Mortality Density Forecasts: An Analysis of Six Stochastic Mortality Models

Abstract

This paper develops a framework for developing forecasts of future mortality rates. We discuss the suitability of six stochastic mortality models for forecasting future mortality and estimating the density of mortality rates at different ages. In particular, the models are assessed individually with reference to the following qualitative criteria that focus on the plausibility of their forecasts: biological reasonableness; the plausibility of predicted levels of uncertainty in forecasts at different ages; and the robustness of the forecasts relative to the sample period used to fit the model. An important, though unsurprising, conclusion is that a good fit to historical data does not guarantee sensible forecasts. We also discuss the issue of model risk, common to many modelling situations in demography and elsewhere. We find that even for those models satisfying our qualitative criteria, there are significant differences between both central forecasts of mortality rates at different ages and the distributions surrounding those central forecasts.

Analysis of Finnish and Swedish mortality data with stochastic mortality models

“…24. Again the greater uncertainty for the higher ages in each case is plausible, but the strong increase of the mortality rates in models M7 and M8 is biologically implausible 8 . For the rest of the models a decreasing or at least stable central trend is uncovered.…”

“…If more than one period effect is present in the model a multivariate random walk with drift and correlated innovations are used to drive the dynamics of the period effects. The following approach was implemented [8]:…”

“…The third component is the cohort effect. As in previous studies I follow the assumption that the dynamics of the cohort effect c t-x are independent of the dynamics of the period effects j t (i) [8,25]. Fitted values for the cohort parameter for the models M2-5 and M7-M9 can be seen in Sect.…”

“…Suitable means, that the model fits well to historical data and gives reasonable and reliable forecasts. A number of recent articles have compared different mortality models with the emphasis on historical data [7,8,14,15,25,31,36]. Renshaw and Haberman [31], for instance, compare models in a quantitative fashion by analysing the pattern of standardised residuals against age, year of observation, and year of birth.…”

“…Dowd et al [13,14] carry out a range of formal, out-of-sample backtesting and goodness-of-fit tests using English and Welsh male-mortality data. Cairns et al [8] asses the forecasts of future mortality rates with reference to the qualitative criteria: plausibility of the forecasts; plausibility of predicted levels of uncertainty in forecasts at different ages; and the robustness of the forecasts relative to the sample period used to fit the model.…”