In yesterday’s post, we showed how inequality in the U.S. has increased by 18% over the previous 40 years according to the most commonly cited measure of inequality, the Gini Coefficient. In tomorrow’s post what we’d like to see from an inequality statistic in an ideal world. Today, I wanted to illustrate how this measure has changed within various subcategories.

According to this Gini Measure (which I emphasize we will learn more about in upcoming posts) it appears that the increase in inequality has occurred within all ethnic classes. Inequality among whites increased at 17.8% since 1967 while among blacks inequality actually increased less (by 11.3%) and among hispanics it increased more (by 22.3%). If there is any ethnic trend apparent it seems to be that there is a convergence of inequality across ethnic groups. Whereas in the beginning of the period the Gini for Hispanics was lowest at .373 and highest for blacks at .432 (about a 16% difference between groups, today all ethnic groups seem to be experience “equal inequality” with only a 5% gap between the most unequal distribution (for blacks) and the least (hispanics).

Now to make this claim more rigorous one would have to do much more serious work than this. Does this “convergence” raise any interesting questions? Whatever has been driving inequality changes seems to be doing it for all ethnic classes. What can you NOT deduce from this information? That income differences across ethnicities is shrinking. It could very well be the case that white incomes are increasing faster than black incomes, but that the dispersion in white incomes is also increasing faster than the dispersion in black incomes. We’d have to couple this information with other income data to say more. The reason I bring this up is that income inequality data, particularly focusing on a single metric, are not sufficient statistics (to use the parlance of statisticians) for identifying many underlying social phenomena.

For those of you forgetting what we mean by a sufficient statistic, it is easiest to show you with an example. Suppose I have an underlying population of two numbers. I know that one of them is the number 7. In this case, if I am told that the arithmetic mean, the average, is 9, then this mean is sufficient to tell me everything else about the distribution without actually needing to be given the number. In other words, I know that the other number must be 11.

OK, so in my view this post was really not all that interesting. This promises to change very soon (I listen to too much talk radio, where they constantly promise you that something really interesting will be delivered to you after the next commercial break).

Here are the previous posts in this series:

• Understanding the Genie in the Bottle, Volume I (showing the overall Gini Index and raising some questions about how to think about it)
• These three posts (here, here and here) show the illusory nature of even the most basic agreed upon properly measured measures of inequality, the distinction between actual consumption and potential consumption, and some ethical questions raised by blindly looking at the data
• This post is an outline of my lecture notes on the basics of measuring inequality.