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
Number of pages9
JournalInsurance: Mathematics and Economics
Publication statusPublished - 1 Jul 2017
Externally publishedYes


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


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