1. Gini and Zenga Indices AVAILABLE for the Analysis of Contextual Income Inequalities within Canada
Bradley A. Corbett, PhD
Associate Research Professor
Richard Ivey School of Business
University of Western Ontario

2. Our Team
Bradley A. Corbett Richard Ivey School of Business, University of Western Ontario, London, Ontario, Canada Francesca Greselin Dipartimento di Metodi Quantitativi per le Scienze Economiche e Aziendali, Universit_a di Milano Bicocca, Milan, Italy Leo Pasquazzi Rebecca Williams University of Western Ontario, Ricardas Zitikis Department of Statistical and Actuarial Sciences, University of Western Ontario, 2 2

3. The study of Income Inequality is…
…a measure of income distribution in a society. 3 3

4. Gini Coefficient Based on Lorenz curve Defined as A/(A+B)
When A=0, Gini=0; represents perfect equality
When B=0, Gini=1; represents perfect inequality
Uses ratio of lower incomes to overall mean of the population

5. The Gini index has been a popular measure of income inequality for a long time (Gini,
1914; see also Giorgi, 1990, 2005): it has a well understood meaning, an easy geometric
interpretation, especially in terms of the Lorenz curve (Lorenz, 1905). Various extensions
and variations of the index have been developed since the pioneering work of Gini (1914),
for obvious reasons such as no index can adequately capture, and thus measure, every
aspect of inequality ([ reference ]).
The Gini index, compares the mean income 1j Σj
i=1 xi of the poor, given the ‘poverty line’ j, with the mean income 1
n Σni=1 xi of the entire population (1.2). But the more skewed (to the right) population is, the less meaningful the mean income 1
n Σni=1 xi is as a measure of the centre, nor is it a sound measure of the mean income of the ‘rich.’
From this point of view, the mean 1n Σni=1 xi does not seem to carry enough meaningful
information to serve a ‘benchmark’ for the mean of the poor. This is one of the issues
that prompts one to think ‘beyond Gini.’

7. Global Changes in the Labour Market, Incomes and the Canadian Context
OECD (2011)
Income inequality is on the rise in nearly all member countries
High earner incomes are increasing twice as fast as low earner incomes
Loss of middle class jobs such as manufacturing in developed countries
Shift from an industrial to a service economy
Increase in technical jobs (higher associated incomes)
Increase in sercvice jobs (lower associated incomes)
Higher education no longer guarantees the prospect of a ‘better life’ but the ‘right education’ is now important
Some additional mitigating factors in Canada
Poverty among aboriginal peoples
Exploitation of natural resources in some provinces

8. Changes in the Tails of the Income Distribution
Frenette, Green & Milligan (2007)
Study of income inequality in Canada from
Argued existing [survey] data sources may have missed changes in the tails of the income distribution
Demonstrated that the Census was a better data source than the standard Survey of Labour and Income dynamics
Also argued many of the changes in the distribution of income have occurred in the tails of the distribution over time
Changes in the tails may not be adequately detected by the Gini Index if the mean remains stable while the tails grow fat

11. Note that the Gini and Zenga have a high level of agreement.

12. Scatter Plot of Canadian Census Divisions: Gini vs. Zenga

13. Gini Index Quintiles in Canada: 2006 Census, After Tax, Census Families

14. Gini and Zenga Indices Available
2006 Canadian Census (2005 Incomes)
a 20% sample from the 2006 Census (~6 Million)
Household incomes
Incentive for low income to submit tax (2000)
Missing data supplemented by tax data
Sampling Weights based on Census
Provincial and Census Division levels of analysis
Income includes market income + government transfers
One family member per household selected

15. Gini and Zenga Indices are AVAILABLE for Merging: Provincial and Census Divisions in Canada (2006 Census; Provincial shown below)
Economic Families
Census Families
No Adjustments
Adjusted
GINI
Before Tax
After Tax BC
Alberta
Saskatchewan
Manitoba
Ontario
Quebec
New Brunswick
Nova Scotia
PEI
Newfoundland & Labrador

16. Contact Info:
Bradley A. Corbett, PhD
Richard Ivey School of Business
University of Western Ontario