Production Sharing and Business Cycle Co-Movements with Heterogeneous Firms

Transcription

1 Producion Sharing and Business Cycle Co-Movemens wih Heerogeneous Firms Andrei Zlae Boson College April 8, 008 Absrac In his paper I examine wheher he co-movemen of business cycles can be explained by he rms decision o relocae he producion of inermediae goods across borders hrough verical FDI. Firs, using daa from Mexico s maquiladora indusry, I show ha o shore producion is pro-cyclical wih he U.S. manufacuring oupu, alhough he iming of he maquiladora s response di ers a he inensive and he exensive margins: hours worked respond immediaely, whereas he number of o shore plans responds wih a lag of hree quarers. Second, I build a dynamic sochasic general equilibrium (DSGE) model wih heerogeneous rms and rm enry dynamics in a wocounry framework (Norh and Souh). The model examines he abiliy of hree inernaionalizaion sraegies of mulinaional rms - verical FDI, horizonal FDI, and endogenous expors - o ac as ransmission channels of aggregae shocks across counries. I derive an asymmeric seady sae in which he relaively lower wage in Souh acs as an incenive for he rms in Norh o relocae producion o shore. A posiive echnology shock in Norh encourages rm enry, riggers he appreciaion of relaive wages and causes more rms o relocae producion o shore. Higher demand for labor in Norh (due o rm enry) and simulaneously in Souh (due o o shoring) generaes posiive co-movemen of wages and aggregae incomes. Relaive o he benchmark models wih eiher endogenous expors or horizonal FDI, o shoring hrough verical FDI increases he comovemen of oupu and decreases he co-movemen of consumpion, resuls which come closer o he empirical correlaions repored in Backus, Kehoe, Kydland (99). JEL classi caion: E, F, F, F4, F4 Keywords: o shoring, verical FDI, horizonal FDI, expors, business cycle co-movemens, heerogeneous rms, rm enry, relaive wages Deparmen of Economics, Boson College, MA 0467, USA; zlae@bc.edu, hp://

2 Inroducion In his paper I examine wheher he rms decision o relocae he producion of inermediae goods across borders can explain he co-movemen of aggregae incomes across counries. Firms ofen follow sraegies ha involve he fragmenaion of producion chain and he esablishmen of foreign a liaes a locaions wih relaively lower labor coss ha serve as expor plaforms, an acion which I refer o as "o shoring hrough verical FDI" (foreign direc invesmen) in his paper. Unlike producion under horizonal FDI - which implies ha foreign a liaes produce mainly for he local marke of he hos counry - his ype of verically-inegraed producion involves foreign a liaes ha add value owards he nal goods purchased by consumers in he mulinaionals counry of origin or in hird counries. Therefore, in my model, verical FDI and rade are complemens: The creaion of producion-based a liaes o shore generaes rade ows, as mulinaionals and heir foreign a liaes exchange inermediae goods wih each oher. Recen lieraure documens empirically ha counry pairs ha exchange inermediae goods more inensely exchanges which ofen ake place beween o shore a liaes and he headquarers of mulinaional rms engaged in verical FDI exhibi higher correlaions of aggregae incomes (Bursein, Kurz, Tesar, 007). Trade daa also shows ha, despie noable variaion across secors and indusries, he exen of cross-border producion under verical FDI in manufacuring has been paricularly large wihin he NAFTA region, Cenral and Souh America. In 005, as much as, 50 and 6 percen of he manufacuring sales of U.S. a liaes from Canada, Mexico and Lain America as a whole were direced owards heir U.S. paren rms, a paern which re ecs he key economic role of producion sharing hrough verical FDI in he region (Bureau of Economic Analysis, 007). I build a dynamic sochasic general equilibrium (DSGE) model ha feaures endogenous o shoring, heerogeneous rms and rm enry dynamics in a wo-counry framework (Norh and Souh). Firms in each economy are monopolisically compeiive, and each rm produces a di eren variey of nal goods using eiher domesic or foreign inpus. Firms also face sunk enry coss, period-by-period xed o shoring coss, and iceberg rade coss. The sunk enry coss re ec he regulaion of saring I aach di eren meanings o "o shoring" and "ousourcing." The former concerns he inegraion of mulinaional rms across borders hrough verical or/and horizonal FDI. In conras o o shoring, ousourcing akes place when a rm purchases inermediae inpus or services from an una liaed supplier - eiher a home or abroad - raher han producing i in house. See Helpman (006) for an ample discussion of he relaed lieraure. In conras, considerably smaller shares of he sales of U.S. a liaes in Europe and Asia-Paci c were direced owards heir U.S. paren mulinaionals ( and 5 percen in 005).

3 a business, whereas he xed coss of producing o shore represen headquarers aciviies and he mainenance of producion plans in he foreign counry. Neverheless, he iceberg rade coss re ec ransporaion, insurance and rade barriers ha a ec he impors of inermediae goods produced by o shore a liaes and sold o heir paren rms in he counry of origin. Thus, when deciding where o locae producion (domesically vs. o shore), rms balance he incenive of lower labor coss agains he xed and iceberg rade coss associaed wih o shore producion. I derive an asymmeric seady sae in which di erences in rm enry regulaion (i.e. he cos of saring a business) a ec labor demand and generae wage di erences across counries. Indeed, empirical evidence shows large variaion in rm enry coss across counries: The cos of saring a business is hree imes higher in Mexico han in he U.S. or Canada; i is six imes higher in Hungary han in he U.K. (World Bank, 007, see Table 4). In my model, I se rm enry coss o be higher in Souh; consequenly, labor demand and he e ecive wage are lower in Souh. Therefore, only rms originaing in Norh have he incenive o relocae producion across he border; all rms ha originae and serve he Souh marke produce domesically. The mechanism ha generaes he co-movemen of aggregae incomes hrough endogenous o shoring in my model works as follows. Firms choose endogenously o locae producion eiher a home or overseas. A posiive echnology shock in he Norh economy encourages rm enry. In urn, rm enry causes wages o rise faser han produciviy, and leads o an appreciaion of he cos of e ecive labor in Norh relaive o Souh. Subsequenly, he more producive rms originaing in Norh choose o relocae producion overseas. Higher demand for labor in Norh (due o rm enry) and higher demand for labor in Souh (due o o shoring) generae posiive co-movemen of wages and aggregae incomes. Throughou his paper I use he erms of labor as a measuremen of he relaive cos of e ecive labor beween Norh and Souh. I de ne he erms of labor as he raio beween he Souh and Norh real coss of e ecive labor expressed in unis of he Norh consumpion baske, T OL = w =Z w =Z Q, where he cos of e ecive labor is he raio beween he real wage and aggregae produciviy, i.e. w Z in he Norh economy. Over he business cycle, rm enry leads o an increase of he relaive cos of e ecive labor (i.e. he erms of labor appreciae/decrease), which in urn causes more rms from Norh o relocae producion o shore. Firm enry and rm heerogeneiy are wo necessary ingrediens of my model. In seady sae, cross-counry di erences in he regulaion of rm enry are ranslaed ino di erences in real e ecive wages across counries, and herefore provide an incenive for some of he rms in Norh o relocae

