Uniform weak convergence of poverty measures with relative poverty lines

TL;DR

This paper develops a unified framework for poverty measures with relative poverty lines, introduces a consistent estimator, and proves a uniform CLT, enabling advanced testing procedures and analysis of poverty data.

Contribution

It presents a general continuous poverty index, a consistent estimator for distribution-dependent poverty lines, and establishes a uniform CLT for the estimator.

Findings

Estimator exhibits asymptotic normality in simulations.

Uniform CLT holds over a broad class of functions.

Application demonstrates impact of relative poverty lines on variance.

Abstract

This paper introduces a general continuous form of poverty index that encompasses most of the existing formulas in the literature. We then propose a consistent estimator for this index in case the poverty line is a functional of the distribution. We also establish a uniform functional Central Limit Theorem for the proposed estimator over a suitable product class of real-valued functions. As a consequence, testing procedures based either on single or simultaneously several poverty indices can be developed. A simulation study showing the asymptotic normality of the estimator is given as well as an application to real data for estimating the effect of relative poverty lines on the variance of the poverty estimates.