Analysis of African Demographic Data as an Air for Economic and Social Planning

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E!CN,14!ASPP/L.6 E!CN.9!CONF.3/L.6 10 August 1962 Original: ENGLISH ,

Ut'\J!TED NATIONS

~

. ECONOMIC

AND

~·OCIAL COUNCIL

--''''''''''.''-:7' !

ECONOMIC COMMISSION FOR AFRICA

Seminar on Population Problems in Afrioa 29 October - 10 November 1962

Cairo, United Arab Republic

DOCUMENTS OFFICE

FILI~ COpy

NO TO BE TAKEN OUT

ANALYSIS OF AFRICAN DEMOGRAPHIC DATA AS AN AID FUR ECONOMIC AND SOCIAL PLANNING

62-11158 62-2170

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ANALYSIS OF AFRICAN IJEM:)GRAPHIC DATA AS--AN AID FOR ECONOMIC AND SOCIAL PLANNING

by .Frank Lorimer

Office of Population Research Princeton University

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CONTENTS

1-2 3-4 5-:1,5 16-26,

27~35

36-48

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I^{.e . ,}INli\OPl£TIO.N.. • • • • ,~"'"

II. ,POPULATIONl?rsTRIllUTION • • •

".:~III. DISTRIBUTION,BY

ssx

^A!'/DAGE

IV,. ESTIMATIQN OF FEIlTILI'l,'Y • • ,.

V. ESTP;1ATJO~,QF, M:l~~:r;TY , . . . . •

h::" ,,' VI. INFI;.\.lEl'lCE OF MIGRATION ON CHANGF.q INLi\.EOURFORCE v:I:;I. ~IMATJml.~ ~~N

TRENt6

Al')D PFOJECTIQNS

A~:FACTQ~ FOR E:lT:r;M/\TION OF CllILD IDRT,OFTY_ (.By U. Brass)

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INTRODUCTION

1. The populations of most African countries have been or soon will be

enumerated in censuses or appraised .tn sampling inquiries. For these countries important progress is assured in tne t'irst phase of programmes to produce useful demoLraphic data. The second, equally important phase, if the aim is to produce information of value in economic and social planning, requires even greater skill and initiative than the first - though rather less financial outlay.

2. This paper will be concerned mainly with methodological questions concerning the use of African ~e~ographic data. Special methods are required because most

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standard method~ of,d~m,?graphic,analysis~r,!, -predicated on tile avail!!bility of reliable vital ~tat~sticsfromcivil registers and on a series of ,several

comparable and reliable,enumerati9ns of the,population. The analysis .of population tren.dsln most ,Mricap COJ.1Ilj;r1e~ at, present must be undertaken without these

resources. Attention, here: is ,r,ocused on certain prob'l.ems cpmmonly encountered_{. ' , - . '}

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inthe~stimation,of population trends under present conditions in Af1:ica. Spee.1.al problems of particular countries are not considered here. In the development of demOGraphic information, as in other matters, it is essential that national planning agencies and statistical organs exercise initiative and ingenuity in adapting general principles of research to their own needs and objectives.

II. POPULATION DISTRIBUTION

3.

Knowledge concerning the distribution of persons and their characteristics byareaJ.units is basic to many aspects of planning. Two different types of area classification are needed for different purposes:

(1)

by political division and (2) by ecological regions. The former usually receives priority, and this

reasonable because such information is needed in administration. It is also important from a research standpoint because some relevant information from some

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other sources will be available only on this basis. It is, nevertheless, important for some purposes to organize information by ecological regions differentiated by type of economy, altitUde, tribal occupancy, etc. One sort of ecological area of special and increasing importance in Africa is the metropolitan district,

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or urbanized are~;' 'including political 1lfiits:outside the central city. One.

approach to these ino.itiple objectives iscto present certain,bllsic demographic data' (e.g~·Pe':fSOh~·:bYSex,broaQ age claSses; ':and ~ertains{lcial ^{and economic}

characteristiClS) f6fthe smallest possibU' units, .along wit)J. measurements of land area -bbth''t'6' meet some adminiStriltive needa and to permit the regrouping of demoBrapliic:!irlkareal information indifferent ways. The data for small areas can also be tiseli'in cartographic presentation on maps of. population distribution (dots and/or sYmbols) and population density (choropleth, isopleth, or

daSymetric»)1' ibreextensive and detailed classifications .of charac,teristics can then be,~resentedfor an intermediate level of political divisions, also capa):Jle of being regrouped into larger regional'divisions defined in different WlyS •.

4. The function of a census, or demographic sample inquiIJ/', as a source of, information on the distribution of popul.atfonTe qutbe distirtctfromits function in

th~: prov{~ion

of data required for'the:analysis of popUlation trends • . The latter

r~~ui;esiabulations'in

detail, 'includingcross-tabulatio!lS of related items, which are not feasible to carry out for small units. They are not

feasibl~ both because of the costs and, especially in the case of data .from a

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sample survey, the risk of obtaining insignificant results oying to reduction in numbers. Both of

th~se

IIlajor functions;f ,8

demog~aphic

si.trvey are oT^Ja low

·Ql'der of imp&tanC.etl'!·~conomicand social planning; their distinct requirements_•...

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must b~'kept clearl~ in mind in planning the d~yelopmentand a~lysis,of demographic data.

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III. DISTRIBUTION BY 'SEx AND AGE

-.1"1";''' :'The' coll\Ii9sition at any moment; of a population by age and sex is determined,

apart from the effects of 'migration, by the numbers.ofbirtljs.in previous years,

JJ.'See articles on population mapping in Africa by Barbour,Kilton and l'rothero in Barb9ur, K.M. and R.M₁ E'r-0t,hi:lro: EssalS on African Population, London, Routledge and Kegan Paul, 1961. The article' by Prothero gives a general review of this subject, including recommendations by committees of the

International Geographical Union and the Commission on Technical Cooperation in Africa (C.C.T.A.). See also Gourou, Piere: Algemene Atlas van Congo, KOninklijke Academie voon Overzeese Welenschaffen, Brussels, 1960.

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the sex ratio

at

birth{'atidthe'prollortioos of"males and of females who have

surviv~ii'ti:J:s\i8ci!~sfite'!ilges.

Iti'ls"possibleth?t the pr-oport Lon of males at birth' 'Ls' 'Mnetallf'~omewhi>tlbweramong'Africaosthao inmost other populations.

