Closed vs. open city models: a new empirical approach to an old question

The empirical literature examining the determinants of city size almost exclusively uses the closed city version of the Mills–Muth model, in which population is exogenous. The closed city approach is particularly useful in that it yields a single equation empirical framework easily estimated with ordinary least squares (OLS). The general theory, however, offers the open city as an alternative, where population and possibly income are endogenous. The open city, in contrast to the closed version, yields a system of equations that should be estimated with seemingly unrelated regression (SUR). This paper finds that population and income are endogenous for broad samples of small and large American urbanized areas and explores the extent to which the empirically preferred open city SUR approach yields empirical results that resemble the closed city OLS model.