Heriot-Watt University. Economic Growth and Migration Ditzen, Jan; Bhattacharjee, Arnab. Heriot-Watt University. Research Gateway

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1 Herio-Wa Universiy Herio-Wa Universiy Research Gaeway Economic Growh and Migraion Dizen, Jan; Bhaacharjee, Arnab Publicaion dae: 2014 Documen Version Early version, also known as pre-prin Link o publicaion in Herio-Wa Universiy Research Poral Ciaion for published version (APA): Dizen, J., & Bhaacharjee, A. (2014). Economic Growh and Migraion. Paper presened a Money, Macro and Finance Research Group 46h Annual Conference, Durham, Unied Kingdom. General righs Copyrigh and moral righs for he publicaions made accessible in he public poral are reained by he auhors and/or oher copyrigh owners and i is a condiion of accessing publicaions ha users recognise and abide by he legal requiremens associaed wih hese righs. If you believe ha his documen breaches copyrigh please conac us providing deails, and we will remove access o he work immediaely and invesigae your claim.

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3 Submied o Mancheser School Economic Growh and Migraion Jan Dizen Arnab Bhaacharjee Spaial Economics and Economerics Cenre (SEEC) Herio-Wa Universiy, Edinburgh, UK The lieraure on growh heory lacks a precise sense of why here are ineracions and dependencies beween counries. Correspondingly, he spaial economerics lieraure on growh empirics accouns for endogenous cross-counry ineracions, bu lacks crucial insighs from economic heory as o how such linkages should be precisely modeled. We address his weakness, by proposing a new economic model as a combinaion of an endogenous Romer-syle growh model and a New Economic Geography model. The model admis wo disinc sources of ineracions beween counries: mobiliy of high skilled workers and iner-counry rade. Boh of hese sources develop from he New Economic Geography models, while he engine of he growh process is adaped from he endogenous growh lieraure. Moivaed by higher wages, highly skilled workers migrae o he richer counry, and here hey work in he R&D secor. This in urn conribues owards economic growh in he richer counry, and leads o divergence beween he wo counries. Trade in he manufacured good reduces he difference beween he wo counries bu does no negae divergence. In is focus on boh migraion of highly skilled labour and is conclusion of divergence, he model capures he phenomenon of he Grea Divergence in he 19h cenury. I is also consisen wih evidence of club convergence in he 20h cenury. The implicaions of he model are verified by simulaion. Keywords: Economic growh; New Economic Geography; Cross-counry ineracions; Convergence; Migraion; Trade. JEL classificaion: O41, F22, F43, O31, N10. Acknowledgemen: We are graeful o many colleagues who have commened on his work, mos noably Paranap Basu, Michael Ben-Gad, Aanas Chrisev, Leandro M. Magnusson, Sephen Millard, Charles Nolan, Rober Tamura and especially Mark Schaffer. The paper was presened a he Annual Conference 2014 of he Money, Macro and Finance Research Group. We hank o he paricipans a he conference for heir valuable commens and suggesions. The usual disclaimer applies. Correspondence: Jan Dizen, Spaial Economics and Economerics Cenre (SEEC), School of Managemen & Languages, Herio-Wa Universiy, Edinburgh EH14 4AS, Scoland, Unied Kingdom, EH14 4AS; jd219@hw.ac.uk 1

4 Submied o Mancheser School Economic Growh and Migraion 1 Inroducion Corrado and Fingleon (2012) argue ha he frequen criicism of he curren growh empirics lieraure in spaial economerics, ha i lacks a link o economic heory, is misplaced. Specifically, in his lieraure spaial exernaliies arise from echnological inerdependence among counries, where knowledge accumulaed in one counry depends on knowledge accumulaed in oher counries. However, he specific paerns of spaial ineracions and dependencies in empirical growh specificaions are no heoreically founded: hey are assumed o depend on geographic disances or rade. This is because a heory of why ineracions beween wo counries maer for economic growh is largely missing. This paper aims o close his gap by combining a Romer (1990) syle endogenous growh model and a New Economic Geography model in he syle of Krugman (1991). The ineracion beween counries is modeled in wo ways. The firs is he migraion of high skilled workers and he second connecion is rade of a manufacured good. The engine of growh draws upon he endogenous growh model and herefore he model predics divergence. Boh he migraion largely of high-skilled workers and he predicion of divergence is in line wih he Grea Divergence in he 19h cenury. Equally, he model can relae o club divergence in curren imes. Our wo counry model is based on hree secors in each counry. The firs, he R&D secor, uses high skilled workers and he exising sock of designs o produce new designs. Designs can be seen as paens or ideas o found new firms in he second secor, he manufacuring secor. Before hese firms can sar producion, hey need o buy exacly one design from he R&D secor. Low skilled labour and a fracion of high skilled workers is employed o produce a firm-specific differeniaed manufacured good. The final secor, a radiional secor, uses solely unskilled labour o produce a homogeneous radiional good. This radiional good secor can be inerpreed as a food producing agriculural secor. The engine of growh is he R&D secor which accumulaes designs. Designs are convered ino new oupu enhancing firms. Therefore he number of designs represens he number of firms operaing in he manufacuring secor. Differen o Romer (1990), is he growh engine in his model is he varieies of goods produced by he manufacuring secor raher han he variey of inermediae goods (for example, machinery) which are ransformed ino one final homogeneous good. In line wih he Romer model, a higher permanen growh rae can only be achieved by an increase in high skilled workers employed in he R&D secor. One counry offers higher wages in he R&D secor, and his provides he incenive for high skilled workers o migrae. Low skilled workers are immobile beween counries bu mobile beween he wo secors, manufacuring and radiional. Some high skilled workers migrae o he higher wage offering counry and conribue o he R&D secor here, allowing ha counry o grow faser. Corner soluions as well as inerior soluions are possible. If he wage differenial is very small, only a fracion of high skilled workers migrae. Wih an increase in he difference beween wages, he inerior soluion moves owards he corner soluion, in which all high skilled workers migrae a once. In a sharp disincion from he lieraure, our model has wo channels for ineracion beween counries: high skilled worker mobiliy and rade. Similar 2

