On the capacity of the Gini index to represent income distributions (original) (raw)
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Comparison of the Gini and Zenga indexes using some theoretical income distributions abstract
Operations Research and Decisions, 2013
The most common measure of inequality used in scientific research is the Gini index. In 2007, Zenga proposed a new index of inequality that has all the appropriate properties of an measure of equality. In this paper, we compared the Gini and Zenga indexes, calculating these quantities for the few distributions frequently used for approximating distributions of income, that is, the lognormal, gamma, inverse Gauss, Weibull and Burr distributions. Within this limited examination, we have observed three main differences. First, the Zenga index increases more rapidly for low values of the variation and decreases more slowly when the variation approaches intermediate values from above. Second, the Zenga index seems to be better predicted by the variation. Third, although the Zenga index is always higher than the Gini one, the ordering of some pairs of cases may be inverted.
On the Limitations of Some Current Usages of the Gini Index
Review of Income and Wealth
Recent popular and professional writing on economic inequality often fails to distinguish between change in a summary index of inequality, such as the Gini Index, and change in the inequalities which that index tries to summarize. This note constructs a simple two class example in which the Gini Index is held constant while the size of the rich and poor populations change, in order to illustrate how very different societies can have the same Gini index and produce very similar estimates of standard inequality averse Social Welfare Functions. The rich/poor income ratio can vary by a factor of over 12, and the income share of the top one per cent can vary by a factor of over 16, with exactly the same Gini Index. Focussing solely on the Gini Index can thus obscure perception of important market income trends or changes in the redistributive impact of the tax and transfer system. Hence, analysts should supplement the use of an aggregate summary index of inequality with direct examination of the segments of the income distribution which they think are of greatest importance.
The generalised entropy index gives a summary measure of concentration of a distribution, where the order of the index determines the sensitivity of the index to top and bottom tail inequality respectively. This paper introduces an adjusted generalised entropy index as a normative and descriptive measure of income inequality. Disagreement over normative and positive issues impacting upon the degree of warranted inequality aversion provides a case for generalising the information within a sample distribution, so that any Atkinson-Kolm-Sen social welfare function which is itself a function of one or many GE indexes may be calculable. This may be achieved by specifying or estimating an adjusted GE curve giving the adjusted GE index for all orders. A method for estimating the GE curve as a two tailed generalised logistic function of order is given. The estimation procedure is accurate; errors are typically less than 1% over a wide range of order.
Contrasting the Gini and Zenga indices of economic inequality
The current financial turbulence in Europe inspires and perhaps requires researchers to rethink how to measure incomes, wealth, and other parameters of interest to policy-makers and others. The noticeable increase in disparities between less and more fortunate individuals suggests that measures based upon comparing the incomes of less fortunate with the mean of the entire population may not be adequate. The classical Gini and related indices of economic inequality, however, are based exactly on such comparisons. It is because of this reason that in this paper we explore and contrast the classical Gini index with a new Zenga index, the latter being based on comparisons of the means of less and more fortunate sub-populations, irrespectively of the threshold that might be used to delineate the two sub-populations. The empirical part of the paper is based on the 2001 wave of the European Community Household Panel data set provided by EuroStat. Even though sample sizes appear to be large, we supplement the estimated Gini and Zenga indices with measures of variability in the form of normal, t-bootstrap, and bootstrap bias-corrected and accelerated confidence intervals.
Evaluation of Income Distribution in OECD Countries with Income Inequality Indexes
2016
Income inequality is an indicator of how material resources are distributed across society. Some people consider high levels of income inequality are morally undesirable. Others focus on income inequality as bad for economic progress of country (OECD Report; 2015). Chile, Mexcio and Turkey had the highest income inequality. OECD Anglophone countries had levels of inequality around or above the OECD average. From this point of view, this study aims to analyze the income inequality for OECD countries. For this aim, we use some indexes to analyze inequality. These indexes are GINI Index, GNI, Atkinson Index and Decile Ratio. * Bu çalışma 24-26 Ağustos 2016 tarihinde İstanbul/Türkiye'de düzenlenmiş olan Politik, Ekonomik ve Sosyal Araştırmalar Kongresinde (ICPESS-2016) özet bildiri olarak sunulmuştur. OECD Ülkelerinde Gelir Dağılımının Gelir Eşitsizliği İndeksleri İle Değerlendirilmesi 154 Research Journal of Politics, Economics and Management, 2016, Year:4, Volume:4, Issue:4 We use...
PLOS ONE, 2017
The Gini index is a measure of the inequality of a distribution that can be derived from Lorenz curves. While commonly used in, e.g., economic research, it suffers from ambiguity via lack of Lorenz dominance preservation. Here, investigation of large sets of empirical distributions of incomes of the World's countries over several years indicated firstly, that the Gini indices are centered on a value of 33.33% corresponding to the Gini index of the uniform distribution and secondly, that the Lorenz curves of these distributions are consistent with Lorenz curves of log-normal distributions. This can be employed to provide a Lorenz dominance preserving equivalent of the Gini index. Therefore, a modified measure based on log-normal approximation and standardization of Lorenz curves is proposed. The socalled UGini index provides a meaningful and intuitive standardization on the uniform distribution as this characterizes societies that provide equal chances. The novel UGini index preserves Lorenz dominance. Analysis of the probability density distributions of the UGini index of the World's counties income data indicated multimodality in two independent data sets. Applying Bayesian statistics provided a data-based classification of the World's countries' income distributions. The UGini index can be re-transferred into the classical index to preserve comparability with previous research.