# Popular Science Monthly/Volume 19/September 1881/Modern Basis of Life Insurance II

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* MODERN BASIS OF LIFE INSURANCE.
By THEODORE WEHLE.
WITH the year 1839 a new phase is reached in the first effort to tabulate the actual experience of insurance companies. Heretofore the average life of towns had furnished the data for mortality tables; now a table was to be deduced from observations of insured lives. Seventeen leading offices appointed a committee, to whom copies of their records were to be intrusted, which, owing to jealousies, were not as perfect as desirable. In 1843, after years of labor, a table was published, now known as "Actuaries' Experience Table No. 1." It was based on 18,282 policies, of which 7,372 had been discontinued, 4,786 had terminated by death, and 6,124 were still in force. The average duration of the policies under observation was eight and a half years,
​In 1869 a table taking a far wider range was compiled, known as "Actuaries' Experience Table No. 2." It comprised the experience of twenty English and Scotch offices, all over twenty years old. It treats of 146,847 lives, which on an average had been under observation for ten years, and records 23,856 deaths. This table was not graduated until recently, and is only beginning to come into use.
About the same time Mr. Sheppard Homans published the "American Experience Table," based principally on twenty-six years' experience of the Mutual Life Insurance Company of New York. For the very young and old ages where the data were insufficient, he also made use of other American and English statistics. This table has been adopted as the official standard for New York and many other States.
The exact numbers and other details that served as a foundation for all these mortality tables have been given rather fully, at the risk of wearying the reader. The object has been to indicate the difficulties of obtaining them in a reliable and sufficient form, and on such a scale as to furnish trustworthy averages.
A little reflection will show that large numbers must be observed for a long term of years, to have deaths occur for every single year of life, and in the proper proportion for each age. Take as an illustration the Carlisle table based upon 1,840 deaths in eight years, which would average 230 deaths per year. According to the present mortality of England, about forty per cent. of the deaths of the whole population occur among children under five years old, forty per cent, between the ages of five and sixty-five, and twenty-per cent, in old age, between sixty-five and one hundred years. Apply these percentages to the 230 deaths at Carlisle, and they would give 92 persons dying under five years old, 92 between five and sixty-five years, and 46 between sixty-five and one hundred years of age. For the last thirty-five years of life only 46 deaths would be likely to take place, because, while the percentage of mortality is high, the number living at those ages is very small. But, when 46 deaths are distributed among thirty-five years of life, it is apparent that they are not likely to prove regularly divided among them. At some ages, and they may be the very highest, no deaths at all may occur. We know, however, that it is not in the course of nature that in any one year of life no human being should die, and properly ascribe it to the small number and the short space of time observed. Here the mathematician steps in and determines, from the insufficient data gathered, what the probable percentage of deaths would be for every year of life, in large communities living under similar conditions.
In illustration of what has been said, and as both interesting and instructive, the actual percentage of deaths comprised under the "Ungraduated Actuaries' Experience Table No. 2" is herewith given in graphic representation:
The table shows the remarkable fact that, out of so large a number ​as 23,800 deaths, not a single individual died at ages eleven, sixteen, and ninety-four. This is due to the insufficient number of persons insured under twenty years, and the very small number living above
English Ungraduated Actuaries’ Experience Table No. 2.
ninety years of age. The other most apparent fluctuations are a fall at age eighty-nine and a sudden rise at ages ninety-two and ninety-three. Here, again, for the same reasons, a very few deaths above or below the average cause large differences in the percentage. But ​more or less deviation was experienced for almost every year of life, although the small scale to which the representation is necessarily confined docs not clearly indicate it. The most superficial examination, however, must convince us that we are not dealing with accidents, but with a clearly pronounced tendency in the rate of mortality, disturbed only by minor causes.
Leaving for the time life-insurance experience, for the wider field of vital statistics generally, we have to note a most important step, in the introduction of the decennial census in England in 1801, and the adoption of a system of registering deaths, births, and marriages, begun in 1836.
The data were thus collected for constructing a mortality table, embracing the whole population of England. This task was undertaken by the Assistant Registrar-General, Dr. Farr, on the census of 1841, and is known as "English Life Table No. 1." It is based on about 16,000,000 lives and 344,000 deaths. In 1863 he published a second, table called "English Life Table No. 2," using the data of the census of 1841 and extending the deaths to three years previous to and three years subsequent to 1841. This period of seven years (1838 to 1844) furnished 2,436,648 deaths. Finally, in 1864, "English Life Table No. 3" was given to the public in the form of a distinct work. It was deduced from the two censuses of 1841 and 1851, and other records for the seventeen years from 1838 to 1854, embracing some 50,000,000 persons living and 6,470,000 deaths. Here, at length, we have a life-table on the largest scale, comprising the population of a whole country from birth upward. A graphic representation of the same is herewith presented, as that conveys a clearer picture to the mind than the reading of the numbers of the living and dying for every age.
