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Slutsky matrix norms: The size, classification, and comparative statics of bounded rationality

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  • Aguiar, Victor H.
  • Serrano, Roberto

Abstract

Given any observed demand behavior —by means of a demand function—, we quantify by how much it departs from rationality. The measure of the gap is the smallest Frobenius norm of the correcting matrix function that would yield a Slutsky matrix with its standard rationality properties (symmetry, singularity, and negative semidefiniteness). As a result, we are able to suggest a useful classification of departures from rationality, corresponding to three anomalies: inattentiveness to changes in purchasing power, money illusion, and violations of the compensated law of demand. Errors in comparative-statics predictions from assuming rationality are decomposed as the sum of a behavioral error (due to the agent) and a specification error (due to the modeller). Illustrations are provided using several bounded rationality models.

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  • Aguiar, Victor H. & Serrano, Roberto, 2017. "Slutsky matrix norms: The size, classification, and comparative statics of bounded rationality," Journal of Economic Theory, Elsevier, vol. 172(C), pages 163-201.
    • Handle: RePEc:eee:jetheo:v:172:y:2017:i:c:p:163-201
    DOI: 10.1016/j.jet.2017.08.007
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    3. Thomas Demuynck & John Rehbeck, 2023. "Computing revealed preference goodness-of-fit measures with integer programming," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 76(4), pages 1175-1195, November.
    4. Victor Aguiar & Roland Pongou & Jean-Baptiste Tondji, 2016. "Measuring and Decomposing the Distance to the Shapley Wage Function with Limited Data," Working Papers 1613e, University of Ottawa, Department of Economics.
    5. Aguiar, Victor H. & Pongou, Roland & Tondji, Jean-Baptiste, 2018. "A non-parametric approach to testing the axioms of the Shapley value with limited data," Games and Economic Behavior, Elsevier, vol. 111(C), pages 41-63.
    6. Roy Allen & John Rehbeck, 2021. "Measuring rationality: percentages vs expenditures," Theory and Decision, Springer, vol. 91(2), pages 265-277, September.
    7. Xavier Gabaix, 2017. "Behavioral Inattention," NBER Working Papers 24096, National Bureau of Economic Research, Inc.
    8. Elias Bouacida & Daniel Martin, 2021. "Predictive Power in Behavioral Welfare Economics," Journal of the European Economic Association, European Economic Association, vol. 19(3), pages 1556-1591.
    9. 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.
    10. Geoffroy de Clippel & Kareen Rozen, 2018. "Consumer Theory with Misperceived Tastes," Working Papers 2018-10, Brown University, Department of Economics.
    11. Maes, Sebastiaan & Malhotra, Raghav, 2024. "Robust Hicksian Welfare Analysis under Individual Heterogeneity," CRETA Online Discussion Paper Series 84, Centre for Research in Economic Theory and its Applications CRETA.
    12. Michael Jerison, 2023. "Social welfare and the unrepresentative representative consumer," Journal of Public Economic Theory, Association for Public Economic Theory, vol. 25(1), pages 5-28, February.
    13. Fernando Luco & Guillermo Marshall, 2021. "Diagnosing Anticompetitive Effects of Vertical Integration by Multiproduct Firms," Review of Industrial Organization, Springer;The Industrial Organization Society, vol. 59(2), pages 381-392, September.
    14. Efe A. Ok & Gerelt Tserenjigmid, 2023. "Measuring Stochastic Rationality," Papers 2303.08202, arXiv.org, revised Dec 2023.
    15. Zheng Fang & Juwon Seo, 2019. "A Projection Framework for Testing Shape Restrictions That Form Convex Cones," Papers 1910.07689, arXiv.org, revised Sep 2021.
    16. Aguiar, Victor H. & Serrano, Roberto, 2021. "Cardinal revealed preference: Disentangling transitivity and consistent binary choice," Journal of Mathematical Economics, Elsevier, vol. 94(C).
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    More about this item

    Keywords

    Consumer theory; Slutsky matrix function; Bounded rationality; Comparative statics; Sparse-max consumer; Collective model;
    All these keywords.

    JEL classification:

    • C60 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - General
    • D10 - Microeconomics - - Household Behavior - - - General

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