Migration, Human Capital Formation and the Beneficial Brain Drain. Hypothesis: A Note

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1 Mgraton, Human Catal Formaton and the Benefal Bran Dran Hyothess: A Note Mehd Chowdhury* Bournemouth Unversty, UK Abstrat: The reent bran dran lterature suggests that the mgraton of hghly sklled eole an be benefal for a ountry as t gves nentves to form addtonal human atal. We rtse ths lam by develong a areer onerns model and roosng that the mgraton oortunty as an nentve mehansm s unrelable. In addton, we show that when an ndvdual forms two tyes of human atal, nreased mgraton oortunty for one tye has a negatve effet on the formaton of the other tye. The eonom beneft and full oly mlatons of the fndngs were not addressed n ths aer. Key Words: Bran Dran, Inentves, Human Catal JEL Classfatons: F *Corresondene to: Mehd Chowdhury, Busness Shool, Bournemouth Unversty 89 Holdenhurst Road, Bournemouth, BH8 8EB, UK. E-mal: mhowdhury@bournemouth.a.uk. Tel: 44 (0) The author would lke to thank Bbhas Saha, Arjt Mukherjee and the semnar artants at Bournemouth Unversty, UK and Dhaka Unversty, Bangladesh for omments and suggestons. The author would lke to thank Sue Barnes for arefully readng the draft of the aer. All the remanng errors are the author s.

2 Mgraton, Human Catal Formaton and the Benefal Bran Dran Hyothess: A Note Abstrat: The reent bran dran lterature suggests that the mgraton of hghly sklled eole an be benefal for a ountry as t gves nentves to form addtonal human atal. We rtse ths lam by develong a areer onerns model and roosng that the mgraton oortunty as an nentve mehansm s unrelable. In addton, we show that when an ndvdual forms two tyes of human atal, nreased mgraton oortunty for one tye has a negatve effet on the formaton of the other tye. The eonom beneft and full oly mlatons of the fndngs were not addressed n ths aer. Key Words: Bran Dran, Inentves, Human Catal JEL Classfatons: F. Introduton The reent bran dran lterature suggests that the mgraton of hghly sklled eole an be benefal for a ountry as t gves nentves to form addtonal human atal. The lterature was oneered by works suh as Stark et al. (997), Mountford (997), Bene et al. (00) and Stark and Wang (00). Doquer and Raoort (0) rovdes a detaled survey of the theoretal and emral lterature surroundng ths ssue.

3 We argue that the entral rooston of the reent bran dran lterature s very smlar to the onet of areer onerns as analysed n Holmstörm (999), Prendergast (999) and Bolton and Dewatront (004). Career onerns refers to the dea that the nentves to exert hgher effort n work may ome from the market. For examle, when an ndvdual works for two erods, the wage of the ndvdual n the seond erod deends on the outut of frst erod as the market regards the outut of the frst erod as a sgnal of the ndvdual s ntrns unobservable ablty. Therefore the market rovdes a mehansm where an ndvdual would exert hgh effort n work wthout the resene of an nentve omatble ontrat. In the seond erod however, wthout any future market, the ndvdual exerts less than the otmum effort level. The nentve to form addtonal human atal n the reent bran dran lterature oerates the same way. The nentve there omes from the nternatonal labour market, as a hgh return of human atal from mgraton ndues the ndvdual to form addtonal human atal. We therefore forwarded our argument by roosng a model, n a smlar way as n the areer onerns lterature. In our model the ndvdual forms human atal n two onseutve erods, whereas mgraton oortunty eases to exst n the seond erod. The nentve rovded by mgraton s only avalable n the frst erod. In addton, we suggest that the mgraton oortunty an dstort the formaton of sklls when sklls are heterogeneous. By heterogenety we mean the heterogenety of skll tyes (suh as Mathemats, Language) as oosed to heterogenety of abltes (hgh or low as n Stark and Wang, 00). The mgraton oortunty may rovde nentve to only one tye of skll. Ths has a smlarty wth the dea of an ndvdual erformng multle tasks (Holmstörm and Mlgrom, 99) Though the dea of multle sklls, n relaton to mgraton, was rased n the ast 3

