Cohort Analysis of Fertility in England and Wales, 1939-50

Brit. J. soc. Med.

(1952),

6,226-244

COHORT ANALYSIS OF FERTILITY IN ENGLAND

AND WALES, BY

1939-50

WALLIS TAYLOR of Medical

Department

Statistics,

and Central

of Birmingham,

University

Is the elimination

(1) Introduction The

to social

relevance

... in the changes little amplifica

of

medicine

as

to interpret a view rate with

of hospital

and on

depends

the

Though in

e.g.

ancillary current the is of

issue

for

demand

the

to

relevance

special

if we reflect upon services

welfare Since mean

of

the National

before,

and

during,

a falling rate birth a decline in primiparae

interpret

medical costing steadiness the

of

rates

accurate

made

services.

the

under

different

Dispute

was

the

and

the

assumptions then about

1939-45

effect

of

war,

This

than

in

about method. Since 1939, the rapid fluctuation of the rates (Fig. 1) has made prognostication without

fruitless

recourse

The need for new methods paper

out

sets

one

such,

to more

refined

cohort

new

in this context although previously employed in medical research (vide infra). This method is then used to analyse recent fertility in England and Wales

and

In one

to estimate of

the very

its significance few

recent

for replacement. analyses

applicable to England and Wales, asks the following questions:

of

Hajnal

be

current

of of

reversal

immediate

the

to demon

adequate

falling fertility and its immediate

age-composition

the population.

the pre-war

post-war work earlier

trend during has en years on the social

rates

to a reason in part adumbrated of composite The credentials

is due remarks.

of fertility

indices

analysis.

method,

idea

earlier

tion

is imperative; and this the

may

the idea that couraged determine has little relevance which fertility agencies to present that forecasts and conditions, suggested of events the inter-war during period by the course are invalid.

arithmetic. rather

the

temporary the war and

reproduction of future births

assumptions

on

A

net

forecasting a matter

rates

fertility

were

demographers

strate consistently

is to be a basis for

Before gross

"full

viz.: What relevance persons, scene have the demographic in the inter-war when period,

contemporary undertaken

other

and

does

and size of family if the outcome

the such

themethods exploited by R. Kuczynski, Enid Charles,

Service,

not necessarily of all parities (which to it is essential occupy beds), hospital a changing rate in terms birth of parities

mainly

of

imply a doubt widely

questions

well-informed

studies

birth.

after

Is

do?

can reveal

development

HajnaFs

and child

the cost of maternity

to marriage

due can

explanation, to rates are due fertility . . . etc.? allowances",

increased

smooth

among to the

spheres, it has

services, Health

of the complications

demographic analysis to resort to "sociological"

expected.

maternities.

in other

importance educational

of Birmingham

that

stage that the

and

the

number

City

no regularity under rates as large as in fertility it would those which have recently occurred, very provide discussion of population trends. little basis for a reasoned assumes that a reasonably For all such discussion orderly

recent changes rapid to appropriate provision the need for which services,

seeks

Office,

employment", "family If demographic analysis fluctuations lying irregular

"old be commonplace. entitled viously age" would is so low in the middle Since mortality age ranges, on of end communication focuses the other this in the birth

all

next

of a community needs age-structure A communication tion. 1951) previous (Taylor, demonstrated of adequate the importance provision to a level pre for a community in which survival

life and

Statistical

such

rapidly-changing

as the gross and net reproduc in a static situation;

a relatively

presume

situation

the picture they disclose

For misleading. highly incentive and imposed powerful rise of in a sudden result may may

be

followed which

by a spectacular

fertility*

does

not

instance, to earlier such

rates

a newly marriage shortly

fall during a period

materially

in

change.

