Examining Fractures: Measuring Inequality
The Gini Index
Inequality by Design and Compounding Fractures sometimes throw around terms and definitions with which our subscribers may be familiar or may need a refresher. In the “Examining Fractures” posts, I will explain measures, concepts, and definitions.
The Gini Index provides a single number between 0 and 100 to describe how far we are from a perfectly equal society by comparing income groups. 100 is the furthest distance the Gini can be from perfect equality, and 0 is the closest it can get to perfect equality. A lower Gini this year means less inequality, while a higher Gini this year means more inequality.
We could think about the Gini by imagining there is a society of five people whose total income per hour is known. Let’s say our five people in order of income from richest to poorest: Jenny (poorest), Janie (second poorest), Marty (middle), Chad (second richest), and Elon (richest). If income was perfectly equal in this group of five people, all of them would each earn $20, for a total of $100 per hour. In this group, Jenny holds 20% of the income since she earns $20 of the $100 ($20 ÷ $100 × 100% = 20%). Jenny and Janie together then would earn $40 of the $100, and so Jenny and Janie together hold 40% of the income. Jenny, Janie, and Chad together would hold 60% of the income. Jenny, Janie, Chad, and Marty would have 80% of the income. All five together make 100% of the income. We can plot them along a line called the “Lorenz Curve,” in which a perfectly income-equal society would be a 45-degree line.
But of course, society is not equal. Suppose Jenny makes $4 per hour, Janie makes $8 per hour, Marty makes $15 per hour, Chad makes $25 per hour, and Elon makes $48 per hour. If we graph the Lorenz Curve of our groups and their income shares, we get a line below the perfectly equal 45-degree line. We can visualize that difference in the graph below where the black line represents everyone in our group holding equal shares of the income, and the red line showing the unequal shares.
The Gini Index is a measure of the distance between that black line and that red line. If Jenny and Janie start making less in income, that red line will shift out, further away from the black line, and the Gini Index, which measures that total distance under the black line to the red line, will increase. The closest that red line gets to the black line is 0 distance, and the furthest away it gets is 100. 0 in this case means the red line is right on top of the black line, and there is no measurable distance between the two. 100 in this case you can imagine as the case where Elon has $100 and everyone else has $0, and this is the most measurably unequal it could be.
The Gini Index is a great measure for inequality in that it satisfies certain properties that other inequality measures do not (more on that in a later post), and we have available data regarding the population of the US broken up into five income levels of 20% of the population each (from the Census Bureau). What the income Gini does not measure is differences in people and necessary spending which can lead to further inequality. If Jenny and Janie are women, they will need to spend a significant amount of their time and income on giving birth and caring for children that Elon will not. If Marty is in an industrial accident and requires a wheelchair, he will need to spend more of his income on accommodating his disability (car and house adjustments, medical bills) that Elon would not. The Gini only measures the person’s income or wealth dimension. Incorporating differences in individuals, especially across a population as large as the United States, really complicates the math. Still, Gini is a useful start to examining inequality at a national (macro) level.
Sources:
Concepts and Methods:
Development Economics, by Debraj Ray. Princeton University Press. 1998. Chapter 6.
Data sources:
Income Inequality, the United States Census Bureau.
Making the Graph:
The graph was made using Google Sheets.