applications and extensions of the karmel formula for reproductivity : i. introduction: ii....

APPLICATIONS AND EXTENSIONS O F THE KARMEL FORMULA FOR REPRODUCTIVITY

I. Introduction. 11. Application t o Queensland.

111. Application to New Zealand.

I Vital Statisticians for many years were content to compare

births only with the size of the population and to obtain figures of birth rates (now designated “crude” birth rates). Gradually this gave place to the slightly more refined concept of a “fertility rate” obtained by comparing the number of births with the number of women of reproductive age. Then, about twenty years ago, came the greatly improved method of measuring reproductivity by gross and net reproduction rates (as a result of the work of R. R. Kuczynski, Dublin, and Lotka). The revolutionary new method of measuring reproductivities which Xr. Kame1 proposed in the June 1944 Ecmomic Record, may prove eventually to be as greatly in advance of the method of gross and net reproduction rates, as that method was in advance of its crude predecessor.

The “fertility rate” was introduced because it was realized that the crnde birth rate might be insufficient for comparing different populations or periods, because the populations con- cerned might contain varying proportions of women aged 15 to 45. The formula for gross and net reproduction rates goes a stage further. It takes into account the possibility that within this age group women may be very abnormally distributed by age. A population, for instance, may contain an unusually high proportion of women aged 20 to 29, which has the effect of raising the number of births. The formula, therefore, calculates the specific fertility of women at each year of age (or in five- year age groups). By adding together these specific fertilities we obtain a gross reproduction rate from which all distortions due to abnormal age distribution of the population have been removed. An allowance for the proportion of children who will probably not survive to maturity gives us the net reproduction rate.

At each stage the result is refined a little more, but there is a further refinement to come. The fertility of a woman

23

24 THE ECONOMIC RECORD J U N E

depends not only upon her age, but upon whether she is married or not and the duration of her marriage. The first few years of married life are the most fertile. Thus the fertility of a normally fertile age group, say 25-29, may be temporarily but seriously reduced if, because of economic depression or similar cause, many marriages are postponed. Conversely, when the years come when these postponements are caught up, or when marriages are accelerated (as they have been during recent years), these causes exert a strong upward influence on the gross and net reproduction rates.

If our measurements of the rate of reproduction are to be purged of such purely temporary influences, a further improve- ment will have been effected. This is what Mr. Karmel’s method has done. Ignoring age, he uses birth statistics to determine the specific fertility of women for each year of duration of marriage. By adding these specific fertilities together he obtains the number of children born from a typical marriage.

The estension now suggested to Mr. Karmel’s formula is one which he himself discussed, namely an allowance for the effect of age at marriage During a period such as he was investigating, in which there was little change in the average age of marriage, this factor can be ignored. But in the longer period, and probably from now onwards, it may be of considerable importance. As will be seen below, the woman who marries young has, on the average, a much larger family than the woman who marries a t a higher age. This is in part because the younger woman has a longer period in front of her in which reproduction is possible, but it is by no means the sole reason. Physiological fertility1 and probably also the willingness to have children are both higher when young. The method adopted in

1. A table in the English Registrar-General‘s Report for 1939 bring8 thia out very clearly. Women marrying at higher ages. and mostly presumably wanting children. a re often unable to bear them. This factor a p p e ~ n to operate from a s early an ago a s 26. Advanced age of the husband is also a contributory factor in infertility.

PERCENTAGE O F WOMEN DYING CHILDLESS-1939 England and W d e s

Husband‘s Age a t Marriage Wife’s Age a t M a m a g e -

Under 25 I 25-44 1 46-64

Under 20 20-24 25-29

3 5 3 9 ao.a4

1 3.0 I 4.9 I - 6.9 8.7 -

28.8 1 1 1 37.6 22.8 38.0 42.6

Unfortunately, the table does not mean exactly what i t appears to mean. because, in the case of second marriages. particulars a re recorded for the last and not the Rmt marriage. A considerable propartion of the women shown as marrying at the age of 36-39. for instance. p r e widow re-marrying. with childen by a previous mnrriaac. Women who marry for the flrst time a t that nge would probnbly show a n even higher Proportion of childlessness.

