Estimating The Linear Expenditure System With Cross-Sectional Data

The linear expenditure system (LES) is a popular model for analysing consumer behaviour in relation to changes in prices and income. The first part of this paper provides a comprehensive review of LES, including its positive and negative attributes. Emphasis is placed on the application to cross-section data where there is no price variation. In such situations, the LES parameters are under identified unless the value of the income elasticity of the marginal utility of income (referred to as the “Frisch parameter”) is known. We evaluate several sources from the literature for this parameter value. The second part of the paper is an empirical illustration of the application of LES with a cross-section of about 10,000 Australian households. To overcome the aggregation and linearity issues of LES, we disaggregated households into income quintiles and estimated a separate LES for each quintile. A comparison of the quintile estimates with the one-consumer case (when the data are pooled) reveals substantial differences in demand responses that are masked when LES is constrained to have the same parameters across the income distribution. We also established the further advantage of disaggregation that the quintile estimates tend to fit the data considerably better than the single LES.