Trade Liberalization, Growth, and Productivity*

Transcription

1 Federal Reserve Bank of Mnneapols Prelmnary June 007 rade Lberalzaon, Growh, and Producvy* Clausre Baona Ryerson Unversy Mark J. Gbson Washngon Sae Unversy mohy J. Kehoe Unversy of Mnnesoa, Federal Reserve Bank of Mnneapols, and Naonal Bureau of Economc Research Km J. Ruhl Unversy of eas a usn BSRC here s a lvely debae abou he mpac of rade lberalzaon on economc growh measured as growh n real gross domesc produc (GDP. Mos of hs leraure focuses on he emprcal relaon beween rade and growh. hs paper nvesgaes he heorecal relaon beween rade and growh. We show ha sandard models ncludng Rcardan models, Heckscher-Ohln models, monopolsc compeon models wh homogeneous frms, and monopolsc compeon models wh heerogeneous frms predc ha openng o rade ncreases welfare, no necessarly real GDP. In a dynamc model where rade changes he ncenves o accumulae facors of producon, rade lberalzaon may lower growh raes even as ncreases welfare. o he een ha rade lberalzaon leads o hgher raes of growh n real GDP, mus do so prmarly hrough mechansms ousde of hose analyzed n sandard models. *hs paper was prepared for he conference New Drecons n Inernaonal rade heory a he Unversy of Nongham. he vews epressed heren are hose of he auhors and no necessarly hose of he Federal Reserve Bank of Mnneapols or he Federal Reserve Sysem.

2 . Inroducon How does rade lberalzaon affec a counry s growh and producvy? How does affec a counry s socal welfare? s Rodrguez and Rodrk (00 pon ou, growh and welfare are no he same hng. rade polces can have posve effecs on welfare whou affecng he rae of economc growh. here s a lvely debae abou he mpac of rade lberalzaon on economc growh measured as growh n real gross domesc produc (GDP. Mos of hs leraure focuses on he emprcal relaon beween rade and growh. he fndngs are med. Many sudes fnd a connecon beween rade, or some oher measure of openness, and growh. Bu Rodrguez and Rodrk (00, among ohers, are skepcal ha hese sudes fnd a connecon beween rade polcy and growh. (We provde an overvew of hese leraures below. furher crcsm of he emprcal leraure, posed by Slaugher (00, s ha largely does no address he specfc mechansms hrough whch rade may affec growh. hs paper nvesgaes he heorecal relaon beween rade polcy and growh. We do so usng smple versons of some of he mos common nernaonal rade models, ncludng Heckscher-Ohln models, Rcardan models, monopolsc compeon models wh homogeneous frms, monopolsc compeon models wh heerogeneous frms, and dynamc Heckscher-Ohln models. hese models allow us o nvesgae a number of specfc mechansms by whch rade lberalzaon s commonly hough o enhance growh or producvy: mprovemens n he erms of rade, ncreases n produc varey, reallocaon oward more producve frms, and ncreased ncenve o accumulae capal. For each model we provde an analycal soluon for he auarky equlbrum and for he free rade equlbrum. We hen look a he ereme case of rade lberalzaon by comparng auarky and free rade. o be conssen wh emprcal work, we measure real GDP n each of hese models as real GDP s ypcally measured n he daa, as GDP a consan prces. In each model he supply of labor s fed, so changes n real GDP are also changes n measured labor producvy. We hen conras real GDP wh a heorecal measure of real ncome, or socal welfare. In each model, rade lberalzaon ncreases socal welfare. hs s o be epeced, bu our resuls on real GDP may come as a surprse o many economss. In he