* the term "fertility" is used, as this communication Throughout all demographers use it, to indicate the current rate of producing progeny. Biologists use the term with emphasis on the ability to produce progeny, a concept for which demographers use the term "fecundity".

fertility

(1947) 226

COHORT ANALYSIS OF FERTILITY IN ENGLAND AND WALES, 1939-50 r22-5

227

A

i

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ill 1875

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Fig. It

is the writer's

aim

i 90

*85

\\\

to

1.?Fertility

show

that

i '05

and marriage

smooth

and

are

Contrary past, we

apparent more to many see

shall

in England

to analytical methods by recourse intricate than previously required. in the recent opinions expressed that

and Wales,

replacement and that

is not a

happening further decline

in fertility is indicated. Such is the cohort method.* The earliest publications illustrating cohort analysis seem

to

McKinlay

be

those

of

Kermack,

(1934) on mortality

McKendrick,

i 'IO

i '15

and

rates, and of Barclay

* This is, of course, analogous to a Family Census, and en passant it is perhaps advisable to detail the reasons for not using the Family on Population. Census conducted by the Royal Commission The the birth boom. first is that the Census took place in 1946?before It is not possible to continue the analysis. The second is that the published volume (1950) has tables for Great Britain not split for age and parity. It is impossible to understand the situation without a complete analysis. The third is that the marriage populations used seem to be erroneous. Fourthly, the Census (a sample census) was voluntary, and of course excluded all data for mothers who had died before the Census date.

are of

the

background then available. was

Registrar-General of births down of application not available. prepared uses but index

on

(1937-8)

contributions

against material

of

first

by maternal the cohort Karmel

material it

l '35

| *30

l *40

l *45

l I95C

fertility;

but

these

1868-1951.

and Kermack pioneer

i '.

\

i 1925

i '20

rates, England and Wales,

trends

did exist in the disturbed period from 1939 to 1949, necessarily

\N-f-^\A

'. ! ,-/ W/\ \

i 1900

i '95

/V

J!

\

YEAR AVERAGE

'80

A REPRODUCTION RATES /

\ GROSS

O-SJ

\

YEARLYFIGURES

ii

YEAR

.

l-O-,-r^r-,-r^M-r

5

20.-FIVE

\

13'

to

current

In the U.S.A.

the

more

creditable

of source inadequacies Until when the 1939, a break to publish able

age, method

for data requisite were to fertility

has (1949) for a suitable an

develop marriage a monograph

since apparently cohort analysis, annual measure?the

fertility

in Australia.

by P. K. Whelpton

has

apparently substantially advanced the analysis of American fertility by cohort methods. Although the work is as yet unpublished, a review by Kiser (1952) describes

a novel

approach,

of less refined data

overcoming

than are available

the

defects

in Great

228 WALLIS TAYLOR Britain

use

the

by

of

"actual"

and

"hypothetical"

period. relevant

cohorts.

(2) The Cohort Method In the domain of mortality or morbidity,

as to the cohort referred procedure is comparatively both in conception simple a breakdown execution. Given of deaths

statistical method and

in

by age over to assemble i.e.

year, and

of

and

rates

at each

are

statistics it is thus marizes

referable.

same

what

would

age The

remained

initial

life of persons in terms of

handicaps, of birth,

time

constant

the

picture precise it is evidently

of

than

laborious

straightforward. cohort life-table of of

for only plete calendar current

the

changing

limited

utility,

cohorts

already and will,

that

of

at each

generation. life-table

is

the alternative,

a much gives hazards of it can

since

extinguished

referable the

utility

in relation

period

of fertile

married

life, especially a small fraction

is quite conditions, its application On the other hand, from the fact that difficulties apart by maternal

age

or

duration

under

more health, be com

is not

as

yet

for

obtainable

the

modern

a generation. involves special a breakdown of of marriage

is

countries.

to know of fertility we need and both calendar year at birth.

analysis age,

by

marriage

births, marriages and duration

tion

in connection

indeed

to

with

when morbidity from arises available

of

cohort,

i.e.

termination

of

the

reproductive

are

current

trends in the

unextinguished over

fertility

has achieved

By segmenting obvious that

already

have

a

for

in,

fertility three

children, which families, of a proportion

small

a further

added

importance of this knowledge the

be

having of such

proportion be only

cohort,

births.

however, stimulated

have

a high themselves

In

fertility

cohort

families

to measure

period,

in the change as a propor

events

external

a short

substantial

any investigated, a small effect measured

rate may have tion of all the previous into it may, parities,

birth.

