Further Analysis of the Zipf's Law: Does the Rank-Size Rule Really Exist?

Abstract

ABSTRACT Zipf's law has two striking regularities: excellent fit and an exponent close to 1.0. When the exponent equals 1.0, Zipf's law collapses into the rank-size rule. This paper alters the sample size, the truncation point, and the mix of cities in the sample to analyze the Zipf exponent. Our results demonstrate that the exponent is close to 1.0 only for a number of selected sub-samples. Small samples of large cities provide higher values, while samples of small cities produce lower values. Using the estimated values of the exponent derived from the rolling sample method revealed elasticity in the exponent with regard to sample size. Our results also suggest that the rank-size rule should be interpreted with caution. Although it is well-known and commonly used, the rank-size rule may be more of a statistical phenomenon than an economic regularity.