Is Economic Activity Really “Distributed Less Evenly” Than It Used To Be? An Attempt To Actually Define That Question.

Ross Douthat wrote a recent column about how we need to break up liberal cities because they’re “bloated megalopolises” or something. I saw Noahpinion Tweeted this in response:

In my view, there’s at least two other problems that we should consider first:

— What exactly does it mean for “economic activity” to be “evenly distributed”?

And (if we don’t have a good answer to that question):

— How do we know how much more “evenly distributed” economic activity used to be, if at all?

Now I don’t know of any historical data source with “economic activity” by “town”, but the Bureau of Economic Analysis API does have county-level wage and salary (“WS_CI”) and population (“POP_CI”) estimates from 1969 to 2015. I don’t know the quirks of this data set and one might choose other metrics. Looking at per capita wages by county should at least suffice for a conceptual illustration of how we might go about answering this question: How “unevenly” is this economic activity distributed?

Update/Clarification: “Wages” here are by place of work, “population” here is by place of residence. I was thinking of “wages” as a proxy for “amount of money sloshing around” anyway, but it’s a distinction worth keeping in mind. More to come.

Update/Clarification 2: For versions of these charts based on earnings/job or personal income/capita, go to http://xenocrypt.github.io/CountyIncomeHistory.html

First, imagine if you had a bar chart with every county in the United States sorted from lowest to highest by wages per capita, with the width of each bar proportional to the population of the county. Here’s what that looks like for 2015, for example:

(I chose this y-axis because technically Butte County, Idaho is recorded as having per-capita wages of over $265,000, even though it’s much too small to actually see.)

One nice thing to note about this graph is that the sum of the areas of the bars — that is, the integral of the shape — is proportional to the national wages per capita. Anyway, since it’s already basically a continuous curve, you lose little information if you collapse the counties into groups:

Since it’s a curve instead of a bar chart, we can compare it to 1969, the earliest year in the data set, using the (urban consumer) CPI to adjust for inflation:

While that’s interesting, it’s not quite a comparison of their distributions of the two years which is the ostensible point of all this. That graph shows both the distributions and levels of wages per capita in both years. In order to compare the curves as distributions, we have to divide each one by its level, or by national wages per capita. That is, we have to normalize the curves so they both integrate to one.

In fact, whenever anyone talks about “clustering” and “even distributions”, they’re mostly really talking about ways of comparing monotonic curves with integral one, whether they realize it or not. “Even distributions” are flat curves like this:

“Clustered distributions” are curves that are lower on one side and higher on the other, like this:

(“A party’s voters should get more or less seats based on the shape of the monotonic curve with integral one they can be arranged in” might sound like a very silly belief, but it is equivalent to the common mantra that you deserve to lose if your voters are “too clustered”.)

If wages were less “evenly distributed” by county in 2015 than in 1969, once we’ve normalized, the 2015 curve should be noticeably higher on the right and lower on the left. So, just how vastly did “clustering of elite wages” and so on increase from 1969 to 2015, according to this data set at least?

Somewhat but perhaps not as vastly as you might think:

The 2015 curve really is a bit higher on the right and lower on the left, especially noticeable at around 90%. That means the highest-wage counties really did take a slightly larger share of national wages in 2015 than in 1969. Specifically, in 1969 the top 10.4% of counties by population accounted for about 20.6% of national wages. By 2015, after nearly half a century of geographic hyper-agglomeration, the top 10.6% of counties by population accounted for about…23.4% of national wages.

That’s about it as far as I can tell. There might be good reasons to orient national policy around making the 2015 curve look like the 1969 curve (if anyone would even notice, since as you can see the distributions appear nearly identical for the bottom 89% of counties). But it’s not like the top 10% of counties used to earn 12% of national wages and now they earn 40%.

That’s not to say there haven’t been winners and losers, especially relatively. Genessee County, Michigan (Flint) had per capita wages of over $3,000 in 1969 dollars, which put it in the top quartile by population. Its 2015 per capita wages of about $15,000 put it in the bottom quartile. On the other hand, Arapahoe County, Colorado had per capita wages of about $1,500 in 1969 dollars, which put it in the bottom quintile or so, and its 2015 per capita wages of about $33,000 put it in the top quintile. But just because Genessee County used to be high-wage and now it’s low wage that doesn’t mean there’s generally more “clustering”. The 1969 and 2015 distribution curves look broadly similar to how they would look if every county was making 10.4 times its nominal 1969 wages per capita.

Update/Clarification 3: Arapahoe County isn’t a great example since it actually declined in residential income per capita relative to the country. I should have used something like Larimer County, Colorado where the residential income per capita went from $21,343 in 1969 (bottom quartile) to $45,318 in 2015 (top half).

Now, there are a million reasons this might not be right — it’s only wages, not total income, I’m not accounting for migration and demographic changes, and I don’t know if the BEA data set does a good job of including the very highest-level wages that might be driving some inequality.

My main goal in writing this piece is not to promote the specific conclusion (as striking as I found that last graph) but to promote the general approach to thinking about distributions. Distributions are curves, so if you’re talking about distributions, try to think about and compare the whole curve as much as possible.

I wrote this very quickly (for me) so feedback is welcome.