Art. LVII.—The Population of New Zealand.

By H. W. Segar, M.A., Professor of Mathematics, University College, Auckland.

In New Zealand statistics Maoris are excluded, and emigration and immigration are to a large extent not taken into account. Every statement cannot be made with an account attached of every small modification that can arise from various sources; if the statement is correct for all practical purposes, it is sufficient.

The same liberality of interpretation must be given here as is necessary on all occasions on which effects depending mainly on one or two principal causes, but at the same time subject to various perturbations, are dealt with.

The Diversity of Age-distribution of Populations.

When we compare the age-distributions of the populations of different countries we find a diversity which is at first astonishing. This is sufficiently illustrated, perhaps, in the following table, in which we compare the populations of New Zealand, England, and France—that is, the populations of a new country, an old country with an increasing population, and an old country with an almost stationary population:—

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This diversity is found to be considerable even between old countries or between new ones, but is naturally more marked, as a rule, when old countries are compared with new ones.

The Stationary Distribution of Population.

For the purposes of comparison it may be of advantage to consider at once the distribution of the ages of the people which we shall speak of as the “stationary distribution.”

The ages of the people will be said to have a stationary distribution when, on comparing the numbers living at any two specified ages, the number living at the greater of the two ages is equal to the number of those at the less that should survive to reach the greater age.

of the New Zealand Institute,” vol. xxix., 1896, pp. 52–60. As these, however, only extend to the age of seventy-five, I have been obliged to fall back for ages beyond this on the English tables of Dr. W. Ogle. The effect of this may be to produce an error, which, however, will not be a very substantial one, on account of the small proportion of our people over seventy-five years of age, and none of the arguments in the sequel can be materially affected by any probable error that can arise on this account. The results in the table were calculated for each year of age, but, for the sake of brevity, are presented here grouped in five-year age-periods. Those of unspecified ages are left out of account, as also those over 100 years of age; but only a very small number of people are thus neglected.

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The total population for a stationary state corresponding to 20,000 births annually—namely, 1,109,563—should be noted. This means that, if the annual number of births in New Zealand were to reach 20,000 and remain at that figure, the total population would only reach about 1,110,000. The common birth-rate and death-rate would be 18.03.

Convergency of Age-distribution.

The falling-off in the number of people living as we rise from any year of age to a greater one may be spoken of as the convergency of the age-distribution, and the age distribution may be said to be more or less convergent according as the numbers fall off more or less rapidly as we ascend to the greater ages. In a stationary state the convergency of the age-distribution will depend on the rates of mortality of the people at the several ages; the more favourable to life the rates are the less will be the convergency of age-distribution. When the actual age-distribution of a population is more convergent than the corresponding stationary distribution the population at the various ages are generally increasing, for at each age there is generally a smaller number living than will survive to that age from amongst those of any less age. Conversely, if the population at the several ages is increasing the actual age distribution must be more convergent than for the stationary state. These facts are verified by an examination of any growing population, and Table II. shows that, in New Zealand, the convergency of age-distribution beyond the fifteenth year was very much greater at the last census than it would be in a stationary state. It is because of this age-distribution of population that the total population of New Zealand has continued to increase rapidly of late years, in spite of the fact that the annual number of births has not been increasing.

Such a state of age-distribution has in general been brought about by a growing annual number of births in the past. The people of reproductive ages generally produce a number of children sufficiently in excess of their own numbers for the survivors to the reproductive age to be greater than the number of their parents, and this goes on continually. In the case of new countries, however, this is not a complete explanation; but this matter will be again adverted to.

The Youth of the Population of New Zealand.

A perusal of Table I. will show that New Zealand has a larger proportion of young people and a very much smaller proportion of old people than either England or France, so that the average age in New Zealand is very much smaller than in either of these other countries. Indeed, the table shows that more than half of New Zealand's population was, at the time of the 1891 census, under twenty years of age, whereas in the case of France there was scarcely more than half under thirty years of age; and in the stationary state

there would be about equal numbers under and over thirty-two years of age. More extended tables might be given and further comparisons made, but we shall let it suffice to state that these would only bear out the statement that, compared with most other populations, that of New Zealand is very young. This fact will be found to have a very important bearing on many points connected with New Zealand population statistics.

The populations of the other Australasian Colonies are largely similar in this respect to that of New Zealand, but there are substantial differences, nevertheless, in the age-distributions of these populations. Thus the proportion of males sixty-five years and over to the total male population varies from 1.63 per cent. in Queensland to 5.55 per cent. in Tasmania, while the proportion at the ages under fifteen years varies from 28.73 per cent. in Western Australia to 38.01 per cent. in New Zealand, and 38.37 per cent. in South Australia. The differences are due chiefly to the histories of the several colonies and the date, character, and extent of immigration.

The Small Death-rate of New Zealand.

