The Demographic Discontinuity of the 1940s

W O R K I I G P A P E R

I n t e r n a t i o n a l l n s t ~ t u t e for Applied Systems Analysis

The Demographic Discontinuity of the 1940s

N a t h a n K e y f i t z

S e p t e m b e r 1987 WP-87-92

Working P a p e r s a r e interim r e p o r t s on work of t h e I n t e r n a t i o n a l I n s t i t u t e f o r Applied Systems Analysis a n d h a v e r e c e i v e d only limited review. Views o r opinions e x p r e s s e d h e r e i n d o not n e c e s s a r i l y r e p r e s e n t t h o s e of t h e I n s t i t u t e o r of i t s National Member Organizations.

INTERNATIONAL INSTITUTE FOR APPLIED SYSTEMS ANALYSIS A-2361 Laxenburg, Austria

Abstract

The expansion of world population in t h e 20th c e n t u r y did not t a k e place as a smooth acceleration, but showed sudden changes in t h e demographic p a r a m e t e r s on at least two occasions. The main o n e w a s in t h e 19409, when t h e amount of i n c r e a s e between c o h o r t s r o s e t h r e e fold within as little as five y e a r s ; a n e a r l i e r similar in- crease took place about 1920. E a r l i e r than these, a r i s e about t h e y e a r 1900 i s suggested. All of this i s i n f e r r e d from censuses taken since 1950. Nothing beyond d a t a on a g e distributions at five y e a r intervals from 1950 onwards i s needed to es- timate i n t e r c o h o r t i n c r e a s e s with small and measurable e r r o r . A check on t h e p r o c e s s i s t o p r o c e e d backwards, and apply t h e calculated a v e r a g e i n t e r c o h o r t in- c r e a s e s t o r e c o n s t r u c t t h e original a g e distributions. I n t e r c o h o r t i n c r e a s e i s a n e t amount t h a t includes some d e c r e a s e of mortality, especially infant mortality, and some i n c r e a s e of fertility.

The technique used provides new information concerning t h e onset of t h e so- called population explosion. For t h e world a s a whole t h a t onset w a s especially sudden because of t h e coincidence of t h e postwar baby boom in developed coun- t r i e s and t h e fall in mortality due t o inoculation and antibiotics in t h e l e s s developed. The measure of discontinuity being l i n e a r and additive, i t c a n b e decomposed precisely by continents and countries. Besides t h e MDCs, t h e mid

1940s showed a leap forward in Malaysia, Egypt and Turkey; t h e corresponding l e a p took p l a c e about five y e a r s later in Pakistan, Vietnam and Indonesia. China a c c e l e r a t e d o v e r a longer period, something like 1 0 y e a r s r a t h e r than 5. The ac- celeration o c c u r r e d also in Latin America but t h e r e i t s t a r t e d e a r l i e r and contin- ued longer and more slowly. Tropical Africa shows little discontinuity in t h e rate of change, but v e r y r a p i d growth throughout, p e r h a p s due t o shortcomings of t h e data.

I a m g r a t e f u l t o Douglas Wolf, Wolfgang Lutz, a n d S h i r o Horiuchi f o r c o r r e c t - ing e r r o r s o n e a r l i e r d r a f t s of t h i s p a p e r , t o Susan S t o c k f o r skilled typing, and t o t h e Ford Foundation a n d IIASA f o r material help. G a r y S i c k a s k e d some of t h e questions t o which t h i s work s e e k s answers.

The

Demographic Discontinuity of

the

19408

Nathan Keyfitz

A remarkable change in t h e world's demographic p a r a m e t e r s took place in t h e 1940s. Its n a t u r e and magnitude c a n b e a p p r e c i a t e d from TABLE 1 and FIGURE 1 , showing a g e distribution from 1950 at five-year intervals as estimated by t h e Unit- ed Nations (1986). One c a n see following t h e bottom c u r v e t h a t r e p r e s e n t s 1950, t h a t t h e difference between t h e number of p e r s o n s under 5 and t h e number 5-9 w a s g r e a t e r t h a n t h e difference between t h e 5-9 and t h e 10-14, and v e r y much g r e a t e r t h a n t h e difference between t h e 10-14 and 15-19. Looked at t h e o t h e r way and comparing t h e bottom c u r v e f o r 1950, with t h e second c u r v e f o r 1955, t h e 5-9 in- crease much more between 1950 and 1955 than do t h e 10-14. The differences fol- low through t h e successive y e a r s , working t h e i r way diagonally down t h e table.

Two s h a r p bends a p p e a r in t h e c u r v e s of FIGURE 1 corresponding t o t h e persons 5-9 and 30-34 in 1950, and so r e f e r r i n g t o t h e c o h o r t s of 1940-45 and 1915-20. The technique developed below i s designed t o measure and account f o r t h e r a d i c a l changes indicated by t h e s e bends, and especially t h a t of t h e 1940s t h a t initiated t h e famous population explosion.