3 sac models, here s no general connecon beween rade lberalzaon and growh of real GDP per capa he relaonshp may even be negave. Moreover, n a dynamc model wh capal accumulaon, some counres wll have slower raes of growh under free rade han under auarky. Openng o rade mproves welfare, bu does no necessarly ncrease real GDP per capa or speed up growh. If openness does n fac lead o large ncreases n real GDP, hese ncreases do no come from he sandard mechansms of nernaonal rade. here s a vas emprcal leraure on he relaonshp beween rade and growh. We can classfy hese papers no wo groups dependng on her nerpreaon of rade. he frs lne of research nerpres rade as epor volume and uses he growh rae of epors or of epors relave o GDP as s measure of changes n rade. he second lne of research nerpres rade as rade polcy and sudes he correlaon of a varey of openness ndcaors and economc growh. Early papers n he frs lne of research nclude Mchaely (977 and Balassa (978. Lewer and Van den Berg (003 presen an eensve survey of hs leraure. hey argue ha mos sudes n hs leraure fnd a posve relaonshp beween rade volume and growh and ha hey are farly conssen on he sze of hs relaonshp. In he second lne of research, fndngs are med. Sudes ha fnd a posve relaonshp beween rade openness and growh (usng dfferen echnques and openness measures nclude, among ohers, World Bank (987, Dollar (99, Sachs and Warner (995, Frankel and Romer (999, Hall and Jones (999, and Dollar and Kraay (004. Rodrguez and Rodrk (00 queson he fndngs of hese sudes. In parcular, hey argue ha he ndcaors of openness used n hese sudes are eher bad measures of rade barrers or are hghly correlaed wh varables ha also affec he growh rae of ncome. In he laer case, he sudes may be arbung o rade he negave effecs on growh of hose oher varables. Followng hs argumen, Rodrk, Subramanan, and rebb (00 fnd ha openness has no sgnfcan effec on growh once nsuonrelaed varables are added n he regresson analyss. Several sudes usng arff raes as her specfc measures of openness have found he relaonshp beween rade polcy and growh o depend on a counry s level of developmen. In parcular, Yankkaya (003

4 and DeJong and Rpoll (006 fnd a negave relaonshp beween rade openness and growh for developng counres. furher crcsm of he emprcal leraure, posed by Slaugher (00, s ha he leraure does no, n general, address he specfc mechansms hrough whch rade may affec growh. Ecepons are Waczarg (00 and Hall and Jones (999. hey fnd ha rade affecs growh manly hrough capal nvesmen and producvy. smaller se of papers sudy he relaonshp beween openness o rade and producvy. Eamples are lcalá and Cccone (004 and Hall and Jones (999, whch fnd a sgnfcan posve relaonshp beween rade and producvy. heorecal sudes on he relaonshp beween rade and growh do no offer a clear vew on wheher here should be a relaonshp beween rade openness (measured as lower rade barrers and growh n ncome. Models followng he endogenous growh leraure wh ncreasng reurns, learnng-by-dong, or knowledge spllovers predc ha openng o rade ncreases growh n he world as a whole, bu may decrease growh n developng counres f hey specalze n he producon of goods wh less poenal for learnng. Young (99, Grossman and Helpman (99, and Lucas (988 are eamples of eamples of papers n hs area. By conras, Rvera-Baz and Romer (99 fnd ha rade leads o hgher growh for all counres by promong nvesmen n research and developmen. Models of rade usng he D-Sglz heory of ndusral organzaon have ypcally focused on welfare. Krugman shows, for nsance, ha rade lberalzaon leads o welfare ncreases because of ncreases n produc varey. Melz (003 ncorporaes heerogeneous frms no a Krugman model and fnds ha rade lberalzaon ncreases a heorecal measure of producvy. Chaney (006 also consders a smple model of heerogeneous frms, close o he one we sudy here. When producvy s measured n he model as n he daa, Gbson (006 shows ha rade lberalzaon does no, n general, ncrease producvy n hese sors of models. he ncrease s, raher, n welfare. Gbson (006 fnds ha addng mechansms o allow for echnology adopon generae ncreases n measured producvy from rade lberalzaon. Models followng he eogenous growh leraure do no have a clear predcon for he relaonshp beween rade and growh. In parcular, n dynamc Heckscher-Ohln 3

