Offshoring Along the Production Chain

Transcription

1 Offshorng Along the Producton Chan Phlpp Harms, Olver Lorz and Deter Urban Workng Paper Ths dscusson paper seres represents research work-n-progress and s dstrbuted wth the ntenton to foster dscusson. The vews heren solely represent those of the authors. No research paper n ths seres mples agreement by the Study Center Gerzensee and the Swss Natonal Bank, nor does t mply the polcy vews, nor potental polcy of those nsttutons.

2 Offshorng Along the Producton Chan Phlpp Harms, a,b Olver Lorz, a and Deter Urban a,c a RWTH Aachen Unversty, b Study Center Gerzensee, c CESfo March 2, 2009 Abstract Recent contrbutons on offshorng often assume that frms can freely splt ther producton process nto separate steps whch can be ranked accordng to the cost savngs from producng abroad. We replace ths assumpton by the noton of a technologcally determned sequence of producton steps. In our model, cost savngs from offshorng fluctuate along the producton chan, and movng unfnshed goods across borders causes transport costs. We show that, n such a settng, frms may refran from offshorng even f relocatng ndvdual steps would be advantageous n terms of offshorng costs, or they may offshore (almost) the entre producton chan to save transport costs. Small varatons n model parameters may have a substantal mpact on offshorng actvtes. JEL classfcaton: D24, F10, F23. Keywords: Offshorng, Internatonal Trade, Vertcal Producton Chan. Address: RWTH Aachen Unversty, Department of Economcs and Busness Admnstraton, Templergraben 64, Aachen, Germany. Emal: harms@rwth-aachen.de, lorz@rwth-aachen.de, deter.urban@ww.rwth-aachen.de.

3 1 Introducton Over the past decade, sgnfcant attenton has been devoted to the phenomenon of offshorng,.e. the fact that frms explot nternatonal cost dfferences by fragmentng ther producton process across natonal borders. The rsng mportance of offshorng has been supported by a number of factors: a strong declne n transportaton costs, the fall of the ron curtan, wdespread lberalzaton of FDI polces, and mprovements n means of nternatonal communcaton through new nformaton technologes. In many rch countres, ths development has rased fears about potental job losses, declnng wages, and rapd de-ndustralzaton. In fact, the publc dscusson abounds wth anecdotes about value-added chans spannng the entre globe and grm forecasts of rch countres eventually degeneratng to mere tradng centers for goods produced at low-cost locatons. Gven ths heghtened publc nterest, t s of no surprse that an ncreasng number of researchers s explorng the determnants and consequences of frms offshorng decsons. Begnnng wth the semnal contrbuton of Jones and Kerzkowsk (1990), varous attempts have been undertaken to analyze the mplcatons of the second unbundlng.e. the dsntegraton of the producton process n a coherent, yet tractable way. 1 Qute recently, Grossman and Ross-Hansberg (2008) [henceforth denoted by GRH] proposed a model that has become very nfluental n ths respect. In ther approach, the producton process conssts of dfferent tasks whch are performed by varous types of labor and whch may be done at home or offshored to a foregn country. 2 Whether offshorng s advantageous depends both on nternatonal wage dfferentals and on task-specfc ceberg costs, whch reflect the frctons assocated wth transmttng nformaton and montorng foregn actvtes. The crucal assumpton of the GRH-framework s that tasks may be ranked accordng to these costs such that there s a unque threshold whch determnes the extent of offshorng: at gven wages, all tasks up to ths threshold level are done abroad whle the rest s performed at home. Changes n relatve wages or n the costs of offshorng shft the extensve margn of offshorng. A declne n offshorng costs, for example, results n more tasks 1 The term second unbundlng goes back to Baldwn (2006) to dstngush the spatal fragmentaton of producton from trade n fnal goods. A short and necessarly selectve lst of contrbutons to the lterature ncludes Jones and Kerzkowsk (1990; 2001a; 2001b), Feenstra and Hanson (1996a; 1996b; 1997; 1999), Arndt (1997), Venables (1999), Glass and Sagg (2001), Jones (2000), Deardorff (2001b; 2001a), Kohler (2004), and Egger and Egger (2007). 2 By usng the term offshorng nstead of nternatonal outsourcng we ndcate that the geographcal locaton of producton s at the center of our nterest whle we abstract from the frms make-or-buy decson. 1

