Is the Zipf law spurious in explaining city-size distributions?

Abstract

The Zipf law, which states that that the rank associated with some size S is proportional to S to some negative power, is a regularity observed in natural and social sciences. One popular application of the Zipf law is the relationship between city sizes and their ranks. This paper examines the rank–size relationship through Monte Carlo simulations and two examples. We show that a good fit (indicated by a high R2 value) can be found for many statistical distributions. The Zipf law's good fit is a statistical phenomenon, and therefore, it does not require an economic theory that determines city-size distributions.