AGE BY AGE DIFFEEZENCES

One way of bringing o u t t h e essential f e a t u r e s of t h e c u r v e s of FIGURE 1 i s by f i r s t differences by age, as in TABLE 2. Thus from TABLE 1 , taking f o r 1950 t h e O- 4 of 3 4 1 million a n d s u b t r a c t i n g t h e 5-9 of 270 million gives t h e 7 1 million as shown at t h e t o p l e f t of TABLE 2.

But w e are more interested in following c o h o r t s than in a g e distributions as such, and to do t h a t w e reassemble t h e same numbers according to c o h o r t . TABLE 3 provides a window into t h e 30 X 1 6 matrix, in which t h e full set of estimates and projections, applying to t h e y e a r s 1950 t o 2025, as provided by t h e United Nations, are reassembled into columns corresponding t o cohorts. I t w a s calculated by sim- p l e offsetting of e a c h successive row of TABLE 1 one f u r t h e r column t o t h e left.

Each column now contains a survivorship table f o r identical individuals. The columns d i f f e r from one a n o t h e r insofar as mortality changed from o n e time t o t h e next, and insofar as b i r t h s w e r e different in different five-year periods. The

TABLE 1. World Population by age, 1950 t o 1980, estimates by t h e United Nations (1986) (millions of persons).

TOTRL 2 5 1 8 2 7 5 1 3 8 1 9 3 3 3 4 3 6 9 3 4 8 7 6 4 4 5 8

TABLE 2. First differences by a g e from TABLE 1 showing estimates and projections from t h e United Nations (1986); world as a whole (millions of persons).

column under t h e heading 1950, 341, 317, 312,

...,

^{i s} a kind of decrement t a b l e f o r t h e 1945-50 generation, and will have a c e n t r a l p l a c e in t h e reconstruction of TABLE 1 t h a t will test t h e model t o b e developed.

TABLE 3. Data of TABLE 1 a r r a n g e d by cohorts; window showing c o h o r t s b o r n 1925-30 t o 1955-60; estimates and projections from United Nations (1986) (millions of persons).

Cohort b o r n I n f l v a y a r r p a r l o d a n d l n g w i t h t h 8 y a r r

n9. 1838 1835 1 8 4 8 1845 1958 1955 1888

Now let us t a k e t h e differences given in TABLE 2 and similarly r e a r r a n g e t h e s e along c o h o r t lines. That i s done in

TABLE

4.

If w e disregard t h e f i r s t row, different from t h e o t h e r s because i t includes t h e e f f e c t of infant mortality, and t h e rows a f t e r about a g e 55 when mortality again starts t o r i s e , t h e r e i s a c e r t a i n uniformity within each column in t h e remainder of t h e table. Thus f o r t h e c o h o r t b o r n in t h e five y e a r s p r i o r t o 1950, i t s i n c r e a s e from a g e 5-9 t o 10-14 is 53 million (checked from TABLE 1 by 317

-

264

=

53), and t h e f u r t h e r numbers down t h e column are 53, 53, 53, 53, 51, etc. Note t h a t t h e s e are not differences of successive a g e s of given cohorts; r a t h e r they are measures of t h e growth from o n e c o h o r t t o t h e next as i n f e r r e d from t h e period difference at any one moment between successive a g e groups. A t least t h r e e f a c t s a p p e a r . 1 ) If f o r t h e moment w e d i s r e g a r d mortality (as w e l l as migration and enumera-

tion e r r o r ) , t h e e x c e s s of t h e 1945-50 c o h o r t o v e r t h e 1940-45 c o h o r t i s given by t h e column u n d e r 1950, and i t shows f o r t h e f i r s t few e n t r i e s a f t e r t h e f i r s t about 53 million. The column f o r t h e just preceding period, t o t h e left of t h i s one, shows only 1 2 o r 13 million persons f o r i t s f i r s t few e n t r i e s . In s h o r t within one five y e a r interval t h e r e w a s a fourfold increase in t h e rate of cohort-to-cohort growth as measured on this preliminary and c r u d e approach.

TABLE 4. F i r s t differences of ages in TABLE 2 r e a r r a n g e d t o show columns f o r cohorts; world as a whole. Window showing 1910-15 t o 1955-60 with each column giving i n c r e a s e o v e r previous five-year period (millions of p e r - sons).

C o h o r t b o r n I n f l v o y o r r p o r l o d o n d l n g w l t h t h o y o r r

4

l 1815 1 9 2 8 1925 1 9 3 8 1835 8 1845 1958 1955 1 8 8 8

2 ) About t h e same thing can b e said f o r t h e c o h o r t born in t h e five y e a r s before 1920. Apparently some dramatic change took place around 1925, corresponding-though at a lower level-to what o c c u r r e d in t h e 1950.

