Measuring and Explaining Economic Inequality: An Extension of the Gini Coefficient

Measuring and Explaining Economic Inequality: An Extension of the Gini Coefficient

C. Chameni Nembua (University of Yaoundé II, Cameroon)
Copyright: © 2014 |Pages: 15
DOI: 10.4018/978-1-4666-4329-1.ch006

Abstract

This chapter proposes a new class of inequality indices based on the Gini coefficient (or index). The properties of the indices are studied and are found to be regular, relative, and to satisfy the Pigou-Dalton transfer principle. A subgroup decomposition is performed, and the method is found to be similar to the one used by Dagum when decomposing the Gini index. The theoretical results are illustrated by case studies, using Cameroonian data.
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2. Notation And Preliminaries

In this chapter, 978-1-4666-4329-1.ch006.m05 is a population with 978-1-4666-4329-1.ch006.m06 members. 978-1-4666-4329-1.ch006.m07 is a positive variable defined in 978-1-4666-4329-1.ch006.m08 and represents an income source distribution between the 978-1-4666-4329-1.ch006.m09 members of 978-1-4666-4329-1.ch006.m10 We denote by 978-1-4666-4329-1.ch006.m11 the values of 978-1-4666-4329-1.ch006.m12on the 978-1-4666-4329-1.ch006.m13members of 978-1-4666-4329-1.ch006.m14 respectively. We assume that 978-1-4666-4329-1.ch006.m15 is partitioned into 978-1-4666-4329-1.ch006.m16 subpopulations 978-1-4666-4329-1.ch006.m17 with, respectively, 978-1-4666-4329-1.ch006.m18978-1-4666-4329-1.ch006.m19978-1-4666-4329-1.ch006.m20 members. The value of 978-1-4666-4329-1.ch006.m21 on member number 978-1-4666-4329-1.ch006.m22 of 978-1-4666-4329-1.ch006.m23 is written as 978-1-4666-4329-1.ch006.m24 The restriction of 978-1-4666-4329-1.ch006.m25 in 978-1-4666-4329-1.ch006.m26 is written 978-1-4666-4329-1.ch006.m27978-1-4666-4329-1.ch006.m28 is the mean of 978-1-4666-4329-1.ch006.m29 in 978-1-4666-4329-1.ch006.m30 (in 978-1-4666-4329-1.ch006.m31 and 978-1-4666-4329-1.ch006.m32978-1-4666-4329-1.ch006.m33 represents the variance of 978-1-4666-4329-1.ch006.m34 in 978-1-4666-4329-1.ch006.m35 (in978-1-4666-4329-1.ch006.m36 Also, 978-1-4666-4329-1.ch006.m37 is the square of the coefficient of variation of 978-1-4666-4329-1.ch006.m38 in 978-1-4666-4329-1.ch006.m39

978-1-4666-4329-1.ch006.m40
and

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