4 producion o Souh, where he cos of e ecive labor is relaively lower. Over he business cycle, rm enry riggered by a posiive echnology shock in he home economy drives he appreciaion of he domesic e ecive wage relaive o Souh, and hus causes more rms o relocae producion o o shore. Firm heerogeneiy i.e. some rms are more producive han ohers is also necessary o generae endogenous o shoring in my model. If rms were idenical and o shoring coss negligible, all rms would prefer o produce inermediae goods a he locaion wih cheaper e ecive labor. However, wih rm heerogeneiy, only some of he rms can a ord he xed coss of o shoring, and heir share in he number of oal rms varies over he business cycle. The relocaion of producion by home rms a ecs wages in Souh in he same way ha rm enry a ecs wages in Norh namely, i induces upward pressure on wages due o higher demand for labor a mechanism which hen generaes co-movemen of aggregae incomes. 4 Given he increased complexiy of mulinaional rms operaions across borders (Helpman, 006), he radiional classi caion of FDI ino verical and horizonal ypes has become increasingly di cul. Therefore, in addiion o o shore producion hrough verical FDI (i.e. moivaed by lower producion coss in he foreign economy), my model ness he benchmark models wih endogenous expors a la Ghironi and Meliz (005) as well as mulinaional producion hrough horizonal FDI (i.e. moivaed no by low producion cos, bu by access o he local marke) a la Conessi (006). Thus, he model examines he abiliy of hree di eren inernaionalizaion sraegies of mulinaional rms o ac as channels hrough which aggregae shocks are ransmied across economies. The analyical momens of my model show ha endogenous o shoring hrough verical FDI increases he co-movemen of naional incomes and decreases he co-movemen of consumpion relaive o he benchmark models wih endogenous expors a la Ghironi and Meliz (005) and horizonal FDI a la Conessi (006), resuls which are more in line wih he corresponding empirical correlaions. This paper is organized as follows. Secion provides an empirical analysis of he cyclicaliy of o shoring o Mexico s maquiladora secor relaive o he U.S. manufacuring oupu. Secion inroduces a DSGE model of o shoring wih heerogeneous rms and rm enry dynamics. Secion Wihou enry, he cos of e ecive labor in Norh would no appreciae relaive o Souh afer a posiive echnology shock, as he increase of home wage relaive o is seady sae level would be jus as large as he increase in aggregae produciviy every period; rms would have no incenive o relocae producion overseas. 4 Firm heerogeneiy is no only a useful feaure of my model, bu also represens a well-esablished empirical regulariy. Firm produciviy varies wihin and across secors, and only he more producive rms impor inermediae goods from overseas (Kasahara and Rodriguez, 005; Yasar and Morrison Paul, 006). 4

5 4 shows he impulse responses and he second momens generaed by he model wih verical FDI relaive o he benchmark models wih endogenous expors a la Ghironi and Meliz (005) and o shore producion hrough horizonal FDI a la Conessi (006). Secion 5 includes an exension of he model wih verical FDI which allows for elasic labor supply, and explores he abiliy of he model o reproduce he empirical momens of o shoring a he inensive and exensive margins. Secion 6 concludes. Measuring he cyclicaliy of o shoring Alhough he link beween rade ows and business cycle co-movemens has received large aenion in empirical lieraure, here is sill lile known abou he ucuaion of o shore producion over he business cycle. Therefore, in his secion I explore he cyclicaliy of o shore producion o Mexico s maquialdora secor relaive o ucuaions in he U.S. manufacuring oupu and in he U.S.-Mexico relaive manufacuring wage.. Trade in inermediae goods and business cycle correlaions Figure. Share of inermediaes in bilaeral rade vs. GDP correlaions. Source: Bursein, Kurz, Tesar (007). Recen lieraure documens he link beween rade in inermediae goods and he co-movemen of aggregae incomes, which is one of he sylized facs ha my heoreical model aemps o replicae. For insance, Bursein, Kurz, Tesar (007) show ha a posiive and signi can link exiss beween () he volume of inermediae goods expored by o shore a liaes back o headquarers, measured as 5

6 he share of a liae expors in he oal expors of he hos economy o heir counry of origin in 00, and () he GDP correlaion beween he pairs of counries involved, measured over (Figure ). 5 This resul suggess ha he cross-counry inerdependencies generaed by he involvemen in producion sharing are associaed wih a closer synchronizaion of business cycle ucuaions across he counries involved.. The cyclicaliy of o shoring wih quarerly daa Nex I explore he cyclicaliy of o shore producion using daa on Mexico s maquiladora and he U.S. manufacuring indusries. In paricular, I explore he link beween () variables describing Mexico maquiladora secor: value added, hours worked, and number of plans, and () variables describing he U.S. manufacuring business cycle: indusrial producion, and he raio of U.S. o Mexico s nominal hourly wage in manufacuring expressed in he same currency. The daa is provided by Mexico s Naional Insiue of Saisics (real value added, hours worked, hourly nominal wages and number of plans in Mexico s maquiladora secor), he Board of Governors of he Federal Reserve Sysem (real indusrial oupu in U.S. manufacuring) and he U.S. Bureau of Labor Saisics (hourly nominal wages in U.S. manufacuring). 6 The maquiladora indusry in Mexico consiues a good example o sudy he paern of o shoring in U.S. manufacuring, due o several reasons. Firs, i represens a classic example of o shoring under verical FDI: Plans ha operae under Mexico s maquiladora program impor inpus, process hem and ship hem back o he counry of origin. On he goods reurn o he counry of origin, ari s are paid only on he value added by he plan in Mexico (Gruben, 00). Second, alhough no all plans in Mexico s maquiladora secor are owned by U.S. rms, mos of maquiladora s value added - roughly 90 percen - is expored o he U.S. (Bursein, Kurz, Tesar, 007). I employ he Baxer-King bandpass ler o he variables expressed in naural logs in order o ler ou ucuaions wih periodiciy lower han 8 monhs and greaer han eigh years. The resuling bandpassed series are ploed in Figure (a). The hree chars on he lef in Figure (a) plo Mexico s maquiladora value added (real), hours worked and number of plans ogeher wih he U.S. manufacuring oupu (indusrial producion, real) a quarerly frequency beween Q-99 and Q4-00. Similarly, he hree chars on he righ in Figure (a) plo Mexico s indicaors ogeher wih he relaive U.S.-Mexico nominal hourly wage in manufacuring. 7 5 The OLS coe cien is posiive (0.65) and signi can a he percen level. 6 Daa on Mexico s maquiladora secor is provided a monhly frequency. I aggregae i ino quarers. 7 The daa on Mexico s maquiladora secor was provided by he Insiuo Nacional de Esadisica, Geogra a e Infor- 6

