ACTUARIAL STUDIES NO. i SOURCES AND CHARACTERISTICS OF THE PRINCIPAL MORTALITY TABLES PRINCIPAL CONTRIBUTOR HENRY MOIR ASSOCIATE CONTRIBUTORS J. D. CRAIG L. K. FILE A. T. MACLEAN H. H. WOLFENDEN PUBLISHED BY THE ACTUARIAL SOCIETY OF AMERICA 346 BROADWAY, NEW YORK 1919 Copyright 1919, by The Actuarial Society of America NEW YORK PRESS OF THE HEW ERA PRINTING COMPANY LANCASTER, PA. GENERAL INTRODUCTION. In view of the fact that, with the exception of a very few modern text books, the literature of Actuarial Science is con- tained in scattered original papers, The Actuarial Society of America proposes to issue a series of small volumes upon im- portant actuarial subjects. Each volume is intended to bring together, as far as space permits, the more important points of information on the subject discussed. The objects in issuing the series are twofold: (1) to assist students of Actuarial Science, and (2) to furnish a means of ready reference for Actuaries. The various subjects are allocated to Fellows of the Society by the Committee in Charge; and, associated with the principal con- tributor, who is primarily responsible for the matter included and the views expressed, are one or more “Associate Contrib- utors.” These are appointed for the purpose of aiding and criticizing the work before publication. It is proposed to avoid discussing subjects already covered in the Text Book of the Institute of Actuaries except as continuity of thought may make occasional references necessary. The title chosen to represent the character of this series is “Actuarial Studies.” The thanks of the Society and of the Committee in Charge are due to all the contributors who have freely given of their time and labor, with the sole purpose of helping others—especially students. III ORIGINAL COMMITTEE. Arthur Hunter Henry Moir P. C. H. Papps Wendell M. Strong A. A. Welch A. B. Wood John K. Gore, Chairman. COMMITTEE NOW IN CHARGE. Robert Henderson J. M. Laird A. T. Maclean A. H. Mowbray Wendell M. Strong J. S. Thompson Hugh H. Wolfenden Henry Moir, Chairman. IV SOURCES AND CHARACTERISTICS OF THE PRINCIPAL MORTALITY TABLES The mortality table is the scientific basis of all life insurance contracts. By means of it the probabilities of living and of dying can be ascertained, on the presumption that what has taken place in the past will be approximately reproduced in the future. A mortality table consists of a schedule showing for each age the number of persons who die and the number who survive out of a known number under observation. Usually the table starts with an arbitrary number, such as 100,000 at the youngest available age, this arbitrary number being called the radix, and gives for each year of age the deaths and the survivors from this original number. By adopting a radix the varying numbers which may have been under observation from year to year are reduced to a common basis suitable for comparisons, and convenient for com- putations of annuity values, premiums, and other functions. The older mortality tables were formed from population statis- tics, but for nearly seventy years the tables which have been most valuable for insurance purposes have been derived from the records of life insurance companies. The information available to com- panies is usually accurate as well as complete in the numbers under observation at each age and the numbers dying, so that the rates of mortality represented by the ratio ~ can be correctly stated for insured lives. The accuracy of this ratio is the fundamental requirement of a good mortality table; and it is of more importance that the deaths be stated at the proper ages and times than that the record of the number living should be so strictly correct, since any error in the numerator of the fraction has much more effect than a similar error in the denominator—at the younger ages the effect is more than one hundred times greater. 1 2 SOURCES AND CHARACTERISTICS OF In forming a mortality table from population statistics, it is necessary, in order to get trustworthy figures, to have a census of the people showing the numbers living at each age, as well as the mortuary registers giving the numbers who have died at each age. The mere death rate, without distinguishing the age distribution of the people, is of practically no scientific value; the ages at death of those dying and also the ages of all who are included in the observations are essential factors. In order to ensure greater accuracy, a census at the beginning and a second census at the end of the period over which the observations extend should be taken; but fairly good approximate results can be obtained from one census only, if it be carefully made, and if the ages and deaths be accurately recorded. The mortality of nations and of cities fluctuates from year to year, and accordingly the observations should extend over a sufficient time to yield good average results. Early Mortality Tables. The earliest mortality tables of which we read were those in use by the Romans for determining the values of life estates. Under the Roman law a man could not bequeath more than three- fourths of his property away from the direct heir; and it was a common practice to bequeath annuities or life interests, the values of which had to be determined by computation. As the Romans made a careful census and recorded deaths with great accuracy, it is usually supposed that they had satisfactory mortality tables, but no proof of this supposition has been forthcoming. The taking of a census has now become a regular custom with civilized nations, having indeed become absolutely necessary for many purposes, such for example as the rearrangement of the methods of repre- sentation under all systems of popular government. In ancient days, however, such an act was regarded with superstition, as for example when the census of the Jews was taken by the Army of David. He believed that the pestilence from which the Jews afterwards suffered was a direct punishment for this act. No records have been disclosed, from the days of the Romans until the close of the seventeenth century, of any reliable tables of mortality. In 1693 Dr. Halley (of comet fame), the British Astronomer Royal, published the first tables of any importance, which are now known.* He formed them from the registers of * See J. I. A., Vol. I, pp. 43-46. THE PRINCIPAL MORTALITY TABLES. 3 deaths in the city of Breslau in Silesia, taken for a period of five years, and they were published in the Transactions of the Royal Society (Great Britain). Before the middle of the eighteenth century a table of mortality was formed from observations made in the city of London, and from this table the original premiums adopted by the old Equitable Society were computed. The mortality rates were very high. In 1746 M. De Parcieux published his “Essai sur les probability de la Duree de la Vie Humaine” in which several tables of mortality were given, constructed from the lists of nominees in the French tontines and from the mortality registers of different religious houses. The mortality shown by this table is generally higher than that of the Carlisle Table, fully described hereafter, with which in other respects it agrees quite closely. This table was never freely used by English-speaking people, although it was more accurate than any of the other tables published in the eighteenth century. It has now only a historical interest. In the early development of scientific mortality tables we owe more to Dr. Richard Price than to any other individual; yet he is popularly remembered as the author of the Northampton Table which is held out as an example of faulty construction. Dr. Price himself was well aware of the difficulties with which he had to contend and he strongly urged the adoption of better systems of registration so that accurate mortality tables could be formed. Amongst other tables formed by Dr. Price were the Chester Tables,* which gave the rates of mortality separately for males and females, and for the time at which they were prepared gave a fair conception of human life. The tables were formed from the birth and burial registers of the small town of Chester, in Eng- land, and the accuracy of the assumptions was tested by an enumeration of the people which included a record of the num- bers living at each age. Unfortunately the tables never came into general use, and the Northampton Tables became much bet- ter known. * See the later editions of “Price on Annuities.” 4 SOURCES AND CHARACTERISTICS OF Northampton Table. The first tables used to any great extent for life insurance purposes were the Northampton Tables, detailed information regarding which is here given as the mode of construction calls attention to one or two errors which should be avoided. Moreover they are still prescribed under certain old statutes as the basis for determining the values of life estates for taxation purposes. There were two tables formed by Dr. Price, the first published in 1771 in his “Observations on Reversionary Payments,” and the second, a more complete table, in 1783, the latter being known as The Northampton Table. The following extract from Dr. Price’s remarks will partially explain the Tables: “In the parish of All Saints, containing the greatest part of the town of Northampton, an account has been kept since 1735 of the ages at which all have died, also an account of the number of males and females that have been christened. Christened 4220 Buried 4689 “Of these died under 2 yrs. of age 1529 aged 2 to 5 362 5 to 10 201 10 to 20 189 20 to 30 373 (351) 30 to 40 329 (351) 40 to 50 365 50 to 60 384 60 to 70 378 70 to 80 358 80 to 90 199 90 to 100 22 4689 “In the fourth edition of this treatise, the following corrections were made: “1st. The table printed in the first three editions haying been formed from the Northampton Bills (of Mortality) for 36 years (i. e., the first North- ampton Table 1735-1770) this table was rendered a little more correct in consequence of being formed from the same Bills for 46 years (1735-1780). “2nd. The Bills give the number dying between 20 and 30 greater than between 30 and 40, but this being a circumstance which does not exist in any other register of mortality, and undoubtedly owing to some accidental and local causes, the decrements were made equal between 20 and 40, preserving the total of deaths the same that the Bills have them. “3rd. The Bills giving only the total of deaths under two years of age and between 2 and 5, the proportion of deaths for every particular year between 2 and 5, and for every quarter of a year after birth till one year of age, were made the same nearly that the Chester register makes them.” Dr. Price formed the table by taking account only of the deaths and without using any enumeration of the population. If a census THE PRINCIPAL MORTALITY TABLES. 