Regression Analyses of Income Inequality Indices

Scientists have analysed different methods for numerical estimation of Gini coefficients. Using Lorenz curves, various numerical integration attempts have been made to identify accurate estimates. Central alternative methods have been the trapezium, Simpson and Lagrange rules. They are all special cases of the Newton-Cotes methods. In this study, we approximate the Lorenz curve by polynomial regression models and integrate optimal regression models for numerical estimation of the Gini coefficient. The attempts are checked on theoretical Lorenz curves and on empirical Lorenz curves with known Gini indices. In all cases the proposed methods seem to be a good alternative to earlier methods presented in the literature.