TRAD, DVLOPMNT AND CONVRGING GROWTH RATS Dynamic Gains From Trade Reconsidered * Theo S. icher Deparmen of conomics Universiy of Washingon Seale, WA 98195 (206) 685 8082 e@u.washingon.edu ABSTRACT: Wihin an endogenous growh framework, we examine dynamic gains from rade for paramerically disinc counries. In he absence of inernaional spillovers or facor mobiliy, previous endogenous growh models generally imply ha rade in goods mus amplify differences in (1) facor endowmens, (2) raes of echnical change and (3) economic growh. ven he dynamic HOS model suggess ha rade inensifies differences in endogenous facor endowmens. In conras, we presen a model where rade in goods alone is sufficien o reduce differences in raes of growh, echnological change and facor endowmens beween leader and laggard economies. The key o he reducion in he gap in growh raes is ha boh human capial and echnological change are no jus endogenous, bu ha heir respecive coss of accumulaion inerac. Since skilled and unskilled labor is endogenous, we can also derive implicaions for cross-counry relaive wage movemens. Key Words: Trade, Convergence, Dynamic Gains, Uneven Growh. (JL F43, 031) Seale, WA 98195, (206) 685 8082, e@u.washingon.edu *I hank wo referees and he edior for careful commens and criicism. I am also graeful o Richard Clarida, Vivek Dehejia, Ronald Findlay, Duncan Foley, Panelis Kalaizidakis, Rober Mundell, B. Ravikumar and Dani Rodrik for encouragemen and helpful suggesions. I also hank seminar paricipans a he Universiies of Pennsylvania, Washingon, Briish Columbia, Souhern California, California Sana Cruz, and he conomeric Sociey s World Congress and he ASSA Meeings for commens. Any errors are my own. 1
I. Inroducion The purpose of his paper is o analyze how inernaional rade affecs facor endowmens, echnical change, and growh, in paramerically disinc economies. The Heckscher Ohlin model, enriched o accoun for endogenous facor accumulaion, predics ha rade amplifies iniial differences in facor endowmens and comparaive advanage. 1 In he absence of capial mobiliy or inernaional knowledge spillovers, endogenous growh models carry even more discouraging implicaions for laggard economies. In his case, rade beween paramerically disinc economies reinforces he posiion of he echnological leader, inensifies he iniial paern of comparaive advanage and increases he dispariies in facor endowmens o furher uneven growh. The implicaion of divergence beween leader and laggard economies in open economy models can cerainly be prevened by assuming inernaional spillovers or facor mobiliy. 2 The conribuion of his paper is o prove ha rade in final goods alone suffices o narrow he echnology gap, and ha spillovers or facor mobiliy are no necessary condiions for condiional convergence wihin an endogenous growh srucure. We also show ha he uneven growh resuls in he previous lieraure depend on he assumpion ha eiher echnology or facor endowmens are endogenous. For example, in models of endogenous echnological change (e.g. Romer 1990), a key deerminan of he growh rae is human capial, whose sock is assumed exogenous. As counries open up o inernaional rade, he reurns o skilled labor change while heir sock do no. Hence rade ends o reinforce raher han aler he exising paern of comparaive advanage as he leader counry generally enjoys dynamic gains, while he laggard economy experiences comparaively minue gains, if no losses. Feensra (1996) shows ha he leader s growh rae may only be slowed in he special case where demand for he R&D inensive good is inelasic. 3 In conras, our model begins wih he premise ha boh endowmens and echnology are endogenous, and ha heir respecive coss and benefis of accumulaion inerac. We 1 This is shown in Sigliz (1970) and Findlay and Kierzkowski (1983) for physical and human capial accumulaion, respecively. 2 Feensra (1996) provides an overview of models and condiions ha imply eiher convergence or uneven growh due o inernaional rade. 3 In his special case he auarchy equilibrium does no exis. 2
show ha i is his ineracion ha generaes he rade induced dynamic gains ha serve o narrow echnology and growh gaps. Our approach is complemenary o previous models of endogenous echnological change ha focus on privae incenives o inves in research (Grossman and Helpman 1991), or on serendipious learning (Young 1991). Here, we specify ha privae incenives induce agens o inves in skills by enering an educaion secor o be insruced by skilled labor. The by-produc of he educaion process is non-rival echnology, whose absorpion ino producion requires skilled workers wih knowledge of he specific vinage. When high and low Tech secors differ in skill-inensiy and echnological sophisicaion, echnological change generaes srong skill-biased labor demand ha exers upward pressure on he relaive wage. This change in he relaive reurns alers no only he cos and benefi of invesmen in human capial, bu