To explain the large differences in labor productivity across U.S. states we estimate two models—one based on local geographical externalities and the other on the diversity of local intermediate services—where spatial density results in aggregate increasing returns. Both models lead to a relation between county employment density and productivity at the state level. Using data on gross state output we find that a doubling of employment density increases average labor productivity by around 6 percent. More than half of the variance of output per worker across states can be explained by differences in the density of economic activity.6% increase in productivity with a doubling of density? That seems small though there is almost certainly some sort of declining curve past a certain point. Still, interesting to see the posited relationship measured. I am seeing a couple of other similar papers in the same ballpark.
Doubling density in metros with above average human capital gain productivity benefits that are roughly twice the average.
[T]he most interesting findings from our paper are that (1) the effect of density on productivity is practically zero (or even negative) in low-human capital metros, but the effect of density on productivity is quite substantial in metros with high college attainment shares; and (2) the interaction effects of population density and college attainment on productivity are highest for the industrial sectors of information, finance, arts and entertainment, and professional services—sectors that place a high premium on creativity and sharing of ideas.