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Beyond the Mean: Testing Consumer Rationality through Higher Moments of Demand

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  • Sebastiaan Maes
  • Raghav Malhotra

Abstract

We study a setting where an analyst has access to purely aggregate information about the consumption choices of a heterogenous population of individuals. We show that observing the statistical moments of market demand allows the analyst to test aggregate data for rationality. Interestingly, just the mean and variance of demand carry observable restrictions. This is in stark contrast to impossibility result of the Sonnenschein-Mantel-Debreu theorem, which shows that aggregate demand carries no observable restrictions at all. We leverage our approach to deliver a characterization of rationality in terms of moments for the common two-good case. We illustrate the usefulness of moment-based restrictions through two applications: (i) improving the precision of demand and welfare estimates; and (ii) testing for the existence of a welfare-relevant representative consumer.

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  • Sebastiaan Maes & Raghav Malhotra, 2024. "Beyond the Mean: Testing Consumer Rationality through Higher Moments of Demand," Papers 2407.01538, arXiv.org.
    • Handle: RePEc:arx:papers:2407.01538
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    References listed on IDEAS

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    1. Yuichi Kitamura & Jörg Stoye, 2018. "Nonparametric Analysis of Random Utility Models," Econometrica, Econometric Society, vol. 86(6), pages 1883-1909, November.
    2. Dette, Holger & Hoderlein, Stefan & Neumeyer, Natalie, 2016. "Testing multivariate economic restrictions using quantiles: The example of Slutsky negative semidefiniteness," Journal of Econometrics, Elsevier, vol. 191(1), pages 129-144.
    3. Michael Jerison, 1994. "Optimal Income Distribution Rules and Representative Consumers," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 61(4), pages 739-771.
    4. Sören Blomquist & Whitney K. Newey & Anil Kumar & Che-Yuan Liang, 2021. "On Bunching and Identification of the Taxable Income Elasticity," Journal of Political Economy, University of Chicago Press, vol. 129(8), pages 2320-2343.
    5. 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.
    6. Mantel, Rolf R., 1974. "On the characterization of aggregate excess demand," Journal of Economic Theory, Elsevier, vol. 7(3), pages 348-353, March.
    7. Hoderlein, Stefan, 2011. "How many consumers are rational?," Journal of Econometrics, Elsevier, vol. 164(2), pages 294-309, October.
    8. P. A. Chiappori & I. Ekeland, 1999. "Aggregation and Market Demand: An Exterior Differential Calculus Viewpoint," Econometrica, Econometric Society, vol. 67(6), pages 1435-1458, November.
    9. Chiappori, P. -A. & Ekeland, I. & Kubler, F. & Polemarchakis, H. M., 2004. "Testable implications of general equilibrium theory: a differentiable approach," Journal of Mathematical Economics, Elsevier, vol. 40(1-2), pages 105-119, February.
    10. Jerry A. Hausman & Whitney K. Newey, 2016. "Individual Heterogeneity and Average Welfare," Econometrica, Econometric Society, vol. 84, pages 1225-1248, May.
    11. Donald J. Brown & Rosa L. Matzkin, 2008. "Testable Restrictions on the Equilibrium Manifold," Lecture Notes in Economics and Mathematical Systems, in: Computational Aspects of General Equilibrium Theory, pages 11-25, Springer.
    12. Pirmin Fessler & Maximilian Kasy, 2019. "How to Use Economic Theory to Improve Estimators: Shrinking Toward Theoretical Restrictions," The Review of Economics and Statistics, MIT Press, vol. 101(4), pages 681-698, October.
    13. Mantel, Rolf R., 1976. "Homothetic preferences and community excess demand functions," Journal of Economic Theory, Elsevier, vol. 12(2), pages 197-201, April.
    14. Stefan Hoderlein & Jörg Stoye, 2015. "Testing stochastic rationality and predicting stochastic demand: the case of two goods," Economic Theory Bulletin, Springer;Society for the Advancement of Economic Theory (SAET), vol. 3(2), pages 313-328, October.
    15. S. Abu Turab Rizvi, 2006. "The Sonnenschein-Mantel-Debreu Results after Thirty Years," History of Political Economy, Duke University Press, vol. 38(5), pages 228-245, Supplemen.
    16. repec:dau:papers:123456789/6427 is not listed on IDEAS
    17. Hildenbrand, Werner, 1983. "On the "Law of Demand."," Econometrica, Econometric Society, vol. 51(4), pages 997-1019, July.
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