Follow the Value Added: Tracking Bilateral Relations in Global Value Chains

Transcription

1 MPRA Munich Peronal RePEc Archive Follow the Value Added: Tracking Bilateral Relation in Global Value Chain Aleandro Borin and Michele Mancini Bank of Italy, Bank of Italy 14 November 2017 Online at MPRA Paper No , poted 17 November :31 UTC

2 Follow the Value Added: Tracking Bilateral Relation in Global Value Chain Aleandro Borin and Michele Mancini* (firt verion June 2015, thi verion November 2017) Abtract Following the pread of global value chain new tatitical tool, the Inter- Country Input-Output table, and new analytical framework have been recently developed to provide an adequate repreentation of upply and demand linkage among the economie. Koopman, Wang and Wei propoe an innovative accounting methodology to decompoe a country total gro export by ource and final detination of their embedded value added. However thi decompoition preent ome limitation and relevant inexactnee in ome of it component. We develop their approach further by deriving a fully conitent counterpart for bilateral trade flow, alo at the ectoral level, addreing the main hortcoming of previou work. We alo provide correct breakdown of the foreign content in total (world) trade flow and a brand new claification of thee component that take the perpective of the exporting country. Finally, drawing on our methodology we derive for the firt time a precie meaure of international trade generated within global production network. Two example of empirical application with relevant policy implication are alo provided. Keyword: global value chain; input-output table; trade in value added; trade elaticity. JEL claification: E16, F1, F14, F15. *Bank of Italy. aleandro.borin@bancaditalia.it, michele.mancini@bancaditalia.it. Thi paper i a revied and updated verion of Borin, A. and M. Mancini, Follow the Value Added: bilateral gro export accounting, Economic Working Paper, Bank of Italy. Section 2.4 ha been added in May 2016, ee Borin, A. and M. Mancini, Participation in Global Value Chain: meaurement iue and the place of Italy, Rivita di Politica Economica. Section 2.3 i brand new. We thank Rita Cappariello, Riccardo Critadoro, Stefano Federico, Alberto Felettigh, Robert Johnon and Julia Wörz for inightful comment. The view expreed in thi paper are olely thoe of the author and do not involve the reponibility of the Bank of Italy. The uual diclaimer applie. 1

3 1 Introduction The international fragmentation of production procee ha challenged the capability of the tandard trade tatitic to truly repreent upply and demand linkage among economie. In general bilateral export differ from the portion of a country GDP related with the production of good and ervice hipped to a certain outlet market. On one hand export alo embed imported intermediate input, on the other hand the directly importing country often differ from the ultimate detination where the good i aborbed by final demand. Whenever production i organized in equential proceing tage in different countrie, trade tatitic repeatedly double-count the ame value added. The diffuion of global value chain (GVC) ha therefore deepened the divergence between gro flow, a recorded by traditional trade tatitic, and the data on production and final demand a accounted for in tatitic baed on value added (above all GDP). Moreover, own to the pread of GVC, new relevant quetion regarding the role of countrie and ector in the international market have emerged. In particular, it ha become crucial to ae the level of participation of countrie and ector into the international haring of production. New data, a the Inter-Country Input-Output table, and new analytic methodologie have been developed in order to addre thee iue. Among the latter Koopman, Wang and Wei (2014) (hereafter KWW) propoe a comprehenive decompoition of total gro export by the ource and detination of their embedded value added, that encompae mot of the methodologie previouly propoed in the literature (e.g. Hummel et al. 2001; Daudin et al., 2009; and Johnon and Noguera, 2012). KWW point out that different cheme of international fragmentation of production yield different proportion of value added content in gro export. In particular, they how that not all the double-counted flow in gro trade tatitic are alike. More pecifically, KWW break gro export down into different component of dometic and foreign value added plu two item of pure double counting. A to the latter, they how that gro export do not in general conit only of value added that can be traced back to GDP generated either at home or abroad. Intead, ome trade flow are purely double-counted, a when intermediate input cro a country border everal time according to the different tage of production. 1 It i worth noting that thee double-counted item are increaingly important in international trade flow (ee Wang et al., 2013 and Cappariello and Felettigh, 2015), making the KWW approach particularly valuable. Albeit providing ueful inight, the original KWW decompoition till preent ome relevant hortcoming and limitation. They correctly meaure the total dometic value added in export, but the breakdown by detination market i imprecie. Furthermore their meaure of the value added generated abroad and of the foreign double counted item in total export are incorrect, ince they overtate the latter component. 2 More in general the KWW decompoition find limited cope for empirical application ince it neglect the bilateral and ectoral dimenion of trade flow. It mean, for intance, that it can not be applied to analyze all the direct and indirect linkage between countrie and ector within the production network. Another relevant limitation i that we can not get a precie meaure of the hare of total trade that i related to 1 A more detailed account of thi mechanim i provided in ection 2.2, where we dicu the difference between the ink and the ource approache of the bilateral decompoition. 2 In ection 2.2 we provide more detailed explanation of the hortcoming that affect the KWW decompoition. 2

