The concept of the "rank" of a demand system is used to unify the literature concerning the aggregation and functional structure of demands. The implication of an extended notion of rank for aggregation, separability, functional form and welfare comparison are derived. These are particularly useful because rank is a scalar, integer attribute of readily available Engle curve data, yet this number has implications for the income and price structure of the demands and for the appropriate structure of models used to estimate and analyze these demands. A simple new nonparametric techniques for estimating the rank of demands is derived based on ordinary linear regressions to construct a matrix that asymptotically has the same rank as the underlying demand system. Applications of other nonparametric estimators are also proposed. Kernel and average derivative estimation will be used to nonparametrically estimate elasticities. They will be combined with rank estimates to suggest appropriate levels of separability, aggregation and parametric or semiparametric functional forms. In developing the new techniques for analyzing demand behavior, the methods will be useful in examining cost and welfare implications for tax, income redistribution and pricing policies and describing the differential impact of such policies on different demographic groups, including the elderly, single parents and the poor. Other potential applications include extensions to production data to reveal analogous information about the structure of factor demands and analysis for financial assets, where rank provides a nonparametric estimate of the degree of mutual fund (portfolio) separation. The principal data sources for the analysis are the Consumer Expenditure Surveys, with prices obtained from the U.S. National Income and Product Accounts. For comparison purposes, British data will be used.
