Technological diffusion and dynamic gains from trade

Transcription

1 MPRA Munch Personal RePEc Archve echnologcal dffuson and dynamc gans from rade Eleonora Cavallaro and Marcella Mulno Sapenza, Unversy of Rome, Unversy of L Aula December 28 Onlne a hp://mpra.ub.un-muenchen.de/3793/ MPRA Paper No. 3793, posed 6. March 29 6:3 UC

2 WORKING PAPER DIPARIMENO DI ECONOMIA PUBBLICA Workng Paper n.7 Eleonora Cavallaro e Marcella Mulno echnologcal Dffuson and Dynamc Gans from rade Roma, ebbrao 29 UNIVERSIA DEGLI SUDI DI ROMA LA SAPIENZA

3 echnologcal Dffuson and Dynamc Gans from rade Eleonora Cavallaro and Marcella Mulno Absrac We consder a echnologcally backward counry and analyse he mplcaons on compeveness and long-run growh of he ualy conen of raded goods. We buld an endogenous growh model where ualy mprovemens sem from research acvy akng place n he R&D secor, and where he relave ualy conen of goods maer for expor and mpor demand funcons. We show ha he possbly of an opmal growh wh a balanced curren accoun and no adverse erms-of-rade effecs s closely relaed o he evoluon of he counry s echnologcal dsance wh respec o he rade parner: wh an unfavourable ualy-dynamcs he counry canno engage successfully n non-prce compeon. hus, long-run growh s coupled wh an adverse expor o mpor rao, and a balanced rade reures a connuous offseng fall n relave prces, eher hrough devaluaons or wage deflaons. We hen allow for nernaonal knowledge spllovers ha ncrease he producvy of labour resources devoed o research n a way whch s proporonal o he echnologcal dsance beween he counres. We show ha he greaer he counry s ably o absorb foregn knowledge and mprove upon foregn echnologes, he greaer he gans n compeveness, and he benefs o long-run growh. A numercal smulaon confrms our fndngs. Keywords: Vercal nnovaon; echnologcal change and cachng up; Economc growh of open economes Sapenza, Unversy of Rome, eleonora.cavallaro@unroma. (correspondng auhor) Unversy of l Aula, mulno@ec.unva. he auhors wsh o hank parcpans n he AISSEC Conference n Parma (June 27) and he INER Workshop n Combra Inegraon and Globalzaon: Challenges for Developed and Developng Counres (June 27) for useful commens. he auhors are graeful o S. Zappacosa for asssance n he numercal smulaon. nancal suppor from he Ialan Mnsry of Unversy s graefully acknowledged.

4 . Inroducon One of he cenral uesons n curren polcy debaes, as well as n heorecal analyses and emprcal nvesgaons, s wha allows laggng-behnd counres o cach up wh more advanced economes. he recen developmen of heores of echnologcal change has gven rse o a new perspecve n he analyss of he relaon among rade, growh, and echnologcal change n open economes. Grossman and elpman (99), Aghon and ow (992), Edwards (998), among ohers, emphasze he exsence of a posve assocaon beween openness and growh drven by echnologcal ransfers and knowledge dffuson, he facors a he bulk of a cachng-up process. he conrbuon of he paper s o address he aforesad ssue wh reference o echnologcally laggng-behnd economes. A he bass of our analyss s he new- Schumpeeran perspecve ha counres compee no so much by varyng prces and uanes, as by nnovang. In hs vew, we conend ha echnologcally backward counres suffer from a srucural lack of compeveness, due o her lower rae of nnovaon, whch s refleced n he relave poor ualy of he goods hey produce. As menoned above, s wdely agreed upon ha openness s among he mos crucal facors for a cachng-up process. he more counres are open o he res of he world, he greaer s her ably o benef by he hgher sock of knowledge capal generaed n leadng counres. In fac, here s wde emprcal evdence ha he nernaonal dffuson of knowledge s promoed, among ohers, by rade n goods and servces, foregn drec nvesmen, mgraon and busness conacs, and ha he negraon of markes favours boh he spread of general scenfc knowledge and he dffuson of more produc-specfc nformaon. he benefs of nernaonal knowledge spllovers accrue n erms of an ncrease n he producvy of labour resources allocaed o research. or nsance, he laggard economy can gan sklls n applyng o he goods manufacures he know-how emboded n producs of he advanced counry; snce raded goods are dfferenaed, enrepreneurs have he possbly o apply a gven know-how o a dfferen ype of good, wh respec o he one whch was orgnally conceved for. ence, n he R&D secor boh nnovaon and maon acves are carred on. 2 On he bass of he above consderaons, we buld an endogenous growh model 3 where a counry rades wh he res of he world n a number of dfferenaed producs. Manufacured producs embody a ualy conen whch reflecs he sock of knowledge capal avalable n he counry a a gven me; as n ualy-ladder models nnovaons sem from research acvy akng place n he R&D secor, and lead o he ualy upgradng of manufacured goods hrough me. We consder he case of a counry ha lags behnd echnologcally, so ha s producs have a lower ualy conen han foregn producs. In he model we derve analycally expor and mpor demand funcons n whch he relave ualy conen of he goods maer. We dscuss he mplcaons on compeveness and long-run growh of a lower rae of nnovaon wh respec o he more advanced rade parners. We show ha he possbly of an opmal growh wh a balanced curren accoun and no adverse erms-of-rade effecs s closely relaed o he Keller (999, 22); Crspol and Marcon (25); Léon-Ledesma (25). 2 Pack and Wesphal (986). 3 In hs paper we exend o a general eulbrum seng he analyss developed n Cavallaro and Mulno (27). 2

