Weak Separability in Applied Welfare Analysis

The focus of this paper is the impact on welfare measurement of a common assumption in applied demand analysis, weak separability. A standard empirical practice is to estimate conditional demand models for a set of goods which are assumed to be weakly separable from all other goods with expenditure as a right-hand-side variable, tacitly assuming that expenditure is predetermined (Alston and Chalfant 1987, 1991; Alston, Carter, Green, and Pick; Blackorby, Boyce, and Russell; Blisard and Blaylock; Brown and Heien; Cashin; Choi and Sosin; Clements and E. Selvanathan; Clements and S. Selvana-than; Deaton 1975; Goddard and Amuah; Gould, Cox, and Perali 1990, 1991; Heien; Heien and Pompelli 1988, 1989; Murray; Safyurtlu, John-son, and Hassan; Theil 1976, 1980; Van Ko-oten; Yen and Chern). Once estimated, such separable demand models often are used to cal-culate exact welfare measures, or changes in the true cost of living index, of the economic effects on consumers due to changes in the prices of the goods under study (Heien; Heien and Pom-pelli 1989; Van Kooten; Blisard and Blaylock). This practice is shown here to produce biased results. There are two sources of the bias and both can be traced to the inappropriate treatment of expenditure as predetermined. In an empiri-cal application to the U.S. dairy program, a comparison of estimates from an incomplete demand system specification versus a weakly separable specification suggests a negative bias of around 17% of the compensating variation due to eliminating price discrimination in federal milk marketing orders in 1990. Results from a Monte Carlo simulation suggest that the downward bias is closer to 40%. I first present the analysis of weak separability, then the empirical application, and a summary and conclusions.