Income Inequality Indices Interpreted as Measures of Relative Deprivation/Satisfaction

Imedio-Olmedo, Luis J.; Parrado-Gallardo, Encarnación M.; Bárcena‐Martín, Elena

doi:10.1007/s11205-011-9912-8

Cited by 9 publications

(3 citation statements)

References 24 publications

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“…Chakravarty and Chakraborty (1984) generalize the aggregate index of relative deprivation proposed by Yitzhaki (1979). Berrebi and Silber (1985) and Imedio-Olmedo, Parrado-Gallardo and Bárcena-Martín (2012) show that many of the commonly used inequality indices can be written as aggregate indices of relative deprivation. The interpretation of a generalization of the Gini index (namely, the single-parameter Ginis; see Donaldson andWeymark, 1980, andWeymark, 1981) as indices of aggregate relative deprivation is due to Duclos (2000) and Verme (2011).…”

Section: Introductionmentioning

confidence: 99%

Proximity-sensitive individual deprivation measures

Bossert

D’Ambrosio

2014

Economics Letters

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Abstract. We propose and characterize a generalization of the classical linear index of individual deprivation based on income shortfalls. Unlike the original measure, our class allows for increases in the income of a higher-income individual to have a stronger impact on a person's deprivation the closer they occur to the income of the individual whose deprivation is being assessed. The subclass of our measures with this property is axiomatized in our second result. Journal of Economic Literature Classification No.: D63.

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Section: Introductionmentioning

confidence: 99%

Proximity-sensitive individual deprivation measures

Bossert

D’Ambrosio

2014

Economics Letters

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“…Among them, welfare implication (see, e.g. Aaberge, 2000; Bárcena‐Martín & Silber, 2013, 2017; Benedetti, 1986; Chakravarty, 2007; Chakravarty & Muliere, 2004), socio‐economic aspects (Bárcena & Imedio, 2008; Bárcena‐Martín & Silber, 2011; Bárcena‐Martín & Silber, 2013; Imedio‐Olmedo et al., 2012; Silber & Son, 2010), application in fuzzy and reliability frameworks (Giordani & Giorgi, 2010; Giorgi & Crescenzi, 2001b) and decomposition by sources or by groups (Bárcena‐Martín & Silber, 2013; Giorgi & Guandalini, 2018; Tarsitano, 1990) have been studied.…”

Section: Introductionmentioning

confidence: 99%

Linearization and Variance Estimation of the Bonferroni Inequality Index

Dong

Tillé

Giorgi

et al. 2021

Journal of the Royal Statistical Society Series A: Statistics in Society

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The study of income inequality is important for predicting the wealth of a country. There is an increasing number of publications where the authors call for the use of several indices simultaneously to better account for the wealth distribution. Due to the fact that income data are usuallyinequality measures, inference, influence function | 1009 DONG et al. | INTRODUCTIONNobel Prize-winning economist, Joseph Stiglitz, stated that income inequality is an important measure for forecasting the wealth of a country (Stiglitz, 2012). The most widely used inequality measure is the Gini index (Gini, 1912(Gini, ,1914. Since Corrado Gini suggested the index, it has been the subject of numerous publications. Its use is not restricted only to the economic field. It is surprising to note that even after a century, different applications of the Gini index pop up in new fields (see, e.g. Giorgi, 2019).Recent studies encourage the use of more than one inequality index simultaneously to better catch the inequality in different parts of the income distribution and thereby to better understand the socioeconomic reality and political significance of inequality (see, e.g. Osberg, 2017;Piketty, 2015). The most suitable candidate to place side by side with the Gini index could be the Bonferroni inequality index (Bonferroni, 1933). In fact, Pundir et al. (2005) show that both can be derived from the Lorenz Curve (Lorenz, 1905). Indeed, the two indices share several properties while maintaining some very interesting peculiarities.The opposition between the Bonferroni index and the Gini index is rooted when Carlo Emilio Bonferroni proposed his index in 1930. In the beginning, the Bonferroni index was fought by Corrado Gini and his followers who were very fond of the Gini index and who tried to avoid the use of any other measures that took the Gini index down the line (Giorgi, 1998). Only in the last 40 years, the Bonferroni index has been rediscovered by Piesch (1975) and Nygård and Sandström (1981). Several extensions and interpretations proposed for the Gini index (see, e.g. Giorgi, 2005, for a comprehensive review) have then been extended to the Bonferroni index, disclosing even more similarities and differences between the two indices.

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“…New and interesting interpretations and extensions of B have been just recently proposed: its welfare implications have been studied by Benedetti (1986), Aaberge (2000), Chakravarty (2007) and Bárcena-Martin and Silber (2013). Giorgi and Crescenzi (2001c) proposed a poverty measure based on B, while other socio-economic aspects have been studied by Bárcena-Martin and Olmedo (2008), Silber and Son (2010), Silber (2011, 2013), and Imedio Olmedo et al (2012). The Bonferroni index has also been investigated in fuzzy and reliability frameworks (Giordani and Giorgi 2010;Giorgi and Crescenzi 2001b) and, in particular cases, a Bayesian estimation is followed (Giorgi and Crescenzi 2001a).…”

Section: Introductionmentioning

confidence: 99%

Decomposing the Bonferroni Inequality Index by Subgroups: Shapley Value and Balance of Inequality

Giorgi

Guandalini

2018

Econometrics

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Abstract:Additive decomposability is an interesting feature of inequality indices which, however, is not always fulfilled; solutions to overcome such an issue have been given by Deutsch and Silber (2007) and by Di Maio and Landoni (2017). In this paper, we apply these methods, based on the "Shapley value" and the "balance of inequality" respectively, to the Bonferroni inequality index. We also discuss a comparison with the Gini concentration index and highlight interesting properties of the Bonferroni index.

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Income Inequality Indices Interpreted as Measures of Relative Deprivation/Satisfaction

Cited by 9 publications

References 24 publications

Proximity-sensitive individual deprivation measures

Proximity-sensitive individual deprivation measures

Linearization and Variance Estimation of the Bonferroni Inequality Index

Decomposing the Bonferroni Inequality Index by Subgroups: Shapley Value and Balance of Inequality

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