5 Submied o Mancheser School Economic Growh and Migraion o he Romer (1990) model, our model predics unbounded growh, an oucome which has imporan implicaions. The counry which receives high skilled workers experiences unbounded growh, while in he case wihou rade he oher counry becomes sagnan, implying divergence. The divergence is moderaed by rade. Simulaions reveal ha convergence in growh levels is possible, bu here always remains a difference in income levels. Therefore he model explains he grea divergence during he 19h cenury which was arguably driven by migraion of high skilled workers. The model is also consisen wih economic developmens in he 20h cenury. A a broad level, i explains convergence clubs, even if he convergence or cach-up processes beween counries wihin each club is no explicily considered. The difference in echnological developmen beween he beginning and he end of he 19h cenury is very vas. 1 In he 19h cenury he Wes (Wesern Europe, US, Canada, Ausralia and New Zealand) sared growing rapidly and lef large pars of he world behind. Maddison (2007, p ) shows ha he Wes experienced a growh rae of 1.07% beween 1820 and 1870 and a rae of 1.56% beween 1870 and GDP per capia increased from $1,202 o $3,988 beween 1820 and The res of he world remained nearly sagnan wih growh raes of 0.1% and 0.86% beween 1820 and 1870 and 1870 and 1913, respecively. Over he cenury (93 years) GDP per capia increased only from $667 o $1, Especially in hese hisorical periods wih lile possibiliies o disribue wrien knowledge, he only way o diffuse knowledge was movemen of human capial, and hence high skilled migraion was imporan. 3 During he 19h cenury he firs migraion wave sared. By he middle of he cenury, approximaely 300,000 migrans dared o underake he journey from Europe o he he Unied Saes each year. The numbers rose unil he end of he cenury o more han 500,000, and furher o more han a million by he beginning of he 20h cenury (Williamson, 2006). Even wihin Europe here were large migraion flows. Abou half of he Ialian emigrans sayed in Europe, especially France and Germany, while 9 percen of he populaion in large Briish ciies were Irish-born (Williamson, 2006). The remainder of his paper is srucured as follows. We review he lieraure in secion 2, followed by he discussion of he model (secion 3). Secion 4 repors on a simulaion of he model and finally secion 5 concludes. 2 Lieraure The lieraure on heories of economic growh and empirical sudies of crosscounry and regional growh are boh vas and very diverse (Temple, 1999, 2003; Islam, 2003). While i is beyond he scope of he curren paper o review his vas lieraure, we discuss seleced conribuions o he lieraure boh as moivaion for, and aid owards, developing our model in secion 3. 1 Jewkes e al. (1961) provides a comprehensive overview of imporan invenions in he 19h cenury, such as he high pressure seam engine and combusion engine, innovaions in he exile indusry, elegraph and elephone, elecric lamps, rubber and seel. 2 See Maddison (2007), p GDP per capia is measured in 1990 inernaional dollars. 3 High skilled workers were no necessarily well educaed. In he conex of he 19h cenury, skill can be seen more as an abiliy o perform sophisicaed jobs and o creae ideas. 3

6 Submied o Mancheser School Economic Growh and Migraion 2.1 Growh Theory and Empirics In discussing he deerminans of long run growh, he lieraure has placed main emphasis on he facors of producion and heir exogenous accumulaion (Solow, 1956; Mankiw e al., 1992; Islam, 1995). Togeher, he endogenous accumulaion of facors of producion has also been explored (Romer, 1990; Grossman and Helpman, 1994). Anoher quesion which was raised wihin his framework was: why is produciviy so differen across counries? Hall and Jones (1999) relae oal facor produciviy o social infrasrucure, a descripion of insiuions and governmen policies; see also Hall and Jones (1999, p. 84). Beer social infrasrucure improves capial accumulaion, educaional aainmen and produciviy and herefore booss oupu per capia. Hall and Jones (1999) consruc an index of social infrasrucure and use as insrumens he disance from he equaor, he prediced rade share of an economy and he fracion of populaion wih a Wesern European language as firs language. 4 Their finding is ha he differences in he social infrasrucure, especially wih he disance from he equaor as he favoured insrumen, accoun for a large proporion of he differences in income across counries. Acemoglu e al. (2001) use a differen measure of insiuions, proecion agains expropriaion, and insrumen his wih seler moraliy. Their esimaion leads o large effecs of insiuions on income per capia. In eiher case, an insrumenal variable approach is necessary because here is poenial for reverse causaliy in he relaionship beween insiuions and economic growh; see Glaeser e al. (2004) and Acemoglu e al. (2005, 2012) and Albouy (2012) for furher discussion. Beer insiuions may foser invesmens ino human and physical capial wha improves growh in income. On he oher hand, higher human capial and income growh poenially aid he developmen of insiuions. The naure of insiuions is closely relaed o geography. This jusifies he approach in Acemoglu e al. (2001) of using a geography relaed insrumen o accoun for he endogeneiy of insiuions. Spolaore and Wacziarg (2013) argue ha he main channels of he geography effec are eiher direcly on he facors of producion or indirecly hrough hisory. Direc effecs include climae and emperaure (Sachs, 2001), while examples for he indirec effecs are diseases (Acemoglu and Johnson, 2007), geneic disance (Spolaore and Wacziarg, 2009), and/or ancesral origin of he curren populaion of a counry (Puerman and Weil, 2010). Also, rade is loosely conneced o geography. Is impac on growh is undoubed, as shown in Frankel and Romer (1999) and in more recen work by Wacziarg and Welch (2007). Basu and Bhaarai (2012) relae rade o invesmens in human capial. They find ha counries wih a well educaed populaion are more open o rade and experience higher growh raes. Finally, in he conex of his paper, here is anoher imporan quesion relaed o geography. Counries poenially inerac wih heir neighbours, so he locaion of a counry is crucial. As an example, for Mexico i is no only imporan o be locaed in Norh America wih is disinc geographical facors, bu being a neighbour o he US is essenial as well. This issue has been addressed in he spaial economerics lieraure by assuming ha neighbouring counries have greaer knowledge spillovers; see, for example, Fingleon and López-Bazo (2006) and Erur and Koch (2007). We urn o his lieraure nex. 4 English, French, German, Poruguese or Spanish; see Hall and Jones (1999, p. 100). 4