This fsa 'stib'j"!!'6i'onWh1chit is very, difficult t.o obtain conclusive evLdence

bec~'u'iJe

ooe' is dealing herewith stnall differences; repQrted ratios may easily bedistlirbed by any small bias 'in reporting and by chance fluctuations._. ' . , - ',- . : In a po~ulation with a central tendency of 1.05 males per female ,at birth, the range, expected to contaio 95 per cent of the ratios observed io samples of 1,000 births, is between 0.93 and 1.19. Even in'ratios based,on samples of 40,000 births

(about the number expected each year in a population of 1 million persons), the correspondiogrange is appreCiable, namely between 1.03 and 1.07. The empirical eVidence'S/ is rather ambiguous, but it is not

'~nconsistent

with the hypothesis tha'" the sex ratio at birth maybe gen",rally somewhat lower ill Ar.ica thall in most other,reglOns;2.1 Sex ratios 'at birth may vary appre<::iablyamong,rel3ions in Africa. ,lnthe absence:Jof reliable, evidence on this subject ;t:or a ,!?e.rticule.r reGion, it ts reasonable to assume a ratio in the vicinity, of,l.O~ or 1.03 as a

\Torting hypothesis"

:,,).:.29 1.54 1.46 1.25 1.43

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French West 'Africa Togo

Cameroon

Fr. Equatorial Africa MadaGascar

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^,'kn,,investigation, of' records ,ofA;t:rican births in hospitals under French

! auspices, ).951-53, yielded the foilo\Ting results: '

Number of Ratio Nilinbet

of'

,Ratio Live Births Males!Females Stillbirths Males/Females

''76.0 1 ; 0 2 2 " 4 . 4 "

4.5 1.072 0.4

10.5 1.028 0.7

14.7 1.036 0.4

62.1,: 1.040 3.0

From'Ministere de la"France d,IQut:l'e~mer. Service des scat.LstIques , Documents et ,Stati$ti9u~" .no, ,X. June, 1953. One must bear in. mind that fadt'9rs'influencing the selection'of"maternity cases 'in hospitals may,influence the seX'r!ilt;i9s)

and to an even greater extent, the ratios of stillbirths to live births.

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This hypothesis receives indirect support frol1ltg.,: observati0t;lthat the '

, ratio ie.il~r among non-vht.tes than. amongwhit!!sin j;heUnited~tates,where the average ratios for the-Years 1940-58, were i"Q58 f.gr'li'hit~s spli,1.023 for non-whites.

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6.

It 'is quite as ,difficult to know how mortality may influence the relative survival of males and females to successive ages, because information on

'mort~lity in Africa is meagre and liable to serious error. In general, mortality in infancy 'and childhood is almost universally higher among males than among females - except in cultures where female infants may be socially rejected or repudiated, which so far as known is, not·, characterist ic of any African societies.

However, some of the meagre evidence" on, sex differences in mortality among African infants is ambiguous. And, certainly, no a priori assumption is warranted

concerning the relative. mortality of males and females during the years of adolescence and active adult life. Finally, the relative numbers of males and females in any district may be strongly influenced by migration. .If so,

'-information on the division of a population by sex, and variations .in r.atios of males to females at different ages cannot be evaluated without, tak~g this effect

into account.

'7.

Information on the ages of Africans by single years is now being obtained in a considerablE'nuinber of countries south of the Sahara, as well ,?S in the

Mediterrahelilnccountries; Information of this sort has been, or is being" provided 'by cens'Uses or national sampling inquiries in ten countries of French expression,

in all' the Portuguese African territories, in Ohana (main census,

1960,

as well as post-enumeration sample survey), Congo (Leopoldyille), and Buganda Province

of Uganda (post-enumeration sample survey) -excluding cases where such information is recorded only for persons able to give information. on ages

immediately and directly, In general, the information thus obtained is found to haire Great value,if used critically, in estimating population characteristics and trends. On the other hand, the reported age ,distributions usually show not Only minor irregularities but also displacements (or relative omi~sions) over broad age ranges.

8. There appear to be three prevalent types of bias in the reporting or

estimation of ages of females in Tropical Africa: (l).a tendency to underestimate the ages of children, beginning with the classification :of too many 9hildren as

"infants" under one year of age; (2) a preference for. the central child-bearing

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ages, 20 to 39 ye~rs, in the classifica'tionof femles;and (3). exaggeration.of ,the ages of elderly women. These tendencies with respect. to females" are

'.i.llustrat~d

by the comparisons 'shown in'figure 1 between reported distributions in several coun1;ries

arid;jeXpect~d"

dIstributionS implied. by mathematical models of stable populations corr~~p~riMngto the estimated'vital rates in these

countries. Comparisons'ol

~i,p6h~d

and expected distributions by' age of females are generally

si~ificant

because', 'even where there is' considerabl.emigratcry movement of women, its influeri~"on, age pattcrrisis usuaj.Ly dampened by an" , ' ,associated movement of other members of their families.

9.

It is morediffic~lt'to discover any characteristic 'types'of' bias in the classification by age of males in African censuses - largelybeceuse in many

',99~yrie~>he

numbers of adult males areitifluencediri different,ways by migration.

H~we~er,~~veralpossibilities reQuir~ Special attention: (1) there is evidence ofvnder-estimation in reporting of ages of flale as well as female children,

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tending,to give over-estimation of the numbers of 'infants (contrary to the bias

"'i\freQuen~lyfound in statist:l.cs for other parts of the world); (2) biases in estimating the ages of males and' females iuthe ,'icinity bf'ad1:llescence may'oe

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," Quite different, with freQuent ovet-est'!.mation cf" the ages' of girls and under-

"estimati~n

of the ages of boys; (3) in come in,,-uiries there maybe 'serious

omissions in enumerating men, especial1.yyoool3 :n",n,because 'of their higl1, mobility.

Extremely low ratios of males to females at ages _20~39 yearsmay,:Ln some cases reflect both under-counts of men and different'scll'ts of' errors 'in the estimation of ages of men and women. This suggestion is supported by 'the low ratios of males to females at all ages f'r'equent.Ly reported. 'in African inquiries. For

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example, according to the results of the demographic inQuiry in the

Congo

(13~azzavill~)

1955-57, there wt,re only

98

males per lOOfeinales in the total population, and only 89.5 males '['ar 100 fe.,;ales at ages 'over 15 years.

