Zipf’s and Gibrat’s laws for migrations

Clemente, Jesús and González-Val, Rafael and Olloqui, Irene (2010): Zipf’s and Gibrat’s laws for migrations. Forthcoming in: The Annals of Regional Science

Abstract

This paper analyzes 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.

• Item Type: MPRA Paper
• Language: English
• Keywords: Migration distribution, Zipf´s law, Gibrat´s law
• Subjects: J - Labor and Demographic Economics > J6 - Mobility, Unemployment, Vacancies, and Immigrant Workers > J61 - Geographic Labor Mobility ; Immigrant Workers; R - Urban, Rural, Regional, Real Estate, and Transportation Economics > R1 - General Regional Economics > R12 - Size and Spatial Distributions of Regional Economic Activity; R - Urban, Rural, Regional, Real Estate, and Transportation Economics > R1 - General Regional Economics > R11 - Regional Economic Activity: Growth, Development, Environmental Issues, and Changes

References

Alesina, A., E. Spolaore and R. Wacziarg, (2000). Economic Integration and Political Disintegration. American Economic Review 90: 1276–1296.

Carrington, W. J., E. Detragiache and F. Vishwanath, (1996). Migration with Endogenous Moving Cost. American Economic Review, 86, 909–930.

Cox, N, I. Salgado-Ugarte, M. Shimizu and T. Toru Taniuchi, (1999). KERNREG2: Stata module to compute kernel regression (Nadaraya-Watson).

Duranton, G., (2007). Urban Evolutions: The Fast, the Slow, and the Still. American Economic Review 97(1), 197–221.

Eeckhout, J., (2004). Gibrat's Law for (All) Cities. American Economic Review, vol. 94(5), 1429–1451.

Gabaix, X., and Y. M. Ioannides, (2004). The evolution of city size distributions. Handbook of urban and regional economics, Vol. 4, J. V. Henderson and J. F. Thisse, eds. Amsterdam: Elsevier Science, North-Holland, 2341–2378.

Ghatak, L., and P. Wheatley, (1996). Migration Theories and Evidence: an Assessment, Journal of Economic Surveys, 10, 159–198.

Gibrat, R., (1931). Les inégalités économiques. Paris: Librairie du Recueil Sirey.

Gonzalez-Val, R., and M. Sanso-Navarro, (2009). Gibrat's Law for Countries. Journal of Population Economics, forthcoming. DOI 10.1007s00148-009-0246-7.

Härdle, W., (1990). Applied nonparametric regression. Econometric Society Monographs. Cambridge, New York and Melbourne: Cambridge University Press.

Harris, J. R., and M. P. Todaro, (1970). Migration, Unemployment and Development: A Two-Sector Analysis. American Economic Review, 60, 126–142.

Ioannides, Y. M., and H. G. Overman, (2003). Zipf’s law for cities: an empirical examination. Regional Science and Urban Economics 33, 127–137.

Jenkins, S. P., and P. Van Kerm, (2007). PARETOFIT: Stata module to fit a Type 1 Pareto distribution.

Larramona, G., and M. Sanso, (2006). Migration dynamics, growth and convergence. Journal of Economic Dynamic and Control, 30(11), 2261–2279.

Pareto, V., (1896). Cours d’Economie Politique. Geneva: Droz.

Rose, A. K., (2006). Cities and countries. Journal of Money, Credit, and Banking, 38(8), 2225–2246.

Spolaore, E., and R. Wacziarg, (2005) Borders and Growth. Journal of Economic Growth 10: 331–386.

United Nations, (2004). Trends in total migrant stock: The 2003 revision. Database maintained by The Population Division of the Department of Economic and Social Affairs.

Zipf, G., (1949). Human Behaviour and the Principle of Least Effort. Cambridge, MA: Addison-Wesley.