Abstract
A common feature in the modelling and extrapolation of the trends in mortality rates over time, based on fitted parametric structures, has tended to involve the treatment of a structured fitted main effects period component (with possibly a cohort component) as a random effects time series. In this paper, we follow the lead of Haberman and Renshaw (Insurance Math Econ 50:309–333, 2012) and other authors in modelling and forecasting mortality improvement rates over time, rather than mortality rates. In this context, we assume linear parametric structures for mortality improvement rates, and we examine the feasibility of modelling the main period effects (and possibly any cohort effects) as a random effect from the outset. We argue that this leads to a more unified approach to model fitting and extrapolation.
Highlights
One of the themes of the recent longevity related academic literature has been the consideration of the modelling of mortality improvement rates (MIR), rather than mortality rates (MR)
Many standard life tables used by actuaries for annuity pricing or reserving are increasingly based on an assumption about the dynamics of suitably defined mortality improvement rates
Our main contribution is to show that, by attributing random effects to the period and cohort components of a main effects ageperiod-cohort structured linear predictor from the outset, it is possible to present a comprehensive self-contained process for modelling and extrapolating mortality improvement rates, which incorporates structured dispersion and an apparent selfselecting time series. We show that this methodology extends to the modelling and extrapolation of mortality rates provided that the predictor structure is linear. We argue that this methodological framework leads to a more unified approach to model fitting and extrapolation as a result of treating the time element as a random effect from the outset, thereby impacting both fitting and extrapolation stages
Summary
One of the themes of the recent longevity related academic literature has been the consideration of the modelling of mortality improvement rates (MIR), rather than mortality rates (MR). Our main contribution is to show that, by attributing random effects to the period and cohort components (or just the period components) of a main effects ageperiod-cohort structured linear predictor from the outset, it is possible to present a comprehensive self-contained process for modelling and extrapolating mortality improvement rates, which incorporates structured dispersion and an apparent selfselecting time series. We show that this methodology extends to the modelling and extrapolation of mortality rates provided that the predictor structure is linear.
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