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Transitivity of Preferences: When Doest it Matter ?

Listed author(s):
  • Laurens Cherchye
  • Thomas Demuynck
  • Bram De Rock

We define the empirical conditions on prices and incomes under which transitivityof preferences has specific testable implications. In particular, we set out necessaryand sufficient requirements for budget sets under which consumption choices canviolate SARP (Strong Axiom of Revealed Preferences) but not WARP (Weak Axiomof Revealed Preferences). As SARP extends WARP by additionally imposingtransitive preferences, this effectively defines the conditions under which transitivityis separately testable. Our findings have considerable practical relevance, as transitivityconditions are known to substantially aggravate the computational burden ofempirical revealed preference analysis. Our characterization takes the form of triangularconditions that must hold for all three-element subsets of normalized prices,and which are easy to verify in practice. We demonstrate their practical use throughtwo short empirical applications.

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Paper provided by ULB -- Universite Libre de Bruxelles in its series Working Papers ECARES with number ECARES 2015-44.

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Length: 22 p.
Date of creation: Nov 2015
Publication status: Published by:
Handle: RePEc:eca:wpaper:2013/221187
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  1. Laura Blow & Martin Browning & Ian Crawford, 2008. "Revealed Preference Analysis of Characteristics Models," Review of Economic Studies, Oxford University Press, vol. 75(2), pages 371-389.
  2. Abi Adams & Laurens Cherchye & Bram De Rock & Ewout Verriest, 2014. "Consume Now or Later? Time Inconsistency, Collective Choice, and Revealed Preference," American Economic Review, American Economic Association, vol. 104(12), pages 4147-4183, December.
  3. Laurens Cherchye & Bram De Rock & Arthur Lewbel & Frederic Vermeulen, 2015. "Sharing Rule Identification for General Collective Consumption Models," Econometrica, Econometric Society, vol. 83(5), pages 2001-2041, 09.
  4. Richard BLUNDELL & Martin BROWNING & Laurens CHERCHYE & Ian CRAWFORD & Bram DE ROCK & Frederic VERMEULEN, 2012. "Sharp for SARP: nonparametric bounds on the behavioural and welfare effects of price changes," Working Papers Department of Economics ces12.11, KU Leuven, Faculty of Economics and Business, Department of Economics.
  5. Federico Echenique & Sangmok Lee & Matthew Shum, 2011. "The Money Pump as a Measure of Revealed Preference Violations," Journal of Political Economy, University of Chicago Press, vol. 119(6), pages 1201-1223.
  6. Laura Blow & Martin Browning & Ian Crawford, 2014. "Never mind the hyperbolics: nonparametric analysis of time-inconsistent preferences," IFS Working Papers W14/17, Institute for Fiscal Studies.
  7. Sam Cosaert & Thomas Demuynck, "undated". "Nonparametric welfare and demand analysis with unobserved individual heterogeneity," ULB Institutional Repository 2013/251988, ULB -- Universite Libre de Bruxelles.
  8. Stoye, Jörg & Kitamura, Yuichi, 2013. "Nonparametric Analysis of Random Utility Models: Testing," Annual Conference 2013 (Duesseldorf): Competition Policy and Regulation in a Global Economic Order 79753, Verein für Socialpolitik / German Economic Association.
  9. Jan Heufer, 2014. "A geometric approach to revealed preference via Hamiltonian cycles," Theory and Decision, Springer, vol. 76(3), pages 329-341, March.
  10. Laurens Cherchye & Bram De Rock & Frederic Vermeulen, 2009. "Opening the Black Box of Intrahousehold Decision Making: Theory and Nonparametric Empirical Tests of General Collective Consumption Models," Journal of Political Economy, University of Chicago Press, vol. 117(6), pages 1074-1104, December.
  11. Richard W. Blundell & Martin Browning & Ian A. Crawford, 2003. "Nonparametric Engel Curves and Revealed Preference," Econometrica, Econometric Society, vol. 71(1), pages 205-240, January.
  12. Thomas Demuynck & Christian Seel, "undated". "Revealed preference with limited consideration," ULB Institutional Repository 2013/251989, ULB -- Universite Libre de Bruxelles.
  13. Richard Blundell & Jean-Marc Robin, 2000. "Latent Separability: Grouping Goods without Weak Separability," Econometrica, Econometric Society, vol. 68(1), pages 53-84, January.
  14. Peters Hans & Wakker Peter, 1994. "WARP Does Not Imply SARP for More Than Two Commodities," Journal of Economic Theory, Elsevier, vol. 62(1), pages 152-160, February.
  15. Ian Crawford & Krishna Pendakur, 2013. "How many types are there?," Economic Journal, Royal Economic Society, vol. 123, pages 77-95, 03.
  16. Richard Blundell & Martin Browning & Ian Crawford, 2008. "Best Nonparametric Bounds on Demand Responses," Econometrica, Econometric Society, vol. 76(6), pages 1227-1262, November.
  17. Stefan Hoderlein & Jörg Stoye, 2014. "Revealed Preferences in a Heterogeneous Population," The Review of Economics and Statistics, MIT Press, vol. 96(2), pages 197-213, May.
  18. Hugh Rose, 1958. "Consistency of Preference: The Two-Commodity Case," Review of Economic Studies, Oxford University Press, vol. 25(2), pages 124-125.
  19. Shafer, Wayne J., 1977. "Revealed preference cycles and the slutsky matrix," Journal of Economic Theory, Elsevier, vol. 16(2), pages 293-309, December.
  20. Gross, John & Kaiser, Dan, 1996. "Two Simple Algorithms for Generating a Subset of Data Consistent with WARP and Other Binary Relations," Journal of Business & Economic Statistics, American Statistical Association, vol. 14(2), pages 251-255, April.
  21. Lewbel, Arthur, 1991. "The Rank of Demand Systems: Theory and Nonparametric Estimation," Econometrica, Econometric Society, vol. 59(3), pages 711-730, May.
  22. Abi Adams & Richard Blundell & Martin Browning & Ian Crawford, 2015. "Prices versus preferences: taste change and revealed preference," IFS Working Papers W15/11, Institute for Fiscal Studies.
  23. Daniel McFadden, 2005. "Revealed stochastic preference: a synthesis," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 26(2), pages 245-264, August.
  24. Bossert, Walter, 1993. "Continuous Choice Functions and the Strong Axiom of Revealed Preference," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 3(2), pages 379-385, April.
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