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

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... e costs of providing for future ageing 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. 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 otherwise of structural breaks in a selection of leading mortality models. We find that structural breaks are present in the majority of cases. In particular, where there is a structural break present we find that allowing for that improves the forecast result significantly. JEL Classification: C51, C52, C53, G22, G23, J11 A c c e p t e d M a n u s c r i p t N o t C o p y e d i t e d Downloaded From: http://risk.asmedigitalcollection.asme.org/ on 03/11/2015 Terms of Use: http://asme.org/terms 2 O'HARE AND LI ASCE-ASME Journal of Risk and Uncertainty in Engineering Systems, Part B: Mechanical Engineering. A c c e p t e d M a n u s c r i p t N o t C o p y e d i t e d Downloaded From: http://risk.asmedigitalcollection.asme.org/ on 03/11/2015 Terms of Use: http://asme.org/terms ASCE-ASME Journal of Risk and Uncertainty in Engineering Systems, Part B: Mechanical Engineering. A c c e p t e d M a n u s c r i p t N o t C o p y e d i t e d Downloaded From: http://risk.asmedigitalcollection.asme.org/ on 03/11/2015 Terms of Use: http://asme.org/terms ASCE-ASME Journal of Risk and Uncertainty in Engineering Systems, Part B: Mechanical Engineering. A c c e p t e d M a n u s c r i p t N o t C o p y e d i t e d Downloaded From: http://risk.asmedigitalcollection.asme.org/ on 03/11/2015 Terms of Use: http://asme.org/terms ASCE-ASME Journal of Risk and Uncertainty in Engineering Systems, Part B: Mechanical Engineering. A c c e p t e d M a n u s c r i p t N o t C o p y e d i t e d Downloaded From: http://risk.asmedigitalcollection.asme.org/ on 03/11/2015 Terms of Use: http://asme.org/terms This can be found at http://www.mortality.org/. A c c e p t e d M a n u s c r i p t N o t C o p y e d i t e d Downloaded From: http://risk.asmedigitalcollection.asme.org/ on 03/11/2015 Terms of Use: http://asme.org/terms IDENTIFYING STRUCTURAL BREAKS IN STOCHASTIC MORTALITY MODELS 7 this is a measure of the overall bias in the projections. The average absolute error, E2, equals As can be seen from the diagrams the trend in each of the time series appears to shift and in particular to accelerate as we move beyond the 1970's. For the Lee-Carter model this is clear in the figure 1 where a peak has occurred around 1970 for each of the countries considers ASCE-ASME Journal of Risk and Uncertainty in Engineering Systems, Part B: Mechanical Engineering. A c c e p t e d M a n u s c r i p t N o t C o p y e d i t e d Downloaded From: http://risk.asmedigitalcollection.asme.org/ on 03/11/2015 Terms of Use: http://asme.org/terms ASCE-ASME Journal of Risk and Uncertainty in Engineering Systems, Part B: Mechanical Engineering. A c c e p t e d M a n u s c r i p t N o t C o p y e d i t e d Downloaded From: http://risk.asmedigitalcollection.asme.org/ on 03/11/2015 Terms of Use: http://asme.org/terms IDENTIFYING STRUCTURAL BREAKS IN STOCHASTIC MORTALITY MODELS 9 ASCE-ASME Journal of Risk and Uncertainty in Engineering Systems, Part B: Mechanical Engineering. A c c e p t e d M a n u s c r i p t N o t C o p y e d i t e d Downloaded From: http://risk.asmedigitalcollection.asme.org/ on 03/11/2015 Terms of Use: http://asme.org/terms ASCE-ASME Journal of Risk and Uncertainty in Engineering Systems, Part B: Mechanical Engineering. A c c e p t e d M a n u s c r i p t N o t C o p y e d i t e d Downloaded From: http://risk.asmedigitalcollection.asme.org/ on 03/11/2015 Terms of Use: http://asme.org/terms 14 O'HARE AND LI The findings are significant in highlighting the importance of the sample period when fitting a model to mortality data; however, they make no reference to possible future structural breaks. Further research could look at more recent developments in the identification of structural breaks in models. Namely, monitoring data for structural breaks as and when they occur, this would then