An Afriat Theorem for the Collective Model of Household Consumption
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.Download Info
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.Bibliographic Info
Paper provided by Tilburg University, Center for Economic Research in its series Discussion Paper with number 2008-72.Length:
Date of creation: 2008
Date of revision:
Handle: RePEc:dgr:kubcen:200872
Contact details of provider:
Web page: http://center.uvt.nl
Related research
Keywords:Other versions of this item:
- Cherchye, Laurens & De Rock, Bram & Vermeulen, Frederic, 2010. "An Afriat Theorem for the collective model of household consumption," Journal of Economic Theory, Elsevier, vol. 145(3), pages 1142-1163, May.
- 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).
- Laurens Cherchye & Bram De Rock & Frederic Vermeulen, 2008. "An Afriat Theorem for the collective model of household consumption," Center for Economic Studies - Discussion papers ces0825, Katholieke Universiteit Leuven, Centrum voor Economische Studiën.
- Cherchye, Laurens & De Rock, Bram & Vermeulen, Frederic, 2008. "An afriat theorem for the collective model of household consumption," Open Access publications from Katholieke Universiteit Leuven urn:hdl:123456789/197557, Katholieke Universiteit Leuven.
- Laurens Cherchye & Bram De Rock & Frederic Vermeulen, 2010. "An Afriat theorem for the collective model of household consumption," ULB Institutional Repository 2013/131711, ULB -- Universite Libre de Bruxelles.
- D11 - Microeconomics - - Household Behavior - - - Consumer Economics: Theory
- D12 - Microeconomics - - Household Behavior - - - Consumer Economics: Empirical Analysis
- D13 - Microeconomics - - Household Behavior - - - Household Production and Intrahouse Allocation
- C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
This paper has been announced in the following NEP Reports:
- NEP-ALL-2009-01-31 (All new papers)
References
References listed on IDEASPlease 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.:
- Chiappori, Pierre-Andre, 1992.
"Collective Labor Supply and Welfare,"
Journal of Political Economy,
University of Chicago Press, vol. 100(3), pages 437-67, June.
- Chiappori, P.A., 1989. "Collective Labour Supply and Welfare," DELTA Working Papers 89-07, DELTA (Ecole normale supérieure).
- Kannai, Yakar, 1977. "Concavifiability and constructions of concave utility functions," Journal of Mathematical Economics, Elsevier, vol. 4(1), pages 1-56, March.
- 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.
- Cherchye, Laurens & De Rock, Bram & Vermeulen, Frederic, 2011. "The revealed preference approach to collective consumption behavior: testing and sharing rule recovery," Open Access publications from Katholieke Universiteit Leuven urn:hdl:123456789/262764, Katholieke Universiteit Leuven.
- Forges, Françoise & Minelli, Enrico, 2009.
"Afriat's theorem for general budget sets,"
Journal of Economic Theory,
Elsevier, vol. 144(1), pages 135-145, January.
- Francoise Forges & Enrico Minelli, 2006. "Afriat's Theorem for General Budget Sets," Working Papers ubs0609, University of Brescia, Department of Economics.
- Francoise Forges & Enrico Minelli, 2006. "Afriat’s Theorem for General Budget Sets," CESifo Working Paper Series 1703, CESifo Group Munich.
- Forges, Françoise & Minelli, Enrico, 2009. "Afriat's theorem for general budget sets," Open Access publications from Université Paris-Dauphine urn:hdl:123456789/4099, Université Paris-Dauphine.
- Varian, Hal R, 1982. "The Nonparametric Approach to Demand Analysis," Econometrica, Econometric Society, vol. 50(4), pages 945-73, July.
- 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.
- 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).
- Laurens CHERCHYE & Bram DE ROCK & Frederic VERMEULEN, 2007. "The revealed preference approach to collective consumption behavior: testing, recovery and welfare analysis," Center for Economic Studies - Discussion papers ces0724, Katholieke Universiteit Leuven, Centrum voor Economische Studiën.
- Pollak, R.A., 1990.
"Distinguished Floow: Houthakker'S Contributions To Economics,"
Working Papers
90-06, University of Washington, Department of Economics.
- 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.
- 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.
- Guesnerie, Roger, 1975. "Pareto Optimality in Non-Convex Economies," Econometrica, Econometric Society, vol. 43(1), pages 1-29, January.
