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The Actuary The magazine of the Institute & Faculty of Actuaries

Mortality: The last post

The use of postcodes in mortality investigations has become increasingly common in the UK, both for individual annuity pricing and in pricing bulk transactions. This article explores some of the pros and cons of the use of postcodes in mortality analyses, and considers how they can most effectively be used.

It is clear that mortality varies with postcode. For instance, Figure 1 shows a map of London in which age-adjusted population mortality for over-50s is displayed. The total range of mortality differentials represents approximately a doubling of mortality, from low (dark blue) to high (red), ignoring extremes of the distribution. Given the existence of such differentials, how can we best use postcodes in designing predictive mortality models?

There are two main ways in which postcodes can be used to help in deriving mortality assumptions:
>> Estimating directly the immediate mortality experience that might be expected in a (typically small to medium-sized) pension scheme or annuity portfolio. Postcodes are used here as a direct proxy for expected mortality rates, allowing for age and gender.
>> Using postcodes as one of a number of factors in a multivariate analysis of the mortality experience of a (typically large) pension scheme or annuity portfolio.

Although superficially similar, these uses are conceptually quite distinct and we consider them separately below. However, they share a common dependence on postcodes, and it is worth noting some immediate weaknesses:
>> Many annuity and pension portfolios have incorrect or missing postcodes on significant proportions of the data, typically ranging from 2% to 3% to around 10%
>> Many annuity and pension portfolios have pensioners living overseas
>> Postcodes provided in pension scheme data almost always relate to a current postcode. However, house moves shortly after retirement are common, as are moves later in life, especially after the death of a partner.

Using postcodes as an immediate mortality proxy
In this method, a base mortality table for a scheme is derived from the results of a prior mortality analysis conducted on some much larger ‘reference dataset’ grouped into postcode clusters. No mortality analysis is conducted on the scheme — the mortality basis is derived by comparing the scheme’s postcode distribution with that of the larger dataset, having regard to the observed mortality of the postcode clusters of the reference dataset.

This method has the notable advantages of speed and simplicity, and the opportunity to find some common ground between negotiators in transactions, leaving aside the question of whether the common ground is or is not correct. However, there are several disadvantages, in addition to those already highlighted:
>> The base table will reflect the mortality experience of a different group of people. The extent of this difference will depend on how the method used to ‘cross-index’ the scheme’s postcodes with those of the larger dataset validly reflects the scheme’s mortality characteristics. The presence of mortality heterogeneity in any postcode groupings used in this process may lead to substantially misleading results
>> The information provided is unlikely to be helpful in informing the choice of mortality improvement assumptions
>> The analysis by a commercial provider may not be transparent and may not permit interrogation or ancillary investigations. This increases the risk of undetected model and user error.

Using postcodes as a factor in a multivariate investigation
In this method, an analysis of a scheme’s mortality experience is conducted with postcodes used as one of the ‘explanatory’ factors. The output of the investigation would typically be a ‘best fit’ table for the scheme’s experience of the form:

“x% of Male standard table 1 or y% of Female standard table 2 × factor relating to postcode group × factor relating to benefit amount × factor relating to [other influences as relevant””

This table would then be applied on a member-by-member basis in any cash flow projection of the scheme. The predictability of this approach depends on how the postcodes are grouped. As far as this aspect is concerned, there are two common ways in which the method can produce misleading results.

First, the postcode modelling may place too much emphasis on pre-defined postcode clusters, for instance those provided by geodemographic or ‘lifestyling’ companies. These can hide significant mortality variations that exist within each postcode cluster, giving a set of postcode factors that do not fully reflect the mortality characteristics of the scheme.

Secondly, if starting with a large number of lifestyle groups and a typically sized scheme, it is easy to fall into the trap of producing a ‘self-prophesying model’ that will be unreliable in predicting experience. If the same data is used both to allocate members to different groups of lifestyle categories and then to calculate the mortality factors relating to those groups, the factors are likely to be wrong. The extent to which they are materially wrong depends on the size of the dataset analysed and the number of lifestyle categories available: the smaller the dataset and, counter-intuitively, the larger the number of lifestyle categories, the greater the probable error.