5 models models ha negrae a neoclasscal growh model wh a Heckscher-Ohln model of rade openng o rade may ncrease or decrease a counry s growh rae of ncome dependng on parameer values. rade may slow down growh n he capalscarce counry even whle rases welfare. Papers n hs leraure are Venura (997, Cuña and Maffezzol (004, and Baona and Kehoe (006. he ranson from heorecal o emprcal resuls s no sraghforward. Besdes he lack of consensus on wheher here should be a relaonshp, he varables suded n he emprcal and heorecal analyss do no necessarly concde. he man problem s he measure of real GDP. Emprcal sudes use measures of real GDP repored n he naonal ncome and produc accouns, whch use eher base-year prces or a chanweghng mehod. Kehoe and Ruhl (007 show ha hese dfferences n measuremen mehods may lead o model predcons no beng refleced n he measured daa. In parcular, hey show ha n sandard models ncome effecs due o changes n he erms of rade are no refleced n daa-based measures of real GDP. Smlar ssues are addressed by Dewer and Morrson (986 and Kohl (983, Do mprovemens n he erms of rade ncrease real GDP? counry s erms of rade s he prce of s mpors relave o he prce of s epors. By decreasng he relave prce of mpors, rade lberalzaon acs as a posve erms-of-rade shock. We consder how mprovemens n he erms of rade affec real GDP n boh a Heckscher-Ohln model and a Rcardan model wh a connuum of goods. (Kehoe and Ruhl (006 consder he same ssue n a small open economy model and arrve a smlar conclusons. In he Heckscher-Ohln model, counres dffer n her relave facor endowmens bu no n her echnologes. In he Rcardan model, counres dffer n her echnologes bu use a common facor of producon... sac Heckscher-Ohln model In each counry,,,..., n, here s measure L of consumers. Each consumer s endowed wh one un of labor and k uns of capal. here are wo radable goods,,. ll quanes are n per capa erms. 4

6 consumer n counry chooses c,,, o mamze a log c + a log c, ( where a+ a, subec o he budge consran p c + p c w + rk. ( Here p s he prce of good, r s he renal rae of capal, and w s he wage rae. Good s produced by combnng capal and labor accordng o he Cobb- Douglas producon funcon θ y k α α, (3 where α > α (ha s, good s relavely capal-nensve. he zero-prof condons are α α α p k r 0, 0 f k > 0 (4 ( α α α Clearng n he facors markes requres ha p k w 0, 0 f > 0. (5 k + k k (6 Under auarky,. (7 + c y. (8 Under free rade, n n Lc Ly. (9 here are analycal soluons for he auarky and free rade equlbra of hs model. o smplfy he noaon, le aα + a α (0 ( α ( α a + a ( D ( α α θ a α α ( α α D D D (3 a a 5

7 µ ( ( α α γ α α a ( ( α α (4 α γ α µ. (5 a hroughou he paper we denoe auarky equlbrum obecs by a superscrp and denoe free rade equlbrum obecs by a superscrp. uarky Prces are p ad α k (6 D r Dk (7 llocaons are w Dk. (8 c y D k α (9 k a α k (0 ( α a. ( In order o compare he model wh he daa, we measure GDP n he model as s measured n he daa. he sandard way of calculang real GDP n he daa s as GDP a consan prces (as opposed o GDP a curren prces. In he sac models n hs paper, our measure of real GDP s smply GDP a auarky prces. Here GDP a auarky prces s GDP p y + p y Dk. ( For each model, we conras our daa-based measure of real GDP wh a heorecal nde of real ncome, or socal welfare. hroughou he paper we calculae 6

8 real ncome as a homogeneous-of-degree-one ransformaon of perod uly. Here real ncome s a ( a v c c Dk. (3 Free rade o oban an analycal soluon, we focus on he case where all counres are n he cone of dversfcaon. ha s, leng k n n Lk L (4 k k γ (5 α κ, (6 α we eamne he case where κ γ κ,,..., n. World prces are p ad α k (7 D r Dk (8 llocaons are w Dk. (9 ( γ c D k α + (30 k y µ (3 D k α a α k µ (3 ( α a µ. (33 Noce ha seng γ gves he same values as for auarky. 7

