O shore Production and Business Cycle Dynamics with Heterogeneous Firms

Transcription

1 O shore Producion and Business Cycle Dynamics wih Heerogeneous Firms Andrei Zlae y Boson College November 8, 2008 JOB MARKET PAPER Absrac Cross-counry variaion in producion coss encourages he relocaion of producion faciliies o oher counries, a process known as o shoring hrough verical foreign direc invesmen. examine he e ec of o shoring on he inernaional ransmission of business cycles. Unlike he exising macroeconomic lieraure, I disinguish beween ucuaions in he number of o shoring rms (he exensive margin) and in he value added per o shoring rm (he inensive margin) as separae ransmission mechanisms. In he model, rms are heerogeneous in labor produciviy. They face a sunk enry cos in he domesic marke and an addiional xed cos o produce o shore. O shoring increases wih he di erence beween he domesic and foreign cos of e ecive labor and wih rm-speci c produciviy. The key resuls are: () The model replicaes he procyclical paern of o shoring and he exensive and inensive margin dynamics ha I documen using daa from Mexico s maquiladora secor; (2) O shoring enhances he comovemen of oupu beween he counries involved; and (3) O shoring reduces price dispersion across counries, because i dampens he real exchange rae appreciaion ha follows a produciviy increase in he paren counry (he Harrod-Balassa-Samuelson e ec). The resuls are relevan for he sudy of macroeconomic inerdependence beween counries separaed by persisen wage di erences, such as he U.S. and Mexico or he original and new EU members. JEL classi caion: F23, F4 Keywords: endogenous o shoring, verical FDI, exensive margin, rm enry, heerogeneous rms, erms of labor, business cycle comovemen, Harrod-Balassa-Samuelson e ec. I hank Fabio Ghironi, James Anderson and Susano Basu for heir paien advice and kind suppor. I would also like o hank Richard Arno, Marianne Baxer, Maeo Iacoviello, Peer Ireland, Sephen Kay, Federico Mandelman, Jim Nason, Francis Neville, Myriam Quispe-Agnoli, Margaria Rubio, Pedro Silos, Vialiy Srohush, Richard Tresch, Chrisina Wang, Adalber Winkler and Sephenie Young for insighful discussions, as well as paricipans a he 4h DYNARE conference in Boson, he FRB of Alana and he FRB of Boson seminars, he Green Line Macro Meeing a Boson College/Boson Universiy, he R@BC and Disseraion Workshop meeings a Boson College. Par of his projec was developed during my disseraion inernships a he FRB of Alana and he FRB of Boson, whose hospialiy I graefully acknowledge. This paper was previously circulaed under he ile "Producion Sharing and Business Cycle Co-Movemens wih Heerogeneous Firms." y Deparmen of Economics, Boson College, MA 02467, USA; zlae@bc.edu, hp://www2.bc.edu/~zlae. I

2 Inroducion Firms ofen follow sraegies ha involve he fragmenaion of producion chains and he esablishmen of foreign a liaes a locaions wih relaively lower labor coss, an aciviy known in he inernaional rade lieraure as o shoring hrough verical foreign direc invesmen (FDI) (Helpman, 984). Unlike producion under horizonal FDI - which means ha foreign a liaes aemp o gain marke access by replicaing he operaions of heir paren rms in he counry where nal consumpion akes place - he ype of verically-inegraed producion ha I model is primarily moivaed by lower producion coss, as foreign a liaes add value o he nal goods sold in he mulinaionals counry of origin or in hird counries. 2 The number of o shoring rms (which I refer o as he exensive margin of o shoring) and he real value added per o shoring rm (he inensive margin) ucuae over he business cycle, and hus a ec oupu, prices and wages in boh he paren and he hos counries. 3 This paper conribues o he inernaional macroeconomics lieraure by analyzing he exensive and inensive margins of o shoring as separae ransmission mechanisms of business cycles beween he paren and he hos counry. I model o shoring as an endogenous, rm-level decision ha depends on he di erence beween he domesic and he foreign cos per uni of e ecive labor, he xed cos of o shore producion, and he rade cos of shipping oupu back o he paren counry. Flucuaions in he number of o shoring rms are linked o domesic rm enry and o he resuling changes in he relaive cos of e ecive labor. Thus, an aggregae produciviy increase in he paren counry encourages domesic rm enry and causes domesic wages o rise faser han produciviy, as labor demand increases o cover enry requiremens. In urn, he increase in he domesic cos of e ecive labor causes more rms o relocae producion o shore. The gradual increase in he number of o shoring rms mirrors he gradual appreciaion of he cos of e ecive labor generaed by domesic rm enry. I documen a se of sylized facs ha characerize he cyclicaliy of o shoring from U.S. manufacuring o Mexico s maquiladora secor. 4 Using he number of maquiladora esablishmens as an 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, he laer 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 (2006) for an exensive discussion of he relaed lieraure. 2 Helpman, Meliz and Yeaple (2004) model horizonal FDI and expors as alernaive inernaionalizaion sraegies for mulinaional rms; Conessi (2006) analyzes his radeo in a dynamic framework. 3 In his paper I mainain a one-o-one ideni caion beween an o shoring rm, a nal good variey, and an o shore plan. Under his assumpion, o shoring a he exensive margin can also be inerpreed as he number of o shoring plans every period; o shoring a he inensive margin can be inerpreed as he value added per o shoring plan. 4 Mexico s maquiladora secor consiss of manufacuring plans ha impor inermediae goods, process hem, and expor he resuling oupu (Gruben, 200). The secor accouns for 20 percen of he Mexico s manufacuring value 2