7 The visual inspecion of he daa suggess ha o shoring o Mexico - measured as value added, hours worked and number of o shore plans - is pro-cylical wih he U.S. manufacuring oupu. More, Mexico s value added is noably more volaile han he U.S. manufacuring oupu. The chars also sugges a delayed response of o shoring a he exensive margin (i.e. he number of plans in Mexico s maquiladora secor) o ucuaions of indusrial producion in U.S. manufacuring. Figure (a). The cyclicaliy of o shoring o Mexico s maquiladora secor relaive o () U.S. manufacuring oupu (lef) and () he U.S.-Mexico relaive wage (righ) maica (INEGI) Mexico. Indusrial producion in he U.S. manufacuring secor a monhly frequency was provided by he U.S. Board of Governors of he Federal Reserve Sysem. 7

8 .. Correlaions wih lags and leads of U.S. oupu In order o accoun for he possibiliy of delayed responses, I compue he correlaion of each of Mexico s maquiladora indicaors (value added, hours worked, numbers of plans) wih various lags and leads of he U.S. business cycle indicaors (indusrial oupu and he U.S.-Mexico relaive wage). Figure (b). Correlaions beween Mexico s mauiladora indicaors and various lags and leads of () he U.S. manufacuring oupu (lef) and () he U.S.-Mexico relaive wage (righ) The chars on he lef in Figure (b) show ha o shoring o Mexico s maquiladora indusry is procyclical wih U.S. manufacuring oupu, alhough he iming of maquiladora s response di ers a he inensive and he exensive margins. On one hand, correlaions show a posiive immediae response 8

9 of maquiladora s hours worked o ucuaions of U.S. indusrial producion in manufacuring. On he oher hand, value added responds wih a lag of one or wo quarers, and he number of plans in Mexico s maquiladora secor (i.e. o shoring a he exensive margin) responds wih a lag of hree quarers o he U.S. manufacuring oupu. The correlaion of he number of maquiladora plans wih he conemporaneous U.S. manufacuring oupu is less han 0.5, whereas he correlaion wih U.S. manufacuring oupu lagged by hree quarers is posiive and exceeds 0.7. I inerpre he correlaions beween Mexico s maquiladora indicaors and he U.S.-Mexico relaive manufacuring wage raio as evidence in favor of he cross-counry ransmission mechanism of business cycles ha I build in my model. The chars on he righ in Figure (b) show ha he correlaions of maquiladora value added, hours worked and number of plans wih he lagged relaive wage raio are posiive, i.e. pas increases in manufacuring wage of he U.S. relaive o Mexico are followed by he relocaion of producion from he U.S. o Mexico a boh he inensive and he exensive margins. However, he correlaions of each of he maquiladora indicaors wih he conemporaneous U.S.-Mexico wage raio are negaive, a resul which shows ha he relocaion of producion o Mexico is associaed wih a conemporaneous increase in Mexico s wage, and herefore a decrease in he relaive wage raio... OLS analysis I use he following economeric speci caion o explore he link beween he ime series described in Figure (a): where he dependen variable Y MEX; ln(y MEX; ) = + ln(oupu US; ) + d NAF T A; + " ; ln(y MEX; ) = + ln( W age US; W age MEX; ) + d NAF T A; + " ; represens alernaively Mexico s manufacuring real value added, hours worked and he number of plans; he dummy variable d NAF T A; conrols for he impac of NAFTA membership on correlaions. I expec o shore value added, hours worked and number of plans o be pro-cyclical wih he U.S. manufacuring oupu, and negaively relaed o he U.S.-Mexico relaive wage in manufacuring. 8 levels) and di erences (for elasiciies of growh raes). I esimae he equaions in boh levels (o obain he elasiciies of 8 The resuls should be inerpreed as correlaions; hey do no provide any insigh on he causaliy beween variables. 9

10 Table. U.S.-Mexico co-movemen in manufacuring, OLS esimaes Equaions in levels Dependen Variables Explanaory + ln(v A MEX; ) ln(hours MEX; ) ln(p lans MEX; ) ln(oupu US ).45*** (0.).854*** (0.0).450*** (0.49) ln( W US W MEX ) (0.074) 0.00 (0.7) (0.095) Equaions in di erences Dependen Variables Explanaory + dln(v A MEX; ) dln(hours MEX; ) dln(p lans MEX; ) dln(oupu US ).5*** (0.95).976*** (0.97) -0.4 (0.8) dln( W US W MEX ) 0.5* (0.070) 0.05 (0.07) (0.079) The resuls in Table show ha Mexico s maquiladora value added, hours worked and he number of plans are indeed pro-cyclical wih U.S. manufacuring oupu. In he equaions in levels, when each of Mexico s value added, hours worked and number of plans alernaively represens he dependen variable, he coe ciens on U.S. oupu are posiive and saisically signi can a he percen level. The equaions in levels also highligh he larger volailiy of Mexico s maquiladora secor relaive o U.S. manufacuring. The coe cien esimaes represen elasiciies and are larger han uni, i.e. a percen increase in U.S. manufacuring oupu is associaed wih a more han percen increase in Mexico s maquiladora secor. The coe cien esimaes on he relaive wage as he explanaory variable are no saisically signi can. In he equaions in di erences wih eiher Mexico s value added or hours worked as he dependen variable, he coe ciens on U.S. oupu are posiive and saisically signi can a he percen level. The sign and magniude of coe ciens show ha faser growh in U.S. manufacuring is associaed wih acceleraed growh in Mexico s maquiladora value added and hours worked. Wih one excepion (value added as he dependen variable), he coe cien esimaes on he relaive wage as he explanaory variable are no saisically signi can. Analyzing he cyclicaliy of o shoring represens a necessary sep which provides empirical grounding for he o shoring-based ransmission channel of business cycles ha I develop in he heoreical secion below. 0

