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1 Online Appendices: No Inended for Publicaion Unless Requesed Appendix A - Theoreical Deails and Proofs In his appendix we give more echnical deails and proofs of our main resuls. We begin wih a full saemen of he equilibrium concep for he closed economy, as well as a characerizaion of he closed-economy seady-sae growh rae referred o in he main ex. We hen sae he open economy equilibrium definiion, characerize seady-sae open economy growh raes, and define he rapped facors rade shock equilibrium. Definiion Closed-Economy Equilibrium Given iniial condiions A, x j, an equilibrium is a pah of wages, ineres raes, sock prices, and inermediae goods prices w, r, q f, p j, ogeher wih sock porfolio decisions, deb levels, final goods firm inpu demands, inermediae goods firms inpu demands, inermediae goods firm innovaion quaniies, inermediae goods dividends, aggregae innovaion quaniies, firm variey porfolios, and aggregae variey quaniies s f, b, H D, x D j,xs j+, M f+, d f,a, A f, M, such ha Households Opimize: Taking wages w, ineres raes r, and sock prices q f as given, he represenaive household maximizes he presen discouned value of is consumpion sream by choosing period consumpion C,debb +, and share purchases s f,i.e. hese decisions solve max C,b +,s j X = b + +C + q f (s f s f ) apple ( + r + )b +w H+ d f s f. f= Final Goods Firm Opimizes: Taking wages w and inermediae goods prices p j as given, he compeiive represenaive final goods firm saically opimizes profis by choosing labor demand H D and inermediae goods inpu demands x D j, i.e. hese decisions solve C f= max (H ) H,x k A (x j ) dj w H A p j x j dj. Inermediae Goods Firms Opimize: Taking marginal uiliies m, perfecly compeiive o-paen inermediae goods prices p j,japplea, and aggregae variey and innovaion levels A, M + as given, inermediae goods firms maximize firm value, he discouned sream of dividends, by choosing he measure of newly innovaed goods M f+ o add o he exising measure of varieies A f in heir porfolios, he supply of all inermediae goods for use nex period x S j+, and he price of on-paen inermediae goods p j,j 2 (A,A ], i.e. hese quaniies solve X max m d f p j,m f+, x j+ =

2 d f + x j+ dj + f apple p j x j dj A f+ A f f = M f+ A, = N Labor, Bond, Sock, and Inermediae Goods Markes Clear: H D = H, b + =,s f =, x D j+= x S j+ Final Goods Marke Clears: Y = C + A + x j+ dj+ f= Innovaion and Variey Consisency Condiions Hold: A + = A +M +,A f+ = A f +M f+,m + = M f+,a = f f= f= A f. Proof of Proposiion To complee he proof of Proposiion, we need o show ha he raes of growh of oupu, consumpion, and varieies are equal on a seady-sae growh pah. Firs, noe ha he firs-order condiions of he inermediae goods firm monopoly pricing decision immediaely yield p M+ = +r +, i.e. hey imply ha he monopoly price in any fuure period + is a fixed markup over firm marginal cos. Marginal cos is given here by he ineres rae r + from he curren period ino he nex period +. The household Euler equaion immediaely implies he ineres rae r + = ( C + C ). We hen immediaely obain he opimal inermediae goods firm pricing rule p M+ = ( C + C ). For laer reference, noe ha he pricing of o-paen varieies, which we will label R goods, is given by p R+ =+r + = ( C + C ) via perfec compeiion and he household Euler equaion. Now wrie he final goods marke clearing condiion C = H M x M + R x a R NP M + x M+ R + x R+ f, f= where we are using he noaion ha he measure of o-paen varieies is given by R and equal o R = A, and he measure of innovaed varieies M = ga. Now, recall he assumpion of seady-sae growh. If we define he growh rae of consumpion by g C, and noe ha he by symmery he individual firm paening raios g f = g n, we can use he inermediae goods firm pricing rules o rewrie he final goods marke clearing condiion 2

3 as C = h A +g H ( ) ( ) ( + gc ) H ( ) + N g N. ( + gc ) i g( ) 2 ( + gc ) H Since C A is consan, we conclude ha g = g C, so ha he innovaion opimaliy condiion, i.e. he firs-order condiion of an inermediae goods firm wih respec o R&D expendiures, reads N ( ) g = ( + g) H. This expression moivaes he choice of he scaling consan = N ( ), so ha he seady-sae growh pah growh raes are invarian o he number of firms or he degree of cos exernaliies across firms as well as he number of firms N. We obain he seady-sae growh pah innovaion opimaliy condiion g = ( + g) H. The lef-hand side, he marginal cos of innovaion, is sricly increasing in g, is equal o when g =, and limis o as g!. The righ-hand side, he discouned monopoly profis from innovaion, is sricly decreasing in g, is equal o a H> when g =, and limis o as g!. We conclude ha a seady-sae growh pah equilibrium exiss and is uniquely deermined by he value of g which saisfies he innovaion opimaliy condiion. This complees he proof. Definiion 2 Open-Economy Equilibrium Given any iniial condiions A, x j, x j, along wih a sequence of rade resricions, an equilibrium in he open economy is a se of erms of rade, ineres raes, wages, sock prices, and inermediae goods prices q, r, r,w,w,q f,qf, p j, and p j, along wih sock porfolio decisions, deb levels, final goods firm inpu demands, inermediae goods firms inpu demands, inermediae goods firm innovaion quaniies, inermediae goods firm porfolios, inermediae goods dividends, aggregae innovaion quaniies, impored variey measures, resriced variey measures, and aggregae variey quaniies s f,s f,b +,b +,HD,H D,x D j,xd j,xs j+, xs j+, M f+, A j,a f, d f,d f, M,I,R, and A such ha Norhern Household Opimizes: Taking wages w, ineres raes r, and sock prices q f as given, he represenaive household in he Norh maximizes he presen discouned value of is consumpion sream by choosing period consumpion C,debb +, and share purchases s f, i.e. hese decisions solve max C,b +,s j X = C 3