also he allocaion of skilled labor beween invening and absorbing echnology. The model endogenously deermines he relaive demand, supply and wage of skilled workers, heir allocaion beween he research and producion, and he raes of echnological change and growh. We label he counry which possesses an endogenously larger supply of unskilled labor, and a comparaive advanage in he Low Tech good he laggard. A change in he erms of rade alers he coss and benefis of boh, human capial invesmen and invenion/absorpion of echnology. Afer opening up o he world s goods marke, he laggard experiences an iniial saic conracion of is skillinensive, echnologically progressive High Tech secor. This lowers he relaive wage of skilled workers and frees resources o expand research and educaion. The resuling dynamic increase in he supply of skilled workers and he rae of domesic innovaion allows he laggard o reduce he gaps in echnology, facor endowmens and growh raes. Since he model feaures skilled and unskilled workers, he srucure also provides implicaions for rade induced relaive wage movemens across counries. High relaive wages and scarciy of skilled labor are ofen menioned as major impedimens o economic growh in laggard counries. Boh feaures of he laggard are generaed endogenously in our model under auarky. Free rade is shown o narrow he relaive wage gap across counries, wih rising wages in he advanced counry and falling 3
relaive wages in he laggard. 4 Previous models sugges similar dynamics. Cariglia (1992) emphasizes he same resource rade off beween oupu and educaion, while Grossman and Helpman (1991, ch. 6) feaure he rade off beween oupu and research which acceleraes growh in he laggard counry in our model. 5 The difference in our paper is ha we examine he effecs when boh radeoffs are endogenous and inerac. In a model of learning by doing, Young (1991) characerizes one of five possible equilibria as one where a laggard migh be capable of closing he echnology gap o he leader. For his equilibrium o occur, he iniial echnology gap mus no be oo large, and he populaion size mus be several orders of magniude greaer in he laggard. Our resuls are independen of iniial condiions or populaion size. While he empirical lieraure on rade and growh is diverse, i does no seem o suppor uneven growh resuls. The iniial comprehensive sudy by Levine and Renel (1992) found no direc effec of rade policy on growh, bu heir posiive correlaion beween rade and invesmen suggesed ha he effecs of rade liberalizaions could operae hrough enhanced resource accumulaion. Subsequen work wih large samples of 30 o 95 developing counries (Dollar 1992 and dwards 1992, 1993) show ha rade liberalizaions improved growh performance. Harrison (1995) surveys he lieraure and inroduces robus evidence ha greaer openness is associaed wih higher growh. Focusing solely on OCD counries, Ben-David (1993) finds ha he iming of rade liberalizaions has been srongly linked wih rade and income convergence in he C. II. The Two Secor conomy This secion oulines he model, which exends he wo secor closed economy in icher (1996) o he hree secor open economy. The join producion in he educaion secor is also essenially equivalen o he one assumed by Fershman, Murphy and Weiss (1996). Consider an 4 This rend is confirmed by Davis (1992) who examines cross-counry relaive wage paerns. 5 Invesmen in human capial is exogenous in Grossman and Helpman (1991, ch 6.), bu heir fifh chaper offers a mechanism o endogenize human capial. Combining he wo chapers implies, however, ha rade leads o a widening of he difference in human capial endowmens. 4
overlapping generaions model wih agens who live for wo periods. One High Tech and one Low Tech consumpion good is manufacured in disinc secors ha differ in echnological sophisicaion and skill-inensiy. An educaion secor produces embodied knowledge (skills) and non-rival knowledge (blueprins) in join producion. In each period, young agens decide eiher o accumulae human capial by enering an educaion secor as sudens, S, or o work in producion as unskilled workers, U. Sudens consiue he fuure sock of skilled workers who choose beween employmen in he educaion secor, or in High Tech producion. Unskilled workers save and consume when young and (for simpliciy) reire when old. To finance human capial invesmen and consumpion, sudens borrow agains heir fuure income a an endogenous ineres rae ha equaes borrowing and saving. Formally, he educaion secor employs eachers, P, sudens, S, and he cuing edge echnological vinage, v (he echnology invened las period), o produce a new, non-rival echnological vinage, v+1. Young agens and eachers ener he educaion secor a an exogenously specified suden-eacher raio, γ 6, [ ] v - v = µ v min γ P,S γ > 1; µ > 0, (1) +1 where µ is a produciviy parameer. We could decompose (1) ino wo alernaive, even simpler, represenaions v+1 - v = v µγp, (1a) and γp = S (1b). The