“Scaling of Atypical Knowledge Combinations in American Metropolitan Areas from 1836–174201014ya”, Lars Mewes2019-03-01 (; similar)⁠:

Cities are epicenters for invention. Scaling analyses have verified the productivity of cities and demonstrate a superlinear relationship between cities’ population size and invention performance. However, little is known about what kinds of inventions correlate with city size. Is the productivity of cities only limited to invention quantity?

I shift the focus on the quality of idea creation by investigating how cities influence the art of knowledge combinations. Atypical combinations introduce novel and unexpected linkages between knowledge domains. They express creativity in inventions and are particularly important for technological breakthroughs. My study of 174 years of invention history in metropolitan areas in the US reveals a superlinear scaling of atypical combinations with population size. The observed scaling grows over time indicating a geographic shift toward cities since the early 20th century.

The productivity of large cities is thus not only restricted to quantity but also includes quality in invention processes.

[Keywords: cities, invention, historic patent data, scaling analysis, atypical knowledge combinations]

Figure 1: Technological diversity as a function of population size at 3 different levels of technological resolution. Diversity is normalized in A by D~max~ for comparability reasons. Scaling relations between population and technological diversity B at the subclass level (D~max~ = 654), C at the group level (D~max~ = 10,154), and D at the subgroup level (D~max~ = 218,570).
Figure 1: Technological diversity as a function of population size at 3 different levels of technological resolution. Diversity is normalized in A by Dmax for comparability reasons. Scaling relations between population and technological diversity B at the subclass level (Dmax = 654), C at the group level (Dmax = 10,154), and D at the subgroup level (Dmax = 218,570).
Figure 3: Scaling exponent of diversity with respect to the number of distinct combinations over time. [Note: Dashed lines indicate the 95% confidence interval.]
Figure 5: Scaling exponent of population size over time for atypical (red line) and typical combinations (blue line). [Note: Dashed lines indicate the 95% confidence interval.]

…I attribute the growing importance to the opportunities given in large cities. In particular, knowledge diversity in large cities provides opportunities for knowledge combinations not found in smaller and less diverse towns. Beyond diversity, larger cities also concentrate the skills to exploit the given diversity. Inventors in large cities realize a disproportionate number of distinct knowledge combinations, which also affects the exploration of new combinations. Given the cumulative nature of knowledge, wealth, innovation, and human skill, my results suggest a self-reinforcing process that favors metropolitan centers for knowledge creation. Thus, knowledge creation plays a major role for creating and maintaining spatial inequalities.

Increasing spatial inequalities have profound implications for regional development and policy making. Inequalities unfold in the form of invention activities, as one crucial economic activity that transforms our economy and society. The benefits of knowledge creation in large cities are not shared by all regions and reinforces a widening divergence between large cities—as centers of knowledge exploration—and smaller towns. Given the importance of geography for knowledge generation, it is unlikely that spatial concentration of invention activities will stop. Earlier research, moreover, observes a decreasing productivity of R&D and highlights that more resources and capabilities are necessary to yield useful R&D outcomes (Lanjouw and Schankerman2004; Wuchty, Jones, and Uzzi2007; Jones, Wuchty, and Uzzi2008). Large cities provide the required resources and capabilities in close geographic proximity. Smaller towns lack the requirements to compete, get disconnected, and fall behind. It should be, furthermore, in the interest of policy makers that all places benefit from urban externalities. That is, policy has to consider how to distribute the novelty created in the centers down the urban hierarchy to smaller towns and lagging regions.

However, much research remains to be done. Why did it take longer for atypical combinations to scale that strongly with city size? Has this process stopped, or will it continue? Moreover, atypical knowledge combinations do not automatically imply a high technological impact or economic value. Thus, it remains unclear precisely how (a)typical combinations relate to the economic performance of cities and how they explain local stories of success and failure.

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Scaling of Atypical Knowledge Combinations in American Metropolitan Areas from 1836–174201014ya