4 b + +C + f= q f (s f s f ) apple ( + r + )b +w H+ d f s f. Souhern Household Opimizes: Taking wages w, ineres raes r, and sock prices qf as given, he represenaive household in he Souh maximizes he presen discouned value of is consumpion sream by choosing period consumpion C,debb +, and share purchases s f, i.e. hese decisions solve X (C ) max C,b +,s f = f= b ++C + qf (s f s f ) apple ( + r + )b +w H + d f s f. f= Norhern Final Goods Firm Opimizes: Taking wages w and inermediae goods prices p j as given, he compeiive represenaive final goods firm in he Norh saically opimizes profis by choosing labor demand H D and inermediae goods inpu demands x D j, i.e. hese decisions solve max (H ) H,x j A (x j ) dj w H A p j x j dj. Souhern Final Goods Firm Opimizes: Taking wages w and inermediae goods prices p j as given, he compeiive represenaive final goods firm in he Souh saically opimizes profis by choosing labor demand H D and inermediae goods inpu demands x D j, i.e. hese decisions solve f= A max (H H ),x j x j dj w H A p j x jdj. Norhern Inermediae Goods Firm Opimizes: Taking marginal uiliies m,perfecly compeiive o-paen inermediae goods prices p j,j apple A, and aggregae variey, rade, and innovaion levels A, R, and M + as given, inermediae goods firms f in he Norh maximize firm value, he discouned sream of dividends, by choosing he measure of newly innovaed goods M f+ o add o he exising measure of varieies A f in heir porfolios, he supply of all inermediae goods in heir porfolio for use nex period x S j+, x S j+, and he price of on-paen inermediae goods p j, j2 (A,A ], i.e. hese quaniies solve X max m d f p j,m f+, x j+,x j+ = d f + (x j+ +x j+ )dj + f apple p j (x j +x j )dj A f+ A f f = M f+ A. Souhern Inermediae Goods Firm Opimizes: Taking marginal uiliies m and perfecly 4

5 compeiive o-paen inermediae goods prices p j,japple A as given, inermediae goods firms f in he Souh maximize firm value, he discouned sream of dividends, by choosing he supply of all inermediae goods in heir porfolios A f for use nex period xs j+, xs j+, i.e. hese quaniies solve d f + max M f+, x j+,x j+ X m d f = (x j+ +x j+)dj apple p j(x j +x j)dj. A f+ A f Labor, Bond, Sock, and Inermediae Goods Markes Clear Final Goods Markes Clear Y = H x j H D = H, H D = H, b + =, b + =, s f =, s f =, x D j = x S j, x D j = x S j. dj = C + R + x R+ + M + (x M+ + x M+)+ f= f Y A =(H ) x j dj = C + R + x R+ + I + (x I+ + x I+) No Arbirage Pricing Condiion Holds Trade is Balanced p j = q p j I p I x I = M p M x M Innovaion and Variey Consisency Condiions Hold: (R +I )=I,I +R = A,I +R +M = A, A f+ = A f +M f+,m = M f,m +R = A f,i +R = A f. f= Souhern Cos Advanage Condiion Holds: O-resricion goods are always produced in he Souhern economy only. Alhough he Fully Mobile economy wih a rade shock has essenially he same equilibrium concep as laid ou in he previous secion iniially discussing he open economy, we mus be more explici abou he Trapped Facors environmen. In he Trapped Facors equilibrium, Norhern inermediae goods firms face an addiional consrain due o he adjusmen coss prevening hem from immediaely responding in heir inpu usage o he 5 f= f=

6 new rade shock. Formally, hey mus solve he modified problem d f + max p f,m f+, x j+,x j+,x f X m d f = (x j+ + x j+)dj + f apple p j (x j + x j)dj A f+ A f A f+ (x j+ + x j+)dj + f X f E,+, where X f E,+ is he opimal inpu demand for period, given expecaions of he rade resricion E,+ for he nex period. X f is also indexed by f and depends boh upon he number of M goods ha he firm plans o produce for nex period, as well as he number of R goods ha he firm has in is porfolio and plans o produce for he nex period. Therefore, alhough hese porfolio shares are only allocaive in a period in which a rade shock occurs, we mus be explici abou he srucure we assume for he pre-shock porfolios of R goods held by each firm f, as well as he acual allocaion of he rade shock liberalizaion among exising firms measures of R goods. We now define some addiional noaion. Le es f be he share of o-paen R goods producion firm f anicipaes doing before he rade shock, where es f =. Then, le he rade shock allocae desrucion of f= R goods producion opporuniies across firms so ha only he proporion f of R goods varieies can sill be produced in each firm. As long as we have he consisency condiion es f f ( ) A =( f= )A, an arbirary choice of f will be consisen wih he rade shock!. We will henceforh make he assumpion ha es f = N for all firms, i.e. ha pre-shock allocaions of R goods producion is uniform across firms. This assumpion grows naurally ou of our srucure in which we assume ha firms coninue o be he producers of goods which hey invened, even afer hese goods fall o-paen and become perfecly compeiive. We also will now assume ha N is even, and ha half of he firms in he economy are in he No Shock indusry, indusry. The oher half of firms in he economy, hose in he Shocked indusry 2, experience a loss of R goods producion opporuniies during he rade shock wih only a fixed proporion 2 of R goods remaining. This framework is a rough approximaion of he heerogeneiy in he direc eecs on firms in developed counries during he rade liberalizaions of he early 2s. Seen in his ligh, indusries such as exiles which experienced a subsanial loss of proecion agains manufacurers in low-wage economies such as China, can be idenified wih indusry 2, while oher indusries would be represened by firms in group in our environmen. We now define a rapped facors equilibrium formally. 6

7 Definiion 3 Trapped Facors Trade Shock Equilibrium Given any iniial condiions A,x j, x j and a sequence of rade resricions,sapple, s=,s>, where he rade shif from o > is unanicipaed and aecs only Shocked indusry 2, leaving he proporion 2 of R goods in indusry 2 resriced, a Trapped Facors equilibrium in he open economy is a se of erms of rade, ineres raes, wages, sock prices, and inermediae goods prices q, r, r,w,w,q f,qf, p j, and p j, along wih sock porfolio decisions, deb levels, final goods firm inpu demands, inermediae goods firms inpu demands, inermediae goods firm innovaion quaniies, inermediae goods firm porfolios, inermediae goods dividends, aggregae innovaion quaniies, impored variey measures, resriced variey measures, and aggregae variey quaniies s f,s f,b +,b +,HD,H D,x D j,xd j,xs j+,xs j+, M f+,a f,a f,d f,d f,m,i,r, and A such ha he following hold. Norhern Household Opimizes: Taking wages w, ineres raes r, and sock prices q f as given, he represenaive household in he Norh maximizes he presen discouned value of is consumpion sream by choosing period consumpion C,debb +, and share purchases s f, i.e. hese decisions solve max C,b +,s f X = C b + + C + q f (s f s f ) apple ( + r + )b + w H + f= d f s f. Souhern Household Opimizes: Taking wages w, ineres raes r, and sock prices qf as given, he represenaive household in he Souh maximizes he presen discouned value of is consumpion sream by choosing period consumpion C,debb +, and share purchases s f, i.e. hese decisions solve X (C ) b + + C + max C,b +,s f = qf (s f s f ) apple ( + r +)b + w H + f= f= d f s f. Norhern Final Goods Firm Opimizes: Taking wages w and inermediae goods prices p j as given, he compeiive represenaive final goods firm in he Norh saically opimizes profis by choosing labor demand H D and inermediae goods inpu demands x D j, i.e. hese decisions solve f= max (H ) H,x j A (x j ) dj w H A p j x j dj. 7

