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An Afriat theorem for the collective model of household consumption

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  • Laurens Cherchye
  • Bram De Rock
  • Frederic Vermeulen

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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Bibliographic Info

Paper provided by ULB -- Universite Libre de Bruxelles in its series ULB Institutional Repository with number 2013/131711.

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Date of creation: 2010
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Publication status: Published in: Journal of economic theory (2010) v.145 n° 3,p.1142–1163
Handle: RePEc:ulb:ulbeco:2013/131711

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References

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  1. Cherchye, Laurens & De Rock, Bram & Vermeulen, Frederic, 2007. "The Revealed Preference Approach to Collective Consumption Behavior: Testing, Recovery and Welfare Analysis," IZA Discussion Papers 3062, Institute for the Study of Labor (IZA).
  2. 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.
  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. 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.
  5. Chiappori, P.A., 1989. "Collective Labour Supply and Welfare," DELTA Working Papers 89-07, DELTA (Ecole normale supérieure).
  6. M. Browning & P. A. Chiappori, 1998. "Efficient Intra-Household Allocations: A General Characterization and Empirical Tests," Econometrica, Econometric Society, vol. 66(6), pages 1241-1278, November.
  7. Starrett, David A., 1972. "Fundamental nonconvexities in the theory of externalities," Journal of Economic Theory, Elsevier, vol. 4(2), pages 180-199, April.
  8. 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.
  9. Diewert, W E, 1973. "Afriat and Revealed Preference Theory," Review of Economic Studies, Wiley Blackwell, vol. 40(3), pages 419-25, July.
  10. Forges, Françoise & Minelli, Enrico, 2009. "Afriat's theorem for general budget sets," Journal of Economic Theory, Elsevier, vol. 144(1), pages 135-145, January.
  11. Pollak, R.A., 1990. "Distinguished Floow: Houthakker'S Contributions To Economics," Working Papers 90-06, University of Washington, Department of Economics.
  12. 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.
  13. Kannai, Yakar, 1977. "Concavifiability and constructions of concave utility functions," Journal of Mathematical Economics, Elsevier, vol. 4(1), pages 1-56, March.
  14. Brown, Donald J & Matzkin, Rosa L, 1996. "Testable Restrictions on the Equilibrium Manifold," Econometrica, Econometric Society, vol. 64(6), pages 1249-62, November.
  15. Mas-Colell, Andreu & Whinston, Michael D. & Green, Jerry R., 1995. "Microeconomic Theory," OUP Catalogue, Oxford University Press, number 9780195102680.
  16. 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.
  17. Guesnerie, Roger, 1975. "Pareto Optimality in Non-Convex Economies," Econometrica, Econometric Society, vol. 43(1), pages 1-29, 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. Laurens Cherchye & Ian Crawford & Bram De Rock & Frederic Vermeulen, 2009. "The revealed preference approach to demand," ULB Institutional Repository 2013/132522, ULB -- Universite Libre de Bruxelles.
  20. 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.
  21. P.-A. Chiappori & I. Ekeland, 2009. "The Microeconomics of Efficient Group Behavior: Identification," Econometrica, Econometric Society, vol. 77(3), pages 763-799, 05.
  22. Cherchye, L.J.H. & Rock, B. de & Vermeulen, F.M.P., 2004. "The Collective Model of Household Consumption: A Nonparametric Characterization," Discussion Paper 2004-76, Tilburg University, Center for Economic Research.
  23. 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.
  24. Starr, Ross M, 1969. "Quasi-Equilibria in Markets with Non-Convex Preferences," Econometrica, Econometric Society, vol. 37(1), pages 25-38, January.
  25. 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.
  26. Varian, Hal R, 1982. "The Nonparametric Approach to Demand Analysis," Econometrica, Econometric Society, vol. 50(4), pages 945-73, July.
  27. Chiappori, Pierre-Andre, 1988. "Rational Household Labor Supply," Econometrica, Econometric Society, vol. 56(1), pages 63-90, January.
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Citations

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Cited by:
  1. Ivar Ekeland & Alfred Galichon, 2013. "The housing problem and revealed preference theory: duality and an application," Economic Theory, Springer, vol. 54(3), pages 425-441, November.
  2. Laurens Cherchye & Bram De Rock & Vincenzo Platino, 2010. "Private versus public consumption within groups : testing the nature of goods from aggregate data," Documents de travail du Centre d'Economie de la Sorbonne 10090, Université Panthéon-Sorbonne (Paris 1), Centre d'Economie de la Sorbonne.
  3. Cherchye, Laurens & De Rock, Bram & Lewbel, Arthur & Vermeulen, Frederic, 2012. "Sharing Rule Identification for General Collective Consumption Models," IZA Discussion Papers 6571, Institute for the Study of Labor (IZA).
  4. Ennio Bilancini, 2010. "On the rationalizability of observed consumers’ choices when preferences depend on budget sets and (potentially) on anything else," Center for Economic Research (RECent) 052, University of Modena and Reggio E., Dept. of Economics.
  5. 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.
  6. Fabrice Talla Nobibon & Laurens Cherchye & Bram De Rock & Jeroen Sabbe & Frits Spieksma, 2011. "Heuristics for Deciding Collectively Rational Consumption Behavior," Computational Economics, Society for Computational Economics, vol. 38(2), pages 173-204, August.
  7. 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".

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