The General Poverty Index

TL;DR

This paper introduces the General Poverty Index (GPI), a unified framework that encompasses most known poverty indices, providing a basis for deriving and analyzing various poverty measures with proven asymptotic normality.

Contribution

The paper presents a comprehensive general formula for poverty indices, unifying existing measures and establishing their asymptotic properties for practical application.

Findings

Derivation of various poverty indices from the GPI framework

Proof of asymptotic normality for the GPI and related measures

Application potential for poverty assessment in poor countries

Abstract

We introduce the General Poverty Index (GPI), which summarizes most of the known and available poverty indices, in the form {equation*} GPI=\delta (\frac{A(Q_{n},n,Z)}{nB(Q,n)}\overset{Q_{n}}{\underset{j=1}{\sum}%}w(\mu_{1}n+\mu_{2}Q_{n}-\mu_{3}j+\mu_{4})d(\frac{Z-Y_{j,n}}{Z}%)),{equation*} where {equation*} B(Q_{n},n)=\sum_{j=1}^{Q}w(j), {equation*} $A(\cdot),$ $w(\cdot),and$ $d(\cdot) $\ are given measurable functions, $Q_{n}$ is the number of the poor in the sample, Z is the poverty line and $Y_{1,n}\leq Y_{2,n}\leq ...\leq Y_{n,n}$\ are the ordered sampled incomes or expenditures of the individuals or households. We show here how the available indices based on the poverty gaps are derived from it. The asymptotic normality is then established and particularized for the usual poverty measures for immediate applications to poor countries data.