the improvement in vitality as disclosed in the british life offices' experience [with...

Institute and Faculty of Actuaries

The Improvement in Vitality as disclosed in the British Life Offices' Experience [withDISCUSSION]Author(s): James BuchananSource: Transactions of the Faculty of Actuaries, Vol. 4, No. 37 (1907-1909), pp. 71-112Published by: Cambridge University Press on behalf of the Institute and Faculty of ActuariesStable URL: http://www.jstor.org/stable/41217582 .

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No. 37-Í 7i

TRANSACTIONS OF THE

FACULTY OF ACTUARIES

The Improvement in Vitality as disclosed in the British Life Offices' Experience, By James Buchanan, M.A., D.Sc, F.F. A., F.I. A., Scottish Widows Fund Life Assurance Society.

[Read before the Faculty, 13 January 1908]

1 HE improvement in vitality is a subject of interest alike to the actuary and to the public statistician. It formed one of the topics for discussion at the Fourth International Congress of Actuaries held in New York in 1903, and papers were submitted by actuaries of different countries dealing with the subject mainly from the point of view of population statistics. The results of most direct interest to us were embodied in a paper by Mr. S. G. Warner On the Improvement in Longevity in the Nineteenth Century. They were based on the summarised returns of the Registrar-General's Reports for England and Wales for the years 1875 and 1900; and, while admitting the defects inherent in the data, Mr. Warner held that the statistics showed " a distinct decrease in the rate of " mortality as the century progresses ; a decrease, on the whole, " so steady and symmetrical that it might fairly be looked on as a " settled and permanent tendency. The improvement is slightly " more marked in female than in male mortality, but it is evident " and indubitable in both." But the outstanding feature of the whole table seemed to him to be that the weight of the improvement fell chiefly on the early years of life.

In the Supplement to the Forty-eighth Annual Report of the Registrar-General for Scotland, published in 1905, is given a series of life tables constructed by Dr. Dunlop, to whom I desire . vol. IV. G



y 2 The Improvement in Vitality as disclosed

to express my acknowledgments for several valuable references. The series consists of twelve tables, three for each of the last

four decades of the past century. They are abbrevi- fo^Scotland ate(* *ê taês> constructed by a method which gives

results closely agreeing with those derived from an extended life table ; and, as the mode of construction is uniform throughout, they form a convenient series for comparison. Expecta- tions of life for selected ages, extracted from these tables, are given in Table I. at the end of this paper. The figures speak for themselves ; generally it will be seen that there has been a progressive improvement at the early and also at the very advanced ages; but a slightly decreased expectation for the middle period of life. For the last decennium of the past century, this decrease begins for both males and females about age 35 and continues in each case to about age 65 or 75. The expectation of life of females is better than that of males at all ages.

An extended life table for Scotland for the period 1891-1900 had previously been published by Dr. Adam, of the Public Health Office in Glasgow, in the Journal of the Royal Statistical Society (lxvii. 448); and the corresponding figures are placed side by side for comparison. Dr. Adam's table was constructed by Milne's Graphic Method, and the expectations agree closely throughout with those obtained from the abbreviated life tables.

The life tables published under the authority of the Registrar- General for England and Wales unfortunately do not form a

similarly convenient series for comparison, owing f ̂Enând to cnan£es which have been made in the method and Wales. °f construction. Speaking in the discussion on

Mr. M. D. Grant's paper on "Canadian Vital Statistics" (J. I. A., xl. 148), Mr. George King said that " the " English Life* Table No. 3 was radically defective, through the u assumption that what Farr called the rate of mortality for an " age group was the force of mortality for the exact middle point " of the group. It was not so. The result of that assumption at " the older ages over 60 was materially to overstate the vitality, so " that in the English Life Table No. 3 the rate of mortality at the " older ages was very much understated, and an entirely erroneous " view was given of the true death-rate in this country. The " English Life Table No. 5 had been correctly constructed, and " it showed a lighter death-rate in the earlier years of life, " and a heavier death-rate later on, than the English Table " No. 3. That was not due to any change in the relative " death-rates in the country ; it was simply due to a change in " the method of constructing the table ; and yet it had given rise " to the heresy which was very prevalent that, at the older ages of



in the British Life Offices Experience J$ " life, the vitality of the country had deteriorated rather than " improved. As a matter of fact it had improved all along, and " it was only the method of constructing the table which gave " a different appearance."

These remarks appear to be strongly supported by the publication of the new English Life Table for 1891-1900 in the Decennial Supplement to the Sixty-fifth Annual Report of the Registrar- General for England and Wales, The method of construction followed by Dr. Tatham is described in the Supplement, and is practically identical with that employed for the English Table No. 5 ; and a reference to the values, given in Table П., of the expectations of life for the last two decennia, shows that there has been an improvement from beginning to end of the table. Annual death-rates for age-groups, recomputed on more accurate estimates of the population, are also given in the Supplement ; and these show an improvement in nearly every age-group. The improvement is greater for females than for males, and the percentage differences are quite marked for the age-period from 15 to 34.

A series of abbreviated life-tables for England and Wales was published in 1901 in the sixty-fourth volume of the Statistical Journal by Dr. T. E. Hayward, the Medical Officer of Health for Haydock, Lancashire. The special method followed in the construction of these tables is fully described x in a paper read before the Statistical Society in 1899 (/. S. S., lxii. 443). Its object was to remove the defects of Fair's short method, which brings out increasingly too large values of the expectations at the advanced ages ; and this whs attained by calculating the Px values for ten- yearly groups by two stages instead of one for ages from 15 to 75 inclusive; by four stages for the next two decennial intervals, and by yearly intervals thereafter. The series extended over the five decades from 1841 to 1890; and it was completed in 1903 by the publication of a similar table for 1891-1900 in the sixty- sixth volume of the Statistical Journal. Where a comparison can be made with Dr. Tatham's figures, the agreement is extremely close; and Dr. Hayward's figures for the two periods 1861-70 and 1891-1900 have accordingly been inserted in Table II. Except for a slight deterioration for the age-period 45-65 for males, and a very minor deterioration about age 55 for females, it will be seen that, even as compared with the earliest decade, the vitality of the last decennium shows an improvement from beginning to end. When a comparison is made between the figures of the last three decades, the expectations of life, even at

1 The method is also described in Newsholme's Vital Statistics, 3rd Ed., pp. 279-286 : and a brief explanation is given in a note appended to this paper, vide p. 84.



74 The Improvement in Vitality as disclosed

the higher ages, in 1881-90, and still more so in 1891-1900, are more favourable than those of 1871-80.

The principal causes which have been assigned for this improvement in vitality are briefly these: - (1) the increased protection

afforded to infant life; (2) the improvements in Suggested sanitary science, which have done much towards Effects. averting epidemics and enabling communities to deal

more intelligently and efficiently with them when they occur; and (3) the great advances in medical and surgical skill, and the improved treatment of sick at home and in hos- pitals, which have saved vast numbers from attacks which would otherwise have proved fatal.

It has been suggested г that each of these causes " indicates, not " an addition to the vitality of the strong, but a diminution of the " fatalities of the weak. Each of them shows a force at work in " the community by which the great natural law of the struggle " for existence, and its consequence in the elimination of the feeble " and the preservation of the fittest, is counteracted. The weak- " lings of the human race are kept alive, so that after these forces " have exerted themselves, the percentage of the whole population " which is of inferior vitality is larger than it was before." The consequence, it has been urged, must inevitably be an increased element of weakness adding more and more to the rate of mortality, so that an age would be reached after which the power of preservation of strong and weak alike is counteracted by the larger percentage mortality due'to the decreased average vitality.

This conclusion does not seem of necessity to follow. There seems to be no reason to believe that a child who, by the aid of medical skill, has passed through the early-risk period of infancy, should not develop into a perfectly healthy man ; or that a man who, in crossing the Bridge of Life, has escaped the marksman Death at the earlier stages, should form a fitter target at the later periods. The fatalities at the older ages will be more numerous, because the number of survivors is greater ; but it does not necessarily follow that they should occur at a more rapid rate. It is fairly certain that the classes, from which assured and annuitant lives are drawn, have profited more largely from the above causes than the general population ; and, if it were the case that these causes had resulted only in the preservation of the weak and not in the production of a more robust type, it might fairly be expected that, in spite of the fact that the lives are selected, some accumulation of weaknesses would show itself in more or less marked degree at the advanced ages.

An experience of assured lives differs essentially from one 1 By Mr. Charlton T. Lewis, at the Fourth International Congress of

Actuaries, New York, 1903 {Proceedings, vol. ii. 116).



in the British Life Offices Experience 75 based on population statistics, in that it takes no account of the lapse of time, but gives us the average rates that have prevailed among a selected body of lives during a given period of time. Both in the case of assured lives and of annuitants at least two investigations of first-class importance have been made in this country J during the past ?2tis^iife , , , , J a - Offices' Ex- century; and , these , ,

possess such , very great

a superi*

- perience.

ority as regards accuracy of data over registration and census returns, that results derived from them are entitled to corresponding weight. We are indebted to Mr. Acidan d and Mr. Chatham for very exhaustive analyses of the New British Life Offices' Experience, more especially in its bearings on premium rates and policy reserves ; and Mr. Ackland's paper also contained a detailed comparison (/. 1. A.} xxxvii. 115-127) of the rates of mortality shown by the aggregate tables of the New Experience and the corresponding tables of the Twenty Offices' Experience. The outstanding feature disclosed by this comparison was the great saving of life shown during the early portion of the OM table. This point was commented on by several speakers in the discussion which followed the reading of the paper, and there seemed to be a general agreement that it was largely due to the influence of selection ; as, quite apart from improvement in longevity due to advances in medical and sanitary science, the machinery of selection has greatly improved of recent years.

There is, however, an essential difference in the materials of which the two experiences were composed, and in the ways in which these materials were compiled. The Old Experience went back to the beginning of the assurances: the New Experience started, on the policy anniversaries in 1863, with a large number of non-select lives already on the books. The Old Experience was composed of all classes of assured lives ; while in the New Experience the mortality of the different classes has been examined separately; and it has been clearly established by Mr. Chatham, in the paper already referred to (T. F. A., i. 109), that the class of assurance is a powerful factor in determining the rate of mortality. The difference of the ways in which the data were compiled - the Old according to calendar years, and the New according to policy years - no doubt had some influence on the deduced rates of mortality, especially during the early years when the influence of selection is at work ; so that differences, revealed by a detailed comparison of the aggregate rates of mortality, can not be referred entirely to changes in the general vitality.

In the New Experience, however, the data are divided into two sections; those relating to contracts already in force when the observations commenced in 1863, have been separately tabulated under the headings of "ОЩ Assurances" and "Old



7 6 The Improvement in Vitality as disclosed

Annuities," while those effected during the period 1863-93 are described as " New Assurances " and " New Annuities." As the materials and mode of compilation are uniform throughout, it seemed that a detailed comparison of the rates of mortality shown by "Old" and "New" in some of the principal sections of the New Experience might lead to important and interesting results.

The OM experience, relating to ordinary whole of life participating assurances on male lives, is statistically and financially by far the most important section of the New Experience ; and a comparison of the rates of mortality shown by the " Old " and " New " sections is of further interest, because of the question that has recently been raised as to the effect on these rates, during the early years following selection, of amalgamating the two sets of data. An annuitant experience differs essentially from one of assured lives, in that annuities are effected for the most part at the older ages. The experience therefore relates almost entirely to the later periods of life, and supplies a useful supplement to that of assured lives. The Annuitant Experience formed the subject of a very recent and valuable contribution to our Transactions by Mr. Ackland ; and it was a study of the results of that investigation which has led to the production of the present paper.

In the experience of assured lives there is strong evidence that the effects of selection are practically exhausted after ten years

from entry, and the ten years' period was accordingly i&pectfSone a(*opted *n the construction of select tables. In the deduced graduated Annuitant Experience the period of selection ftom ult*; has been limited to five years ; but in Mr. Acklanďs Assured Uves. recent paper it was shown that, while a good junction

between the select and the ultimate data was possible and was actually effected after five years, there was evidence of the persistence of selection for a longer period. In order to eliminate the effects of selection in the comparison of the Old and New sections of the experience, the statistics of the first ten years were accordingly excluded, both in the case of assured and of annuitant lives; even though in the latter case the exclusion resulted in a serious curtailment of the data.

In the graduation of the 0[MJ table, Mr. Hardy merged the select experience of the first ten years in a select and ultimate ten-year table, given on p. 145 of the Account of the Principles and Methods, etc. This table is constructed from the Select data for the Combined Old and New Assurances, excluding the first ten years, and duplicate policies on the same life were not eliminated unless effected in the same year of age. Similar tables have been constructed from the Select data of the Old and New Assurances separately, and the resulting figures are given in Table III. at the end of this paper. The numbers exposed to risk and the numbers



in the British Life Offices Experience 77 of deaths for the Old and New Assurances, taken together, make up the corresponding figures of Mr. Hardy's table ; and rates of mortality and curtate expectations of life have been deduced from each set of data separately for all ages from 20 up to the end of life. As might have been expected, the rates of mortality run with considerable irregularity ; but a comparison of the expectations shows that, nearly to the end of the table, the vitality of the " New " lives is better than that of the " Old/' At first sight, it seems strongly to support the view that the improvement in vitality has taken place almost entirely at the younger ages. But the rapid falling away in the numbers of the " New " lives exposed to risk at the advanced ages renders the comparison for these ages of minor importance; and much of the apparent decrease in vitality for these ages is accounted for by the fact that there are no recorded observations after age 94, and at that age the only cases recorded have passed out of observation by death. We shall return later on to the apparent convergence in the vitality of " Old " and " New " lives towards the latter end of the table.

