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Nonparametric Analysis of Random Utility Models: Computational Tools for Statistical Testing

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  • Bram De Rock
  • Laurens Cherchye
  • Bart Smeulders

Abstract

Kitamura and Stoye (2018) recently proposed a nonparametric statistical test for random utility models of consumer behavior. The test is formulated in terms of linear inequality constraints and a quadratic objective function. While the nonparametric test is conceptually appealing, its practical implementation is computationally challenging. In this note, we develop a column generation approach to operationalize the test. We show that these novel computational tools generate considerable computational gains in practice, which substantially increases the empirical usefulness of Kitamura and Stoye’s statistical test.

Suggested Citation

  • Bram De Rock & Laurens Cherchye & Bart Smeulders, 2019. "Nonparametric Analysis of Random Utility Models: Computational Tools for Statistical Testing," Working Papers ECARES 2019-19, ULB -- Universite Libre de Bruxelles.
    • Handle: RePEc:eca:wpaper:2013/292215
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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. George B. Dantzig & Philip Wolfe, 1960. "Decomposition Principle for Linear Programs," Operations Research, INFORMS, vol. 8(1), pages 101-111, February.
    3. 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.
    4. Yuichi Kitamura & Jorg Stoye, 2019. "Nonparametric Counterfactuals in Random Utility Models," Papers 1902.08350, arXiv.org, revised May 2019.
    5. Varian, Hal R, 1982. "The Nonparametric Approach to Demand Analysis," Econometrica, Econometric Society, vol. 50(4), pages 945-973, July.
    6. Rahul Deb & Yuichi Kitamura & John K.-H. Quah & Jorg Stoye, 2017. "Revealed Price Preference: Theory and Stochastic Testing," Cowles Foundation Discussion Papers 2087, Cowles Foundation for Research in Economics, Yale University.
    Full references (including those not matched with items on IDEAS)

    Citations

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    Cited by:

    1. Roy Allen & Pawel Dziewulski & John Rehbeck, 2019. "Revealed statistical consumer theory," Working Paper Series 1119, Department of Economics, University of Sussex Business School.
    2. Nobuo Koida & Koji Shirai, 2024. "A dual approach to nonparametric characterization for random utility models," Papers 2403.04328, arXiv.org.
    3. Changkuk Im & John Rehbeck, 2021. "Non-rationalizable Individuals, Stochastic Rationalizability, and Sampling," Papers 2102.03436, arXiv.org, revised Oct 2021.
    4. Turansick, Christopher, 2022. "Identification in the random utility model," Journal of Economic Theory, Elsevier, vol. 203(C).
    5. Christopher Turansick, 2023. "On Graphical Methods in Stochastic Choice," Papers 2303.14249, arXiv.org, revised Sep 2023.
    6. Mike Tsionas & Valentin Zelenyuk, 2021. "Goodness-of-fit in Optimizing Models of Production: A Generalization with a Bayesian Perspective," CEPA Working Papers Series WP182021, School of Economics, University of Queensland, Australia.
    7. 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.
    8. Daniele Caliari & Henrik Petri, 2024. "Irrational Random Utility Models," Papers 2403.10208, arXiv.org.

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    Keywords

    computational tools; statistical testing;

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