### Asymmetrical Information - Megan McArdle

02.06.137:13 AM ET

# Department of Awful Statistics: Income Inequality Edition

Think the middle class is disappearing? Look again.

"When I was growing up in Canada," says Jon Evans of Techcrunch, "I was taught that income distribution should and did look like a bell curve, with the middle class being the bulge in the middle. Oh, how naïve my teachers were. This is how income distribution looks in America today"

"That big bulge up above? It’s moving up and to the left. America is well on the way towards having a small, highly skilled and/or highly fortunate elite, with lucrative jobs; a vast underclass with casual, occasional, minimum-wage service work, if they’re lucky; and very little in between."

This seems to be the fear of the week.  Something--outsourcing, robots, immigration, or maybe just the greedy rich hoarding all the good jobs in their massive bank vaults--is stealing all the prosperity from the bottom of the income distribution.  Pretty soon, those people will be reduced to begging in the streets while the rich stride past them with their robot servants in tow.

And it's certainly a striking graph.  So striking that I was initially very surprised.  Income is one of those things that follows a pretty predictable distribution: big bulge at the low end, trailing off to a few households at the top.  Has American income inequaltiy gotten so bad that it's actually broken a statistical regularity?

Er, no.  Look closely at those last two brackets.   Now look at the brackets immediately to the right of them? What do you notice?

Probably, you notice the same thing that immediately struck me: the last two brackets cover a much, much wider income band than the rest of the brackets on the graph.

Each bar on that graph represents a \$5,000 income band: Under \$5,000, \$5000 to \$9,999, and so forth.  Except for the last two.  The penultimate band is \$200,000 to \$250,000, which is ten times as wide as the previous band.  And the last bar represents all incomes over \$250,000--a group that runs from some law associate who pulled down \$251,000 last year, through A-Rod's \$27 million annual salary, all the way to some Silicon Valley superstar who just cashed out the company for a one time windfall of hundreds of millions of dollars.  Unsurprisingly, much wider bands have more people in them than they would if you kept on extrapolating out in \$5,000 increments.

In 2011, the \$195,000 to \$199,999 segment had 312,000 households in it.  If you multiply by ten, you get 3 million households.  But the \$200,000 to \$250,000 segment had just 2.2 million households.  In other words, as incomes rise, the number of households-per-\$5,000-of-income falls--just as Jon Evans learned it should, in those long ago Canadian days.

To put it another way, the apparent clustering of income along the rich right tail of the distribution is just an artifact of the way that the Census presents the data.  If they kept running through \$5,000 brackets all the way out to A-Rod, the spreadsheet would be about a mile long, and there would only be a handful of people in each bracket.  So at the high end, where there are few households, they summarize.

Meanwhile, there's no evidence that the middle class is getting poorer.  Here's the Census's Households by Total Money Income table, summarized for 1967 through 2011, which shows the percent of households in each bracket. (Figures are in inflation-adjusted dollars)  As you can see, there's no big movement "up and to the left", other than a slight expected income downshift during the Great Recession.

However, Jon Evans is right about one thing in the chart he linked: income does not, quite, follow the skewed bell curve that you'd expect.  Look at the bars around nice, round income numbers like \$50,000 or \$100,000.  Suddenly, instead of falling slightly as you'd expect, they climb back above their leftward neighbors.  Someone is rounding off to 5's and 10's--either the bosses who set salaries, or the folks who report their incomes.  Probably both.

So there is an interesting statistical anomaly here.  But it's not a result of rising American income equality.  It's a product of an entirely different historical accident: the fact that human hands have five fingers.

This post has been updated to add the historical figures.