A Poisson common factor model for projecting mortality and life expectancy jointly for females and males

Abstract

We examine the application of a Poisson common factor model for the projection of mortality jointly for females and males. The model structure is an extension of the classical Lee–Carter method in which there is a common factor for the aggregate population, while a number of additional sex-specific factors can also be incorporated. The Poisson distribution is a natural choice for modelling the number of deaths, and its use provides a formal statistical framework for model selection, parameter estimation, and data analysis. Our results for Australian data show that this model leads to projected life expectancy values similar to those produced by the separate projection of mortality for females and males, but possesses the additional advantage of ensuring that the projected male-to-female ratio for death rates at each age converges to a constant. Moreover, the randomness of the corresponding residuals indicates that the model fit is satisfactory.