3 empirical proxy for he exensive margin, I nd ha he value added o shore is procyclical wih U.S. manufacuring oupu, and also ha he exensive margin varies noably over he business cycle (Figure 6). 5 I also show ha expansions in U.S. oupu precede increases in he number of maquiladora esablishmens by a leas hree quarers, a resul ha highlighs he iner-emporal link beween U.S. manufacuring and he exensive margin of o shoring. Bergin, Feensra, and Hanson (2008) also analyze he exen o which ucuaions in he exensive margin of o shoring accoun for variaions in Mexico s maquiladora employmen. They show ha more han one hird of he adjusmen in indusry-level employmen and nearly one half of he adjusmen in maquiladora s oal employmen occur a he exensive margin (i.e. hrough variaion in he number of esablishmens over ime). 6 Despie he empirical evidence, he heoreical macroeconomic lieraure addressing he business cycle implicaions of o shore producion does no fully capure he iner-emporal dynamics of o shoring a he exensive and he inensive margins. For insance, Bursein, Kurz, and Tesar (2008) examine he role of producion sharing in he ransmission of business cycles in a wo-counry model in which he locaion of plans is xed over ime. 7 Bergin, Feensra, and Hanson (2007) also focus on he imporance of o shore producion in amplifying he ransmission of shocks across counries, bu hey do so wih a model in which he inensive margin does no reac, and he number of o shoring rms makes an abrup shif raher han a gradual adjusmen over ime (as in he daa) in response o aggregae shocks. I address hese de ciencies by incorporaing he endogenous deerminaion of he number of o shoring rms in a wo-counry (Norh and Souh), dynamic sochasic general equilibrium (DSGE) model wih rm enry and rm heerogeneiy, along he lines of Meliz (2003) and Ghironi and Meliz (2005). Firm enry is subjec o a sunk cos re ecing he regulaion associaed wih saring a business in he counry of origin. Following enry, each rm can use eiher domesic or foreign inpus in he producion of a di eren variey of nal goods. The use of foreign inpus involves he esablishmen added (INEGI), nearly 50 percen of he Mexico s expors, and approximaely 25 percen of Mexico s employmen (Bergin, Feensra, Hanson, 2007, 2008). 5 Alhough no enirely owned by U.S. mulinaionals, he maquiladora plans impor mos of heir inpus (82 percen) and send mos of heir gross oupu (90 percen) from/o he U.S. (Hausman and Kayko, 2003; Bursein, Kurz and Tesar, 2008). For his reason, I use he number of maquiladora esablishmens as an empirical proxy for he exensive margin of o shoring. 6 Recen empirical lieraure highlighs he role of he exensive margin in inernaional rade and he presence of xed exporing coss: Baldwin and Harrigan (2007) show ha he number of raded goods (he exensive margin) decreases wih disance and increases wih he size of he imporing counry. Besedes and Prusa (2006) nd ha he survival rae of expors for di ereniaed good varieies increases wih he iniial ransacion size and also wih he lengh of he relaionship. Hummels and Klenow (2005) show ha larger economies have larger expors, and ha he exensive margin accouns for as much as 60 percen of his di erence. 7 In Bursein, Kurz and Tesar (2008), he low subsiuabiliy beween he domesic and foreign varieies enering an Armingon composie enhances he cross-counry co-movemen of oupu. 3

4 of an o shore producion plan and is subjec o a xed o shoring cos per-period. Also, o shoring involves he so-called iceberg rade coss ha re ec ransporaion, insurance, and rade barriers, coss incurred in he shipping of nal good varieies produced o shore back o he counry of origin. Thus, when deciding on where o locae producion (domesically vs. o shore), each rm balances he lower foreign coss of e ecive labor agains he xed and rade coss associaed wih o shore producion. 8 Since rms are heerogeneous in produciviy, he decision o produce o shore is rm-speci c: Only he more producive rms can a ord he xed coss of o shoring, and heir number varies over ime. The model also implies ha he relocaion of producion o shore akes place one-way: Since he cos of e ecive labor is relaively lower in he Souh, only Norhern rms have he incenive o relocae producion o shore. All Souhern rms produce domesically. 9 The implicaions of he model are consisen wih he empirical evidence provided by recen sudies on he deerminans of verical producion neworks. For insance, Hanson, Maaloni, and Slaugher (2005) show ha U.S. mulinaional rms impor more inermediae inpus when heir foreign a liaes bene from lower wages and lower rade coss in he hos economy. Kurz (2006) shows ha U.S. rms choosing o o shore are ex-ane larger and more producive han heir domesic counerpars, as heir higher idiosyncraic produciviy levels allow hem o cover he xed coss of o shoring. The key resuls of he paper are as follows. Firs, he model generaes a procyclical paern of o shoring ha is consisen wih he sylized facs from Mexico s maquiladora indusry. In paricular, following an economic expansion in he paren counry, he value added per o shoring rm spikes on impac. However, domesic rm enry leads o an appreciaion of he erms of labor and generaes a gradual increase in he number of o shoring rms over ime. 0 Second, o shoring enhances he comovemen of oupu relaive o he benchmark model wih expors developed in Ghironi and Meliz (2005). As rm enry places upward pressure on he domesic e ecive wage and causes more rms o relocae producion o shore, higher demand for domesic labor (due o rm enry) and sequenially higher demand for o shore labor (due o he relocaion of producion) enhance he comovemen of wages and aggregae incomes. The resul is consisen wih he empirical regulariy documened by 8 I de ne he cos of e ecive labor as he raio beween he real wage and aggregae produciviy (w =Z in he Norh and w =Z in he Souh). 9 I derive an asymmeric seady sae in which di erences in he regulaion of rm enry in he counry of origin are ranslaed in di erences in real e ecive wages across counries. In he model, I se rm enry coss o be higher in he Souh; in urn, since he more regulaed economy aracs a smaller number of rms, labor demand and he cos of e ecive labor are lower in he Souh. 0 The erms of labor is de ned as he raio beween he Souhern and Norhern real cos of e ecive labor expressed in unis of he same consumpion baske, T OL = Q w =Z w =Z, as in Ghironi and Meliz (2005). An increase in he cos of e ecive labor in he Norh would cause he erms of labor o appreciae (i.e. T OL decreases). In conras, in he radiional IRBC lieraure, a domesic increase in aggregae produciviy leads o increased 4