8 Souhern Final Goods Firm Opimizes: Taking wages w and inermediae goods prices p j as given, he compeiive represenaive final goods firm in he Souh saically opimizes profis by choosing labor demand H D and inermediae goods inpu demands x D j, i.e. hese decisions solve A max (H H ),x j x j dj w H A p jx jdj. Norhern Inermediae Goods Firm Opimizes: Taking marginal uiliies m, perfecly compeiive o-paen inermediae goods prices p j,japple A, and aggregae variey, rade, and innovaion levels A, R, M + as given inermediae goods firms in he Norh maximize firm value, he discouned sream of dividends, by firs choosing he quaniy of inpus X E f,+ given heir expecaions of rade policy nex period, hen choosing he measure of newly innovaed goods M f+ o add o he exising measure of varieies A f in heir porfolios, he supply of all inermediae goods in heir porfolio for use nex period x S j+, x S j+, and he price of on-paen inermediae goods p j,j2 (A,A ], i.e. hese quaniies solve X max m d f p j,m f+, x j+,x j+,x f d f + = (x j+ + x j+)dj + f apple p j (x j + x j)dj A f+ A f A f+ (x j+ + x j+)dj + f X f E,+ f = M f+ A where we have ha E, s apple s,s+=, s >. Souhern Inermediae Goods Firm Opimizes: Taking marginal uiliies m and perfecly compeiive o-paen inermediae goods prices p j,j apple A as given, inermediae goods firms in he Souh maximize firm value, he discouned sream of dividends, by choosing he supply of all inermediae goods in heir porfolios A f for use nex period x S j+,xs j+, i.e. hese quaniies solve X max m M f+, x j+,x d f j+ = d f + (x j+ + x j+)dj apple p j(x j + x j)dj. A f+ A f 8

9 Labor, Bond, Sock, and Inermediae Goods Markes Clear Final Goods Markes Clear: Y = H Y x A =(H ) H D = H, H D = H, b + =, b + =, s f =, s f =, x D j = x S j, x D j = x S j. j dj = C + x j+ dj + (x j+ + x j+)dj + R + M + x j No Arbirage Pricing Condiion Holds f= dj = C + x j+dj + (x j+ + x j+)dj R + I + f Trade is Balanced p j = q p j I p I x I = M p M x M Innovaion and Variey Consisency Condiions Hold: (R +I )=I,I +R = A,I +R +M = A, A f+ = A f +M f+,m = M f,m +R = A f,i +R = A f. f= Souhern Cos Advanage Condiion Holds: O-resricion goods are always produced in he Souhern economy only. Proof of Proposiion 2: Open Economy Seady-Sae Growh Pah The demand schedules for inermediae goods, based on he Norhern and Souhern final goods firms echnologies, are given by f= f= x j =( ) Hp j x j =( ) H p j, where p j and p j are he prices of inermediae good variey j in Norhern and Souhern oupu unis, respecively, and p j = q p j. The opimaliy condiions for he Norhern inermediae goods firm, combined wih he Euler equaions of he Norhern represenaive 9

10 household for deb and equiy, are given by p R+ =+r + p M+ = f+ f+ = +r + p M+ (x M+ + x M+). Diereniaing he cos funcion and subsiuing in he opimal pricing rules we have ha he hird condiion, he innovaion opimaliy condiion, is given by (g f + )( ) = a ( C + C ) (H + q + H ). Now he balanced rade condiion can be wrien M p M x M = I p I x I ( + r ) g A ( ) H ( + r ) = A q ( + r )( ) (q ( )) H q ( ) H 2 +r 2 q =, g H +r where =( ) 2. Applying he assumpion of seady-sae growh, we immediaely obain from he Euler equaions of boh represenaive households ha ineres raes in he Norhern and Souhern economies, as well as he erms of rade, are consan. Also, exacly as in he proof of Proposiion A, he final goods marke clearing condiions for each economy, ogeher wih he assumpion of seady-sae growh, imply ha he raios C A, C A are consan, so ha we conclude ha ( + r) =(+r )= ( + g), q = H gh 2. Now he innovaion opimaliy condiion can be rewrien as g = a ( + g) (H + q H ). Also, subsiuing he erms of rade formula/balanced rade condiion ino he innovaion opimaliy condiion yields! g = H 2 a ( + g) H + gh H.

11 As a funcion of g, he marginal cos of innovaion on he lef-hand side is sricly increasing in g, saring a and growing exponenially o as g!. The righ-hand side, he discouned monopoly profis from sale of newly paened goods in he Norh and he Souh, is sricly decreasing in g, asympoing o as g! and o as g!.we conclude boh ha here exiss a seady-sae growh pah equilibrium for his economy, and ha i is he unique seady-sae growh pah growh rae. For any given fixed value of, we denoe his growh rae, and he associaed erms of rade, by g( ) and q( ). This complees he proof.

