Life Office Experience Tables and Selection (1829-1881)

Despite John Finlaison’s scepticism, by the 1820s there was a strengthening conviction amongst life office actuaries that the selection effects of life underwriting practices were likely to have a material impact on the mortality rates that their business experienced. But no quantification of the impact of selection had been made. How could selection effects be measured? If selection effects existed, did they have a permanent impact on the mortality behaviour of policyholders relative to the broader population, or a more temporary one? If temporary, for how long did the effect persist? These questions could only be answered through an analysis of the life offices’ mortality experience data.

The first analysis of mortality experience at a British life office was conducted by William Morgan in 1776 at the behest of Richard Price. As noted earlier, this investigation led Morgan to conclude that ‘the probabilities of life in the Society had been higher than those in Mr Dodson’s Table, from which its premiums were computed, in the proportion of three to two’. Fifty years later, as the life assurer with by far the most data on the mortality rates experienced in its business, the Equitable was naturally positioned to take the lead on further exploring selection effects. But William Morgan resisted the development or application of mortality tables based on Equitable’s mortality experience for as long as possible. Like most of Morgan’s later resistance to change, it was at least partly motivated by reasoned argument as well as mere intransigence. Morgan held a firm belief that the Equitable’s lighter mortality experience relative to the Northampton table was due to a transient selection effect which would be imprudent to pass on to policyholders via the premium basis. In 1828, Morgan also argued that moving the valuation of Equitable’s business onto the much-lighter experience mortality basis would motivate the release of an inequitable amount of surplus to older policyholders relative to younger policyholders.[1]

For once, Morgan’s resistance proved futile. Charles Babbage and Griffith Davies, both leading actuaries of the time, each published their own versions of Equitable experience mortality tables based on the limited statements Morgan had made about the Equitable experience relative to the Northampton table. An Equitable member formally proposed that the Equitable’s liability valuations (and hence assessments of surplus) should be based on the experienced mortality rates. Whilst the Equitable’s legal counsel found in favour of maintaining the status quo, the pressure from Equitable policyholders was sustained and Morgan recognised that it might be more counterproductive to continue to resist. He finally published an Equitable experience mortality table in 1829, though this was clearly done through gritted teeth and with heavy caveats: ‘The following tables ... are still deduced from documents, particularly in the earlier parts of life, much too defective to be depended upon, and have been constructed merely for the purpose of effecting some calculations directed to be made by the last General Court of the Society.’[2]

Morgan’s table confirmed the substantial extent to which the Equitable’s experience was lighter than the Northampton table that it used in its pricing and valuations. However, the information provided by Morgan could not provide much new insight on the source of this differential in mortality. Was it simply that the segment of society that purchased Equitable life assurance tended to be richer and healthier than the population at large? Or had mortality significantly improved since the time of Price’s data due to improvements in economic and social conditions? Or were the Equitable’s rigorous underwriting processes and the rejection of lives with above average mortality rates the main reason for the lighter mortality experience? To answer these questions, a more comprehensive analysis of the behaviour of the mortality experience would be necessary (particularly if and how mortality experience varied as a function of the duration of policy). But the reluctant Morgan would not sanction any further exploratory work on the Equitable experience data.

William Morgan retired in 1830 and passed away in 1833, aged 83. His son, Arthur, who was a member of the Equitable’s actuarial staff when Morgan senior retired, was elected actuary. Arthur Morgan’s first major task was to construct mortality tables of the Equitable experience on a more thorough basis than his father’s somewhat half-hearted effort of 1829. His analysis included all 21,398 lives who had been members of the Equitable during its first 67 year years since inception (1762-1829). The data included a total of 5,144 deaths. This work appears to have been regarded highly by his actuarial peers—he was elected as a Fellow of the Royal Society in 1835 primarily for his work on the experience tables, and his Royal Society sponsors included leading actuaries of the day such as Benjamin Gompertz and Griffith Davies.[3]

Arthur Morgan’s Equitable experience analysis was the first statistical analysis of mortality rates that considered the behaviour of mortality rates as a function of the duration of membership as well as age of member. This demonstrated that the Equitable’s experienced mortality rates had varied significantly with duration of policy. For example, a 40-year-old who had been admitted to the society within the previous five years experienced a mortality rate of around 5 %, whilst a member of the same age who had been a member for between 15 and 20 years experienced a mortality rate of around 7.5 %.[4] This strongly supported the hypothesis that the selection effect of underwriting was a significant driver of the gap between the mortality experience and the pricing basis, and that the selection effect, whilst substantial, was temporary.