decomposiion highlighs ha he educaion secor is an amalgam of he sandard research secor (1a) in models ha follow Romer (1990), and he simples formulaion of he educaion process (1b), firs inroduced by Bhagwai and Srinivasan (1977). The direc (uiion) cos per suden, z, jus equals he eacher-suden raio imes he eachers wage, w P γ, which implies ha privae incenives o inves in educaion finance non rival echnological change. While he endogenous sock of skilled labor is consan in equilibrium, echnology coninues o evolve resuling in endogenous increases in he qualiy of he sock of educaed workers. The economy manufacures wo consumpion goods. The High Tech good uilizes he cuing edge echnological vinage, v, and unskilled workers, U H, who perform rouine asks. To absorb ever imposes γ. 6 Alernaively, one could follow Shell (1966) by specifying ha a research manager, who maximizes oupu, 5
new echnologies he High Tech secor also employs skilled labor,, wih knowledge of he vinage H = v U ρ H 1- ρ 0 < ρ < 1. (2) Once a echnology has been absorbed ino producion, is use requires only unskilled workers. Thus, he Low Tech consumpion good, employs only old echnology, v 1, and unskilled labor, U L, o perform he now rouine asks L = v-1δ U L ; δ > 0, (3) Producion of he High and Low Tech goods akes place in perfecly compeiive secors. We choose he price of he High Tech good as he numeraire hroughou, so ha π represens he relaive price of he Low Tech good. The facor marke equilibrium requires ha unskilled workers wages are equalized across secors, w UL which is he marginal produc in he High Tech secor, w = w UH, and ha he wages of eachers equal heir opporuniy cos, P = w. quaing he marginal producs of unskilled in he wo secors yields an expression for he unskilled o skilled worker raio in he High Tech secor, which can be simplified by using equaion (1). To derive he relaive wage in he economy we subsiue his expression ino he relaive wage of he High Tech secor o obain w w = ρ 1- ρ U 1+ µ S δ π -1 ( 1- ρ) -1 1 ρ. (4) In parial equilibrium, he relaive wage is decreasing in he relaive price of he Low Tech good. Neverheless, he producion srucure yields a posiive, ineracive relaionship beween pas human capial invesmen and oday s relaive wage (or, beween pas echnological change and oday s skilled labor demand). The feaure of he model ha drives his posiive ineracion is ha he wo secors differ no only in facor inensiies bu also in echnological sophisicaion. More human capial invesmen raises no only he fuure sock of skilled workers, bu also finances more echnological change ha mus be absorbed ino producion. Given he srucure of he wo secors, he absorpion process is skill inensive and creaes skill-biased labor demand ha dominaes he increase in he supply of skilled workers. To close he producion side, we specify zero populaion growh, which allows us o normalize he size of each generaion o uniy. The labor consrains in period hen becomes 6
U = U L + U H, (5) 1 = S + U, (6) S-1= P +. (7) III. Uiliy Opimizaion Individuals share idenical ases, and he preferences of hose born a ime can be represened by a wo-level uiliy funcion. An agen born in period consumes C1 when young and C2+1 when old. The upper level uiliy funcion may wrien as = β β (8) k W lnc 1 + lnc 2 +1, > 0, where k=u, S superscrip represens he respecive career pahs of sudens and unskilled workers. To minimize noaion, we suppress his superscrip unless necessary. Wihin a represenaive period, he insananeous subuiliy over High and Low ech consumpion for young and old can be expressed as We now define per capia expendiures in period, y k i, as lnc i = α ln c i L + ln c i H, α > 0; i = 1,2. (9) y k L H = π c + c (10) i i i Then, from our specificaion of he subuiliy in equaion (9), demand for he wo goods by a consumer in period saisfies π c L i H = αc (11) i To deermine he sock of sudens we examine he ineremporal allocaion in erms of saving and borrowing. From equaions (8)-(11) we derive he indirec uiliy for each individual born a ime [ ] ( ) ( 1 1 ) π α β +1 (8') k k k k V y, = 1+ ln y + lny, plus a consan erm, which reflecs he ime pah of relaive prices. ach unskilled worker receives a wage when young and saves, x, for reiremen. ach suden borrows, b, agains fuure income o finance uiion, z, and firs period consumpion. Thus, he respecive budge consrains of unskilled and skilled workers are, y U = w U - x, (12) 7
