Estimation of Complete Demand Systems from Household Budget Data: The Linear and Quadratic Expenditure Systems

Abstract

In this paper we explore two issues in empirical demand analysis-the estimation of complete systems of demand equations using household budget data (Section I), and the incorporation of demographic characteristics into such systems (Section II). Although there are numerous studies which use time-series data to estimate complete demand systems, and many which estimate Engel curves from household budget data, there are virtually none which combine budget data from different periods to estimate complete systems. Since each budget study corresponds to a single price situation, one might conjecture that estimation of complete systems would not be possible unless budget studies were available from a large number of periods. This is incorrect. In Section I we argue that interesting complete demand systems can be estimated from a small number of budget studies, despite the limited price variability represented in such data. To demonstrate this, we use budget study data for two periods to estimate a pair of related demand systems: the familiar linear expenditure system (LES) and a quadratic expenditure system (QES), a generalization of LES in which the demand equations are quadratic in total expenditure.' The inclusion of demographic variables in the analysis of household consumption patterns is desirable because there are likely to be systematic differences in the consumption behavior of households with different demographic characteristics. But the effects of demographic characteristics have seldom been studied within the framework of complete demand systems. In Section II we propose as a general method for incorporating demographic variables into complete systems of demand equations. This method has not previously been discussed as a general technique for bringing demographic variables into demand systems, although it has been employed in several studies. To improve the estimates of the LES and the QES presented in Section I, we reestimate these two systems using translating to incorporate family size.