Sensitivity Analysis of Population Projections: Models Structured by Age and Sex

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

Cohort-component projections can be written as time-varying matrix operators: n(t+1)=A[t]n(t)+b(t) where n(t) is the population vector, A[t] the projection matrix, and b(t) the migration vector, at time t. Projection results depend on mortality, fertility, and migration time series used to generate A[t] and b(t). Here we present novel matrix calculus methods to analyse the sensitivity and elasticity of any projection output, in any projection year, to changes in age-specific mortality, fertility, and migration at any time during the projection. This approach can reveal the consequences of unforeseen changes in vital rates, evaluate potential policy interventions, and approximate projection uncertainty. We apply our methods to a projection of the population of Spain from 2012 to 2052. We present the elasticity of the total population, school-age population, population suffering from dementia, and the dependency and the economic support ratios, to changes in mortality, fertility, emigration, and immigration.