3) The enormous impetus given in t h e late 1940s was followed by a n even g r e a t e r increase in t h e e a r l y 1950s, but i s gradually wearing itself out. W e must b e careful in drawing conclusions on c o h o r t s much a f t e r 1970; t h e table includes both estimates of what happened in t h e p a s t and projections f o r t h e future, and insofar as w e r e l y on t h e latter w e are merely reading o u t t h e assumptions put in by t h e United Nations' authors.

The differences of TABLE 4 in effect include t h e whole of mortality along with t h e cohort-to-cohort differences. Can w e obtain c l e a r e r r e s u l t s by taking t h e differences in t h e o t h e r direction? Instead of a c o h o r t arrangement of t h e a g e to a g e differences, suppose w e t a k e a c o h o r t arrangement of t h e period-to-period in- c r e a s e s at given ages. In TABLE 1 f o r example, t h e persons under 5 y e a r s of age, are 400 million in 1955 and 341 million in 1950, s o t h e difference i s 5 9 million, as shown under 1955 in TABLE 5. That i s a different way of measuring cohort-to- c o h o r t increases, and w e see t h a t i t produces even more consistent r e s u l t s (TABLE 5). I t i s t h i s uniformity of t h e numbers in each column of TABLE 5. in p a r t deriving from t h e rapidly improving mortality of t h e postwar y e a r s , t h a t i s t h e basis of t h e

p r e s e n t unconventional approach.

TABLE 5. I n c r e a s e at given a g e group o v e r preceding five y e a r s , a r r a n g e d in c o h o r t form; world as a whole (millions of persons).

C o h o r t b o r n I n f i v e y e a r p e r l o d a n d l n g w i t h t h e y e a r Age 1 8 2 8 1 8 2 5 1 8 3 8 1 8 3 5 1 8 4 8 1 8 4 5 1 8 6 8 1 8 5 5 1 8 6 8 1 8 8 5

DIFFERENCES BETWEEN POINTS OF TIME AT GIVEN AGE

The five-year i n c r e a s e s of t h e given a g e groups in TABLE 5, a r r a n g e d in c o h o r t form, a r e even more strikingly uniform down columns (i.e. in measuring t h e i n c r e a s e from one c o h o r t to t h e next) t h a n t h e numbers of TABLE 4 and t h a t makes t h e c o n t r a s t between columns more impressive. Under t h e column headed 1950 w e have various more o r less independent estimates of t h e amount by which t h e 1945- 50 c o h o r t e x c e e d s t h e 1940-45 c o h o r t , as measured by census t y p e information from t h e s e v e r a l ages. This f i g u r e , 47 o r 48 million, i s itself topped by t h e next column, t h a t shows 58 o r 59 million.

A l l of t h e above t a b l e s showing c o h o r t s are windows in a diamond-shaped con- figuration t h a t i s 29 columns wide, with t h e window opening on t o t h e middle p a r t of t h e diamond. T h e r e i s not much i n t e r e s t in t h e p a r t t h a t was omitted on t h e r i g h t hand side, since i t consists largely in p r o j e c t e d figures, but t h e t r i a n g l e omitted on t h e l e f t could tell u s about what w a s happening p r i o r t o 1915. In f a c t (TABLE 6) i t even gives indications as f a r back as 1880-85. What i t tells is t h a t t h e 19th centu- ry rate of population i n c r e a s e w a s remarkably slow, and at t h e new c e n t u r y t h e r e

FIGURE 1. Age distribution, world as a whole, based on estimates and projections provided by the United Nations (1986), millions of persons.

FIGURE 1A.Enlargement of part of FIGURE 1. The intervals marked 4 a r e the a g e differences of Table 4; those marked 5 a r e t h e time differences of Table 5.

w a s a jump to double t h e previous rate of increase. With t h e exception of t h e 1915-20 c o h o r t t h a t double level continued to 1920, when t h e r e was again a s h a r p r i s e , t h a t approximately continued, with a falling back during World War ^11. And then came t h e big jump between 1940-45 and 1945-50 t h a t i s a main i n t e r e s t of t h i s p a p e r , shown in TABLE 5.

When world population growth i s s e e n as a s e r i e s of period totals i t i s a rela- tively smooth c u r v e , until t h e 1970s rising with more t h a n exponential steepness.

When c o h o r t differences are taken t h e acceleration a p p e a r s as s t e p s , clearly measurable from a g e distributions derived from censuses in 1950 and subsequently.

There were distinct jumps about 1900, about 1920, and about 1945, each one some- thing like a doubling of t h e rate of growth from t h e previous step.

TABLE 6. Left c o r n e r of diamond-shaped f i g u r e of which TABLE 5 gives middle;

world as a whole (millions of persons).