Arthur Morgan made his experience analysis publicly available, providing the opportunity for other actuaries to contribute to the investigation of the data. T.R. Edmonds, a widely published economist and demographer who had been appointed actuary of Legal & General in 1832, published an important paper in The Lancet in 1837 that discussed the implications of Morgan’s results.[5] Edmonds argued that the bulk of Equitable’s mortality profit had likely arisen from this selection effect—the mortality rates of long duration policies were not significantly different to the premium basis. This had been William Morgan’s consistent position. Edmonds also warned about expecting this effect to be a permanent feature of the future of life assurance:

At the present day, such is the competition among various life offices, that a large proportion of lives proposed for insurance are now accepted, who would formerly have been rejected.[6]

In 1841 Thomas Galloway, the actuary of the Amicable, followed Morgan’s example and published the mortality experience analysis of his office. This data covered the period 1808—1841.[7] The Amicable was the second-largest British life office of the time and the volume of the data was approximately one third of that available to the Equitable (1,792 deaths). Galloway performed some innovative analysis that suggested that the selection effect was not unique to the Equitable. He divided his dataset into two parts: one for policyholders who were already members at the start of 1808; and another for those who joined in 1808 or thereafter. His reasoning for this was that the office’s pricing and underwriting standards were fundamentally altered in 1808. Galloway wanted to measure the selection impact of this change in underwriting practice. His two mortality experience tables are shown below in Fig. 3.3.

Amicable mortality experience (1808-1841)

Fig. 3.3 Amicable mortality experience (1808-1841)

The post-1808 members experienced materially lower mortality rates than the pre-1808 members, particularly between the ages of 50 and 70. Galloway’s experience analysis provided a measure of the impact of changes in underwriting practices on mortality experience. This measure of the effect of selection would, however, have been somewhat over-stated if life expectancies had improved over the 33-year period, as the average calendar year of experience of, say, a 60 year-old would have been earlier for the pre-1808 members than for the post-1808 members.[8] Galloway did not note this possible effect, which itself highlights that no systematic allowance for mortality improvements tended to be considered during this era.

The next important step in the development of experience mortality tables was initiated at a meeting held at the London Coffee House on Ludgate Hill on 19 March 1838. There, the actuaries of many of the leading British life offices met and agreed to jointly share their experience data for the purposes of producing mortality tables based on their pooled experience. A committee of senior actuaries including Benjamin Gompertz, Joshua Milne and others was appointed to oversee the effort. Seventeen life offices submitted data that totalled 83,905 policies and 3,928 deaths. The Equitable and Amicable were amongst the contributors to the combined experience, but they did not contribute the full data that they used in their own individual experience studies, partly because the Seventeen Offices dataset only used policies written on single lives (to avoid potential double-counting of lives). The combined analysis was eventually published in 1843 and the mortality tables became known as the Seventeen Offices tables.[9]

The average duration of the policies in the combined data set was only eight years. The committee decided that this data could not support an analysis of mortality rate as a function of duration of policy as well as age of policyholder. This had two important implications for the results: given the published results of the Equitable and Amicable experience, it was reasonable to assume that the relative immaturity of the business being analysed meant that long-term mortality rates experienced by life offices were likely to be higher than those estimated from this dataset; and, secondly, it restricted the ability to quantify selection effects. The committee had also set out to analyse cause of death but found that ‘the returns ... were deficient in so many of the Lists, that is was not considered desirable to make any classifications of them’.[10]

These limitations meant that no new fundamental insights were obtained from the combined data. The report’s main conclusion was that the combined experience was very similar to that published by the Equitable a decade earlier. Nonetheless, the Seventeen Offices table is notable for representing the beginning of a long and important tradition of actuaries pooling experience data for the purposes of combined mortality studies. The table itself was also used widely in life office premium bases both in Britain and overseas.

