Beyond the Beta Lorenz Curve: A New Parametric Family for Poverty and Inequality Estimation

TL;DR

This paper introduces a new parametric family of Lorenz curves to improve poverty and inequality estimation from aggregated income share data, outperforming existing models like the GQ Lorenz curve.

Contribution

It identifies limitations of the Beta Lorenz curve and proposes a corrected, more flexible four-parameter family that ensures theoretical validity and enhances estimation accuracy.

Findings

The new model outperforms the GQ Lorenz curve in over 80% of cases.

It provides highly accurate estimates of poverty and inequality measures.

The analysis is based on over 2,000 datasets.

Abstract

The estimation of inequality and poverty measures is frequently constrained by a lack of individual data. Many countries, including China, continue to report income data in the form of aggregated income shares. In this context, the Beta Lorenz curve, introduced by Kakwani (Econometrica, 48, 1980), has become a standard tool for reconstructing income distributions at both academic and institutional levels. Notably, alongside the General Quadratic (GQ) Lorenz curve, it represents the primary specification used by the World Bank to construct its official poverty estimates when microdata is unavailable. In this paper, we demonstrate that Kawani's model fails to satisfy the formal requirements of a genuine Lorenz curve. To address this, we identify the specific constraints that ensure the theoretical validity of this model and introduce a new family of Lorenz curves derived from the corrected parametric space. Our analysis, conducted across more than 2,000 datasets, reveals that our proposed four-parameter specification provides highly accurate estimates of several poverty and inequality measures. Our results show that this model consistently outperforms the GQ Lorenz curve, which we find tends to underestimate poverty in over 80 percent of the analyzed cases