allow for these breaks to be incorporated into mortality models more efficiently reducing any future forecast errors. A c c e p t e d M a n u s c r i p t N o t C o p y e d i t e d Downloaded From: http://risk.asmedigitalcollection.asme.org/ on 03/11/2015 Terms of Use: http://asme.org/terms IDENTIFYING STRUCTURAL BREAKS IN STOCHASTIC MORTALITY MODELS 15 Population Studies, 13, 1-18. ASCE-ASME Journal of Risk and Uncertainty in Engineering Systems, Part B: Mechanical Engineering. A c c e p t e d M a n u s c r i p t N o t C o p y e d i t e d Downloaded From: http://risk.asmedigitalcollection.asme.org/ on 03/11/2015 Terms of Use: http://asme.org/terms IDENTIFYING STRUCTURAL BREAKS IN STOCHASTIC MORTALITY MODELS 17 [36] Zeileis, A. A c c e p t e d M a n u s c r i p t N o t C o p y e d i t e d represent models with both small and large numbers of factors. ASCE-ASME Journal of Risk and Uncertainty in Engineering Systems, Part B: Mechanical Engineering. A c c e p t e d M a n u s c r i p t N o t C o p y e d i t e d Downloaded From: http://risk.asmedigitalcollection.asme.org/ on 03/11/2015 Terms of Use: http://asme.org/terms IDENTIFYING STRUCTURAL BREAKS IN STOCHASTIC MORTALITY MODELS 23 FIGURE 2. Cumulative sum of residuals test for the Lee-Carter model for (from top left clockwise) US, UK, Netherlands and Australia with boundaries shown in red. A c c e p t e d M a n u s c r i p t N o t C o p y e d i t e d Downloaded From: http://risk.asmedigitalcollection.asme.org/ on 03/11/2015 Terms of Use: http://asme.org/terms 24 O'HARE AND LI FIGURE 3. Test of the structural break for the Lee-Carter model for (from top left clockwise) A c c e p t e d M a n u s c r i p t N o t C o p y e d i t e d Downloaded From: http://risk.asmedigitalcollection.asme.org/ on 03/11/2015 Terms of Use: http://asme.org/terms ASCE-ASME Journal of Risk and Uncertainty in Engineering Systems, Part B: Mechanical Engineering. A c c e p t e d M a n u s c r i p t N o t C o p y e d i t e d Downloaded From: http://risk.asmedigitalcollection.asme.org/ on 03/11/2015 Terms of Use: http://asme.org/terms IDENTIFYING STRUCTURAL BREAKS IN STOCHASTIC MORTALITY MODELS 29 Appendix: Additional Figures and Tables FIGURE 8. Cumulative sum of residuals test for the CBD model for (from top left clockwise) US, UK, Netherlands and Australia with boundaries shown in red. A c c e p t e d M a n u s c r i p t N o t C o p y e d i t e d Downloaded From: http://risk.asmedigitalcollection.asme.org/ on 03/11/2015 Terms of Use: http://asme.org/terms IDENTIFYING STRUCTURAL BREAKS IN STOCHASTIC MORTALITY MODELS 31 FIGURE 10. Cumulative sum of residuals test for the O'Hare and Li model for (from top left clockwise) US, UK, Netherlands and Australia with boundaries shown in red. A c c e p t e d M a n u s c r i p t N o t C o p y e d i t e d Downloaded From: http://risk.asmedigitalcollection.asme.org/ on 03/11/2015 Terms of Use: http://asme.org/terms 32 O'HARE AND LI FIGURE 11. Test of the structural break for the CBD model for (from top left clockwise) A c c e p t e d M a n u s c r i p t N o t C o p y e d i t e d Downloaded From: http://risk.asmedigitalcollection.asme.org/ on 03/11/2015 Terms of Use: http://asme.org/terms IDENTIFYING STRUCTURAL BREAKS IN STOCHASTIC MORTALITY MODELS 33 FIGURE 12. Test of the structural break for the Plat model for (from top left clockwise) A c c e p t e d M a n u s c r i p t N o t C o p y e d i t e d Downloaded From: http://risk.asmedigitalcollection.asme.org/ on 03/11/2015 Terms of Use: http://asme.org/terms ASCE-ASME Journal of Risk and Uncertainty in Engineering Systems, Part B: Mechanical Engineering. A c c e p t e d M a n u s c r i p t N o t C o p y e d i t e d Downloaded From: http://risk.asmedigitalcollection.asme.org/ on 03/11/2015 Terms of Use: http://asme.org/terms Figure 13: Test of the structural break for the O'Hare and Li model for (from top left clockwise) A c c e p t e d M a n u s c r i p t N o t C o p y e d i t e d Downloaded From: http://risk.asmedigitalcollection.asme.org/ on 03/11/2015 Terms of Use: http://asme.org/terms