C o h o r t b o r n I n f i v e y a r r p a r l o d o n d l n g w i t h

1885 1898 1885 1998 1985 1918 1815 1928

- - - - - - - ^-

- - - - - - - -

¹

- - - - - -

^{7 8}

- - - - -

^{11 8 8}

- - - -

^{11 12 9 8}

- - -

^{8 12 12 18 8}

- -

^{5 5 12 12 18 1}

-

^{5 5 5 12 11 9 1}

5 5 5 3 18 11 8 2

3 4 4 3 9 8 8 2

From t h e viewpoint of FIGURES 1 t h e differences shown in TABLE 4 are each taken along a single c u r v e , and t h e columns are what a p p e a r from successive c u r v e s along a (more or less because of mortality) horizontal section. The differ- e n c e s of Tables 5 and 6 , on t h e o t h e r hand, are also taken along horizontal sec- tions, but they are t h e height of each of t h e c u r v e s of FIGURE 1 above t h e c u r v e beneath. The distinction i s shown in FIGURE lA, which i s a n enlargement of FIG- URE 1.

The e x t r a o r d i n a r y uniformity of t h e numbers in e a c h column of Tables 5 and 6 i s crucial t o t h e p r e s e n t analysis of a g e distributions, o u r use of t h e s e r e s u l t s , and in TABLE 7 t h i s uniformity i s measured by s t a n d a r d deviation and r a n g e and then put to use in t h e reconstruction of TABLE 1.

AVERAGE COHOBT INCREASE

Tables 5 and 6 show t h e i n c r e a s e in given a g e g r o u p s from one point of time t o a point of time five y e a r s l a t e r ; each of t h e i r numbers c a n b e i n t e r p r e t e d as t h e i n c r e a s e from one five-year c o h o r t to t h e next. The a p p a r e n t homogeneity of t h e numbers within columns, plus this i n t e r p r e t a t i o n t h a t makes them out t o r e p r e s e n t t h e same entity, tempts one t o a v e r a g e them in o r d e r to s e c u r e t h e b e s t available estimate of t h e i n c r e a s e from one c o h o r t t o t h e next, overlooking ( b e t t e r assimi- lating) mortality changes. This w e do f o r t h e world in TABLE 7. W e only go as f a r as t h e 70-74 a g e group, deleting t h e last row in o r d e r t o exclude t h e somewhat ragged numbers t h a t t h e oldest a g e s would show. Thus t h e f o u r t h figure, f o r 1900, in TABLE 7, t h e i n c r e a s e from t h e 1880-85 t o t h e 1885-90 c o h o r t , i s t h e t o t a l of t h e t h i r d column of TABLE 6, i.e. 6

+

5

+

5

+

³

=

1 9 , and i t i s h e r e divided by 4, which i s t h e number of rows of TABLE under 1900 and above 75-79. The t o t a l s and a v e r - a g e s are rounded independently, s o t h e numbers of Tables 5 and 6 d o not always quite add t o column 2 of Table 7.

This convenient uniformity of absolute differences depends on t h e f a c t t h a t mortality improvement w a s steady and l a r g e during t h e post-war period. Our con- stant i n t e r c o h o r t differences, virtually invariant with r e s p e c t to t h e d a t e at which they are measured, depend on t h e f a c t t h a t mortality improvement o v e r time just about offset t h e increasing mortality with age, at l e a s t o v e r considerable intervals of age.

The t h e t h i r d column of TABLE 7 i s t h e payoff on o u r labors. To emphasize i t s message,

1 ) T h e r e was a level and low rate of i n t e r c o h o r t i n c r e a s e in t h e 19th c e n t u r y , as f a r back as w e c a n deduce from t h e a g e d a t a of 1950 onwards;

2) A f i r s t doubling o c c u r r e d with t h e i n c r e a s e of t h e c o h o r t b o r n in 1900-05;

3 ) A f u r t h e r r i s e , t o a level twice as high as t h a t of 1900-15, o c c u r r e d with t h e c o h o r t of 1920-25, a f t e r a c o h o r t t h a t showed no i n c r e a s e at all, presumably as a r e s u l t of World W a r I;

4 ) Again a doubling to an unprecedented level with t h e c o h o r t of 1945-50;

5 ) A somewhat i r r e g u l a r tendency to decline since 1955;

6 ) The decline at t h e v e r y end of t h e t a b l e i s mostly a n assumption of t h e projec- tion, and this applies even more t o t h e c o h o r t s from 1975 onwards t h a t are omitted from t h e table.

TABLE 7 . Averaging t h e amount of i n c r e a s e between successive five-year cohorts;

world as a whole (millions of persons). Totals and a v e r a g e s r e f e r t o t h e 5 y e a r s p r i o r t o t h e d a t e given, and t h e y show t h e i n c r e a s e o v e r t h e c o h o r t b o r n five y e a r s b e f o r e t h a t .

