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

Research output: Contribution to journalArticle

Abstract

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.

Details

Authors
Organisations
External organisations
  • Maastricht University
Research areas and keywords

Subject classification (UKÄ) – MANDATORY

  • Probability Theory and Statistics

Keywords

  • Age–period model, Age–period–cohort model, Identifiability, Lee–Carter model, Plug-in Lee–Carter model, Time series model
Original languageEnglish
Pages (from-to)117-125
Number of pages9
JournalInsurance: Mathematics and Economics
Volume75
Publication statusPublished - 2017 Jul 1
Publication categoryResearch
Peer-reviewedYes