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Heuristics for deciding collectively rational consumption behavior

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  • Talla Nobibon, Fabrice
  • Cherchye, Laurens
  • De Rock, Bram
  • Sabbe, Jeroen
  • Spieksma, Frederik

Abstract

We propose a directed graph for testing whether observed household consumption behavior satisfies the Collective Axiom of Revealed Preferences (CARP). More precisely, the data satisfy CARP if the graph allows a node-partitioning into two induced subgraphs that are acyclic. We prove that partitioning the obtained graph into two acyclic subgraphs is NP-complete. Next, we derive a necessary condition for CARP that can be verified in polynomial time, and we present an example to show that our necessary and sufficient conditions do not coincide. We also propose and implement fast heuristics for testing the sufficient condition. These heuristics can be used to check reasonably large data sets for CARP, and can be of particular interest when used prior to computationally demanding approaches. Finally, based on computational results for both real-life and synthetic data, we conclude that our heuristics are effective in testing CARP.

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Bibliographic Info

Paper provided by Katholieke Universiteit Leuven in its series Open Access publications from Katholieke Universiteit Leuven with number urn:hdl:123456789/268772.

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Date of creation: 2011
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Publication status: Published in Computational Economics (2011) v.38, p.173-204
Handle: RePEc:ner:leuven:urn:hdl:123456789/268772

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Web page: http://www.kuleuven.be

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  1. Varian, Hal R, 1982. "The Nonparametric Approach to Demand Analysis," Econometrica, Econometric Society, vol. 50(4), pages 945-73, July.
  2. 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.
  3. Mette Christensen, 2007. "Integrability of Demand Accounting for Unobservable Heterogeneity: A Test on Panel Data," The School of Economics Discussion Paper Series 0713, Economics, The University of Manchester.
  4. 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.
  5. P.-A. Chiappori & I. Ekeland, 2009. "The Microeconomics of Efficient Group Behavior: Identification," Econometrica, Econometric Society, vol. 77(3), pages 763-799, 05.
  6. Chiappori, Pierre-Andre, 1988. "Rational Household Labor Supply," Econometrica, Econometric Society, vol. 56(1), pages 63-90, January.
  7. 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.
  8. Cherchye, Laurens & De Rock, Bram & Vermeulen, Frederic, 2008. "An Afriat Theorem for the Collective Model of Household Consumption," IZA Discussion Papers 3794, Institute for the Study of Labor (IZA).
  9. Mette Christensen, 2007. "Integrability of demand accounting for unobservable heterogeneity: a test on panel data," IFS Working Papers W07/14, Institute for Fiscal Studies.
  10. Cherchye, L.J.H. & Rock, B. de & Vermeulen, F.M.P., 2007. "The collective model of household consumption: A nonparametric characterization," Open Access publications from Tilburg University urn:nbn:nl:ui:12-194157, Tilburg University.
  11. Donald J. Brown and Chris Shannon., 1997. "Uniqueness, Stability, and Comparative Statics in Rationalizable Walrasian Markets," Economics Working Papers 97-256, University of California at Berkeley.
  12. Diewert, W E, 1973. "Afriat and Revealed Preference Theory," Review of Economic Studies, Wiley Blackwell, vol. 40(3), pages 419-25, July.
  13. 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.
  14. 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.
  15. 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.
  16. Chiappori, Pierre-Andre, 1992. "Collective Labor Supply and Welfare," Journal of Political Economy, University of Chicago Press, vol. 100(3), pages 437-67, June.
  17. repec:bla:restud:v:75:y:2008:i:2:p:371-389 is not listed on IDEAS
  18. 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.
  19. Starr, Ross M, 1969. "Quasi-Equilibria in Markets with Non-Convex Preferences," Econometrica, Econometric Society, vol. 37(1), pages 25-38, January.
  20. Starrett, David A., 1972. "Fundamental nonconvexities in the theory of externalities," Journal of Economic Theory, Elsevier, vol. 4(2), pages 180-199, April.
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Cited by:
  1. Cherchye, Laurens & Demuynck, Thomas & De Rock, Bram, 2011. "Testable implications of general equilibrium models: an integer programming approach," Open Access publications from Katholieke Universiteit Leuven urn:hdl:123456789/311998, Katholieke Universiteit Leuven.
  2. Mark Dean & Daniel Martin, 2011. "Testing for Rationality with Consumption Data: Demographics and Heterogeneity," Working Papers 2011-11, Brown University, Department of Economics.

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