12 Appendix B - Daa and Model Robusness Checks This Appendix firs describes he firm-level daa sources and variable consrucion used in for he producion of Table in Secion 2. Then, we describe he aggregae daa sources used o calibrae our model and for various figures hroughou he paper. We conclude by lising he empirical sraegy behind some alernaive rade policy calibraion exercises used in his paper and previous versions of he projec. Innovaion & Trade Daa The empirical analysis in Table in Secion 2 of his paper draws from a daase buil from 4 disinc sources. The firs source is Bureau van Dijk s Amadeus daabase, conaining firm-fiscal year level accouning saemens of public and privae firms in European naions. Work by Bloom, Draca, and Van Reenen (25) mached his daase o microdaa on paening from he European Paen O ce, he second source of daa. We use wo measures from his mached daase - described furher in Bloom, Draca, and Van Reenen (25) - as dependen variables in Table. For Panel A, we define ln(patents) ijk =ln(+pat ijk ), where PAT ijk is he number of successful paen applicaions per worker filed by firm i in indusry j in counry k in year. The dependen variables is he five-year dierence of his variable. For Panel B, he dependen variable is he five-year growh rae of employmen. The hird source of informaion we use is he UN Comrade daabase, from which we exraced HS-6 digi produc by year rade flows from China ino each of he naions in our Amadeus sample, plus he US. We concord he HS-6 digi produc flows ino 4- digi SIC indusry codes, which is he uniform indusrial classificaion mached by Bloom, Draca, and Van Reenen (25) o he European firm-level daa. The fourh source of informaion we use is indusry producion ables from he US and Europe. We use he US NBER-CES manufacuring daabase, providing informaion on US producion by SIC 4-digi manufacuring indusry and year, as well as aggregaes from he European Prodcom daabase in he Bloom, Draca, and Van Reenen (25) daabase. To pull hese ogeher, we compue base-year producion Y jk996 in each 4-digi SIC manufacuring indusry j in 996 in he counries k including he US and he European naions in our sample. We define IMPjk CH as he raio of impors from China ino indusry j in counry k in year scaled by base-year producion in ha indusry. Then, he change in Chinese impors Imp CH jk for indusry j in counry k in year is simply he 5-year dierence of his variable. In Table, when k includes European naions his impor growh measure is he endogenous rade oucome on he righ hand side, and when k = US we use he variable as he insrumen for our IV specificaions. We combine hese source of infromaion o obain a firm-fiscal year daase ha afer censoring ouliers in he rade flows resuls in a sample of paen growh, employmen growh, and Chinese impor flows for around 25, firm-fiscal years for around 7, firms in 235 manufacuring indusries based on daa from spanning he eleven European naions Ausria, Germany, Denmark, Spain, Finland, France, Grea Briain, Ireland, Ialy, Norway, and Sweden. = M jk CH Y jk996 Calculaing he raio of H o H for model calibraion To calculae he raio of H o H, we follow he human capial accouning approach in Hall and Jones (999) and compue he human capial endowmen in counry c from he Barro and Lee (2) daa as H c = e µcsc P c,wheres c is he average number of years of schooling compleed in he adul populaion above age 25, and P c is he size of he populaion of he counry c in 2. We ake ino accoun he dierences in educaional qualiy and he reurns o schooling across counries by using he Mincerian reurns o educaion of immigrans in he Unied Saes from counry c, µ c, from Table 4 in Schoellman (2). 2

13 If Mincerian reurns for a counry c are no available in Schoellman (2), we ake µ c = 7% for non-oecd counries and µ c = 9% for OECD counries. These are he averages of reurns o schooling P for he wo caegories in Schoellman s sample. We finally define H non OECD =2. H c, where he raio 2. correcs for he fac ha no all non- c/2oecd OECD counries are represened in he Barro and Lee daa. In paricular 2. is equal o he raio of he non-oecd o OECD populaion raio in 2 in he Wolfram Alpha daabase (wih full global coverage) o he non-oecd o OECD populaion raio in 2 in he Barro and Lee daa. Such a procedure relies on he implici assumpion ha he schooling raes and reurns o educaion in counries no represened in he Barro and Lee daa are similar o hose wih daa presen. From he procedure above we obain H H 2.96, which we round o 3. in he ex discussion. Calculaing he Trade Shares for Figure The real per-capia oupu growh rae is from he US NIPA ables, compued as he average annual real GDP per capia growh rae from Trade daa was downloaded from he OECD-STAN daabase, and OECD GDP daa comes from he Penn World Tables, Version 9.. The non-oecd counry o OECD impors o OECD oupu raios were compued over he years All of he daa and simple calculaions performed in he calibraion procedure are available on Nicholas Bloom s websie: hp:// Figure plos he non-oecd impors o OECD GDP raio over his period, ogeher wih Chinese impors ino he OECD. Compuing Paen Raios for Figure B We downloaded Unied Saes Paen and Trademark O ce (USPTO) microdaa on paens graned from he mid-97s onwards from he USPTO PaensView websie. Figure B plos he raio of all paens wih a foreign (non-us) assignee, non-oecd assignee, or Chinese assignee o he oal number of paens graned from Trade Policy Subsiuion away from China Toal observed low-wage impor growh ino he OECD as a share of GDP from is equal o 4.9%. Growh in Chinese impor shares was equal o 2.5%, implying ha non-china/non-oecd counries saw heir impor shares ino he OECD increase by 2.4%. The no China counerfacual in he main ex assumed ha he growh in Chinese impor shares was compleely removed from liberalizaion over his period. If, however, policy-makers parially subsiued owards oher non-oecd impors in lieu of Chinese impors, we would sill see impor share growh in he counerfacual. To analyze he quaniaive magniude of his subsiuion eec, we consider a case where exacly one half of Chinese impor growh is realized in he no China counerfacual, via subsiuion owards oher non-oecd counries. Saring wih a low-wage impor share of 3.5%, his half subsiuion case exhibis impor share growh of.5* = 3.65%, so ha he resuling arge impor o oupu raio pos-liberalizaion in he counerfacual is = 7.5%. Figure B2 plos he resuling wo rapped facors ransiion pahs, analogous o Figure 9, in he oal observed impor liberalizaion and Half China cases. As can be seen immediaely, he ransiion pahs dier by less han he case in which all Chinese impor growh is removed, which works o reduce he marginal conribuion of China o 3

14 US Paens from Foreign Counries Percen of all US Paens Toal Foreign (mean = 45.%) Non OECD (mean = 9.57%) China (mean =.2%) Applicaion Year Figure B: Non-OECD Paen Raios are Small Noe: Paen fracions are compued from he USPTO PaensView daabase. The classificaion of paens by assignee o he required OECD, non-oecd, and Chinese caegories is done by he naionaliy of assignee, and a given counry s OECD member saus as of he applicaion year. Each series is normalized by he oal number of graned US Paen and Trademark O ce applicaions in he same year. The repored mean raios are compued over model calibraion range

15 A: Variey Growh Annual % Baseline No China Pre Shock BGP Baseline Pos Shock BGP Period B: Souhern Terms of Trade Norh/Souh Period Figure B2: Trade Liberalizaion wih Half of Chinese Impor Growh Noe: The figure displays he ransiion pah in response o rade liberalizaion in wo scenarios. The firs ransiion pah, in solid black, Baseline, replicaes he Trapped Facors ransiion pah displayed in Figure 6 above. A permanen and unanicipaed rade liberalizaion from o > is announced in period o become eecive in period. The second ransiion pah in green wih riangle symbols, Half China, plos he Trapped Facors ransiion pah, saring wih he same iniial condiions as Baseline bu insead considering a counerfacual increase of o a level beween and which maches pos-liberalizaion impors o GDP raios assuming ha half he growh in Chinese impors ino he OECD occurs hrough policy subsiuion o non-china, non-oecd counries. The upper horizonal solid blue line is he pos-shock seady-sae growh pah, and he lower horizonal dashed red line is he pre-shock seady-sae growh pah.

