Structural Breaks in Mortality Models and their Consequences

In recent years, the issue of life expectancy has become of upmost importance to pension providers, insurance companies and the government bodies in the developed world. Significant and consistent improvements in mortality rates and, hence, life expectancy have led to unprecedented increases in the cost of providing for older ages. This has resulted in an explosion of stochastic mortality models forecasting trends in mortality data in order to anticipate future life expectancy and, hence, quantify the costs of providing for future aging populations. Many stochastic models of mortality rates identify linear trends in mortality rates by time, age and cohort, and forecast these trends into the future using standard statistical methods. The modeling approaches used failed to capture the effects of any structural change in the trend and, thus, potentially produced incorrect forecasts of future mortality rates. In this paper, we look at a range of leading stochastic models of mortality and test for structural breaks in the trend time series.

Identifying Structural Breaks in Stochastic Mortality Models

In recent years, the issue of life expectancy has become of utmost importance to pension providers, insurance companies, and government bodies in the developed world. Significant and consistent improvements in mortality rates and hence life expectancy have led to unprecedented increases in the cost of providing for older ages. This has resulted in an explosion of stochastic mortality models forecasting trends in mortality data to anticipate future life expectancy and hence quantify the costs of providing for future aging populations. Many stochastic models of mortality rates identify linear trends in mortality rates by time, age, and cohort and forecast these trends into the future by using standard statistical methods. These approaches rely on the assumption that structural breaks in the trend do not exist or do not have a significant impact on the mortality forecasts. Recent literature has started to question this assumption. In this paper, we carry out a comprehensive investigation of the presence or of structural breaks in a selection of leading mortality models. We find that structural breaks are present in the majority of cases. In particular, we find that allowing for structural break, where present, improves the forecast result significantly.

Models of Mortality - Analysing the Residuals

The area of mortality modelling has received significant attention over the last 20 years owing to the need to quantify and forecast improving mortality rates. This need is driven primarily by the concern of governments, professionals, insurance and actuarial professionals and individuals to be able to fund their old age. In particular, to quantify the costs of increasing longevity we need suitable model of mortality rates that capture the dynamics of the data and forecast them with sufficient accuracy to make them useful. In this paper we test several of those models by considering the fitting quality and in particular, testing the residuals of those models for normality properties. In a wide ranging study considering 30 countries we find that almost exclusively the residuals do not demonstrate normality. Further, in Hurst tests of the residuals we find evidence that structure remains that is not captured by the models.