WHAT THE AGE COMPOSITION OF MIGRANTS CAN TELL US (1982)

8/3/2019 WHAT THE AGE COMPOSITION OF MIGRANTS CAN TELL US (1982)

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WORK I N G PAPERWHAT T H E A G E C O M P O S I T I O N O F M I G R A N TSCA N T E L L U S

L u i s J . C a s t r oA n d r e i R o g e r s

O c t o b e r 1 9 8 2W P - 8 2 - 9 4

1~ASALmI n t e r n a t i o n a l I n s t i t u t efor Applied Systems Analysis


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NOT FOR QUOTATIONWITHOUT PERMISSIONOF THE AUTHORS

WHAT THE AGE COMPOSITION OF MIGRANTSCAN TELL US

Luis J. CastroAndrei Rogers

October 1982WP-82-94

Working Papers are interim reports on work of theInternational Institute for Applied Systems Analysisand have received only limited review. Views oropinions expressed herein do not necessarily repre-sent those of the Institute or of its National MemberOrganizations.INTERNATIONAL INSTITUTE FOR APPLIED SYSTEMS ANALYSISA-2361 Laxenburg, Austria


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PREFACE

The evo lu t i on o f human po pu la t ion s o ve r t i m e a nd s p a c e h a sb ee n a c e n t r a l c o n c e r n o f many s c h o l a r s i n t h e Human Se t t l e m e n t sa nd S e r v i c e s Ar ea a t I I A S A d u r in g t h e p a s t s e v e r a l y e a r s . From1975 t h r o ug h 1978 some o f t h i s i n t e r e s t was m a n i f e s t e d i n t h ework o f t h e Mig ra t io n and Se t t l em en t Task , which was fo r ma l lyc o n c lu d e d i n November 1 97 8. S i n c e t h e n , a t t e n t i o n h a s t u r n e dt o d i s s em i n a t i n g t h e T a s k ' s r e s u l t s , t o co nc lu di ng i t s compara-t i v e s t u dy , and t o e x p lo r i n g p o s s ib l e f u t u r e a c t i v i t i e s t h a tm ig ht a p p l y t h e m a t h e m a t ic a l me th od olo gy t o o t h e r r e s e a r c h t o p i c s .

T h i s p a p e r i s p a r t o f t h e Ta s k ' s d i ss e mi n at io n e f f o r t . Itshows how f a m i l y r e l a t i o n s h i p s among m i g r a n t s a r e r e f l e c t e d i nt h e i r a g g re g a te a ge p r o f i l e s . By d i s a g g r e g a t i n g m i g r an t s i n t od ep en d en t an d in d ep e nd e nt c a t e g o r i e s , t h e p a pe r i l l u m i n a t e s t h eways i n w hic h t h e a g e p r o f i l e o f m i g r a t i n g p o p u la t i o n s a r e s en -s i t i v e t o r e l a t i v e changes i n dependency l e v e l s and i n r a t e s o fn a t u r a l i n c r e a s e a nd m o b i l i t y .Andre i RogersChairmanHuman Set t lementsa n d S e r v i c e s


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C O N T E N T S

I N T R O D U C T I O N 1

E S T A B L I S H I N G THE R E G U L A R I T I E S : MI GR ATI ON MEASUREMENT 5S U M M A R I ZI N G T H E R E G U L A R I T I E S : M OD EL M I G R A T I O N S C H E D U L ES 1 1E X P L A I N I N G T H E R E G U L A R I T I E S : F A MI LY S T A T U S 2 0

C O N C L U S I O N S 29R E F E R E N C E S 3 1


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WHAT THE AGE COMPOSITION OFMIGRANTS CAN TELL US

INTRODUCTIONA population pyramid graphically displays the age and sex

distribution of a population; Figure 1 presents such pyramidsfor Mexico and Sweden. Mexico's population, with its largefraction of children and small fraction of elderly, may becalled a "young" population in contrast to Sweden, which clearlyexemplifies and "old" population.

The age composition of a population reflects the past his-tory of fertility and mortality to which the population hasbeen exposed. For example, high rates of natural increase giverise to age pyramids that taper more rapidly with age, and zerogrowth rates ultimately produce age pyramids that are nearlyrectangular until ages 50 or 60 and that decline rapidly there-after as death rates increase among the aged. Thus one mayconclude t.hat the age composition of a population tells ussomething about past patterns of fertility and mortality.


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Ma l e s

AGE

F ema l e s

Mexico 1970

AGE

Males F ema l e s

Sweden 1974

F i g u r e 1 . N a t i o n a l p o p u l a t i o n a g e c o m po s i t i o n s : Mexico 1 9 7 0a nd Sweden 1 9 7 4. S o ur c es : F e d e r a l S t a t i s t i c a l O f f i c e1 9 7 0 ; A n d e r s s o n a n d H o l mb e rg 1 9 8 0 .


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S i n c e m i g ra n ts a r e a s u b s e t o f t h e p o p u l a t i o n , d o e s t h e i r a gec om po si ti on r e f l e c t a n al og ou s c h a r a c t e r i s t i c s o f r e c e n t p a t t e r n so f f e r t i l i t y , m o r t a l i t y , and m ig ra ti on ?

F i g u r e 2 s e t s o u t t h e n a t i o n a l m i g r a t i on p yra mid s f o rMexico and Sweden. They e x h i b i t a fundamen ta l common f i n d i n go f c o u n t l e s s m i g r a t i o n s t u d i e s : t h e a ge co m p os i ti o n o f m i g r a nt sr e f l e c t s a g e s e l e c t i v i t y , w i t h young a d u l t s and i n f a n t s g e n e r a l l yb e i n g t h e m ost m o bi le g ro u p i n any p o p u l a t i o n . M i g r a t i o n pr o-p e n s i t i e s a r e h i g h among c h i l d r e n , v a r y i n g f rom a p ea k a t a ge1 t o a low p o i n t a r o un d a g e 1 6 . Beyond t h a t a g e , m i g r a t i o n i n -c r e a s e s s h a r p l y t o a n o t h e r peak a ro un d ag e 2 2 , a f t e r w hich itd e c l i n e s r e g u l a r l y u n t i l p o s s i b l y i n t e r r u p t e d by a r e t i r e m e n tpeak a t t h e o l d e r a ge s .

T h is p ap e r s e e k s t o i d e n t i f y some o f t h e f a c t o r s t h a t a r er e s p on s i b le f o r t h e wi de sp re ad r e g u l a r i t i e s i n age p r o f i l e se x h i b i t e d by e m p i r i c a l s c h e du l e s o f m i g r a t i o n r a t e s . W eb e g i n by b r i e f l y c o n s i d e r i n g t h e p ro b le m o f m i g r a t i o n mea-s u re m e nt an d t h e n g o on t o a d o p t a m a t h e m at i c al f u n c t i o n a ld e s c r i p t i o n o f m i g r a t i o n a g e c o m p o s it i o ns . Armed w i t h t h i ss u c c i n t r e p r e s e n t a t i o n o f t h e ag e s t r u c t u r e o f m i g ra n t s , w ego on t o exam ine how d i f f e r e n c e s i n f a m il y s t a t u s p a t t e r n ss t r u c t u r e t h e a g e p r o f i l e o f m i gr an ts .


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Males

AGE

80

Females

a. I n t e r s t a t e m i g r a t i o n , M ex ico 1 97 0.

Males Females

b. I n t e r r e g i o n a l m i g r a t i o n , Sweden 1 974 .

F i g u r e 2 . N a t i o n a l m i g r a t i o n a g e c om po si t i o ns : ~ e x i c o 970a n d S we de n 1 9 74 . S o u r c e s : O n e - p e r c e n t s a m p l e o f t h e1 9 7 0 M e x ic a n P o p u l a t i o n C e n s u s ; A n d e r s s o n a n d H olr nb erq1980 .


