Longevity: Back to first principles

Andrew Hunt and David Blake present a new, general procedure for constructing mortality models that unbundles the age, period and cohort dimensions in the data, resulting in better understanding of historic changes in mortality and more reliable forecasts of future mortality rates

Longevity risk is one of the key demographic risks faced by pension plans and life assurers. Many plan sponsors have been asked to contribute millions of pounds to cover deficits caused by rising projections of life expectancy. The world’s oldest life office, the Equitable Life Assurance Company, closed to new business, in part due to a catastrophic failure to assess the impact of longer life spans on the guarantees it had offered policyholders.

But it is not just the increasing trend, but the uncertainty around how that trend will evolve which has spawned the global multi-billion dollar pension fund derisking and longevity reinsurance markets. To manage this risk, it needs to be measured and that is why the ‘general procedure’ (GP) for constructing mortality models has been developed. It specifically addresses the need for more reliable forecasts of mortality, both at specific ages and for specific years of birth, which conventional models struggle to provide.
Mortality rates for men and women from a national population can be analysed in terms of three factors – age, period and year of birth (or cohort).  

In terms of age, we know that old people are more likely to die than the young. But infant mortality rates can also be high. Even now, the first six months of our lives can be as dangerous as the following three decades. We also know that, due to reckless behaviour, mortality rates increase in the late teens and early 20s – especially for men – the so-called accident hump.

It is also important to take account of the year being investigated. For example, mortality rates generally fall for everyone as healthcare improves, so we would expect to have higher mortality rates in 1950, say, than in 2013. However, this trend is not continuous; freezing winters and hot summers can both raise mortality rates, especially among the elderly, and there is the ever-present threat of a natural disease or pandemic disease occurring.

Finally, we know that year of birth can make an important difference. Some birth cohorts have higher rates of mortality than others separated by only a few years for reasons that are not always obvious. Of the three factors, year of birth is by far the most subtle and it can easily confused with the other two. This is because we are unable to change one variable while holding the others fixed. For example, we can look at the same group of individuals at different times, with the same year of birth, but they will be older and be observed in different years. Similarly, we can look at different ages in the same year, but they will have different years of birth.

Most existing mortality models attempt to analyse rates by imposing a structure on mortality rates across these three factors, which is why they are known as age-period-cohort models. The earliest of these models were too simplistic to effectively describe the complex structure observed in the data, which led to inaccurate projections for mortality rates. These naive models were then subject to some ad hoc fixes in order to correct their weaknesses, which merely generated new issues later on. To solve this problem, we came up with the GP to construct mortality models from first principles and so avoid the need for makeshift solutions.

The GP is not a model itself; rather, it provides a method for building mortality models tailored to specific national populations, driven by a forensic examination of the data.

The GP identifies every significant demographic feature in the data in sequence, starting with the most important. For each feature, we need to apply expert judgement to give it a functional form which can be estimated from the data. By following the GP, we believe that it is possible to build mortality models which capture accurately all the significant information present in the data in the age, period and cohort dimensions. In particular, the GP prevents structure in the data which is genuinely associated with an age or period effect being wrongly allocated to a cohort effect. This is important in itself, but especially so when we come to make forecasts of future mortality rates.

In summary, a mortality model generated by the GP will:
• make stochastic projections of future mortality rates, since the future is uncertain and a good model needs to quantify uncertainty by indicating a range of possible outcomes for future mortality rates;
• be able to accurately describe the features observed in the past;
• be simple to calibrate and explain to other stakeholders;
• capture the specific features of mortality for different years of birth and project these as individuals age; and
• provide reasonable forecasts of mortality rates at specific ages for some longevity risk management strategies based on derivatives.

When we applied the GP to data for the UK, we found that the model needed more terms than simply those governing the average level of mortality rates across ages and how rapidly rates increase as people age. To describe the past accurately we also need to take account of the evolution of mortality rates for infants and children, the higher rates of mortality during the accident hump and the nuanced impact of medical progress on different ages late in life. Once these features are accounted for, the true impact of year of birth is revealed and the differing life stories for those born during the First World War, the Great Depression and the Swinging Sixties can be told.

The post-war baby boomer generation has started retiring, purchasing annuities and drawing pensions that may last for decades. To charge them a fair price for their benefits and accurately assess the risks of providing them with pensions, we need better models which are able to analyse the factors which will affect their mortality rates and project them into the future.

Models produced by the GP outperform all of the alternative models proposed to date in achieving this and have been successful in predicting mortality rates when tested against historical data. The GP also avoids the problems many alternative models have, with either terms being added as ad hoc fixes to fundamental problems or being generated by black-box algorithms. The models produced are also robust to new and revised data, such as that which resulted from the revision of populations at high ages caused by the 2011 census in the UK.

To sum up, the general procedure offers a new and better set of tools for measuring and monitoring one of the key risks of our age – that we will outlive our savings. It represents a step forward for pension plans and life assurance companies in assessing this risk and so can help safeguard the retirement security of millions.

Andrew Hunt, a former pensions consultant, is a PhD student at Cass Business School and a fellow of the Pensions Institute; David Blake is professor of pension economics at Cass Business School and director and fellow of the Pensions Institute. The full paper is available at

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