These ratios are not unusual' for African inQUiries, and are selected for citation here because in tllis case th~y cannot be ascr'fbed lJiainly to the effects of

migration; (4) the ages of elderly Africanmeri 'dre ~uite as ,much, or possibly even more, subject to over~estimati:6n^{as those} bf elderly women. ' Exaggeration of the ages of elderly persons is a nearly unive~sal phenomenon, but this has

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FIGURE 1

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REPORTED AND STABLE FEMALE AGE DISTRIBUTIONS, PERCENTAGES

20

15

10

5

o

STABLE UPPER VOLTA

25

20

15

10

5

o

20 15

10

5

o

0-5 5-10 10-15 15-20 20-2525-30 30-35 35-4040-4545-5050-55 55-60 60-65 65-70 70 PLUS

IVORY COAST

0- 5 5 -10 10-15 15 -20 20-25 25-30 30-35 35-4040-45 45-50 50-55 55-6060-65 65-70 70 PLUS

CONGO (LEOPOLDVILLE)

0-5 5 -10 10-15 15-20 20-25 25-30 30-35 35- 45

AGE

~: Office ot Population Research, Princeton University.

45-55 55 PLUS

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rather secondary importance in Africa, because the relative numbers of such persons are generally rather small here.

10. So~e of the problems encountered in estimating sex and age distributions can be avoided in certain types of demographic analysis. For example, one can obtain reasonable estimates of fertility from data on tpe age distribution of females witbout regard to the age distribution of males. Estimates of the complete distribution of a population by sex and ages are, however, needed for many purposes.

lOa. The methods cOlllll1only used to smooth reported age distribution by graduation are useful only in eliminating sbort-range displacements, such as those resulting from a tendency to report ages in "round numbers" and similar "digit preferences".

These methods do not meet the most important needs of countries wbere the reporting of ages may be affected by relatively long-range displacements. An excellent treatment of this subject is presented in a paper by Carrier and Farrag,

,~th

specific reference to

E~JPt.~

Unfortunately, many of the specific methods described in this article are also inappropriate to the needs of most countries of Tropical Africa for two reasons (though some of the principles set forth by these authors are applicable to any situation): (1) many of the methods are dependent on the examination of detailed data on ages from two or more comparable censuses; (2) tbese methods are not _des~gncd to measure and correct any important bias in reports on numbers of young children; and, as already noted, this is a , major problem in the treatment of age distributions of many African populations.

lOb. The most efficient procedure in many situations is to find the sex and age distribution to be expected in a "stable population" with the vital rates of the population under observation. This method is appropriate only where it can be assumed that there has been no important cbange in the level of fertility in recent decades and no major calamities, but it can be used where there are ~no'fD

to have been gradual changes in mortality becau3e, as has been shown, these do not generally induce important changes in the distribution of a population by ages. The stable population gives the pattern to be expected in the absence of

'if

^{Carrier, N.H. and A.~} Farrag, The reduction for' statistically under-developed cOlli~tries,

vol. 12 (3): 240-285. March, 1959.

of errors in census ~opulations

Population Studies (London)

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11. The basic technique for the required calculation ;i.s simple, but its application involves important and difficult questions. The combination of (1) a model life table at an appropriate level of mortality and (2) a factor representing the influence of the rate of population increase (e-ra) gives the r'equired stable population - i f the "pattern" of mortality (Le. relations among specific rates at different ages) in the model table is similar to that in the actual pOPulation.

21

The United Nations life table models are constructed on the assumption that deviations in pattern, from a set of relations obtained by averagings'large series of life tables, can be ignored. Unfortunately this assumption may sometimes lead to errors in application to particular situations, especially in the proportion of elderly persons, say at ages beyond 50 years, A precise determination of the proportions surviving from birth to successive aces requires not only information on the general level of mortality but also some knowledge of the age Pattern of mortality, and considerable skill in the application of this knowledge.£! Unfortunately no reliable information on this subject can be obtained at present in the case of many African countries.

Nevertheless, even in the absence of such information, the construction of a hypothetical stable populstion corresponding to the observed vital rates of a particular African population, on the assumption implied in the United Nations life table models, may still be the most useful approach to the estimation of sex and age distributions in many African countries, if it is applied critically and the results are interpreted with caution. The proportion of population at

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In the expression given in parenthesis, e denotes the base of the system of natural logarithms, r denotes the rate of natural increase, and a denotes successive ages. The latter, of course, refer to the centres of the age classes under consideration (ages 0.5, 1.5, etc.) not their initial limits

(0,1.0, etc.). -

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This topic, among others, will be treated at some length in a forthcoming monograph on the analysis of African demographic data presenting the results of work during the academic year 1961-62 at Princeton University, Office of Population Research.

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older, ages, where the error is likely to b~,greatest,_. is generallY,less in

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Africa than inmost occidental countries. Al,so, although there are probably considerable differences in age-patterns of mortality among regions in Africa, the fragmentary evidence available to date does not indicate any general tendency toward an extreme deviation from average relations. Finally, variations in age distribution are in general more sensitive, to differences in levels of fertility

th~n to di~erences in levels of mortality.

12.' It is necessary to apply a constructed' stable population in a particular situation with great caution. A first step is naturally to compare the

constructed age distribution for persons of each sex, e.g. the curve of the cumulated proportions under successive ages, with the reported distributionsll giving special attention to the comparison for females. The problem then becomes ,one 'of considering how and to what extent the divergencies between these

,.distributions might have arisen from migration or errors in enumerat Ion or the reporting of ages or, on the other hand, from discordance between the assumed vital rates On which the constructed population is based and the actual rates that determined the age distribution of the present population. The results of :this investigation capbe.helpful in forming.a f1.,;,al estimate of the true

distri'9ution. '

13. A procedure, similar in principle to that d;i.~cussed above but more arbitrary and Less fleXible, is the comparison of ther~port~~age distribution of some other popu1.ation assumed to have similar vital trends, with that of the population

un~er consideration.

14., , It ..is difficult 100 evaluate the accuracy of reported, divisions of a_{. ;" -} - . . . . , , ' . . ','," ; r:-

population classified only by sex and by proad age,cl,asses_{• ' " . ,. (s~ch.• L} as infants under one year, children 1-14 years or som~-otherlimit intli!s'-'V:i6friity;-and older persons with or without one or two other age breaks) because such a classification

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conceals tendencies toward ;yst~lnati6 omission at, certain ages or transfers within certain ranges due fo under-estImation or over-estiJnation of ages, which might

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have been revealed by more detailed reports on ages. \f.here only such broad

The technique of' transforming the ogtve curves obtaioed in this way described by Carrier and Farrag (0'1'. cit.) is useful for: this purpose.

