The sensitivity analysis of population projections

Abstract

In this study, the authors' goal is to derive and apply theory to compute the sensitivity and the elasticity of any projection outcome to changes in any of the parameters, where those changes are applied at any time during the projection interval. The authors use matrix calculus to derive a set of equations for the sensitivity and elasticity of any vector valued outcome at time t to any perturbation of a parameter vector at any time s. The results appear in the form of a set of dynamic equations for the derivatives that are integrated in parallel with the dynamic equations for the projection itself. The authors show results for single-sex projections and for the more detailed case of projections including age distributions for both sexes. They apply the results to a projection of the population of Spain, from 2012 to 2052 and determine the sensitivity and elasticity of the total population, the school-age population, the population subject to dementia, the total dependency ratio, and the economic support ratio.