U y +1 y S y = x(1+r). (12 ) = b - z, (13) = w + 1 - b(1+r). (13 ) Subsiuing he respecive consrains in o he objecive funcion (8 ) yields firs order condiions ha can be solved for per capia borrowing and saving, respecively x = θ w, (14) U b = θ z + w+1, (15) β(1+ r ) where θ β / (1 + β) 1 denoes he marginal propensiy o save. Since skilled workers receive a wage when old, heir opimal borrowing is increasing in heir fuure discouned income ( w / β 2(1+r)). + 1 More paience ( β increases)3 depresses sudens demand for funds, since more consumpion is deferred ino he fuure. Higher uiion, z, decreases he presen period consumpion possibiliy and induces sudens o ransfer income from he fuure o he presen hrough increased borrowing. Borrowing and saving are regulaed by an endogenous ineres rae. The financial marke clearing condiion requires ha oal borrowing equals oal saving, or Sb = Ux. Using his clearing condiion and subsiuing for (14) and (15) yields an ineres rae ha is coningen on he relaive supply of skilled labor. w+1 1+ r = U U β w z S. (16) The marke clearing ineres rae reflecs he simple supply and demand for credi by individuals. The larger he supply of unskilled labor (sudens), he lower (higher) he ineres rae. The higher he discouned reurn o educaion (unskilled labor), he greaer (lower) he demand for credi and he higher (lower) he ineres rae. To close he model, he deerminaion of he equilibrium ineres rae, and hus he sock of sudens, requires he addiional condiion ha agens mus be idenical beween career pahs, or W U S = W. Since agens share idenical uiliy funcions, and face idenical ineremporal raes of 8
ransformaion we know ha y U = y S and y U +1 = y. We can now equae (12) and (13) and subsiue for opimal borrowing and lending from (14) and (15), plug in for he ineres rae (16) and use he labor consrain (6) o derive invesmen in human capial S θ = w + 1 γw (17) quaion (17) ogeher wih equaion (1), immediaely deermines he sock of human capial allocaed o he educaion secor, P. The sock of sudens depends posiively on he consan saving rae, θ, because i increases savings and lowers he ineres rae. Alernaively, we can wrie equaion (17) as ( ) U S = θ w / w / γ + w, 1 which highlighs he posiive effec of increased lending, θ w, and he U U negaive impac of an increase in he direc (uiion) and indirec (opporuniy) cos of human capial invesmen ( w / + w U ) γ. Noe ha an increase in w raises he uiion expense, and hus effecs he sock of sudens oday negaively. Tha sudens care abou he wage hey receive as skilled workers when old, which has been facored ino he ineres rae (16). Having obained he sock of sudens, we derive he equilibrium ineres rae U ( ) 1+ r = w+1 w + w / γ, which urns ou o simply be he benefi/cos (direc and indirec) raio of invesing in human capial. Higher invesmen in human capial creaes a higher rae of echnological change, whose fuure absorpion ino producion raises he relaive wage. As sudens expec he relaive wage o rise omorrow, heir borrowing demand rises, which increases he ineres rae. Simply saed, as higher economic growh raises he marginal rae of subsiuion, i mus also raise he marginal rae of ransformaion. IV. Auarky quilibrium H H L L In auarky, domesic supply mus equal demand, or c + c = H and c + c = L. Afer aggregaing per capia consumpion as expressed in equaion (11) over all individuals, we obain an 1 2 1 2 expression for he demand price from he inverse relaive demand funcion, ( c 2 H + c1 H ) ( c 2 L + c1 L ) π α α = = 9 H L, Given equaion (18), we can use he facor marke clearing condiion w UL = w UH (18) ogeher wih he
producion srucure (1)-(4) and he labor consrains (5), (6) o deermine he relaive price and he relaive wage, respecively π = ( 1+ µ S )( ρ) 1 1 ( 1 ρ + α)( S 1 S γ ) δ ( 1 ρ)( 1 S ) w w U = ρ( 1 S ) ( 1 ρ + α)( S S γ ) 1 ρ (19) (20) The relaive wage in he closed economy deserves a closer look. As discussed above, he parial equilibrium effec of increased pas invesmen in human capial is o raise he relaive wage. quaion (20) shows, however, ha his effec is being reversed once he demand side of he economy is considered. In general equilibrium, higher levels of pas human capial invesmen depress he relaive wage, as he homoheic demand forces he labor supply effec o dominae he absorpion effec. The resul is reminiscen of Rosensein-Rodan (1943), who proposed ha lack of demand migh resric developmen in a dynamic economy wih increasing reurns. Our model exhibis, however, consan reurns o scale in each period, while invesmen in human capial creaes ineremporally increasing reurns. The srong ineremporal supply response generaed by human capial invesmen acually resuls from wo separae supply effecs. Firs, ceeris paribus, here is a Rybczynski effec, since higher invesmen in human capial oday increases he supply of skilled labor in he nex period, which increases he oupu of he High Tech good and decreases ha of he Low Tech good. Second, higher human capial invesmen oday creaes higher echnological change, which creaes Hicks neural echnological change in he nex period ha is biased o he High Tech secor. Thus, a consan relaive prices, higher invesmen in human capial and higher raes of echnological change increases he raio of he High o Low Tech good. Since he share of consumpion expendiures allocaed o he High Tech good remains consan, however, he relaive price mus increase, which hen depresses he relaive wage. Wih he expression for he relaive wage in hand, we may now examine he deerminans of human capial invesmen, relaive prices and growh in auarchy. Subsequenly, proposiions I and II serve as a summary discussion of he characerisics of each equaion. Afer subsiuing for he relaive wage in equaion (17), invesmen in human capial can be expressed by he following difference 10