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classes are used, it is especially important to compare the apparent divisions

·)"i;l;hthose to berexpect.ed in stable populations with similar vital trends. In such a situatiOQ, resort to any mecbanical process tbat relieves the investigator , of responsibi1.ity fOr examining, his data critically in all possible ways is

especially dangerous., For example, the derivation of a detailed age distribution by fitting a polynomial function to the apparent values for broad age divisions

yi~lcds,a4eoeptivelysmooth series of specific values that may be quite erroneous.

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15 •. Statist,icalofficials may reasonably decide th~ adjusted or smoothed 1ge distributions at'e more useful for most purposes than the results obtained by simple tabulation of the data as reported. An adjusted or smoothed distribution may then be given primary emphasis in the report of the census or other

demographic,inq\liry, and the unadjusted data may in some cases be relegated to an appendiX. But complete suppression of the unadjusted data, which could be 'used by'other,·statisticians to evaluate the official estimates ·or to derive other estimates, ~ers the ,advancement of knowledge.

IV. ESTIMATION OF FERTILITY

16 •. Many demographic surveys in Africa now provide two distinct series of data on births: (A)'teports of births, cLas sdf'Led by age of mother, during a

specifiedihtE!rVa'l (usually one year) prior to the survey, and (B) reports,by wOlllen'f~f(§:{rferentage classes numbers of children ever born alive to them. The

fo~r

maY be'

referred to as "current" reports, the latter as "retrospective"

~epbfts^': Bbth sets are' subject to bias but, ,at least to a large extent , t o di,rrE;rent kinds of bias •

17. 'A major problem with respect, to; ,the current data is the difficulty und.er Afr:i.c'ancbnditibns of applYing effectively a precise definition of the time_{- . . , - .¥}

within'which'births are to be taken into account. ,If the informants sh6ul! tend to iriclude atl births, for example, during the previous fifteen months"~s

occurring (Within the last year, the reported number would be inflated byabout

25

^{per 'cent.} A tendency in this direction may sometimes result from a habit of regarclingall children still nursing or carried by their mothers as "infants".

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On the, other ,hand, the reports may err in the opposite w~y, referring. to events

"'ithi;~

shorter period than the prescribed interval. There

may

also be omissions through negligence i~ reporting, especiallY in the case of infants who died

shortly after birth. Because the reports on births and deaths during the previous year are usually obtained from interviews with the head of the family, and in

sD~e cases are not supported by a separate question on children born but no longer living, these reports may be less complete than those obtained from interviews with women concernfng births to them. The numbers of reported births during the .prevt.ous ye;,ar may, therefore, be either too high or too low. There is evide.nce

that eJ;"rors in one direction are prJi,ponderant in some surveys, 'snd'thosein:the opposite direction in other surveys. The:re is, howeve:r,Db :reason. to suppose that errors in "current" dataoh birthssre sppreciablyaffectedbytlhe ages ()f,the ~~hers.

18. On the other hand, there is abundant evidence that "retr05pee,tive" reports by older women on numbers of chi.Ldren ever born to them are 'frequently less

complete than comparable reports by younger women. The older women, many of them mothers of large families, a're

likely't~

fdrget (or neglect to report) some of the childre'nbornto them

at

an earliertime,espepiallytllQs,e lRng dead. ,There is little'possibilityof great ove:r-reporting of births by women at any age, though somk;\,oSsibilit:l:es in this direcHon '. must be .conai dared, Some stillbirths may be reported as live births and some·,aQ.qpted,chndrenmay be reported as

born to their foste:rmothers _but questions Qn fertili1;y,are usually framed explicitlY"t6"avoid confusion on. these; points • ..One can assume that retrospective reports by women rarely yield excessive estimates of,fertility; on the ~ontrary,

they teb'd:'tbkrd under-statement; especially in the case of.Q1,derwomen.

Exa~inatiori;of^{data 'DOW} available 'from ,inquiries in,Africa.(incl~?~ngche~ks against t-ep()t-tedage dis'tributions) shOWs that in thepase ofY0UD{lerJNomen, repoi-ts' oftriuIilbe:r'g ''of child:ren ever bornaI1e gel1erally fairly r,eliable.

19. AcoirrPeirison of retJ:'ospectivereportsonfe;rtility (series B) with current teports oft'births (sedes A) to women ,'incomparable age classes provides a basis

!l •

fo{'acl..iustingtheage~s'pecific

'rates .of series; A, and thus o1;ltl'\ining 1'\ reasonable

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estimate of'tqtal fertility - on the assumptions that (l) retrospective reports by young women provide the most reliable information on this subject and

(2) errors in current reports on births are proportionately the same for women at,different ages.

20. ' An'approximate graphic method of making this comparison will first be described as, follows: (1) Plot the numbers of children ever born to women in successive age classes (series B), assigning the average for each class to the exact age withitrthRt class at which the accumulated fertility is estimated to be equal to the average for group. For this purpose, the mid-ages of five-year classes (22.5, 27.5, etc.) can be used for all classes except the first

(15-19 years). In view of the rapid increase of fertility during the teens, it is best to plot the average for this class in the vicinity of 18 years. (2) Plot the successive sums of the current specific rates (series A) at their terminal ages, minus one-half the interval covered by the reports, e.g. at ages

19.5,

24.5, etc. (3) Examine these curves, which should be approximately identical if all the data were correct, to observe the general pattern"of their relations.

(4) Read off values from curve B at the ages used in plotting curve A (19.5, 2!f.5, etc. ),and take the differences between th~se values to give a series of cUrrent age-specific fertility rates for successive age classes i5-i9, 20-24, etc.

(5) Compute B/A ratios at successive age classes (ratios of the series obtained in step

(4)

to the series A current rates).

(6)

If a smooth series is obtained in this way, the B/A ratio at ages 20-24 years, or an average of the ratios at 20-24 and 25-29 years, can be zpplied as ^R correction factor to all the specific rates of series A. (7) The sum pf the series A values so corrected gives an estimate of "total fertility", Le. average number of live births per weiman livinG through the childbearing period.

21. TIlis is a crude procedure, and in mapy cases the B/A ratios obtained in this way will form a quite errati~ series. A better series of estimated specific fertility rates from the retrospective reports - and therefore a better series of B/A ratios and a better estimate of total fertility - can be obtained by using an appropriate method of graduation developed by

Brass.~/

The application of

'1/

^Functions,

/ ...