1946 FORMULA FOR REPRODUCTIVITY 25

the calculations below, therefore, is to work out the Karmel formula separately for women married at the ages of 15-19, 20-24, 25-29, 30-34 and 35-39.

In order to determine whether the fertilities thus shown are s a c i e n t to maintain or increase population in the long run, these separate marriage fertilities can be combined in ratios determined either by the usual proportion of women marrying within each age group, or by the proportions prevailing in any particular period, such as the present wartime period, when there has been an acceleration of marriage. The resulting reproduction rate indicates the reproductivity of the population had the assumed proportions been constant for the last generation.

The Authors would like to express their gratitude to Mr. S. E. Solomon for invaluable advice throughout the prepara- tion of this paper, and for some suggestions which cleared u p difficulties which had appeared insoluble.

The data to which the Karmel formula is applied below are as follows:

(1) Queensland. Hitherto unpublished data obtained from punched cards of vital statistics beginning 1938 (with earlier data for marriages).

(2) New Zealand. Tables of Live Legitimate Births classified by age of mother and duration of marriage, from published vital statistics, for years from 1926 onwards, with earlier data for marriages.

I1 Legitimate births registered in the years 1938-1944 inclusive

in Queensland were classified according to the calendar year of the marriage of the mothers. This enabled marriage fertilities to be calculated directly from the marriage statistics of each calendar year. The results are shown in Table 1.2

The figure of 2,522 for 1938 is 3 per cent. higher than the fignre of 2,447 for the same year obtained by a separate calcu- lation using Mr. Karmel’s method, that is, the classification of births by duration of marriage and the redistribution of marriages to calculated durations.

In order to make’further refinement in the calculations to take account o f age a t marriage, the machine cards recording data for legitimate births registered in 1939 and 1944 were sorted to give a classification by age of mother a t marriage and calendar year of marriage.

2. For Tab!- I-V see end of Section 11 ( DF. 90-34).


By dividing each figure by the number of marriages recorded in each year for each quinquennial age group, a series of marriage fertilities was obtained as in Tables I1 and 111.

Having a marriage fertility rate for each quinquennial age group, it now becomes possible to test what the general marriage fertility (for all ages) would have been if the present (or any other) marriage habits had been consistently customary over the last thirty years, and the population had been stationary.

Starting with an assumed stationary population with 1,000 births per annum, we fhd that on Queensland experience 487 births per annum would be females. We then calculate from the Australian Life Tables 1932-4 the survivors in each quinquennial age group in the reproductive period of 487 female births per annum (Table IV, column 2). Columns 3, 4 and 5 of that table showing the percentage of women in each age group who are married or have been married are based on 1936 data. In order to find the total percentage who marry during each quinquennium it is necessary to interpolate to get figures f o r the end of each age group rather than a t the mid-point. Column 6 is the result of such interpolation of the figures in column 5. This shows what may be called the “normal” percentages of women who have married by the time they reach the end of each age group.

Column 7, derived from Conjugal Condition Tables based on 1941 figures, instead of the peace-time experience of 1938, shows the “war-time” percentages as opposed t o the “normal” figures. Column 8 is a similar set based on Australian 1933 or “normal” rates.

Columns 9, 10 and 11 differ from columns 6, 7 and 8 respectively in that they show the percentages of women who marry for the first time within each age group rather than the percentages who are married by the time they reach the end of each age group. Allowance is made for re-marriages by adding to the figures in columns 9, 10 and 11 respectively, the percentages shown in column 12. Applying these combined percentages to the number of women in column 2, we get the number of women in a stationary population who marry a t each age assuming that they follow :

(1) Queensland “normal” marriage habits (column 13). (2) Queensland “war-time ” marriage habits (column 14). (3) Australian “normal” marriage habits (column 15). By using these figures as weights and applying them to

the marriage fertility for each age group a t marriage, we obtain


a figure representing the number of births expected from the stationary population within each five years, if the three assump- tions above were applicable to all marriages in the last thirty years. Dividing by five, we get the number of births expected in a single year from such a stationary population. If the figure is exactly 1,000, one generation is just replacing itself, since the stationary population is based on 1,000 births per annum. This figure, then, is a net reproduction rate. Table V shows that 1944 reproduction is slightly lower than the 1939 rate, if the same marriage rate be assumed in each case, but 1944

war-time” rates show a higher reproductivity than the 1939 “normal” rates.