equaion ha characerizes he general equilibrium, S = θ ρ ( 1-S) ρ α γ γ ( 1- + ) -1 ( S-1 -S ) + 1. (21) Defining he seady sae level of sudens S * = S = S-1, we can solve equaion (21) for he closed form soluion of S * in erms of he parameers of he model ( ) where ξ ρ ( γ- )( - ρ+ α ) * S = θ -ξ 1-ξ, (21 ) 1 1. To rule ou violaions of he 2of he labor consrain (6), we require * * * * * ξ 3< θ. Thus, S ξ < 0; or S θ, S γ, S α > 0, and S ρ < 0. 4 The appendix proves ha he sysem is monoonically sable. We now express he equilibrium relaive wage and price as π * = * w * U w = 1- ξγ - ( µ ) ( ρ) ( ρ α ) ( γ ) * δ ( 1-S )( 1- ρ) θ θ ξ, (20 ) * -1 * 1+ S 1-1- + 1- S ρ, (19 ) which we wrie in erms of he equilibrium sock of sudens o reain some inuiion abou how price movemens relae o human capial invesmen. Finally, by aggregaing (12)-(13 ) we can obain a closed form expression for he long-run growh rae by logarihmically differeniaing oal seady sae income of he economy, Y * =w U* U * +w * *. Defining ^ variables as growh raes, he seady sae values of $ * U, $ *, π $ * equal zero, and * U* * $w = $w = $v. Then 5he long-run growh rae, φ, is simply * * * * φ = Y $ = C $ = $v = µ S = ( - ) µ θ ξ 1- ξ. (22) We are now in a posiion o examine he deerminans of he saic comparaive advanage, which highlighs he couner-balancing influences of he absorpion and consumpion demand effecs in response o changes in human capial invesmen and he rae of echnological change. Proposiion I An increase in he marginal propensiy o save, θ, or an increase in he 11
suden-eacher raio, γ, causes increases in human capial invesmen, in he raes of echnological change and growh. However, he relaive wage declines as he relaive price of he Low Tech good rises. An increase in he saving rae increases he supply of funds and decreases borrowing demand. An increase in he suden-eacher raio lowers he borrowing demand due o a lower direc cos of invesmen in human capial. Thus an increase in eiher β 6 or γ creaes excess supply in he bond marke o lower he ineres rae on impac, which renders invesmen in human capial more aracive. As he sock of suden increases, so do he raes of echnological change and growh (22). The higher rae of echnological change generaes Hicks neural echnological change ha is biased o he High Tech secor. This increases he relaive demand for skilled labor a consan relaive prices, consequenly he oupu of he High Tech good ends o expand, which raises π * (equaions (18) and (19 )). Wih a larger supply of skilled workers, a higher rae of echnological change, bu also wih a higher relaive price of he Low Tech good, he relaive wage of skilled workers mus decline (see equaion (20 )). The oupu and skilled labor supply effecs hus dominae he absorpion effec in he closed economy. This depresses he wage differenial despie he fac ha he economy experiences higher raes of echnological change and growh. Proposiion II An increase in consumer preferences for H, or in he share of skilled workers in H resuls in decreases in he human capial invesmen, in he raes of echnological change and growh. However, he relaive wage rises as he relaive price of he Low Tech good falls. A decrease in α, or an increase in ρ poses wo imporan resource coss o he economy. Ceeris paribus, increased demand for he High Tech good decreases he relaive price of he Low Tech good, (18), which leads o a rise in he relaive wage as producion of he High Tech good expands o saisfy consumer demand. Alernaively, an increase in he share of skilled workers in he High Tech secor raises he relaive wage since more skilled workers are required o absorb echnology in order o produce he same level of High Tech oupu. Thus, in boh cases he share of skilled labor devoed o he producion of he High Tech good increases. This drains skilled workers from he educaion secor, and increases he direc cos of human capial accumulaion. As he number of eachers and 12
