The sensitivity and elasticity analysis of multistate population projections

Nora Sánchez Gassen, University of Amsterdam
Hal Caswell, University of Amsterdam

Multistate population projections extend the usual projections by age and sex by adding one or more additional dimensions (e.g., educational categories, marital states, health conditions, etc.). The projection results depend on the mortality, fertility and migration rates and numbers as well as the rates of transition between states on which the projections are based. If any parameter is changed, the results of the projection will be different. Our goal is to systematically analyse the links between any projection result (e.g. population sizes, age distributions, dependency ratios) and any age-, sex- or state-specific projection parameter or parameter group on which projections are based. To do so, we present the equations necessary conduct sensitivity and elasticity (proportional sensitivity) analyses of multistate projections, using matrix calculus. We apply our method to a population projection of Germany, which projects the population by age, sex, and citizenship from 2014 to 2050. We identify the parameters which have the largest impact on projected sizes of population subgroups, age groups and ratios. Overall, sensitivity and elasticity analyses provide valuable information on how projection results are driven by mortality, fertility, migration and transition parameters; which parameters deserve particular attention when projection scenarios are prepared; and it may help us to recommend more targeted policy measures to address demographic changes.