Quality of Imports Relative to Exports, and the Transmission of Sustained Growth through the Terms of Trade

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1 Qualy of Impors Relave o Expors, and he Transmsson of Susaned Growh hrough he Terms of Trade Carmen D. Álvarez-Albelo Unversdad de La Laguna and CREB Móna Pgem-Vgo Unversa de Barelona and CREB ABSTRACT: Ths paper shows ha an eonomy an mpor susaned growh from abroad, n spe of no possessng mehansms o absorb foregn ehnal progress. To do ha, develops a wo-ounry model of exogenous growh wh nvesmen-spef ehnologal hange. In auary, one ounry enjoys perpeual growh, whle he oher eonomy remans sagnan. In he rade suaon, he erms of rade beome nreasngly favourable o he sagnan eonomy, whh resuls n he ransmsson of growh. The onnuous mprovemen n he qualy of mpored apal goods relave o expored onsumpon goods s he reason why hs ours. Moreover, ounres onverge n per apa nome f rade s haraersed by nomplee spealsaon. KEY WORDS: rade; erms of rade; qualy-adjused pres; growh ransmsson; onvergene JEL CLASSIFICATION: F43, O33, O4 RUNNING TITLE: Transmsson of Susaned Growh hrough he Terms of Trade Correspondene: Deparamen de Teora Eonóma, Esola d Empresarals, Unversa de Barelona, Avnguda Dagonal, 696, Barelona, Span. Tel. (34) ; fax: (34) ; e-mal: pgem@ub.edu. We are deeply ndebed o Fernando Perera for hs ommens. We anowledge fnanal suppor from Mnsero de Cena y Tenología (SEC ). The usual dslamer apples.

2 . Inroduon The leraure lnng eonom growh wh nernaonal rade has manly foused on he dffuson of ehnology or nowledge. To hs respe, reen empral evdene has shown ha he man soures of ehnal hange leadng o produvy growh ome from overseas (e.g. Coe, e. al., 997; Keller, 00). As repored by Keller (004), he leraure has largely onenraed on sudyng ehnologal spllovers as a mehansm of dffuson. A less developed ounry an drely learn from blueprns and desgns ha have been generaed abroad, and ndrely learn from he ehnology emboded n mpored npus. Ths learnng nreases ounry s so of nowledge and, hene, he produvy of s nvenve avy and/or of s worers. Ths vew mples ha ounres possess mehansms, as R&D seor and/or some ype of learnng proess, o absorb foregn ehnal hange. However, he resul obaned by Dewer and Morrson (986) suggess ha he aess o lower pres may also onsue a way of mporng foregn produvy gans. More onreely, hey developed an empral model based on ndex numbers, and proved ha an nrease n he pre of expors relave o mpors has he same effe as an nrease n oal faor produvy (TFP). One ould argue ha, pung smple, an mprovemen n he erms of rade perms o ge more nermedae or apal goods by less, for nsane, onsumpon goods. Ths nrease n npus rases produvy and physal apal aumulaon and, hene, he growh rae of oupu. In hs ase, he exsene of absorpon mehansms would no be neessary for ehnology dffuson o ae plae, sne nowledge s emboded n mpored goods. Emboded ehnal progress onnuously hanges goods feaures, mang hem more produve. Therefore, auses

3 he need for properly defnng pres. Noe ha, holdng quanes onsan, an mprovemen n he qualy of mpored goods relave o expored goods amouns o an mprovemen n he erms of rade. Thus, pres mus be defned per qualy or effeny un, nsead of per quany un. Ths paper s onerned wh he nernaonal dssemnaon of ehnology n absene of any nd of absorpon mehansm. More spefally, goes furher han Dewer and Morrson (986), and poses he followng queson: mgh erms of rade movemens a as he sole engne of growh for a ounry? An affrmave answer would mply ha he effes of free rade on growh ould be powerful enough o ae an eonomy ou of sagnaon. A smple wo-ounry model of exogenous growh and rade s developed o offer a heoreal answer o hs queson. Sne he paper fouses on long run growh, he analyss s lmed o he long run equlbrum. The sruure of he model s as follows. Counres produe wo poenally raded fnal goods, apal good and onsumpon good, usng apal and labour as faor npus. The eonomes only dffer n her nal endowmen of apal and he qualy of he apal good. More spefally, he qualy of apal permanenly upgrades n one of he ounres (ounry ), whle holds onsan n he oher eonomy (ounry ). The qualy of onsumpon good n ounry and boh goods n ounry are denal and reman onsan over me. Therefore, ehnologal progress n ounry s nvesmenspef or emboded n apal. Thus, apal faor n he model s undersood as he Solow (960) jelly apal, and s measured n qualy or effeny uns. In auary, ounry enjoys permanen growh, whle ounry remans sagnan n he long run. The hanges n relave qualy of goods wll deermne he omparave 3

