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What Do Revealed Preference Axioms Reveal about Elasticities of Demand?

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  • Hjertstrand, Per

    ()
    (Research Institute of Industrial Economics (IFN))

  • Jones, Barry E.

    ()
    (Department of Economics)

Abstract

It is well-known that observed data on prices and quantities of a set of goods is consistent with rational choice if the data satisfy revealed preference. In this paper, we derive estimators for demand and substitution elasticities at the observed data points for datasets satisfying the Strong version of the Strong Axiom of Revealed Preference (SSARP) from Chiappori and Rochet (1987). We find that these estimators are identified only up to a strictly positive parameter, which must be small enough that the utility function rationalizing the dataset satisfies certain properties. We show that the estimated elasticities of substitution approach zero in the limit as this parameter approaches zero. Thus, if the dataset satisfies SSARP, then it is consistent with negligible substitutability between any pair of goods at all observed data points. Our estimators are derived directly from results in Brown and Shannon (2000) and Brown and Kannan (2005).

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Bibliographic Info

Paper provided by Research Institute of Industrial Economics in its series Working Paper Series with number 972.

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Length: 16 pages
Date of creation: 04 Sep 2013
Date of revision:
Handle: RePEc:hhs:iuiwop:0972

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Keywords: Strong Axiom of Revealed Preference; Afriat Inequalities; Elasticities of Demand;

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References

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  1. Jones, Barry E. & De Peretti, Philippe, 2005. "A Comparison Of Two Methods For Testing The Utility Maximization Hypothesis When Quantity Data Are Measured With Error," Macroeconomic Dynamics, Cambridge University Press, vol. 9(05), pages 612-629, November.
  2. repec:ecj:econjl:v:122:y:2012:i::p:305-331 is not listed on IDEAS
  3. Jones, Barry E. & Stracca, Livio, 2008. "Does money matter in the IS curve? The case of the UK," Working Paper Series 0904, European Central Bank.
  4. Barnett, William A. & Serletis, Apostolos, 2008. "Consumer preferences and demand systems," Journal of Econometrics, Elsevier, vol. 147(2), pages 210-224, December.
  5. Varian, Hal R, 1982. "The Nonparametric Approach to Demand Analysis," Econometrica, Econometric Society, vol. 50(4), pages 945-73, July.
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  8. Hal R. Varian, 2012. "Revealed Preference and its Applications," Economic Journal, Royal Economic Society, vol. 122(560), pages 332-338, 05.
  9. Epstein, Larry G. & Yatchew, Adonis J., 1985. "Non-parametric hypothesis testing procedures and applications to demand analysis," Journal of Econometrics, Elsevier, vol. 30(1-2), pages 149-169.
  10. Chiappori, Pierre-Andre & Rochet, Jean-Charles, 1987. "Revealed Preferences and Differentiable Demand: Notes and Comments," Econometrica, Econometric Society, vol. 55(3), pages 687-91, May.
  11. Jones, Barry E. & Dutkowsky, Donald H. & Elger, Thomas, 2005. "Sweep programs and optimal monetary aggregation," Journal of Banking & Finance, Elsevier, vol. 29(2), pages 483-508, February.
  12. Diewert, Erwin, 2011. "Afriat's Theorem and Some Extensions to Choice under Uncertainty," Economics working papers erwin_diewert-2011-22, Vancouver School of Economics, revised 01 Sep 2011.
  13. Fleissig, Adrian R. & Whitney, Gerald A., 2005. "Testing for the Significance of Violations of Afriat's Inequalities," Journal of Business & Economic Statistics, American Statistical Association, vol. 23, pages 355-362, July.
  14. Chavas, Jean-Paul & Cox, Thomas L., 1997. "On nonparametric demand analysis," European Economic Review, Elsevier, vol. 41(1), pages 75-95, January.
  15. Diewert, W E, 1973. "Afriat and Revealed Preference Theory," Review of Economic Studies, Wiley Blackwell, vol. 40(3), pages 419-25, July.
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  17. Fleissig, Adrian R & Whitney, Gerald A, 2003. "A New PC-Based Test for Varian's Weak Separability Conditions," Journal of Business & Economic Statistics, American Statistical Association, vol. 21(1), pages 133-44, January.
  18. Varian, Hal R., 1985. "Non-parametric analysis of optimizing behavior with measurement error," Journal of Econometrics, Elsevier, vol. 30(1-2), pages 445-458.
  19. William Barnett & Apostolos Serletis, 2009. "Measuring Consumer Preferences and Estimating Demand Systems," WORKING PAPERS SERIES IN THEORETICAL AND APPLIED ECONOMICS 200901, University of Kansas, Department of Economics, revised Jan 2009.
  20. Barnhart, Scott W & Whitney, Gerald A, 1988. "Nonparametric Analysis in Parametric Estimation: An Application to Translog Demand Systems," The Review of Economics and Statistics, MIT Press, vol. 70(1), pages 149-53, February.
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  23. Diewert, W. E. & Parkan, C., 1985. "Tests for the consistency of consumer data," Journal of Econometrics, Elsevier, vol. 30(1-2), pages 127-147.
  24. Varian, Hal R, 1983. "Non-Parametric Tests of Consumer Behaviour," Review of Economic Studies, Wiley Blackwell, vol. 50(1), pages 99-110, January.
  25. Davis, George C & Gauger, Jean, 1996. "Measuring Substitution in Monetary-Asset Demand Systems," Journal of Business & Economic Statistics, American Statistical Association, vol. 14(2), pages 203-08, April.
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