Further, the death-rate of New Zealand is exceptionally small. This fact is almost invariably quoted as being due to our climate and the conditions of life of our people. These factors must have some influence on the death-rate, no doubt, but before any conclusions can be drawn from the actual death-rate the distribution of the population according to age must be taken into account. The rates of mortality vary exceedingly according to age. According to data given by Mr. C. E. Adams, B.Sc., A.I.A., in the “Transactions of the New Zealand Institute,” the death-rate per thousand for males in New Zealand is 102 in the first year, 21 in the second year, 7.5 in the third year, and continues to diminish until it becomes as small as 2.2 for the ages 10–15. From then onwards, however, the rate increases, though it does not become considerable again until the ages 55–60, when it is 22; but after that it increases very rapidly, reaching as high as 95.8 for the ages 75–80. The course of the death-rates for females is much the same.

If, then, we had a population either of young babies only or old people only our general death-rate would be excessively high; and it must be obvious that the distribution of population according to age must have a great influence in determining the general death-rate. If one nation has a greater proportion of population at the ages for which the death-rate is small and a smaller proportion at the ages for which the death-rate is large than another, we must expect the first to

have the smaller death-rate if other conditions are the same. It is little use comparing the general death-rates of two countries unless these considerations are taken into account, and the proper way of comparing the vitality of the people of one country with that of the people of another is by comparing the death-rates of the two peoples for the several ages. This was done for New Zealand, Victoria, and England by Mr. C. E. Adams, B.Sc., A.I.A., and the results given are very favourable to New Zealand, so that, even if the age-distributions were the same in these three countries, New Zealand would still have the smallest death-rate, though it would not be so small relatively to the others as it actually is.

Again, the average death-rate in Sweden for the years 1887–96. was 16.48. This was the smallest in Europe, but is large compared with that of New Zealand, which was 9.87 during the same period. If, however, the age-distribution in New Zealand had been the same as in Sweden, the death-rate for New Zealand would have been about 14 instead of 9.87 during the same period, and in 1894 would have reached as high as 14.44.

We have already seen that, if the ages of the people had a stationary distribution, the death-rate would be 18.03, whereas the actual rate is about 10. The sniallness of this actual rate, then, is due mainly to the youth of the people.

The Annual Number of Births and the Birth-rate of New Zealand.

Up to and including the year 1880 the number of births per annum in New Zealand always increased from year to year. The number for 1880, which was 19,341, was not reached again, however, till 1884, in which year the number of births was 19,846, and up to the present moment this remains the record. For the last twenty-one years the births have been as exhibited in the following table:—

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Thus the average for the last five years is somewhat less

than that for the last twenty-one years; and during the whole of these twenty-one years the numbers of births in the several years did not vary from the average for the whole period by more than 5 per cent. in either direction. Further, for each of the six years 1882–87 the number of births exceeded 1,900; but this number has never since been attained, with the consequence that, at the last census, the number of children in the colony of ages 5–10 was actually less than that recorded at the previous census.

Effects of a Constant Annual Number of Births.

For some twenty years we have thus had a practically constant annual number of births, and in consequence, and by reason also of the growth of the population as a whole, a rapidly diminishing birth-rate. This is a phenomenon of the highest importance. If it continues it must bring about a practically stationary state of the whole population in a comparatively short period. At the time of the census of 1896 it had already brought about a practically stationary distribution of population of the ages 0–17, and at the present time the distribution of ages 0–20, must be stationary. The consequences have already begun to appear in the schools of the colony, the attendances at which rose continuously until 1898, but in that year the first falling-off in numbers was recorded. In the North Island the number of children attending school continues to increase, but this increase is counterbalanced by the decrease in the South Island, where the falling-off in school-attendance has led in many cases to the discharge of teachers.

So long as the annual number of births remains constant this stationary portion of the population will continue to spread; five years later the distribution of ages 0–25 will be stationary, and so on until the whole population is reduced to this state. A greater and greater portion of the population will fill up to the stationary level corresponding to the annual number of births and will there remain.

We have seen that an annual number of births equal to 20,000 will produce a population only of about 1,110,000, and if the annual number of births were not to reach 20,000 the total population could not even reach this number, except so far as it is aided by immigration; the annual increase would become less and less, and the total population would approach its limit more and more slowly, until at last the annual increase would not be worth taking into account.

Future Births in New Zealand.

What, then, are the chances that the state of things begun twenty years ago and continued to the present time may yet

continue for a period long enough to produce serious effects in the direction indicated ? This is a question to which no certain answer can be given; yet there are considerations worthy of attention in connection with this very important matter.