- Martin Browning & Pierre-Andre Chiappori, 1994.
"Efficient Intra-Household Allocations: a General Characterization and Empirical Tests,"
Department of Economics Working Papers
1994-02, McMaster University.
- 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.
- 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).
- 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.
- Starr, Ross M, 1969. "Quasi-Equilibria in Markets with Non-Convex Preferences," Econometrica, Econometric Society, vol. 37(1), pages 25-38, January.
- 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.
- Laurens Cherchye & Bram De Rock & Frederic Vermeulen, 2007. "The Collective Model of Household Consumption: A nonparametric characterization," ULB Institutional Repository 2013/98559, ULB -- Universite Libre de Bruxelles.
- 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.
- 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.
- 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.
- 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.
- Cherchye, Laurens & Vermeulen, Frederic, 2008. "Nonparametric analysis of household labor supply: Goodness-of-fit and power of the unitary and the collective model," Open Access publications from Katholieke Universiteit Leuven urn:hdl:123456789/183144, Katholieke Universiteit Leuven.
- Cherchye, L.J.H. & Vermeulen, F.M.P., 2006. "Nonparametric Analysis of Household Labor Supply: Goodness-of-Fit and Power of the Unitary and the Collective Model," Discussion Paper 2006-13, Tilburg University, Center for Economic Research.
- 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).
- Laurens Cherchye & Frederic Vermeulen, 2003. "Nonparametric Analysis of Household Labour Supply: Goodness-of-Fit and Power of the Unitary and the Collective Model," Public Economics Working Paper Series ces0302, Katholieke Universiteit Leuven, Centrum voor Economische Studiën, Working Group Public Economics.
- Cherchye, Laurens & Vermeulen, Frederic, 2003. "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:123456789/121561, Katholieke Universiteit Leuven.
- 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.
- Cherchye, Laurens & De Rock, Bram & Sabbe, Jeroen & Vermeulen, Frederic, 2008. "Nonparametric tests of collectively rational consumption behavior: An integer programming procedure," Journal of Econometrics, Elsevier, vol. 147(2), pages 258-265, December.
- Cherchye, Laurens & De Rock, Bram & Sabbe, Jeroen & Vermeulen, Frederic, 2008. "Nonparametric tests of collectively rational consumption behaviour: an integer programming procedure," Open Access publications from Katholieke Universiteit Leuven urn:hdl:123456789/177075, Katholieke Universiteit Leuven.
- Laurens Cherchye & Bram De Rock & Jeroen Sabbe & Frederic Vermeulen, 2008. "Nonparametric tests of collectively rational consumption behavior: an integer programming procedure," ULB Institutional Repository 2013/131712, ULB -- Universite Libre de Bruxelles.
- Cherchye, L.J.H. & Rock, B. de & Sabbe, J. & Vermeulen, F.M.P., 2008. "Nonparametric Tests of Collectively Rational Consumption Behavior: An Integer Programming Procedure," Discussion Paper 2008-2, Tilburg University, Center for Economic Research.
- Cherchye, Laurens & De Rock, Bram & Sabbe, Jeroen & Vermeulen, Frederic, 2008. "Nonparametric tests of collectively rational consumption behavior: an integer programming procedure," Open Access publications from Katholieke Universiteit Leuven urn:hdl:123456789/183147, Katholieke Universiteit Leuven.
- 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.
- 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.
- 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.
- Donald J. Brown & Chris Shannon, 1998. "Uniqueness, Stability, and Comparative Statics in Rationalizable Walrasian Markets," GE, Growth, Math methods 9802003, EconWPA, revised 02 Mar 1998.
- P.-A. Chiappori & I. Ekeland, 2009. "The Microeconomics of Efficient Group Behavior: Identification," Econometrica, Econometric Society, vol. 77(3), pages 763-799, 05.
- Chiappori, Pierre-Andre, 1988. "Rational Household Labor Supply," Econometrica, Econometric Society, vol. 56(1), pages 63-90, January.
- Browning, M. & Bourguignon, F. & Chiappori, P.A. & Lechene, V., 1992.
"Incomes and Outcomes: A structural Model of Intra-Household Allocation,"
DELTA Working Papers
92-23, DELTA (Ecole normale supérieure).
- 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.