5 Bursein, Kurz, and Tesar (2007) ha counries wih higher producion-sharing rade links end o exhibi higher correlaions of manufacuring oupu. Third, o shoring narrows he price dispersion across counries, as i dampens he appreciaion of he real exchange rae ha follows an increase in aggregae produciviy in he paren counry (he Harrod-Balassa-Samuelson e ec). This resul is driven by several channels, including he upward pressure on he foreign wage, he decrease in he size of he domesic non-raded secor, he decline in impor prices and in he availabiliy of foreign varieies as o shoring crowds ou he less producive foreign exporers. Fourh, o shoring enhances he procyclicaliy of invesmen and rm enry in he paren counry relaive o he benchmark model wih expors only, as he lower-cos alernaive of o shoring increases he pro abiliy of domesic rms. In urn, he employmen loss caused by o shoring is parially o se by he employmen gain generaed by greaer domesic rm enry. This paper is relaed o a growing body of macroeconomic lieraure ha focuses on endogenous rm enry and adjusmens along he exensive margin of expors (bu no of o shoring). For example, Ghironi and Meliz (2005) sudy he expor decision of rms in he presence of xed exporing coss, in a framework wih rm enry and rm heerogeneiy. Alessandria and Choi (2007) analyze he exensive margin of expors in a model wih sunk and coninuaion xed coss ha explains he "exporer hyseresis" behavior. 2 Corsei, Marin, and Peseni (2007) examine he erms-of-rade implicaions of produciviy improvemens a ecing he enry of rms and he producion secor, in a model in which he exensive margin of expors is endogenous. And Mejean (2006) emphasizes he implicaions of endogenous rm enry in he radable secor for he real exchange rae dynamics and he Harrod-Balassa-Samuelson e ec. The sudy of macroeconomic implicaions of o shoring hrough verical FDI is paricularly relevan for pairs of counries and for economic areas ha are separaed by persisen di erences in he cos of e ecive labor. For insance, o shoring hrough verical FDI has been imporan for he U.S. mulinaional rms acing wihin he NAFTA region, and also wihin Cenral and Souh America: As much as 50 percen of he manufacuring sales of U.S. a liaes in Mexico and 26 percen in Lain America as a whole were direced owards heir U.S. paren rms in 2005 (as opposed o only 3 percen for he U.S. a liaes in Europe and 5 percen in he Asia-Paci c region; BEA, 2007). A similar paern exiss beween Wesern Europe and he new member counries of he European Union (Marin, 2006; Meyer, 2006). producion a home bu no o shore, such as in Backus, Kehoe, Kydland (992). 2 "Exporer hyseresis" refers o he behavior of rms ha coninue o serve he foreign marke even afer a real exchange rae appreciaion reduces heir expor compeiiveness. 5

6 The res of his paper is organized as follows: Secion 2 inroduces a DSGE model of o shoring ha allows for ucuaions in o shoring a boh he exensive and he inensive margins; Secion 3 de nes he average produciviy levels of he rms producing domesically and o shore; Secion 4 discusses he model calibraion; Secion 5 presens he resuls, including he macroeconomic dynamics in he presence of aggregae produciviy shocks, as well as a comparison of he empirical momens of o shoring o Mexico and heir model counerpars; Secion 6 concludes wih a summary and proposed exensions of he model. 2 Model of O shoring wih Heerogeneous Firms 2. Model Seup: Markes and Producion Sraegies This secion summarizes he wo-sage model of rm enry and o shore producion, illusraed in Figure. In he rs sage, an unbounded pool of poenial enran rms face a rade-o beween he sunk enry cos (re ecing he cos of saring a business in he rms counry of origin), he expeced sream of fuure monopolisic pro s, and he probabiliy of exi very period, as in Ghironi and Meliz (2005, henceforh GM2005). Only afer paying he sunk enry cos, each rm is assigned an idiosyncraic labor produciviy facor ha is drawn independenly from a common disribuion over a suppor inerval, and ha he rm keeps for he enire duraion of is life. Figure. Desinaion markes and producion sraegies of rms 6

7 In he second sage, pos-enry rms are monopolisically compeiive and heerogeneous in labor produciviy. Every period afer enry, rms choose he desinaion marke(s) ha hey serve as well as he locaion of producion, as follows: () Firms serving heir domesic marke can use eiher domesic or foreign inpus in producion. The use of foreign labor involves he esablishmen of o shore producion plans (o shoring hrough verical FDI). I o ers he advanage of a lower producion cos, bu is subjec o a per-period xed o shoring cos, and o an iceberg rade cos ha a ecs he nal goods shipped back o he counry of origin for nal consumpion. (2) Some of he rms can also serve he foreign marke. To his end, hey use domesic labor as he only inpu in he producion of nal goods which hey expor subjec o a per-period xed exporing cos, as in GM2005. Thus, I nes he model of GM2005 (expors only, no o shoring) as a special case in my model wih o shoring. 3 The following secions describe in deail he model wih rm enry and o shore producion, saring wih he laer (secions 2.2) and ending wih he former (secion 2.5). 2.2 Firms Serving he Domesic Marke: Domesic Producion vs. O shoring This secion describes he mechanisms of domesic and o shore producion for he Norhern rms. I does no concern he Souhern rms, as o shoring akes place one-way, from he Norhern economy o he low-wage Souh. In he Norh, a coninuum of monopolisically-compeiive rms produce nal goods for he domesic marke. Firms are heerogeneous in produciviy, wih each rm producing a di eren variey of nal goods. 4 Since each rm produces one variey, he rm-speci c labor produciviy z also serves as an index for he exising varieies of nal goods. Every period, rms producing for he domesic marke can choose one of wo possible locaions of producion: 3 I absrac from he possibiliy of o shoring hrough horizonal FDI: As an alernaive o expors, rms serving he foreign marke may produce abroad using he local labor of he counry whose marke hey arge, as in Conessi (2006), a sraegy which I refer o as o shoring hrough horizonal FDI. The di erence beween o shore producion under verical and horizonal FDI is ha, under verical FDI, rms serving heir domesic marke shif par of he producion chain o shore in order o ake advanage of he relaively lower cos of e ecive labor. This re ecs he relocaion of downsream producion aciviies o shore (e.g. manufacuring, assembly and packaging) by he verically-inegraed rms ha coninue o perform he upsream operaions (e.g. research, markeing and sales) in he counry of origin. In conras o verical FDI, producion under horizonal FDI is moivaed by improved access o he foreign marke (i.e. obained by avoiding he rade cos), and involves he simulaneous producion of he same nal good boh a home (i.e. o be sold in he home marke) and o shore (i.e. o be sold in he hos marke). 4 The model implies ha rms wih produciviy below he endogenous produciviy cuo z V; (i.e. he less producive rms) produce heir varieies of nal goods domesically, whereas hose above he cuo produce o shore. 7

