 The general procedure for constructing mortality models is a new approach based on analysing mortality rates across the dimensions of age, period and year of birth. It uses a combination of statistical methods and expert judgement to identify sequentially every significant demographic feature in the data and give it a specific functional form. This means that it can be used to give a better understanding of the historic changes in mortality and therefore more reliable forecasts of future mortality rates.
Longevity risk is one of the key demographic risks faced by pension plans and life assurers. In recent years, a host of different competing models for measuring and monitoring longevity risk have been created; however many of them give poor fits to historic data or make unfeasible forecasts of mortality rates. To overcome these problems, 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 do.
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). However, year of birth is by far the most subtle and it can easily be 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.
Most existing mortality models attempt to impose 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, such as the Lee-Carter model, 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. Other, more complicated models were generated using statistical algorithms (such as those based on principal component analysis). However, these tend to be “black box” procedures which sacrifice any demographic significance or meaning to the terms in them in favour of maximising the fit to historic data. This is not an adequate approach for most model users, who are required to explain their models to non-specialist users. They would also often fail to give cohort effects that were believable or consistent with the history of the population. Furthermore, they tended not to provide more plausible forecasts of future mortality rates. To solve these problems, we came up with the GP to construct mortality models from first principles.
The GP is not a model itself: rather it provides a method for building mortality models tailored to specific populations, driven by a forensic examination of the data. Through an iterative process, the GP categorises every significant demographic feature in the data in sequence, starting with the most important. At each step, the most important feature is identified by finding a new term which fits the data best. Then, we need to apply expert judgement to give this term a simplified functional form which has greater demographic significance and can be estimated more robustly. 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, which is important in itself, but especially so when we come to make forecasts of future mortality rates. Models produced by the GP outperform all of the alternative models proposed to date in fitting the historic data and have been successful in predicting mortality rates.
When we applied the GP to data for the UK, we found that we needed to go beyond terms governing just the average level of mortality across ages and how rapidly it increases as we age. The extra terms we needed to include 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. Their identification would not have been possible using alternative black box methods, or guessed in advance as the solution to problems with a simpler model.
In summary, the General Procedure offers a new and better method of building the tools needed to measure and monitor longevity risk. It therefore provides a blueprint for actuaries and mortality modellers to enhance their ability to face this key risk.
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