4 advanage of ounres. Counry and evenually have omparave advanage n he produon of apal and onsumpon good, respevely. The rade suaon may be haraersed by omplee spealzaon of ounres, or by nomplee spealzaon of ounry. In eher ase, he erms of rade beome nreasngly favourable o ounry, whh resuls n he ransmsson of susaned growh. The reason s ha permanen rases n he erms of rade preven he value of he margnal produvy of apal from delnng n ounry, n spe of dereasng margnal produvy of apal. The fndngs also show ha he omsson of relave qualy hanges may lead o wrong onlusons when denfyng he hannels hrough whh rade operaes n mpang growh. If relave qualy hanges n he model were gnored, nernaonal relave pres per quany un would be onsdered as he erms of rade. Sne hese pres beome onsan and ounres mpors and expors n quany uns permanenly nrease, one would onlude ha rade operaes va rade volume. An aurae reamen of qualy would reveal ha ounry s erms of rade permanenly mprove and, hene, ha rade operaes va relave pres. Furhermore, under nomplee spealzaon he world eonomy behaves as an negraed eonomy, and ounres onverge n per apa nome. Several empral and heoreal sudes have also arrved o he onluson ha free rade promoes onvergene (e.g. Ben-Davd and Kmh, 004; Ben-Davd and Loewy, 003). Ths resul n hese heoreal sudes les on he exsene of mehansms o absorb foregn ehnology. The fndng from hs model, however, s enrely due o movemens n relave pres. 4

5 Whle he mprovemen n he qualy of goods has been already reaed n he heoreal leraure on growh and rade, he possbly of growh ransmsson hrough he erms of rade has been relegaed o a seond plane. The reason mgh be relaed o he resuls n he empral leraure ndang a deeroraon of less developed ounres erms of rade (e.g. Sarar and Snger, 99; Hwang and Wllamson, 003). However, alhough hs s a well-esablshed resul for hese ounres as a group, fals o hold for some eonomes (Auhoorola, 998 and 000). The debae on developng ounres erms of rade s no losed a all. In hs regard, Ahuorala (993) emphassed he unrelably of un value ndexes as ndaors of genune pre movemens, sne hey are nfluened by hanges n he qualy of goods. Due o he la of suable sasal nformaon, researhers are resred o usng hs ype of ndex. Therefore, her fndngs refer o pres per quany un, and no o he rue erms of rade. A proper adjusmen of nernaonal pres for hanges n qualy beomes rual when ounres rade n apal goods. A srand of he leraure has found srong suppor for a posve effe of rade on growh hrough nvesmen (e.g. Jones, 994; Lee, 995; Harrson, 996). The presene of ehnologal hange emboded n apal as Several heoreal wors have onenraed on analysng rade beween developed eonomes (e.g. Rvera-Báz and Romer, 99). Oher sudes have shown ha qualy upgradng n advaned eonomes may have he effe of leavng less developed ounres ou of nernaonal mares (e.g. Murphy and Shlefer, 997; Fan, 004). Noneheless, hs ssue has been wdely analysed from an empral pon of vew. See, for example, Kohl (004). Some publ sasal agenes, as he Ameran Bureau of Labor Sass (BLS), have made a onsderable effor n provdng researhers wh qualy-adjused nernaonal pres. However, hese daases do no nlude nformaon for less developed ounres. 5

6 amplfyng hs posve effe. Reen empral sudes have found a onrbuon of nvesmen-spef ehnal progress o TFP as hgh as sxy per en (Greenwood e al.,997; Cummns and Volane, 00; Saellars and Wlson, 004). In lgh of hese fndngs, he ransmsson of susaned growh hrough he erms of rade seems more han jus a heoreal possbly. Of ourse, a rgorous empral analyss s needed o deermne o wha exen he ype of phenomenon desrbed here has aen plae n less developed eonomes. The remander of hs paper s organsed as follows. Seon desrbes he model and oulnes agen s desons. Seon 3 haraerses he auary equlbrum. Seon 4 analyses he rade suaon. Seon 5 summarses and onludes. Lasly, hree appendxes onan some deals on alulaons.. The Model and Agens Desons Ths seon desrbes he bas sruure of he model and oulnes agens desons... The Envronmen The world eonomy s modelled as onssng of wo large ounres, =,. Tme s onnuous and endless. There are wo ypes of agens: frms and households. As s usual, agens have perfe foresgh. All mares n boh eonomes are ompeve, and nernaonal faor flows are no allowed. Eah ounry produes wo poenally raded fnal goods: a onsumpon good, and a apal good. Counres are nhabed by a onnuum of denal households ha s normalsed o one. There s no populaon growh. Households are endowed wh one un of me a every perod ha an only be alloaed o wor. These assumpons mply ha he 6