Similar tables for male and female annuitants, corresponding to Tables VI. and VIII. of Mr. Ackland's paper which are based on the Combined Old and New data, were constructed from the data for the Old and New separately. At certain points of these tables there are apparent discrepancies between the numbers exposed to risk and the numbers of deaths ; for the figures of the Old and New, taken together, do not in all cases agree with the figures of Mr. Ackland's paper. These discrepancies are accounted for by the fact that, for certain ages at entry - 63 for males, and 61, 68, and 76 for females - " New " annuities were excluded from the Combined Old and New data, because an "Old" annuity, purchased at the same age, had already been tabulated for the same life. In the case of the New data, for both male and female lives, the experience is incomplete, and the figures for the last few years of life were supplied on the assumption that the experience of the " Old " annuities would be repeated for the "New."

The exclusion of the first ten years' experience seriously curtails the data, especially in the case of male annuitants; but the proportion which the Old and New data bear to one another, for both male and female lives, is much more uniform than in the case of assured lives. The effect of this meagreness of data is to produce considerable irregularities, even in the columns headed " expectations of life " ; but the general tendency is to show a superior vitality among the " New" annuitants, which is rather more marked than in the case of assured lives, and which extends to a later period of life. Although at the advanced ages the differences are ßmall, still at no point of either table is there that marked falling




away, which might have been expected if the saving of life shown during the early years had meant not an addition to the vitality of the strong, but a diminution of the fatalities of the weak. Of course it may be urged that the experiences are limited to lives that are select at entry, and that those who showed any past history of weaknesses would be excluded altogether. But it is satisfactory to be able to record the opinion that, in the past, no such accumulation of weaknesses,. inherited from the early years of life, has remained latent for a long period, only to make itself shown at the advanced ages.

Attention has already been drawn to the fact that, in the case of the New Assurances, the numbers exposed to risk decrease very rapidly after age 55, so that for the advanced ages - say above 70 - the experience has to be supplied chiefly from the statistics of the Old Assurances. Taking, for example, attained age 70, the numbers of Old Assurances exposed to risk during the period of observations, 1863-93, would include cases entering under observation at all ages from 40 to 70 ; and, in the case of those of that number who came under observation at ages below 50, the experience recorded at age 70 must belong to the last decade of the period. A very large portion of the experience recorded at the advanced ages, must therefore be of comparatively recent date, and more nearly contemporaneous with the much more limited experience of the New. It is, therefore, only to be expected that the vitality of " Old " and " New " should approximate more and more closely towards the latter end of the table ; and the fact that this approximation does take place is not a proof that the improvement in vitality has been confined to the early years of life.

It would be wrong to found too strongly on a comparison of the relative vitality of the Old and New sections of the experiences of assured and annuitant lives ; but in the annuitant experience the differences are generally greater than at the corresponding ages of the assurance experience. Now, annuities are effected for the most part at ages over 50, and the observations, recorded for the advanced ages of the Old annuitants, would belong to an earlier period of the experience than the corresponding observations for assured lives. It is therefore possible that these excess differences may be due in part to this cause. A careful consideration of all the facts seems to justify the conclusion that, while the improvement in vitality of assured and annuitant lives is most marked for the earlier ages, it is not confined to them ; but that, towards the end of life, it is obscured by the fact that the statistics of the Old section are later in point of time and more nearly contemporaneous with the corresponding data of the New,



in the British Life Offices Experience 79 We now pass to an examination of the rates of mortality

deduced from the Old and New sections of the experience during the first ten years, when the influence of selection is still in operation. The Old data are so meagre for individual ages, that some mode of grouping was necessary in order to produce ungraduated rates showing some degree seSctTratee of regularity. In the volume of the Unadjusted deduced from Data of the Annuitant Experience tables are given Old and New (pp. 172-3 and 178t9), showing the probabilities of dying in each of the ten years following entry, deduced from the combined data for quinquennial groups (1) of ages at entry, and (2) of ages attained; and on p. 478 of the volume of Whole-life Assurance data a similar table is given for ages attained only. In constructing similar tables from the select data of the Old and New sections separately, the same age-groupings were adhered to.

Tables VI. and VII. give the figures deduced from the data of the Old and New Assurances ; and, to facilitate comparison, the greater of each pair of corresponding rates is set in heavy type. In Table VI. the Old rates are in excess ¿ves^ in fifty-six cases out of eighty- one, and in a large number of these cases the difference is considerable. In a fair number of the cases in which the New rate is in excess the difference is trifling, and is probably due to accidental irregularities of the data. A careful comparison shows clearly that the vitality of the New lives is better than that of the Old, and that for the younger ages the improvement is almost universal. It also seems to show that amongst the New lives the effects of medical selection have been more persistent; for during the last three years of duration the New rate is almost invariably lower, and considerably lower, than the Old.

Table VII. perhaps illustrates more clearly the relative durations of selection in the two sections ; for it gives us the rates of mortality, for the same groups of ages attained, of lives in each year of assurance up to the ninth. In fifty-nine cases out of eighty-one, the Old rates are in excess ; and, as in the case of the other table, the differences are almost invariably in favour of the New during the last three years of duration. The tendency to increase from year to year is also more marked in the New rates, and, in this section at any rate, there seems to be strong evidence of the persistence of selection for at least ten years from entry.

In the case of the Old Annuitant data, the numbers exposed to risk, even when age-groupings were employed, were so very small that a few deaths more or less often produced violent fluctuations in the deduced rates of mortality. In- stead of giving, as in the case of Assurances, rates for Old



8o The Improvement in Vitality as disclosed

and New Annuities separately, the New rates have щ Tables VIII. and IX. been compared with the corresponding rates deduced from the combined Old and New data, and given on pp. 172-3 and 178-9 of the volume of Unadjusted Data. To facilitate comparison as before, the greater of each pair of corresponding rates has been set in heavy type ; but the superiority of the New lives is not nearly so apparent as in the case of assured lives. For male annuitants, the Old rates are actually the smaller in the majority of cases ; but, for females, there is a slight preponderance in favour of the New.

This again supports the view that the improvement in vitality at the older ages has been relatively small ; but it also seems to show that the self-selection exercised by annuitants has not improved to nearly the same extent as the medical selection exercised by the office. Especially in the case of male annuitants, the data are so very meagre that no very reliable conclusions can be drawn from them ; but there seems to be some justification for the view that self-selection is more efficiently exercised by females than by males.

In order to illustrate the differences between the Old and New rates more clearly, and also the probable effect on the deduced Actual and rates of mortality of amalgamating the two sets of Expected data, a further comparison is made in Tables X. and Deaths. xitj so as to give effect to the proportions in which the Old data entered into the Combined Experience. These tables give the numbers of deaths actually recorded for certain age-groups in the Combined Old and New data, and the numbers by which they are in excess or defect of the "expected" deaths, calculated on the assumption that the total numbers exposed to risk were throughout subject to the rates of mortality experienced by the New. A table, similar in form, but with different age-groupings, was given by Mr. Ackland in the discussion which followed the reading of Mr. Elderton's paper on Spurious Selection (/. 1. A., xl. 242) ; but the figures were there stated in the form of percentages, and it seemed that valuable additional information would be obtained by showing the actual numbers of deaths recorded and the numbers by which they deviate from the expected. The general results of the two tables entirely confirm one another. In a total of 33,089 recorded deaths the deviation between the actual and the expected is only 532, or little more than one and a half per cent : and the bulk of this deviation is accounted for (1) in the younger age-groups, and (2) in the last three years of duration for practically all age- groups. In the annuitant experience the deviations are small, especially when the limited extent of the data is kept in view. Positive and negative deviations are fairly evenly distributed, so



in the British Life Offices' Experience 81

that the aggregate difference is relatively smaller than in the case of assured lives. It seems, therefore, that the effect of amalgamating the Old and New data on the apparent duration of selection must be slight, if not practically non-existent.

It has been remarked above that, in the case of assured lives, the chief part of the deviation of the actual from the expected deaths occurs (1) in three or four age-groups, and (2) in the last three years of duration for practi- selection^ cally all age-groups. The inference seems to be that the influence of medical selection has been more persistent among the New lives than the Old, and that the improvement in the results of selection has shown itself most conspicuously in the case of the younger lives. It is possible, therefore, that for these age-groups and durations, the effect of amalgamating the Old and New data may be to produce appreciable variations in the values of q, and so to give rise to a measur- able amount of what has been technically called Spurious Selection. This question has a practical bearing, because of its possible effects on the apparent duration of medical selection as shown by the New tables. That spurious selection does exist under certain conditions, both when medical selection is still in operation and when it has ceased to operate, is undoubted ; and in both cases it is theoretically capable of measurement. But, while the effect of amalgamating two experiences, showing different rates of mortality and different results of medical selection, may be to introduce an element of this kind, it will also give us a measure of medical selection intermediate between those shown by the two experiences; and it is quite possible that the effect in the Combined Assurance Experience may be to make the duration of selection appear to be shorter than it really is, and shorter than that likely to prevail in the future.

A point of decided practical importance is that the amalgamation of the Old and New data has materially raised the rates of mortality, as compared with those shown by the New section. It has, in fact, given us a series of average rates for the period of observations, corresponding probably to some point of time in the latter half of the period. The exclusion of the first ten years' experience, in the comparison of the ultimate rates of the Old. and New sections, was practically equivalent to contrasting two bodies of non-select assured lives - one coming under observation in 1863, and the other in 1873 - the experience in each case being carried up to 1893. Population statistics seem to show that the improvement in vitality has been going on steadily since these observations were closed ; and, if a difference of ten years in point of time has meant so much in the resulting rates of mortality, the question naturally suggests itself - how far do the




rates of the combined experience differ from those prevailing at the present time, or from those likely to prevail in the future 1 It seems not unlikely that life offices may still look forward to a continuance of favourable mortality experiences in the case of assured lives; while in the case of annuitants the effects may probably be the other way. General To recapitulate briefly the main conclusions to Conclusions, which a study of these statistics seems to lead :

(1) The improvement in vitality has been marked during the earlier years of life ; but it has not been confined to them, that at the older ages having been to a great extent obscured by the fact that the statistics of the " Old " and " New " lives are more nearly contemporaneous.

(2) The influence of medical selection has been more persistent among the " New " Assured lives than the " Old," and the improvement in the results of selection is most conspicuous in the case of the younger lives.

(3) The self-selection exercised by annuitants has not improved to nearly the same extent as the medical selection by the office ; though there appears to be some reason to believe that it is more efficiently exercised by females than by males.

(4) We are not justified in asserting that the apparent duration of selection has been materially increased by the amalgamation of the " Old " and " New " data. On the contrary, it is quite possible that the result has been to under-estimate the effects of medical selection, both as regards extent and duration, as compared with those likely to prevail in the future.

We have seen that, in the case of a table based on population statistics, the expectation of female life is better than that of males at all ages; and the question is sometimes asked why the practice of life offices seems to run counter to this teaching. Life offices must base their premium rates on their own experience, and the results of Mr. Chatham's investigation (T. F. A., i. 116-119) showed that that experience does not agree throughout with the evidence of population statistics. It is, however, quite beyond the scope of this paper to contrast the mortality of class with class ; its object is to compare the mortality of the same class at different periods of time. A comparison of the mortality experience of the Old and New sections of female assured lives would no doubt have been of interest; especially as, in the case of assurances for the whole of life with participation in profits, the number of years of risk is very evenly divided between the two



in the British Life Offices Experience 83 sections. But the construction of further comparative tables would have involved a very considerable additional amount of labour ; and it seems probable that it would only have led to a similar conclusion.

A comparison of the expectations of life of assured and annuitant lives with those of the general population seems to show clearly that the improvement has been more marked in the former classes; and in view of the steadily increasing vitality shown by population statistics, it is quite possible that the tables of the British Offices' Experience may already be obsolete, as an indication of the mortality prevailing at the present time or likely to prevail in the future. But in spite of this possible continued improvement, offices will hesitate to reduce their premium rates in face of a rate of expenditure which has a tendency to rise. The evidence seems to point to a probable continuance of mortality profit in the case of assured lives, and a possible mortality loss in the case of annuitants. Participating policyholders may look to have any increased mortality gains returned to them in the shape of bonus ; while those assured on the non-participating scale may trust to keenness of competition to keep rates down to the lowest level compatible with safety.

The opinion has often been expressed that, as regards reserves, the closest approximation to the truth is given by the use of select tables. Hitherto the labour involved in making such a valuation has probably been the chief deterrent to its adoption by many ; but this objection has been largely removed by the ingenious methods which have recently been devised so as to permit of a select valuation being made with a minimum of trouble. On the other hand, the recognition of the select reserve as a standard has been criticised both in this country and abroad. The most recent criticisms have been based on the possible effects on the apparent duration of selection of the amalgamation of hetero- geneous material; but, while admitting the existence of these effects, I am unable to agree as to their extent, or in the conclusions which have been based on them. The select reserves of the British Offices7 Experience mark a substantial advance on those of the Twenty Offices1 Experience, and the moral to be drawn from the steady improvement in vitality appears rather to be the advisability of continually strengthening reserves.