- Browning, M & Bourguignon, F & Chiappori, Pa & Lechene, V, 1994. "Income And Outcomes - A Structural Model Of Intrahousehold Allocation," Open Access publications from University College London http://discovery.ucl.ac.u, University College London.
- 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.
- Bram De Rock & Laurens Cherchye & Frederic Vermeulen, 2008. "Analyzing cost efficient production behavior under economies of scope: a nonparametric methodology," ULB Institutional Repository 2013/7536, ULB -- Universite Libre de Bruxelles.
- Cherchye, Laurens & De Rock, Bram & Vermeulen, Frederic, 2006. "Analyzing Cost Efficient Production Behavior Under Economies of Scope: A Nonparametric Methodology," IZA Discussion Papers 2319, Institute for the Study of Labor (IZA).
- Starrett, David A., 1972. "Fundamental nonconvexities in the theory of externalities," Journal of Economic Theory, Elsevier, vol. 4(2), pages 180-199, April.
- repec:bla:restud:v:76:y:2009:i:2:p:503-528 is not listed on IDEAS
- 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.
- Diewert, W E, 1973. "Afriat and Revealed Preference Theory," Review of Economic Studies, Wiley Blackwell, vol. 40(3), pages 419-25, July.
- Mas-Colell, Andreu & Whinston, Michael D. & Green, Jerry R., 1995. "Microeconomic Theory," OUP Catalogue, Oxford University Press, number 9780195102680, July.
- 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.
- Brown, Donald J & Matzkin, Rosa L, 1996.
"Testable Restrictions on the Equilibrium Manifold,"
Econometrica,
Econometric Society, vol. 64(6), pages 1249-62, November.
- 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.
- 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.
Citations
Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.Cited by:
- 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.
- Cherchye, Laurens & De Rock, Bram & Lewbel, Arthur & Vermeulen, Frederic, 2012. "Sharing rule identification for general collective consumption models," Open Access publications from Katholieke Universiteit Leuven urn:hdl:123456789/348268, Katholieke Universiteit Leuven.
- Laurens Cherchye & Bram De Rock & Arthur Lewbel & Frederic Vermeulen, 2012. "Sharing Rule Identification for General Collective Consumption Models," Boston College Working Papers in Economics 809, Boston College Department of Economics.
- Cherchye, L.J.H. & Rock, B. de & Lewbel, A. & Vermeulen, F.M.P., 2012. "Sharing Rule Identification for General Collective Consumption Models," Discussion Paper 2012-041, Tilburg University, Center for Economic Research.
- 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).
- 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".
- 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.
- 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.
- 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.
- Cherchye, Laurens & Demuynck, Thomas & De Rock, Bram, 2009. "Degrees of cooperation in household consumption models: a revealed preference analysis," Open Access publications from Katholieke Universiteit Leuven urn:hdl:123456789/252064, Katholieke Universiteit Leuven.
- Laurens CHERCHYE & Thomas DEMUYNCK & Bram DE ROCK, 2009. "Degrees of cooperation in household consumption models: a revealed preference analysis," Center for Economic Studies - Discussion papers ces09.20, Katholieke Universiteit Leuven, Centrum voor Economische Studiën.
- 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.
- 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.
- Talla Nobibon, Fabrice & Cherchye, Laurens & De Rock, Bram & Sabbe, Jeroen & Spieksma, Frederik, 2011. "Heuristics for deciding collectively rational consumption behavior," Open Access publications from Katholieke Universiteit Leuven urn:hdl:123456789/268772, Katholieke Universiteit Leuven.
- Fabrice Talla Nobibon & Laurens Cherchye & Bram De Rock & Jeroen Sabbe & Frits Spieksma, 2011. "Heuristics for deciding collectively rational consumption behavior," ULB Institutional Repository 2013/131710, ULB -- Universite Libre de Bruxelles.
- Fabrice Talla Nobibon & Laurens Cherchye & Bram De Rock & Jeroen Sabbe & Frits C.R. Spieksma, 2008. "Heuristics for deciding collectively rational consumption behavior," Center for Economic Studies - Discussion papers ces0824, Katholieke Universiteit Leuven, Centrum voor Economische Studiën.
- 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.
Lists
This item is not listed on Wikipedia, on a reading list or among the top items on IDEAS.Statistics
Access and download statisticsCorrections
When requesting a correction, please mention this item's handle: RePEc:dgr:kubcen:200872For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Corry Stuyts).
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.

