Bilateral Gini Index

Abstract

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, this index 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 some 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 in how privileges and facilities are distributed into them.

A new inequality index?

“…In an article published in volume 2 of this Journal, Esparza et al (2020) propose a new measure of inequality: a modification of the Gini index, which they call the "Bilateral Gini index".…”

“…After that Esparza et al (2020) define the Bidimensional Bilateral Gini index as the pair G e GB. They state (p. 11), without any explanation, that this index obeys the Pigou-Dalton's condition.…”

“…Because the regressive transfers cause the value of to fall from more than 0.5 to less than 0.5, the value of changes from positive to negative, contrary to Pigou-Dalton's condition. In fact, the "Bilateral Gini" of Esparza et al (2020) is not an appropriate measure of inequality and it is very inappropriate to denominate it using the name of the most usual of the inequality measures.…”

“…Esta es una crítica a un artículo publicado en el volumen 2 de la Revista Brasileira de Economia Social e do Trabalho. La modificación del índice de Gini propuesta por Esparza et al (2020) implica definiciones arbitrarias e injustificadas. Ya existen métodos establecidos para comparar la distribución de ingreso en diversas regiones sin que el análisis se limite a la desigualdad, como, por ejemplo, las curvas de Lorenz generalizadas.…”

“…Il s'agit d'une critique d'un article publié dans le volume 2 de la Revista Brasileira de Economia Social e do Trabalho. La modification de l'indice de Gini proposée par Esparza et al (2020) implique des définitions arbitraires et injustifiées. Il existe déjà des méthodes établies pour comparer la distribution des revenus dans différentes régions sans que l'analyse se limite aux inégalités, comme par exemple les courbes de Lorenz généralisées.…”