During the years 1881–96 the population of females at the reproductive ages increased from 96,139 to 158,201, or by 64.5 per cent. It has still further increased during the last four years; but the number of children born last year only just exceeded the number born in 1881, and was decidedly less than the number born in 1880. Moreover, the past few years have been years of exceptional prosperity, and the marriage-rate has been higher than for very many years; yet, though there had been a small steady increase in the annual number of births from 1892 to 1898, last year showed another falling-off, and the number for the year was over a thousand less than the record number of 1884. Thus, for some twenty years, in good times and in bad, the growth of the practice of rearing only small families has counteracted the tendency of the growth of the population to produce an increased number of births from year to year. This practice may have reached its full development or it may not. This question the future only can decide for us; but, if the practice continues for many years more to grow sufficiently to keep the annual number of births constant, the reproductive ages will be included in those having a stationary distribution, and will cease to increase in numbers. Then, no increase in the annual number of births can be expected except from a diminution in the practice of restricting births; and, unless this change takes place, it will only be a matter of time for the older ages to fill up in the same way, and for the whole population to become stationary.

Change of Age-distribution in New Zealand.

Not only when we compare the age-distribution for different countries, but when we compare the age-distribution of the population of the same country at different periods, we sometimes find a very great variability. The following table illustrates this for the case of New Zealand:—

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of the number of people at the marrying-ages has recently been so much more rapid than that of the people as a whole.

The other section of the people that has been increasing with special rapidity is that consisting of those of fifty-five years of age and over. This feature is of special importance, and we shall discuss it in particular in the next section.

The Increasing Proportion of Old People in New Zealand.

A glance down the percentage column of Table V. will reveal at once the extraordinary increase that took place between the last two censuses in the number of old people compared with the increase in the population as a whole. This disproportionate increase has been taking place for a very long time, for Table IV. shows that the percentage of old people has grown steadily from 0.63 in 1864 to 2.95 in 1896

It is a matter not only of deep interest, but of national importance, to inquire how rapid will be this increase, and how far it will extend in the future. To calculate the percentage at any future period, however, involves knowing the population at the time, and this involves some hypothesis as to what the number of births will be in future years. We shall, consequently, consider at present only the increase that may be expected in the actual number of old people, leaving the question of ratio to the whole population for consideration later on.

By means of life-tables we may predict, with all reasonable accuracy, how many persons out of any sufficiently large number at any given age will survive after any given number of years. Persons 100 years of age and over we may neglect. Let us, then, investigate what the number of old people in New Zealand may be expected to be at the time of the census of 1911. The persons that will be from sixty-five to ninety-nine years of age eleven years hence will be the survivors of those that were from fifty to eighty-four years of age at the last census (1896), neglecting, of course, the effect of immigration and emigration, which, even if it were to take place again on a fairly large scale, would but slightly affect this particular question.

The following table gives in the second column the number of persons alive at the census of 1896 at all ages from fifty to eighty-four, and in the fourth column the number of each of these that may be expected to survive in the year 1911:—

will be the survivors of the present population, but what ratio this population of old people will bear to the whole population depends on what the whole population will be. If, for instance, the annual number of births were 20,000, the total population would reach ultimately about 1,110,000, while of these no less than about 120,000, or 10.8 per cent., would be old people of sixty-five years or over. This represents a limiting case, useful for comparison, however, for, as the annual number of births tends towards a state of constancy, so will the distribution of the population tend towards the condition that would follow from a constant annual number of births. The general and continued fall of birth-rates renders it probable that in the near future many populations, including that of New Zealand, that have been very progressive hitherto will not differ greatly from this stationary state.

It may seem utterly improbable at first that a population can come into existence having such a large proportion of old people as 10.8 per cent., or almost four times the proportion there was in New Zealand at the time of the last census. It should be borne in mind, however, that the state of things which can produce this large proportion—namely, an approximately constant annual number of births—has hitherto only obtained in one country having reliable statistics. That country is France, and there already the proportion of old people reaches 8.1 per cent., although even in France the annual number of births has not been approximately constant for a length of time sufficient for the maximum effect to have been produced. Considering this actual example, and the fact that life is longer in New Zealand on the average than in France, the possibility I have pointed out may continue to astonish, but there can be no room left for incredulity.

Effect on Death-rate.

We have previously pointed out the dependence of the death-rate upon the age-distribution of the people, as well as upon the rates of mortality at the several ages. A great increase in the proportion of old people, amongst whom the death-rate is many times the general death-rate, must tend to increase that general rate. But, on the other hand, a decrease in the proportion of children in the first two years of age tends to diminish the general death-rate, for the mortality amongst young children is very great. Further, the increase in the proportion of old people will not have a very great influence in affecting the death-rate so long as that proportion is still small. Consequently, we find that until comparatively

recently the death-rate of New Zealand had no permanent tendency to increase, and was even very much less in 1896, when it was 9–10 per thousand, than in 1891, when it was 10.35. Since 1896, however, the increase has been substantial and steady, the death-rates for the years 1896–99 being 9–10, 9–14, 9.84, and 10–24 respectively.