4 (Todaro, 996 ted n Doquer and Raoort, 0), only reently ths has started to reeve attenton of the theoretal bran dran lterature, suh as Corrado and Stryszowsk (009), Stark and Zakhrenko (0). Our aer ontrbutes to ths lterature by roosng a multtask tye model wth dfferent sklls and shows that the mgraton oortunty for one skll negatvely affets the otmal formaton of another tye of skll. The aer therefore, to some extent, s aganst the benefal bran dran hyothess. It should also be noted that the aer s tself not a work on the theory of nentves. We only utlse the strutures develoed by the theory as suh, nternatonal mgraton an be vewed from that ersetve. It s one of the ontrbutons of ths short aer, n addton to our regular analyss of the bran dran ssue. The rest of the aer s as follows. The seond seton rovdes the bas assumtons and analyses a model wth a sngle tye of human atal. In the thrd seton we analyse a model wth two tyes of human atal. The forth or fnal seton onludes the aer.. One Tye of Human Catal We assume that the reresentatve rsk neutral ndvdual exerts effort to form human atal n two erods. There exsts one tye of human atal, we denote t by h. denotes the effort level. The formaton of human atal as a funton of s, ( ) β ln( ) h ln () 4

5 Where s eonomy wde average effort,, β > 0 are oeffents. Assume that the utlty funton s u ( x) x and s the syhologal dsutlty of makng addtonal effort. For smlty assume that human atal h gves return equal to h. The net utlty of the ndvdual n term of effort s, u ( ) ( ) β ln( ) ln () The equatons () and () are smlar to the equatons used n Stark and Wang (00) but our nterretaton s dfferent. In Stark and Wang (00) the term stands for the level of human atal, s the ost of er unt human atal and s the eonomy wde average human atal. We nstead defne as the effort, as the dsutlty of effort and as the eonomy wde average effort. Ths nterretaton rovdes a learer ture of the roess of formaton of human atal. As our equatons are almost the same as Stark and Wang (00) t also shows that a slght modfaton of the orgnal nterretaton an rodue a drastally dfferent result. Stark and Wang (00) foused on the ostve externalty of human atal, atured by, whh otental mgrants do not nternalse. The externalty s not the fous of our analyss hene β s onsdered equal to zero. Now dfferentatng equaton () wth reset to and assumng nteror soluton, u 0 Or, (3) 5

6 Followng the bran dran lterature, assume that there exsts an exogenous mgraton robablty. Assume that the mgrants get, π h where π >, that s mgraton gves hgher return to human atal. The exeted utlty wth mgraton s therefore, ( πh) ( ) u( h) π ln( ) ( ) ln( ) ( π ) ln( ) u (4) The net exeted utlty wth mgraton s, u m ( ) ( π ) ln( ) (5) Dfferentatng equaton (5) wth reset to and assumng nteror soluton, ( π ) As π >, the otmal effort to form human atal and the otmal level of human atal are hgher. We an now nororate externalty n the model and show that the oortunty of mgraton an at as a soluton to the externalty roblem as shown n Stark and Wang (00). We omt the analyss as t s now merely a routne alulaton. In our ontext what s mortant s the otmal effort of the ndvdual n the seond stage of the lfesan. The otmal effort of an ndvdual nreases n the frst erod. However f we assume that the mgraton oortunty s not avalable n 6

7 the seond erod then wthout the resene of mgraton oortunty the effort of the ndvdual dros n that erod. The smle model we roose s aable of rovdng gudelnes n atual ssues ertanng to the formaton of human atal. For examle, the researh oututs of many unverstes of develong ountres are very oor though they do not lak the requred exertse (e.g. PhDs from world s best unverstes). It s sometmes sad the faulty members of these unverstes are not motvated enough to undertake further researh after omleton of ther PhDs. What s often not onsdered s the role of nentves on ndvduals researh atvtes. The faulty members obtan PhD degrees to mrove ther CVs, to seure better ostons and/or to mgrate to better unverstes n the West. Wth full, artal or no realsaton of these objetves, the need to aqure further human atal falls. Hene emhass should to be laed on the ontnuty of nentves, nstead of relane on a market that s beyond any ontrol. 3. Two Tyes of Human Catal In the revous seton we develoed a model where an ndvdual exerts effort to form only one tye of human atal. In realty the ndvduals often exert effort to form dfferent tyes of human atal (e.g. Mathemats and Mus). The multdmensonalty of effort to erform multle tasks has been wdely analysed n the lterature followng the semnal work of Holmström and Mlgrom (99). The We do not rovde the alulatons for the seond erod as t s also qute straght forward. It should be also noted that the human atal aqured n the frst erod may ease the roess of aqurng human atal n the seond erod, resultng n a redued effort for the same level of human atal. We assume no suh reduton of effort n the seond erod whh s obvously an overly smlfed assumton. Together total human atal of two erods s hgher, but here we emhass on the lak of mgraton motvated effort n the seond erod. 7