9 GDP a curren prces s gdp p y + p y ( γ Dk +. (34 Noce ha we use he lowercase gdp o dsngush curren prces under free rade so as no o confuse wh our measure of real GDP, GDP a auarky prces. Here GDP a auarky prces s Real ncome s GDP p y + p y α ( ( + ( γ γ α α γ α γ α α Dk α α a ( a v c c ( γ + Dk. (35. (36 Effec of rade lberalzaon I s sraghforward o show ha each counry s erms of rade mprove followng rade lberalzaon (smply compare relave prces under auarky and under free rade. hs leads o an ncrease n real ncome. Bu real GDP acually decreases followng rade lberalzaon. Proposon. If γ, real ncome srcly ncreases followng rade lberalzaon. Proof. We wan o show ha or equvalenly ha ( Dk Dk γ + >, (37 Defne he funcons γ + > γ. (38 ς f z z+ ς (39 g( z z ς. (40 8

10 hen f ( z ς (4 ς g z z ς. (4 he lnear funcon f s angen o he funcon g a z (boh funcons have he same value and slope a z. Snce g s srcly concave, f ( z g( z > f z. Proposon. If γ, GDP a auarky prces srcly decreases followng rade lberalzaon. Proof. We wan o show ha Defne he funcon p y + p y > p y + p y. (43 α ( p, p, k ma p k α α α + p k π θ θ s.. k + k k +. (44 k 0, 0 Snce α > α, hs funcon s srcly concave. Noce ha (,, π p p k p y + p y. (45 he free rade allocaon also sasfes he feasbly consrans n (44, so p y + p y > p y + p y, (46 where he src nequaly follows from he src concavy of π. Fgure llusraes he proof. 9

11 .. Rcardan model wh a connuum of goods here are wo symmerc counres. In each counry,,, he represenave consumer s endowed wh uns of labor. here s a connuum of radable goods, z [ 0,]. he represenave consumer chooses c ( z, z [ 0,] subec o he budge consran, o mamze log c 0 z dz (47 Here p ( z s he prce of good z and w s he wage rae. where where 0 p z c z dz w 0. (48 he echnology for producng good z n counry s α >. Here a n counry. he zero-prof condons are Clearng n he labor marke requres ha Under auarky, Under free rade, y z z a z, (49 a ( z e α z (50 ( a z e α z, (5 z s he quany of labor requred o produce one un of good z p z a z w 0, 0 f y z > 0. (5 0 z dz. (53 c z y z. (54 c z + c z y z + y z. (55 0

12 uarky We normalze w. he prces of he goods are p z e α he consumpon and producon levels are z (56 ( z p z e α. (57 he allocaon of labor s GDP a curren prces s Real ncome s c z y z p ( z. (58. (59 z 0 GDP p z y z dz. (60 v ep log c 0 z dz. (6 e α Free rade Snce he counres are symmerc, we normalze w w. Counry produces and epors goods z [ 0,0.5] and counry produces and epors goods z ( 0.5,]. he prces of he goods are he consumpon levels are p ( z e e α z α ( z z z [ 0,0.5] ( 0.5,]. (6 c z c z For goods z [ 0,0.5], he producon plans are p ( z. (63

13 y ( z ( z p ( z y ( z ( z 0 For goods z ( 0.5,], he producon plans are y ( z ( z, (64. (65 (66 0 GDP a curren prces s GDP a auarky prces s Real ncome s y ( z, ( z p (67 ( z 0 gdp p z y z dz. (68 0 GDP p z y z dz. (69 v ep log c 0 z dz. (70 Effec of rade lberalzaon fer rade lberalzaon, he prces of each counry s mpors decrease, resulng n an mprovemen n he erms of rade. Real ncome ncreases from a auarky prces remans consan a. e α o. GDP 3. Do ncreases n produc varey from rade lberalzaon ncrease real GDP? I s well known ha, n sandard monopolsc compeon models wh homogeneous frms, rade lberalzaon leads o an ncrease n he number of produc varees avalable o he consumer. hs ncrease n produc varey leads o an ncrease n real ncome, bu does lead o an ncrease n real GDP? We fnd ha hs depends on

