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

Eric Beutner*, Simon Reese, Jean-Pierre Urbain

*Corresponding author for this work

Research output: Contribution to journalArticleAcademicpeer-review


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 realizations, 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.
Original languageEnglish
Pages (from-to)117-125
JournalInsurance: Mathematics and Economics
Publication statusPublished - Jul 2017


  • Time series model
  • Identifiability
  • Lee Carter model
  • Plug-in Lee Carter model
  • Age period model
  • Age period cohort model

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