Agglomeration effects as spatially embedded social interactions: identifying urban scaling beyond metropolitan areas

Agglomeration is the tell-tale sign of cities and urbanization. Identifying and measuring agglomeration economies has been achieved by a variety of means and by various disciplines, including urban economics, quantitative geography, and regional science. Agglomeration is typically expressed as the non-linear dependence of many different urban quantities on city size, proxied by population. The identification and measurement of agglomeration effects is of course dependent on the choice of spatial units. Metropolitan areas (or their equivalent) have been the preferred spatial units for urban scaling modeling. The many issues surrounding the delineation of metropolitan areas have tended to obscure that urban scaling is principally about the measurable consequences of social and economic interactions embedded in physical space and facilitated by physical proximity and infrastructure. These generative processes obviously must exist in the spatial subcomponents of metropolitan areas. Using data for counties and urbanized areas in the United States, we show that the generative processes that give rise to scaling effects are not an artifact of metropolitan definitions and exist at smaller spatial scales.