Group Public Economics.
  2. Martin Browning & P.A. Chiappori, 1996. "Efficient Intra-Household Allocations - A General Characterization and Empirical Tests," Discussion Papers 96-10, University of Copenhagen. Department of Economics.
  3. Donald J. Brown & Chris Shannon, 2000. "Uniqueness, Stability, and Comparative Statics in Rationalizable Walrasian Markets," Econometrica, Econometric Society, vol. 68(6), pages 1529-1540, November.
  4. Cherchye, Laurens & De Rock, Bram & Vermeulen, Frederic, 2007. "The Revealed Preference Approach to Collective Consumption Behavior: Testing, Recovery and Welfare Analysis," IZA Discussion Papers 3062, Institute for the Study of Labor (IZA).
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  6. Francoise Forges & Enrico Minelli, 2006. "Afriat’s Theorem for General Budget Sets," CESifo Working Paper Series 1703, CESifo Group Munich.
  7. 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).
  8. Laurens Cherchye & Bram De Rock & Jeroen Sabbe & Frederic Vermeulen, 2008. "Nonparametric tests of collectively rational consumption behavior: an integer programming procedure," Working Papers ECARES 2008-001, ULB -- Universite Libre de Bruxelles.
  9. Varian, Hal R, 1982. "The Nonparametric Approach to Demand Analysis," Econometrica, Econometric Society, vol. 50(4), pages 945-73, July.
  10. 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.
  11. Donald J. Brown & Rosa L. Matzkin, 1995. "Testable Restrictions on the Equilibrium Manifold," Cowles Foundation Discussion Papers 1109, Cowles Foundation for Research in Economics, Yale University.
  12. Browning, M. & Bourguignon, F. & Chiappori, P.A. & Lechene, V., 1992. "Incomes and Outcomes: A structural Model of Intra-Household Allocation," DELTA Working Papers 92-23, DELTA (Ecole normale supérieure).
  13. 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.
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  16. François Bourguignon & Martin Browning & Pierre-André Chiappori, 2009. "Efficient Intra-Household Allocations and Distribution Factors: Implications and Identification," Post-Print halshs-00754386, HAL.
  17. 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, 03.
  18. W. E. Diewert, 1973. "Afriat and Revealed Preference Theory," Review of Economic Studies, Oxford University Press, vol. 40(3), pages 419-425.
  19. Kannai, Yakar, 1977. "Concavifiability and constructions of concave utility functions," Journal of Mathematical Economics, Elsevier, vol. 4(1), pages 1-56, March.
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  22. Guesnerie, Roger, 1975. "Pareto Optimality in Non-Convex Economies," Econometrica, Econometric Society, vol. 43(1), pages 1-29, January.
  23. 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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  26. Starrett, David A., 1972. "Fundamental nonconvexities in the theory of externalities," Journal of Economic Theory, Elsevier, vol. 4(2), pages 180-199, April.
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