The proportion of old people, in fact, has now reached a magnitude which makes the number of deaths of old people bear a very substantial ratio to the total number of deaths, and consequently the increase in the proportion of old people in the population will have a considerable influence, by reason of the corresponding increase in the number of deaths of old people, in affecting both the total annual number of deaths and the death-rate. This is illustrated by the following table, giving the annual number of deaths of people over sixty years of age, the total number of deaths, and the percentage the former are of the latter for the years 1896–99:—

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We may thus expect the death-rate to increase in the future to a figure considerably greater than that at which it stands at present.

Increase of Population of New Zealand.

Increase of population is due to two causes, excess of births over deaths and excess of immigration over emigration.

Now, the excess of births over deaths in New Zealand reached its maximum in 1884, while for 1899 the excess was not as great as it was in 1876—i.e., twenty-four years ago.

The following table gives the excess of births over deaths for the last twenty-four years:—

it is not part of my present plan, but it is important to observe that the nature of both is such as to leave us no hope for its diminution in the future, whereas there is no necessary limit to its growth short of the disappearance of the family, though the love of parenthood instinctive in the race gives us a moral guarantee that the child will not altogether disappear from the home. The child, however, may still be with us and yet not in numbers sufficient to increase or even to keep up the population; and, whatever will be the limit ultimately reached in this or in any other country, the steady unchecked fall of birth-rates makes it appear unlikely that in the course of a few years the practice of restricting families will fall very far short of the limit required to produce a stationary state.

That this prospect is of vast moment all will allow, but that it is to be regretted all will not agree. Many will, from religious motives, refuse to grant the possibility of good arising from a condition of things consequent on what may appear a vice; but there is no escaping the fact that a voluntary stoppage of increase of population is the only thing that can prevent the same effect being brought about ultimately by misery, hardship, and disease. True, we might increase and multiply much further yet, in this part of the world at least, with no risk of consequent suffering; but it happens that the very populations to whom increase might even be beneficial are the very ones that have most conspicuously adopted the practice that must make future increase slow indeed, when in a few years, by reason of the changed agedistribution of the people, the death-rate has risen to a higher and more permanent level.

It will indeed be remarkable if, in these parts of the world, the future shows that we are already near the time when governments, colonial and municipal, may cease to allow for future increases of requirements, and the unearned increment will cease to annoy financial reformers.

Old-age Pensions.

We have seen that the population of sixty-five years of age and over, and therefore qualified in respect to age for the receipt of old-age pensions, will reach by 1911 a total of about 43;737. If the number of old-age pensioners and the cost of the pensions increase proportionally with the number of old people, the rate of increase in the cost of old-age pensions will be altogether out of proportion to the rate of increase of the population, and consequently, under normal circumstances, to the rate of increase of the resources of the country. How far this disproportionate increase may extend has already been pointed out. If New Zealand had permanently

about £400,000 per annum, or double what it is costing at present, while the resources of the colony are not likely to be very much greater than they are to-day. But in any case the cost of the scheme must continue to grow rapidly, and far more rapidly than the population; it is because of the small proportion of old people that it is at present as small as it is.

Though I have brought forward this reflection on the old-age-pension scheme, I would not be understood to be arguing in any way against the principle of the scheme; but it is right that its probable future cost as well as its present cost should be known. When the scheme was introduced an estimate of the growth of the cost of the scheme for at least a generation to come should have been made, so that the people of the colony might have known what was involved in the future as well as the present, and not have acted on the rough assumption that the cost of the scheme would increase only in proportion to the population and its resources. Yet there is a chance of the community being able to bear the greater cost of the future as easily as it bears the present cost, for, with a smaller proportion dependent on it by reason of immature age, it would be well able to maintain the provision recently made for a greater number of those dependent on it by reason of old age. Whether it should do so in a manner such as to discourage thrift even on the smallest scale is the question of most importance perhaps in connection with the scheme, but one of a character not falling within the province of this paper.

Other Consequences of Change of Age-distribution.

The changes in age-distribution that are taking place in New Zealand and elsewhere, and the causes contributing thereto, are full of interest in connection with many other matters of very practical import.

The prospects of insurance companies must interest most of us. Now, insurance companies as a whole have hitherto enjoyed, especially in these parts, receipts from premiums greatly in excess of the outgoing payments due to deaths and maturing of policies, and this has resulted in a rapid accumulation of funds and the establishment of vast capitals. This is due to the great convergency in the age-distribution of those assured, the younger section of those assured being much more numerous in proportion than the older section, and this is, as in the case of the general population, due to continued growth. Unless this growth can be kept up, unless companies can continue to obtain, year after year, a greater volume of new business, the inequalities in receipts and payments on account of members must get less and less. It is not remarkable, then, that so many companies should