84 The improvement in Vitality as disclosed

APPENDIX

On the Abbreviated Method of Constructing Life Tables from Population Statistics

As a fairly extensive use has been made in the accompanying tables of the values of the expectation of life obtained by the " abbreviated method," a brief explanation of the method, accompanied by an example of its appli- cation to an actual case, may be of interest. As is usual in life tables based on population statistics, the notation is Farr's notation ; thus, in an extended life table, Px and Qx correspond to Lx and Tx of the Institute notation ; while in an abbreviated life table, Px denotes the sum of the Lx values for the age-group.

The same preliminary work is involved in finding the estimated mean populations and the average annual deaths for the various age-groups ; and, for the first five years of life, the lx values are determined in exactly the same way for an abbreviated life table as for an extended one.

From this point onwards, Farr's short method consisted in finding the mean probability of living a year for an age-group from the ratio

Population - ' Deaths Population + ' Deaths

To obtain a good working value of p05i differences based on the four or five preceding values had better be employed.

Starting with ř5, and the mean values of p so obtained, the succeeding values Zl0, lìòì 12& . . . were found as follows : -

ho = h Л - io : hõ = ho V'o - ió • hõ = lu Pl0u - 25 : etc. and then ?A-io = 4(Í6 + Wx6:Pio-ie = i(^o + Wx5:P15.a5 = i(r16 + r2õ)xlO:etc.

The above ratio gives mean values of p increasingly too large, and the values of P are increased in greater proportion than those of I ; so that, for the advanced ages, the expectations of life are much too great.

Dr. Hay ward found empirically that a better approximation to the values of the expectation was obtained by making the calculation of the Px values in two stages instead of one : thus

■Pee-Ts-o^ÍK + W + i^ + W] Z70 and lVo being derived from 10Г) in the same way as before. Extending this idea at the advanced ages, he made the calculation by four stages instead of one for the age-periods 75-85, and 85-95, and by yearly intervals thereafter : and the expectations of life so obtained agree with great closeness with those derived from an extended table. The values of lx however, would apparently have to be used with caution.

The following Extract from one of the life tables for Scotland (1891-



in the British Life Offices Experience 85

1900), (Supplement to the Forty-Eighth Annual Report of the Eegistrar- GenercUfor Scotland, p. xcvi.) will illustrate the method : -

Estimated Average bÄ2f **£* Ah* "*•«■* Äed *g£

Акв. Popula. *» Average Annoii ! I bÄ2f a « »S* Г«* t Í «¿ih in»ud of A. Акв. Popula. *» Annoii *«»• I ! îft iAge-i a «

*g£ »S* Г«* ¡y-Ä t Í «¿ih

идя* in»ud д of

¿x CÍx J?x ! ¿x Px Çx ^x _

! i 1 - ^

бббб 112565 40261 '964862 55 478744 4034833 ! 75.57706 15*79 ; 65-76 60771 4155*2 i -933886 65 334655 2447397 3522873 10*53 75-85 21664 2992*7 '870783 75 168864 | 923619 1075476 6*37 85-95 2824 792' -754037 85 42329 146830 151857 3*59 05+ 104 44*7 -630011 95 2515 5027 5027 2Ю7 I ; I ; ,

The Px values, for the age-periods 65-75 and 75-85, are obtained as follows : -

= 5 [| (334655 + 168864) + 237720] = 2447397. ¿'75-85 = 2.5 '1(175+ Zn.6)+ . . . +i(/ar5 + /85)]

= 25 [i (l7s + řK) + /77.5 + lw + /82.J = 2-5 [| (168864 + 42329) + 119485 + 84545 + 59822] = 923619.

The principle underlying the method appears to consist in assuming that the lx values for a ten-yearly group decrease in geometrical progression, the common ratio being the mean probability of living a year for the age- group. Up to age 75, the ten-yearly sections of the life curve do not differ very much from a straight line, so that the " years of life lived in each year of age " for each age-group, represented by the area of the corresponding portion of the life curve, can be obtained very nearly by dividing the area into two part$ of equal width, joining the end of the dividing ordinate to the ends of the bounding ordinates, and taking the area so obtained. Above age 75, the life curve becomes more and more convex, and to get a good approximation it is necessary to divide each area into four (or ten) portions of equal width and to find the corresponding areas.



86 The ïtnprovenient in Vitality as disclosed

Table I.- Complete Expectations of Life based on Life Tables for Scotland

Males Females

Age Dunlop Adam Dunloj Adam Age

1861-70 1881-90 1891-00 1891-00 1861-70 1881-90 1891-00 1891-00

0 40*33 43-92 4468 44*71 43 85 46 33 47 44 47*47 0 5 48*86 51*38 52*29 52*36 50*95 52*84 53*95 54*02 б

15 42*26 43*93 44*26 44*34 44*51 45*59 46*18 46*26 15 25 35-68 36*66 36*68 36*75 37*72 38*39 38*54 38*63 25 36 2906 29*46 29*22 29 30 31*12 31*51 31*27 31*37 35 46 22*70 22*55 22*16 22*24 24*51 24*59 2415 24*27 46 55 16*45 16*24 15*79 15*85 17*81 17*78 17*32 17*42 56 65 10*75 10*81 10*53 10*57 11*61 11*85 1154 11*60 66 75 6*26 6*48 6*37 6*38 6*67 7*07 7*01 705 75 85 3 36 3*51 3 59 3*38 3*59 i 3*85 3*92 3*75 85 95 1*65 1*78 2-07 1*78 1*87 1*98 2*49 1*96 95




Table II. - Complete Expectations of Life based on Life Tables for England and Wales

Males Females

Age Hayward Tatham Hayward Tatham Age

1861-70 1891-00 1881-90 1891-00 1861-70 1891-00 1881-90 1891-00

0 39-65 44-12 43-66 4413 42-39 47*72 4718 47*77 0 5 49-82 53*44 5275 53*50 51-38 55 69 54 92 5579 б

15 42-80 4513 44*47 45*21 4436 47*51 46*55 47*61 15 26 35-65 36-93 36-28 37*01 37*35 39*27 3850 39*37 25 35 28-86 2916 28-91 29*24 30*66 31*42 31*16 31*52 35 45 22*32 2211 2206 22*20 2396 2408 2405 2420 45 55 1606 15*71 15*74 15*79 17*19 17*13 17*23 17*24 55 65 10*43 10*28 10*31 10*34 11*17 11*18 11*26 11-27 65 75 603 6-12 610 615 645 666 6*68 6'70 75 85 3-25 3*52 3*29 3*45 3*54 381 3*71 3*80 85 95 166 1*95 1*72 1*95 1*88 211 205 2*23 95

VOL. IV. H




Table III. - Whole-Life Participating Assurances - OM[10] Male Lives. Excluding first ten years of Experience 0м [101

Old Assurances New Assurances

Age Curtate Curtate Age Exposed TV ,, Rate of Expecta- Exposed Vlea n. ,, Rate of Expecta- to Risk

TV mea ,, Mortality tion to Risk Vlea n. ,, Mortality tion

of Life of Life

20 39 i 1 02664 40-108 '

46 1 02222 42-032 20 21 84 ... -00000 40-163 86 ... -00000 41-987 21 22 137 2 -01460 39-163 166 2 Ю1290 40*987 22 23 201 3 -01492 38-743 266 ... -00000 40-623 23 24 316 2 -00604 38-330 432 4 -00926 39-623 24 25 486 3 -00617 37-624 726 2 -00276 38-892 26 26 700 6 -00700 36-768 1,196 7 -00586 37*999 26 27 976 11 -01123 36-017 1,862 10 -00637 37*223 27 28 1,312 9 -00686 36*428 2,787 22 Ю0789 36*424 28 29 1,793 14 -00781 34-673 4,163 30 -00722 36-714 29 30 2,473 | 22 -00890 33-946 6,267 63 -00847 34-973 30 31 3,662 I 25 -00685 33-261 10,060 60 -00597 34-273 31 32 6,396 64 -01001 32-480 14,638 100 -00683 33-479 32 33 7,613 72 -00946 31*808 20,373 163 -00800 32*709 33 34 10,294 106 01030 | 31-112 26,883 209 -00777 31*973 34 36 13,641 142 01041 j 30-436 34,219 291 -00860 31-223 36 36 17,319 174 01006 i 29-766 41,387 363 -00877 30-491 36 37 21,260 218 -01026 29*068 48,036 436 -00906 29761 37 38 25,687 265 00993 28-369 64,318 461 -00830 29033 38 39 30,306 306 -01010 27-643 60,114 484 -00806 28276 39 40 36,478 397 -01119 26-926 66,692 619 -00944 27*606 40 41 40,418 426 01054 26*230 69,718 716 -01026 26*767 41 42 46,512 495 -01088 26-609 72,988 764 -01033 26*046 42 43 60,390 622 -01234 24*790 76,448 800 01060 25-317 43 44 55,435 711 01283 24*100 77,024 922 -01197 24-588 44 46 60,400 810 01341 23-413 77,876 874 -01122 28-886 46 46 66,101 892 -01370 22-730 77,963 942 -01208 23-167 46 47 69,609 974 -01399 22046 77,076 929 -01206 22-441 47 48 73,674 1,126 -01628 21/359 76,536 1,027 -01360 21-715 48 49 77,434 1,196 -01546 20*690 73,436- 991 01349 21*014 49 60 81,268 1,331 -01638 20-015 71,253 1,049 -01472 20-301 60 61 84,560 1,449 -01714 19-348 68,269 1,029 -01507 19-604 61 62 87,506 1,663 -01776 18-686 64,886 1,022 -01676 18-904 62 63 90,083 1,712 -01900 18023 61,114 1,097 -01796 18-207 63 64 91,798 1,807 -01968 17-372 67,260 1,022 -01786 17*640 64 66 93,233 1,916 -02064 16*721 63,782 1,172 -02179 16*869 66 66 94,016 2,149 -02286 16*072 60,083 1,104 -02204 16*285 66 67 94,150 2,266 -02407 16448 46,343 1,103 -02380 16*601 67 58 93,984 2,248 -02392 14-829 42,636 1,012 -02374 14-981 68 69 93,531 2,626 -02700 14 192 39,293 1,027 -02614 14-346 59 60 92,430 2,764 -02990 13-585 36,129 1,033 -02869 13-730 60 61 90,683 2,717 -02996 13004 32,888 964 -02901 13-185 61 62 88,636 2,923 -03302 12*406 29,961 965 -03187 12*527 62 63 85,871 3,056 -03559 11-830 27,020 982 -03634 11-939 63 64 82,957 3,311 -03991 11-267 24,287 933 -03841 11*389 64




Table III. {continued). - Whole-Life Participating Assurances OM[101 Male Lives. Excluding first ten years of Experience OM[101

Old Assurances New Assurances

Age Curtate Curtate -Age Exposed п.л/1 Died Rate of Expecta- Exposed Died n.H Rate of Expecta- Exposed toRisk

п.л/1 Died Mortality tion toRisk Died n.H Mortality tion

of Life of Life

65 79,617 3,306 -04166 10-736 21,682 872 04040 10-844 66 66 76,813 3,366 04440 10-200 19,166 840 -04386 10-300 66 67 71,983 3,506 -04871 9-674 16,766 803 -04790 9-772 67 68 67,646 3,643 -06386 9169 14,670 813 06680 9-264 68 69 63,249 3,681 -06662 8691 12,663 699 '06664 8*812 69 70 68,766 3,677 -06267 8212 10,898 646 -06928 8-331 70 71 04,112 3,606 -06664 7-760 9,286 607 '06637 7*866 71 72 49,884 3,730 Ю7663 7*314 7,783 661 -07080 7*406 72 73 44,683 3,641 07926 6*912 6,469 490 '07676 6*970 73 74 39,921 8,419 '08664 6*607 6,346 464 -08681 6*641 74 76 86,470 3,235 -09120 6-116 4,338 402 -09267 6-163 76 76 31,348 3,172 -10119 6-730 3,467 340 '09807 6-793 76 77 27,271 2 929 -10740 6376 2,688 283 -10628 6*423 77 78 23,679 2,793 *U846 , 6022 2,112 242 *11466 6*061 78 79 20,084 2,666 -12722 ! 4697 1,620 209 -12901 4-716 79 80 16 939 2,388 -14097 i 4*383 1,238 163 -13166 4*416 80 81 14,037 2,097 14939 I 4102 907 126 13892 4084 81 82 11,428 1 882 -16468 | 3*822 666 106 '16031 3*743 82 83 3,229 1,604 -17380 3676 482 80 '16697 3*468 83 84 7,334 1,469 -20030 3*328 346 89 -26723 3-146 84 86 6 636 1,119 -19866 3-160 217 43 -19816 3234 86 86 4,367 903 -20726 2943 148 27 '18243 3034 86 87 8804 766 -23184 2-712 96 22 -22916 2-712 87 88 2Д30 689 -24239 2-531 63 13 -20636 2-518 88 89 1*762 464 -26766 2341 46 10 '21739 2173 89 90 1222 321 -26269 2-154 27 7 '26926 1*776 90 91 '849' 239 -28160 1-921 17 7 -41177 1*397 91 92 598 194 -32442 1673 8 1 '12600 1-376 92 93 886 161 -39119 1-476 7 3 -42867 *671 93 94 2U 91 -40625 1*424 2 2 1*00000 *000 94 96 126 67 -46600 1-398 »Ö 96 66 15 -23077 1-669 96 97 46 20 -43478 1040 »7 ' 98 25 13 -62000 '840 »8 99 8 5 -62500 *750 99

