On the influence of the Theil-like inequality measure on the growth

TL;DR

This paper develops a unified theoretical framework using functional empirical processes to analyze how inequality measures influence growth, covering various poverty and inequality indices with practical R code applications.

Contribution

It introduces a coherent, unified approach to study the interaction between poverty and inequality indices using Gaussian fields and asymptotic laws.

Findings

Derived asymptotic laws for index variations over time

Provided confidence intervals for index changes

Applied methods to Senegal pseudo-panel data

Abstract

We set in this paper a coherent theory based on functional empirical processes to consider both the poverty and the inequality indices in one Gaussian field enabling to study the influence of the one on the other. We use the General Poverty Index (\textit{GPI}), that is a class of poverty indices covering the most common ones and a functional class of inequality measure including the Entropy Measure, the Mean Logarithmic Deviation, the different inequality measures of Atkinson, Champernowne, Kolm and Theil called Theil-like Inequality Measures \textit{TLIM}. Our results are given in a unified approach with respect to the two classes instead of their particular elements. We provide the asymptotic laws of the variations of each class over two given periods and the ratio of the variation and derive confidence intervals for them. Although the variances may seem somehow complicated, we provide R codes for their computations and apply the results for the pseudo-panel data for Senegal with simple analysis.