11 Model of o shoring wih heerogeneous rms The model describes hree main aciviies in each economy. () Households supply labor inelasically, consume an aggregae consumpion baske, and nance rm enry. () Firms (monopolisically-compeiive, heerogeneous in produciviy) produce nal goods for he domesic marke using inermediae goods under wo possible sraegies: (a) use only domesic inpus; or (b) use a mix of inermediae goods produced boh domesically and o shore hrough verical FDI, i.e. relocae he producion of some inpus o o shore locaions where labor is cheaper. () Some of he rms also produce nal goods for he foreign marke under wo possible sraegies: (a) produce domesically and expor he nal good, like in Ghironi and Meliz (005); or (b) use a mix of inermediae goods produced boh domesically and o shore hrough horizonal FDI as in Conessi (006). Figure. Inernaionalizaion sraegies of mulinaional rms Figure describes he various producion sraegies available o rms ha serve he domesic and foreign markes. The di erence beween producion under verical and horizonal FDI is ha he former sraegy is adoped by rms serving he domesic marke, is moivaed by he relaively lower labor coss abroad, and involves he relocaion of producion o shore simulaneously wih shuing down he domesic faciliy. In conras, producion under horizonal FDI is moivaed by access o he o shore marke, and involves he simulaneous producion of he same variey of inermediae goods

12 boh a home (for he domesic marke) and o shore (for he foreign marke). The following secions describe he deailed model while focussing on he Norh economy. The equaions for Souh are similar unless indicaed oherwise. Variables in Souh are denoed wih a sar superscrip.. Households Households in each counry maximize he expeced lifeime uiliy and provide labor inelasically, subjec o he budge consrain: max fb ; x g " E X s= s C s # ; s:: B + + ev (N + N E; ) x + + C = ( + r )B + ( d e + ev )N x + w L; where (0; ) is he subjecive discoun facor, C is aggregae consumpion, and > 0 is he inverse of he iner-emporal elasiciy of subsiuion. The represenaive household in Norh purchases wo ypes of asses. Every period, he household buys he risk-free bond B + denominaed in unis of he consumpion baske C. I also purchases x + shares in a muual fund of rms in Norh ha include: (i) N rms ha already produce a ime, eiher domesically or o shore, and (ii) N E; new rms ha ener he marke in period. Each share is worh is marke value ev, which equals he ne presen value of he expeced sream of fuure pro s of he average rm, measured in unis of he Norh consumpion baske. The household eners every period wih real bond holdings B and muual fund share holdings x whose marke value is ev N. I receives ineres r B on bond holdings, and dividend income d e N on he muual fund socks equal o he pro of he average rm imes he number of exising home rms in period, in proporion wih is sock holdings x. 9 Finally, he represenaive household also receives labor income equal o he real wage w. I se L =, i.e. labor is supplied inelasically. 9 In his version of he model (complee nancial auarky), socks in he muual fund and bonds are no raded across counries; hence, he equilibrium condiions for sock and bond holdings are x = x + = ; B = B + = 0.

13 The rs-order condiions generae he Euler equaions for bonds and socks: 0 C = ( + r + ) E h C + i ; () ev = ( )E C+ C ( e d + + ev +): () Households in Norh consume he consumpion baske C, which includes varieies of nal goods produced by Norh rms (! NN ) using a mix of domesic and foreign inpus, hrough eiher domesic or o shore producion under verical FDI. In addiion, he consumpion baske C also includes nal good varieies produced by Souh rms (! SN ) and which are eiher impored or produced in Norh under horizonal FDI: z Z V; C = y D; (!) 6z 4 min d! {z } Domesic producion + Z d! y V; (!) z V; {z } O shore producion Z + yh;(!) d! zh; 7 {z } 5 SN where > is he symmeric elasiciy of subsiuion across goods. ; Le p (!) denoe he price of each variey of nal goods y (!); hen he price index of he home consumpion baske is P = R p (!) d! for! NN [ SN, and he demand for each variey of nal goods! is y (!) = (p (!)=P ) C. Using he home consumpion baske C as he numeraire good and de ning he real price of variey! as (!) = p (!)=P, I wrie he consumpion-based price index as: Z = (!) d! ;! NN [ SN : (). Firms serving he domesic marke: domesic producion vs. verical FDI The Norh economy includes a coninuum of monopolisically compeiive rms ha produce nal goods. Each rm produces a di eren variey of nal goods - herefore, he rm-speci c labor produciviy z also serves as an index for he exising varieies on he suppor inerval [z min ; ). As shown in he expression for he Norh consumpion baske C above, rms wih produciviy below 0 As described below, rms - including he new enrans - encouner a random exi shock wih probabiliy a he end of every period. Moreover, new enrans a ime do no produce and do no obain any pro unil period +. Thus, he law of moion for he number of producing rms is N + = ( )(N + N E;). The represenaive household a ime purchases socks in a muual fund of N + N E; rms, among which some will experience he random exi shock a he end of period.

14 he endogenous cuo z V; produce heir varieies of nal goods using exclusively domesic inpus, whereas hose above he cuo use foreign inpus. Thus, each rm producing for he domesic marke can choose one of wo possible sraegies: () Under domesic producion, he home rm wih idiosyncraic labor produciviy z employs an amoun of labor l and obains oupu: y D; (z) = Z zl ; where Z is he aggregae produciviy of labor in Norh; () Under verical FDI, he same rm uses a combinaion of domesic and foreign inpus produced wih labor from Norh and Souh, l and l ; respecively. Following Anras and Helpman (004), oupu of every variey z of nal goods is a Cobb-Douglas funcion of he inpus: y V; (z) = Z zl Z zl : Under di eren calibraions of he model, I vary he share of foreign inpus conribued by o shore a liaes. The smaller is, he more inensive he producion process is in inpus produced by o shore a liaes. Seing = 0 implies ha verical FDI rms use exclusively foreign inpus in he producion of nal good varieies. A he oher exreme, = shus down o shore producion under verical FDI as a ransmission channel for aggregae shocks. Given he demand for nal goods produced domesically, y D; (z) = D; (z) C, and he demand for nal goods produced under verical FDI, y V; (z) = V; (z) C, rms se prices by solving he following pro -maximizing problem: max f D; (z)g d D(z) = D; (z)y D; (z) max f V; (z)g d V (z) = V; (z)y V; (z) w Z z y D;(z); w w Q w w Z z Z z y V;(z) f Q V : Z Z The cos of producing one uni of oupu eiher domesically or under verical FDI varies according o di erences in labor produciviy z across rms and di erences in he cos of e ecive labor across counries. Given he domesic and o shore real wages w and w, he uni cos of producing inerme- Using l Hôpial s rule, lim = lim!0! = = lim! e(=) ln = e lim [(=) ln ]! = e lim (=)! = e 0 = : Appendix shows he derivaions of he aggregae price index and he demand funcions of inermediae goods produced domesically and o shore. 4