'$/CN~{4JASPp/L,6 E/CN.9/CONF.3/L.6 English

PaGe 16

this ~thod is simPle and straightforward, and gives

a

smoother series of B values. The A values (wh:i.chh::lve"not been smoothed) and therefore the B/A ratios may stillee more or less erratic due to sampling variations or other ,fluctuations.

In particular, all values for the age class unde~ 20 years, representing'a time when fertility is rising rapidly, must be viewed with extreme caution; the. B/A ratio at ages 15-19 years should not be used as a correction factor. In theory, the B/A;r~tio ^{at ages} 20-24 provides the best basis for the adjustment of

series A• However, us th:cs r'at.Lo may be i,nfluenced by sampling error or some other irregularity, it should not be applied without attention to the adjacent values, especially that at ages 25-29 years. The estimated total, fertility obtained in this way appears to be the ~ost reliable index of fertility possible unde? present conditions in most African countries.

22. 'An estimate 'of the crude birth rate is given directly by this procedure - applying the same' adjustment factor to the total number of births dpring, the preced:Lng year. The ad.justed age-spacific fertility rat'es (tran'sformed into female or male rates by s?plication of tbe sex ratio at birth) can be used, in conjunction with an appropriate life taale to construct a one-sex stable

population. It is, hONever, quite satisfactory for most purposes to use & measure

,,'

'ofthecen'tral age of t;,e childbearing per-Led (the mean age of the fertility distribut:i.on) as an inde}: ^0,0 the pattern ef f<;rtility. This measure in

conjunctf.on with an estiLlate of tLe proportion of' females surviving from birth to ttd.~ age gives t.he approximate value of the mean interval between successive

felnale ' generations.

23.

'Useful 'supplemental i:-:fornat10n of fertility can be obtained from the data a{f~"adY·menhonea.by tabulating the distribution of women in successive age classes by specific numb8rs of childreneve~born. The information so obtained on theptbportions of childless worren at successive aGes may be especially useful.

Condition~responsiblefor very 10" fertility in Africa (below levels that can reasonably be attributed to prOlonged intervals between births, ·as a result of

, ,

prolongea lactat:i.on or· other factors, or to a fairly rapid decline of fertility in theiater childbearing ages)' are likely to involve both a high frequency of

I ...

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17

; , - ,

.

even possible that in some cases non-reporting validity of the .results.

childlessness and a low average njllll!:ler of births pe;r JIlother, Apparent evidence of one of these cOndition,s without the other should lead one to question the

"

Numbers of enunerated women from whom nO reports on fertili.t;)' are obtained should always .be tabulated. and reported, This information is omitted from some reports. It is

/

\{Omen have been erroneouslyclassifiedaitthildless~

~4. EEitimates of current fertility may bedepresEied by a net transfer of females ',from adjacent ages to aees "ith!"! the reproductive period, exaggerating the

denominator of specific birth rates or a general fertility rate - or inflated by an opposite tendency, though this is less. likely. (There may be under- enumeration. of "omen in some areas, b~t there is no "ell-documented evidence to this effect. Also, i f this occurs, it is Ukely to be associated with under- reporting of births and of children.) T'1e possible effects of erroneous

estimation of ages on retrospective ratios of births to women are complex, but

·",pos/>'ible influences of this sort merit .ser Ious attention.

"! .

25. The risk of error in the estirr.atiQn 0:" fertility is. greatly increased if the types of information described above are not availa1ele to the satistician

,~esponsiblefor population esti~ates - because, in that case, he cannot

.efficiently check one type of data.agairst others to determine their consistency

•. or to take inconsistencies into accourrt , D3t3 cnl.y on births during the previous year, especially if relatedcnly t.o womon 0:" ell ages or to women "between menache and menopause", IIJ!3y lead e.ither to over-estimation or under-estimation of

fertility - without valid a pr~ori reaSC;18 for specifying the probable direction of the error. Data on numbers oi children ever born, especially if given only for _~omen beyond _~he childbearing ages, can gen2rally be expected to yield

, '

uncler,estiIIJ!3tes of fertility - but there is no good'way of estimating'theprobable wagnitudeQf the errors.

C,\:.26.•. '+:he use of detailed in:'or"'Otio'1 on the distribution of a population by sex an~j~y.ages.in conjunctionlTith the use of one type of specific information on fertility (current or retrospective reports) does make possible some' cross-checking of estimates - if

~geS

are reported, or

e~tinated,

fairly well and if the age

structure of

thefema~e p~pulation ha~

not been,distorted by an important change

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E!CN.14!~/~.6 E!CN.9!CO'NF' .'3/t.6 English ^{C '} Page 18

in fertility', or by calami ties, or by large-scale selective migration. But a high level of sophistication is required for an efficient use of the available data in this situation, and even so the final results will necessarily be less reliable than they might be if more complete information were available.

V. ESTIMATION OF MORTALITY

27. Reports on deaths during the current year are notoriously unreliable. If there is no other information on mortality, and if there is no firm basis for an estimate of natural increase during a recent period that can be used in

conjunction with a reliable estimate of fertility, proper basis for any

estimation of death rates does not exist. As a crude stop-gap measure, it might be assumed that mortality in the country or region concerned is similar to that in some other area for which there is more adequate information, but this is a very dangerous procedure because there is conclusive evidence that there are large variations in mortality among Africans - and frequently between populations in apparently rather similar circumstances.

28. Fortunately, significant information on child mortality can be obtained from the sort of data discussed in the previous section. Recent experimentation shows that surprisingly reasonable results can be obtained from reports by women, especially younger women, on numbers of children ever born and numbers surviving, This information has the great advantage that it does not involve relating sets of data from different sources, each of which may have its own peculiar biases. By taking information on fertility into account, the experience under ris)t of death of children born to women in successive age classes can be estimated with

satisfactory approximation. This possibility is greatly enhanced by the nature of childhood mortality, which was high intensity innnediately after birth but

diminishing intensity in subsequent intervals. Therefore a considerable error

in estimating the upper age limit of the experience at risk causes only a relatively small error in the estimation of the proportions surviving from birth to successive childhood ages - or their complement, the proportions dying.

29. Applying adjustment factors, developed by Brass, which have relatively narrow'ranges, one obtains estimates of successive mortality quotients from successive ratios of surviving children to children ever born by age of mother as follows:

/ ...