4 GVC participation from the tandalone application of the KWW decompoition. Beide thee iue there are everal other reaon why we might be intereted in tracing value added flow between countrie. In fact firm trade with bilateral partner, even when participating in more complex multi-country production network. In tudying GVC, it i relevant to analyze the overall tructure of production network and to identify all the international and interectoral link. Methodologie like KWW can track the value added linkage between the country of origin and the final detination. But we may alo be intereted in the poition of a country (or a ector) within the production proce and in identifying it direct uptream and downtream trade partner. Thi might be relevant in order to map geographically the production network and to analyze the international propagation of macroeconomic hock, a exchange rate variation. Deepening the knowledge of thee mechanim alo provide ueful inight to interpret the hort-term dynamic of trade flow. 3 Moreover, countrie participation in GVC affect bilateral trade balance (Nagengat and Stehrer, 2016); thi and other feature of bilateral hipment, a their merchandie compoition, unambiguouly influence trade policie (e.g. international trade and invetment agreement). More in general, the potential policy implication of all the apect mentioned above are clearly ignificant. Our aim i to extend KWW methodology in order to obtain a conitent decompoition of bilateral (and ectoral) trade flow that offer additional information on a good many matter that cannot be invetigated uing imple gro trade data or aggregate trade in value added. For intance, by conidering the bilateral dimenion of trade-production relation it i poible to meaure the amount of trade generated within global production network. We alo intend to overcome hortcoming and limitation that affect the KWW decompoition and other previou attempt to get a bilateral counterpart of the KWW cheme. In particular we provide proper definition for ome component that are incorrectly pecified by KWW: i) the dometic value added that i directly (and indirectly) aborbed by the final demand of the importing country; ii) the foreign value added (FVA) in export; iii) the double counted item produced abroad. At the world level our corrected variant of the KWW FVA component reemble the meaure propoed by Johnon (2017), which i derived in a completely different framework. Indeed the two meaure do not coincide when computed for a ingle exporting country. 4 Beide improving the meaure of FVA and foreign double counted (FDC) within the KWW framework, we alo propoe a completely alternative approach to plit thee two component. According to the KWW logic, which in thi apect i hared alo by Johnon (2017), FVA and FDC are defined referring to world trade flow. 5 However, from the perpective a particular 3 Although ICIO data are only available with a lag, we can till ue thee tool to interpret and project hort-term development in international trade, inofar a the value added tructure of bilateral export i quite peritent over time. For example, if we know that in motor vehicle manufacturing a coniderable hare of the intermediate component exported from Italy to Germany are ued to produce car for the North American market, we preume that a lackening of US demand i likely to reult in a reduction in hipment of part from Italy to Germany. 4 We alo preent an extended verion of the FVA indicator propoed by Johnon (2017), with a breakdown by country of ultimate detination. 5 In KWW a certain component of value added embedded in another country export i recorded a FVA only once in all (world) trade flow. If along the value chain the ame component croe everal other border, even of different countrie, all thee other time it i conidered a foreign double counted. Note that thi definition of double counted flow differ from that ued for 3

5 exporting country thi might not be economically meaningful and it produce an arbitrary allocation of trade flow, depending on the number of upward (or downward) tage of production that tand between the exporter and the country in which the value added wa generated (or the market of final detination). In order to addre thi iue we propoe two brand new meaure of FVA and of FDC conitent with thoe adopted for the dometic content of export. A better explained later on, thee meaure can be derived in different way for bilateral trade flow, then generating ditinct reult at thi level of diaggregation. Neverthele, they all um up to the ame indicator of FVA and of FDC when computed at the country level. We alo overcome the main problem that make imprecie and at leat partially incorrect the value added decompoition of bilateral export previouly propoed in the literature. In thi regard our work i related to that of Nagengat and Stehrer (2016) and Wang et al. (2013). Nagengat and Stehrer (2016) point out that there are different way to account value added in bilateral trade. Indeed they propoe two alternative methodologie: a firt one take the perpective of the country where the value added originate (the ource-baed approach), a econd one take the perpective of the country that ultimately aborb it in final demand (the ink-baed approach). However, neither methodology in Nagengat and Stehrer (2016) are correctly pecified, o that they do not include the entire dometic value added embedded in each bilateral trade flow. We propoe two alternative breakdown of bilateral export that overcome thi hortcoming, while maintaining two eparate framework for the ource-baed decompoition and for the inkbaed one. Both our decompoition correctly take into account the dometic value added, the foreign value added and the double-counted component of bilateral export. In both cae there i a precie correpondence with the item in the KWW decompoition when we conider the total export of a country (apart from the component that are erroneouly defined in KWW). Having pecific and internal conitent methodologie both for the ink-baed and the ource-baed approach allow to chooe the mot appropriate framework to the purpoe of the analyi. Wang et al. (2013) follow KWW cloely and propoe a ingle breakdown of bilateral export that can be exactly mapped into the original KWW decompoition umming all the export flow acro the detination. Thi alo mean that the drawback of the KWW methodology mentioned above apply alo thi bilateral variant (e.g. the incorrect identification of of the foreign value added component). Moreover, Wang et al. (2013) mix ink and ource approache to ingle out the different component, o that their methodology uffer from internal inconitency. Finally and more importantly, they can not identify the trade flow that are generated within global upply network, which ha emerged a a key quetion in the literature. According to the definition firt propoed by Hummel et al. (2001) and commonly acknowledged in thi field, GVC cheme hould entail at leat two eparate production tage in different countrie, before the good i ultimately hipped toward the final market. In other word there hould be at leat a re-hipment of intermediate or final good toward a third country (or back to the country of origin). Converely, traditional production and trade pattern reult in good and ervice produced in a certain country and conumed by the direct importer. Wang et al. (2013) methodology, which in part follow a ink-baed approach, doe not allow to ditinguih between thee two cae, while our ource-baed decompoition i uited to tackle thi iue. Indeed in ection 3.2 we propoe for the firt time a meaure of GVC-related trade that i conitent with Hummel et al. (2001) the item produced dometically, which KWW conider a double counted only when they cro the ame national border more than once. 4