16 welfare o a oal of 4.6% (Norh) and 4.5% (Souh). In his alernaive counerfacual, he impac of China is equal o 8% (Norh) and 9% (Souh) of he overall welfare gains from rade observed in he daa. Alernaive Calibraion from 23 Paper Noe ha a previous version of our calibraion sraegy, wih resuls published in A Trapped Facors Model of Innovaion, (American Economic Review: Papers and Proceedings, 23) yielded smaller dynamic impacs of rade liberalizaion. Our improved calibraion sraegy here diers from ha earlier work in four respecs. Firs, we consider a model period of en years raher han one year o mach a more plausible eecive monopoly lengh. Second, we base he calibraion on impors o value added raios raher han impors o gross oupu raios, since daa availabiliy for China is beer for value added. Third, insead of calibraing he pos-liberalizaion rade openness via a limiing highes which sill mainained produc-cycle rade (i.e. q( ) < ), he firs wo calibraion changes allow us o now direcly mach observed pre- and pos-liberalizaion rade raios, which resuls in larger growh impacs more aligned wih observed rade liberalizaion. Fourh, we now have access o daa on impor liberalizaion spanning a larger number of years insead of In he larger ime span, liberalizaion expanded before sabilizing, increasing he implied dynamics gains from rade. 4

17 Appendix C - Soluion Technique and Equilibrium Condiions for he Calibraion Please find code for he quaniaive resuls in he paper on Nicholas Bloom s websie a hp:// We solve each of he sysems of nonlinear equaions laid ou below using paricle swarm opimizaion as implemened in R. This is a robus global nonlinear opimizaion echnique. Seady-Sae growh Pah As documened in he proof of Proposiion 2, he seady-sae growh pah growh rae g( ) of he open economy given rade resricion is fully characerized by he equilibrium innovaion opimaliy condiion g( ) = a ( + g( )) H + H g( )H! 2 H. All oher long-run quaniies, in paricular he ineres raes and exchange rae, are direc funcions of his seady-sae growh pah growh rae hrough he Euler equaions and balanced rade condiion ( + r( )) = ( + r ( )) = ( + g( )) q( )= H g( )H 2. Fully Mobile Transiion Dynamics To compue he ransiion dynamics of he fully mobile model in response o a rade shock in period, saring from he seady-sae growh pah associaed wih rade resricion, we firs pick a horizon T. We also normalize A =. Then, we assume ha he model has converged o he seady-sae growh pah associaed wih by period T.Thissrucure requires ha we solve for 3(T ) prices, {q,r,r } T =2. These 3(T ) prices are pinned down by 3(T ) equaions: he balanced rade condiion, he Norhern Euler equaion, and he Souhern Euler equaion, in periods =,...,T. These equaions are given by q = H g H C+ C 2 C + C +r +r = ( + r + ), = ( + r + ). 2, We noe ha all allocaions in he ransiion pah are a funcion of hese hree prices. 5

18 Inermediae goods prices follow he monopoly markup or compeiive pricing condiions p M = +r,p R= (+r ),p I = q ( + r ) p M= q +r,p R= (+r ),p I =(+r ). The final goods firms demand schedules hen yield x j =( ) Hp j, x j =( ) H (p j), The firs-order condiion for innovaion a Norhern inermediae goods firms, ogeher wih symmery across firms and he equilibrium price and quaniy decisions laid ou above, yields he innovaion opimaliy condiions g+ = ( + r + ) H + q + H, which uniquely pin down he variey growh rae g + as a funcion of erms of rade and ineres raes. Given our characerizaion of g as a funcion of prices, i only remains o pin down C and C as a funcion of prices. Bu his is easily accomplished by noing ha C +M + (x M+ +x M+)+R + x R+ + = Y Y = H M x M + R x R + I x I = f = g+ A f= C +I + (x I+ +x I+)+R + x R+= Y Y =(H ) M (x M) + R (x R) + I (x I) A + =(+g + )A M + = g A R + =( + )A I + = + A. Since all allocaions in his economy are herefore a funcion of he 3(T ) prices, we can consruc he errors in 3(T ) equaions above given any inpu sequence of prices. The percenage squared errors of his sysem of equaion are minimized using paricle swarm opimizaion. Afer solving for he ransiion pah price pahs, we check o see if he cos advanage for I goods producion is mainained by he Souh, jusifying our M, R, I goods 6

19 pariioning. This is equivalen o checking ha, for each period ( + r )q apple ( + r ). In he baseline resuls shown in Secion 5, we choose T =7. Trapped Facors Transiion Dynamics The equilibrium condiions which we mus solve o compue he ransiion dynamics for he rapped facors model are idenical o hose in he fully mobile economy, for period 2,...,T. There are, however, dierences in he equilibrium condiions in he period of he shock. In paricular, here is heerogeneiy in he response of he aeced and unaeced indusries o he shock, and insead of solving for simply he 3(T ) prices {q,r,r } T =2 as in he fully mobile case, we mus solve for hese prices and he four addiional variables {g2,g2 2,µ,µ 2 }. These variables are paening raes and shadow values of inpus wihin Norhern firms in he unaeced indusry () and he aeced indusry (2). Therefore, we mus pin down 3(T ) + 4 quaniies, which we do wih 3(T ) + 4 equaions: 2 q = 4 H H h n 2 (µ ) g + n 2 (µ 2 ) g 2 q = H g H C+ C C + C 2 +r +r 3 2 i5 +r +r 2, 2,...,T = ( + r + ),=,...,T = ( + r + ),=,...,T (Ng ) = ( + r ) (µ ) (H + q H ) (Ng 2 ) = ( + r ) (µ 2 ) (H + q H ) 2 N ( )( ) g( ) g( ) ( + r( )) H+ + N N ( ) 2 ( + r( )) (H + q( ) H ) = N ( )( ) (µ ) ( + r ) H+ N g +g ( ) 2 ( + r ) (µ ) (H + q H ) N ( )( ) g( ) g( ) ( + r( )) H+ + N N ( ) 2 ( + r( )) (H + q( ) H ) = N 2 ( )( ) (µ 2 ) ( + r ) H+ N g 2 7

