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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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    File URL: http://www.cemmap.ac.uk/wps/cwp361313.pdf
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    References listed on IDEAS

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    1. Varian, Hal R, 1982. "The Nonparametric Approach to Demand Analysis," Econometrica, Econometric Society, vol. 50(4), pages 945-973, July.
    2. Blundell, R. & Browning, M. & Cherchye, L.J.H. & Crawford, I. & de Rock, B. & Vermeulen, F.M.P., 2012. "Sharp for SARP : Nonparametric Bounds on the Behavioural and Welfare Effects of Price Changes," Discussion Paper 2012-065, Tilburg University, Center for Economic Research.
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    9. Hoderlein, Stefan, 2011. "How many consumers are rational?," Journal of Econometrics, Elsevier, vol. 164(2), pages 294-309, October.
    10. Canay, Ivan A., 2010. "EL inference for partially identified models: Large deviations optimality and bootstrap validity," Journal of Econometrics, Elsevier, vol. 156(2), pages 408-425, June.
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    18. Daniel McFadden, 2005. "Revealed stochastic preference: a synthesis," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 26(2), pages 245-264, August.
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    Citations

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    Cited by:

    1. Sam Cosaert & Thomas Demuynck, "undated". "Nonparametric welfare and demand analysis with unobserved individual heterogeneity," ULB Institutional Repository 2013/251988, ULB -- Universite Libre de Bruxelles.
    2. Boneva, Lena & Linton, Oliver & Vogt, Michael, 2015. "A semiparametric model for heterogeneous panel data with fixed effects," Journal of Econometrics, Elsevier, pages 327-345.
    3. Sokbae Lee & Kyungchul Song & Yoon-Jae Whang, 2014. "Testing For A General Class Of Functional Inequalities," KIER Working Papers 889, Kyoto University, Institute of Economic Research.
    4. Cherchye, Laurens & De Rock, Bram & Demuynck, Thomas, 0. "Transitivity of preferences: when does it matter?," Theoretical Economics, Econometric Society.
    5. 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.
    6. repec:spr:etbull:v:3:y:2015:i:2:d:10.1007_s40505-014-0061-5 is not listed on IDEAS
    7. 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.
    8. 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.
    9. Kim, Byung-Yeon & Choi, Syngjoo & Lee, Jungmin & Lee, Sokbae & Choi, Kyunghui, 2013. "Do Institutions Affect Social Preferences? Evidence from Divided Korea," IZA Discussion Papers 7567, Institute for the Study of Labor (IZA).
    10. Kawaguchi, Kohei, 2017. "Testing rationality without restricting heterogeneity," Journal of Econometrics, Elsevier, vol. 197(1), pages 153-171.
    11. Hubner, Stefan, 2016. "Topics in nonparametric identification and estimation," Other publications TiSEM 08fce56b-3193-46e0-871b-0, Tilburg University, School of Economics and Management.
    12. Laurens Cherchye & Sam Cosaert & Bram De Rock & Pieter Jan Kerstens & Frederic Vermeulen, 2017. "Individual Welfare Analysis for Collective Households," Working Papers ECARES ECARES 2017-44, ULB -- Universite Libre de Bruxelles.

    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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