In 2013, Chetty and a phalanx of economists produced a one-of-a-kind study on intergenerational mobility—that is, the odds that low-income households can work their way into the middle class and above. Comparing social mobility by metro area, they discovered that the American Dream is alive in many cities, like Salt Lake City, Pittsburgh, and San Jose. But it's dying in others, particularly across the southeast and the Rust Belt, where cities are spread out, segregated, and blighted by bad schools and broken families.

But many young people aren't choosing to move to a city because they've heard that a Harvard economist said it was really good for intergenerational mobility. They move for more short-term financial reasons. They want to live affordably. As Kolko explains, "the five most affordable markets are in Ohio, Indiana, and upstate New York... the South is relatively affordable too."*

But now look what happens when you compare Chetty's map of economic opportunity (red is bad) ...

Economic Opportunity, by Location

Chetty

with Kolko's map of affordable housing by city (red is still bad).

Percent of For-Sale Homes That Are Affordable With a Median Household Income

Kolko/Trulia

Climbing the income ladder is easiest in the west and northeast. But finding an affordable home is easiest in the south and the Great Lakes/Appalachian region. California, home to six of the seven least affordable housing markets, has four of the 11 best cities for upward mobility.

If you plot the 50 largest metro areas by Kolko's affordability metric and Chetty's absolute mobility metric, the inverse relationship is unavoidably clear. Upwardly mobile cities have more expensive homes.

Percent of Homes Millennials Can Afford vs. Social Mobility

There are the only three cities in the United States with (a) at least 50 percent of houses affordable to middle-class Millennials and (b) a top-10 finish in Chetty's mobility calculations. These are the outliers: Pittsburgh, Minneapolis, and Salt Lake City.

In the graph below, I've isolated the 10 best cities for upward mobility and arranged them by affordability to give you a sense of how steep the drop-off is after our trio of outliers. Less than half of all homes are affordable to middle-class Millennials in Boston, NYC, and across California's major metros, all of which are sterling cities for working your way into and past the middle class.

Top 10 Cities for Social Mobility, Ranked by Affordability

Chetty/Kolko

Here are the 10 major U.S. cities with the worst upward mobility by Chetty's measure. I've arranged them by Kolko's affordability metric again. What stands out immediately: More than half of the houses in all of these cities are affordable for young families. (These are all major metros, and the worst places for upwardly mobility could well be in exurban and rural America.)