6 definition, providing empirical evidence about it evolution at the global level. While we how a couple of poible implementation of our decompoition by uing ICIO table (the World Input Output Databae, WIOD, and the OECD-WTO Trade in Value Added, TiVA) the detailed breakdown of bilateral/ectoral gro export preented here might find a much broader cope for empirical invetigation on global production network. In particular, it provide the baic information needed to ae country/ector poition and participation in GVC and to develop meaure about the overall length of international upply chain (Antrà and Chor, 2013; Wang et al., 2016; Borin and Mancini, 2016). In thi way it will be poible to invetigate at the macro (country-ector) level ome feature of production network that have emerged from cae tudie (Dedrick et al., 2010; Ivaron and Alvtam, 2011) and firm level analye (Sturgeon et al., 2008, Brancati et al., 2017). The ret of the paper i organized a follow. The econd ection recall KWW accounting, preent two novel decompoition of bilateral export that overcome the main drawback in KWW methodology, propoe an alternative approach to account for the foreign value added in export, illutrate how to include three different ectoral dimenion in the decompoition and dicue how thee new tool can contribute to analyze international production network. The third ection how two empirical application: the firt one adopt the ink-baed approach to explore the forward linkage of the world larget exporter; the econd one take the ource-baed perpective to derive a meaure of GVC-related trade and to ae how it evolution ince the mid-1990 ha affected the relationhip between world trade and income. Section four conclude. 2 The decompoition of bilateral gro export 2.1 KWW breakdown of total export The methodology propoed by KWW contitute a innovative and comprehenive accounting framework for gro foreign trade. The way in which thi tool can improve our evaluation of countrie trade relationhip i offered by the two tylized production-conumption-trade cheme hown in Figure 1. In panel 1.a) production i organized in tage, each in a different country. Firt country A produce 1 USD worth of intermediate component uing only it own reource and hip them to B, which add 1 USD of value to produce more refined intermediate product, which are ent to C. Here they undergo a final proceing tage, worth another 1 USD, before being old a final good back to A for 3 USD. In panel 1.b, intead of having equential tage of production in A and B, initially each country produce intermediate component worth 1 USD uing only it own productive factor and hip them to C; here the different input are aembled, adding another 1 USD of value to produce final good that are aborbed by final demand in A, a before. Gro trade tatitic indicate that in cae 1.a country A export are generated by demand from country B, and in cae 1.b. by demand from C. Since KWW trace both the origin and the final detination of value added, however, their decompoition how that in both cae the export are actually activated by country A own dometic demand. Before analyzing bilateral trade flow, let u tart from the accounting framework for total 5

7 export introduced by Koopman, Wang and Wei (2014). Their methodology i baed on a global input-output model with G countrie and N ector (for detail ee Appendix A which alo give an exhautive definition of our notation, which i eentially identical to KWW). Here let u only recall that Y r indicate the demand vector of final good produced in and conumed in r, B i the global Leontief invere matrix for the entire inter-country model, A i the global matrix of input coefficient, V incorporate the value added hare embedded in each unit of gro output produced by country, E i the vector of total export of country for the N ector, and u N i the 1 N unit row vector. The eential decompoition of total export of country (u N E ) in KWW i ummarized by the following accounting relationhip: u N E = + V B Y r + V V B r Y r + V G G G + V B r A r (I A ) 1 E + + B r Y rr + V G,r B r Y rt B r A r (I A ) 1 Y V t B t Y r + V t B t A r (I A rr ) 1 Y rr V t B t A r (I A rr ) 1 E r (1) KWW define the nine item in equation (1) a follow: G 1. V B Y r : dometic value added in direct final good export; G 2. V B ry rr : dometic value added in intermediate export aborbed by direct importer; G G 3. V,r B ry rt : dometic value added in intermediate good re-exported to third countrie; G 4. V B ry r : dometic value added in intermediate export reimported a final good; G 5. V B ra r (I A ) 1 Y : dometic value added in intermediate input reimported a intermediate good and finally aborbed at home; G 6. V B ra r (I A ) 1 E : double-counted intermediate export originally produced at home; G G V tb t Y r : foreign value added in export of final good; G G V tb t A r (I A rr ) 1 Y rr : foreign value added in export of intermediate good; G G V tb t A r (I A rr ) 1 E r : double-counted intermediate export originally produced abroad. 6

8 Although KWW methodology allow to improve the knowledge of value added content of total export, it provide no inight into the tructure of ingle bilateral flow. A already mentioned, from a policy perpective thi could be relevant for everal reaon. Conider, for example, the aement of bilateral trade balance. In Figure 1.a A run a 1 USD urplu with B and a 3 USD deficit with C, all evaluated in term of gro trade flow; in cae 1.b, A how a net bilateral balance of -2 USD toward C and zero with repect to B. However, in value added term, A ha a net trade deficit poition of 1 USD with B and C in both panel. Thu while A overall deficit i exactly the ame in value added a in gro term (2 USD), it bilateral poition differ coniderably between the two accounting method. Uing baic accounting relationhip and inter-country I-O table, we can compute the bilateral poition in value added term. 6 Yet thi i not enough to dientangle the international production linkage and the ultimate demand force that generate a particular urplu/deficit between two countrie in gro term; nor doe the original KWW breakdown hed light on thee matter when multiple trade partner and ource of final demand are involved. Moreover ome of KWW definition are quetionable and, to ome extent, incorrect, but thi will become clear by going though the analyi of bilateral trade flow, o we prefer to dicu thee iue in the following ection. A VA=1 Y=3 A VA=1 Y= C VA=1 2 B VA=1 C VA=1 1 B VA=1 (1.a) (1.b) Figure 1: Value added veru gro export accounting of bilateral trade balance 2.2 The decompoition of bilateral trade By focuing on bilateral trade flow we can follow the pattern of value added in export along the different phae of the value chain. However the input-output framework potentially allow for infinite round of production. Hence we face a trade-off between adding detail about the international production linkage and providing an analytically tractable and conceptually intelligible framework. Our compromie i to track the direct importing country, then - if the value added i not aborbed there - we conider the additional detination of re-export from the direct importer. 6 See equation (A.7) in Appendix A. 7

