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

The estimation of inequality and poverty measures is frequently constrained by a lack of individual data.

When only income shares are available, the Beta Lorenz curve introduced by Kakwani (Econometrica, 48, 1980) has become a standard tool for reconstructing income distributions.

Together with the General Quadratic (GQ) Lorenz curve, it is used by the World Bank to produce official poverty estimates when microdata are unavailable.

In this paper, we show that Kakwani's specification does not generally satisfy the formal requirements of a genuine Lorenz curve and introduce a new Lorenz curve rooted in the corrected parameter space.

Using more than 1,700 datasets, we show that the proposed model yields valid Lorenz curves in all applications and consistently outperforms competing specifications in both accuracy and sampling precision.

The GQ, by contrast, fails to provide genuine curves in 15 percent of datasets and underestimates extreme poverty severity in 98 percent of them.