C o h o r t To t r I N o . A v a r r g r S t r n d a r d

b o r n In f o r r v r l l r b h o f a v a ilab la d a v f a t l o n F r o m Tab la8

5 y a a r m c o h o r t 8 c o h o r tm w ith in 5 a n d 6

p r r c r d h g (1 (2) (311 (1)/(2) c o h o r t m In n a x

I t b e a r s r e p e a t i n g t h a t e a c h of t h e numbers in TABLE 7 e x c e p t t h e f i r s t i s t h e a v e r a g e of more t h a n o n e measure of t h e i n c r e a s e of successive cohorts. These measures are in general in close agreement, as summarized in t h e last columns of TABLE 7 t h a t show t h e s t a n d a r d deviation of t h e s e v e r a l measures t h a t are a v e r - aged, as w e l l as t h e smallest and t h e l a r g e s t of these. In t h e majority of instances t h e standard deviation i s much less than 10 p e r c e n t of t h e mean. The calculated s t a n d a r d deviations confirm t h e impression given by t h e a p p e a r a n c e of Tables 5 and 6 t h a t t h e i n c r e a s e of t h e s e v e r a l a g e s o v e r time i s consistently estimated f o r any one c o h o r t , and hence t h e differences between c o h o r t s are t o b e taken seri- ously.

The point i s emphasized by FIGURE 2 and FIGURE 2A, t h a t show t h e middle value, along with t h e lowest and highest values, f o r e a c h of t h e estimates of inter- c o h o r t increase.

FIGURE 2. Intercohort increases 1895-1975, as calculated from population age distributions 1950-2020 estimated and projected by the United Nations (1986), world a s a whole, millions of persons.

FIGURE 2A. Intercohort increases 1890-1970, as calculated from population age distributions 1950-2020 estimated and projected by the United Na- tions (1986), more developed and l e s s developed countries, millions of persons.

M e n DNdopcd Ceuntrlcs 16

RECONSTRUCTION OF THE ORIGINAL

AGE-PERIOD

TABLE

The uniformity of t h e c o h o r t - b c o h o r t differences provides a n opportunity t o reconstitute t h e conventional age-period d a t a given as TABLE 1. Such a reconsti- tution i s at one and t h e s a m e time a test of what w e c a n now consider as a model, and a n opportunity to experiment with t h e model t o see what amounts of cohort change are capable of producing t h e s h a r p discontinuity in rates of growth shown in TABLE 1.

The mean differences in t h e t h i r d column of TABLE 7 c a n b e successively ad- ded to some initial population and s o reconstitute t h e orignal age-time table. If w e t a k e t h e c o h o r t b o r n in t h e y e a r 1945-50, shown as t h e main diagonal of TABLE 1 , and r e p e a t e d in TABLE 8 as t h e initial values f o r t h e model, then by successively adding t h e a v e r a g e i n t e r c o h o r t differences shown as t h e t h i r d column of TABLE 7 w e c a n build up t h e p a r t of TABLE 1 above t h e main diagonal. By subtracting from t h a t main diagonal. values t a k e n from t h e same t h i r d column of TABLE 7 w e can build up t h e p a r t of TABLE 1 below t h e main diagonal, all t o a n approximation t h a t i s t o b e investigated. If i t i s possible t o r e c o n s t r u c t TABLE 1 with 29 numbers from TABLE 7(and i t s continuation, not h e r e shown), plus a column of 15 numbers f o r s t a r t i n g values given as t h e main diagonal of TABLE 1 and r e p e a t e d as TABLE 8, then w e have a greatly improved chance t o analyse and compare continents and countries. With 29 plus 15

=

44 numbers r a t h e r than t h e 17 x 15

-

255 intercoun- t r y and o t h e r differences should come out more clearly.

What t h i s amounts t o i s t h a t t h e numbers provided by TABLE 7 being differ- e n c e s w e need s t a r t i n g values t o a t t a c h them t o and TABLE 8 provides those in- dispensable s t a r t i n g values. In a f u r t h e r development t h e s e starting values will b e a suitable cohort life table survivorship, but f o r want of d a t a on t h e world as a whole they are h e r e simply taken from t h e original TABLE 1. TABLE 9 shows t h e r e c o n s t r u c t e d c o h o r t s , intended t o approximate TABLE 3. In TABLE 9 t h e r e i s no limitation to t h e diamond form of TABLE 3 since w e have released outselves from t h e d a t a r e s t r i c t i o n s of t h a t table, and TABLE 1 0 could b e extended t o l a t e r and e a r l i e r years. The technique may h a v e some potential f o r forecasting.

The calculation i s unconventional, in t h a t i t uses absolute differences r a t h e r than t h e more usual r a t i o s , and t h e s e include t h e e f f e c t s of mortality and f e r t i l i t y changes. Y e t t h e e r r o r of t h i s p r o c e s s is small, as t h e reconstruction will show, and i t h a s t h e advantage of being l i n e a r , and hence additive. The additivity will en- a b l e u s t o trace any peculiarity, in p a r t i c u l a r t h e discontinuity of t h e 1940s. down t o t h e continents. c o u n t r i e s e t c . t h a t make up t h e total.

TABLE 8. C o h o r t b o r n 1945-50, t h a t s e r v e s as b a s e f o r r e c o n s t r u c t i o n ; world as a whole (millions of persons).

TABLE 9. R e c o n s t r u c t i o n of t h e c o h o r t a r r a n g e m e n t of TABLE 3, using only t h e t h i r d column of TABLE 7 a n d t h e d e c r e m e n t information of TABLE 8; world as a whole (millions of p e r s o n s ) .

