The sensitivity analysis of multistate pension projections based on a vec-permutation approach

The cohort component method in the context of pension projections can be translated into a multistate matrix model, in which beneficiaries of a pension scheme are classified jointly by their age and status (active contributor, invalid, retiree, widows/widowers), using the vec permutation matrix. The projection results depend on the mortality, retirement, disability, marital percentage and remarriage rates as well as the number of new entrants into the scheme on which the projections are based. Any change to a parameter will result in a corresponding change in the projection outcomes. Our objective is to systematically examine the relationships between various key projection outcomes—such as status-specific population sizes, dependency ratio, totalcash flows, and PAYG cost rate—and the underlying age- and sex-specific projection parameters. To achieve this, we present the set of equations required to perform sensitivity and elasticity (i.e., proportional sensitivity) analyses of multistate projections, utilizing matrix calculus. We apply our methodology to a projection of the Moroccan pension system, which estimates population and cash flows disaggregated by age, sex, and status over the period 2020 to 2080.