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ESTABLISHING THE REGULARITIES: MIGRATION MEASUREMENTM i g ra t io n s t u d i e s hav e i n t h e p a s t e x h i b i t e d a c u r i o u s l y am-

b i v a l e n t p o s i t i o n w i t h r e g a r d t o t h e m easu rem en t o f g e o g r a p h i c a lm o b i l i t y . T h i s a m b iv a le n ce i s p a r t i c u l a r y s t r i k i n g b ec au se oft h e c o n t r a s t it p os es w i t h r e s p e c t t o t h e c o r re sp o nd in g s t u d i e so f m o r t a l i t y a nd f e r t i l i t y - s t u d i e s t h a t a r e r i c h l y endowed w i t hd e t a i l e d d i s c u s s i o n s o f m ea su re me nt p r o bl e m s. H a en s z el ( 1 96 7 )a t t r i b u t e s t h i s p a r a d o x t o t h e s t r o n g i n f l u en c e o f R a v en s te in ' se a r l y c o n t r i b u t i o n s t o m ig r a t i on a n a l y s i s :

Work o n m i g r a t i o n a nd p o p u l a t i o n r e d i s t r i b u t i o n a p p e a r st o ha ve b ee n s t r o n g l y i n f l u e n c e d by t h e e a r l y s u c c e s s e so f R a v e n s t e i n i n f o r m u l a t i n g "l a w s o f m i g r a t i o n " . Sub-s e q u e n t p a p e r s h av e p l a c e d a prem ium o f t h e d e v el o pm e n tan d t e s t i n g o f new h y po th es es r a t h e r t h a n o n d e s c r i p t i o n so f f a c t s an d t h e i r c o l l a t i o n ... T h i s i s i n c o n t r a s t t ot h e h i s t o r y o f v i t a l s t a t i s t i c s . W hile Grau nt more th a ntwo c e n t u r i e s b e f o r e R a v e n ~ t e i n ~ h a d m a d ee v e r a l i m p o r -t a n t g e n e r a l i z a t io n s from t h e s t u d y of " b i l l s o f m o rt a l -i t y " i n London, h i s s u c c e s s o r s c o n t i n u e d t o c o n c e n t r a t eon d e s c r i p t i o n s o f t h e f o r c e s o f m o r t a l i t y a nd n a t a l i t yby means o f r a t e s b a se d on p o p u l a t i o n s a t r i s k .(Ha ens ze l 1967 :260)I t i s n a t u r a l t o l o o k t o t h e s t a t e o f m o r t a l i t y an d f e r t i l i t y

m ea su re me nt f o r g u i d a n c e i n d e v e l o p i n g m e a su r e s o f m i g r a t i o n . L i k em o r t a l i t y , m i g r a t i o n may b e d e s c r i b e d a s a p r o c es s o f i n t e r s t a t et r a n s f e r ; h ow ev er , d e a t h c a n o c c u r b u t o n c e , w he re as m i g r a t i o n i sa p o t e n t i a l l y r e p e t i t i v e e v e n t . T hi s s u g g e s t s t h e ad op t i on o f af e r t i l i t y a n a l o g , i . e . , i n s t e a d o f b i r t h s p e r m ot he r, moves p e r m i -g r a n t ; b u t m i g r a t i o n ' s d e f i n i t i o n a l d epend ence o n s p a t i a l bound-a r i e s a n d on d i f f e r e n t f orm s of d a t a c o l l e c t i o n i n t r o d u c e s m easure-ment d i f f i c u l t i e s t h a t d o n o t oc cu r i n t h e a n a l y s i s of f e r t i l i t y .

One o f t h e c e n t r a l pr ob le m s i n m i g r a t i o n m ea su re me nt a r i s e sa s a co ns eq ue nc e o f t h e d i f f e r e n t s o u r c e s o f m i g r a t i o n d a t a . Mosti n f o r m at i o n r e g a r d i n g m i g r a t i o n i s o b t a i n e d f r om p o p u l a t i o n c en -s u s es o r p o pu la t i o n r e g i s t e r s t h a t r e p o r t m i gr a t io n d a t a , f o r ag i v e n t i m e i n t e r v a l , i n t e r m s o f c o u n t s o f m i g r a n t s o r o f m oves,r e s p e c t i v e l y . Y e t a n o t h e r s o u r c e o f m i g r a t i o n d a t a i s t h e s a m p l es u r v e y , w hi ch may b e d e s i g n e d t o p r o v i d e i n f o r m a t i o n a b o u t b o t hm i g r a n t s a n d m oves. M i g r a t i o n d a t a p ro d u ce d by c e n s u s e s a r e u su -a l l y i n t h e fo rm o f t r a n s i t i o n s . P op ul at io n r e g i s t e r s t r e a tr i g r a t i o n a s a n e v e n t and g e n e r a t e d a t a on moves.


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A m o v e r i s a n i n d i v i d u a l who h a s made a move a t l e a s t o n ced u r i ng a g iv en i n t e r v a l . A m i g r a n t on t h e o t h e r ha n d, i s ani n d i v i d u a l who a t t h e e nd o f a g iv en i n t e r v a l n o l o n g e r i n h a b i t st h e same community o f r e s i d e n c e a s a t t h e s t a r t o f t h e i n t e r v a l .Thus p a r a d o x i c a l l y a m u l t i p l e mover c a n b e a n on m ig ra n t, i f a f t e rm o v i n g s e v e r a l t i m e s h e r e t u r n s t o h i s i n i t i a l p l a c e o f r e s id e n ceb e f o r e t h e end o f t h e u n i t t i m e i n t e r v a l .

B ec au se m i g r a t i o n o c c u r s o v e r t i m e a s w e l l a s a c r o s s s p a c e,s t u d i e s o f i t s p a t t e r n s must t r a c e i t s o c c ur r en c e w i t h r e s p e c tt o a t i m e i n t e r v a l , a s w e l l a s o v e r a s y st em o f g e o g r a ph i c a la r e a s . I n g e n e r a l , t h e l o ng e r t h e t i m e i n t e r v a l , t h e l a r g e r w i l lb e t h e number o f r e t u r n m o ve rs a n d n o n s u r v i v i n g m i g r a n t s a n d ,h e n ce , t h e more t h e c o u n t o f m i g r a n t s w i l l u n d e r s t a t e t h e numbero f i n t e r r e g i o n a l mov ers ( a n d, of c o u r s e , a l s o o f m ov es ) .

Most m i g r a t i o n d a t a c o l l e c t e d by p o p u l a t i o n c e ns u s e s c o m e f ro mr es p on se s t o f o u r t y p i c a l q u e s t io n s : p l a c e o f b i r t h , d u r a t i o nof r e s i d en c e , p l a c e o f l a s t r e s i de n c e , and p l a c e o f r e s i d e n c e a ta f i x e d p r i o r d a t e ( U n i t e d N a t io n s 1 9 7 0 ) . From t h e s e q u e s t i o n sit i s p o s s i b l e t o e s t a b l i s h t h e c ou n t o f s u r v i v i n g m i gr an t s l i v -i n g i n a r e g i on a t t h e t i m e o f t h e c e n s u s , d i s a g g r e g a t e d by d i f -f e r e n t r e t r o s p e c t i v e t i m e i n t e r v a l s . The l o n g er t h e t im e i n t e r -v a l , t h e l e s s a c c u r a t e becomes t h e m i g r a t i o n m e a s ur e.

