Zipf’s and Gibrat’s laws for migrations

Abstract

This paper analyses the evolution of the size distribution of the stock of emigrants in the period 1960-2000. Has the distribution of the stock of emigrants changed or has there been some convergence? This is the question discussed in this work. In particular, we are interested in testing the fulfillment of two empirical regularities studied in urban economics: Zipf's law, which postulates that the product between the rank and size of a population is constant; and Gibrat's law, witch states that growth rate of a variable is independent of its initial size. We use parametric and non-parametric methods and apply them to absolute (stock of emigrants) and relative (migration density, defined as the quotient between the stock of emigrants of a country and its total population) measurements.

On the Economic Geography of International Migration

“…In keeping with the findings of Clemente et al. (), we find, at least across most of the distribution of the stock of immigrants, that Gibrat's law holds. The major exceptions are those countries in the lower end of the distribution, which tend to grow faster than the other countries in the distribution.…”

“…Both immigrant levels and densities are log‐normally distributed as was the case in Clemente et al. () . As if Gibrat's law were to hold, the resulting distributions of the relevant variables will be log‐normal, we proceed by examining whether Gibrat's law holds for our various measures of international migration.…”

“…As such estimators are sensitive to atypical values, we follow Clemente et al. () and drop the bottom 5 per cent of observations. Figures and plot the results from these regressions, and we would expect these values to be flat and concentrated around zero if Gibrat's law were to hold.…”

“…The only study examining Gibrat's and Zipf's laws in international immigration is Clemente et al. (). In the context of immigrant levels and densities, they find Zipf's law only holds for immigrant levels for the top 50 countries.…”

Did Zipf Anticipate Socio-Economic Spatial Networks?

“…As mentioned above, there is a large number of studies which show the validity of Zipf's law, particularly in the upper (truncated) tail (Clemente et al, 2011;Krugman,1996a;Levy, 2009;Mansury, 2010;Rosen and Resnick, 1980). It should noted that Soo (2005) has shown that the degree of variability of Zipf's law also depends on the estimation method used: he found contrasting results using OLS or Hill 4 estimators.…”