Having spoken to many life and pensions actuaries about this aspect of modelling, it is clear that most are unaware of this problem — despite it being commonly recognised in the non-life sector.

Problems with lifestyle clusters
Both postcoding methods discussed above are vulnerable to the deficiencies of the method used to group postcodes. Although lifestyle-derived postcode clusters have been shown empirically to be reasonable proxies for mortality, by definition a mortality proxy is only ever an approximation. Lifestyle postcode clusters are typically derived with reference to such census statistics as educational attainment levels, as observed in 2001. Each lifestyle group, typically containing in the order of 10 000 to 50 000 postcodes, is likely to hide a large variety of different mortality characteristics, even after allowing for age and gender and so on.

Given the substantial mortality variations that can remain in lifestyle groupings, it is interesting to consider postcodes can be used more precisely. How can we construct more homogeneous postcode clusters that better explain mortality characteristics?

Intelligent postcoding
It is possible, with large datasets, to conduct detailed postcode analyses of mortality by using the scheme’s own mortality experience to derive mortality-related postcode clusters. This is done by first arriving at a decent predictive model for the data in question, without any geographical component. This model allows us to calculate an ‘actual versus expected’ measure in every micro-region, typically postcode sector. This indicates the apparent effect of the micro-region on mortality. These mortality effects are often termed ‘residuals’, as they indicate the residual mortality effect reasonably attributable to the postcode, or other micro-regions, in question.

These apparent effects will be somewhat influenced by random fluctuations, particularly in those parts of the portfolio with low exposure. We can, therefore, use credibility-based spatial smoothing algorithms to improve the estimated mortality effect of low-exposure microregions, with reference to a suitably independent data portion.

Having arrived at smoothed mortality residuals, we can combine all postcode sectors with similar residuals into mortality ‘clusters’. These scheme clusters, where each cluster will generally comprise many potentially distant and unconnected postcodes, can then be calibrated in a fuller multivariate model to the scheme’s mortality experience. Great care is needed to partition the data into independent portions at the various stages of the analysis, in order to avoid over-fitting and deriving a ‘self-prophesying model’.

Mortality-derived postcode clusters can also be derived from population statistics, and these can give good predictive results when applied as ready-made mortality groups to model the experience of a scheme. Public domain information allows the derivation of such groups at below the postcode sector level.

To date, we have found that on large portfolios, mortality-derived postcode clusters can give factors with an ‘explanatory power’ of well over 200%. This compares extremely favourably with the effect of basing models around such proxies as lifestyle groupings. As we might expect, mortality-derived postcode clusters will generally be more predictive of mortality than lifestyle-based postcode clusters. Mortality-based clustering is also substantially cheaper than lifestyle clustering, the only cost being that of some basic cartographic coordinates — for example, of postcode sector centroids — and is typically a one-off cost of several thousand pounds, an order of magnitude lower than the cost of geodemographic and lifestyle information.

The methods noted so far — scheme mortality-derived clusters, population mortality-derived clusters and lifestyle (and related) clusters — are not necessarily exclusive. It may be the case that the models based on mortality clusters can be made even more predictive by incorporating the information provided by other clustering methods, especially in areas where the dataset in question lacks good exposure. Wise practitioners should test a variety of approaches. Mortality modelling is a completely empirical field, and what works is what can be shown to be predictive on an independent part of the data.

Mortality models can, in general, be made more predictive by deriving postcode clusters with reference to mortality experience, ideally that of the portfolio in question, otherwise some population mortality equivalent. We have found such ‘mortality clustering’ to be extremely predictive. Given the competitive nature of the current bulk purchase annuity market, and the general proliferation of postcoding techniques based on crude proxies, it is interesting to consider the extent of competitive advantage open to those players who switch from proxy-based clustering to mortality-based clustering.

Matthew Edwards is a senior consultant in the insurance and financial services practice of Watson Wyatt. He has a particular interest in wider applications of generalised linear models.