7 populaon amouns o he labour fore of he eonomes, and ha varables are expressed n per apa erms. Capal and Consumpon Good Seors Eah seor s omposed of a onnuum of measured one of denal frms. The nex expresson summarzes he assumpons on produon ehnologes: Capal Good Seor Consumpon Good Seor ϕ γ γ ϕ ( ) ϕ ϕ = = y l, y l, y = q y, y = q y, q = e > 0, q =, q = q =, () ϕ 0,, =,. From now on, sub-ndexes and wll denoe varables referred o apal and onsumpon good seor, respevely. Qualy s emboded n goods and, hene, he dfferene beween physal or quany uns and qualy or effeny uns maers. The wggle symbol (~) wll ndae ha he varable s measured n qualy uns. The quanes of apal and onsumpon good n ounry a me, y and y, are produed wh onsan reurns o sale Cobb-Douglas ehnologes. The produon funons use apal, ( ) and ( ), and labour, l and l, as faor npus. Faor nenses are assumed o be he same aross seors. The produon of goods n qualy uns or qualy-adjused oupu, ( ) y and y, omes from mulplyng qualy ndexes q and q ( ) by he respeve quanes. 7

8 In ounry q grows a an exogenous rae γ a eah perod, whle q, q and q reman onsan over me and ae he same value ha s normalsed o he un. Therefore, measuremen uns wll only be relevan for he apal good, sne he res of qualy ndexes are se equal o one. These assumpons mply ha ehnal hange n ounry s emboded n apal, and ha here s no ehnologal progress n ounry. The dfferene beween quany and qualy also maers for defnng relave pres of goods. In boh ounres he pre of a qualy un of onsumpon good s aen as numerary. 3 The pre of a physal un of apal a s denoed by p, whle one qualy un of apal oss p uns of onsumpon good. The relaonshp beween hese pres s: =. p p ( ) p p = q p p =, γ e () In he rade suaon super-ndex n pres wll dsappear, sne hey wll be deermned n nernaonal mares. A eah, frms reeve nome from sales and pay wages and nvesmen oss. Thus, NCF = p y p I w l ) and ne ash flows (NCFs) of frms are ( =, where I ( ) and I NCF y p I w l are apal good demands measured n physal uns (gross physal nvesmen), and w represens 8

9 he renal rae of labour or wage. I s assumed ha frms have a fxed number of equy shares ousandng ha s normalsed o one, and ha NCFs are pad ou as dvdends o he shareowners. 4 Therefore, he mare values of frms a me zero or pres per share a Π me zero, and Π 0, are equal o presen values of NCFs beween mes zero 0 and nfny, dsouned a he mare rae of reurn or neres rae ounry see o maxmze: r. Hene, frms n Π r ( τ) dτ 0 = 0 ( ) 0 e p y p I w l d, (3) Π r ( τ) dτ 0 = 0 ( ) 0 e y p I w l d. (4) The neres rae wll urn ou o be he rae of reurn o shareowners. Eques ssued by frms n apal and onsumpon good seors are perfely subsue and, onsequenly, hey mus have he same rae of reurn. The apal faor n he model s undersood as he Solow (960) jelly apal, whh s measured n qualy uns. As shown by Hulen (99), jelly apal an be expressed as = and = Q ( ) ( ), where Q ( ) Q s he average emboded ehnal effeny, and and ( ) are apal sos measured n physal uns (physal apal). Physal apal aumulaes wh physal nvesmen, whle he 3 The pre of a quany un of onsumpon good an also be onsdered as numerary, sne a qualy un amouns o one physal un. 4 Ths se-up s smlar o ha n Barro and Sala (995: 0). Negave dvdends are allowed, so he seup s well defned. 9

10 aumulaon of jelly apal depends on nvesmen n qualy uns, I = q I and I = q I ( ). Thus, he moon laws of apal n ounry ae he form: q I, = δ (5) = q I δ, (6) where he so of apal depreaes a he same rae δ > 0 n boh ounres and seors. Here and hroughou he paper, he do over a varable denoes dervave respe o me. In a rade suaon, qualy ndexes n he above expresson wll depend on wheher he apal good was produed n ounry or. Households Counres do no dffer regardng preferenes. Eah household n ounry derves uly of he onsumpon and maxmzes s neremporal uly dsouned a he posve rae ρ : 5 j ( q j ) σ ρ j = σ > σ 0 U 0 e d, 0, q =,, j =,, (7) where j denoes household s demand n ounry of onsumpon good produed n ounry j. The onsumpon n he uly funon s measured n qualy uns. However, sne qualy ndex of onsumpon good equals one, hs dfferene beomes rrelevan. Noe ha n a rade suaon household s onsumpon mgh beome he sum of wo demands. ( j ) j 5 Curren uly defnes as u = ln f σ =. 0

