Your manager recently participated in a mortality modelling seminar where the

presenter successfully used the following simplified Lee$$Carter model to forecast

mortality rates:

$,=$ exp$(+$ kt $+,)$ with $,$ N$(0,\backslash$sigma $2$

$)($Model $3)$

where $$ and kt are unknown parameters that can be estimated.

Based on that experience, your line manager suggests that the team should consider

Model $3.$

$($iii$)$ Demonstrate that Model $3$ is not identifiable. $[1]$

$($iv$)$ Describe how you would achieve identifiability when fitting Model $3.[2]$

$($v$)$ Comment on the suitability of Model $3.[3]$