4 beng performed abroad. Whle the approach of GRH provdes an elegant framework to open the black box of producton t neglects three mportant aspects of realty: Frst, n many ndustres technology determnes the sequence of tasks or producton steps such that a rearrangement accordng to offshorng costs alone seems mplausble. 3 The panels for a car-body are frst pressed, then joned together and then sprayed; an arplane s rewred before the seats can be attached; the producton chan for mcrochps begns wth makng slcon from quartz, purfyng the slcon n a second step before wafers are produced, mcrochps are bult on these wafers, and, fnally, wafers are cut apart; n the textle ndustry one frst needs to produce cotton or wool, then to spn yarn before ths yarn can be woven or kntted. All these steps follow each other and cannot be smply re-organsed accordng to offshorng costs or other crtera. Second, performng a certan producton step often requres the unfnshed good or at least a component of t to be physcally present: sprayng a car s mpossble wthout havng the car-body n the factory, weavng fabrc requres the yarn etc. Fnally, movng these ntermedate goods across borders s assocated wth sgnfcant costs, whch encompass physcal transport costs as well as the costs of uncertan or delayed delvery. In ths paper, we present a formal framework that ncorporates these observatons n a transparent and tractable fashon. We set up a stylzed partal equlbrum model of an ndustry that apples a technology wth a contnuum of producton steps each of whch can be located n the home country or abroad. We devate from the prevous lterature assumng that producton steps have to be undertaken n a predetermned sequence, a producton step always requres the physcal presence of the unfnshed good, and shpment of the unfnshed good across borders causes transport costs. To see why and how these devatng assumptons matter, suppose there exsts a sequence of producton steps, say A, B, C, D, and steps A and C can be done more cheaply abroad whle the converse s true for producton steps B and D. To offshore only steps A and C, producton begns abroad wth step A, then the unfnshed good must be shpped shpped back to perform 3 The dfference between tasks and producton steps s subtle, but mportant: GRH assgn a task to a specfc type of labor.e. there are hgh-sklled tasks and lowskll-tasks. By contrast, the producton steps we have n mnd potentally employ varous types of labor (as n Dxt and Grossman, 1982; Feenstra and Hanson, 1996a, 1997; Kohler, 2004). Offshorng of producton steps mposes the technologcal requrement that certan tasks, each performed by one partcular producton factor, must be bundled together to a producton step at one locaton. Offshorng of sngle tasks assumes, nstead, that each sngle task can be performed at a certan locaton ndependent of where other tasks are performed. 2

5 step B at home, shpped abroad agan for step C, and fnally shpped back home to perform step D. If transport costs for the unfnshed good at ts varous stages are large, then such a strategy of partal offshorng may not be proftable. But ths does not necessarly mply that there s no offshorng at all. Instead, although n tself t s not worthwhle to offshore step B, the frm may relocate ths producton step as well because steps A and C are worthwhle to offshore and addng step B saves transport costs twce. We call such a strategy full offshorng. The decson to offshore one partcular step thus essentally depends on the proftablty to offshore adjacent steps, whch may result n a tendency to lump together several parts of the producton chan n one locaton. The extent to whch ths happens depends on a range of ndustry-specfc parameters characterzng the producton process, transport costs, and offshorng costs. We thus combne the argument that...offshorng s an ndustry-specfc phenomenon, relatng to the dosyncratc way n whch the value added process of certan ndustry may be slced up, or fragmented, nto dfferent tasks (Kohler, 2008, p. 11) wth the concept of a technologcally determned sequence of producton steps. Ths has an mmedate consequence for how the extent of offshorng n a partcular ndustry reacts to parameter varatons: our framework suggests that such changes may occur n the form of dscretonary regme shfts. Ths contrasts wth the GRH-model where a mnor varaton of exogenous parameters leads to a smooth adjustment of the number of tasks that are performed abroad. We obtan such a catastrophc shft between ndustry-specfc offshorng regmes even though we assume a CRS-technology. The mere exstence of transport costs combned wth the predetermned sequence of producton steps s suffcent to lump together producton steps, causng an nternatonal bundlng or unbundlng of large chunks of a producton chan at margnal changes of transport-, producton-, or offshorng costs. Our model thus not only offers an explanaton for why dfferent ndustres may have qute dfferent fragmentaton ntenstes even though factor cost dfferences and offshorng costs are not obvously dfferent (see Geshecker and Görg, 2008). It also ratonalzes a dscrepancy between estmates of the offshorng potental for certan ndustralzed countres and the actual volume of offshorng actvtes. In our model, such a dfference drectly follows from the jont assumptons of sequental producton and transport costs: despte a large offshorng potental n terms of relatve cost advantages, frms may choose to perform certan producton steps at a sngle locaton snce they are frmly ted nto a technologcally determned producton chan. The remander of the paper s structured as follows: The followng secton 2 descrbes the model, secton 3 derves the offshorng pattern, comparatve 3