8 () Domesic producion: The Norhern rm wih idiosyncraic labor produciviy z employs labor l o obain an amoun of nal goods: y D; (z) = Z zl ; () where Z is he aggregae produciviy of labor in he Norh and z is he rm-speci c labor produciviy; (2) O shore producion: Alernaively, he rm wih idiosyncraic labor produciviy z may choose o relocae producion o shore using Souhern labor l as he only inpu in producion: y V; (z) = Z zl : (2) Thus, I assume ha while he o shoring rm becomes subjec o he Souhern aggregae labor produciviy Z ; i is able o carry is own idiosyncraic labor produciviy z o he Souhern economy. 5 Given he demand for nal good varieies produced domesically, y D; (z) = D; (z) C, and also he demand for varieies produced o shore by he verically-inegraed rms, y V; (z) = V; (z) C, 6 he monopolisically-compeiive rms solve heir pro -maximizaion problem: max f D; (z)g d D(z) = D; (z)y D; (z) w Z z y D;(z); (3) max f V; (z)g d V (z) = V; (z)y V; (z) w Q Z z y V;(z) w Q f V Z : (4) The cos of producing one uni of oupu eiher domesically or o shore varies no only wih he cos of e ecive labor w Z and w Q Z across counries, bu also wih he level of idiosyncraic labor produciviy 5 Sraegies () and (2) are exreme cases of a broader framework of o shoring, which would allow he o shoring rm wih idiosyncraic labor produciviy z o use a mix of Norhern and Souhern labor, l and l. Following he speci caion in Anras and Helpman (2004), I wrie oupu of every variey of nal goods z as a Cobb-Douglas funcion of he domesic and foreign inpus: Zzl y V;(z) = Z zl : In his paper, I explore he economic implicaions of o shoring of wo exreme scenarios under di eren calibraions of parameer : A one exreme, seing = shus down o shoring under verical FDI, as rms use exclusively domesic inpus in producion. A he oher exreme, seing = 0 implies ha o shoring rms use exclusively foreign inpus in he producion of nal goods. The smaller is, he more inensive producion is in foreign inpus, i.e. he larger is he range of operaions ha he mulinaional rm locaes o shore (e.g. manufacuring, assembly, packaging, cusomer service). For he wo exreme cases, I use he l Hôpial rule o obain: lim = lim!0! = = lim! e(=) ln = e lim! ln l0h ^opial = e lim (=)! = e 0 = : 6 I provide heir derivaion in he Appendix. 8

9 z across rms. 7 I de ne he real exchange rae Q = P " P as he raio beween he price indexes in he Souh and Norh expressed in he same currency, where " is he nominal exchange rae. In addiion o he marginal cos, he Norhern rms producing o shore incur a period-by-period xed o shoring cos equal o f V unis of Souhern e ecive labor, a cos ha re ecs he building and mainenance of he o shore producion faciliy. 8 They also face an iceberg rade cos ( > ) associaed wih he shipping of goods produced o shore back o he paren counry: For every unis produced o shore, only one uni reaches he Norhern consumers, as he di erence is los due o coss associaed wih rade barriers, ransporaion, insurance, language barriers, and di erences in he legal sysems, as discussed in Anderson and Wincoop (2004). The pro -maximizaion problem under monopolisic compeiion implies he following equilibrium prices per uni of oupu produced domesically and o shore, respecively: 9 D; (z) = V; (z) = w Z z (5) w Q Z z : (6) The resuling pro s from domesic and o shore producion, boh expressed in unis of he Norhern consumpion baske C, are: 20 d D; (z) = D;(z) C ; (7) d V; (z) = V;(z) w Q C f V Z : (8) To summarize he above, he pro s associaed wih domesic and o shore producion depend on he cos of e ecive labor in he Norh and Souh, he xed o shoring cos, he iceberg rade cos, as well as he rm-speci c labor produciviy. Firms producing o shore bene from he relaively lower cos of e ecive labor, bu heir pro s decline wih he per-period xed o shoring cos, and also wih he iceberg rade cos. Thus, when deciding upon he locaion of producion every period, he rm wih produciviy z compares he pro d D; (z) i would obain from domesic producion wih he 7 Given he domesic and o shore real wages, w and w respecively, he marginal cos of producing one uni of variey z domesically is w, and he marginal cos of producing i o shore is w Q Z z Z. The real wage w = W=P in Norh z 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. 8 The mix of f V unis of Souhern e ecive labor is equivalen o f V w =Z unis of he Souhern consumpion baske. 9 The derivaions are provided in he Appendix. 20 Using he demand y D(z) = D(z) C and he price D(z) = w for domesic producion, he corresponding Zz pro is d D(z) = D(z)yD(z): The pro from o shore producion is analogous. 9

10 pro d V; (z) i would obain from producing he same variey o shore. The model implies ha only he relaively more producive Norhern rms nd i pro able o locae producion o shore every period. Despie he lower cos of e ecive labor in Souh relaive o Norh, only rms wih idiosyncraic produciviy above a cerain cuo (z > z V; ) obain pro s ha are large enough o cover he xed o shoring cos and he iceberg rade cos. This implicaion of he model is consisen wih he empirical evidence provided by Kurz (2006) ha rms choosing o produce o shore are ex-ane larger and more producive han heir domesic counerpars, as he larger idiosyncraic produciviy levels allow hem o cover he xed coss of o shoring. 2 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 accouning for he xed o shoring cos and he iceberg rade cos, he rm a he cuo obains equal pro s from domesic and o shore producion, a propery which I use o solve for he endogenous produciviy cuo z V; ha governs he locaion decision of producion: z V; = fz j d D; (z V; ) = d V; (z V; )g : (9) Exisence of he equilibrium produciviy cuo Nex I show ha he exisence of he equilibrium produciviy cuo z V; requires a cross-counry asymmery in he cos of e ecive labor, so ha some of he Norhern rms will always mainain an incenive o produce o shore. I begin by re-wriing he expressions for pro s obained from domesic and o shore producion as d D; (z) = B w Z z and d V; (z) = B w Q z, respecively, where B C Z is a measure of he marke size in he Norh. In Figure 2, I plo he corresponding pro s as funcions of he idiosyncraic produciviy parameer z over he suppor inerval [z min ; ). The verical inerceps represen he annualized value of he sunk enry cos for he case of domesic producion w ( f E Z ), and he annualized value of he sunk enry cos plus he period-by-period xed cos for w he case of o shore producion ( f w E Z f Q ( ) V Z ), where parameer ( ). The exisence of equilibrium produciviy cuo z V; requires ha he following condiion holds every period: The pro funcion for o shoring mus be seeper han ha for domesic producion, slope fd V; (z)g > slope fd D; (z)g. When he condiion is me, o shoring generaes greaer pro s han domesic producion for he Norhern rms wih idiosyncraic produciviy z along he upper range 2 A useful implicaion of rm heerogeneiy along he lines of Meliz (2003) is ha he more producive rms have larger oupu and revenue. Given wo rms wih idyodyncraic produciviy z 2 > z, he raios of oupu and pro s are y(z 2 ) = z2 y(z ) z > ; r(z 2 ) = z2 r(z ) z > : Empirical sudies show ha rms using impored inpus in producion no only are more producive, bu also are larger and employ more workers (Kurz, 2006; Yasar and Morrison Paul, 2006). 0

