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

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  • Anthony F. J. Raan

    (Leiden University)

  • Jos J. Winnink

    (Leiden University)

Abstract

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.

Suggested Citation

  • Anthony F. J. Raan & Jos J. Winnink, 2025. "Urban scaling of patents and relation with socioeconomic strength for German cities and their urban areas," Scientometrics, Springer;Akadémiai Kiadó, vol. 130(8), pages 4339-4367, August.
    • Handle: RePEc:spr:scient:v:130:y:2025:i:8:d:10.1007_s11192-025-05388-x
    DOI: 10.1007/s11192-025-05388-x
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    References listed on IDEAS

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    1. Fritsch, Michael & Wyrwich, Michael, 2021. "Is innovation (increasingly) concentrated in large cities? An international comparison," Research Policy, Elsevier, vol. 50(6).
    2. Paul Cheshire & Stefano Magrini, 2009. "Urban growth drivers in a Europe of sticky people and implicit boundaries," Journal of Economic Geography, Oxford University Press, vol. 9(1), pages 85-115, January.
    3. Tom Broekel & Louis Knuepling & Lars Mewes, 2023. "Boosting, sorting and complexity—urban scaling of innovation around the world," Journal of Economic Geography, Oxford University Press, vol. 23(5), pages 979-1016.
    4. J. Lobo & D. Strumsky & J. Rothwell, 2013. "Scaling of patenting with urban population size: evidence from global metropolitan areas," Scientometrics, Springer;Akadémiai Kiadó, vol. 96(3), pages 819-828, September.
    5. Pierre-Alexandre Balland & Cristian Jara-Figueroa & Sergio G. Petralia & Mathieu P. A. Steijn & David L. Rigby & César A. Hidalgo, 2020. "Complex economic activities concentrate in large cities," Nature Human Behaviour, Nature, vol. 4(3), pages 248-254, March.
    6. Anu Ramaswami & Daqian Jiang & Kangkang Tong & Jerry Zhao, 2018. "Impact of the Economic Structure of Cities on Urban Scaling Factors: Implications for Urban Material and Energy Flows in China," Journal of Industrial Ecology, Yale University, vol. 22(2), pages 392-405, April.
    7. Dieter Franz Kogler & Gaston Heimeriks & Loet Leydesdorff, 2018. "Patent portfolio analysis of cities: statistics and maps of technological inventiveness," European Planning Studies, Taylor & Francis Journals, vol. 26(11), pages 2256-2278, November.
    8. Michael Fritsch & Michael Wyrwich, 2021. "Does Successful Innovation Require Large Urban Areas? Germany as a Counterexample," Economic Geography, Taylor & Francis Journals, vol. 97(3), pages 284-308, May.
    9. Luiz G A Alves & Renio S Mendes & Ervin K Lenzi & Haroldo V Ribeiro, 2015. "Scale-Adjusted Metrics for Predicting the Evolution of Urban Indicators and Quantifying the Performance of Cities," PLOS ONE, Public Library of Science, vol. 10(9), pages 1-17, September.
    10. Carolina Castaldi, 2024. "The geography of urban innovation beyond patents only: New evidence on large and secondary cities in the United States," Urban Studies, Urban Studies Journal Limited, vol. 61(7), pages 1248-1272, May.
    11. Luís M A Bettencourt & José Lobo & Deborah Strumsky & Geoffrey B West, 2010. "Urban Scaling and Its Deviations: Revealing the Structure of Wealth, Innovation and Crime across Cities," PLOS ONE, Public Library of Science, vol. 5(11), pages 1-9, November.
    12. Rudiger Ahrend & Emily Farchy & Ioannis Kaplanis & Alexander C. Lembcke, 2017. "What Makes Cities More Productive? Evidence From Five Oecd Countries On The Role Of Urban Governance," Journal of Regional Science, Wiley Blackwell, vol. 57(3), pages 385-410, June.
    13. Jamie Peck, 2005. "Struggling with the Creative Class," International Journal of Urban and Regional Research, Wiley Blackwell, vol. 29(4), pages 740-770, December.
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