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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. 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.
  2. 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.
  3. 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).
  4. 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.
  5. Forges, Françoise & Minelli, Enrico, 2009. "Afriat's theorem for general budget sets," Economics Papers from University Paris Dauphine 123456789/4099, Paris Dauphine University.
  6. 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.
  7. 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.
  8. Chiappori, P.A., 1989. "Collective Labour Supply and Welfare," DELTA Working Papers 89-07, DELTA (Ecole normale supérieure).
  9. 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.
  10. Diewert, W E, 1973. "Afriat and Revealed Preference Theory," Review of Economic Studies, Wiley Blackwell, vol. 40(3), pages 419-25, July.
  11. 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).
  12. Brown, Donald J & Matzkin, Rosa L, 1996. "Testable Restrictions on the Equilibrium Manifold," Econometrica, Econometric Society, vol. 64(6), pages 1249-62, November.
  13. Starr, Ross M, 1969. "Quasi-Equilibria in Markets with Non-Convex Preferences," Econometrica, Econometric Society, vol. 37(1), pages 25-38, January.
  14. Starrett, David A., 1972. "Fundamental nonconvexities in the theory of externalities," Journal of Economic Theory, Elsevier, vol. 4(2), pages 180-199, April.
  15. 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.
  16. 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.
  17. Chiappori, Pierre-Andre, 1988. "Rational Household Labor Supply," Econometrica, Econometric Society, vol. 56(1), pages 63-90, January.
  18. 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.
  19. Donald J. Brown & Chris Shannon, 1998. "Uniqueness, Stability, and Comparative Statics in Rationalizable Walrasian Markets," Cowles Foundation Discussion Papers 1170, Cowles Foundation for Research in Economics, Yale University.
  20. 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).
  21. repec:ner:tilbur:urn:nbn:nl:ui:12-194157 is not listed on IDEAS
  22. P.-A. Chiappori & I. Ekeland, 2009. "The Microeconomics of Efficient Group Behavior: Identification," Econometrica, Econometric Society, vol. 77(3), pages 763-799, 05.
  23. 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.
  24. Mas-Colell, Andreu & Whinston, Michael D. & Green, Jerry R., 1995. "Microeconomic Theory," OUP Catalogue, Oxford University Press, number 9780195102680, March.
  25. Varian, Hal R, 1982. "The Nonparametric Approach to Demand Analysis," Econometrica, Econometric Society, vol. 50(4), pages 945-73, July.
  26. repec:dgr:kubcen:20082 is not listed on IDEAS
  27. Kannai, Yakar, 1977. "Concavifiability and constructions of concave utility functions," Journal of Mathematical Economics, Elsevier, vol. 4(1), pages 1-56, March.
  28. Guesnerie, Roger, 1975. "Pareto Optimality in Non-Convex Economies," Econometrica, Econometric Society, vol. 43(1), pages 1-29, January.
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