5 evoluon of he counry s echnologcal dsance wh respec o he rade parner: an unfavourable ualy-dynamcs deermnes he nably o engage successfully n nonprce compeon. I follows ha long-run growh s coupled wh an adverse expor o mpor rao so ha a balanced rade reures a connuous offseng fall n relave prces, eher hrough devaluaons or wage deflaons. We hen allow for nernaonal knowledge spllovers. ormally, we le foregn knowledge ener he sock of knowledge capal avalable o domesc researchers, and allow for a hgher effcency of he economy n makng ha sock of knowledge capal useful n R&D acvy. Overall, hese effecs deermne an ncrease n he producvy of labour resources devoed o research, n a way whch s proporonal o he echnologcal dsance beween he counres. 4 In he paper, we derve analycally he mpac of he echnologcal cachng up on expor and mpor demand funcons and show ha he greaer he counry s ably o absorb foregn knowledge and mprove upon foregn echnologes, he greaer he gans n compeveness, and he benefs o long-run growh. A numercal smulaon confrms our fndngs. 2. he model: he basc se-up We consder a laggng-behnd economy radng wh he res of he world whch s echnologcally more advanced. or he sake of smplcy, we wll name he res of he world as he advanced counry. As n more recen rade leraure, he conex s ha of a sem-small open economy, where mpored goods are purchased a gven world prces, whereas he counry faces a downward slopng demand schedule for s expors, because hese are perceved o be mperfec subsues for he radable goods of oher counres. In addon, we assume here are no arffs, ransporaon coss or oher rade barrers, and ha only fnal goods are nernaonally raded Consumers behavour ouseholds have a preference for dversy and herefore derve uly from he consumpon of dfferen producs, whch are manufacured domescally and abroad, and whch subsue mperfecly for each oher. We assume he se of avalable producs o be fxed hrough me snce we are no concerned wh he ssue of brand prolferaon, whereas he ualy conen of such producs vares hrough me: as n ualy ladder models, 5 each produc can poenally be produced n an unlmed number of uales, and he pace nnovaon n a gven counry deermnes he ualy upgradng of he producs manufacures. We assume ha a each me he ualy dfference beween domesc and foregn producs s refleced n households (sac) choce of consumpon. We hus descrbe neremporal preferences of he represenave consumer wh he sandard form: U ρ ( τ ) e log u dτ () where ρ represens he subjecve dscoun rae and u each household s nsananeous uly: τ 4 Edwards (998); Smulders (24). 5 Grossman and elpman (99); Aghon and ow (992). 3

6 θ n θ m θ θ θ θ u C + C j (2) j he specfcaon of uly n euaon (2) reflecs he consan elascy of subsuon beween producs, eual o θ >, 6 and he preference for ualy: he n domesc and m foregn producs ener n each consumer s preferences n relaon o her ualy conen, ha s, n proporon o and. Each represenave household supples labour servces nelascally, earns labour ncome and receves profs whch are pad ou by frms as dvdends from hs share of domesc asses holdngs. Moreover, each household can borrow freely on he world marke a he nernaonal rae o fnance he excess of expendure over labour and nonlabour ncomes. he dynamc budge consran s herefore: n m ds P C + xpjc j + W L + r S for all (3) j d where P and P j represen he prces of good and j produced n he domesc and foregn economy, respecvely, x s he exchange rae, S s he value of he consumer s oal asse holdngs ne of foregn lables, W s he wage rae, L s labour supply, r s he rae of reurn on ne asse holdngs. In order o preven ndvduals o choose pahs wh explodng deb, we mpose he ransversaly condon ha reures each household s deb, B, no ncrease asympocally faser han he neres rae: r lm B e (4) he soluon o he above maxmzaon problem leads o he followng sac demand funcons for he domesc good and for he foregn good j: 7 C C P θ n m θ θ θ θ ( ) P + ( ) xpj j xp j j n m θ θ θ θ ( ) P + ( ) xpj j where E denoes he represenave consumer s expendure, as resulng from he dynamcal budge consran n euaon (3). Euaons (5) and (6) may be resaed as: θ E E θ θ θ ( ) E P θ E θ δ ( + ) P P P C (5a) θ P (5) (6) 6 o save on noaon, we assume he same value of he elascy of subsuon among all goods, rrespecve of her place of producon. 7 Pollack (97). 4

