This paper documents key elements and their mathematical representation of a projection methodology for international migration. The methodology rests on the well-established multiregional model in demography, but was reformulated to allow for more realistic migration assumptions that depend on sending and receiving countries. The paper develops the methodology in a consistent and transparent way in matrix notation. The starting point is the generating matrix of multiregional models, followed by the multiregional life table and corresponding projection model. The paper distinguishes between two types of multiregional projection models—the standard model, which implements migration solely in terms of emigration intensities, and a model that allows for interactions between the regions or countries involved. The second projection model is nonlinear and requires an iterative approach. The paper implements procedures to estimate the demographic events that are associated with the multiregional model. In the classical formulation of the multiregional projection model, births are (implicitly) covered, but deaths and migrants by age are neglected. The explicit inclusion of all vital events adds considerably more analytical power to multiregional population projections. The last addition to the multiregional methodology is the replacement of the common assumption of a uniform distribution of (decrement) events within age groups by a more realistic assumption that rests on approximations by local fits and an empirical model especially for the first age group. The methodology was implemented in a multiregional analysis and projection software package and coded in the high-level statistical language R.

See Working Paper 30: Modeling Alternative Projections of International Migration here.