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

Giorgi, Giovanni Maria; Guandalini, Alessio

doi:10.3390/econometrics6020018

Cited by 3 publications

(3 citation statements)

References 25 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The trapezoidal rule of defining the income inequality indices is here introduced. Following the insight of Pietra (1915) who used this rule for computing the concentration area between the Lorenz curve and the equidistribution line for the Gini index, Giorgi & Guandalini (2013) adopt it for estimating the Bonferroni index. Needless to say, this technique can be extended to the generalised index and to all the income inequality indices associated.…”

Section: Trapezoidal Rulementioning

confidence: 99%

Generalised Income Inequality Index

Dong,

Tille,

Giorgi

et al. 2023

Int Statistical Rev

View full text Add to dashboard Cite

SummaryThis paper proposes a deep generalisation for income inequality indices. A generalised income inequality index that depends on two parameters and that involves a large set of income inequality indices in the same framework is proposed. The two parameters control the sensitivity of the generalised index to different levels of the income distribution. A thorough investigation of the generalised index paves the way for understanding the influence of the low, middle and high incomes on various income inequality indices and thereby facilitates the choice of multiple indices simultaneously for a better analysis of inequality as advocated by several recent studies. Moreover, two methods for estimating the generalised index in the case of finite populations are shown. A new method for estimating the inequality indices is proposed.

show abstract

Section: Trapezoidal Rulementioning

confidence: 99%

Generalised Income Inequality Index

Dong,

Tille,

Giorgi

et al. 2023

Int Statistical Rev

View full text Add to dashboard Cite

show abstract

“…Not as popular as the Gini index, yet no less profound, is the Bonferroni index [57][58][59][60][61][62][63]. This subsection addresses the Bonferroni index I Bonf of the input T.…”

Section: Bonferroni-index Criteriamentioning

confidence: 99%

Mean-performance of sharp restart: II. Inequality roadmap

Eliazar

Reuveni

2021

J. Phys. A: Math. Theor.

View full text Add to dashboard Cite

Restarting a deterministic process always impedes its completion. However, it is known that restarting a random process can lead to an opposite outcome—expediting completion. Hence, the effect of restart is contingent on the underlying statistical heterogeneity of the process’ completion times. To quantify this heterogeneity we introduce a novel approach to restart research: the methodology of inequality indices, which is widely applied in economics and in the social sciences to measure income and wealth disparities. Utilizing this approach we establish an ‘inequality roadmap’ for the mean-performance of sharp restart: a whole new set of universal inequality criteria that determine when restart with sharp timers (i.e. with fixed deterministic timers) impedes/expedites mean completion. The criteria are based on key Lorenz-curve inequality indices including Bonferroni, Gini, and Pietra. From a practical perspective, the criteria offer researchers highly useful tools to tackle the common real-world situation in which only partial information of the completion-time statistics is available. From a theoretical perspective, the criteria yield—with unprecedented precision and resolution—a powerful and overarching take-home-message: restart impedes/expedites mean completion when the underlying statistical heterogeneity is low/high, respectively. As sharp restart can match the mean-performance of any other restart protocol, the results established here apply to restart research at large.

show abstract

“…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

Self Cite

View full text Add to dashboard Cite

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.

show abstract

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

Cited by 3 publications

References 25 publications

Generalised Income Inequality Index

Generalised Income Inequality Index

Mean-performance of sharp restart: II. Inequality roadmap

Linearization and Variance Estimation of the Bonferroni Inequality Index

Contact Info

Product

Resources

About