The traditional approach to estimating systems of share equations is to append a multivariate normal stochastic component to the deterministic component. The aggregation restrictions are then exploited to delete one equation and estimation is then carried out by maximum likelihood. Such an approach does not exploit the aggregation restrictions to their full extent, as there remains a non-zero probability of shares being negative or greater than unity. In this paper -we take an approach, compositional data analysis, and a distribution familiar to statisticians, the additive logistic normal, and apply them to the estimation of a system of demand share equations. The results of this new approach are then compared to those of the traditional approach.