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Nonparametric Analysis of Random Utility Models

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  • Yuichi Kitamura
  • Jörg Stoye

Abstract

This paper develops and implements a nonparametric test of random utility models. The motivating application is to test the null hypothesis that a sample of cross‐sectional demand distributions was generated by a population of rational consumers. We test a necessary and sufficient condition for this that does not restrict unobserved heterogeneity or the number of goods. We also propose and implement a control function approach to account for endogenous expenditure. An econometric result of independent interest is a test for linear inequality constraints when these are represented as the vertices of a polyhedral cone rather than its faces. An empirical application to the U.K. Household Expenditure Survey illustrates computational feasibility of the method in demand problems with five goods.

Suggested Citation

  • Yuichi Kitamura & Jörg Stoye, 2018. "Nonparametric Analysis of Random Utility Models," Econometrica, Econometric Society, vol. 86(6), pages 1883-1909, November.
  • Handle: RePEc:wly:emetrp:v:86:y:2018:i:6:p:1883-1909
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    File URL: https://doi.org/10.3982/ECTA14478
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    References listed on IDEAS

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    1. Hiroaki Kaido & Francesca Molinari & Jörg Stoye, 2019. "Confidence Intervals for Projections of Partially Identified Parameters," Econometrica, Econometric Society, vol. 87(4), pages 1397-1432, July.
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    3. Richard Blundell & Martin Browning & Laurens Cherchye & Ian Crawford & Bram De Rock & Frederic Vermeulen, 2015. "Sharp for SARP: Nonparametric Bounds on Counterfactual Demands," American Economic Journal: Microeconomics, American Economic Association, vol. 7(1), pages 43-60, February.
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    6. Wolak, Frank A, 1991. "The Local Nature of Hypothesis Tests Involving Inequality Constraints in Nonlinear Models," Econometrica, Econometric Society, vol. 59(4), pages 981-995, July.
    7. Blundell, Richard & Kristensen, Dennis & Matzkin, Rosa, 2014. "Bounding quantile demand functions using revealed preference inequalities," Journal of Econometrics, Elsevier, vol. 179(2), pages 112-127.
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    9. Dette, Holger & Hoderlein, Stefan & Neumeyer, Natalie, 2016. "Testing multivariate economic restrictions using quantiles: The example of Slutsky negative semidefiniteness," Journal of Econometrics, Elsevier, vol. 191(1), pages 129-144.
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    11. 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.
    12. 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.
    13. Abi Adams, 2015. "Mutually consistent revealed preference bounds," IFS Working Papers W15/20, Institute for Fiscal Studies.
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    Cited by:

    1. repec:ucp:jpolec:doi:10.1086/692808 is not listed on IDEAS
    2. à ureo de Paula & Seth Richards†Shubik & Elie Tamer, 2018. "Identifying Preferences in Networks With Bounded Degree," Econometrica, Econometric Society, vol. 86(1), pages 263-288, January.
    3. 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.
    4. Whitney K. Newey & Sami Stouli, 2018. "Heterogenous Coefficients, Discrete Instruments, and Identification of Treatment Effects," Papers 1811.09837, arXiv.org.
    5. Victor H. Aguiar & Maria Jose Boccardi & Nail Kashaev & Jeongbin Kim, 2018. "Does Random Consideration Explain Behavior when Choice is Hard? Evidence from a Large-scale Experiment," Papers 1812.09619, arXiv.org, revised Jun 2019.
    6. repec:eee:mateco:v:81:y:2019:i:c:p:74-83 is not listed on IDEAS
    7. Adams, Abigail, 2019. "Mutually Consistent Revealed Preference Demand Predictions," CEPR Discussion Papers 13580, C.E.P.R. Discussion Papers.
    8. Whitney K. Newey & Sami Stouli, 2018. "Control variables, discrete instruments, and identification of structural functions," CeMMAP working papers CWP55/18, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    9. Victor H. Aguiar & Nail Kashaev, 2019. "Discrete Choice and Welfare Analysis with Unobserved Choice Sets," Papers 1907.04853, arXiv.org, revised Jul 2019.
    10. Victor H. Aguiar & Nail Kashaev, 2018. "Stochastic Revealed Preferences with Measurement Error," Papers 1810.05287, arXiv.org.
    11. Charles F. Manski, 2014. "Identification of income–leisure preferences and evaluation of income tax policy," Quantitative Economics, Econometric Society, vol. 5, pages 145-174, March.
    12. Bhattacharya, D., 2018. "The Empirical Content of Binary Choice Models," Cambridge Working Papers in Economics 1883, Faculty of Economics, University of Cambridge.
    13. Jerry Hausman & Whitney K. Newey, 2014. "Individual Heterogeneity and Average Welfare," CeMMAP working papers CWP42/14, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    14. Arthur Lewbel & Krishna Pendakur, 2017. "Unobserved Preference Heterogeneity in Demand Using Generalized Random Coefficients," Journal of Political Economy, University of Chicago Press, vol. 125(4), pages 1100-1148.
    15. Rahul Deb & Yuichi Kitamura & John Quah & Jorg Stoye, 2018. "Revealed price preference: theory and empirical analysis," CeMMAP working papers CWP57/18, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    16. repec:eee:econom:v:211:y:2019:i:2:p:483-506 is not listed on IDEAS
    17. repec:eee:ecolet:v:177:y:2019:i:c:p:66-68 is not listed on IDEAS
    18. Matias D. Cattaneo & Xinwei Ma & Yusufcan Masatlioglu & Elchin Suleymanov, 2017. "A Random Attention Model," Papers 1712.03448, arXiv.org, revised Aug 2019.
    19. Natalia Lazzati & John K.-H. Quah & Koji Shirai, 2018. "Nonparametric analysis of monotone choice," Discussion Paper Series 184, School of Economics, Kwansei Gakuin University.
    20. Stoye, Jörg, 2019. "Revealed Stochastic Preference: A one-paragraph proof and generalization," Economics Letters, Elsevier, vol. 177(C), pages 66-68.
    21. 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.
    22. Charles F. Manski, 2012. "Identification of Preferences and Evaluation of Income Tax Policy," NBER Working Papers 17755, National Bureau of Economic Research, Inc.
    23. Cherchye, Laurens & Demuynck, Thomas & Rock, Bram De, 2019. "Bounding counterfactual demand with unobserved heterogeneity and endogenous expenditures," Journal of Econometrics, Elsevier, vol. 211(2), pages 483-506.

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    JEL classification:

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

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