6 statcs are performed n secton 4, secton 5 extends the model to analyze as to how a modularzaton of the producton process and the presence of multple foregn countres wth heterogeneous cost structures nfluence offshorng, and secton 6 concludes. 2 Model Setup Consder a compettve frm n sector whch produces a homogeneous good under constant returns to scale. Technology conssts of a contnuum of producton steps whch can be offshored abroad to explot factor cost dfferences. Each producton step n ths ndustry combnes hgh- and low-sklled labor. The nput coeffcents of producton step t n ndustry are denoted by a h (t) for hgh-sklled labor and by a l (t) for low-sklled labour. Factor prces are exogenously gven. We follow GRH n assumng dentcal factor ntenstes for each producton step,.e. a s (t) = a s, for s = l, h. If producton takes place n a domestc plant, then unt factor costs of each producton step t n ndustry are gven by c (w l, w h ) = a l w l + a h w h, where w l, and w h are the domestc wage rates for hgh- and low-sklled labor, respectvely. For brevty, we wll omt the arguments of c wherever applcable. If producton step t s offshored, then producton costs are rased by offshorng costs of the ceberg-type, that s, foregn producton costs are multpled by the term d (t) > 1. Ths reflects the addtonal costs assocated wth performng step t n the foregn country (e.g. costs of communcaton between headquarter and producton unt or supervson costs). 4 Wthout loss of generalty we normalze unt factor costs abroad to c = 1. The unt cost functon of the offshored producton step t n ndustry s then gven by d (t). We devate from the prevous lterature wth respect to the orderng of producton steps. Whle exstng models of offshorng generally assume that producton steps can be lned up accordng to ther offshorng costs, ths may not be the case n realty. Assumpton 1 There s a techncally determned sequence t, n whch producton steps have to be processed one after the other. Our second crucal assumpton s based on the noton that every producton step requres the presence of the unfnshed good produced at the 4 Instead of assumng offshorng costs, we could also consder dfferences between the home and the foregn country wth respect to total factor productvty. The term d (t) then represents the productvty advantage of the home country relatve to the foregn locaton wth respect to performng producton step t. 4

7 precedng step. Whle transportaton s assumed to be costless wthn natonal borders, any nternatonal change of locaton s costly: Assumpton 2 Any crossng of borders between two adjacent producton steps s assocated wth constant costs T per goods unt. The varable T captures not only the costs arsng from physcal transportaton, but also from the rsk of delayed delvery. Note that the magntude of T s ndependent of the stage of the producton process. To capture the dea that the costs of offshorng may go up and down along the producton chan, we assume that d (t) takes the form of a cosne functon. 5 Assumpton 3 Offshorng costs are gven by d (t) = A cos (α t)+b, where t [0; 2n π] and B A 1. The restrcton on B A ensures that d (t) 1 for all t.e., offshorng costs are always postve. Although the specfc functonal form for the offshorng costs may appear somewhat unfamlar n the context of nternatonal producton, ts parameters have a straghtforward and natural nterpretaton (see Fgure 1): the shft parameter B determnes average offshorng costs,.e., f B s very hgh, the frctons assocated wth communcaton and supervson render offshorng relatvely unattractve for the average producton step. The ampltude A of the cost functon reflects dfferences n offshorng costs between ndvdual producton steps. A hgh value of A mples a wde range between lowest and hghest offshorng costs over the producton chan. The parameter α specfes the perod (2π/α ) of the offshorng cost functon. It determnes how frequently offshorng costs of sngle producton steps alternate around the average value of B along the producton chan. If α s hgh, closely-lnked producton steps dffer substantally n relatve offshorng costs. Conversely, f α s low, the sets of adjacent producton steps whch are characterzed by lower or hgher than average offshorng costs are large, makng t advantageous ceters parbus to perform comparatvely large chunks of the producton process n one locaton (at home or abroad). Fnally, n determnes the total length of the producton chan 2πn, dstngushng producton processes wth many from those 5 The choce to fx the foregn cost level whle allowng the costs of delegaton d (t) to vary across producton steps s nconsequental n our partal-equlbrum setup. We could as well have fxed offshorng costs and allowed factor costs to vary along the producton process wth ths varaton beng due to ether changng nput coeffcents or a varyng total factor productvty. Of course, when our model s extended to a general-equlbrum framework such dstnctons may become mportant. 5

8 d t 2 A B 2n t Fgure 1: Offshorng Costs wth only a few producton steps. To keep the analyss tractable whle stll beng able to perform comparatve-statc analyss wth respect to α and n, we assume α n N +. The offshorng cost functon d (t) then exhbts α n full cycles. Dfferent values of α or n thus mply dfferent numbers of cycles whle the overall shape of d (t) for t [0; 2n π] keeps beng symmetrc. Hence, n addton to the transport cost T, we have four parameters to descrbe the technologcal envronment of the offshorng decson. We later capture technologcal or nsttutonal change by varyng these parameters by lowerng average offshorng costs and the heterogenety of these costs (lowerng B and A, respectvely), by allowng for an ncreased heterogenety n the producton process (rasng α ) or by changng the length of the producton chan n. Our last assumpton anchors the producton chan n the domestc economy. Assumpton 4 The fnal product s sold n the home market. Ths assumpton mples that frms have to shp ther fnal nput back home (at a cost T ) even f they choose to perform all producton steps abroad. Whether such a decson s proftable wll be analyzed n the followng secton. 6