11 of he suppor inerval. The slope inequaliy is equivalen o: w Q =Z w =Z < ; (0) which implies ha he e ecive wage in he Souh mus be su cienly lower han ha in he Norh, so ha he di erence covers he iceberg rade cos ( > ) and hus provides an incenive for some of he Norhern rms o produce o shore every period. 22 Figure 2. Exisence of equilibrium produciviy cuo z V ;. 2.3 Firms Serving he Foreign Marke: Expors In his secion I describe he problem of he exporing rms originaing in he Norh. The equaions for he Souh are similar unless indicaed oherwise. Variables for he Souhern economy are marked wih he (*) superscrip. Firms in each economy have he opion o serve he foreign marke hrough expors, as in GM2005. Thus, he Norhern exporing rm wih idiosyncraic produciviy z uses an amoun of domesic labor l in he producion of nal good varieies y H; (z) expored he Souhern marke: See Appendix 9. A second condion, necessary o avoid he corner soluion when all rms would produce o shore, is ha he produciviy cuo mus be larger han he lower bound of he suppor inerval: z V; > z min: This condiion is equivalen o d D;(z min) < f E w Z w + f Q V Z ;which shows ha he rm wih idiosyncraic produciviy equal o he lower-bound level z min would obain zero pro s from domesic producion and negaive pro s from o shore producion. 23 I view exporing as a special case wihin a broader framework which allows rms o serve he foreign marke using a

12 y H; (z) = Z zl : () The pro maximizaion problem of he Norhern exporing rms generaes he following price and pro funcions: H; (z) = w Q Z z ; (2) d H; (z) = H;(z) C Q f H w Z : (3) In paricular, serving he foreign marke involves a period-by-period xed exporing cos equal o f H unis of Norhern e ecive labor as well as he iceberg rade cos. The model implies ha every period, he Norhern rms wih idiosyncraic labor produciviy above a cerain cuo (z > z H; ) nd i pro able o expor o he Souhern marke a he same ime wih serving heir domesic marke (Norh). They obain pro s ha are large enough o cover boh he xed cos and he iceberg rade cos of exporing. In he presence of rm heerogeneiy, he opion o expor is endogenous o he model. As in GM2005, he rm wih he idiosyncraic labor produciviy equal o he cuo obains zero pro s from exporing. Thus, he ime-varian produciviy cuo z H; is obained as: z H; = inf fz j d H; (z V; ) > 0g : (4) mix of domesic and foreign inpus in producion. Producion is described by he following Cobb-Douglas speci caion: Zzl Z y H;(z) = zl ; where a larger accouns for a smaller conen of foreign inpus conribued by he o shore a liaes owards he producion of nal goods sold in he Souhern marke. Thus, In addiion o nesing he model wih endogenous expors as in GM2005 (which is focus of his paper, under he calibraion = ), my model wih o shoring can also nes he case in which rms serving he Souhern marke produce exclusively hrough heir foreign a liaes as in Conessi (2006) (which I revisi by seing = 0). Producion in Souh hrough horizonal FDI allows rms o avoid he rade cos by using!0 local inpus. Using he l Hôpial rule, lim = lim! = = lim The corresponding price and pro funcions are H;(z) = w f w Q H Z Z :! e(=) ln = e lim! w Q Z z ln l0h ^opial = e lim! (=) = e 0 = : w Z z and dh;(z) = H;(z) C Q 2

13 2.4 Households Financial auarky Households in each counry maximize he expeced lifeime uiliy (as a funcion of consumpion) and provide labor inelasically: subjec o he budge consrain: max fb + ; x + g " E X s= s C s # ; (5) (ev + e d )N x + ( + r )B + w L > ev (N + N E; ) x + + B + + C ; (6) where 2 (0; ) is he subjecive discoun facor, C is he consumpion baske, and > 0 is he inverse of he iner-emporal elasiciy of subsiuion. The Norhern household sars every period wih muual fund share holdings x (whose marke value is ev N ) and real bond holdings B. I receives dividend income e d N on he muual fund socks (equal o he pro of he average rm imes he number of producing rms) in proporion wih is sock holdings x ; ineres r B on bond holdings, and also labor income equal o he real wage w for he amoun of labor L = ha i supplies inelasically. The Norhern household purchases wo ypes of asses every period. Firs, i purchases x + shares in a muual fund of Norhern rms ha includes: (i) N rms already producing a ime, eiher domesically or o shore, and (ii) N E; new rms ha ener he domesic marke in period. Each share is worh is marke value ev, equal o he ne presen value of he expeced sream of fuure pro s of he average rm. Second, he household buys he risk-free bond B + denominaed in unis of he Norhern consumpion baske. (Bond holdings play a role in he exended model wih inernaional rade in bonds, which I presen in he Appendix.) 24 In addiion, households purchase he consumpion baske C, which includes varieies of nal goods produced by Norhern rms (! 2 NN ) eiher domesically or o shore; i also includes he impors of nal good varieies produced by he Souhern rms (! 2 SN ): 2 z Z V; C = y D; (!) 6z 4 min d! {z } Domesic producion + Z d! y V; (!) z V; {z } O shore producion 3 Z + yh;(!) d! zh; 7 {z } 5 SN ; (7) 24 In he model wih complee nancial auarky (i.e. socks in he muual fund and bonds are no raded across counries), he equilibrium condiions for sock and bond holdings are x = x + = and B = B + = 0. 3

