WHAT THE AGE COMPOSITION OF MIGRANTS CAN TELL US

Luis J. Castro* and Andrei Rogers**

Sutvtuany

The present paper seeks to identify some of the factors that are responsible for thewidespread regularities in age profiles exhibited by empirical schedules of migration.

It shows how family relationships among migrants are reflected into their aggregateage profiles. By disaggregating migrants into dependent and independent categories, thepaper illuminates the ways in which the age profile of migrating populations is sensitive torelative changes in dependency levels and in rates of natural increase and mobility.

Just as population age compositions reflect particular characteristics of fertility andmortality régimes, so do observed migration age compositions reflect key aspects of familystructure and migration patterns. A framework for assessing the impacts of natural increase,family dependencies, and differing migration propensities is proposed.

)

,I

INtRooucnoN

A population pyramid graphically displays the age and sexdisribution of a population; figure I presents such pyramidsfor Mexico and Sweden. The population of Mexico, with itslarge fraction of children and small fraction of elderly, D&ybe called a "young" population in contrast to Sweden,which clearly exemplifies an "old" population.

The age composition of a population retlects the pasthistory of fetility and mortality to which the population hasbeen exposed. For example, high rates of natural increasegive rise to age pyramids that taper more rapidly with age,and zero growth rates ultimately produce age pyramids thatare nearly rectangular until ages 50 or 60 and that declinerapidly thereafter as death rates increase among the aged.Thus, one may conclude that the age composition of a popu-lation tells us something about past patterns of fertility andmortality. Since migrants are a subset of the population, doestheir age composition reflect analogous characteristics ofrecent patterns of fertility, mortality and migration?

Figure II sets out the national migratron pyramids tbrMexico and Sweden. They exhibit a fundamental commonfinding of countless migration studies: the age compositionof migrants reflects age selectivity, with young adults andinfants generally being the most mobile group in any popula-tion. Migration propensities are high among children, vary-ing from a peak at age I to a low point about age 16. Beyondthat age, migration increases sharply to another peak aboutage 22, after which it declines regularly until possibly inter-rupted by a retirement peak at the older ages.

*Former Research Scholar, Human Settlements and Services, Interna-tional Institute for Applied Systems Analysis, Laxenburg, Austria.

**Chairman, Human Settlements and Services, International Institute forApplied Systems Analysis, Laxenburs. Austria.

The present paper seeks to identify some of the factorswhich could explain the widespread regularities in age pro-files exhibited by empirical schedules of migration rates. Webegin by briefly considering the problem of migration meas-urement and then go on to adopt a mathematical functionaldescription of migration age composiüons. Armed with thissuccinct representation of the age structure of migrants, wego on to examine how differences in family status patternsstructure the age profile of migrants.

EsTngITs}ilNG THE REGULARITIES:MIGRATION MEASUREMENT

Migration studies have in the past exhibited a curiouslyambivalent position with regard to the measurement of geo-graphical mobility. This ambivalence is particularly strikingbecause of the contrast it poses with respect to the cone-sponding studies of mortality and fertility, studies that arerichly endowed with detailed discussions of measurementproblems. Haenszel (1967) attributes this paradox to thestrong influence of Ravenstein's early contributions tcmigration analysis:

"Work on migratron and population redistributionappears to have been strongly influenced by the earlysuccesses of Ravenstein in formulating 'laws of migra-tion'. Subsequent papers have placed a premium on thedevelopment and testing of new hypotheses rather than ondescriptions of facts and their collation. . . This is incontrast tu the history of vital statistics. While Graunt,more than two centuries before Ravenstein, had madeseveral important generalizations from the study of 'bills

of mortality' in London, his successors continued to con-centrate on descriptions of the forces of mortality andnatality by means of rates based on populations at risk"(Haenszel, 1967:260).

63

Figure I. National population age comlDsitions: Mexico, 1970, and sweden. 1974

Mexico,1970

Age

9080

70

60

5040

30

20

100

L

128(percentage)

Age90

T

812(percentage)

Sweder, 1974

80

70

60

50

40

30

20

100

16 l2g4O(percentage)

sources: Federal Statist-ical otfice, rr70; Ándersson and Hormberg, 19g0.

Figure rI. Nationar migration age compositions: Mexico, 1970, and sweden. 1974

J

A fnterctate migraüon, Mexi@, lgl}

Age

80

70

60

50

40

30

20

f0

0

J

B- Intenegionaf mignaüon, swedeñ, 1974

Age

80

70

60

50

40

30

20

t0

016rzBi 048n(Rercenage¡ -r r;o- ^_

r¿(Fercentage)sources: lo'ne per cent sample of the t97Ó Mexican population census; Andersson and Eolmberg, lgso.

r2B(percentage) 8t2

(percentage)

65

It is nanral to look to the state of mortality and fertilitymeasurement for guidance in developing measures of migra-tion. Like mortality, migration may be described as a processof interstate transfer; however, death can occur but or¡ce,whereas migration is a potentially repetitive event. Thissuggests the adoption of a fertility analogue, that is, insteadof births per mother, moves per migrant; but migration'sdefinitional dependence on spatial boundaries and on differ-ent forms of data collection introduces measurement difficul-ties that do not occur in the analysis of fertility.

