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Nonparametric analysis of random utility models: testing

Author

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  • Yuichi Kitamura

    (Institute for Fiscal Studies and Yale University)

  • Jorg Stoye

    (Institute for Fiscal Studies and Cornell University)

Abstract

This paper develops and implements a nonparametric test of Random Utility Models (RUM) using only nonsatiation and the Strong Axiom of Revealed Preference (SARP) as restrictions on individual level behaviour, allowing for fully unrestricted unobserved heterogeneity. The main application is the test of the null hypothesis that a sample of cross-sectional demand distributions was generated by a population of rational consumers. Thus, the paper provides a finite sample counterpart to the classic theoretical analysis of McFadden and Richter (1991). To do so, it overcomes challenges in computation and in asymptotic theory and provides an empirical application to the U.K. Household Expenditure Survey. An econometric result of independent interest is a test for inequality constraints when they are represented in terms of the rays of a cone rather than its faces.

Suggested Citation

  • Yuichi Kitamura & Jorg Stoye, 2013. "Nonparametric analysis of random utility models: testing," CeMMAP working papers CWP36/13, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    • Handle: RePEc:ifs:cemmap:36/13
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    References listed on IDEAS

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    Cited by:

    1. Sam Cosaert & Thomas Demuynck, 2018. "Nonparametric Welfare and Demand Analysis with Unobserved Individual Heterogeneity," The Review of Economics and Statistics, MIT Press, vol. 100(2), pages 349-361, May.
    2. Ho, Kate & Rosen, Adam M., 2015. "Partial Identification in Applied Research: Benefits and Challenges," CEPR Discussion Papers 10883, C.E.P.R. Discussion Papers.
    3. Bugni, Federico A. & Canay, Ivan A. & Shi, Xiaoxia, 2015. "Specification tests for partially identified models defined by moment inequalities," Journal of Econometrics, Elsevier, vol. 185(1), pages 259-282.
    4. Cherchye, Laurens & Cosaert, Sam & De Rock, Bram & Kerstens, Pieter Jan & Vermeulen, Frederic, 2018. "Individual welfare analysis for collective households," Journal of Public Economics, Elsevier, vol. 166(C), pages 98-114.
    5. Lee, Sokbae & Song, Kyungchul & Whang, Yoon-Jae, 2018. "Testing For A General Class Of Functional Inequalities," Econometric Theory, Cambridge University Press, vol. 34(5), pages 1018-1064, October.
    6. Natalia Lazzati & John K.-H. Quah & Koji Shirai, 2015. "A revealed preference theory of monotone choice and strategic complementarity," Discussion Paper Series 138, School of Economics, Kwansei Gakuin University, revised Dec 2015.
    7. Kaplan, David M. & Zhuo, Longhao, 2021. "Frequentist properties of Bayesian inequality tests," Journal of Econometrics, Elsevier, vol. 221(1), pages 312-336.
    8. Mira Frick & Ryota Iijima & Tomasz Strzalecki, 2019. "Dynamic Random Utility," Econometrica, Econometric Society, vol. 87(6), pages 1941-2002, November.
    9. Cherchye, Laurens & Demuynck, Thomas & De Rock, Bram, 2018. "Transitivity of preferences: when does it matter?," Theoretical Economics, Econometric Society, vol. 13(3), September.
    10. Richard Blundell & Dennis Kristensen & Rosa Matzkin, 2017. "Individual counterfactuals with multidimensional unobserved heterogeneity," CeMMAP working papers CWP60/17, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    11. Laurens Cherchye & Thomas Demuynck & Bram De Rock & Frederic Vermeulen, 2017. "Household Consumption When the Marriage Is Stable," American Economic Review, American Economic Association, vol. 107(6), pages 1507-1534, June.
    12. Alexander Torgovitsky, 2019. "Partial identification by extending subdistributions," Quantitative Economics, Econometric Society, vol. 10(1), pages 105-144, January.
    13. Jerry A. Hausman & Whitney K. Newey, 2016. "Individual Heterogeneity and Average Welfare," Econometrica, Econometric Society, vol. 84, pages 1225-1248, May.
    14. Cherchye, Laurens & Demuynck, Thomas & De Rock, Bram, 2018. "Transitivity of preferences: when does it matter?," Theoretical Economics, Econometric Society, vol. 13(3), September.
    15. Hubner, Stefan, 2016. "Topics in nonparametric identification and estimation," Other publications TiSEM 08fce56b-3193-46e0-871b-0, Tilburg University, School of Economics and Management.
    16. David M. Kaplan, 2015. "Bayesian and frequentist tests of sign equality and other nonlinear inequalities," Working Papers 1516, Department of Economics, University of Missouri.
    17. Rahul Deb & Yuichi Kitamura & John Quah & Joerg Stoye, 2017. "Revealed Price Preference: Theory and Stochastic Testing," Working Papers tecipa-582, University of Toronto, Department of Economics.
    18. Yuichi Kitamura & Jorg Stoye, 2019. "Nonparametric Counterfactuals in Random Utility Models," Papers 1902.08350, arXiv.org, revised May 2019.
    19. Bart Smeulders, 2018. "Column Generation Algorithms for Nonparametric Analysis of Random Utility Models," Papers 1812.01400, arXiv.org.
    20. Giovanni Compiani & Yuichi Kitamura, 2016. "Using mixtures in econometric models: a brief review and some new results," Econometrics Journal, Royal Economic Society, vol. 19(3), pages 95-127, October.
    21. 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.
    22. Ian Crawford & Matthew Polisson, 2015. "Demand Analysis with Partially Observed Prices," Discussion Papers in Economics 15/12, Division of Economics, School of Business, University of Leicester, revised Dec 2016.
    23. Kawaguchi, Kohei, 2017. "Testing rationality without restricting heterogeneity," Journal of Econometrics, Elsevier, vol. 197(1), pages 153-171.

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    More about this item

    Keywords

    stochastic rationality;

    JEL classification:

    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General

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