7 Submied o Mancheser School Economic Growh and Migraion 2.2 Growh Empirics and Spaial Economerics Wihin a growh model, channels for he effec of space on growh are mobiliy of he facors of producion or echnology. Koch (2008) akes space explicily ino accoun wihin a growh empirical seing, emphasizing in paricular he imporance of inerdependence of he oal facor produciviy across counries. In his esimaion of a spaial error model, facor produciviy as capured by he error erm no only depends on he counry iself bu on oher counries produciviy as well. The paper finds ha if spaial effecs are ignored, radiional resuls are biased. Similarly, Erur and Koch (2007, 2011) show ha spaial dependencies in TFP maers for a muli-counry Schumpeerian growh as well as a Solow Growh model. Boh models were augmened wih echnological inerdependencies beween counries. Lesage and Fischer (2008) esimae a growh equaion wih a spaial Durbin model on daa for 255 regions in 25 EU counries. Their findings are ha characerisics of neighbouring regions, how he region is conneced o is neighbours and he srengh of his connecion are more imporan han direc effecs of he region iself. Fingleon and López-Bazo (2006) sress he imporance of echnological diffusion and pecuniary exernaliies for he long run growh of regions. In a recen paper, Ho e al. (2013) esimae a spaial lag model using a spaial weigh marix based on rade daa. They find posiive spillover effecs of growh beween counries, when such spillover is measured by bilaeral rade. This relaionship drives he rae of convergence o a higher level han in radiional models. In summary, all papers in his lieraure have he common conclusion, ha ignoring spaial effecs such as endogenous spaial lags leads o biased and inconsisen esimaes of empirical growh models. Therefore, he radiional resuls obained in he lieraure so far are no valid and canno as such be used o refue or accep any specific heory of growh. Addiionally, spaial dependencies are included in he models. Spillovers are assumed o exis, bu a heoreical jusificaion as o why hey should depend on geographic disance or rade is absen. Specifically, here is no clear sense from his lieraure as o why spillovers should be relaed o geographic disances, or indeed o oher poenial channels of cross-counry linkage such as labour mobiliy (migraion) or rade. This is he domain of he curren paper. 2.3 New Economic Geography New Economic Geography (NEG) models, iniiaed by Krugman (1991), provide a naural way o inegrae space ino heories of economic growh. The woregion wo-secor model, sandard in his lieraure, explains he concenraion of skill inensive manufacuring firms in a region wih respec o he consumpion maximizaion behaviour of mobile, highly skilled workers. While he NEG models provide useful explanaion for agglomeraion, hey do no have an explici source or engine of growh, and are herefore no adequae for modelling he growh process in iself. An exension of he NEG models are New Economic Geography and Growh (NEGG) models, such as Baldwin and Forslid (2000), Baldwin and Marin (2004) and Cerina and Pigliaru (2007). A capial accumulaing secor is added o he economy and works as he engine of growh. However, from a growh 5

8 Submied o Mancheser School Economic Growh and Migraion heory perspecive here are some drawbacks. Firs, he concep of capial is no clearly defined in he NEGG models. Baldwin and Marin (2004) describe immobile capial as human capial while mobile capial would be physical capial or paens. From a growh heory perspecive, his ambiguiy is problemaic because here is considerable disincion beween physical and human capial which is crucial for inerpreaion and policy. 5 Second, here is in hese models no disincion beween highly skilled workers and low skilled workers. This rules ou he role of migraion of high-skilled workers as a driver of cross-counry ineracions. Finally, he effec of geographical agglomeraion on income growh lies a he core of hese models, while economic growh is only a by-produc of agglomeraion. We will address hese issues in developing our growh model in he secion Migraion Migraion and is impac on he hos counry as well as on he counry of origin are widely discussed opics in economics, mainly in labour and developmen economics. 6 By conras wih he exising lieraure, our work here focuses on he connecion beween high skilled migraion and economic growh. I is relaively obvious why high skilled migrans should have an effec on he income of he hos counry. Prominen anecdoal evidences are pleny. Consider, for example, Alexander Graham Bell who was born in Edinburgh (Scoland, U.K.) and migraed o he Unied Saes, where he founded he Bell Telephone Company. Marie Curie immigraed in 1891 from Poland o France, where she conduced her research on radioaciviy. Furher noable examples are Alber Einsein, Ludwig von Mises and Oskar Morgensern, who all lef heir counry of birh and developed heir ideas o he benefi of heir adoped counries. Likewise, many German rocke engineers migraed, parly forced, afer he 2nd World War o he US and he USSR, where hey played a key role in he consrucion of he firs space rockes. The above anecdoal evidence is suppored by empirical work. Hornung (2014) analyzes he effec of well educaed 18h cenury Hugueno immigrans ino Prussia on produciviy 100 years laer and finds a posiive long run effec. Afer he collapse of he Sovie Union, over 1,000 Sovie mahemaicians migraed o oher counries, wih a large fracion seling in he Unied Saes. Borjas and Doran (2012) find ha inernaional differences in produciviy can be explained by hese migraion flows. Likewise, Moser e al. (2014) sudy Jewish migraion ino US afer he akeover of he NSDAP (Naionalsozialisische Deusche Arbeierparei - Naional Socialis German Workers Pary) in Germany. Their baseline esimaes indicae ha he arrival of German Jewish immigrans led o a 31 percen increase in innovaion in he research fields of hese emigres. Wadhwa e al. (2007) esimae ha he conribuion of non-us ciizens o inernaional paens increased from 7.3% in 1998 o 24.2% in The discussion of he role human capial plays in economic growh is widely discussed in he lieraure. See, for example, Lucas (1988), Mankiw e al. (1992), Benhabib and Spiegel (1994), Barro and Sala-i Marin (2004) and reviews by Temple (1999) or Barro (2001). 6 See, for example, reviews by Borjas (1994) or Oaviano and Peri (2012) for he effecs on labour markes. In developmen economics an imporan opic is he drain brain from underdeveloped counries (Docquier and Rapopor, 2012; Dequied and Zenou, 2013). The lieraure has also considered he effec of migraion on he income disribuion wihin a counry; see, for example, Ben-Gad (2004). 6