5 had been used a different result would have been reached, and the tables would have been much more accurate. In view of the difference between the number of christenings and of burials (469 or 10% of the burials) he assumed that not only 10% but 13% of the deaths were those of persons who immigrated to Northamp- ton at the age of twenty; his reason for adopting the higher percentage is not stated. The excess of deaths over births was probably caused almost entirely by deaths among Dissenters, whose children were not entered in the Parish Register of Christenings. Dr. Farr pointed out that if effect had been given to the increas- ing nature of the population, the table would have shown lower and more accurate mortality rates, and would have been much more valuable. The mortality amongst male children appears heavier than amongst females, a feature which has been confirmed in other tables. Age. Deaths. Numbers Liv- ing at First Age in Group (if Population had been Stationary). Numbers in Column 3 Raised to Radix of 10000. Column 4 Less 1300 up to Age 20 (i. e. 13 of Discontinuance. Rate % of Discontinuance. Rate i of Discontinuance. Year. Age 35. All Ages. Year. Age 35. All Ages. Year. Age 35. All Ages. 0 2.5 2.7 5 2.7 2.8 110-14 1.4 1.4 1 6.2 7.0 6 2.2 2.4 15-19 1.0 .9 2 4.2 5.0 7 3.2 3.6 20-24 .8 .7 3 3.8 4.1 8 1.9 1.8 25-29 .4 .5 4 2.9 3.3 9 1.5 1.6 30 and over .4 .4 Sprague’s Select Mortality Tables.* In 1879 Mr. T. B. Sprague published the results of an investiga- tion he made from the Hm statistics to determine the effect of selection, and to show the uses to which Select Tables could be put. He first reduced the figures for each age at entry to a common radix of 100,000; and, in order to lessen the irregularities arising from small numbers, he grouped the entrants at five ages to get the rate of mortality for the central age of the group. The same assumptions were made as to ages at entry as were made in compiling the Institute Experience, namely, that the entrants at any age next birthday attained that age at the end of the year, also that the initial period, “year 0,” covered half a year. To deduce the mortality for age 30, the five year group contained: 100,000 of exact age 29|] 100,000 of exact age 30§ J which gave 200,000 of mean age 30. 100,000 of exact age 28|'| 100,000 of exact age 31 |j which gave 200,000 of mean age 30. 50,000 of exact age 50,000 of exact age 32§J which gave 100,000 of mean age 30. 500,000 of mean age 30. The reason for taking only 50,000 at the two last named ages was of course that the balance of 50,000 in each case entered into the adjacent groups; i. e., the other 50,000 at age were included in the group for age 25 at entry, and the 50,000 at age * J. I. A., Vol. XXI, p. 229 et seq. 48 SOURCES AND CHARACTERISTICS OF 32§ in the group for age 35. By reducing the figures to a common radix, the facts at each age had the same weight assigned to them in the final table. The following table indicates the method and gives the figures used for age 30: Time Elapsed. Assumed Age at Entry. Average Age at Entry 30. 27} 28} 29} 30} 31} 32} Survi- vors. Total Deaths. Age At- tained. (1) (2) (3) (4) (5) (6) (7) (8) (9) (10) Years 0 1 2 1§ 2! 31 4! 5! 50,000 49,962 49,550 49,167 48,672 48,345 47,986 100,000 99,788 99,346 98,655 97,940 96,823 95,868 100,000 99,931 99,394 98,644 97,490 96,166 95,142 100,000 99,754 99,316 98,594 97,839 96,926 96,024 100,000 99,676 99,115 98,347 97,573 96,841 95,960 50,000 49,864 49,609 49,256 48,818 48,315 47,860 500,000 498,975 496,330 492,663 488,332 483,416 478,830 0 1,025 3,670 7,337 11,668 16,584 21,170 30 30| 31! 32! 33! 34! 35! This table gives the numbers living at the end of 1§, 2\, etc., years; and in order to obtain the numbers at the end of full years, Mr. Sprague divided the deaths in Column 9 of the above table into half-years by a method of differences. The deaths in the first and second half-years were then added together and di- vided by the corresponding numbers exposed to risk to give the rate of mortality for the first full year, and so on for subsequent years. The tables were computed on the further assumption that the H table represented the ultimate rate of mortality. Accord- ingly having deduced the Select rates for the first five years, and having graduated them by the Graphic Method, these graduated rates were joined to the Hm(5) rates. When the former exceeded the latter in the years one, two, three or four, the Hm(5> rates were adopted from that year onwards; after the first five years the tfm(5> Table was adopted in all cases. This saved labor in calcula- tions, because all the more useful values had been published for the Table, and those for the early years only had to be added. From the rates of mortality for quinquennial ages, found as above shown, the rates for intermediate ages were obtained by a process of osculatory interpolation. THE PRINCIPAL MORTALITY TABLES. 49 These tables quickly came into general use, especially for the calculation of premiums; and, as compared with ordinary life net premiums under the Hm Table, those by the Select Tables are higher up to age 43, but after that age they are lower. King’s Analyzed Tables gave similar results. As the method of com- puting the rate of mortality for the first year introduced a function involving the second year’s mortality, the rate deduced by Mr. Sprague was probably too high, while Mr. King’s method left the same factor avowedly too low. In addition to the painstaking work of Mr. Sprague in this investigation there were four original ideas introduced by him at that time which deserve special emphasis: 1. The facility obtained by using a Common Radix; 2. The happy combination of his figures with the Hm(-B> Table; 3. The use of a new formula of Interpolation; and 4. The development of an excellent Notation for Select Tables. Moreover, Mr. Sprague, in an elaborate and very valuable paper* showed the many uses to which select tables could be put whereby information could be obtained on points regarding which nothing could be learnt from the old aggregate tables. Those uses opened a new field of vision to many actuaries, and enabled them to solve problems, which some had scarcely even ventured to guess at previously. The result was the immediate acceptance by nearly all actuaries of the Select Table Principle. British Offices’ Life Tables, 1893.f A growing opinion that the mortality of insured lives had de- veloped on lines which made the Hm Table obsolete, with a strong desire for more truly representative tables, especially Select Tables, led to the formation of a Joint Committee of the Institute and the Faculty of Actuaries to compile new statistics. In 1894 cards were issued to the contributing offices, and sixty sent in returns. Males and females were dealt with separately by means of colored cards. Rated up lives and those subject to extra hazard were excluded, the experience being confined to healthy lives resident * J. I. A., Vol. XXII, p. 40Q. t British Offices Life Tables—several volumes published by C. & E. Lay- ton, London. See especially “An Account of the Principles and Methods, etc.,” 1903. 50 SOURCES AND CHARACTERISTICS OF in Britain when the policies were issued. If extra premiums were afterwards incurred for foreign residence or occupation, the lives were continued under observation without modification on this account. The experience extended from the Policy Anniversary in 1863, or subsequent date of entry, to the anniversary in 1893 or previous exit. One of the objections to the Hm Table was thus avoided, namely—that the data for that table extended back to the earliest history of the oldest companies when sanitary and economic surroundings were entirely different. The rates of mortality are shown separately for different classes of policies, as follows: Symbols Used. No. of Years of Experience. No. of Lives. Approxi- mate Mor- tality Ratio.* Whole Life Participating 0M 7,056,863 551,838 100 Whole Life Non-participat- ing ONM 602,591 56,807 110 Endowment OEM 897,673 132,043 75 Limited payments OEM 410,251 36,839 81 Increasing scale premiums OIM 207,709 23,280 109 Temporary OTM 36,489 11,603 Contingent OCM 15,586 3,482 Joint Lives 0JM 90,171 9,195 Select Tables are expressed OlNM], 0[M1, etc.; while for female lives the letter / is substituted in the above symbols instead of m. Select mortality tables have been accurately formed for the first time and show the effect of the company’s and the policy holder’s selection. The effect of selection is shown to be of little impor- tance after 5 or 6 years yet unadjusted tables are given which exclude: 1. The first 5 years; 2. The first 6 years; etc., etc., up to the first 10 years. By excluding the first ten years we probably get the ultimate rate of mortality. Select values during the first ten years have * This “Approximate mortality ratio” is obtained by comparing the actual deaths between the principal insurance ages 30-50 with the expected deaths by the 0M(5) table. The select period (first five years) was excluded in making the comparison. In the last three classes the non-select experience is scarcely sufficient to make a satisfactory comparison. THE PRINCIPAL MORTALITY TABLES. 