“Engel Curve Based Linear Expenditure Demand System”

Citation: Ganesh-Kumar, A. and G. Darbha 1996. “Engel Curve Based Linear Expenditure Demand System”. Paper presented at the 32^nd Indian Econometric Society Conference, Indian Statistical Institute, Bangalore, Mar.21-23.

Abstract: Fischer et. al. (1988) proposed a procedure for estimating the linear expenditure system (LES) through a locally linear approximation of commodity-wise estimated Engel curve parameters. The estimated Engel curves for different commodities are combined into a complete demand system by defining a measure of “real” income that ensures the adding-up requirement of the budget constraint. Such a measure of implicit real income is derived as an iterative solution to a system of nonlinear demand equations based on Newton-Raphson algorithm. The LES parameters are then derived from the Engel functions evaluated at that level of real income. Additionally, this procedure permits impostion of calorie consumption constraint on the demand system, such that the calorie consumption associated with the projected demand would lie within reasonable levels. A great advantage with this procedure is that one can estimate a demand system for a large number of commodities from the time series data on aggregate consumption even when household survey data are not available at the desired level of commodity disaggregation. However, the robustness of this procedure to alternate initial specification of Engel functional forms and its performance vis-à-vis an econometrically estimated LES have not been studied.

In this paper we study the robustness of this procedure to different combinations of Engel functional forms and parameter values. We construct randomised parameter configurations of different Engel parameters around their point estimates using normal random numbers generated from a population with the same standard error as those of the Engel parameters. Distributional properties of the corresponding estimated LES parameters are then analysed. We find that the procedure is robust to different functional forms for the Engel curves and also to different parameter configurations. We also find that the associated LES parameters are normally distributed and are comparable with those of the econometrically estimated LES in terms of their mean and standard errors.

Additionally, we extend this procedure to estimate classwise LES parameters from a set of aggregate Engel functions. This modification, while retaining all the above mentioned properties of additivity and consistency, ensures that the estimated classwise demands are consistent with the aggregate household demand. This procedure, in our view, would be useful while constructing Social Accounting Matrix (SAM) which is a pre-requisite for a Computable General Equilibrium Model.

---