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A Comprehensive Approach to Revealed Preference Theory

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  • Hiroki Nishimura

    () (Department of Economics, University of California Riverside)

  • Efe A. Ok
  • John K.-H. Quah

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.
(This abstract was borrowed from another version of this item.)

Suggested Citation

  • Hiroki Nishimura & Efe A. Ok & John K.-H. Quah, 2016. "A Comprehensive Approach to Revealed Preference Theory," Working Papers 201614, University of California at Riverside, Department of Economics.
  • Handle: RePEc:ucr:wpaper:201614
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    References listed on IDEAS

    as
    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. John Quah & Matthew Polisson & Ludovic Renou, 2015. "Revealed preferences over risk and uncertainty," Economics Series Working Papers 740, University of Oxford, Department of Economics.
    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. Yoram Halevy & Dotan Persitz & Lanny Zrill, 2018. "Parametric Recoverability of Preferences," Journal of Political Economy, University of Chicago Press, vol. 126(4), pages 1558-1593.
    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. repec:eee:gamebe:v:112:y:2018:i:c:p:67-77 is not listed on IDEAS
    19. Matthew Polisson & John K.-H. Quah & Ludovic Renou, 2017. "Revealed preferences over risk and uncertainty," Discussion Paper Series, Department of Economics 201706, Department of Economics, University of St. Andrews, revised 16 Apr 2019.
    20. Francoise Forges & Enrico Minelli, 2009. "Afriat's theorem for generalized budget sets," Post-Print hal-00360726, HAL.
    21. Efe A. Ok & Gil Riella, 2014. "Topological Closure of Translation Invariant Preorders," Mathematics of Operations Research, INFORMS, vol. 39(3), pages 737-745, August.
    22. Fishburn, Peter C., 1975. "Separation theorems and expected utilities," Journal of Economic Theory, Elsevier, vol. 11(1), pages 16-34, August.
    23. Heufer, Jan, 2014. "Nonparametric comparative revealed risk aversion," Journal of Economic Theory, Elsevier, vol. 153(C), pages 569-616.
    24. Stiglitz, Joseph E, 1974. "On the Irrelevance of Corporate Financial Policy," American Economic Review, American Economic Association, vol. 64(6), pages 851-866, December.
    25. 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.
    26. Dziewulski, Paweł, 2018. "Revealed time preference," Games and Economic Behavior, Elsevier, vol. 112(C), pages 67-77.
    27. Fishburn, Peter C, 1976. "Representable Choice Functions," Econometrica, Econometric Society, vol. 44(5), pages 1033-1043, September.
    28. Hal R. Varian, 1983. "Non-parametric Tests of Consumer Behaviour," Review of Economic Studies, Oxford University Press, vol. 50(1), pages 99-110.
    29. Green, Richard C. & Srivastava, Sanjay, 1986. "Expected utility maximization and demand behavior," Journal of Economic Theory, Elsevier, vol. 38(2), pages 313-323, April.
    30. 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.
    31. Andreu Mas-Colell, 1978. "On Revealed Preference Analysis," Review of Economic Studies, Oxford University Press, vol. 45(1), pages 121-131.
    32. 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.
    33. 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.
    34. Matzkin, Rosa L, 1991. "Axioms of Revealed Preference for Nonlinear Choice Sets," Econometrica, Econometric Society, vol. 59(6), pages 1779-1786, November.
    35. W. E. Diewert, 1973. "Afriat and Revealed Preference Theory," Review of Economic Studies, Oxford University Press, vol. 40(3), pages 419-425.
    36. repec:dau:papers:123456789/4099 is not listed on IDEAS
    37. 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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    More about this item

    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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