7 C j P xp θ θ θ j ( ) E ( + ) θ xpj P θ ( δ ) where δ represens he relave ualy conen of domesc goods, whch + should be nended as he relave amoun of servces provded by domesc goods, and θ θ n m θ θ θ where P δ ( δ ) P + xp j s he prce ndex conssen wh he j preference specfcaon gven n euaon (2). Euaons (5a) and (6a) show ha he represenave household s demands for good and for good j, respecvely, are funcons of relave prces, wh elascy θ, real ncome, wh unary elascy, and ha he relave ualy conen of domesc and foregn goods mpacs on he magnude of he expendure proporonaly. he mporance of he ualy conen n he srucure of demand appears clearly by akng he rao beween euaons (5a) and (6a): C P (7) C j xpj Euaon (7) shows ha relave demand depends on he goods prce rao and he know-how conen rao; o pu dfferenly, relave demand s decreasng n ualyadjused prces. As sandard n endogenous growh models, he ndvdual opmal spendng profle obeys he Ramsey rule: E ~ r ρ, where E ~ denoes he growh rae of expendure. 8 Marke demand for good s obaned by summng over resdens and non-resdens ndvdual demands. Domesc demand for good, C, akes exacly he same form as euaon (5a), bu wh expendure E referred o naonal-wde expendure. 9 As o foregn demand, C, we make he usual assumpon ha consumers preferences n he wo counres are symmerc, so ha: θ θ P θ R P θ E C δ δ (8) xp P P P where xp P s he foregn prce ndex n erms of he domesc currency, and xr E s foregn expendure n erms of he domesc currency. he overall demand for good a each me akes he followng form: θ θ P θ E P θ E D C + C δ + δ (9) P P P P rms behavor he supply sde of he economy s characerzed by he secor ha manufacures fnal goods, and he secor ha manufacures nermedaes; n he laer frms underake wo θ θ E P (6a) 8 In he paper, he symbol ~ over a varable denoes s rae of growh. 9 In he aggregae he economy s expendure s gven by oal wages and profs earned n he dfferen secors of he economy plus he flow of exernal borrowng ne of neres paymens on deb. hs follows from he assumpon ha consumers preferences n he wo counres are symmerc. 5

8 acves: hey creae blueprns by engagng n R&D acvy, and hey manufacure nnovave nermedaes. he frms ha succeed n up-fron research have he ably o gan ndusry leadershp for he nnovave produc and o capure he monopoly profs accrung from he producon of he nermedae unl nex research success. In he fnal secor here s a fxed number of frms, each producng a dfferenaed fnal produc wh a consan-reurn-o-scale echnology where labour and nermedaes goods are he wo npus: α α Y L A () Y where s an arbrary consan reflecng he choce of uns, L Y s employmen of labour and A he amoun of nermedaes n he manufacure of produc. We follow Grossman-elpman (99) n assumng ha frms employ a fxed assormen of nermedae npus whch are vercally dfferenaed, ha s, each npu can be produced n varous uales. We shall hus employ he followng ndex of nermedae npus: log A log τ Zτ h dh () τ where Z τ h represens he componen h n he ndex whose ualy s τ. he nnovaon process s such ha each new nermedae provdes γ addonal servces wh respec o he good of he prevous generaon, ha s τ γ τ, where τ denoes he ualy of he τ h generaon good. he nermedae ndex () has he propery ha vercally dfferenaed npus n a gven ndusry h subsue perfecly for one oher when ualy dfferences are appropraely accouned for. Moreover, each nermedae h eners he ndex symmercally, and herefore eners symmercally n he producon of fnal goods, oo. We assume ha each frm producng he fnal produc s a monopolsc compeor n he world marke, so ha he behavour of frm s descrbed by a sandard prof maxmzaon problem, gven he echnology and he demand consran (euaons () and (9), respecvely). he opmal prce rule followed by producers n he fnal secor mples a fxed margn over he margnal coss of producon. he analycal se-up s ha of monopolsc compeon, as n Blanchard Kyoak (987). In our model P W PA each frm solves he followng maxmzaon programme: max Y L A, subjec o he Y P P P P θ α α P θ E + E echnology consran: Y L A and o he demand consran: Y C C Y + δ P P, where P A s he prce of he nermedae ndex A. Each frm akes he wage rae and he prce of he nermedae ndex as gven. Moreover, due o he assumpon of a large number of frms n he world marke, each frm akes he prce ndex P as gven, oo. he opmal prce rule mples a fxed margn over he θ W LY θ P A A margnal coss of producon: P and P. he above condons lead o he θ α Y θ ( α ) Y θ PY followng demand funcons for labour and for he aggregae nermedae: LY α and θ W 6

9 As o nnovaon acvy, we follow closely Grossmann-elpman (99). Recall ha each frm ha manufacures an nermedae produc underakes also research acvy: each frm may ener freely no R&D and ssue euy o fnance nnovaon coss. he successful research effor leads o ndusry leadershp for he manufacure of he nermedae, and o he sream of monopoly profs unl he nex research success. We assume ha an enrepreneur engages labour resources n R&D a nensy ι for a me nerval of lengh d. 2 he probably of ganng success n lab acvy s proporonal o he resources devoed: o acheve a research nensy of ι, s necessary o nves L R lι uns of labour servces per un of me, where l s a parameer reflecng he producvy of labour n research. he enrepreneur wll nves labour n research acvy up o he amoun for whch he cos of R&D acvy, W lι, euals he expeced revenues υι. I follows ha: W l υ, wh eualy whenever ι > (2) he above euaon (2) may be nerpreed as an arbrage condon beween he sock marke value of he nnovang frm υ and he expeced cos of ualy upgradng. As o he nnovave nermedaes, each componen Z h s manufacured wh a consan-reurn-o-scale echnology where labour s he only npu. or he sake of smplcy, we choose uns so ha one un of he nermedae npu reures one un of labour npu. Gven monopolsc compeon n he ndusry and lm prcng oucome all nermedaes bear he same prce, ha s PZ h PZ. Such a prce s deermned on he bass of a mark-up γ over un coss, where γ s he ncrease n ualy emboded n he superor, sae-of-he-ar nermedae, ha s: P Z γw. Snce beer ualy npus are more producve, producers of he fnal goods buy only he sae-of-he-ar varees; and snce all demanded componens Z h are employed n eual uanes, he aggregae nermedae A can be expressed as A Z where Z denoes he aggregae volume of nermedaes and s an ndex of producvy of nermedaes. he above assumpons PZ mply also ha PA A PZ Z, so ha P A. As o he producvy ndex, reflecs he counry s sae of knowledge emboded n he fnal producs, a a gven me, and s proporonal o he oal number of R&D successes. 3 he prcng sraegy n he nnovave secor leads o a flow of profs per frm eual o: A θ θ ( α ) PY. he opmal prcng sraegy leads o a flow of monopoly profs a each me eual P A o Π Y P Y. θ 2 We are hus assumng ha success n nnovaon and maon arses randomly, followng a Posson processes, wh ι denong he parameer of he densy funcon. 3 rom euaon () we have log A log h dh + log Z, where h represens he ualy of he sae-ofhe-ar brand of nermedae h. ence, he ndex s number of R&D successes from me up o. I γ, where I ι ( ) d represens he oal 7

