Income Inequality and the contribution of Geography

by Charles Liebenberg

Want the details? Keen on some formulas? Technical Details

This work was inspired by a green paper authored by actuaries Hugh Miller and Laura Dixie Inspiration

Community level mental illness, violence, imprisonment, teenage births and drug abuse are conditions of a society that rhyme (are correlated) with inequality (Wilkinson and Pickett, 2009). The form of inequality that is perhaps most on the public consciousness in 2024 is economic inequality.

What is economic inequality? Put simply, it is the concentration of economic resources among a population. Economists like to calculate economic inequality through income inequality, as it's measurement is easier with data readily available.
A useful tool to measure the concentration of income among a population is the Lorenz Curve.
ⓘ The Lorenz curve is a "concentration curve" for income, that plots the cumulative share of income against the cumulative share of the population.

This Lorenz curve describes Australia's income share at various proportions of the population.

The orange and blue lines describe a universe where one person has all the income and universe where all income is evenly shared, respectively.

Finally, the red line describes Australia: somewhere in the middle. It follows then, that the shaded area represents inequality.

Generated Graph
But how can this inequality be quantified into a measurement for comparison?

Enter the Gini Coefficient: a measure of the size of the shaded area.

Australia has a Gini coefficient of 0.48, with the top 10% earning roughly 23.5 times the bottom 10%. But what does this actually look like in terms of dollars?

Income distributions are heavily skewed towards higher incomes. To model this, economists use families of statistical distributions with long tails to the right. These tails represent the small group of ultra-high incomes.

ⓘ This analysis uses the Pareto and Log-normal distributions for modelling. It is theorised that the first 97-99% of the population follows a log-normal distribution and the remaining a pareto distribution.

Generated Graph

Modelling income distributions allows for interesting and simplified analysis in the absence of individual-level data.

Have you ever wondered how you stack up against your peers?

How about your peers in your suburb?




How was this calculated?
ⓘ Once parameters are estimated for a given area, the probability that any individual point is below or equal to any given value is given by the cumulative probability function (CDF). The inequality driven by geography is calculated using Lerman and Yitzhaki decomposition.