On comparing Life Table No. 3 from ten years upward with the "Ungraduated Actuaries' Experience Table No. 2," it will be observed that the direction of the curve is very similar in both; but, while the one is absolutely smooth and even, the other is disturbed by the more or less violent deviations already referred to. The process of removing these unevennesses in the line, actuaries call graduating or adjusting. It is a very delicate and most important problem, for it involves no less than the effort to determine the law of mortality, freed from the accidental influences which experience has recorded. The outline of this law is, indeed, clearly defined, and can be traced in every table—a high rate of mortality in the first year of life, decreasing until the minimum is reached somewhere near the age of puberty, then rising very gradually, until with old age a very rapid increase takes place. But, while these general traits are well established, the details are subject to continual deviations.
We must assume that there is a fundamental law of life accompanying the organization of the human being, but that it is
English Life Table No. 3.
frequently traversed by many artificial and accidental influences. To determine the normal and eliminate the accidental conditions is the aim of theoretical inquiry. On the other hand, it may be urged that there is no normal standard of life nor of its surroundings, and that ​length of life is merely an expression of the sum total of social influences upon the organism. A community may be divided into ever so many groups, each of which will have its peculiarity, and the summary of all these units will give as resultant the average of life. Every graduated mortality table may, therefore, be considered only an approximate expression of the death-rate under the conditions and at the time of observation.
We may now follow "English Life Table No. 3" more in detail. It gives a separate record of both male and female life, and we may examine the mortality of males first.
The notation adopted refers to the percentage of death in the current year; meaning from birth to end of first year, 1 from beginning to end of second year of life, and so on:
| Age. | Percentage of deaths. | Age. | Percentage of deaths. | Age. | Percentage of deaths. | Age. | Percentage of deaths. |
| 0 | 16·36 | 15 | ·52 | 40 | 1·30 | 70 | 6·73 |
| 1 | 6·40 | 20 | ·83 | 45 | 1·54 | 80 | 14·18 |
| 5 | 1·36 | 25 | ·92 | 50 | 1·88 | 90 | 26·41 |
| 10 | ·56 | 30 | 1·00 | 55 | 2·45 | 95 | 34·21 |
| 13 | ·47 | 35 | 1·13 | 60 | 3·25 | 100 | 41·78 |
The table ends with age 107. :
| Taking | birth | as a starting- | point, | the mortality | for the first | 5 | years of life is | 27·64 | per cent. |
| " | " | " | " | " | " | 10 | " | 31·02 | " |
| " | " | " | " | " | " | 20 | " | 34·82 | " |
| " | " | " | " | " | " | 4412 | " | 50·00 | " |
| The rate of | mortality | of age | 5 | is again | reached | at about | age | 41 |
| " | " | " | 1 | " | " | " | " | 70 |
| " | " | " | 0 | " | " | " | " | 82 |
| About | 1 | in | 412 | of all | children | born | will reach | age | 70 |
| " | 1 | " | 10 | " | " | " | " | " | 78 |
| " | 1 | " | 100 | " | " | " | " | " | 90 |
Let us now compare male and female mortality. There are born 511,745 males to 488,255 females, being an excess of 23,490 males $=$ 4·81 per cent.
| During | age | 0 | , the deaths are 83,719 males to 65,774 females: leaving males | , the deaths are 83,719 males to 65,774 females: leaving males | , the deaths are 83,719 males to 65,774 females: leaving males | , the deaths are 83,719 males to 65,774 females: leaving males | , the deaths are 83,719 males to 65,774 females: leaving males | , the deaths are 83,719 males to 65,774 females: leaving males |
| | | | in excess | | | 1·31 | per cent. | |
| At | " | 8 | the excess | of males | living is | 1·00 | per cent. | |
| " | " | 15 | " | " | " | 1·18 | " | |
| " | " | 37 | " | " | " | 2·08 | " | |
| " | " | 50 | " | " | " | ·93 | " | |
| " | " | 53 | | the sexes are about even in number. | the sexes are about even in number. | the sexes are about even in number. | the sexes are about even in number. | the sexes are about even in number. |
| " | " | 70 | the excess | females | living is | 8·00 | " | |
| " | " | 80 | " | " | " | 19·00 | " | |
| " | " | 90 | " | " | " | 41·00 | " | |
| End of table for | male | life is | 107 | years, | for | female | life is | 108 | years |
| Equation of | " | " | 4412 | " | of | " | " | 4612 | years |
| Of | males | living | at age | 20, | about | 1 | in | 3 | will | reach | 70 | years, of | females | 1 | in | 212 |
| " | " | " | " | " | " | 1 | " | 8 | " | " | 70 | " | " | 1 | " | 634 |
| " | " | " | " | " | " | 1 | " | 70 | " | " | 90 | " | " | 1 | " | 49 |
​Thus it appears that, with the exception of the period from fifteen to thirty-seven, where the larger mortality can be easily explained on physiological grounds, females have a far better chance of life than males. This is particularly marked in the first year of life, and after fifty-three years of age.