11 A eah me perod he represenave household reeves apal nome and labour nome, and faes he budge onsran: a = r a + w,,j =,. (8) j where a represens wealh, whh wll urns ou o be equal o he sum of mare values of frms n apal and onsumpon good seors. A me zero, eah household s endowed wh 0 > 0 qualy uns of physal. Thus, he value of he nal endowmen of apal onsues household s nal wealh: > gven ϑ 0 0, a 0 = 0 0, =,, (9) where ϑ ( 0) s he pre of one qualy un of apal owned by households a me zero... Agens Desons Ths subseon desrbes agens desons ha orrespond o he auary suaon. Seon 4 wll ndae he modfaons ha agens desons experene when he eonomes are n he rade suaon. Frms n Capal Good Seor The problem of he represenave frm n ounry onsss of maxmsng (3) subje o (5). The frs order ondons of he problem are expresson (5) and: ( ϕ ) ϕ w p l ϕ, = (0) r 0 ( τ) dτ λ e p + q = 0, ()

12 r ( τ) dτ 0 ϕ ϕ ϕ ( ) λ = e p l λ δ (), where λ s he urren Lagrangan mulpler. In addon, he ransversaly ondon lmλ = 0 mus be sasfed. Frms n Consumpon Good Seor Smlarly, he frm s problem n ounry onsss of maxmsng (4) subje o (6). The frs order ondons of he problem are expresson (6) and: ( ϕ ) ϕ (3) w l ϕ =, r 0 ( τ) dτ λ e p + q = 0, (4) r ( τ) dτ 0 ϕ ϕ ( ) ϕ λ = e l λ δ (5), where λ s he urren Lagrangan mulpler. The soluon of he problem mus also sasfy he ransversaly ondon lmλ = 0. Households The represenave household n ounry maxmses (7) subje o (8) and he nal endowmen n (9). The frs order ondons of he problem are (8) and: σ ( j ) μ = 0, (6) = μ μ ρ r, (7)

13 where μ s he dsouned Lagrangan mulpler. The soluon of he problem has also o sasfy ha lm e μ a 0 =. 3. The Auary Suaon The nex wo subseons solve for he auary equlbrum n eah ounry. The ompeve equlbrum s a se of alloaons and pres ha sasfy frms and households problems, and ha lear all mares n eah eonomy. More onreely, he equlbrum n onsumpon and apal good mares requres ha = y and = + y I I. Appendx A onans he deals on he alulaons. 3.. Auary Equlbrum of Counry Two equvalen expressons for neres rae are obaned afer some manpulaon of (), (), (4) and (5). The equalzaon of hese wo expressons perms o wre he relave pre per physal un as: ϕ = l = ϕ δ + ϕ p l r q r y p q y p = ϕ + p p δ p. (8) The mare rae of reurn n (8) nludes ne margnal produvy of apal and he hange n he pre per qualy un. The faor alloaon among seors an be obaned from expressons (0), (3) and (8): κ, -κ κ = l, -κ = l, (9) 3

14 where oal apal of he eonomy s equal o he sum of frms apal n boh seors, ha s, = +. Counry s auary pres ome from nrodung he resuls n (9) n he relave pre n (8): = = (0) p, p. e γ Therefore, one physal un of apal oss one un of onsumpon good, whle he pre of one qualy un of apal srly dereases over me. The faor alloaon n (9) and auary pres perm o wre he neres rae n (8) n erms of oal apal: γ ϕ = δ γ () r e. The long run equlbrum of ounry s haraersed by a balaned growh pah (BGP), n whh apal and onsumpon grow a a onsan rae, and proporons and l κ reman onsan over me. From now on, he omsson of me n varables wll denoe saonary values over he BGP. A onsan growh rae for onsumpon requres ha neres rae holds onsan. Loong a () and (), follows ha apal and he produon of apal n qualy uns grow a a hgher rae, θ, han onsumpon and he produon of apal n physal uns, ϕθ : γ θ = θ = θ = θ ϕθ = θ = θ (), y, y ϕ. 4