B ec au se p o u p l a t i o n r e a i s t e r s f o c u s on mo~res a nd n o t t r a n s i -t i o n s , d i f f e r e n c e s w i l l a r i s e betw ee n d a t a o b t a i n e d f ro m r e g i s -t e r s a nd f rom p o p u la t i o n c e n s u s e s . I n t h e a nne x t o t h e U . N .Manual on Methods of Mea surin g'lnt ernal Migration ( U n i t e dN a t i o n s 1 9 7 0 ) i t i s s t a t e d :

S i n c e a t l e a s t some m i g r a n t s , by ce n su s d e f i n i t i o n ,w i l l h av e be en i n v o lv e d , by r e g i s t r a t i o n d e f i n i t i o n ,i n more t h a n o n e m i g r a t o r y e v e n t , c o u n t s f ro m r e g i s -t e r s s h o u l d n o rm a l ly e x c e ed t h o s e f ro m c e n s u s e s . . .O nly w i t h J a p a n e s e d a t a h a s it s o f a r been p o s s i b l et o t e s t t h e c o r r e s p on d e n c e b et we en m i g r a t i o n s , a sr e g i s t e r e d d u r i n g a o n e- ye ar p e r i o d a n d m i g r a n tse nu me ra te d i n t h e c e n s u s i n terms o f f i x e d - p e r i o dc h an ge o f r e s i d e n c e . ( U n i t e d N a t i o n s 1 97 0: 50 )


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T a b l e 1 , t a k e n f r o m t h e UN a n a l y s i s , i l l u s t r a t e s how t h er a t i o o f r e ~ i s t e r - t o - c e n s u s m ig r a t i on d a t a i s i n g e n e r a l b i g-g e r t h a n u n i t y , i n c r e a s in g w i t h d e c re a s in g d i s t a n c e , a s f o rexam ple , i n t h e c a s e o f i n t r a - v e r s u s i n t e r p r e f e c t u r a l m igra-t i o n i n J ap an . I n g e n e ra l , t h e r a t i o o f r eg i s te r - to - c en s u sm i gr a ti o n d a t a s ho ul d t e n d t o u n i t y a s l o ng e r d i s t a n c e s a r e i n -v o l v ed , a n d a l s o a s t i m e i n t e r v a l s become s h o r t e r ( F i g u r e 3 ) .C l e a r l y , t h e r a t i o s h ou l d b e g r e a t e r t h a n u n i t y when s h o r t d i s -t a n c e s a r e c o n s i d e r e d an d c l o s e t o u n i t y when t h e t i m e i n t e r v a li s s h o r t , b e ca u se t h e p r o b a b i l i t y o f moving a c r o s s l o n g d i s t a n c e ss e v e r a l t i m e s s h o u l d be e x p e c t e d t o b e l e s s t h a n t h e p r ob a bi -l i t y o f moving t h e 'same number o f t i m e s b et we en s h o r t d i s t a n c e s .And, t h e p r o b a b i l i t y o f moving s e v e r a l t i m e s d u r i n g a l o ng i n -t e r v a l o f t i m e s ho ul d b e g r e a t e r t h a n t h e p r o b a b i l i t y o f ex-p e r i e n c i n g t h e s ame number of moves d u r i n g a s h o r t e r p e r i o dof t i m e .

A f u nd a me n ta l a s p e c t o f m i g r a t i o n i s i t s c ha nge ove r t i m e .A s Ryder (19 64) h a s p o i n t e d o u t f o r t h e c a s e o f f e r t i l i t y , p e r io dan d c o h o r t r e p r o d u c t io n r a t e s w i l l d i f f e r w hen ever t h e a ge d i s -t r i b u t i o n o f c h i l d b e a r i n g v a r i e s f rom o ne c o h o r t t o a n o th e r . Theu s e fu l n es s o f a c o h o r t ap pro ach i n m i g r a t i o n, a s i n f e r t i l i t ya n a l y s i s , l i e s i n t h e i mp or ta nc e o f h i s t o r i c a l e x p e r i en c e a s a ne x p l a n a t i o n o f c u r r e n t b e h a vi o r . M o rr is on ( 19 70 ) i n d i c a t e s t h a tm i g r a t i o n i s i nd uc ed by t r a n s i t i o n s f rom o ne s t a g e o f t h e l i f ec y c l e t o a n o t h er , and " c h ro n ic " m i gr an t s may a r t i f i c i a l l y i n f l a t et h e m i g r a t i on r a t e s o f o r i g i n a r e a s t h a t a r e h e a v i ly p o pu la te d withm i g r at i o n -p r o n e i n d i v i d u a l s . B oth i n f l u e n c e s o n p e r i o d m i g r a t i o na r e r e a d i l y a s s e s se d by a c o h o r t a n a l y s i s .

I t i s t h e m i g ra t i o n o f a p e r i o d , h ow ev er , a n d n o t t h a t o f ac o h o r t , t h a t d e t e r m in e s t h e sudden r e d i s t r i b u t i o n o f a n a t i o n a lp o p u la t io n i n r e s p o ns e t o e conom ic f l u c t u a t i o n s , a nd i t i s i n -f o rm a ti o n on p e r i o d m i g r a t i o n t h a t i s needed t o c a l c u l a t e s p a t i a lp o p u la t io n p r o j e c t i o n s .

C u r r en t p e r io d m i g r a t i o n i n d i c e s do n o t d i s t i n g u i s h t r e n dfro m f l u c t u a t i o n and t h e r e f o r e may be d i s t o r t e d ; c u r r e n t c o h o r tm i g r a t i o n i n d i c e s a r e i n c om p l e te . Thus it may be u s e f u l t o dr awo n R y d e r ' s ( 1 96 4) t r a n s l a t i o n t e c h n i q u e t o ch an ge f ro m o ne t ot h e o t h e r . A s K e y f i t z ( 19 77 :2 50 ) o b s e r v e s , t h e c o h o r t an d p e r i o d


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T a b l e 1 . Compari son of mi gra t io n by s ex and typ e based on th ep o p u l a t io n r e g i s t e r and t h e c en s us f o r t h e o ne -y ea rper iod be tween Oc tober 1 9 5 9 and October 1 9 6 0 , Ja pa n .- - -- -

Sex and type of m i g ra t i on R eg i s t er D ata C ens us Data R a t i o x 100Both Sexe s

I n t ra - p re f e c t u r a l 2 ,9 6 6 ,6 2 1 1 , 9 9 8 , 1 7 1 148.47I n t e r p r e f e c t u r a l 2 ,6 2 5 ,1 3 5 2 ,5 9 0 ,7 5 1 1 0 1 .3 3

I ntra -pre fe c tura l 1 ,4 8 8 ,9 3 5 1 ,0 0 1 ,7 4 5 148 .63I n t e r p r e f c c t u r a l 1, 50 ,817 1 ,466 ,898 98 .90

I n t r a - p r e f e c t u r a lI n t e r p r e f e c t u r a l

Source: Uni ted Na t ions ( 1 9 7 0 Table 4 2 : S O ) .

r e g i s t e r / c e n s u s r a t i o

d i s t a n c e

F i g u r e 3 . R a t i o o f r e g i s t e r t o ce n su s m i g r at io n d a t a w i th r e s -p e c t t o d i s t a n c e and t i me i n t e r v a l .

r c g i s t e r / c e n s u s r a t i o

1 ..0-

13-t i m e i n t e r v a l


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moments i n R y d e r ' s f o r m ul a s c a n " b e i n t e r p r e t e d , n o t a s c h i l d -b e a r i n g , b u t a s m o r t a l i t y , m a r r i a g e , s c h o o l a t t e n d a n c e , in co me ,o r some o t h e r a t t r i b u t e o f i n d i v i d u a l s " . M ig ra t i on i s c l e a r l ys u ch an a t t r i b u t e .

The im p or ta nc e o f h i s t o r i c a l e x p e r i e n ce i n i n t e r p r e t i n g an du n d e r s t a n d in g c u r r e n t m i g r a t i o n b e h a v io r l e d P e t e r Pl or ri so n(1970:9) t o d e f i n e t h e n o t i o n o f s t a g i n g a s b e in g " an y l i n k a g eb et we en a p r i o r s e q u e n c e a nd s u b s e q u e n t m i g r a t i o n b e h a v i o r " .M or ri s on r e c o g n i z e s f o u r k i n d s o f s t a g i n g : g e o g ra p h ic , l i f ec y c l e , s o ci oe c on o m ic , a nd e x p e r i e n t i a l . G e o gr a ph ic a l s t a g i n gr e f e r s t o r e t u r n m i g r a t io n and t o what i s c o n v e n t i o n a l l y u n de r-s t o o d t o mean " s t a g e m i g r a t i o n " , i . e . , t h e i d e a t h a t m i g ra n tst e n d t o move t o p l a c e s n o t v e ry d i s s i m i l a r f rom th o s e t h e y l e f tb eh in d. L i f e - c yc l e s t a g i n g v ie ws m i g r a t i on a s a r i s i n g o u t o fb r e a k s i n an i n d i v i d u a l ' s o r a h o u s eh o l d ' s l i f e c y c l e , s u ch a se n t r y i n t o t h e l a b o r f o r c e , m a r r ia g e , a nd r e t i r e m e n t . S oc io ec on -omic s t a g i n g s e e s m i g r a t i o n s e q u e n c e s a s b e i n g c o n d i t i o n e d b y s o -c i o s t r u c t u r a l f a c t o r s su ch a s oc c u p at i on , e d u c a t i o n a l a t t a in m e n t ,a nd income l e v e l . F i n a l l y , e x p e r i e n t i a l s t a g i n g r e f e r s t o move-m en t e x p e r i e n c e i n t e r m s o f n um ber o f p r e v i o u s m oves a n d d u r a t i o ns i n c e t h e l a s t move; i t i s t h e " p a r i t y " d i me ns io n o f m i g r a t i o na n a l y s i s .

