Nonparametric Analysis of Random Utility Models: Testing

48 Pages Posted: 30 Jul 2013

See all articles by Yuichi Kitamura

Yuichi Kitamura

Yale University - Cowles Foundation

Jörg Stoye

Cornell University - Department of Economics

Date Written: July 29, 2013


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.

Keywords: Stochastic rationality

JEL Classification: C14

Suggested Citation

Kitamura, Yuichi and Stoye, Jörg, Nonparametric Analysis of Random Utility Models: Testing (July 29, 2013). Cowles Foundation Discussion Paper No. 1902, Available at SSRN: or

Yuichi Kitamura (Contact Author)

Yale University - Cowles Foundation ( email )

Box 208281
New Haven, CT 06520-8281
United States

Jörg Stoye

Cornell University - Department of Economics ( email )

414 Uris Hall
Ithaca, NY 14853-7601
United States

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