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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 (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 Katholieke Universiteit Leuven, Centrum voor Economische Studiën in its series Center for Economic Studies - Discussion papers with number ces0825.

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Date of creation: Sep 2008
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Handle: RePEc:ete:ceswps:ces0825
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  1. Cherchye, L.J.H. & de Rock, B. & Vermeulen, F.M.P., 2007. "The collective model of household consumption : A nonparametric characterization," Other publications TiSEM 0a104373-4fb6-4ef2-9d2b-2, Tilburg University, School of Economics and Management.
  2. Martin Browning & Pierre-Andre Chiappori, 1994. "Efficient Intra-Household Allocations: a General Characterization and Empirical Tests," Department of Economics Working Papers 1994-02, McMaster University.
  3. Cherchye, L.J.H. & de Rock, B. & Vermeulen, F.M.P., 2006. "Analyzing Cost Efficient Production Behavior Under Economies of Scope : A Nonparametric Methodology," Discussion Paper 2006-81, Tilburg University, Center for Economic Research.
  4. Kannai, Yakar, 1977. "Concavifiability and constructions of concave utility functions," Journal of Mathematical Economics, Elsevier, vol. 4(1), pages 1-56, March.
  5. Donald J. Brown & Chris Shannon, 1998. "Uniqueness, Stability, and Comparative Statics in Rationalizable Walrasian Markets," GE, Growth, Math methods 9802003, EconWPA, revised 02 Mar 1998.
  6. 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.
  7. Mas-Colell, Andreu & Whinston, Michael D. & Green, Jerry R., 1995. "Microeconomic Theory," OUP Catalogue, Oxford University Press, number 9780195102680, March.
  8. Laurens Cherchye & Bram De Rock & Jeroen Sabbe & Frederic Vemeulen, 2008. "Nonparametric tests of collectively rational consumption behavior: an integer programming procedure," Center for Economic Studies - Discussion papers ces0801, Katholieke Universiteit Leuven, Centrum voor Economische Studiën.
  9. Starr, Ross M, 1969. "Quasi-Equilibria in Markets with Non-Convex Preferences," Econometrica, Econometric Society, vol. 37(1), pages 25-38, January.
  10. 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.
  11. Chiappori, Pierre-Andre, 1988. "Rational Household Labor Supply," Econometrica, Econometric Society, vol. 56(1), pages 63-90, January.
  12. 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.
  13. Francoise Forges & Enrico Minelli, 2006. "Afriat's Theorem for General Budget Sets," Working Papers ubs0609, University of Brescia, Department of Economics.
  14. 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.
  15. Chiappori, Pierre-Andre, 1992. "Collective Labor Supply and Welfare," Journal of Political Economy, University of Chicago Press, vol. 100(3), pages 437-67, June.
  16. P.-A. Chiappori & I. Ekeland, 2009. "The Microeconomics of Efficient Group Behavior: Identification," Econometrica, Econometric Society, vol. 77(3), pages 763-799, 05.
  17. Diewert, W E, 1973. "Afriat and Revealed Preference Theory," Review of Economic Studies, Wiley Blackwell, vol. 40(3), pages 419-25, July.
  18. Starrett, David A., 1972. "Fundamental nonconvexities in the theory of externalities," Journal of Economic Theory, Elsevier, vol. 4(2), pages 180-199, April.
  19. 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.
  20. Varian, Hal R, 1982. "The Nonparametric Approach to Demand Analysis," Econometrica, Econometric Society, vol. 50(4), pages 945-73, July.
  21. 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.
  22. Guesnerie, Roger, 1975. "Pareto Optimality in Non-Convex Economies," Econometrica, Econometric Society, vol. 43(1), pages 1-29, January.
  23. Laurens CHERCHYE & Bram DE ROCK & Frederic VERMEULEN, 2007. "The revealed preference approach to collective consumption behavior: testing, recovery and welfare analysis," Center for Economic Studies - Discussion papers ces0724, Katholieke Universiteit Leuven, Centrum voor Economische Studiën.
  24. 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.
  25. 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.
  26. 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.
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