Income and Price Elasticities of Demand in South Africa: An Application of the Linear Expenditure System

• Date: 01 December 2017
• Author: Neil Andrew Rankin,Rulof Petrus Burger,Lodewicus Charl Coetzee,Carl Friedrich Kreuser
• DOI: http://doi.org/10.1111/saje.12167
• Published date: 01 December 2017

INCOME AND PRICE ELASTICITIES OF DEMAND IN

SOUTH AFRICA: AN APPLICATION OF THE LINEAR

EXPENDITURE SYSTEM

RULOF PETRUS BURGER

†

,LODEWICUS CHARL COETZEE

†

,CARL FRIEDRICH KREUSER*

†

AND

NEIL ANDREW RANKIN

†

Abstract

This paper investigates the expenditure patterns of South African households using detailed

cross-sectional expenditure and price data that varies across region and time. Linear expenditure

system parameter estimates are used to calculate income and price elasticities for a number of

product categories at different points of the income distribution. We find substantial variation in

the price and income elasticities of demand for items across the income distribution, with the

bottom quartile being extremely sensitive to increases in the price of food and clothing items,

and the top quartile being as sensitive as households in developed countries.

JEL Classification: D11, D12, D31

Keywords: Linear Expenditure System, Demand Estimation, Price Elasticity, Income Elasticity

1. INTRODUCTION

Few topics in economics have been studied as extensively as demand systems. Demand mod-

els help us understand how consumers respond to changes in the economic environment,

and are therefore an integral part of general equilibrium modelling of the economy. This

paper estimates a linear expenditure system (LES) using household income and detailed price

data. Despite being less flexible than several other demand models, this model remains popu-

lar due to its consistency with consumer demand theory and its relative simplicity.

The LES was first introduced as a theory by Klein a nd Rubin (1948), while Samuel-

son (1948) and Geary (1949) developed a corresponding system of demand equations.

Stone (1954) was the first to apply the concept empirically and developed the model fur-

ther in Stone (1964) and Stone et al. (1964). Prior to Stone, empirical demand studies

were characterised by single equation methods that ignored the demand restrictions of

adding-up, homogeneity, and Slutsky symmetry. The LES assumes a strongly separable

utility function, which means that these theoretical restrictions are maintained. This con-

sistency with theoretical models of consumer demand, combined with its relative simplic-

ity are highly desirable properties for general equilibrium modelling.

Unfortunately, this simplicity comes at the cost of restrictive behavioural assumptions

such as linear Engel curves, constant marginal budget shares, proportional income and

* Corresponding author: Researcher, Department of Economics, Stellenbosch University, Private

Bag X1, Matieland, Stellenboach, Western Cape 7602, South Africa. E-mail: cfkreuser@gmail.com

†

Department of Economics, Stellenbosch University

This paper is reproduced here with acknowledgement of UNU-WIDER in Helsinki which

commissioned the original research.

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C2017 Economic Society of South Africa. doi: 10.1111/saje.12167

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South African Journal of Economics Vol. 85:4 December 2017

South African Journal

of Economics

price elasticities and an inability to account for complementary relationships between

goods (Sola, 2012). In response to evidence that the assumption of additive separability

is often violated in practice (Deaton, 1974), a number of non-additive generalisations of

the LES were proposed (including Pollak, 1971; Brown and Heien, 1972; Blackorby

et al., 1978). Many of these models retained weak separability of the utility function and

continued to imply linear Engel curves (Blundell and Ray, 1982). Non-separable general-

isations of the LES followed (e.g. Carlevaro, 1976), but such models often violated some

of the theoretical requirements of representative agent models. Howe et al. (1980) derive

a class of theoretically plausible demand functions that are quadratic in expenditure, or

quadratic expenditure systems (QES), and illustrate the estimation of one such function

on United States per capita time series data. Blundell and Ray (1982) present another

non-separable generalisation of the LES which permits non-linear Engel curves.

Computable general equilibrium (CGE) models remain a popular tool

1

for modelling

general equilibrium effects to the South African economy data, and this typically requires

LES parameter estimates as an input. Case (2000) investigated consumption patterns in

South Africa in order to examine the potential effects of trade liberalisation on household

behaviour and wellbeing. The study was based on the 1993 Project for Statistics on Living

Standards and Development (PSLSD) data, which included data from which a food price

index could be constructed. This index is separately constructed for the African and white

population groups, due to the substantial differences in total earnings and possible differen-

ces in purchased product quality. In our analysis below we choose to rather disaggregate our

sample by income quantiles. From this index the price and expenditure elasticity for all

other commodity groups could be estimated. Case (2000) finds that food, fuel, alcohol/

tobacco and other goods are necessities for the African population group, and that food,

fuel and alcohol/tobacco are also price inelastic for this group. Necessities for the white pop-

ulation group include food, fuel, alcohol/tobacco, clothing, personal items and other goods,

with food, fuel and alcohol/tobacco also being price inelastic. She finds that the African

population group are generally more price sensitive than the white population group.

The above models are all based on the primal problem of utility maximisation, and

demand equations are derived directly from the utility function. An alternative modelling

approach derives demand functions from the consumer’s expenditure function, or the

dual problem of expenditure minimisation.

2

The almost ideal demand system (AIDS),

developed by Deaton and Muellbauer (1980), is perhaps the best known model of this

class and remains one of the most widely applied in empirical demand studies. In the

South African context, most demand system analyses are variations on the AIDS model,

with most focusing on the demand for food or meat.

3

Koch and Bosch (2009) analyse

1

For example, Alton et al. (2014) uses LES estimation as a sub-component in a CGE model

studying the implication of carbon taxes, while Maisonnave and Decaluwe (2010) use the model

to investigate whether South Africa’saffirmative action policy has been efficient.

2

Selvanathan and Clements (1995) and Edgerton et al. (1996) provide comprehensive reviews of fur-

ther alternative specifications and functional forms. Koch (2015) compares the South African Engel

curve estimates obtained from quadratic almost ideal demand system (QUAIDS) and fractional multi-

nomial logit models and Boysen (2015) used a QUAIDS in the analysis of food prices in Uganda.

3

See for example: Balyamujura et al. (2000); Agbola et al. (2003); Selvanathan and Selvanathan

(2003); Taljaard et al. (2003); a study by the Human Sciences Research Council (2004); Bopape

(2006); Bopape and Myers (2007); and Dunne and Edkins (2008).

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