10 n θ Π Z ( α ) P Y h (3) θ γ he above flow of profs, ogeher wh he expeced capal gans or losses, consue he overall reurn o he owner of he nnovave asse. In a perfec-foresgh eulbrum, arbrage n he capal marke reures ha he overall reurn o capal be eual o he reurn on a rskless loan r. We hen have: Π Z + & υ ι υ rυ (4) h where & υ ι υ s he expeced capal gans or losses on he value of he euy clams Long-run growh and he exernal balance We now urn o he macrodynamcal behavour of he model n a general eulbrum conex. Gven ha he demand funcons for each domesc produc are dencal, and ha he producon funcons of each frm are dencal, oo, we have symmery among frms. ence, n a general eulbrum he prces se by frms n he fnal- good secor are dencal, ha s P P. he eulbrum condon beween aggregae producon n n PY P Y PD P D and aggregae demand, a each me, may be saed by P P P P recallng euaon (9): θ P Y P θ E + E P P δ (5) P We now consder he marke clearng condons for he labour and he nermedae good markes. As o he aggregae nermedae, has only a sngle use and s supply s eual o he derved demand by fnal good producers; as o labour, s used n R&D, n he manufacure of he consumpon producs and of nermedaes. herefore, he marke clearng condon, a each me, s obaned by euang he fxed labour supply, L, and he derved demands for labour n research, and n he nermedae and fnal secors: θ P Y θ P Y ι l + ( α ) + α L (6) θ γ W θ W where now ι denoes he aggregae nensy of research argeed a a sae-of-he-ar produc. 5 We may hus reformulae he arbrage condon as: V& Π Z V ι ρ (7) V where Π Z s he aggregae prof n he nnovave secor and V υ s he nverse of he aggregae value of he sock marke. he dynamcal behavour of he economy hrough me s descrbed by he above arbrage condon, ogeher wh he labour marke eulbrum condon. We concenrae on he seady-sae properes, when he value of he sock marke s consan, ha s, V &. 4 Wh effcen markes υ s eual o he dscouned value of he flow of fuure profs, so ha no bubbles arse. 5 he specfcaon of he nermedae goods secor mples ha he oal measure of prof makng frms euals, and herefore he aggregae value of he sock marke s υ. 8

11 Euaons (6) and (7), ogeher wh he sde euaons (2) and (5), deermne he seady-sae rae of nnovaon: L α ι ( ξ ) ξρ, < ξ + α < (8) l γ I appears ha he economy s pace of nnovaon s posvely nfluenced by he degree of monopoly power enjoyed by he nnovave secor larger values of γ, as well as by a relavely hgh share of nermedaes n he echnology for he producon of he fnal good lower values of α. As n Grossman-elpman (99), n he long run he pace of economc expanson depends on he resless process of producvy growh ha akes place n he nnovave secor. In fac, gven he frm s echnology n euaon (), growh accounancy relaonshps mply ha n a symmerc eulbrum he growh rae of aggregae oupu s proporonal o he growh rae of he aggregae nermedaes A: Y ~ ( α ) A ~ (9) Snce A Z, and gven ha each new generaon nermedaes provde γ addonal servces wh respec o he prevous generaon goods wh probably ι, so ha ~ ι log γ, euaon (9) may be reformulaed as ~ Y ( α ) ι logγ (2) In seady sae growh wll be coupled wh exernal balance. Ye, we do no rule ou he possbly for an economy o absorb above s level of producon for some perod of me, by spendng n mpored producs above he receps from expors, and hus o accumulae exernal deb. In fac, hs appears clearly from he economy s dynamcal budge consran as obaned by aggregang euaon (3) over all households. Naonal ncome accounng denes mply ha he excess of consumpon expendure over dsrbued ncome, ne of domesc asse accumulaon, euals he change n he economy s sock of foregn deb, B : db NX + rb (2) d where NX s he rade balance. Ye, he decson of an economy o consume early n me a a rae above he level of oupu, ne of domesc asse accumulaon, s refleced n he reuremen of a rade surplus n a seady-sae eulbrum, n order o offse neres paymens on deb. 6 Gven ha he economy s long-run growh s characersed by an exernal eulbrum, we may as well focus on he curren accoun eulbrum condon: n m PC xpjc j + rb j (22) 6 By negrang he economy s budge consran from me o some me, and by akng no accoun he ransversaly condon we ge he sandard condon ha he presen value of consumpon s eual o oal wealh a me, where he laer s gven by aggregae non-human wealh S and he presen value of labour ncomes. As usual, n eulbrum he presen value of consumpon s also eual o he presen dscouned value of oupu - ne of domesc asse accumulaon - mnus he nal level of deb. 9

