Economic Properties of Statistical Indices: The Case of a Multidimensional Gini Index (original) (raw)
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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 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
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.
International Journal of Economic Theory, 2018
A central problem in constructing multidimensional inequality indices is that of devising weights on the dimensions. There are two different approaches to the problem: the normative and the data-driven. Indices derived from data-driven weights have the limitation that they may violate normatively desired properties. This paper asks whether it is possible to obtain normatively acceptable inequality indices from a data-driven approach. A multidimensional Gini index is derived from an endogenous weighting scheme and is shown to possess a number of desired properties. The existing literature does not seem to contain a Gini index that satisfies all of these properties.
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.
An elementary characterization of the Gini index
Mathematical Social Sciences, 2015
The Gini coefficient or index is perhaps one of the most used indicators of social and economic conditions. In this paper we characterize the Gini index as the unique function that satisfies the properties of scale invariance, symmetry, proportionality and convexity in similar rankings. Furthermore, we discuss a simpler way to compute it.
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.
Bilateral Gini index: Application for regional studies and international comparisons
Bilateral Gini index: Application for regional studies and international comparisons, 2020
In this paper, we have considered a new contextualization of the Gini index, giving a particular interpretation of inequality. The Gini index is the most widely used measure of inequality in the world, however, it does not meet some desirable properties of an inequality indicator. Even so, as it is a measure adopted by most countries through the years, makes it a valuable statistical input, which requires adjustments that provide information, making the study of inequality more robust by adding different indicators that can account for their economic, political, and social environment. This article provides a variation of the Gini index with the purpose of compare and classify different territories (the States of Mexico, as well as selected countries) with similar Gini index. The classification is carried out into groups (called turbines) with either positive equality, negative equality, positive inequality or negative inequality. The main contribution of this paper lies on distinguish territories with similar Gini index but different average income, from what can be inferred the conditions of each one and how privileges and facilities are distributed into them.
Inequality Measures: The Kolkata index in comparison with other measures
2020
We provide a survey of the Kolkata index of social inequality, focusing in particular on income inequality. Based on the observation that inequality functions (such as the Lorenz function), giving the measures of income or wealth against that of the population, to be generally nonlinear, we show that the fixed point (like Kolkata index k) of such a nonlinear function (or related, like the complementary Lorenz function) offer better measure of inequality than the average quantities (like Gini index). Indeed the Kolkata index can be viewed as a generalized Hirsch index for a normalized inequality function and gives the fraction k of the total wealth possessed by the rich (1-k) fraction of the population. We analyze the structures of the inequality indices for both continuous and discrete income distributions. We also compare the Kolkata index to some other measures like the Gini coefficient and the Pietra index. Lastly, we provide some empirical studies which illustrate the difference...