9 Submied o Mancheser School Economic Growh and Migraion According o Kerr (2013), immigrans represen 16% of he US workforce wih a bachelors degree and hey accouned for a majoriy of he increase in he Science, Technology, Engineering, and Mahemaics workforce in he US since Thus, OECD (2011, p. 52) saes: In absolue numbers, highly skilled foreign-born individuals conribue heavily o he human capial endowmens of regions in he Unied Saes, Canada and Ausralia. The above-menioned examples underline he imporance of highly skilled migrans o heir hos counries. Mobiliy of high skilled workers as a channel for ineracions beween counries is negleced in heoreical models of economic growh. A he same ime he growh empirics lieraure assumes spillovers, mainly diffusion of knowledge, wihou providing adequae heory for how and why knowledge spreads. Ineracions beween counries are modeled in he New Economic Geography lieraure. However, hese models eiher lack an engine of growh or are limied by a lack of richness in modelling physical and human capial. 3 A Growh Model wih Mobile Labour In his secion, we develop our model of economic growh, as a combinaion of he endogenous growh model by Romer (1990) and models from he New Economic Geography lieraure, especially Krugman (1991), Baldwin and Marin (2004) and Forslid and Oaviano (2003). This is a wo-counry model. The economy in an index counry i consiss of hree secors: a R&D, a manufacuring and a radiional goods secor. The R&D secor produces designs which are used by he manufacuring secor o found firms. Each firm in he manufacuring secor produces a unique heerogeneous good. Boh he manufacuring secor and he radiional goods secor use unskilled labour, which is immobile, while he R&D secor employs highly skilled mobile labour. Besides relying on he work of Romer (1990), he model lends emphasis o he imporance of human capial for economic growh, a poin sressed by Lucas (2009a,b). Our poin of difference wih he laer work is ha his model does no include any diffusion of knowledge. Insead of diffusion, he spread of knowledge in his model is hrough migraion, and hus by movemens of highly skilled persons. The paper can be undersood as emphasizing he imporance of labour movemens in he Lucas fashion and swiching off diffusion of knowledge. Exensions o include knowledge diffusion lies in he domain o fuure work. 3.1 R&D Secor The R&D secor in each counry i is oriened on Romer (1990), and produces designs under perfec compeiion. Inpu facors are he exising sock of designs A i and he number of highly skilled workers Hi R. Ȧ i is he number of new designs in counry i and produced according o Ȧ i = δh R i A i. (1) The producion funcion has wo implicaions. Firs, a higher number of employees in he R&D secor implies a higher oupu of designs. Secondly, he designs 7

10 Submied o Mancheser School Economic Growh and Migraion are accumulaed and increase he produciviy in fuure periods. Therefore here are wo effecs of an exogenous increase in he number of highly skilled workers, a growh effec and a level effec. The firms in he R&D secor sell he designs a a price p A i in a perfecly compeiive marke o he manufacuring firms. R&D firms pay he highly skilled workers heir marginal produc, wi R = δa i p A i. Thus he profi equaion of a R&D firm is: πi A = p A i Ȧ i wi R Hi R. I is assumed ha designs produced in one counry remain wihin his counry. This implies ha here is no echnology or knowledge diffusion. However, in he open economy case, he oher counry benefis from he availabiliy of a higher variey of manufacured goods. 3.2 Manufacuring Secor A firm in he manufacuring secor produces variey s wih a consan marginal produc of unskilled labour. 7 Before a firm can sar producing, i has o buy exacly one design from he R&D secor a price p A i.8 This implies ha in counry i, here are exacly A i firms. Moreover each manufacuring firm requires a share Hi x α = H i A i of high skilled workers. These employees can be inerpreed as adminisraive saff or managers required o run a firm. Each firm produces one unique inermediae good x i (s) wih he following producion funcion: x i (s) = φa i L x i. (2) x i (s) is decomposed ino wo pars. One par is sold in counry i and he res expored o counry j wih iceberg coss τ. Thus he oal amoun of he manufacured good produced in counry i is x ii (s) + τx ij (s). 9 τ measures he number of unis of he manufacured good ha have o be produced in order o saisfy he foreign demand of one uni, implying τ 1. In he case of zero ransporaion coss τ equals 1. As rade coss increase o infiniy, rade becomes so expensive such ha any rade beween he counries is precluded. Denoing he wage for unskilled labour as wi x, he profi equaion for a firm in counry i is: π x i = p ii (s)x ii (s) + p ji (s)x ji (s) w x i L x i w H i H x i p A i. (3) The cos funcion has wo pars: variable coss of unskilled labour, wi xlx i, and fixed coss he price of he design, p A i, and labour coss for he high skilled 7 For simpliciy, he marginal produc of labour is assumed o be consan. The main advanage of his simplifying assumpion is ha he price does no depend on he quaniy of x i and he level of echnology. Therefore, compuaion of he price index P i becomes more sraigh forward. The assumpion is in line wih Forslid and Oaviano (2003). 8 This assumpion comes from he Romer model. In he NEG models, a fixed inpu requiremen is included bu his is no seen as a requiremen for firm enry. Buying a second design would no improve he oupu of a firm. Therefore he manufacuring secor has increasing reurns o scale. 9 The firs subscrip refers o he counry of consumpion, he second o he counry where he produc is produced. Thus x ji is produced in counry i and expored o or consumed in counry j. Noe ha, by assumpion he prices of x ii and x jj are he same in boh counries, oherwise i would be possible ha highly skilled migrans migrae due o a higher real income ha is only due o lower prices. Such migraion moives may no be very realisic. 8

