The Area and Population of Cities: New Insights from a Different Perspective on Cities

2205 This paper builds on a recently proposed algorithm to construct cities based on geographical features of high-quality micro data (Hernán D. Rozenfeld et al. 2008), rather than informative but somewhat arbitrary legal or administrative definitions. It allows us to take a fresh look at key quantities in urban economics, namely the population and the area of cities. We find that Zipf’s law for population holds quite well, and well below the very upper tail of the city size distribution, where it had been shown to hold to a good degree of approximation (Gabaix and Yannis M. Ioannides 2004). We also find that the distribution of city areas follows a power law, with an exponent close to one, the Zipf value. These findings help constrain further theories of cities and theories of geography. A key difficulty in studying cities is finding a practical way to define them (George K. Zipf 1949; Paul Krugman 1996; Jonathan Eaton and Zvi Eckstein 1997; Linda Harris Dobkins and Ioannides 2001; Jan Eeckhout 2004; Kwok Tong Soo 2005; Batty 2006). A canonical method involves defining Metropolitan Statistical Areas (MSAs) obtained in the United States from the Office of Management and Budget and available from the US Census Bureau (2009). MSAs are defined for each major agglomeration and attempt to capture their extent by merging administratively defined entities, counties in the US, based on their social or economic ties (other countries use similar criteria). For instance, the MSA of Boston, MA, includes not only the administrative unit of Boston, but also adjacent Cambridge. MSAs derive their appeal from a strong economic logic, but their construction requires qualitative analysis and is very timeconsuming. Therefore, MSAs have been constructed only for the 276 most populated cities in the US, and the corresponding Zipf’s law has been documented only for the upper tail of the distribution (Gabaix and Ioannides 2004; Soo 2005). Two main alternatives to the MSAs have been proposed in the literature. One method is to use administrative or legal borders of cities to define so-called “places” The Area and Population of Cities: New Insights from a Different Perspective on Cities