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Transitivity of preferences: when does it matter?

Author

Listed:
  • Cherchye, Laurens

    (Department of Economics, KULeuven)

  • Demuynck, Thomas

    (Ecares, Université Libre de Bruxelles)

  • De Rock, Bram

    (Ecares, Université Libre de Bruxelles)

Abstract

We define necessary and sufficient conditions on prices and incomes under which quantity choices can violate SARP (Strong Axiom of Revealed Preference) but not WARP (Weak Axiom of Revealed Preference). As SARP extends WARP by additionally imposing transitivity on the revealed preference relation, this effectively defines the conditions under which transitivity adds bite to the empirical analysis. For finite datasets, our characterization takes the form of a triangular condition that must hold for all three-element subsets of normalized prices, and which is easy to verify in practice. For infinite datasets, we formally establish an intuitive connection between our characterization and the concept of Hicksian aggregation. We demonstrate the practical use of our conditions through two empirical illustrations.

Suggested Citation

  • Cherchye, Laurens & Demuynck, Thomas & De Rock, Bram, 2018. "Transitivity of preferences: when does it matter?," Theoretical Economics, Econometric Society, vol. 13(3), September.
  • Handle: RePEc:the:publsh:2733
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    References listed on IDEAS

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    1. 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.
    2. 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, September.
    3. Blundell, R. & Browning, M. & Cherchye, L.J.H. & Crawford, I. & de Rock, B. & Vermeulen, F.M.P., 2012. "Sharp for SARP : Nonparametric Bounds on the Behavioural and Welfare Effects of Price Changes," Discussion Paper 2012-065, Tilburg University, Center for Economic Research.
    4. 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.
    5. Cherchye, Laurens & Demuynck, Thomas & De Rock, Bram & Hjertstrand, Per, 2015. "Revealed preference tests for weak separability: An integer programming approach," Journal of Econometrics, Elsevier, vol. 186(1), pages 129-141.
    6. John Quah, 2006. "Weak axiomatic demand theory," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 29(3), pages 677-699, November.
    7. Sam Cosaert & Thomas Demuynck, 2018. "Nonparametric Welfare and Demand Analysis with Unobserved Individual Heterogeneity," The Review of Economics and Statistics, MIT Press, vol. 100(2), pages 349-361, May.
    8. Yuichi Kitamura & Jörg Stoye, 2013. "Nonparametric analysis of random utility models: testing," CeMMAP working papers 36/13, Institute for Fiscal Studies.
    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. repec:hal:spmain:info:hdl:2441/f0uohitsgqh8dhk9820172631 is not listed on IDEAS
    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. Laura Blow & Martin Browning & Ian Crawford, 2008. "Revealed Preference Analysis of Characteristics Models," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 75(2), pages 371-389.
    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. 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.
    15. Ian Crawford, 2010. "Habits Revealed," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 77(4), pages 1382-1402.
    16. Hugh Rose, 1958. "Consistency of Preference: The Two-Commodity Case," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 25(2), pages 124-125.
    17. Richard Blundell & Martin Browning & Ian Crawford, 2008. "Best Nonparametric Bounds on Demand Responses," Econometrica, Econometric Society, vol. 76(6), pages 1227-1262, November.
    18. Timothy K. M. Beatty & Ian A. Crawford, 2011. "How Demanding Is the Revealed Preference Approach to Demand?," American Economic Review, American Economic Association, vol. 101(6), pages 2782-2795, October.
    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. Samiran Banerjee & James Murphy, 2009. "A simplified test for preference rationality of two-commodity choice," Experimental Economics, Springer;Economic Science Association, vol. 12(2), pages 252-252, June.
    21. Kihlstrom, Richard E & Mas-Colell, Andreu & Sonnenschein, Hugo, 1976. "The Demand Theory of the Weak Axiom of Revealed Preference," Econometrica, Econometric Society, vol. 44(5), pages 971-978, September.
    22. Thomas Demuynck & Ewout Verriest, 2013. "I’Ll Never Forget My First Cigarette: A Revealed Preference Analysis Of The “Habits As Durables” Model," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 54(2), pages 717-738, May.
    23. 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.
    24. Thomas Demuynck & Christian Seel, 2018. "Revealed Preference with Limited Consideration," American Economic Journal: Microeconomics, American Economic Association, vol. 10(1), pages 102-131, February.
    25. 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.
    26. Varian, Hal R, 1982. "The Nonparametric Approach to Demand Analysis," Econometrica, Econometric Society, vol. 50(4), pages 945-973, July.
    27. Philip J. Reny, 2015. "A Characterization of Rationalizable Consumer Behavior," Econometrica, Econometric Society, vol. 83, pages 175-192, January.
    28. Chambers,Christopher P. & Echenique,Federico, 2016. "Revealed Preference Theory," Cambridge Books, Cambridge University Press, number 9781107087804.
    29. Lewbel, Arthur, 1996. "Aggregation without Separability: A Generalized Composite Commodity Theorem," American Economic Review, American Economic Association, vol. 86(3), pages 524-543, June.
    30. 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.
    31. 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.
    32. Ian Crawford & Krishna Pendakur, 2013. "How many types are there?," Economic Journal, Royal Economic Society, vol. 123, pages 77-95, March.
    33. 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.
    34. Lewbel, Arthur, 1991. "The Rank of Demand Systems: Theory and Nonparametric Estimation," Econometrica, Econometric Society, vol. 59(3), pages 711-730, May.
    35. 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.
    36. 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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    Cited by:

