Do the world's largest cities follow Zipf s and Gibrat's laws?

摘要

We examine whether the size distribution and the growth process of the world's largest cities follow Zipf s law and Gibrat's law. The parametric results of the size distribution analysis reject Zipf s law for all sample sizes and also show the Zipf exponent systematically declines as the sample size increases. The growth process analysis confirms Gibrat's law and yields a local Zipf exponent of one for cities with a normalized population less than 0.53%, which includes about 95% of the total observations. The deviations from Zipf's law occur at the extreme upper tail and are likely a result of restricted mobility of population across countries. However, given that Gibrat's law holds, we can expect the size distribution to converge to Zipf's law with a decline in the barriers to immigration.