8 mgraton lterature however has not looked at the mult-dmensonalty of effort to form multle human atal. The frst seton of the aer onneted human atal wth ndvduals effort level. Ths seton onnets dfferent tyes of efforts wth dfferent tyes of human atal. In artular, we develoed a model wth two tyes of efforts and two tyes of human atal. In relaton to the bran dran lterature, we are nterested n the analyss of the effets of nreased mgraton robablty of one artular human atal on the formaton the other human atal. To do so we utlse a smlfed verson of multtask model smlar to the one used n Bolton and Dewatront (004, age 0). Denote human atal by h where,. The ndvdual exerts effort to form human atal h. Assume for smlty that skll h gves a return equal to h n mgrant s home. There exsts a mgraton robablty of for skll h. If suessful then mgraton gves return π for skll. Assume also that the relatonsh between h effort and human atal s gven by smlar equatons as was n (). Wth the resene of mgraton robabltes, the exeted return of the ndvdual s, π h π ln π h ( )( h h ) ( ) π ln( ) ( )( ln( ) ln( ) ).. (6) Assume that π h > h so that mgraton gves a hgher return just from a, sngle skll. We ensure t by assumng that π s suffently large. Let ψ (, ) ( ) δ be the ost or dsutlty of effort. If δ 0, the efforts are ndeendent. Assume δ > 0. The net utlty n term of effort s, 8

9 9 ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ln ln ln ln, δ π π u.. (7) Dfferentatng wth reset to and assumng nteror soluton we get, ( ) 0 δ π u (8) We also have ( ) ( ) ( ) u π and δ u. Assume δ > so that the margnal ost of an effort tye resonses more to the hange of that effort tye than that of the other effort tye. It ensures j u u > as suh the own seond order artal dervatve s hgher n absolute value than the ross seond order artal dervatve. From (8) we obtan, ( ) 0 δ δ π (9) By dfferentatng (7) wth reset to, ( ) 0 δ δ π (0)

10 Dfferentatng totally and assumng π, from equatons (9) and (0),, and unhanged, we obtan π d d d d δ d δ d δd 0 () and, d d d δ d δ d δd 0 () From equatons () and () we obtan, d π π π δ δ δ δ d D where D 4 δ δ δ δ δ δ δ > 0 as requred for the stablty. Also we have, π π π δ δ δ δ ostve by d assumton. Therefore, > 0. Hene, when efforts are substtutes, the effort for a d tye of human atal nreases as mgraton oortunty of that tye nreases. Smlarly we obtan, Substtutablty s however not essental to obtan a smlar result (see Aendx). 0

11 d d < δ δ π δ δπ δ D 0 Therefore the effort and onsequently the human atal of one tye falls as the mgraton oortunty of the other tye rses. The result we obtaned was not surrsng. It was also not dffult to alulate. However, the strength of the analyss les n ts ablty to learly llustrate the effets of the hgher mgraton robablty of one tye of human atal on the otmal formaton of dfferent tyes of human atal. As the mgraton robablty of one tye nreases, the formaton of that human atal nreases and the formaton of the other human atal dereases. The results hene rovde an nsght on the asymmetr nature of the effets of mgraton on human atal formaton. Assume further that the eonomy faes an external shok that nreases the mgraton oortunty n the frst erod. Wth the hgher mgraton oortunty, the ndvdual nreases the effort n formng h and redues the effort n formng the other atal h. However, the ndvduals efforts return to the re-shok levels n the seond erod. Therefore, f the mgraton oortunty dstorts the formaton of human atal n the frst erod, an absene of that n the seond erod hels to onfront the dstorton. The effet of a shok, however, an be ermanent. As dsussed n footnote, f the seond erod s human atal to some extent deends on the frst erod s human atal, the addtonal human atal of one tye n one erod may result n an nreased formaton of that tye and a dereased formaton of the other tye n the seond erod. Hene an nreased mgraton oortunty may have a lastng effet on the overall formaton of human atal of an eonomy.

