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

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.

Original languageEnglish
Pages (from-to)117-125
Number of pages9
JournalInsurance: Mathematics and Economics
Volume75
DOIs
Publication statusPublished - 1 Jul 2017
Externally publishedYes

Funding

The first author was partially supported by CRoNoS COST ActionIC1408. The second author received funding from the Jan Wallander and Tom Hedelius Foundation under research grant numbers P2014-0112:1 and H2014-0467:1.

FundersFunder number
Jan Wallander and Tom Hedelius FoundationP2014-0112:1, H2014-0467:1

    Keywords

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

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