C a l c u l a t i o n s o f m i g r a t i o n r a t e s o f i n c r e a s i n g s p e c i f i c i t ys e e k t o un co nfo un d t h e " t r u e " m i g r a t i o n r a t e s f ro m w e i gh t s t h a tr e f l e c t t h e a r i t h m e t i c a l i n f l u e n c e o f t h e p a s t . T h i s p ro c e ss o fm e a s u r i n g m i g r a t i o n... t d i f f e r e n t l e v e l s o f s p e c i f i c i t y o f o c cu r r en cea nd e x po s u re y i e l d s p r o d u c t s wh ic h dra w e v e r f i n e r

d i s t i n c t i o n s b etw ee n c u r r e n t b e ha v i or a nd t h e r e s i -d ue of p a s t b e ha v io r r e f l e c t e d i n t h e e xp o su red i s t r i b u t i o n a t a ny t i m e (Ryder 1975:lO).S uc h p r o d u c t s may b e w e i g h te d a n d a g g r e g a t e d t o p ro d u c e t h e

" c ru d e " r a t e s o f h i g h e r l e v e l s o f a g g re g a t i o n . F o r e xa mp le , t h ea ge -se x s p e c i f i c m i g ra t io n r a t e i s a w e i g ht e d a g g r e g a t i o n w i t hr e s p e c t t o t h e m i gr a t i o n " p ar i t y -d u ra t i o n " d i s t r i b u t i o n j u s t a st h e c ru d e m i g ra t io n r a t e i s a w ei g ht ed a g g r e g a t i o n w i t h r e s p e c tt o t h e a ge - s ex d i s t r i b u t i o n .


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The ag e p r o f i l e o f a s c he d u l e o f m i g ra t io n r a t e s r e f l e c t st h e i n f l u e n c e s o f two a ge d i s t r i b u t i o n s : t h e a ge c o m po s it io n o fm i g r a n t s an d t h a t o f t h e p o p u l a t i o n o f w h ic h t h e y w e r e a p a r t( R o g e r s 1 9 7 6 ) . T h i s c a n b e e a s i l y d e m o n s t r a t e d by d ec om po sin gt h e n um er at or a nd d en om in at or o f t h e f r a c t i o n t h a t d e f i n e s a na g e - s p e c i f i c m i g r a t io n r a t e , M ( x ), s a y .

I f O ( x ) d e n o t e s t h e number o f o u t m i g r a n t s o f a g e x , l e a v i n ga r e g i o n w i t h a p o p u l a t io n o f K ( x ) a t t h a t a g e , t he n

N x )(x ) - O * N ( x ) = .( x ) =-K (x) K 0C(x ) C ( x )0 = t o t a l number o f o u t m i g r a n t s

N ( x ) = p r o p o r t i o n o f m i g r a n t s ag e d x y e a r s a t t h e t i m e o fm i g r a t i o n

K = t o t a l p o p u l a t io nC ( x ) = p r o p o r t i o n o f t o t a l p op u l a t i on a ged x y e a r s a t m id-year

o = c ru d e o u tm i g ra t io n r a t eW e d e f in e t h e c o l l e c t i o n o f N ( x ) v a l u e s t o be t h e m i g r a t i o n

p r o p o r t i o n s c h e d u l e a n d t h e s e t o f M(x) v a l u e s t o be t h e migra -t i o n r a t e s ch ed u l e .


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SUMMARIZING THE REGULARITIES: MODEL M IGRA T I ON SCHEDULESO bserved a g e - s p e c i f i c m i g r a t i o n r a t e s c h e d u l e s u n i v e r s a l l y

e x h i b i t a common s h a p e ( R o g e r s a n d C a s t r o 1 9 8 1 ) . T he same s h a p ea l s o c h a r a c t e r i z e s t h e a ge co m p os i t io n o f m i g r a n t s , i . e . , migra -t i o n p r o p o r t io n sc h e d u le s . S t a r t i n g w i t h r e l a t i v e l y h i gh l e v e l sd u r i n g t h e e a r l y c h i ld h oo d a g e s , m i g ra t io n r a t e s o r p r o p o r t i o n sd e c r e a s e m o n ot o ni c al ly t o a low p o i n t a t a ge x s a y , i n c r e a s e1'u n t i l t h e y r e a c h a h i g h p ea k a t ag e x h, a nd t h e n d e c r e a s e o n cea g a i n t o t h e a g e s o f r e t i r e m e n t b e f o r e l e v e l i n g o f f a ro un d somec o n s t a n t l e v e l , c s a y . O c c a s i o n a l l y a " p o s t - l a b o r f o r c e " com-p o n en t a p p e a r s , s ho wi ng e i t h e r a b e l l- s h a pe d c u r v e w i t h a r e t i r e -m en t pe ak a t a g e x r o r a n u pward s l o p e t h a t i n c r e a s e s m o n o t o n ic a l lyt o t h e l a s t a ge i n c l u de d i n t h e s ch e d u l e , a g e w s a y . T hu s t h em i g r a t i o n a ge p r o f i l e may be d i v i d e d i n t o c h i l d ( d e p e n d e n t ) ,a d u l t , a nd e l d e r l y co m po n en ts ; h ow ev er , w e s h a l l c o n f in e o u r a t -t e n t i o n i n t h i s p a p e r t o o n ly t h e f i r s t two. Bu t o u r a rgum enti s e q u a l l y v a l i d f o r p r o f i l e s showing a r e t i r e m e n t p eak o r a nupw ard r e t i r e m e n t s l o p e .

The o b s e r v e d a g e d i s t r i b u t i o n o f m i g r a n t s , N ( x ) may b ed e s c r i b e d by a f u n c t i o n o f t h e f orm :

where-0. X

N ( x ) = a l e1f o r t h e c h i l d ( d e p en d e n t) c om po ne nt ,

f o r t h e a d u l t ( i n d e p e n d e n t ) c om po ne nt , a nd c i s t h e c o n s t a n tt e r m t h a t im pro v es t h e f i t when m i gr a t i o n d i s t r i b u t i o n s a t o l d e ra g e s a r e r e l a t i v e l y h i gh . F i gu r e 4 i l l u s t r a t e s t h e f em al e mo-d e l m i g ra t i o n p r o p o r t i o n s c h e du l e s o f t h e o b se rv ed d a t a p r e -s e n te d i n F i gu r e 2 , w hic h b y d e f i n i t i o n show a n a r e a o f u n i t yu n d e r e a c h c u r v e .


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Females

a. Interstate migration, Mexico 1970.

X-- 0 .0sZ Females

b. Interregional migration, Sweden 1974.

Figure 4. Components of the model migration-proportionschedule.


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An a l t e r n a t i v e way o f e x p r e s s i n g e q u a t i o n ( 2 ) i s a s aw e ig ht ed l i n e a r c o m b in a ti on o f t h e d e n s i t y f u n c t i o n s r e p r e s e n t i n gt h e ab o ve t h r e e co m po ne nt s ( C a s t r o a n d R o g er s 1 9 8 1 ) :

where w i s t h e l a s t a g e i n c l ud ed i n t h e s c h e d ul e , $, a nd $ 2 a r et h e r e l a t i v e s h a r e s o f t h e c h i l d an d a d u l t co mp on en ts , $c i st h e s h a r e o f t h e c o n s t a n t t e r m , f l ( x ) and f 2 ( x ) a r e r e s p e c t i v e l y ,t h e s i n g l e a nd do u bl e e x p o n e n t i a l d e n s i t y f u n c t i o n s

-a xf l ( x ) = a l e 1

a n d I ' ( a 2 / h 2 ) r e p r e s e n t s t h e gamma f u n c t i o n v a l u e o f a 2/ A2 . N o tet h a t + $ 2 + $C = 1 by d e f i n i t i o n .

