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Parametric Lorenz Curves and the Modality of the Income Density Function

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  • Melanie Krause

Abstract

type="main"> 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.

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  • Melanie Krause, 2014. "Parametric Lorenz Curves and the Modality of the Income Density Function," Review of Income and Wealth, International Association for Research in Income and Wealth, vol. 60(4), pages 905-929, December.
    • Handle: RePEc:bla:revinw:v:60:y:2014:i:4:p:905-929
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    File URL: http://hdl.handle.net/10.1111/roiw.12047
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    Cited by:

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    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. Bluhm, Richard & de Crombrugghe, Denis & Szirmai, Adam, 2018. "Poverty accounting," European Economic Review, Elsevier, vol. 104(C), pages 237-255.
    5. 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.
    6. 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.
    7. Liang Frank Shao & Melanie Krause, 2020. "Rising mean incomes for whom?," PLOS ONE, Public Library of Science, vol. 15(12), pages 1-20, December.

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    More about this item

    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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