One of the central problems in migration measurementarises as a consequence of the different sources of migrationdata. Most informatiori regarding migration is obtained frompopulation censuses orpopulation registers that report migra-tion data, for a given time interval, in terms of counts ofmigrants or of moves, respectively. Yet another source ofmigration data is the sample survey, which may be designedto provide information about both migrants and moves.Mgration data produced by censuses are usually in the formof transitions. Population registers treat migration as an eventand generate data on moves.

A mover is an individual who has made a move at leastonce during a given interval . A migrant, on the other hand, isan individual who at the end of a given interval no lo¡gerinhabits the same community of residence as at the start of theinterval. Thus, paradoxically, a multiple mover can be a non-migrant, if after moving several times he returns to his iniüalplace of residence before the end of the unit time interval.

Because migraüon occurs over time as well as acrossspace, studies of its patterns must trace its occurrence withrespect to a time interval, as well as over a system of geo-graphical areas. In general, the longer the time interval, thelarger will be the number of return movers and non-sunrivingmigrants and, hence, the more the count of migrants willunderstate the number of interregional movers (and, ofcourse, also of moves).

Most migration data collected by population censusescome fromresponses to fourtypical questions: place of birttr,duration of re.sidence, place of last residence and place ofresidence at a fixed prior date (United Nations ,l97O). Fromthese quesüons it is possible to establish the count of surviv-ing migrants living in a region at the time of the census,disaggregated by different retrospective time intervals. Thelonger the time interval, the less accurate becomes the migra-üon measure.

Because population registers focus on moves and ngttransitions, differences will arise between data obtained fromrcgisters and from population censuses. In the annex to theUnited Nations manual on Metlnds of Measuring Interno.lMigration (United Nations, 1970) it is stated:

"Since at least some migrants, by census definition,will have been involved, by registration definition, inmor€ than one migratory event, counts from registersshould normally exceed those from oensuses. . . . Onlywith Japanese data has it so far been possible to test thecorrespondence between migrations, as registered duringa one-year perid and migrants enumerated in the oensusin üerms of ñxed-period change of residence" (UnitedNations, 190:50).

TnsI-e I . Corrlpnrusox oF MrcRATroN By sEx AND TypE BASED oN THE PoPU-LATION REGISTER AND THE CENSUS FOR TT{E ONE-YEAR PERTOD BETWEENOcrosen 1959 ll.Io Ocrosen 1960. J¡p¡rN

Sex and type of migration Register dota Census data Ratio x I0O

Both s*eslnta-prefccturalIntqprcfectural

Malcslntra-prefcctural ..Intcrprcfectural . . : : : : : :

Fenul¿sIntra-prcfecturalInterp'refectural

1998 l7l 14.472 59075t r01.33

1001745 148.63I ¡ló6 898 9t.90

29óó62126í25 t35

I ,f88 935I 450 El?

| 477 86| 174 3r8

99642ftl 123 853

148.30104.4e

Sourcc: Unitod Naüons (ln0, table 42:f)).

Table 1, taken from the United Nations analysis, illus-trates how the ratio of register-to-census migraüon data is ingeneral bigger than unity, increasing with decreasing dis-tance, as, for example, in the case of intra- ven¡us inter-prefectural migration in Japan. In general, the ratio ofregister-to-census mrgration clata snould tend to unity aslonger distances are involved, and also as time intervalsbecome shorter (figue III). Clearly, the raüo should begreater than unity when short distances are considered andclose to unity when the time interval is short, because theprobability of moving across long distances several timesshould be expected to be less than the probability of movingthe same number of times between short distances. And, theprobabillty of moving several times during a long interval oftime should be greater than the probability of experiencingthe same number of moves during a shorter perid of time.

A tundamentat aspect of nügration is its change over tíme.As Ryder (1964) has pointed out for the case of fertility,period and cohort reproduction rates will differ whenever theage distribuüon of child-bearing varies from one cohort toanother. The usefulness of a cohort approach in migration, as¡in fertility analysis, ües in the importance of historical expe-rience as an explanation of current behaviour. Morrison(1970) indicates that migration is inducedby transitions fromone stage of the life cycle to another, and "chronic"migrants may artificially inflate the migration rates of originareas that are heavily populated with migration-prone indi-viduals. Both influences on period migration are readilyassessed by a cohort analysis.

It is the migraüon of a period, however, illd not that of acohort, that determines the sudden redistribuüon of .anational population in response to economic fluctuations,and it is information on period migration that is needed tocalculate spatial population projections.

Current period migration indices do not distinguish trendfrom fluctuaüon and therefore may be distorted; currentcohort migration indices are incomplete. Thus it may beuseful to draw on Ryder's (1964¡ translation technique tochange from one to the other. As Keyfitz (1977:25O)observes, the cohort and period moments in Ryder's for-mulae can 'be interpreted, not as child-bearing, but asmortality, marriage, school attendance, income, or someother athibute of individuals". Migration is clearly such anattribute.