14 where > is he symmeric elasiciy of subsiuion across nal good varieies. I use he home consumpion baske C as he numeraire good; I de ne he real price of variey z in unis of he Norhern consumpion baske as (z) = p (z)=p. Thus, he he consumpion-based price index in he Norh is: 25 Z = (!) d! ;! 2 NN [ SN : (8) The rs-order condiions generae he Euler equaions for bonds and socks: C h i = ( + r + ) E C + ; (9) " C+ )E ( d e + + ev +)# : (20) ev = ( C 2.5 Firm Enry and Exi Following GM2005, rm enry akes place every period. I requires a sunk enry cos (re ecing he cos of saring a business in he rms counry of origin) equal o f E unis of Norhern e ecive labor. 26 Poenial enrans become aware of heir idiosyncraic labor produciviy z only afer enering he marke. Afer paying he sunk enry cos, each rm is randomly assigned an idiosyncraic labor produciviy z which is drawn independenly from a common disribuion G(z) wih suppor over he inerval [z min ; ), and which he rm keeps for he enire duraion of is life. The poenial enran rms are forward looking and correcly anicipae heir expeced pos-enry value ev, which is given by he expeced sream of fuure pro s e d and by he exogenous probabiliy wih which hey receive an exi-inducing shock every period. The forward ieraion of he Euler equaion for socks (20) generaes he expression for he expeced pos-enry value of poenial enrans: ev = E ( X s=+ ) [( )] s Cs eds : (2) C In equilibrium, rm enry akes place unil he value of he average rm ev equals he sunk enry cos f E w Z, boh expressed in unis of he Norhern consumpion baske: ev = f E w Z : (22) 25 If p (z) denoes he price of each variey z, he price index of he home consumpion baske is P = R p (!) d! for! 2 NN [ SN. The demand for each variey of nal goods z is y (z) = (p (z)=p ) C. 26 Or f Ew =Z unis of he consumpion baske in he Norh. 4

15 The N E; rms enering a ime do no produce unil period +. Irrespecive of heir idiosyncraic produciviy, all rms - including he new enrans - are 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; ); (23) where N = N ;D + N ;V consiss of rms producing eiher domesically or o shore every period. 3 Solving he Model wih Firm Heerogeneiy A necessary sep in solving he model wih rm heerogeneiy is o derive analyical soluions for he average produciviy, prices and pro s of he represenaive Norhern rms ha produce domesically and o shore every period. This secion also provides he expressions for aggregae accouning and he balance of inernaional paymens ha close he model wih o shoring. 3. Average Firm Produciviy Levels Firms serving he domesic marke I de ne wo average labor produciviy levels: () he average produciviy ez D; of he Norhern rms producing domesically, and (2) he average produciviy ez V; of he Norhern rms producing o shore. I illusrae hem in Figure 3, in which I plo he densiy of he rm-speci c labor produciviy levels z over he suppor inerval [z min ; ). Every period, here are N D; of he relaively less producive Norhern rms (z < z V; ) ha choose o produce domesically; heir average produciviy is ez D;. The remaining N V; of he relaively more producive Norhern rms (z > z V; ) choose o produce o shore; 27 heir average produciviy is ez V;. 28 Since he rm-speci c labor produciviies z are random draws from a common disribuion G(z) wih densiy g(z), I wrie he average idiosyncraic produciviies of he Norhern rms producing domesically and o shore as: 2 ez D; = 4 G(z V; ) zz V; z min z 3 g(z)dz5 2 Z 6 and ez V; = 4 G(z V; ) z V; z 3 7 g(z)dz5 : (24) 27 The oal number of Norhern rms is N = N V; + N D;: 28 The di erence beween ez V; and z V; is ha he former is he average produciviy of o shoring rms, whereas he laer is he cuo produciviy above which rms produce o shore. 5

16 Figure 3. Average labor produciviies for rms serving he domesic marke hrough domesic (ez D ; ) and o shore (ez V ; ) producion Pareo-disribued rm produciviy Following Meliz (2003) and GM2005, I assume ha he rm-speci c labor produciviy draws z are Pareo-disribued, wih p.d.f. g(z) = kz min =z k+ and c.d.f. G(z) = (z min =z) k over he suppor inerval [z min ; ): Using his assumpion, I derive analyical soluions for he average produciviies of he wo represenaive Norhern rms producing domesically and o shore as funcions of he ime-varian produciviy cuo z V; : 29 ez D; = z min z V; 2 ( ) k ( ) zk 4 V; zmin zv; k zmin k 3 5 and ez V; = z V; ; (25) h where he produciviy cuo 30 is z V; = z min (N =N V; ) (=k), and he parameers are k k ( ) i and k >. 3 Since o shoring akes place one-way, from Norh o Souh, he Souhern rms serving heir domesic marke (exclusively hrough domesic producion) have a consan average produciviy ez D = z min : 29 I provide heir derivaion in he Appendix. 30 The shares of Norhern rms producing domesically and o shore, respecively, are N D;=N = G (z V;) and N V;=N = G (z V;), where he oal number of Norhern rms in every period is N = N D; + N V;. I use he funcional form for he Pareo c.d.f. in order o derive he produciviy cuo as z V; = z min(n =N V;) (=k) : 3 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. Also, he condiion k > ensures ha he variance of rm size is nie, given he average produciviies of he rms producing domesically and o shore. 6

