This second special issue of Statistica & Applicazioni provides a selection of papers, which were presented and discussed at the International Conference to Honor Two Eminent Social Scientists. Dedicated to the memory of Corrado Gini and Max Otto Lorenz, the conference highlighted how remarkable and permanent is their seminal contribution in research carried out by the community of scholars in the last century. It was held in May 2005 at the Certosa di Pontignano of Siena University, following the initiative of Professors Camilo Dagum and Samuel Kotz.
The purpose of this paper is to extend Dagum’s Gini decomposition (“A New Approach to the Decomposition of the Gini Income Inequality Ratio”, Empirical Economics 22(4), 515-531, 1997a) following three types of theoretical modelisations. The first one deals with a “poor/non-poor” decomposition within a sub-group multilevel framework. The second one exhibits a multi-decomposition technique, that is, the combination of the multilevel sub-group decomposition and the income source decomposition. Finally, we provide a parametric multidecomposition in order to capture different dimensions of income inequality within groups and between groups.
Keywords: Gini, Income Source Decomposition, Multi-decomposition, Poverty, Subgroup Decomposition.
This paper intends to highlight a few considerations on the choice of a variability measure and its estimate, focusing on the standard deviation, the mean deviation and the mean difference. We have considered the non-parametric case, the normal and the Pareto distribution. All the examined characteristics point out that the mean difference can be re-evaluated. The sample mean difference presents exact results in terms of expected value and variance, moreover this variance exists finite
even if, in the parent population, the moments of order greater than two are infinite; instead the approximate variance of the sample standard deviation is finite only if, in the parent population, the fourth moment is finite. This aspect should be taken into account when the observed data are well described by a heavy tail distribution
model. In the normal distribution the estimator of the standard deviation based on the sample mean difference has the variance very close to that of the estimator
based on the sufficient statistics.
Keywords: standard deviation, mean deviation, mean difference, unbiased estimator, mean square error.
The aggregates of the System of National Accounts are composite values which measure the result of economic activity without considering where the flows come from or where they go to. The cost of the necessary micro data was probably the main cause of this omission in the past. However, nowadays the greatest obstacles are the absence of political will to produce them and the lack of consensus on the inequality measure to be used as an international standard. The current revision of the SNA provides a good opportunity to include some norm of aggregation that takes into account distributive issues. In order to contribute to the achievement of that goal this paper compares the Gini and Euclidian norms (and their related families) using three dimensional representations. After discussing some of the most relevant theoretical issues, we display the income within-countrydistributions to explore the empirical relevance of using different inequality metrics.
Keywords: inequality measurement, system of national accounts, poorest and richest triangle.
This paper investigates the Ordered uniform spacings and produces the associated moment generating function of the Gini coefficient of inequality. Using the expected values of the individual spacings, it gives the consequential Lorenz curve and discusses its characteristics. Following this, it suggests some extensions, producing families of Lorenz curves. Finally, it proposes a number of areas for further work.
A variety of measures are used to compare income inequalities, many of which have been derived from Lorenz curve. However, classical Gini coefficient and its variations are probably the most commonly used measures of income inequality. They are considered as the best measures by many scientists, but it is also recognized that the choice of age-grouping affects the Gini measures (Formby, et al.1989). Bhattacharya and Mahalanobis (1967) recognized that because income
distributions overlap extensively, the effect of age group on inequality is overestimated. Many procedures are available for ordering and ranking income
distributions where the ordering is not linear. However, the researchers often are not interested in ordering the populations but selecting the best (or worst) of available populations indicating a lower (or higher) level of disparities in incomes within the population. This paper will discuss the approximation to the sampling distribution of Gini Measure of inequality and selection of a population with most diversity in its constituents as measured by it.
Keywords: Selection procedure, Least favorable configuration, probability of correct selection, Gini coefficient.
This paper analyzes inequality of income distribution, looking at consumption expenditure per capita, over the period 1990-2002. Using three-yearspan micro-data set drawn from Susenas, we determine the pattern of distribution, mainly on the basis of Gini coefficient, with Lorenz curve and cumulative frequency distribution for complete description of distribution. Results are compared with Atkinson, Variance of Logarithm and Theil indices. We examine sources of income inequality by decomposing Theil indices into urban and rural components. The main findings are, first, the overall income inequality was increasing both before and after
the economic crisis of 1997. Second, urban inequality was higher not only than rural inequality but also than overall inequality. Third, population movement from rural to urban area worked to increase the degree of inequality.
Keywords: Decomposition, Indonesia, Inequality, Micro-data.
This paper assesses prospects of achieving the Millennium Development Goal (MDG) of income poverty in developing countries by 2015. A system of equations is estimated by 3SLS where institutional indicators are endogenous to historical and geographical factors and openness and inequality are also made endogenous. Our simulations confirm (i) the role of institutional quality improvement in raising income which in turn lowers poverty, and (ii) the needs for growth acceleration –especially in South Asia- and for reduction of inequality in achieving the MDG. A somewhat striking result is that even modest institutional improvements have significant poverty reducing effects through income growth.
There are several functional forms of Lorenz curves and corresponding Gini coefficients. A new multi-parametric Lorenz curve (Ahmad, 2005) generated from the initial Lorenz curve is presented. The new curve is fitted to Pakistan consumption data and compared the results with Ortega et al. (1991) and Kakwani (1980) curves and computed Gini coefficients. The Gini coefficient based on the new Lorenz curve provides more information on consumption inequality closer to the data than Ortega et al. (1991) and Kakwani (1980) curves.
The aim of the paper is to investigate the role of income from selfemployment in accounting for both the level and the change in the overall inequality among the Italian households from 1998 to 2002. The data come from the Survey of Household Income and Wealth (SHIW) conducted by the Bank of Italy. Through a decomposition analysis of Gini index by income source we find that in the more recent years the income from self-employment is the main disequalizing factor even if its effect is offset at the aggregate level by the forces played by the other sources. The Gini decomposition by population groups provides the evidence of widening gaps in the average income among the groups. Indeed a strong increase in the average income for managers and self-employed other than entrepreneurs and professionals has increased the segmentation of the different groups.
Keywords: Gini decomposition, Income from self-employment, Relative Economic Affluence.