We derive asymptotic properties of an estimator for supply and demand models extended with additional moments relating consumer demographics to the characteristics of purchased products. We clarify the structure of a practical sampling scheme in which the extended estimator is consistent, asymptotically normal, and more efficient than the original estimator. We provide conditions guaranteeing the asymptotic theorems hold for the random coefficient logit model of demand with oligopolistic suppliers. Extensive simulation studies demonstrate significant benefits of the additional moments in estimating the random coefficient logit model.