9 3 The Offshorng Decson Gven our specfcaton of the offshorng cost curve, we may now characterze the offshorng decson. Ths s done n Fgure 2. To make the model nterestng we only consder the case B A < c < B + A,.e. both locatons have a cost advantage for at least some producton steps. Snce B A 1 ths also mples c > 1. Thus, we exclude factor prce equalzaton by assumpton. 6 Gven that the d (t)-functon exhbts α n full cycles n the nterval [0, 2n π] we can defne the set of crtcal producton steps (t 1,..., t m) where the( offshorng ) costs exactly offset the factor cost savngs abroad;.e. where d t j = c. Ths set s determned by as well as t 1 = 1 ( ) c B arccos α t j = (j 1) π α + t 1 for j U, and t j = j π α t 1, for j E, where U are the uneven ntegers {1, 3,..., m 1} and E the even ntegers {2, 4,..., m }, wth m 2α n representng the total number of crtcal producton steps. By the perodcty of the offshorng cost functon d (t) and the assumpton concernng the parameter range of c, offshorng costs are lower than factor cost savngs n the nterval ( t j; tj+1,), j U, whereas offshorng costs are at least as hgh as factor cost savngs along [t j; t j+1,], j E, as well as at the begnnng and the end of the producton chan,.e. n [0; t 1] and [t m ; 2πn ]. Fgure 2 depcts the case of m = 4. For all steps n the nterval [0; t 1] producton costs abroad (ncludng offshorng costs) are at least as hgh as domestc producton costs. For all steps n (t 1; t 2) producng abroad s cheaper than producng at home, even f offshorng costs are taken nto account. In the nterval [t 2; t 3] domestc producton weakly domnates foregn producton etc. If there were no transport costs, the frm n sector would obvously explot all cost dfferences and produce abroad whenever d (t) < c. However, once the costs of shppng ntermedate goods back and forth are strctly postve, the sze of cost savngs matters as well. We denote the total cost savngs assocated wth offshorng the sequence (t 1; t 2) by D. It follows 6 In general equlbrum, factor costs would be endogenous. A falure of nternatonal factor prce equalzaton may then be the result of trade costs or dfferent total factor productvtes. A (1) 7

10 (t) d 1 1 D * * t 1 t D * * 2 t 3 t 4 2 D 2 c D D t Fgure 2: Cost Savngs from Offshorng from the symmetry of the cosne functon that: D = = 2 t 2 t 1 [c d (t)] dt = t j+1, [ )] A sn (α t α 1) + (B c ) (t 1 πα t j [c d (t)] dt, for j U (2) Takng the dervatve of (2) wth respect to t 1 and usng (1), we can show that D / t 1 = 0: Offshorng addtonal producton steps has no effect on cost savngs D at the margn. Increasng the ampltude of the d (t) functon obvously ncreases D,.e. D / A > 0. Moreover, t 1 < π/α mples that D / B < 0 and D / c > 0: hgher average offshorng costs reflected by an upward shft of the d (t)-curve render offshorng less advantageous, whereas a hgher factor cost-advantage of the foregn country reflected by a hgher value of c has the opposte effect. To determne the nfluence of α on D we cannot smply look at the dervatve, because α n s an nteger. However, nsertng t 1 nto (2) shows that the product α D does not change n α, whch means that D declnes n α. Recall that a hgher value of α reflects greater heterogenety of adjacent producton steps n terms of relatve offshorng costs. Techncally, rasng α ceters parbus rases the frequency of the d (t)-functon, reduces the length of the nterval (t 1; t 2) and thus dmnshes the cost savngs assocated wth offshorng a sequence of producton steps. Lkewse, the cost savngs from performng producton steps n the nterval 8.

11 [t 2; t 3] at home are gven by D + = = 2 t 3 t 2 [d (t) c ] dt = t j+1, t j [ ] A sn (α t α 1) + (B c ) t 1 [d (t) c ] dt, for j U (3) where we have exploted the fact that (t 3 t 2) = 2t 1. As wth D we can show that D + / t 1 = 0 and that D + / A > 0. Conversely, but for obvous reasons, D + / B > 0 and D + / c < 0. The nfluence of α on D + s strctly negatve. From (2) and (3) we obtan, D D + = 2π α (c B ). (4) Ths equaton compares cost savngs from offshorng producton segments for whch the foregn country has lower unt costs wth cost savngs from leavng other segments wth d (t) > c at home. The cost dfference D D + s postve f and only f factor costs at home c exceed average offhorng costs B. For ths case we can say that the foregn country has a total cost advantage to produce good. Note, fnally, that the absolute value of cost savngs decreases n α : f the foregn country offers a cost advantage for shorter segments of the producton process ths reduces the relatve benefts of offshorng these segments. The last term to be determned s the cost advantage from producng the frst or the last producton sequence at home: t 1 0 [d (t) c ] dt = n π t m [d (t) c ] dt = 1 2 D+. (5) We can now turn to the offshorng decson of frms n sector. Obvously, the last sequence [t m ; 2n π] always takes place at home, because, frst, t s cheaper to produce these steps at home and, second, the fnal good needs to be present at home by Assumpton 4. Wth respect to the other producton steps we can dstngush the followng offshorng regmes: no offshorng at all, full offshorng, and partal offshorng. Defnton 1 Full offshorng: the sequence of producton steps n the nterval [0, t m ) s offshored. 9

