Income distribution and inequality measurement: The problem of extreme values

Abstract

International audienceWe examine the statistical performance of inequality indices in the presence of extreme values in the data and show that these indices are very sensitive to the properties of the income distribution. Estimation and inference can be dramatically affected, especially when the tail of the income distribution is heavy, even when standard bootstrap methods are employed. However, use of appropriate semiparametric methods for modelling the upper tail can greatly improve the performance of even those inequality indices that are normally considered particularly sensitive to extreme values

Robust estimation of the Pareto tail index: a Monte Carlo analysis

“…12 This data set was previously used by Alfons et al (2013) in the context of robust estimation of the Gini index of inequality from survey data. The reason for robust estimation arises in this context because survey samples may contain extreme observations, which have large influence on estimates on many of the standard inequality measures (Cowell and Flachaire 2007). In the presence of extreme outliers, both estimation and inference for inequality indices can be unreliable.…”

“…The latter is a sum of a nonparametric inequality measure estimated for the non-rich and a parametric inequality index for the rich (see, e.g. Cowell and Flachaire 2007). 15 The Gini index of the Pareto model with the tail index α is: G = 1/(2α − 1).…”

“…Since then, the Pareto distribution has become the most popular model to describe top income and wealth values (see, e.g. Drȃgulescu and Yakovenko 2001;Kleiber and Kotz 2003;Clementi and Gallegati 2005;Klass et al 2006;Cowell and Flachaire 2007;Cowell and Victoria-Feser 2007;Ogwang 2011;Alfons et al 2013). 1 However, the model is also heavily used in several other areas of economics to model the right-hand tails of fluctuations in stock prices (Lauridsen 2000;Gabaix et al 2003Gabaix et al , 2006Balakrishnan et al 2008), exchange rates (Wagner and Marsh 2005), firm sizes (Axtell 2001;Luttmer 2007), city sizes (Soo 2005), countries' interactions in international trade (Hinloopen and van Marrewijk 2012), CEO compensation (Gabaix and Landier 2008), supply of regulations (Mulligan and Shleifer 2005), tourist visits (Ulubaşoglu and Hazari 2004), claims in actuarial problems (Ramsay 2003), macroeconomic disasters (Barro and Jin 2011), and macroeconomic fluctuations (Gaffeo et al 2003).…”

Intermediation Services and Search Frictions

“…The three measures differ in their sensitivity towards changes in the mean or changes in the tails (see e.g. Bendel et al, 1989;Cowell and Flachaire, 2007). The coefficient of variation and the Gini coefficient are more sensitive to shifts in the mean compared to the variance of logs.…”

A new multidimensional population health indicator for policy makers: absolute level, inequality and spatial clustering - an empirical application using global sub-national infant mortality data

“…We have assumed that this level of data would be sought only when developing intra-country interventions using specific data for the country concerned. The inclusion of gender, however, in future research on the development of multidimensional health indicators is suggested Lastly, previous literature (Cowell and Flachaire, 2007) has suggested that inequality measures are in general sensitive to extreme values (due to war, famine and natural catastrophes) or "data contamination". Thus data quality would affect the analysis in our present study as outlying or erroneous subnational IMR's may thus have affected the calculated Theil measures.…”