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Nonparametric Analysis of Random Utility Models: Testing

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Abstract

This paper develops new tools for the analysis of Random Utility Models (RUM). The leading application is stochastic revealed preference theory, that is, the modeling of aggregate choice behavior in a population characterized by individual rationality and unobserved heterogeneity. We test the null hypothesis that a repeated cross-section of demand data was generated by such a population, without restricting unobserved heterogeneity in any form whatsoever. Equivalently, we empirically test McFadden and Richter's (1991) Axiom of Revealed Stochastic Preference (ARSP, to be defined later), using only nonsatiation and the Strong Axiom of Revealed Preference (SARP) as restrictions on individual level behavior. Doing this is computationally challenging. We provide various algorithms that can be implemented with reasonable computational resources. Also, new tools for statistical inference for inequality restrictions are introduced in order to deal with the high-dimensionality and non-regularity of the problem at hand.

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File URL: http://cowles.econ.yale.edu/P/cd/d19a/d1902.pdf
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Bibliographic Info

Paper provided by Cowles Foundation for Research in Economics, Yale University in its series Cowles Foundation Discussion Papers with number 1902.

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Length: 47 pages
Date of creation: Jul 2013
Date of revision:
Handle: RePEc:cwl:cwldpp:1902

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Postal: Cowles Foundation, Yale University, Box 208281, New Haven, CT 06520-8281 USA

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Keywords: Stocastic rationality;

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References

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  1. Varian, Hal R, 1982. "The Nonparametric Approach to Demand Analysis," Econometrica, Econometric Society, vol. 50(4), pages 945-73, July.
  2. 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.
  3. Blundell, R. & Browning, M. & Cherchye, L.J.H. & Crawford, I. & Rock, B. de & 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.
  4. Jörg Stoye, 2010. "Partial identification of spread parameters," Quantitative Economics, Econometric Society, vol. 1(2), pages 323-357, November.
  5. 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.
  6. Wolak, Frank A, 1991. "The Local Nature of Hypothesis Tests Involving Inequality Constraints in Nonlinear Models," Econometrica, Econometric Society, vol. 59(4), pages 981-95, July.
  7. 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.
  8. 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.
  9. Stefan Hoderlein, 2009. "How many consumers are rational?," CeMMAP working papers CWP32/09, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
  10. Jorg Stoye, 2009. "More on Confidence Intervals for Partially Identified Parameters," Econometrica, Econometric Society, vol. 77(4), pages 1299-1315, 07.
  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. Daniel McFadden, 2005. "Revealed stochastic preference: a synthesis," Economic Theory, Springer, vol. 26(2), pages 245-264, 08.
  13. Arthur Lewbel, 2001. "Demand Systems with and without Errors," American Economic Review, American Economic Association, vol. 91(3), pages 611-618, June.
  14. 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.
  15. 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.
  16. 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.
  17. 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.
  18. 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.
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Citations

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Cited by:
  1. 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.
  2. 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.
  3. Cherchye, Laurens & Demuynck, Thomas & De Rock, Bram & Vermeulen, Frederic, 2014. "Household Consumption When the Marriage Is Stable," IZA Discussion Papers 8070, Institute for the Study of Labor (IZA).
  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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