Forecasting Mortality Trends Allowing for Cause-of-Death Mortality Dependence

Abstract

Longevity risk is among the most important factors to consider for pricing and risk management of longevity products. Past improvements in mortality over many years, and the uncertainty of these improvements, have attracted the attention of experts, both practitioners and academics. Since aggregate mortality rates reflect underlying trends in causes of death, insurers and demographers are increasingly considering cause-of-death data to better understand risks in their mortality assumptions. The relative importance of causes of death has changed over many years. As one cause reduces, others increase or decrease. The dependence between mortality for different causes of death is important when projecting future mortality. However, for scenario analysis based on causes of death, the assumption usually made is that causes of death are independent. Recent models, in the form of Vector Error Correction Models (VECMs), have been developed for multivariate dynamic systems and capture time dependency with common stochastic trends. These models include long-run stationary relations between the variables and thus allow a better understanding of the nature of this dependence. This article applies VECMs to cause-of-death mortality rates to assess the dependence between these competing risks. We analyze the five main causes of death in Switzerland. Our analysis confirms the existence of a long-run stationary relationship between these five causes. This estimated relationship is then used to forecast mortality rates, which are shown to be an improvement over forecasts from more traditional ARIMA processes, which do not allow for cause-of-death dependencies.

Acknowledgments

The authors acknowledge the financial support of the Australian Research Council Centre of Excellence in Population Ageing Research (project number CE110001029).

Notes

Future researches might be interested in comparisons across countries.

In this article, we consider variables that are integrated of order one. In that special case, cointegrating relations are necessarily stationary. For a more general framework, see Hamilton (1994) and Lütkepohl (2005).