17 Exporing rms Under he assumpion of Pareo-disribued produciviy draws, GM2005 de- ne he average produciviy levels of he exporing rms originaing in each economy: =k N ez H; = z min and ez H; = zmin N H; N D; N H;! =k : (26) 3.2 Average Prices and Pro s Afer deriving he average produciviies, I re-wrie he model in erms of hree represenaive Norhern rms: one producing domesically, anoher producing o shore (each serving he Norhern marke), and a hird rm exporing o he foreign marke. Since he Souhern rms do no produce o shore due o he wage asymmery across counries, here are only wo represenaive Souhern rms, one producing domesically for he local marke, and he oher exporing o he Norh. I use he average rm produciviies de ned above o wrie he prices and pro s associaed wih each represenaive rm, as shown in Table : Table. Average prices and pro s Producion sraegy Desinaion marke Prices Pro s Domesic Domesic e D; = e D; = w Z e dd; e z D; = (e D;) C w d e D; = e D; C Z ez D; O shore Domesic e V; = w Q Z ez V; Domesic Expor e H; = e H; = w Q w Q Z ez H; ed V; = (e V;) C f V w Q Z Z dh; e ez H; = (e H;) C w Q f H Z ed H; = e H; C Q fh w Z Endogenous produciviy cuo for o shoring Using he Pareo assumpion and he propery ha he rm a he produciviy cuo z V; is indi eren abou he locaion of producion, I wrie he link beween he pro s of he wo represenaive rms as: 32 ed V; = k zv; edd; + k ( ) ez D; k ( ) f V w Z w Q : (27) The produciviy cuo for expors is also endogenous, as in GM2005. Using he propery ha he rm a he produciviy cuo z H; obains zero pro s from exporing, he average pro s from 32 See he Appendix for he derivaion. Z 7

18 expors are: ed H; = k ( ) f w H ; and d Z e H; = k ( ) f H w Z : (28) Price indexes The consumpion price index in he Norhern economy is an expression of he average prices of goods produced domesically and o shore by he Norhern rms, as well as of he average price of goods impored from he Souh: = N D; (e D; ) + N V; (e V; ) + N H; e H; : (29) Due o he relaive wage asymmery, here is no represenaive Souhern rm producing o shore. The consumpion price index in he Souh includes only he average price of goods produced domesically by Souhern rms and ha of goods impored from he Norh: = N D; e D; + NH; (e H; ) : (30) Toal pro s The oal pro s of he Norhern rms include he average pro s from domesic producion, from o shore producion, and from exporing: N e d = N D; e dd; + N V; e dv; + N H; e dh; : (3) In conras o he Norhern economy, he oal pro s of he Souhern rms combine he pro s from domesic producion and from expors only: N D; e d = N D; e d D; + N H; e d H;: (32) 3.3 Aggregae Accouning and he Balance of Inernaional Paymens I use value added as a measure of he aggregae incomes of he wo economies. The measure avoids he double-couning of o shore producion by he Norhern rms, which is capured by he value added of he Souhern economy hrough he wage bill. Thus, I de ne value added as he sum of he wage bill and he amoun of sock dividends ha households in each counry obain every period: Y = w + N e d and Y = w + N D; e d : (33) Under nancial auarky in he markes for boh bonds and socks (i.e. B + = B = 0 and 8

19 x + = x = in equilibrium), aggregae accouning implies ha households spend heir income from labor and sock holdings on consumpion and invesmen in new rms: C + N E; ev = Y and C + N E;ev = Y : (34) Finally, he real exchange rae Q is deermined by he balanced curren accoun condiion for he Norhern economy, which re ecs he corresponding balance for he Souh: CA Auarky = N H; (e H; ) C Q + N V;dV; e {z } {z } Expors Repariaed pro s N V; (e V; ) C {z } O shore value added N H; e H; C {z } Impors from Souhern rms Under nancial auarky, he balanced curren accoun condiion (CA Auarky = 0) implies ha he sum of (a) expors by he Norhern rms o he Souh and (b) repariaed pro s of o shore a liaes mus equal he sum of (c) he value of impors from o shore a liaes and (d) impors of nal good varieies produced by he Souhern rms. 3.4 Model Summary As shown in Appendix A., he baseline model wih nancial auarky for he Norhern economy can be summarized by 6 equaions in 6 endogenous variables: N, N D;, N V;, N H;, N E;, e d, e d D;, e d V;, ed H;, ez D;, ez V;, ez H;, ev, r, w and C. As he Souhern rms do no o shore o he high-wage Norh, he Souhern economy is described by only equaions in endogenous variables: There are no Souhern counerpars for N, N V;, e d V;, ez D; and ez V;. In paricular, he average labor produciviy of he represenaive Souhern rm producing for he domesic marke (ez D ) is consan over ime. Variables N D;, r, N and r are predeermined. 4 Calibraion I use a sandard quarerly calibraion by seing he subjecive rae of ime discoun = 0:99 o mach an average annualized ineres rae of 4 percen. The coe cien of relaive risk aversion is = 2. Following GM2005, I se he inra-emporal elasiciy of subsiuion a = 3:8, a value which corresponds o he U.S. plan and macro rade daa. Alhough he resuling markup of 35.7 percen over he marginal cos migh appear oo large compared o he sandard macroeconomic lieraure, is magniude mus be considered in he conex of he sunk enry cos ha places a wedge beween 9

20 he rms marginal and average cos. I also calibrae he probabiliy of rm exi = 0:025 o mach he annual 0 percen job desrucion in he U.S. As summarized in Table 2, I calibrae he xed coss of o shoring (f V ) and exporing (f H and f H ) as well as he Pareo disribuion parameer (k) so ha he model maches he imporance of o shoring and rade for he Mexican economy, as illusraed by four empirical momens: () Maquiladora s value added represens approximaely 20 percen of Mexico s manufacuring GDP (INEGI, 2008), as compared o 25 percen in he model; (2) Maquiladora s expors represen approximaely half of Mexico s oal expors (Bergin, Feensra, and Hanson, 2008), as compared o 60 percen in he model; (3) Employmen in he maquiladora secor accouns for approximaely 25 percen of Mexico s oal manufacuring employmen (Bergin, Feensra, and Hanson, 2008), as compared o 22 percen in he model; (4) Toal impors represen he equivalen of 33 percen of Mexico s GDP (INEGI, 2008), as compared o 32 percen in he model. To his end, I se f V for Norhern rms), f H = 0:032 and f H = 0:0057 (he xed cos of o shoring = 0:08 (he xed coss of exporing for Norhern and Souhern rms, respecively), as well as k = 4:2 (he Pareo disribuion coe cien). 33 Wihou loss of generaliy, I se he lower bound of he suppor inerval for rm-speci c produciviies in he Norh and Souh a z min = z min =. In order o derive an asymmeric seady sae in which he cos of e ecive labor is lower in he Souh han in Norh, I se he sunk enry cos (i.e. which re ecs he cos of saring a business) o be larger in he Souh han in Norh (f E = 4f E, while seing f E = wihou loss of generaliy). 34 The calibraion re ecs he considerable variaion in he cos of saring a business across counries: he moneary cos is 3.3 imes higher in Mexico han in he U.S. or Canada; i is 6.2 imes higher in Hungary han in he U.K. (World Bank, 2007; see Appendix 5). The asymmeric sunk enry coss, along wih he rade iceberg cos ( = :3) and he values for f V, f H and fh repored above, generae a seady sae value for he erms of labor ha is less han one (T OL = 0:76). Thus, he seady sae cos of e ecive labor in he Souh, de ned as he real wage divided by he aggregae produciviy 33 In he model wih expors only, I se f H = 0:0260 and f H = 0:0226 so ha he fracion of Norhern exporing rms (0 percen) and ha of Souhern exporing rms (63 percen) mach he corresponding seady sae values in he model wih o shoring. 34 The asymmeric sunk enry cos is one mehod ha generaes di eren e ecive wages across counries. The same resul would be achieved wih a leas wo oher modeling devices: () Inroduce a cross-counry asymmery in he size of rms (raher han in heir number) hrough he price elasiciy of demand. Wih idenical sunk enry coss and equal average labor produciviy levels in he wo economies, rms in he economy wih he lower price elasiciy of demand charge higher markups and produce relaively lower oupu; in urn, he lower labor demand generaes lower wages. (2) Anoher way o generae di eren rm sizes across counries, similar o he one I use in his paper, would be o allow for muli-produc rms and sunk coss of creaing new produc varieies. While keeping he sunk rm enry coss equal across counries, here will be fewer varieies per rm and lower demand for labor in he economy wih he higher sunk cos of creaing a new variey. 20

