🤖 AI Summary
This study addresses a critical flaw in the existing Beta Lorenz curve, whose parameter space fails to satisfy the theoretical constraints inherent to Lorenz curves, leading to systematic bias in estimating poverty and inequality from grouped income data. The authors explicitly identify this deficiency for the first time and propose a novel four-parameter family of Lorenz curves that rigorously adheres to all formal properties of genuine Lorenz curves while retaining practical usability. Through parametric modeling, derivation of necessary constraints, and extensive empirical validation across more than 2,000 datasets, the new model demonstrates superior performance in estimating poverty and inequality metrics. Specifically, it significantly reduces the systematic underestimation of poverty levels observed in over 80% of cases compared to the widely used General Quadratic (GQ) Lorenz curve.
📝 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