A Quantitative Comparison of Stochastic Mortality Models Using Data from England & Wales and the United States

Abstract

We compare quantitatively eight stochastic models explaining improvements in mortality rates in England &Wales and in the US. On the basis of the Bayes Information Criterion (BIC), we find that an extension of the Cairns, Blake & Dowd (2006b) model that incorporates the cohort effect fits the England & Wales data best, while for US data, the Renshaw & Haberman (2006) extension to the Lee & Carter (1992) model that also allows for a cohort effect provides the best fit. However, we identify problems with the robustness of parameter estimates of these models over different time periods. A different extension to the Cairns, Blake & Dowd (2006b) model that allows not only for a cohort effect, but also for a quadratic age effect, while ranking below the other models in terms of the BIC, exhibits parameter stability across different time periods for both data sets. This model also shows, for both data sets, that there have been approximately linear improvements over time in mortality rates at all ages, but that the improvements have been greater at lower ages than at higher ages, and that there are significant cohort effects.

Keywords: Stochastic mortality, CBD-Perks models, Lee-Carter models, age effect, period effect, cohort effect, maximum likelihood, Bayes Information Criterion, robustness