C o h o r t b o r n I n f l v e y e a r s p r a c a d l n g t h a y a a r

Now all t h a t i s n e e d e d i s t o o f f s e t t h e s u c c e s s i v e r o w s of TABLE 9 in s u c h a fashion as to l i n e u p p o i n t s of time u n d e r o n e a n o t h e r , a n d we e n d with TABLE 10.

This last s t e p i s t h e r e v e r s e of t h a t b y which TABLE 3 was d e r i v e d f r o m TABLE 1.

FIGURE 3. Age distributions as given by the United Nations, and as reconstructed from intercohort increases of TABLE 7, shown in FIGURE 2, and base of 1945-50 cohort, world as a whole, millions of persons. No other data

FIGURE 4. Original age distributions (as estimated and projected by the United Nations) and a g e distributions a s reconstructed from intercohort in- creases and base of 1945-50 cohort, aggregate of Less Developed Coun- tries, 1950-2025.

EZ- 8 - '8

E 8 S 8 E E E 8

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8ST LET

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szs

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8 LST LST 89T

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8 8 9 ELE LTE ELZ T89 6 1 9 86E T9E

'71 aalnbea qou seop Xpnqs quesead eqq qnq 'Xq?ppou Bul%rreqo a o j e p e u e q ueo uolqoeuoa .Xqllqaou %u?%ueqo Xq peqoejje qsou e l q q eqq u? seoeld eqq 'pue pue Buluulaaq eqq Jsau smoa eqq e a e daoqeejslqes ueqq s s e l s l qlj eqq eaeqm s e o e ~ d e u '~eulalao eqq uroy uolqonaqsuooea eqq jo seanwedep eqq smoqs TT

xqav~,

Having developed t h e method, w e c a n go on to obtain a profile, similar to t h a t given by t h e t h i r d column of TABLE 7 , f o r t h e s e v e r a l continents.

GEOGRAPHIC DECOYPOSITION OF THE DISCONTMUITY

Since t h e whole of our calculation i s linear, t h e discontinuity ought to b e allo- catable without residue to t h e s e v e r a l countries and continents.

As a n example, in TABLE 1 2 w e find t h a t t h e 1920 number f o r t h e world i s 3, and t h i s i s t h e n e t balance between -70 f o r t h e MDCs and 73 f o r t h e LDCs, all in thousands. In t h e following c o h o r t w e have a n i n c r e a s e to 233 f o r t h e world, i.e.

t h e i n c r e a s e increased by 233

-

3

=

230. Corresponding numbers f o r t h e MDCs were 1 9 0 and 40. T h e r e was a discontinuity f o r t h e world as a whole, and i t was o v e r 8 0 p e r c e n t due to t h e developed countries. Very different was t h e discon- tinuity of t h e 19409, t h a t was at least half due to t h e LDCs.

The conveniently additive c h a r a c t e r of t h e measure of c o h o r t change permits u s to partition t h e total at any point. Thus of t h e 1885 i n c r e a s e of 45 (hundred thousands) 22 i s in t h e MDCs and 2 3 in t h e LDCs, both as presently classified (first row of TABLE 12).

Evidently t h e discontinuity t h a t starts f o r t h e world with t h e c o h o r t born 1945-50 a p p e a r s both in t h e MDCs and t h e LDCs, but t h e latter have much more weight. For t h e MDCs, moreover, i t i s only one item of a s e r i e s of r e p e a t e d and i r - r e g u l a r fluctuations. F o r t h e LDCs t h e c o h o r t of 1945-50 initiates a level t h a t i s from 2 to 4 times t h a t of t h e precedfng decades. For t h e s e latter t h e r e i s a de- cisive r i s e from t h e line marked 1945 to t h a t marked 1950, and a n o t h e r from 1950 to 1955.

I t seems to h a v e been t h e baby boom, s t a r t i n g just a f t e r t h e war, and ending with t h e c o h o r t of 1955-60, t h a t joined in with what was happening in t h e LDCs to give such a decisive t u r n to t h e p i c t u r e f o r t h e world as a whole.

As among t h e continents, Africa shows no discontinuity, but r a t h e r a steady acceleration, and something of t h e same kind c a n b e said, though less emphatically, about Latin America. I t i s Asia t h a t i s more than any o t h e r continent responsible f o r t h e discontinuity in t h e world picture.

The sudden r i s e t h a t began with t h e 1920-25 c o h o r t i s more uniformly s p r e a d around t h e continents, with Europe having a n especially l a r g e p a r t of it.

TABLE 12. Average amount of i n c r e a s e of successive cohorts, as estimated from available ages, f o r c o h o r t s born in t h e five y e a r s preceding 1885 t o c o h o r t s b o r n t h e five y e a r s b e f o r e 1970 (hundreds of thousands of p e r - sons).