5

6

t

The impctance of historical experience in interpreting andunderst¡nding current migration behaviour led Peter Morri-son (190:9) to define the notion of staging as being "anylinkage between a prior sequence and subseguent migraüonbchaúq". Morrison recognizes for¡r kinds of staging: geo-graphic, life cycle, socio-cconomic ad experiential. Geo-graphical staging rpfcrs to r€hrn migration and to what isconventionally understood to mean "stage migration", thatis, thé idea üat migrants tend to move to places not verydissimilar from those they left behind. Life-cycle stagingviews migration as arising out of breaks in an individual's ora household's life cycle, such as entry into the labour force,marriage and rotirement. Socio-oconomic staging seesmigration scqucnoes as bcing conditioned by socio-stnrctural

Iturc m. Rrüo of rcabcr !o ccrn¡ n[retbn drtrttlh rl¡pcct to dllrncc ¡Dd dn hicrvd

dis;hnce

factors, such as occupation, educational athinment andincome level. Finally, experiential staging refers to move-ment experience in terms of number of previous moves andduration since the last move; it is the '?arity" dimension ofmigration analysis.

Calculations of migration rates of increasing specificityseek to unconfound the "tn¡e" migration rates from weightsthat reflect the arithmetical influence of the past. This pro-cess of measuring migration

". . . at different levels of specificity of occunence andcxposur€ yielrls products which draw ever finer dtstinc-tions betrreen current behavior and the residue of pastbehavior reflected in the exposure distribution at anytim€" (Rydcr 195:10).Such products may be weighted and aggregated to produce

the "cn¡de" rates of higherlevels of aggreganon. Forexam-ple, the agc-scx-specific migration rate is a weightedaggregation with respect to the migration "parity-duration"distribution just as the crude migration rate is a weightedaggregation with respect to the age-sex üstribution.

The age profile of a schedule of migration rates reflects theinfluences of two age distributions: the age composition ofmigrants and that of the population of which they were apart(Rogers, lnq. This can be easily demonstrated by decom-posing the numerator and denominator of the fraction thatdefines an age-specific migration rate, M (x), sy.

lf O (x) denotes the number of out-migrants of age x,leaving a region with a populaüon of K (x) at that age, then

M (x) : o (x) : o'N (x) : o. N (x) ( l)

K (x) K 'C (x) C (x)

where

O : total number of out-migrantsN (x) : proportion of migrants aged r years at the

time of migrationK : total population

C (x) : proportionof total population aged x years atmid-year

o : cnrde out-migration rate

We define the collection ofN (.r) values to be the migrationproportion schedule and the set of M(x) values tq be themigration rate schedule.

Suuuan¡axc rHE REGI LARrrrEs:MODEL MIGRATION SCHEDULES

Observed age-specific migration rate schedules univer-sally exhibit a conunon shape (Rogers and Casüo, l98l).The same shape also cbaracterizes the age composition ofmigrants, that is, migration proportion schedules. Startingwith relatively high levels druing the early childhood tg€s,migration rates or proportions decrease monotonically to alow point atagex,, sy, increase until they reach a high peakat age,r¡, aod then decrease onee again to the ages of retire-ment before leaving off aro¡nd some constant level, c, ey.Occasionally a "post-labour force" component appears,

regisb/cen$s ratio

reglsb/cens¡s ratio

üme inbrual

6l

showi4g either a be[-shaped curye with a retirement peak atage x¡or an upward slope that incrpases mondonically to thelast age included in the schedule, age lr, say. Thus, themigration age profile may be divided into child (dependenD,adult anc etcerly aomponents; however, we shall confine ouratlention in the present paper to only the first two. But ourargument is equally valid for profiles strowing a retirementpeak or an upward retirement slooe.

The observod age distribution of migrants ,N (x), may bedescribed by a ñrdction of the form:

where

N ( x ) : N r 6 ) + N 2 @ ) + c ( 2 )

Nt @) - 41 e-at x

fa the child (dependent) component,

NZ 6 ) : a2 e -%k

- t l z ) - e -x26 - t t z )

rbr the aü¡lt (independent) component, and c is the constantterm that improves the fit when migration distributions atolder ages are relatively high. Figure IV illustrates the femalemodel migraüon proportion schedules of the observed datapresented in figure II, which by definition show an area ofunity under each curve.

An anernaüve way of expressing equatron (2) is as aweighted linear combination of the density functions représenüng the above three components (Castro and Rogers,l98l):

N (x ) : h f i 6 ) + h fz@ + óc ( I lw ) (3 )

where w is the last age included in the schedule, ótand @2 aretbc relative shares of the child and adult components, ó" istbc share of üe constant tsrm,f,(x) andfr(i) u", respec-tivcly, tbc single and double ex¡nnential dcnsity funcüons

h @) : er e-at x (4)

fz @) - #

e-azk - Fz) - e-\26 - t2) (5)

and I (o.2llQ reprcsents the gamma function value of a2l\2.Note that ó, + óz * ó" : I by definition.

Equations (2) through (5) imply that

4 I : Ó , q ,

Tr¡u 2. hnrcpr¡, n¡ucns DEFTNTNc oBsERvBD AcB-sp¡oFtcMIORATION OTARACTEruSTTCS

Clwara¡istic

hoportion of child¡e, (dcpcndants),

Qt allal

Proportion of adultsa, Q (labourforce)

fr- r @2t\)

Labour asymm€try, az \21a2

I-abour dominancc, 62¡ a2la 7

Parental-shift, Br2 a7la2

Ctild-adult dependency migration Iratio, Do

Thc reciprocal index is also of interest inasmuch as it reflects üe Otal

number of migrants per adult, s, = ;#.

stope; anÍ p2 positions the adult component on the age axis.Taken as a group, these parameters suggest a number ofuseful and robust measures for describing an observed migra-tion sclrcdule (table 2). For example, the ratio Do : ü lh,the child-adult dependency migration ratio, is one of severalimportant ratios that may be used to interpret particularpatterns of dependency among migrants. It assumes a centralrole as an indicator of family dependency structure by defin-ittg the number of dependants per adult migrant.