14 he naure of compeon n he produc marke. If here s a connuum of produc varees, hen real GDP does no change. If here s a fne number of produc varees, hen real GDP ncreases. he reason s ha, wh Courno (or Berrand compeon among frms, markups over margnal cos decrease when he number of frms supplyng goods o a marke ncreases. We make hs pon usng a monopolsc compeon model wh a fne number of produc varees. monopolsc compeon model wh homogeneous frms In each counry,,,..., n, he represenave consumer s endowed wh uns of labor. Le J be he number of goods avalable o he consumer n counry. Consumer chooses c,,,..., J, o mamze J ( log (7 c subec o he budge consran J p c w. (7 Here p s he prce of good and w s he wage rae. frm producng good n counry has he ncreasng-reurns-o-scale echnology y b ma f, 0, (73 where f s he fed cos, n uns of labor, of operang. here s Courno compeon among frms. akng as gven he consumer s demand funcon and he decsons of all oher frms, a frm s problem s o choose he quany of oupu ha mamzes s profs. here s free enry of frms, so here are no aggregae profs. Clearng n he labor marke requres ha J. (74 Under auarky, c y. (75 Under free rade, f good s produced n counry, 3

15 y n c. (76 uarky Normalze w. Each frm akes he consumer s ndrec demand funcon as gven. Consumer s ndrec demand funcon for good s p c. (77 J c m m he frm n counry producng good chooses y o mamze profs, Pluggng (77 no (78, he epresson for profs becomes y p y by f. (78 J y m m y by f. (79 Prof mamzaon mples ha margnal revenue s equal o margnal cos, so J ( m J ( y m m y y m y y y J b. (80 y m m Imposng symmery across frms (he subscrps are omed, we oban he profs of a frm are c y p J ( J ( J b bj ( J (8. (8 ( J ( J p y by f f. (83 Snce here s free enry, frm profs mus be zero n equlbrum: f J J 0 (84 4

16 Le N be he number of frms n counry. Usng he quadrac formula, we solve for he number of varees and frms: + + 4f J N. (85 f Noce ha he number of goods s no necessarly an neger. lernavely, we could allow for aggregae profs and calculae N as he neger such ha here are nonnegave profs bu ha, f one more frm enered, profs would be negave. GDP a curren prces s Real ncome s GDP N p y ( v J c ( J ( J J b. (86. (87 Free rade We can use he above approach o solve for he negraed equlbrum of he world economy, n whch he supply of labor s and oban n. We agan normalze w J + + 4f y f ( J ( J b (88 (89 Dsaggregang proporonally, p bj ( J. (90 5

17 c y. (9 N J. (9 Noce ha he equlbrum values for free rade are he same as hose for auarky f. GDP a curren prces s GDP a auarky prces s Real ncome s GDP gdp N p y N p y J ( J ( J J ( ( v J c ( J ( J J b. (93. (94. (95 Effec of rade lberalzaon Proposon 3. If < lberalzaon., hen real ncome n counry srcly ncreases followng rade Proof. We wan o show ha ( J ( J ( J. (96 > ( J J b J b I suffces o show ha J J >, whch s evden from comparng (85 and (88. 6

18 Proposon 4. If < followng rade lberalzaon., hen GDP a auarky prces n counry srcly ncreases Proof. We wan o show ha J ( J ( J J >. (97 gan, hs follows from he fac ha J J >. Real GDP ncreases because markups decrease. Snce J J >, here are more frms compeng n each marke. Wh Courno compeon, hs lowers he markup over margnal cos: J < J ( J ( J. (98 If here s a connuum, raher han a fne number, of produc varees, hen he markup over margnal cos s consan a, regardless of rade polcy. In hs case, GDP a auarky prces remans consan followng rade lberalzaon. 4. Does reallocaon across heerogeneous frms followng rade lberalzaon ncrease measured producvy? Wh heerogeneous frms and fed coss of eporng, rade lberalzaon can lead o a reallocaon of resources across frms. In a smple model, rade lberalzaon causes he leas producve frms o e and he mos producve frms o become eporers. Inuvely, hs reallocaon of resources oward more producve frms should ncrease aggregae producvy. Bu we fnd ha does no. he fndng here s eplored furher n Gbson (007, where a posve mechansm s also provded. 7

