Distribution of City Size: Gibrat, Pareto, Zipf

The exact shape of the distribution of city size is subject to considerable scholarly debate, as competing theoretical models yield different implications. The alternative distributions being tested are typically the Pareto and the log-normal, whose finite sample upper tail behavior is very difficult to tell apart. Using data at different levels of aggregation (census blocks and cities) we show that the tail behavior of the distribution changes upon aggregation, and the final result depends crucially on the shape of the distribution of the number of elementary units associated with each aggregate element.