12 Defnton 2( Partal ) offshorng: the sequences of producton steps n the ntervals t j ; t j+1, are offshored. j U Full offshorng mples that all producton steps except for the last sequence [t m ; 2n π] are done abroad. Hence, t causes transport cost T only once for shppng the ntermedate good back to the home country. Partal offshorng nstead nvolves sendng forth and back the good, wherever segments of the producton chan are manufactured abroad. Hence, the unfnshed good crosses the border 2m tmes n the producton process. Because the offshorng cost functon s symmetrc, frms offshore all segments wth c > d (t) f t s worthwhle offshorng one of them. By the same type of argument we can exclude offshorng patterns other than no-, partal- or full offshorng. 7 For example, producng the frst sequence t [0, t 1] at home gves a cost advantage of D + /2 but rases transport costs by T. Ths s exactly half of the cost advantage and addtonal transport costs that would occur from producng a sequence [t j; t j+1,], j E at home. If partal offshorng s worthwle later n the producton chan, t s so for the frst sequence as well. To determne the optmal offshorng pattern for a frm n sector we smply have to compare costs under the three dfferent regmes. If there s no offshorng, total costs C n to produce one unt of the good are C n = 2πn c. Cost savngs from full offshorng compared to no offshorng C n C f are gven by C n C f = m 2 D m 1 D + T. (6) 2 These cost savngs ncrease n D and declne n D + and n the transport costs T. By settng C f = C n we can determne a crtcal level of transport costs T f,n for whch the cost advantage of full offshorng compared to no offshorng vanshes: T f,n 1 2 D+ + m ( D D + 2 ). (7) Cost savngs from partal offshorng compared to no offshorng C n C p can be obtaned as C n C p = m 2 D m T. (8) 7 To check for robustness of our results, we also have consdered versons of our model n whch the cosne functon s shfted horzontally. Then the model may produce addtonal regmes wth offshorng ntervals dfferng from full offshorng as t s defned here. The basc nsghts of our model, however, reman: A partal offshorng regme exsts for low transport costs whereas for hgher transport costs the frm may offshore longer segments of the producton chan. 10

13 Ths dfference s postve as long as transport costs are below a crtcal value, whch s defned as T p,n T p,n 1 2 D. (9) Fnally, the cost advantage from partal offshorng versus full offshorng s gven by the condton C f C p = m 1 D + (m 1) T. (10) 2 Partal offshorng saves costs compared to full offshorng as long as transport costs are below a crtcal value T p,f, gven by T p,f 1 2 D+. (11) We are now ready to lay out the choce of an offshorng regme for ndustry n Proposton 1. 8 Proposton 1 Suppose Assumptons 1 to 4 hold. Then we can dstngush two cases: Case 1: c > B T p,f < T p,n < T f,n. There s partal offshorng for T < T p,f, and no offshorng for T T f,n T f,n Case 2: c B T p,f T p,n. T f,n. There s partal offshorng for T < T p,n, full offshorng for T p,f < T and no offshorng for T T p,n. Proof. The orderng of the crtcal values of T for c > B and c B can be establshed from (7), (9) and (11). The results of Proposton 1 then follow mmedately. Fgure 3 llustrates Proposton 1 by depctng the cost dfferences C n C p and C n C f as functons of the transport costs T. The lne C n C p s steeper than C n C f, and ts ntercept wth the ordnate s hgher. Both lnes therefore ntersect, makng ether partal or full offshorng more attractve (to the left or rght of ths ntersecton). Fgure 3.a represents Case 1, where the ntersecton T p,f s n the frst quadrant, mplyng a postve cost advantage compared to no offshorng. In ths case, we can dstngush three areas: partal offshorng for low transport costs T, full offshorng for ntermedate T and no offshorng for hgh transport costs. In Case 2 (Fgure 3.b) the lnes 8 In Proposton 1 we assume that the frm chooses the offshorng mode assocated wth the lowest transport actvtes whenever t s ndfferent between several modes. 11

14 C C n p p n T, p f T, T C C n f C C n f p f T, T p, n T f, n T C n C p Partal offshorng Full offshorng No offshorng Partal offshorng No offshorng (a) (b) Fgure 3: Partal and Full Offshorng C n C p and C n C f ntersect n the fourth quadrant, such that the area of full offshorng vanshes. The relatonshp between c and B that dstngushes the two cases n Proposton 1 s mportant snce t determnes whether the foregn country has a total cost advantage or not: f c > B ths s the case and full offshorng becomes attractve once transport costs decrease below the crtcal threshold. Conversely, f c B the factor cost advantage of the foregn country s too small to make up for the offshorng costs on average. Ths excludes full offshorng and nduces frms to choose the partal offshorng regme once transport costs are suffcently low.e. smaller than T p,n. Proposton 1 reveals that offshorng actvtes may change n a catastrophc way f certan transport cost thresholds are passed. Note that for ths result we do not assume network effects or agglomeraton economes Moreover, n Case 1, a hump-shaped pattern of offshorng actvtes emerges: As transport costs decrease, there s frst a large ncrease n offshorng actvtes as the sector moves from no offshorng to full offshorng. At a further reducton of transport costs the offshorng volume declnes agan whle swtchng to the partal offshorng regme. 9 T f,n 9 For a related result n the context of a two-stage producton process see Barba Navarett and Venables (2004). 12

