Another wrinkle in the density discussion.

Density is one of the most important, and at times contentious, topics in urban development. We cover it a lot here at Cities.

It's clear that density plays an important role in economic growth. Density brings people and firms closer together which makes it easier to share and exchange information, invent new technologies, and launch new firms.

But the question remains: How exactly — in what ways and through which channels — does density make our cities more productive?

That’s where a recent study published in the Journal of Regional Science breaks new ground. Conducted by economists Jaison Abel of the Federal Reserve Bank of New York, Ishita Dey of the University of Georgia, and Todd Gabe of the University of Maine, the study provides new evidence of the relationships between density, human capital, and urban productivity. It uses detailed statistical models to gauge more precisely the effects of density and human capital, separately and together, on productivity of more than 350 metro areas.

In doing so, the study overcomes a couple of nagging problems that have confounded previous research. The relationship between density and productivity is vexed by the nature of urban "sorting," the study points out, where more productive people are attracted to more productive places. To get around this, the researchers employ "instrumental variables" as proxies for density and use a two-step modeling approach that allows them to essentially portion out the effects of industry structure on metro productivity. This enables them to get a more precise level of productivity that is directly attributable to density.

The graph above, from the study, shows the wide variation in productivity across U.S. metros. The most productive metro generated $114,798 in average output per worker, more than three times that of the least productive ($35,867). As the authors point out, the "average output per worker in the twenty most-productive metropolitan areas was two times larger than in the twenty least-productive metropolitan areas, and more than one-half larger than the value for the median metropolitan area…"

"[These maps] really show the difference (especially for places like Denver) between the 'standard' density measure (population per square mile) and the weighted density measure," writes Gabe in an email. It's a concept we recently explored on Cities.

The study’s findings lead to several important conclusions about the role of density in urban productivity. 

First, it finds that density plays a considerable role in the productivity of metro areas. Specifically, doubling density increases productivity by an average of two to four percent.

Second, it notes that density plays a bigger role in cities where levels of skill and human capital are higher. Metro areas with below average levels of human capital realize no productivity gains from density, the study finds, while doubling density in metros with above average human capital gain productivity benefits that are roughly twice the average. This "negative net agglomeration effect" found in less skilled metros leads the authors to conclude that the negative effects of congestion swamp the positive effects of urbanization in less skilled places.

Third, the study finds the effects of density to be even more substantial in industries with high levels of knowledge and creativity. It thus goes well beyond previous studies that look at economic output in the aggregate to hone in on the effects of density and human capital on the productivity and performance of individual industrial sectors. The authors find clear evidence that both the effects of density per se and the density of skilled people are highest in knowledge-based and creative industries. This is particularly true in the information, arts and entertainment, professional services, and finance industries where "the exchange of information and sharing of ideas are important parts of the production process." This provides important empirical evidence of Jane Jacob's and Robert Lucas's theories of the interplay of density and talent as forming the basic underlying mechanism of economic growth.

Based on this, the authors conclude that the overall results of their analysis...

…provide an enhanced understanding of the mechanisms by which agglomeration enhances output in the most productive U.S. metropolitan areas—important given that the 50 most productive metropolitan areas account for 60 percent of U.S. GDP. Relative to conventional models of urban agglomeration, we show that incorporating the density of human capital explains the highly nonlinear distribution of productivity observed across the most productive metropolitan areas. Knowing the keys to productivity in these places helps us understand factors influencing the overall level of economic activity in the United States.

Or as Gabe summarized their key results in an email to me:

[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.

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