11 Submied o Mancheser School Economic Growh and Migraion workers, wi HHx i.10 Since each firm produces a differeniaed good, he marke is characerized by monopolisic compeiion. Unskilled workers are paid he marginal produc of labour in he radiional secor; wi x = φa i. Finally, o ensure ha high skilled workers have no incenive o move from one secor o anoher, wages in he manufacuring and he R&D secor have o be equal, wi H = wi R = δa i p A i. 3.3 Tradiional Goods Secor The Tradiional Goods secor uses unskilled labour L T i as an inpu and produces a homogeneous radiional good. For simpliciy i is assumed ha one inpu produces exacly one uni of oupu. 11 Firms in he secor produce he good under perfec compeiion according o he following producion funcion: T i = L T i. The firms sell heir produc a a price p T i following profi equaion: and pay wages wi T. This forms he π T i = p T i T i w T i L T i. (4) Since he compeiive firms make no profis, he paid wage equals he price for he radiional good, wi T = p T i. In equilibrium, unskilled labour is paid he same wage in boh secors o preven workers moving from he radiional o he manufacuring secor or vice versa. This assumpion quanifies he wage in he manufacuring secor o be: wi x = wi T = p T i. Following sandard NEG models he radiional good can be raded a no cos. 3.4 Consumers The represenaive consumer in counry i maximizes a Cobb-Douglas uiliy funcion wih boh goods: U i = X µ i T γ i (5) wih he composie X i [ Ai Aj X i = x ii (s) 1 1 σ ds + = σ > 1. 0 [ Ai+A j 0 x C i (s) 1 1 σ ds ] 1 1 1/σ 0 x ij (s) 1 1 σ ds ] 1 1 1/σ The choice of he varieies depends on a CES funcion, wih σ denoing he elasiciy of subsiuion beween he differen varieies. Each consumer faces he 10 The wages of he high skilled workers is fixed in he R&D secor, and manufacuring firms ake his as given. 11 This assumpion is also made in Krugman (1991) and Forslid and Oaviano (2003). 9

12 Submied o Mancheser School Economic Growh and Migraion following budge consrain, which can be expressed by wo differen equaions: Y i = w T i L T i + w x i L x i + w R i H R i + w H i H x i (6) = p T i T i + Ai 0 p ii (s)x ii (s)ds + Aj 0 p ij (s)x ij (s)ds (7) = p T i + P i X i. (8) Eq. (6) is he income of he households from working and has o equal he spending of he household (Eq. (7) and (8)). Wages in he R&D secor are denoed by a superscrip R, while wages in he wo oher secors are denoed by x for he manufacuring and T for he radiional goods secor. H i is he supply of high skilled workers, including boh domesic and migran foreign workers. L i = A i L x i + LT i is he oal supply of unskilled labour which is he sum of he wo remaining secors. Furher, households consume a subsisence level of he radiional good, T i Ti min, which can be inerpreed as he necessary consumpion of food. As menioned before, high skilled workers are mobile; hey can move from counry j o counry i. They migrae if heir income in he counry of desinaion is higher compared o heir home counry. There is no moive for migraion if he income in boh counries is equal. Hence he oal amoun of high skilled workers in counry i is: H i = m i (w H i, w H j ) = (1 m ij )L H i + m ji L H j m ij = { 0, if w H i w H j (0, 1], if w H i < w H j m ji = { 0, if w H j w H i (0, 1], if w H j < w H i, where m ij is he fracion of high skilled workers (in counry i) who migrae from counry i o counry j. The same holds for counry j. H j = m j (w H i, w H j ) = (1 m ji )L H j + m ij L H i. There are wo poenial equilibrium oucomes. In he corner soluion, all high skilled workers migrae o he counry wih higher wages, while in he inerior soluion only a fracion of he high skilled workers migrae. The inerior soluion implies ha he wage differenial beween he wo counries is relaively small. Migraion will occur unil eiher wages are equalized or all high skilled workers have migraed, which is again he corner soluion. In he inerior soluion, he disribuion of high skilled workers is more balanced and boh counries grow. 3.5 The Growh Engine In our model, he sole engine of growh is he R&D secor producing new designs. If a new design is invened (or produced), a new firm in he manufacuring secor can be founded. The imporance of he designs o he manufacuring firms is similar o Romer (1990). In he conex here, designs can be seen as paens or echnologies which are used o produce a good. A firm buys he paen and has he righ o produce and sell he produc based exclusively on he paen, acing as a monopolis in he specific differeniaed good. The number of designs 10

13 Submied o Mancheser School Economic Growh and Migraion increases he number of firms, making he R&D secor crucial for he growh process of an economy. The growh of designs A i depends on he number of highly skilled workers and he exising invenions. A higher number of highly skilled workers increases he number of new designs. Also, a large sock of designs increases he number of new designs. The firs implicaion is ha counries which are on he echnology fronier have a higher producion of new designs. Second, even hough he firm in he R&D secor sells he design exclusively o one firm in he manufacuring secor, he research firm is allowed using i for he producion of furher designs. Then, he growh rae of designs is: A i A i = δh R i. (9) Equaion (9) implies ha a permanen increase in he growh rae of designs is possible only wih an increase in he number of highly skilled workers. Therefore he differeniaion beween he growh and he level effec is imporan. If he number of highly skilled workers increases from period 1 o, he growh effec will be he increase in he growh rae of he designs a he end of period, while he level effec will se in from period + 1 in he form of a higher sock of designs A i. The implicaion is ha, wo counries wih he same number of persons employed in he R&D secor may have he same growh rae bu may be a differen number of designs (or echnology) and hus income. This implies ha he iniial income level is deermined by he iniial level of echnology. A counry s growh rae depends solely on he number of high skilled workers bu no on he echnology level. Addiionally he model implies ha here is no cach up effec. Even hough he counry lef behind will benefi from rade, immobiliy of ideas means ha a echnological cach up (or designs cach up) is ruled ou. Finally, as in Romer (1990), our model predics unbounded growh. 3.6 Closing he model Afer he hree secors, he behaviour of he consumers and highly skilled workers are explained, he model is closed. I is assumed ha he size of he skilled and unskilled labour force (L H i and L i ) are predeermined and fixed. Wihin each period, he number of firms (A i ) is exogenous as well. Firs, we derive he price index and quaniies demanded by consumers. A wo sage opimizaion of (5) wih respec o (8), based on Dixi and Sigliz (1977), leads o he following values for x ii (s), x jj (s), x ij (s) and x ji (s): x ii (s) = σ 1 ( Yi pt i T ) i (10) σ R i R i ( x jj (s) = σ 1 Y j pt j T ) j (11) σ R j R j x ij (s) = τ σ σ 1 ( Yi pt i T ) i (12) σ R i R i ( x ji (s) = τ σ σ 1 Y j pt j T ) j (13) σ R j R j 11