12 We mght onlude that the mgraton motvated addtonal human atal s a bran waste. From our analyss of the aer, however, we annot yet make suh a onluson. The human atal s a bran waste when t s not useful for the ountry of emgraton. To analyse t, we requre a better understandng of a ountry s objetves and the onneton between the human atal and a ountry s objetves. We have not defned any suh objetve and/or a model that s aable of analysng the welfare mlatons of mgraton. Instead we restrted the analyss n showng a weakness of reent bran dran lterature that does not ay attenton to the dstortve nfluene of mgraton n the omoston of dfferent tyes of human atal wthn a ountry. 4. Conluson In ths aer we suggested that nternatonal mgraton, when beyond the ontrol of a ountry, s rather an unrelable nentve mehansm to suort the formaton of human atal. The ndvduals n dfferent erods of lfesan fae dfferent mgraton oortuntes. Mgraton oortuntes may gve nentves to form addtonal human atal n one erod and none n other erods. In addton when sklls are heterogeneous, the mgraton oortunty may dstort the omoston of human atal formaton. We have not analysed how ths dstorton nfluenes the overall eonomy but ths aer suggests for a reonsderaton of the dea of the benefal bran dran. The analyss of the aer s also dretng towards some nterestng future researhes on multle human atal. A natural extenson of the analyss n ths aer would be to desgn an nentve mehansm that s aable of the offsettng the

13 negatve effets, f any, of mgraton oortuntes. Another ossble way s to onsder how t shaes the nternatonal trade of a ountry by enouragng the roduton of mort substtutng sklls. We may also want to study the effets of a temorary mgraton oortunty on the long run formaton of human atal. In future, attemts to be made for extenson of the analyss n these dretons. 3

14 Referenes: Bene, M., Doquer, F. and Raoort, H. (00). Bran Dran and Eonom Growth: Theory and Evdene, Journal of Develoment Eonoms, Vol. 64, No., Bolton, P. and Dewatront, M. (004). Contrat Theory. MIT Press. Corrado, D. M. and Stryszowsk, P. (009). Mgraton, Human Catal Aumulaton and Develoment, Journal of Develoment Eonoms, Vol. 90, No., Doquer, F. and Raoort, H. (0). Globalzaton, Bran Dran and Develoment, Journal of Eonom Lterature, Vol. 50, No. 3, Mountford, A. (997). Can a Bran Dran be Good for Growth n the Soure Eonomy?, Journal of Develoment Eonoms, Vol. 53, No., Holmström, B. (999). Manageral Inentve Problems: A Dynam Persetve, Revew of Eonom Studes, Vol. 66, No., Holmström, B. and Mlgrom, P. (99). Multtask Prnal-Agent Analyss: Inentve Contrats, Assets Ownersh, and Job Desgn, Journal of Law, Eonoms and Organzaton, Vol. 7, Prendergast, C. (997). The Provson of Inentves n Frms, Journal of Eonom Lterature, Vol. 37, No., Stark, O., Helmensten, C. and Prskawetz, A. (997). A Bran Gan wth Bran Dran, Eonoms Letters, Vol. 55, Issue, Stark, O. and Wang, Y. (00). Indung Human Catal Formaton: Mgraton as a Substtute for Subsdes, Journal of Publ Eonoms, Vol. 86, No.,

15 Stark, O. and Zakharenko, R. (0). Dfferental Mgraton Prosets, Skll Formaton and Welfare, Revew of Internatonal Eonoms, Vol. 0, No. 4, Todaro, M. (996). Eonom Develoment, 5th ed., Longman Publshng. 5

16 Aendx In ths aendx we assume that δ 0, The equatons (9) and (0) resetvely beome, ( ) 0 (A) π π d d d d 0 (A) Therefore, ( π ) d d > 0 The equatons () and () resetvely beome, ( ) δ 0 (A3) π δ d d d 0 (A4) Imlyng that, d d < 0 Therefore substtutablty s not essental to demonstrate that the nreased mgraton oortunty of one skll has a negatve effet on the formaton of the other skll. 6