Table VI shows the marriage fertility averaged for a11 marriages :

1 1

( i ) as actually shown in Tables I1 and 111; (ii) as obtained by weighting the marriage fertility a t each

age by the percentage marrying in that age group.

TABLE VI Marriage Fertility per 1,000 marriages

1939 1944 Actual (Tables I1 and 111) .. 2,601 2,580 Assuming Queensland “normal ”

rates of marriage over the last thirty years . . . . . . . . 2,515 2,487

Assuming Queensland ‘ war- time” rates of marriage over the last thirty years . . . . . . 2,690 2,658

Assuming Australian “normal ” rates of marriage over the last thirty years . . . . . . . . 2,493 2,468

In order to make comparisons of total fertility it is necessary to allow for illegitimate births. This may be done briefly by increasing the factors already obtained in the same ratio as total births bear to legitimate births. The ratio for each year is shown below:

1938 . . . . . . . . . . . . . . 1.051 1939 . . . . . . . . . . . . . . . 1.052 1940 . . . . . . . . . . . . . . 1,049 1941 . . . . . . . . . . . . . . 1.052 1942 . . . . . . . . . . . . . . 1.050 19.13 . . . . . . . . . . . . . . 1.070 1944 . . . . . . . . . . . . . . 1.077

28 THE ECONOMIC RECORD JUNE

Year of Blrtb

1938 1939 1940 1941 1942 1943 1944

Children Born in Wedlock All Chlldren

(including 4 ~ e a n of 4 Yean of Lerptirnate lue@timte) Mamage Mamage Clulhn

*I04 .987 1.535 2-522 2.626 a 1 1 1 1.043 1.558 2.601 2.712 -093 1.003 1.513 2.516 2.609 -107 1.004 1-622 2.526 2.833 .085 .903 1.525 2.428 2.513 *I52 -918 1.665 2.483 2.635 -152 .882 1.698 2.580 2.732

Illegitimate Chlldren In Fuat After Fuat Total

Making these adjustments we have the following comparisons :

TABLE VII Net Reproduction Rates

From Marriage Fertility Data (Table V) (a) Assuming Queensland ‘ ‘ normal ”

(b) h s u m i n g Queensland “war-time”

(c) Assuming Australian “normal”

1939 1944

marriage rates . . . . . . . . . . . . 1,153 1,167

marriage rates . . . . . . . . . . . . 1,239 1,254

marriage rates . . . . . . . . . . . . 1,120 1,135 B y Kuczynski’s method . . . . . . . . . . . . 1,161 1,319

A study of Table I shows that births to marriages of less than four years’ duration have declined during the war years. The following dissection brings this out more clearly. It also makes allowance for illegitimate births in arriving at total fertility. The number of illegitimate children per marriage in each year is based on the number of marriages in that year, on the grounds that a large proportion of illegitimate births are fol- lowed by the marriage of the parents. The rise in illegitimacy in the last two years is probably due to war service increasing the period between extra-marital conceptions and subsequent marriages.

TABLE VIII Number of Children per Average Marriage-Queensland

The decline in the figure for the first four years of marriage is to be explained by the large number of war-time marriages and consequent separations due to war-service, etc. ; the number of servicemen’s wives engaged in industry; and the lack of adequate housing. However, the increase in the numbers born


after the first four years of marriage appears to be quite genuine. It might first be thought that this increase is due to delayed first births to parents who have been separated by the war, but this is not so. Only the small normal proportion of first births is included in this figure, Morever, the weighted average interval between marriage and first birth increased by only 2 . 1 months between 1938 and 1942 on Australian figures while the Queensland figure for 1944 is only 2 . 4 months greater than the Australian figure for 1938.