14 Submied o Mancheser School Economic Growh and Migraion wih R i = A i + τ 1 σ A j Demand for he good produced by he radiional goods secor equals: ( ) γ Y i T i = max µ + γ p T, Ti min i (14) Nex, we derive prices. The manufacuring firms maximize heir profis using he inverse demand funcions for he manufacured goods. Thus, hey se he following prices for each good: p ii (s) = p ii = p jj = σ σ 1, p ji(s) = p ji = p ij = σ σ 1 τ = p iiτ In eiher case, he second equaliy holds because of symmery in he producion funcions of he wo counries. The goods price is independen of he quaniy of he manufacured good or he echnological level A i, depending only he elasiciy of subsiuion beween he differen varieies. Moreover he price for each variey is he same. Then, he price index for counry i is: [ Ai ] 1 Aj 1 σ P i = p ii (s) 1 σ ds + p ij (s) 1 σ ds 0 0 = σ σ 1 R 1 1 σ i. The price index falls wih an increase in he number of domesic and foreign firms. In erms of workers, a larger R&D secor wih a large oupu implies a falling price index. In he following i is assumed ha only he subsisence level of he radiional good is consumed, as implied by γ = 0 and µ = 1. Similar o Romer (1990), manufacuring firms make no profis because hey bid for he design produced by he R&D secor. Therefore he price for a design is: πi x = p ii x ii + p ji x ji wi x L x i wi H Hi x p A i = 0 p A i = p iix ii + p ji x ji wi xlx i x i = 1 + δαh i (σ 1) (1 + δαh i ) w H i = p A i Ȧ i = δa i x i (σ 1) (1 + δαh i ). As he price for each variey is he same, all firms in he manufacuring secor produce he same quaniy of he firm specific variey, implying x i (s) = x i = x ii + τx ji. Thus, he price for he designs depends negaively on he number of high skilled workers residing in counry i. In addiion o he adverse dependence of high skilled workers, he wage for he same depends posiively on he number of designs. This rules ou he possibiliy ha he ordering of wages for high skilled workers in he wo counries reverses. In oher words, if counry i has a higher wage and receives more high skilled workers in, he wage will be higher for all following periods. 12

15 Submied o Mancheser School Economic Growh and Migraion Under he assumpion ha all labour markes clear: income can be expressed as: Y i = σr ( i σ 1 L i + p T i or as: wih Y i = z i = σr ( i σ 1 L i + p T i H i = A i H x i + H R i L i = A i L x i + L T i σr ) i T i + τ 1 σ R i p T j T j τ 1 σ R i Y j σ 1 R j R j 1 ( zi τ 1 σ ) z 1 + τ 2(1 σ) j σr ) i T i + τ 1 σ R i p T j T j. σ 1 R j Since σ > 1, as ransporaion coss increase o infiniy, ha is τ, here is lierally no rade and τ 1 σ 0. Then, he price level only depends on he number of domesic designs (R i = A i ) and he growh rae can be expressed as: ( ) A σ i σ 1 L i φ(σ 1) σ σ 1 T i Y i Y i = A i ( σ σ 1 L i φ(σ 1) σ σ 1 T i ) = A i A i = δh R i = δh i ( 1 α A i ) = δ ( (1 m ji ) L H j + m ij L H i ) ( 1 α A i ). Under auarky, he resul is he same as Romer (1990). A higher growh rae is only obained if he number of workers employed in he R&D secor increases. 3.7 High Skilled Worker Migraion High skilled workers migrae if he wage differenial beween he counries is posiive. 12 Since ordering of wages is preserved and high skilled workers are homogeneous, migraion flows will be only in one direcion. If migraion is cosless, migraion will happen unil wages are equalized: x i x i δa i 1 + δα [ (1 m ij )L H i + m ji L H j w H i = w H j x j δa i = δa j 1 + δαh i 1 + δαh j ] = δa j x j 1 + δα [ (1 m ji )L H j + m ijl H i Since here are only labour movemens from counry j o i (implying m ji > 0 and m ij = 0), labour movemen becomes: ( 1 m ji = A2 i Lx i δα + ) ( LH j A 2 j L x 1 j δα + ) LH i ( A 2 j L x j + ). (15) A2 i Lx i L H j 12 Since he inerior soluion moves owards he corner soluion if he wage differenial is large, we discuss only he inerior soluion wih a maximum of 1, which is he corner soluion. ]. 13

