On the Problem of Inference for Inequality Measures for Heavy‐Tailed Distributions

29 Pages Posted: 17 Feb 2012

See all articles by Christian Schluter

Christian Schluter

University of Southampton - Division of Economics

Date Written: February 2012

Abstract

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 studentized 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 studentized and standardized 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 stabilizing transforms are proposed and shown to improve inference significantly.

Keywords: Asymptotic expansions, Inequality measures, Inference, Statistical performance, Variance stabilization

Suggested Citation

Schluter, Christian, On the Problem of Inference for Inequality Measures for Heavy‐Tailed Distributions (February 2012). The Econometrics Journal, Vol. 15, Issue 1, pp. 125-153, 2012. Available at SSRN: https://ssrn.com/abstract=2006810 or http://dx.doi.org/10.1111/j.1368-423X.2011.00356.x

Christian Schluter (Contact Author)

University of Southampton - Division of Economics ( email )

Southampton, SO17 1BJ
United Kingdom
+44 2380 59 5909 (Phone)
+44 2380 59 3858 (Fax)

HOME PAGE: www.economics.soton.ac.uk/staff/schluter/

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