sudens decreases, so do he raes of echnological change and growh. The decrease in human capial invesmen and he rae of echnological change leads o a decline in he relaive price of he Low Tech good, equaion (19 ), which hen raises he relaive wage above is previous equilibrium level, equaion (20 ). Afer having clarified he mechanics ha deermine he saic comparaive advanage, we urn o he characerisics ha disinguish he leader and laggard counries. One approach wih a long radiion in he rade lieraure is o assume ha he leader possesses he higher savings rae. 7 The comparaive saics have shown ha he saic comparaive advanage generaed endogenously by differen raes of ime preference fis he common descripion of a leader and laggard quie well. From proposiion I we know ha he more paien leader is endogenously endowed wih more human capial and experiences higher raes of echnological change and growh as compared o he laggard. Given he assumpion of idenical, homoheic demand across counries, he auarky relaive price of he Low Tech good in he advanced counry, π N, mus hen exceed ha of he laggard, π S, which implies ha he relaive wage in he advanced counry lies below he relaive wage observed in he laggard. The closed economy analysis exposes, however, one couner-facual implicaion. While he comparaive saics confirm ha higher raes of human capial invesmen and echnological change creae skill-biased labor demand, he homoheic demand srucure limis he reurn o human capial invesmen and echnological change in he economy and relaive wages falls in response o higher raes of echnological change. The recen empirical lieraure has documened ha several indusrialized counries experienced rising relaive wages due o higher raes of echnological change, which induced skill-biased labor demand (see icher 1996 for a discussion). One exension ha would preven he rise in he relaive price of he Low Tech good in response o higher raes of echnological change would be o relabel he Low Tech good as agriculure and o assume income inelasic demand for food as in Masuyama (1992). ngel s Law would hen allow for a coninuous decline in he Low Tech good s relaive price. Given he objecive 7 A common jusificaion for his assumpion ha more advanced counries have higher savings raes is ha savings raes across counries are posiively correlaed wih he degree of financial developmen (i.e. dwards 1995). 13
of his paper, we explore an alernaive approach: we examine how inernaional rade affecs he raes of growh, and he relaive demand, supply and wage of skilled workers in he leader and laggard economy. V. The Small Open conomy Criical o he small counry analysis is he perfecly elasic demand on he world marke, which immediaely implies ha he raes of echnological change, growh and reurn o educaion (he relaive wage) are no longer consrained by he auarky demand (prices). Wihou inending o imply ha inernaional spillovers are irrelevan o developmen, convergence and rade paerns, we examine how rade affecs he endogenous variables o foser growh wihou reliance on inernaional diffusion of knowledge. Thus for he purposes of his paper we assume incomplee specializaion and absrac from inernaional diffusion of knowledge, inernaional borrowing and lending, and migraion. Given a world price π, he relaive wage and he number of sudens can be obained by subsiuing for π in equaions (4) and (17), yielding, 8 w w U j ρ 1+ S = µ 1- ρ δ π -1 j ( 1- ρ) -1 1 ρ, (23) S = j ρ θ ( 1- ρ) γ δ π ( 1- ρ) j 1+ µ S -1 j -1 1 ρ + 1,, (24) Afer imposing he seady sae condiion S j = S j -1 = S *j in equaions (23) and (24), i can easily be verified ha he growh rae of he economy is sill φ j = µ S *j, where S *j is now deermined by he difference map in equaion (24). 9 For a given a world price, figure 1 characerizes he ineracion beween echnological change and human capial accumulaion in he small open economy. The S j S j schedule, equaion (17), represens he supply of sudens for each relaive wage level and he inuiion 8 s w n where j = n (leader), s (laggard) and w (world) and θ < θ < θ. 9 The ransiion dynamics and sabiliy condiions for his class of difference maps wih more general funcional forms have been invesigaed by icher (1996). 14
o is shape has been discussed above. Much like equaion (4), whose inuiion has been discussed a lengh above, he G j G j schedule given by equaion (23) relaes pas human capial invesmen (echnological change) o fuure relaive wage movemens. The small open economy resuls conras sharply wih hose observed under auarky. Recall ha in he closed economy, higher raes of echnological change and human capial invesmen lead o a lower relaive wage, due o he increase in he relaive price of he Low Tech good. In clear conras, he small open economy experiences an increase in he relaive wage in response o higher human capial invesmen and higher raes of echnological change, since increases in he relaive supply of he High Tech good may now be expored. This leads o he dominance of he absorpion effec, as he skill-biased labor demand is now srong enough o increase he relaive wage. In he nex secion we examine wheher rade can serve as an engine for growh, developmen and convergence. To disenangle he saic and dynamic gains (or losses) from rade in he advanced and he laggard counries, we examine eiher economy as i moves from auarky o free rade. VI. Trade, Developmen and Convergence When we examine how inernaional rade affecs he economy, our ineres focuses on he quesion of how rade affecs he relaive demand, supply and wages of skilled labor. These endogenous variables fully deermine he growh