Engel Analysis with Lorenz and Concentration Curves

Economic analysis of income transfer programs requires knowledge of how households with different incomes alter expenditure patterns as their incomes change. Classical demand theory, however, provides little guidance for quantifying these income response parameters. Consequently, researchers have relied on statistical approaches to find functional forms which "best" describe the relationship between expenditures and income. The most commonly used specifications (linear, semilogarithmic, and double-logarithmic) imply that the Engel (expenditure) elasticities are monotonically increasing, decreasing, or constant across the income spectrum. However, serious errors may occur if actual elasticities do not adhere to one of these patterns. This paper utilizes a nontraditional approach, based on income and expenditure distributions, to estimate expenditure elasticities. The method places less emphasis on the mathematical specification of the Engel relation and allows for increased flexibility in elasticity patterns. The primary purposes of this article are to examine household income and expenditure distributions in order to deduce the underlying Engel relationship and to measure inequality within each distribution. When other relevant factors (e.g., prices) are held constant, the expenditure distribution on a commodity is directly related to the income distribution via the commodity's Engel function. A recently proposed technique for the estimation of Lorenz and concentration curves is employed (Kakwani and Podder). These curves are directly related to the cumulative distributions of income and expenditures. Expenditure elasticities and measures of income and expenditure inequality can be calculated from the estimated parameters of the Lorenz and concentration curves (Kakwani). Elasticities thus estimated are not constrained to be monotonic or constant across the income spectrum, and may vary across commodities. Related objectives are to (a) introduce a generalized functional form to describe the Lorenz and concentration curves, (b) compare estimated expenditure elasticities among three urbanizations for several food groups using U.S. data, (c) examine elasticity patterns within each urbanization, and (d) examine inequality of food expenditure and income distributions for each urbanization.