12 where he LS s oal expor receps and he RS s oal paymens for mpors and neres oblgaons on ousandng deb. By aggregang he expor and mpor demand ndvdual funcons we ge: n θ θ θ + P P P m xp θ E j δ xpj ( ) P j P δ θ and by recallng ha P δ + reformulae he curren accoun eulbrum condon as: E P rb n m θ j θ δ and + ( δ ) θ P xp j θ θ (23), we n m P xp j P E xpj E + rb j (24) ~ ~ ~ Snce P P, P j P, and E P + Y boh home and abroad, he above condon may be resaed n dynamcal erms as: Y ~ Y ~ θ ( P ~ x~ P ~ ) + θ ( ~ ~ ) (25) I appears clearly ha he fulflmen over me of condon (25) wll depend on he evoluon of boh he pure prce erm and he ualy dfferenal erm. If he economy sars wh an exernal defc, gven he rae of change of foregn varables (ha s, ncome, prces and ualy), an acceleraon n s pace of nnovaon can enhance foregn demand whle keepng prces consan. In such a case, an opmal growh pah n our model mples a non-deflaonary eulbrum rajecory, wh derved facor demands proporonal o aggregae oupu, consan producvy-adjused npu prces and consan relave facor prces. On he conrary, wh an unfavourable dynamcs of ualy upgradng he counry faces a srucural lack of compeveness so ha connuous changes n relave prces - eher exchange rae devaluaons or wage deflaons are needed o ensure he exernal balance. I s clear ha he laer scenaro s one of mmserzng growh where he economy faces a deeroraon n s erms of rade, snce, over me, an ncreasng amoun of s expors - wh a gven ualy conen has o be exchanged for a gven amoun of mpors - wh a hgher ualy conen - n order for a curren accoun eulbrum o be acheved. he resuls obaned follow drecly from our assumpons on households preferences, ha lead o expor and mpor demand funcons where he relave ualy conen of producs mpacs on he expendure proporonaly. If growh s coupled wh an unfavourable relave ualy dynamcs, he expor o mpor rao wll move adversely, and a balanced rade wll reure a perssen offseng fall n relave prces. Our model shows ha demand condons are endogenous, snce hey are closely relaed o a counry s pace of nnovaon. In hs sense, may provde an answer o he Keynesan srucurals approach o growh, where exogenously gven demand condons consran long-run growh. As known, he so-called balance-of-paymens consran approach 7 emphasses ha erms of rade changes are neffecve n adjusng exernal defcs because mos rade occurs n hghly dfferenaed goods. Ye, n ha approach a counry s expors are assumed o depend on ncome elasces of expors whch are aken as gven, whereas n our analyss we oban apparen ncome elasces whch vary θ 7 hrlwall (979); McCombe, hrlwall (994); McCombe (998).

13 wh he relave ualy conen of raded goods, and hence wh he counry s pace of nnovaon. 8 Anoher feaure of our model s ha he exen o whch growh can be mmserzng wll ulmaely depend on he counry s ably o compee n ualy domnaed markes. he economy wh a lower pace of nnovaon ha s unable o engage n ualy compeon s forced o engage n prce compeon, and sell an ncreasng amoun of producon a fallng relave prces. hs mples ha growh s coupled wh favourable apparen ncome elasces only o he exen ha he counry s able o close s echnologcal gap wh respec o he mos advanced counres. In fac, n our model an ncrease n producon wll generae an euvalen demand wh no changes n relave prces, only f he ualy-conen of manufacured producs s compeve. 9 If he counry s unable o cach-up echnologcally domesc prces wll have o fall perssenly so as sasfy he long-run eulbrum condon saed n euaon (25). 4. Inernaonal knowledge spllovers, echnologcal cachng up and growh he analyss developed above pons o he fac ha a echnologcally backward counry s unfavoured n rade because he goods produces lag behnd as o her knowhow conen. o see hs, recall ha wh a research nensy of ι devoed o oban he nex generaon good, he growh rae of ualy n he echnologcally backward economy s: ~ ι log γ (26) or euvalenly: d ι log γ (27) d he above specfcaon makes explc he publc good naure of he sock of exsng domesc knowledge n he ualy upgradng process. In fac, he producvy of he resources devoed o research s posvely nfluenced by he ualy level a a gven me,, ha s, by he sae-of-he-ar know-how emboded n he ualy of manufacured goods. Analogously, for he foregn counry we assume he followng: ~ logγ (28) where s he rae of nnovaon n he advanced counry. Gven ha a laggng-behnd counry s ypcally characersed by a lower rae of R&D acvy,.e., > ι, we ge an unfavourable dynamcs of he ualy dfferenal erm n euaon (25). Ye, f we allow for knowledge spllovers o be nernaonal n scope, we may undersand why openness may favour growh. Indeed, openness s a crucal facor n promong he dffuson of knowledge. As emphassed n recen conrbuons of he leraure on nnovaon and endogenous growh, 2 laggng-behnd counres benef by he 8 Whn hs analycal perspecve Cavallaro and Mulno (28) provde an emprcal assessmen of he mporance of ualy upgradng n he performance of marke shares for some EU new member saes. 9 In Krugman (989) he economy s characersed by ncreasng produc dfferenaon and households love for varey, so ha he expanson of producon wll brng abou an ncrease n demand a gven prces. Dfferenly, n our model an ncrease n producon wll generae an euvalen demand wh no changes n relave prces only f he ualy-conen of manufacured producs s compeve. 2 See, for nsance, Connolly and Valderrama (24); Smulders (24); Léon-Ledesma (25).

