Distorted Lorenz curves: models and comparisons

Sordo, Miguel Á.; Navarro, Jorge; Sarabia, José Marı́a

doi:10.1007/s00355-013-0754-y

Cited by 15 publications

(6 citation statements)

References 52 publications

(62 reference statements)

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“…Like the numerator of the Gini index, these measures are linear combinations of order statistics and there is a large literature deriving their large sample distributions (David and Nagaraja 2003;Greselin et al 2009;Giorgi and Gigliarano 2016). Similarly, the Lorenz curve and related functions or transformations of it (Sordo et al 2014;Arnold 2015;Gastwirth 2016) can be used to emphasize the region of the income distribution of primary concern.…”

Section: Summary and Discussionmentioning

confidence: 99%

Is the Gini Index of Inequality Overly Sensitive to Changes in the Middle of the Income Distribution?

Gastwirth

2017

Statistics and Public Policy

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The Gini index is the most commonly used measure of income inequality. Like any single summary measure of a set of data, it cannot capture all aspects that are of interest to researchers. One of its widely reported flaws is that it is supposed to be overly sensitive to changes in the middle of the distribution. By studying the effect of small transfers between households or an additional increment in income going to one member of the population on the value of the index, this claim is reexamined. It turns out that the difference in the rank order of donor and recipient is usually the most important factor determining the change in the Gini index due to the transfer, which implies that transfers from an upper income household to a low income household receive more weight that transfers involving the middle. Transfers between two middle-income households do affect a higher fraction of the population than other transfers but those transfers do not receive an excessive weight relative to other transfers because the difference in the ranks of donor and recipient is smaller than the corresponding difference in other transfers. Thus, progressive transfers between two households in the middle of the distribution changes the Gini index less than a transfer of the same amount from an upper income household to a lower income household. Similarly, the effect on the Gini index when a household in either tail of the distribution receives an additional increment is larger than when a middle-income household receives it. Contrary to much of the literature, these results indicate that the Gini index is not overly sensitive to changes in the middle of the distribution. Indeed, it is more sensitive to changes in the lower and upper parts of the distribution than in the middle.

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Section: Summary and Discussionmentioning

confidence: 99%

Is the Gini Index of Inequality Overly Sensitive to Changes in the Middle of the Income Distribution?

Gastwirth

2017

Statistics and Public Policy

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“…Hence, we are dealing with the distorted Bonferroni function¯ (B F (p)), 0 < p < 1, which is analogous to the distorted Lorenz function upon which Sordo et al (2014) have built their research (see Aaberge (2000) for earlier results on the topic). We do not pursue this research venue in the present paper because the Bonferroni function, just like that of Lorenz, incorporates a pre-specified reference measure, which is the mean income µ F .…”

Section: From Egalitarian Lorenz To the Mean Referencementioning

confidence: 99%

From the Classical Gini Index of Income Inequality to a New Zenga-Type Relative Measure of Risk: A Modeller’s Perspective

Greselin

Zitikis

2018

Econometrics

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Abstract: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, which could be point measures like the population mean or median, or curves like the hypotenuse of the right triangle into which every Lorenz curve falls. 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, and 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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“…Coming now back to the index A F , we note that with the generic relative-value function v(x, y) = ℓ(x/y), the index can be rewritten as E[l(B F (π))], wherel(t) = ℓ(1 − t). Hence, we are dealing with the distorted Bonferroni functionl(B F (p)), 0 < p < 1, which is analogous to the distorted Lorenz function upon which Sordo et al (2014) have built their far-reaching development of Aaberge's (2000) work. We do not pursue this research venue in the present paper because the Bonferroni function, just like that of Lorenz, incorporates a pre-specified reference measure, which is the mean income µ F .…”

Section: From Equalitarian Lorenz To the Mean Referencementioning

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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Distorted Lorenz curves: models and comparisons

Cited by 15 publications

References 52 publications

Is the Gini Index of Inequality Overly Sensitive to Changes in the Middle of the Income Distribution?

Is the Gini Index of Inequality Overly Sensitive to Changes in the Middle of the Income Distribution?

From the Classical Gini Index of Income Inequality to a New Zenga-Type Relative Measure of Risk: A Modeller’s Perspective

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

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