100 3 2 -66667 1000 100 101 1 ... -00000 2000 101 102 1 ... -00000 1000 102 103 1 1 1-00000 000 ЮЗ



9 o The Improvement in Vitality as disclosed

Table IV. - Annuitant Experience- Male Lives Oam m Excluding first ten years Qam [10]

Old Annuities New Annuities

Age Curtate Curtate AoK Exposed Diea n. H Rate of Expecta- Exposed nl mea , Rate of Expecta- toRisk Diea n. H

Mortality tiou to Risk nl mea Mortality tion I of Life of Life

60 40 ... 00000 19-315 32 ... -00000 19 507 60 61 44 1 02273 18-315 39 1 -02564 18 507 61 62 52 2 -03846 17*741 41 1 02439 17 994 62 63 61 1 -01639 17-450 47 ' 1 02128 17*444 . 63 64 66 1 -01515 16-741 53 ... -00000 16-825 64 66 75 ... -00000 15-999 57 1 -01754 15-825 66 66 97 ... -00000 14-999 71 4 -05634 15*107 66 67 111 3 02703 13-999 78 1 -01282 15 009 67 68 127 10 -07874 13 389 89 2 -02247 14-204 68 69 140 7 05000- 13-532 108 5 -04630 13 531 69 60 151 5 03311 13-244 120 6 -05000 13 188 60 61 163 6 03681 12-698 140 8 -05714 12-882 61 62 180 9 -05000 12183 156 4 -02564 12662 62 63 208 6 -02885 11 -825 161 8 Ю4967 11996 63 64 241 14 -05809 11*176 189 13 -06878 11623 64 66 255 9 -03529 10 865 210 5 -02381 11480 66 66 278 13 -04676 10-263 230 11 -04783 10*759 66 67 293 14 04778 9766 259 10 -03861 10-3C0 67 68 324 15 04630 9 256 278 6 02158 9713 68 69 342 14 Ю4094 8706 304 18 -05921 8*930 69 70 382 28 -07330 8-077 346 18 -05202 8*490 70 71 389 24 -06170 7*715 391 31 -07928 7*955 71 72 409 43 -10514 7 223 413 24 05811 7 640 72 73 400 31 07750 7 072 443 33 -07449 7*112 73 74 425 26 06118 6 666 434 29 -08986 '6 684 74 76 440 47 10682 6100 437 39 -08924 6 344 76 76 454 32 -07048 5 830 443 47 -Ю609 5 '966 76 77 465 44 -09464 5 272 438 35 -07991 5*674 77 78 458 62 -13537 4823 438 49 -11188 5'167 78 79 433 63 -14550 4578 409 45 -11003 4-817 79 80 392 61 -15561 4-357 395 51 -12911 4'413 80 81 354 56 -15819 4160 346 55 -15896 4067 81 82 320 56 -17500 3 942 300 44 -14667 3836 82 83 286 51 -17832 3-778 253 50 -19763 3-495 83 84 253 39 -15415 3-598 199 40 20101 3-356 84 86 224 42 -18750 3254 178 39 -21910 3201 86 86 194 43 -22165 3 005 133 28 -21053 3 099 86 87 164 33 -20122 2 861 104 18 -17307 2925 87 88 139 39 -28058 2 582 85 23 -27059 2 537 88 89 105 30 -28571 2*589 64 23 -35937 2 478 89 90 77 27 -35065 2*624 41 10 -24390 2*869 90 91 49 13 -26530 3 041 29 7 -24138 2*794 91 92 35 6 -17143 3139 22 4 -18182 2683 92 93 29 7 -24138 2789 18 7 -38889 2 279 93 94 24 7 -29167 2 676 8 2 -25000 2729 94 95 18 6 -33333 2778 6 1 -16667 2*639 96 96 12 2 -16667 3*167 3 1 -33333 2167 96 97 10 3 -30000 2-800 2 1 -50000 2*250 97 98 7 1 -14282 3*000 1 ... -00000 3*500 98 99 4 ... 00000 2*500 2*500 89

100 4 1 -25000 1-500 1*500 100 101 3 ... 00000 1-000 1-000 101 102 3 3 100000 -000 -000 102



in the British Life Offices Experience 91 Table V. - Annuitant Experience - Female Lives

0*™ Excluding first ten years CK[10] Old Annuities New Annuities

д0Е Curtate Curtate age Exposed «. mea A Rate of Expecta- Exposed ~. mea л Rate of Expecta- toRisk mea A

Mortality tion to Risk mea л Mortality tion

of Life of Life 50 125 2 -01600 22-321 124 4 -03226 22-839 60 61 141 2 -01418 21*684 143 ... -00000 22600 61 52 164 2 -01299 20996 157 2 -01274 21*600 52 53 184 5 -02717 20-272 176 2 Ю1136 20 879 53 54 204 ... -00000 19838 199 3 -01508 20119 54 55 232 7 -03017 18-838 216 3 01389 19*427 55 56 266 5 -01880 18-425 251 4 -01594 18-701 56 57 292 2 -00685 17778 295 7 -02373 18-004 57 58 331 6 -01813 16-900 329 5 -01520 17 441 58 69 362 7 -01934 16-213 358 7 -01902 16 '711 59 60 423 14 -03310 15-533 429 4 -00932 16035 60 61 484 7 -01446 15064 482 12 02490 15186 61 62 553 16 -02893 14-285 546 8 -01465 14-57.3 62 63 631 18 -02853 13-711 627 14 -02233 13*789 63 64 695 25 -03597 13-113 699 23 -03290 13*104 64 65 779 22 -02824 12-603 759 26 -03426 12550 65 66 853 25 -02931 11969 873 31 -03551 11-995 66 67 937 30 -03202 11-331 975 37 -03795 11-437 67 68 1,029 35 -03401 10706 1.073 47 -04380 10-888 68 69 1,111 59 -05311 10083 1,150 40 -03478 10*387 69 70 1,223 55 -04497 9-648 1,312 68 -05183 9-761 70 71 1,320 64 -04849 9*102 1,438 62 -04312 9295 71 72 1,404 76 -05413 8*566 1,601 90 -05621 8*714 72 73 1,483 94 -06339 8-056 1,676 111" -06621 8*233 73 74 1,547 93 -06012 7*602 1,726 106 -06141 7*817 74 75 1,629 108 -06630 7'088 1,751 117 -06682 7*328 75 76 1,666 136 -08163 6-591 1.782 141 -07912 6-853 76 77 1,681 161 -09578 6-176 1,766 136 -07701 6-441 77 78 1,647 163 -09886 5-831 1,706 155 -09086 5'979 78 79 1,595 170 -10658 5-470 1,588 137 Ю8627 5-577 79 80 1,517 190 -12565 5*123 1,492 168 -11260 5-103 80 81 1,407 172 -12225 4-857 1,376 184 -13372 4-751 81 82 1,301 157 -12067 4-534 1,214 159 -13097 4*484 82 83 1,215 170 -13992 4156 1,034 140 -13540 4-160 83 84 1,086 185 -17035 3 831 853 144 -16882 3-812 84 85 925 154 -16649 3'618 694 120 -17291 3*586 85 86 806 151 -18735 3*341 559 110 -19678 3*335 86 87 672 141 -20982 3-111 444 93 -20941 3*162 87 88 553 113 -20431 2*937 329 75 -22797 2*987 88 89. 448 98 *21875 2 -692 231 58 «25108 2*869 89 90 357 92 -25770 2446 176 37 -21023 2832 90 91 268 70 -26120 2*295 125 25 *20000 2*586 91 92 200 53 -26500 2*106 100 20 -20000 2-232 92 93 142 55 '38732 1-866 69 26 -37681 1790 93 94 87 30 -34482 2 045 43 15 -34883 1*873 94 95 58 16 -27687 2-121 25 5 -20000 1*877 95 96 41 14 -34147 1-930 15 5 33333 1-345 96 97 24 6 -25000 1*931 8 3 «37500 1*021 97 98 18 7 -38889 1'574 5 4 -80000 -633 98 99 11 3 -27273 1*576 2 ... -00000 2*167 99

100 8 4 -50000 1167 2 1 -50000 1*167 100 101 3 1 -33333 1-333 1*133 101 102 2 1 -50000 1*000 1*000 102 юз i ... -ooooo l-ooo l-ooo юз IO* 1 1 1*00000 -000 -000 104.




Table VI. - Whole-Life Participating Assurances - Male Lives- 0м.

Probability of Dying in each of the ten years following Entry, deduced from the Data for Quinquennial Groups of Ages at Entry

Tears elapsed since Entry Ages at Entry

0123456789

Old Assurances

20-24 ... 00535 00623 00728 00744J00879 00893 01 188 00891 -00896 25-29 ... 00380 -00685 OO823 -00770 -OOÓQO -00003 -00936 -00873 -00994 30-34 .... 00431 00523 -00717 -00864 01113 00877 01017 -OIO55 01101 35-39 ... 00640 00873 00900 00953 "00810 00981 -01133 oi^'oi^ 40-44 ... 00698 -00961 00893 -01172 -01350 -01444 -01526 -01674-01723 45-49 ... .01245 OIIOO 01169 01338 01679 01436 01921 02012 -02280 50-54 ... 00817 -01961 01468 -02087 02246 02282 .02364 -02831 02969 55-59 ... 02374 02003 02152 02527 02649 02622 -04023 03828 -04200 60-64 ... .04516 01604 -02973 04000 -03618 04967 04616 .05907 06738

New Assurances

20-24 -00258 00472 00543 -00544 -00671 00597 -00710 -00678 00714 00785 25-29 00280 -00419 -00507 00550J 00598 -00638 0077б| -00746 00763 -00783 30-34 -00355 .00489 -ообю 00629; 00693 -00810 -00869 00802 -00978 -00988 35-39 00361 .00607 00697 00766 -00813 00896 -01004 01098 -01074 -01092 40-44 00516 .00696 00828 .00952 00907 -01043 01141 01389 01441 -01427 45-49 00576 Ю0926 01023 -01333 -01362 -01599 -01575 01912 01863 -02136 50-54 00888 -01405 01524 .01686 01728 -02287 -02452 02167 02408 .03236 55-59 01196 01790 02068 -02213 02291 -02481 -02957 03616 03733 03960 60-64 01664 02331 -02885 02782 -04060 -05179 04018 -05678 04266 -06968

9m... и^=£™+!1™+}™+^-^^




Table VII. - Whole-Life Participating Assurances- Male Lives- 0^.

Probability of Dying in each of the ten years follomng Entry, deduced from the Data for Quinquennial Groups of Ages Attained

Years elapsed since Entry

Attained I : 0123456780

Old Assubances

20-24 . . 00531 -00781 00790 -01154 00676 00567 00513 00844 00820

25-29 ... 00369 00598 00771 00721 00879 OO995 01068 00933 -00859 80-34 ... -00456 .00619 00740 00856 00690 00871 -0I0Z2 OO887 -00921 35-39 ... -00470 -00677 -00784 00807 -0III3 00881 OIO52 -00931 -00086

40-44 ... 00678 00845 OO883 0X012 00810 00969 00987 -01103 -OII20

45-49 ... .00943 'O1216 -00991 01284 -01350 01272 -01412 -01296 .01274 50-54 ... 01014 .01694 01467 01 336 01679 01554 01812 -01884 -01763 55-59 ... -01696 01489 '01678 -02299 02246 02014 01862 -02144 -02337

60-64 ... .042XX 02551 02242 02299 -02650 02311 -02957 -03071 03377

New Assurances

i i i 20-24 -00268 -00470 -00664 00697 00669 -00749 00467 00871 00480 01309 25-29 -00280 -00422 00607 '00616 00668 00697 00721 00667 -00622 00844

30-34 -00866 .00479 -00666 -00677 00616 00638 00747 00729 00748 00796

35-89 Ю0361 -00584 -00640 -00699 -00726 -00810 00854 -00766 -00840 O0826

40-44 -00616 -00666 -00781 00846 -00844 -00806 -01012 00986 01038 -00966

45-49 -00676 -00889 00947 -01017 00954 01043 01062 Ю1210 01112 01164

50-54 '00888 .0x297 01264 -01515 -01454 -01509 01379 01746 01696 01560

55-59 -01196 01675 01874 01834 01806 02287 -02351 02081 01986 02413 6O-«4 -01664 02162 02470 -02753 -02506 02481 02836 02805 02769 08261

y __ fl[86]+4 + 0[87j+4 + 0[88]+4 + ¿4891+4 + ^[403+4

Е[8вн.4+Е[з7]+4+Е138]+4+Е[89]+4+ E[40]+4




Table VIII. - Annuitant Experience

Probability of Dying in each of the ten years following Entry, deduced from the Data for Quinquennial Groups of Ages at Entry

