Decomposition by sources, by subpopulations and joint decomposition by subpopulations and sources of Gini, Bonferroni and Zenga 2007 inequality indexes digital
Recently, the authors have illustrated the decompositions by subpopulations of the Gini (1914), Bonferroni (1930) and Zenga (2007) inequality measures. These decompositions were illustrated by a numerical example involving non-overlapping subpopulations and by a numerical example involving overlapping subpopulations...
Decomposition by subpopulations of Gini, Bonferroni and Zenga inequality measures digital
This paper presents a common framework for the decompositions by subpopulations of Gini, Bonferroni and Zenga synthetic inequality measures. These three synthetic indexes are the weighted arithmetic means of the corresponding point measures and applying the Zenga two-step approach, decompositions based on means comparison are obtained. In the first step additive decompositions are derived for the point indexes and in the second step, using the decompositions of the point measures, we obtain the decompositions by subpopulations of the synthetic indexes...
Joint decomposition by subpopulations and sources of the point and synthetic Bonferroni inequality measures digital
The total income Y is the sum of c sources Xj : Y = X1 + . . . + Xc: The N units of the population are partitioned in k different subpopulations. In the frequency distribution framework the Bonferroni (1930) point inequality index is given by Vh(Y) = [M(Y) - ̅Mh.(Y)]/M(Y), M(Y) and ̅Mh.(Y)are the mean and the lower mean of Y...
Decomposition by subpopulations of the point and the synthetic Gini inequality indexes digital
Keywords: Gini Index, Point Inequality Index, Synthetic Inequality Index, Decomposition by Subpopulatios
On the decomposition by subpopulations of the point and synthetic Bonferroni inequality measures digital
This paper, by using the ‘‘two-step’’ approach proposed in Radaelli (2008, 2010) and in Zenga (2016) for the decomposition of the Zenga (2007) index, obtains the decomposition of the Bonferroni (1930) inequality measure. In the first step the Bonferroni point measure Vh(Y) is decomposed in a weighted mean of k x k relative differences between the mean Mg(Y) of subpopulation g and the lower mean Mhl(Y) of the subpopulation l...
Joint decomposition by subpopulations and sources of the Zenga inequality index I(Y) digital
Keywords: Zenga Inequality Index, Income Inequality, Joint Decomposition by Subpopulations and Sources, Point and Synthetic Inequality Indexes.
The reordering variates in the decomposition by sources of inequality indexes digital
Keywords: Reordering Variate, Income Inequality, Decomposition by Sources, Point Inequality, Uniform Cograduation
A longitudinal decomposition of Zenga’s new inequality Index
The paper proposes a three-term decomposition of Zenga’s new inequality index over time. Given an initial and a final time, the link among inequality trend, re-ranking, and income growth is explained by decomposing the inequality index at the final time into three components: one measuring the effect of re-ranking between individuals, a second term gauging the effect of disproportional growth between individuals’ incomes, and a third component measuring the impact of the inequality existing at the initial time. The decomposition allows one to distinguish the determinants of inequality change from the contribution of the inequality at the initial time to the inequality at the final time. We applied the decomposition to Italian household income data collected by the Survey on Household Income and Wealth of the Bank of Italy, waves 2008-2010.
Application of Zenga’s distribution to a panel survey on household incomes of European Member States
In this paper Zenga’s distribution is applied to 114 household incomes distributions from a panel survey conducted by Eurostat. Previous works showed the good behaviour of the model to describe income distributions and analyzed the possibility to impose restrictions on the parametric space so that the fitted models comply with some characteristics of interest of the samples. This work is the first application of the model on a wide number of distributions, showing that it can be used to describe incomes distributions of several countries. Maximum likelihood method on grouped data and methods based on the minimization of three different goodness of fit indexes are used to estimate parameters. The restriction that imposes the equivalence between the sample mean and the expected value of the fitted model is also considered. It results that the restriction should be used and the changes in fitting are analyzed in order to suggest which estimation method use jointly to the restriction. A final section is devoted to the direct proof that Zenga’s distribution has Paretian right-tail.