On a method of estimating the expenditure elasticity from concentration curves

Abstract

In 1960 N.S. Iyengar developed a new method of estimating the expenditure elasticity of a specific item from two concentration curves the Lorenz curve of total expenditure (or income) and a generalized Lorenz curve which relates the proportion of consumption of the specific item to the proportion of consumers spending up to a given level of the total expenditure. On the assumptions of log normality of total expenditure distribution and of constancy of elasticity, the author derived an expression for elasticity that is valid just for two particular points of the range of the concentration curves. In this work we give a new expression for elasticity that can be calculated for any point of the range of the concentration curves. Iyengar's results follows as particular cases of it. Moreover, the two underlying hypotheses can be easily checked through this same expression. A generalization of a concentration curve recently studied by M. Zenga is also considered giving rise to an equivalent formula for elasticity Finally, a numerical illustration based on expenditure data in Italy shows the advantages of the new suggested approach compared to former results obtained by R. Guarini.