The child-adult dependency migratron ratio vanes as afunction of the parameters that define the age profile ofmigrants. If the constant term c is close enough to zero to beignored, as normally is the case, then {" : 0 and

Do:t:ffiSince

l (q l \ r ) :W

we obtain the result

D o :9,, 6r,I ¡l + I lo)

where ür : qla¡ Fn = a,b¡ (r2: Itrlq are tüe labor¡rdominanc€, pÍlr€ritll-shift and labour asymmetry indexesdefined in Rogers and Castro (1981). These three ratios andpzmay be used to fully characterize observed migration ageprofiles.

Another useful indicator of the average size of familyamong migrants is the value so : I lS2, which reflects thetotal number of migrants per adult. In a single-sex formula-tion, for instance, if adults are considered as heads of eachmigrant family (interpreting single individuals as one-personfamilies) then the sum of the two sex-specific values of soclosely approximates the average size of family amongmigrants.

(e)

and

c- h_w

The six parameüerse1, e¡, a2, e, ! and pz do not seemto have demographic inúerpretations. Both c¡ and a2 reflectthe heights of their respective parts of the profile; a1 and a2refer to the descending slopes; 12 reflects the ascending

(ó)

(7)

(8)

6E

-x

*oct)(E+,(trEoEeeo-

0.03

0.02

0.01

0

0.05

0.04

0.03

o.o2

0.01

0

IISUrc IV. Componcnts of ihc nodel mlgrrtbn proportbn schcdute

A Inbrstate migraüon, Mexi@, 1970

-, .2 k-p2) - "

^t ( ' -Pz)

a2 e

) 20.0 30.0 40.0 50.0 60.0Age

B. Intenegional migraüon, Swedeñ, 1974

Females

t

s>ioCD(u

TEo€eeo-

30 40Age

69

Figure V. Model migration proportion schedules for selected cities around the worldand a typical nation¡l immigration flow

0.05

> 0.04=xoP o.o3(EcoEg o.o2eo-

0.01

0

0.06

0.05

-x

{ 0.O{ooo(E

E 0.03EIpd o.o2

0.01

0

l1

l¡

oCD(o+.|Eco€eeo-

Figure V (continuedl

Gr€abr Kharh¡m

. - --Sources.' Alberts, l!77.; gne pe_r:gg!!-t'gpte of the 197-9 polrllation census of Mexico; Géorge antlEigbéfoh,1973; Kawabe and Farah, tgz¡: nr-oérssoñ-al-¿ Hóhnberg, lffiÜñiG¿-ñltioris,lgTg.

-

7 l

s ofH

)t

$ ooote

.9E oo2g

> o ( ES-

x'oP o.o4.rt.EEoF

E000E

s ofH

*

$ on.{rr.E

Ef, o.ozeo,

0.01

3 0 4 6 -Stockholm

lmmlgratbn b Kuvmit

Tr¡t¡ 3. PlteMsrgRs AND vARIABLES DEFTNTNc oBsERvED MoDEL MIGRATToN pRoFoRTroN scHEDr,JLEs FoR sELEcTED crrrEsAnouND THE woRLD AND A TyprcAL NATToNAL rMMrcRATroN n o#¡

Rb dc taaá¡o llcxico City Grcatcr Klutau¡t Stültholm Innigration to KuwaitPomqvtúb Faml¿s

a1a1a2

,L2a2lU

0.0¿:t o.(Xl0.075 0.oy20.051 0.037

15.394 14.9050.()69 0.0590.6A 0.583

0.065 0.048 0.u20.101 0.081 0.0990.u27 0.02r o.ú2

15.765 13.878 t7.2230.ü/0 0.060 0.w21.107 t.2Á3 0.291

0.025 0.0230.116 0.0950.088 0.096

rc.ns 19.6480.098 0.1100.$t 0.334

0.018 0.u270.056 0.0470.086 0.084

19.65r t9.%0.108 0.1610.229 0.301

0.03E0.0650.0,18

rr.ffi0.0980.318

0.0310.0990.054

15.053ó.oog0.531

NqrE Ou¡ .ssumplion th'r c = 0 cont¡irs the paramcters to satisry the rclationshipfl- a ,?--f @y'XrrÉ;l

fiowrc, ot rt¿ciUu did ¡ú paúúi3 u¡ b aúta¡ this ¡rrt¡ictiotr. HGtrcc, somc p¡r¿otcr v¡luc¡ ¡¡p 'iüghtly birséd" úd in rucb iD¡t¡¡caa 6c abovc cqudig¡ 4jri.lt ná, W. e ¡ndru r frcjücr fa4cnr to¡ O¡ oüac¡var¡¡.-! Dl c pú¡rllclcr vd¡¡c w¡6 3e1 equ¡l to zem rn tlre non-túea¡ pa¡arnetcr €stimarion pfocedur€.