15 diae goods domesically is w Z, and he uni cos of producing o shore is w z Z z w Q Z z real exchange rae Q = P " P. The is de ned as he raio of consumer price indexes expressed in Norh and Souh in he same currency, where " is he nominal exchange rae. In addiion o he uni producion coss, rms producing under verical FDI also incur he periodby-period xed o shoring coss equal o a mix of f V unis of e ecive labor from Norh and Souh, coss which re ec headquarer operaions as well as he building and mainenance of he producion faciliy o shore. 4 They also face an iceberg rade cos ( > ) which applies o he value of inpus produced by o shore a liaes and incorporaed in he nal good varieies consumed in Norh. 5 The iceberg rade coss represen ransporaion coss, insurance and fees, as well as language barriers and di erences in he legal sysems, as discussed in Anderson and Wincoop (004). Hence, he opimal prices per uni of oupu produced eiher domesically or o shore are: 6 D; (z) = w Z z ; V; (z) = w w Q Z z Z z : The resuling pro s from domesic and o shore producion, boh expressed in unis of he Norh consumpion baske C, are: 7 d D; (z) = D;(z) C ; d V; (z) = V;(z) w w C f Q V : Z To summarize he above, he srucure of producion coss depends on he rm-speci c produciviy facor z, he cos of e ecive labor in Norh and Souh ( w Z Z and w Q Z, respecively), he xed coss The laer is ranslaed ino unis of he consumpion baske in Norh. The real wage w = W =P in Norh is expressed in unis of he domesic consumpion baske; he o shore real wage w = W =P is expressed in unis of he consumpion baske in Souh. 4 w The mix of f V unis of e ecive labor is equivalen o f w Q V Z Z unis of he consumpion baske in Norh. 5 The assumpion ha he iceberg rade coss apply only o he inpus produced o shore is a normalizaion. Domesic inpus ha undergo o shore processing and hen are re-impored in he counry of origin, alhough exemp from ari s, are sill subjec o ransporaion and insurance coss. However, I assume ha he iceberg rade coss applying do domesic inermediaes are less han hose applying o impored o shore inermediaes. 6 Appendix shows he derivaion of he opimal price formulas for inermediae goods produced by he monopolisically-compeiive rms domesically and o shore. 7 Given he demand y D(z) = D(z) C and opimal price D(z) = z produced domesically, he pro formula is derived as d D(z) = producing hrough verical FDI is derived in a similar fashion. w Zz charged for he inermediae good variey w yd(z) = D(z)yD(z): The pro from Zz 5

16 of o shoring f V as well as he iceberg rade coss. Firms ha produce inermediae goods o shore bene from he relaively lower cos of e ecive labor, bu incur xed o shoring coss every period and iceberg rade coss when shipping inermediaes for nal assembly back in Norh. Hence, when deciding he locaion of producion faciliies, rms compare he pro s hey would obain from domesic producion d D; (z) o hose obained from producing inermediaes o shore d V; (z), a feaure of he model which generaes endogenous o shoring. Every period, rms wih idiosyncraic produciviy z above a cerain cuo z V; nd i pro able o locae he producion of inermediae inpus o shore. Given he di erence beween he coss of e ecive labor in Norh and Souh, he relaively more producive rms (z > z V; ) obain pro s ha are large enough o cover he xed o shoring cos f V and he iceberg rade cos of shipping he inpus back home. On he conrary, rms wih relaively low labor produciviy (z < z V; ) are unable o ake advanage of he lower cos of e ecive labor in Souh, since heir pro s would fall shor of covering he xed and he iceberg rade coss. As a paricular case, he rm wih labor produciviy equal o he cuo z V; is indi eren beween producing domesically or o shore: Afer subracing he o shoring and rade coss, he pro s i would obain from domesic and o shore producion are equal. The equaliy of pro s allows o solve for he endogenous produciviy cuo z V; ha governs he locaion decision of producion under verical FDI: z V; = fz j d D; (z V; ) = d V; (z V; )g : Exisence of equilibrium. Below I show ha he exisence of equilibrium produciviy cuo z V; requires cross-counry asymmeries wih respec o he cos of e ecive labor. In oher words, rms need he incenive of a lower cos of e ecive labor in order o relocae producion o shore hrough verical FDI. Seing = 0; I re-wrie he pro funcions for domesic and o shore producion hrough verical FDI, respecively, as d D; (z) = B w Z z and d V; (z) = B w Q Z z ; where > and B C is a measure of marke size: Figure (b) plos pro s as funcions of z. The verical inerceps are he annualized value of he sunk enry cos (for d D; (z)) and he annualized value of he sunk enry cos plus he xed o shoring coss (for d V; (z)). The exisence of equilibrium cuo z V; requires: () d V; (z) o be seeper han d D; (z); and () z min < z V; mus hold every period: 6

17 Figure (b). Exisence of equilibrium produciviy cuo z V ; The rs condiion implies ha e ecive wages in Souh mus be low enough (T OL < ) in order o o se he iceberg rade coss ( > ): w Q Z < w Z z () T OL < : The second condiion, discussed in Appendix 4, implies: where = w w Q d D; (z min ) < f E + f V ; Z ( ) ( ) : The inequaliy shows ha he pro obained from domesic producion by he rm wih he minimum produciviy z min is less han he per-period value of he sunk enry cos plus he xed o shoring cos. In oher words, he rm ha obains zero pro from domesic producion would make negaive pro s if i engages in o shore producion, i.e. he rm wih produciviy z min does no produce in eiher counry. Z. Firms serving he foreign marke: expors vs. horizonal FDI Firms in he Norh economy also have he opion o serve he foreign marke hrough one of wo possible sraegies: () Under endogenous expors, rms in Norh use only domesic inpus in he producion of nal goods which hey expor o he Souh marke; 7