15 4 Comparatve-Statc Analyss We are now ready to determne the nfluence of our model parameters on the offshorng pattern. Apparently, these parameters have consequences for both the crtcal transport costs whch separate the dfferent offshorng-regmes and the nternatonal allocaton of producton steps wthn a gven regme. We start by consderng the extent of offshorng gven that the sector s n a certan offshorng regme. The emprcal lterature measures the extent of offshorng as producton value of ntermedate nputs from abroad relatve to total producton value (e.g. Feenstra and Hanson, 1996b, 1999). In our framework, the length of the nterval ( t j, tj+1), j U multpled by α n reflects ths extent of offshorng. Settng ths nterval n relaton to the length of the entre producton chan 2πn, we may determne the share of foregn producton s p n the partal offshorng regme as s p = α n (t 2 t 2πn 1) = 1 1 ( ) π arccos c B. (12) A Wth full offshorng the respectve share s f s gven by s f = t m = 1 1 ( ) 2πn 2α n π arccos c B A. (13) From dfferentatng (12) or (13) we obtan the followng comparatve-statc results: Proposton 2 Suppose sector s n the partal or n the full offshorng regme. The share of producton that s offshored rses n c and declnes n B. Furthermore, t declnes n A ff c > B. In the full offshorng regme the share of producton that s offshored also rses n α and n. The nfluence of the domestc factor costs c and of the average offshorng cost B s straghtforward. 10 For the effects of changng the ampltude A we have to dstngush whether the foregn country has a total cost advantage (Case 1, c > B ) or not (Case 2, c B ). In case 1, an ncrease n the value of A, reflectng starker contrasts between total costs at home and abroad, lowers the extent of offshorng. In case 2, the opposte holds. Due to the symmetry of the functon d (t) the length n of the producton chan (and smlarly α ) nfluences the share of foregn producton only n the full offshorng regme. The longer the producton chan and the hgher 10 Recall that the functon arccos(x) decreases n x. 13

16 the frequency of the d (t) functon, the shorter s the last sequence whch s produced at home relatve to the total mass of tasks that are performed. Apart from affectng the nternatonal allocaton of producton steps n the partal or the full offshorng regme, a change n the technologcal envronment may also shft the regme borders of Fgure 3 as summarzed n the followng proposton. Proposton 3 The crtcal transport costs depend on the model parameters as follows: T f,n ncreases n c and A and declnes n B and α. It also ncreases n n ff c > B. T p,n ncreases n c and A and declnes n B and α. T p,f ncreases n B and A and declnes n c and α. Proof. The results can be obtaned from (7), (9), and (11) and the nfluence of the exogenous varables on (2) and (3). Interpretng these results, we begn wth the nfluence of the average offshorng costs B. In addton to a reducton n transport costs T globalzaton may materalze n a declne n B : a general mprovement of communcaton and nformaton technologes lowers average offshorng costs and thereby shfts the d (t) curve downward. Accordng to Proposton 3 full offshorng then becomes more attractve compared to both alternatves, partal offshorng and no offshorng. The range of transport costs that yelds full offshorng n Fgure 3.a ncreases. For c B, (Fgure 3.b) we have to compare partal offshorng wth no offshorng. Partal offshorng becomes more advantageous for a larger range of transport costs f B declnes. Thus, a declne n average offshorng costs causes a tendency towards more offshorng not only n terms of the number of tasks that are offshored wthn a certan regme but also n terms of a potental shft towards a regme wth more offshorng. Fgure 4 depcts the combned nfluence of T and B on the regme borders. Partal offshorng only occurs f transport costs T are low and average offshorng costs are nether too large nor too small. If transport costs T are hgh, but average offshorng costs are low, frms prefer full offshorng. In all other cases there s no offshorng Note that the dvdng lnes for the regmes are generally not lnear. 14

17 Full offshorng No offshorng Partal offshorng Fgure 4: Offshorng Regmes Wth respect to the other parameters, we see from Proposton 3 that an ncrease n the ampltude A or the perod 2π/α of the offshorng cost functon rases all crtcal transport costs: as cost dfferences between adjacent producton steps dmnsh and the sze of potental cost savngs ncreases, partal offshorng becomes more attractve at gven costs of transportaton. The length of the producton chan n only nfluences the border T f,n between the full offshorng regme and no offshorng. The longer the producton chan, the more attractve full offshorng becomes snce the transport costs assocated wth repatratng the unfnshed good before the fnal producton segment become less mportant relatve to potental cost savngs. 5 Extensons: Modularzaton and Global Producton Networks 5.1 Modularzaton In the analyss so far we have taken the producton chan for good as nondvsble,.e. a frm that decded to relocate a producton step or a seres of producton steps had to shp the entre unfnshed good to the plant n the foregn country and back. In most ndustres, however, the producton process can be sub-dvded nto dfferent components or modules that are manufactured ndvdually and then assembled n a fnal producton step. Our model can be easly extended to ncorporate such a modularzaton of producton. For ths, we may vew a component as a secton of the 15