Ages of mothers in years

15-19 20-24 25-29

30-34

35-39 40-44

45-49

50-54 55-59 60-64

E/CN.14/ASPP/L.6 E/CN.9/CONF.3/L.6

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Mortality ~uotients by age intervals in years

0-1 0-2 0-3 0-5 0-10 0-15 0-20 0-25

0-30

0-35

30. The first of these derived values is likely to be quite erratic for reasons stated in the discussion of fertility. The next two or three values are, it is expected, fairly stable though subject to some fluctuations due to sampling variation, mis-statements of age, errors in estimates of fertility, et cetera.

These should be used as a series without attaching undue importance to each individual estimate. The significance of the subsequent values becomes

increasingly problematic with advancing age of the mothers. There are two main reasons for this: (1) Ratios of children surviving to children born may be influenced·by differential non-reporting as the ages of women rise. (2) There may have been changes in the level of child mortality during the intervals between the births of children to the older and the younger women. The values in the series for the higher age groups must, therefore, be used with caution.

31. In general, the values thus obtained for 2Qo' 3~, 5qo can be regarded as approximately true or minimum estimates of mortality. Mothers are not likely to "invent" deceased children. It is possible that in some cases the values obtained may be inflated by the inclusion of stillbirths, but any bias in this direction is likely to be partially offset or out-weighed by some omission of infants who died SOon after bir:th. Of c,?urse, one cannot assume that this index of mortality has absolute validity; but it is the best available index on this

subject for African populations in the absence of reliable vital statistics from well established civil registers - apart from information obtained from well controlled longitudinal studies or the continuous observation of selected populations. Factors to be used in deriving these estimates are shown in the annex.

/ ...

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32. An estimate of child mortality is, in itself, an important index more

useful for many purposes than a crude death rate or an estimation of expectation of life at birth. Given an estimate of child mortality, such as 5~, other indices can be obtained by various methods - though with variable and in some cases, large margins of error. The simplest procedure is, of course, to assume that mortality values at other ages as given by a model life table which has the same specific child mortality (or the values obtained by interpolation between two model tables with somewhat similar child mortality) are applicable to the population in question. On this assumption other intrinsic indices and 'the crude death rate of the population under consideration can be estimated.

However, this procedure neglects the possible influence of a difference between the pact.ern of mortality in this population and the schedule of ,mortality implied . ,_by,J;!1e, model table. This neglect may cause appreciable errors in the derived

es'cimates ,- and this source of error must be kept in mind in any use of the results.

" 33. There is no simple answer to the problem thus presented. There,are some obvious first steps, but they may not lead to satisfactory results. First of all, one may compare the whole series of mortality quotients described above with those of a selected model or other comparable life table - but, in view of the cautions already expressed, this ccmparison may be inconclusive. Similarly, if reports on deaths during the previous year by sex and age of the deceased persons have been obtained, sex-and-age-specific death rates can be computed from these data, in conjunction with information on the population at risk.

These rates can then be compared with those obtained from reports by mothers , and with sets of life table values. In the light of these comparisons the

statistician may, but probably will not, find that he has a fairly substantial basis for compiling a whole set of estimated mortality values.

31f . Vore elaborate, methods may yield more satisfactory, though hardlY conclusive. results. No amount of skill can overcome deficiencies in the

basic 'data. EXperimentation in the development of new methods in this field is now in progress.

35. Estimates of age-speCific death'rates for Egypt can be derived by comparing the numbers of persons in corresponding age groups enumerated in the successive

! ...

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'Engli~h ' Page 21

censuses. This"is hardly possible as, yet in most of the other countries in Africa, though this may become possible in several other countries one or two deca.des hence. ~ntilmore reliable basic.data are provided, all estimates of mortality in Africa will remain subject to large errors.

VI. INFLUENCE OF MIGRATION ON CHANGES IN LABOUR FORCE

noi36.' It is particU1~rlydifficult in transitional societies with a changing

mixture of subsistence and commercial activities to malee a, meaningful, quantitative division between the productive and the nan-productive segments of a papulation.

The diViding lines between childhood dependency and productive maturity, and between full economic activity and complete or partial withdrawal to the status accorded elderly; persons are, in large part, culturally deflnetland differ radically in different segments of the society. The proportion ,of papulation above any given age, such as 12, 16 or 20 years (determinedcmainly by previous levels of fertility) differs among African popUlations; but really very large differences are' rather unusual except in zonss with large migrant elements • ." '". r Variations.ih' these proportions are in any case partially ,offset -by variations,

usually in the apposite direction, in the proportions of aged persons. The different ecOnomic roles of men and women also vary widely in relation to traditional culture and'in different segments of the economy.

37. The economy of some African countries is highly dualistie,' with sharp

differentia'tioll between the comnercial- ibdustrtaland the , traditional -subs is tence

"'segments - thUs' inducing and becoming 'dependent onacbnstant flow of short-term

~abourers :from the subsistence sector to the comnercial, se¢tor in eXchange for wages. In some other African countries the traditional rural economy has been considerably modified by the introduction of commercial crops and the

intensification and extension of markets and transportation - with associated changes in the urban economy. This· distinction between dualistic and mixed eccinomiesis real, but never ebsoliite. There is a whole range of intermediate types. Voreover, among countries generally char-acter-Laed by a mixed economy, there iswidE!'vBriation'iri theirilportance bf large-scale ibdustrisl and

co~ercial activities.

38.

These d1f¥erehces in economic structure and associated migratory movements stronglyou1;'Welgh differences Hlthe sex and age structure 'of the populations

/ ...

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. E!C}l.J.4!AS?P!L.6 E!CN.9!CONF.3!L.6

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in various countries, as factors infJ.uencing the size and composition· of the labour force available for productive activity. Questions about the trend of the population as whole, its regional distribution and migration· as a process of population redistribution and as a mechanism of accommodation among different sectors of the economy are, therefore, of more immediate importance with respect to labour force trends in Africa. For this reason, attention is focused here on the measurement of migration and its reJ.ations to the formation and utilization of. the labour force.

39.

There is great diversity and considerable confusion in the provision of information on migratory movements in Africa today. This stems in part from differences in the nature of migration and in possible sources of information on this subject. Information on migrants empJ.oyed in corporate enterprises can be obtained from establishment reports. Moreover, where migration for empJ.oyment is mainly directed to J.arge-scale operations or othereasiJ.y

distinguished enterprises, data on migrant workers can be obtained Without undue difficulty from periodic censuses of employment in such enterprises as in the

. Fecleration of Rhodesia and Nyasaland, Nigeria, United Arab Republic, etc. Problems of measurement are more complex where employment is Widely diffused or "here

micration involves the movement of individuals and famiJ.ies in response not

onJ.y ·00 opportunities for wage work but aJ.so to opportunities for self-empJ.oyment or share croplling.