    1. Khushboo Surana, 2022. "How different are we? Identifying the degree of revealed preference heterogeneity," Discussion Papers 22/09, Department of Economics, University of York.
    2. Takashi Kunimoto & Roberto Serrano, 2020. "Rationalizable Incentives: Interim Implementation of Sets in Rationalizable Strategies," Working Papers 2020-15, Brown University, Department of Economics.
    3. Victor H. Aguiar & Roberto Serrano, 2018. "Cardinal Revealed Preference, Price-Dependent Utility, and Consistent Binary Choice," Working Papers 2018-3, Brown University, Department of Economics.
    4. Alvaro Sandroni & Leo Katz, 2024. "The leveling axiom," Theory and Decision, Springer, vol. 96(1), pages 135-152, February.
    5. Sam Cosaert, 2019. "What Types are There?," Computational Economics, Springer;Society for Computational Economics, vol. 53(2), pages 533-554, February.
    6. Cherchye, Laurens & Demuynck, Thomas & Rock, Bram De, 2019. "Bounding counterfactual demand with unobserved heterogeneity and endogenous expenditures," Journal of Econometrics, Elsevier, vol. 211(2), pages 483-506.
    7. Aguiar, Victor H. & Hjertstrand, Per & Serrano, Roberto, 2020. "A Rationalization of the Weak Axiom of Revealed Preference," Working Paper Series 1321, Research Institute of Industrial Economics.
    8. Christopher P. Chambers & John Rehbeck, 2022. "Nonparametric market supply with variable participants," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 74(3), pages 899-921, October.
    9. Zhibin Wu & Rong Yuan & Jiancheng Tu, 2021. "Group Decision Making with Transitive Preferences Under Ordinal and Cardinal Consistencies: An Optimization Approach," Group Decision and Negotiation, Springer, vol. 30(1), pages 221-250, February.

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    More about this item

    Keywords

    Revealed preferences; warp; sarp; transitive preferences; testable implications; Hicksian aggregation;
    All these keywords.

    JEL classification:

    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • D01 - Microeconomics - - General - - - Microeconomic Behavior: Underlying Principles
    • D11 - Microeconomics - - Household Behavior - - - Consumer Economics: Theory
    • D12 - Microeconomics - - Household Behavior - - - Consumer Economics: Empirical Analysis

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