Some of the results deduced from this table will no doubt surprise many. It is not commonly assumed that age thirteen is the healthiest in life, or that so large a proportion of infants will reach as high an age as is here indicated. Nor is it generally known that more boys are born than girls, and that the weaker sex has such decided advantages in life over the stronger. But, while nearly five per cent, more male than female infants are born, the very reverse appears in the whole population, there being about five per cent, more females living than males. Of course, these proportions refer to England only, and they vary in different countries, according to conditions and influences that the reader can readily picture to himself.
English Life Table No. 3 marks an epoch in statistical science, and the results obtained are valuable and sufficiently reliable for practical purposes, but much yet remains to be done to satisfy scientific inquiry. An annual census, which is strongly urged, would allow a closer and more frequent examination of facts, and reduce mathematical speculation to a minimum.
One question of grave importance can not yet be considered as definitively settled; it is whether the rate of mortality is steadily declining, and the duration of life is correspondingly extending. In a general way, and as compared with former centuries, there can be no doubt that a marked improvement is to be found. Take the population of England as an illustration:
| It was | estimated in | 1651 at | 5,450,000 |
| " | " | 1751 at | 6,400,000 |
| | Census of | 1801 at | 8,892,536 |
| | " | 1851 at | 17,927,609 |
This shows an increase of seventeen and a half per cent, for the century from 1651 to 1751, of thirty-nine per cent, for the fifty years to 1801, and of one hundred and one and a half per cent, for fifty years to 1851.
These rapid strides are not astonishing when we consider the epidemics, the internal strife, the famines, and insufficient means of communication, the disorderly and unsettled habits of former times, and compare them with the better hygiene, the greater comforts, and the generally refining influences of the present. But this increasing ratio of growth may be due either to a larger percentage of births, or to a smaller proportion of deaths, or to both causes combined. Statistics seem to indicate that both factors are even now contributing to this result. In 1841, out of 1,000 of the population, 15·4 were married ​during the year, and in 1876 the number had gradually risen to 17 per 1,000. So that, in spite of large cities and the greater difficulty of supporting families, the growing tendency to settled and more regular habits is exhibited in the larger number of marriages. The result is an increasing number of births in proportion to the population. In 1841, 512,158 children were born, being 32·2 per 1,000, while in 1870 the number was 887,464, or 36·6 per 1,000, which is an increase of about twenty-five per cent. The deaths, on the other hand, remained nearly stationary, being 21·6 per 1,000 in 1841 to 21·9 in 1876. The ratio of deaths to births, therefore, stood as 1 to 1·49 in 1841, while in 1876 it was as 1 to 1·74.
The preponderance of young families, however, ought to make the death-rate very much higher, as the mortality at the young ages is very large. Since it remained nearly unchanged, while the marriages and births increased, it would indicate that the average duration of life was being extended. For special localities like large cities, it is well known that sanitary measures and other causes are producing constant improvement; but there are many counteracting conditions to be considered. With an improved system of registration and more frequent enumerations of the people, data will be obtained for computing and comparing life tables at shorter intervals, and there can be no doubt that, in spite of increasing difficulties, the beneficial influences of higher civilization will be found to tend to a steady prolongation of human life.