E q u a t i o n s ( 2 ) t h r o u g h ( 5 ) im ply t h a t

and

The s i x p a r am e te rs a l , a l , a 2 , a 2 , A 2 , an d p 2 d o n o t s e e mt o h av e d em og rap hic i n t e r p r e t a t i o n s . Both a l and a 2 r e f l e c tt h e h e i g h t s o f t h e i r r e s p e c t i v e p a r t s o f t h e p r o f i l e ; a l and a 2r e f e r t o t h e d e sc en di n g s l o p e s ; h 2 r e f l e c t s t h e a s c en d i ng s l o p e ;and p 2 p o s i t i o n s t h e a d u l t com ponent o n t h e ag e a x i s . T a ke n a sa g ro u p , t h e s e p a r a m e t e r s s u g g e s t a number o f u s e f u l a n d r o b u s t


18/36

m e as ur es f o r d e s c r i b i n g a n ob s e rv e d m i g r a t i o n s c h e d u l e ( T a bl e 2 ) .F or e xa mp le , t h e r a t i o Do = , t h e c h i l d - a d u l t d ep en de nc ym i g ra t io n r a t i o , i s on e o f s e v e r a l i m p o rt a n t r a t i o s t h a t may beuse d t o i n t e r p r e t p a r t i c u l a r p a t t e r n s o f d e p e n d e n c y among mi g r an t s .I t assum es a c e n t r a l r o l e a s a n i n d i c a t o r o f f a m i l y dep ende nc ys t r u c t u r e by d e f i n i n g t h e number o f d e p en d e nt s p e r a d u l t m i g ra n t .

The c h i l d - a d u l t d ep en de nc y m i g r a t i o n r a t i o v a r i e s a s a f un c-t i o n o f t h e p a ra m et e r s t h a t d e f i n e t h e a g e p r o f i l e o f m i g ra n ts .I f t h e c o n s t a n t t e r m c i s c l o s e enough t o z e r o t o be i g n o r e d , a sn o r m a l l y i s t h e c a s e , t h en $c = 0 and

S i n c e

w e o b t a i n t h e r e s u l t

where 6 2 1 = a 2 / a l , B 1 2 = a l / a 2 , o2 = h / a a r e t h e l a b o r do mina nc e,2 2p a r e n t a l - s h i f t , a nd l a b o r asy mm etry i n d e x e s d e f i n e d i n R og er s a ndC a s t r o ( 1 9 8 1 ) . T he se t h r e e r a t i o s and p 2 may be u s e d t o f u l l yc h a r a c t e r i z e o bs e rv e d m i g r a t io n a g e p r o f i l e s .

A no th er u s e f u l i n d i c a t o r o f t h e a v e ra g e s i z e o f f a m i l yamong migran ts i s t h e v a l u e so = w hic h r e f l e c t s t h e t o t a lnumber o f m i g r a n ts p e r a d u l t . I n a s i n g l e - s e x f o r m u l a t i o n , f o ri n s t a n c e , i f a d u l t s a r e c o ns i de r e d a s h ea ds o f e ac h m i gr a nt f a m i ly( i n t e r p r e t i n g s i n g l e i n d i v i d u a l s a s one -p er s on f a m i l i e s ) t h e n t h esum o f t h e two s e x - s p e c i f i c v a l u e s o f so c l o s e l y a p pr ox im a te st h e a v e r a g e s i z e o f f a m i l y among m i g r a n t s .

F i q u r e 5 s e t s o u t s e v e r a l aTe ? r e f i l e s o f i n t e r n a l m ig ra -t i o n f lo ws t o d i f f e r e n t c i t i e s a rou nd t h e w o r ld , t o g e t h e r w i t h


19/36

Tab l e 2 . P r i n c i p a l i n d i c e s d e f i n i n g o bs e rv e d a g e - s p e c i f i cm i g ra t io n c h a r a c t e r i s t i c s .C h a r a c t e r i s t i c I nd ex

- P r o p o r t i o n o f c h i l d r e n( d ep en d en t s ) , a l / a l$1- P r o p o rt i on of a d u l t s I a( l a b o r f o r c e ) $2- Labor asymmetry, a 2 h 2 / U 2- Labor dominance,6 2 1 a2 /a l

- C h i l d - ad u l t d ep en d en cym i g ra t io n r a t i o , Doa The r e c i p r o c a l i n d e x i s a l s o o f i n t e r e s t ina sm uc h a s i t r e f l e c t s t h e t o t a l

a,Lnumber o f mi g ran t s p e r a d u l t , s =0 a 2 r ( a 2 / A 2 )

a t y p i c a l i n t e r n a t i o n a l m i g ra t io n ( im m ig ra tio n) a ge d i s t r i b u t i o nf o r ma le s and f ema l es . These p r o f i l e s w er e g en e r a t ed by mode lm i g r a ti o n p r o p o r t i o n s c h ed u l e s f i t t e d t o ob se rv ed d a t a , t h ep a r a m e te r s o f w h ic h a r e i n c l u d e d i n T a b l e 3 . T h e q u a n t i t a t i v ei n d i c e s p r e s e n t e d i n T a b le 4 c on fi r m t h e r e g u l a r i t i e s i l l u s -t r a t e d i n F i g u r e 5 . F or e xa m pl e, t h e m i g r a t i o n f lo w s t o M exicoC i t y a nd t o Lagos d i f f e r s h a r p l y from t h e c o r r e s p o nd i n g f lo w st o St ock ho lm. The f o r mer show ab o u t d o u b l e t h e p r o p o r t i o n o fd e pe n de n ts e x h i b i t e d by t h e l a t t e r . The same t a b l e a l s o in -d i c a t e s t h a t t h e a v e ra g e s i z e o f f a m il y i n t h e f lo w t o MexicoC i t y , w i t h a b o u t 2 . 6 5 + 2 . 2 0 = 4.85 members pe r m ig ra t i ngf a m i l y , i s t h e l a r g e s t among t h e e xa m ple s p r e s e n t e d .

A l l of t h e m i g ra t io n c h a r a c t e r i s t i c s i n F ig u re 5 and Ta bl e4 i n d i c a t e low o r h i g h f a m i ly de pe nd enc y p a t t e r n s . I n t h e n e x ts e c t i o n , we s e e k a n e x p l a n a t i o n f o r su ch c h a r a c t e r i s t i c s byl i n k i n g them w i t h t h e f a m i ly c h a r a c t e r i s t i c s o f t h e p o p u la t i ona s a w h o l e .


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h - 1 6 -X

I R i o d e J a n e i r o

hU\u:z 1 Mexico C i t y

L a g o s

AGEF i g u r e 5 . M ode l m i g r a t i o n p r o p o r t i o n s c h e d u l e s f o rs e l e c t e d c i t i e s a r o un d t h e w o r l d a n d a t y p i c a l

n a t i o n a l i m m i g r a t io n f l ow . S o u rc e s : A l b e r t s1 97 7; o n e - p e r c e n t s a mp le o f t h e 1 9 70 P o p u l a t i o nC e n s u s o f M e x i co ; G e o r ge a n d E i g b e f o h 1 9 7 3 ;Kaw abe a n d F a r a h 1 9 7 3 ; A n d e r s s o n a n d H o lm b e r g1 9 8 0 ; UN 1 9 7 9 .


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hX-. .05" 1 Greater Khartoum

Stockholm

0.4 : +0 10 20 30 40 5 U 6

z 0.0s Immigratian to Kuwait

AGE

Figure 5 continued.


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Table 3. Parameters and variables defining observed model migration proportion schedulesfor selected cities around the world and a typic al national immigration flow.a

Rio de Jan eir o Mexico C ity Lagos G. Khartoum Stockholm Immig ration t oBraz i l Mexico N ig er ia Sudan Sweden KuwaitParameter or

v ar ia b le Males Females Males Females Males Females To ta l Males Females Males Females

a ~ h e parameter value was se t equal to zero in the nonlinear parameter est imat ion procedure .


