Metropolitan areas with population densities of about 4,000 people per square mile tend to produce the highest rate of patenting, according to a recent article in the American Journal of Economics and Sociology. In a study of U.S. metro areas over a ten-year period, the authors found that metro population density has a significant positive correlation with patenting rates. At about 4,000 people per square mile, the benefits of agglomeration, such as knowledge spillovers and diverse labor pools, are at their highest, compared to negative effects of congestion, such as increasing costs of real estate and other scarce resources. Few U.S. cities, however, approach this level of population density. The authors advise against taking the averaged optimal density level as a basis for policy, but use their data to suggest that cities play a vital role in the innovation economy and that increasing urban density could lead to higher innovation rates in some U.S. urban areas.