Urban growth and the emergent statistics of cities

Urban theory models cities as spatial equilibria to derive their aggregate properties as functions of extensive variables, such as population size. However, this assumption seems at odds with cities' most interesting properties as engines of fast and variable processes of growth and change. Here, we build a general statistical dynamics of cities across scales, from single agents to entire urban systems. We include agents' strategic behavior to produce predictable growth rates, which requires balancing relative incomes and costs over time. We implement these dynamics using stochastic differential equations and control theory to demonstrate a number of general emergent properties of cities deriving from limit theorems applied to growth rates. This framework establishes necessary conditions for scaling to be conserved by urban dynamics and shows how exponent corrections can be calculated. These ideas are tested using stochastic simulations and a long timeseries for 382 US Metropolitan Areas over nearly five decades.

All data needed to evaluate the conclusions in the paper are present in the paper and/or the Supplementary Materials. The data and python code used in the analyses of the paper and generation of each figure are available at https://github.com/mansueto-institute/Urban-Growth-Emergent-Statistics. A continuously updated version of the data is available from the U.S. Bureau of Economic Analysis website as Table CA30 Economic Profile: Wages and Salaries (www.bea.gov/regional/downloadzip.cfm). Additional data related to this paper may be requested from the author.