That would suggest that any two American metropolitan areas with similar populations ought to have very similar average incomes. I decided to check West’s assertion by choosing a couple of US “Metropolitan Statistical Areas” and comparing them with the help of census figures.
Not all of 2010 census statistics are available yet, so I used figures from 2000 to compare metropolitan Denver — which at that time had a population of 2,157,756 — and metropolitan Pittsburgh, whose population was 2,431,087. According to West and Bettencourt’s theory, Pittsburgh, with an advantage of 12.7 percent in population, should be a little wealthier per capita than Denver.
The median household incomes, however, were actually the other way around, if the Census was accurate. Median household income in the Pittsburgh area was $35,908, while Denver’s figure was $39,910, or 11.1 percent higher.
That might be a fluke, of course. So I compared two smaller metro areas of almost identical population; Madison, Wisconsin, whose population in 2000 was 501,774, and Augusta-Richmond County, Georgia, South Carolina, home to 499,684 people. The census identified Madison’s median family income as $55,159 and Augusta’s as $44,491, or 24 percent less.
The general rule about population size and average income, as spelled out in Lehrer’s article, didn’t hold true, at least in those two comparisons. Perhaps other factors needed to be included, such as the geographical spread of the metro area, age of the city, the area’s racial composition, or variations between one region and another. Something must have been left out. (italics added)
But let’s return to West and Bettencourt.
Why return to West and Bettencourt if their initial prediction appears to be so wrong? Indeed, "Something must have been left out." But it's all interesting anyway.