21 level, is 76 percen of he corresponding value in he Norh. The calibraion provides an incenive for he Norhern rms o produce o shore in seady sae. Table 2. Baseline model wih o shoring: calibraion f E = Sunk rm enry cos, Norh k = 4:2 Pareo disribuion coe cien fe = 4f E Sunk rm enry cos, Souh = 0:99 Sandard quarerly calibraion f V = 0:0057 Fixed cos of o shoring = 2 CRRA coe cien f H = 0:0320 Fixed cos of exporing, Norh = 0:025 Probabiliy of rm exi f H = 0:080 Fixed cos of exporing, Souh = 3:8 Inra-emporal elasiciy of subsiuion The resuling seady-sae fracion of he Norhern rms ha use inpus impored from heir o shore a liaes (N V =N) is :4 percen; he raio of exporing rms in oal (N H =N) is 0: percen. 35 Since I model o shoring in an asymmeric wo-counry framework ha absracs from exchanges beween U.S. rms and he res of he world (oher han Mexico), he seady sae values repored above are less han heir empirical counerpars ha include all U.S. manufacuring rms. In he daa, approximaely 4 percen of he U.S. rms (oher han domesic wholesalers) used impors from boh Mexico and he res of he world in 997 (Bernard, Jensen, Redding and Scho, 2007), 36 ou of which inra- rm impors (as opposed o arm s lengh ransacions) represened half of he oal (Bardhan and Jafee, 2004); approximaely 2 percen of he U.S. manufacuring plans were exporers in 992 (Bernard, Eaon, Jensen and Korum, 2003). The calibraion also implies ha he seady-sae share of Norhern expendiure on he varieies produced by Norhern rms domesically (66.0 percen) - rms which are relaively less producive han he average - is less han heir fracion in he oal number of varieies available o Norhern consumers (89.2 percen). In conras, since he o shore varieies are produced by he relaively more producive Norhern rms, heir marke share (2.2 percen) is more han heir fracion in he oal number of varieies available in Norh (.2 percen) In he Souhern economy, he raio of exporing rms in he oal is 63 percen. 36 The value would undersae he fracion of plans ha use impored inpus if he imporing rms end o operae muliple plans manufacuring muliple produc varieies. 37 The marke share of he Souhern varieies in he Souhern marke is 6.66 percen. Their fracion in he oal number of varieies available in Souh (62.77) exceeds heir marke share. 2

22 5 Resuls 5. O shoring Dynamics Under nancial auarky, I log-linearize he model wih o shore producion around he seady sae and compue he impulse responses o a ransiory percen increase in aggregae produciviy in he Norh. I assume ha produciviy is described by he univariae process log Z + = log Z + u, wih he persisence parameer = 0:9. O shoring a he inensive margin Figure 4 shows he impulse responses of he model wih o shoring (solid line), and conrass hem wih he impulse responses of he benchmark model wih endogenous expors and no o shoring as in GM2005 (doed line). For each variable, he horizonal axis illusraes quarers afer he iniial shock, and he verical axis shows he percen deviaions from he original seady sae in each quarer. On impac, he percen increase in aggregae labor produciviy in he Norh generaes an equal increase in he real wage w. The increased demand for he nal good varieies already produced o shore (o shoring a he inensive margin) causes he real wage in he Souh (w ) and he erms of labor T OL = Qw =Z w =Z o spike upward on impac: Since he increase in aggregae labor produciviy in he Norh is no replicaed in he Souh, on impac here is excess demand for he Souhern unis of e ecive labor. Therefore, he number of Norhern rms ha produce o shore (N V; ) declines on impac due o: () he increase in he cos of producing o shore, and (2) he increase in he xed cos of relocaion, boh of which are sensiive o he cos of e ecive labor in he Souh. O shoring a he exensive margin Over he business cycle, as aggregae labor produciviy in he Norh persiss above he iniial seady sae, he larger marke size encourages rm enry, which causes he number of Norhern rms (N ) o increase (Figure 4). The larger number of incumben rms causes an increase in labor demand in he Norh, and hus leads o an appreciaion of he cos of e ecive labor in he Norh relaive o ha in he Souh in he medium run (as shown by he decline of T OL below he iniial seady sae). Following he appreciaion of he erms of labor, more of he Norhern rms have an incenive o relocae producion o he Souh (o shoring a he exensive margin). Hence, following he iniial drop, he number of Norhern rms ha relocae producion o he Souh (N V; ) rises above he original seady sae 4 quarers afer he shock. The iniial upward spike in he Souhern real wage, caused by he increased demand for nal good varieies ha were already produced o shore when he shock occurred (o shoring a he inensive 22