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The predominant way of modelling mortality rates is the Lee-Carter model andits many extensions. The Lee-Carter model and its many extensions use a latentprocess to forecast. These models are estimated using a two-step procedure thatcauses an inconsistent view on the latent variable. This paper considersidentifiability issues of these models from a perspective that acknowledges thelatent variable as a stochastic process from the beginning. We call thisperspective the plug-in age-period or plug-in age-period-cohort model. Defininga parameter vector that includes the underlying parameters of this processrather than its realisations, we investigate whether the expected values andcovariances 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 haveidentifiability in a certain sense it does not necessarily carry over to theplug-in models.

Identifiability issues of age-period and age-period-cohort models of the Lee-Carter type