14 hgher level of scenfc and echnologcal knowledge of advanced counres, and he knowledge dsadvanage urns o be a he bass of a process of echnologcal cachng up. In fac, wh he negraon of markes boh he spread of general scenfc knowledge and he dffuson of more produc-specfc nformaon ake place. As o he laer, he backward economy can gan sklls n applyng o he goods manufacures he know-how emboded n producs of he advanced counry; moreover, snce raded goods are dfferenaed, enrepreneurs have he possbly o nven around he paen,.e., o apply a gven know-how o a dfferen ype of good, wh respec o he one whch was orgnally conceved for. ence, we assume ha n he R&D secor boh nnovaon and maon acves are carred on. We rea analycally he wo acves n a smlar way, as maon reures labour resources much lke he oher ype of research. In fac, has been sressed ha n laggng-behnd economes maon reures nvesmen n echnologcal capably whch mples effor o apply exsng knowledge n new crcumsances. 2 Buldng on he above consderaons we modfy he specfcaon of he echnology for nnovaon n euaons (26) and (27) and assume ha, hanks o ncreased openness o nernaonal rade, frms ake advanage n her R&D acvy of a broader sock of knowledge capal, whch ncludes he know-how of he advanced counry. I follows ha he producvy of labour resources n research now ncreases wh domesc knowledge as well as wh foregn knowledge ha flows no he economy, so ha ualy changes over me ake place accordng o he followng law: d LR ϕ [( ) ( ) ] log γ (29) d l where he erm n suare brackes s a measure of he sock of knowledge capal useful n research. By comparng euaons (27) and (29), appears ha he process of ualy upgradng benefs by he nernaonal dffuson of knowledge. In fac, now he producvy of labour resources allocaed o research depends boh on domesc srucural facors and on he aforesad nernaonal spllovers. he coeffcen ( ) s he degree o whch foregn knowledge flows no he economy and s ncorporaed no he overall sock of knowledge capal; hence reflecs he relevance of he sock of foregn knowledge capal for he specfc research acvy underaken n he laggng economy, and depends, among ohers, on he degree of markes negraon. he parameer ϕ reflecs he effcency wh whch he overall sock of knowledge capal s convered no R&D acvy; we assume o be above uny, n order o ake no accoun ha wh ncreased marke negraon ualy upgradng n mos laggng-behnd economes s enhanced by boh nnovaon and maon acves. In fac, a gven sock of knowledge capal wll have a greaer mpac on ualy upgradng because s exploed no only o produce general knowledge, bu also o generae ualy developmen by maon and reverse engneerng. By rearrangng euaon (29), we can express he growh rae of ualy as: L ~ ϕ R log γ (3) l 2 Pack and Wesphal (976), p. 5. 2

15 where s he measure of he counry s echnologcal dsadvanage. Euaon (3) shows ha when knowledge spllovers are nernaonal n scope he producvy of labour resources n research depends posvely on he echnologcal gap, gven he values of ϕ and. Snce ϕ >, he producvy of labour resources n research s greaer n euaon (29), wh nernaonal spllovers, han n euaon (27). We can now address he ssue of he mpac of he echnologcal cachng up on compeveness and growh. By nspecon of euaon (3) appears ha a counry s relave echnologcal dsadvanage can be a posve deermnan of a cachng-up process, provded ha he counry s able o fully capure he benefs of he nernaonal dssemnaon of knowledge. Indeed, he possbly of benefng by he nernaonal dffuson of knowledge s relaed o he counry s ably o absorb foregn echnology, ha s, o maser and evenually mprove upon echnologes conceved n oher counres. he facors whch make a counry recepve of he echnology emboded n foregn goods are closely lnked, among ohers, o he counry s degree of openness, ha s, o rade and fnancal lberalsaon, as well as o an adeuae nsuonal seng. As well known from earler conrbuons n developmen leraure, 22 he laggng-behnd economy should have acured he so-called socal capables n order for he benefs of he nernaonal dssemnaon of echncal knowledge o be fully capured. In our specfcaon of he echnology for ualy upgradng hs occurs for ( ) and ϕ suffcenly hgh. I urns ou ha he counry whch s able o capure he knowledge emboded n foregn goods and echnologes 23 wll engage successfully n a reducon n he ualy gap over me. hs mples ha he erm ( ~ ~ ) n euaon (25) wll move favourably, ha s, he counry wll mprove s compeveness. In he Appendx we sudy he possble paerns of condonal ualy convergence for dfferen values of he parameers ϕ and. We derve formally he behavour of he rao and fnd ha he rao ncreases over me and ends o a consan value,, for large enough, ha s: 24 ι lm ϕ (3) ence, he laggng counry s pace of nnovaon and s level of ualy convergence depend on s srucural parameers: he smaller, and he greaer ϕ, he beer he 22 Abramovz (986), and Baumol e al. (989) consder mporan facors n deermnng a counry s socal capables he avalably of human capal, he srucure and flexbly of radng and fnancal nsuons, he degree of openness o nernaonal rade and nvesmen n R&D. 23 Gven he small open economy assumpon, he rae of nnovaon of he advanced counry s ndependen from he nnovaon akng place n he backward counry. 24 See Appendx, condon [A.6]. 3

