CHAPTER IX RATES OF MORTALITY AND SICKNESS BY VARIOUS TABLES IT is interesting to compare the rates of mortality that have been observed at different times among the general population and among that special class of the general population that seeks the protection of insurance, and as such study is also useful in im- pressing on the mind the rates of mortality at various ages and the influence of selection, we shall devote this concluding chapter to a consideration of the results that have actually been obtained. We shall confine our attention to the published tables, which are, or have been, of general use and shall not discuss the many tables constructed from time to time by various methods from miscellaneous data. Much of the work done in this direction was valuable at the time, and some of the tables have assumed a more or less historical interest, owing to the adoption in them for the first time of an improvement in the methods of construction; but it is impracticable to go into such detail here, and anyone who is interested in the subject on the historical side can obtain all the in- formation he wants with comparatively little difficulty. 101 102 MORTALITY AND SICKNESS TABLES To bring together, in full, even a few of the moat important published tables would require a prohibitive amount of space and would make the comparison very laborious. In this chapter, therefore, the rates of mortality are given at a few selected ages only, and— in the case of insurance office tables—at two or three durations of insurance. The tables examined were based on a large amount of data and, generally, give the rates of mortality, etc., after graduation, i.e. after adjustment to remove accidental irregularities in their general progression—and they can be compared as they stand without using the method of "expected deaths." The ages have been so chosen as to indicate the general nature of each table, and the trend of the rates of mortality at the intervening ages may be judged from the examples given. The rates of sick- ness and withdrawal that have been found to prevail in a few large experiences are also included. It must be pointed out that the cause of the changes shown is not always apparent, and care must be taken not to draw wrong conclusions. For example, the change that has taken place in the mortality among insured persons depends not only upon the mortality of the community as a whole, but also on the selection of lives by the life insurance offices and on the policy of these offices, which may have altered sufficiently to have attracted a different class of person from that assured in older days. In Table XXVIII the mortality in England and Wales at various times is shown, and it will be noticed that there has been, on the whole, a general improve- ment, except at the oldest ages and in early infancy. TABLE XXVIII.—CENSUS TABLES—BATE OF MOKTALITY X 100
104 MORTALITY AND SICKNESS TABLES Part of the change at the older ages is probably due to more accurate returns: there is evidence that people who are advanced in years are less likely to overstate their ages than they were in the days of the earlier censuses—except in Ireland, where there is still much inaccuracy—and the members of the fair sex seem either to have developed better memories or to have leamt how to resist the temptation of giving themselves the benefit of a year or two when the census return is made. Apart, however, from these considerations, the mortality has probably changed, and several reasons have been advanced in explanation. One probable explanation is the improvement in methods of sanitation, while it is also held that increasing knowledge among the masses of the proper treatment of children may have resulted in reduction of the mortality in childhood and youth, but may at the same time have led to the preservation up to middle age of people with feeble constitutions who would formerly have died young. The effect of the latter result would be to reduce the average vitality of those at the older ages, and would account for an increase in the rate of mortality at these ages. It should be noticed that the change in mortality of men has been less than that of women, and that the lighter mortality in favour of men shown at some ages, when the earlier censuses were taken, has practically disappeared and their mortality is now heavier almost all through life. Some part of this change may be due to the improvement in the returns as regards age, to which we have already referred. RATES OF MORTALITY AND SICKNESS 105 The following lines of the table show the results of the most important investigations in countries outside the United Kingdom, and the last two lines relate to one mortality table (the Northampton Table) which is obsolete, and another (the Carlisle Table) which is nearly so. The Northampton Table was constructed on un- sound methods by Dr. Price in 1783 from the deaths in the Parish of All Saints, Northampton, during the years 1735-1780. Price's method would only have been accurate if the population had been stationary for a century before the date when the deaths he used were recorded. The table showed too heavy a mortality, especially at the younger ages. It was in general use until better tables replaced it, and in spite of the heavy mortality shown it was used by the Government in Pitt's time as the basis for the calcula- tion of the annuities granted by the National Debt Office, the consequence being that the country must have lost heavily on such transactions. It is a standing example of the impossibility of constructing reliable tables of mortality from deaths or populations alone. The Carlisle Table was based on the deaths for the years 1779-1787 and two censuses taken, January 1780 and December 1787, of