15 Tehnal hange emboded n apal nfluenes he growh of y ( ) q γ ), bu also nreases Q ( ) nrease n drely rases oupu ( oupu (ϕγ ). Lasly, an nrease n q physal apal and oupu ( ( ) n hree ways. An and onsequenly nreases physal nvesmen and hene ϕ γ ϕ ). The mpa on he growh of y and y only nludes he wo las effes. Ineres rae a long run derves from he Euler equaon governng onsumpon evaluaed over he BGP. Consderng expressons (6), (7), () and (), neres rae a long run resuls o be r = σθ +ρ. The resoures alloaon over he BGP an be obaned from apal aumulaon (addng up (5) and (6)), he Euler equaon, and () and (): ( + ) ( + ( ) ) ϕθ δ ϕ γ ϕ δ κ = l = =. r + δ + γ σϕγ + ϕ ρ + δ + γ (3) In boh seors, an addonal un of apal yelds he margnal produvy of apal ( r δ γ + + ). Aordng o desons on onsumpon and savng, a par ϕ ( θ δ) + of suh addonal un s alloaed o apal good seor, whle he res s alloaed o he produon of onsumpon good. 3.. Auary Equlbrum of Counry The auary equlbrum of ounry mmedaely follows from ounry s, sne he only dfferene s γ = 0. Therefore, ounry s auary pres boh per quany and per qualy un are onsan: 5

16 p p. = = (4) From he expresson of neres rae n equlbrum, r ϕ = δ, s lear ha he long run equlbrum of ounry s a seady sae n whh all varables hold onsan hrough me. Thus, hs eonomy does no enjoy susaned growh. The neres rae n seady sae equals he dsoun rae of uly, r = ρ, and he proporon of apal and labour alloaed o he apal produon s equal o κ l ϕδ ( r δ ) = = The Free Trade Suaon Capal goods produed by ounres are no homogeneous. A physal un of apal produed n ounry embodes more qualy uns han one un generaed n ounry. Therefore, he omparave advanage of ounres mus be deermned by he omparson of relave pres per qualy un of apal. To hs respe, expressons (0) and (4) learly demonsrae ha ounry and have omparave advanage n he produon of apal and onsumpon good, respevely. The nex sep s o show ha he rade suaon n he long run may be haraersed by eher omplee spealzaon or nomplee spealzaon of ounry. Some ehnal deals an be found n Appendxes B and C. 4.. Trade Equlbrum under Complee Spealzaon Under omplee spealzaon resoures of ounry and are enrely alloaed o apal and onsumpon good seors, respevely. Aordngly, frm s problem n onsumpon and apal good seor does no apply for ounry and, respevely. 6

17 The ompeve equlbrum of he world eonomy mples ha a par of apal good produon s expored o ounry and he res s used whn ounry, = + y I I. Smlarly, a par of onsumpon good produon s expored o ounry, whle he remanng produon s onsumed whn ounry, = + y. Moreover, he rade balane mus be always n equlbrum, p I =. The las equlbrum ondon an be rewren n erms of he expored-mpored proporons of goods by ounres as: ϕ I v u, v p =. y y u (5) Ineres raes of ounres are obaned by proeedng as n he auary suaon: γ ϕ r = ϕe δ + γ, γ r e p p ϕ p = ϕ ( ) δ + γ, p p (6) The long run equlbrum of he world eonomy s a BGP n whh apal and onsumpon n boh ounres grow a a onsan rae, and proporons u and v reman onsan over me. From he law of moon of apal of ounres evaluaed over he BGP follows ha. Several resuls an be derved from hs = ( ) u u relaonshp beween apals. Frs, long run growh raes of ounres are denal o ounry s n auary: γ θ =, θ = θ = θy, ϕθ = θ = θy, =, (7) ϕ 7

18 Seond, neres rae of ounres equalze a long run and hene ( ) ( ) = v ( u) and u = v. Therefore, rade does no lead o wage equalzaon among ounres. Thrd, gross world nome s spl among ounry and n he proporons u and u, respevely. Lasly, he pre of a physal un of apal s onsan, whle he pre per qualy un srly dereases over me. The value of u s obaned from he law of moon of apal of eher ounry or, he Euler equaon and long run growh raes, and ondes wh ha n (3). Thus, nernaonal relave pres over he BGP are: where ϕ ϕ u u p =,p =, γ u e u ( + ( ϕ) δ) ( ) ϕ γ u =. σϕγ + ϕ ρ + δ + γ (8) The omparson beween auary pres n expressons (0) and (4), and nernaonal pres over he BGP n (8) reveals ha rade a long run wll be haraersed by omplee spealzaon of ounres only n he ase ha u : p p > p p. f ( + ( ϕ) δ) ( ) ϕ γ σϕγ + ϕ ρ + δ + γ, (9) Counry wll always evenually ompleely spealze n he produon of onsumpon good. However, ounry wll ompleely spealze only f s share n gross world nome s greaer han or equal o a half. A onluson from he resuls n hs subseon s ha ounry mpors susaned growh smply by radng. The mprovemen n ounry s erms of rade onsues he 8

