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An Afriat Theorem for the Collective Model of Household Consumption

  • Cherchye, Laurens

    ()

    (KU Leuven)

  • De Rock, Bram

    ()

    (ECARES, Free University of Brussels)

  • Vermeulen, Frederic

    ()

    (KU Leuven)

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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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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  1. Donald J. Brown and Chris Shannon., 1997. "Uniqueness, Stability, and Comparative Statics in Rationalizable Walrasian Markets," Economics Working Papers 97-256, University of California at Berkeley.
  2. Cherchye, L.J.H. & de Rock, B. & Vermeulen, F.M.P., 2004. "The Collective Model of Household Consumption : A Nonparametric Characterization," Discussion Paper 2004-76, Tilburg University, Center for Economic Research.
  3. Pollak, Robert A, 1990. "Distinguished Fellow: Houthakker's Contributions to Economics," Journal of Economic Perspectives, American Economic Association, vol. 4(2), pages 141-56, Spring.
  4. Starrett, David A., 1972. "Fundamental nonconvexities in the theory of externalities," Journal of Economic Theory, Elsevier, vol. 4(2), pages 180-199, April.
  5. Cherchye, Laurens & Vermeulen, Frederic, 2006. "Nonparametric Analysis of Household Labor Supply: Goodness-of-Fit and Power of the Unitary and the Collective Model," IZA Discussion Papers 2004, Institute for the Study of Labor (IZA).
  6. Cherchye, L.J.H. & de Rock, B. & Sabbe, J. & Vermeulen, F.M.P., 2008. "Nonparametric Tests of Collectively Rational Consumption Behavior : An Integer Programming Procedure," Discussion Paper 2008-2, Tilburg University, Center for Economic Research.
  7. Browning, Martin & Francois Bourguignon & Pierre-Andre Chiappori & Valerie Lechene, 1994. "Income and Outcomes: A Structural Model of Intrahousehold Allocation," Journal of Political Economy, University of Chicago Press, vol. 102(6), pages 1067-96, December.
  8. François Bourguignon & Martin Browning & Pierre-André Chiappori, 2006. "Efficient Intra-household Allocations and Distribution Factors: Implications and Identification," CAM Working Papers 2006-02, University of Copenhagen. Department of Economics. Centre for Applied Microeconometrics.
  9. Kannai, Yakar, 1977. "Concavifiability and constructions of concave utility functions," Journal of Mathematical Economics, Elsevier, vol. 4(1), pages 1-56, March.
  10. 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.
  11. Forges, Françoise & Minelli, Enrico, 2009. "Afriat's theorem for general budget sets," Economics Papers from University Paris Dauphine 123456789/4099, Paris Dauphine University.
  12. 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).
  13. 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.
  14. Brown, Donald J & Matzkin, Rosa L, 1996. "Testable Restrictions on the Equilibrium Manifold," Econometrica, Econometric Society, vol. 64(6), pages 1249-62, November.
  15. P.-A. Chiappori & I. Ekeland, 2009. "The Microeconomics of Efficient Group Behavior: Identification," Econometrica, Econometric Society, vol. 77(3), pages 763-799, 05.
  16. Chiappori, Pierre-Andre, 1992. "Collective Labor Supply and Welfare," Journal of Political Economy, University of Chicago Press, vol. 100(3), pages 437-67, June.
  17. Mas-Colell, Andreu & Whinston, Michael D. & Green, Jerry R., 1995. "Microeconomic Theory," OUP Catalogue, Oxford University Press, number 9780195102680, March.
  18. 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.
  19. Bram De Rock & Laurens Cherchye & Frederic Vermeulen, 2008. "Analyzing cost efficient production behavior under economies of scope: a nonparametric methodology," ULB Institutional Repository 2013/7536, ULB -- Universite Libre de Bruxelles.
  20. Diewert, W E, 1973. "Afriat and Revealed Preference Theory," Review of Economic Studies, Wiley Blackwell, vol. 40(3), pages 419-25, July.
  21. Starr, Ross M, 1969. "Quasi-Equilibria in Markets with Non-Convex Preferences," Econometrica, Econometric Society, vol. 37(1), pages 25-38, January.
  22. 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.
  23. Richter, Marcel K. & Wong, K.-C.Kam-Chau, 2004. "Concave utility on finite sets," Journal of Economic Theory, Elsevier, vol. 115(2), pages 341-357, April.
  24. Chiappori, Pierre-Andre, 1988. "Rational Household Labor Supply," Econometrica, Econometric Society, vol. 56(1), pages 63-90, January.
  25. Guesnerie, Roger, 1975. "Pareto Optimality in Non-Convex Economies," Econometrica, Econometric Society, vol. 43(1), pages 1-29, January.
  26. Varian, Hal R, 1982. "The Nonparametric Approach to Demand Analysis," Econometrica, Econometric Society, vol. 50(4), pages 945-73, July.
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