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

Eric Beutner, Simon Reese and Jean-Pierre Urbain

Insurance: Mathematics and Economics, 2017, vol. 75, issue C, 117-125

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.

Keywords: Time series model; Identifiability; Lee–Carter model; Plug-in Lee–Carter model; Age–period model; Age–period–cohort model (search for similar items in EconPapers)
Date: 2017
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (3)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:insuma:v:75:y:2017:i:c:p:117-125

DOI: 10.1016/j.insmatheco.2017.04.006

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