19 dffuson mehansm. Ths fndng omes ou from dfferenang ounry neres rae over he BGP wh respe o me: ϕ p γ r = ϕ( ) δ γ = =. p ϕ p ϕ (30) I s obvous from expressons (8) and (30) ha growh s generaed by an mprovemen n he erms of rade of ounry. The onsumpon good s nreasngly expensve n nernaonal mares, whh prevens he value of he margnal produvy of apal from fallng n ounry, n spe of dmnshng margnal produvy of apal. Thus, free rade s benefal for ounry beause perms an nrease n real nome and welfare. However, he remarable benef here s ha ounry s allowed o susanably grow. A seond onluson arses from hs subseon, namely he rual mporane of onsderng qualy-adjused nernaonal pres. The omsson or msreamen of qualy hanges may lead o naurae onlusons regardng he mehansm hrough whh rade operaes n ransmng growh. If qualy hanges n he model were gnored, ounres erms of rade p ( ) would be onsan n he long run, and expors and mpors n quany uns would grow a he same rae ϕθ. The observaon of hose fas would lead o he wrong onluson ha openness mpas growh hrough he rade volume. A orre reamen of relave qualy hanges would show ha ounry s erms of rade p ( ) permanenly mprove, and s expors n qualy uns grow a a lower rae (ϕθ ) han s qualy-adjused mpors (θ ). I s obvous ha ounry s rade volume onnuously nreases, bu hs s due o he me evoluon of he erms of rade. 9

20 4.. Trade Equlbrum under Inomplee Spealzaon Trade wll be haraersed by nomplee spealzaon f he ondon n (9) does no hold. In hs ase, ounry produes boh apal and onsumpon good, expors he frs good and mpors he laer one. Counry only produes he good of onsumpon and, onsequenly, he frm s problem n apal good does no apply. Therefore, he y = I + I + I ), ompeve equlbrum of he world eonomy mples ha ( y = and y ( ) = ( ) + ( ). The rade balane of ounres mus also be n equlbrum. Sne ounry produes boh goods, resoures mus be alloaed among seors. The same seps followed n he auary ase perm o show ha he resoures alloaon s denal o ha n (9), p ( ) and p ( ) onde wh ounry s auary pres n (0), and neres raes of ounres are equal o hose n (6), bu wh p( ) =. Consderng expored-mpored proporons of goods defned n (5) and he above resuls, he exernal equlbrum ondon an be rewren o oban a relaon beween ounres apal sos: ϕ v p =. = (3) u l The long run equlbrum of he world eonomy s agan a BGP, n whh apal and onsumpon n boh ounres grow a a onsan rae, and κ ( ), l, u and v hold onsan over me. From he requremen of onsan neres raes a long run, follows ha he growh raes of ounres are he same as hose n (7). The equalzaon 0

21 of neres raes mples ha = ( ) and, from (3), ha v ( u ) l =. The fa ha apal sos beome equal n he long run also mples ha wage equalzes among ounres. The value of u s obaned usng he laws of moon of apal of boh ounres. The value of l omes from he law of moon of apal of eher ounry or and he Euler equaon. The nex expresson onans hese values: ( + ( ϕ) δ) ϕ γ u =, l =, v= l ( u). (3) σϕγ + ϕ ρ + δ + γ Over he BGP all relave pres equalze among ounres and, hene, he long run equlbrum replaes he equlbrum of a fully negraed world eonomy. In addon, he rade suaon under nomplee spealzaon leads o ounres onvergene n per apa nome. The prevous fndngs perm o wre gross world nome (GWI) and gross domes nome of ounry and ( GDI and GDI ) as: γ γ ( ) ϕ ϕ ( ) ϕ ( ) ( ) GWI p e y + y = +, GDI p e y + y = l + l, GDI y =, ϕ ϕ (33) Afer mposng = n (33), beomes lear ha ounres shares n GWI are equal o one half. The world produon of onsumpon good, y, s also equally dsrbued among ounry and : + = ( )( ) + ( ) = ( )( ) ϕ ϕ ϕ l v, v, + l + v v = =, = =. y l y l (34)

22 Sne all faor npus n ounry are devoed o produe onsumpon good and labour s a non-reproduble faor, boh faor alloaon and expor deson n ounry wll depend on ounres relave amouns of apal. If ounry s apal so sars beng hgher han ounry s, hen durng he ransonal perod he reurn o apal wll be lower n he frs eonomy han n laer one. Consequenly, he proporons l and u are nally low, and rase as ounry aumulaes apal and he gap beween neres raes narrows. Inenves o modfy faor alloaon and expor deson n ounry ease o exs when, ha s, when pres of boh ounres = equalze. Over he BGP, mpors from ounry allow ounry o double he proporon of labour and apal o produe apal good wh respe o he auary suaon. Therefore, he onluson s agan ha free rade propagaes permanen growh o ounry. The explanaon for hs resul s he same as n he ase of omplee spealzaon. Lasly, onvergene n per apa nome omes ou as a hrd benef ha ounry obans from free rade. 5. Conluson Ths paper has shown ha a sagnan eonomy an overome dereasng reurns o apal aumulaon and susanably grows f s erms of rade permanenly nrease. The onnuous mprovemen n he qualy of mpored apal goods relave o expored onsumpon goods s he reason why hs ours. Thus, he effes of rade on growh operae hrough relave pres. Moreover, ounres onverge n per apa nome f rade s haraersed by nomplee spealsaon.