18 Full Offshorng Full Offshorng Component 1 Component 2 Fgure 5: Modularzaton and Offshorng total producton chan that can be separated from other sectons and manufactured ndvdually. To keep our symmetrc set-up, we assume that the producton chan can be subdvded nto k such sectons of equal length (the components).transport costs for each component are T /k, and the length of each segment s 2n π/k. We furthermore assume that n α /k N +,.e. each segments covers one or multples of a full cycle. Modularzaton makes full offshorng more attractve compared to our baselne model as t breaks up the producton chan. Some segments whch can be produced cheaper at home now move to the end of the producton chan. They can be produced at home as they are no longer captured between offshored segments n the mddle of the producton chan (Fgure 5). Consequently, the crtcal transport cost T f,n k : T f,n = k 2 D+ + m ( D D + 2 ) and ncreases and T p,f decreases n T p,f = m k 2 (m 1) D+. (14) The range of transport costs whch leads to full offshorng expands whereas the partal offshorng regme becomes smaller. 5.2 Global Producton Networks So far we have assumed that frms n the domestc economy may offshore producton steps to a homogeneous rest of the world. In realty, however, 16

19 domestc producers face a multtude of foregn countres whch dffer substantally n terms of relatve factor prces and offshorng costs, and they may explot these dfferences by establshng global producton networks. To show how our framework can be modfed to analyze ths scenaro we dstngush between two foregn countres ( country I and country II ). Wthout loss of generalty we normalze factor costs n ndustry to equal one n both countres. The offshorng cost functon of ndustry n country j s d j (t) = Aj cos ( α j t + θj ) + B j, (15) wth j {I, II} and θ j [0, 2π]. To demonstrate the mplcatons of ths modfcaton for offshorng patterns n the smplest possble framework we make the followng assumptons: A j = A, α j = α, B j = B for both countres. Moreover, we set θ I = 0, θ II = π, and B = c, 12 and we assume that transport costs T are the same between all locatons. Fgure 6 depcts the resultng pattern of offshorng costs n countres I and II (relatve to the domestc economy) for m = 4. Gven the above assumptons, there s a perfectly negatve correlaton between the two countres cost advantages: whenever country I offers lower costs, country II s at a dsadvantage, and vce versa. Note, however, that we stll stck to the assumpton that the fnal good s sold n the domestc economy. Hence, f the last producton step s performed n one of the two foregn countres, frms have to account for the costs of fnal shppng. Gven ths setup, we may stll dstngush between three offshorng regmes, however, the regme types now dffer from our baselne model. The frm now produces n both foregn countres, and we call such a stuaton a global network. 13 Dependng on transport costs, the home country may be ncorporated as a producton ste or not. More precsely, we may defne a partal global network as a regme n whch all producton steps n the nterval [0, t m ) are located abroad n country I and country II and the steps n the nterval [t m, 2πn ] are performed n the domestc economy. In a full global network, the frm produces entrely abroad n the two foregn countres. Note that the mportant dfference between the two global network regmes s that a full global network requres one addtonal run of transportaton, but allows the frm to save costs for a wder range of producton steps. 12 Note that the latter assumpton mples D + D = Gven our assumpton B = c, t s never optmal for the frm to perform all producton steps n a sngle foregn country. 17

20 I 1 2 D D D D 1 2 D 1 2 D D D D 1 2 D II Fgure 6: Offshorng Costs wth Two Foregn Countres Cost savngs from a full and a partal global network are gven by C n C n C f,global = m D (m + 1)T and (16) ( C p,global = m 1 ) D m T, (17) 2 where we have used the superscrpt global to ndcate the presence of global producton networks. The cost dfferences as a functon of T are depcted n Fgure 7. As n the benchmark model, no offshorng s optmal for very hgh transport costs. As T decreases, a partal global network becomes preferable,.e. frms shft a large part of the producton process abroad, but the fnal sequence of steps s performed at home. As transportaton costs decrease further, movng ntermedate goods between countres s cheap enough to make a full global network optmal. Note that ths result contrasts wth the constellaton derved n the benchmark model: There, decreasng costs of transportaton eventually caused a shft to partal offshorng and a large share of producton was performed n the domestc economy. By contrast, the possblty to establsh a global producton network and to explot cost dfferences between dfferent foregn countres leads to a dramatc ncrease n the offshorng volume once transport costs fall below a crtcal threshold. 18

