Persistence and stability in city growth

Abstract

The overall growth and expansion of cities has been of long-standing interest to economists because of the association of urbanization and industrialization with economic growth. Relative city growth provides information on shifts in production patterns, changes in income distribution, and economic growth in a spatial context. Previous empirical work that examines relative city growth uses a Markov chain method to answer the question of how cities of different sizes grow relative to each other. Those studies find that cities of different sizes grow at similar rates, i.e., city growth is parallel. While intriguing, the treatments are inadequate in this particular context for two reasons. First, the authors do not perform statistical inference on the estimated transition matrices. Second, it fails to explain city growth dynamics. A more useful way to explain the dynamic behavior of city size is to use a time-series approach in which present size is determined by past size. This paper examines growth rates of city populations in a time-series context using Indian population data from 1901–1991. The purpose of this paper is to answer two questions regarding cities and their evolution. The first is to determine the effect of shocks on city populations in terms of the length of time for which they affect the city, i.e., to determine the non-stationarity of city population series. The second is to examine evolution of the hierarchy of cities (or relative urban growth) given the effect of time-varying shocks. Unit root tests show that city populations may be non-stationary. Cointegration of city population and total urban population suggests that the growth of cities may be parallel in the long-run. In the short-run there are deviations from the long-term parallel growth of cities due to exogenous shocks. These shocks take less than a decade to dissipate and for the city to return to its long-run growth rate.