19 monopolsc compeon model wh heerogeneous frms here are wo symmerc counres. In each counry,,, he represenave consumer s endowed wh uns of labor and measure µ of poenal frms (poenal frms may choose no o operae. Each frm produces a dfferenaed good. z Z Le Z be he se of goods avalable o consumer. he consumer chooses, o mamze subec o he budge consran ( log c z dz Z c z, (99 p z c z dz w + π. (00 Z Here p ( z s he prce of good z, w s he wage rae, and π s he profs of frms. Frms dffer n her producvy levels. Le ( z be he producvy level of he frm ha produces good z. he frm producng good z n counry has he ncreasngreurns-o-scale echnology y z ma z z fd, 0, (0 where f d s he fed cos, n uns of labor, of operang. If he economes are open o rade, hen a frm can choose o epor by payng an addonal fed cos of f e uns of labor. Poenal frms draw her producves from a Pareo dsrbuon F γ, (0. he choce of one as he lower bound on he Pareo dsrbuon can be hough of as a normalzaon. For reasons ha wll be clear laer, we mpose he resrcon ha γ > ma,. akng he consumer s demand funcons as gven, he frm s problem s o choose he prof-mamzng prce. Each frm decdes wheher o operae. If here s free rade, each frm decdes wheher o epor. Clearng n he labor marke requres ha 8

20 Z z dz. (03 uarky here are wo possbles: Eher all poenal frms choose o produce or no. We eamne he laer case. In hs case, here s a cuoff d, d >, such ha a frm wh producvy produces f. d Snce he counres are symmerc, counry subscrps are omed. Se w. he prof-mamzng prces are he aggregae prce nde s p ( P µ p df d. (04 ( γ ( γ( ( γµ ( d he demand for a good produced by a frm wh producvy frm wh producvy. (05 d s ( + π c y p P ( ( ( + γ π ( γµ ( d Pluggng (04 and (06 no (07, we oban γ( d mus make zero profs n equlbrum, so ( d. (06 c p ( d c ( d fd 0. (07 d µγ f d ( γ ( ( + π d γ, (08 9

21 where ( c π µ p ( c ( f d df d. (09 γ Pluggng (09 no (08, he cuoff for operang s GDP a curren prces s Real ncome s d µ ( γ fd ( γ ( γ GDP µ p y df d γ γ ( µ v c df d γ ( γ P. (0. (. ( Free rade We agan eamne he case n whch no all frms choose o produce. ha s, frm z produces f ( z d, >. Wh free rade, each frm faces an addonal decson: d wheher o pay he fed cos f e o epor. here s a cuoff z epors f ( z e. e, e >, such ha frm d Snce he counres are symmerc, we se w w. he prof-mamzng prces are he aggregae prce nde s p (. (3 0

22 ( P µ p ( df( µ p ( + df( d e γ ( γ( γ( ( γµ ( d ( + e he demand n a counry for a good produced by a frm wh producvy. (4 d s hen ( + π c p P ( ( ( + ( γµ ( d + ( e y ( γ π. (5 γ( γ( c d < c e e. (6 he cuoff for operang, so d, mus sasfy ( d c p ( d c ( d fd 0, (7 ( γ ( ( + π ( d γµ Smlarly, he cuoff for eporng, so ( d + ( e d γ( γ( e, mus sasfy ( e fd 0. (8 c p ( e c ( e fe 0, (9 e

23 Here ( γ ( ( + π ( e γµ ( d + ( e γ( γ( ( c π µ p c f d df d c ( + µ p ( c ( f e df e γ ( ( π µ fe 0. (0 γ ( d fd e fe + +. ( Noce ha (8, (0, and ( gve us a sysem of 3 equaons n 3 unknowns o be solved for d, e, and π. he soluon s d γ( µ ( γ fd ( fe fd + ( γ ( γ ( e γ( µ ( γ fd + ( fe fd f e fd ( γ ( γ (3 GDP a curren prces s GDP a auarky prces s π. (4 γ gdp µ p y df d γ γ GDP µ p y df d γ γ. (5. (6