rae and he srucural ransformaion of he paern of producion. The new equilibrium sock of human capial under free rade is crucial since i deermines he rae of echnological change and hus he dynamic comparaive advanage. As we shall see, he effec of rade on eiher counry depends on he economy s endogenous facor endowmen, is rae of echnological change, and is relaive wage before engaging in free rade. If rade frees skilled workers from he absorpion of echnology in High Tech producion, boh he direc cos of educaion and he resource cos of human capial invesmen decline wih he saic fall in he relaive wage. Subsequenly, increased human capial invesmen generaes a higher rae of echnological change o creae a dynamic gain. As produciviy increases in he High Tech secor accelerae, he share of he High Tech good in producion increases again, ogeher wih he rae of economic growh. We show ha rade serves as an effecive engine of growh in he echnologically laggard counry. Wih a rae of ime preference ha exceeds ha of he res of he world, he laggard generaes 15
fewer savings o finance fewer sudens. This renders he laggard no only unskilled labor abundan under auarky, bu also less capable of generaing and absorbing echnological change. Due o he laggard s saic comparaive advanage in he Low Tech good, inernaional rade raises he relaive price of he Low Tech good and forces a conracion of he High Tech secor. On impac, figure 2 shows how he ensuing excess supply of skilled labor lowers he relaive wage (and hus he direc cos of educaion) in he laggard (A-B). In he long run, he laggard experiences an dynamic gains (B-C), due o he reallocaion of skilled labor from producion o he educaion secor, and he simulaneous increase in sudens and echnology. The economy approaches a long run equilibrium, characerized by a higher rae of human capial invesmen, a higher rae of echnological change, bu a lower relaive wage. To isolae he saic and he dynamic gains, we differeniae equaion (23) wih respec o he world price * j * j U ( / w ) d w d π = where ψ = ψγ σ *j ( 1+ S ) π µ ρ *j *j ( πµ S / π - ( 1+ µ S )) 1+ µ S *j ( 1- ρ) γ δπ ( 1- ρ) -1 1 ρ. (25) We can sign he expression by implicily differeniaing equaion (24), which yields πµ S π µ σ ψ θ 2 µ σ ψ θ 1 + 1 + * j j = ( ψ ) 2 *j ( 1 + ψ ) ( 1 + µ S ) j. (26) As long as sabiliy is assured, equaion (26) mus lie beween zero and uniy, which esablishes he familiar Solper-Samuelson resul ha he relaive wage of skilled workers declines in he relaive price of he unskilled labor inensive good. The wo separae effecs of world price on he relaive wage can be represened by he wo erms in brackes in equaion (25). As he laggard experiences an increase in he relaive price of he Low Tech good, on impac, he relaive wage falls in proporion o he sock of human capial from A o B. The conracion of he High Tech secor depresses he demand for skilled labor in producion 16
and he relaive wage mus rise o clear he marke for skilled labor. In he long run, however, he laggard experiences he dynamic benefi generaed by a srucural ransformaion of he economy, represened by he firs erm in brackes in equaion (25). No only do skilled workers in producion relocae o become eachers, bu over ime he sock of skilled labor increases, which hen also raises he rae of echnological change. This consiues he movemen from B o C in figure 2. Noe ha his version of "indusrializaion" is based on he explici modeling of he coss and benefis of invesing in human capial and heir ineracion wih he rae of echnological change ha needs o be absorbed in producion. The engine of growh for he echnologically laggard counry is ha inernaional rade allows for he reducion in he absorpion cos of echnology in he High Tech secor, and for he expansion of educaion and innovaion. In conras, free rade diminishes he echnological leadership of he advanced economy. Wih a saic comparaive advanage in he High Tech good, free rade lowers he advanced counry s relaive price of he Low Tech good and creaes an expor marke for is High Tech good. These saic gains are offse by a dynamic loss as he economy approaches is new long run equilibrium, one characerized by lower invesmen in human capial, a lower rae of echnological change, and a higher relaive wage. The dynamic loss can be aribued o he decline in he rae of echnological change caused by a dynamic decrease in human capial invesmen. To isolae he saic gain and he dynamic loss, we noe ha rade generaes expor demand of he High Tech good which increases he demand for skilled labor in he advanced counry. Thus he relaive wage in he advanced counry mus rise o clear he marke for skilled labor. In he long run, however, higher oupu of he High Tech good is generaed a wo imporan resource coss, represened by he firs erm in brackes in equaion (25). No only do eachers relocae o become High Tech producion, bu over ime he sock of sudens declines (due o a higher direc cos of human capial invesmen), which decreases he rae of echnological change. These long run dynamics beg he quesion of wha degree of cross-counry convergence in skill endowmens, growh raes and relaive wages is implied by he model. Figure 3 summarizes he adjusmen process for he advanced counry and he laggard. Since he counries share idenical producion srucures, boh mus share he same G W G W schedule afer having adjused o he world 17
