The coherence of US cities

Diversified economies are critical for cities to sustain their growth and development, but they are also costly because diversification often requires expanding a city's capability base. We analyze how cities manage this trade-off by measuring the coherence of the economic activities they support, defined as the technological distance between randomly sampled productive units in a city. We use this framework to study how the US urban system developed over almost two centuries, from 1850 to today. To do so, we rely on historical census data, covering over 600M individual records to describe the economic activities of cities between 1850 and 1940, as well as 8 million patent records and detailed occupational and industrial profiles of cities for more recent decades. Despite massive shifts in the economic geography of the United States over this 170-y period, average coherence in its urban system remains unchanged. Moreover, across different time periods, datasets, and relatedness measures, coherence falls with city size at the exact same rate, pointing to constraints to diversification that are governed by a city's size in universal ways.