A Parsimonious Approach to Stochastic Mortality Modelling with Dependent Residuals
Abstract
A standard approach to the tting of stochastic mortality models is to maximise a likelihood function underpinned by an assumption that deaths follow a conditionally independent Poisson
distribution. This, in turn, has led researchers to develop increasingly complex models in an effort to improve in-sample explanatory power. This paper, using the Cairns-Blake-
Dowd (CBD) model as an example, proposes an alternative framework that models residuals as dependent rather than conditionally independent random variables. The extension introduces
short-term dependencies between adjacent cells of the population that, amongst other things, can be structured to capture cohort eff ects in a parsimonious and transparent manner.
Using a Bayesian framework, the posterior distribution of the resulting hierarchical model is considered in order to explore the extent of parameter uncertainty. Samples from
the posterior predictive distribution are used to project mortality, and the outcomes are compared to the Poisson maximum likelihood results of the original CBD model and one
of its cohort-enhanced versions, model M7. The resulting model yields predictive distributions of mortality rates with greater spread compared to its two competitors, especially as
the projection horizon prolongs. Those increased levels of uncertainty are then inherited by mortality related indices and metrics.
Keywords: Stochastic mortality, Bayesian VAR, CBD model, Parameter uncertainty, Robustness.