Multiregional Migration Projection

A single-region projection adds a net-migration term on top of births and deaths, which conceals the gross two-way flows and can violate consistency: the same person may be implicitly counted as leaving one place without arriving anywhere. Multiregional projection instead tracks directional origin-to-destination flows for all regions at once inside one growth matrix, so every departure is an arrival and the system is closed. This not only improves accounting but also lets you study how the whole regional system redistributes and yields multistate quantities a net-migration model cannot produce.

The matrix needs age-specific migration probabilities for every origin-destination pair, but these raw rates are often noisy or have gaps, and feeding erratic single-age values into a long projection makes results unstable. Fitting Rogers-Castro model migration schedules imposes the regular childhood-labour-retirement age shape, smooths the rates, fills missing ages, and makes flows comparable. The graduated schedules therefore act as the stable, theoretically grounded migration inputs that the multiregional growth matrix advances through time.

It is the population structure — by age and region — toward which the system would converge if the current survival, fertility, and migration rates were held constant indefinitely, obtained as the dominant eigenvector of the growth matrix. It is an analytical equilibrium that reveals the long-run spatial tendency embedded in present rates, not a prediction of the actual future, since real rates change. Demographers use it to characterize and compare migration regimes, much as the intrinsic growth rate characterizes a single population.