  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 rely on any restriction on 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 polyhedron rather than its faces. An empirical application to the U.K.
Household Expenditure Survey illustrates computational feasibility of the
method in demand problems with 5 goods.
