Invention volatility and urban systems dynamics

Large firms generate most American inventions. We know that cities are host to organizations of varying size and prevalence, but are these conditions important to urban system dynamics? This article presents volatility in patenting as a novel instrument for distinguishing between cities reliant on many or few organizations. Volatility is the standard deviation of a city's inter-annual patenting growth rate over a period. We attest an inverse-size hypothesis between volatility and metropolitan size -- as metropolitan size increases volatility decays. This hypothesis belongs to a family of urban scaling power laws, but our approach is distinctive in linking invention volatility, city size, and the organization of technological progress. A focus on volatility facilitates an unraveling of intertwined place attributes and organizational characteristic. Place attributes include the level of engagement in invention and the growth rate of patenting by resident inventors. Organizational characteristics pertain to patentee type with an emphasis on the proportion of grants in a city to corporate champions, individual inventors, universities, and Federal agencies. Results show that while place attributes are influential beyond the largest metropolitan areas, organizational characteristics are key to understanding volatility in big cities.