Boosting, sorting and complexity-urban scaling of innovation around the world

It is widely understood that innovations tend to be concentrated in cities, which is evidenced by innovative output increasing disproportionately with city size. Yet, given the heterogeneity of countries and technologies, few studies explore the relationship between population and innovation numbers. For instance, in the USA, innovative output scaling is substantial and is particularly pronounced for complex technologies. Whether this is a universal pattern of complex technologies and a potential facilitator of scaling, is unknown. Our analysis compared urban scaling in urban areas across 33 countries and 569 technologies. Considerable variation was identified between countries, which is rooted in two fundamental mechanisms (sorting and boosting). The sorting of innovation-intensive technologies is found to drive larger innovation counts among cities. Among most countries, this mechanism contributes to scaling more than city size boosting innovation within specific technologies. While complex technologies are concentrated in large cities and benefit from the advantages of urbanization, their contribution to the urban scaling of innovations is limited.