21 C C n f global C C n p global Full global network Partal global network No offshorng Fgure 7: Global Producton 6 Summary and Concludng Remarks Ths paper has ntroduced a new approach to analyze frms offshorng decsons. In contrast to exstng models, n whch sngle tasks or producton steps can be arranged accordng to ther offshorng costs, we have taken nto account that, due to technologcal constrants, the sequence of producton steps can rarely be vared at wll. Combned wth the plausble assumpton that shftng ntermedate goods between dfferent locatons s costly, ths may lead to a clusterng of ndvdual producton steps, such that the decson to produce a sngle step at home or abroad depends on the locaton of precedng or subsequent steps. In our framework, ths leads to three dfferent offshorng regmes: partal, full or no offshorng. We have shown that the borders between these regmes depend n a non-trval way on costs of transportaton and on offshorng costs. Thus, the nfluence of globalzaton defned as mproved nternatonal communcaton and reduced barrers to nternatonal trade on the offshorng pattern s far from straghtforward: on the one hand, frms may be reluctant to offshore certan producton steps although, consdered n solaton, these steps could be performed at far lower costs abroad. On the other hand, mnor changes n the costs of offshorng or technologcal nnovatons affectng the structure of the producton process may result n the relocaton of consderable parts of the producton chan all at once. Wth regard to further advances n theory, the next logcal step s to embed our offshorng model nto a general equlbrum framework of nternatonal trade. We may then be able to obtan new nsghts nto the relaton- 19

22 shp between the condtons for offshorng and factor rewards. Moreover, t should be possble to emprcally test the mplcatons of our approach. Our model suggests that one needs to take nto account that varous ndustres dffer wth respect to the sequentalty and potental modularzaton of ther producton chans, the sze and relevance of transport costs, as well as the costs of relocatng ndvdual producton steps. In our vew, a frm grasp of these technologcal constrants holds the key for a better understandng of the extent and evoluton of offshorng. References Arndt, S. W. (1997). Globalzaton and the open economy. North Amercan Journal of Economcs and Fnance 8, Baldwn, R. (2006). Globalsaton: The great unbundlng(s). Paper for the Fnnsh Prme Mnster s offce. Barba Navarett, G. and A. J. Venables (2004). Multnatonal Frms n the World Economy. Prnceton Unversty Press, Prnceton, NJ. Deardorff, A. V. (2001a). Fragmentaton across cones. In S. W. Arndt and H. Kerzkowsk (Eds.), Fragmentaton: New Producton Patterns n the World Economy. Deardorff, A. V. (2001b). Fragmentaton n smple trade models. North Amercan Journal of Economcs and Fnance 12, Dxt, A. K. and G. M. Grossman (1982). Trade and protecton wth multstage producton. Revew of Economc Studes 49, Egger, H. and P. Egger (2007). Outsourcng and trade n a spatal world. Journal of Urban Economcs 62, Feenstra, R. C. and G. H. Hanson (1996a). Foregn nvestment, outsourcng and relatve wages. In R. C. Feenstra, G. M. Grossman, and D. A. Irwn (Eds.), Poltcal Economy of Trade Polcy: Papers n Honor of Jagdsh Bhagwat. MIT Press, Cambrdge, MA. Feenstra, R. C. and G. H. Hanson (1996b). Globalzaton, outsourcng, and wage nequalty. Amercan Economc Revew, Papers and Proceedngs 82,

23 Feenstra, R. C. and G. H. Hanson (1997). Foregn drect nvestment and relatve wages: Evdence from Mexco s maquladoras. Journal of Internatonal Economcs 42, Feenstra, R. C. and G. H. Hanson (1999). The mpact of outsourcng and hgh-technology captal on wages: Estmates for the Unted States. Quarterly Journal of Economcs 114, Geshecker, I. and H. Görg (2008). Wnners and losers: A mcro-level analyss of nternatonal outsourcng and wages. Canadan Journal of Economcs 41, Glass, A. J. and K. Sagg (2001). Innovaton and wage effects of nternatonal outsourcng. European Economc Revew 45, Grossman, G. M. and E. Ross-Hansberg (2008). Tradng tasks: A smple theory of offshorng. Amercan Economc Revew 98, Jones, R. W. (2000). Globalzaton and the Theory of Input Trade. Press, Cambrdge, MA. MIT Jones, R. W. and H. Kerzkowsk (1990). The role of servces n producton and nternatonal trade: A theoretcal framework. In R. Jones and A. Krueger (Eds.), The Poltcal Economy of Internatonal Trade. Basl Blackwell, Oxford. Jones, R. W. and H. Kerzkowsk (2001a). A framework for fragmentaton. In S. W. Arndt and H. Kerzkowsk (Eds.), Fragmentaton: New Producton Patterns n the World Economy. Oxford Unversty Press, Oxford. Jones, R. W. and H. Kerzkowsk (2001b). Globalzaton and the consequences of nternatonal fragmentaton. In G. M. Calvo, M. Obstfeld, and R. Dornbusch (Eds.), Money, Captal Moblty, and Trade, Essays n Honor of Robert A. Mundell. MIT Press, Cambrdge, MA. Kohler, W. (2004). Internatonal outsourcng and factor prces wth multstage producton. Economc Journal 114, C Kohler, W. (2008). Offshorng: Why do stores dffer? CESIfo Workng Paper Venables, A. J. (1999). Fragmentaton and multnatonal producton. European Economc Revew 43,