The established life offices naturally accumulated more experience data as the years moved on, and by 1869 the available data could facilitate a much richer combined experience analysis. A committee of some of the eminent actuaries of their generation—Brown, Sprague, Bailey, Woolhouse and others—superintended the development of a new set of combined tables.[11] This time 20 life offices contributed their experience, providing data on 160,426 lives and 26,721 deaths. The 1869 tables are most notable for their treatment of selection. As we saw above, Galloway’s Amicable analysis of 1843 had statistically demonstrated that rigorous underwriting, and the selection of healthy lives for assurance, could generate a significantly lighter mortality experience. But questions remained. In particular, would this selection effect be experienced for the entire duration of the policy, or would its effect be transient, only impacting on mortality for the first few years of the policy’s duration? Arthur Morgan’s Equitable experience analysis suggested the latter, but no other evidence had yet been produced to corroborate this. Samuel Brown, the President of the Institute at the time, even worried that the mortality rates of select lives may ultimately be poorer than other lives[12]:

It is essential to the prosperity and good management of an office to know not merely whether the selection of lives affords unusual profits within a short period after admission of the assured, or how long that period continues, but also whether it may not require some reserves out of those profits to meet a permanent excess of mortality hereafter.

When the Seventeen Offices tables were constructed, actuaries were asking these questions, but the volume and spread of data could not support a rigorous answer. By 1869 the British life offices had been in existence long enough to generate the experience data required to build a two-dimensional mortality table that recorded mortality as a function of the age of the policyholder and the number of years the policy had been in-force. This data analysis yielded significant new insights and quantifications on the duration of selection effects: ‘For all practical purposes, the benefit of selection may perhaps be said to be lost after the fifth year of assurance.’[13] It also highlighted how substantial the selection effect was in the early years of the policy. For example, the mortality rates of 40-44 year-old healthy males in the first year of assurance were found to be only 37 % of the mortality rate of the same category in their fifth year or later.[14]

By the mid-nineteenth century, significant life assurance businesses were developing outside Europe, particularly in the British colonies and the United States of America. In the USA, a small number of life assurers had existed since the second half of the eighteenth century, but it was legislation in New York State in 1840 that provided a catalyst for rapid growth in the sector. It was estimated that 50,000 life assurance policies were in-force in 1859, and that this number increased to 800,000 by 1872.[15] During this period, in the absence of any local data, American actuaries used British mortality tables, most typically Price’s Northampton table, Milnes’ Carlisle table or the Seventeen Offices table.

In 1859, the first US life office experience table was produced by Sheppard Homans, based on the experience of the Mutual Life Insurance Company of New York, of which he was the actuary. This table was updated in 1868 and was commonly referred to as the American Experience Mortality Table. This table was used widely by US life offices over the following fifty years.[16] In 1881, American actuaries set a new world record for the amount of experience data used in a mortality table when the Thirty American Offices’ Table was published.[17] This table was based on a 30-year experience up to the end of 1874, and, as its name suggests, 30 life offices contributed their mortality experience. It included experience data on over one million policies and 46,543 deaths. It claimed to represent a full three quarters of all experience of life offices in the United States over the 30-year period considered.

Like the Institute of Actuaries table that came before it, the Thirty American Offices’ Table provided strong evidence of the impact of underwriting and selection on mortality experience. For example, for males aged 40-45, the mortality rate experienced in the first year of the policy was found to be around two thirds of the rate experienced for policies’ with durations of five years or more.[18] In general, the results were consistent with the Institute’s conclusions that the selection effect was evident for the first five years of policies’ duration and was not significant thereafter.

By 1881, the practice of pooling experience mortality data was well- established in developed life assurance markets around the world. Actuarial thinking moved on from the quantification of selection effects to considering the implications that this should have for pricing and reserving.

  • [1] See Ogborn (1962), p. 200.
  • [2] Morgan (1829), Appendix.
  • [3] Ogborn (1962), p. 215.
  • [4] Edmonds (1837), p. 159.
  • [5] Edmonds (1837).
  • [6] Edmonds (1837), p. 162.
  • [7] Galloway (1841).
  • [8] I am grateful to D.C.E. Wilson for highlighting this point to me.
  • [9] Ansell et al. (1843).
  • [10] Ansell et al. (1843), p. xi.
  • [11] Institute of Actuaries (1869).
  • [12] Institute of Actuaries (1869), p. 19.
  • [13] Institute of Actuaries (1869), p. 25.
  • [14] Institute of Actuaries (1869), p. 22.
  • [15] Meech (1881), Preface, p. 4.
  • [16] Maclean (1948), p. 284.
  • [17] Meech (1881).
  • [18] Meech (1881), p. 31.
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