Assuming that, if it had not been for the war, there would have been a similar increase in births within the first four years of marriage (and, also, that illegitimacy had remained stationary at its 1938 proportion), then the figures showing the average number of children per marriage would have been:

1938 . . . . . . . . . . . . . . 2.626 1942 . . . . . . . . . . . . . . 2.525 1943 . . . . . . . . . . . . . . 2.676 1944 . . . . . . . . . . . . . . 2.894

To calculate a net reproduction rate from these figures, it is necessary to know the number of children necessary to pro- vide for the bare maintenance of population. From Trlble IV, which is calculated on the basis of a stationary population of 1,000 births per annum, it appears (by summing the figures in column 13) that such a population will result in 2,179 marriages in each quinquennium at “normal” marriage rates, or 435.8 per annum. If these 435.8 marriages produced eventually 2.295 b i r t h each, they would have produced a total of 1,000 births and their generation would have exactly reproduced itself. The number of children per marriage necessary barely to maintain the population is then 2.295. If we assume a con- tinuance of “wartime” ages of marriage, a slightly lower figure will suffice.

If this figure is divided into the figures.above o f the total number of children per marriage we can obtain a net reproduction rate for each year as under. For comparison, figures obtained by the Kuczynski method are also shown.

It will be noted that this method gives practically the same results with “normal” marriage rates, as does the Kuczynski formula in the years 1938-1941. However, the Kuczynski formula assumes, in effect, no violent disturbances from year to year in the number of marriages of the female population of reproductive age, and takes no account of the fact that from 194.2 onwards the population has contained an abnormally high

30

2.626 2.712 2.609 2.633

THE ECONOMIC RECORD

1.144 1.091 1.182 1.161 1.137 1.148 1,147 1.192

J U N E

Net Reproduction Rate

I I 1 I

Total Number of Childnn per Marriage

Y m

-- 1938 1939 I940 1941

1942 1943 1944

With Adjustments Asin toButhswithin C+mnZ Column3 By Kuczynsld

Table VIII 1 F%;z:y 1 -2.285 I - 2296 1 Formula

2.513 2.535 1.095 2.635 I ::?(:: 1 1.148 2.732 1.190

1.100 1.166 1.261

1.160 1.249 1.319

TABLE I Births per 1,000 Marria,ges-Queensland

Year of Birth WendarYear

& 2 n T e a r of BLth

n -

n- 1 n- 2 n- 3 n- 4 n- 5 n- 6 n- 7 n- 8 n- 9 n- 10 n-11 n- 12 n- 13 n-14 n- 15 n- 16 n- 17 n- 18 n- 19 n - 20 n- 21 n - 22 n-23 n-24 n-25 11-26 n-27 n-28 n-29 n-30

- 1938

~

1939

150 392 259 242 200 182 180 154 138 117 99 80 67 56 54 46 38 31 30 21 22 16 10 6 5 3 1 1 1

-

- -

- 1943

85 343 250 240 211 189 167 142 120 108 105 87 80 75 61 46 37 30 28 22 17 11 8 6 6 4 2 2 1 1

-

-

1941 1B42 1944

157 377 240 213 195 195 187 152 133 112 91 77 63 62 52 45 36 33 26 28 21 15 12 9 6 3 2 1 1 - I -

138 374 247 244 209 169 154 152 128 116 99 83 67 56 49 45 39 33 25 21 17 16 12 8 5 4 2 1 1 - -

133 376 246 219 214 191 150 136 134 112 101 90 73 58 48 42 38 32 26 19 14 12 10 8 5 4 3 2 1' - -

73 349 243 238 212 182 154 130 118 116 98 88 84 68 53 43 34 33 26 21 16 14 11 10 7 4 2 2 1 - -

78 346 229 229 215 199 170 156 139 119 106 103 ' 85 78 72 58 44 34 29 26 20 15 10 7 5 3 2 1 1 1 -

Total .. 2,522 l- - 1,601 -

1,516 -

!,5?6 -

1,428 -

!,483 -

'.580 -


proportion of married women, and in particular an abnormally high proportion of newly-married women who were still i n the most fertile period of their marriages. For this reason this formula gave an exaggerated index of fertility. The marriage fertility formula where the greater number of births was related to the greater number of married women, and to the greater number of marriages of short duration, gave a more realistic result.

