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Parametric L orenz Curves and the Modality of the I ncome Density Function
Author(s) -
Krause Melanie
Publication year - 2014
Publication title -
review of income and wealth
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.024
H-Index - 57
eISSN - 1475-4991
pISSN - 0034-6586
DOI - 10.1111/roiw.12047
Subject(s) - parametric equation , parametric statistics , function (biology) , mathematics , curve fitting , econometrics , statistics , geometry , evolutionary biology , biology
Similar looking L orenz curves can imply very different income density functions and potentially lead to wrong policy implications regarding inequality. This paper derives a relation between a L orenz curve and the modality of its underlying income density: given a parametric L orenz 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 L orenz curves such as the P areto, W eibull, S ingh– M addala parametrizations and hierarchical families of L orenz curves are discussed. A L orenz curve performance comparison with M onte C arlo simulations and data from the UNU – WIDER W orld I ncome I nequality D atabase underlines the relevance of the theoretical result: curve‐fitting based on criteria such as mean squared error or the G ini difference might lead to a L orenz curve implying an incorrectly‐shaped density function. It is therefore important to take into account the modality when selecting a parametric L orenz curve.