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T a b l e 4 . E s t i m a te d c h a r a c t e r i s t i c s o f o b s e r ve d m od el m i g r a t i o n p o p u l a t i o n s c h e d u l e sf o r s e l e c t e d c i t i e s a ro u n d t h e w o rl d a nd a t y p i c a l n a t i o n a l i m m i g r at i on f l o w .

-- - -- -R i o d e ~ a n e i r d t e xi c o C i t y L a g o s G . I S ha r t o u d i ~ t o c k h o l f i ~ u i c j r a t i o n o fB r a z i 1 1 9 6 8 - 7 2 M e x i c o 1 9 6 9 -7 0 N i g e r i a 1 9 67 - 68 S u d a n 1 9 6 0 - 6 4 s w e d e n 1 9 7 4 K u w a i t 1 9 6 5 - 7 0C h a r a c t e l -

; c t ; r . Male F e m a l e 'Male F e m a l e Male F e m ul e T o t a l Male F e m a l e Male F e m a l e

P r o p o r t i o n o f 3 3 , . 7 0 4 4 . 8 1 6 4 . 2 9 5 9 . 5 0 4 2 . 2 8 5 7 . 8 0 3 1 . 6 0d e p e n d e n t s ( $ 1P r o p o r t i o n ofa d u l t s ( $1T o t a l n um be ro f m i g r a n t s 1 , ~ 4 3 1 . 6 8 2 .6 5 2 . 20 1 . 6 7 2 . 28 1 . 36 1 . 2 8 1 . 2 2 1 . 42 2 . 1 6p e r a d u l tL a b o r a s : , m m e t r y 1 0 . 0 3 9 . 8 3 1 5 . 7 4 2 1 . 0 1 3 . 2 0 3 . 2 4 7 . 7 3 3 . 0 4 5 . 1 8 2 . 1 2 1 . 8 7L a b o r d o m i n a n c e 2 . 0 2 0 . 9 0 0 . 4 2 0 . 5 8 1 . 4 7 1 , 2 7 1 . 7 2 4 . 1 8 3 . 5 5 4 . 8 8 3 . 1 2P a r e n t a l s h i f t 1 . 0 8 1 . 5 6 1 . 4 3 1 . 3 4 1 . 0 8 0 , 6 7 1 . 4 4 0 . 8 7 1 . 1 8 0 . 5 2 0 . 2 9C h i l d - a d u l t 0 . 4 8 0 . 7 5 1 . 7 1 1 . 3 1 0 . 7 1 L . 3 2m i g r a t i o n r a t i o 0 . 4 3

S o u r c e s : * A l b e r t s 1 9 77O n e - p e rc e n t s a m p l e o f t h e 1 9 70 M e xi ca n C en s u s o f P o p u l a t i o nG e or ge a nd E igb e f oh 1973Kawabe and Far ah 1973A nde r s son a nd H olmbe rg 19 80f U n i t e d N a t i o n s 1 97 9


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EXPLAINING THE REGULARITIES : FAMILY STATUSI t i s w id el y r e co gn iz ed t h a t a l a r g e f r a c t i o n o f t o t a l m i -

g r a t i o n i s a c c o u n t e d f o r by i n d i v i d u a l s whose moves a r e de p e n d e n to n t h o s e o f o t h e r s . I nd e ed f a m i l y m i g r a t i o n i s s u c h a w e l l -e s t a b l i s h e d phenom enon t h a t Ry de r ( 19 7 8) h a s e v e n s u g g e s t e d i t su se a s a c r i t e r i o n f o r i d e n t i f y i n g f a m i ly mem bership: a f a m i l yc o m p ri s e s o f t h o s e i n d i v i d u a l s who w ould m i g r a t e t o g e t h e r .

To u n d e r s t a n d t h e i n f l u e n c e s t h a t f a m i l y a nd de pe nd en cy re -l a t i o n s h i p s ha ve o n m i g r a t i o n a g e c o m po s i t i on s , it i s u s e f u l t oexamine how such p r o f i l e s r e sp on d t o f u nd a m en ta l c h an g es i n de -pendency p a t t e r n s . To i l l u s t r a t e t h i s , c o n s i de r a s i nq l e - s exp o pu l a t i on t h a t i s d i v i d e d i n t o tw o g r ou p s : d e p e n d e n ts a ndh e a d s , w he re d e p e n d e n t s a r e si m ? l y i n d i v i d u a l s who h a v e n o tl e f t home t o become h e a d s . ( I n c l ud e d a s h e a d s a r e i n de p e n d e n ts i n g l e i n d i v i d u a l s who may b e v ie w ed a s o n e -p e r so n f a m i l i e s . !~ h u s t h e g e d i s t r i b u t i o n o f t h e f e m al e p o p u l a t i o n C ( x ) may be corn-p os ed by w e i g h t i n g t h e d e n s i t y f u n c t i o n s o f d e p e n d e n ts an d h e a ds :

w he re $ l c a nd $ 2 c a r e t h e p r o p o r t i o n s o f d e p e n d e n ts a nd he a d s i nt h e t o t a l f em ale p op u l a t io n a nd , f l c ( x ) a n d f 2 c ( x ) a r e t h e i r c or -r es po nd in g ag e d i s t r i b u t i o n s , r e s p e c t i v e l y .

The r a t i o o f t h e w ei gh t s a s s o c i a t e d w i t h t h e a g e p r o f i l e so f d e p e n d e n ts a nd h e ad s d e f i n e s t h e c h i l d - a d u l t d ep en de nc y popu-l a t i o n r a t i o , Dc , which i s s i m i l a r t o t h e D d e f in e d e a r l i e r f o r0t h e m i g ra n t p o p u l a t i o n :

A s i n t h e c a s e o f m i g r a t io n , w e c an a l s o d e f i n e t h e t o t a l numbero f p er s o n s p e r a d u l t ( he a d) a s s c= l / $2 c. To i n v e s t i g a t e a n a l y t i -c a l l y some o f t h e u n d e r l y i n g p a t t e r n s o f " he ad fo r m a t i o n" r e q u i r e ss o m e m a t h e m a t i c a l t h e o r i z i n g .


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L e t yo d e n o te t h e a g e a t wh ic h a n a p p r e c i a b l e n umber o ff em a le s f i r s t l e a v e home t o e s t a b l i s h t h e i r own h o us eh o ld . S i n c em a r r i a g e i s a n i m p o r t a n t r e a s o n f o r l e a v i n g t h e f a m i l y home, iti s l i k e l y t h a t t h e p r o b a b i l i t y d e n s i t y f u n c t i o n d e s c r i b i n g t h ep a t t e r n o f h ea d f o r m a t i o n by a g e i s s i m i l a r t o t h e on e f oun d i ns t u d i e s of n u p t i a l i t y , i . e . , t h e d o u b l e e x p o n e n t i a l f u n c t i o n d e-f i n e d i n e q u a t i o n ( 5 ) . I f g ( y ) i s s u ch a f u n c t i o n t h e n

d e f i n e s t h e p r o p o r t i o n o f f e m a le s who ha ve e v e r l e f t home by a g ex , i . e . , who a r e h ea ds a c c o r d i n g t o o u r d e f i n i t i o n .

