Greater population density drives innovation and productivity. Albeit a theory, urbanists rally around the idea. I'm skeptical of the claim. The conclusion supports the preferred geography, raising a red flag. Some actual research from Wei Pan suggesting, perhaps, I'm wrong and urbanists are correct:
"If you think about productivity, it’s all about ideas, information flows, how easily you can access ideas and opportunities," Pan says. "We believe that the interaction mechanism is what drives the productivity of the city."
The study tells a compelling story about the magic of cities, solving a long-standing mystery. I remain unimpressed. A bit further down in the article from The Atlantic Cities:
"What really happens when you move to a big city is you get to know a lot of different people, although they are not necessarily your 'friends,'" Pan says. "These are the people who bring different ideas, bring different opportunities, and meetings with other great people that may help you."
Emphasis added. Moving to a big city is a very different experience from being born in a big city. From the Center for an Urban Future:
Entrepreneurship has been a proven ticket to financial empowerment and economic mobility for countless immigrants—a fact that the Center documented in our 2007 report, “A World of Opportunity.” In that study, we showed that massive numbers of immigrants in New York, Boston, Houston, and Los Angeles have turned to entrepreneurship and in doing so have transformed neighborhoods as well as their own economic fortunes. Some of these entrepreneurs have been wildly successful, generating numerous jobs for their communities and significant financial rewards for themselves. Many others simply make enough to live on. Most turned to entrepreneurship in the first place because they saw it as the quickest and most logical path for them to provide for their families.
But while so many immigrants—including newcomers who are both poor and poorly educated—have turned to entrepreneurship, many fewer native-born poor people have done so.
Citywide, the native-born self-employment rate is 8.6 percent, which is considerably lower than the foreign-born self-employment rate of 10.9 percent. But even this modest rate is inflated because it includes affluent native-born entrepreneurs, particularly in Manhattan and Brooklyn. For example, in Manhattan, roughly 97,000 native-born residents—or 13.3 percent of the working-age native born population—are self-employed, compared to only 124,000 (or just 6.7 percent) in the other four boroughs combined.
The innovation geography in Big City is uneven. The productivity gains occur in a few places with most residents left behind. Dense, parochial neighborhoods are isolated. The wealth generated stays in the core and migrates out to the affluent suburbs, effectively gating the benefits of globalization.
If you are geographically mobile, then you have little concern. The magic of big cities is migration. A sprawling residential pattern doesn't dampen the effect. Talent can live in the core or super-commute into downtown. Concerning innovation, better to be an immigrant than work in Big City. Migration matters more, much more, than density.