51 been graduated to join this ultimate table. Those tables which exclude a portion of the data have been called truncated—a word which does not seem expressive for the particular purpose in view. Duplicate lives were eliminated from the aggregate tables; but all except simultaneous policies were retained in the select statistics, since two policies taken at different dates on the same life do not come into the same section of a select mortality table. Accordingly the Select Tables purport to deal with a larger number of lives and a greater number of years of exposure. In the aggregate and ultimate tables if two policies appeared on the same life, but with an uninsured interval between the discon- tinuance of the one and the issue of the other, the first was treated as withdrawn and the second as a new issue. The 0M and the 0M(5) as compared with the American Experience Table show the following results: Age. Complete Expectation of Life Bate of Mortality qx per 1000. American. 0M 0M(5) American. 0M 0M(5) 20 42.20 43.68 42.39 7.81 4.04 6.52 30 35.33 35.57 35.06 8.43 5.95 7.47 40 28.18 27.86 27.67 9.79 9.15 9.78 50 20.91 20.61 20.52 13.78 15.04 15.45 60 14.10 14.07 14.04 26.69 28.87 29.21 70 8.48 8.71 8.71 61.99 62.07 62.19 80 4.39 4.84 4.84 144.47 138.44 138.50 The rate of mortality qx by the American Table is higher than the 0M at ages under 43, then considerably lower from that age to age 70, after which it is again higher. Net premiums for Whole Life insurance follow generally the same course; but at the prin- cipal entry ages 25 to 40 there is never so much difference as $1.00 per thousand. At age 25 the American Experience rate is 87 cents more than the 0M and at age 40 it is 49 cents less. The Expectations of life by the American Experience and the 0M(5) show a remarkable agreement while annuity values, premium rates, etc., also differ but slightly. Female Experience is given for: (1) Ordinary Life participating, (2) Ordinary Life non-participating, and (3) Minor Classes. As compared with male mortality the same characteristics appear as 52 SOURCES AND CHARACTERISTICS OF had been noted in earlier investigations; there is also an indication of general superiority of female over male vitality; but medical selection does not appear to be quite so effective. A full analysis of female in comparison with male mortality was made by Mr. C. W. Kenchington* and a further investigation was afterwards made by Mr. A. J. C. Fyfe.f Amongst the “Old Assurances” in force in 1863, there were comparatively few recent policies, and the method whereby such Old Assurances were included, while extending greatly the expe- rience at the older ages, had the effect of introducing an increased number of non-select and aged lives into the aggregate 0M expe- rience, as well as into the select experience. This would make the mortality curve of the aggregate table unduly steep after middle life; it probably accounts for the high reserves by this table. Although the Hm net premiums are lower than Sprague’s Select up to age 43, the 0M are lower than the 0[MI Select only up to age 29 —a result possibly arising from the same cause. Net premiums by the 0M Table are less than those by the older Hm Table, but policy values average greater, a condition caused by the different slope of the mortality curve. The mortality in the various classes confirms the belief that the larger the rate of premium paid, the lower the mortality—an effective illustration of the selection exercised by policy holders. A careful study of the new statistics as compared with earlier compilations appears to show 1. A marked improvement in vitality; 2. The influence of medical selection is more persistent, and especially conspicuous amongst younger men; 3. Self selection by annuitants had not improved to the same extent as medical selection of applicants for insurance. One of the new features of this experience is the publication for the first time of complete tables of withdrawals. These are given for ages at issue grouped around quinquennial points and for each year of duration from 0 to 9 inclusive, also for “10 and upwards.” The rates of discontinuance per cent, according to the 0M expe- rience! were as follows: * J. I. A., Vol. XLIV, p. 105. JT. F. A., Vol. IV, p. 82. t T. F. A., Vol. VII, p. 21. § See J. I. A., Vol. XXXVII, p. 463. THE PRINCIPAL MORTALITY TABLES. 53 Year. Central Age at Entry. Year. 25 35 45 55 1 3.05 2.42 2.25 1.98 1 2 8.59 6.56 5.70 5.17 2 3 5.81 4.44 3.88 3.46 3 4 4.21 3.40 2.92 2.64 4 5 3.27 2.66 2.44 1.95 5 6 2.78 2.34 2.09 1.77 6 7 2.30 2.08 1.70 1.41 7 8 2.17 1.72 1.49 1.11 8 9 1.91 1.67 1.33 1.02 9 10 1.68 1.52 1.21 1.11 10 The rates of discontinuance per cent, on non-participating whole life policies differed materially from the above as is shown by the following rates for central age at issue, 35, that is for the group of ages 32-37. Rates of Discontinuance per cent, Onm Experience. Central Age 35. Year. Bate. 1 4.36 2 10.13 3 7.36 4 6.57 5 4.90 6 3.88 7 3.20 8 2.72 9 2.49 10 2.31 The graduation of the entire experience was placed in charge of Mr. George F. Hardy; and the 0M(5> Table was graduated by Makeham’s Law, constants being determined by a new method somewhat similar to the method of moments. In the adjustment of the 0M Table the use of Makeham’s formula alone was not practi- cable; but the graduated table was built up on the basis of the gradu- ated 0M(5) by a double frequency curve connecting the two tables. As it was necessary to abandon or modify Makeham’s formula the only object in view was to obtain a perfectly smooth curve for the 0M Table, and to represent as nearly as possible the ungraduated facts. But Makeham’s Law was applied to the graduation of the qnm(5) experience,* and was found to give good results from age 20 onwards. *J. I. A., XXXVIII, p. 501. 54 SOURCES AND CHARACTERISTICS OF An ultimate table, excluding the first ten years of the participat- ing experience, was graduated by Makeham’s Law and the select values were graduated to join this Ultimate Table by an extension of the same law, introducing a function dependent on the duration of the insurance. Specialized Mortality Investigation.* This is not strictly a mortality table but rather an investigation into the relative mortality as affected by certain special features, such as: nationalities resident in the United States, occupations, personal and family histories, and localities. The work was under- taken in 1901, under the direction of the Actuarial Society of America, from thirty years’ experience (1870-1899) of thirty-four life insurance companies in the United States and Canada. Its object was to supply those officers who have to decide upon the acceptance of risks with material for ascertaining whether a particular class is better or worse than normal. The investigation was based upon policies except that if several policies were issued on one application in the same year only one, the longest in force, was reported. The duration of policies can- celled was computed by subtracting the calendar year of issue from that of termination, and of policies in force by taking the exact duration at the anniversaries in 1900. The mortality experience in the different classes was compared with a table adopted to represent Standard Mortality amongst healthy lives. The expected deaths were computed by such Standard Table, which was based upon Farr’s Healthy English Male Table, modified for ages 15 to 21, inclusive, and for 52 to 61, inclusive. For ages 15 to 21, eleven-tenths of the annual mortality of the then new male experience Ow(5) was taken, while at ages 52 to 61, five-sixths of the Om(5) mortality was adopted. In order to allow for the effect of selection during the early years, the following percentages of mortality by the Standard Table were used: Ages at Entry. Percentages of Standard Mortality to Allow for Selection. Year 1. Year 2. Year 3. Year 4. Year 5. Year 6 and After. 15 to 28 45 64 79 90 97 100 29 to 42 50 68 82 92 98 100 43 to 56 55 72 85 94 99 100 57 to 70 60 76 88 96 100 100 * Volume published by A. S. A., 1903, 479 pp., folio. THE PRINCIPAL MORTALITY TABLES. 55 The final results were published in 1903, with the actual and expected deaths for each class in the four age groups above shown as well as in total. The detailed facts were also published to permit of individual study, and from which more accurate con- clusions may be deduced. The classes of risks may be briefly described as follows: 1. Policies for large amounts; one class over $20,000. 2. Policies granted on terms other than applied for; 2 classes. 3. Nationality; divided into 4 classes. 4. Occupation; divided into 35 classes and covering army, navy, and marine service; the more important hazardous trades; liquor dealing; and railway service. 5. Personal Disability; covering 32 classes, including past history of diseases such as gout, blood-spitting, etc., unusual weights and unusual heights. 6. Family history unsatisfactory; covering 2 classes, dealing re- spectively with cancer and insanity. 