Tsars elapsed since Entry Ages at Entry i i I

O'l 2 3 4 б 6 7 8 ! 9 I I 1

Combined Old and New Annuities- Males- OLam] i i i i ■

50-54 00943 02754 02476 01646 «02434 03325 /02660. «03966 -03040 -03679 55-59 01469 «01474 «01726 02886 -03180 02778 «01018-03272 «04270 -03865 60-64 02406 02790 -03610 03946 -03493] -05947, -04406 06142 .05152 -06355 65-69 03209 «04687 0458 i -04153 «06337! 05925 08180 06928 -09630 -07679 70-74 «04603 .06532 -06125 07277 -09116 08800 -10575 ..xi93x!-14171 '16033

I I i I New Annuities- Males- Otamí

50-54 00943 -02812 -02589 -01774' -02723 -03581 02885J04255 02789 03182

55-59 01469 .01496 -01798 02928 03169 03239 01602 03061 .04360 03671 60-64 02406 -02862 -03622 -03969 «03333-06548 0386з| «06939 «05094 06047 65-69 03209 .04618 «04467 «04016 ¡.06379' -06139 -08424 «06602 «09551 07339 70-74 04603 06403 -об2о8 -07421 O8869.08893 «09666 «11370 -16013 15678

Combined Old and New Annuities- Females- Ota/]

50-54 01074 «01646 -00982' «01261 01426 .01490 01171 01613 «02030 «02072 55-59 00792 00842 01751 01944 -02329 01791 -02910 02666 02917 03180 60-64 01424 «02030 -01715 02823.03069 «03260 03621 04375 04329 -04378 65-69 02126 02860 -03148 -03918 «03949 04639 -O5O22 -0606706971 07381 70-74 03093 04592 -04410 -05268 06722 «08664 -07308 -10729 .10038 10667

New Annuities- Females- O[a/i _ . . .

50-54 01074 .01571 -00882,- 01344 <>I497 01423 01290 01653 -02381 02381 55-59 00792 .00862 -01786 01708 -02260 -02040 02830 -02941! «02581 «03019 60-64 01424 02030 -01664 02819 03020 .03299 0371 1 04383I.04367 04210 65-69 02126.O2OO8 -03114 03900 -04100 -04766 04803 05860| 06638 .07825 70-74 «03098 -04668 -043 10 «06178 «06636 -08754 «07010 «10128 Ю991 8 -10141




Table IX. - Annuitant Experience

Probability of Dying in each of the ten years following Entry > deduced from the Data for Quinquennial Groups of Ages Attained

YE4R8 ELAPSED 8ПГСВ ENTRY

Attained i T 0 1 2 3 4 5 6 780

! !

Combined Old and New Annuities- Males- Otami

| j j i 60-64 00943 02662j 01866 01462 -01718 00980 02532 04959 03093 03947 55-59 -01469 -01436 -01838 -02682 .03320 -03326 02703 -04089 .0363o' -03297 60-64 02406 -02429-03627 02807 02782 02778 01174 -03104 03369( .02516 66-69 03209 04333 -03323 -04572 04139 05947 -03922 -05288 03013 04968 70-74 04603 06561 .05712 04671 07087 05926 07710 -05955 07883! -06745

New Annuities- Males- Otawi

60-54 00943 02724 01966 01597 , -01687; -015x7 00840 04446 02899 01818 55-69 01469 -01461 01920 02799' 03266 -03581 -02930 -04206 03614, -04000 60-64 02406 02490 03589 .02868-02914 03239 01174 03030 .03754J 02137 66-69 03209 -04367 03170 04238 04064 '05648 03364 04962 02619J 01360 70-74 04608 .05561 05664 osois'ctf^o .06139 07909 06632 .08257 06696

Combined Old and New Annuities- Females- О^Я

60-64 01074 01326 00994 01608 .01131 01363 -01230 00941 -02254 -02X13 55-59 -00792 00964 -01532 -01658 -01386 -01490 01022 01643 03017 -01657 60-64 -01424 01788 01403 -02184 -02565 01791 02518 01617 01997 02276 66-69 02126 02792 -02823 03306 -03089 03260 03400 04439 -03669 03108 70-74 03093 04154 03908 -03076 04610 04639 -04496 -O4777 -05181 06268

New Annuities- Females- O[a/]

50-64 01074 01349 -01032 -01613 -00974 -01369 00728 -01146 01799 01396 66-59 00792 00976 01496 01694 01382 01423 -01215 -02044 -03083 01446 60-64 -01424J 01779 01400 01960 02669 -02040 02406 01666 -02061 -02456 65-69 O2126J02838 02694 -03405 03087 -03299 -03617 -04636 08487 02718 70-74 03093| 04180,-03936 08897 -04729 -04766 04131 04607 05000 .05456 i 1 I !



ç6 The Improvement in Vitality as disclosed

Table X. - Actual Deaths in the Combined Old and New Assurances, and numbers by which they deviate from the Expected Deaths, calculated on the assumption that Old amd New are throughout subject to the rates of mortality experienced by the New.

Tears elapsed since Entry

ЧЗЁ i Du^ 0 1 2 3 4 5 6 7 8 9 tions

Actual Deaths- 0™

20-24 168 261 ! 278 267 268 274 805 301 283 294 2689

25-29 305 417 485 511 528 531 628 592 578 584 5154

30-34 366 466 i 546 650 592 682 669 626 713 705 5916

35-39 277 433 479 505 519 534 584 627 599 588 5145

40-44 272 341 392 426 409 459 486 659 571 558 4473

45-49 190 290 j 802 373 869 417 389 467 445 497 3739

50-54 168 246 261 267 275 340 j 345 305 335 406 2948

55-59 109 155 167 172 175 j 181 198 245 j 242 250 1894

60-64 64 88 95 91 126 148 117 139 116 153 1132

All Ages 1909 2697 J8005 3162 3261 3661 3721 3861 3877 4036 38089

In Excess ( + ) or Defect ( - ) of thb Expected

i 20-24 ... 9 21 6*6 77 14-4 104 322 121 82 946

25-29 ... -I' 86 18-9 15-2 5*4 148 252 16- 334 1364

30-34 ... -1*6 -4-4 6-8 15*8 33-4 11 808 12*2 198 1134

35-39 ... -1*5 71 78 103 -7-6 -25 4-2 10- 61 339

40-44 ... -1-6 4*1 -2-6 16-2 20*9 23*5 122 227 31*6 1259

45-49 ... 3-3 1-5 -4-8 - 8 - -8 -67 5 9*6 95 113

50-54 ... -3-6 4-9 -3-6 7*6 -I- -4*8 6*4 15-1 -102 108

55-59 ... 20 - -4 - -5 26 22 -6*6 8*8 1-8 61 15-

60-64 ... 3-4 -8-7 6 - -3 -9- 5*7 -8*9 117 -9- -95

All Ages ... -3 19-7 28-7 78-8 579 349 111-4 111*2 94 4 6318




Table XL- Actual Deaths in the Annuitant Experience, AND NUMBERS BY WHICH THEY DEVIATE FROM THE EXPECTED

Deaths, calculated on the assumption that Old and New are throughout subject to the rates of mortality experienced by the New.

Years elapsed since Entry An Ages at : Years elapsed since Entry

„*£. An

^0123456789 *0П8

Actual Deaths- Males- OlewJ

50-54 6 16 13 8 11 14 10 ! 14 10 11 118 55-59 13 12 13 20 20 16 8 16 19 16 168 68-64 34 37 44 44 35 54 36 46 34 89 403 65-69 49 65 59 49 68 57 71 ! 53 65 44 580 70-74 53 71 58 62 67 | 55 57 ! 55 53 46 677

AU Ages 155 201 187 183 201 196 182 184 181 156 1826 | 1

In Excess ( + ) or Defect ( - ) of the Expected

50-54 ... - -3 - 6 - 6 -18 -11 - -8 -11 -8 1-6 -86 55-59 ... - 2 - 5 - -3 -1 -2-7 - 4 1- - '4 12 -22 60-64 ... -1- 1- - -3 15 35 4-4 ! 1*4 -3 27 186 65-69 ... - -4 1-е 1-е - '4 -21 -21 2*6 -6 19 31 70-74 ... 1-4 - -8 -12 1-9 - 6 6*4 26 -69 -2- - 2

All Ages ... - -6 -7 - 8 1*8 -3- 65. 6-4 -6-7 6-8 10*7

Actual Deaths -Females- O^

50-54 20 26 '

16 18 19 18 13 17 20 19 186 55-56 23 23 44 45 50 36 53 45 46 48 412 60-64 60 81 64 99 100 98 101 112 102 94 911 65-69 82 104 108 126 117 126 125 139 145 137 1209 70-74 78 108 96 105 121 136 101 181 106 96 1077

All Ages 263 342 326 893 407 413 893 444 419 394 8794 i

In Excess ( + ) ob Defect ( - ) of the Expected

50-54 ... - -4 1*5 -1-2-1- -8 -13 - -4 -3*4 -28 -8*2 55-59 ... - -6 - -9 5-4 15 -49 15 -46 63 34 62 60-64 ... 0- 28 1 1*6 -1*5 -2*6 - -2 - -9 36 2*4 65-69 ... -1-8 11 6 -4-5 -3 6-4 4*7 6-9 -8:3 4-8 70-74 ... -9 2-2 1-8 84 -3- 41 7*4 18 44 22-8

All Ages ... -1-8 6*2 6-6 1- -8-3 71 6-9 9-2 6 27 6




DISCUSSION

Mr. Chatham wrote : - I have been asked to open the discussion on Dr. Buchanan's valuable paper, and it is a matter of great regret to me that, through circumstances over which I have no control, I am unable to do so personally. His paper is on a subject of great importance to insurance companies, because I need hardly remind you that any lengthening of the lifetime of assured persons - and they form the great bulk of our business - has a double effect, inasmuch as more premiums are received, and the payments of sums assured are longer deferred. I have no hesitation in saying that this has played an important part in the prosperity of life assurance offices, and no more fitting subject could have been brought forward for discussion by the Faculty. Great credit must be given to Dr. Buchanan for the manner in which he has treated his subject, and there are many points on which I find myself in agreement with him. Instead of dwelling upon them, I will rather take up the points, the few points, where I differ from him, and thereby endeavour to throw some fresh light on the subject.

But first of all I would direct your attention to what seems to me to be of the nature of an omission. The title of his paper is " The Improvement in Vitality as disclosed in the British Life Offices' Experience," but he gives at the outset an account - an interesting account - of the improvement in vitality as disclosed in returns based upon population statistics, and then he proceeds to deal with the British Life Offices' Experience, and compares the " Old" portion of it with the " New," and bases his conclusions upon it. Now it is not essential that the statistics should be contemporaneous to show that there has been an improvement in vitality - indeed, it would rather be an advantage if they were not, and I do not know why Dr. Buchanan has altogether omitted from the scope of his paper the valuable statistics published under the auspices of the Institute of Actuaries, which form the beginning of the " Old" portion of the British Offices' Experience. Probably his difficulty was to get a proper basis of comparison, because, as he says, the Institute Experience consists of all classes of policy, whereas the recent experience is divided into separate classes. But, as was shown by Mr. King (J. I. A., xix. 383), the Institute Experience consisted almost entirely of Whole Life policies by uniform premiums. He gave an analysis of the business on the books, when last they valued, of nineteen out of the twenty offices contributing their experience, and I reproduce part of his table here :



in the British Life Offices' Experience 99

TkaoAiWt/tr. Description nf of Assurances А«,в««1»,/.Ла Amounts Assured, Percentage to TkaoAiWt/tr. Description nf of Assurances А«,в««1»,/.Ла le8S ъыыхя&ыы Total Burine«

Whole Life, Uniform Premiums . £97,377,672 90*33 Do. Other Descriptions . 5,410,688 5*02

Joint Lives 682,297 63 Endowment Assurances . . . 1,662,165 1*54 Short Term 1,113,001 103 Contingent Survivorship . . 756,999 '70 Last Survivor 701,173 *65 Endowments 108,175 *10

Total . . £107,812,070 1004)0

It will be seen that 90 per cent, of the business is whole life policies by uniform premiums, but the real percentage of the experience is probably greater, as the special classes, having been introduced later in point of time, would form an even smaller proportion of the exposures than shown in the above table. The mortality on the whole would be rather better than for whole life policies alone, because limited payment and endowment assurance policies would together be greater than all the other special classes, and we know that the mortality in them is lighter than in the case of whole life policies.