18 () Under horizonal FDI, rms use a combinaion of domesic and foreign inpus and sell he resuling nal goods o consumers in he Souh marke. The producion funcion for boh sraegies can be summarized as: Z zl Z y H; (z) = zl ; where a smaller corresponds o a larger conen of inpus produced by o shore a liaes and ha is incorporaed in he nal goods sold o consumers in he hos marke. Thus, my model of o shoring ness boh Ghironi and Meliz (005) and Conessi (006). On one hand, seing = implies ha rms serve he Souh marke exclusively hrough endogenous expors, as in Ghironi and Meliz (005). On he oher hand, seing = 0 implies ha rms produce exclusively hrough heir o shore a liaes in order o serve o Souh marke, like in Conessi (006). Boh expors and horizonal FDI imply a xed cos equal o a mix of f H unis of e ecive labor in Norh and Souh. In addiion, expors also require he iceberg rade cos which applies o he impored conen of nal goods consumed in Souh. Unlike o shore producion hrough verical FDI, which is moivaed by lower labor coss, o shore producion hrough horizonal FDI is moivaed by marke access, since i allows rms o avoid he rade coss associaed wih inpus ha are produced in he hos economy raher han impored. Under producion hrough horizonal FDI, rms coninue o produce in heir counry of origin (in order o serve he home marke) a he same ime wih producing he same variey of nal goods a he o shore locaion (in order o serve he marke of he hos economy),. Following he approach described above, pro -maximizing rms from Norh serving he souhern marke se opimal prices for oupu ha is eiher expored or produced under horizonal FDI: H; (z) = w Q w Z z Z z : Every period, rms wih idiosyncraic produciviy z above a cerain cuo z H; nd i pro able o serve he foreign marke (Souh) - a he same ime wih serving heir domesic marke (Norh) - hrough eiher expors or horizonal FDI. Their pro s are large enough o cover he xed cos of serving he foreign marke f H. In addiion o ha, rms save he iceberg rade cos when using inpus produced locally hrough horizonal FDI in he counry which hey serve (i.e. = 0). The pro funcion is: d H; (z) = H;(z) C w w Q f Q H : Z The opion o serve he foreign marke (in addiion o serving he domesic one) is endogenous: Z 8

19 he produciviy cuo z H; is ime-varian: z H; = inf fz j d H; (z V; ) > 0g :.4 Firm averages Firms serving he domesic marke: Following he approach in Meliz (00), I de ne wo average produciviy levels ha correspond o: () rms producing nal goods using enirely domesic componens (average produciviy level ez D; ), and () rms producing nal goods hrough verical FDI using inpus produced boh domesically and hrough o shore a liaes (average produciviy level ez V; ). Then I solve he model in erms of wo represenaive Norh rms: () he average home rm producing domesically, and () he average home rm producing o shore hrough verical FDI. Figure 4. Average labor produciviies for rms serving he domesic marke: domesic producion (ez D ; ) and o shore producion hrough verical FDI (ez V ; ) As shown in Figure 4, in every period here are N D; home rms producing domesically wih average rm-speci c labor produciviy ez D;, and N V; rms producing o shore hrough verical FDI wih average rm-speci c labor produciviy ez V;. 8 Since he rm-speci c labor produciviies z are random draws from a common disribuion G(z) wih densiy g(z) and suppor on he inerval 8 One should disinguish beween ez V; and z V;. The former is he average rm-speci c labor produciviy of rms producing o shore, whereas he laer is he labor produciviy cuo on suppor inerval [z min; ); all rms above cuo z V; esablish producion faciliies o shore. 9

20 [z min ; ), I wrie he domesic and o shore average produciviies respecively as: ez D; = 4 G(z V; ) zz V; z min z Z 6 ez V; = 4 G(z V; ) z V; z g(z)dz5 7 g(z)dz5 Afer de ning he wo average produciviies, I re-wrie he model in erms of wo represenaive rms, one producing domesically and he oher producing o shore hrough verical FDI. I sar by re-wriing he prices charged by each of he wo represenaive rms as: The corresponding pro s are: ; e D; = w ; (4) Z ez D; e V; = w w Q Z ez V; Z ez : (5) V; : ed D; = (e D;) C ; (6) ed V; = (e V;) w w C f Q V : (7) Z Due o he wage asymmery across counries, rms originaing in Souh do no engage in verical FDI, i.e. hey do no use inermediaes produced o shore - in he high-wage Norh economy - when serving heir domesic marke. Their average price and pro s are: Z e D; = w Z ez ; (8) D; ed D; = e D; C : (9) Firms serving he foreign marke: As in Ghironi and Meliz (005), he pro -maximizing represenaive rms in Norh and Souh ha serve he foreign marke - hrough eiher expors or horizonal FDI - charge he following prices: e H; = e H; = w Q Z ez H; w Q Z ez H;! w Z ez H; w Z ez H; ; (0)! : () 0

21 The corresponding average pro s are: ed H; = (e H;) C w w Q f Q H ; () ed H; = e H; C Q f H Z w Z Z w Q Z : () Price indexes: The consumpion price index in Norh include he average price of he nal good produced domesically, he average price of he good produced by domesic rms under verical FDI, and he average price of he good supplied by Souh rms hrough eiher expors or local producion under horizonal FDI, respecively: = N D; (e D; ) + N V; (e V; ) + N H; e H; (4) In conras o rms originaing in he Norh economy, none of he rms in Souh has an incenive o esablish o shore producion faciliies in Norh, where labor is relaively more expensive. Therefore, none of he rms in he Souh economy produces inermediaes hrough o shore a liaes under verical FDI. The consumpion price index in Souh includes he average price of goods supplied by souhern rms hrough domesic producion and he price of goods provided by norhern rms hrough eiher expors or horizonal FDI: = ND; e D; + NH; (e H; ) (5) Toal pro s: The oal pro of he average rm originaing in Norh includes pro s from domesic producion, verical FDI and horizonal FDI: N d e = N D;dD; e + N V;dV; e + N H;dH; e : (6) In conras o norhern rms, none of he rms in Souh engages in verical FDI: N D; e d = N D; e d D; + N H; e d H;: (7).5 Pareo-disribued rm produciviy Firms serving he domesic marke: I solve he model in erms of wo represenaive rms - producing eiher domesically or hrough verical FDI, respecively - under he assumpion ha rmspeci c labor produciviy z is Pareo disribued over he suppor inerval [z min ; ), wih p.d.f. g(z) = kz min =z k+ and c.d.f. G(z) = (z min =z) k as in Meliz (00). Parameer k re ecs he dispersion of he produciviy draws: A relaively larger k implies a smaller dispersion and a higher concenraion of produciviies z owards he lower produciviy bound z min.

