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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," VfS 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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    Cited by:

    1. Edwin Fourrier-Nicolaï & Michel Lubrano, 2021. "Bayesian Inference for Parametric Growth Incidence Curves," Research on Economic Inequality, in: Research on Economic Inequality: Poverty, Inequality and Shocks, volume 29, pages 31-55, Emerald Group Publishing Limited.
    2. 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.
    3. Soondong Hong & Heejoon Han & Chang Sik Kim, 2020. "World distribution of income for 1970–2010: dramatic reduction in world income inequality during the 2000s," Empirical Economics, Springer, vol. 59(2), pages 765-798, August.
    4. Vanesa Jorda & Jos Mar a Sarabia & Markus J ntti, 2020. "Estimation of Income Inequality from Grouped Data," LIS Working papers 804, LIS Cross-National Data Center in Luxembourg.
    5. Liang Frank Shao & Melanie Krause, 2020. "Rising mean incomes for whom?," PLOS ONE, Public Library of Science, vol. 15(12), pages 1-20, December.
    6. Bluhm, Richard & de Crombrugghe, Denis & Szirmai, Adam, 2018. "Poverty accounting," European Economic Review, Elsevier, vol. 104(C), pages 237-255.
    7. Santiago Pindado & Carlos Pindado & Javier Cubas, 2017. "Fréchet Distribution Applied to Salary Incomes in Spain from 1999 to 2014. An Engineering Approach to Changes in Salaries’ Distribution," Economies, MDPI, vol. 5(2), pages 1-19, May.

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    More about this item

    Keywords

    Lorenz Curve; Income Distribution; Modality; Inequality; Goodness of Fit;
    All these keywords.

    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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