U o r I d ~ D C LDC R f r l c a a L a t Rim E u r o p e N. Rim.

And now f o r t h e c o u n t r i e s where t h e events of World War I1 made a n especially deep impression on t h e demography, r e f l e c t e d in t h e r i s e from 8,900,000 of t h e 1940-45 c o h o r t t o a r i s e of 24,900,000 f o r t h e c o h o r t of 1945-50 (Table 12). In- donesia i s a n impressive case, and w e see (TABLE 1 3 ) t h a t t h e i n c r e a s e of t h e 1950 figure (representing t h e c o h o r t b o r n 1945-50) w a s 300 thousand, a v e r a g e d o v e r t h e 1 4 age-dates f o r which information (including U N projections) i s available. In c o n t r a s t t o t h i s t h e 1955 figure w a s 1900 thousand, averaged o v e r 15 points of time and age, a six-fold r i s e .

China evidently made a major contribution t o t h e mid-century discontinuity t h a t shows in t h e world picture, India much less, Bangladesh and Pakistan less yet.

A s far as t h e r i s e a f t e r World War I i s concerned, t h e five countries in TABLE 13 show i t weakly o r not at ^all. Someone with b e t t e r knowledge of t h e history of those countries about t h e t u r n of t h e century may b e a b l e t o speculate more con- vincingly than can t h i s w r i t e r about t h e events t h a t a r e r e f l e c t e d in t h e c o h o r t changes of TABLE 13. The only point t h a t i s worth mentioning again i s t h a t f o r e a c h of t h e c o h o r t s a f t e r t h e f i r s t one in t h e table (that f o r 1875-80) t h e r e are at least two points, and t h e s e are more o r less independent, and in almost all c a s e s

a g r e e closely with o n e a n o t h e r .

TABLE 13. Average i n c r e a s e between c o h o r t s , based on population estimates and f o r e c a s t s , from c o h o r t b o r n in five y e a r s b e f o r e 1885 to c o h o r t b o r n in five y e a r s b e f o r e 1970 (hundreds of thousands of persons).

C o h o r t 1885 1888 1885 19 8 8 1885 18 1 8 18 15 1828 1825 1838 1835 1848 1845 1958 1955 1868 1865 1878

B a n g l a d a s h 8.

8.

8.

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1 8 7 1 8 1 2 17 1 8 2 8 2 5 3 1 3 2 2 0 2 7 4 7 7 5 8 7 7 8 8 1

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8.

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3 4 3 1 5 9 8 8 3 3 18 2 4 14 2 4

Pak i s t a n -8.

8.

-2 8.

-8.

2 2 1 2 4 2 3 3 0 17 1 8 13 14

TABLE 1 4 shows t h e l a r g e r European c o u n t r i e s in t h e s a m e way. They show b i r t h and mortality losses during e a c h of t h e wars, and a boom at t h e end of e a c h w a r . France's l o w b i r t h rate of t h e 1 9 t h c e n t u r y comes through, as d o e s t h a t of t h e UK.

F o r individual c o u n t r i e s of o v e r 15 million population a sequencing w a s made of t h e s h a r p n e s s of t h e bend in a g e distribution f o r d i f f e r e n t points of time. Four of t h e c o u n t r i e s t h a t showed s h a r p bends a p p e a r in FIGURE 5.

THE THBEE-DIMENSIONAL GEOMETRY OF THE DISCONTINCJLTY

Some understanding of t h e argument of t h i s p a p e r c a n b e obtained from t h e three-dimensional r e p r e s e n t a t i o n of such numbers as t h o s e of TABLE 1 , or func- tions of them. FIGURE 7 c h a r t s f i r s t differences, and i t s even r i d g e s c o r r e s p o n d to t h e uniformity down diagonals of TABLE 2 and t h e uniformity down columns of TABLE 3. The g r e a t e r uniformity of Tables 5 a n d 6 c o r r e s p o n d s to a d i f f e r e n t an- gle on t h e ridge.

TABLE 14. Average i n c r e a s e between cohorts, based on population estimates and f o r e c a s t s , from c o h o r t b o r n in five y e a r s b e f o r e 1880 t o c o h o r t b o r n in five y e a r s b e f o r e 1970. Major countries of western Europe. Thousands of Persons.

C o h o r t 1 8 8 8 1 8 9 8 1895 1 9 0 8 19 85 19 19 18 1 5 1 9 2 8 1925 1 8 3 8 19 35 1 8 4 8 1945 1 9 5 8 1955 1 9 6 8 1985 1 9 7 8

F r a n c e 8 8 5 1 5 3 2 8 3 24 8 3 8 - 2 8 8 - 7 5 1 1 2 2 1

8 - 1 9 -23 1

-3 3 1 2 8 3 3 8 .

