The Lorenz dominance index: a continuous measure for inequality and social welfare comparisons

Lorenz dominance is a classical criterion for comparing income distributions with respect to inequality and social welfare. However, its binary nature, in which one distribution either dominates another or does not, often leads to inconclusive results when empirical Lorenz curves intersect. To overcome this limitation, we introduce the Lorenz dominance index (LDI), a continuous measure that quantifies the extent to which one Lorenz curve lies above another. The LDI provides an interpretable assessment based on the population, allowing for the evaluation of partial or near dominance and improving its usefulness in empirical settings. We derive the asymptotic distribution of the LDI and propose a nonparametric bootstrap procedure to construct confidence intervals and perform inference. Monte Carlo simulations confirm the estimator’s strong performance in finite samples and its nominal coverage. An application to household income data from China highlights the practical value of the LDI in distributional analysis.