9 In ummary, our trategy i to decompoe gro bilateral trade flow identifying the following actor: i) the country of origin of value added; ii) the direct importer; iii) the (eventual) econd detination of re-export; iv) the country of completion of final product; v) the ultimate detination market. C VA=0 Y=3 A VA=1+1= B VA=1 Figure 2: Value added and double counting in bilateral trade flow Another conceptual iue that arie in conidering the ingle bilateral flow regard the purely double counted item. A pointed out by Nagengat and Stehrer (2016), when a certain portion of value added croe the ame border more than once it ha to be aigned to a particular gro bilateral trade flow, while it hould be recorded a purely double counted in the other hipment. The iue i clearly pointed out by the cheme reported in Figure 2: here the 1 USD of value added originally produced in A i firt exported to B a intermediate input, proceed there, then hipped back to A and ued to produce final good for re-export to C. In thi cae, the value added generated in the very firt tage of production in A i counted twice in it gro bilateral export to B and C. The quetion i the following: in which cae hould we conider it a dometic value added and in which a double counted? Nagengat and Stehrer (2016) point out that it i an arbitrary choice and propoe two alternative approache: a firt one take the perpective of the country where the value added originate (the ource-baed approach), a econd one that of the country that ultimately aborb it in final demand (the ink-baed approach). A regard the example in Figure 2, according to the ource-baed approach the original 1 USD of production of country A would be conidered a dometic value added in the gro export to B (and double counted in the hipment to C); vice-vera uing the ink-baed approach it would be conidered a dometic value added in the export to C (and double counted in the hipment to B). In hort we can ay that the ource-baed method account the value added the firt time it leave the country of origin, while the ink-baed approach conider it the lat time it croe the national border. The choice between the two framework depend on the particular empirical iue we want to addre. For intance if one i intereted in inquiring the trade linkage through which the value added reache a certain market of final detination, the ink-baed approach i probably more appropriate. On the contrary the ource-baed method allow to trace the very firt detination of value added from the country of origin. In ection 3 we how two different empirical application, each one adopting one of the two approache decribed above. Hereafter we preent two decompoition of bilateral trade flow. The firt one follow a ink-baed approach, the econd one a ource-baed logic. We how how our methodologie 8

10 addre critical apect of KWW and other previou contribution by Wang et al. (2013) and by Nagengat and Stehrer (2016). In Appendix B we alo provide the full analytical derivation for the ink-baed approach, which i the mot complex. 7 Sink-baed breakdown of bilateral export A full ink-baed decompoition of bilateral export from country to country r can be expreed by the following accounting relationhip: u N E r = 1 V B Y r Y rr + + V B A r (I A rr ) 1 [ 2a, 2b [ 3a + V B A r (I A rr ) 1 Y rj V B A r (I A rr ) 1 [ 4a 5 + V B A r (I A rr ) V B A r (I A rr ) 1 A rj Y r + G G A rj B jr Y rr + 3c G k,r A rj B j Y A rj B j E A rj 3b G l,r B jk Y kr + 4b A rj B jr Y r V t B t Y r + V t B t A r (I A rr ) 1 Y rr [ 9a + V r B r A r (I A rr ) 1 Y rj + + 9c V t B t A r (I A rr ) 1 E r,r + V r B r A r (I A rr ) 1 9d G A rj B jr Y rl A rj A rj 2c G k,r G B jk Y kk k,r,l l,r ] 3d ] B jk Y kl 4c G k,r 9b ] A rj (I A jj ) 1 Y jj B jk Y k A rj (I A jj ) 1 E j (2) 7 The reult for the ource-baed decompoition could be eaily derived following a imilar logic and they can be provided upon requet. 9 ]

11 where B (I A ) 1 i the Leontief invere matrix derived from the input coefficient matrix A, which exclude the input requirement of other economie from country : 8 A 11 A 12 A 1 A 1G A = 0 0 A A G1 A G2 A G A GG We can define the item that form the bilateral decompoition of gro export a follow: 1 dometic value added (VA) in direct final good export; 2a dometic VA in intermediate export aborbed by direct importer a local final good; 2b dometic VA in intermediate export aborbed by direct importer a local final good only after additional proceing tage abroad; 2c dometic VA in intermediate export aborbed by third countrie a local final good; 3a dometic VA in intermediate export aborbed by third countrie a final good from direct bilateral importer; 3b dometic VA in intermediate export aborbed by third countrie a final good from direct bilateral importer only after further proceing tage abroad; 3c dometic VA in intermediate export aborbed by direct importer a final good from third countrie; 3d dometic VA in intermediate export aborbed by third countrie a final good from other third countrie; 4a dometic VA in intermediate export aborbed at home a final good of the bilateral importer; 4b dometic VA in intermediate export aborbed at home a final good of the bilateral importer after additional proceing tage abroad; 4c dometic VA in intermediate export aborbed at home a final good of a third country; 5 dometic VA in intermediate export aborbed at home a dometic final good; 6 double-counted intermediate export originally produced at home; 7 foreign VA in export of final good; 8 foreign VA in export of intermediate good directly aborbed by the importing country r; 9a and 9b foreign VA in export of intermediate good re-exported by r directly to the country of final aborption. 9c and 9d double-counted intermediate export originally produced abroad. 8 In Appendix B we decribe in detail how and for which purpoe the B matrix i derived. 10

