Mortality projections for non-converging groups of populations

We propose a nested multi-population mortality projection model in which the forces of mortality are modelled via an extended version of the Cairns–Blake–Dowd model for middle and higher ages, and the resulting model parameters are forecast using a vector error correction model. Dependencies between different populations are accounted for by the joint parameter dynamics through lag coefficients (short-term predictability between the marginals), cointegration relations (long-run equilibriums), and error terms (correlated shocks). Bayesian inference assures integrated estimation and prediction of all hierarchical parameters in one step and allows for quantifying the underlying joint uncertainty. Our hierarchical set-up—yet flexible and easily interpretable—leads to a wider range of biologically plausible forecasts including, e.g., long-lasting, possibly varying discrepancies or phases of temporal divergence. We study two empirical examples in European mortality which suggest that the common a priori coherence assumption in actuarial projection models is too restrictive.