On the problem of inference for inequality measures for heavy-tailed distributions

We consider the class of heavy-tailed income distributions and show that the shape of the income distribution has a strong effect on inference for inequality measures. In particular, we demonstrate how the severity of the inference problem responds to the exact nature of the right tail of the income distribution. It is shown that the density of the studentised inequality measure is heavily skewed to the left, and that the excessive coverage failures of the usual confidence intervals are associated with excessively low estimates of both the point measure and the variance. For further diagnostics, the coefficients of bias, skewness and kurtosis are derived and examined for both studentised and standardised inequality measures. These coefficients are also used to correct the size of confidence intervals. Exploiting the uncovered systematic relationship between the inequality estimate and its estimated variance, variance stabilising transforms are proposed and shown to improve inference significantly.