Parametric Lorenz Curves and the Modality of the Income Density Function
AbstractSimilar 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. --
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Bibliographic InfoPaper provided by Verein für Socialpolitik / German Economic Association in its series Annual Conference 2012 (Goettingen): New Approaches and Challenges for the Labor Market of the 21st Century with number 67390.
Date of creation: 2012
Date of revision:
Lorenz Curve; Income Distribution; Modality; Inequality; Goodness of Fit;
Find related papers by JEL classification:
- C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
- C16 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Econometric and Statistical Methods; Specific Distributions
- D31 - Microeconomics - - Distribution - - - Personal Income and Wealth Distribution
- O57 - Economic Development, Technological Change, and Growth - - Economywide Country Studies - - - Comparative Studies of Countries
This paper has been announced in the following NEP Reports:
- NEP-ALL-2013-01-12 (All new papers)
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