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An Afriat Theorem for the Collective Model of Household Consumption

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  • Cherchye, L.J.H.
  • Rock, B. de
  • Vermeulen, F.M.P.

    (Tilburg University, Center for Economic Research)

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 su¢ cient 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 Tilburg University, Center for Economic Research in its series Discussion Paper with number 2008-72.

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Date of creation: 2008
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Handle: RePEc:dgr:kubcen:200872

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  1. Chiappori, Pierre-Andre, 1992. "Collective Labor Supply and Welfare," Journal of Political Economy, University of Chicago Press, vol. 100(3), pages 437-67, June.
  2. Kannai, Yakar, 1977. "Concavifiability and constructions of concave utility functions," Journal of Mathematical Economics, Elsevier, vol. 4(1), pages 1-56, March.
  3. Laurens Cherchye & Bram De Rock & Frederic Vermeulen, 2011. "The Revealed Preference Approach to Collective Consumption Behaviour: Testing and Sharing Rule Recovery," Review of Economic Studies, Oxford University Press, vol. 78(1), pages 176-198.
  4. Forges, Françoise & Minelli, Enrico, 2009. "Afriat's theorem for general budget sets," Journal of Economic Theory, Elsevier, vol. 144(1), pages 135-145, January.
  5. Varian, Hal R, 1982. "The Nonparametric Approach to Demand Analysis," Econometrica, Econometric Society, vol. 50(4), pages 945-73, July.
  6. Cherchye, Laurens & De Rock, Bram & Vermeulen, Frederic, 2007. "The revealed preference approach to collective consumption behavior: testing, recovery and welfare analysis," Open Access publications from Katholieke Universiteit Leuven urn:hdl:123456789/122664, Katholieke Universiteit Leuven.
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  11. Starr, Ross M, 1969. "Quasi-Equilibria in Markets with Non-Convex Preferences," Econometrica, Econometric Society, vol. 37(1), pages 25-38, January.
  12. 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.
  13. Cherchye, Laurens & Vermeulen, Frederic, 2006. "Nonparametric analysis of household labour supply: Goodness-of-fit and power of the unitary and the collective model," Open Access publications from Katholieke Universiteit Leuven urn:hdl:123456789/120923, Katholieke Universiteit Leuven.
  14. 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.
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  19. Cherchye, L.J.H. & Rock, B. de & 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.
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  22. 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.
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Citations

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Cited by:
  1. Laurens CHERCHYE & Bram DE ROCK & Arthur LEWBEL & Frederic VERMEULEN, 2012. "Sharing rule identification for general collective consumption models," Center for Economic Studies - Discussion papers ces12.05, Katholieke Universiteit Leuven, Centrum voor Economische Studiën.
  2. 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".
  3. Ennio Bilancini, 2011. "On the rationalizability of observed consumers’ choices when preferences depend on budget sets and (potentially) on anything else," Journal of Economics, Springer, vol. 102(3), pages 275-286, April.
  4. Cherchye, L.J.H. & Demuynck, T. & Rock, B. de, 2009. "Degrees of Cooperation in Household Consumption Models: A Revealed Preference Analysis," Discussion Paper 2009-91, Tilburg University, Center for Economic Research.
  5. Nobibon, Fabrice T. & Cherchye, Laurens & De Rock, Bram & Sabbe, Jeroen & Spieksma, Frits C.R., 2008. "Heuristics for deciding collectively rational consumption behavior," Open Access publications from Katholieke Universiteit Leuven urn:hdl:123456789/198271, Katholieke Universiteit Leuven.
  6. 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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