J>y
P. C O M P T O N
Of th e th ree v ita l processes, fe rtility , m o rtality an d m igration, th e la st is th e m ost im p o rta n t fa c to r determ ining differential p o p u latio n g row th in H ungary.
The n o rth ea st portion] of th e co u n try , H ajd ú -B ih ar, S zabolcs-S zatm ár and th e ru ra l p a rts of B orsod counties, h as consistently contained th e hig h est rates of n a tu ra l increase while th e n u m b er of people living there has d rastically declined in the la s t tw o decades. O n th e o th er h a n d , during th e p a s t te n years d ea th s have slig h tly surpassed b irth s in B u d ap est h u t th e p o p u latio n of the ca p ita l has still grow n enorm ously. A lthough th e ra te of p o p u latio n grow th th e re has not been th e highest in th e country, th e absolute increase in popula
tion has been g re a te r th a n anyw here else and th is includes th e provincial cities an d th e new socialist tow ns. In th ese tw o exam ples th e decisive fa c to r influenc
ing population g ro w th has been m igration, and if one cares to exam ine o th er regions and se ttle m e n ts w ithin th e country, th e sam e p a tte rn em erges. The reasons for th is v a s t te rrito ria l tu rn o v e r of p o p u latio n are in b ro a d outline well know n, a lth o u g h as y e t no m u ltiv ariate studies h av e been u n d erta k en to assess th e re la tiv e im po rtan ce of th e various o p erativ e factors. Suffice it to say t h a t th e process is in tim a te ly linked w ith th e rap id in d u strialisatio n of som e tow ns re su ltin g in m ore pronounced regional co n trasts in th e level and possibilities of living and in th e desire of th e p o p u latio n to m axim ise them . This is a situ atio n w hich is ch aracteristic of n o t only H u n g ary b u t of m ost o th e r developed a n d in some instances of developing countries in th e world.
A clear m an ife sta tio n of this is th e g re at increase of u rb a n populat ion th ro u g h o u t th e world.
W e find in dem o g rap h y , how ever, th a t th e degree of so phistication th a t exists in th e analysis of birth s an d deaths is no fa r lacking in th e stu d y of m ig ratio n processes. D escription is very difficult in m ost countries including th e U n ited S ta te s of A m erica an d G reat B ritain , tw o countries w ith a long dem ographic tra d itio n , owing to th e lack of m ig ratio n d ata. C onsequently, s ta tistic a l analyses are even m ore difficult to u n d e rta k e . F o rtu n a te ly , th e situ a tio n in H u n g ary is m ore favourable, where an excellent system of d a ta collect
ing a n d ta b u la tio n exists, b u t even so, little is know n ab o u t th e p re se n t m ig ra
tio n processes a p a r t from th e basic facts of te rrito ria l m igration rates, th e d istrib u tio n of m ig ra n ts b y age and sex an d som e of th e m ore obvious tre n d s in gross a n d n et m igration. U nder th e stim u latio n of th e H u n g aria n d a ta , th e w rite r of this p ap e r has o u tlin e d a m ethod of analysing th e effects of m ig ratio n on a closed population system w hich does give a realistic p ic tu re of how p o p u latio n can be expected to develop, p rovided certain conditions are h eld co n stan t w ith in the system , a n d th e ir im plications fully
re alise d .1 The p rin cip a l draw back in accepting th is m eth o d as a possible way of m ak in g p o p u latio n forecasts is t h a t new b irth s a n d deaths are com pletely ig n o red . I t does, how ever, give a su c c in t picture of th e influence of m igration on a given p o p u latio n d istrib u tio n a n d the m eth o d can thus p ro v id e new a n d m eaningful m ig ra tio n indices to supplem ent existing ty p es. M ethods h a v e been outlined fo r stu d y in g m ig ra tio n processes w ith in an open po p u la
tio n system , i.e. w h e re b irth s an d d e a th s are in clu d ed , b u t th e a d d itio n of th e l a tt e r masks th e effects of m ig ra tio n while th e m eth o d is of little use in p o p u la tio n forecasting since only cru d e b irth and d e a th rates for th e whole of th e p o p u latio n can b e used if th e an a ly sis and forecast technique is n o t to b e
com e u n d u ly com p licated . If age specific rates could be utilised, th e n the o p en system could b e used w ith g re a te r facility an d confidence.
T h e principal aim of this p a p e r is to o btain a p ic tu re of how th e annual te rr ito r ia l p attern s of m igration b etw e en 1959 an d 1965 woud h av e influenced th e populations of B u d ap est, th e p ro v in cia l tow ns an d the counties of H u n g ary la te r on, provided th e m igration pro b ab ilities com p u ted were held co n stan t w ith in each system . S econdarily, tre n d s which ta k e into consideration the in te ra c tio n betw een th e size of th e p o p u latio n w ithin each te rrito ry an d m igra
tio n w ill be com puted. In so far as th e s e in teractio n s are tak en in to acco u n t, it is t h e w rite r s considered opinion t h a t such indices are n o t only superior to b u t also supplem ent th e tre n d s co m p u ted on th e basis of th e m igration b alan ce and of gro ss in- and o u t-m ig ratio n . The tre n d s which will b e com puted in th is paper a re tre n d s in th e so-called lim itin g p o p u latio n d istrib u tio n s o b tain ed from the ite ra tio n of a m a trix of in te rte rrito ria l m ig ratio n probabilities.
T H E ANALYSIS
1 P a u l Compton: A régiók k ö zö tti v á n d o rlás vizsgálata m a trix m ódszerrel (I n te r
reg io n al m igration stu d ied by m a trix m e th o d ). Demográfia, B udapest, 1966, Yol. 9 , No. 1, p p . 475-496.
T h e model ad o p ted in this analysis assum es th a t a n y given m ig ratio n system d u p lic a te s th e p ro p e rtie s of a M arkov chain. I t is th u s a pro b ab ilistic or s to c h a stic model. T he fa c t th a t a M arkov chain progressively develops th ro u g h tim e a n d reaches a lim it afte r w h ich it does n o t change is th e m o st useful p ro p e rty of this m odel. The m odel is best form alised in term s of m a trix alg eb ra.
T h e first step in th e analysis is to c o n stru c t a d a ta m atrix , D, co n tain in g a cross tab u la tio n of m ig ratio n b etw een th e areas to be exam ined, w here D is of th e form
The elem en ts in each ro w of the m a tr ix D contain th e absolute figures of o u t
m ig ra tio n while th e elem ents in t h e columns co n tain th e corresponding figures for in-m igration. Each e le m e n t along th e principal diag o n al is th e p o p u la tio n th a t will re m a in in th e g iv e n area afte r out-m igration. If each ele
m en t in each row of th e m atrix is d iv id e d b y th e n u m b er of p o p u la tio n in th e area represented b y th e row, th e n th e d a ta m a trix D is c o n v e rted into a p ro b a b ility m atrix, P , w here the ro w s of th e m a trix contain th e p robabilities of o u t-m ig ratio n from a given region, w hile th e colum ns contain th e p ro b a b ili
ties of in-m igration to a given region. T he sum of th e elem ents of each row is u n ity . M atrix P is of th e form
P u P12 • ■ • P i n
P21 P2 2 • ■ • P i n
P n l P n2 ■■ ■ P nn
w h ere p u = —P , • • ■ p ni — ~^~ e tc ., N x, . . ., N n being th e populations
N i N n
of a reas 1 ,. . ., n.
If w e pre-m ultiply m a trix P by a v e c to r e0 w here e0 is th e p o p u la tio n d istri
b u tio n for areas 1, . . ., n, we shall th e n o b tain a new v ecto r vx re p resen tin g a new population d istrib u tio n for th e areas 1, . . ., n a fte r one step o r in m ore p ra c tic a l term s a fte r one tim e in te rv a l. The length of one in te rv a l of tim e is d eterm in e d by the tim e period for w h ic h th e m a trix P is co n stru cted . If itis for one y e a r th en vector v x represents a p o p u latio n d istrib u tio n one y e a r la te r th an th a t represented b y e0, b u t if on th e o th e r hand m a trix P is com puted for a five y e a r period then vx re p resen ts a p o p u la tio n d istrib u tio n five y ea rs la te r th a n th a t given by e0. In th is m anner a w hole series of new vectors can be ob
ta in e d fro m ' P , rep resen tin g p o p u latio n d istributions which re s u lt from th e dev elo p m en t of th e m igration sy ste m th ro u g h tim e, u p to a lim itin g vector es, since P -*■ lim. T h u s v0P = iq, vxP = e2, . . ., es_ xP = es. To fa c ilita te com p u ta tio n on an electro n ic com puter, how ever, th e system is b e st view ed in te rm s of th e developm ent of m a trix P w here, since e0P —vx and <qP = e 2, e2 is also given by e0P 2. T hus e0P = vx, . . ., e0P s — es. The lim iting m a trix ’ and v e c to r are most easily calculated b y th is second m ethod, since b y squaring th e m a trix , then sq u a rin g the re su lt a n d so on, P 256 can be reach ed a fte r nine ite ra tio n s of the m a tr ix P . This l a t t e r m a trix operation is of g re a t use to us sin
ce w e shall be m ost in te re ste d in th e lim itin g m at rix and lim iting p o p u latio n in th e succeeding analysis.
A d etailed d escrip tio n of the an a ly sis is as follows. F or each y e a r betw een 1959 an d 1965 inclusive, a sep a rate m igration p ro b a b ility m a trix w as com
p u te d . The basic d a ta for these co m p u ta tio n s were ob tain ed from T ab le 9.12 in th e 1959 D em ographic Yearbook, from Table 9.16 in th e 1960, from Table 9.22 in th e 1961, a n d from Tables 8.22 in th e Y earbooks betw een 1962 and 1965 inclusive. T hese tables co n tain a cross tab u la tio n of p e rm a n e n t m igra
tio n betw een the coun ties, the p ro v in cia l tow ns an d B udapest for each indi
45
v id u a l year. T e m p o ra ry and te m p o ra ry re tu rn m ig ratio n were n o t considered in th is analysis. T h e m igration pro b ab ilities were calcu lated from th e m id-year populations of th e s e territories, on th e assu m p tio n th a t th e y represented a close ap proxim ation of the p o p u latio n s exposed to th e possibility of m igration d u rin g one year. T h u s for in stan ce, th e m ig ratio n probabilities for th e year 1961 were c o m p u te d on the basis of th e J u n e 1st 1961 populations of each te rrito ry . The re s u ltin g seven p ro b a b ility m atrices were th en ite ra te d to sta b ility on th e M e rc u ry electronic co m p u ter a t Sheffield U niversity, E ngland, a n d th e tra n sitio n a l p ro b a b ility m atrice s relatin g to each m a trix itera tio n and th e corresponding v ec to rs were p rin te d out. R esu lts were th u s obtained for P, P 2, P 4, P s. . . ., _P1024, the la tte r b eing th e lim it for each m atrix . In every case th e initial v ector a d o p te d was th e p o p u latio n d is trib u tio n for J a n u a ry 1st 1966.
T his renders th e re s u lts from each m ig ratio n system stric tly com parable.
R ESU LTS
Two types of in fo rm atio n are o b ta in e d from th e analysis. F irst, for each S eparatem ig ratio n sy stem from 1959 to 1965 we can trac eh o w th ep o p u latio n of e v e ry area develops fro m th e in itia l to th e lim itin g population. We are thus view ing changes th ro u g h tim e in th is instance. S econdly, we can ta k e a cross sectio n of co rresp o n d in g results from each system re la tin g to a given tim e or in o th e r words re la tin g to th e same stag e of m a trix ite ra tio n . So for exam ple, we ca n com pare th e size of the lim iting populations, o r an y other populations we m a y think in tere stin g . In this m an n er, we can co m p u te population tren d s w ith in th e country fo r e v e ry te rrito ry , re la tin g to a given tim e, w here th e trends d em o n strate th e ch a n g in g effects of th e annual m ig ratio n system s on popula
tio n redistrib u tio n .
S even separate sets of results are o b tain ed from th e analysis each relating to th e annual m ig ra tio n system s for th e period 1959 to 1965. In th e ensuing discussion we shall b e referring to a dem ographic situ a tio n th a t w ould occur if each system w ere allow ed to ru n unchanged to its lim it. This is n a tu ra lly a v e r y idealised a n d h y p o th e tic a l condition since th e territo ria l p a tte rn s of m ig ratio n are alw a y s changing an d we cannot ex p e ct th e m igration proba
b ilities com puted fo r ea ch system to rem ain c o n sta n t th ro u g h tim e. A dditional
ly b irth s and d e a th s h a v e been le ft o u t of (lie analy sis and an y population d istrib u tio n re la tin g t o the fu tu re t h a t is given in th is paper m u st no t be re g ard e d as a p o p u la tio n forecast. T he term co n d itio n al projection is pre
fe rred , the ro u tin e h a v in g b u t one object, to an a ly se th e im plications of m ig ratio n under c e rta in very s tric t conditions.
T able 1 shows th e expected d evelopm ent of populatio n s of th e counties, provincial towns a n d B u d ap est on th e basis of th e 1965 territo ria l p a tte rn of m ig ratio n . The in itia l v ec to r is th e J a n u a ry 1st 1966 population. The lim it is reached at the 1 ,0 2 4 th itera tio n of th e m atrix , w hich converted in to years is 1,024 years hence. T his result can b e regarded as an in v aria n t characteristic of th e 1965 m ig ratio n system . W e m u s t note, how ever, th a t th e approach to th e lim it is c o m p a ra tiv e ly rapid a n d is closely a p p ro x im a te d a t th e 256th ite ra tio n of the m a tr ix t h a t is 256 y e a rs hence. The resu lts for th e o th er
migra-Ta b l e 1
The developm ent of the 1965 m igration system from th e initial population to th e lim iting population as shown b y th e population vectors v (in 1,000s)
^0 ^2 1 * **8 ^18 e32 c,, *■*1*8 ^10 2 4
B udapest 1,952 1,977 2,002 2,049 2,136 2,282 2,490 2,702 2,821 2,847 2,849
Debrecen 148 151 154 158 163 167 161 147 138 137 137
Miskolc 171 174 178 185 196 212 226 229 220 215 214
Pécs 136 142 149 161 182 210 238 251 253 252 252
Szeged 116 119 121 126 134 145 156 160 157 155 155
B aranya 278 274 271 265 255 245 234 230 228 228 228
Bács-K iskun 563 558 552 542 524 495 460 432 423 423 424
Békés 443 437 431 420 400 369 328 294 282 281 281
Borsod-A.-Z. 593 590 586 579 565 543 511 475 448 439 438
Csongrád 320 318 316 311 303 291 274 259 249 247 247
Fejér 385 389 393 401 415 437 463 484 492 494 494
G yőr-Sopron 400 400 400 400 400 399 398 398 398 397 397
H ajdú-B ihar 367 358 350 335 310 275 239 213 204 203 203
Heves 342 341 340 337 332 323 309 292 282 279 279
K om árom 299 303 307 315 330 353 384 412 425 427 427
Nógrád 236 236 235 235 233 230 226 221 218 217 217
P est 849 860 870 889 921 969 1,023 1,065 1,086 1,092 1,092
Somogy 362 359 356 352 343 329 311 295 288 288 288
Szabolcs-Sz. 552 540 529 507 471 416 354 311 298 297 297
Szolnok 443 436 429 416 394 360 319 287 278 277 277
T olna 256 253 250 244 235 220 203 192 189 189 189
Vas 276 274 272 269 261 249 230 208 192 188 187
Veszprém 410 411 411 412 413 414 414 413 410 409 409
Zala 263 261 258 253 244 229 209 190 181 179 179
Total* 10,160 10,161 10,160 10,161 10,160 10,160 10,160 10,160 10,160 10,160 10,160
* D ifferen c es in th e to t a ls a re d u e to r o u n d in g e rro rs.
tio n system are c o m p arab le, each a tta in in g s ta b ility a t th e 1,024th itera tio n
t h a t are affected b y th e vital processes. As an exam ple of th is p ro p erty , an
e n t re su lt w ith D ebrecen, G yőr-Sopron and V eszprém being grouped w ith
iii. L im iting populations in itially increasing in sizeb u t su b seq u e n tly decreas
G roup ii. co n tain s b y far the la rg e st num ber of counties. W ith th e exception
tria lly developed. I t is again n o t u n n a tu ra l th a t P est c o u n ty and th e p ro v in cial towns of M iskolc and Szeged should fall in to th e category. P est co u n ty in w hich large areas are dorm ito ry regions for B udapest is in stru c tu re n o t unlike a tow n. T he a p p a re n t slowing dow n of population g ro w th m ig ratio n in Miskolc and Szeged can be linked to th e p o p u latio n upsurge shown by counties in G roup ii. B u d a p e st and Pécs h ave been lin k ed to g eth er in one group, s tric tly on th e m ag n itu d e of th e lim iting p o p u latio n s and not on th e ir tren d p a tte rn s . In this la tte r re sp ect th e y are very unsim ilar. W ith th e physical re stric tio n s th a t exist on m ig ratio n to B u d ap est and w ith th e rapid developm ent t h a t is going on in th e countryside, it is n o t u n ex p e cted th a t th e size of th e lim itin g populations of B u d ap est should decline in tim e. The p resent analysis does show t h a t the declining ra te of p o p u latio n g ro w th of th e ca p ita l is an u n derlying ten d en cy and n o t som ething t h a t m ay change as th e te rrito ria l p a tte r n of m igration develops. W hy Pécs should h a v e a grow th te n d e n c y so m uch la rg e r th a n th e o th er provincial tow ns is n o t re a d ily ap p aren t. T he relationship, as fa r as m igration is concerned, of so u th ern T ransdanubia w ith th e rest of th e co u n try is n o t so developed as in o th er areas. So although th e re is v ery h ig h m obility w ith in th is p a rt of T ra n sd an u b ia, th e in- and o u t-m ig ratio n ra te s to an d from this p a r t of th e co u n try are g enerally lower th a n th o se betw een o th e r regions. In th is resp ect, we can view the p o p u la tio n grow th p o ten tial of Pécs as som ething p ec u lia r to so u th ern m o st T ra n sd an u b ia.
This paper h a s trie d to exam ine m ig ratio n from a new a n d possibly u n u su a l view point. M arkov chains are a v ery pow erful m ath e m a tic a l tool, how ever, w hich will p ro b a b ly be increasingly used in dem ography an d o th er social sciences in th e fu tu re . This p ap e r has been dealing w ith only one of th e v ita l processes d eterm in in g population gro w th an d so any re s u lts are n o t to be in terp re ted as popu latio n forecasts. The ex am in atio n of open population sy s
tem s by this te c h n iq u e is ju s t beginning an d as y e t is no t su ita b le for forecasting th e future. B u t w ith fu rth e r developm ent and so p h isticatio n and w ith th e g re a t increase in m achine facilities for d a ta processing a n d analysis, sim ilar techniques will re su lt in increasingly m ore reliable in fo rm atio n in th e field of population forecasting, alth o u g h even a t th is early stage it provides us w ith an insight of how spatial m igration processes work.
GEOGRAPHICAL ASPECTS OF DUNAÚJVÁROS