A Note on α‐Gini Measures

• Published date: 01 September 2019
• Author: Stéphane Mussard,Pauline Mornet
• Date: 01 September 2019
• DOI: http://doi.org/10.1111/roiw.12373

A Note on a-Gini Measures

by St

ephane Mussard*

CHROME, Universit

edeN

^

ımes

and

Pauline Mornet

LAMETA, Universit

e Montpellier I

This note provides a characterization of a-Gini inequality measures. These measures generalize the

standard Gini index by including one sensitivity parameter a, which captures different value judg-

ments. The a-Gini measures are shown to be weaklydecomposable and unit consistent. Weak decom-

position provides within-groupand between-group inequalities. Unit consistency keeps unchanged the

ranking of two income distributions when the income units vary. It is shown that the a-Gini measures

are relevant with either “leftist” or“rightist” views.

JEL Codes: D63, D31, C43

Keywords:a-Gini measures, unit consistency, weak decomposition

1. Introduction

The Gini index is one of the most popular indices employed in economics. It

is expressed in various ways and its applications are concerned with concentra-

tion, income inequality, poverty, segregation, diversity, health, mobility, and

many other fields. In recent decades, the Gini index has been generalized in order

to bring out wider families of income inequality; for example, the S-Gini family

due to Donaldson and Weymark (1980), the extended Gini index proposed by

Yitzhaki (1983), and, among others, the P-Gini family introduced by Gajdos

(2002). The measures of those families may depend on a parameter of sensitivity

toward inequality. The parametrization and the structure of those measures vary

from one family to another; however, each member of these families inherits from

the basic properties satisfied by the Gini index, highlighting either its connection

with the Lorenz curve or with the dual social welfare function of Yaari (1987).

The aim of this note is to propose a characterization of the a-Gini measures,

introduced by Chameni (2006) and Ebert (2010). A subgroup decomposition

property (WDEC) is proposed and appears to be a generalization of the weak

decomposition properties (DEC) of Ebert (2010) and ðd

DECðeÞÞ. Such a property

Note: An anonymous referee of ROIW is gratefully acknowledged. The usual disclaimer

applies.

*Correspondence to: St

ephane Mussard, Research fellow, GR 

EDI, University of Sherbrooke,

and LISER, Luxembourg (stephane.mussard@unimes.fr).

V

C2018 International Association for Research in Income and Wealth

1

Review of Income and Wealth

DOI: 10.1111/roiw.12373

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Series 65, Numb er 3, September 2019