16 Submied o Mancheser School Economic Growh and Migraion There is no labour movemen if he difference beween he erms in he numeraor equals zero. Assuming ha he radiional secor requires a consan share of unskilled labour, he amoun of unskilled labour in he manufacuring secors, L x i and Lx j, remains consan. As he model does no include any populaion growh, he oal number of high skilled workers across he wo counries is consan as well. Therefore, labour mobiliy depends solely on he sock of varieies or he number of firms. Migraion increases wih an increase in he difference of he number of firms beween he wo counries. Thus, in erms of firms, he larger counry aracs more high skilled workers. Migraion flows are posiive as A i > A j implies wi A > wj A. Migraion can be hen summarized as min m ji = min m ij = ( A 2 i Lx i ( 1 δα +LH j ) A 2 j Lx j ( 1 δα +LH i ) L H j (A 2 j Lx j +A2 i Lx i ) ( A 2 j Lx j ( 1 δα +LH i ) A 2 i Lx j ( 1 ), 1, if w H i > w H j 0 ), if wi H wj H δα +LH j ), 1, if wj H > wi H L H i (A 2 i Lx i +A2 j Lx j ) 0, if w H j w H i 3.8 Incorporaing Migraion Coss The assumpion of zero migraion coss is unrealisic. Migrans incur coss o esablish social neworks, learn and work using a foreign language and culure, and so on. These coss can be summarized as uiliy coss. On he oher hand, he ac of migraion iself bears coss. In he following main emphasis is pu on he laer. Coss of moving from counry j o counry i are k, wihou any furher assumpions abou he origin of he coss. 13 There will be migraion if he wage in he hos counry minus he coss is larger han in he domesic counry: wi H k > wj H Assuming again ha here is no migraion from counry i o j, migraion flows from j o i can be described as: m ji = 1 1 { ( kδα(σ 1) L H 2 k(σ 1)δαL H j L H ) ( i + δφ A 2 i L x i + A 2 jl x ) j j [ k 2 (σ(σ 2) + 1) ( 4 + δα 2 (L H i + L H j ) 2 + 4δα(L H i + L H j ) ) + δ 2 φ 2 ( A 2 i L x i + A 2 jl x ) 2 ( j + (σ 1) A 2 j L x j A 2 i L x ) i ( ( 2σ + δα L H i L H ))] 1 } 2 j (16) Compared o he case wihou migraion coss, inerpreaion of equaion (16) is somewha complicaed. 14 The main driver of migraion is sill he difference 13 Including migraion coss in he consumer budge consrain does no lead o subsanial changes in he demand funcions for he wo goods, so long as he coss are independen of x i and T i. This condiion holds if T i = Ti min. If T i > Tj min hen L x i and Lx j depend on T i, which would hen as well depend on x i. 14 Apar from equaion (16), here is anoher poenial soluion for m ji. In his soluion, he erm in squared brackes, ha is [...], would have a posiive sign in fron of i. This soluion is inadmissible as i would predic migraion flows from counry i o j even in he case of wj H > wi H. 14

17 Submied o Mancheser School Economic Growh and Migraion in he sock of firms, since he oher variables remain consan. Migraion coss will have he effec of posponing migraion unil he wage differenial is large enough o cover he coss. The influence of coss of migraion is furher discussed in he conex of simulaions in secion 4. This complees descripion of our proposed model. The model has he following key characerisics. Firs, a higher number of highly skilled workers leads o a higher number of designs which in urn enhances growh. In addiion, he richer counry receives more highly skilled workers and herefore he difference beween he wo counries increases. In he seady sae, when a fracion or he enire sock of high skilled workers moves o one counry, he model explains divergence. Counries are linked o each oher by wo facors: labour migraion and rade. The counry wih more manufacuring firms aracs high skilled workers from he oher counry and benefis from a higher growh rae. The counry wih he smaller number of manufacuring firms remains sagnan a a lower level. The second linkage is rade. The counry wih a lower variey of manufacured goods benefis from he growh in he richer counry by imporing a higher number of varieies, while a he same ime exporing a fixed quaniy of is manufacured good. Like any oher heoreical growh model, he above model represens an absracion of realiy. To obain realisic inerpreaions, i is useful o consider concepual disincions beween cross-counry or iner-region migraion and growh dependences. World hisory offers a huge range of examples of labour movemen beween counries or regions. By varying he srucural parameers, our model can be applicable o boh he above cases. Divergence emerges as an essenial oucome of he model. As oulined in he Inroducion (secion 1), subsanial divergence across counries was an essenial feaure of he 19h cenury. In he 20h cenury, here is evidence of clubconvergence (Baumol, 1986; Islam, 2003), where groups of counries converge o a common equilibrium, bu uncondiional convergence across all counries is absen. 15 Thus, he divergence oucome of our model is also consisen wih conemporary evidence on convergence clubs. I may be noed, however, ha our model has no mechanism for cach-up or convergence wihin each such club. Therefore his model should be seen more as an aemp o consider ineracions beween counries or regions wihin a growh model, raher han offering a full explanaion for economic growh and convergence/ divergence across counries and regions. Anoher poenial criique is ha he model focuses on wage differences raher han on uiliy as he moive for migraion. However, as he Cobb- Douglas uiliy funcion is sricly increasing in boh goods and boh because boh goods are normal goods, boh moives are coinciden. Finally, in our model he decision o migrae is purely economic. Poliical or geographical reasons such as conflic or naural disasers ofen moivae migraion. In he conex of our 15 Empirical analysis in Baumol (1986) suggess convergence for 16 OECD counries, bu no for a broader sample of counries. Islam (2003) wries: [P]rodded by Romer, Baumol also considers he relaionship in an exended sample of 72 counries. In his larger sample, however, he does no find evidence of convergence.... The numerical resuls of his regression were no presened, bu Baumol repored ha i yielded slighly posiive slope, indicaing a process of raher divergence. 15

18 Submied o Mancheser School Economic Growh and Migraion model, such moives may be viewed as reducing he migraion coss, k. 4 Simulaion In his secion, we carry ou a simulaion o undersand he impac of migraion and rade on income, in he conex of he economic model developed in secion 3. For his purpose, we inroduce dynamics in he accumulaion of designs. The number of designs over subsequen periods evolves as: A i,+1 = Ȧi, + A i, = A i, (δh R i, + 1). (17) For our simulaions, he choice of he iniial values and he parameers are of crucial imporance. Assume ha boh counries have he same number of firms (or designs) and he same populaion size, bu one counry has a higher number (proporion) of high skilled workers. We consider he following iniial values for he designs and sock of workers: A i = 10 A j = 10 L i = 6 L j = 8 L H i = 4 L H j = 2 The above parameers imply ha counry i will have higher income due o a larger number of highly skilled workers. Therefore highly skilled workers will migrae from j o i whenever such migraion is allowed. In he following, we assume ha he manufacuring and he radiional secor boh require wo unis of unskilled labour for each uni produced. The demand for he radiional good is resriced o be 1 in boh counries. We also assume he following parameers for he marginal rae of subsiuion beween he manufacured goods and he radiional good: δ = 0.5 σ = 8 φ = 0.5 α = 0.1 µ = 1 γ = 0 T i = T min i = 1 T j = T min j = 1 For rade, we consider wo cases: (a) Very high ransporaion coss so ha here is no rade, implies rade coss are se such ha τ 1 σ = 0; (b) oherwise, for each raded uni 1.5 unis have o be produced (τ = 1.5). When migraion is allowed, i is inroduced only from period 5 onwards. In addiion here are no consrains for migraion, implying ha from one period o he nex, a fracion of all highly skilled workers are allowed o move beween counries. Firs, he model is simulaed wihou migraion or rade. This case is used as a baseline and compared o simulaions wih migraion and/ or rade. 4.1 Baseline (no migraion, no rade) Figure 1 shows simulaion resuls of he baseline model wihou migraion and rade (τ, τ 1 σ = 0). Oupu (1a), he number of firms (1b) and he relaive 16

