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Parametric Lorenz Curves and the Modality of the Income Density Function

Melanie Krause ()

Annual Conference 2012 (Goettingen): New Approaches and Challenges for the Labor Market of the 21st Century from Verein für Socialpolitik / German Economic Association

Abstract: 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). Several single- parameter Lorenz Curves such as the Pareto, Chotikapanich and Rohde forms are associated with zeromodal densities. The paper contrasts these Lorenz Curves with the ones derived from the (unimodal) Lognormal density and the Weibull density, which, remarkably, can be zero- or unimodal depending on the parameter. A performance comparison of these five Lorenz Curves with Monte Carlo simulations and data from the UNU-WIDER World Income Inequality Database underlines the relevance of the theoretical result: Curve-fitting of decile data based on criteria such as mean squared error 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.

Keywords: Lorenz Curve; Income Distribution; Modality; Inequality; Goodness of Fit (search for similar items in EconPapers)
JEL-codes: C13 C16 D31 O57 (search for similar items in EconPapers)
Date: 2012
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Journal Article: Parametric Lorenz Curves and the Modality of the Income Density Function (2014) Downloads
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