Recurring after this digression to the experience of life-insurance companies, we will compare English Life Table No. 3 from twenty years upward with the two tables most in use, the Actuaries' Experience Table No. 1 and the American Experience Table. The percentages are given, in preference to the number of living and dying for each period:
| AGES. | ENGLISH LIFE NO 3. | ENGLISH LIFE NO 3. | ACTUARIES' EXPERI- ENCE NO. 1. | ACTUARIES' EXPERI- ENCE NO. 1. | AMERICAN EXPERIENCE. | AMERICAN EXPERIENCE. |
| AGES. | Percentage of deaths. | Percentage of deaths. | Percentage of deaths. | Percentage of deaths. | Percentage of deaths. | Percentage of deaths. |
| 20 | · | 83 | · | 73 | · | 78 |
| 25 | · | 92 | · | 78 | · | 81 |
| 30 | 1· | 00 | · | 84 | · | 84 |
| 35 | 1· | 13 | · | 93 | · | 89 |
| 40 | 1· | 30 | 1· | 04 | · | 98 |
| 45 | 1· | 54 | 1· | 22 | 1· | 12 |
| 50 | 1· | 88 | 1· | 59 | 1· | 38 |
| 55 | 2· | 45 | 2· | 17 | 1· | 86 |
| 60 | 3· | 25 | 3· | 03 | 2· | 67 |
| 65 | 4· | 59 | 4· | 41 | 4· | 01 |
| 70 | 6· | 73 | 6· | 50 | 6· | 20 |
| 80 | 14· | 18 | 14· | 04 | 14· | 45 |
| 90 | 26· | 41 | 32· | 37 | 45· | 45 |
| 95 | 34· | 21 | 58· | 43 | 100· | 00 |
| 99 | 41· | 04 | 100· | 00 | . . . | . . |
| 107 | 100· | 00 | . . . | . . | . . . | . . |
​While the two experience tables are very similar, and represent about the same social conditions, the well-to-do middle classes, in this country and in England, the American table has a peculiarity characteristic of life in the United States. At the younger ages, up to thirty years, the mortality is greater, while from thirty to seventy years it is somewhat less than in England. During this latter, the most active period of life, the strain upon the system is very great in this country, and the vital forces are used up to such an extent that after seventy years the death-rate rises rapidly. The table ends at ninety-five, while the English is carried to ninety-nine. It may also be mentioned here that female life has proved less favorable than male life to insurance companies, while it will be remembered that the very reverse has been observed in the community at large. The next point that will attract attention is, that the English life table, representing the average life of the whole population, does not range so much above the insurance tables as might be supposed. Insurance companies select only healthy individuals by medical examination, and almost exclusively from the better classes and occupations. Why, then, is the difference not greater? Some of the reasons can be readily given. First, there is a constant effort on the part of the public to foist impaired lives upon the insurers. No amount of care or precaution can detect all misrepresentation or trace every inducement to fraud and self-destruction, and, while it may amount to less than some assume, it undoubtedly reduces the standard of absolute health. Of far greater importance is the observation that the effect of selection nearly wears away in about five years. Taking a class of live? selected by medical examination, say at twenty-five years, it will show a reduced mortality during the first year; but after five years, at age thirty, very nearly the usual average is again reached. For, while the diseased are excluded from the selected class, a certain number of these sound lives will find their health to fail from year to year. Were those admitted at twenty-five years to be reexamined at age thirty, so many sick and ailing would be among them that the advantages of selection would be found to have largely disappeared.
Registrar-General Farr estimates 27 out of 1,000 of the whole population, between the ages of twenty and sixty, to suffer from some kind of disease or other, be it hereditary, chronic, recurrent, or acute. Consumption, he thinks, though varied in duration, seems to average about two years. The higher the age, the greater the value of selection; and, the older the members of a life-insurance company become, the more do they approximate the health of the community at large.
Another factor that operates as a selection against the mortality experience is what is called lapses. A large number of policies are constantly allowed to terminate through the indifference of the insured, and for various other reasons. But, while the healthy often forfeit ​their insurance upon slight provocation, there are few indeed, of those that think their health impaired, that will do so. The result is, that an undue proportion of the sickly will remain, and exert a deteriorating influence upon the average mortality.
Finally, it must not be forgotten that there is, after all, a considerable difference in the middle ages between the English life table and the insurance tables, particularly the American Experience Table. This latter, Mr. Romans states, has the effect of selection carefully eliminated, and therefore indicates a higher rate of mortality than the actual experience. As a matter of fact, all well-managed insurance companies, doing a sufficiently large business to furnish the basis for reliable averages, and having a constant accession of new lives experience more or less gain over the tables in use.
Before dismissing this subject, one question of a general character yet remains to be answered, viz., how do, or may, epidemics affect the average rate of mortality?
As regards the possibilities of the future, it is strictly a problem for medical and sanitary science; but we may be allowed to draw some inferences from the past records of a well-ordered state.
In 1849 a cholera epidemic, of a very malignant type, prevailed in England, considerably increasing the mortality for that year.
The number of deaths for the five years from 1848 to 1852 were as follows:
| 1848 | 398,385 |
| 1849 | 440,883 |
| 1850 | 368,602 |
| 1851 | 395,396 |
| 1852 | 407,135 |
| | 2,010,401 |
It will be noticed that in 1849 the increase over the previous year was about 42,000, while in the following year, 1850, there was a falling off to 30,000 below the number of deaths in 1848. For the period of five years from 1848 to 1852 the annual average of 400,000 remained undisturbed. This would indicate that, when through a powerful influence an excessive death-rate prevails, a large proportion of the weak and sickly is carried off, so that by way of compensation the surviving, healthier population will for a time show a mortality below the average. It is also well known that such inflictions are largely confined to the dirtiest and most crowded quarters, and carry off principally the poor and improvident. As these classes do not insure their lives, the mortality experience of insurance companies is no more likely to be seriously affected by epidemics in the future than it has been in the past.