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Stochastic Revealed Preferences with Measurement Error

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  • Victor H. Aguiar
  • Nail Kashaev

Abstract

A long-standing question about consumer behavior 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 nonparametric, allows for unrestricted heterogeneity in preferences, and requires only a centering 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 \emph{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). The second finding reverses the conclusions drawn from the deterministic RP test of Afriat (1967) and Varian (1982).

Suggested Citation

  • Victor H. Aguiar & Nail Kashaev, 2018. "Stochastic Revealed Preferences with Measurement Error," Papers 1810.05287, arXiv.org, revised Sep 2020.
  • Handle: RePEc:arx:papers:1810.05287
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    Cited by:

    1. Rahul Deb & Yuichi Kitamura & John K. -H. Quah & Jorg Stoye, 2018. "Revealed Price Preference: Theory and Empirical Analysis," Papers 1801.02702, arXiv.org, revised Apr 2021.
    2. Roy Allen & Pawel Dziewulski & John Rehbeck, 2019. "Revealed statistical consumer theory," Working Paper Series 1119, Department of Economics, University of Sussex Business School.
    3. Serletis, Apostolos & Xu, Libo, 2021. "Consumption, Leisure, And Money," Macroeconomic Dynamics, Cambridge University Press, vol. 25(6), pages 1412-1441, September.
    4. Mikhail Freer & Cesar Martinelli, 2018. "A Representation Theorem for General Revealed Preference," Working Papers ECARES 2018-28, ULB -- Universite Libre de Bruxelles.
    5. Heufer, Jan & Hjertstrand, Per, 2019. "Homothetic preferences revealed," Journal of Economic Behavior & Organization, Elsevier, vol. 157(C), pages 602-614.
    6. Roy Allen & John Rehbeck, 2020. "Counterfactual and Welfare Analysis with an Approximate Model," Papers 2009.03379, arXiv.org.
    7. Changkuk Im & John Rehbeck, 2021. "Non-rationalizable Individuals, Stochastic Rationalizability, and Sampling," Papers 2102.03436, arXiv.org, revised Oct 2021.

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