16 counry s performance. As argued above, such condons are lkely o be me wh an ncreasng negraon of markes. he presence of nernaonal spllovers allows a echnologcally laggng counry o ncrease he producvy of labour resources devoed o research, so ha a each me he pace of ualy upgradng s deermned on he bass of euaon (29). In a seady-sae he economy has a hgher long-run growh rae of aggregae oupu, proporonal o he hgher growh rae of ualy resulng from euaon (3). hs can be verfed by calculang he long-run rae of nnovaon n he presence of nernaonal spllovers. When he echnology for nnovaon s he one descrbed n euaon (3) he producvy of labour resources devoed o research s Q ϕ, so ha he euaons ha deermne he long-run rae of nnovaon, ha s, euaons (6) and (7), ogeher wh he sde euaons (2) and (5), lead o he followng seady-sae rae of nnovaon n he presence of nernaonal spllovers: Q α ιs ( ξ ) L ξρ, < ξ + α < (32) l γ where Q s he seady-sae value of Q, ha s, he producvy of labour resources devoed o research when he benefs of he nernaonal dffuson of knowledge are all exploed so ha euaon (3) s verfed. 5. A numercal llusraon We frs derve some resrcons on he parameers ha ensure condonal ualy convergence, on he reasonable assumpon ha he ualy level of he advanced counry s never reached by he laggng counry. Recallng euaon (3), hs mples ha ι ϕ <, and hence 25 ϕ, (33) ι ι In fgure we represen he se of pons correspondng o condon (33). 25 See Appendx, condon [A.9]. 4

17 gure Admssble range for parameers ϕ and We now perform some numercal smulaons n order o analyse he paerns of condonal ualy convergence when nernaonal knowledge dffuson akes place. We consder he followng values:. 6; 5 ; γ. 3, and compare he behavour of ι he ualy rao hrough me for dfferen values of he effcency parameer ϕ, and evenually for dfferen values of parameer - he wegh of foregn capal n he sock of avalable capal avalable o domesc researchers. We frs carry ou he smulaon wh ϕ 4. 5 and ϕ , when. 2 ; we hen perform he same exercse wh. 2 and. 6, when ϕ In fgure 2 we show he resuls of he frs smulaon, where. 2. Recallng ha he ualy growh rae n he advanced counry s consan (euaon 28), he dfference observed n he rao s all explaned by he dynamcs of hrough me. By choosng ϕ 4 5, a value whch s close o he maxmum admssble value (euaon 3), we ge ι. he hgher curve correspondng o a faser dynamcs of ualy. Asympocally, he curve ends o a lm value, marked by he doed lne, whch les always below uny. he lower curve corresponds oϕ , whch s an nermedae value n he range of he admssble ones. he smulaon shows ha, oher hngs eual, he more he laggng counry s effcen n makng he overall sock of knowledge capal useful for s R&D acvy, he hgher and he faser wll be s convergence o he ualy level of he advanced economy. 5

18 gure 2 Qualy rao dynamcs for dfferen values of parameer ϕ In fgure 3 we represen wo alernave scenaros correspondng o dsnc values of parameer, when ϕ 3. 5 he hgher curve s relave o a hgher wegh of foregn capal n he overall sock of knowledge capal, ha s,. 2. he lower curve represens he dynamcs of he echnology gap when. 6. I appears ha he more foregn knowledge s ncorporaed no he nnovaon acvy of he laggng counry, he beer wll be he counry s performance, and, conseuenly, he lower s echnologcal dsance wh respec o he advanced counry n seady sae. gure 3 Qualy rao dynamcs for dfferen values of parameer 6

19 6. Some fnal remarks he conrbuon of he paper s o address he ssue of rade and growh for a counry ha echnologcally lags behnd. We focus on vercal nnovaon, and follow new- Schumpeeran models n assumng ha he ualy conen of he goods manufacured n a gven counry reflec he avalable sock of knowledge capal, and he counry effcency n converng ha capal no nnovaon. In he model we derve analycally expor and mpor demand funcons where we make explc he role of goods ualy conen, and show he mplcaons for a counry s compeveness and long-run growh of a lower pace of nnovaon wh respec o s rade parners. In lne wh he neo-schumpeeran vew ha frms compee no so much by varyng prce and uany as by nnovang, we show ha he possbly of long-run growh wh no adverse erms of rade effecs depends on he ably of he laggard counry o cach-up echnologcally and o compee n ualydomnaed markes. ence, he more a counry s able o absorb foregn knowledge and o mprove upon echnologes conceved n oher counres, he greaer he gans n compeveness, and he benefs o long-run growh. References Abramovz, M. (986) Cachng Up, orgng Ahead, and allng Behnd, Journal of Economc sory, 2, pp Aghon, P. and ow, P. (992) A Model of Growh hrough Creave Desrucon, Economerca, 6, pp Aghon, P. and ow, P. (998) Endogenous Growh heory (Cambrdge, MA: MI Press). Baumol, W. J., Bael Blackman, S.A. and Wolff, E.N. (989) Producvy and Amercan Leadershp: he Long Vew (Cambrdge, MA: MI Press). Blanchard, O. and Kyoak, N. (987) Monopolsc Compeon and he Effecs of Aggregae Demand, Amercan Economc Revew 77, 4, pp Cavallaro, E. and Mulno, M. (27), Vercal Innovaon and Cachng Up: Implcaons for rade and Growh, CIDEI Workng Paper 75. Cavallaro E., Mulno M. (28), Vercal Innovaon and Cachng Up: Implcaons of EU Inegraon for CEECs-5, Inernaonal Advances n Economc Research,4, 3, Connolly, M. and Valderrama, D. (24) Norh-Souh echnologcal Dffuson and Dynamc Gans from rade, ederal Reserve Bank of San rancsco Workng Paper 24. Crspol, V. and Marcon, D. (25) echnology ransfer and Economc Growh n Developng Counres: An Economerc Analyss, Banca d Iala: em d dscussone 564. Edwards, S. (998) Openness, Producvy and Growh: Wha do We Really Know?, he Economc Journal, 8, pp Grossman, G. M. and elpman, E. (99) Innovaon and Growh n he Global Economy (Cambrdge, MA: MI Press). Keller, W. (999) ow rade Paerns and echnology lows Affec Producvy Growh, NBER Workng Paper 699. Keller, W. (22) Inernaonal echnology Dffuson, CEPR Dscusson Paper

