04 May 2011

Two Charts on Inequality

The Economist: Free Exchange | R.A. | Rich and poor, growing apart

Think income inequality growth is primarily an American phenomenon? Think again:


American society is more unequal than those in most other OECD countries, and growth in inequality there has been relatively large. But with very few exceptions, the rich have done better over the past 30 years, even in highly egalitarian places like Scandinavia.
I don't have much to say about this chart in particular, but I do have something to say about the metric it uses.

I do not like the Gini coefficient. Well, specifically I do not like it for income distributions. It's served me well in some Machine Learning applications, but that is not the point.

(1) Contra some libertarians, I do believe relative income levels are worth considering, but I still think they are not as important as absolute income levels. These sorts of comparisons of Gini coefs completely disregard absolutes. For instance, even a purely Pareto improvement can result in a "worse" Gini coefficient.

(2) Measuring changes in Gini over time is especially tricky because it ignores lifetime effects. The median person ten years ago is not the same as the median person now. I would hope that there is inequality between me-right-now, while I'm a research assistant, and me-in-ten-years, when I've got my doctorate.

(3) Gini coefs reduce a curve to a scalar value. Indeed, that's their whole point. But that unavoidably entails a huge loss of information. Be wary.

(4) This isn't specific to the Gini coefficient, but I am distrustful of measures of household rather than individual income. Actually, distrustful isn't the right word. I find them irrelevant for normative purposes. And even for positive purposes, they are fraught with complications, especially when making comparisons through time.

(5) Gini coefficient charts are always presented, often explicitly, with an interpretation that higher is worse and lower is better.

But — and this is my main point — that isn't true. A society with Gini=1.0 would be terrible. But a society with Gini=0.0 would also be terrible.

Some people are more talented than others. Some are more conscientious. Some place higher value on income than leisure, or vice versa. These people should be earning different incomes. That will make the Gini coefficient greater than zero.

I have a particular cousin who is a narcissistic, profligate wastrel. He is Aesop's grasshopper. He is Sumner's One Marshmallow Eater. We all know someone like this. Do you want that person to have the same income as you? As Sergey Brin? As JK Rowling? That will make the Gini coefficient greater than zero.

What is the "American Dream" to you? To me it is the goal of providing my children with a more comfortable life than I had. I believe many others share my goal. For this to be possible the correlation in intergenerational income must be positive. (I don't want peoples income to be perfectly correlated with their parents — my wastrel cousin's father is hard-working and has achieved much financially, for instance — but it shouldn't be strictly independent either.) That in turn requires some people will have higher incomes than others, and that will give us Gini > 0.

So the "desired" Gini coefficient is somewhere between 0.0 and 1.0. I don't know where it is. But I do know that you can't assert that a Gini cofficient rising from x1 to x2 is bad unless you know the "correct" level is less than x1.

Robert Frank and I arent going to agree what that right level is. He would guess it's higher than I would. Neither of us is right. (Or rather, neither of us is Right.) There is no single, correct, moral value for a Gini coefficient.

And even if one of us were right the "correct" value changes over time. Technology will change. Culture will change. Our ability to produce and to consume will change. That will lead to a different level of inequality, maybe for the better, and maybe for the worse.

(A world with a Cure for Cancer will see, I would imagine, better compensated oncologists.  Ceteris paribus, that will lead to a higher Gini coef.  And I'm cool with that.)

Furthermore why the "correct" level changes through time matters. Has inequality changed because of fiddling with the the tax code to advantage the relatively wealthy? (*Ahem* mortgage interest deduction *ahem*) Is it due to assortive mating? Immigration? The first we ought to shut down, the second I would say we ought to ignore, and the last we ought to celebrate.

All that gets lost when people start fretting about the US having a Gini coefficient of .37 while Sweden's is .27.

~ ~ ~

Here's a chart I find much more interesting.

It still has drawbacks, of course, but overall I find it much more illuminating that one based on Gini coefficients. (This chart was posted back in January and I never got around to commenting on it.)
Economix | Catherine Rampell | The Haves and the Have-Nots

I had a review this weekend about “ The Haves and the Have-Nots,” a new book by the World Bank economist Branko Milanovic about inequality around the world. My favorite part of the book was this graph, next to which I actually wrote “awesome chart” in the margin:


Here the population of each country is divided into 20 equally-sized income groups, ranked by their household per-capita income. These are called “ventiles,” as you can see on the horizontal axis, and each “ventile” translates to a cluster of five percentiles. [...] Now on the vertical axis, you can see where any given ventile from any country falls when compared to the entire population of the world.

Brazil’s bottom ventile — that is, the poorest 5 percent of the Brazilian population, shown as the left-most point on the line — is about as poor as anyone in the entire world, registering a percentile in the single digits when compared to the income distribution worldwide. Meanwhile, Brazil also has some of the world’s richest, as you can see by how high up on the chart Brazil’s top ventile reaches. In other words, this one country covers a very broad span of income groups.

Now take a look at America.

Notice how the entire line for the United States resides in the top portion of the graph? That’s because the entire country is relatively rich. In fact, America’s bottom ventile is still richer than most of the world: That is, the typical person in the bottom 5 percent of the American income distribution is still richer than 68 percent of the world’s inhabitants.

Now check out the line for India. India’s poorest ventile corresponds with the 4th poorest percentile worldwide. And its richest? The 68th percentile. Yes, that’s right: America’s poorest are, as a group, about as rich as India’s richest.

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