The

if we wish

is obvious

relative

and reaction of efficacy to fertility. of to the the application the cohort method our problem reason of fertility, is for a further stimulus

study less simple

than

those

the

experience,

which

our

When

of

year

in

arise

concern

of

study

mortality a constituent indi

of

birth

the

is with

vidual is a sufficient criterion for the identification of

the

cohort.

our

When

we to have experience, same in one and the at

different

to

special

trend fertility and successively and

delay

of

fertility

and

at

marriage

the

fertility

a

calendar particular to different age The

reader to make

necessary

may this

year, groups here ask distinc

the same criterion by identifying define

of in

birth. this

obscured

our The

fertility answer

context by

promoting procreation.

for

cohorts

the

if we

year

concern

age

year. be of

i.e.

type, the mother's

individuals

year

Since

referable

tion if we adopted constitution

fertility that fact

the

it will thus be necessary of births, not merely of all the history

all marriages in the one calendar it would

is with

with

calendar

total

i.e. spacing pattern, to follow separately referable marriages

either

concern

reckon

ages.

both

influences

the are

the fact that procreation as is death, a unique event. is not, To marriages in one and the same year there may and will commonly be more before the extinction than one birth of the fertility

can

labour,

to peculiar to draw

subject if we

about

as yet

investigate

durations

whether

in contradistinc fertility the data requisite

conclusions cohorts

but

A special difficulty besetting the use of the cohort method

if we

the

marry

cohort

are primiparae is also essential

it

the cohort

mortality.

we need of mortality, to know analysis and deaths calendar births and year age only by at death, to relate deaths at age x in calendar in order ? x. to birth For cohort ym back ym year year

For

and

segmented

of

most

we

defined.

may

available only in recent British statistics (since 1939) and

that

but

example, so that

is of much greater approach to our present theme the because

cohort

i.e.

stated,

external

at

one

how the propor analysis, exhibiting births is changing first, etc., second, pari with the changing size of the completed family. is useful refinement for the reason already

hazards,

at

be most year, therefore, our concern when is with trends only to a much earlier date. From this point of

instructive

births

a

by

for

of

Thus, to

our

confine

tabulated

of marriage by duration are available, calendar year but with considerable additional

sense

embodies

of death

throughout a cohort such

if we

If figures

as

any legitimate on the basis of

subjected conditions

which

of assembly same cohort

the

even

laborious,

as well parity and the same

passu Such

age the

in contradistinction

life-table composite if current risks happen

more naturally is otherwise but

view,

of

life up to the to which

date

to total births.

tion

cohorts completed sum life-table which

a

duration

constitution

While

For

to make

possible the mean

at prevailing the customary

year of the latest

at

the cohort

by

more

the

make, a more refined

it is possible long period, born in a given calendar the same the death cohort,

one

somewhat

attention

also

a sufficiently for all persons

survival

attained

to the

the

of course, makes to one and referable

This, data

agencies both From

to

is

problems cohorts is that

of by our the

evaluate

simultaneously earlier marriage this

point

of

view,

COHORT ANALYSIS OF FERTILITY IN ENGLAND AND WALES, 1939-50 the fertility calendar

us

tells year age at marriage,

her

know

of a woman

experience

lar

in a particu do not

born

if we

little

very

the fertility

e.g.

of

experience

a woman

married

in

1940

at

the

age

of 30 will be different from that of a woman married same

in the

at

year

the

20.

of

age

on

rate

reproduction from

the

one

the

cohort

approach

hand, on

and

what

the

other,

is to liken the first to a snapshot of a procession the second

and

to a moving

If the procession

picture.

is orderly and uniform, the latter may give little information beyond that disclosed by the former, our

of

indices

acceptance as informative

health

is consistent

with

and

is not

community calamities. such

If we

great

the

life-table

customary measures of

or some

of

the

inadequacies will be actuary

the

ingly ; but the effect is operative for each completed during by

cordingly Consequently

one

year

the

prevailing there is no

ac is diluted and only in previous risks years. of the secular distortion

trends except in so far as the risk of death depends on

the year by the cohort during in which is our concern situation an epidemic situation is essentially this investigation more in which for diverse, though comparable, reasons the snapshot is wholly misleading. approach

of

the

reached

age

The

epidemic.