Figure V sets out s€veral age profiles of internal migrationflows to different cities around the world, together with aqpical international migration (immigration) age distribu-tion for males and females. These profiles were generated bymodbl migration proportion schedules fitted to observeddata, the parameters of which are included in table 3. Thequantitative indices presented in Able 4 confirm the reg-ularities illustrated in ñgure V. For example, the migrationflows to Mexico City and to Lagos differ sharply from theoüresllonding flows to Stoclüolm. The former show aboutdouble the proportion of dependants exhibited by the latter.Tbe same table also indicates that the average size of familyin theflow-to Mexico City, with about2.65 + 2.20: 4.85members per migrating family, is the largest among theerarqtles _p_ resented .

All of the migration characteristics in figure V and table 4indicate low or high family dependency patterns. In the nextsecüon, we s€ek an explanation for such characteristics bylinking them with the family characteristics of the populationas a whole.

EXpI¡T¡uNc TTTE REGULARITIES :FAMILY STATUS

It is widely recognized that a large fraction of total migra-tion is accounted for by individuals whose moves aredependent on those of others. Indeed, family migration issuch a well-established phenomenon that Ryder (1978) haseven suggested its use as a criterion for identifying familymembership: a family comprises those individuals whowor¡ld migrate together.

To understand thé influences that family and dependencyrelationships have on migration age compositions, it is usefulto examine how such profiles respond to fundamentalchanges in dependency patterns. To illustrate this, consider asingle-sex population that is divided into two groups: depen-dants and heads, where dependants are simply individualswho have not left home to become heads. (Included as headsare independent single individuals who may be viewed asone-person families.) Thus, the age distribution of the femalepopulation C (x) may be composed by weighting the density

L

Tr¡I.E 4. Esnrr¡rsD cHARAgrERIsrtcs oF oBsERvED MoDEL MIcRATIoN x)puLATtoN scrrEDULEs FoR SELEcTED cITtEsAROIJND THE WORLD AND A TYPICAL NATIONAL IMMIGRATION FI.oW

'Rb dc Julci¡orI%t-rn2

-auu-c¡j

I%tr-t970Lagosc ciu¿r xtuitnd stnl,l-l^'

1967-IX,E l%t0-r%4 Iy74Innigruioato ,

Kuxyait I%5-IY/O'

Clwrcteñsüc Fciule llal¿ Fctml¿ Malc Fcnal¿ Tdol Malc F¿rrulc Aab Fdrulc

hoportion of dependants(pcrecntage) 33.70

hopction of adults(percentage) 70.14

Total number of migrantsper adult 1.43

I¡bor¡r asymrnetry 10.03I¡bour dominancc 2.U2Parcnal shift l.0BGild-adult migration ratio 0.4t

4 .8 t &.29

59.54 37.67

1.68 2.659.83 t5.740.90 0.421.56 t.430.75 t .7 l

59.50 42.28

45.55 59.90

2.20 r.672t.0t 3.200.58 t.47r.34 1.08l .3 l o.7l

24.07 21.31

78.06 82.17

t.28 t.223.04 5. r84.18 3.550.87 l . l80.31 0.26

3t.6 57.09

70.9 6.n

1.42 2. t62. t2 1.874.88 3. t20.52 0.290.45 r.23

57.80

43.88

2.283.24t . no.67r.32

31.60

73.77

1.367.73r.721 .40.43

Swces::Alberts, 197.bnc pcr cent sample of the 19/0 Mexican population oensus.p*t!" and Eigbeioh, ln3.Tkwabe and Farah, 193.lAndersson and HoLnberg, 1980.¡Unitpd Nations, 1919.

72

functions of dependants and heads:

C (x) : ót"ft"@) + ór"fr,(x)

where Ór" and Ór, *" the proportions of dependants andheads in the total female population andJ" @) andfr,(x) uetheir corresponding age distributions, respectivelv.

The ratio of tne weignts associated witn tne age profiles ofdependants and heads defines the child-adult dependencypopulation ratio, D", which is similar to theQ¿ defined earlierfor the migrant population:

n - ó t ,u c - ó r "

As in the case of migration, we can also detine the totalnumber of persons per adult (head) ffi r" : I ló2". To invesü-gate analytically some of the underlying patterns of "headformation " requires some mathematical theorizing.

Irt yr'.denote the age at which an appreciable number offemale3irst leave home to establish their own household.Since mariage is an imporüant reason for leaving the familyhome, it is likely that the probability density functiondescribing the pattern of head formation by age is similar tothe one found in studies of nuptiality, that is, the doubleexponential function defined in equation (5). Ifgly) is such afunction then

f ^G@) : l s0 )dy

tro

defines the proportion of females who have ever left home byage x, that is, who are heads according to our definition.

Since fr" (x) defines the proportion of the population ofheads that are of age x , and G f¡) defines the proportion of thepopulation who are heads by age ¡, it is evident that in astable population growing at an intrinsic rate of growth r,

fz" 6) _ _e-rx I (x) G (x)

e-a I 0 G (y) dy

where / l¡) denotes the probability of surviving from birth toage x. For similar reasons

ft" @)e - r x I ( x ) Í I - G ( x ) I

Figure VI illustrates the above argument with hypotheticaldata. It presents the survivorship curve, I (x) , which is that ofthe Brass standard with a : -0.80 and B : 1.75 with anexpectation of life at birth of approximately ó9 years (Brass,l97l); and the head formation curve G (x) is the Coale-McNeil double exponential (Coale and McNeil, 1972)expressed by the Rodriguez and Trussell (1980) standardwith mean (22years'¡ and variance (5 years) of age of becom-ing a head. Figure VII shows the resulting dependant, headand population (dependants plus heads) distributions of sta-ble populations growing at intrinsic rates r : 0 and r : 0.03,respectively.