7. Place of Residence; 22 classes, each relating to a different county in the United States, principally in the South. Care must be exercised in using the results for the following reasons: All the lives investigated were accepted by companies and therefore may not show average results in some of the specialized classes. While those who were charged an extra solely on account of occupation were included in the experience, no risks were in- cluded if they had been treated as under average on account of personal or family history. Accordingly all the classes in the latter category may be viewed as the better selected risks of each class. Again, the standard of measurement (Farr’s Table Modi- fied) has not been universally accepted as representing the normal risk. If the standard mortality were too low for any group of ages the result would be to give apparently unfavorable results for those ages and vice versa. Medico-Actuarial Mortality Investigation. The Association of Life Insurance Medical Directors and the Actuarial Society of America felt that the work of the Specialized Mortality Investigation should be extended, and a joint commit- tee was formed for the purpose, October, 1909; memorandum of instructions issued May, 1910. Forty-three companies supplied 56 SOURCES AND CHARACTERISTICS OF the basic information and the work of compiling, tabulating, and recording the data was conducted at a central bureau in New York City. The experience covered about 93 per cent, of the policies issued in the United States and Canada by all legal reserve companies during the years 1885-1909, traced to policy anniversaries in 1909. It dealt with the following: a. 68 groups involving occupational hazard; b. 76 groups of medical impairments; c. 4 groups of women; d. 3 groups of colored risks; e. 4 groups of joint life policies; /. A study of the influence of build on longevity. Policies which had been treated as sub-standard for medical reasons were excluded; policies rated as sub-standard for family history alone, or for occupation, were included. The experience was based on policy years, and mean durations; in case of death the duration was curtate, thereby placing each death in the proper policy year. To investigate the influence of build on longevity, the com- panies furnished records of their business on standard lives for one month in each of the sixteen years, 1885-1900, January being taken in the odd years and July in the even years, by this means securing an average of summer and winter weight. The mortality rates from this data were much lower than the stand- ard table assumed in the Specialized Investigation. They were however confirmed by the experience of two large companies, and were therefore used for purposes of comparison. The rates of mortality were low at the younger ages, the ultimate mortality for the eleventh and succeeding policy years being less than 60 per cent, of the American Experience for attained ages below 40. After the first year the mortality by policy years for entrants under 50 showed the effects of selection to be relatively slight. The committee asked the companies to furnish additional data to examine further the improvement in mortality and a standard table was thereafter formed. The following shows the extent of statistics: THE PRINCIPAL MORTALITY TABLES. 57 Years of Issue. Number of Entrants. Total Number of Years’ Exposure. Deaths. Expected Deaths. Ratio. 1885-1892 1893-1900 1901-1908. 80,976 148,995 270,404 781,852 1,106,316 926,108 7,180 8,000 5,042 6,850.03 6,911.45 5,441.91 105% 101% 93% Totals 500,375 2,814,176 20,222 20,203.39 100.3% The final table shows the mortality rates for the first four years of duration and thereafter is merged into a general table excluding these years,—now commonly mentioned as the M. A. Table. Only the first two years showed a distinctly lower mortality than the ultimate. The Committee was satisfied that the table might with confidence be used for the particular purpose for which it was constructed. Subdivision of the data according to years of issue showed a continuous improvement in mortality. The committee issued a warning against the general use of this table for any purpose other than that for which it was prepared. It is based upon policies and should not be applied to the solution of financial problems, since mortality rates are higher when based upon amounts insured. Five volumes of statistics were published from 1912 to 1914, the first volume containing details of the investigation and basic facts for the investigation of build, also the adjusted mortality table. Tables of average height and weight were prepared and in Volume II are published mortality ratios in groups of lives according to the extent of departure from the average build.* These tables should be used with caution, as the preponderance of recent business has the effect of indicating a lower mortality than normal in some cases, in others a higher. In addition to showing the effect of build on mortality Volume II contains an analysis of the causes of death amongst men at different ages; also tables of mortality amongst womenf divided into four classes— a. Spinsters; b. Married women, beneficiary husband; c. Married women, beneficiary other than husband; d. Widows and divorcees. * T. A. S. A., Vol. XV., p. 315, and XVII., p. 17. f See also T. A. S. A., XVIII., pp. 318-326. 58 SOURCES AND CHARACTERISTICS OF Classification by plan shows that endowments are favored by unmarried women, whereas life and limited payment forms are more often taken by married women, including widows and di- vorcees. The volume closes with statistics of mortality amongst North American Indians and certain colored groups. The mor- tality amongst negroes was shown to be about 40 per cent, in excess of the expected in spite of the careful selection of such risks. Vol. III. deals with the “Effect of Occupation on Mortality,” the most important divisions being the Liquor Industry, Rail- road, Metal Trades, and Mining. The causes of death are not given. Vol. IV contains statistics of cases showing medical impair- ments, including the effects of alcohol, also diseases affecting the various physical organs, the arteries, etc., including certain surgical conditions. It must be remembered that cases ac- cepted without rating, although coming within these classes must have been unusually good in every respect except for the par- ticular impairment. High mortality appears among those who have suffered from syphilis, even after two years’ continuous treatment and one year’s freedom from symptoms; also in cases in which albumen or sugar were found, cases of alcoholic habits, high pulse rate, abdominal girth greater than chest expanded, etc. Questions of family history (especially history of tuberculosis), habitat mostly in southern states, malaria, and joint life insur- ance, are covered in Vol. V. It was developed that under joint policies to men and women, there was a high mortality among women at the younger ages, but at the middle and older ages they appeared better than men. Students should read with close attention the warnings con- tained in “An Interpretation of the Results of the M. A. In- vestigation,” T. A. S. A., Vol. XV., pp. 62-76. Experience of Canada Life Office. Published 1895, covering years, 1847-93. One of the principal objects of this investigation, made by Mr. Frank Sanderson, was to find out the effects of selection in the northern half of North America. All lives rated-up, or charged an extra, as well as female lives, were excluded. The investi- THE PRINCIPAL MORTALITY TABLES. 59 gation was made according to the lives assured, and particulars were taken out on cards of somewhat similar form to those of the Institute 1893 Experience. The policy year method of investigation was adopted, but some slight complication arose in regard to the ages on account of the next-birthday age having been inserted in the cards. The expe- rience was reduced from fractional to even ages by means of the formula lx — lx—\ 3^x—l) it having been found from actual experience that on the average the assurances were taken one-third of a year prior to the attain- ment of the age next birthday. But this assumption was ingeni- ously avoided in graduating the aggregate tables, constants hav- ing been determined from the facts at fractional ages. In filling in the mode of exit four subdivisions were used: (1) Existing, (2) Matured, (3) Withdrawn, and (4) Died. The matured contained expired term assurances and endowments. The existing were carried to the anniversaries in 1893, and the dura- tion was found by subtracting the year of entry from 1893, thus giving an integral number of years in all such cases. The nearest integral duration of exposure was adopted for the Matured and Withdrawn, while those who died were carefully located in the policy year in which death took place and assumed to be under exposure to the end of that year. Duplicate lives were eliminated, it would appear, from the select experience as well as from the aggregate. The total number of entrants was 35,287 covering 296,481 years of life. 55% of the entrants were “Existing” in 1893; 37% had “Withdrawn” and “Matured”; and 8% had “Died.” The average age at entry was 32; the average duration nearly 834 years. Of the total years of exposure, more than one-half relate to ages below 40 and four-fifths to ages below 50, a fact that prob- ably accounts for the small percentage of deaths for so high an average exposure, although for the “Died” alone the average duration was 13.55 years. The tables deduced include an Aggregate Table, a table excluding experience of first five years, some Select Tables, as well as full particulars under each age at entry of the exposed to risk and deaths for each year of duration. Statistics are given of the 60 SOURCES AND CHARACTERISTICS OF withdrawals, and it is shown that nearly half of these took place at the end of the first year. Makeham’s formula for graduation was used for the aggregate table, the method of determining the constants being that introduced by King and Hardy; log c .