Margaret de Valois Lowe gives us a clue
The dawn of the new millennium saw the publication of Continuous Mortality Investigation Report no 18. This sophisticated process of analysing and drawing conclusions on death data is now considered normal in the actuarial world. But how did this morbid obsession begin, and who formally concluded that we could use data to predict a person's lifespan, sometimes to financial gain?
I took a trip to the Institute library to find out. Captain John Graunt appears to be a likely candidate for starting death analysis for mortality. He used a list of reasons for death to produce a set of survival rates in 1662. But who was John Graunt, why and how did he develop his survival rates, and what influence did he have on other similar work on mortality?
Who was he?
John Graunt was a London shopkeeper, born in 1620. His life story is one of an industrious, highly respected individual but ends somewhat sadly, with bankruptcy and the loss of many of his friends through religious disagreements. Graunt spent much of his life working as a draper in Birchin Lane, close to the current site of the Royal Exchange. Graunt was the captain of a trained band of soldiers, and was probably quite affluent in the earlier years of his life, having a fine collection of prints and antiquities. One of his greatest achievements came in 1662 when he was admitted to the Royal Society. Graunt's contribution to the society was varied, ranging from a paper on the number of carp in a pond to supplying Macassar poison for analysis.
This was the time of Pepys, the plague, and Pudding Lane fires. Graunt's house was destroyed in the Great Fire and he became bankrupt. To his friends' disgust, Graunt converted from puritan to Roman Catholic and then appeared twice under the accusation of recusancy before dying of jaundice at the age of 54.
What did he achieve and why?
In 1662 Graunt published the first known mortality table to be based on real data, survival rates being produced at ten-year age intervals. The real data used were the fascinating 'bills of mortality'. These were lists of deaths and their causes, split by parish. Graunt looked at the bills covering the beginning of the 17th century. He then produced a list of 106 conclusions.
But why did Graunt study these bills in so much detail? Dr William Petty may have been an inspiration for Graunt. The bills refer to various diseases of the 17th century, so we can assume that the author had some medical knowledge. Dr Petty was a friend of Graunt who edited the reprint of the bills in 1676, although Graunt's actual involvement in the production of the bills is questionable. Graunt was admitted to the Royal Society very soon after the publication of his observations on the bills. Undoubtedly, his admittance to the society was on the strength of this work.
As well as producing the mortality table which could be used in predicting numbers of deaths, Graunt's conclusions may well have been useful in the economic and social planning of 17th century London. For example, Graunt used the bills to:
- estimate the population of London, which he then used to estimate the number of eligible 'fighting men' available to the king;
- dispel the myth that the plague was more rife in years of monarchy changes; and
- investigate how London was expanding.
Searchers v the GAD and the census
So how did Graunt put together his tables and where did the bills of mortality come from?
The first stage in the compilation of the bills involved old women 'ancient matrons sworn to their office' called searchers. Every week the searchers would view bodies, making enquiries to form a decision as to the cause of death. How much of this decision was influenced by the intake of ale is unknown.
The searchers then reported to the parish clerk, who published the results every Thursday. The results were then distributed to families (on the Thursday or Friday) who paid a small fee for this privilege of early warnings of plague epidemics.
Graunt's analysis of the data was detailed and contains evidence of modern actuarial methods. For example, allowances for possible errors were made. An illustration of this can be seen in Graunt's assumption that some reasons for death were incorrectly recorded. Graunt assumed these recording errors were due to the old women searchers 'after the mist off a cup of ale, and the bribe of a two groat fee, instead of one' being unable to decipher correctly the cause of death. Graunt also used data reconciliation in his argument, following the declining care in recording christenings, the actual figures not being as expected. Graunt also made assumptions such as the number of women fleeing London owing to the plague, this also being an early example of the use of withdrawal rates.
Graunt deduced that the population of London was 384,000. A proof by contradiction was used to show the original estimate of 6m to 7m was wrong. A final figure was then derived by assuming:
- each woman to have one child every two years, so 12,000 births thus implies 24,000 women of childbearing age;
- that there were twice as many families as women;
- that there were eight members of each family, hence a population of 384,000.
Graunt confirmed his population estimate using the following geographical argument:
- using a 1658 map he assumed that there were 54 families living in each space of 100 yards square;
- within the walls of London there were 220 such squares, making 11,880 families there;
- the number of deaths in London as a whole, both within and outside the walls, was four times the number of deaths within the walls alone.
Hence the number of families in London as a whole was 4¥11,880=47,520. This is consistent with the 48,000 families obtained in Graunt's first estimate.
Mortality figures were then deduced using the observation that around a third die of infant ailments. This led to the assumption that only 64% of children conceived survive to age six. The bills showed that around 7% of the deaths were among the 'aged'. Graunt guessed that this meant aged 70, or more, which led to the assumption that only 1% of children conceived would survive to age 76. Graunt also recognised that men do not die in actual proportion to their age. The rates shown in figure 1 left were then produced.
Graunt makes it clear that his survival rates are mathematical assumptions, not derived from data. Each number is 5/8 of the previous one up to age 56, with an arbitrary run-off thereafter.
What happened to Graunt's work?
Graunt's observations were very successful both in England and on the Continent, with five editions being published within 14 years of their completion. Survival rates were used to price annuities during the 17th century by the Dutch prime minister, De Witt. Although De Witt did not use Graunt's actual rates, the observations on the bills could have been an influence in Holland.
It was inevitable that the observations would receive some criticism. For example, objections were voiced to the assumptions used, particularly Graunt's assumption of eight people per family. This was considered too high in comparison with Gregory King's estimate in 1696 of just five people.
Most importantly, perhaps, Graunt was influential for academics and set the pace for much more demographic and statistical work. Sir Richard Corbet went on to produce the first set of mortality tables subdivided by all ages, although these were not based on real data.
We can certainly class John Graunt as one of our actuarial forefathers, even though he restricted himself to demography without considering any financial implications. As well as being highly analytical, he possessed the highly coveted actuarial skill of being able to communicate new ideas in an interesting, clear, informative way that is also fun to read. He was the first person to demonstrate that valid conclusions could be drawn about the likely experience of a group of people, even though the future experience of a single individual was impossible to predict.
John Graunt pioneered techniques still used today to become one of the first people to draw conclusions from mortality data. Graunt produced a realistic estimate of the population size of 17th century London as well as the first mortality table based on real information. On the back of his work Graunt was accepted into the Royal Society a worthy member.