Variance Estimation and Prediction of Gini Coefficient for Income Distribution Using Asymptotic Expansions and Resampling Methods

In the present paper we consider the Coefficient of Gini (Kendall and Stuart, 1982), for income distribution. This statistic is derived from data showing the annual taxes paid by the Greek taxpayers, for years 1960 to 1996. An intractable issue is the estimation of its variance because of the complication of its distribution. Applying von Mises asymptotic expansions for differentiable statistical functionals (Hinkley, 1978), (Frangos, 1980) we estimate the variance of Gini coefficient for a set of frequency data regarding a particular year. Robust confidence intervals for Gini coefficient are constructed using the jackknife statistical methodology. Treating the series of Gini estimates from 1960 from to 1996 as a time series from an autoregressive model, we estimate its parameters using the bootstrap methodology, (Davison and Hinkley, 1997) and we compare the bootstrap confidence intervals for the parameters with the least squares ones. Finally, three autoregressive models for prediction of Gini Coefficient are compared with respect to their predictive errors. A simple autoregressive model is selected for prediction purposes. The above comparisons support the argument of a clear superiority of the bootstrap confidence intervals, with respect to their length, over the quot;classicalquot; method of least squares