We have to deal with a period inwhich two variables distort

the of

tions

There

picture.

in

nuptiality

have

been

fluctua large which have

circumstances

of both hastened and delayed the assumption the responsibilities of parenthood. The essential difference between the snapshot and the moving picture is felt in more than one medical situation. Since it would be true to say that hospital reports still publish figures of duration of

stay

based

on

averages,

current-year

it

is not

trivial to remark that only two indices of duration are

We

meaningful.

might a census

approach

by

applying

the conventional

interpret

taking

its meaning

adopt on a

the given

snapshot date and

life-table method

as an overall

patients of

picture

the

base

in

practice,

liable

a

to we

therefore,

figures

and

discharged, to referable same

the

are

an appropriate procedure, for duration of stay

any

already duration

for

available

figures

small,

being In

calendar

to

therefore not

admissions In

year.

all

short,

circumstances force us to adopt what is in principle the cohort method; but we then do so less because hospital populations are subject to violent fluctuation than because the snapshot approach would be inconvenient and the disadvantages of the cohort vis a

approach referable

to

situations.*

the

in view, are

end

i.e. a

regard to duration

that may say and exaggerates

the

statement in most

trivial

conditions,

With

one

hospital

vis

current

of stay in

snapshot approach the disadvantages

all

of crude birth and death rates.

the evident. snapshot rates of an epidemic, death In the year prevailing a wide the so of age groups, and rise over range i.e. mean duration of life, called mean expectation on the basis of current falls accord calculated rates, cohort

on

day, error.

in choosing

must

figures

the

when

to major epidemics of the occurrence

imagine

catastrophe, of approach

large sampling have no option i.e. we

because

question census

duplicates

community

experience

subject

to one

any

necessarily

to bring into focus the A helpful metaphor differences between indices such as the expectancy of life in the customary life-table and the gross emerges

conditions; but the usefulness of this procedure, not as yet applied to the writer's knowledge, is open

experience

of a woman born in 1900, up to the end of her reproductive life (say 1945) will be different if she is married in 1930 from what it will be if she is not married until 1940. Similarly, the fertility

229

of current

to

It may

to clarify

help

for a new

the need

approach

to an evaluation of current trends of fertility if we contrast in which situations the schematically of marriages and alter without may

incidence taneously,

births, any

singly concurrent

or

simul change

in fertility as exhibited in Tables I - III below. Table I exhibits the fertility experience of a hypothetical static population with fixed size of the completed family throughout the period covered, the only variable to the total number of births being a temporary

rise

compensatory stable level

temporary to which it

illustrative

we purposes, 2-child families

the returns.

of

significance

For

all marriages the same way,

there is evidently no difficulty

Here the

occurring second birth

a

eventually assume that

by a former

followed

below

in spaced in the second year of marriage in the fifth of marriage. year

produce a first birth and

rate

in the marriage fall

the

relevant

in recognizing

situation.

Table II exhibits a hypothetical static population with fixed nuptiality. As before, fertility is also constant

over

the

and

covered

period

at

level the spacing of the family being in Table

I.

Here,

we

however,

same

the

initially as a

interpolate

tem

porary phase during which the second birth follows more rapidly after the first, the second birth then occurring

in

the

may distinguish last,

all

second

third

year

three periods. births

will

be

of marriage.

Thus

we

In the first and in the referable

to one

cohort

but during the middle period they will be referable to different cohorts. Again it is not difficult to see what has really happened.

*Mental hospitals constitute a special case since clearance for most other types of hospital cases does not involve a delay of more than 18months if we base our figures on discharge dates.

230 WALLIS TAYLOR Table I OF MARRIAGE

IN INCIDENCE

CHANGE

BEING

(BIRTHS

CONSTANT)

Births Marriages

First Second

Year Number

100

PhaseNumber

?

1y

y +1001

50

100 100 100

Corresponding date of marriage of cohort

{stable)

200 j/ + 7

{temporary rise)

y + 8 3 50 + 9 .y

{secondary fall)

12 4 13 14

j>+ y + >>+

62 200 y + 100 200

?

j

OF

ZZ

200 >>+ 7 50 j>+ y + 9 y + 10

+

200

1

100 .y

+

200

2

50 >>+ll 100 ^ + 12 100 y + 13 ^+14 j>+ 15

Table BIRTHS

300+ 4 150 + 5 250 6 250 7

100 y 100 j> 200 j> + 200j +

8

50j> y50 + 50 ^ 150 50 ^+11 100y

Total

?? ?? ??

y200100 100 j>

j + 5 6 +3300 + 100 ^

15 100 y +100 100 100y +16

IN INCIDENCE

Z Z y y +?2 j; + 3 y + 4

50 50y +10 50 50 j +11

0ta6/