20 +g 2 ( ) 2 ( + r ) (µ 2 ) (H + q H ). The firs 3(T ) equaions are simply he balanced rade and Euler equaions for he Norhern and Souhern households in periods,...,t. The balanced rade condiion mus be modified in period o reflec he fac ha flows of M goods from Norh o Souh come from boh indusry and indusry 2, wih dieren prices and quaniies for each. The final four equaions represen he innovaion opimaliy condiions for firms in indusry and indusry 2, as well as he rapped facors consrains for firms in each indusry. The innovaion opimaliy condiions are simply he firs-order condiions of firms wih respec o he mass of new varieies o be innovaed in period for use in period. Noe ha we are defining µ = and µ 2 = 2,wherem and m 2 are he mulipliers on he rapped facors inpu consrains in he opimizaion problem for Norhern inermediae goods firms in period. A fall in µ below represens a fall in he shadow value of inpus for an inermediae goods firm. Also, if M f is he number of new paens innovaed by a firm in indusry f in period for use in period, we are following he convenions g f = M f A, and imposing he consisency condiion N g = (g 2 ). The rapped facors consrains are simply he inpu demands for R goods producion and M goods innovaion and producion expendiure pre-shock (lef-hand side) and posshock (righ-hand side). The inpu consrains dier across indusries because he R goods available in he pos-shock period in indusry 2 for producion are reduced by he facor 2,where 2 saisfies + 2 =, 2 which is he consisency condiion discussed in he equilibrium definiion. Also, he righhand side on he rapped facors consrains ake ino accoun he following opimal pricing rules in he period of he shock: p M = µ +r,p R =(+r ), p 2 M = µ 2 +r,p2 R =(+r ). The demand condiions are idenical o hose laid ou in he fully mobile secion. Inermediae goods firm innovaion coss on he righ hand side of he rapped facors consrain are given by = N g 2 = N g 2, which is a direc applicaion of he definiion of he innovaion cos funcion. All of he oher quaniies needed for consrucion of he Euler equaion errors and balanced rade 8

21 condiions are idenical o hose in he fully mobile economy, wih he excepion of he resource consrains in he Norh and Souh in periods and which mus be modified o read Y = C + N g 2 A (x M +x M)+ Y = H apple N 2 Y = C +( ga (x M) + N ( ) apple Y =(H ) N g 2 A (x M) + N g 2 2 A (x 2 M +x2 M) N 2 2 )A x R+ A (x I +x I) N g 2 2 A (x 2 M) + N 2 A (x 2 R) + A x I g 2 A (x 2 M) +( N 2 2 A x R+ A (x R) + N ( ) 2 A x 2 R 2 2 )A (x R) + A (x I). Afer compuing he ransiion pah in he above manner, we mus verify ha µ,µ 2 <, jusifying our imposiion of he rapped facors inequaliy consrain as an equaliy consrain. We mus also check he Souhern cos dominance condiion for I goods in each period, i.e. min (µ,µ 2 )( + r ) q ( + r ), ( + r ) q ( + r ),=2,..,T, q,q T apple. Welfare Calculaions We illusrae our mehod of compuing he consumpion equivalen variaion by explicily laying ou he formulas used o compue he welfare gains o rade from he fully mobile rade shock. All oher welfare calculaions are similar. W NS = X = C NS,W NS = X = C NS W FM = X = C FM,W FM = X = C FM where he consumpion allocaions on he fully mobile FM compued ransiion pah from,...,t are direcly compued and consumpion is assumed o grow a he rae g( ) for all economies from period T onwards. The no shock NS case is consumpion assuming ha allocaions are hose of he pre-shock seady-sae growh pah wih consan, 9

22 growh a rae g( ). Then, we solve for x and x, X = C NS ( + x) = X = C FM, X = C NS ( + x ) = X = C FM The welfare numbers repored in he ex are x and x.. Decomposing Oupu Growh Figure and he discussion in Secion 4.6 in he main ex inroduce a decomposiion of oupu growh ino componens due o various price and variey facors. For any wo periods and beween which we wan o decompose oupu growh, noe ha Norhern oupu in each period is given by Y = H M x M + R x R + I x I Y = H M x M + R x R + I x I. Clearly, oal oupu growh beween he wo periods is dependen on he raio Y Y. However, o perform he decomposiion displayed in Figure, we simply define wo inermediae values of oupu. The firs value Y RoI = H M x M +(R I + I )x R + I x I simply convers he mass of goods which are resriced R goods in ino impored I goods varieies a he exensive margin which will prevail in period. The change from Y o Y RoI is driven solely by he reduced prices and higher inensive margins on I goods in he Norh, alhough he oal mass of varieies remains fixed. The second value Y MoR = H R x R + I x I furher convers he exising monopoly M varieies ino o-paen R goods varieies. The change from Y RoI o Y MoR is driven solely by he lower price on pre-exising M goods in ha are convered ino lower-cos R goods and used more inensively. Clearly, he remaining dierence from Y MoR o he observed Y is driven mosly by he inroducion of new M goods varieies, i.e., new exensive margin eecs, alhough he swich from inensive margins prevailing in o also has a minor eec. We now urn o a more deailed explanaion of he figure iself. The boom black area labelled Cheaper R o I Goods wihin each bar in Figure reflecs he raio Y RoI Y.The middle blue area wihin each bar reflecs he raio Y MoR Y. And he bar heigh iself reflecs he oal raio Y Y. Each of hese raios is expressed in annualized percenage changes, i.e., 2

23 we compue " Y gy RoI RoI = Y " Y gy MoR MoR = Y g Y = " Y Y # #, # and Figure plos hese growh raes cumulaively in he order gy RoI,hengY MoR,hen g Y. For he Souhern economy, he growh raes are defined analogously, alhough he lack of a price dierence for Souhern final goods firms beween R and I goods implies ha he souhern equivalen of gy RoI = for all periods. 2

