Cross‐Section Application of Linear Expenditure Systems: Responses to Sociodemographic Effects

Abstract

Analysis of consumption allocation with expenditure systems is well known in aggregate, time-series applications. Yet, until recently, studies of individual household behavior have not generally brought available demand theory to bear on the empirical estimates. Pollak and Wales cited two advantages of using complete demand systems for the study of demographic effects on consumption. Demand systems incorporate the budget constraint into the analysis and permit the separation of demographic effects from ownand cross-price effects as well as from income effects. Unless these effects are separated, the demographic effects estimated with one set of prices cannot be presumed to apply in a different price situation. This paper discusses the interpretation of linear Engel curves as reduced forms of the linear expenditure system (LES) and the extended linear expenditure system (ELES). Parameters of these systems can be made functions of the sociodemographic characteristics of the household. With constant prices, the marginal budget shares in the LES are identified, but the subsistence expenditures are not. The ELES, which uses income in place of total expenditure, is exactly identified; all its parameters can be estimated by indirect least squares. Subject to the assumption of additive separability underlying the LES and the savings behavior implicit in the ELES, price effects can be estimated with data from a single cross section.