We may assume therefore that the Institute Experience consists of whole life policies, but we cannot compare it directly with the British Offices' Ex- perience, which is divided into "with profit" and " without profit" policies. I have made an investigation into the point, and find the proportion of the "without profit

" policies is small, only about 17 per cent. In order to eliminate selection, the HM(5) curtate expectations of life may be compared with those of the British Offices' Experience, and this is done in the following table :

British Offices' Experience

excluding excluding Age H»№ first five years first ten years

With Without With Without Profits Profits Profits Profits '

20 39-72 4219 4104 4192 4150 30 33-43 34*57 33*64 3441 33*82 40 26*46 2715 26-40 2706 26*41 50 19*52 20 03 19*51 20 00 19*52 60 1319 13*56 1318 13*53 1316 70 7*94 8-19 7*90 8*19 788 80 4*20 4'36 416 4*36 4'16 90 1*81 218 1*96 218 1*96

The expectations in the case of the "with profit" class are in every case higher than the HM(5), and substantially so at the younger ages. In the case of the " without profit

" class the expectations are slightly less, except at ages 20 and 30. But we may go a step further, and exclude the first ten years in the British Offices' Experience, and the same remarks still hold good when they are compared with the HM(6), as shown in the above table. One curious result is brought out in the table, that in the "without profit" class at ages 20 and 30 the expectations of life, excluding the first five years only, are appreciably less than the expectations excluding the



loo The Improvement in Vitality as disclosed

first ten years. For a proper comparison of the British Offices' expectations with the HM(6), we ought to make a small deduction from the " with profit " class to allow for the percentage of " without profit " policies in the HM(5) experience, but it is, generally speaking, so small that it is hardly worth while. It is clear, therefore, that there has been a considerable improvement in the mortality of the recent experience over the HM(6), and it would probably have been greater still if there had been time to separate the " Old " portion of the recent experience from the " New."

Dr. Buchanan gives three causes which have been assigned for this improvement in vitality, and says : "It is fairly certain that the classes, from which assured and annuitant lives are drawn, have profited more largely from [them] than the general population." I do not think he would have made this statement, at all events of the earlier periods of life, if he had been acquainted with the statistics of the great Friendly Societies, which draw their members from the industrial classes. These statistics are compiled with great care, and afford a very good indication of the improvement in mortality. The following table shows the rate of mortality of the Manchester Unity of Oddfellows in the two great experiences they have constructed - namely, for the periods 1866-70 and 1893-97. The rate of sickness is also given, for the reason I will explain presently.

Rath of Mortality per cent. Rate of Sickness in Weeks I Ages ■

1866-70 1893-97 1866-70 j 1893-97

20-24 -64 -37 75 -90 25-29 '76 -46 81 -95 30-34 -82 -55 93 106 36-39 '98 -70 106 127 40-44 1*26 '95 1*26 1*58 45-49 1*43 117 1*64 1-99 50-54 1-91 1*69 2-22 2*75 55-59 249 242 305 402 60-64 3-54 356 4-72 631 65-69 5-21 5*41 724 10*59 70-74 7*81 809 1206 17*40 75-79 j 9*95 1204 16*87 2515 80-84 11*88 17*66 . 20*59 3227 85-89 19*61 23*26 29*63 3612 90-94 ... 28*47 ... 38*89 95-100 ... 4400 ... 3857

Up to ages 55-59 the rates of mortality in the later experience are less than in the earlier, the reduction being specially marked at the younger ages ; but after age 60 the mortality in the later period is greater, and increases very rapidly. This rather bears out the authority Dr. Buchanan quotes, that an age would be reached after which the power of preservation of strong and weak alike is counteracted by the high percentage mortality due to the decreasing average vitality.

Dr. Buchanan says it has been suggested that each of the causes for improvement above referred to " indicates, not an addition to the vitality of the strong, but a diminution of the fatalities of the weak." This seems to be borne out by the great increase in sickness shown in the same two periods of the Manchester Unity Experience, as disclosed in the above table. I may add that these features have been confirmed by other similar experiences, and I am afraid that his poetical allusion to the man crossing the Bridge of Life is more imaginary than real.



in the British Life Offices' Experience ioi

There are several other points I should have liked to allude to, but I have already trespassed too much upon your time, and will content myself with referring to the last one dealt with in the paper - namely, the valuation of the liabilities of Life Offices by means of select tables. However ingenious the methods devised of valuing by such tables, the labour must always be considerable, and it has always seemed to me a much simpler plan to value select premiums by ultimate annuity values, and of course sums assured by ultimate assurance values. This makes a provision for the deficiency to which Dr. Buchanan calls attention, and it will approximate more closely to the real reserve which should be made. Each table as it has been published has, as a rule, required larger reserves ; and as improvement in vitality of both lives assured and annuitants is likely to continue, tables in the future will probably require larger reserves still.

Mr. Low. - The object of this paper is to investigate how far the improvement which is held to have taken place in the death-rate of the general population, is manifested in the statistics of assured and annuitant lives. Dr. Buchanan has applied himself to the problem with his usual ability and thoroughness, and he has produced results which, at all events, are worthy of very careful consideration. If those results are not absolutely convincing, that is due to the nature of the material with which Dr. Buchanan has had to deal, rather than to any want of skill on his part in the manipulation of it. Now, I am not at all disposed to quarrel with or criticise the conclusions Dr. Buchanan has drawn with regard to annuitant lives. From all our observations they certainly show a tendency to " dis- improve " in the interest of the Insurance Companies and to improve in their own interest. Like the "waeftť wife" in Outram's well-known lyric, these people live for their annuity and their annuity keeps them alive, and if they have gone far towards converting themselves into what he termed "a leevin' perpetuity" none of us need be surprised. But as regards the experience of assured lives, I think something may be said in qualification of the general conclusions which Dr. Buchanan has drawn. In the first place, however, I should like to call attention to some features in the population tables which Dr. Buchanan has presented to us, and which I read with a rather different emphasis from that which he puts upon them. They all speak with one voice as to the progressively enhanced expectation at the beginning of life. It would seem that an infant bom in these days has before it the prospect of a considerably longer average life than one born in former times. The improvement shown by the population table in thirty years- between the period 1861-1870 and the period 1891-1900 -represents an addition to the expectation of life at birth of something like 11 per cent. Coming down the tables, however, we find a progressive diminution in the percentage as the age increases, until, in nearly all of them, we reach a point somewhere between ages 35 and 45 at which the expectation of life in 1891-1900 appears no greater than it was in 1861-1870. From that point onwards until past the age of sixty-five the expectation indicated by the figures of the later period is actually less than that indicated in the earlier period. Then there is a rally, and for older people the prospect of life again becomes better. These features appear in all the tables except that for females in England and Wales, and there the difference in favour of the later period, for the tract of life in which the figures elsewhere are reversed, is so insignificant as to suggest that the causes which led to increased vitality at younger ages had virtually ceased to operate, while those which led to improvement in later life had not yet begun to take effect. The same features are to be observed in Dr. Dunlop's tables for males in Scotland for the bst two decennial periods, 1881-1890 and 1891-1900. I speak with great diffidence in that gentleman's presence,



IO2 The Improvement in Vitality as disclosed

but perhaps he will kindly put me right if necessary. There had been improvement almost throughout - though more marked at the beginning of the table - in the former period as compared with the earlier decennium 1861-1870, but much of this was lost in the later period 1891-1900, and during the tract of life which I have mentioned the expectations had become still lower, both for males and females, than in the period 1861-1870. As the mode of construction of the tables was uniform throughout, there is here evidence of progressive deterioration, rather than of improvement, at the very period of life which is of most importance to the community. It would seem therefore that instead of congratulating ourselves on an improvement in vit »lity of the population, we in Scotland have cause to regret that the amount of vitality during the effective period of life has become somewhat lessened. The deterioration is probably even greater than appears from the tables, because the expectation at each age is in these tables taken to the extreme limit of life and includes the later period during which the tables show improvement rather than retrogression. The English statistics do not show the same deterioration as between the last two decennial periods, but any improvement that has taken place is so slight as not to have compensated (in the case of male lives) for the loss which took place between 1861-1870 and 1881-1890. Probably the greater part, if not the whole, of the apparent improvement would disappear if the expectations were calculated only up to the age of sixty -five and not beyond.

We have then, as the characteristic of our population statistic?, an improvement at the early ages, deterioration when the battle of life has well begun and all through the working period, and again improvement later on.

Dr. Buchanan has mentioned certain causes which have been adduced to account for the assumed general improvement in vitality, and he goes on to say that if it were true, as has been suggested, that the causes indicate, not an addition to the vitality of the strong, but a diminution of the fatalities of the weak, it would follow that some accumulation of weaknesses would show itself at the advanced ages. That conclusion, however, would follow only up to a certain point. I think the consequence of a general deterioration in stamina would rather be this, that we should have, during a certain period of life, a race of men who were not capable of procreating such a strong healthy progeny as their predecessors, and the effect would be shown not so much in an increased death-rate at the extreme end of the table, as in the deterioration of succeeding generations. That is something very like what has come out in Dr. Dunlop's table for Scotland, which, as we have seen, exhibits a progressive deterioration for the working period of life. This is no doubt a pessimistic view of the causes affecting vitality that are at work around us. At the same time it seems to be one that is to some extent warranted by the statistics presented. It may quite well be that deterioration holds only up to a certain age, and improvement takes place later, because after the process of elimination has been completed - after the weaker men have succumbed in the battle of life - the survivors may have a greater vitality as compared with the lives which preceded them.

Now it is a very interesting inquiry whether these same appearances can be traced among assured lives, and it is to this that Dr. Buchanan has directed attention in the paper. It is greatly to be regretted that he was not able to find - it is not his fault, for the thing does not exist - two sets of data that were strictly comparable. I think it an ingenious and excellent idea of his to take these " Old " and " New " Assurances of the New Experi- ence, but a little consideration serves to show that we have not here a very satisfactory basis of comparison. I think it very probable that the element of selection enters much more largely than would appear from the tables. Dr. Buchanan suggests that these experiences may be regarded as prac-



in the British Life Offices' Experience 'щ

tically equivalent to tracing two bodies of под-select lives- one coming under observation in 1863 and the other in 1873- up to 1893. In that case the comparison would have been better than it is, but it is not strictly the case. One set of non-select lives came under observation in large bulk in 1863. They were gradually added to for ten years by introducing the lives which entered up to 1873, and then they ceased to have any addi- tions made to them. But in the case of the " New " Assurances the first non-select lives came under observation in 1873, and these were added to year by year up to 1893, so that the interval between the two experiences would be much greater than the ten years suggested by Dr. Buchanan.

I come, however, to what is a more important point. Dr. Buchanan has shown in bis tables of the mortality for the first ten years that the effect of selection persists markedly up to the end of the tenth year. It is Dot to be assumed that it is then immediately stopped. It would, no doubt, be traceable in the statistics for some time further. It follows that if we have in the " New " Assurances, as compared with the " Old," a preponderance of lives coming under observation shortly after the ten years, we should expect to find the mortality in the "New" Assurances rather lighter than the corresponding mortality in the " Old," because of the effect, of selection. Now that is exactly what we do find, but the difference is not very great, as you will see from the tables. Again, if you look at the difference in the effective period of life, you will find that, as between the " New " and the " Old " it is very small indeed. That is especially significant to the Insurance Offices, for the great increase in the proportion of Endow- ment Assurances has rendered it less and less important to them what the rate of mortality is after about the age of 60. Now if, instead of taking the expectations, as in Table III., up to the end of life, we take them only up to the age of 60, we find the differences are very small indeed. I haye calculated the complete expectations ('w^x) for the period between certain quinquennial ages and the age of 60, and find them to be as follows : -

Cúmplete Expectation up to Age 60

Age, 30 ! 36 ! 40 ¡ 45 60 55

" Old "Assurances, . . 25*35 ! 21*42 1741 j 13*30 9*10 4*73 ''New" do. . . 25-90 21*76 1764 | 13*46 916 4*72

The apparent improvement at age 30 is 2*18 per cent. ; at 35, and again at 40, it is 1*28 per cent. ; at 45 it is 1*17 per cent. ; at 50 it has fallen to 0*64 per cent., and at 55 the difference has turned very slightly the other way.

These small differences up to the age of 50 may be quite well accounted for by more recent selection, there being among the " New " Assurances, as compared with the " Old," a preponderance of lives towards the beginning of the period following the first ten years.

Well, all this means simply that we are unable to say whether the clnss of people from whom Assurances are drawn have benefited materially during the effective period of life from the new conditions which have prevailed in recent times. Dr. Buchanan suggests in one part of his paper that they have benefited more than the other classes. I do not know upon what he bases that view, for I should have thought quite the contrary, namely, that any improvement in the modern conditions of life has been more in favour of the working classes and of children than in favour of the adult middle class from which Assurances are drawn. Yet in the case of the general population we have an apparent deterioration, and I think all we

VOL. IV. J



iO4 The Improvement in Vitality as disclosed

can at present say is that we have no evidence of this having shown itself in the class from which insured lives are drawn. I cannot conclude these remarks without saying that Dr. Buchanan's figures have excited in my mind great admiration, not only for the manner in which he has handled them, but for the industry he has shown in putting these figures together. I think this is a subject that will bear a great deal of further investigation, and I hope that some day we may find statistics that will give us real light upon it and produce results that will hold their own against any criticism.