24 Appendix D - Semi-endogenous Growh Model In his Appendix we consider he semi-endogenous growh model approach o show ha i delivers quaniaively similar resuls o our fully endogenous growh model. As documened in Jones (995a,b) he implicaion of a model like ha considered in he main ex, wih srong scale eecs implying ha he long-erm growh rae is dependen upon he level of human capial, is rejeced by he ime series evidence which documens he concurrence of rising populaions and researcher numbers wih consan growh raes. Jones proposes a small modificaion o he producion funcion for new varieies, or alernaively, o he cos funcion for innovaion, which implies smaller reurns from he exising sock of varieies in he producion of new paens. This change o he model convers he srucure ino a semi-endogenous growh model wih weak scale eecs, since he long-erm growh rae is now proporional o he growh rae of human capial raher han he level of human capial. Analogously, in our conex wih produc-cycle rade, such a modificaion of he model leads o long-erm growh raes proporional o human capial growh raes and, crucially, independen of he rade liberalizaion policy. As we will see, however, a reasonable calibraion of a semi-endogenous growh model consisen wih he daa on boh per-capia growh raes and populaion growh displays exremely long ransiion dynamics and considerable emporary eecs on variey growh raes from rade liberalizaion. Therefore, he emporary growh eecs of liberalizaion (and he permanen level eecs), imply similar resuls for welfare regardless of wheher one considers a srong or weak scale eecs model. Given ha he model wih srong scale eecs delivers closed-form expressions for he seady-sae growh pah growh raes dependen upon he rade policy parameer, and given ha he ransiion dynamics for he srong scale eecs model are of a more reasonable lengh, we prefer o work wih he srong scale eecs model as our baseline version. Model We now lay ou he model srucure and equilibrium concep in he semi-endogenous growh framework, for he fully mobile environmen only. Populaion and Human Capial: We assume ha in he Norh and in he Souh here is a coninuum of idenical households of measure, each wih an expanding se of members [,L ] and [,L ], respecively. We furher assume ha here is an consan level of human capial per member of he populaion, i.e. H = hl and H = hl,respecively. This assumpion implies ha preferences of he CRRA form defined over per-capia consumpion or over consumpion expressed relaive o human capial dier only by a consan, and for convenience we express preferences as per uni of human capial. Norhern Households: Given a sequence of wages w,firmsockpricesq f,firmdiv- Noe ha we omi below a erm muliplying per capia preferences by he size of he populaion, which would be proporional o H given our assumpions. Such an assumpion, as will be seen below, resuls in a level shif in ineres raes. However, and imporanly, our assumpion prevens he mechanical inflaion of he welfare gains from rade liberalizaion (relaive o our baseline srong scale eecs model wih no populaion growh) simply because liberalizaion gains occur in he fuure wih a larger populaion. In unrepored resuls, however, we also solved an alernaive model wih per-capia preferences weighed by populaion size. Predicably, his resuled in larger welfare gains from rade liberalizaion. 22

25 idends D f, and ineres raes r, a Norhern household supplies labor inelasically and chooses consumpion C, porfolio posiions S f, and bond purchases B + o solve he problem X C H max C,B +,S f C + B + + = q f (S f S f ) apple w H +(+r )B + f= S f D f Souhern Households: Given a sequence of wages w,firmsockpricesqf,firmdividends Df, and ineres raes r, a Souhern household supplies labor inelasically and chooses consumpion C, porfolio posiions Sf, and bond purchases B + o solve he problem f= max C,B +,S f X = C H C + B+ + qf (S f Sf ) apple w H +(+r )B + f= f= S f D f Norhern Final Goods Firms: Taking as given a sequence of wages w and inermediae goods prices p j for each variey j 2 [,A ] as given, perfecly compeiive Norhern final goods firms choose inpu demands H and x j o solve he saic problem max H,x j Y A p j x j dj w H max H,x j H A x j dj A p j x j dj w H Souhern Final Goods Firms: Taking as given a sequence of wages w and inermediae goods prices p j for each variey j 2 [,A ] as given, perfecly compeiive Souhern final goods firms choose inpu demands H and x j o solve he saic problem max Y H,x j A p jx jdj w H max H,x j A (H ) (x j) dj A p jx jdj w H Norhern Inermediae Goods Firms: Taking as given a sequence of ineres raes r, along wih aggregae variey socks A, as well as Norhern and Souhern final goods firms inermediae demand schedules, each of N Norhern inermediae goods firms f makes monopoly producion x Mj+ and x Mj+, perfecly compeiive producion x Rj+, and 23

26 innovaion decisions M f+ o solve he following problem max x Rj+,x Mj+,x Mj+,M f+ X m D f, = D f + f + (x j+ + x j+)dj apple A f+ A f p j (x j + x j)dj, where m + +r + or m = = +r. This is equivalen o sock price or value maximizaion as can be seen from ieraion on he Norhern Household s firs order condiion for S f and inserion of he Norhern household firs order condiion for B +. A all imes, he innovaion cos funcion is given by m = f = M f+ A, where = and 2 (, ), and = N is again a scaling consan discussed in more deail below. This innovaion cos funcion is idenical o he srong scale eecs innovaion cos funcion, wih he excepion ha < here and = in ha case. Souhern Inermediae Goods Firms: Taking as given a sequence of ineres raes r, as well as Norhern and Souhern final goods firms inermediae demand schedules, each Souhern inermediae goods firm makes perfecly compeiive producion x Ij, x Ij, and x Rj decisions o solve he following problem = +r + max x Ij,x Ij,x Rj X m Df, = Df A + (x j+ +x j+)dj apple p j (x j +x j)dj f+ A f +r where m + m or m = =. This is equivalen o sock price or value maximizaion as can be seen from ieraion on he Souhern Household s firs order condiion for S f and inserion of he Souhern Household s firs order condiion for B+. Terms of Trade Noaion/No Arbirage Condiion: p j = q p j Trade Resricions and Monopoly Srucure: There is one-period monopoly proecion for any newly innovaed M goods, rade resricion for an exogenously se proporion of o-paen goods labeled R goods, and impors from Souh o Norh of he exogenously se proporion of o-paen goods labeled I goods. Equilibrium Summary Some sequence of is exogenously se by he Norhern governmen Norhern households opimize consumpion, savings, and equiy purchase decisions 24

27 Souhern households opimize consumpion, savings, and equiy purchase decisions Perfecly compeiive Norhern final goods secor opimizes human capial and inermediae goods demand Perfecly compeiive Souhern final goods secor opimizes human capial and inermediae goods demand Norhern inermediae goods firms opimize M goods innovaion, M goods monopoly producion, and perfecly compeiive R goods producion decisions Souhern inermediae goods firms opimize perfecly compeiive R and I goods producion decisions Trade is balanced: I p I x I = M p M x M Bond markes clear: B = B = Equiy markes clear: S f + S f = Human capial marke clear H D = H,(H ) D = H Final goods marke clears/resource consrain is saisfied in he Norh Y = H A x j dj = C + (x j+ +x j+)dj+ A + f= f Final goods marke clears/resource consrain is saisfied in he Souh Y = H A x j dj = C + (x j+ +x j+)dj A + Consisency condiions hold M f+ = M + = A + f= A = I, ( H H = H H = H H )A = R A Souhern cos dominance for I goods q ( + r ) < ( + r ) 25

