Zipf’s and Gibrat’s laws for migrations

TLDR: In this paper, the authors analyzed the evolution of the size distribution of the stock of immigrants in the period 1960-2000 and found that the growth rate of a variable is independent of its initial size, which could be explained by the lower birth rates of host countries and the reduction in the cost of emigration produced by the presence of a previous stock in the country.

Abstract: This paper analyses the evolution of the size distribution of the stock of immigrants in the period 1960–2000. In particular, we are interested in testing the validity of two empirical regularities: Zipf’s law, which postulates that the product between the rank and size of a population is constant; and Gibrat’s law, according to which the growth rate of a variable is independent of its initial size. We use parametric and nonparametric methods and apply them to absolute (stock of immigrants) and relative (migration density, defined as the quotient between the stock of immigrants of a country and its total population) measurements. We find that both the stock of immigrants and migration density follow similar size distributions to those of cities and of countries. Contrary to what traditional migrations models predict, growth in the stock of immigrants is independent of the initial stock. Moreover, the growth of migration density shows a divergent behaviour, which could be explained by the lower birth rates of host countries and the reduction in the cost of emigration produced by the presence of a previous stock of immigrants in the country.