Dr. J. C. Dunlop, Superintendent of Statistics in the Office of the Registrar- General. - It is apropos of Dr. Buchanan's first conclusion that I will venture to make some remarks. That conclusion is distinctly of an un- committing description. He states that " the improvement in vitality has been marked during the earlier years of life, but has not been confined to them." It may be of some interest to consider whether the improvement has been found to occur in all periods of life. It was for the elucidation of that subject that I constructed the series of life tables which Dr. Buchanan quotes in the earlier part of his paper. These were based on similar information, worked out by similar methods, and are, I believe, thoroughly comparable with each other ; and the changes observed in them, in my opinion, are indicative of the changes of expectation of life resulting from the influences to which lives were exposed at the end of last century as compared with the expectation of life resulting from the influences earlier in that century. The principal points shown by the series of tables are that there is a marked increase of the expectation of life at early ages and for both sexes, but as life advances the increase becomes less marked, and at the middle periods of life, 35 to 65, the increase not only disappears, but there is a diminution evident. These tables then, so far as they go, show that the increased vitality, so marked in the younger age-periods, does not extend throughout all age-periods. An increase of expectation is also observable in the later periods, 75 to 95. The only other really comparable study known to me is Dr. Hayward's, also quoted by Dr. Buchanan. It deals with the expectation of life in England, and in its results it closely agrees with mine, for those tables show the expectation of male life to have markedly increased in the early age-periods, but to have somewhat diminished at the age-periods from 45 to 65, and the expectation of female life to have similarly increased at the early ages, but not to have done so later, from 55 to 65. Further corroboration is afforded by the life tables published in the English Registrar-General's Reports, though differences in the method of construction make this comparison rather less satisfactory.

For a further study of the subject I have prepared the following table, which shows the relative increase or diminution in the death-rate of age- groups which is found by comparing the Scottish death-rates of the period 1861 to 1870 with those of the period 1891 to 1900. From the table it may be ascertained that the death-rate of infants of less than one year old was slightly increased, the death-rates of all age-periods, both male and female, from 1 to 55 have been diminished, the percentage diminution reaching a maximum at the age-period 5-10 for males and at the period 3-4 for females, at which ages the diminution was nearly fifty per cent., and that the diminution of death-rate of both sexes became less and less until the age of 55 was attained. In the subsequent age-periods, instead of a diminution being observable there is an increase for both sexes, that increase being at the age-period 55-65 for both sexes fully 13 per cent., and at the age-period 65-75 fully 6 per cent. Subsequent to 75 a small diminution of death-rate is observable in both sexes. These changes of death- rate explain the differences between the life tables of the decades, - the



in the British Life Offices Experience 105 increased expectation of life at the earlier ages, and the absence of that increase at the later age-periods.

Scottish Death-rates, 1861-1870 and 1891-1900

Males Females

A0E »я_ Death-rate Difference Death-rate Difference A0E »я_ per 1000 Differ- per cent. per 1000 Differ- per cent.

- enee of 1861-70 enee of 1861-70 1861-18701891-1900 rate 1861-18701891-1900 rate

0- 1 150-74 159-37 + 8-63 i 57 125*76 128*10 + 2-34 +19 1-2 70-20 54-32 -15-88 -226 67*77 51*57 -16*20 -239 2-3 36*90 22-38 -1452 -393 3676 22*13 -14*63 -39 8 3-4 25*50 13*34 -12*16 -47*7 26*21 13*53 -12*68 -48*4 4-6 18*44 9-40 - 904 -490 1872 9*76 - 8*96 -47*9 6-10 9-65 4*91 - 4*74 -491 931 5-25 - 406 -437

10-16 5*15 3-18 - 1-97 -38*2 5*36 3*61 - 175 -32*7 16-20 7-35 516 - 219 -29*9 7*21 5*18 - 203 -28*2 20-26 10-36 685 - 3-51 -33*9 8*48 602 - 2*46 -290 26-36 10*45 7*72 - 2-73 ! 26*2 9*89 7*80 - 209 -21*1 36-46 1404 11-43 - 2-61 -18*6 1216 10*41 - 1*75 -144 46-66 1908 1903 - 005 - 02 1555 15*23 - 0*32 - 21 66-66 31*42 35*77 + 4*35 +138 2567 29*09 + 342 +13*3 66-76 6402 68*37 + 4*35 + 6*8 54*77 58*33 + 3*56 + 65 76-86 139-94 13814 - 1*80 - 1*3 128*24 12098 - 726 - 5*7

A similar conclusion is also derived from a consideration of the causes of death which are found to be less prevalent now than they were in the sixties, for the causes of death which are now found to be less fatal, than formerly are almost exclusively those which affect children and young adults. As examples of such causes of death, I may mention smallpox, scarlet fever, diphtheria and croup, typhus fever, enteric fever, and tubercle, all of which are now less fatal than they were in the sixties. . I would also like to point out that the outcome of insurance experience, as formulated in Dr. Buchanan's Tables III., IV., V., and X., can hardly be said to be contrary to the view that the increased vitality of modern times does not extend to all age-periods. In Tables III., IV., and V., it may be noticed that the increased expectations after 40 are so small as practically to be insignificant, while in Table X. the demonstrated saving of life is practically confined to age-periods under 45.

Two other points I may mention; one, the question whether ^ there is any probability of a further increase of vitality at the early ages in ^ future years, the other the comparative expectation of male and female life. As bearing on the former I show a chart which was published in the Fiftieth Detailed Annual Report of the Registrar-General of Scotland (Cd. 2794) which compares the death-rates of the urban and rural districts of Scotland of each year from 1855 to 1904, and it will there be seen that while there has been a very marked reduction of the urban death-rate during the period, the rural death-rate has been practically unchanged. It is extremely improbable that the urban death-rate will ever fall much if at all below the rural death-rate, and as the urban death-rate recently has been very little above the rural, and the rural rate is not declining, the conclusion is that much further diminution of the urban death-rate, with the consequent diminution of the national death-rate, is unlikely.

Regarding the superiority of female expectation of life as shown by



i об The Improvement in Vitality as disclosed

population statistics, Dr. Buchanan quotes Mr. Chatham's investigation as showing that insurance experience does not altogether agree therewith. On this matter the evidence got from population statistics is both decided and consistent, for the expectation of female life in very many countries has been found to be superior to that of male life. Among other observations, I may quote life tables prepared in Scotland, England, London, Denmark, Norway, Sweden, Switzerland, Germany, Prussia, Berlin, Fin- land, Hamburg, Breslau, Holland, Belgium, France, Italy, Massachusetts, New South Wales, Western Australia, and India. It is of interest to me to observe in Dr. Buchanan's Tables IV. and V. a similar superiority of female expectation of life, for by comparing those tables I note that" the female expectation at all ages from 50 to 89 in both the " Old " and the " New " annuity experience is better than the male expectation.

Mr. Thomas G. Ackland wrote :- I am much obliged to the Council of the Faculty for their invitation to send a few notes on Dr. Buchanan's valuable and interesting contribution to our Transactions. I am more particularly interested in the author's investigation into the improvement of vitality amongst assured lives and annuitants, as illustrated by a comparison of the "Old" and "New" experience included in the OCMJ Table, and in the OtawJ and Ola/i Tables, respectively. Dr. Buchanan has investigated the comparative mortality, in quinary groups of ages at entry and attained, during each of the first ten years of duration ; and, as regards later durations combined together, at individual attained ages. This plan conveniently separates the period during which selection may be assumed to be in operation from the later period, over which the influence of first selections, at any rate, may be deemed to be eliminated.

The comparison for assured lives is significant and interesting. The rates of mortality during the period of selection, as set out in Tables VI., VIL, and X., show a decided preponderance of mortality amongst the "Old" assurances, as compared with the "New," at practically all grouped ages ; but most notably up to attained age 49 (where 46 cases out of 54 show an excess mortality for the " Old" cases), and in the 8th, 9th, and 10th years of assurance (where, in 24 cases out of 27, the " Old " experience is in excess). The "ultimate" assurance Table III. shows, even more definitely, the preponderance of "Old" mortality over "New"; the expectations of life for the former class being less than by the latter at all ages from 20 to 80 inclusive. I agree that the superior vitality of " New " assurances, thus clearly demonstrated, must be attributed to two main causes : (1) the greater value of life, from improvement in sanitary conditions, and in the scientific treatment of disease ; (2) the improvement in the selection of lives for assurance, both as regards the medical man and the actuary.

As regards the annuitant experience, the results, while clearly tending in the same direction, are not nearly so marked as in the assurance experience. I suppose that this partly arises from the fact that, owing to paucity of data, Dr. Buchanan has felt obliged to combine, in Tables V1IL, IX., and XL* the " Old" and " New" data, and compare the combined rates with those of the "New" annuitants. This would tend to minimise the differences between the "Old" and "New" rates, especially in the first ten years of assurance, where the "New" data largely preponderate. Not- withstanding this, there are clear evidences of superior vitality amongst " New " annuitants in the first ten years' duration, especially in the fast three years of that period for male lives, and generally for female lives. In the " ultimate " annuitants' Table V., the expectations for " New " lives are throughout greater than for " Old " lives, between ages 50 and 79 inclusive, excepting at ages 53, 55, 59, and 60 for male lives, and at ages 64 and 65



in the British Life Offices' Experience 107 for female lives. In the case of annuitants, the medical and actuarial selection of the life is replaced by the self-selection of the annuitant, no doubt an important factor, but one in respect of which we should not, I think, have grounds to anticipate any marked improvement or differentia- tion, over the period 1863-93, as compared with an earlier period.

During the last few months, I have been investigating the comparative mortality óf " Old " and " New " annuitants, on lines partly identical with those followed by Dr. Buchanan, but including also comparisons on somewhat more extended lines. I first got out tables identical with his Tables IV. and V., showing the comparative mortality of "Old" and "New" cases, as deduced from a ten years' ultimate table, based upon select data. My results are practically identical with those given in Tables IV. and V., excepting for a slightly different mode of dealing with the data at the oldest age in the "New" experience, where it happens that, both for male and female annuitants, a single life, tabulated at ages 98 and 100 respectively, survived as " existing " on the policy anniversary in 1893. I know of no method for theoretically dealing with such a case (which frequently arises where expectations are computed for individual ages at entry) in computing the expectations of life ; and I adopted the device of assuming that the life, so surviving, died in the year following that at which it was tabulated as "existing." Dr. Buchanan deals with this difficulty by assuming that the single life subsequently experienced the mortality of " Old " annuitants, in which class the ultimate age was 102 for male and 104 for female lives. This tends to overstate the author's "New" expectations as compared with mine at all ages, although the excess is practically negligible in respect of ages younger than 75 or 80.

It is not perhaps entirely satisfactory to deal, as in Dr. Buchanan's Tables III. to V., with a truncated ten-year table based upon select data, because this cannot be deemed in any real sense to be a "non-select" table ; and this, not because of any persistence of first selections after ten years, but, as I have shown in my paper read before the Faculty in March last (T.ÍP.A., iii. 316-319) because the rate of mortality in a truncated table, bused upon select data, is, practically at all ages, appreciably lower than that deduced from a similarly truncated table based on aggregate data. This arises from the fact that, in the select data, the cases of re-selection, introduced when lives, already recorded, effect second and subsequent annuities (or assurances), are included, whilst in the aggregate data they are excluded ; thus giving, in the select ultimate table, an added weight to the data in respect of these healthy lives. As I thought it probable that the inclusion of these cases of re-selection might tend to vitiate any comparison between " New " and "Old" rates of mortality, I got out, separately, four truncated ten-year tables for "Old "and "New" male and female annuitants, based upon aggregate data. For this purpose the data given in the published volume was of no service (the aggregate data not having been tabulated in select form), but I obtained the necessary data from the manuscript working sheets and abstracts of data, available in bound volumes at Staple Inn Hall. From the four ultimate tables thus deduced, Ï computed rates of mortality and expectations of life at all ages.

I give here two tables showing, for male and female annuitants, the curtate expectations at every fifth age from 50 onwards, as deduced from (1) "Old" aggregate data ; (2) "Old" select data ; (3) "New" aggregate data ; (4) " New " select data ; those numbered (2) and (4) being identicnl with Dr. Buchanan's Tables IV. and V,



io8 The Improvement in Vitality as disclosed

Annuitant Experience, excluding first ten years Curtate Expectations of Life

Males Females

Age i '■ Г Age "Old" "Old" "New" "New" "Old" "Old" "New" "New"

Aggreg'te Select Aggregate Select Aggreg'te Select Aggreg'te Select

Õ) (2) (¡) õ) (Õ (¡) (¡) ~п) 50 19038 19*315 19 442 19 504 22*256 22*322 22*616 22*839 50 55 15*809 15*999 15*753 15*820 18*809 18*839 19*236 19*427 66 60 13093 13*245 12*944 13182 15*453 15*532 15*876 16034 60 65 10*839 10*865 11*286 11*474 12*488 12*603 12*440 12*550 65 70 8032 8 077 8*382 8'484 9*585 9*648 9*633 9*761 70 75 6060 6*100 6*242 6*336 7001 7087 7*226 7*327 75 80 4*359 4-357 4*297 4*399 5050 5123 5098 5102 80 85 3*127 3*254 3*330 3165 3*604 3*618 3*518 3583 85 90 2162 2-624 2*869 2719 2445 2446 2*612 2823 90 96 2*231 2*778 1*944 1944 2*043 2122 1*735 1*833 95

100 1000 1-500 Г556 1167 '500 -500 100 _J i

It will be seen that the vitality of both " Old " and " New " lives is greater in the select than in the aggregate data, at practically all ages ; also that the expectations, deduced from aggregate data, are, for both sexes, and at almost all ages, greater for " New " annuitants than for " Old " annuitants ; thus confirming the author's results. This investigation does not, however, fully bear out my anticipations, that the effect of comparing " Old " and u New " lives from aggregate data might materially differ from the comparison based on select data.