22 Under he Pareo assumpion, I re-wrie he average produciviy levels of he home rms producing domesically and o shore as follows: 9 h where k k ( ) ez D; = z min z V; ( ) k ( ) zk 4 V; zmin zv; k zmin k 5 ; (8) ez V; = z V; ; (9) i, z V; = z min (N =N V; ) (=k) and k >. 0, Since rms originaing in Souh serve heir domesic marke exclusively hrough domesic producion, he average produciviy of souhern rms is consan: ez D; = z min: (0) Finally, using ha he rm a he produciviy cuo z V; is indi eren abou he locaion of is producion plans - since i obains equal pro s from domesic and o shore producion, d D; (z V; ) = d V; (z V; ), I derive he link beween he pro s of he wo average rms as follows: k zv; ed V; = edd; + k ( ) k ( ) f w w Q V : () ez D; Firms serving he foreign marke: Under he assumpion of Pareo-disribued produciviy, I re-wrie he average produciviy levels of he rms serving he foreign marke hrough eiher expors or horizonal FDI as follows: ez H; = z min N N H; Z Z =k ; () ez H; = z min N D; N H;! =k : () Using ha he rm a he produciviy cuo z H; obains zero pro s from serving he foreign marke hrough eiher expors or horizonal FDI, d H; (z H; ) = 0, I derive he following pro cuo s: ed H; = k ( ) f w w Q H Z Z ; (4) ed w H; = k ( ) f H w Q : (5) Z 9 See Appendix. 0 I derive he shares of home rms producing domesically and o shore, respecively, as N D; N Z = G (z V;) and N V; N = G (z V;), where he oal number of rms in every period is N = N D; + N V;. Then I use he expression for he Pareo c.d.f. G(z V;) o derive he produciviy cuo z V; from he share of o shoring rms, z V; = z min(n =N V;) (=k) : The condiion ha k > ensures ha he variance of rm size is nie, since he average produciviies of he h i domesic-based and ousourcing rms are, respecively, ez V; = z V;. See Appendix 4. k k ( )

23 .6 Firm enry and exi Firm enry and exi ake place every period. Following Gironi and Meliz (005), rm enry requires a sunk enry cos i.e. which re ecs he cos of saring a business equal o f E unis of home e ecive labor. Poenial enrans do no become aware of heir idiosyncraic labor produciviy z unil afer hey ener he marke. Afer paying he sunk enry cos, each rm is randomly assigned an idiosyncraic labor produciviy z drawn independenly from a common disribuion G(z) wih suppor on he inerval [z min ; ), which he rm keeps for he enire duraion of is life. Poenial enrans are forward looking and correcly anicipae heir expeced pro s e d as well as he probabiliy of receiving an exi-inducing shock every period. Hence, poenial enrans do anicipae heir expeced pos-enry value given by he presen discouned value of heir expeced sream of pro s: ev = E X s=+ [( )] s Cs eds : C Therefore, rm enry akes place unil he value of he average rm equals he sunk enry cos: ev = f E w Z : (6) Each of he N E; rms enering a ime does no produce unil period +, which inroduces a one period ime-o-build ino he model. Irrespecive of heir produciviy, rms - including he new enrans - are also subjec o a random exi shock ha occurs wih probabiliy a he end of every period afer producion has aken place. Thus, he law of moion for he number of producing rms is: N + = ( )(N + N E; ): (7).7 Aggregae demand and value added In order o quanify he business cycle co-movemens generaed by my model, I use value added as a measure of he aggregae incomes of he wo counries. Thus, he model akes ino accoun he fac ha inpus produced in Souh and used in he producion of he nal good consumed in Norh are par of he value added of he Souh economy, and herefore mus no be double-couned in he value added of Norh. Under nancial auarky on he marke for boh bonds and socks (i.e. B + = B = 0 and x + = x = in equilibrium), value added is equal o he wage bill plus he oal amoun of sock Or f Ew =Z unis of he consumpion baske in Norh.

24 dividends derived by households in each counry: Y = w L + N d e : Finally, aggregae accouning under nancial auarky implies ha households spend heir income from labor and sock holdings on consumpion and invesmen in new rms: C + N E; ev = w L + N d e : (8).8 Balanced rade Under nancial auarky, he real exchange rae Q is pinned down by he balanced curren accoun condiion for Norh (which re ecs he corresponding balance for Souh): ( )N V; (e V; ) C + NH; e {z } H; C {z } () VFDI impors () HFDI impors + ( ) N H; e d H;Q {z } () HFDI pro s* = N H; (e H; ) C Q + ( ) N V;dV; e + ( ) N H;dH; e : {z } {z } {z } (4) HFDI expors (5) VFDI pro s (6) HFDI pro s The equaions shows ha he sum of () Norh s impors of inpus manufacured by o shore a liaes under verical FDI, () Norh s impors of inpus used by Souh rms for local producion under horizonal FDI, and () he repariaed pro s of Souh rms acive in Norh hrough horizonal FDI mus equal he sum of (4) Norh s expors of inpus used by Norh rms serving he Souh marke hrough horizonal FDI, (5) and (6), i.e. he repariaed pro s of Norh rms obained from verical and horizonal FDI, respecively..9 Model summary and asymmeries beween Norh and Souh As shown in Table, he model for he Norh economy is summarized by 6 equaions in 6 endogenous variables: N, N D;, N V;, N H;, N E;, e d, e dd;, e dv;, e dh;, ez D;, ez V;, ez H;, ev, r, w and C, plus he equaion describing aggregae produciviy Z. Firms in he Souh economy produce domesically for he domesic marke, and serve he foreign marke hrough eiher expors or local producion under horizonal FDI, bu have no incenive o engage in verical FDI since e ecive labor in Norh is relaively more expensive. Therefore, he Souh economy is described by only equaions in endogenous variables, i.e. here are no counerpars for N, N V;, e dv;, ez D; and ez V;. In paricular, since no rms from Souh produce o shore, he average labor produciviy of he Souhern rms is a h i consan, ez D = z min, where = k : Finally, I use he pricing and pro formulas de ned k ( ) by equaions (6) - (5) and summarized in Table. 4

