An elementary characterization of the Gini index (original) (raw)
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Economic Properties of Statistical Indices: The Case of a Multidimensional Gini Index
Journal of quantitative economics, 2018
This paper seeks to construct a Gini index of the distribution of standard of living. Since standard of living has various dimensions, we need a multidimensional Gini index (MGI). The literature on index numbers contains two distinct approaches: the statistical and the economic. In the context of MGIs the statistical approach (which obtains the indices from conditions based on statistical or data-related considerations) seems to be open to the criticism that it sometimes yields indices that violate economic norms. However, the economic approach (where the indices are derived from norms based on economic theory) also does not seem to have succeeded so far in obtaining an MGI satisfying the various normative requirements that have been proposed in the literature. This paper shows that it is possible to obtain an MGI from the statistical approach ensuring, at the same time, that the economic norms are satisfied. In this sense it is an attempt to bring the two disparate traditions in index construction referred to above closer to each other. The index that is developed here does not appear in the existing literature. Moreover, the literature does not seem to contain any other MGI satisfying all of the proposed economic norms. Keywords Multidimensional inequality • Gini index • Transfer principle • Uniform majorisation For insightful comments on an earlier version of the paper and useful discussions on related matters I am grateful to Dipankar Dasgupta, Pradip Maity, Mihir Rakshit and Soumyen Sikdar as well as to the participants in a seminar at the Indian Statistical Institute, Kolkata. Needless to say, none of them is responsible for any error that the paper may contain.
Journal of quantitative economics, 2019
This paper seeks to construct a Gini index of the distribution of standard of living. Since standard of living has various dimensions, we need a multidimensional Gini index (MGI). The literature on index numbers contains two distinct approaches: the statistical and the economic. In the context of MGIs the statistical approach (which obtains the indices from conditions based on statistical or data-related considerations) seems to be open to the criticism that it sometimes yields indices that violate economic norms. However, the economic approach (where the indices are derived from norms based on economic theory) also does not seem to have succeeded so far in obtaining an MGI satisfying the various normative requirements that have been proposed in the literature. This paper shows that it is possible to obtain an MGI from the statistical approach ensuring, at the same time, that the economic norms are satisfied. In this sense it is an attempt to bring the two disparate traditions in index construction referred to above closer to each other. The index that is developed here does not appear in the existing literature. Moreover, the literature does not seem to contain any other MGI satisfying all of the proposed economic norms. Keywords Multidimensional inequality • Gini index • Transfer principle • Uniform majorisation For insightful comments on an earlier version of the paper and useful discussions on related matters I am grateful to Dipankar Dasgupta, Pradip Maity, Mihir Rakshit and Soumyen Sikdar as well as to the participants in a seminar at the Indian Statistical Institute, Kolkata. Needless to say, none of them is responsible for any error that the paper may contain.
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.
Mathematical Social Sciences, 2010
This paper considers the problem of construction of a multidimensional Gini index (MGI) of relative inequality satisfying normatively acceptable conditions. One of the conditions considered is that of Correlation Increasing Majorization (CIM) which has been studied in the existing literature. A new condition called Weighting of Attributes under Unidirectional Comonotonicity (WAUC) is introduced. It requires that, in the case where the allocation of all attributes are comonotonic and attribute i is more unequally distributed than attribute j, a reduction of inequality of i is socially more beneficial than that of inequality of j. An MGI is constructed by taking each individual's well-being to be a weighted average of the attribute levels and applying the univariate Gini formula to the resulting vector of individual well-beings. The weights, same for all individuals, are determined by the attribute levels of all the individuals. It is shown that the suggested MGI satisfies both CIM and WAUC. The existing literature does not seem to contain any other MGI satisfying these two conditions simultaneously.
A Class of Estimators : A Unifying Tool Towards the Estimation of Gini Index and Its Variant
2014
The Gini index and its variant are widely used as a measure of income inequality. Finding reliable estimators of these measures and studying its asymptotic properties has been an important area of research in the last two decades. Due to the fragmentation of literature among statistician and economist, several results in this direction have been republished often with a clear lack of reference to previous work. In this paper, we propose a simple unique approach to find the estimators of different income inequality measures. Asymptotic properties of these estimators can be proved in an identical way. The method described here provides an explicit formula for finding the asymptotic variance of the proposed estimators. A consistent estimator of the asymptotic variance can also find by plug-in method. We bring several research problems related to the estimation of Gini index and related concepts into our uniform framework. The asymptotic distribution obtained for Gini covariance has far...
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.
On the capacity of the Gini index to represent income distributions
Metron-International Journal of Statistics, 2020
Almost all governmental and international agencies use the Gini index to summarize income inequality in a nation or the world. The index has been criticized because it can have the same value for two different distributions. It will be seen that other commonly used summary measures of inequality are subject to the same criticism. The Gini index has the advantage that it is able to distinguish between two distributions that have identical integer valued generalized entropy measures. Because no single measure can fully summarize a distribution, researchers should consider combining the Gini index with another measure appropriate for the topic being studied. Keywords Generalized entropy measures • Gini index • Lorenz curve • Measures of income inequality • Pareto distribution • Moment problem
Computing the Gini index: A note
Economics Letters, 2019
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