  We introduce two models of non-parametric random utility for demand systems:
the stochastic absolute risk aversion (SARA) model, and the stochastic
safety-first (SSF) model. In each model, individual-level heterogeneity is
characterized by a distribution $\pi\in\Pi$ of taste parameters, and
heterogeneity across consumers is introduced using a distribution $F$ over the
distributions in $\Pi$. Demand is non-separable and heterogeneity is
infinite-dimensional. Both models admit corner solutions. We consider two
frameworks for estimation: a Bayesian framework in which $F$ is known, and a
hyperparametric (or empirical Bayesian) framework in which $F$ is a member of a
known parametric family. Our methods are illustrated by an application to a
large U.S. panel of scanner data on alcohol consumption.