25 Euler equaion, bonds Table. Model summary h i = ( + r + ) E C + = + r+ i E hc + C C Euler equaion, socks ev = ( )E C+ C ( d+ e + ev + ) ev C = ( )E + C ( d e D;+ + ev + ) Free enry ev = f Ew Z ev = f E w Z Rule of moion, # rms N + = ( )(N + N E; ) Aggregae accouning N D;+ = ( )(N D; + N E; ) C + N E; ev = w L + N e d C + N E; ev = w L + N D; e d D; Consumpion price index = N D; (e D; ) + N V; (e V; ) + NH; = ND; e D; + NH; (e H; ) e H; Toal pro s N e d = N D; e dd; + N V; e dv; + N H; e dh; Number of rms (Home) N D; e d = N D; e d D; + N H; e d H; N = N D; + N V; VFDI pro s link (Home) e dv; = k k ( ) zv; HFDI pro s link e dh; = k ( ) f H Dom. produciviy (Home) VFDI produciviy (Home) HFDI produciviy ed H; = k ( ) f H ez D; = z min z V; ez D; edd; + w w Q Z Z wq w Z k ( ) zv; z ez V; = z min N N V; =k ez H; = z min N ez H; = z min z k V; =k N H; N =k D; N H; k ( ) min zmin k k ( ) f V Z Balanced rade ( )N V; (e V; ) C + NH; e {z } H; C {z } VFDI impors HFDI impors = N H; (e H; ) {z C Q + ( } ) N V;dV; e {z } Expors VFDI pro s w w Q Z Z + ( ) NH; d e H;Q = {z } HFDI pro s* + ( ) N H; e dh; {z } HFDI pro s 5

26 Table. Pricing and pro formulas Producion Prices Pro s Domesic e D; = e D; = VFDI e V; = HFDI e H; = 4 Resuls e H; = 4. Seady sae w Z e dd; e z D; = (e D;) C d e D; = e D; C dv; e = (e V;) C f w V w Z ez D; w Z ez V; w Q w Q Z ez V; Z ez H; w Q Z ez H; w Z ez H; w Z ez H; ed H; = Z w Q Z dh; e = (e H;) C Q f w w Q H Z Z e H; C Q fh w Z wq Z Inuiively, rms from Norh have an incenive o relocae inpu producion o Souh only if he di erence in he cos of e ecive labor is large enough o cover boh he xed coss of o shoring and he iceberg rade coss of shipping he inpus produced o shore back home. In line wih his inuiion, in his secion I demonsrae analyically he need for an asymmeric seady sae wih respec o wages. Under = 0; he seady sae soluions for all variables of my model can be obained analyically afer solving for he labor produciviy of he average rm ha produces inermediae goods o shore, ez V. The soluion is described by he hyperbola: ez V + ez k V = ; wih parameers > 0 and > 0 for all plausible calibraions, k > 0 and >. In Figure 5, I plo he hyperbola described above for he cases of > 0 (squares) and < 0 (diamonds). 4 The gure shows ha he seady-sae soluion for ez V lies wihin he suppor inerval [z min ; ), wih z min, if and only if: = zmin k (T OL) k ( ) (T OL) > 0; where he erms of labor, T OL = w =Z w=z Q, represen a measure of he relaive cos of e ecive labor 4 ez V is on he horizonal axis, is on he verical axis. 6

27 beween he wo counries. Figure 5. Seady sae soluion for ez V The resuling condiion, T OL <, can be sais ed in wo di eren ways: (a) T OL = and < ; (b) > and T OL <. Wih mehod (a), he model would have a symmeric seady sae in which real e ecive wages in Norh and Souh are idenical, i.e. T OL =. In absence of cross-counry di erences in wages, rms would be moivaed o relocae producion o shore by he exisence of an iceberg subsidy, < ; ha reduces he marginal cos of inermediae goods manufacured o shore and shipped home. Wih mehod (b), he model would have an asymmeric seady sae in which he cos of e ecive labor is relaively higher in Norh han in Souh, i.e. T OL <. The cross-counry di erence in he cos of e ecive labor acs as an incenive for rms originaing in Norh o relocae producion o Souh. The di erence in he cos of e ecive labor mus be large enough o cover he xed o shoring cos and he iceberg rade cos >. I follow mehod (b): I impose fe > f E, i.e. he cos of saring a business is higher in Souh han in Norh, o obain an asymmeric seady of e ecive wages. The calibraion is suppored empirically by he daa on cross-counry di erences in he cos of saring a business described in Table 4. 7

28 4. Calibraion I se he cos of saring a business o be imes larger in Souh han in Norh (fe = f E), where I assume f E = wihou loss of generaliy. As shown in Table 4, his calibraion re ecs he considerable variaion in he cos of saring a business across counries: he moneary cos is imes higher in Mexico han in he U.S. or Canada; i is 6 imes higher in Hungary han in he U.K. Table 4. Firm enry coss, seleced economies (Source: World Bank, Doing Business, 007) The asymeric sunk enry coss - ogeher wih he xed o shoring cos f V = 0:00, he rade iceberg cos = :, and he xed cos of serving he foreign marke f H = 0:006 - generae T OL = 0:74: In seady sae, he cos of e ecive labor in Souh de ned as real wage over aggregae produciviy is 74 percen he value of he corresponding measure in Norh. Inerpreing periods as quarers, I se he subjecive rae of ime discoun = 0:99 and he coe cien of relaive risk aversion =. Following Ghironi and Meliz (005), I se he probabiliy of rm exi = 0:05 o mach annual 0 percen job desrucion in he U.S. Following Bernard, Eaon, Jensen and Korum (00), I also se he inra-emporal elasiciy of subsiuion = :8, calibraed afer U.S. plan and macro rade daa. Finally, I se he Pareo disribuion coe cien k = 5:5 and he lower bound of he suppor inerval of idiosyncraic rm produciviies z min = wihou loss of generaliy. In fuure work, I aim o neune he calibraion of k, f V and f H in order o mach empirical paerns such as he fracion of rms ha use impored inpus in producion (4 percen, as documened by Bernard, Jensen, Redding and 8