‘I Dream of Gini’ – Measuring Income Inequality

One of the problems with economics is that economists use complex words like “coefficient,” making a term like “Gini coefficient” unpopular before people even know what it means. If the term referred to some abstract number that people use to explain recessions it probably wouldn’t be worth explaining. This number, however, has been connected to fetal mortality and the likelihood that crazies will go shooting up our preschools, so it’s worth a little more than a dismissive glance.

The simple description of the Gini coefficient is that it’s a measure of income inequality. If everyone in a group made the same amount of money, then its value would be zero. If only one person in the population made all of the money, then its value would be one. Neither extreme is desirable, and in the real world, it falls between .23 (Sweden) and .65 (South Africa). This value is usually expressed as a percentage, making those numbers 23 and 65.Inequality chart

Political wrangling aside, calculating the number isn’t complicated. I’ll use US numbers as an example. You start with a square chart on which the width is 100% of the earning population (around 150 million) and the height is the total amount of money that everyone earn each year (around 12 billion). Take the half of the population that makes the least amount of money (75 million) and add up all of the money they make (can you guess this number?). This puts a point on the chart halfway from left to right, and at a height similar to the height of a stack of those people’s money, if the height of the full chart were all of the money earned. If you repeat this process for enough points on the line, you get a curve below the equality line.

The equality line is what the curve would look like if everyone made the same amount of money. The blue area is the difference between the “equal income” line and the numbers we just described. Mathematicians have no problem finding the area of a shape like this. They divide the area of the light blue area by everything under the equality line and the number they get is the Gini coefficient. This turns the complexities of income inequality into a simple number that goes up when inequality is high and down when inequality is low.

Richard Wilkinson has been studying this kind of inequality for decades. We intuitively know that letting big guys step on little guys has poor societal outcomes, but he’s put a lot of effort into applying numbers to the problem. He found financial inequality to be correlated with worse overall outcomes in every category of social woe that he and his team cared to study. Infant mortality, child well-being, mental health, homicide, teenage births — all of these issues and many more are demonstrated to worsen as financial inequality increases. He can explain it all better than I can. It’s difficult to apply a causal relationship, but in-group psychology readily describes how stronger financial differentiation can cause negative social outcomes, and it would be much more difficult to argue reverse causation, that infant mortality causes income inequality.

GiniVsIMChartA bit of quick math with data from various internet sources allows us to home in on the scale of the problem. The following chart takes the last known Gini index for every country for which it is available and compares it to the 2010 infant mortality rate. A bit of simple math draws a trend line through the chart. The trend line demonstrates that, on average, the infant mortality rate can be expected to double with every 12.2 points of Gini index increase.

We can then check this against real-world numbers. For instance, the Gini index of the European Union is 30.4, and that of the US is 45, the increase being 14.6. That trend line suggests that the increase in infant mortality should be around 2.3x. The actual numbers (3.4 and 6.81, respectively) find the difference to be a 2x increase, suggesting that we’re in the right ballpark.

Even with this back-of-the-napkin math, we can identify that the difference between social inequality in the US vs. the European Union is responsible for somewhere in the area of fourteen thousand infant deaths per year in the US. This doesn’t count the increase in murder rate, poor health care, or any other form of death that is increased, and it doesn’t even touch upon the increase in human misery.

Income inequality has been creeping up on us for decades, and the historical answer to it is to overthrow the nobles and cut their heads off. Before it all gets that bad, I’d like to suggest a less extreme form of remediation.

Calculating the Gini index for a large population is challenging because it involves collecting the records for millions of individuals and deciding whether or not they count as income earners. For a corporation, however, calculating the Gini index is comparatively effortless. Skip the rest of this paragraph if you don’t care about math. For the rest of you, take all of the income earners in the company and sort them from least well-paid to most well-paid. For each person, add their pay in pile A, and put the amount of money they would be making if everyone were paid equally in pile B. After each person is added to A and B, then add A into pile C and B into pile D. When you’re all done, the Gini index for the company is (D-C)/D.

Now that you have a Gini index for the company, you use this to determine the taxes for the corporation on a sliding scale. Companies that overpay their executives or underpay their employees will then be taxed extra to pay for the increase in infant deaths, poor healthcare outcomes, and mental health care caused by their pay policies. Either way, society wins.