two parishes in the City of Carlisle, and was constructed on sound lines by Joshua Milne in 1815. The particular district had a population which was fairly stationary, and in the term with which Milne was concerned there had been no epidemics nor other disturbing influences. The weakness in the table is that the ages were 106 MORTALITY AND SICKNESS TABLES stated very inaccurately, but in spite of this it was for many years used for the calculation of premiums and the valuation of the liabilities of assurance companies, and it is still used to some extent for the valuation of reversions and in a few other special circumstances. Table XXIX shows how the rates of mortality vary with the number of years since selection. The first example is taken from the "20 Offices" Table (Healthy Males: H^) which was constructed by a method similar to that described on p. 30. This table was formed from the combined experience of twenty British Offices and related only to cases accepted at ordinary rates of premium, which were on the books of the offices at any time before 1863. It was first published as an aggregate table,—or rather as two aggregate tables, for the full aggregate and the table excluding the first five years of assurance were both given. Some years later Dr. T. B. Sprague made a further investigation of the original data and gave approximate values for the Select rates. The next two examples are taken from the " British Offices Tables," which were constructed by the method of Chapter II, from the experience of sixty British Offices during the period 1863-1893. The Om Table gives the mortality under whole life with profit policies, and the 0"™1 the mortality under whole life without profit policies. Tables for other classes of assurance were published and show very different rates of mortality, but they have not been used in practical work and it is unnecessary to reproduce them here. RATES OF MORTALITY AND SICKNESS 107 The differences between the H1"' and O1"1 Tables are very noticeable, but not more so than between the Om and 0^. The explanation of the latter result probably is that there is a certain amount of self-selection. A man who thinks he will live long is more likely to take a with profit policy than one who has doubts as to his prospects of reaching old age: it is also possible that the higher rate of premium is paid by a provident class, while many without profit policies are effected for purposes of loans among a class which we should not expect to be long lived. The remaining examples relating to assured lives have been selected from the best-known tables published in other countries. The extent of the observations in each case is indicated in the table, and the methods of construction were similar to that employed for the O1111 Tables. The reader will be able to draw his own conclusions from a comparison of these figures with those for the English Tables, but some allowance must be made for chronological differences. In connection with the Japanese Offices experience, it may be mentioned that the extra mortality due to the war with Russia has been excluded in arriving at the figures given. The second part of the table shows the results of Annuity Experiences. Here the selection is effected entirely by the annuitant. Obviously, a man or woman does not buy an annuity if he or she thinks there is much chance of early death, and the effect of this self-selection is remarkable. The first two examples of both male and female TABLE XXIX.—LIFE OFFICE TABLES—SELECT BATES—RATE OF MORTALITY x 100
110 MORTALITY AND SICKNESS TABLES annuitant mortality are from the experience of persons purchasing annuities from the National Debt Office; the first experience extending from 180 8-1875 1 and the second from 1875—1904. It will be noticed that the mortality among male annuitants has improved appreciably, but to a less extent than that among female annuitants. The same result is given by a comparison of these figures with those from the British Offices Annuity Experience, 1863-1893, which was investigated at the same time as the Assurance Experience and by a similar method. Table XXX contains examples from Aggregate Tables of Mortality. It is possible for a comparison of such tables to give results which do not seem consistent with those given by a comparison of the corresponding Select Tables, because the proportion of recently selected lives included in the experiences may vary (see p. 91). The figures given are, however, interesting, and it is useful to compare the Aggregate Tables with the rates found from the Census returns (Table XXVIII). A rather more useful comparison may be made between the rates of mortality of the general com- munity and those given by aggregate tables, excluding the years of insurance when selection is most import- ant (see Chapter III, page 24). Table XXXI gives such a comparison, but it is again necessary to notice chronological differences in making use of this Table. In Table XXX are included the rates of mortality 1 The method of construction of this table was different from that of the other tables discussed. TABLE XXX.—AGGREGATE RATES OF MORTALITY—RATB OF MORTALITY X 100 MALE LIVES
TABLE XXXI.—AGGREGATE BATES OF MORTALITY (EXCLUDING THE EXPERIENCE OF THE FIRST FIVE YEARS OF INSURANCE) X 100 COMPARED WITH RATES OF MORTALITY SHOWN BY ENGLISH LIFE NO. 6 TABLE—MALE LIVES