I may perhaps also be allowed to refer to an investigation which I made in 1897 as to the comparative mortality in the class of " Old" and " New }; annuitants. The results are set out on pp. 12, 13 of my Fourth Report to the Joint Mortality Committee, being Document No. 30 in the volume of Reports and Documents, which is available, I believe, at the Halls of the Institute and the Faculty for reference by members. In this investigation I compared, for male and female annuitants, the actual deaths during the first ten years of duration, with those which would have occurred if the rates experienced amongst " New " annuitants during that period had been in operation for the "Old" lives also. Dr. Buchanan gives the results of a similar comparison, but, as his investigation is limited to ages 50 to 74 inclusive, whilst mine extended over the whole of life, it may be interesting to give the more extended results, for purposes of comparison : -

" Old " Annuitants : Males. Females. Actual Deaths, 267* 636' Expected by " New " rates, . . 267*36 581*

" Combined " Annuitants : Actual deaths, 2384* 4786" Expected by " New J; rates, . . 2384*14 4732*

It will be seen that, on the whole, the operation of the "Old" and " New " rates gave identical results for male lives ; whilst, for female lives, the "Old'' rate of mortality is, on the whole, somewhat less than 10 per



in the Éritish Life Offices Experience 109 cent, in excess of the "New" rate, or slightly more than 1 percent, in excess of the "Combined" rate. These results are closely in accord with those given in the author's Table XI.

I might also refer to a diagram, appended to my Fourth Keport, cited above, which was intended to illustrate the question, dealt with by the author in the present paper, as to the approximate proportionate distribution of " Old " and " New " data in the " Combined " annuitant experience, having regard to years of duration and calendar years of observation, and also to years of entry. This diagram shows the large preponderance of the " New " experience in the early years of duration, up to about the fifteenth year ; and, for subsequent years of duration, the increasing preponderance of the " Old" experience. These results have, of course, to be "weighted," according to the proportionate number of cases actually entering into the " Old " and " New " experience in particular years of duration and observation; an operation which will give a further preponderance to the " New " experience.

I consider that Dr. Buchanan has given us a suggestive and most valuable contribution, and entirely agree with his four "general conclusions." In particular, I think he has clearly demonstrated that "spurious selection" has not, to any appreciable extent, arisen from the combination of " Old " and " New " data ; and his letter on this subject, published in the current number of the Journal of the Institute (J. I. -4., xlii. 141), is, in this connection, well worthy of study.

On the question of the method of constructing Life Tables from Popula- tion Statistics, dealt with by Dr. Buchanan in the Appendix to his paper, members of the Institute and Faculty will read witn interest a valuable paper on the subject to be submitted by Mr. George King at the next meeting of the Institute of Actuaries.

Mr. Gr. W. Richmond, F.I.A. - There is a reference in the paper to the English Life Table No. 3 as understating the mortality at the advanced ages, owing to the method of its construction. Beyond that there is another cause working in the same direction, viz. the erroneous statement of ages in the Census Returns. Old people have a tendency to exaggerate their ages, and the effect would of course be to bring out lower death-rates than really apply to the ages as given. At the beginning of the table there is a difficulty (referred to, I think, by the late Dr. Farr) in getting out the correct death-rate owing to the tendency of people to set down age 1 in the case of their children who die in the first year of life. Notwithstanding the contrary view of such an authority as Dr. Dunlop, I believe there has been a diminution of mortality, taking Great Britain as a whole. Any evidence on the point furnished by Assurance statistics I should be inclined to rely upon more than in the case of population statistics, the data, if more restricted, being much more reliable. Even if the improvement as indicated by the individual " expectation " be small, yet being shared by vast numbers of lives, it represents a very considerable addition to the number of years of life in the aggregate. One aspect of the matter is very important to Assurance Offices, viz. the effect upon reserves. It is obvious that a diminution of mortality means a lessening of premiums somewhere, but of course it does not follow that reserves will be reduced. I believe the tendency is the other way, as would undoubtedly be the case if the diminution in mortality were more prominent at the younger ages, at which most assurances are effected. In Germany the Gotha Office has gone into the question. A series of mortality tables was constructed, analysing the mortality separately for each of three successive periods since 1829 when the Office commenced business. The mortality experience of each period was found during that period and during each succeeding period. The results



t io The improvement in Vitality as disclosed

have been very useful» They show with few exceptions a steady -diminution in the mortality of the successive periods, and Dr. Karup, of the Gotha Office, one of the most eminent actuaries in Germany, constructed a hypothetical table on the assumption that this diminution would continue, in order to ascertain what would be the effect on premiums and reserves. The reserves were found to remain approximately the same as before. I may state, however, that the reserves required by German tables are much larger than by ours in consequence of the peculiar form of German mortality. At young ages the mortality is lighter than ours, but at fifty or fifty-five the curves cross and their mortality is then heavier ; hence their larger reserves, the slope of their mortality curve being so ni uch steeper.

The improvement in the mortality of assured lives suggests three question«. How far is it due to improvement in the health of the general population? How far to more skilful medical selection? But to my mind the third question is still more important, viz. How much is due to the fact that the Offices are now dealing with a different stratum of the population from that which principally furnished their business formerly '( That we are doing so is indicated by the decline in the average amount oí" policy, as well as by the change in the kind of assurance. The lower middle class is coming more and more into our business, and the apparent improvement in mortality may simply be due to the fact that we are getting another and better class of lives. That is the case in Sweden, where the Offices are getting a larger proportion of healthy country lives than formerly, where, moreover, the distinction between town and country lives is very clearly marked. This point has been made use of in Germany in connection with an attack there upon Select Tables arising out of a proposal to render compulsory the use of Select Tables in valuations. Such a course would prove a severe strain upon the smaller Offices, and the proposal is consequently exciting their opposition.

Mr. W. A. Robertson, - Dr, Buchanan's most interesting paper compels us to consider tbe various methods of measuring the mortality experience among lives assured. The material for select tables may be chosen (1) by using the complete experience of the Offices. But a great portion of this material is really out of date, since it is acknowledged that the $election of lives is more efficient than say forty years ago. (2) By limiting the period of observations and bringing in survivors. This perhaps improves upon the first method. It involves, however, the bringing together of two sets of statistics. The idea is a modification of u final series," a replacing of the " existing " by means of the survivors. It is known, however, that the latter show far heavier mortality than the former, and it is difficult to grasp the full effect of this mixing of statistics, since the force as represented by the survivors is bound to increase with the, duration of the con- tract. The further point arises as to whether an interval of thirty years is not too long a period of investigation, and whether for the purpose in view a period of say ten years is not sufficient. That was the period usually employed in measuring the experience of the population. (3) Perhaps the best method of investigating the effect of selection would be to fix on a particular year for entry, even a particular date, and trace new entrants at each age at entry from date of entry until they all passed out by death or withdrawal. While, however, the tables so formed would be true select tables, they would be open to the criticism that they were out of date owing to tne increased efficiency of present-day selection.

The general conclusions as given in the paper are very interesting. Conclusion No. 1 would seem to follow from the nature of the statistics, since it is doubtful if the full force of the improved selection has had time to operate at the older ages. Then the fact that the vitality of the " New "



in the British Life Offices Experience ill

is superior to the " Old " raises another point. The Endowment Assurance experience is practically all " new," while the Whole Life experience is " mixed." Might not this account to some extent for the difference in the mortality experienced ?

It would have been instructive had Dr. Buchanan been able to compare the " new " with the " old " mortality among females. It is the case, as he points out, that the female mortality experience of the population compares favourably with male mortality, and similarly in the case of annuitants. It is also the case that in industrial assurance statistics the difference between female and male mortality is nothing like so great as in the ordinary offices' experience. Mr. Chatham's figures (T. F. A.> i. 117), deduced from the British Life Offices' Experience, indicate an extra rate for females, especially in the case of term risks including endowment assurances. Yet the tendency of present-day practice is to ignore this teaching.

The probable effect of the relative improvement in vitality upon the reserves of Offices is touched upon in the paper. If the aggregate experience should continue to exhibit an appreciably lighter mortality at the younger than at the older ages, this would appear to involve increased reserves. As to select valuation, is it the case that the select reserve is the correct standard ? It might be so if the expenses of the Office were uniform from year to year, and always covered by the loading on the select net premium, if a true rate of interest were employed in the calculations, and if a correct reserve were made for future bonus at the rate to be declared. As things are, however, may we not say with Mr. Sorley that valuation by an aggregate table is. a convenient compromise, not algebraically correct, but still defensible on the broad principle of averages Ì

The Chairman (Mr. N. B. Gunn). - In view of the lateness of the hour, and as Dr. Buchanan has still to reply, I shall not, before calling upon him, detain you further than to move that we accord him a hearty vote of thanks for his excellent paper. Its preparation must have involved considerable work, and we are very much indebted to him, not only on account of the admirable way in which he has dealt with the subject, but also for having elicited such an interesting discussion.

Dr. Buchanan. - I thank you very sincerely for the reception you have given to my paper, and the gentlemen who have spoken for their criticisms. I recognise that a number of the points put forward in the paper are of a controversial nature ; but they seemed to be the better fitted to promote a good discussion, and I can only express myself as extremely gratified at the excellent discussion we have had to-night. As regards Mr. Chatham's remarks about my having confined the examination to the new British Life Offices' Experience, my object was to get a basis of comparison which would be as nearly homogeneous as possible, both as regards material and mode of compilation. My aim was also to eliminate the effects of selection as far as possible ; for there appears to be little doubt that selection has been more persistent in the British Offices' Experience than in the Twenty Offices' Experience. Besides, very exhaustive comparisons of these experiences have already been made by Mr. Chatham himself and by Mr. Ackland, and to have introduced further comparisons would have been going over ground which had been traversed before. As regards the question of whether the improvement in the vitality of the general population has been continued for the whole period of life, my object in introducing figures based on population statistics was not in any way to attack the evidence of these statistics, but simply to add to the interest of the paper, to show how far the evidence of these statistics was reproduced in the experience of assured and annuitant lives, and in what directions there

VOL. IV. К



1 1 2 The Improvement in Vitality were differences. At the same time the evidence of population statistics as to deterioration at the later periods of life seemed to me to be incon- clusive. Certainly, the life tables for Scotland show a small but marked deterioration during the middle period of life ; but that is not confirmed by the most recent life tables for England and Wales, and, as far as I could judge from an examination of Dr. Hayward's tables, there appeared to be a fairly general and continued improvement for the last three decennia of the past century. Dr. Dunlop has pointed out that the reduction in death- rates has chiefly affected young lives. That is a point on which all are agreed ; but it does not seem to be a necessary consequence of this improvement that there should be deterioration in after life. Certain risks appear to be peculiar to certain periods of life, and a susceptibility to a particular risk at a given period of life does not necessarily imply a similar susceptibility to an entirely different risk at a later period of life. My reference to the Bridge of Life was prompted by Professor Karl Pearson's well- known and highly suggestive analysis of the mortality curve. He has shown that the mortality curve may be resolved into five distinct frequency curves, corresponding to five periods of life ; and, while he does not claim that his resolution of the curve is final, he expresses himself as fairly con- fident that the various diseases to which human life is subject may be grouped into five great classes centreing about five periods of life. He has pictured five grim marksmen, of different degrees of " skewness " of aim, aiming with weapons of different degrees of precision at the procession of human beings crossing the Bridge of Life. Is it not possible that medical skill has clothed that crowd in a kind of armour which has enabled them to pass safely through the line of fire when it strikes them with a given degree of obliquity ?

When we turn to the statistics of assured and annuitant lives we find an improvement practically from beginning to end of the table. I admit that it is possible that this continued improvement may be due to the fact that the lives had been selected ; but in Tables III. to V. the comparison has been made between two bodies of lives in which the benefit of selection may be regarded as exhausted, so that they may fairly be regarded as a fair average population of a life office. With all deference to the opinions expressed by Mr. Low, I am rather inclined to think that if there had been deterioration at the later period of life in the class from which assured and annuitant lives are drawn, it would have shown itself even in this selected body once the benefit of selection was exhausted. But even granting that the advance of medical science has resulted in the preservation of the weak, and that the effect of medical selection has been to eliminate these undesirables entirely, do the comparisons made in these tables not show clearly that there has been a marked addition to the vitality of the strong Í The advance of medical science has resulted in the preservation of the few, but it has also meant an addition to the vitality of the many. I am very glad to find myself in complete agreement with Mr. Ackland, both because of his unique knowledge acquired as Official Supervisor of the New Experience, and because he has independently investigated the same question on very similar lines. It is very satisfactory to find that his comparisons of the "Old" and "New" Aggregate data of the Annuitant Experience confirm those of the " Old" and "New" Select data. He has gone so minutely into the whole matter that he has left me nothing to say beyond expressing my sincere thanks for the amount of trouble he has taken.

