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Stochastic Revealed Preferences with Measurement Error
[Consistency between Household-level Consumption Data from Registers and Surveys]

Author

Listed:
  • Victor H Aguiar
  • Nail Kashaev

Abstract

A long-standing question about consumer behaviour is whether individuals’ observed purchase decisions satisfy the revealed preference (RP) axioms of the utility maximization theory (UMT). Researchers using survey or experimental panel data sets on prices and consumption to answer this question face the well-known problem of measurement error. We show that ignoring measurement error in the RP approach may lead to overrejection of the UMT. To solve this problem, we propose a new statistical RP framework for consumption panel data sets that allows for testing the UMT in the presence of measurement error. Our test is applicable to all consumer models that can be characterized by their first-order conditions. Our approach is non-parametric, allows for unrestricted heterogeneity in preferences and requires only a centring condition on measurement error. We develop two applications that provide new evidence about the UMT. First, we find support in a survey data set for the dynamic and time-consistent UMT in single-individual households, in the presence of nonclassical measurement error in consumption. In the second application, we cannot reject the static UMT in a widely used experimental data set in which measurement error in prices is assumed to be the result of price misperception due to the experimental design. The first finding stands in contrast to the conclusions drawn from the deterministic RP test of Browning (1989, International Economic Review, 979–992). The second finding reverses the conclusions drawn from the deterministic RP test of Afriat (1967, International Economic Review, 8, 6–77) and Varian (1982, Econometrica, 945–973).

Suggested Citation

  • Victor H Aguiar & Nail Kashaev, 2021. "Stochastic Revealed Preferences with Measurement Error [Consistency between Household-level Consumption Data from Registers and Surveys]," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 88(4), pages 2042-2093.
    • Handle: RePEc:oup:restud:v:88:y:2021:i:4:p:2042-2093.
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    File URL: http://hdl.handle.net/10.1093/restud/rdaa067
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    Cited by:

    1. Roy Allen & Paweł Dziewulski & John Rehbeck, 2024. "Revealed statistical consumer theory," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 77(3), pages 823-847, May.
    2. Serletis, Apostolos & Xu, Libo, 2021. "Consumption, Leisure, And Money," Macroeconomic Dynamics, Cambridge University Press, vol. 25(6), pages 1412-1441, September.
    3. Changkuk Im & John Rehbeck, 2021. "Non-rationalizable Individuals, Stochastic Rationalizability, and Sampling," Papers 2102.03436, arXiv.org, revised Oct 2021.
    4. Heufer, Jan & Hjertstrand, Per, 2019. "Homothetic preferences revealed," Journal of Economic Behavior & Organization, Elsevier, vol. 157(C), pages 602-614.
    5. Im, Changkuk & Rehbeck, John, 2022. "Non-rationalizable individuals and stochastic rationalizability," Economics Letters, Elsevier, vol. 219(C).
    6. Sam Cosaert & Tom Potoms, 2024. "Intertemporal Consumption With Anticipating, Remembering, And Experiencing Selves," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 65(3), pages 1283-1322, August.
    7. Schennach, Susanne M., 2020. "Mismeasured and unobserved variables," Handbook of Econometrics, in: Steven N. Durlauf & Lars Peter Hansen & James J. Heckman & Rosa L. Matzkin (ed.), Handbook of Econometrics, edition 1, volume 7, chapter 0, pages 487-565, Elsevier.
    8. Thomas Demuynck & Tom Potoms, 2022. "Testing revealed preference models with unobserved randomness: a column generation approach," Working Papers ECARES 2022-42, ULB -- Universite Libre de Bruxelles.
    9. Rahul Deb & Yuichi Kitamura & John K H Quah & Jörg Stoye, 2023. "Revealed Price Preference: Theory and Empirical Analysis," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 90(2), pages 707-743.
    10. Javier A. Birchenall, 2024. "Random choice and market demand," Canadian Journal of Economics/Revue canadienne d'économique, John Wiley & Sons, vol. 57(1), pages 165-198, February.
    11. Laurens Cherchye & Thomas Demuynck & Bram De Rock & Joshua Lanier, 2020. "Are Consumers Rational ?Shifting the Burden of Proof," Working Papers ECARES 2020-19, ULB -- Universite Libre de Bruxelles.
    12. Roy Allen & John Rehbeck, 2020. "Counterfactual and Welfare Analysis with an Approximate Model," Papers 2009.03379, arXiv.org.
    13. Wilfried Youmbi, 2024. "Nonparametric Analysis of Random Utility Models Robust to Nontransitive Preferences," Papers 2406.13969, arXiv.org.
    14. Dazhuo Wei, 2024. "Random Attention Span," Papers 2405.11578, arXiv.org.
    15. Mikhail Freer & Cesar Martinelli, 2018. "A Representation Theorem for General Revealed Preference," Working Papers ECARES 2018-28, ULB -- Universite Libre de Bruxelles.
    16. Daniele Caliari & Henrik Petri, 2024. "Irrational Random Utility Models," Papers 2403.10208, arXiv.org, revised May 2025.
    17. Aguiar, Victor H. & Kashaev, Nail & Allen, Roy, 2023. "Prices, profits, proxies, and production," Journal of Econometrics, Elsevier, vol. 235(2), pages 666-693.
    18. Laurens Cherchye & Thomas Demuynck & Bram De Rock & Joshua Lanier, 2025. "Are Consumers (Approximately) Rational? Shifting the Burden of Proof," The Review of Economics and Statistics, MIT Press, vol. 107(6), pages 1652-1666, November.
    19. Banzhaf, H. Spencer & Liu, Yaqin & Smith, Martin D. & Asche, Frank, 2024. "Non-parametric tests of behavior in the commons," Journal of Economic Behavior & Organization, Elsevier, vol. 224(C), pages 521-536.

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