IDEAS home Printed from https://ideas.repec.org/
MyIDEAS: Log in (now much improved!) to save this paper

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.

If you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.

File URL: http://ftp.iza.org/dp3794.pdf
Download Restriction: no

Paper provided by Institute for the Study of Labor (IZA) in its series IZA Discussion Papers with number 3794.

as
in new window

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
Contact details of provider: Postal:
IZA, P.O. Box 7240, D-53072 Bonn, Germany

Phone: +49 228 3894 223
Fax: +49 228 3894 180
Web page: http://www.iza.org

Order Information: Postal: IZA, Margard Ody, P.O. Box 7240, D-53072 Bonn, Germany
Email:


References listed on IDEAS
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.:

as in new window
  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. Laurens Cherchye & Frederic Vermeulen, 2008. "Nonparametric Analysis of Household Labor Supply: Goodness of Fit and Power of the Unitary and the Collective Model," The Review of Economics and Statistics, MIT Press, vol. 90(2), pages 267-274, May.
  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. Mas-Colell, Andreu & Whinston, Michael D. & Green, Jerry R., 1995. "Microeconomic Theory," OUP Catalogue, Oxford University Press, number 9780195102680, December.
  5. 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.
  6. Browning, M. & Chiappori, P.A., 1994. "Efficient Intra-Household allocations: A General Characterization and Empirical Tests," DELTA Working Papers 94-16, DELTA (Ecole normale supérieure).
  7. François Bourguignon & Martin Browning & Pierre-André Chiappori, 2009. "Efficient Intra-Household Allocations and Distribution Factors: Implications and Identification," Review of Economic Studies, Oxford University Press, vol. 76(2), pages 503-528.
  8. Guesnerie, Roger, 1975. "Pareto Optimality in Non-Convex Economies," Econometrica, Econometric Society, vol. 43(1), pages 1-29, January.
  9. 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.
  10. 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.
  11. Francoise Forges & Enrico Minelli, 2006. "Afriat's Theorem for General Budget Sets," Working Papers ubs0609, University of Brescia, Department of Economics.
  12. 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.
  13. 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.
  14. 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.
  15. 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.
  16. Laurens Cherchye & Bram De Rock & Jeroen Sabbe & Frederic Vermeulen, 2008. "Nonparametric tests of collectively rational consumption behavior: an integer programming procedure," Working Papers ECARES 2008-001, ULB -- Universite Libre de Bruxelles.
  17. Laurens Cherchye & Bram De Rock & Frederic Vermeulen, 2008. "The Revealed preference approach to collective consumption behavior: testing, recovery and Welfare analysis," Working Papers ECARES 2008-029, ULB -- Universite Libre de Bruxelles.
  18. Varian, Hal R, 1982. "The Nonparametric Approach to Demand Analysis," Econometrica, Econometric Society, vol. 50(4), pages 945-73, July.
  19. Starrett, David A., 1972. "Fundamental nonconvexities in the theory of externalities," Journal of Economic Theory, Elsevier, vol. 4(2), pages 180-199, April.
  20. 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.
  21. W. E. Diewert, 1973. "Afriat and Revealed Preference Theory," Review of Economic Studies, Oxford University Press, vol. 40(3), pages 419-425.
  22. 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.
  23. Kannai, Yakar, 1977. "Concavifiability and constructions of concave utility functions," Journal of Mathematical Economics, Elsevier, vol. 4(1), pages 1-56, March.
  24. Starr, Ross M, 1969. "Quasi-Equilibria in Markets with Non-Convex Preferences," Econometrica, Econometric Society, vol. 37(1), pages 25-38, January.
  25. Chiappori, Pierre-Andre, 1988. "Rational Household Labor Supply," Econometrica, Econometric Society, vol. 56(1), pages 63-90, January.
  26. P.-A. Chiappori & I. Ekeland, 2009. "The Microeconomics of Efficient Group Behavior: Identification," Econometrica, Econometric Society, vol. 77(3), pages 763-799, 05.
Full references (including those not matched with items on IDEAS)

This item is not listed on Wikipedia, on a reading list or among the top items on IDEAS.

When requesting a correction, please mention this item's handle: RePEc:iza:izadps:dp3794. See general information about how to correct material in RePEc.

For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Mark Fallak)

If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

If references are entirely missing, you can add them using this form.

If the full references list an item that is present in RePEc, but the system did not link to it, you can help with this form.

If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your profile, as there may be some citations waiting for confirmation.

Please note that corrections may take a couple of weeks to filter through the various RePEc services.

This information is provided to you by IDEAS at the Research Division of the Federal Reserve Bank of St. Louis using RePEc data.