As actuaries and the others in the longevity community await additional updates to the UK Continuous Mortality Investigation (CMI) 2023 Mortality Projections Model (“CMI_2023”), it is a valuable exercise to revisit the models underlying CMI_2023 and critically analyze their appropriateness.
Of particular interest is the effect of the models when examining the mortality of UK residents currently aged 50-70 years. This 14-million-person cohort, the industry’s next massive group of retirees, arrives with unique mortality experience that may be negatively skewing mortality model outputs.
This analysis of that specific cohort is another effort by ˿ƵAPP actuaries to study the CMI model and share insights on its proposed calibration. (Earlier this year, ˿ƵAPP released a longer paper investigating the implications of the default calibration of the CMI_2023 version of the model.)
Modeling expected future mortality is a complex topic. When building models, actuaries consider changes in healthcare provision and medical advances, changes in diet and lifestyle, and the impact of new technologies such as artificial intelligence, among many other factors.
One frequently used starting point is to fit statistical models to past data and extrapolate trends into the future. A common approach is to break down those trends into components, including:
The industry mortality projection model in the UK (the CMI model) follows this approach. The model estimates age, period, and cohort effects from past data and projects them into the future. These effects are then separately blended into assumed long-term rates at different speeds, depending on age at the start of the projection period.
Of key interest here is that cohort effects can be projected forward up to 40 years for certain ages. Once actuaries estimate these separate projections, they add them together to estimate the change in mortality rate for each age in each calendar year.
The changes from year to year are typically referred to as “mortality improvements,” although the change could be negative, meaning mortality rates become worse (and mortality has therefore “dis-improved”). When dealing with a complex model like the CMI model, it is important to ensure the output is reasonable and can be justified from a qualitative point of view.
The heatmap above shows the model output by age and calendar year for a recent version of the CMI model (CMI_2023) using the default model calibration. Warmer colors represent higher positive improvements and cooler colors depict lower or negative improvements. Cohort effects appear as diagonal patterns in this type of chart because the effect is assumed to stay with specific people as they age (moving upwards) over time (moving left to right). Whether the projected patterns produced by the model are sensible is explored further below.
For males who were aged 20-40 in the early 1990s (i.e. currently aged 50-70), the model identifies a strong negative cohort effect in the data (blue area), which will have a material effect on the projected trend in mortality for this group. As seen in the circled area, the model then projects that cohort effect forward 40 years, indicating negative mortality improvements for this group over the next several decades.
Interestingly, the same effect is not present for females. What could be driving this effect? Is it reasonable to include in a model of future improvements for this group? This is an important consideration because this age group is approaching retirement. The mortality outlook for this cohort will soon affect annuity pricing and is already relevant for deferred annuity pricing under pension risk transfer transactions.
Source: ˿ƵAPP analysis of total improvements by age and calendar year for males, based on data from the UK Office for National Statistics
Drilling into the details by exploring cause of death data helps explain why the models are fitting this effect. In the tables above we consider total improvements by age group and calendar year for males on the left, with contributions to these improvements from specific causes in the middle and right hand tables. Here we see a pattern of low mortality improvements, mainly for males aged 20-40 in the early 1990s, which can be shown when using a different segmentation of the data to be concentrated on the least affluent socioeconomic groups. These deaths are largely driven by drug overdoses and external causes including self-harm. This suggests “deaths of despair” and could be related to deindustrialization in the U.K. at that time, which spurred significant job losses and economic hardship for families across the country.
Since the balance of causes of death at older ages shifts to non-communicable diseases such as cardiovascular disease, cancer, and Alzheimer’s disease, and dementia, some careful thought needs to be given as to whether these earlier deaths are relevant at the current and future older ages of this group. If not, then using the default version of the model without adjustment could project significantly higher mortality rates for this group than turns out to be the case (i.e. underestimating the liabilities relating to younger pensioners).
Modeling the future progression of mortality rates is challenging and often requires complex statistical methods when using a data-driven approach. The features of these models need to be carefully reviewed to ensure the results make sense and can be reliably applied when estimating future mortality rates. Users should confirm they are comfortable with and can justify the results, rather than simply unquestioningly relying on default values.
