The Rank of Demand Systems: Theory and Nonparametric Estimation

W. M. Gorman's (1981) concept of Engel curve "rank" is extended to apply to any demand system. Rank is shown to have implications for specification, separability, and aggregation of demands. A simple nonparametric test of rank using Engel curve data is described and applied to U.S. and U.K. consumer survey data. The test employs a new general method for testing the rank of estimated matrices. The results are used to assess theoretical and empirical aggregation error in representative consumer models, and to explain a representative consumer paradox. Copyright 1991 by The Econometric Society.