S i n c e f 2 c ( ~ ) e f i n e s t h e p ro p o r t i o n o f t h e p o pu l a t i o n o fh e a d s t h a t a r e o f a g e x, a n d G ( x) d e f i n e s t h e p r o p o r t i o n o f t h ep o p u l a t i o n who a r e h e a d s by a g e x , it i s e v i d e n t t h a t i n a s t a b l ep o p u la t io n g row ing a t an i n t r i n s i c r a t e o f g row th r ,

where 1 x ) d e no t es t h e p r o b a b i l i t y o f s u r v i v i n g from b i r t h t oa g e x . F o r s i m i l a r r e a s o n s

G iv en t h e s e e q u a t i o n s , t h e c h i l d - a d u l t d ep en de nc y p o p u l a t i o nr a t i o Dc may b e d e f i n e d a s


26/36

F i g u r e 6 i l l u s t r a t e s t h e above argum en t w i t h h y p o t h e t i c a ld a t a . I t p r e s e n ts t h e s u r v i v o r sh i p cu rv e, l ( x ) , w hich i s t h a t o ft h e B r as s s t a n d a r d w i t h a = -0 .80 and B = 1 .7 5 w i t h a n e x p e c t a t i o no f l i f e a t b i r t h o f a pp ro xi ma te ly 69 y e a r s ( B ra ss 1 9 7 1 ) ; and t h eh ea d f o r m a t i o n c u r v e G ( x ) i s t h e C oa le- Mc Neil doub le e xp on e n t i a l( C oa l e a nd M cNeil 1972 ) e xp r e s s e d by t h e R odriguez a nd T r u s s e l l( 1 9 8 0 ) s t a n d a r d w i t h mean ( 2 2 y e a r s ) a nd v a r i a n c e ( 5 y e a r s ) ofa g e o f b ec om in g a h ea d . F i g u r e 7 shows t h e r e s u l t i n g d e p e n d e n t ,h e ad , and p o p u l a ti o n ( d ep e nd e nt s p l u s h e a d s ) d i s t r i b u t i o n s o fs t a b l e po p ul a t io n s g rowing a t i n t r i n s i c r a t e s r = 0 and r = 0 . 03 ,r e s p e c t i v e l y .

AGE

F i g u r e 6. P r o p or t io n s u r v i v i n g t o a ge x , l ( x ) , and p ro po r-t i o n o f i n d i v i d u a l s who ha ve e v e r l e f t home by a g ex , G(x).


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" al ha, F dF a Q)a 3F: -4@ O + 'a - d U4J 0)mas4 J d U)G 7 a lo a ka 0g " Ga m 0a l ca - d 04J

L 0 7 CU) aG a l6 0 0


28/36

To d e r i v e t h e c o r r e s p o n d i n g a g e c o m p o s i t i o n s o f m i g r a n t s wei n t ro d u c e t h e p r o b a b i l i t i e s p l ( x ) and p 2 ( x ) t h a t a d e pe nd en t a nda h ea d , r e s p e c t i v e l y , m i gr a t e a t ag e x i n an i n t e r v a l o f t i m e .The a g e d i s t r i b u t i o n o f m i g r a n ts i s d e f i n ed a s b e f o r e :

where

and

The c h i ld - d ep e n d en c y m i g r a t i o n r a t i o Do, e q u i v a l e n t t o e qua-t i o n ( 9 ) , may now be d e f in e d as :

B oth c h i l d - a d u l t d ep en de nc y r a t i o s , Dc a nd Do , may be a na ly ze d byu s i n g h y p o t h e t i c a l p o p u l a t i o n s o nc e a g a i n . To s p e c i f y c o r r e c t l yt h e p r o b a b i l i t i e s p l ( x ) and p 2 ( x ) f rom d i f f e r e n t s o u r c es o f m i -g r a t i o n d a t a , i t i s n e c es s a r y t o i d e n t i f y f i r s t t h e number ofmoves a p e r s o n u n d e r t a k e s d u r i n g a u n i t i n t e r v a l . However, f o ro u r p u r p o s e s w e may as su m e t h a t b o t h d e p e n d e n t s a n d h e a d s f o l l o wa n e g a t i v e e x p o n e n t i a l p r o p e n s i t y t o m i g ra t e w it h r e s p e c t t o a g e ,w i t h t h e f u n c t i o n ' s p a ra m e te r r e f l e c t i n g t h e a v e r a g e r a t e o f m ovingp e r u n i t of t i m e . Fo rma l ly , we have th en

and


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w here yo d e n o t e s , a s b e f o r e , t h e a g e a t w hich a n a p p r e c i a b l enumber o f f e ma le s f i r s t l e a v e home t o e s t a b l i s h t h e i r ownh o u s e h o l d , a nd o , a nd o 2 d e n o t e t h e a v e r a g e r a t e s o f m ovingp e r u n i t o f t i m e o f d e p e n d e n t s a nd h e a d s , r e s p e c t i v e l y . Onem ig ht e x p e c t t h a t t h e a v e r a g e r a t e o f moving p e r u n i t o f t i m ef o r de p e nd e n ts , o , , s h o u ld n o t ex ce ed 02 , t h e c o r r e s p o n d i ngr a t e f o r h e ad s . I n g e n e r a l , d e pe n de n ts ( c h i l d r e n ) move w i t ht h e i r p a r e n t s and i n de p en d en t , s i n g l e i n d i v i d u a l s a r e mostl i k e l y t o b e f ou nd among a d u l t s .

F i gu r e 8 p r e s e n t s t h e v a r i a t i o n o f Do w i th r e s p e c t t o Dcf o r t h e h y p o t h e t i c a l p o p u l a t i o n s of F i g ur e 7 , u n d er v a r i o u sm o b i l i t y c o n d i t i o n s a s e xp r es s ed by t h e r a t i o 01/02. I t maybe s ee n t h a t t h e r a t i o Do/Dc more c l o s e l y a p p r oa c h es u n i t y a st h e m i g r a t i o n o f h e ad s i n c r e a s e s .

The p a ra m e t e r s d e f i n i n g t h e m o b i l i t y c o n d i t i o n s may b eused t o s e t o u t a t y po lo gy of m i g r a t io n p r o f i l e s t h a t h e l p s t oi d e n t i f y how a p a r t i c u l a r f a m il y m i g r a t i o n p a t t e r n may be r e -f l e c t e d i n a m i g r a t i o n a g e c o m p o s i t i on , a nd how i m p o r t a n t t h em i g r a t i o n p r o p e n s i t i e s among h e a ds a nd d ep e n d en t s a r e i n s t r u c -t u r i n g t h a t a g e c o m p os i t io n . F i g u r e s 9 and 1 0 p r e s e n t a s e t ofp r o f i l e s c l a s s i f i e d a cc or di ng t o two d i s t i n c t l y d i f f e r e n t r a t e so f n a t u r a l i n c r e a s e . F o r e a ch o f t h e h y p o t h e t i c a l p o p u l a t io n sw e show t h r e e a l t e r n a t i v e c om b in at io ns o f p r o p e n s i t i e s t o m i -g r a t e among h e a d s a nd d e p e n d e n t s . F i r s t , F i g u r e 9 s e t s o u t ,f o r low he ad m i g r a t i o n p r o p e n s i t i e s ( 0 2 = 0 .0 8 ) 1 p r o f i l e s show-i n g a s i g n i f i c a n t d eg r ee of f am i ly m i gr a t i o n ( 0 , = 021 anda l s o o f low f a m i l y d ep en de nc y (0, = 0 . 1 0 0 ~ and o, = 0 . 2 0 0 ~ ) .I n a s i m i l a r f o r m at , F i g u r e 10 p r e s e n t s t h e c o r r e s p o n d i n gp r o f i l e s f o r h ig h h ea d m ig r at io n p r o p e n s i t i e s (02 = 0 . 1 6 ) .With t h e a i d o f t h e s e two f i g u r e s we ca n s e e t h a t p a t t e r n ss u ch a s t h o s e o f S to ck ho lm i n d i c a t e a r e l a t i v e l y low f a m i lym i g r a t i o n d ep en de nc y w i t h h i g h h e ad m i g r a t i o n p r o p e n s i t i e s an dlow p o p u l a t i o n g ro wth r a t e s , w h er ea s p r o f i l e s s u ch a s t h o s e o fM exico C i t y p r e s e n t c h a r a c t e r i s t i c s t h a t c o r r e sp o n d t o hicyhf a m i l y m i g r a t i o n d ep en de nc y an d r e l a t i v e l y h i q h d e p en d en t a ndh ead m i g r a t io n p r o p e n s i t i e s .


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0.4 1 I 1 I I I I I , 10. 10.0 20.0 30.0 40.0 50.0 60.0 7 U . C 80.0 30.0100.~

0, /02 ( p e r c e n t )

F i g u r e 8 . V a r i a t i o n o f c h i l d - a d u l t d ep en den cy r a t i o sa mong mig ra n t s ( D ) a nd t h e p o p u l a t i o n ( D c )w i t h r e s p e c t t o d y f f e r e n t l e v e l s o f n a t u r a li n c r e a s e ( r ) f a m i ly m i g r a t i o n ( o / 0 2 ) , a n dm i g r a t i o n p r o p e n s i t i e s o f h ea ds ( A 2 ) .


