Is There a 'Great Gatsby Curve' in America?

The famous "Great Gatsby Curve" suggests that, on an international level, there's a positive correlation between inequality and immobility -- the bigger the gap between rich and poor in a given country, the more likely people are to stay in the class into which they were born.

Over at National Review, J.D. Vance raises some issues with the curve -- and, intriguingly, he makes a Great Gatsby Curve comparing different areas of America, using data from the recent study on mobility from the Equality of Opportunity Project. It's not as curvy as you might expect: