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A general equilibrium model of guest-worker migration
Journal of International Economics 25 11988) 335-351. North-Holla:td
A GENERAL EQUILIBRIUM M O D E L O F GUEST-WORKt'P MIGRATION
The S w ~ t - C o n ~ P
~
Slobodan DJAJI~ Graduate Imai~tae of imerm~foeml $1whes, 1211-Germ, Swu:erlaM
Ross MILBOURNE* Owt,n's UmdrL.rm~y.KUq.~om. 0 t ~ o . Cm*m~mKTL 3;/6
Itemved Novembu ig~6, fc~,4,mi ~.tQon rectived Februtn/ lCgLq •rkm impt., ~ i m m kkutiad, u f i l i t y ~
tkg Imu~m ot Immt.,,,,od~ mimmm From ~ eoomom3, ~ by imdividm~ ~ fmmimew o d d q ~ The d E i m ~o migrate, time
nine d m ~ while Mxoul, as 111 as dm b q ~ d a milmm'o tuq im tlk, foNilm ©mintS, m.e MI vimqd as pwt of a ,drama to m ~m, ummpoml otaiiamaiom Im,Olmn. In ,dditio, to studyil,~,. • . aspemsM,mpwmTmqrmiom ,a,..impammlymUmdmm wmmu o( dU mla.'Mlx~mmSow o( mi~'mu, dm ~ m s p o s d i q dommic wsW.. ,md me k ' ~ oC =dfare m~oymdbT, tylpiml worker. IMms d ms ~iermion m ~re dm m v m i p ~
I. Immmlmgtl~
The relative importance of temporary as o p p m e d to permanent migration hat grown considerably since the end of World War !1. This is particulady true with respect to the pattern of migration olxgrved between the Mediterranean countrie~ and the economies of northern and central Europe. The recent flows of labor into the oil-rich c o u n t r i a of the P~slun Gulf from the less prosperous neighboring economies provide another example in which migration is primarily of the guest-worker type. The system of temporary migration offers rome attractive features to both the guest-workers and the host countries. From the point of view of the guest-worker, this type of international labor mobility enab!es one to take advantage of the higher w a f t s abroad, without having t¢~ incur the relatively *This paper was pgaeated to the Fourth Annual C.mdkgmceon International Trade Theory at the U-ivenity of Watem Ontm'io. 23-24 Man:h, 1985. We ~ to thank the gonkrmoe pmiapnm and two anonymous referees for their hdphd rammers. Very tmdul digumiom ~ Rmm~ ~3~r ,mi I t ~ H m Lm srsl~l~lly ~ Any d the n:msiainS m o ~ o ~
0022-19%/85/$3..q0 ~ 1968. ElsevierScimm PuldiMtt~ B.V.(Nortb-Holhmd)
3~
S. Djaj/~and R. M//botm~.G.e~-workerW~/on
high economic asld psychic costs of permanent migration. From the perspective of the host country, the guest-worker system presents an appealing way of dealing with iabor-market shortaKes, particularly those perceived to be transitory is'. nature. In spit,; of the considerable economic importance of guest-worker migrefi,~, to both the countries of immigration and emigration, theoretical problems 8ssoclated with this type of internatiomd labor mobility are only beginning to attract attention. Among the few o , isting studies is the contribution by Ethkr (1985), which focuses on 8 number of host-country issues/ However, t~os~ aspects of the problem which are of the greatest concern to both the 8uest workers and to the remaining residents of the source country, have not been adequately acldrt~ed in the theoretical literature. 2 The purpasc of the Fegsent study is to cxmnine the problem of guestworker migrdtiun from the perspective of the potential miiprut and his country of origin, in section 2 we dcvdop a simple mocld of a small monomy from which individuals m i g r ~ in order to sink temporary employmmt a l x o ~ F m a p l i c i t y and on the I m m of the oboer~tion that temporary misratiou involves primarily ~ labor, we asmsme that all w o r ~ , n are idmticsL Each of them has a fmite workin8 Ilk o v ~ which be nmximizm utility from ~ ~,, the f,x u g n and domestic monouties. Thus, the da:bion to mipatc, '.he rate of m v i n j u b i k shroud, M wall 8s the iensth of a tnqp~t's stay in the forcqgn country, are all viewed as perts of a solution to an intertemporal u t i l i t y - ~ t i o n wobkm. Afta s n a l y s ~ t h ~ m i c r ~ ~ of gue,t-wo~ka misration, we turn in section 3 to the woblem of detOgl~mmS the market ~ in the soumc country and the equilibrium flow of mifgrants. In m:tion 4 we employ a ,imple d i q r a m m a t i c technique to study the e t : t s of c h a n ~ in certain of the model or, the p a t t m t of inteTnational misration and the levd of welfare enjoyed by the citizens of our economy. The disturbances cons/doted include a clumlc in ~ cost of international migration, a shift in preferenoes of migrants between consumption at home and consumption abroad, and a change in the wage available to guest worlk~rs in the host tSgg 8ho Bbmqgwati(1976) for ms ~sportut survey of the issues rdmted to the pmbkm of inta~Jtion,i mL"~i~ indudins pu~t-worl~ migration, and the wm~ of ~ Scbatz and Won8 (1984), i)jaji&(IM6Lb), Etl~r (1984). Kntum (1976), and Ri~raohtiz (1~3). An ,trick by Hill (1987) takes an alqmm~ somewlmtsimilar to that of the pmcm pqx~. Thug 8re also several emldrkadstudks and informaldiscmskmson the eamcqngs of ipmt-wodus milpltion. See, for exmnpk. Blitz (1977), Chandsva~a~ (!980), Maami]llau(1982), Mdutiuder (1980), P~ore (1979~ Swmny (19QI). and Richardsand Marlin (1983). 'The extensiveliterature ms the *tmdn-drain"proidemfocusmon a number of ~ t r y m indudin8 thme invdviu8 the w d ~ of mqputs ,nd of tUe remainm8 rmdmU. Hovmva, it trats millmtJon as permanmt u d does not 6~1 ~th the proMam which am spetiftc to the 8ue~t-~k~ qy,,t.,~u.
$. Djaj~ and R. Milbourne, Guest. worker nuRratWn
337
country. The effects of an emigration tax are considered in section 5. Finally, section 6 o~ers some roncluding t~'marks and suggestions for future research.
Z. 1"m ,te,~.im te Jlp~.te in an attempt to highlight what we perceive to be the central issues, we make ~everal simp:ifying assumptions. We assume that at every instant there are N identical workers born in our economy, each enaowed with one unit of labor, in addition to workers, then: is a class of landlords who competitively employ workers, but do not supply any labor themselves. Each worker is assumed to be continuously employed throughout his working life, a period defined to last from the alle of 0 to T. in order to further simplify the analysis, we assume that the work/ economy produces • single commodity with the aid of land and labor. Moreover, the home country is small in relation to the resl of the world and relatively abuuadant in labor. A c c o r d ~ y , the ~ real walle, w, is lower than tbe prevailin8 foreign wage, w*. W o r k e n are free to milp'at~ across international borders and to seek employment abroad. 3 However, the p r a e n ~ of movin8 costs - both economic m d i~,chic - prevents the equalization of w with w*. T h e problcn, facing each polestinJ m i l p a n t is whether o r not t o incur the
moving costs in excbanlpe for the opportunity to re~ve a bqlber Walle abroad. Moreover, if he de~ks to millrate, he faces the problems of choosing the length o~ lus foreign slay and of dividing ha lifetime income between consumption in one country and consumption in the other In analysing the,e interrelatedproblems, we shall assume that the migrants have a stronger preference for consumption in their homeland than they do for consumption abroad. More specifically, lettins u*(c*) denote the flow of utility from the consumption rate c* abroad and u[c) denote the flow of utility eujoyed at home from the consumption rate c, we assume that u*'(x) < u'(x),
V x.
(I)
That is, the marginal utility of consumption at home is always higner than that associated with the same rate of consumption abroad. This assumption on the marginal utilities results in behavior consistent with st)iized facts that migrants have a higher savings rate while aborad and that their rate of )The modd could easily be extended to a world in which mignmtq arc permitted to work in the host country only for a q~ecifu: period of time (ue l)ja~ (lgSGb)]. The case of unimpeded millratioa, u within an ¢¢ouo4mk: community, seems to be a more logical staxtin8 Feint for
anazpu.
S. D~aj~ and R. Milbownt, Gwst.worker migrmion
338
consumption rises upon returniag to the homeland? Both utility functions u*(-) and u(-) are taken to be increasing, ,..!~!y conca,'e, and '..,~..'~ continuously differentiable. Let us assume further that the cost of moving to ~ foreign country in order to become a guest worker is an increasing function of the migrant's abe, t. Thus, in the absence of any advantages to migrating iateT on in life, each migrant will minimize his moving cc4ts by so:king employment abroad at age 0. The corresponding :ound-trip cost of tr~gration is denoted p and assumed to be the same for all citizens. Finally, let us a u u m e that caigta' markets are perfect and that me constant rate of time preference, &, is equal to the world rate of interest, r. The latter assumption is made in an a~empt to mmpi~, the analysis and to hilgltlisht the role of factors influencing savin$ which are spechtc to the problem of gnat-worker migration. The manner in which the optimal consumption pettern is affected when 6 ~ • is well known, s Considering only statm~mry equilibria, we may now formulate the problem facinlg each of the migrants as follows. He must choose the lensth of his foreilgn stay, T, and the rates of consumption abroad and at home, c*(t) and c(t), so as to maximize the discounted flow of utility,
Y " = i ue(ce(t)) e - * dt + i u(c(t)) c - k dr, 0
(2)
•
subject to the budget constraint, t
T
v
T
I ¢"(t) e - * dt + I c(t) e - * d t + p = w-e I e - k d t + . , I e - * c~. 0
•
0
(3)
s
4Prekten~ and constraints faua~ by a typical 8uest worker fgivet ~ to e~nomic behavior which often has O,: foUowin8 two featur~ First, his uvinSS rate while abroad tends to be unusually high. In Germany in 1972, for example, mVinlp of m',~'ants amounted to 25 percem of their averap dispoud~ income (Blitz (19T7, pp. 49~499)]. For the fiimures on the other European countries, see Macmillan (19~$2)and the referem~ cited therein. ~ esngJen~ that a typical pest-worker's consumption undcrsms an upward jump following his mum to the homeland, ~ y wit5 respect to his ra:c at" c-Jneumpziouof luxmy floods wb.ich vnJd to be more expenmveat home th~qnthey are abroad, hu been reported by C"handa~trkar (1980L On the basis of these observations and informal interviews with 8umt workers, one mi~,ht advance the followin8 hypothmis. A pest-worker's utility is it function of both his coosumption rate c and the amber .q of relatives 8ud friends in whose preaence commmption o u r s . If c and R 8re Edlleworth compkmenu, so that the marginal utility of colummp6on is increuin8 in R, and if~ is ~ in the homelud than it is abroad, one would indeed obee~ tlmt• 8nest wot,ket" has t rdJItivdy higher [N~lrerelgN~for coMumptioflat home in the MBSeOf ineqtJB~i) ~,~). sit 6~r, comumptiou Imtlu ~rc not conmmt at bom~ and a ~ - commmption declines (tiara) over tune if 6 > ~ 6 < r ) - bqtt none d o u r qualitstive result- is affected, in p B f t i ~ , eqL (?)-(15) below hold for both c u d c° just tJter the jutt before abe z. r e ~ v d y .
S. Djaji~ and R. Mi!bc".'.':.:. G,,*~r-wor/~erm.fratio,i
339
Defining Z as the Lagrangian assoctated with the migrant's maximizatton problem~ the first-order conditions are
OZ Oc*(t)= u*'(c*(t)) e- ~' - ;. e - 6' = 0, ~Z
....
?c(t}
= u'(c(t)}e
(4)
"-;.c~'=0,
(5)
~Z ~:r =" u ' ( c ' ( T ) )
e -'-
-tc(t)) •
"-
,.[c'(t)-~)-
,~'" -,- . , ] e
"=0,
(6)
and of course, the budget constraint (3). Sinoe the shadow value of wealth. ,;. is independent of time, eqs. (4) and (5) imply that c*(t):c', clt)=c, and u * ' ( c ' ) = u'(c) = ;..
(7l
Eq. (7) is the familiar arbitrage condition: the margina] utility of consumption at home must be equal to that al~road. From (I) and t'/) it follows that c* O.
(8)
That is, the Izn.Jth of a migrant's foreign stay i.; optimal one) if u(c) -u*(c*), the utility ~.lh'ked by remaining an extra instant abroad, is just equal to the gain in utility fro;iz ~ ' ; ' S w * - w + c - c * additior,ai units of output for consumption at home. Moreover, eq. (7) enables us to express c* as a function of c* = ¢(c),
(9)
where ¢~'= de*/& ~- .'(c)/u*'(c*)>0. With the aid of (9), we may rewrite (8) as t , ( c ) - u*( ~ c ) ) = u ' ( c ) [ w * - w + c - 4,(c)~.
(lO)
which relates c to the international wage differential, w ' - w . That it does so uniquely, may be seen by differentiating (10) to obtain dr./d(w*-w)=u'tcl/ u'(c)[.~cl - c - w* + .~,]>0. Thi.~ enables us to write ca. (10) as c=~(w*-w),
~'=c/pEw*-w+c-~c)]>Oo
(11)
NO
$. DJ~/~ ald R. Mi/botmw,
Gues.~rk~r mit,rm/ow
where p = - u"(c}c/u°(c)>0 is the elasticity of marginal utility with respect to consumption. T.be.. rmsitive relationship betweec, c and w * - w may be interpreted as follows. For a given pattern of a migrant's consumption i.-. the two economies, the higher the intm'national w a F ~ i a l , the greater the value of w * - w ÷ c - c * , his 'net' rate of assm accumulation abroad. To restor~ balance between the cost and the benefit of staying abroad and accumulatin~ assets, c must rise to lower u'(c) and hence lower ~ e utility value of the hishcr savings rate.' The sons/tivity of consumption to clumps in w * - w is invenJely related to p, a measure o( the degree of concavity of the utility fumgtion. in summary, the flurst-order conditions (4)-(6) determine by themselves c, c°, and ,t as functions of w * - w . " I ~ remaining first-mdcr condition, the b u d F t constraint, then ckterm'_mm the optimal value of t, given c and c*. Integrating the terms in (3), and rcarransins, we have
e - " : e "'r+ ('v* -c')(I - e -'r) -,5# ( c - c " + w ' - w)
(t2)
Because c - c" + w* - w • 0, it follows that z < T if and only if
~ < ( ~ , -c*) (I - e6 -'r)
(13)
That is to say, an internal solution for t emerBes if and o n l y if the cost of migration, /a, is smaller than the present value of savings in the foreign country by a migrant who follows the optimal consumption program and spends Ms ontire working lik abroad. Substituting the optimal values of c and c* into (12), we obtain the followin8 relationship betweon the length of a migrant's foreign stay, % and the parameters of the model: { w * - ¢~[¢~w'- w)]}(1 - e - ' ) - a . c - " = c - ' T + ~ ( ~ ' _ w) - ¢~[~w* - w)] + w* - w'
(14)
which we shall denote as ~ : 6 ( ~ , w*,,).
(15)
6It sboukl be noNd ~mul while u i ~ in w (for a 8iwn we) lowers c and c'. it does not lo~.r z m ~ = t ' s disco~¢~l utility..ks n show~ in section 3 bdow. dmcoumed u ~ t y d • m~nml r i ~ with w u be m~poncb to in i n c m ~ in the d o m e ~ ~ by mlucin8 ¢b= dmckm of his stay ~xoed.
S. Djaj~ and R. Milbrzrne, Gwsx-worker nugrat~
341
To find the effects on r of changes in w, w*. and p, we differentiate (14). Throughout the rest of the paper, c* and ~(c)---¢~[ddw*-:;')], and c and ~ ( ~ " - w ) , will be used interchangeably where it simpliEes t.he a!gebra. In addition, let us define
k ---(I - e - ~ ' ( - ) + ' ( - ) + ( e * -
e-'r)#'(-) > O,
where the derivatives of functions arc with rc~jx~t to t,t~eir arguments (which are suppressed). For a 8Jven value of r, k16 measures the change in the d~:ounted vaine of a migrant's opttmal consmup~v, stre~tm Jrom a one Ultit increase in the internabonal wage difkr~tiaL Because both c* and c increase with this wage dilSkr~tial, k/.~.%0. From (14) it follows that the partial derivatives of the function 0 are 0 . -= [(e -6, - e -
'T) 4" k]/4~l~ - 4k(Ce --C -- We ~" W) <~0,
O.. = [ ( I - - e - ~ ) -- k ] / ' ~ - k(g * - c -
w" + w) t 0 ,
(16)
117) 118)
O p = - I/e-k(c* - c - w * + w) >0.
The signs in 116).-118) m y he expll~iz~ -t, An inaume in w reduces the international w a F differential and, a,~,xding to eqs. (9) and (IJ), Iowen a mqgant's rate of cxxmmtptkm both at home and abroad. A; the same time it raisu the present value of his liktime earninjts for any 8iven z < T. Thus, an increase in w ena134m a ~ t to attain his op~mal consumption p r o o a m w~th a slzortet stay alxoad lt.e. O. <0). On the other hand, an i ~ . m ~ widens the intL'rnatiomd wast differential, lending to an increase in a r a t ' s optnnal rates of consumption in both c o u n ~ Althongh for a giwm t the m t value of his lifetime income also rises with w*, it may increase by more or k:s than desired spending, depeedins on the smsitivity of c to chanl~ in w * - w Because this sensitivity is invcngly related to the d e l p ~ of ,-~lativc risk a v e r ~ we may covdude that for relatively high (low) values o~ p, the cost of a migrant's
optimal consumption prngram rises by less (more) than his incoug, resulting in a reduction (increase) in the required length of his foreign stay. FinnHy, we notc that an increase in the cost of migration, F, does not affect the rates of consumption enjoyed by a migrant in either economy, it does, however, !-~wex the present ;'~uc of . ~ net lifctimc income. Thus, ;,, order to satudy his i n ~ p o r a l budget constraint, a migrant must stay in the foreign country for a longer period of time.
z Tin ~
flu, of m ~ . , m J
Mffm
lr. considering a migrant's maximization problem, we have treated the
342
S. Dja/'ii and R. MiIbourne,GK~..wc~r ndo'mion
domestic wage -'ate as exogeno "s. Given the technology and the economy's endowment. of land, the equilibrium value of w is inversely related to the size of the country's labor for~e. It is therefore a d i r e r fai,~,~;o, of ~,;, the nurabcr of citizens of the home country employed abroad. The purpose o; this section is to solve for the stationary value of w and the corresponding flow of migrants, M / t , to and from the home country. In our analysis, we shall deal ~ t h internal solutions which yield an equilibrium flow of migrants smaller than N, the number of individuals born at each instant. Eqs. (9), (11), and (15) provide the solutions for the optimal pattern of consumption mid tl~ l¢:ngth of a migrant's foreign stay as functions of w and the exogenous variables. Noting that w is a direct function of the number of migrants, M, and that the equilibrium value of : is given by eq. (15), we may express the discounted utility of a typical migrant [defined by (2)] as qu,(Ml: w'. ~1
V,,=u*lOl~[w*-w(Ml]})
I
e-"dt
o T
w(M)]})
¢IQl
e-*dt.
O[~M): w'./,l
A resident who chooses not to migrate (referred to as a remaining worker) maximizes JoTu(c~t))e-"dt, subject to the budget constraint, F
g
J ~(t)e-a' dt=w j e-~' dt. o
o
The solution to this problem is ~(t)---w for all to so that the discounted utility achieved by a remain.lng worker is given by T
v, = u[,,(M)] j e-" dr.
(20)
0
We observe that both ~ and $.~~u¢ ruzictions of w(M). By differentiating (!9) and (20) with respect to w(M) and rearran&Jng terms, we can express the slopes of these/unctions as
OK. u'(c)(e-" - , T Ow(M)= 5 -e )>0, ~V, ~w(M) Since
(2t)
u'!'w(M)1(l - e -'r) >0. 6
(22)
..............................
c > ~M),
u'(c)
Moreover,
e- j' < I.
Consequently,
S. D)~.ii~ and R. Milbourne. G ' ~ s t - w o r k o migrcuio,,
343
,-.v,.! !
I
Vm
/
'
!
I
I I
I,
'!
! °
T4
I I
e.,
I
e . . . .
F - ~ ;. Omter--,,,mation o f equilibrium w and t.
~?V,/c~(M)>c~V~/~w(M). Assnming that V.>V, when M=O (otherwise it would not pay for anyone to migrate), we may use the schedules V. and V, in the top panel of fi& I to depict the relationships between w(M) on the one hand, and the levels of discounted utility enjoyed by the migrants and by the remninin~ workers on the other. Because all workers are identical, in a stationary equilibrium there can he no advantage to being a migrant rather than a remaining worker. The value of V_ must thg'refore he equal to g, as at the point of intersection between the V. and V, schedules. Corresponding to this point is the equilibrium domestic wage @. Once this wage is dete.mined, one can easi|y solve (wi:b the a ~ of the production function) foi the corresponding rumher of migrants, A). The Iow~ panel of fig. I displays the relationship between the domestic
344
,5. Djaji~ and R. Millx~wne, Cmesg-workermigralion
wage and the optimal length of a migrant's foreign stay. From (IS), ¢ and w are inversely related so that the link between the two can be . ~ . ~ t e d by the negatively sloped 88 schedule. This schedule may now be used to determine ~, the optimal value of z corresponding to the equilibrium Wal~ ~(M). Finally, if A~ is the equilibrium number of migrants and ~ is the length of time that each of them spends abroad, F - ~ / ~ is the stationary flow of migrants leaving and retumin 8 to the home country per unit of time. 4. Comparative tuttia This section examines the effects of dumges in certain parameters of the model on the pattern of misratiou and welfare in a stationary equilibrium it is most convenient to proceed with the analysis Ip~aett~zdly;, algebraic derivations are presented where appropriate.
4.1. A decline M the cost of intenmt~tal migration
Consider a fall in the cost of milp'ation due, for example, to a reduction in traml~rt and mmmunication coets. How does tim fall allect the duration of a typical migeut', stay m the tmeign country and hi~ mvinlp rate abroad? How does it s l o t the flow o f ~ t s tad file level of wdfare ~ y ~ I by the workers n m m i n ~ in the source country?. From (I 8), at each level of w, a decline in ~t reduee8 the optimal value o( :. This slfif~ the m schedule down to 6'0' in the lo..-~r p m ~ of fill. 2. In addition, becaux a reduction in raises the discounted value of a migrant's lifetime utility by - a ' ( c ) d ~ > 0 at each value of w~ it shift, the V= locus upward to g~,,, as illustrated in tbe top wmel of fiB, 2. Given that a change in/~ has no e t c t on V,, the point of intersection between the V. and V, schedules must he above and to the right of the initial equilibrium. The kvel of welfare enjoyed by each worker rises from Po to Pt, while the equilibrium domestic ~ increases from ~o to F t. The corresponding increase in the number of migrants is from ~ o to 5]t. Because an increase in ~ narrows the international wade differenth0, it lowers the migrant's optimal rates of consumption both at home and abroad [see eqs. (9) and (11)]. With 8 constant w*, this implies that each migrant saves a larger fraction of his foreign income. In the lower panel of fig. 2 the optimal length of a typical guest worker's stay in the foreign country falls from io to ~t. This is because a redjgtion in # lowers the optimal value of z both directly (by relaxing the misrant's intertemporal budget constraint at each value of w) and indirectly (by raising the equilibrium Ic~! ¢-f w). An implication of a fall in ~ is that the stationary flow of milgants, P, incraaes proportionately more than the numhet of misnm~ ~.
S. Djaji~ a'Td a. q4ilhourvu, (;,,,,¢t-~,.,,,~,.,
.,,iet,~ioPi
v,,,'v~I
/ J
A T
I
I
I
I
T,
i
, e
J
I ....
e
w. t~.) %~1}
w(Id)
F'q. 2. Emlecz of a red~z/~s m ~.
4.2. An increase in the foreign wage It was shown in eq, (l7) that an increase in w* has an ambiguous effect on the po6ition of the. ~ schedule. However, it improves the welfare of migrants at each level of w, shifting the Y. locus up and to the left. This can be seen by differentiating (19) and obtaining ~ Y . / 0 w * = u ' ( c ) [ l - e - ~ ] / 6 > 0 . At the same time, a c h s n F in w* laves the position of the V, locus unaffected. Thus, as in the case of a reduction in/4 (depi¢:~ in fi& 2) the level of welfare of each, worker rises trom, ssy, ['o to ['t and the domestic wase rises from ~o to ~t. The corresponding increase in the stock of migrant labor is from '~ to ~ t . l ~ g effect of an incrua~ m w* on ~ is ambiguous. However, because an increase in w* ~ the domestic walg., x must fall if the 08 schedule shifts
346
S. Dj'aj~ and R. Milbourne, Gue.n-wor/~.i,~frmion
downward (i.e. if 0v,<0). Alte~atively, in the event that 0~,>0, as when p is relatively 'small" [see the discussion following eq. (17)], there exists the possibility that d~/dw* >0.
4.3. ,4 shift in preferences Consider next the effects of a change in tastes which in~eas~ the flow of utility and the marginal utihty a~tociated with each rate of consumption abroad Such a .~he.-.=e in te.-.e~. ~,~'.:id, for example, be the result of an improvement in the social a t m m p l ~ that the migrants face in the host country. It will be viewed in what follows as an upward shift of the function ¢(.) in eq. (9). Differentiation ofeq. (10) with respect to 4q') reveals that this shift in ~ raises c* while leaving c unchanged for any given values of w* and w3 In order to finance the higher rate of consumption abroad. each migrant must now work in the forciipn country for a longer period of time. Accordingly, in fiB- 3, the 80 schedule sb.;fts up and to the right. The rise in the flow of utility associated with any given rate of consumption abroad shifts the It. schedule up and to the ~ in the upper panel of fig. 3. in consequence, the stationary level of welfare enjoyed by both the migrants and the remamm$ wv, kcas incrmsm from Fo to Ft. The: domestic wage & aim increases, as does the equilibrium number of migrants. However, the net effect on the length of each migrant's forei~rt stay (shown in the lower panel of fig. 3 to he positive) is ambiguous. Whik the direct effect of an inen:ase in the attmctivenem of living abroad tends to increase T, the associated rise in the domestic wage operates in the opposite direction. 5. Emigration tax and welfare
The effects of taxing emigration have been analysed primaA'i]y in the context of modeb where the earning power d~ers among individuals3 Assuming that the foreign wage is higher than that available at home, there is an economic rent associated with the opportunity to migrate for all but the marginal migrant (the individual who is just indifferent between being a migrant and a nonmigrant). By taxing this rent, the gover--ment of the so,.trce countr) can improve the welfare of the remaining residents as we!! zs the distribution of income among them. In contrast with the assumptions made in these studies, we have posited that all workers are identical. This assumption is particularly appropriate for the analysis of temporary migration of manual workers whose abilities at~ essentially the same as those of the remaining residents. Consequently, each 71t im:nmsm,however,the eJuticity of c with t~spectto the ittiecuttional wNledilknmtiai. tSw, for aample, BhalgWatiand Hamada (1982L Baumol(1962L ~ (IMSL MeCulloch and Ydlua (19"/5),Mirrlm (IM2k and Wilson(1982).
S. Djr.jil and R. A4ilbourne. Guest-aorker mig;~ "",,
347
v~ , v~l v~,
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.
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.
.
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,
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.,
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io (~,) i,(~,) Fi& 3. Effect of a clsanF in I m t r c n c a
.
w(M) favohng consumptmn abroad.
migrant is a 'marginal migrant', earning no rent that could be taxed and used by the authorities to improve the welfare of the remaining residents. On the contrary, it can be shown that the imposition of an emigration tax necessarily lowers welfare, not only of migrants, but also of those workers who choose not to migrate, it is only the landlords who benefit from this policy measure. Let us assume that the government of the source country imposes an exit tax on those who leave tl~ economy in order to seek employment abroad. This tax raises the cost of migration, the effocts of which are already familiar, given the analysis of a change in/A in subsoction 4. !. Thus, as shown in fig. 4, the V= schedule shifts dov, n from Vr to V'_, while the 00 schedule shifts tip and to the right. Assuming that the tax rcv¢nue is given to the la~dlor,'.; position of the V, schedule remains unaffocted. Under those conuition~ the
348
$. Djdj~ ,.and R. M i ~ ,
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.--,
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~ ~b~n p o ~ o , of ~ e..sra~on tax.
level of welfare of ~ worker falls from P, to Pz, tl~ equilibrium wal~ d~.li~s from ~! to &2, and the I ~ s t h of each ~ t ' $ stay a ~ from ~, to ~2. AIt~-mLtivcly, if the pro(x~(L~ of tbc tax arc r~iistribulml to-tko~ worke~ who qpr~ n e ~ to mi~ate., the welfare locus of tim re~dnmg workers shifts up from V, to Y',. This is i:a:ausc at any si~'n w, the incom= of worker is now hillhar due to the trand~r. As a ~ u l t of this shift of the V, locus, w falls to ~ and the statiomu'y k'wl of ~ ~joyed by ~ h worker ~ to Ps- Thus, the welfare loss of w o r k m i s / ~ e r than that e x ~ when the tax prooemls are turned over to the landlords. The intuition behind these som~vhat parsdoxk:ld results is r a t l ~ idmp~. In the tbeen~ of mom)poly powar in the international mark~ for labor, an emilp'tti~ tax b a welfare-reduciq distortion for the economy M a whole.
$. Djaji~ and I~. Milbourne, Guest-worker mi~,ra,,on
349
Moreover, by discouraging emigration, the tax is an instrument which shtfts the economy'g distribution of income, away from labor ..nd in favor of the landlords. Thus~ given ti~ assumption that all worken ~re ideatical, each of them must unambiguously suffer a welfare it,~s, regard;c~, of whether he chooses to migrate or to remain at home. If the fax revenue is distributed to the remaining workers, the si~ of the distortion is greater, and heree the welfare loss experienced by workers laqler? It is interesting to examine the effects of the emigration tax on the standards of living enjoyed m tke home comm'), by the returning migrants and by the nmmining workers, if the tax prcx:eeds are distributed to the landlord& ~ falls to ~2,/ower/,~ the constant rate of comumption and utility enjoyed by the remaining workers. The full in t~, however. ~reases the international wage ditgeatial aad hence the. rate of consumption that the migrants undertake alter reuettling in their bomehtnd. ]'bus, the p p between the raU= of commumptiou mjoyed in the home country by the two groups of worken, is now wider. This gap can be shown to incrense even furthn if the Woceeds of t.".e tax are no¢ di~trilmted to the lamilord& but rather to the wo:lters who agree not to migrate., it was argued earlier that t h~ c l u m F in the manner of distriixnin~_ the proc0eds s b ~ thg F, scheduk up and to the left in fig 4 and lowers the discounted utility of encb um4ca from P~ to Ps. ~ constant rate
of comumptim enjoyed by the rmmim
woden mum be co,'m,pondingly
low~ in q3ite of the tmm&r. On tl~" o t h ~ lured, the furtl~r f,Ml in w from • , to ~'s increm~ the iatenmtioaal wase d i ~ e n t i a l and hmze the migrant's rate of conmmption at home. It follows that the act of distributing the tax proceeds to the remaining worker, lower, th,'Ar rate of consumption, while raising tha: enjoyed in the borne country by the rcturnins milwants. Thus, in the context of the present model, the policy <4 taxing emigraUon in an attempt to reduce the gap between the :',.,tndard of living enjoyed by the returning m i ~ a n ~ and by t|g remaining workers will generate prechely the opposite effects. It should he emphasized, however, that the migrants enjoy a higher consumption level at home at the ccr.t of a longer period of low-utility consumption abroad. & Ceulml~ mm~ .The m~n contribution of this paper fie; in its approach (o the problem of international migration, in contrast with most of the earlier studies, the approach is based on the notion that migrants are utility-maximizing individuals with finite working lives. Accordingly, the decision to migrate, the YOur results rely, of coente, on tl~ structure of our model if we consi(~ instead am economy wlmne ~ and unskilled ~ r k e r ~ - .atbor than land and labor - awe used to produge output. • tax on , . - - i , u t i ~ t of Jilled (umkilJed) worken would be,~yi: va~killed (liJied) worken..
350
S. Djaji~ and R. Milbos.Tne, Guest-wov'-kevmigration
len~h of a guest-worker's stay and his rate of asset accumulation in the for~:ign country, are. all viewed as parts of a solution to an intertemporai optimization problem. In addition to analysing the behaviour of guest workers and their optimzd response to a number of exogenous disturbances, we have examined the effects of these disturbances on the equilibrium flow of migrants, the domestic wage, and the level of weJf~:c enjoyed by the remaining worLcrs of the source country. Although none nf the results was found to be particularly striking, they all serve to highlight the present model's unique ability to deal wi:l,, ~,or.,s relz~:,~ to the optimal length of a migrant's stay in the foreign
country and his intertemporal patte~ of consumption within a generai equilit'~:'.;m Cramework. While the model is capable of addressing a range., of important sourcecountry issues, its ability 0o explain a number of observed phenomena is limited by so.,ne of our simplifying assumptions. For example,, by dropping t,~e assumptions that all individuals arc identical and that a migrant's p r c k r e m ~ arc invariant with rcspect to the l e q t h of time spent away from the home country, one would be a b k to offer economic reasons why some migrants make several tripe to the foreign country, why some stay I o n l ~ than others, and why some migruts never rcturn. F u r t h e r m o ~ to relax the assumption of perfect capital markets and to introdnec physical capital into the model as a factor of wodnetion would allow one to p i n insights into the important and controversial Iclatiomhip between intcrmttimml misration and e ~ n o m i c growth of the source country. Explicit consideration of tariffs - ,'l,ich in the context of the present model amount to a tax on remittar~es - and other ec~n~mic policies which ha:'= a dire.: :.~quen~ on t ~ 4..~.~.'n. to migrate Le.g. nummum-wage laws, inmdgration restrictions, ~qcl labormarget subsidies) woutd aiso be us~ul in future research. RefeNmces Baumoi, WJ, 1982,The incomedistribution frontier and taxation of miwuts, Journal of Public Economi~ 18, MY-~I. BImswati, J.N., 1976, The internattomd brain drain and taxation" A survey of issues, in: J.N. Bhagwati,ed., The brain drain and taxation (North-Hohnd, Amsterdam)3-27. Bhagwati, J.N. and K. Hsm~J. 1982, Tax policy in the pt~smt~ of emilgration,Journal of Public Economics18, 291-317. Bhagwali, J.N.,K.-W. Schatz and K.-Y. Worts, 1984, The West German gnstarbeitersystem of migration,European Economic Re~'w 26, 277-294.
Blitz, R.C., 1977, A bmn~fit..costanalysis of foreign workers in West Ocmumy, 1957-1973, Kyklos 30, 479-502. Clumdavagkar,A.G., 1980, Use of migrant remittancesin inbor-ezportingcountries, Finance and l ~ ~ t 17, .~6-39. l~qji6, ,5., 1985, Skills and the I~tte.~ of international migration. Di~-ussion paper no. 612, ~haeen'sUniversity. D~tji~ S., 191Vat,fntenmtiomudmisration, rmuittanccs and welfare in a ¢kpmdent economy, Journalof DevelopmentEconomics21,229-234.
S. Djaji? and ~. Miihourne, Guest-wo~~ r migration
351
Djaji~ S.. 1986b Milpa,zt~ in a 8uest-worker system: A utility-maximizin 8 approach. Discussien paper no. 661, Queen's University, forthcoming, JournAl of Development Economics. I=thzer wJ., 19z[4, International trade theory and intcmationa~ milp'a*.ion, Discussion paper no. ~, Mi~r~,;.,,, ,~nd r~-velo.mnenl Pfowrarn. Harvard Unive~ilv Ethier, WJ., 1985, International trade and labor migration. American Economic Review 75, 691-707. Hill J.K., 1987, Immigrant decisions concernln8 duration of stay and m~rat.on ~requency, Journal of Development Economics 25, 221-234. Kralxss, M.B., 19"/6, The economic~ of "he Ipuu~l-worker problem: 4 Ne~-Heckr~her-Ohlin approac~ ScamliuviM Journal of Ecot~nk~ 78. 470-476. Mmumillmz, M J , Iq~?, The e~nomic effects or international migration: A survey. Joumzd of Common Market Sl,,m,~ 20, 245-267. McCuiloch. it, and J. Ydlea, 1975. Comequmces of • tax oe the Imun-drain for unemployment aid im:ome iaeqmdity in less dcvcio.Ded ommtrkL Journal of Development Econom.cs 2, 24q-2M Mehrh~d=r, U. 19~0, The human-resource probkm ta Z~ur,~., M,ip~-'zt ~bor m the F~der.=l PaepubSc of ~ y . in: U. Ra'aaaa. ed, EOsmc ~ m modem democratic states (Papmou Prin. New YorkL Mirdem, ".A~ 1987.. Milpatioa and optimal im:oaz tssa, Journal of Public Economics IS. 319-341. ~,~, 19"/'9, B6rds of pmmal~. Mqprzml labor in industrial lociezic.s ICambndge t,nlvcrmty Prom, Loudoe~. Rk:han~ A. aud P.L. Martia. 19113,TI~ I.,umtz4aire aplwoac~ to mtenutttmud labor milpratioa: TI~ cu~ olr Arab Middle Eal. Eammmc l ~ t n d Cultural ClhumF 31. 455-474. IU~l-Batiz. F. 1983. 1'1he u ; o o o ~ (dr tl~ "to mad fro' m~plm: Soo~ w,~r-,c-themr~zcal cc,mideratiom..5,cu~llmaviu Jounud of' F.,coaom~ 8~, 403-413 Sammy. G . 19~i. iolmtatiomal mui~'amt woftkas" r e m i t ~ Some ~ theoretical coeuad~. atom, World lbudc Sudr w m t m 8 paper uo. 48j. Wadui~zou. IX:. Wiboa. J.D, 19~2, Optimal ~ lautiou m the p r a a t ~ o( cmisratma. Journal of Pebhc F,couomi~ !8. 363-379.
A GENERAL EQUILIBRIUM M O D E L O F GUEST-WORKt'P MIGRATION
The S w ~ t - C o n ~ P
~
Slobodan DJAJI~ Graduate Imai~tae of imerm~foeml $1whes, 1211-Germ, Swu:erlaM
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tkg Imu~m ot Immt.,,,,od~ mimmm From ~ eoomom3, ~ by imdividm~ ~ fmmimew o d d q ~ The d E i m ~o migrate, time
nine d m ~ while Mxoul, as 111 as dm b q ~ d a milmm'o tuq im tlk, foNilm ©mintS, m.e MI vimqd as pwt of a ,drama to m ~m, ummpoml otaiiamaiom Im,Olmn. In ,dditio, to studyil,~,. • . aspemsM,mpwmTmqrmiom ,a,..impammlymUmdmm wmmu o( dU mla.'Mlx~mmSow o( mi~'mu, dm ~ m s p o s d i q dommic wsW.. ,md me k ' ~ oC =dfare m~oymdbT, tylpiml worker. IMms d ms ~iermion m ~re dm m v m i p ~
I. Immmlmgtl~
The relative importance of temporary as o p p m e d to permanent migration hat grown considerably since the end of World War !1. This is particulady true with respect to the pattern of migration olxgrved between the Mediterranean countrie~ and the economies of northern and central Europe. The recent flows of labor into the oil-rich c o u n t r i a of the P~slun Gulf from the less prosperous neighboring economies provide another example in which migration is primarily of the guest-worker type. The system of temporary migration offers rome attractive features to both the guest-workers and the host countries. From the point of view of the guest-worker, this type of international labor mobility enab!es one to take advantage of the higher w a f t s abroad, without having t¢~ incur the relatively *This paper was pgaeated to the Fourth Annual C.mdkgmceon International Trade Theory at the U-ivenity of Watem Ontm'io. 23-24 Man:h, 1985. We ~ to thank the gonkrmoe pmiapnm and two anonymous referees for their hdphd rammers. Very tmdul digumiom ~ Rmm~ ~3~r ,mi I t ~ H m Lm srsl~l~lly ~ Any d the n:msiainS m o ~ o ~
0022-19%/85/$3..q0 ~ 1968. ElsevierScimm PuldiMtt~ B.V.(Nortb-Holhmd)
3~
S. Djaj/~and R. M//botm~.G.e~-workerW~/on
high economic asld psychic costs of permanent migration. From the perspective of the host country, the guest-worker system presents an appealing way of dealing with iabor-market shortaKes, particularly those perceived to be transitory is'. nature. In spit,; of the considerable economic importance of guest-worker migrefi,~, to both the countries of immigration and emigration, theoretical problems 8ssoclated with this type of internatiomd labor mobility are only beginning to attract attention. Among the few o , isting studies is the contribution by Ethkr (1985), which focuses on 8 number of host-country issues/ However, t~os~ aspects of the problem which are of the greatest concern to both the 8uest workers and to the remaining residents of the source country, have not been adequately acldrt~ed in the theoretical literature. 2 The purpasc of the Fegsent study is to cxmnine the problem of guestworker migrdtiun from the perspective of the potential miiprut and his country of origin, in section 2 we dcvdop a simple mocld of a small monomy from which individuals m i g r ~ in order to sink temporary employmmt a l x o ~ F m a p l i c i t y and on the I m m of the oboer~tion that temporary misratiou involves primarily ~ labor, we asmsme that all w o r ~ , n are idmticsL Each of them has a fmite workin8 Ilk o v ~ which be nmximizm utility from ~ ~,, the f,x u g n and domestic monouties. Thus, the da:bion to mipatc, '.he rate of m v i n j u b i k shroud, M wall 8s the iensth of a tnqp~t's stay in the forcqgn country, are all viewed as perts of a solution to an intertemporal u t i l i t y - ~ t i o n wobkm. Afta s n a l y s ~ t h ~ m i c r ~ ~ of gue,t-wo~ka misration, we turn in section 3 to the woblem of detOgl~mmS the market ~ in the soumc country and the equilibrium flow of mifgrants. In m:tion 4 we employ a ,imple d i q r a m m a t i c technique to study the e t : t s of c h a n ~ in certain of the model or, the p a t t m t of inteTnational misration and the levd of welfare enjoyed by the citizens of our economy. The disturbances cons/doted include a clumlc in ~ cost of international migration, a shift in preferenoes of migrants between consumption at home and consumption abroad, and a change in the wage available to guest worlk~rs in the host tSgg 8ho Bbmqgwati(1976) for ms ~sportut survey of the issues rdmted to the pmbkm of inta~Jtion,i mL"~i~ indudins pu~t-worl~ migration, and the wm~ of ~ Scbatz and Won8 (1984), i)jaji&(IM6Lb), Etl~r (1984). Kntum (1976), and Ri~raohtiz (1~3). An ,trick by Hill (1987) takes an alqmm~ somewlmtsimilar to that of the pmcm pqx~. Thug 8re also several emldrkadstudks and informaldiscmskmson the eamcqngs of ipmt-wodus milpltion. See, for exmnpk. Blitz (1977), Chandsva~a~ (!980), Maami]llau(1982), Mdutiuder (1980), P~ore (1979~ Swmny (19QI). and Richardsand Marlin (1983). 'The extensiveliterature ms the *tmdn-drain"proidemfocusmon a number of ~ t r y m indudin8 thme invdviu8 the w d ~ of mqputs ,nd of tUe remainm8 rmdmU. Hovmva, it trats millmtJon as permanmt u d does not 6~1 ~th the proMam which am spetiftc to the 8ue~t-~k~ qy,,t.,~u.
$. Djaj~ and R. Milbourne, Guest. worker nuRratWn
337
country. The effects of an emigration tax are considered in section 5. Finally, section 6 o~ers some roncluding t~'marks and suggestions for future research.
Z. 1"m ,te,~.im te Jlp~.te in an attempt to highlight what we perceive to be the central issues, we make ~everal simp:ifying assumptions. We assume that at every instant there are N identical workers born in our economy, each enaowed with one unit of labor, in addition to workers, then: is a class of landlords who competitively employ workers, but do not supply any labor themselves. Each worker is assumed to be continuously employed throughout his working life, a period defined to last from the alle of 0 to T. in order to further simplify the analysis, we assume that the work/ economy produces • single commodity with the aid of land and labor. Moreover, the home country is small in relation to the resl of the world and relatively abuuadant in labor. A c c o r d ~ y , the ~ real walle, w, is lower than tbe prevailin8 foreign wage, w*. W o r k e n are free to milp'at~ across international borders and to seek employment abroad. 3 However, the p r a e n ~ of movin8 costs - both economic m d i~,chic - prevents the equalization of w with w*. T h e problcn, facing each polestinJ m i l p a n t is whether o r not t o incur the
moving costs in excbanlpe for the opportunity to re~ve a bqlber Walle abroad. Moreover, if he de~ks to millrate, he faces the problems of choosing the length o~ lus foreign slay and of dividing ha lifetime income between consumption in one country and consumption in the other In analysing the,e interrelatedproblems, we shall assume that the migrants have a stronger preference for consumption in their homeland than they do for consumption abroad. More specifically, lettins u*(c*) denote the flow of utility from the consumption rate c* abroad and u[c) denote the flow of utility eujoyed at home from the consumption rate c, we assume that u*'(x) < u'(x),
V x.
(I)
That is, the marginal utility of consumption at home is always higner than that associated with the same rate of consumption abroad. This assumption on the marginal utilities results in behavior consistent with st)iized facts that migrants have a higher savings rate while aborad and that their rate of )The modd could easily be extended to a world in which mignmtq arc permitted to work in the host country only for a q~ecifu: period of time (ue l)ja~ (lgSGb)]. The case of unimpeded millratioa, u within an ¢¢ouo4mk: community, seems to be a more logical staxtin8 Feint for
anazpu.
S. D~aj~ and R. Milbownt, Gwst.worker migrmion
338
consumption rises upon returniag to the homeland? Both utility functions u*(-) and u(-) are taken to be increasing, ,..!~!y conca,'e, and '..,~..'~ continuously differentiable. Let us assume further that the cost of moving to ~ foreign country in order to become a guest worker is an increasing function of the migrant's abe, t. Thus, in the absence of any advantages to migrating iateT on in life, each migrant will minimize his moving cc4ts by so:king employment abroad at age 0. The corresponding :ound-trip cost of tr~gration is denoted p and assumed to be the same for all citizens. Finally, let us a u u m e that caigta' markets are perfect and that me constant rate of time preference, &, is equal to the world rate of interest, r. The latter assumption is made in an a~empt to mmpi~, the analysis and to hilgltlisht the role of factors influencing savin$ which are spechtc to the problem of gnat-worker migration. The manner in which the optimal consumption pettern is affected when 6 ~ • is well known, s Considering only statm~mry equilibria, we may now formulate the problem facinlg each of the migrants as follows. He must choose the lensth of his foreilgn stay, T, and the rates of consumption abroad and at home, c*(t) and c(t), so as to maximize the discounted flow of utility,
Y " = i ue(ce(t)) e - * dt + i u(c(t)) c - k dr, 0
(2)
•
subject to the budget constraint, t
T
v
T
I ¢"(t) e - * dt + I c(t) e - * d t + p = w-e I e - k d t + . , I e - * c~. 0
•
0
(3)
s
4Prekten~ and constraints faua~ by a typical 8uest worker fgivet ~ to e~nomic behavior which often has O,: foUowin8 two featur~ First, his uvinSS rate while abroad tends to be unusually high. In Germany in 1972, for example, mVinlp of m',~'ants amounted to 25 percem of their averap dispoud~ income (Blitz (19T7, pp. 49~499)]. For the fiimures on the other European countries, see Macmillan (19~$2)and the referem~ cited therein. ~ esngJen~ that a typical pest-worker's consumption undcrsms an upward jump following his mum to the homeland, ~ y wit5 respect to his ra:c at" c-Jneumpziouof luxmy floods wb.ich vnJd to be more expenmveat home th~qnthey are abroad, hu been reported by C"handa~trkar (1980L On the basis of these observations and informal interviews with 8umt workers, one mi~,ht advance the followin8 hypothmis. A pest-worker's utility is it function of both his coosumption rate c and the amber .q of relatives 8ud friends in whose preaence commmption o u r s . If c and R 8re Edlleworth compkmenu, so that the marginal utility of colummp6on is increuin8 in R, and if~ is ~ in the homelud than it is abroad, one would indeed obee~ tlmt• 8nest wot,ket" has t rdJItivdy higher [N~lrerelgN~for coMumptioflat home in the MBSeOf ineqtJB~i) ~,~). sit 6~r, comumptiou Imtlu ~rc not conmmt at bom~ and a ~ - commmption declines (tiara) over tune if 6 > ~ 6 < r ) - bqtt none d o u r qualitstive result- is affected, in p B f t i ~ , eqL (?)-(15) below hold for both c u d c° just tJter the jutt before abe z. r e ~ v d y .
S. Djaji~ and R. Mi!bc".'.':.:. G,,*~r-wor/~erm.fratio,i
339
Defining Z as the Lagrangian assoctated with the migrant's maximizatton problem~ the first-order conditions are
OZ Oc*(t)= u*'(c*(t)) e- ~' - ;. e - 6' = 0, ~Z
....
?c(t}
= u'(c(t)}e
(4)
"-;.c~'=0,
(5)
~Z ~:r =" u ' ( c ' ( T ) )
e -'-
-tc(t)) •
"-
,.[c'(t)-~)-
,~'" -,- . , ] e
"=0,
(6)
and of course, the budget constraint (3). Sinoe the shadow value of wealth. ,;. is independent of time, eqs. (4) and (5) imply that c*(t):c', clt)=c, and u * ' ( c ' ) = u'(c) = ;..
(7l
Eq. (7) is the familiar arbitrage condition: the margina] utility of consumption at home must be equal to that al~road. From (I) and t'/) it follows that c*
(8)
That is, the Izn.Jth of a migrant's foreign stay i.; optimal one) if u(c) -u*(c*), the utility ~.lh'ked by remaining an extra instant abroad, is just equal to the gain in utility fro;iz ~ ' ; ' S w * - w + c - c * additior,ai units of output for consumption at home. Moreover, eq. (7) enables us to express c* as a function of c* = ¢(c),
(9)
where ¢~'= de*/& ~- .'(c)/u*'(c*)>0. With the aid of (9), we may rewrite (8) as t , ( c ) - u*( ~ c ) ) = u ' ( c ) [ w * - w + c - 4,(c)~.
(lO)
which relates c to the international wage differential, w ' - w . That it does so uniquely, may be seen by differentiating (10) to obtain dr./d(w*-w)=u'tcl/ u'(c)[.~cl - c - w* + .~,]>0. Thi.~ enables us to write ca. (10) as c=~(w*-w),
~'=c/pEw*-w+c-~c)]>Oo
(11)
NO
$. DJ~/~ ald R. Mi/botmw,
Gues.~rk~r mit,rm/ow
where p = - u"(c}c/u°(c)>0 is the elasticity of marginal utility with respect to consumption. T.be.. rmsitive relationship betweec, c and w * - w may be interpreted as follows. For a given pattern of a migrant's consumption i.-. the two economies, the higher the intm'national w a F ~ i a l , the greater the value of w * - w ÷ c - c * , his 'net' rate of assm accumulation abroad. To restor~ balance between the cost and the benefit of staying abroad and accumulatin~ assets, c must rise to lower u'(c) and hence lower ~ e utility value of the hishcr savings rate.' The sons/tivity of consumption to clumps in w * - w is invenJely related to p, a measure o( the degree of concavity of the utility fumgtion. in summary, the flurst-order conditions (4)-(6) determine by themselves c, c°, and ,t as functions of w * - w . " I ~ remaining first-mdcr condition, the b u d F t constraint, then ckterm'_mm the optimal value of t, given c and c*. Integrating the terms in (3), and rcarransins, we have
e - " : e "'r+ ('v* -c')(I - e -'r) -,5# ( c - c " + w ' - w)
(t2)
Because c - c" + w* - w • 0, it follows that z < T if and only if
~ < ( ~ , -c*) (I - e6 -'r)
(13)
That is to say, an internal solution for t emerBes if and o n l y if the cost of migration, /a, is smaller than the present value of savings in the foreign country by a migrant who follows the optimal consumption program and spends Ms ontire working lik abroad. Substituting the optimal values of c and c* into (12), we obtain the followin8 relationship betweon the length of a migrant's foreign stay, % and the parameters of the model: { w * - ¢~[¢~w'- w)]}(1 - e - ' ) - a . c - " = c - ' T + ~ ( ~ ' _ w) - ¢~[~w* - w)] + w* - w'
(14)
which we shall denote as ~ : 6 ( ~ , w*,,).
(15)
6It sboukl be noNd ~mul while u i ~ in w (for a 8iwn we) lowers c and c'. it does not lo~.r z m ~ = t ' s disco~¢~l utility..ks n show~ in section 3 bdow. dmcoumed u ~ t y d • m~nml r i ~ with w u be m~poncb to in i n c m ~ in the d o m e ~ ~ by mlucin8 ¢b= dmckm of his stay ~xoed.
S. Djaj~ and R. Milbrzrne, Gwsx-worker nugrat~
341
To find the effects on r of changes in w, w*. and p, we differentiate (14). Throughout the rest of the paper, c* and ~(c)---¢~[ddw*-:;')], and c and ~ ( ~ " - w ) , will be used interchangeably where it simpliEes t.he a!gebra. In addition, let us define
k ---(I - e - ~ ' ( - ) + ' ( - ) + ( e * -
e-'r)#'(-) > O,
where the derivatives of functions arc with rc~jx~t to t,t~eir arguments (which are suppressed). For a 8Jven value of r, k16 measures the change in the d~:ounted vaine of a migrant's opttmal consmup~v, stre~tm Jrom a one Ultit increase in the internabonal wage difkr~tiaL Because both c* and c increase with this wage dilSkr~tial, k/.~.%0. From (14) it follows that the partial derivatives of the function 0 are 0 . -= [(e -6, - e -
'T) 4" k]/4~l~ - 4k(Ce --C -- We ~" W) <~0,
O.. = [ ( I - - e - ~ ) -- k ] / ' ~ - k(g * - c -
w" + w) t 0 ,
(16)
117) 118)
O p = - I/e-k(c* - c - w * + w) >0.
The signs in 116).-118) m y he expll~iz~ -t, An inaume in w reduces the international w a F differential and, a,~,xding to eqs. (9) and (IJ), Iowen a mqgant's rate of cxxmmtptkm both at home and abroad. A; the same time it raisu the present value of his liktime earninjts for any 8iven z < T. Thus, an increase in w ena134m a ~ t to attain his op~mal consumption p r o o a m w~th a slzortet stay alxoad lt.e. O. <0). On the other hand, an i ~ . m ~ widens the intL'rnatiomd wast differential, lending to an increase in a r a t ' s optnnal rates of consumption in both c o u n ~ Althongh for a giwm t the m t value of his lifetime income also rises with w*, it may increase by more or k:s than desired spending, depeedins on the smsitivity of c to chanl~ in w * - w Because this sensitivity is invcngly related to the d e l p ~ of ,-~lativc risk a v e r ~ we may covdude that for relatively high (low) values o~ p, the cost of a migrant's
optimal consumption prngram rises by less (more) than his incoug, resulting in a reduction (increase) in the required length of his foreign stay. FinnHy, we notc that an increase in the cost of migration, F, does not affect the rates of consumption enjoyed by a migrant in either economy, it does, however, !-~wex the present ;'~uc of . ~ net lifctimc income. Thus, ;,, order to satudy his i n ~ p o r a l budget constraint, a migrant must stay in the foreign country for a longer period of time.
z Tin ~
flu, of m ~ . , m J
Mffm
lr. considering a migrant's maximization problem, we have treated the
342
S. Dja/'ii and R. MiIbourne,GK~..wc~r ndo'mion
domestic wage -'ate as exogeno "s. Given the technology and the economy's endowment. of land, the equilibrium value of w is inversely related to the size of the country's labor for~e. It is therefore a d i r e r fai,~,~;o, of ~,;, the nurabcr of citizens of the home country employed abroad. The purpose o; this section is to solve for the stationary value of w and the corresponding flow of migrants, M / t , to and from the home country. In our analysis, we shall deal ~ t h internal solutions which yield an equilibrium flow of migrants smaller than N, the number of individuals born at each instant. Eqs. (9), (11), and (15) provide the solutions for the optimal pattern of consumption mid tl~ l¢:ngth of a migrant's foreign stay as functions of w and the exogenous variables. Noting that w is a direct function of the number of migrants, M, and that the equilibrium value of : is given by eq. (15), we may express the discounted utility of a typical migrant [defined by (2)] as qu,(Ml: w'. ~1
V,,=u*lOl~[w*-w(Ml]})
I
e-"dt
o T
w(M)]})
¢IQl
e-*dt.
O[~M): w'./,l
A resident who chooses not to migrate (referred to as a remaining worker) maximizes JoTu(c~t))e-"dt, subject to the budget constraint, F
g
J ~(t)e-a' dt=w j e-~' dt. o
o
The solution to this problem is ~(t)---w for all to so that the discounted utility achieved by a remain.lng worker is given by T
v, = u[,,(M)] j e-" dr.
(20)
0
We observe that both ~ and $.~~u¢ ruzictions of w(M). By differentiating (!9) and (20) with respect to w(M) and rearran&Jng terms, we can express the slopes of these/unctions as
OK. u'(c)(e-" - , T Ow(M)= 5 -e )>0, ~V, ~w(M) Since
(2t)
u'!'w(M)1(l - e -'r) >0. 6
(22)
..............................
c > ~M),
u'(c)
Moreover,
e- j' < I.
Consequently,
S. D)~.ii~ and R. Milbourne. G ' ~ s t - w o r k o migrcuio,,
343
,-.v,.! !
I
Vm
/
'
!
I
I I
I,
'!
! °
T4
I I
e.,
I
e . . . .
F - ~ ;. Omter--,,,mation o f equilibrium w and t.
~?V,/c~(M)>c~V~/~w(M). Assnming that V.>V, when M=O (otherwise it would not pay for anyone to migrate), we may use the schedules V. and V, in the top panel of fi& I to depict the relationships between w(M) on the one hand, and the levels of discounted utility enjoyed by the migrants and by the remninin~ workers on the other. Because all workers are identical, in a stationary equilibrium there can he no advantage to being a migrant rather than a remaining worker. The value of V_ must thg'refore he equal to g, as at the point of intersection between the V. and V, schedules. Corresponding to this point is the equilibrium domestic wage @. Once this wage is dete.mined, one can easi|y solve (wi:b the a ~ of the production function) foi the corresponding rumher of migrants, A). The Iow~ panel of fig. I displays the relationship between the domestic
344
,5. Djaji~ and R. Millx~wne, Cmesg-workermigralion
wage and the optimal length of a migrant's foreign stay. From (IS), ¢ and w are inversely related so that the link between the two can be . ~ . ~ t e d by the negatively sloped 88 schedule. This schedule may now be used to determine ~, the optimal value of z corresponding to the equilibrium Wal~ ~(M). Finally, if A~ is the equilibrium number of migrants and ~ is the length of time that each of them spends abroad, F - ~ / ~ is the stationary flow of migrants leaving and retumin 8 to the home country per unit of time. 4. Comparative tuttia This section examines the effects of dumges in certain parameters of the model on the pattern of misratiou and welfare in a stationary equilibrium it is most convenient to proceed with the analysis Ip~aett~zdly;, algebraic derivations are presented where appropriate.
4.1. A decline M the cost of intenmt~tal migration
Consider a fall in the cost of milp'ation due, for example, to a reduction in traml~rt and mmmunication coets. How does tim fall allect the duration of a typical migeut', stay m the tmeign country and hi~ mvinlp rate abroad? How does it s l o t the flow o f ~ t s tad file level of wdfare ~ y ~ I by the workers n m m i n ~ in the source country?. From (I 8), at each level of w, a decline in ~t reduee8 the optimal value o( :. This slfif~ the m schedule down to 6'0' in the lo..-~r p m ~ of fill. 2. In addition, becaux a reduction in raises the discounted value of a migrant's lifetime utility by - a ' ( c ) d ~ > 0 at each value of w~ it shift, the V= locus upward to g~,,, as illustrated in tbe top wmel of fiB, 2. Given that a change in/~ has no e t c t on V,, the point of intersection between the V. and V, schedules must he above and to the right of the initial equilibrium. The kvel of welfare enjoyed by each worker rises from Po to Pt, while the equilibrium domestic ~ increases from ~o to F t. The corresponding increase in the number of migrants is from ~ o to 5]t. Because an increase in ~ narrows the international wade differenth0, it lowers the migrant's optimal rates of consumption both at home and abroad [see eqs. (9) and (11)]. With 8 constant w*, this implies that each migrant saves a larger fraction of his foreign income. In the lower panel of fig. 2 the optimal length of a typical guest worker's stay in the foreign country falls from io to ~t. This is because a redjgtion in # lowers the optimal value of z both directly (by relaxing the misrant's intertemporal budget constraint at each value of w) and indirectly (by raising the equilibrium Ic~! ¢-f w). An implication of a fall in ~ is that the stationary flow of milgants, P, incraaes proportionately more than the numhet of misnm~ ~.
S. Djaji~ a'Td a. q4ilhourvu, (;,,,,¢t-~,.,,,~,.,
.,,iet,~ioPi
v,,,'v~I
/ J
A T
I
I
I
I
T,
i
, e
J
I ....
e
w. t~.) %~1}
w(Id)
F'q. 2. Emlecz of a red~z/~s m ~.
4.2. An increase in the foreign wage It was shown in eq, (l7) that an increase in w* has an ambiguous effect on the po6ition of the. ~ schedule. However, it improves the welfare of migrants at each level of w, shifting the Y. locus up and to the left. This can be seen by differentiating (19) and obtaining ~ Y . / 0 w * = u ' ( c ) [ l - e - ~ ] / 6 > 0 . At the same time, a c h s n F in w* laves the position of the V, locus unaffected. Thus, as in the case of a reduction in/4 (depi¢:~ in fi& 2) the level of welfare of each, worker rises trom, ssy, ['o to ['t and the domestic wase rises from ~o to ~t. The corresponding increase in the stock of migrant labor is from '~ to ~ t . l ~ g effect of an incrua~ m w* on ~ is ambiguous. However, because an increase in w* ~ the domestic walg., x must fall if the 08 schedule shifts
346
S. Dj'aj~ and R. Milbourne, Gue.n-wor/~.i,~frmion
downward (i.e. if 0v,<0). Alte~atively, in the event that 0~,>0, as when p is relatively 'small" [see the discussion following eq. (17)], there exists the possibility that d~/dw* >0.
4.3. ,4 shift in preferences Consider next the effects of a change in tastes which in~eas~ the flow of utility and the marginal utihty a~tociated with each rate of consumption abroad Such a .~he.-.=e in te.-.e~. ~,~'.:id, for example, be the result of an improvement in the social a t m m p l ~ that the migrants face in the host country. It will be viewed in what follows as an upward shift of the function ¢(.) in eq. (9). Differentiation ofeq. (10) with respect to 4q') reveals that this shift in ~ raises c* while leaving c unchanged for any given values of w* and w3 In order to finance the higher rate of consumption abroad. each migrant must now work in the forciipn country for a longer period of time. Accordingly, in fiB- 3, the 80 schedule sb.;fts up and to the right. The rise in the flow of utility associated with any given rate of consumption abroad shifts the It. schedule up and to the ~ in the upper panel of fig. 3. in consequence, the stationary level of welfare enjoyed by both the migrants and the remamm$ wv, kcas incrmsm from Fo to Ft. The: domestic wage & aim increases, as does the equilibrium number of migrants. However, the net effect on the length of each migrant's forei~rt stay (shown in the lower panel of fig. 3 to he positive) is ambiguous. Whik the direct effect of an inen:ase in the attmctivenem of living abroad tends to increase T, the associated rise in the domestic wage operates in the opposite direction. 5. Emigration tax and welfare
The effects of taxing emigration have been analysed primaA'i]y in the context of modeb where the earning power d~ers among individuals3 Assuming that the foreign wage is higher than that available at home, there is an economic rent associated with the opportunity to migrate for all but the marginal migrant (the individual who is just indifferent between being a migrant and a nonmigrant). By taxing this rent, the gover--ment of the so,.trce countr) can improve the welfare of the remaining residents as we!! zs the distribution of income among them. In contrast with the assumptions made in these studies, we have posited that all workers are identical. This assumption is particularly appropriate for the analysis of temporary migration of manual workers whose abilities at~ essentially the same as those of the remaining residents. Consequently, each 71t im:nmsm,however,the eJuticity of c with t~spectto the ittiecuttional wNledilknmtiai. tSw, for aample, BhalgWatiand Hamada (1982L Baumol(1962L ~ (IMSL MeCulloch and Ydlua (19"/5),Mirrlm (IM2k and Wilson(1982).
S. Djr.jil and R. A4ilbourne. Guest-aorker mig;~ "",,
347
v~ , v~l v~,
I
1
I
.
I
!
.
.
L ........
~ I
i i
,
r
io(go ) ,,
8
!
U\I
\\',
,
.....
~,(~,)
-
w(M)
', ,
.,
i ',\/o. •
~
io (~,) i,(~,) Fi& 3. Effect of a clsanF in I m t r c n c a
.
w(M) favohng consumptmn abroad.
migrant is a 'marginal migrant', earning no rent that could be taxed and used by the authorities to improve the welfare of the remaining residents. On the contrary, it can be shown that the imposition of an emigration tax necessarily lowers welfare, not only of migrants, but also of those workers who choose not to migrate, it is only the landlords who benefit from this policy measure. Let us assume that the government of the source country imposes an exit tax on those who leave tl~ economy in order to seek employment abroad. This tax raises the cost of migration, the effocts of which are already familiar, given the analysis of a change in/A in subsoction 4. !. Thus, as shown in fig. 4, the V= schedule shifts dov, n from Vr to V'_, while the 00 schedule shifts tip and to the right. Assuming that the tax rcv¢nue is given to the la~dlor,'.; position of the V, schedule remains unaffocted. Under those conuition~ the
348
$. Djdj~ ,.and R. M i ~ ,
G~st-wm'kev m/~'m/on
4
~m,V,
.v; °/m
V2
. . . . .
!
-/:
I
I
I I
I '!
! I I
I ! J
E3
~2
w,
I I
I
I
,
:
~
,
1" ~
~
:
.__oN _ _ ~,,~__'~
~2 . . . . .
I
,
----
I
i i .,'k,"k, I
T .... I
.-~ Fil~ 4. ~
wlM) ~
'
l
.-'2
z
.--,
w(M) =
~ ~b~n p o ~ o , of ~ e..sra~on tax.
level of welfare of ~ worker falls from P, to Pz, tl~ equilibrium wal~ d~.li~s from ~! to &2, and the I ~ s t h of each ~ t ' $ stay a ~ from ~, to ~2. AIt~-mLtivcly, if the pro(x~(L~ of tbc tax arc r~iistribulml to-tko~ worke~ who qpr~ n e ~ to mi~ate., the welfare locus of tim re~dnmg workers shifts up from V, to Y',. This is i:a:ausc at any si~'n w, the incom= of worker is now hillhar due to the trand~r. As a ~ u l t of this shift of the V, locus, w falls to ~ and the statiomu'y k'wl of ~ ~joyed by ~ h worker ~ to Ps- Thus, the welfare loss of w o r k m i s / ~ e r than that e x ~ when the tax prooemls are turned over to the landlords. The intuition behind these som~vhat parsdoxk:ld results is r a t l ~ idmp~. In the tbeen~ of mom)poly powar in the international mark~ for labor, an emilp'tti~ tax b a welfare-reduciq distortion for the economy M a whole.
$. Djaji~ and I~. Milbourne, Guest-worker mi~,ra,,on
349
Moreover, by discouraging emigration, the tax is an instrument which shtfts the economy'g distribution of income, away from labor ..nd in favor of the landlords. Thus~ given ti~ assumption that all worken ~re ideatical, each of them must unambiguously suffer a welfare it,~s, regard;c~, of whether he chooses to migrate or to remain at home. If the fax revenue is distributed to the remaining workers, the si~ of the distortion is greater, and heree the welfare loss experienced by workers laqler? It is interesting to examine the effects of the emigration tax on the standards of living enjoyed m tke home comm'), by the returning migrants and by the nmmining workers, if the tax prcx:eeds are distributed to the landlord& ~ falls to ~2,/ower/,~ the constant rate of comumption and utility enjoyed by the remaining workers. The full in t~, however. ~reases the international wage ditgeatial aad hence the. rate of consumption that the migrants undertake alter reuettling in their bomehtnd. ]'bus, the p p between the raU= of commumptiou mjoyed in the home country by the two groups of worken, is now wider. This gap can be shown to incrense even furthn if the Woceeds of t.".e tax are no¢ di~trilmted to the lamilord& but rather to the wo:lters who agree not to migrate., it was argued earlier that t h~ c l u m F in the manner of distriixnin~_ the proc0eds s b ~ thg F, scheduk up and to the left in fig 4 and lowers the discounted utility of encb um4ca from P~ to Ps. ~ constant rate
of comumptim enjoyed by the rmmim
woden mum be co,'m,pondingly
low~ in q3ite of the tmm&r. On tl~" o t h ~ lured, the furtl~r f,Ml in w from • , to ~'s increm~ the iatenmtioaal wase d i ~ e n t i a l and hmze the migrant's rate of conmmption at home. It follows that the act of distributing the tax proceeds to the remaining worker, lower, th,'Ar rate of consumption, while raising tha: enjoyed in the borne country by the rcturnins milwants. Thus, in the context of the present model, the policy <4 taxing emigraUon in an attempt to reduce the gap between the :',.,tndard of living enjoyed by the returning m i ~ a n ~ and by t|g remaining workers will generate prechely the opposite effects. It should he emphasized, however, that the migrants enjoy a higher consumption level at home at the ccr.t of a longer period of low-utility consumption abroad. & Ceulml~ mm~ .The m~n contribution of this paper fie; in its approach (o the problem of international migration, in contrast with most of the earlier studies, the approach is based on the notion that migrants are utility-maximizing individuals with finite working lives. Accordingly, the decision to migrate, the YOur results rely, of coente, on tl~ structure of our model if we consi(~ instead am economy wlmne ~ and unskilled ~ r k e r ~ - .atbor than land and labor - awe used to produge output. • tax on , . - - i , u t i ~ t of Jilled (umkilJed) worken would be,~yi: va~killed (liJied) worken..
350
S. Djaji~ and R. Milbos.Tne, Guest-wov'-kevmigration
len~h of a guest-worker's stay and his rate of asset accumulation in the for~:ign country, are. all viewed as parts of a solution to an intertemporai optimization problem. In addition to analysing the behaviour of guest workers and their optimzd response to a number of exogenous disturbances, we have examined the effects of these disturbances on the equilibrium flow of migrants, the domestic wage, and the level of weJf~:c enjoyed by the remaining worLcrs of the source country. Although none nf the results was found to be particularly striking, they all serve to highlight the present model's unique ability to deal wi:l,, ~,or.,s relz~:,~ to the optimal length of a migrant's stay in the foreign
country and his intertemporal patte~ of consumption within a generai equilit'~:'.;m Cramework. While the model is capable of addressing a range., of important sourcecountry issues, its ability 0o explain a number of observed phenomena is limited by so.,ne of our simplifying assumptions. For example,, by dropping t,~e assumptions that all individuals arc identical and that a migrant's p r c k r e m ~ arc invariant with rcspect to the l e q t h of time spent away from the home country, one would be a b k to offer economic reasons why some migrants make several tripe to the foreign country, why some stay I o n l ~ than others, and why some migruts never rcturn. F u r t h e r m o ~ to relax the assumption of perfect capital markets and to introdnec physical capital into the model as a factor of wodnetion would allow one to p i n insights into the important and controversial Iclatiomhip between intcrmttimml misration and e ~ n o m i c growth of the source country. Explicit consideration of tariffs - ,'l,ich in the context of the present model amount to a tax on remittar~es - and other ec~n~mic policies which ha:'= a dire.: :.~quen~ on t ~ 4..~.~.'n. to migrate Le.g. nummum-wage laws, inmdgration restrictions, ~qcl labormarget subsidies) woutd aiso be us~ul in future research. RefeNmces Baumoi, WJ, 1982,The incomedistribution frontier and taxation of miwuts, Journal of Public Economi~ 18, MY-~I. BImswati, J.N., 1976, The internattomd brain drain and taxation" A survey of issues, in: J.N. Bhagwati,ed., The brain drain and taxation (North-Hohnd, Amsterdam)3-27. Bhagwati, J.N. and K. Hsm~J. 1982, Tax policy in the pt~smt~ of emilgration,Journal of Public Economics18, 291-317. Bhagwali, J.N.,K.-W. Schatz and K.-Y. Worts, 1984, The West German gnstarbeitersystem of migration,European Economic Re~'w 26, 277-294.
Blitz, R.C., 1977, A bmn~fit..costanalysis of foreign workers in West Ocmumy, 1957-1973, Kyklos 30, 479-502. Clumdavagkar,A.G., 1980, Use of migrant remittancesin inbor-ezportingcountries, Finance and l ~ ~ t 17, .~6-39. l~qji6, ,5., 1985, Skills and the I~tte.~ of international migration. Di~-ussion paper no. 612, ~haeen'sUniversity. D~tji~ S., 191Vat,fntenmtiomudmisration, rmuittanccs and welfare in a ¢kpmdent economy, Journalof DevelopmentEconomics21,229-234.
S. Djaji? and ~. Miihourne, Guest-wo~~ r migration
351
Djaji~ S.. 1986b Milpa,zt~ in a 8uest-worker system: A utility-maximizin 8 approach. Discussien paper no. 661, Queen's University, forthcoming, JournAl of Development Economics. I=thzer wJ., 19z[4, International trade theory and intcmationa~ milp'a*.ion, Discussion paper no. ~, Mi~r~,;.,,, ,~nd r~-velo.mnenl Pfowrarn. Harvard Unive~ilv Ethier, WJ., 1985, International trade and labor migration. American Economic Review 75, 691-707. Hill J.K., 1987, Immigrant decisions concernln8 duration of stay and m~rat.on ~requency, Journal of Development Economics 25, 221-234. Kralxss, M.B., 19"/6, The economic~ of "he Ipuu~l-worker problem: 4 Ne~-Heckr~her-Ohlin approac~ ScamliuviM Journal of Ecot~nk~ 78. 470-476. Mmumillmz, M J , Iq~?, The e~nomic effects or international migration: A survey. Joumzd of Common Market Sl,,m,~ 20, 245-267. McCuiloch. it, and J. Ydlea, 1975. Comequmces of • tax oe the Imun-drain for unemployment aid im:ome iaeqmdity in less dcvcio.Ded ommtrkL Journal of Development Econom.cs 2, 24q-2M Mehrh~d=r, U. 19~0, The human-resource probkm ta Z~ur,~., M,ip~-'zt ~bor m the F~der.=l PaepubSc of ~ y . in: U. Ra'aaaa. ed, EOsmc ~ m modem democratic states (Papmou Prin. New YorkL Mirdem, ".A~ 1987.. Milpatioa and optimal im:oaz tssa, Journal of Public Economics IS. 319-341. ~,~, 19"/'9, B6rds of pmmal~. Mqprzml labor in industrial lociezic.s ICambndge t,nlvcrmty Prom, Loudoe~. Rk:han~ A. aud P.L. Martia. 19113,TI~ I.,umtz4aire aplwoac~ to mtenutttmud labor milpratioa: TI~ cu~ olr Arab Middle Eal. Eammmc l ~ t n d Cultural ClhumF 31. 455-474. IU~l-Batiz. F. 1983. 1'1he u ; o o o ~ (dr tl~ "to mad fro' m~plm: Soo~ w,~r-,c-themr~zcal cc,mideratiom..5,cu~llmaviu Jounud of' F.,coaom~ 8~, 403-413 Sammy. G . 19~i. iolmtatiomal mui~'amt woftkas" r e m i t ~ Some ~ theoretical coeuad~. atom, World lbudc Sudr w m t m 8 paper uo. 48j. Wadui~zou. IX:. Wiboa. J.D, 19~2, Optimal ~ lautiou m the p r a a t ~ o( cmisratma. Journal of Pebhc F,couomi~ !8. 363-379.