SPECIFICATION OF COMMODITY SUBSETS FOR SEPARABLE UTILITY FUNCTIONS

Abstract

The present paper differs from previous works since it is concerned with the conditions under which commodities are grouped in separable utility functions. The conditions are derived theoretically and then tested empirically. This provides a solid basis under which commodities can he properly grouped without employing an a priori reasoning process that could result in misspecification of the utility function. The conditions are derived and tested for three principal types of separable utility functions: utility tree, block additivity, and additivity. In the case of directly additive utility functions, the goods are treated as Hicksian composite commodities rather than specific goods. The general conditions for grouping apply to directly additive functions so that each composite commodity is treated as belonging to a separate subset. The data for commodity expenditure in constant dollars and prices of commodities are taken from The National Income and Product Accounts of the United States, 1929–1965, Statistical Tables, Table 2.6 and Table 8.6 respectively. The conditions necessary for specification of the commodity subsets are derived from the properties of each Separability situation and are empirically tested in an iterative fashion similar to the cochranc‐orcutt autoregressive technique.