Multistate Dynamics: The Convergence of an Age-by-Region Population System

Abstract

This paper uses Rogers's (1975) discrete model of multiregional demographic growth to study the convergence properties of a fourteen-age-group, eight-region, female Canadian population system, which is subject to the 1966–1971 age-specific rates of births, deaths, and interregional migration. The focus is on (1) the changes in the age-by-region population distribution and (2) the evolution of regional growth and component rates. For the youngest age group, the fluctuations in regional population size are almost entirely determined by a small number of low-frequency and long-durability cyclical components. As age increases, the high-frequency and short-durability cyclical components tend to play a more important role. The half-lives of major cyclical components are related to the shapes of regional fertility schedules. The legacy of the postwar baby boom is nationwide, so that the population waves in different regions tend to have similar phases and periodicities. The slow and persistent spatial convergence is noncyclical, but one region overshoots and two others undershoot their respective long-run regional shares. Over a hundred years the convergence toward the long-run regional age profiles is practically completed, while the spatial convergence has gone only halfway. The difference in sensitivity among regional birth, death, in-migration, and out-migration rates to moving population waves and changing slopes of regional age profiles depends on the characteristics of regional schedules of fertility, mortality, and interregional migration. The persistent interregional contrast in growth rates is mainly determined by the relative competitiveness in the interregional migration transaction. The fluctuations of regional growth rates are dominated by the cyclical pattern of regional birth rates in early stages and by the fluctuations of regional death rates in later stages. The interpretation of long-run (intrinsic) regional in-migration or net migration rates as indices of regional attractiveness or competitiveness can be more misleading than the interpretation of long-run regional death rates as indices of regional mortality.