23 Three man onlusons arse from hese fndngs. Frs, erms of rade movemens an a as an engne of growh for sagnan eonomes. The exsene of mehansms o absorb foregn ehnologal progress s no neessary for he ransmsson of susaned growh o ae plae, sne ehnal advanes are emboded n mpored npus. Seond, o properly adjus he erms of rade for qualy hanges of mpored-expored goods s rual for denfyng he hannels hrough whh rade mpas growh. In hs sense, he omsson or msreamen of qualy hanges mgh lead o he wrong onluson ha rade affes growh hrough rade volume, nsead of hrough relave pres. Lasly, openness may emerge as an mporan fore leadng o ounres onvergene n per apa nome, even hough poor eonomes do no possess an own soure of permanen growh. Therefore, he radonal lose-eonomy approah for he sudy of onvergene should be reonsdered. As sad above, he denfaon of he erms of rade movemens as an engne of growh requres of qualy-adjused nernaonal pres. Though some publ sasal agenes, as he Ameran BLS, have made a onsderable effor n provdng researhers wh qualy-adjused pres, he avalable daases do no nlude nformaon for developng ounres. Ths sasal nformaon would open broad avenues for fuure empral and heoreal researh on he role of erms of rade movemens n promong growh. Referenes Ahuorala, Prema-handra, (993), Manufaured Expors from Developng Counres and Ther Terms of Trade: A Reexamnaon of he Sarar-Snger Resuls, World Developmen, (0), Oober,

24 Ahuorala, Prema-handra, (998), Trade Poly Issues n Asan Developmen, London and New Yor: Rouledge. Ahuorala, Prema-handra, (000), Manufaured Expors and Terms of Trade of Developng Counres: Evdene from Sr Lana, Journal of Developmen Sudes, 36(5), June, Barro, Rober and Xaver Sala--Marn, (995). Eonom Growh, New Yor: MGraw Hll. Ben-Davd, Dan and Ayal Kmh, (004), Trade and he Rae of Inome Convergene, Journal of Inernaonal Trade and Eonom Developmen, 3(4), Deember, Ben-Davd, Dan and Mharl B. Loewy, (003), Trade and he Neolassal Growh Model, Journal of Eonom Inegraon, 8(), Marh, -6. Coe, Davd T., Elhanan Helpman, and Alexander W. Hoffmaser, (997), Norh-Souh R&D Spllovers, Eonom Journal, 07(440), January, Cummns, Jason G., and Govann L. Volane, (00), Invesmen-Spef Tehnal Change n he Uned Saes ( ): Measuremen and Maroeonom Consequenes, Revew of Eonom Dynams, 5(), Aprl, Dewer, W. Erwn and Caherne J. Morrson, (986), Adjusng Oupu and Produvy Indexes for Changes n he Terms of Trade, Eonom Journal, 96(383), Sepember, Fan, C. Smon, (004), Qualy, Trade and Growh, Journal of Eonom Behavor and Organzaon, 55(), Oober,

25 Greenwood, Jeremy, Zv Herowz, and Per Krusell, (997), Long-Run Implaons of Invesmen-Spef Tehnologal Change, Ameran Eonom Revew, 87(3), June, Harrson, Ann, (996), Openness and Growh: A Tme Seres, Cross Counry Analyss for Developng Counres, Journal of Developmen Eonoms, 48(), Marh, Hulen, Charles R., (99), Growh Aounng when Tehnal Change s Emboded n Capal, Ameran Eonom Revew, 8(4), Sepember, Hwang, Jason and Jeffrey G. Wllamson, (003), The Terms of Trade and Eonom Growh n he Perphery, , NBER Worng Paper No Jones, Charles I., (994), Eonom Growh and he Relave Pre of Capal, Journal of Moneary Eonoms, 34(3), Deember, Keller, Wolfgang, (00), Trade and he Transmsson of Tehnology, Journal of Eonom Growh, 7(), Marh, 5-4. Keller, Wolfgang, (004), Inernaonal Tehnology Dffuson, Journal of Eonom Leraure, 4(3), Sepember, Kohl, Ulrh, (004), Real GDP, Real Domes Inome, and he Terms-of-Trade Changes, Journal of Inernaonal Eonoms, 6(), January, Lee, Jong-Wha, (995), Capal Goods Impors and Long-Run Growh, Journal of Developmen Eonoms, 48(), Oober, 9-0. Murphy, Kevn M. and Andre Shlefer, (997), Trade and Qualy, Journal of Developmen Eonom, 53(), June, -5. 5