= .0425. In forming select tables the experience after five years was first investigated, and connecting mortality rates were formed during the first five years between the ages of 20 and 50 in the following manner: The first year’s mortality was investigated by itself in three groups of ages, and then graduated for each age. The third year’s mortality was found by combining the second, third and fourth years, the resulting mortality rates being graduated by Makeham’s formula; and lastly, the second, fourth and fifth years’ mortality were got by interpolation. In the published volume there were included comparative tables showing the death rate as compared with that of the more im- portant mortality tables in individual offices and groups of offices. The mortality of the Canada Life appears to have been exceedingly favorable, being practically the same as that of the Australian Mutual Provident. Statistics deduced from census returns would indicate that the conditions in Canada are peculiarly favorable to longevity. The satisfactory experience of the Canada Life office may be caused to a considerable extent by climatic influences, combined with strict medical selection and a goodly proportion of risks from rural communities. D and N commutation columns and annuity values at 4% in- terest are given, and it is found that the reserves by this table are high as compared with the standard tables. The government of the Province of Ontario adopted the experi- ence as the basis for the calculation of minimum rates for fraternal societies. A separate investigation was made into the mortality amongst substandard lives, but the paucity of data and combination of various classes of risks renders any conclusions from this class of doubtful practical value. Mortality Experience of Gotha Life Office, 1829-1896.* This investigation, made under the supervision of Dr. Johannes Karup, embraces the experience of the Gotha Life Office on all classes of life and endowment insurances from 1829 to 1895; the observations ceasing on the policy anniversaries in 1896. The * This account has been taken from T. F. A., Vol. V, p. 87 et seq. THE PRINCIPAL MORTALITY TABLES. 61 policy year method was used and there were 150,594 lives with 2,255,813 years of exposure, and 46,480 deaths. All joint life, survivorship, and short term insurances were excluded. The experience was analyzed by lives, and by amounts; also according to sex and classes of insurance (life, endowment, etc.), all according to the duration of policies, thus producing select tables. The nearest age at entry was taken, and the nearest duration method used. Duplicate lives were excluded whether of the same class or not, except for ascertaining the rate of claim, i. e., mortality by amounts. The treatment of withdrawals followed the British Offices’ Experience, except that exact calculations were made for the first year. An investigation of the manner in which the mortality changed during the period was made, by tracing the new business of different periods separately, and dividing 1829-1896 into four parts, namely: (1) 1829-1852, (2) 1852-1867, (3) 1867-1881, and (4) 1881-1896. The mortality of each period was compared with (1) the whole experience 1829-1896, and (2) the partial experience 1852-1896 by convenient age groupings for (a) the first five years, and (6) the sixth and subsequent years. The results showed that the mortality diminished from period to period, especially during the first five insurance years, indicating an improvement in methods of selection. The final graduated Select Tables are joined to the ultimate table after 7 years. The first year’s mortality declines from age 15 to age 28, and until age 40 continues less than for age 15; this char- acteristic is observed in a less pronounced form in subsequent durations. The practice of the company had been to accept many risks on endowment plans where the excess mortality might be expected to fall mainly after maturity of the endowment; indeed this seems to be the only method used for treatment of substandard lives. Endowment policies were divided into three classes: (1) “Volun- taries,” i. e., those who apply for such of their own accord, (2) “Involuntaries,” i. e., those upon whom such policies were imposed, and (3) a class of policies issued as collateral for loans. These three divisions taken together show a mortality lighter than that for whole life policies, being 84% during the first five years and 96.3% thereafter. The voluntary endowment class shows an unusually low mortality and each of the other classes a mortality 62 SOURCES AND CHARACTERISTICS OF considerably in excess of the whole life, the involuntary class being slightly the worst, the heavier mortality of this last named class being also distinctly observed during the first five years after entry. The female experience was not extensive, there being 2,735 deaths. During the first year women appear as favorably as men, but during the second and subsequent years for ages under forty there is a noticeably higher mortality amongst females. From about age 40 onward the excess of male mortality over female is quite appreciable. Japanese Life Tables.* These tables are the first to give the mortality of an Oriental race, scientifically deduced from life insurance records. The tables, formed by Mr. K. Ebihara, F. I. A., were published in 1912. The material, furnished by three Japanese life companies, is of recent character, the oldest company having been founded in 1881. The experience closed in 1905 and to avoid special risks incurred during the Russo-Japanese war, all emigrants and lives in military service effecting policies in 1903 or after, were excluded. The system of investigation followed closely that of the British Offices’ Life Tables. 484,815 cards were sent in, of which 203,- 143 related to endowments. Special features were: 1. Very heavy mortality at young ages and marked improve- ment between ages 20 and 30—generally heavier mor- tality than British or American standard. 2. The method of handling selection. The actual deaths in the first year were 62 per cent, of the expected by the Ultimate Japanese Table. This ratio of 62 per cent, was used for all ages; similarly for the second, third, and fourth years, the ratios were 87 per cent. 95 per cent, and 97 per cent. 3. The use of the function B[*]+f, meaning “Brought down” or “net movement.” * J. I. A., Yol. XLVII., pp. 100-105. THE PRINCIPAL MORTALITY TABLES. 63 Government Annuitants—No. I, 1829. MORTALITY OF ANNUITANTS. In 1808 the National Debt Commissioners of Great Britain commenced to grant life annuities, and they applied to Mr. W. Morgan, the Actuary of the Old Equitable, to compute tables for this purpose; these tables he based on the Northampton Table. In 1819 Mr. John Finlaison who had been appointed Government Actuary pointed out that the prices charged for annuities were too small, and that the Government was losing heavily. Specula- tors had discovered the excellent values in such annuities, and had been buying annuities on carefully selected lives, sometimes also protecting themselves against loss by life insurance on the same lives. The loss to the government in the eleven years from 1808 amounted to nearly $10,000,000, yet a period of about ten more years elapsed before the error was corrected. Mr. Finlaison had in the meantime been taking steps to ascertain the rate of mortality amongst annuitants. He took for his materials the nominees of* 1. Various English and Irish Tontines from 1693 to 1789; 2. Life annuities issued at the Exchequer from 1745 to 1779, and 3. Life annuities chargeable on Sinking Fund from 1808 (as above). In each case the facts were carefully tabulated, and in extracting them duplicate lives were eliminated. The ages last birthday were given in each case, and on an average the lives were assumed to be half a year older. Those stated to be 30 were assumed on the average to be 30§, the sum of the numbers at 29 and 30 were assumed to give double the number exposed to risk at age 30. Mr. Finlaison drew up twenty-one tables, two of which he ad- justed by the formula: Graduated ?x = Mv'x-i + 2pl_3 + 3px_2 + 4p'_j + 5p' + 4Vx+\ + 3p*+2 + 2px+3 + p'+4]. called Finlaison’s Method of Graduation. There is reason to believe, however, that he subjected his data to some modification before applying his method of adjustment. One of the most important features of this investigation was the marked superiority of female life over male. Values of annuities were deduced from his results and employed by the government. 64 SOURCES AND CHARACTERISTICS OF Government Annuitants—No. II, 1860. This table was formed by Mr. A. G. Finlaison (son of Mr. John Finlaison), the Actuary of the National Debt, the materials used being the nominees of: 1. The Irish Tontines of 1773-1777 . 3,384 persons. 2. The English Tontines of 1789 . 8,171 persons. 3. The annuities granted by National Debt Commissioners 1808-1850 . 16,812 persons. 28,367 Of these 28,367 persons, 11,829 were males and 16,538 females; 19,434 had died during the period over which the observations extended; while amongst the males were 675 carefully selected lives nominated by speculators who had purchased the annuities. This practice has been stopped by law. The Tables were never extensively used, and are now of but little interest. Government Annuitants—No. Ill, 1883. Formed by Mr. A. J. Finlaison (grandson of Mr. John Fin- laison), Actuary to the National Debt Commission, exclusively from the records of the annuities issued from the National Debt Office during the period from 1808 to 1875. The number included was 30,788, of whom 10,929 were males, and 19,859 females. The 675 selected nominees previously referred to were also included amongst the males. 22,998 had died during the period and 7,790 were alive at the close of the observations. The tables published give the following particulars for each age: 1. Number of entrants. 2. Number alive at close of observations. 