Test of two hypotheses explaining the size of populations in a system of cities

TL;DR

This study tests two hypotheses explaining city population sizes using Bulgarian city data, finding that growth depends on city size and follows a double Pareto log-normal distribution, supporting the Yule process hypothesis.

Contribution

It provides empirical evidence that Bulgarian city growth aligns with the Yule process and a double Pareto log-normal distribution, challenging the size-independence hypothesis.

Findings

City growth is size dependent in Bulgaria.

Population distribution fits a double Pareto log-normal model.

Supports the Yule process hypothesis for city growth.

Abstract

Two classical hypotheses are examined about the population growth in a system of cities: Hypothesis 1 pertains to Gibrat's and Zipf's theory which states that the city growth-decay process is size independent; Hypothesis 2 pertains to the so called Yule process which states that the growth of populations in cities happens when (i) the distribution of the city population initial size obeys a log-normal function, (ii) the growth of the settlements follows a stochastic process. The basis for the test is some official data on Bulgarian cities at various times. This system was chosen because (i) Bulgaria is a country for which one does not expect biased theoretical conditions; (ii) the city populations were determined rather precisely. The present results show that: (i) the population size growth of the Bulgarian cities is size dependent, whence Hypothesis 1 is not confirmed for Bulgaria; (ii) the population size growth of Bulgarian cities can be described by a double Pareto log-normal distribution, whence Hypothesis 2 is valid for the Bulgarian city system. It is expected that this fine study brings some information and light on other, usually considered to be more pertinent, city systems in various countries.