To derive the corresponding age compositions of migrantswe inhoduce the probabilitiesp,(x) andpr(x) that a depen-dant and a head, respectively, migrate at age x in an intervalof time. The age distribution of migrants is defined as before:

where

f , ( x ) :

N (x) : ótfi @) + üf, (x)

e-rx I (x)l,I - G (x\pt @)

t [, e-rY I (Y) tt - G (Y)] Pt 0) dY

[,

I: ,T

and

fr (x) :fI e-'Y I (y) G (y) pz 0) dy

Jo

The child-dependency migration ratio Do, equivalent toequation (9), may now be defined as:

e-u I (y) Ít - G (v)lpt 0) dy

Do :

-'Y I (y) G (y) pz 0) dy

Both child-adult dependency ratios, D" and Do, may beanatysed 6y using hlpothetical populations once again. Tospetify correctly the probabilities pt @) and p, l¡) fromdifferent sources of migraüon data, it is necessary to identifyfirst the number of moves a person undertakes during a unitinterval. However, for our purposes we may assume thatboth dependants and heads follow a negative exponentialpropensity to migrate with respectto age, with the function'sBarameter reflecting the average rate of moving per unit oftime. Formally, we have then

and

pt @) : 6, ¿-o¡x

PZ Q,- Yd : o2 e-oz$ - Yo)

:rI e-'Y I (y) ÍI - G (il) dy

J ^0

Given these equations, the child-adult dependency popula-tion ratio D" may be defined as

@

I e-rY I (y) II - G (y)l dyI

D r : - *

TC73

I

-n'I 0) G (y) dy

Figure VI. Proportion surviving to age x, I (x), and proportion of individualswho have ever left home by age x, G (x)

r .000

0.900

0.800

0.700

0.600

0.500

0.400

0.300

0.200

0. t00

0.

where yo denotes, as before, the age at which an appreciablenumber of females first leave home to establish their ownhousehold, ord o/ and o, denote the average rates of movingper unit of time of dependants aüd heads, respectively. Onemight expect that the average rate of moving per unit of timefor dependants, o¡, should not exceed or,the correspondingrate for heads. In general, dependants (children) move withtheir parents and independent, single individuals are mostlikely to be found among adults.

Figure VIII presents the va¡iation of Dowith respect to D.for the hypothetical populations of figure VII, under variousmobility conditions as expressed by the ratio o , lo 2.lt may beseen that the ratioD o lD,rnoreclosely approaches unity as themigration of heads increases.

The parameters deñning the mobiüty conditions may beused to set out a typology of migration profiles that helps toidentify how a particular family migration pattern may be

reflected in a migration age composition, and how importantthe migration propensities among heads and dependants arein stn¡cturing that age composition. Figures IX and X presenta set of profiles classified according to two distinctly differ-ent rates of natural increase. For each of the hypotheticalpopulations we show three alternative combinations of pro-peñsities to migrate among heads and dependants. First,figure IX sets out, for low head migration propensities (o2 :0.08),profiles showing a significant degree of family migra-üon (o, : or) and also of low family dependency @t =0.10o2 and o, : 0.20o). In a similar format, ñgure Xpresents the corresponding profiles for high head migrationpropensities (o, -- 0.16).lVith the aid of these two figures wecan see that patterns such as those of Stocküolm indicate arelatively low family migration dependency with high headmigration propensities and low population growth rates,whereas profiles such as those of Mexico City present char-

*oo(tr(E

co€eeo-

74

Figure vII. Proportion of dependanls.at ase x,fiq@), proportion of heads at age x'f2¿$)' and the

resulting population age composition, C (i,ío: íniiíns¡c rates of growth r of zaro end 0'03' respectively

$ o.o,o

EI oo2

&

x- 0.o4oI6

g o.os

F,,

f o m i l ¡ m s oAs€

o t o 2 0 O ¿ o 5 ( r 6 0Age

)

¡a$ ooo6c

II oo3Io-

o l o z o 3 O ¿ m 5 0Age

20 30 ¡o 5(,AgP

acteristics that correspond to high family migrafon.depen-

d;t .rd áatively'high de,pendant and head migraüon

propensities.

Coxct ustoNs

The aim of the present paper has been to show how the

regularities that .pptut in migiation age compositions can be

,o-r-rrirrd in iüseful manner and to suggest what such

regularities may be telling us about patterns of natural

ññ;;,- family relationships and mobiüty levels among

migrants.--Í dir"ggr"gation of migranr* intg depe$ent and indepen-

dent cateió¡á, and the adoption of model migrationpropof-

tion schedules, illuminates the ways rn which the age protile

of .igation is sensitive to relative changes-in.dependencylevels and in rates of natural increase and mobüty' Viewing

the migration process within a framework of depeldent and

indepe-ndent rirovements allows one to observe that if the

indeirendent component mainll comprises single. persons'

tfr"n'tfr" associateá dependent migration may be insignificant

in terms of its relativl share of the total migration.pn the

,tfr.t tt""¿, if migfation tends to consist principally of family

;;"tú,'tt "n

tie share of dependent children may become

" n-"ty important part of total migration'- OUr"*in migáüon disributións, when analyse! in tlrc

context of the family status approach, confirm the indicaüons

gi""o by the puruto"t"ts of ttré associated model proportion

icheduies. Fór example, high migration dependencies were

75

Figure VIII. Variation of child-adult dependency ratios among migrants (Do) an¿ the population (Ds) with respect to different levels ofnatural increase (r), family migration (o7lo2\ and migration propensities of heads (o2)