3. Deaths, and 4. Exposed to risk. In the case of those alive at the close of the observations—1875— they were each kept under observation until their birthdays that year in order to avoid fractional years of age. The following is an extract from the table of elementary facts, age at purchase 60: Number of Entrants 475. Age. Alive at Close of Observations. Deaths. Number Exposed to Risk. 60 _ 4 316.7 61 4 16 467 62 6 11 445 63 7 14 427 etc. etc. etc. etc. THE PRINCIPAL MORTALITY TABLES. 65 The ages at purchase of the annuities were stated as those last birthday, and it was found that, on an average, the annuitants were actually four months older. Accordingly, the true average age of the 475 entrants above mentioned was and up to the age of 61 these were exposed to risk for two-thirds of a year. Mr. Finlaison, to get the mortality for the first year, and for age 60 at entry, divided the four deaths above mentioned by two- thirds of 475, i. e., 316.7, this being equivalent to an assumption that the rate of mortality during the four months from the birth- day to purchase was the same as for the eight months immediately following. A similar assumption was of course made for other ages. For the second year’s mortality at age 61, the four who died, and the four alive at close of observations must be deducted from the entrants, thus giving 467 exposed to risk at age 61, among whom 16 deaths occurred, which showed a rate of mortality of .0343; similarly for subsequent years. The formula for deducing the exposed to risk would therefore be: or E[x]+n — E[x]+n—1 d[x]+n_l 6[x]+nj and for the general mortality table where the entrants at all ages were combined: Ex = 2nx_ i -f f n* — 2ex — 2dx_i = 22x_i + |nx_i + f nx — ex — dx_i, where nx represents the new entrants. An analysis of the facts was made to ascertain the effect of the selection which the annuitants exercise, and it was found to be unimportant after four years. The entrants at each age were accordingly traced separately for the first four years of their existence (for ages 40 to 80) and thereafter combined with the entrants at all previous ages, thus giving Select Mortality Tables. The treatment was equivalent to a “life-year” method, the annuitants being traced on the average from birthday to birthday. It has been suggested that the method of graduation by Wool- house’s formula distorted the table, and resulted in higher mor- tality rates than the facts justified; but this is now only of academic interest. 66 SOURCES AND CHARACTERISTICS OF Government Annuitants—No. IV, 1910.* The Actuary to the National Debt Commissioners of Great Britain, Mr. J. Blakey, submitted a report dated 12th October, 1910, in which he gave particulars of an investigation into the mortality of government annuitants from 1st January, 1875, to 31st December, 1903, including new annuities issued during that time and annuitants living on the anniversary of purch. se date in 1875. Where two or more annuities were granted, only the experience of the first was included. The following table gives a summary of the data: Males. Females. Total. Number of lives under observation 5,504 13,863 19,367 Number of years of risk 57,652 163,378 221,030 Number of deaths 4,168 9,333 13,501 Number of lives existing at the close of the observation 1,336 4,530 5,866 Government Annuity Experience, 1875-1904. Summary of Data. The investigation proceeds on the policy year plan, tracing the mortality from the date of admission to the next anniversary, and so forth, from anniversary to anniversary of the purchase of the annuity, following the method of the latest British Offices’ Experience. The ages at entry were taken as the nearest age at date of purchase. An investigation as to the effect of using this showed that the assumption had the effect of understating the tabular ages by about 20 days in the case of male lives and about 15 days in the case of female lives—a trivial difference. A considerable number of annuities are purchased at the Na- tional Debt Office under wills, etc., where the nominees do not exercise any option, but in most cases the nominees themselves are the purchasers. The new tables are based on the assumption that the effects of selection are practically exhausted after the expiration of four years and the rates of mortality were, therefore merged into the aggregate table after that period. The tables were graduated by Makeham’s method, satisfactorily in the case of aggregate tables, but modified for select tables in a manner similar to that employed in the graduation of the British Offices Annuitant * J. I. A., XLVII, p. 66. the principal mortality tables. 67 Tables. The following table compares the new values with other important tables of annuitant mortality. Males. Age. Government Annuitants. Select. British Offices, Select. McClintock’s. 1808-1875. 1875-1904. 40 $16.37 $17.34 $17.60 $17.41 50 13.83 14.24 14.40 14.29 60 10.64 10.82 10.88 10.73 70 7.36 7.45 7.44 7.15 80 4.64 4.59 4.54 4.08 Females. 40 $18.17 $18.69 $18.26 $19.32 50 15.28 15.78 15.51 16.03 60 11.82 12.29 12.23 12.28 70 8.06 8.59 8.41 8.42 80 5.02 5.27 5.05 5.01 Annuity Values—Three Per Cent. British Offices’ Life Annuity Tables, 1893.* This investigation relates entirely to the experience of annuitants under contracts purchased from 43 life assurance and annuity institutions, including the British annuity experience of three American companies. Particulars of each annuity current at the commencement of the observations in 1863 and of those subse- quently granted up to 1893 were supplied upon cards, a separate card being written for each annuity. The total of such cards was 9,700 for male and 24,300 for female lives, reduced by elim- ination of duplicates, etc., to 8,641 and 23,056, respectively. In the select male section 4,214 were existing; there had been 4,427 deaths; and 67,250 years of exposure. The corresponding figures in the female section were 11,956, 11,100, and 207,324. The tables are published in the form of select tables, the entrants at each age having been traced separately during the first five years, the rates of mortality thereafter being those of a modified ultimate experience formed by omitting the observations of the select period. It had long been felt that the government tables were not applicable to the annuitants’ experience of life assurance com- * See “An Account of the Principles and Methods adopted in the Compi- lation of the Data, etc.,” C. & E. Layton, London, 1903. 68 SOURCES AND CHARACTERISTICS OF panies, the rates of mortality in the latter being lighter than the rates in the government tables. The fact that the observations for the government experience extended from 1808 to 1875 was in itself a deterrent influence, since it was believed that mortality had continued to improve. Moreover, the selection exercised against insurance companies is probably more intelligent, because government annuities are often bought for small amounts under the provisions of a will to pension old servants. Still further, Life Office annuitants are doubtless of a better social class than the government nominees. In the case of females, forming the great proportion of the annuitants, the British Offices annuity values approximate to those of the government at an age one year younger. In the case of the males at the older ages the difference is about half a year. The difference in reserves in case of a “model office” is roughly 3}^%. Notation. Male Annuitants Table aggregate Oam Female Oaf “ “ “ select The graduation was performed by Mr. George F. Hardy. A preliminary graduation of the Aggregate Table excluding the first five years, showed that the male mortality from 40 upward could be well represented by Makeham’s formula. The female mortality could only be thus represented at ages above 65, and a sup- plementary curve had to be introduced below that age. The con- stants for these curves were obtained by equating to zero the sum of the deviations of the adjusted and unadjusted deaths, also the sum of the accumulated deviations. Three trial graduations of the male table were made, for assumed values of log c equal to .040, .038, and .036; and the final value adopted was .038 as giving on the whole the most practical results, while following closely the ungraduated facts. An arbitrary adjust- ment was made in one of the constants, so as to make the male annu- itants’ mortality at the younger ages nearly the same as the mortality amongst assured lives. The facts at these ages were meagre; and, but for this adjustment the annuity values of the annuitants would have been appreciably smaller (i. e., higher mortality) than those of assured lives. The graduation of the Select Tables for the first five years was made by introducing into Makeham’s formula a function dependent upon duration after entry. THE PRINCIPAL MORTALITY TABLES. 