TABLE I1 Marriage Fertility Rates in Each Quinquennial Age Group

Based on Births Registered in 1939-QueensZand Illegitimate Births Excluded-Multiple Births Included

Wendar Year of

Marriage

1939 1938 1937 I936 1935

1934 1933 1932 1931 1930

1929 1928 1927 I926 1935

1924 1923 1922 1931 1920

1919 1918 1917 1916 1915

1914 1913 1912 1911 1910

Total

19 and Under

290 528 323 311 290

297 227 210 195 190

150 136 133 101 98

102 79 84 71 56

57 60 35 34 16

11 17 7 7 4

L. 122

-

-

3&24

155 435 280 270 210

217 183 154 138 120

110 78 81 67 61

61 48 44. 34 33

29 19 10 8 2

1 1

-

-

- !,848 -

B h t h per 1,ooO Marriages at Age at Marriage

%29

100 353 249 238 198

191 176 142 120 106

103 70 65 44 35

16 11 10 8 8

3 2

1

-

-

- !,248 -

90 290 252 172 139

164 101 103

66 31

37 19 18 4

11

4

73 200 105 71 54

64 33 21 14

-- ,501 1 635

4 0 4 4

29 97 42 32

6

15 8

-

- 229

45 and O v a -

8 10

18 -

u1 A g e

150 392 259 242 200

182 180 154 138 117

99 80 67 56 64

46 38 31 30 21

20 16 10 6 5

3 1 1 1

!,601 -


TABLE I11 Marriage Fertility Rates in Each Quinquennial Age Group

Based on All Legitimate Births Registered in 1944-Queensland

CallXldar Year of Marriage

1944 1943 1942 1941 1940

1939 1938 1937 1936 1935

1934 1933 1932 1931 1930

1929 I928 1927 1926 1925

1924 1923 1922 1921 1920

1919 1918 1917 1916 1915

Total

- 19 and Under

140 490 278 275 281

248 213 200 174 159

153 135 108 148 123

112 96 80 76 67

68 54 65 27 21

24 8 7 6 7

3,832 - -

76 364 250 252 236

217 186 176 160 150

129 117 98 89 77

69 58 46 36 30

25 18 9 7 4

2 2 - - 1

2,884 -

- 25-29

53 316 224 228 211

200 183 153 135 123

92 88 64 62 43

33 20 16 5 2

3 1

--

Age of Mother at Marriage

2,244 -

- 30-34

52 265 186 200 177

166 119 101 85 48

39 30 23 11 7

4 4

2

1,519 -

- 35-3s

60 208 126 97 93

63 27 38 32 7

7 5

6

- 768

- 4&44

21 70 23 22 10

6

L_

- -

6

- 158

- 45 and Over - - 6

- 6 -

- - 78 346 229 229 215

199 170 156 139 119

106 103 85 78 72

68 44 34 29 26

20 15 10 7 5

3 2 1 1 1

1,580 - -

.. ..

..

Z.1

P,t

8.8

9.12

9.96

0.9

1

"'0

E*L

8

0.98

9.P8

E.08

O*P

9

E.LI

2.18

0.9

8

9.18

8.ZL

E.19

0.91:

8.9 I8

9.6 18

0.2

9L

L.0

E9

2.0 PE

v - --

1Z"Z

691'Z

90Z'Z

BEZ'Z

292'Z

188'7; -

Irp-oP

8E-9E

VEQE

82-92

PZQZ

81-91


I11 Calculations for New Zealand were based for each year on

a table in the Annual Report on Vital Statistics entitled “Living Legitimate Births-Duration of Marriage and Age of Mother. ” The durations given as 0, 1, 2, 3 . . . years, were taken on the average to be f, 14, 24, 33 . . . years, and these durations sub- tracted from the given age of the mothers at the birth of the children gave the average age of the mothers a t marriage in each case. Similarly, the date of marriage was calculated by subtracting the durations f , If, 2&, 34 . . . years, from the mid- point of the year for which the table was constructed, i.e., for instance, births in 1941 of “0 years” duration were assumed to come from marriages in the six months on either side of December, 1940, i.e., marriages in 1940-41. Similarly, births in 1941, of “1 year’s” duration were taken to come from marriages in 1939-40, and so on. This treatment, it will .be seen, was less refined than Mr. Karmel’s.

The original table was then marked off into sections corres- ponding to quinquennial age groups of the mothers at marriage. For each quinquennial age group, a table was constructed showing duration of marriage horizontally and date of marriage (in financial years) vertically. The entries from the original Vital

TAEILE X New Zealand Marriage Fertilities by Age Groups at Marriage

( B a e d on Living Legitimate Births)

Year

1936

1928 1939 1930 1931

1933 1934 1935 1936 1937

1938 1939 1940 1941

15-18

3.935

3.710 3.559 3.636 3.828

3.384 3.433 3.280 3.316 3.264

3.359 3.280 3.583 3.606

Age Gmup of Mothen a t Marriage

20-24

3.112

2.970 2.898 2.881 2.814

2.645 2.650 2.525 2.495 2.496

2.541 2.618 2.794 2.839

25-29

2.669

2.568 2.469 2.408 2.360

2.166 2.067 2.024 2.042 2.041

2.046 2.105 2.223 2.419

30-34

1.963

1.780 1.705 1.711 1.693

1.440 1.402 1.348 1.380 1.418

1.413 1.426 1.522 1.659

35-39

.871

~ 7 0 5 .760 .73? .7?3

-713 .659 -636 -59.4 -695

.648 -666 .624 .640

4 M 4

a181

,176 .158 *I96 .135

.128 *I08 -158 .135 . I 2 0

. I11 ,159 .126 -149


Statistics Table for any one year appeared in this new table as a diagonal line. The figures for births to marriages of any given date were then divided by the total number of marriages in that financial year within the particular age group under consideration. The quotient was a specific fertility rate for marriages in each year based on births in the year of the original Vital Statistics Table. The sum of these specific fertilities gave the total fertility (or total number of children espected) throughout the whole duration of marriage of the average woman who married within the age group under consideration. This method was repeated for each of the age groups between the ages of 15 and 44.

The whole process was performed for original Vital Statis- tics Tables fo r the years 1926-1941, with the exception of 1927 and 1932 for which years figures did not happen to be available.

The resulting marriage fertilities are shown below in Table X.

In order to convert these figures into comparative net reproduction rates, it was necessary to find the relative distribution of marriages according to the quinquennial age grouping of brides :

(a) under normal conditions; and (b) under war-time conditions.

This was done on lines which are fully explained in the Queens- land section of the text referring to Table IV. In a stationary population of 1,000 births, 485 would be female births. Using New Zealand life-tables, it is calculated that a stationary population of 485 female births per annum would show the following age distribution of females:

Age G r w p Population 15-19 . . . . . . . . . . . . . . 2,290 20-24 . . . . . . . . . . . . . . 2,268 25-29 . . . . . . . . . . . . . . 2,242

30-34 . . . . . . . . . . . . . . 2,205 35-39 . . . . . . . . . . . . . . 2,165 40-44 . . . . . . . . . . . . . . 2,124

Applying to these figures the prevailing marriage rates, wc find that we may expect the following number of marriages in each quinquennium :

