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A Comprehensive Approach to Revealed Preference Theory

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  • John Quah
  • Hiroki Nishimura
  • Efe A. Ok

Abstract

Richter's theorem and Afriat's theorem are two fundamental results underlying modern revealed preference analysis. In this paper, we provide a version of Richter's theorem that characterizes the rationalizability of a choice data set with a continuous utility function (rather than simply a complete preorder as in the original result) and extend Afriat's theorem so it becomes applicable in choice environments other than the classical setting of consumer demand. Furthermore, while standard treatments give very different proofs for these two results, we introduce a framework within which both results can be formulated and established in tandem. We also demonstrate how our generalized versions of these theorems can be used in empirical studies. In particular, we apply our results to devise tests for rationalizability in the context of choice data over lotteries, contingent consumption, intertemporal consumption, and positions in policy space. Some new results on the revealed preference theory of consumer demand (for instance, on the possibility of deriving utility functions from estimated Engel curves) are also reported.

Suggested Citation

  • John Quah & Hiroki Nishimura & Efe A. Ok, 2015. "A Comprehensive Approach to Revealed Preference Theory," Economics Series Working Papers 752, University of Oxford, Department of Economics.
  • Handle: RePEc:oxf:wpaper:752
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    References listed on IDEAS

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    1. Varian, Hal R, 1982. "The Nonparametric Approach to Demand Analysis," Econometrica, Econometric Society, vol. 50(4), pages 945-973, July.
    2. Edward J. Green & Kent Osband, 1991. "A Revealed Preference Theory for Expected Utility," Review of Economic Studies, Oxford University Press, vol. 58(4), pages 677-695.
    3. Herden, G., 1989. "On the existence of utility functions," Mathematical Social Sciences, Elsevier, vol. 17(3), pages 297-313, June.
    4. Matthew Polisson & John Quah & Ludovic Renou, 2015. "Revealed preferences over risk and uncertainty," IFS Working Papers W15/25, Institute for Fiscal Studies.
    5. Forges, Françoise & Minelli, Enrico, 2009. "Afriat's theorem for general budget sets," Journal of Economic Theory, Elsevier, vol. 144(1), pages 135-145, January.
    6. Philip J. Reny, 2015. "A Characterization of Rationalizable Consumer Behavior," Econometrica, Econometric Society, vol. 83, pages 175-192, January.
    7. Chiappori, Pierre-Andre & Rochet, Jean-Charles, 1987. "Revealed Preferences and Differentiable Demand: Notes and Comments," Econometrica, Econometric Society, vol. 55(3), pages 687-691, May.
    8. Herden, G., 1989. "On the existence of utility functions ii," Mathematical Social Sciences, Elsevier, vol. 18(2), pages 107-117, October.
    9. James Andreoni & Charles Sprenger, 2012. "Estimating Time Preferences from Convex Budgets," American Economic Review, American Economic Association, vol. 102(7), pages 3333-3356, December.
    10. Halevy, Yoram & Persitz, Dotan & Zrill, Lanny, 2012. "Parametric Recoverability of Preferences," Microeconomics.ca working papers yoram_halevy-2012-20, Vancouver School of Economics, revised 28 Aug 2015.
    11. Efe A. Ok & Lin Zhou, 1999. "Revealed group preferences on non-convex choice problems," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 13(3), pages 671-687.
    12. Nash, John, 1950. "The Bargaining Problem," Econometrica, Econometric Society, vol. 18(2), pages 155-162, April.
    13. Jean-Paul Chavas & Thomas L. Cox, 1993. "On Generalized Revealed Preference Analysis," The Quarterly Journal of Economics, Oxford University Press, vol. 108(2), pages 493-506.
    14. Walter Bossert & Kotaro Suzumura, 2012. "Revealed preference and choice under uncertainty," SERIEs: Journal of the Spanish Economic Association, Springer;Spanish Economic Association, vol. 3(1), pages 247-258, March.
    15. Kalandrakis, Tasos, 2010. "Rationalizable voting," Theoretical Economics, Econometric Society, vol. 5(1), January.
    16. Thomas Demuynck, 2009. "Absolute and Relative Time-Consistent Revealed Preferences," Theory and Decision, Springer, vol. 66(3), pages 283-299, March.
    17. 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.
    18. Francoise Forges & Enrico Minelli, 2009. "Afriat's theorem for generalized budget sets," Post-Print hal-00360726, HAL.
    19. Efe A. Ok & Gil Riella, 2014. "Topological Closure of Translation Invariant Preorders," Mathematics of Operations Research, INFORMS, vol. 39(3), pages 737-745, August.
    20. Fishburn, Peter C., 1975. "Separation theorems and expected utilities," Journal of Economic Theory, Elsevier, vol. 11(1), pages 16-34, August.
    21. Heufer, Jan, 2014. "Nonparametric comparative revealed risk aversion," Journal of Economic Theory, Elsevier, vol. 153(C), pages 569-616.
    22. Stiglitz, Joseph E, 1974. "On the Irrelevance of Corporate Financial Policy," American Economic Review, American Economic Association, vol. 64(6), pages 851-866, December.
    23. Syngjoo Choi & Raymond Fisman & Douglas Gale & Shachar Kariv, 2007. "Consistency, Heterogeneity, and Granularity of Individual Behavior under Uncertainty," Economics Working Papers 0076, Institute for Advanced Study, School of Social Science.
    24. Pawel Dziewulski, 2015. "Revealed time-preference," Economics Series Working Papers 748, University of Oxford, Department of Economics.
    25. Fishburn, Peter C, 1976. "Representable Choice Functions," Econometrica, Econometric Society, vol. 44(5), pages 1033-1043, September.
    26. Hal R. Varian, 1983. "Non-parametric Tests of Consumer Behaviour," Review of Economic Studies, Oxford University Press, vol. 50(1), pages 99-110.
    27. Green, Richard C. & Srivastava, Sanjay, 1986. "Expected utility maximization and demand behavior," Journal of Economic Theory, Elsevier, vol. 38(2), pages 313-323, April.
    28. Shane Frederick & George Loewenstein & Ted O'Donoghue, 2002. "Time Discounting and Time Preference: A Critical Review," Journal of Economic Literature, American Economic Association, vol. 40(2), pages 351-401, June.
    29. Andreu Mas-Colell, 1978. "On Revealed Preference Analysis," Review of Economic Studies, Oxford University Press, vol. 45(1), pages 121-131.
    30. Syngjoo Choi & Raymond Fisman & Douglas Gale & Shachar Kariv, 2007. "Consistency and Heterogeneity of Individual Behavior under Uncertainty," American Economic Review, American Economic Association, vol. 97(5), pages 1921-1938, December.
    31. Browning, Martin, 1989. "A Nonparametric Test of the Life-Cycle Rational Expectations Hypothesis," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 30(4), pages 979-992, November.
    32. Matzkin, Rosa L, 1991. "Axioms of Revealed Preference for Nonlinear Choice Sets," Econometrica, Econometric Society, vol. 59(6), pages 1779-1786, November.
    33. W. E. Diewert, 1973. "Afriat and Revealed Preference Theory," Review of Economic Studies, Oxford University Press, vol. 40(3), pages 419-425.
    34. repec:dau:papers:123456789/4099 is not listed on IDEAS
    35. Evren, Özgür & Ok, Efe A., 2011. "On the multi-utility representation of preference relations," Journal of Mathematical Economics, Elsevier, vol. 47(4-5), pages 554-563.
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    Cited by:

    1. Sürücü, Oktay, 2016. "Welfare improving discrimination based on cognitive limitations," Research in Economics, Elsevier, vol. 70(4), pages 608-622.
    2. Fabio Galeotti, 2017. "The Attraction and Compromise Effects in Bargaining: Experimental Evidence," Post-Print halshs-01657317, HAL.
    3. Ronayne, David & Brown, Gordon D.A., 2016. "Multi-attribute decision by sampling: An account of the attraction, comprimise and similarity effects," The Warwick Economics Research Paper Series (TWERPS) 1124, University of Warwick, Department of Economics.
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    6. John Quah & Matthew Polisson & Ludovic Renou, 2015. "Revealed preferences over risk and uncertainty," Economics Series Working Papers 740, University of Oxford, Department of Economics.
    7. Dino Borie & Dorian Jullien, 2017. "Description-dependent Choices," Working Papers halshs-01651086, HAL.
    8. Mauricio Ribeiro & Gil Riella, 2017. "Regular preorders and behavioral indifference," Theory and Decision, Springer, vol. 82(1), pages 1-12, January.
    9. Georgios Gerasimou, 2016. "Partially dominant choice," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 61(1), pages 127-145, January.
    10. Fabrizi, Simona & Lippert, Steffen & Puppe, Clemens & Rosenkranz, Stephanie, 2016. "Manufacturer suggested retail prices, loss aversion and competition," Journal of Economic Psychology, Elsevier, vol. 53(C), pages 141-153.
    11. Georgios Gerasimou, 2016. "Asymmetric dominance, deferral, and status quo bias in a behavioral model of choice," Theory and Decision, Springer, vol. 80(2), pages 295-312, February.
    12. Shaofang Qi, 2016. "A characterization of the n-agent Pareto dominance relation," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 46(3), pages 695-706, March.
    13. Hassan Nosratabadi, 2017. "Rational Filters," Departmental Working Papers 201706, Rutgers University, Department of Economics.
    14. Buturak, Gökhan & Evren, Özgür, 2017. "Choice overload and asymmetric regret," Theoretical Economics, Econometric Society, vol. 12(3), September.
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    18. Hassan Nosratabadi, 2017. "Referential Revealed Preference Theory," Departmental Working Papers 201705, Rutgers University, Department of Economics.
    19. Anujit Chakraborty & Evan M. Calford & Guidon Fenig & Yoram Halevy, 2017. "External and internal consistency of choices made in convex time budgets," Experimental Economics, Springer;Economic Science Association, vol. 20(3), pages 687-706, September.
    20. Lamiraud, Karine & Oxoby, Robert & Donaldson, Cam, 2016. "Reference Dependence and Incremental WTP," ESSEC Working Papers WP1609, ESSEC Research Center, ESSEC Business School.
    21. Guney, Begum & Richter, Michael, 2015. "An experiment on aspiration-based choice," Journal of Economic Behavior & Organization, Elsevier, vol. 119(C), pages 512-526.
    22. repec:eee:mateco:v:71:y:2017:i:c:p:63-73 is not listed on IDEAS
    23. Nishimura, Hiroki & Ok, Efe A., 2016. "Utility representation of an incomplete and nontransitive preference relation," Journal of Economic Theory, Elsevier, vol. 166(C), pages 164-185.
    24. Nocke, Volker & Schutz, Nicolas, 2017. "Quasi-linear integrability," Journal of Economic Theory, Elsevier, vol. 169(C), pages 603-628.

    More about this item

    Keywords

    Revealed Preference; Rational Choice; Afriat's Theorem; Richter's Theorem; Engel Curves.;

    JEL classification:

    • D11 - Microeconomics - - Household Behavior - - - Consumer Economics: Theory
    • D81 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Criteria for Decision-Making under Risk and Uncertainty

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