A modified common factor model for modelling mortality jointly for both sexes

There is an increasing attention on the joint modelling of multiple populations. Populations are related in several ways, such as neighbouring countries, females and males, and socioeconomic subgroups within a population. They are associated due to certain common driving forces, and mortality projection models should be constructed to allow for such underlying relationships. One such example is the Poisson common factor model. In this paper, we consider some extensions of the original Poisson common factor model. The first is to use a different number of additional factors for each sex. With this, the potential trend differences between the two sexes can be captured. The second is to incorporate a common age sensitivity effect into the additional factors. It may help improve parameter parsimony. A hybrid version between these two extensions is also considered. Overall, the modified versions deliver better fitting and projection results than the original model, using mortality data from eight developed countries. Qualitatively speaking, the new models provide much more flexibility in modelling populations with different mortality patterns. Empirically, they are shown to be able to produce improved performance in fitting and projection. The models are selected as the optimal choices based on information criteria statistics, and they tend to produce more accurate forecasts of the male-to-female ratios of death rates.