1946 FORMULA FOR REPRODUCTIVITY

1926

1928 1929 1930 1931

1933 1934 1935 1936 1937

1938 1939 1940 1941

TABLE XI

1.139 1.189

1.080 1.129 1.047 1 095 1.042 1.091 1.028 1.080

-948 -997 -938 .991 - 901 . 960 -900 * B47 *go1 .947

*913 ~962 -931 *980 a993 1-046

1 * 029 1.077

37

Age Group

15-19 20-24 25-29 30-34 3&39 4044

~~

Total Marriages in Five Years

At "Nmmal" R a t a

252 890 615 238 98 46

.Of MaITbgO

2.038

At "War-the" R a t a af muriage

298 1,073 399 146 82 46

2,043

Weighting the marriage fertilities of Table X by these relative numbers of marriages a t each age group, apd dividing by 5 to reduce the fi,oues from a quinquennial to an annual basis, we get the total number of children a stationary population of 1,000 births per annum would produce if the fertility rates of each year remained constant far a generation. Hence, by dividing the total number of children by 1,000 we get a net reproduction rate appropriate to each of the two rates of marriage. (Table XII.)

TABLE XI1 New Zealand N e t Reproduction Rates

( B a e d an Marriage Fertilities)


1.221

1.150 1.113 1.111 1.093

1.006 -99% * 953 -952 -955

-964 .979 1.045 1.081

obtain results showing total fertility, these births should be included. The net reproduction rates above are then increased:

(a) in the proportion which all live legitimate births bear

(b) in the proportion which all live births bear to births to births shown in the table; and

shown in the table. The results are shown in Table XI11 below.

1.209

1.141 1.106 1.104 1.092

1.008 1.002 -961 -956 .957

-973 -990 1.057 1.090

YUr

1926

1928 1929 1930 1931

I933 1934 1935 1936 1937

1938 1939 1940 1941

TABLE XI11 New Zealand N e t Reproduction Rates

(Baed on Marriage Fertilities)

Assuming Normal Marriage Ratu I Assuming War-time Myriage Ratn

la) Adjusted to

Cover all Live Le ‘timate

f L h s

1-158

1.091 1-058 1.055 1.040

-958 .949 -912 909 -911

* 923 -941 1.004 1.041

Cover all Live (i.a. including Illegitimate)

(b) Adjusted ta Cover

all Live B k t b (i.e.. induding Illegitimate)

1.275

1.202 1.164 1.164 1.149

1.057 1.052 1-005 1.001 1.004

1.016 1.031 1.100 1.131

New Zealand peace-time rates of marriage are such that a stationary population with 1,000 births per annum would only produce 2,038 marriages in five years or 407.6 .per year, so that each marriage would have to produce 2.453 children to maintain a stationary population. Queensland peace-time rates of marriage yield 2,179 marriages per five years of such a population, i.e., only 2.295 children per marriage are needed to maintain a stationary population.

In other words, part of the difference between Queensland and New Zealand reproduction rates & explained by earlier marriage in Queensland, rather than by higher marital fertility.

The New Zealand figures in Table XI11 can be espressed as marriage fertilities (weighted according to peace-time or


war-time ages of marriage respectively) by multiplying by 2.453 in the case of the first two columns, or 2.447 in the case of the two latter columns.

The difference between New Zealand and Queensland marriage rates is to be explained by the greater percentage of unmarried women in N.Z. In New Zealand in 1936 72.1 per cent. of the women in the age group 20-24 were single, as against only 67.3 per cent. in Queensland in 1933. This difference persisted, on a diminishing scale, through all the higher ages. This in turn may be attributed to the higher degree of mascu- linity in Queensland as shown in Table XIV below. Age groups down to 10-15 are shown since this par t of the population in 1933 has grown into the reproductive ages by now.

TABLE XIV killscztlinity Rates

~

Age Croup

10-15 15-19 20-24 25-29 30-34 3 6 3 9 40-44

Total Population

Qukolland Cauw, 1933

104-6 103.8 110-2 116.9 113.7 106-6 113-7

110.4

New zulaad Census, lOaa

104.2 103.8 102.7 104.0 104.8 99.3 91.4

102.9 I I

COLIN C U R X R. E. DYNE.

Brisbane.

applications and extensions of the karmel formula for reproductivity : i. introduction: ii....

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