69 McClintock Annuity Tables. In 1896 a paper appeared in the Transactions of the Actuarial Society of America* giving particulars of the annuity experience of fifteen American companies collected by Mr. Rufus W. Weeks, Actuary of the New York Life. At first all the annuities issued prior to 1890 were used and this material was afterwards carried forward to 1892 with additional new issues in the meantime. A feature of the experience was the preponderance of foreign business; about three fourths of the lives were European and one fourth American. The experience was based on lives; duplicates were eliminated. The age was taken at the birthday nearest to the date of first exposure; observation began on entry into any one of the companies and continued until death or the anniver- sary in 1892 when the experience closed. The exposure of a few deferred annuities in the experience was taken from the date at which the first annuity payment became due—at which date there is usually an option to take a cash settlement. Men and women were investigated separately, and complete select data is given for each age at entry. The number of lives included in the experience was 4,365 men, and 4,821 women. Mr. McClintock took this data and derived two aggregate mortality tablesf for male and female annuitants respectively. They were graduated by Makeham’s Formula and have a com- mon value for the constant c—namely: log c = .04. Mr. McClintock stated that the tables differ somewhat from those which might be formed from a mere adjustment of Mr. Weeks’ data but that he had endeavored to admit only such diversions as seem reasonable. His female table, for example, shows a somewhat higher mortality at ages under 70, because he con- sidered that the experience at those ages had been materially affected by the large proportion of recent entries. With reference to the male table Mr. McClintock stated that he thought it best, if any departure from Mr. Weeks’ experience should be permitted, that such departure should be on the safe side. That is to say, the mortality in Mr. McClintock’s adjustment would be lighter than that actually shown by a direct application of the experience. This table has been adopted by the State of New York and several other states as the standard for annuity valuations. The * T. A. S. A., Vol., IV, .p. 275. t T. A. S. A., Vol. VI., pp. 13 and 137. 70 SOURCES AND CHARACTERISTICS OF following table illustrates the manner in which McClintock figures vary from those of other standard tables: Complete Expectation op Life ex. Males. Females. Age. Government Oam McClintock Age. Government Oaf McClintock 1883 Select. Select. Aggregate. 1883 Select. Select. Aggregate. 40 26.04 28.31 28.08 40 29.84 30.16 32.47 50 20.26 21.23 21.11 50 22.92 23.49 24.53 60 14.38 14.82 14.64 60 16.26 17.01 17.22 70 9.33 9.54 9.18 70 10.30 10.88 11.00 Annuitants Resident in the United States and Canada. An unusually low rate of mortality amongst annuitants resident in the United States and Canada was indicated by the investigation into the experience of American and Canadian companies by Arthur Hunter in 1904. As the number of lives observed at that time was relatively small, the Council of the Actuarial Society recommended to the companies that additional data be furnished when the then available statistics should be doubled. This con- dition was fulfilled in 1910; and the companies supplied their data up to the year of issue 1909, the exposures being carried to the anniversaries in 1910. All the companies represented in the Actuarial Society granting annuities furnished their figures. Only immediate annuities were included, issued on single lives for the whole of life, under which the consideration had been paid in cash. Accordingly all temporary, deferred, joint, and survivorship annuities were excluded, as were also annuities issued in exchange for dividends. In the experience to the anniversaries of the annuities in 1910 thirty companies contributed 12,174 cards, 6,620 relating to women, and 5,554 relating to men; more than three-quarters of the expe- rience was supplied by six companies. After eliminating simul- taneous contracts, there were 5,510 annuities on women, with 1,585 deaths; and 4,042 (42 per cent, of the total) on men with 1,295 deaths. The average ages at purchase were 63 for women and 61 for men. The nearest integral age was taken, and the duration of the existing was obtained by deducting the year of purchase from 1910. Duplicates were brought together by sorting, (1) according to year of birth, and (2) according to name. THE PRINCIPAL MORTALITY TABLES. 71 As compared with the British Offices’ Annuity Tables (Select), the mortality among women was 84 per cent, by lives and 87 per cent, by amounts of annuity. While among men the corresponding percentages were 85 per cent, and 95 per cent, respectively, both sexes indicating a lower mortality in the United States and Canada than in Great Britain. There was no evidence that the mortality differed widely by ages at entry in its relation to the British Offices’ Annuity Table. A comparison of the experience to the anniversaries of 1904 with that to the anniversaries of 1910 showed that there had been very little change in the experience for the 6th and succeeding annuity years, the ratio of the 1910 table being for all ages and years of issue 85 per cent, of the British Select Annuity experience for men and 88 per cent, for women. During the first five annuity years, however, the experience on the issues of 1904 to 1910 showed a marked increase over the experience for the same annuity years to the anniversaries in 1904. Two hypotheses have been advanced as explaining this change: (a) that there has been greater care in obtaining proof of the ages of the annuitants at the date of purchase; and (6) that the proportion of people seeking annuities was lower than formerly, and the proportion of those actively canvassed was higher,—hence less selection by the annuitants. This table formed by Christian Jensen is based upon data de- rived from the experiences of voluntary survivorship annuities, granted by “ Statsanstalten for Livsforsikring,,, the Danish State’s Life Insurance Institution. The investigation deals with female beneficiaries—Danish women only. No tables were com- puted showing death rates of the insured lives. Obligatory annuities on Civil Servants were not included. The period of observation is 1842 to 1900 and the experience is by lives, carried forward until the last policy for any particular beneficiary terminated. Exact ages from birthday to birthday were used, and the observations ceased on the birthday of the beneficiary in 1900, or with the first birthday after death prior to 1900. The graduation was by Makeham’s Formula. The constant log c — .04579609 is the same as that used in Hunter’s Makehamized American experience, thus facilitating the use of Danish Survivorship Annuity Table.* * T. A. S. A., Vol. X., p. 253. Survivorship Annuity Tables. Dawson, p. vi. 72 SOURCES AND CHARACTERISTICS OF the two tables for joint lives. The other constants were derived by the “Method of Least Squares” from the table at age 40 up- wards, involving 4,041 deaths. The experience showed an improvement in the death rate towards the end of the period. The mortality of the Danish population is said to be as good as that in the healthier parts of the United States, so that the tables may be used until American Tables for Survivorship Annuities are available. In the absence of other authoritative tables showing the rates of mortality of annuitants under Survivorship Annuity Contracts, this table has been adopted as the standard for workmen’s compensation allow- ances in the State of New York. THE PRINCIPAL MORTALITY TABLES. 73 MISCELLANEOUS MORTALITY INVESTIGATIONS. In addition to the tables herein described there have been many- other investigations, some of which are of great interest; but space will not permit that they be discussed in detail, although references to the more important of these experiences may with advantage be given. Those who may have occasion to study any particular phase of mortality may thus have some knowledge of the lines of research and may be guided in the way towards which their further inquiries can profitably be directed. These special investigations may be placed in general divisions as follows: 1. Investigation of death rates of different races; 2. Mortality rates in various countries and localities; 3. Observations according to class or occupation; 4. The experience of individual insurance companies. The mortality of different races has not been scientifically analysed with any completeness. Of course, it is necessary that the various peoples should be under similar conditions in order that proper comparisons may be made. At various times investigations into the mortality of the colored race in the United States have been undertaken, as in the Specialized Investigation of the Actu- arial Society and the U. S. Life Tables, 1&10. The experience of individual companies on the same subject has also been dealt with, but the results have seldom been made public, although they have frequently been stated incidentally. The mortality rates in different countries may be viewed either as affecting Caucasians resident in foreign lands, or as affecting the native population. Conditions as affecting whites resident in tropical countries have changed greatly in recent years through a better knowledge of malaria and other tropical diseases which are frequently transmitted by causes formerly unsuspected, often by mosquito bites. Yellow fever has disappeared from certain countries, while notable changes have been observed in such regions as Cuba and the Panama Canal Zone, making the older investi- gations of mortality in such regions of doubtful value. Some of the less progressive countries do not seem to have taken advantage of this growth of scientific knowledge. The Journal of the Institute of Actuaries contains many refer- 74 SOURCES AND CHARACTERISTICS OF ences to mortality in different countries, as for example mortality in certain parts of Africa;* the mortality in certain parts of Australia;f the mortality among the natives of India;! assured lives in the West Indies,! etc. Much valuable information with reference to the mortality in semi-tropical and tropical countries is given in the Transactions of the Actuarial Society, Vol. X, p. 395; and by James Chatham in Trans. 3rd International Congress, p. 338. Under the division of mortality according to class or occupation one most important publication is the Supplement to the Report of the Registrar General in England and Wales, Part II, published in 1908, dealing with the death rates in different occupations in England during the years 1900-’01-’02. This report succeeded another of the same nature, less complete, published ten years earlier. The question of mortality amongst dealers in alcoholic liquors was investigated by the Associated Scottish Life Offices, || also in the Specialized and Medico-Actuarial Investigations. The question of comparative mortality among abstainers and non- abstainers from the use of alcohol has been a subject of much controversy.