12 The enumeration of the item recall the original KWW component, which can be obtained a a imple ummation over the importing countrie r of the correponding item in our bilateral decompoition (e.g. the econd term in KWW i equal to the um acro the r detination of 2a+2b+2c). A formal proof of thi equivalence for each item in equation (2) i provided in Appendix C. We can now compare the definition of the item here above with thoe originally aigned by KWW, which have been quoted below equation (1). Depite the algebraical conitency between the two claification, there are a few dicrepancie, due to the hortcoming that affect KWW methodology. Firt KKW do not properly allocate the dometic value added embedded in intermediate export between the hare going to direct importer and the hare aborbed in third market (ee alo Nagengat and Sterher, 2016 on the ame point). Second, the term 9a and 9b of equation (2) are erroneouly claified a double-counted by KWW. By correcting thee two ditortion our breakdown of bilateral trade flow reult alo in a ubtantial refinement of the original KWW claification of aggregate export. According to KWW, the firt and econd component of dometic value added of export go entirely to direct importer final demand. Uing the decompoition of bilateral export in equation (2), we oberve that only ub-item 2a and 2b are actually part of the direct importer final demand. Converely, part of the third item (3c), which KWW claify a third countrie final demand, hould be alo conidered a direct importer aborption of dometic VA. Thi make the total value added produced at home and finally aborbed by the bilateral trade partner equal to the um acro detination of: 1, 2a, 2b and 3c. Thi clearly differ from KWW definition (i.e. 1+2). The cheme reported in Figure 3 may clarify the difference between the two approache. Panel 3.a diagram a imple trade relationhip in which country A produce 1 USD of intermediate input, which are ued by B to produce 4 USD of local final good. In thi cae, both KWW and our own bilateral decompoition claify (in component 2 and 2a repectively) the export from A to B a dometic VA in intermediate export aborbed by direct importer. In panel 3.b we now aume that B perform only a partial proceing tage (worth 1 USD of VA) before ending the intermediate product to C, which aemble and conume the final good. The 1 USD of dometic VA exported by A i now aborbed in a third country (C), not the bilateral importer (B). Thi i correctly traced in our bilateral breakdown, a the A-B trade flow i allocated to component 2c (i.e. dometic VA in intermediate export aborbed by third countrie a local final good ). In KWW breakdown, however, it would be recorded by the term V A B AC Y CC and improperly claified a dometic VA of country A aborbed by the direct importer C, ince in thi cae only B directly import from A. Indeed the B AC, being part of the global invere Leontief matrix, account for all the poible way in which the intermediate input of country A contribute to final good produced in C, not only thoe directly imported by C. In the example diagrammed in Figure 3.c, the intermediate product are proceed in two ubequent production tage in B and C, then returned to B for a final tage before erving final demand. The very firt hipment from A to B i correctly claified a dometic VA in intermediate export aborbed by direct importer both in KWW and in our own decompoition. But only our decompoition correctly recognize that the dometic VA i aborbed by direct importer a local final good only after additional proceing tage abroad (2c). Thi alo indicate the difference between the two arrangement of international fragmentation of production in ub-cheme 3.a 11

13 A VA=1 A VA=1 1 1 B VA=3 Y=4 4 C VA=2 Y=4 4 2 B VA=1 (3.a) (3.b) A VA=1 A VA=1 1 1 C VA=1 2 3 B VA=1+1=2 Y=4 4 C VA=2 2 4 B VA=1 Y=4 (3.c) (3.d) Figure 3: Accounting of the aborption of dometic value added of export by direct importer 12

