Visualizing Income Distributions

Clive Crook describes a very interesting visualization exercise for understanding income distribution. The article is in the latest, September 2006, Atlantic Monthly. An excerpt is available on the website. Here’s a long quote that starts the story and describes the visualization.

In 1971, Jan Pen, a Dutch economist, published a celebrated treatise with a less-than-gripping title: Income Distribution. The book summoned a memorable image. This is how to think of the pattern of incomes in an economy, Pen said (he was writing about Britain, but bear with me). Suppose that every person in the economy walks by, as if in a parade. Imagine that the parade takes exactly an hour to pass, and that the marchers are arranged in order of income, with the lowest incomes at the front and the highest at the back. Also imagine that the heights of the people in the parade are proportional to what they make: those earning the average income will be of average height, those earning twice the average income will be twice the average height, and so on. We spectators, let us imagine, are also of average height.

Pen then described what the observers would see. Not a series of people of steadily increasing height—that’s far too bland a picture. The observers would see something much stranger. They would see, mostly, a parade of dwarves, and then some unbelievable giants at the very end.

As the parade begins, Pen explained, the marchers cannot be seen at all. They are walking upside down, with their heads underground—owners of loss-making businesses, most likely. Very soon, upright marchers begin to pass by, but they are tiny. For five minutes or so, the observers are peering down at people just inches high—old people and youngsters, mainly; people without regular work, who make a little from odd jobs. Ten minutes in, the full-time labor force has arrived: to begin with, mainly unskilled manual and clerical workers, burger flippers, shop assistants, and the like, standing about waist-high to the observers. And at this point things start to get dull, because there are so very many of these very small people. The minutes pass, and pass, and they keep on coming.

By about halfway through the parade, Pen wrote, the observers might expect to be looking people in the eye—people of average height ought to be in the middle. But no, the marchers are still quite small, these experienced tradespeople, skilled industrial workers, trained office staff, and so on—not yet five feet tall, many of them. On and on they come.

It takes about forty-five minutes—the parade is drawing to a close—before the marchers are as tall as the observers. Heights are visibly rising by this point, but even now not very fast. In the final six minutes, however, when people with earnings in the top 10 percent begin to arrive, things get weird again. Heights begin to surge upward at a madly accelerating rate. Doctors, lawyers, and senior civil servants twenty feet tall speed by. Moments later, successful corporate executives, bankers, stock­brokers—peering down from fifty feet, 100 feet, 500 feet. In the last few seconds you glimpse pop stars, movie stars, the most successful entrepreneurs. You can see only up to their knees (this is Britain: it’s cloudy). And if you blink, you’ll miss them altogether. At the very end of the parade (it’s 1971, recall) is John Paul Getty, heir to the Getty Oil fortune. The sole of his shoe is hundreds of feet thick.

This is true in every economy, but in some more than others. Back when Pen wrote his book, incomes were already more skewed in America than in Britain. Over the past thirty-five years, and especially over the past ten, that top-end skewness has greatly increased. The weirdness of the last half minute of today’s American parade—even more so the weirdness of the last few seconds, and above all the weirdness of the last fraction of a second—is vastly greater than that of the vision, bizarre as it was, described by Pen.

I think this kind of stuff is brilliant. I remember reading somewhere that about 20 percent of people in the United States think they are in the top 1 percent of the income distribution. So a lot of confusion about income distribution in America is due to perception. Scott Winship echoes this idea at the Democratic Strategist while discussing a recent paper by economist Jacob Vigdor.

Finally, and perhaps most importantly for the Kansas question, Vigdor’s theory predicts that if voters compare themselves to people who are in a similar economic situation, then working- and middle-class voters should be less likely than poor or rich voters to support the Democrats. That’s because of the particular way that income is distributed in the U.S.

As income increases from $0 to a working-class income, the number of people at each income level gets larger and larger. That means that more often than not, when people in this income range (“the poor”) compare themselves to other poor people, they will find that there are more poor people doing better than them than worse. They will thus tend to support redistribution.

On the other hand, as income increases from a working-class income to an upper-middle-class income, the number of people at each income level gets smaller and smaller. When people in this income range (“the working and middle classes”) compare themselves to other similarly-situated people, they will find (more often than not) that there are more working- and middle-class people doing worse than them than better. Consequently, they will tend to oppose redistribution.

Finally, as income increases from an upper-middle-class income to an upper-class income, the number of people at each income level continues to get smaller and smaller, but the decline is not very steep. When the rich compare themselves to their peers, they will tend to find that there are nearly as many people doing worse than them as there are doing better. The rich will tend to be indifferent toward redistribution.