Examining Fractures: "Good" Inequality Measures
The Gini Index and the 1%
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.
At minimum, a “good” inequality measure should increase as a number if inequality in a society increases. Economists broadly agree that any “good” inequality measure should not be dependent on who is earning, should distinguish between groups within the population, and should increase if you take from the poor to give to the rich. The popular “top 1% of earners” measure given much media attention, fails this last italicized principle, while the Gini Index satisfies it. Gini measures the hollowing out of the middle-class, while the 1% myopically focuses on the extremely wealthy.
In a related post, we covered measuring inequality through the Gini index and took a quick look at how it might be represented on a graph. More popularly you will see the “1%” inequality measure, or the amount of income held by the richest 1% of the country. In broad terms it is preferable to use the Gini Index because it looks at more groups than the 1%, which is a special case of what economists would call a “Kuznets Ratio.” The 1% Kuznets Ratio splits the total population into two groups: “rich” (the 1%) and “not rich” (the 99%). This is a good examination of the extremes, but it may fail to miss an important concept in economics for inequality called “The Dalton Principle,” or as I like to call it, “the Reverse Robin Hood.” According to the Reverse Robin Hood, an inequality measure should increase if one were to take income from a poorer group and give it to the richer group. Suppose a policy were to increase taxes on the bottom 20% of income earners but cut taxes for those who fall between the 60%-80% band of earners. Would inequality increase or decrease? It should increase. But the 1% Kuznets Ratio fails, because it only measures those transfers that occur at the highest extreme. Indeed, the Kuznets ratio would be unchanged by this Reverse Robin Hood, and the dynamics of increasing inequality would be missed. The Gini Index would not miss this, as it captures that transfer of income between those two groups of income earners.
Is Gini perfect? Of course not. Let’s assume we take from a household that falls into the 20%-40% income band and give it to a less poor household in that same band. Gini will miss that. But we can, given data, re-define the Gini to take into account these multiple groups of income earners. We cannot do that with the 1%, which only includes two ill-defined groups: the rich, and the not rich.
Let’s consider our group of Jenny, Janie, Marty, Chad, and Elon from the post on the Gini Index and the Lorenz Curve, and let’s consider how the 1% measure changes and the Gini Index changes through some simple math and how the graphs are changing. Remember that the Lorenz Curves measuring how unequal that group was look like this:
Mathematically, the 1% Kuznets ratio is simple with our five-person group. Elon in this case is the top 20% as well as the top 1% since he has the highest of the five incomes. We can take a simple ratio of Elon’s income to the total income of all five to get the 1% measure most are familiar with in the popular media
Which is to say that the top income earner receives 48% of the total economy’s income. Or we could take the ratio of Elon’s share to those below him on the income distribution to get
Or that is to say, Elon’s income is 92% of the total income share of Jenny, Janie, Marty, and Chad combined.
So let’s Reverse Robin Hood this bad boy.
Suppose I take $2 from Jenny, Janie, Marty, and Chad, and give it to Elon (I rob from the poor and give to the rich. I think that’s how that story went anyway). The Lorenz Curve will show a clear increase in inequality, and we can safely conclude our much-harder-to-compute Gini Index also increases as the distance from perfect inequality to our new inequality has increased at every point.
Very clearly the transfer of income from everyone else to Elon increases inequality. But what crazy kind of policy would do that? That just seems cruel and irrational to take from the not rich and give to the rich to increase their wealth. And in this case, we can recalculate the 1% income ratio to be
That is to say, Elon’s income is 127% of the sum total of Jenny, Janie, Marty, and Chad’s income. Ouch.
But what if the income transfer is not so clear? In this last Reverse Robin Hood, I’m going to take $4 from Marty’s $15 income and $0.50 from Elon’s $48 income, and distribute it such that Jenny now has $5.25, Janie now was $9.25, Chad now has $27, and Elon has $47.50. Just consider first the 1% measure, and that Elon has lost $0.40
Oh my God, you guys. We’ve solved inequality in our five-person group. The 1% are now holding less income share than they were before. Mission accomplished, hand me my ‘merican flag and aircraft carrier. Let’s end this. Blog post done. Awesome.
Oh wait. Except Marty lost $4 of his income. Maybe we should figure out if that had an affect on that inequality measure? Alright. I got a few minutes before lunch. Let’s get to it. Here are the Lorenz curves.
Now we have a measure problem. In some instances (Jenny and Janie) income has gone up, so the inequality measure should go down. But Mary’s has gone down, and Chad’s has gone up (and yes, Elon’s went down a bit). It is not clear that the distance from perfect equality is uniformly increasing or decreasing.
This post has gone on long enough, and I don’t think anyone wants me to whip out the Gini formulae, but the point is made that measuring inequality is difficult, and even in a simplified fable-economy of five people it can get complex very quickly. We need good measures that communicate clearly that when a number goes a certain direction, that means something. The 1% measure very clearly communicates that if it goes up then the richest of the rich are getting more income share. But to truly grasp an increase or decrease in inequality across many income groups, one must use the Gini Index, or a similar “good” measure.
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.