Estimation of Variance of Gini Coefficient for Income Distribution

Gini coefficient is a Statistical measure for Income Distribution. This paper is an exposition of data concerning the Gini Coefficients for the Greek Income Tax Service for the years 1960 to 2000. Using von Mises Expansions we find second-order properties of Gini Coefficient. We estimate its variance and we find confidence intervals for it. An Exponential Smoothing Time Series Model is constructed. The trend of the Greek Gini coefficient based on the annual declaration of income is calculated. Using the Jackknife Statistical method of setting robust nonparametric confidence intervals, we estimate the Variance of Gini Coefficient and we find the 95% confidence limits for the true Gini Coefficient. The conclusion is two-fold: a) We found that the trend of Greek Gini Coefficient is upwards; b) We found that the Jackknife method for variance estimation works very satisfactorily in the case of Gini Coefficient and it produces trustworthy Confidence Intervals for it.