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 language | English |
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Pages (from-to) | 117-125 |
Number of pages | 9 |
Journal | Insurance: Mathematics and Economics |
Volume | 75 |
DOIs | |
Publication status | Published - 1 Jul 2017 |
Externally published | Yes |
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.
Funders | Funder number |
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Jan Wallander and Tom Hedelius Foundation | P2014-0112:1, H2014-0467:1 |
Keywords
- Age–period model
- Age–period–cohort model
- Identifiability
- Lee–Carter model
- Plug-in Lee–Carter model
- Time series model