Urban Scaling of Patenting in Europe. Addressing the Endogeneity of City Size

Patenting is strongly concentrated in cities, and innovation-related outputs tend to scale superlinearly with urban population. Yet the interpretation of this relationship remains contested. This paper examines whether the superlinear scaling of patenting persists once the endogeneity of city size is addressed. Using across-section of 362 European Functional Urban Areas, we estimate the elasticity of patent output with respect to population using ordinary least squares and two-stage least squares. Contemporary population is instrumented by terrain ruggedness and historical rural population in 1770. The results confirm that patenting scales super-linearly with city size, and that instrumental-variable estimates are substantially larger than the corresponding OLS estimates. These findings suggest that the urban scaling of patenting in Europe is consistent with a positive e!ect of urban scaleon innovation. The paper contributes to the urban scaling literature by providing instrumental-variable evidence for the European context.