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

•We examine the size distribution and the growth process of the world's largest cities.•We analyze Gibrat's and Zipf's laws by applying nonparametric estimation.•Gibrat's law holds for largest cities in the World.•The local Zipf exponent is around one for 95% of the total observations.•The deviations from Zipf's law occur at the extreme upper tail.

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.