Exact aggregation of consumer demand systems

This paper is divided into two parts which deal with closely connected issues. The first section of the paper explores the structure of consumer demand systems necessary and sufficient for exact aggregation. The second section addresses a related empirical question: what, if anything, do the restrictions imposed on exactly aggregable demand systems buy the econometrician engaged in estimating integrable consumer demands? In particular, if the objective of an empirical exercise is to estimate the demand systems of individual utility maximizing consumers and only aggregate expenditure information and information on the income and demographic composition of the population are available, then under what conditions can the parameters of the estimated aggregate expenditure system be used to uniquely identify the parameters of the underlying individual demand systems?