We develop a model of demand where consumers trade-off the utility of consumption against the disutility of expenditure. This model is appropriate whenever a consumer’s demand over a strict subset of all available goods is being analyzed. Data sets consistent with this model are characterized by the absence of revealed preference cycles over prices. The model is readily generalized to the random utility setting, for which we develop nonparametric statistical tests. Our application on national household consumption data provides support for the model.
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.