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What Do Revealed Preference Axioms Reveal about Elasticities of Demand?

Author

Listed:
  • 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).

Suggested Citation

  • Hjertstrand, Per & Jones, Barry E., 2013. "What Do Revealed Preference Axioms Reveal about Elasticities of Demand?," Working Paper Series 972, Research Institute of Industrial Economics.
  • Handle: RePEc:hhs:iuiwop:0972
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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. 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.
    3. 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.
    4. 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.
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    6. 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.
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    More about this item

    Keywords

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

    JEL classification:

    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • D12 - Microeconomics - - Household Behavior - - - Consumer Economics: Empirical Analysis

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