Sensitivity analysis in multiregional demographic models

Abstract

The theory of multiregional mathematical demography investigates how fertility, mortality, and migration combine to shape the growth of multiregional population systems. Population dynamics have been studied for cases where the structural parameters, namely the age-specific rates of fertility, mortality, and migration, are fixed. This paper addresses the question of how the system behaves under changing structural parameters. By applying the technique of matrix differentiation, sensitivity functions are derived which link changes in multiregional life-table statistics and in population projections to changes in the age-specific rates. A review of the technique, which may be used for the sensitivity analysis of any matrix model, is given in the appendix.