Scott Sumner  

America: A dromedary, not a Bactrian camel

The Widerquist-Caplan UBI Deba... Russ Roberts's Wonderful Loaf...

It's now becoming fashionable to describe America in binary terms, such as red and blue, coastal and middle, affluent and struggling. In my view these generalizations are often misleading.

Let's take the case of income distribution. If you listened to many pundits, you would assume that America is divided into two groups---struggling non-college educated people who shop at Walmart, and affluent professionals who shop at Whole Foods. These articles create an image of a two-class society, that is, an income distribution that looks like the back of a Bactrian camel:

Screen Shot 2017-05-03 at 1.37.35 PM.png
In fact, America's income distribution is one hump not two. The vast majority of people are neither highly affluent nor struggling to survive. Indeed the largest group (of middle aged people) is middle class, people such as teachers and other state and local workers, unionized industrial workers, pharmacists, tax preparers, skilled carpenters, nurses, plumbers, electricians, ordinary office workers, miners, small businesspeople, typical (full time) farmers, long haul truckers, and many others. Here's the actual income distribution---do you see two humps?

Screen Shot 2017-05-03 at 1.23.14 PM.png
Neither do I.

These binary descriptions of America tend to mislead us. The left wonders why inequality is not a bigger issue. Maybe because the huge group in the middle isn't sure whether the Dems want to redistribute money from the rich to them, or from them to the poor.

Interestingly, back in 1970 we did live in a Bactrian camel world:

Screen Shot 2017-05-03 at 1.26.23 PM.png
We moved to a dromedary world when China went from being poor to being middle income:

Screen Shot 2017-05-03 at 1.28.34 PM.png
See that $60,000 figure in the lower right corner? I feel very lucky right now. If you are a typical reader of this blog, you may feel that way too.

Why do pundits mislead us? Perhaps because they like to think about the world in terms of stories. This boring post doesn't have an interesting story to tell.

PS. A comment on the median income in the US---which might seem rather low. That figure includes lots of young people working part time, as well as lots of retired people picking up a few extra bucks. Middle-aged full time workers tend to earn more, and of course family incomes tend to be higher than individual incomes.

Comments and Sharing

CATEGORIES: Income Distribution

COMMENTS (13 to date)
ThisPers0n writes:

The income distribution may be one hump in the middle, but being on the left hand of the distribution is far greater a misery than being on the far right hand side of the income distribution is a pleasure, which I think justifies talking about the poor more than the rich.

Sam writes:

While I agree with the point that the income distribution is unimodal, I'm not sure I believe your plot was an actual histogram of incomes, as opposed to some smoothed version or a fit to some parametric family of distributions. First of all, it seems to show 200K people with an annual income in some (presumably narrow, if the plot is to be believed) bin around exactly $1000. Doesn't seem plausible. Second of all, it seems to use implausibly narrow log-dollar bins for income. It beggars belief that you wouldn't see at least some round-number effects if the bins are actually that narrow.

Am I off base here? Genuinely curious if any commenters are familiar with the raw data set here.

This is mostly a nitpick, as Scott's actual point is obviously correct. It's just a pet peeve of mine when media presents plots of models and claims they are plots of data.

Scott Sumner writes:

Sam, Good question, I'm not sure if there was any smoothing of the data.

Nick writes:

It's entirely possible to have a two-class society in which the income distribution appears to be unimodal.

Here's a simple illustration that looks very similar to the global income distribution in 2000.

Thomas Hutcheson writes:

Doesn't looking only at wages and salaries incomes sort of ignore the phenomenon being worried over? And was the worry ever about two humps as opposed to the two tails getting farther apart or the top tail receding from the median?

Ironman writes:

I can confirm that the chart is "smoothed". It was generated using the actual cumulative distribution of income from actual data reported by the U.S. Census Bureau, which was then modeled using a best-fit logistic function. That model was then used to generate the log-normal bell curve shown in the chart.

If this chart had been generated directly from the binned data, it would show much more of a sawtooth pattern attributable to the kind of rounding effects that Sam describes, but more significantly from noisy variation in the raw data, which would never-the-less generally trace the indicated distribution.

The best way to think of the chart is that it's the equivalent what you see when you look at a faraway mountain. When you get closer, you see the jagged edges, but it still follows the general shape that you saw from far away.

Scott Sumner writes:

Nick, The problem there is that the two classes are then not defined in terms of income. So it's OK to talk of two groups, as long as you understand that (for instance) lots and lots of Walmart shoppers are richer than lots and lots of Whole Foods shoppers. And in a way, that's my point.

Thomas, It seems to me that if you are worried about the two tails getting further apart, you are actually describing a three class society. (As long as the middle was bigger than each tail.)

Thanks Ironman, It sounds like that smoothing would not affect the number of major "humps", is that right? Do you have a picture of the un-smoothed data?

Ironman writes:

The smoothing that was done won't affect the number of humps - the original cumulative income distribution that it was built from was a "Single-S", so it would only produce a single major hump. Here's a post from 2016 (showing income distribution data for 2015) that shows the kind of cumulative income distribution that we used to build the chart, where you can see how the model fits to the raw data. The main difference between it and the data from 2012 is that the incomes have shifted to the right.

I do have an example of what the raw data would look really like if it weren't smoothed, but it's for the world individual income distribution for 2013. I would describe it as a single hump with a slight bulge.

This post has a chart featuring the smoothed cumulative income data for the world, the U.S. and China. The Chinese cumulative income distribution comes closest to forming a "double-S", which is what it would really take to have a bimodal double-hump distribution, but its really more of an "elongated-S".

Lorenzo from Oz writes:

While it is useful to remind folk that income distribution is rather bell curve like, given the strong territoriality of voting patterns, it is hardly surprising that income is not a good differentiator.

mbka writes:


I am stunned by how well the raw data fit the model. It's as if this were a result from physics.

Ironman writes:

mbka: I think you mean vice-versa - it's a lot easier to fit models to raw data than the other way around! In this case, we also assumed that the income distribution naturally follows a lognormal distribution, which helped to better fit the model to the data.

mbka writes:


that's an interesting a philosophical point! Ideally, the mental model should come before the raw data are compared to it, i.e. one should have a clear theory as to why one would expect such a distribution, and this theory is then tested by comparing data to it. But I do agree that in reality data usually come first, and then one starts wondering which model could explain (or fit) the data.

Nick writes:

@Scott Sumner

Or, perhaps, income is an imperfect proxy for wealth (which is true). And the peaks for the respective income distributions need not be that close to each other, so there may not be much overlap. Or, the income distribution of the upper class may be a left-truncated log-normal distribution, the income distribution of the lower class a right-truncated log-normal distribution, and they meet in the middle, so that every lower-class individual makes less money than every higher-class individual, but the overall income distribution appears log-normal.

I'm making this point not because I think you're wrong, but because I don't think we can draw any substantive conclusions from the modality of the distribution of income about the class structure of the United States.

Comments for this entry have been closed
Return to top