An RGA analysis comparing the Canadian Institute of Actuaries (CIA) model and a Canadian calibration of the 2019 Continuous Mortality Investigation (CMI) mortality improvement model highlights the significant impact the choice of a model has on mortality projections.
Different models produce different results. This analysis set out to provide valuable insights into the nuances in two prominent models and the importance of understanding how and why they diverge. The goal is to help insurers see through the fog inherent in attempting to predict future mortality improvements.
For this summary analysis, we have not delved into the full technical details of each model. Instead, we have focused on four key aspects of the models. These are:
The waterfall charts below (Figures 1A and 1B) move from CMI_2019 to the CIA model, covering three of the items mentioned above. The LTR does not feature on this chart because we have used the CIA LTR in the CMI model.
The waterfall charts show how the life expectancy for a 65-year-old varies as we move from the CMI model to the CIA model. The components of the APCI model are linked, and the impact associated with each step would vary if these steps were taken in a different order. However, the waterfalls are still useful to show how different components drive the difference between the CIA and CMI models. They show that the CIA model produces higher life expectancies than the CMI model, and almost every aspect considered contributes to this.
The initial rate is the rate of improvement in the last year of known data, the jumping-off year. It is composed of age, period, and cohort components and follows this formula:
Total improvement = age component + period component + cohort component
The level of the initial rate influences the overall rate of improvement in the future projection. The breakdown of the rate among age, period, and cohort components influences how the rates will vary based on an individual’s year of birth and age. To derive the initial rate, the APCI model is fitted to known data. The age, period, and cohort improvement components are then backed out from this model. The initial rate from our analysis was then compared to the initial rates from the CIA scale. (Figures 2A and 2B)*
Improvements by age are smoother under the CMI model than the CIA scale, which may feel more intuitive when projecting this rate into the future. On the other hand, it is likely that the CIA model will more closely reflect recent experience, and we may only expect the mortality rates to be smooth in the future projection, not the improvement rates.
The CIA initial rate is higher at older ages than the CMI’s. This contributes to the higher life expectancies projected by using the CIA initial rate.
The table below outlines the different input parameters used to derive the initial rate in each model.
Both models project the initial rate from the jumping-off year (2019) toward an LTR at the end of a convergence period. Multiple parameters in the model influence the shape and length of the convergence. The key ones are the direction of travel (DT), which is the rate of change of the improvements just after the jumping-off point, and the convergence period, which is the number of years taken to reach the LTR. The age, period, and cohort components can each have different DTs and convergence periods.
The graphs below show how the future projection differs for different combinations of DT and convergence period (conv), using various CIA and CMI parameters (Figures 3A and 3B).
It is clear the choice of parameter can greatly influence the future projection. Table 2 describes the convergence and DT parameters.
The CIA set an LTR by projecting their stochastic model forward using a time series and estimating the age-independent LTR that most closely matched its central stochastic forecast (CIA paper section 6). This is a very data-driven method. The CMI chooses not to set an LTR.
As mentioned in the previous section, the CIA has chosen a convergence period of 30 years, placing more reliance on recent data. In contrast, the CMI’s often shorter convergence period and zero DT may mean the LTR is a more material parameter for this model.
Both models use the APCI model to fit a range of ages. The CIA fits ages 40 to 90 and the CMI fits ages 20 to 100. To extend the model to older ages, an extrapolation is needed. The CMI fits ages up to 120 by linearly extrapolating mortality rates based on the age 99 and age 100 rates. The CIA takes a different approach. It obtained access to older age administrative datasets and used these to identify a mortality plateau in the data. It then used Hermite splines to model mortality from age 90 to the mortality plateau of 113/112 for males/females.
The waterfall chart suggests the CIA approach leads to higher mortality improvement rates than the CMI approach. This will become more material for life expectancies at older ages.
This analysis has demonstrated that different implementations of a similar mortality projection model (APCI in this case) can lead to materially different results. A multitude of models exist, and each would most likely produce a different answer. When factoring in potential model adjustments – for example, to tailor the projection to an insured population or to reflect future drivers of mortality improvement – the interval of possibilities becomes even wider. Future mortality improvement comes with a high level of uncertainty, and for that reason it may be one of the most challenging assumptions for an actuary to determine.
RGA is here to help. As an established leader in actuarial modeling, RGA combines a long track record of success with innovative new approaches. Contact us today to learn how our team of experts can help you more effectively manage mortality risk.
