**DISCUSSION PAPER PI-0802**

Evaluating the goodness of fit of stochastic mortality models

Kevin Dowd, Andrew J.G. Cairns, David Blake, Guy D. Coughlan, David Epstein, and Marwa Khalaf-Allah

This study sets out a framework to evaluate the goodness of fit of stochastic
mortality models and applies it to six different models estimated using English
& Welsh male mortality data over ages 64–89 and years 1961–2007.
The methodology exploits the structure of each model to obtain various residual
series that are predicted to be iid standard normal under the null hypothesis
of model adequacy. Goodness of fit can then be assessed using conventional
tests of the predictions of iid standard normality. The models considered
are: Lee and Carter’s (1992) one-factor model, a version of Renshaw
and Haberman’s (2006) extension of the Lee–Carter model to allow
for a cohort-effect, the age-period-cohort model, which is a

simplified version of the Renshaw–Haberman model, the 2006 Cairns–Blake–Dowd
two-factor model and two generalized versions of the latter that allow for
a cohort-effect. For the data set considered, there are some notable differences
amongst the different models, but none of the models performs well in all
tests and no model clearly dominates the others.

Key words:- Goodness of fit, Mortality models, Standard normality