Measuring economic inequality and risk: a unifying approach based on personal gambles, societal preferences and references

The underlying idea behind the construction of indices of economic inequality is based on measuring deviations of various portions of low incomes from certain references or benchmarks, that could be point measures like population mean or median, or curves like the hypotenuse of the right triangle where every Lorenz curve falls into. In this paper we argue that by appropriately choosing population-based references, called societal references, and distributions of personal positions, called gambles, which are random, we can meaningfully unify classical and contemporary indices of economic inequality, as well as various measures of risk. To illustrate the herein proposed approach, we put forward and explore a risk measure that takes into account the relativity of large risks with respect to small ones.Comment: 29 pages, 4 figure

Zenga’s new index of economic inequality, its estimation, and an analysis of incomes in Italy

For at least a century academics and governmental researchers have been developing measures that would aid them in understanding income distributions, their differences with respect to geographic regions, and changes over time periods. It is a challenging area due to a number of reasons, one of them being the fact that different measures, or indices, are needed to reveal different features of income distributions. Keeping also in mind that the notions of ‘poor’ and ‘rich’ are relative to each other, M. Zenga has recently proposed a new index of economic inequality. The index is remarkably insightful and useful, but deriving statistical inferential results has been a challenge. For example, unlike many other indices, Zenga’s new index does not fall into the classes of L-, U-, and V -statistics. In this paper we derive desired statistical inferential results, explore their performance in a simulation study, and then employ the results to analyze data from the Bank of Italy’s Survey on Household Income and Wealth.Zenga index, lower conditional expectation, upper conditional expectation, confidence interval, Bonferroni curve, Lorenz curve, Vervaat process.

A robust approach to model-based classification based on trimming and constraints

In a standard classification framework a set of trustworthy learning data are employed to build a decision rule, with the final aim of classifying unlabelled units belonging to the test set. Therefore, unreliable labelled observations, namely outliers and data with incorrect labels, can strongly undermine the classifier performance, especially if the training size is small. The present work introduces a robust modification to the Model-Based Classification framework, employing impartial trimming and constraints on the ratio between the maximum and the minimum eigenvalue of the group scatter matrices. The proposed method effectively handles noise presence in both response and exploratory variables, providing reliable classification even when dealing with contaminated datasets. A robust information criterion is proposed for model selection. Experiments on real and simulated data, artificially adulterated, are provided to underline the benefits of the proposed method

Analyzing the Gender Gap in Poland and Italy, and by Regions

High-income inequality, accompanied by substantial regional differentiation, is still a great challenge for social policymakers in many European countries. One of the important elements of this phenomenon is the inequality between income distributions of men and women. Using data from the European Union Statistics on Income and Living Conditions, the distributions of income for Italy and Poland were compared, and the gender gap in these countries was assessed. No single metric can capture the full range of experiences, so a set of selected tools were adopted. The Dagum model was fitted to each distribution, summary measures, like the Gini and Zenga inequality indices, were evaluated, and the Zenga curve was employed to detect changes at each income quantile. Afterward, empirical distributions were compared through a relative approach, providing an analytic picture of the gender gap for both countries. The analysis moved beyond the typical focus on average or median earnings differences, towards a focus on how the full distribution of women’s earnings relative to men’s compares. The analysis was performed in the different macroregions of the two countries, with a discussion of the results. The study revealed that income inequality in Poland and Italy varies across gender and regions. In Italy, the highest inequality was observed in the poorest region, i.e. the islands. On the contrary, in Poland, the highest inequality occurred in the richest region, the central one. The relative distribution method was a powerful tool for studying the gender gap