a 4 - 1 8 3

U. Germ.

9 2 1 8 7 2 3 8 4 4 8 4 8 4 1 8 4 -244 -1 1 2 6

1111 8 2 -7 9 6 8 - 5 4 8 - 3 4 8 3 3 8 3 8 1 5 7 9 - 3 88

I t a l y 1 7 8 1 2 5 8 5 1 9 7 2 4 2 3 0 7 1 5 s - 7 8 7 1 8 4 2

4 3 - 3 8 1 5 2 - 3 2 1 5 17 -2 3 8 1 8 7 4 4 1 - 1 8

Spa I n 4 1 1 8 8 4 7 17 2 114 115 5 3 4 295 14 7 187 -18 1

-6 5 27 8 9 8 2 8 8 28 8 11 1

THE YODEL

AS A BASIS FOR EXPERIMENTS

Plainly t h e full detail of t h e d a t a i s not needed in o r d e r t o produce on a c h a r t t h e discontinuity h e r e under study, and i t i s illuminating t o produce i t with t h e minimum of data, even no d a t a at all. Suppose t h a t instead of t h e a g e distribution of t h e c o h o r t born in 1945-50 w e t a k e as t h e s t a r t i n g point t h e geometric progres- sion 20, 16, 12.8, 10.24,

... .

Beyond t h a t let t h e profile (that w e have taken as t h e t h i r d column of TABLE 7 in t h e reconstruction) consist in 1 f o r all c o h o r t s up t o 1940-45, and 3 f o r all c o h o r t s beyond (FIGURE 6). This provides a discontinuity in t h e i n c r e a s e s of about t h e o r d e r of magnitude of t h a t shown in some LDCs.

The plan f o r f u r t h e r experimenting is t o t r y conditions more realistic than those of FIGURE 6, but s h o r t of t h e u s e of actual data. In p a r t i c u l a r one would like t o s e e what kinds of changes in b i r t h rates. and in a g e specific mortality r a t e s , will produce t h e bend actually observed. No one e x p e c t s t h a t a unique answer c a n b e found t o t h e question "What changes in b i r t h and death rates brings about t h e a g e distribution?" and what will b e sought i s t h e r a n g e of possibilities.

FIGURE 5. Age distributions 1950-2025, four populations leading in sharpness of discontinuity: Malaysia. Pakistan, Egypt, Turkey.

0 ,

a

In. f-

P -

In. 9

0

-

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-

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t 0

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0 -

n

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FIGURE 6. Synthesized s e t of age distributions, based only on initial values 20, 16, 12.8, 10.24,

...,

and on change of 1 p e r five y e a r s from 1880 to 1945, and 3 from 1945 to 2020. No actual data used.

FIGURE 7. Three-dimensional representation of age-time dNribution correspond- ing to TABLE 1 (prepared by Wolfgang Lutz).

WORLD ABSOLUTE DIFFERENCES 1 950- 2025

APPENDIX

The Lexis diagram (FIGURE 8) shows some of t h e cells of Tables 1-5. For ex- ample on t h e lowest row, t h e 0-5 counts, f o r 1950 w e have 341 million; f o r 1955 at a g e 5-9 w e have 317 million. These both concern t h e cohort b o r n in 1945-50, and w e expect them t o include t h e mortality loss by a g e as t h e i r difference. When w e compare t h e s e losses w e find along horizontal lines t h e differences given in parenthesis, and along c o h o r t lines these come close t o constancy. The differ- ences between t h e 1950-55 c o h o r t and t h e prece.rding, along a diagonal. comes out as 59, 59, 58, 58 when estimated from t h e successive censuses as in Table 5. When t h e i n t e r c o h o r t differences are estimated from one census at a time, as in Table 2, they also show some uniformity, but not as much (Figures in square brackets).

The differences t h a t a p p e a r in t h e diagram have t h e i r uniformity as a result of combining mortality and fertility change. I t i s planned t o s e p a r a t e t h e s e in later r e s e a r c h , but f o r t h e present purpose such separation i s unnecessary.

-

²⁶

-

FIGURE 8. Lexis diagram: world population

Lexis diagram: world population

1 9 5 0 1 9 5 5 1 9 6 0 1 9 6 5

Y E A R S

REFERENCES

Preston, S.H. and A. J. Coale (1982) Age S t r u c t u r e , Growth, Attrition and Accession:

A N e w Synthesis. Population Indez 48217-259.

Ryder, N.B. (1980) Ihe Cohort Approach: E s s a y s i n the Measurement of Tem- p o r d V a r i a t i o n s i n Demographic Behavior. New York: Arno Press.

United Nations (1984) Demographic Indicators of a u n t r i e s : E s t i m a t e s a n d Pro- jections us Assessed i n 2382. New York: United Nations.

United Nations (1986) Computer tape containing estimates and projections of t h e 1984 assessment.

Wriggings, H.W. and J.F. Guyot (eds.) (1973) Population, Politics, a n d the F h t u r e oj'Sauthern A s i a . Columbia University Press.

Yuen-chung Yu and S. Horiuchi (1986) Population Aging and Juvenation in MaJor Regions of t h e World. P r e s e n t e d at t h e Annual Meeting of t h e Population As- sociation of America.