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Nonparametric analysis of random utility models: testing

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  • Yuichi Kitamura

    ()
    (Institute for Fiscal Studies and Yale University)

  • Jörg Stoye

    (Institute for Fiscal Studies and New York 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.

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Bibliographic Info

Paper provided by Centre for Microdata Methods and Practice, Institute for Fiscal Studies in its series CeMMAP working papers with number CWP36/13.

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Date of creation: Aug 2013
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Handle: RePEc:ifs:cemmap:36/13

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Keywords: stochastic rationality;

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References

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  1. 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.
  2. Daniel McFadden, 2005. "Revealed stochastic preference: a synthesis," Economic Theory, Springer, vol. 26(2), pages 245-264, 08.
  3. Arthur Lewbel, 2001. "Demand Systems with and without Errors," American Economic Review, American Economic Association, vol. 91(3), pages 611-618, June.
  4. Gourieroux, Christian & Holly, Alberto & Monfort, Alain, 1982. "Likelihood Ratio Test, Wald Test, and Kuhn-Tucker Test in Linear Models with Inequality Constraints on the Regression Parameters," Econometrica, Econometric Society, vol. 50(1), pages 63-80, January.
  5. Jorg Stoye, 2009. "More on Confidence Intervals for Partially Identified Parameters," Econometrica, Econometric Society, vol. 77(4), pages 1299-1315, 07.
  6. Stefan Hoderlein & Jörg Stoye, 2009. "Revealed Preferences in a Heterogeneous Population," Boston College Working Papers in Economics 745, Boston College Department of Economics.
  7. Richard BLUNDELL & Martin BROWNING & Laurens CHERCHYE & Ian CRAWFORD & Bram DE ROCK & Frederic VERMEULEN, 2012. "Sharp for SARP: nonparametric bounds on the behavioural and welfare effects of price changes," Center for Economic Studies - Discussion papers ces12.11, Katholieke Universiteit Leuven, Centrum voor Economische Studiën.
  8. Jörg Stoye, 2010. "Partial identification of spread parameters," Quantitative Economics, Econometric Society, vol. 1(2), pages 323-357, November.
  9. Epstein, Larry G. & Yatchew, Adonis J., 1985. "Non-parametric hypothesis testing procedures and applications to demand analysis," Journal of Econometrics, Elsevier, vol. 30(1-2), pages 149-169.
  10. Stefan Hoderlein, 2009. "How many consumers are rational?," CeMMAP working papers CWP32/09, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
  11. Victor Chernozhukov & Han Hong & Elie Tamer, 2007. "Estimation and Confidence Regions for Parameter Sets in Econometric Models," Econometrica, Econometric Society, vol. 75(5), pages 1243-1284, 09.
  12. Wolak, Frank A, 1991. "The Local Nature of Hypothesis Tests Involving Inequality Constraints in Nonlinear Models," Econometrica, Econometric Society, vol. 59(4), pages 981-95, July.
  13. Laurens Cherchye & Ian Crawford & Bram De Rock & Frederic Vermeulen, 2009. "The revealed preference approach to demand," ULB Institutional Repository 2013/132522, ULB -- Universite Libre de Bruxelles.
  14. Federico A. Bugni, 2010. "Bootstrap Inference in Partially Identified Models Defined by Moment Inequalities: Coverage of the Identified Set," Econometrica, Econometric Society, vol. 78(2), pages 735-753, 03.
  15. Varian, Hal R, 1982. "The Nonparametric Approach to Demand Analysis," Econometrica, Econometric Society, vol. 50(4), pages 945-73, July.
  16. Federico Echenique & Sangmok Lee & Matthew Shum, 2011. "The Money Pump as a Measure of Revealed Preference Violations," Journal of Political Economy, University of Chicago Press, vol. 119(6), pages 1201 - 1223.
  17. Fishburn, Peter C., 1992. "Induced binary probabilities and the linear ordering polytope: a status report," Mathematical Social Sciences, Elsevier, vol. 23(1), pages 67-80, February.
  18. Itai Sher & Jeremy T. Fox & Kyoo il Kim & Patrick Bajari, 2011. "Partial Identification of Heterogeneity in Preference Orderings Over Discrete Choices," NBER Working Papers 17346, National Bureau of Economic Research, Inc.
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Cited by:
  1. Sokbae 'Simon' Lee & Kyungchul Song & Yoon-Jae Whang, 2014. "Testing for a general class of functional inequalities," CeMMAP working papers CWP09/14, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
  2. Laurens CHERCHYE & Thomas DEMUYNCK & Bram DE ROCK & Frederic VERMEULEN, 2014. "Household consumption when the marriage is stable," Center for Economic Studies - Discussion papers ces14.08, Katholieke Universiteit Leuven, Centrum voor Economische Studiën.
  3. Jerry Hausman & Whitney Newey, 2013. "Individual heterogeneity and average welfare," CeMMAP working papers CWP34/13, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
  4. Federico Bugni & Ivan Canay & Xiaoxia Shi, 2013. "Specification for Partially Identified Models defined by Moment Inequalities," CeMMAP working papers CWP01/13, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.

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