RATES OF MORTALITY AND SICKNESS 113 found from a few friendly society experiences. These societies have, in the past, consisted mainly of members of the superior artisan and labouring classes, who joined their friendly society more or less as a matter of course on attaining manhood. There is consequently not so much " selection" of the kind already referred to found as that observed in the experience of life insurance offices, but if the rates of mortality are compared with those of the general population it will be seen that there is a " selection " of another kind, due to the fact that these figures represent the experience of the more prosperous and provident portion of the community. Table XXXII contains examples of the rates of sickness that have been experienced by some of the oldest friendly societies. Here, as elsewhere, different methods influence the results to some extent, and too much stress must not be laid on small differences. It is, however, interesting to notice that the rates of sickness have steadily increased from time to time, especially at the older ages and the longer durations, whereas the rate of mortality among the same people has steadily decreased. The tables examined were formed from the experience of the Independent Order of Oddfellows (Manchester Unity) and the returns made to the Registrar of Friendly Societies by all registered English Friendly Societies during 1876-1880. The second Manchester Unity Experience here dealt with (1893-1897) was very extensively analysed. The rates of mortality given in Table XXX will be seen to relate to three different areas of the country, and the sickness rates in Table XXXII are 8 114 MORTALITY AND SICKNESS TABLES
TABLE XXXII.—RATES OP SICKNESS
* Group A.H.J. consists of inembers engaged in agricultural and miscellaneous occupa- tions. B.O.D., of outdoor building trades, casual and unskilled outdoor labour, railway service, seafaring, fishing, etc. E.F., of quarry work, iron, steel, chemical, and glass work. 0., of mining occupations. Whole Society, of all occupations. t These rates refer to the sickness after the first year; rates of sickness for the second twelve months were not calculated. jfote.—The rates of sickness in the first two columns are based on the number of person! commencing at each age; the rates of sickness in the remaining columns are based on the average number alive during the year of age.
RATES OF MORTALITY AND SICKNESS 115 those found in four groups of occupations. This experience is particularly interesting, as the " Whole Society " rates formed the sickness basis of the calcula- tions under the National Insurance Act. Table XXXIII is added to show how rates of withdrawal vary with the age and period of member- ship. The figures, of course, depend almost entirely on the voluntary action of the members themselves, but it is interesting to notice how comparatively regular such action is, the general principle shown being, as one would expect, that those who have most to lose are least inclined to cancel their contracts. The rates of withdrawal found from the experience of any society are peculiar to that society, and if employed in any calculations they must be used with great caution, and care must be taken to see that the conditions of the society have not changed so as to affect them in any way. The figures from one experience can seldom, if ever, be used in making investigations in connection with another society. The reader will probably have noticed that it is sometimes a little difficult from a study of tables like those given in this chapter to form a general idea of the differences between the mortality shown by various experiences. The difficulty is greater when we are dealing with the unadjusted rates of mortality, i.e. before a graduation has been made. To overcome this inconvenience and to facilitate comparisons other functions are sometimes employed by actuaries. We have already mentioned the method of comparing the actual deaths with those expected by a- standard table, and we can extend its usefulness by making the TABLE XXXIII.—BATES OF SECESSION PER CENT. PER ANNUM IN MANCHESTER UNITY FRIENDLY SOCIETY DURING 1893-1897 (Extract/Tom a table given ty Mr. A. W. Watson, in his introduction to the account of the investigation of the experience of the Society)
RATES OF MORTALITY AND SICKNESS 117
TABLE XXXIV.—VALUES OF TEMPOBABY ANNUITIES BY VABIOUS TABLES—INTEREST, 3 PEE CENT.
118 MORTALITY AND SICKNESS TABLES comparison between the totals of the figures in groups of ages and for all ages. A method used by the Eegistrar-General of Births, Deaths, and Marriages is to show how many persons remain alive at each age in various experiences out of 1,000,000 births, and another method in frequent use is to compare the " expectations of life " shown by different tables. The last function is simply the average number of years lived by persons of any age after the attainment of that age, i.e. the average future lifetime. Against the use of this function the objection may be made that although it may give a good general idea of the mortality shown throughout a particular table, it disguises even appreci- able differences in the rates of mortality if they tend to counterbalance one another; so that it is possible for the expectation of life at a certain age to be the same in two tables which show rates of mortality differing widely throughout. A surer comparison could be made by the use of " temporary expectations of life," that is to say, the average duration of life during a few years only from the attainment of any age. Such values are not often calculated, but an exactly similar function is the value of a temporary annuity, payable until the expiration of a fixed number of years and subject to earlier discontinuance if the annuitant should die. Table XXXIV has therefore been added, and contains examples of the values of such annuities at a few ages and for specified terms, on the basis of some of the Mortality Tables discussed in this chapter. The reader should examine the figures given and see how the conclusions arrived at compare with those obtained from a study of the earlier tables.