Annals, Anecdotes and Legends: A Chronicle of Life Assurance

by of the Bank of England John Francis

It is sufficiently known that the coffee-houses of the eighteenth century were the resort of all who sought intelligence or loved the company of the wits and fine men about town. To one of these, in St. Martin’s Lane, De Moivre went, where it was customary to apply to him for the solution of many questions connected with annuities, and for answers to queries concerning games of hazard, which were propounded to him by those who hoped to turn the chance of loss into a certainty of gain. The payment of these questions was his chief mode of subsistence; and there is something unpleasant in the memory of this man, compelled, in his old age, to be at the bidding of gamesters, and to consort with men who lived on the town by their wits.

The opinion of posterity is divided upon his merits. “By the most simple and elegant formulæ,” says Francis Baily, “he pointed out the method of solving all the most common questions relative to the value of annuities on single and joint lives, reversions, and survivorships.” The subsequent editions of his works prove that he was aware of his errors of detail, by correcting them. He enlarged the boundaries of the science which he loved, and encouraged others to follow in the same path. Although his hypothesis may not be applicable to all occasions and circumstances, and though later discoveries proved that it could not be always safely adopted, “nevertheless it is still of great use in the investigation of many cases connected with this subject, and will ever remain a proof of his superior genius and ability.” Such is the opinion of Baily on the merits of De Moivre; but it has been added by Morgan, that “on the whole the hypothesis of De Moivre has probably done more harm than good, by turning the attention of mathematicians from investigating the true laws of mortality.”

In 1737, an attempt was made to calculate the number of the people, which was estimated at 6,000,000, an amount probably not very far from the mark; as in 1688 the population was reckoned at a little over 5,000,000. Some important assistance was rendered in 1738, by the publication of Kersseboom’s tables, taken from the records of life annuities in Holland[10]; and as the ages of the annuitants had been there recorded for 125 years, they proved a considerable aid to those interested. So small was the progress made in England by 1746, that Dr. Halley’s Breslau Tables and those of M. Kersseboom were the only ones which gave anything like a representation of the true laws of mortality. In this year, however, the “Essai sur les Probabilités de la Durée de la Vie Humaine” of M. De Parcieux, with several valuable tables deduced from the mortuary registers of religious houses in France, and from the nominees in the French tontines, were an additional contribution to our information.

The first effort to show the value of annuities on lives from the London Bills of Mortality is attributable to James Hodgson. Nor was this endeavour uncalled for or unnecessary. Many assurance offices had arisen, undertaking to grant these annuities; and the tables principally in use were founded on the decrease of life at Breslau. But by the Breslau Tables, half the people lived till they were about 41 years of age, while in London half did not reach the age of 10. This was a vast difference in the estimate of mortality, and affected the price of annuities in a proportionate degree. But if the Breslau Tables calculated life at too high a rate, it was equally evident that the London Tables made them too low; it is obvious, therefore, that the value of a life annuity founded on any confined observations would be unsuitable to the general annuitant; and it is evident that a scale of prices should have been based on a more enlarged foundation.

The work of Mr. Hodgson deserves very great attention, and the notice of the reader is called to its investigation, as the conclusions were arrived at after great labour, and are a specimen of the time and trouble bestowed on the subject. “The easy way of raising money for public uses,” says Mr. Hodgson, “by granting annuities upon lives, has met with so great encouragement that there is no room to doubt it will be carried down to future times.” The following statements of this gentleman will be read with surprise by those who are acquainted with the chances of life as calculated at the present day. He estimated that “1000l. would purchase an annuity of 70l. per annum for a life of 29 years 10 months, when money is valued at 3 per cent. per annum; that the same sum will purchase the same annuity for a life of 23 years, when money is valued at 4 per cent. per annum; and that the same sum will purchase the same annuity for a life of 23 years, when money is valued at 5 per cent. per annum; and that it will purchase the same annuity for a life of 16 years 2 months, when money is valued at 6 per cent.

“It appears that the highest value of a life is when the person is about 6 years of age, and that from the birth to that time the value of lives decrease, as they do from that time to the utmost extremity of old age; that a life of 1 year old is nearly equal in value to a life of 7 years old; that a life of 3 years old is nearly equal in value to a life of 12 years old; that a life of 4 years old is nearly equal in value to a life between 9 and 10 years; and that a life of 5 years is nearly equal in value to a life of 7 years of age. And hence arose the custom of putting the value of the lives of minors upon the same value with those of a middling age, which at the best is but a bold guess, and made use of for no better reason, than that they knew of no better way to find the true value.”

Such was a portion of Mr. Hodgson’s contribution in 1747 to vital statistics. This work was followed in 1751 by the “Observations on the past Growth and present State of the City of London” of Corbyn Morris, containing tables of burials and christenings from 1601 to 1750. The tables were important in themselves, and the book is noticeable as containing a proposal to remodel the Bills of Mortality.

The topic was particularly interesting to mathematical men. In 1753, Mr. James Dodson pursued the subject, and solved in his “Repository” an immense variety of questions. Hitherto a table deduced by Simpson from the London Bills of Mortality, was the only one taken from real observation. But it need not be said that London was a very limited theatre on which to found the payment of premiums. The number of persons who died there in a given time, doubled that of other and more healthy cities. It was impossible to separate the casual visitors from the natives, in the record of deaths. It was equally difficult to divide those who had been born there, from those who were naturalised by virtue of a long and continued residence. The city, which has ever been the land of promise to the country, brought adventurers from the rural districts in a continued stream. The difficulties which prevented correct information from spreading may be judged by the statement that, from 1759 to 1768 a third more deaths than births were registered, the average annual burials being 22,956 to 15,910 of births. In the previous 10 years, the excess had been 10,500, or near half the burials. The baptismal registries were also very deficient in that large class denominated sectarians; Jews, Quakers, Roman Catholics, and all who refused to recognise the rites of the English Church being excluded. It required, therefore, care and calculation of no ordinary character to make any approximation to the truth; and Mr. Dodson believed he would be nearer it, by adopting the opinions of De Moivre as the ground work of his tables, rather than by entering on a sea of uncertain and hypothetical calculations.

In 1754, a further “valuation of annuities on lives,” deduced also from the London Bills of Mortality was published. By this it appeared that the work of Mr. Hodgson had not produced much effect in sending the Breslau Tables out of general use; for, says the author, “I think it very unreasonable that a poor citizen of London should be made to pay for an annuity according to the probability of the duration of life at Breslau, where, as appears from the bills of mortality, one-half of the people that are born live till they are about 41 years of age, whereas at London one-half die before they arrive at the age of 13.”