24 Real ncome s ( µ µ v c df + c df d e γ ( γ P. (7 Effec of rade lberalzaon Proposon 5. he cuoff for operang srcly ncreases followng rade lberalzaon. Proof. Compare (0 and (. Proposon 6. GDP a auarky prces does no change followng rade lberalzaon. Proof. Compare ( and (6. Proposon 7. Real ncome ncreases followng rade lberalzaon. Proof. Comparng ( and (7, suffces o show ha and (4, we see ha hs follows from Proposon 5. P > P. Comparng (05 he effec of reallocaon across frms he e of he leas producve frms and he movemen of resources oward he mos producve frms whch sar eporng ncreases welfare, no real GDP. 5. How does rade lberalzaon affec growh raes? rade lberalzaon can change he ncenves o accumulae capal, whch n urn affecs growh raes. Does rade lberalzaon have any effec on growh raes? o analyze hs, we consder a dynamc Heckscher-Ohln model wh endogenous capal accumulaon as n Baona and Kehoe (006. 3

25 dynamc Heckscher-Ohln model In each counry,,,..., n, here s measure L of consumers. Each consumer s endowed wh one un of labor and k 0 uns of capal. here are wo radable goods,,. consumer n counry chooses {,, } c k,,, 0,,..., o mamze β ( alog c + alog c, (8 0 where a+ a, subec o he budge consran and he law of moon of capal p c + + p c + w + r k (9 a a ( δ k + k +, (30, gven k0 k0. Here p s he prce of good, rae of capal. Each counry has he Cobb-Douglas echnologes θ where α > α. he zero-prof condons are w s he wage rae, and r s he renal y k α α, (3 α α α p k r 0, 0 f k > 0 (3 ( α α α Clearng n he facors markes requres ha p k w 0, 0 f > 0. (33 k + k k (34 Under auarky,. (35 + c + y. (36 Under free rade, n n L ( c + L y. (37 o oban an analycal soluon, we assume ha here s complee deprecaon, δ. We use he same noaonal convenons ha we used for he sac Heckscher- 4

26 Ohln model. Gven k, he equlbrum values n he dynamc model for perod are he same as n he sac model, ecep ha oupu s spl beween consumpon and nvesmen. uarky he analycal soluon s r D k (38 p w D k (39 ad α k (40 D where α y D k (4 k a α k (4 ( α a (43 ( β c D k α (44 β (45 D k α GDP a curren prces s ( ( β β, 0 k D k D k. (46 gdp p y + p y ( D k. ( β D Dk a Noce ha GDP a curren prces s equal o ( ( GDP a perod-0 prces s a y y. 5

27 GDP p y + p y 0 0 α α k k a + a Dk 0 k0 k 0. (48 Real ncome s α α a D k + a D k Dk β 0 β 0 0 a ( ( a v c c ( β D( k. ( ( β ( β D Dk Free rade o oban an analycal soluon, we assume ha he nal facor endowmens are such ha facor prces are equalzed n he frs perod. Baona and Kehoe (006 show ha, n hs case, facor prce equalzaon occurs along he enre equlbrum pah for he Cobb-Douglas model. hs mples ha he model can be solved by calculang he equlbrum of he negraed economy he economy wh nal endowmens equal o he world endowmens and hen splng producon, consumpon, and nvesmen across counres n each perod. If all counres are n he cone of dversfcaon, hen where k γ k (50 k 0 γ (5 k0 k n Lk 0 0 n L. (5 he analycal soluon for he case where κ γ κ,,..., n, s r D k (53 6

28 p w D k (54 ad α k (55 D ( γ γ β c D k + (56 α γβ (57 D k α where α y µ D k (58 k a α µ k (59 ( α a µ, (60 ( ( β 0 k βd k D k. (6 GDP a curren prces s gdp p y + p y ( γ D( k +. ( ( γ ( β + D Dk GDP a perod-0 prces s GDP p y + p y 0 0 α α k k a + a Dk µ µ 0 k0 k 0. (63 α α a D k + a D k Dk µ β 0 µ β 0 0 If he counres are nally n auarky, we can measure real GDP as GDP a perod-0 auarky prces: 7

