Wednesday, July 4, 2018

A Lake Woebegone Problem

Back in 2001, when we were colleagues in the Economics Department at the University of Montana, Tom Power and I wrote a book - Post Cowboy Economics - in which we tried to pick apart the relationships between environmental protection, natural resource exploitation and family incomes in the Mountain West. One of the troubling questions that we had to confront was why incomes in places like Missoula were so much lower than they were in the rest of the United States. And the answer, at least in part, lay in geographical differences in the cost of living (COL for short).

The simple fact was that when we compared the incomes of Missoula families to the incomes of other  Americans, those other Americans were living predominately in pretty large cities.  And while they typically took home bigger pay checks than Missoulians, they also had higher living costs, particularly when it came to housing. In fact, when Tom and I did the math, to a pretty substantial degree, the earnings disadvantage from living in Missoula and not, say, Los Angeles, was offset by the lower cost of living in the Garden City.

Now flash forward to today’s Missoulian, which reports that the Missoula Economic Partnership has just released a study of the city’s competitiveness in attracting new business, which includes, among its findings, that while Missoula families have incomes below the national average, their living costs, rather than being low, are above the national average. Evidently, what worked for Tom and me a couple of decades ago just isn’t working any more.

Or is it? After all, don’t most American still live in big, expensive cities and pull down wages commensurate with those high living costs?

Well, yes they do, but here’s the problem: when we talk about average earnings and the average cost of living, we’re talking about different kinds of averages. US average family earnings are calculated across all the families in the nation, while average cost of living is calculated across all the cities in the nation, regardless of each city’s population. That means that New York City, with a COL index of 166, and Missoula, with a COL index of 103, count equally in computing the US average COL (100), even though New Yorkers outnumber Missoulians by about 100 to 1. If big, high COL cities carried more weight in computing the national average, that average would be higher, and Missoula would come in below, not above it.

Here’s an entirely hypothetical numerical example of the problem. Suppose we have three cities; call them Big, Medium and Small.  There are 300,000 families in Big that earn an average of $57,150 per year and face a COL index of 120.  There are 30,000 families in Medium, with an average income of $50,000 and a COL index of 105, and 20,000 families in Small, with average incomes of $35,700 and a COL index of 75.

Now the first thing to notice here is that real incomes (that is, income adjusted for the cost of living) are the same in all three of these communities. $35,700 goes just as far at the store in Small as $50,000 does in Medium and $57,150 does in Big. 

The next thing to notice is that the average COL index for these three cities is 100 (that’s the average of 120, 105 and 75). So by that calculation Medium has a cost of living 5 percent above the national average and Big's COL is 20 percent above the average. Viewed in terms of families instead of cities, the situation is a little like Lake Woebegone's. When it comes to cost of living, nearly all families - 330 out of 350 thousand - are above average.

The last thing to notice is that if we average the incomes of all 350,000 families living in the three cities, the result is $55,790, so income in Medium is below the national average.*  And there you have it. Medium, like Missoula, has below average income and above average living costs. That sounds like there’s a significant economic disadvantage to living in Medium. But there’s not. In this example, at any rate, real incomes in Medium are the same as real incomes anywhere else.

To be clear, I am not claiming here that the difference between average income in Missoula and the rest of the country can be entirely accounted for by differences in living costs.  But there is a sort of Lake Woebegone problem with the way the MEP report measures COL. The fact is that for most Americans, who inhabit places like San Francisco or Chicago or Seattle or New York, Missoula would be a relatively cheap place to live, and if they were contemplating coming to Missoula to take a job in some spanking new startup, the cost of living here would be the least of their worries.

*To calculate average family income for the 350,000 families, you need to compute the total income they earn and divide by 350,000. The total income earned by families in any city equals (average income) x (number of families), so for Big, for example, total income is 300,000 x $57,150. For all three cities the total is (300,000 x $57,150) + (30,000 x $50,000) + (20,000 x $$35,700). Divide that number by 350,000 and you get $55,790.