Discussion Paper 1009, "On the Problem of Inference for Inequality Measures for Heavy-Tailed Distributions", by Schluter, C.
The received wisdom about inference problems for inequality measures is that these are caused by the presence of extremes in samples drawn from heavy-tailed distributions. We show that this is incorrect since the density of the studentised inequality measure is heavily skewed to the left, and the excessive coverage failures of the usual confidence intervals are associated with low estimates of both the point measure and the variance. For further diagnostics the coefficients of bias, skewness and kurtosis are derived for both studentised and standardised inequality measures, and the explicit cumulant expansions make also available Edgeworth expansions and saddlepoint approximations. In view of the key role played by the estimated variance of the measure, variance stabilising transforms are considered and shown to improve inference.
Keynames: Inequality measures, inference, statistical performance, asymptotic expansions, variance stabilisation.
JEL Classification: C10, D31, D63.