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a. Family migration b. Low family dependency

Low Population Growth, r = 0Low Head Migration Propensity,02=0.08; o =0.08, 0.016, and 0.008

High Population Growth, r = 0.03Low Head Migration Propensity,02=0.08; o =0.08, 0.016, and 0.0081

0.10-

0.09..

0.09.-

0.07

0.06-

0.05..

o.o*--

a:01 0.- . -- I6 0 I. 40 10 20 30 40 so 0 I0 20 30 40 SO 60

9.10-

hx 0.03.-V

0.0s.-.0.07..

Ww 0.06.-

A CF1

c. Family migration

0.09::::!.070.0s-

AGE

c. Low family dependency

0.0s.-

0.04..

-4SO10 20 3c a0 SO

Figure 9 . A typology of age migration distributions for low andhigh population growth, family migration dependencies,and low head migration propensities.


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Low Po p ul a t io n Growth, r = 0H ig h Head M i g r a t i o n P r o p e n s i t y ,o = 0 . 1 6 ; o = 0 . 1 6 , 0 . 0 3 2 , a n d 0 . 01 62 10.t0-

0.09..

0.0~--

0.07.-

0.06-

a . F a mi ly m i g r a t i o n0. ; -4o 10 PO 10 *O. pp . G J

b. Low fa m i l y depen dency

H i g h P o p u l a t i o n G r o w t h , r = 0 . 0 3H igh Head M i g r a t i o n P r o p e n s i t y ,0 2 = 0 . 1 6 ; 0 =0.16 , 0 .032 , and 0 .0161

AGEc . F a m i l y m i g r a t i o n AGEd. Low fa m il y dep end enc y

F i g u r e 1 0 . A t yp o lo g y o f a g e m i g r a t i on d i s t r i b u t i o n s f o r d i f -f e r e n t p o p u l a t i o n g ro w th , f a m i l y m i g r a t i o n d ep en -d e n c i e s a nd h i g h h ea d m i g r a t i o n p r o p e n s i t i e s .


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CONCLUSIONSThe a i m o f t h i s p a p e r h a s b ee n t o show how t h e r e g u l a r i t i e s

t h a t a p p e a r i n m i g r a t i o n a g e c o m po s i ti o n s c a n b e sum marized i na u s e f u l m anner a nd t o s u g g e s t w ha t s uc h r e g u l a r i t i e s may b et e l l i n g us a bo u t p a t t e r n s o f n a t u r a l i n c r e a s e , f am i l y r e l a t i o n -s h i p s , and m o b i l i t y l e v e l s among m i g r a n t s .

A d i s a g g r e g a t i o n o f m i g r a n t s i n t o de p e nd e n t a nd i n d e pe n d en tc a t e g o r i e s , a nd t h e a d o p t i o n of m odel m i g r a t i o n p r o p o r t i o n s c he -d u l e s , i l l u m i n a t e s t h e ways i n which t h e a g e p r o f i l e o f m i g r a t i o ni s s e n s i t i v e t o r e l a t i v e c ha ng es i n dependency l e v e l s a nd i nr a t e s o f n at ur al i n c r e a s e a n d m o b i l i t y . V iew in g t h e m i g r a t i o np r o c e s s w i t h i n a f ramework o f depe nden t and i nde pen den t move-m en ts a l l o w s on e t o o b s e r v e t h a t i f t h e i n d e p e nd e n t com ponenti s m a in l y c om pr is ed of s i n g l e p e r s o n s, t h e n t h e a s s o c i a t e d de-p e n de n t m i g r a t i o n may b e i n s i g n i f i c a n t i n t e r m s o f i t s r e l a t i v es h a r e of t h e t o t a l m i g r a t i o n , On t h e o t h e r h an d, i f m i g r a t i o nt e n d s t o c o n s i s t p r i n c i p a l l y o f f a m il y m i g ra t i on , t h e n t h esh a re o f dependen t c h i l d r e n may become a v e r y i m po r t a n t p a r to f t o t a l m ig ra t io n .

O bs er ve d m i g r a t i o n d i s t r i b u t i o n s , when a n a ly z e d i n t h ec o n t e x t of t h e f a m i l y s t a t u s a pp ro ac h, c o nf i rm t h e i n d i c a t i o n sg i v e n by t h e p a r a m e t e r s o f t h e a s s o c i a t e d model p r o p o r t i o ns c h e d u l e s . F o r e xa mp le , h i g h m i g r a t i o n d e p e n d e n c ie s w er ec o r r e c t l y i n d i c a t e d f o r Mexico C i t y ; f o r St oc khol m t h e y w e r el ow ; and f a l l i n g som ew here i n b e tw een th e s e two ex t r em es w a st h e case o f R i o d e J a n e i r o .

The d eg r ee o f p r o p en s i ty t o m ig r a t e among in d ep en d en t mi- .g r a n t s i s a l s o e v i d e n t from o b se r ve d a g e p r o f i l e s . S t r o n g l yskewed d i s t r i b u t i o n s i n t h e a d u l t a g e s , c o rr es p on di n g t o h ig hX 2 and a2 p ar am et er v a l u e s , i n d i c a t e r e l a t i v e l y h ig h e r m i g r a t i o np r o p e n s i t i e s f o r t h e i nd e pe n de n t com ponent. P r o f i l e s w i t h h i g hdependency l e v e l s show much more weakly skewed a d u l t mi gr at io nc o m p os i t io n s du e t o l ow er p r o p e n s i t i e s f o r i n d i v i d u a l movesamong heads.


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J u s t a s p o pu l a t i on a ge c om po si tio ns r e f l e c t p a r t i c u l a rc h a r a c t e r i s t i c s o f f e r t i l i t y and m o r t a l i t y re gi me s, s o doo b se r ve d m i g r a t i o n a g e c om p o si t io n s r e f l e c t ke y a s p e c t s o ff a m i l y s t r u c t u r e a nd m i g r a t i o n p a t t e r n s . A lt ho ug h, manyof t h e r e l a t i o n s h i p s s e t o u t i n t h i s p ap er a r e s t i l l con-j e c t u r a l , a m od es t s t a r t h a s b ee n made. A f ramework f o ra s s e s s i n g t h e i m p a ct s o f n a t u r a l i n c r e a s e , f a m i l y de pe nd en-c i e s , and d i f f e r i n g m ig r at i on p r o p e n s i t i e s h a s be en s e t o u t .


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0A n de rs so n , A. E . , a nd I . H ol mb er g ( 1 9 8 0 ) M i g r a t i o n a n d S e t t l e m e n t :3. Sweden. RR-80-5. L a x en b u rg , A u s t r i a : I n t e r n a t i o n a l I n s t i t u t ef o r A p pl i e d S y s te m s A n a l y s i s .A l b e r t s , J . ( 1 9 7 7 ) ~ i ~ r a c i d na c i a a r e a s m e t r o p o l i t a n a s d e ~ m g r i c aL a t i n a ( M i g r a t i o n i n L a t i n A mer ic an M e t r o p o l i t a n A r e a s ) .

R io d e J a n e i r o : C e n t r o L a t i n oa m e r i c an o d e ~ e m o g r a f i a .B r a s s , W. ( 1 97 1 ) On t h e S c a l e o f M o r t a l i t y . P a g e s 69-1 10 i nB i o l o g i c a l A s p e c t s o f Demography e d i t e d b y W . B r a s s .L ond on: T a y l o r a n d F r a n c i s L t d .C a s t r o , L . J . , a n d A. R o g e r s ( 1 9 81 ) M odel M i g r a t i o n S c h e d u l e s :

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t h e Fr eq ue nc y o f F i r s t M ar r i ag e i n a F e m a l e C o h o r t .J o u r n a l o f t h e A m er ic an S t a t i s t i c a Z A s s o c i a t i o n 67 :743-749 .F e d e r a l S t a t i s t i c a l O f f i c e ( 19 7 0 ) I X C enso G e n er a l d e ~ o b l h c i o n

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