29 GDP p y + p y 0 0 α α k k a + a Dk µ µ 0 k0 k 0. (64 α α a + a Dk ( βd k0 βd k0 µ µ 0 k 0 k 0 Real ncome s a ( ( a v c c ( γ γβ D( k ( γ γ β ( β + D Dk. (65 Effec of rade lberalzaon We begn wh he analyss of real ncome and dscuss real GDP laer. Frs we analyze raes of growh of real ncome under boh auarky and free rade. Proposon 8. Under auarky, f k 0 < k 0, hen he growh rae of real ncome s hgher n counry han n counry n every perod. Proof. Under auarky, he growh rae of real ncome n counry s hs s decreasng n k 0. v, +, + v k k. (66 β D k ( β D ( + + k0 Proposon 9. Under free rade, real ncome grows a he same rae n every counry. 8

30 Proof. Wh free rade, he growh rae of real ncome s hs s ndependen of. v, + + β D k0 v ( +. (67 Noce ha, under free rade, ncome n counry relave o ncome n he world s consan over me. Proposon 0. If k 0 > k0, hen real ncome n counry grows a a faser rae under free rade han under auarky n every perod. If k 0 < k0, hen real ncome n counry grows a a slower rae under free rade han under auarky n every perod. Proof. hs follows drecly from he prevous wo proposons. Despe he fac ha rade lberalzaon leads o slower growh of real ncome n some counres, rade lberalzaon ncreases welfare n every counry. Proposon. If γ, welfare s srcly hgher under free rade han under auarky. Proof. Welfare n counry under auarky s W β log v 0 0 Welfare n counry under free rade s + + β log ( β βd Dk0. (68 ( β β ( β ( log D log D log k + + β β β β 0 9

31 W We wan o show ha W β log v β log ( γ β βd Dk0. (69 ( γ + β β ( β ( log D log D log k + + β β β β 0 > W, or equvalenly ha ( β ( β γ + > γ β β From here, he proof s he same as ha for Proposon. ( β β. (70 Wha happens o real GDP followng rade lberalzaon? We can nfer from he sac model ha, f a counry s nally n auarky, hen rade lberalzaon nally causes a decrease, or a leas a decrease n he growh rae of, real GDP n ha counry. Proposon. If γ, GDP a perod-0 auarky prces s srcly lower under free rade han under auarky n perod 0. Proof. hs follows from Proposon. hs pon we would lke o analyze he growh raes of GDP a perod-0 prces under boh auarky and free rade. he epressons for hese growh raes are no analycally comparable, however. We nsead provde an llusrave numercal eample. here are wo counres, and counry s relavely capal-rch. We se L L, β 0.96, a a 0.5, θ θ, α 0.6, α 0.4, k , and k he resuls on growh raes of real GDP are smlar o hose on growh raes of real ncome. s Fgure shows, under auarky he capal-poor counry grows much faser han he capal-rch counry, us as we would epec from a sandard growh model. hs compleely changes under free rade. Fgure 3 shows ha he capal-rch counry grows 30

32 faser han he capal-poor counry. Fgures 4 and 5 reerae hs fndng from he perspecve of each ndvdual counry. 6. Concluson o he een ha rade lberalzaon leads o hgher producvy or hgher raes of growh n real GDP, does so hrough mechansms ha are, for he mos par, ousde of hose analyzed n sandard models. Deermnng he relaon beween rade lberalzaon and growh s no us a challenge for emprcal research bu also for heorecal research. 3

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36 Fgure p y y p 35

37 Fgure uarky: GDP a perod-0 prces capal-poor counry nde ( world capal-rch counry perod 36

38 Fgure 3 Free rade: GDP a perod-0 prces 50 nde ( capal-rch counry capal-poor counry perod 37

39 Fgure 4 Capal-rch counry: GDP a perod-0 prces nde ( free rade world 0 00 auarky perod 38

40 Fgure 5 Capal-poor counry: GDP a perod-0 prces auarky nde ( free rade world perod 39