14 and 3.c. Scheme 3.d differ from 3.c only in that the final aembly tage i performed in C rather than B, which i till the country of final detination. A regard country A, B i both the direct importer and the final demand aborber, o it export to B hould be conidered a dometic VA aborbed by a direct importer, which i how they are mapped in our decompoition (in item 3c), wherea in KWW method they are allocated to third countrie aborption of dometic VA of export. The value added decompoition of bilateral trade flow offer ueful information for valuing trade balance between countrie, reconciling the gro export data with value added accounting. For intance, going back to the example in Figure 1, in cae 1.a we ee that the export from A to B are generated by A demand for C final good, ince they are claified in item 4c of equation (2) (i.e. of a third country ). dometic VA in intermediate export aborbed at home a final good In example 1.b, intead, export from A to C are claed under 4a (i.e. dometic VA in intermediate export aborbed at home a final good of the bilateral importer ). Thi differentiation, which i not enviaged in KWW original framework, give inight into the tructure of international production and demand linkage, epecially in dealing with the ort of complex production network that prevail in the real world. Our ink-baed decompoition ummarized by equation (2) differ ubtantially alo from the one in Nagengat and Sterher (2016). In fact they claify a dometic value added aborbed by direct importer only that embedded in good that do not leave thi country again, aigning the remainder to the double counted component. In thi way they do not take into account what we have claified in the 2b and 3c component, underetimating the dometic value added aborbed by direct importer. It mean that, for intance, in the cheme 3.c and 3.d decribed above, the export from country A to country B would be entirely claified a double counted in the decompoition of their bilateral flow. Alo their definition of the dometic value added finally aborbed at home and by third countrie turn out to be imprecie, leading in thi cae to an overetimation of the dometic value added in export. The cheme diagrammed in Figure 4 highlight thi particular iue. In thi cae, two tage of production, each worth 1 USD of value added, are performed both in country A and B, before the final good being hipped from B to the detination market C. The total bilateral gro export from A to B are equal to 4 USD, which conit of 2 USD of VA generated in A, 1 USD of VA generated in B and 1 USD of double counted VA, originated in the firt tage of production in A and embedded in the econd hipment from A to B. In Nagengat and Sterher (2016) thi 1 USD of double counted item would be aigned to the dometic value added of A aborbed by third country C, overetimating thi component. 9 Thi 9 Thi overetimation tem from the double ue of the global invere Leontief matrix in ome of the term of the decompoition of Nagengat and Sterher (2016). In fact in the example of Figure 4, the dometic value added aborbed in third countrie would be calculated a V A B AA A AB B BB Y BC (both in ink and ource-baed methodology). Since B AA account for all the poible way in which the intermediate input of country A contribute to the production in A, V A B AA encompae the entire value added of A generated both in the firt and the econd tage of production. Then the V A B AA matrix hould be applied only to the econd export flow to B, in order to extract A value added following the ink-baed logic. Intead, ince they account the B gro output neceary for the production of the final good exported to C through the B BB matrix, they are recording both the firt and the econd tage of production in B and hence both the hipment of intermediate input from A. So they end up with an overetimation of the 13

15 drawback applie both to their ink and ource-baed decompoition. Thi inaccuracy in defining ome of the item entail that neither methodology propoed by Nagengat and Sterher (2016) can retrieve the entire dometic value added exported by a country umming the correponding item acro the bilateral flow. On the contrary both our ink-baed decompoition and ource-baed breakdown, hown below, meet thi requirement. C VA=0 Y=4 A VA=1+1= B VA=1+1=2 Figure 4: countrie Dometic value added and double counting with final detination in third Figure 4 can be alo ued to point out another relevant iue of KWW methodology and of it bilateral verion by Wang et al.(2013): the erroneou claification of part of the foreign value added in export (i.e. the excluion of item 9a and 9b of equation (2) from the foreign value added). KKW claification fail to record the VA originated in the uptream tage of the production proce by the country that export to the market of final detination (i.e. country r). We can make thi point clearer by referring again to the cheme in figure 4. The 1 USD of value added produced by B in the econd production phae hould be conidered a FVA in country A re-export to B (i.e. the flow worth 3 USD), but in KWW claification thi i recorded a double counted, a B i not the market of final detination. Intead braking down A export according to equation (2) thi component produced by B i correctly claified a foreign value added (within term 9a). Source-baed breakdown of bilateral export The ource-baed decompoition of bilateral export from country to country r can be expreed a follow: 1a* u N E r = V (I A ) 1 Y r [ 1b* + V (I A ) 1 A r (I A rr ) 1 A rj B j Y r + VA produced in A. A rj 1c* G k,r B j Y k ] 14

16 [ 2a* 2b* + V (I A ) 1 A r (I A rr ) 1 Y rr + A rj B jr Y rr +, [ 3a* + V (I A ) 1 A r (I A rr ) 1 Y rj + + A rj 3c* G k,r A rj 3b* G l,r B jk Y kr + A rj 2c* G k,r B jr Y rl [ 4a* 4b* + V (I A ) 1 A r (I A rr ) 1 Y r + A rj B jr Y r + 5* + V (I A ) 1 A r (I A rr ) 1 6* + V (I A ) 1 G A t B t E r A rj A rj B jk Y kk ] 3d* ] B jk Y kl G k,r,l l,r 4c* G k,r G A rj B j Y B jk Y k ] [ 7* 8* ] + V t (I A tt ) 1 A t (I A ) 1 Y r + A r (I A rr ) 1 Y rr 9a* G + V t (I A tt ) 1 A t (I A ) 1 A r (I A rr ) 1 Y rj 9b* G G + V t (I A tt ) 1 A t (I A ) 1 A r (I A rr ) 1 A rj B jk Y kl k l [ 9c* 9d* ] + V t (I A tt ) 1 A tj B j E r + A t (I A ) A t B t E r (3) j t, We can define the item above a: 1a* dometic value added (VA) in final good export directly aborbed by bilateral importer; 1b* dometic VA in intermediate export aborbed by bilateral importer a dometic final good after additional proceing tage; 1c* dometic VA in intermediate export aborbed by third countrie a dometic final good after additional proceing tage; 2a* dometic VA in intermediate export aborbed by direct importer a local final good; 2b* dometic VA in intermediate export aborbed by direct importer a local final good only after further proceing tage; 2c* dometic VA in intermediate export aborbed by third countrie a local final good; 15