19 Submied o Mancheser School Economic Growh and Migraion prices (1d) and he wage in he manufacuring secor (1f) are ransformed in logarihms. The model behaves as expeced from an endogenous Romer syle model. Oupu increases wih a consan rae, he number of firms and hence varieies increase wih he same rae. The wages of high skilled workers increases a a consan rae as well. The increase is smaller han for he number of varieies as wage is scaled down by δ and he price of he varieies, which falls wih an increase in A i. Since here is no migraion, he number of high skilled workers remains he same. The number of low skilled workers employed in a single firm in he manufacuring secor decreases over ime as he number of firms increases. In he firs period 0.7 unskilled workers are employed in each of he 10 firms of he manufacuring secor in counry j. More workers are employed in each firm in counry j as less addiional firms are founded han in i. 4.2 Migraion, bu no Trade Figure 2 shows a simulaion wih and wihou migraion bu no rade. A solid line refers o he case wih and a dashed line o he case wihou migraion in all graphs. As soon as migraion is inroduced in period 5 (indicaed by a verical dashed line), high skilled workers sar moving o counry i as shown in Panel 2c. Afer wo periods all high skilled workers employed in he R&D secor have moved o counry i, leaving he R&D secor in counry j empy. This movemens booss he amoun of produced designs in counry i while he amoun of designs in counry j remains a he same level. The number of designs, and so he number of firms, do no change anymore and herefore demand remains he same. As before, he amoun of unskilled labour allocaed o he manufacuring secor in boh counries decreases bu says consan for counry j afer he inroducion of migraion. The wage for high skilled workers and he relaive price in counry j do no change anymore, because he number of designs remains consan. The simulaion clearly shows ha he counry which receives more high skilled worker benefis from migraion by increasing he growh rae of designs and herefore experiencing a higher oupu growh rae. Thus, migraion leads o divergence. 4.3 Trade, bu no Migraion To find ou how rade affecs he model, Figure 3 shows simulaion resuls wih (τ = 1.5) and wihou rade (τ 1 σ = 0). High skilled workers are immobile and no allowed o move beween counries. Therefore rade is he only ineracion beween counries. In he case wihou rade, he model is exacly as he baseline specificaion in Figure 1. Below we highligh differences o his baseline wih he case wih rade. The number of varieies, or firms, is he same in boh cases, since rade does no lead o any changes in he disribuion of he high skilled workers. Therefore he number of low skilled workers employed in each firm as shown in Panel 3d does no change as well. The oupu increases because he demand for he manufacured goods increases due o he possibiliy of rade. Boh counries benefi from rade, even hough counry j benefis more, as Panel 3a shows The rade benefis for counry i are very small and almos impossible o disinguish from he graphs. Noe ha he graph plos logarihm of oupu. 17

20 Submied o Mancheser School Economic Growh and Migraion Thus, rade inroduces a degree of cach-up or convergence. Counry j impors more goods as counry i offers a higher variey of differen goods. The changes in he relaive prices are small. Again he change is larger for counry j han for counry i. The reason is he number of foreign designs eners he price level only by a facor The simulaion reveals ha, in comparison wih migraion, he effec of rade is of a smaller magniude. The counry wih he smaller manufacuring secor is he main beneficiary. 4.4 Boh Migraion and Trade In Figure 4 we allow for boh migraion and rade from period 5 onwards. Coss of rade are se o τ = 1.5, implying ha for each uni of he manufacured good which is sold abroad, half a uni is los in ransporaion. As in he case of migraion only (see Figure 2), all high skilled workers migrae o counry i wihin 2 periods. Therefore counry i produces more designs, while he sock of designs remains consan in counry j. As he number of designs remains consan, no new firms can be founded and herefore counry j is no able o expor more of he manufacured good o counry i (see Panel 4d). However he impors of he manufacured good ino counry j increases. Producing more designs leads o a higher growh rae of income in counry i, similar o he case wih migraion bu no rade. Similarly o he case of rade only (see Figure 3) he growh rae of counry j converges o he growh rae of counry i. Thus rade dampens he negaive effec of migraion. Despie rade, he growh rae of he poorer counry canno overake he growh rae of he richer counry. A hough experimen can be used o illusrae his. If rade is possible wihou any coss, τ = 1, hen he demand for he domesic and impored manufacured good will be he same. Therefore he locaion of producion does no make any difference o he availabiliy of he manufacured good; boh counries benefi from a higher number of firms in any counry. To pu i differenly, rade coss of zero would merge he wo counries and heir growh raes would be he same. Furher, convergence in growh raes does no imply convergence in income he richer counry remains a a higher income level. The simulaion shows ha rade offses he negaive effecs of migraion for he counry which loses high skilled workers. The richer counry benefis more from he addiional high skilled workers han from he opporuniy of rade. 4.5 Migraion Coss Figure 5 shows simulaion wih cosless migraion and migraions coss of 200, which is in he order of he wage in he R&D secor in period 5. Panel 5c shows ha migraion is shifed by 1 period ino he fuure. Moreover all highly skilled worker migrae immediaely in he nex period. This is because he difference in he number of he firms does no increase linearly over ime. All high skilled workers moved o counry i wihin 2 periods or 1 period, wihou and wih coss respecively. The shif due o migraion coss causes a delay unil counry i s growh rae of oupu o reaches he same rae as in he case wihou coss. 17 The main driver for he price changes is R i = A i + τ 1 σ A j, where τ 1 σ =