Gibrat 's law for cities revisited

The aim of this work is to test empirically the validity of Gibrat's Law in the growth of cities, using data for all the twentieth century of the complete distribution of cities (without any size restrictions) in three countries: the US, Spain and Italy. For this we use different techniques (parametric and non-parametric methods), obtaining mixed evidence. Our results confirm that Gibrat's law for means holds only as a long-run average. In the short term, considered decade by decade, we find that growth was divergent in all three countries. Despite this, the distribution of growth in the cities can be approached as a lognormal. In the long term, panel data unit root tests confirm the validity of Gibrat's Law in the upper tail distribution. Finally we find evidence in favour of a weak Gibrat's Law (size affects the variance of the growth process but not its mean) when using non-parametric methods which relate the growth rate to city size.