price. The SS schedules differ, however, due o he differing saving raes beween counries. From (24) i is clear ha he counry wih he higher savings rae mus possess a higher rae of echnological change. The level of he skill endowmen gap narrows and in he long run "condiional" convergence wihin he endogenous growh srucure occurs. Condiional convergence was inroduced By Barro (1991) and Mankiw e al. (1992) in recogniion of he fac ha paramerically differen counries canno be expeced o converge o idenical seady sae posiion. When counries differ paramerically (i.e. in heir savings rae), he erm describes he process of convergence o disinc saionery saes, in conras o consan or even diverging seady saes. Hence convergence is condiional on conrolling for parameric differences such as savings raes. VII. Conclusion In he absence of inernaional diffusion of knowledge or facor mobiliy, previous models of endogenous growh necessarily imply ha rade eiher reinforces he posiion of he leading naion, or leaves he laggard counry wih few alernaives bu o rely on inernaional knowledge spillovers for developmen. These conclusions have sood in sharp conras o he empirical evidence, which documens a rend owards condiional convergence, and ha rade and openness do serve as an engine for growh, facor accumulaion, and a narrowing of he echnology gap. This paper suggess ha if boh echnological change and human capial accumulaion are endogenous, and if incenives o inves in educaion inerac wih he rae of echnological change, rade does narrow he differenial in facor endowmens and raes of growh and echnological change. Our model exposes he ineracion beween human capial and he rae of echnological change as he driving force behind convergence. Opening o rade generaes a dynamic gain o he laggard counry, whose conracion of he skill-inensive High Tech secor frees skilled labor, which lowers he relaive wage and he direc cos of educaion. The dynamic increase in is research and educaion effor hen allows he laggard o narrow he echnology gap and increase is human capial endowmen. I is imporan o noe ha his paper does no inend o sugges ha spillovers, or privae incenives o innovae, or learning on he job, may no have a significan impac on he developmen and convergence process. Raher, he objecive was o qualify he srong implicaions of he HOS model and he recen endogenous growh models ha endogenous facor accumulaion and rade in 18
goods highly likely o lead o divergence beween he leader and he laggard, as long as we rule ou inernaional spillovers. We also do no rule ou ha acive policy on he par of a planner may influence developmen. Allowing for inernaional migraion presens anoher appealing exension, which may provide new insighs as o why boh skilled and unskilled labor seeks o migrae from poor o rich counries. Trade in goods does no subsiue for rade in facors in our model, as he advanced counry s higher auarky rae of growh and echnological progress creaes incenives for migraion owards he advanced counry. The model suggess an inriguing relaion beween brain drain and migraion since he advanced counry gains by increasing is sock of skilled workers, no only o increase he oupu of is High Tech secor, bu also o increase is educaion and research effor. 19
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Appendix I. Local Behavior Around The Fixed Poin S* In Auarky. The firs order difference equaion which governs he dynamics of he sysem is given by (21) whose asympoic sabiliy is assured as long as ds ds -1 ( ) ( ) * ψ ξ θ θ ξ = 1- -. Implici differeniaion of (21) yields ds ds -1 * S = * ψ θ * * * * * ( 1/ γ ) S ( 1+ ψ ) + ψ θ (( γ 1) S ) ( 1 S ) < 1. quaions (25) and (20 ) imply ha. ( ) (A1) 2 1 1 which proves ha he sysem approaches he equilibrium monoonically. From (A1) we find ( ψ ) 2 * * 1 + S - 1 *-1 ( γ -1 ) + ( S -1 ) > 0. θ ξ As γ and 1/S * exceed uniy, i suffices o show ha he very lef erm in (A2) is posiive. Given he definiion of * ψ ha erm can be rearranged o ( ) ( ) (A2) θ + ξ 1-θ 1- ξ > θξ, which mus always hold since we required ha θ > ξ 7 o assure U * and S * o be non negaive. Sabiliy is assured if (A1) can be shown o be smaller han 1. By he same procedure ha proved sabiliy, edious calculaions show ha his condiion is also assured for θ > ξ. 22
8FIGUR 1 quilibrium in a Small Open conomy 23
FIGUR 2 Trade Liberalizaion in a Laggard Counry 24
FIGUR 3 Trade Liberalizaion in he Leader and Laggard Counries Condiional Convergence o a World Growh Rae ω j = U j w w 25