40.

Recognition of problems presented by the rapid growth of African cities 'rhas led to a considerable number of special urban surveys. There have also been

surveys of particula:r:< regions that p:r:<esent speciaJ. probJ.ems of some sort, often involving migration. There have been some investigations of major streams of migrants in transit. FinaJ.ly, there have been many intensive, official and unoffiCial investigations of particular situations or particular aspects of rural economy,urbanization, and migration. The problems involved in the interpretation of data collected in these diverse undertakings are too complex for treatment· in this paper. Our attention here is directed mainly to the analysis of data on migration and the allocation of human resources that can be drawn from cepsus-type inquiries.

41. In view of the importance of short-term migratory movements in Africa and of changes in the composition of migrant streams under different circumstances,

/

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^L

. 6

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inveptigation of the characteristics of migrants an~ durations of sta¥ is as important' as the determination of the total number of ~ersons displaced by

migration'at a given moment. ' In most cases one must work with data on the status of in-migrants in given localities, or of out-migrants from giyen localities, at a G;iven moment rather than data on persons in a stream of migrants.

F'urther)llOre, in A~ican countrieD, even data, oc) the status of migrants defined in terms of duration of stay are very scanty. Even so, the consideration of

methodologic~~problc=c involv2d in an3lysic o~ such data is of importance in the African context. In any tabulation of reports on "length of stay" the distribution

of replies is, dependent on the type of inquiry. If there is a constant flo\{

of miGrants from one area to another, and all migrants return after varying, lenc;thsof' stay, the chanc e that in_migrants. wilJ, be included in a momentary survey in the area of destination is proportional to their length of stay, and the same relation holds for reports on out-migrnnts by their kinsmen in the area of oriGin. ' For example, twice as many t"ro-Y2ar xi,grants as one-year migrants, relative: to the numbers moving each year, ,.,ill. bo LneLuded in a census - whereas the chances of being recorded in an Lnvest.t.gat.Lon of migrants en route is,

proportional to the number of' trips aUQ in~2penueut of the length of stay.

Similarly, if reports are obtained from migrants in anylicality concerning present and previous trips, U", reporkd. o.u:r,'1ti0?:} of the present visit will tend on the average to be only on",..half oC: th·" tot,,:'. ~.'lration, whereas the previous durations will be completely reported. T"nE:se're1ations can, of course, be taken into account in interpreting th2 results. R~ports are sometimes made on the, proportion 'of all persons in an area \{ho r~ve been present, more than £ years.

In that case it is best to exclu.de these under !!. years of age from both the numerator and the denomirlator of the ratio. The value of any information on length of stay can be greatly increasei by the ~resentationof specific rates by seX and by age classes~ If it is not [ocsiblz to tabulate the information separately by age classes, it may be ~se~cl a~v5.sable to present the information onlY for personsag~d15 years or over,

42. The persi.stence of tribal affiliations in a positive asset in the

investiGation of migration in m.~ny African countries. This provides a useful approach, though it is beset by some Itr,itations.' Some tribes are rather widely

/ ...

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dispersed. Replies to questions on tribal affiliation may be ambiguous. But these difficulties are hardly more serious than those encountered in any detailed ,classification of persons by place of birth. Information'on tribal affiliatipn,

wanted for many reasons, is obtained in most large-scale inquiries', in Africa.

For example, in the 1960 PopUlation Census of Ghana a number of detailed

classifications are being tabulated to indicate the relationship between tribe and other socio-economic characteristics. Tribal affiliation provides a basis for classifying individuals into groups that persist through changes in location and in social conditions. Analysis of the tribal components, by sex, age, and other characteristics such as, type of economic activity and marital status can throw light on patterns of migration.

43. If comparable information on the tribal components of an area's population is obtained in successive inqUiries, it may be possible to estimate increments or decrements resulting from migration during the inter-census intervals.

Incidentally, this procedure can be important in deriving an estimate of natural increase from the results of successive inquiries by focusing attention during an inter-census period on the numbers and characteristics of a tribal component cap, of course, be greatly improved if information is available from both

censuses on its sex and age composition. However, highly signific?nt information can also be obtained, from a single inquiry on the demographic characteristics of, tribal components.

4h.

It is more difficult to obtajn reliable information on persons who have moved away from a given area than on in-migrants. In the case of out-migrants, the information may be obtained (1) by collating data on in-migrants into

different areas classified by place of origin (obtained from a census of census- type surveyor taken from emplo~ent reco~ds or official registers), or (2) by addressing questions concerning absentees to other persons in the locality of oriGin, in a special purpose household survey, or (3) examining local reGisters in areas of out-migration, Each cf these methods is beset by difficulties.

Collation of data concerning migrants who cross international lines is dependent on the comparability of data collected in different countries.' Even collation of data on migrants to different 8reas within the same country may place a heavy

/ ...

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j-'- .demand on modeststat:lst;Lca1 resources unless it is l1l!lited. (a) to major divisions of thecount;ry, or (~) to t~e l;lreas that are the princ;Lpal ;sources of migration. Again, col<lai;;!.onof tribal data, mentioned in the preceding paragraphs,1Il!lY yield good information on migrants from some districts· that are occupied mainlY by ~ll-df'!fined groups, though not for other areas with more

he~erogeneous populations.

45.

It is, however, often important for economic and social purposes to obtain information on the demographic effects of out-migration from small areas affected i'l>y particular conditions. Such information must generally be drawn from reports

.concerning absentees made by their .relatives, neighbours, or local officials, in the· area under consideration. This information, even though.subject to

.considerable erl'ors, can'be expected to show important variations under. different

conditi.()n~,.,r:Ipquiries may also be designed to throw light on migr!\ci;iQn patterns and processes. For example, in the recent sampling demographic inquiry in Upper

~olta (a count;ry of heavy periodic out-migration) data were _ob~ained on absentees classified by duration of absence - 11l!lited to persons away les.s than.five years, on the assumption that useful information could not be obtained in the case

of persons absent a longer time. In this inqui;ry a special schedule on previous .migration experience was used in all interviews with men present at that time

i . _ . . . . . _ , . •

in the s!\mple areas. Each man was asked about numbers of trips of six months or more duration (a) within this country.and.(b) outside this count;ry. Detailed information was then reCJ.uired with respect to (a) his first trip outside the country and (b) his most recent trip - on age, residence, family status and Occup!\tionat the time of departure; date and type of travel, and whether or not accompanied by wife.and children; duration of stay, employment, and whether or not married during absence; conditions of return trip, and money or goods

brought back; and duration of next continuous stay in Upper V6ita. Unfortunately, the results of this experimental investigation are not yet available.

l~6. Observations on seasonal migrations present a special difficulty, and information on this subject is often vague. One possible way

61'

getting at the magnitude of' seasonal changes of population, where such changes are important,

is to estimate the peaks and troughs by sajllpling studies in. the same locality at two or more different t1l!les of. the year. If more complete descriptions of

/ ...

