The multiregional matrix growth operator and the stable interregional age structure

Summary Current population-forecasting efforts generally adopt minor variants of the cohort-survival projection method. This technique focuses on a population disaggregated into cohorts, a group of people having one or more common characteristics at a point in time and, by subjecting each cohort to class-specific rates of fertility, mortality, and net migration, generates a distribution of survivors and descendants of the original population, at successive intervals of time. Although cohort-survival methods take on a large number of variations, they all are essentially trend-based, dynamic, aspatial models of growth. The temporal element is introduced by a recursive structure which operates over a sequence of unit time intervals. The spatial dimension, when it is included at all, typically is accommodated by replicating the analysis over as many areal units as comprise the study area. Realistically, however, time and space need to be considered jointly in population-forecasting models. The need for interregional models which systematically introduce place-to-place movements and simultaneously consider the spatial as well as the temporal character of interrelated population processes is becoming increasingly apparent. Recently several demographers have taken advantage of the conceptual elegance and computational simplicity of matrix methods of population analysis. Their models, however, assume a “closed” population which is subject only to the processes of fertility and mortality. These, therefore, are not directly applicable to interregional “open” systems in which migration is frequently a much more variable and important contributor to population change than births or deaths. However, a natural extension of the demographer's matrix model allows one to incorporate place-to-place migration and provides an integrated interregional population-forecasting model which easily may be programmed for any of the current generation of digital computers. Such a model is outlined in this paper.