17 3a* dometic VA in intermediate export aborbed by third countrie a final good from direct bilateral importer; 3b* dometic VA in intermediate export aborbed by third countrie a final good from direct bilateral importer only after further proceing tage; 3c* dometic VA in intermediate export aborbed by direct importer a final good from third countrie; 3d* dometic VA in intermediate export aborbed by third countrie a final good from other third countrie; 4a* dometic VA in intermediate export aborbed at home a final good of the bilateral importer; 4b* dometic VA in intermediate export aborbed at home a final good of the bilateral importer after further proceing tage; 4c* dometic VA in intermediate export aborbed at home a final good of a third country; 5* dometic VA in intermediate export aborbed at home a dometic final good; 6* double-counted intermediate export originally produced at home; 7* foreign VA in export of final good; 8* foreign VA in export of intermediate good directly aborbed by the importing country r; 9a* and 9b* foreign VA in export of intermediate good re-exported by r; 9c* and 9d* double-counted intermediate export originally produced abroad. A for the ink-baed decompoition, the enumeration of the item here above recall the original KWW component. However while for the dometic content (term 1a* to 6*), the correpondent KWW item can be obtained a a imple ummation over the importing countrie r, 10 thi property doe not hold for the foreign content part. At the level of the ingle exporter term 7* to 9d* differ from thoe propoed in the ink-baed decompoition of equation (2) becaue the notion of FVA and FDC in KWW are defined at world level (not at country level like the DVA and the DDC). The ource bae claification of FVA and FDC of equation (3) follow a imilar logic. 11 However while in the ource-baed approach a certain item i recorded a FVA the firt time that it i re-exported by a foreign country (and a FDC in all the other re-export), in the ink-baed framework all the FVA i accounted the lat time that it i embedded in a export flow. Since the firt re-exporter may not coincide with the lat one, alo the ource-baed indicator of foreign content and the ink-baed one uually differ when computed at the level of the exporting country. However both the approach account a given item a FVA only once in world trade flow. It mean that aggregating at the world level the FVA and FDC component of equation (2) and (3) we obtain exactly the ame meaure. In ection 2.3 we preent an alternative approach to claify the foreign double counted from the perpective of the exporting country that lead to a unique meaure of FVA and FDC both in a ink-baed framework and in a ource-baed one. 10 A formal proof i available upon requet. 11 In particular the definition of FVA in (3) correpond to the meaure propoed by Johnon (2017) diaggregated by country of final detination. 16

18 Another feature of the ource-baed decompoition in (3) i that it identifie eparately the dometic value added directly aborbed by the bilateral partner (term 1a* and 2a*), i. e. croing jut the border between the two countrie, from the dometic value added aborbed by the bilateral partner only after further proceing tage abroad or at home (term 1b*, 2b* and 3c*). A we how in the empirical application preented in ection 3.2, thi i key to meaure global value chain related trade, defined a good and ervice croing more than one border, both at the bilateral and at the aggregate level. Thi i alo one the main feature that differentiate our methodology from the one propoed by Wang et al. (2013). Their decompoition doe not allow to ingle out the good that never leave the direct importing country ince: i) the dometic value added in export of final good i meaured through a ink-baed accounting (i.e. V B Y r ); ii) it doe not identify intermediate good aborbed by the bilateral importer without additional proceing tage abroad (notice that the term 2a* i only part of the correpondent component in Wang et al. (2013), V (I A ) 1 A r B rr Y rr ). More in general Wang et al. (2013) ue different approache (ink and ource) to ingle out the different component, o that their methodology uffer from internal inconitency. Thi make the item of the decompoition not comparable with each other. Since the trade in intermediarie and that in final good are treated in different way it could be tricky alo to ue their methodology to compare the value added tructure of two (or more) ditinct trade flow, a in the analyi of bilateral trade balance An alternative breakdown of the foreign content of export A already mentioned, in equation (2) and (3) FVA and FDC are defined referring to world trade flow. 13 It mean that a certain item i conidered a VA only the firt (or the lat) time it croe a foreign border, while all the other time it i claified a double counted, even in the export of different countrie. On the other hand, the item produced dometically are conidered a double counted only when they cro the ame (national) border more than once. The world perpective ued to define the FVA and the FDC make thee meaure particularly unatifactory when analyzing the export of a given country. Indeed thi may make ene only in the breakdown of total world trade, 14 but in the breakdown of a country export thi ditinction of FVA and FDC turn out to be totally arbitrary. Conider the following example: Italy import intermediarie directly from Germany and indirectly from France; according to a ource-baed approach the German VA i conidered a FVA in Italian export while the French 12 Indeed in a recent paper Wang et al. (2016) themelve adopt our ource-baed decompoition of equation (3). 13 Thi approach i adopted by all the other contribution in the literature that conider the ditinction between FVA and FDC, including Koopman et al. (2014), Wang et al. (2013), Nagengat and Sterher (2016) and Johnon (2017). 14 It i worth noting that alo in thi cae the previou definition of FVA and FDC are quetionable. At world level all the FVA component are alo recorded a DVA in the flow other countrie, meaning that they are already double counted GDP in export. Then, it i arguable to claim that a certain item hould be recorded a FVA only once in world trade flow in order to avoid double counting of the ame production. 17