2.00

1.90

1.80

1.70

l.ó0

1.50

1.40

1.30

1.20

l . l 0

J.(X'

0. 10.0 20.0 30.0 40.0 50.0

or lo2

= o.o3= o.16

=Q= o.16

= o.o3= o.og

-o= o.o8

ó0.0 70.0 90.0 100.0

(per cent)

tionships set out in the present paper are still conjectural, amodest start has been made. A framework for assessing theimpacts of natural increase, family dependencies and differ-ing migration propensities has been set out.

The arguments set out in the present paper are related to anumber of earlier efforts by the authors to examine reg-ula¡ities in age patterns of migration. For example, our focushas been on a single-sex formulation. However, it appearsthat differences between the age composition of migrantsmay be a consequence of differences in sex-dependencystructures. To study these relationships, a matrix approachhas been recently proposed in Castro and Rogers (1983).

Causes of migration are related to a person's age and sex.For example, migration motivated by health reasons is aphenomenon characteristic of old people, whereas educa-

ro2

o2

ro2

ro2

{

Qo o.eo0,80

0.70

0.ó0

0.50

0.40

0.30

0.20

0 .10

0.

correctly indicated for Mexico City; for Stockholm they werelow; and falling somewhere in between these two extremeswas the case of Rio de Janeiro.

The degree of propensity to migrate among independentmigrants is also evident from observed age profiles. Sronglyskewed distributions in the adult ages, corresponding to hightr, and a2 paraÍreter values, indicate relatively higher migra-tion propensities for the independent component. Profileswittr higb dependency levels show rnuch more weaklyskewed adult migration compositions due to lower propen-siües for individual moves among heads.

Just as population age compositions reflect particular char-acteristics of fertility and mortality régimes, so do observedmigration age compositions reflect key aspects of familystructure and migration patterns. Although many of the rela-

76

olo

ooe

0.6

o.g,

* n *x

$t o G

5En '

oqt

o@

oo

ngurc lX. .l,ry'ry9q f "¡: mlgrrrbn dhrlburlon¡ for br rd hbb populrrbo gmrrh,

frdry nEr¡rbn depcndcncig r¡d br hd nlrtbo plo¡iniltlcr

l¡wpg¡¡üongulfr,r 'Olow hcd nfgraüon fp.n¡ty,

or.Ofit o¡.O.08, O.OIE tnd 006

s*I¡

F

oo

b. towffiyd¡rrdÍct

lspn5oog:orrútr rOLtrttrdrdglrümffiy,

or.Oüt 0r.O.6. O.Ot6 tr5 O00t

X¡üeogffongwdr,r rO.GlLwhd nú¡nüonplup.rüy,

or.OOO ot.OOO 0.016 md 0003

OD

OO

q@

OO

OG

oof

q6

oc

oül

o.o

o.o r 0

c. F.Ítfnügr!ücl

ot 'oo16orr o'c

ot 'ool8or'ofi

or ' o'oo8or. OOB

20 0 ¡to 50 toAet

g¡'I¡

É

or0

OD

oc

g.g,

o0c

OG

o0a

o@

o@

oo

¡ 0 S ¡ | o 5 0 OAg.

o t o

d. Lwffiyd¡p¡nd¡rv

& t O ¡ O l 0 OAot

X¡ü mC¡ongu¡trru O.CBlow hrrd nfg[üon prop.üfry.

or.O& ot.Ooo, O.OIO üd Om

ol . o2. 0(D

oo

0.6

o@

$o-*

¡ o c¡l * .É

ogt

77

Figure X. { typgloqv. of 1Be migration distributions for different population growth,family migrntion dependencies and high head migration piofensities

:

l-ovv popt¡lalion groudh, r = OHigh fnad migraüon propensity,

or=0.16; or=O.16, 0.O32 and 0.016

$o*x'sf; o.os

EF"*

-* 0.06toCDoñ 0.05c

€R o.*o-

= o r= Q.16

It

Age

High popr¡hlion grornrlfr, r = O.O3High head mQration propensity.

o r=O.16 ; o l=0 .16 ,0 .032 and 0 .016

b. Lowfamilydependency

2A 30 40 50 60Age

S o.o.x'

$É b.osEE

F o'*

Hi$t pogdation grorndfr,r = 0O3Hagh h€d rrúf¡rdliorl prop€rx*V

or-0.16; o, =O.16, 0.o32 and 0o16

o, = O.O16

o, = 0.16

o, = O.O3202 = 0'16

L= or= 0.16

20 30 40 50 60Age

I

Lour popr¡lation grorarlh, r = OH¡gh head m¡gration properu*ty,

or=0.16; o, =0.16, O.O32 and O.016

0.