20 Krugman, P. R. (989) Dfferences n Income Elasces and rends n Real Exchange Raes, European Economc Revew, 35, pp Léon-Ledesma, M. A. (25) Expors, Produc Dfferenaon and Knowledge Spllovers, Open Economes Revew, 6, pp McCombe, J. S. L. (998) arrod, Economc Growh and Inernaonal rade, n: G. Rampa, L.Sella and A. P. hrlwall (Eds), Economc Dynamcs, rade and Growh, pp (Basngsoke/London: McMllan). McCombe, J. S. L. and hrlwall, A. P. (994) Economc Growh and he Balance-of- Paymens Consran (Basngsoke/London: McMllan). Pack,., and Wesphal, L. E. (986) Indusral Sraegy and echnologcal Change: heory versus Realy, Journal of Developmen Economcs, 22, pp Pollak, R. A. (97) Addve Uly uncons and Lnear Engel Curves, he Revew of Economc Sudes, 38, pp Porer, M. (99) he Compeve Advanage of Naons, (New York: ree Press). Smulders, S. (24) Inernaonal capal marke negraon: Implcaons for convergence, growh, and welfare, Inernaonal Economcs and Economc Polcy,, pp hrlwall, A. P. (979) he Balance of Paymens Consran as an Explanaon of Inernaonal Growh Rae Dfferences, Banca Nazonale del Lavoro Quarerly Revew, 28, pp Mahemacal Appendx. Explc soluons for and he ualy levels n he advanced and n he laggng-behnd counres a me are he soluons o he dfferenal euaons (28) and (3), respecvely. We hus oban for he advanced counry: ( τ ) dτ γ [A.] where s he nal ualy level. As o he laggng counry, we frs reformulae euaon (3) as: d d ϕ( ) ι() lnγ ( ) and hen negrae n he me nerval beween and : d s ϕ( s ) ι() s lnγ ds ( s ) We hus oban: [( ) ( ) ] ϕ lnγ ι()( s s ) ds where s he nal ualy level of he laggng counry. By furher smplfyng, we ge: ( ) ( ) ( ) () ( ) s ( τ ) τ + ϕ γ ι γ d ln s ds [A.2] 8

21 9 2. Convergence relaonshps In wha follows we derve he condons for ualy convergence among he wo counres, by lookng a he behavour of he rao hrough me. Gven ha ( ) d τ τ whch mples ha on average he number of jumps on he ualy ladder s, when s large enough, he lm of euaon [A.] for s: γ lm [A.3] Analogously, we calculae he lm of euaon [A.2] for : lm ( ) ( ) ( ) () ( ) γ ι γ ϕ + s ds s ln ( ) ( ) ( ) ( ) ( ) γ γ ι γ ϕ + ln ln By rearrangng he above formula, we ge: ( ) ( ) ( ) ( ) γ ι ϕ ι ϕ + [A.4] urnng o he rao, as resulng from euaons [A.3] and [A.4], wh some algebra we ge: ( ) ι ϕ γ ι ϕ + [A.5] and, by akng he lm of he above rao for ι ϕ lm [A.6] snce he erm ( ) γ n euaon [A.5] ends o vansh wh ( ),. On he assumpon ha he ualy level of he advanced counry s never reached by he laggng-behnd counry, we have he followng condon: lm < ι ϕ [A.7] whch mples < ι ϕ, or euvalenly: ι ϕ, [A.8]

22 Moreover, from euaon [A.5] appears ha when he sgn of he erm n suare brackes s negave we have monoonc convergence, and hence any value ress always below ι he lm ϕ. We hus oban he followng condons for he parameers: ln ϕι ϕ > ; < ι ln ln By akng no accoun condon [A.8], and he assumpons (,), > ι, > we ge he wo euvalen condons ln ϕ, ; ϕι, [A.9] ι ι ln ln whch are depced n fgure n he ex. 2

23 Pubblcao n propro Dparmeno d Economa Pubblca acolà d Economa Unversà degl Sud d Roma La Sapenza Va del Casro Laurenzano 9 6 Roma ISSN

24 Workng Paper del Dparmeno d Economa Pubblca Unversà degl sud d Roma La Sapenza Va del Casro Laurenzano 9 6 Roma COMIAO SCIENIICO Eleonora Cavallaro Guseppe Croce Debora D Goacchno Maurzo ranzn Lusa Gurao Domenco Maro Nu Anono Pedone Enrco Salar Annamara Smonazz I Workng Paper vengono pubblca per favorre la empesva dvulgazone, n forma provvsora o defnva, de rsula delle rcerche sulla eora e la polca economca. La pubblcazone de lavor è soggea all approvazone del Comao Scenfco, seno l parere d un referee. I Workng Paper del Dparmeno d Economa Pubblca oemperano agl obblgh prevs dall ar. del D.L.: n. 66 e dal Decreo del Presdene della Repubblca 3 maggo 26 n.252, ar.37.