Cobus Daneel and Jon Palin describe the challenges in producing the CMI’s Mortality Projections Model for 2020
The exceptional nature of mortality in 2020 is challenging for mortality projections that rely on recent experience to inform future trends. Models may need to be adapted if they are to produce plausible results. To avoid an over-reaction to one year’s data, the CMI has modified its mortality projections model.
Mortality in 2020
COVID-19 led to exceptional mortality experience in 2020. Figure 1, based on the CMI Mortality Monitor (bit.ly/3scIRnI), compares standardised mortality rates (SMRs) in 2020 to those in corresponding weeks in the previous decade. (An SMR is an average mortality rate for a range of ages, assuming it has a standard age and gender profile; this enables a consistent comparison of mortality rates over time.) As this analysis is based on registered deaths, there are dips around public holidays, when register offices tend to be closed.
Mortality in the first quarter of 2020 was relatively low, as in 2019. The pandemic then led to a severe spike in mortality during the second quarter, before we saw record low mortality in the third quarter. The second wave of the pandemic saw elevated mortality during the winter of 2020-21, but not as high as during the fi rst wave or what the number of deaths ascribed to COVID-19 may have suggested.
Figure 2 shows mortality improvements derived from SMRs, based on the dataset used to calibrate CMI_2020 – the latest annual update of the CMI Mortality Projections Model, published in March 2021. (The working paper for CMI_2020 may be found at bit.ly/3saFxJS) These are ‘crude’ improvements, derived from the data without smoothing to separate signal from noise. The 2020 mortality improvement of -12% is well outside the range of improvements for 1981-2019, and our analysis of longer-term data from the Human Mortality Database suggests 2020 had the largest year-on-year increase in mortality since 1929.
How the CMI Model works
To ensure relevance for a variety of populations, the CMI Model models mortality improvements. Users can apply projected mortality improvements to a recent mortality table of their choice to derive projected mortality rates. In line with other ‘targeting’ models, the CMI Model interpolates between:
- ‘Initial’ mortality improvements, applying at the start of the projection period. These are based on recent historical mortality improvements, which are usually considered to be a good guide to short-term future improvements.
- ‘Long-term’ mortality improvements. As the long-term influences on mortality could be quite different to recent influences, the long-term improvements are not based on historical data. As a matter of policy, the CMI does not give a view on a suitable value for the long-term rate, and users of the CMI Model must form their own view. The model is therefore a framework for mortality assumptions – it does not give a single answer. This is important to bear in mind when setting mortality assumptions in 2021 in particular, as the pandemic may have changed longer-term mortality rates.
Figure 3 shows crude SMRs for each year since 2000, together with a smooth fitted trend from CMI_2020. We see that, while there is some volatility from year to year, this was relatively modest for 1980 to 2019, with crude rates being within 3% of the trend during that period. The SMR for 2020 was well outside that range.
The CMI Model ‘expects’ that the fitted underlying trend would likely be within 3% of the crude SMR, in line with the volatility for previous years shown in Figure 3. In a business-as-usual model, the SMR in 2020 would exert significant upward pressure on the fitted trend, corresponding to a negative initial mortality improvement of about -0.7%. As the initial rate is used as the starting point for future projections, this would in turn lead to a substantial fall in cohort life expectancy
A business-as-usual version of CMI_2020 would have led to a fall in life expectancy at age 65 of more than 10 months for females and nearly 15 months for males compared to the previous version of the CMI Model, CMI_2019. This is more than what most users would have thought reasonable, given a single year of additional data. Because of this, we have modified the model to reduce the impact of experience in 2020, following a broadly supported consultation.
We have amended the smoothing process so users can place less weight on data for individual years. Specifically, we place no weight on the data for 2020 in the Core version of CMI_2020. This reflects our view that mortality in 2020 was exceptional and is unlikely to be a good guide to mortality improvements in the coming years.
Other ways to cope with the exceptional mortality in 2020 were also considered, including:
- Increasing the period smoothing parameter – a parameter in the model that affects how rapidly mortality improvements can change over time. However, to avoid excessive changes in life expectancy, the parameter would need to be increased to the extent that the model wouldn’t produce a realistic fit over earlier periods and would almost certainly have required further tweaks in later versions of the model.
- Adjusting the number of deaths in the dataset to exclude those linked to the pandemic. While this seems reasonable, there could be considerable subjectivity in deciding which measure of pandemic-related deaths to use. And it would be difficult to argue that the resulting dataset represents a valid counterfactual of mortality in the absence of a pandemic.
Illustrative results from CMI_2020
Users of the CMI Model are required to form their own view on the long-term rate of mortality improvements, and users can apply the projections of the model to their chosen mortality table. For the purpose of illustration, we have used the S3PMA and S3PFA UK pensioner mortality tables and a long-term rate of 1.5% a year – a commonly used value, rather than a CMI recommendation.
Figure 4 shows illustrative cohort life expectancies at age 65 on 1 January 2021 from different versions of the CMI Model. It shows that CMI_2020 produces cohort life expectancies at age 65 that are about four weeks lower for males and one week lower for females than in CMI_2019, when using these illustrative assumptions for both models. The highest life expectancies shown are for CMI_2012, which are nearly 18 months higher than for CMI_2020 for both males and females.
The CMI Model is a framework that allows users to project life expectancy based on their views. We continue to encourage users of the model to consider adjusting the ‘core’ parameters to reflect their views and their particular population – for example, recognising that in recent years, mortality improvements in England and Wales have been higher for those living in less deprived areas.
Responses to our recent consultation showed that, among CMI Model users, there is broad consensus that it is reasonable and pragmatic at this time to disregard 2020 when assessing ‘initial’ improvements. However, views may shift in time, and users can modify CMI_2020 to put weight on 2020 data if they wish.
There is also an open question about the longer-term effects of the pandemic and what that may mean for long-term rates. Different actuaries can reasonably have a range of views, and we expect some lively discussions in 2021.
Cobus Daneel is the chair of the CMI Mortality Projections Committee
Jon Palin is secretary to the CMI Mortality Projections Committee