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seasonal migration are required, the surveys at different times in the year might be, complemented by small, continuous surveys of movements at key points.

47. Information on the characteristics of in-migrants or absentees, at a given moment c!;ill throw light on the underlying processes. Variations in' sex and age

,_{\ ' - , '}tomposit~~'~mong_{,', \ .. ,-',} population segments formed by migration provide a hasis for

inferenc~s about the nature of migration processes. Information on other characteristics, e.g. marital status and occupation -evenwithout a direct question on lengt'h of residence - can be used to check inferences from data on sex and age ~6mPosition:Ifthe adUlt'§ex ratio ina migrant segment approaches nornu:.lcy, it' if'iikely'that the, segment has been largely formed by permanent,

.

^-

or at least lohg-term, migrant~. In short, it may be said that data on the . ,., demographic and !ioeial charac ter-ist.tcs of migrants in a given area at a 'given

time provide ~basis for reasonable, though sometimes inconclUsive, inference about migration processes.

48. There~ifno one best way under all circumstances of measuring migration in Afri;a,

"ev~n

with'the limited objective of measuring its

resid~l

^{effects on}

-: :",.'- -: ..-'..~;

the status, of populations. There are, however, several useful ways, among , which the use of tribal data is cne of the most promising. Other important

procedures' include the use of information on in-migrants, defined by a question on place of birth or place of residence at some previous'date, and inquiries

(es~eciallY i~

rural areas) ooncez-nlng absentees. A clearer recognition of the importance of knowledge about migration will almost certainly lead to the

'1:

provision of more extensive and useful information on this subject. It is helpful here, as at many other points, to bear in mind a working principle, advanced by some persons with experience in African inquiries, that on any important topic one should try to get information in at least two different ways.

VII. ESTIVATION OF POPULATION TRENDS AND PROJECTIONS

49.

I~ is now becoming possible, in a few African countries to obtain e~timates

of natural increase from estimates of fertility and mortality and,. taking the effects of migration into account or excluding tribal groupsappreci.ahly affected

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those indicated by successive censuses, comparable in methods and coverage. But,

unfortyn~t~+~"oneor more of the elements required for proceeding in this way .arecstill l~Cki~g in most countries. So the statistician attempting to estimate

either natural increase or the trend of the total population is generally forced

tcr,~ercisehis jUdgement concerning sources of error in discordant or incomplete statistics in finding a range of values which can be assumed to include the

true rate of increase.

50.

In the case of rapidly growing urban centres and zones strongly influenced by migration, direct estimates of total population change from successive surveys,

s,

which often have a longer history and can be repeated with less difficulty than nation-wide inquiries, will often have greater validity than the estimates of their components: fertility, mortality, and migration. In such cases it is reasonable to place primary relio~ce on an estimate of the crude rate of population growth as a basis for a projection of future population trends, as

required for planning and administration. I f there is positive evidence of changes in the composition of a local population, with respect to sex, ages, ethnic

groups, etc., this can be taken into account. Otherwise, one may assume a coptinuation of the proportional distribution found in the present population.

51. In the case of most national and some regional populations it is possible and desirable to distinguish at least the two major components of population

chan~e, natural increase and migration, and to treat these separately. A distinction can·then be made with respect to migration between

(1)

temporary movements which may augment or diminish particular segments of the population but need not be taken into account in projecting subsequent trends in natural increase and (2) changes in the size and composition of the established

population through access or loss of migrants which must be taken into account in estimates of subsequent births and deaths.

52. Any projection of the natural increase of a population is dependent

on the selection of working assumptions. One possible (though ordinarily rather unlikely) hypothesis is that the rate of natural increase will remain unchanged.

Another possible hypothesis is that there will be a gradual rise in this rate,

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due to the persistence of relatively constant fertility in combination with some specified diminution in mortality. In some circumstances, however, it may be more plausible to assume a rise· in mortality or a decrease in fertility.

It is rarely possible in'Africa at the present time to find any firm empirical basis for such hypotheses because, even though it begins to be possible to make reasonable·estimates of cUrrent fertility, child mortality, aod natural increase in· some AfTican countries, i t is usually impossible to accol!lPlish the more

difficult task of measuring recent changes in these factors.

53. The pi-eferred method of population projection for count.rl es With detailed .: and reliable demographic 'statistics Ls some form of the "components method"

'involving the application of specific mortality and fertility rates (changing over time in accordance with stated trends) to the observed aex-end-age segments of the initial population, usually with some adjustments by smoothing or other methods of correction. This is hardly feasible today in most African countries, The' selection of a hypothetical series of specific factors, subject to stated itrends,,,ould require many arbitrary jUdgements; distor.tions in the initial

;estinmtes might be exaggerated in' their projection; and the significance of the final results would be obscure •. Some simpler, more comprehensible method is generally required. There seem to be two major alternatives.

51~. TIle simplest procedure is to work with hypothetical trends of the

crude birth ,and death rates. If constancy in the crude birth rate is assumed, a constancy of the proportional division of the popUlation by sex and age classes' may also be assumed without great risk of gross error. However, if a

change infertility is assumed (or a change in infant mortality not balanced by corresponding changes in death rates at later ages); important changes in age structure and consequently in the crude death rate, in addition to the effects of changing death conditions, must be expected. The simple procedure Just suggested is, therefore, hardly acceptable except in situations where it can be assumed thatfcrtiii'~y ".ell be fairly constant. At best this procedure;

though by no means absurd in some situations, is not very satisfactory.

55. As pointed out bef'or-e ; the construction of a theoretical "stable

population", fi:tted,to the estimated characteristics of a population, is the nost promising approach in many situations to the estimation of the distribution

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