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# NIASRA Seminar Series

## June 13 @ 2:30 pm - 3:30 pm

##### Speaker

Professor Murray Aitkin, Department of Statistics, University of Melbourne

**Title**

An alternative measure of income inequality over successive surveys

##### Abstract

In Australia, there has been a recent major argument over the claim by the Australian Bureau of Statistics that inequality had not worsened in Australia over the period 2014-2016. The then Commonwealth Government Treasurer (now Prime Minister), Scott Morrison, gave a speech at the time to the Australian Industry Group, in which he said:

*“Analysis of the more recent census data for the 2016 census shows the Gini coefficient based on gross household income has declined from 0.382 to 0.366 since 2011.”*

In a separate comment, he said

*“The last census showed that on the global measure of inequality, which is the Gini coefficient – that is the accepted global measure of income inequality around the world – and that figure shows that it hasn’t got worse, inequality, that it’s actually got better.”*

Mr Morrison’s figures were derived using gross income data taken from the census, and are based on internal, unpublished calculations.

There are at least three problems with the Gini coefficient for income inequality comparisons.

The first is that countries or years with widely different income distributions may have the same Gini index.

The second is that its calculation formally requires access to individual-level income data, to develop both the percentiles of the individual income distribution and the proportion of national income received by each income percentile group. These data are generally confidential to the national statistical office and are not publicly available, except by personal application through a recognised University. What is publicly available, at least in Australia, is the numbers of households receiving income in ABS-defined income intervals.

This information is insufficient to compute the Lorenz curve, from which the Gini index is computed.

The third and principal problem with the Gini index, or any other single number, is that it cannot represent variability in the income distribution. A Gaussian distribution can be summarised by two numbers, but only a single-parameter distribution, like the Poisson or exponential, can be summarised by one number. Recognition of this allows us to develop a statistical modelling approach to changes in income inequality over repeated surveys or censuses, using publicly available income data. I give an example of publicly available total household income reported in percentile ranges from the Australian censuses of 2006, 2011 and 2016. The alternative analysis uses a four-moment distribution to model the income distribution and graduate its reported percentiles.

It is clear from the analysis that the reported income distribution changed very little from 2006 to 2011, but changed substantially – mean and variability both increasing – from 2011 to 2016. This would appear to represent a decrease in inequality from 2011-2016, but the voluntary response makes almost any conclusion doubtful.