Consumer Demand—Separability and Commodity Aggregation

A significant problem to address prior to empirical implementation of the theory of consumer demand is the problem of degrees of freedom. In particular, because of the large number of goods purchased by the consumer, there are literally thousands of individual goods and, therefore prices of related goods, one would need to include in the analysis to make it complete. Even for a modest number of commodities, there are still a relatively large number of elasticities to estimate requiring a relatively large data sample. This chapter considers the alternative approaches to this problem, though restrictions on price movements and separability and two-stage budgeting. The focus is on two-stage budgeting with an effort to clarify understanding of application to systems of demand functions. The main result is that either strong separability or homogeneous separability, in addition to weak separability, is required for consistent estimation of two-stage demand functions. The chapter concludes with a discussion on how to empirically implement two-stage budgeting for a complete system of demand functions.