The addition of a set of cohort parameters to a mortality model can generate complex identifiability issues due to the collinearity between the dimensions of age, period and cohort. These issues can lead to robustness problems and difficulties making projections of future mortality rates. Since many modern mortality models incorporate cohort parameters, we believe that a comprehensive analysis of the identifiability issues in age/period/cohort mortality models is needed. In this paper, we discuss the origin of identifiability issues in general models before applying these insights to simple but commonly used mortality models. We then discuss how to project mortality models so that our forecasts of the future are independent of any arbitrary choices we make when fitting a model to data in order to identify the historical parameters.

For many pension schemes, a shortage of data limits their ability to use sophisticated stochastic mortality models to assess and manage their exposure to longevity risk. In this study, we develop a mortality model designed for such pension schemes, which compares the evolution of mortality rates in a sub-population with that observed in a larger reference population. We apply this approach to data from the CMI Self-Administered Pension Scheme study, using U.K. population data as a reference. We then use the approach to investigate the potential differences in the evolution of mortality rates between these two populations and find that, in many practical situations, basis risk is much less of a problem than is commonly believed.