Enter "urban economics" density, creativity, innovation in Google Scholar and you get quite a few papers, many of which report a statistical link between local population density and some measure of creativity or success. Many of the authors admit that their measure of population (or employment) density (at the metropolitan area level) is crude and possibly problematic. Many of these areas are counties or combinations of counties and the average U.S. county is over 1,000 square kilometers. Even if just the urbanized portions of these counties are studied, an average over such a large area can be very misleading. The state of small-area data is the bane of urban economics.
I am late to the party and have just been introduced to the recent PUMS data. These are interesting because many of the PUMS areas are smaller than counties. The file provide information on in- and out-migrants by education level. For the 2006 PUMS data, the most educated migrants are coded as MA+ (Masters degree or higher). One can rank PUMS areas with the most arrivals and the most departures of these highly educated folks. A propos the expectations of Richard Florida and others, I calculated the population densities of the the 100-top sending and the 100-top receiving areas. The correlation of receiving area density and inflow of highly educated is 0.277. The correlation of sending area density and outflow of highly educated is 0.225.
Most of us have been to Manhattan as well as to Silicon Valley. Each attracts large numbers of smart and creative people. Beyond that, they have little in common, least of all population density. That would be way too simple.