26 Rvera-Báz, Lus and Paul M. Romer, (99), Eonom Inegraon and Endogenous Growh, Quarerly Journal of Eonoms, 06(), May, Saellars, Pluarhos and Danel J. Wlson, (004), Quanfyng Emboded Tehnal Change, Revew of Eonom Dynams, 7(), January, -6. Sarar, Prabrj and Hans W. Snger, (99), Manufaured Expors of Developng Counres and Ther Terms of Trade Sne 965, World Developmen, 9(4), Aprl, Solow, Rober, (960), Invesmen and Tehnal Progress, n Kenneh J. Arrow, Samuel Karln, and Par Suppes (eds.), Mahemaal Mehods n Soal Senes, Sanford, C.A.: Sanford Unversy Press. U.S. Deparmen of Labor (Bureau of Labor Sass), Inernaonal Pre Program, hp:// Appendx A Ths appendx desrbes he seps o solve he auary equlbrum of ounry. The desrpon onernng ounry equlbrum s omed. The ompeve equlbrum requres ha mares n he eonomy lear. The learng ondons for fnal and apal good mares appeared n he ex. The learng ondon of labour mare has been already nrodued n he model. If hese mares lear, hen equy mare also lears, a Π ( ) Π ( ) = +. The fulflmen of he las ondon follows from dfferenang he value of frms a, addng up hem, and nrodung he oher learng ondons: 6

27 a Π + Π = r Π + Π a y w p y + p I + I + w l + w l y. (A.) I also holds ha he sum of frms values s equal o he value of oal apal, = Π + Π, and ha 0 p ( 0 ) p ϑ =. Ths resul an be easly proven proeedng as Barro and Sala (995: 0). The dfferenaon of expressons () and (4) respe o me yelds: λ p q p q r = λ λ, r. λ + p q = + p q (A.) Expresson (8) omes from pluggng () no (), and (4) no (5), and nrodung he resulng expressons no (A.). The Euler equaon s obaned dfferenang (6) respe o me and pluggng (7). Ths equaon evaluaed over he BGP perms o ge: ϕ( ϕ) ϕγ ϕ ϕ γ γ σϕγ + ϕ ρ + δ + γ = e ( ) δ γ e ( ) =. ϕ (A.3) Addng up (5) and (6) and evaluang he resulng expresson over he BGP allow obanng he value for n (3): l = κ n (A.3) ϕ γ γ = l e δ. (A.4) ϕ Lasly, he ransversaly ondons an be rewren as: 7

28 λ λ μ a 0, 0, - < 0. (A.5) λ λ μ + < + < ρ + + a Expressons (A.), (7) and (), and he long-run value for neres rae perm o show ha he fulflmen of (A.5) requres ha: ϕγ θ < r ( σ) ρ < 0. (A.6) ϕ Hene, he usual ondon ha a long run neres rae mus be greaer han he growh rae of onsumpon mus hold n order for dsouned uly o be bounded. The fulflmen of (A.6) ensures ha he value n (3) s smaller han one, ha s, κ = l ( 0,). Appendx B Ths appendx onenraes on some deals on he alulaons of rade equlbrum under omplee spealzaon. Those alulaons ha an be easly derved from he explanaons n he ex and n he prevous appendx are omed. The ompeve equlbrum of he world eonomy mples he learng ondons n he ex are sasfed and, hene, ha a = Π ( ) and Π ( n he prevous appendx, s obaned ha: a = ). Proeedng as a a Π = r Π + w p y p I, a a Π = r + w y p I. Π (B.) 8

29 Consderng he defnons n (5), he aumulaon of apal of ounres an be rewren as: y y = u δ, = ( u) δ. (B.) Sne he growh raes of apal equalze a long run, follows ha u= v. Appendx C Ths appendx explans he dervaon of some resuls n subseon IV.. As n Appendx B, only some alulaons wll be desrbed. Mare learng ondons mply ha: a ( ) ( ) a w Π + Π = r Π + Π + w l + w l p y p I + I y, (C.) and he seond expresson n (B.). The value of u s obaned by proeedng as n Appendx B, bu s frs neessary o add up (5) and (6) for ounry. The long run value of ϕ γ s alulaed usng e he Euler equaon, and ondes wh ha n (A.3). Gven u, ( ) γ e ϕ and he resul ha θ θ =, he moon law of apal of eher ounry or perms o solve for l = κ : y y = ul δ, = ( u) l δ. (C.) 9