Frequency of purchase and the estimation of demand systems

In this paper we consider a joint model for frequency of purchase and consumer demand. We discuss sufficient identifying assumptions for the estimation of consumer demands from survey data for the general case of nonlinear (or linear) Engel curves. Moreover we show that in many cases the actual number of purchases is necessary in order to obtain consistent parameter estimates for the demand system. The empirical application relates to the estimation of a demand system for French foodstuffs.