Parametric Lorenz Curves and the Modality of the Income Density Function

type="main"> <p>Similar looking Lorenz curves can imply very different income density functions and potentially lead to wrong policy implications regarding inequality. This paper derives a relation between a Lorenz curve and the modality of its underlying income density: given a parametric Lorenz curve, it is the sign of its third derivative which indicates whether the density is unimodal or zeromodal (i.e., downward-sloping). The density modality of several important Lorenz curves such as the Pareto, Weibull, Singh–Maddala parametrizations and hierarchical families of Lorenz curves are discussed. A Lorenz curve performance comparison with Monte Carlo simulations and data from the UNU–WIDER World Income Inequality Database underlines the relevance of the theoretical result: curve-fitting based on criteria such as mean squared error or the Gini difference might lead to a Lorenz curve implying an incorrectly-shaped density function. It is therefore important to take into account the modality when selecting a parametric Lorenz curve.