On the suitability of income inequality measures for regional analysis: Some evidence from simulation analysis and bootstrapping tests Boris A. Portnov a, * , Daniel Felsenstein b a Department of Natural Resources and Environmental Management, Graduate School of Management, University of Haifa, Israel b Department of Geography, Hebrew University of Jerusalem, Mount Scopus, Jerusalem, Israel article info Article history: Available online 13 April 2010 Keywords: Regions Inequality measures Bootstrapping Random permutation tests abstract The paper looks at the sensitivity of commonly used income inequality measures to changes in the ranking, size and number of regions into which a country is divided. During the analysis, several test distributions of populations and incomes are compared with a ‘reference’ distribution, characterized by an even distribution of population across regional subdivisions. Random permutation tests are also run to determine whether inequality measures commonly used in regional analysis produce meaningful estimates when applied to regions of different population size. The results show that only the population weighted coefficient of variation (Williamson’s index) and population-weighted Gini coefficient may be considered sufficiently reliable inequality measures, when applied to countries with a small number of regions and with varying population sizes. Ó 2010 Elsevier Ltd. All rights reserved. 1. Introduction The study of inequality across regions is rather different to the study of inequality between individuals. This derives from the fact that regions are groups formed by individuals. This is not as obvious as it may sound. For example, a tradition exists in the regional income convergence literature that treats regions as individual observations regardless of the size of the former (cf. e.g., [1]). As such, large and small regions are assumed to carry equal weight, just as fat and thin people are treated equally when looking at inequality between them. The computational issues associated with multi-group compar- isons of income inequality were noticed (apparently for the first time) by the American economist Max Lorenz. In his seminal paper published in 1905, Lorenz highlighted several drawbacks associated with the comparison of wealth concentrations between fixed groups of individuals. In particular, he found that while an increase in the percentage of the middle class is supposed to show the diffusion of wealth, a simple comparison of percent shares of persons in each income group may often lead to the opposite conclusion. For instance, while the upper income group in a particular period may constitute a smaller proportion of the total population, the overall wealth of this group may be far larger compared to another time period under study ([2]: 210e211). The remedy he suggested was to represent the actual inter-group income distribution as a line, plotting ‘along one axis cumulated percents of the population from poorest to richest, and along the other the percent of the total wealth held by these percents of the populations’ (ibid. p. 217). In an essay published in 1912, the Italian statistician Corrado Gini moved Lorenz’s ideas a step further, suggesting a simple and easy comprehendible measure of inequality known as the Gini coefficient. Graphically, the calculation of this coefficient can be interpreted as follows: Gini coefficient ¼ Area between Lorenz curve and the diagonal Total area under the diagonal Mathematically, the Gini coefficient is calculated as the arith- metic average of the absolute value of differences between all pairs of incomes, divided by the average income (see Table 1). 1 The coefficient takes on values between 0 and 1, with zero interpreted as perfect equality [3]. A few years later, Dalton [4] carried out the first systematic attempt to compare the performance of different inequality measures against ‘real world’ data. As he noted, many inequality measures, though having intuitive or mathematical appeal, react to changes in income distribution in an unexpected fashion. For * Corresponding author. E-mail address: portnov@nrem.haifa.ac.il (B.A. Portnov). 1 The computation includes the cases where a given income level is compared with itself. Contents lists available at ScienceDirect Socio-Economic Planning Sciences journal homepage: www.elsevier.com/locate/seps 0038-0121/$ e see front matter Ó 2010 Elsevier Ltd. All rights reserved. doi:10.1016/j.seps.2010.04.002 Socio-Economic Planning Sciences 44 (2010) 212e219