78

tion-related migration is predominantly associated withyoung people. Thus, in order to understand better why peo-ple move, it is important to disaggregate cause-specificmigration databy age and by sex. This "mortality" analogyis followed in Rogers and Castro (l98la), where it is shownthat it is possible to account for some of the differences in agepatterns of migration by linking them to differences in theirunderlying cause-specific structureS.

Drawing on techniques used in the corresponding litera-ture in fertility and mortality, Rogers and Castro (l98lb)proposed procedures for adopting model migraüon schedules

to infer migration patterns in the absence of accurate migra-tion data. Such model migration schedules may be used tograduate inadequate data, thereby smoothing out irreg-ularities and ascribing to the data summary measures that canbe used for comparative analysis. They also may be used tointerpolate to single years of age observed reliability ofempirical migration data, and indications of appropriatestrategies for their correction are aided by the availability ofstandard families of migration schedules. Finally, suchschedules may also be used to help resolve problems causedby missing data.

Rr¡sn¡¡¡css

I

Alberts, J. Migración hacia óreas metropolitanas de América Latina(Migration in t atin American Meropolitan A¡eas). Rio de Janeiro,Centro Latinoamericano de Demografia, 1977.

Andcrsson, A. E., and I. Holmberg . Migration and Scttlcnvnt: 3 . Swcdcn.Laxenburg, AusEia, International lnstitute for Applied Systems Analy-sis, 19t0. RR-80-5.

Brass, W. On the scale of mortality. Biological Aspects of Demography, W .Brass, ed. London, Taylor and Francis Ltd.,lnl. pp. 69-110.

Castro, L. J., and A. Rogers. Model Migration Schedules: A SimplifiedFormulation and an Altertutive Parameter Esti¡nation Method. I-axen-burg, Austria, International Institute for Applied Systems Analysis,1981. wP-8r-63.

Casro, L. J., and A. Rogers. Patterns of family migraüon: two meth-odological approaches. Environnent and Planning ^r{, vol. 15, 1983.

Coale, A. J., and D. R. McNeil. The distribution by age of the frequency offirst marriage in a female cohort. Journal of the Amcrican StatisticalAssociation 67 :7 43-7 49, 197 2.

Federal Staüstical Office. D( Censo General de Población (Ninth GeneralPopulation Census). Mexico City, 1970.

George, M. V., and A. A. Eigbefoh. Population growth and migration inLagos, l9l l-1963. Urbanization and Migration in Some Arab andAlrican Countries. Cairo, Cairo Demqgraphic Center, 1973.

Haenszel, W. Concept, measurement, and data in migration analysis.Demograplry 4:253-261, 1967 .

Kawabe, H., and A. A. M. Farah. An ecological study of Greater Khar-toum. Urbanizption and Migration in Some Arab and African Countries.Cairo, Cairo Demographic Center, 1973.

Keyfitz, N. Applied Mathe¡natical Demography. New York, Wiley,lW .

Morrison, P. M. Implications of Migration Histories for Model Design.Santa Monica, California, The Rand Corporation, lnO. p. 4342,

Rodriguez, G., and J. Trusseü. Mücimum ükelihood Estination of theParatneters of Coale's Model Nuptiality Schedule from Suley Data.World Fertility Survey, Technical Bulletin 7, Tech. 1261. Voorburg,Netherlands, International Staüstical Institute, 1980.

Rogers, A.Two Methodological Notes on Spatial Population Dynamics inthe Soviet Union. laxenburg, Austria, International Instiote fq AppüedSysrcms Analysis, 196. RM-7648.

Rogers, A., and L. J. Castro. Age patrcrns of migraüon: cause-speciñcprofiles. IIASA Rcporrs 4: l2!l-ló0, l9Ela.

Ryder, N. B. The process of demographic transition. Demograplry,l:7482,1964.

Fertility measurement through cross-sectional surveys. SocialForces, 54l.7-35,lÍ15.

Methods in Measuring the Family Life Cycle. Proceedings of theInternational Populaüon Conference, International Union fm the Scien-üfic Study of Populaüon , lnt.

Soboleva, S. Migration and Settlernent: 8. Soviet Ilüon.I-axenburg, Aus-tria, International Institute for Applied Systems Analysis, 19E0.RR-8G36.

United Naüons. Department of Economic and Social Affairs. Methods ofMeasuring l¡tertul Migration. Population Stuües, No.47. (ST/SOA/Series A/47) Sale.s No. E.70.XIU.3.

Tre¡ús and Clnracteristics of lternartonal Migration Since 1950 .Demographic Stuües No. 64. 19/9. (ST/ESA/SER.A/64) Sales No.8.7t.Xm.5.

t

f

79

CONTENTS

Recent trends and conditions of fertilityUnited Nations Secretariat

Fertility and family structureNorman B. Ryder

Population distribuüon policiesHarry W. Richardson .

Metropolitan migration and population growth in seleoted developing countries, lfbG 1970United Nations Secretariat

What the age composition of migrants can tell usLuis J. Castro and Andrei Rogers

The long-term impact of war on mortality: old-age mortality of the First World lVarsurvivors in the Federal Republic of Germany

Shiro Horiuchi

15

80

DEPART]IIENT OF INTERNATIONAL ECONOMIC AND SOCIAL AFFAIRS

ST/ESA/SER.N/15

aPOPULATION BULLETI NOFTHE UNITED NATIONS

15 -1983

rat

WH*T*J?J*,-'

No.

t