19 VA i claified a FDC, even if the two component contribute in very a imilar way to the value embedded in Italian export. 15 From the perpective of the exporting country, we are uually intereted in meauring the hare of export that can be traced back to the dometic GDP and the hare that correpond to the foreign one, independently from the number of uptream or downtream production tage that eparate the exporter from the country of origin and/or the market of final detination. To thi aim we need a notion of foreign double counting that follow the ame logic adopted for the dometic double counting: we want to exclude from the FVA only the item that cro the ame (dometic) border more than once. Building on thi intuition, we have developed a new ink-baed decompoition of FVA and FDC and new ource-baed one defined according to the perpective of the exporting country. The FVA in bilateral export from country to country r baed on a ink-baed approach can be expreed a follow: FVAink r = V t B t Y r + V t B t A r (I A rr ) 1 Y rr 9a V t B t A r (I A rr ) 1 9b V t B t A r (I A rr ) 1 9b V t B t A r (I A rr ) 1 G Y rj G A rj G G k B jk Y kl l A rj B j Y (4) The correponding double counted component originated in foreign countrie i the following: FDCink r = 9c V t B t A r (I A rr ) 1 G A rj B j E (5) where the enumeration of the item recall that of equation (2) ince they have imilar interpretation, however only the term 7 and 8 are exactly the ame. A in equation (2) the ue of B (I A ) 1 allow u to take into account the entire foreign value added in export of, excluding only the trade flow that are re-exported more than once by the country itelf. In particular in equation (4) the FVA i recorded the lat time that it leave the national border, in line with the ink-baed approach. Alo in thi cae it i poible to derive a ource-baed counterpart of the decompoition of bilateral flow, in which the value 15 Likewie the ink-baed claification produce arbitrary allocation too. 18

20 added i recorded in the firt hipment from country. 16 7* FVAource r = V t B t Y r 8* + V t B t A r (I A rr ) 1 Y rr 9a* + V t B t A r (I A rr ) 1 9b* + V t B t A r (I A rr ) 1 G Y rj G A rj G k B jk Y kl (6) l FDCource r = 9c* G V t B t A j B j E r (7) j t, Both the decompoition of the foreign component are completely conitent with each other when we um acro all detination market (i.e. they produce the ame value of FVA and FDC for the aggregated export of a country, FVAink r = G FVAource r ). Thu thi new approach lead to a ingle meaure of FVA (and FDC) at the country level. Thee new indicator can be ued alo to addre other intereting empirical quetion: which i the portion of a country GDP that i embedded into the export of another country? How thi i related to the market of final detination? 2.4 The decompoition at the bilateral ector level Our bilateral decompoition can be eaily extended to the ectoral level. 17 In particular, we focu on three different decompoition: i) by ector of origin of the value added, either dometic or foreign, ii) by ector of export (the only one conidered in the work of Wang et al., 2013) and iii) by ector of final aborption. To get a decompoition by ector of origin, it i neceary to ubtitute in equation (2) or (3) the V and V t vector with V and V t, the N N diagonal matrice with the direct value added coefficient along the principal diagonal and zero elewhere. Intead, the decompoition by ector of export i obtained imply by ubtituting V B and V t B t with V B and V t B t, the N N diagonal matrice with the value added hare in final production along the principal diagonal and zero elewhere, a defined in Appendix A. Finally the 16 Again we ue an enumeration that recall the one aigned in the ource-baed decompoition in (3), even if all the correponding term differ in the two decompoition. 17 See alo Borin and Mancini (2016) on thi point. 19

21 decompoition by ector of final aborption i obtained by replacing the vector of final demand, for intance for country a and b, Y ab, with Ŷab, the N N diagonal matrice with country b demand for final good produced in a along the principal diagonal and zero elewhere. 18 Therefore, depending on the particular empirical application, it will be poible to chooe the appropriate bilateral ectoral decompoition. Thee decompoition can alo be combined: in order to meaure imultaneouly the value added embedded in a bilateral trade flow in a particular ector of origin detined for a particular ector of aborption, it i ufficient to ue at the ame time V and Ŷ in equation (2) or (3). 3 Two empirical application We ue the OECD Trade in Value Added ICIO Table (TiVA-ICIO, ee OECD-WTO, 2012) and the World Input-Output Databae (WIOD, ee Dietzenbacher et al. 2013, Timmer et al. 2015) to how two different way of exploiting the value added decompoition of bilateral trade. The firt application follow the ink-baed approach and focue on the eight larget world export, tracing their dometic VA in export from direct importer to final demand. The econd follow the ource-baed approach and derive a new meaure of the hare of GVC-related trade in order to determine how it evolution ince the mid-1990 ha affected the long-run relationhip between global demand and world trade. Matlab code for the ink and ource-baed decompoition are available upon requet, both for WIOD and TiVA, a well a thoe to reproduce the empirical application in the next eion. A Stata command implementing the method decribed in thi paper i alo available. It can be intalled from within Stata by typing net intall icio, from( Major exporter forward connection The decompoition of bilateral export flow provide ueful information on the downtream tructure of the production network in which a country i involved. In particular, in thi ection we invetigate the channel through which the world top exporter reach the market of final detination. We plit the dometic value added in export (DVA) into a hare that i directly exported to the country of ultimate aborption and a hare of DVA that pae through one or more intermediate countrie before reaching the final market. For each exporter and region of final detination we identify the five mot important intermediate importer. Thu, for thi exercie, the ink-baed decompoition preented in equation (2) i better uited, ince it account the value added the very lat time it croe the national border, which i the export flow more cloely related with the market of ultimate aborption. 20 The exercie i 18 See Appendix A for the derivation of V and Ŷ. The matrix VB i obtained in the ame way. 19 Notice that the command cannot be downloaded from the webite but jut directly intalled through the Stata oftware. 20 To further clarify thi point we refer to the example hown in Figure 2. With the ink-baed approach all the value added generated in A and finally aborbed in C i entirely accounted within the bilateral export of final good from A to C, while with the ource-baed approach a part of thi would be aigned to the bilateral flow from A to B. See ection 2.2 for further detail on thi 20