On the joint distribution of variations of the Gini index and Welfare indices

TL;DR

This paper investigates the joint asymptotic behavior of the Gini index and welfare measures using Gaussian process representations, enabling analysis of their mutual influence and applications to growth fairness with practical R code implementations.

Contribution

It introduces new Gaussian field-based representation theorems for the joint distribution of Gini and welfare indices, facilitating their asymptotic analysis and applications.

Findings

Derived joint asymptotic distributions for Gini and welfare indices.

Provided R codes for variance computation and confidence intervals.

Unveiled relationships between inequality, growth, and fairness measures.

Abstract

The aim of this paper is to establish the asymptotic behavior of the mutual influence of the Gini index and the poverty measures by using the Gaussian fields described in Mergane and Lo(2013). The results are given as representation theorems using the Gaussian fields of the unidimensional or the bidimensional functional Brownian bridges. Such representations, when combined with those already available, lead to joint asymptotic distributions with other statistics of interest like growth, welfare and inequality indices and then, unveil interesting results related to the mutual influence between them. The results are also appropriate for studying whether a growth is fair or not, depending on the variation of the inequality measure. Datadriven applications are also available. Although the variances may seem complicated at a first sight, their computations which are needed to get confidence intervals of the indices, are possible with the help of R codes we provide. Beyond the current results, the provided representations are useful in connection with different ones of other statistics.