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An Afriat Theorem for the collective model of household consumption

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Author Info
Laurens Cherchye
Bram De Rock
Frederic Vermeulen

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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 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. Chiappori, Pierre-Andre, 1992. "Collective Labor Supply and Welfare," Journal of Political Economy, University of Chicago Press, vol. 100(3), pages 437-67, June. [Downloadable!] (restricted)
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  2. Kannai, Yakar, 1977. "Concavifiability and constructions of concave utility functions," Journal of Mathematical Economics, Elsevier, vol. 4(1), pages 1-56, March. [Downloadable!] (restricted)
  3. Starrett, David A., 1972. "Fundamental nonconvexities in the theory of externalities," Journal of Economic Theory, Elsevier, vol. 4(2), pages 180-199, April. [Downloadable!] (restricted)
  4. Laurens Cherchye & Bram De Rock & Jeroen Sabbe & Frederic Vermeulen, 2008. "Nonparametric Tests of Collectively Rational Consumption Behavior: an Integer Programming Procedure," ECARES Working Papers 2008_001, Université Libre de Bruxelles, Ecares. [Downloadable!]
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  5. Varian, Hal R, 1982. "The Nonparametric Approach to Demand Analysis," Econometrica, Econometric Society, vol. 50(4), pages 945-73, July. [Downloadable!] (restricted)
  6. 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. [Downloadable!] (restricted)
  7. Laurens Cherchye & Bram De Rock & Frederic Vermeulen, 2008. "The Revealed Preference Approach to Collective Consumption Behavior: Testing, Recovery and Welfare Analysis," ECARES Working Papers 2008_029, Université Libre de Bruxelles, Ecares. [Downloadable!]
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  8. 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. [Downloadable!] (restricted)
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  9. FRANÇOIS BOURGUIGNON & MARTIN BROWNING & PIERRE-ANDRÉ CHIAPPORI, 2009. "Efficient Intra-Household Allocations and Distribution Factors: Implications and Identification," Review of Economic Studies, Blackwell Publishing, vol. 76(2), pages 503-528, 04. [Downloadable!] (restricted)
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  10. 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. [Downloadable!] (restricted)
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  11. 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.
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  12. 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.
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  13. Laurens Cherchye & Bram De Rock & Frederic Vermeulen, 2006. "Analyzing Cost Efficient Production Behavior Under Economies of Scope: A Nonparametric Methodology," IZA Discussion Papers 2319, Institute for the Study of Labor (IZA). [Downloadable!]
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  14. Diewert, W E, 1973. "Afriat and Revealed Preference Theory," Review of Economic Studies, Blackwell Publishing, vol. 40(3), pages 419-25, July. [Downloadable!] (restricted)
  15. 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. [Downloadable!] (restricted)
  16. Brown, Donald J & Matzkin, Rosa L, 1996. "Testable Restrictions on the Equilibrium Manifold," Econometrica, Econometric Society, vol. 64(6), pages 1249-62, November. [Downloadable!] (restricted)
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  17. Chiappori, Pierre-Andre, 1988. "Rational Household Labor Supply," Econometrica, Econometric Society, vol. 56(1), pages 63-90, January. [Downloadable!] (restricted)
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(explanations, Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.)

  1. Fabrice Talla Nobibon & Laurens Cherchye & Bram De Rock & Jereon Sabbe & Frederic Vermeulen, 2008. "Heuristics for Deciding Collectively Rational Consumption Behavior," ECARES Working Papers 2008_028, Université Libre de Bruxelles, Ecares. [Downloadable!]
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