  The predominant way of modelling mortality rates is the Lee-Carter model and
its many extensions. The Lee-Carter model and its many extensions use a latent
process to forecast. These models are estimated using a two-step procedure that
causes an inconsistent view on the latent variable. This paper considers
identifiability issues of these models from a perspective that acknowledges the
latent variable as a stochastic process from the beginning. We call this
perspective the plug-in age-period or plug-in age-period-cohort model. Defining
a parameter vector that includes the underlying parameters of this process
rather than its realisations, we investigate whether the expected values and
covariances of the plug-in Lee-Carter models are identifiable. It will be seen,
for example, that even if in both steps of the estimation procedure we have
identifiability in a certain sense it does not necessarily carry over to the
plug-in models.
