Urban scaling of patents and relation with socioeconomic strength for German cities and their urban areas

We combine the fields of quantitative studies of science and technology, in particular patent analysis on the one hand, and on the other quantitative urban studies, in particular the urban scaling methodology. We focus on knowledge production in terms of patents, and we analyze the urban scaling of patents for German cities with urban agglomerations (functional urban areas, FUAs) larger than 500,000 inhabitants. We assign patents to cities and FUAs on the basis of applicant-addresses as well as of inventor-addresses. We study how cities differ in patenting activities as compared to their entire urban area. Patenting activity increases with city size and FUA size but it is not certain that this increase is superlinear. Next to socioeconomic indicators based on urban scaling measures we also use employment data and data on new businesses. We find a reasonably strong indication that cities and FUAs with a relatively high patenting activity are predominantly the socioeconomically stronger cities and FUAs. Our results show high patenting activity is not necessarily a largest cities issue. We find that the scaling relation between patent numbers and publication numbers of cities is approximately linear, also for the industry-relevant publications. Co-publications with industry does not necessarily reinforce patenting activity in cities. Our study revealed some striking differences between cities and their FUAs. For a given population size cities have a higher GUP as compared to FUAs. Applicant addresses of patents tend to focus more on cities whereas inventor addresses are more spread out over the FUAs.