A regression method for estimating Gini index by decile

Based on the three-parametric Lorenz curve proposed by Kakwani (1980), this paper builds a multiple linear regression model to estimate the parameters by the weighted least square method named the regression method. Using the Lorenz curve, the Gini index and its variance are then calculated. Compared to the error minimization technique, the regression method has a better performance in estimating the Gini index using Kakwani (1980)’s Lorenz curve and a dataset of sixteen economies from the United Nation University-World Income Inequality Database (UNU-WIID). The results also suggest that the regression method has an advantage when estimating the Gini index and fitting the income shares by decile for the medium and higher inequality economies. We find that the three-parametric Lorenz curve has a better performance than the double-parametric Lorenz curve, and the double-parametric Lorenz curve is superior to the single-parametric Lorenz curve, judged by the RMSE of the actual Gini index and the estimated ones.