28 Equilibrium Condiions for Reference For laer reference in he proof of Proposiion D, we now lis he equilibrium condiions in his environmen. Norhern Households (HH) Firs Order Condiions (FOC) H C = =(+r + ) + (D f q f )+ + q f+ =! ( + r + )= H + C+ H = c+ ( + g H ) H H + C c X Y! q f = m D f, m = = +r = Souhern Households FOC s! ( + r +) = H + H C + H + H C = c ( + g H ) + c, c C H, c C H! qf = X m Df, = Norhern Final Goods Firm FOC s m = Y = +r Souhern Final Goods Firm FOC s ( )H xj p j =! x j =( ) p j H x j w = ( )(H ) (x j) p j =! x j =( ) (p j ) H Norhern Inermediae Goods Firm FOC s (H ) (x j) w = max x M+,M f+,x R+ X m D f D f = p j (x j + x j)dj f (x j+ + x j+)dj A f A f+ m f + x M+ + x M+ + m + p M+ (x M+ + M+) = f+ = H p M+ = arg max p m ( ) p (H+ +q + H +)+m + ( ) p (H+ +q + H +) 26

29 p M+ = m m + m + m + p R+ =! p M+ = +r +, x M+ =( ) 2 (+r+ ) H+, x M+ =( ) 2 (+r+ ) q! p R+ =+r +, x R+ =( ) ( + r+ ) f+ = f+! = A+ A f = g A+ A+ f=! g A+ A Souhern Inermediae Goods Firm FOC s, imposes symmery g Af+ =(/N )g A+, imposes symmery g Af+ =(/N )g A+ = ( + r + ) max X m Df, = D f = A f p j (x j + x j)dj m + m +p R+ = m + m +p I+ = H + + q + H+ A f+ (x j+ + x j+)dj! p R+ =(+r +), x R+ =( ) ( + r + ) H +! p I+ =(+r +),p I+ = q + p I+, x I+ =( ) ( + r + ) H +, Balanced Trade Condiion x I+ =( ) ( + r + ) q + H + I p I x I = M p M x M A q ( + r )( ) ( + r ) +r q H = g A A ( ) 2 ( + r ) q H 2 +r 2 q = g A H +r, =( ) 2 Norhern Resource Consrain Y = H M x M + R x R + I x I = C + M + x M+ + x M+ + R + x R+ + H + H + 27

30 Souhern Resource Consrain Y =(H ) M (x M) + R (x R) + I (x I) = C + R + x R+ + I + (x I+ + x I+) Consisency Condiions and Terms of Trade Noaion Convenion M + = A + A, R + =( +)A, I + = + A M + = M f+, Souhern Cos Dominance for I Goods f= p j = q p j q ( + r ) apple ( + r ) Proposiion D A seady-sae growh pah wih consan exiss and is unique. On his seady-sae growh pah he growh rae g A of varieies saisfies ( + g A ) =(+g H ), ineres raes saisfy +r =+r = ( + g H )( + g A ), and he erms of rade saisfies q = g A H 2 H, =( ) 2. On his unique seady-sae growh pah, oupu and consumpion grow as he facor ( + g H )(+g A ) and per capia consumpion has growh rae equal o he number of varieies g A. Proof of Proposiion D: Semi-endogenous Seady-sae Growh Pah Assume consan growh raes of quaniies and a consan. Then he HH Euler equaions yield +r = ( + g H )( + g c ) +r = ( + g H )( + g c ), which implies ha ineres raes are consan. Bu he BT condiion is hen H 2 +r q = g A H +r 2, 28

31 which implies ha he erms of rade are consan. Bu he innovaion FOC is g A A LHS / = ( + r) ( + g A ), H + + q H +. RHS / ( + g H )! ( + g A ) =(+g H ) on any BGP. Now noe ha prices of all goods are consan because hey are funcions of ineres and erms of rade, so he inensive demand margins are also consan muliples of human capial. In paricular, x M =( ) 2 ( + r) H, x M =( ) 2 ( + r) q H x R =( ) ( + r) H, x R =( ) ( + r ) H x I =( ) ( + r ) q H x I =( ) ( + r ) H Noe also ha by he consisency condiions M = g A A,R =( )A,I = A are all consan muliples of A (given he fac ha A = +g A A ). Y = H Now from he uses ideniy we also have M x M + R x R + I x I Y / H A / (( + g H )( + g A )) Y = C + M + x M+ + x M+ + R + x R+ + Bu from above M + x M+ + x M+ / H A = ga A + R + x R+ / H A / A + / ( + g A ) + Bu since + g H =(+g A ) on any BGP by he innovaion FOC, we have / (( + g H )( + g A )), Therefore, we have C / (( + g H )( + g A )), c / ( + g A ), implying ha g c = g A, so ha +r = ( + g H )( + g A ). 29

32 Now similar reasoning shows ha Y / H A, C / H A, c / A, so ha q = g A +r =+r H 2 +r 2 H +r = g A H 2 H. Noe ha his final expression implies ha for su cienly small, q<, which is equivalen along he BGP o Souhern cos dominance in I goods. Finally, uniqueness follows from he innovaion FOC g = ( + r) H + + q H +. A A Afer dividing boh sides by ( + g H ), we have ha ga / ( + r) H + q H. Since >, he LHS is increasing in g A.Sincer is increasing in g A and q is decreasing in g A, here is a mos one soluion for g A. Since all oher prices are funcions of g A,hey are unique as well. Exisence is shown by noing ha he increasing LHS asympoes o as g A! and o as g A!. The decreasing RHS asympoes o as g A! (see he formula for q ) and o as g A! (see he formulas for r and q ). By he coninuiy and monooniciy of everyhing involved, as well as he inermediae value heorem, g A exiss uniquely. This complees he proof. Calibraion Sraegy We would like o consider, as in he Fully Mobile environmen described above, he ransiion pah associaed wih a shock from he balanced growh pah associaed wih rade policy parameer o he balanced growh pah associaed wih rade policy parameer. As before, we will consider he impac of a permanen and unanicipaed shock moving he policy parameer from o. The iming convenions are idenical o hose discussed in he Fully Mobile rade shock iming secion in he main ex. According o he OECD Naional Accouns Main Aggregaes daase and Populaion daase, as curren in early May 23, he average oal OECD real GDP per-capia growh rae from is equal o approximaely 2.37% per year. The average OECD populaion growh raes over his same period is approximaely equal o.78% per year. Now noe ha he seadysae growh pah relaionship above beween g H and g A is a logarihmic equaion whose soluion yields = log( + g H) log( + g A ). Above, noe ha g A and g H are -year versions of he annual growh raes aken 3