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

Andrew J.G. Cairns, David Blake, Kevin Down, Guy D. Coughlan,
David Epstein, Alen Ong and Igor Balevich


We compare quantitatively eight stochastic models explaining improvements
in mortality rates in England and Wales and in the United States. On the basis
of the Bayes Information Criterion (BIC), we find that, for higher ages, an
extension of the Cairns-Blake-Dowd (CBD) model that incorporates a cohort
effect fits the England and Wales males data best, while for U.S. males data,
the Renshaw and Haberman (RH) extension to the Lee and Carter model that
also allows for a cohort effect provides the best fit. However, we identify
problems with the robustness of parameter estimates under the RH model,
calling into question its suitability for forecasting. A different extension to the
CBD 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 datasets. This model also shows,
for both datasets, 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.