Distributional Comparisons Using the Gini Inequality Measure

• Published date: 01 December 2023
• Author: John Creedy
• Date: 01 December 2023
• DOI: http://doi.org/10.1111/1467-8462.12534

The Australian Economic Review, vol. 56, no. 4, pp. 538–550DOI: 10.1111/1467-8462.12534

Perspective

Distributional Comparisons Using the Gini Inequality Measure

John Creedy*

Abstract

This article is aimed at undergraduate and

graduate economics students, as well as

public sector economists, who are interested

in inequality measurement. It examines the

use of the Gini inequality measure to compare

income distributions. The implicit distribu-

tional value judgements are made explicit, via

the use of a particular form of Social Welfare

Function. Emphasis is given to the interpreta-

tion of changes in inequality.

JEL CLASSIFICATION

D331; D63

1. Introduction

The most widely used summary measure of

income inequality in official statistics and

public debates is the Gini index.

1

This was

devised in 1914 by the Italian statistician

Corrado Gini (1884–1965).

2

An attractive

feature of Gini's index is that it can be related

to the famous Lorenz curve: this plots the

cumulative proportion of total income against

the corresponding proportion of people, after

ranking all incomes in ascending order.

3

It is

drawn in a square box with sides of unit length:

an illustration is shown in Figure 1. The case of

complete equality in the diagram is represented

by a

°4

5

diagonal line: any given proportion of

income is obtained by the same proportion of

people. Extreme inequality, where only on,

person has all the income, implies—for a large

population—a curve that follows the base and

right‐hand side of the square box. A inter-

mediate amount of inequality produces a curve

lying below the diagonal (the poorest

x

per cent

of people have less than

x

percentoftotal

income).

The ‘distance’between the actual Lorenz

curve and the line of equality therefore provi des

a convenient visual indication of the extent of

inequality. Gini defined his index using an area

measure of distance: it is the area between the

Lorenz curve and the diagonal line of equality,

divided by the area for the case of extreme

inequality. As the latter is 1/2 (since the area of

the whole box is 1), the Gini is simply twice the

former area. The calculation of this area can

conveniently be carried out using a range of

formulae, as shown below.

4

*Creedy: Victoria University of Wellington, Wellington,

New Zealand; email: <john.creedy@vuw.ac.nz>.

This article is part of a project on ‘Measuring Income

Inequality, Poverty, and Mobility in New Zealand’,

funded by an Endeavour Research Grant from the

Ministry of Business, Innovation and Employment

(MBIE) and awarded to the Chair in Public Finance. I

am grateful to Norman Gemmell, Ivica Urban and a

referee for helpful comments on an earlier draft.

© 2023 The University of Melbourne, Melbourne Institute: Applied Economic & Social Research, Faculty of Business

and Economics.

Published by John Wiley & Sons Australia, Ltd