This thesis focuses on the measurement of income inequality.
Gini coefficient as a distributive measure is widely used because of its computational and graphically interpretational ease, but it also has several problems. First, the Gini coefficient does not account for the differences in distributional form when the concentration areas in Lorenz curve are the same size because the Gini coefficient is computed by measuring the concentration area. Second, the Gini coefficient has a theoretical range of 0 ～ 1, but actually the revealed range of income distribution change is very narrow. Thus it is doubtful whether it can sensitively reflect the change in income distribution.
Therefore, this thesis reviews the properties and problems involved in the measurement and use of the Gini coefficient and attempts to analyze the sensitivity of the Gini coefficient to the change in income distribution.
For the measuring the change in income distribution, I relied on the concepts of utility theory and social welfare function. Atkinson's index was used as a proxy variable of social welfare change. Atkinson's index has the merit of providing a measurement of income inequality without finding the shape of utility function because it uses an utility function with a constant rate of risk aversion in decision making theory under uncertainty.
In the simulation analysis for reviewing the sensitivity of the Gini coefficient to the change in Atkinson's index, a proxy of social welfare, I did not use actual data but rather computer generated data. Based on the actual data the Gini coefficient ranged from 0.25 to 0.55. A more comprehensive data therefore is needed for the simulation analysis. Thus by the use of IMSL, which is random number generating package, I produced various income distributions with a more approperiate range of the Gini coefficient.
From theses distribution data, Atkinson's indices and Gini coefficients were computed and ranked before the rank correlation analysis was attempted. I also undertook a regression analysis with differentials of these distributive measurements. Finally, a situational descriptive analysis of 22 randomly selected income decile data was attempted.
