Revisiting a functional form for the Lorenz curve

“…One should be aware that the structural assumptions underlying parametric LCs might be a limitation, but they offer the only feasible estimation approach in the presence of grouped data. As Sarabia et al (2010) have pointed out, this form can be considered a reformulation of the parametrization proposed by Aggarwal (1984). 3 Because the density functions of these parametric LCs are known, one could also look at them directly to check their zeromodality.…”

Section: The Pareto Chotikapanich and Rohde Lcsmentioning

confidence: 99%

“…As Sarabia et al . () have pointed out, this form can be considered a reformulation of the parametrization proposed by Aggarwal ().…”

mentioning

confidence: 98%

Parametric Lorenz Curves and the Modality of the Income Density Function

Krause

2013

Review of Income and Wealth

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Standard-Nutzungsbedingungen:Die Dokumente auf EconStor dürfen zu eigenen wissenschaftlichen Zwecken und zum Privatgebrauch gespeichert und kopiert werden.Sie dürfen die Dokumente nicht für öffentliche oder kommerzielle Zwecke vervielfältigen, öffentlich ausstellen, öffentlich zugänglich machen, vertreiben oder anderweitig nutzen.Sofern die Verfasser die Dokumente unter Open-Content-Lizenzen (insbesondere CC-Lizenzen) zur Verfügung gestellt haben sollten, gelten abweichend von diesen Nutzungsbedingungen die in der dort genannten Lizenz gewährten Nutzungsrechte. 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 singleparameter 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. Terms of use: Documents inJEL Classification: C13, C16, D31, O57

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“…and the equalitarian Lorenz function L E (p) = p, 0 ≤ p ≤ 1, which is the hypotenuse of the right triangle that we have eluded to in the abstract. For parametric expressions of L F (p), we refer to Gastwirth (1971), Kakwani & Podder (1973), as well as to more complete and recent works by Kleiber & Kotz (2003), Sarabia (2008), Sarabia et al (2010), and references therein. Hence, the Gini index is…”

Section: The Classical Gini Index Revisitedmentioning

confidence: 99%

Measuring Economic Inequality and Risk: A Unifying Approach Based on Personal Gambles, Societal Preferences and References

Greselin

Zitikis

2015

SSRN Journal

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The underlying idea behind the construction of indices of economic inequality is based on measuring deviations of various portions of low incomes from certain references or benchmarks, that could be point measures like population mean or median, or curves like the hypotenuse of the right triangle where every Lorenz curve falls into. In this paper we argue that by appropriately choosing population-based references, called societal references, and distributions of personal positions, called gambles, which are random, we can meaningfully unify classical and contemporary indices of economic inequality, as well as various measures of risk. To illustrate the herein proposed approach, we put forward and explore a risk measure that takes into account the relativity of large risks with respect to small ones.

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Revisiting a functional form for the Lorenz curve

Cited by 22 publications

References 10 publications

A general method for generating parametric Lorenz and Leimkuhler curves

A general method for generating parametric Lorenz and Leimkuhler curves

Parametric Lorenz Curves and the Modality of the Income Density Function

Measuring Economic Inequality and Risk: A Unifying Approach Based on Personal Gambles, Societal Preferences and References

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