** Those who use alcohol freely are unquestionably on the average poor risks for insurance purposes. The low mortality amongst the clergy generally was long ago indicated by investigations made by the late James Meikle into the Church of Scotland Ministers’ Widows Fund, and this experience has been confirmed again and again, the most recent investigation of this type being that into the Presbyterian Ministers’ Fund by L. G. Fouse, details of which have not been published. Several interesting tables have also been prepared showing the mortality of British Peerage Families, the statistics being taken from books published from time to time giving information regard- ing the individual members of the Peerage. These publications also afforded a means of investigating the numbers of marriages and of births, and thus computing premiums for insurance against the birth of issue, ft Peerage and clergy statistics have also been used for determining the mortality in infancy and in childhood * Vol. XXXIII, p. 285, XLVI, 308. J Vol. XXV, p. 217, XLIII, 365. t Vol. XXXVI, p. 151. § Vol. XXVII, p. 161. |! See J. I. A., Vol. XXXIII, p. 245. ** See paper and discussion, J. I. A., Vol. XXXVIII, p. 213; correspondence, same Vol., p. 273; and Transactions 5th International Congress, Vol. I, pp. 517-545. ft See especially J. I. A., Vol. XXVIII, p. 350. THE PRINCIPAL MORTALITY TABLES. 75 which has depended in the past very greatly upon the class of the parents, so that the ordinary census tables of mortality in infancy are not applicable for calculations relating to children’s endowments.* There have been many important investigations conducted by individual companies which have furnished information on par- ticular points. For example, the Mutual Benefit Life Insurance Company investigated especially the mortality on policies con- tinued under Extended Insurance.! Several companies, following the Mutual Life investigation of 1857, have taken up the causes of death of insured lives. These have not been discussed much by actuaries though they prove of great interest to medical men. The experience of the Connecticut Mutual Life Insurance Co. from its commencement to 1878 was published in 1884, and amongst other features showed that the mortality under term insurance had been excessive as compared with other classes, but it is explained that this might partly be accounted for by term policies taken out by the early Californian miners. Tables of discontinuance were also given, but under present day conditions these are not now of much value. More recent rates of discon- tinuance were given by the New York Life,! but even these rates have been greatly improved upon since 1907. The information contained in the Medico-Actuarial publication with reference to height and weight was recently supplemented by the publication of “Standard Mortality Ratios incident to Variations in Height and Weight among men” compiled by a joint committee of the Actuarial Society and the Association of Medical Directors. This publication deals not only with devi- ations from standard weight as affected by age, but treats of (1) Medium sized, (2) Tall, and (3) Short men; also (4) Abdominal girth of stout men. A Practical Rating for Overweights was submitted by A. A. Welch in T. A. S. A., XVII, p. 17. The Washington Life Insurance Company published mortality results in 1889 containing amongst other interesting data an investigation into the rates of mortality amongst policy holders taking their dividends as reversionary additions as compared with those taking cash. The latter were found to be very much the better lives confirming the results of a previous investigation by Mr .G. F. Hardy. § The mortality experience of the Provident * See J. I. A., Vol. XVII, p. 26. t T. A. S. A., Vol. X, p. 597. t T. A. S. A., Vol. IX, p. 103. § J. I. A., Vol. XXIII, p. 1. 76 SOURCES AND CHARACTERISTICS OF Life & Trust Company from 1866 to 1875 showed unusually low mortality rates, apparently due in part to the large proportion of endowment policies issued by the company. Further investiga- tions of the same company up to 1911 (T. A. S. A., XIV, p. 277) show low mortality in Endowment policies as compared with Life, and unexpectedly low rates in Term policies. An interest- ing investigation of mortality by plan of insurance, as experienced by the Aetna Life Insurance Company, appears in Vol. XVII, p. 246. The mortality rates applicable to policy issues from 1885 to 1905 are relatively high in relation to the entire experience; while all issues indicate a low mortality during the years from 1905 to 1913. The experience on deferred dividend policies after the dividend period expires, policies being continued, was submitted by Arthur Hunter, Vol. XIV, p. 38. The results show a clear condition of selection by policyholders adverse to the company. On more than one occasion it has been shown that when an automatic provision for extended insurance or even for paid-up insurance goes into effect, there is a tendency towards high mortality in the first year or two after lapse. Probably the policyholders “ allowed their policies to lapse as a direct result of serious im- pairment in health and without regard to consequence.”* These and many other phases of the mortality question have been ably discussed, yet the conditions of life have been changing so rapidly that results obtained some years ago while possibly indicating the trend of events or showing that certain causes may lead to good or evil effects, are not necessarily applicable to present day conditions. Accordingly there is almost unlimited scope for further research, and we may expect to see a still closer scientific study leading especially towards the improvement of conditions in unhealthy regions or occupations. *T, A S.A.,XV. p. 303. THE PRINCIPAL MORTALITY TABLES. 77 Table Showing the Rate op Mortality (qx) According to Certain Tables. Thirty Age. American Experience. Actuaries Table. American Offices. O* 0*<5> Age. (Males). 20 .0078 .0073 .0068 .0063 .0040 .0065 20 25 .0081 .0078 .0070 .0066 .0048 .0069 25 30 .0084 .0084 .0075 .0077 .0060 .0075 30 35 .0090 .0093 .0082 .0088 .0074 .0084 35 40 .0098 .0104 .0094 .0103 .0092 .0098 40 45 .0112 .0122 .0112 .0122 .0115 .0120 45 50 .0138 .0159 .0142 .0160 .0150 .0154 50 55 .0186 .0217 .0189 .0210 .0204 .0208 55 60 .0267 .0303 .0265 .0297 .0289 .0292 60 65 .0401 .0441 .0386 .0434 .0420 .0422 65 70 .0620 .0649 .0578 .0622 .0621 .0622 70 75 .0944 .0956 .0878 .0984 .0926 .0927 75 80 .1445 .1404 .1341 .1447 .1384 .1385 80 Age. Gotha 1852-95 Whole Life —Males. Healthy English No. 1 (Males). English Life No. 3 (Males). English Life No. 6 (Males) Carlisle Table. North- ampton Table. Age. 20 .0053 .0070 .0083 .0046 .0071 .0140 20 25 .0047 .0078 .0092 .0057 .0073 .0158 25 30 .0045 .0082 .0101 .0067 .0101 .0171 30 35 .0058 .0086 .0113 .0090 .0103 .0187 35 40 .0078 .0094 .0130 .0119 .0130 .0209 40 45 .0104 .0108 .0154 .0148 .0148 .0240 45 50 .0144 .0130 .0188 .0194 .0134 .0284 50 55 .0213 .0166 .0246 .0257 .0179 .0335 55 60 .0320 .0237 .0325 .0360 .0335 .0402 60 65 .0467 .0368 .0459 .0497 .0411 .0490 65 70 .0709 .0556 .0673 .0721 .0516 .0649 70 75 .1061 .0840 .0988 .1054 .0955 .0962 75 80 .1619 .1249 .1418 .1520 .1217 .1343 80 78 SOURCES AND CHARACTERISTICS OP Table Showing the Complete Expectation op Life (e*) According to Certain Tables. Age. American Experience. Actuaries’ Table. Thirty American Offices. (Males.) hm OW 0M 03f(5) Age. 20 42.2 41.5 43.1 42.1 42.9 43.7 42.4 20 25 38.8 38.0 39.5 38.4 39.2 39.6 38.7 25 30 35.3 34.4 35.8 34.7 35.6 35.6 35.1 30 35 31.8 30.9 32.2 31.0 31.9 31.7 31.4 35 40 28.2 27.3 28.5 27.4 28.2 27.9 27.7 40 45 24.5 23.7 24.8 23.8 24.7 24.2 24.0 45 50 20.9 20.2 21.2 20.3 21.2 20.6 20.5 50 55 17.4 16.9 17.8 17.0 17.9 17.2 17.2 55 60 14.1 13.8 14.6 13.8 14.9 14.1 14.0 60 65 11.1 11.0 11.6 11.0 12.1 11.2 11.2 65 70 8.5 8.5 9.0 8.5 9.7 8.7 8.7 70 75 6.3 6.5 6.7 6.4 7.6 6.6 6.6 75 80 4.4 4.8 4.9 4.7 4.8 4.8 80 Age. Gotha Healthy English No. 1 (Males). English English Carlisle Table. North- Select. Aggre- gate. Life No. 3 (Males). Life No. 6 (Males). ampton Table. Age. 20 43.0 43.6' 43.4 39.5 41.0 41.5 33.4 20 25 39.2 39.7 39.9 36.1 37.0 37.9 30.8 25 30 35.3 35.6 36.4 32.8 33.1 34.3 28.3 30 35 31.3 31.4 32.9 29.4 29.2 31.0 25.7 35 40 27.4 27.4 29.3 26.1 25.6 27.6 23.1 40 45 23.6 23.5 25.6 22.8 22.2 24.5 20.5 45 50 20.0 19.8 22.0 19.5 18.9 21.1 18.0 50 55 16.8 16.3 18.5 16.4 15.8 17.6 15.6 55 60 13.9 13.1 15.1 13.5 12.9 14.3 13.2 60 65 11.4 10.4 12.0 10.8 10.3 11.8 10.9 65 70 7.9 9.4 8.4 8.0 9.2 8.6 70 75 5.9 7.2 6.5 6.2 7.0 6.5 75 80 4.3 5.4 4.9 4.6 5.5 4.8 80 THE PRINCIPAL MORTALITY TABLES. 79 Tab lb Showing Percentages which the Rates op Mortality According to Certain Tables, Bear to the Rates According to the American Experience. Age. Actuaries Table. Thirty Ameri- can Offices. H M qU 0«( 5) Age. 20 93 87 81 52 84 20 25 96 87 82 60 85 25 30 100 89 92 71 89 30 35 104 92 98 82 94 35 40 106 96 105 93 100 40 45 109 100 109 103 108 45 50 116 103 116 109 112 50 55 117 102 113 110 112 55 60 114 99 111 108 109 60 65 110 96 108 105 105 65 70 105 93 100 100 100 70 75 101 93 104 98 98 75 80 97 93 100 96 96 80 Age. Gotha 1854-95, Whole Life, Males. Healthy English No. 1 (Males). English Life No. 3 (Males). English Life No. 6 (Males). Carlisle Table. North- ampton Table. Age. 20 68 89 106 59 91 180 20 25 58 96 114 70 91 196 25 30 53 97 119 80 120 203 30 35 65 97 126 100 115 209 35 40 80 96 132 122 133 214 40 45 93 96 138 133 133 215 45 50 104 94 137 140 97 206 50 55 115 89 132 138 97 180 55 60 120 89 122 135 125 151 60 65 116 92 114 124 102 122 65 70 114 90 109 116 83 105 70 75 112 89 105 112 101 102 75 80 112 86 98 105 84 93 80