International migration beyond gravity: a statistical model for use in population projections.

International migration will play an increasing role in the demographic future of most nations if fertility continues to decline globally. We developed an algorithm to project future numbers of international migrants from any country or region to any other. The proposed generalized linear model (GLM) used geographic and demographic independent variables only (the population and area of origins and destinations of migrants, the distance between origin and destination, the calendar year, and indicator variables to quantify nonrandom characteristics of individual countries). The dependent variable, yearly numbers of migrants, was quantified by 43653 reports from 11 countries of migration from 228 origins and to 195 destinations during 1960-2004. The final GLM based on all data was selected by the Bayesian information criterion. The number of migrants per year from origin to destination was proportional to (population of origin)(0.86)(area of origin)(-0.21)(population of destination)(0.36)(distance)(-0.97), multiplied by functions of year and country-specific indicator variables. The number of emigrants from an origin depended on both its population and its population density. For a variable initial year and a fixed terminal year 2004, the parameter estimates appeared stable. Multiple R(2), the fraction of variation in log numbers of migrants accounted for by the starting model, improved gradually with recentness of the data: R(2) = 0.57 for data from 1960 to 2004, R(2) = 0.59 for 1985-2004, R(2) = 0.61 for 1995-2004, and R(2) = 0.64 for 2000-2004. The migration estimates generated by the model may be embedded in deterministic or stochastic population projections.