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Parametric Lorenz Curves and the Modality of the Income Density Function

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  • Krause, Melanie

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.

Suggested Citation

  • Krause, Melanie, 2012. "Parametric Lorenz Curves and the Modality of the Income Density Function," Annual Conference 2012 (Goettingen): New Approaches and Challenges for the Labor Market of the 21st Century 67390, Verein für Socialpolitik / German Economic Association.
  • Handle: RePEc:zbw:vfsc12:67390
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    1. Sarabia, J. -M. & Castillo, Enrique & Slottje, Daniel J., 1999. "An ordered family of Lorenz curves," Journal of Econometrics, Elsevier, vol. 91(1), pages 43-60, July.
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    Cited by:

    1. Richard Bluhm & Denis de Crombrugghe & Adam Szirmai, 2016. "Poverty Accounting. A fractional response approach to poverty decomposition," Working Papers 413, ECINEQ, Society for the Study of Economic Inequality.
    2. repec:eee:eecrev:v:104:y:2018:i:c:p:237-255 is not listed on IDEAS

    More about this item

    Keywords

    Lorenz Curve; Income Distribution; Modality; Inequality; Goodness of Fit;

    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, Innovation, Technological Change, and Growth - - Economywide Country Studies - - - Comparative Studies of Countries

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