Is the relationship causal? You can easily think of reasons for spurious correlation: sprawl is associated with being in the sunbelt, with voting Republican, with having weak social safety net programs, etc.. Still, it’s striking.
Matt Yglesias adds additional data about what happens with kids who move into high density urban areas as well as a few other possible explanations:
So what drives this? The study does not really make a high-powered effort to draw strong causal inferences. But the study does show that kids who moved into a high-mobility area at a young age do about as well as the kids born in high-mobility areas, but kids who move as teenagers don't. So there seems to be a factor that isn't parent-driven. The authors report that tax policy, the existence and affordability of local colleges, and the level of extreme local wealth do not appear to be strong correlates of intergenerational mobility. Metro areas where the poor are geographically isolated from the middle class have less intergenerational mobility, while metro areas with more two-parents households, better elementary and high schools, and more "civic engagement" (measured through membership in religious and community groups) have more.So clearly it would be a mistake to over-interpret these data. But they do have one major policy piece embedded into them -- it makes absolutely no sense to subsidize sprawl as a positive good. It may not be worth it to try and discourage it, but generally there are a lot of laws (think zoning laws and car centered transportation grids) that implicitly subsidize sub-urban communities.
There are still pieces to be considered -- like does the poorest quintile do objectively better or worse in the low social mobility environments (you can justify low mobility if everyone is better off as a result). However, the two extremes in Paul Krugman's graph are Atlanta (low density and mobility) and Los Angeles (high density and mobility). It's not 100% clear that it is better to be poor in California than Georgia, but it isn't like it is far worse in California so far as I can tell. Maybe Mark can weigh in here?
But this all points to a big picture that urban planning is actually a much bigger deal than I had previously realized.