Gestimate Of Value Added And Gross Trade Flows

Transcription

1 WO R K I N G PA P E R S E R I E S N O 1695 / J U LY 2014 COLLATERAL IMBALANCES IN INTRA-EUROPEAN TRADE? ACCOUNTING FOR THE DIFFERENCES BETWEEN GROSS AND VALUE ADDED TRADE BALANCES Arne J. Nagengast and Robert Stehrer THE COMPETITIVENESS RESEARCH NETWORK In 2014 all ECB publcatons feature a motf taken from the 20 banknote. NOTE: Ths Workng Paper should not be reported as representng the vews of the European Central Bank (ECB). The vews expressed are those of the authors and do not necessarly reflect those of the ECB.

2 CompNet The Compettveness Research Network Ths paper presents research conducted wthn the Compettveness Research Network (CompNet). The network s composed of economsts from the European System of Central Banks (ESCB) -.e. the 28 natonal central banks of the European Unon (EU) and the European Central Bank a number of nternatonal organsatons (World Bank, OECD, EU Commsson) unverstes and thnk-tanks, as well as a number of non-european Central Banks (Argentna and Peru) and organsatons (US Internatonal Trade Commsson). The objectve of CompNet s to develop a more consstent analytcal framework for assessng compettveness, one whch allows for a better correspondence between determnants and outcomes. The research s carred out n three workstreams: 1) Aggregate Measures of Compettveness; 2) Frm Level; 3) Global Value Chans CompNet s chared by Flppo d Mauro (ECB). Workstream 1 s headed by Chara Osbat, Govann Lombardo (both ECB) and Konstantns Benkovsks (Bank of Latva); workstream 2 by Antone Berthou (Banque de France) and Paloma Lopez-Garca (ECB); workstream 3 by João Amador (Banco de Portugal) and Frauke Skudelny (ECB). Jula Frtz (ECB) s responsble for the CompNet Secretarat. The refereeng process of CompNet papers s coordnated by a team composed of Flppo d Mauro (ECB), Konstantns Benkovsks (Bank of Latva), João Amador (Banco de Portugal), Vncent Vcard (Banque de France) and Martna Lawless (Central Bank of Ireland). The paper s released n order to make the research of CompNet generally avalable, n prelmnary form, to encourage comments and suggestons pror to fnal publcaton. The vews expressed n the paper are the ones of the author(s) and do not necessarly reflect those of the ECB, the ESCB, and of other organsatons assocated wth the Network. Acknowledgement Dscusson Papers represent the authors personal opnons and do not necessarly reflect the vews of the Deutsche Bundesbank. Comments by an anonymous referee are gratefully acknowledged. We also thank Thomas Knetsch for comments on an earler verson of ths manuscrpt. Arne J. Nagengast Deutsche Bundesbank; e-mal: [email protected] Robert Stehrer WIIW European Central Bank, 2014 Address Kaserstrasse 29, Frankfurt am Man, Germany Postal address Postfach , Frankfurt am Man, Germany Telephone Internet All rghts reserved. Any reproducton, publcaton and reprnt n the form of a dfferent publcaton, whether prnted or produced electroncally, n whole or n part, s permtted only wth the explct wrtten authorsaton of the ECB or the authors. Ths paper can be downloaded wthout charge from or from the Socal Scence Research Network electronc lbrary at Informaton on all of the papers publshed n the ECB Workng Paper Seres can be found on the ECB s webste, ISSN ISBN EU Catalogue No (onlne) (onlne) QB-AR EN-N (onlne)

3 Abstract One of the man stylsed facts that has emerged from the recent lterature on global value chans s that blateral trade mbalances n gross terms can dffer substantally from those measured n value added terms. However, the factors underlyng the extent and sgn of the dfferences between the two measures have so far not been nvestgated. Here, we propose a novel decomposton of blateral gross trade balances that accounts for the dfferences between gross and value added concepts. The blateral analyss contrbutes conceptually to the lterature on double countng n trade by dentfyng the trade flow n whch value added s actually recorded for the frst tme n nternatonal trade statstcs. We apply our decomposton framework to the development of ntra-eu27 trade balances from and show that a growng share of ntra-eu blateral trade balances s due to demand n countres other than the two drect tradng partners. Keywords: Trade balances; Global value chans; Vertcal specalsaton; Value added; Input-output tables JEL classfcaton: F1, F2, C67, R15 ECB Workng Paper 1695, July

4 Non-techncal summary The avalablty of global nput-output tables has sparked a growng lterature on global value chans and has rendered t possble to compute the value added content of trade (Detzenbacher et al., 2013; Johnson and Noguera, 2012; Koopman et al., 2014). Value added trade between two countres descrbes n whch country the partcular parts of a good consumed n one country are produced. Value added trade flows can dffer from gross trade flows due to trade n ntermedate goods whch are used as nputs to produce fnal goods. Ths s because an ntermedate good, such as a subcomponent of a car engne, mght cross several nternatonal borders untl the fnal good, n ths case the car, s purchased by a clent abroad. Intermedate goods trade also leads to consderable dscrepances between blateral value added and gross trade balances, whch are a senstve topc n the economc polcy debate. For example, Johnson and Noguera (2012) fnd that n 2004 the trade defct of the US wth Japan was approxmately 33% larger when measured on a value added bass, whereas the US trade defct wth Chna was approxmately 30-40% smaller. Value added measures of blateral trade arguably better reflect whch countres beneft from trade n terms of ncome and employment (Foster-McGregor and Stehrer, 2013; Tmmer et al., 2013). In contrast, measures of blateral trade flows based on gross concepts can lead to msjudgng the nfluence of domestc demand and relatve prce adjustments on blateral trade balances (Bems and Johnson, 2012). Despte the mportance of blateral trade balances n polcy debates, the proxmate factors that explan why value added and gross trade balance are dfferent have so far not been nvestgated. Therefore, n ths artcle we frst dentfy to what extent gross and value added concepts overlap, whch s a conceptual contrbuton to the trade n value added lterature n general. Second, we descrbe the factors that account for the dfferences between value added and gross trade balances. We provde a novel dstncton between value added that s due to demand of the drect tradng partner, and value added that s due to demand n thrd countres. Whle both are ultmately the results of trade n ntermedates, the dfference between these two categores proves to be mportant from a polcy perspectve as demand n thrd countres s by defnton unaffected by domestc demand n the two tradng partners, whch s often one of the man targets for current account adjustments. We apply our decomposton framework to the development of ntra-eu27 trade balances from 1995 to A major determnant of the dfference that emerges along wth foregn value added s demand n countres other than the two tradng partners. The latter accounted for 25% of the total varance of ntra-eu gross blateral trade balances n 2011, whch marks a consderable rse from 3% n We fnd that the extent of ntra-european mbalances has been overestmated, whle trade mbalances wth countres outsde of the European have been underestmated usng data of gross trade flows. A smlar result holds for the euro area. Our results matter for polcy as, partcularly n a currency unon, t s mportant to establsh wth whom trade mbalances exst snce the burden of adjustment may dffer between trade defcts vs-á-vs member countres and thrd partes (d Mauro and Pappada, 2014). Even though ther lmtatons are wdely acknowledged gross blateral trade balances stll fgure wdely n the lterature and polcy debates (Davs and Wensten, 2002; Bahman-Oskooee and Brooks, 1999). Our paper therefore provdes a strong case for consderng value added nstead of gross blateral trade balances snce a szable porton of gross blateral trade balances cannot be nfluenced by the two countres between whch the mbalance exsts. ECB Workng Paper 1695, July

5 1 Introducton One of the man stylsed facts that has emerged from the recent lterature on global value chans s that blateral trade balances n gross terms can dffer substantally from those measured n value added terms, whle aggregate trade balances are the same n both cases (Johnson and Noguera, 2012). Value added balances capture the dfference between any two countres domestcally produced value added that s absorbed n fnal demand by ther respectve tradng partner. In contrast to gross trade balances, they dscount the part of trade flows that s double counted n offcal trade statstcs (Koopman et al., 2014). Trade n ntermedate nputs can lead to consderable dscrepances between the two concepts. For example, consder the stylsed global producton network depcted n Fgure 1. The gross trade balance between country 3 and country 2 s 4 USD. However, the gross trade flow between the two countres also contans value added worth 1 USD of country 1 due to the presence of trade n ntermedate goods. The value added balance between country 3 and country 2 s only 3 USD once foregn value added s dscounted. In practce, value added and gross trade balances often dffer substantally from each other. For example, Johnson and Noguera (2012) fnd that n 2004 the trade defct of the US wth Japan was approxmately 33% larger when measured on a value added bass, whereas the US trade defct wth Chna was approxmately 30-40% smaller. Value added measures of blateral trade arguably better reflect whch countres beneft from trade n terms of ncome and employment (Foster-McGregor and Stehrer, 2013; Tmmer et al., 2013). In contrast, measures of blateral trade flows based on gross concepts can lead to msjudgng the nfluence of domestc demand and relatve prce adjustments on blateral trade balances (Bems and Johnson, 2012). Whle the mportance of value added trade balances n economc theory and polcy s begnnng to gan recognton, the underlyng factors that determne the sgn and magntude of the dfferences between the two concepts have so far not been nvestgated. The prevous lterature has generally ascrbed dscrepances between gross and value added balances to dfferent characterstcs of nternatonal producton networks such as trangular producton sharng and the relatve poston of countres n global value chans (Johnson and Noguera, 2012; OECD, 2013; Antras et al., 2012). However, a mathematcal framework that clarfes the relaton between the two concepts at the blateral level 1 s stll lackng and hampers the nterpretaton of blateral gross balances, whch are currently the only data avalable n a tmely manner. In ths paper, we compute and analyse the proxmate factors that account for the dfferences between gross and value added blateral trade balances. In order to do so, we propose a novel decomposton of blateral gross trade balances. Ths requres a conceptual framework that relates blateral value added and gross trade flows to each other. A caveat whch turns out to be nherent n the subject matter s that the relaton between value added and gross trade flows s theoretcally ll-defned, and therefore necessarly a queston of what value added flows are defned to be n relaton to physcal trade flows. A frst conceptual contrbuton s that we are, to the best of our knowledge, the frst to dentfy ths problem and dscuss the two most parsmonous solutons to t, whch determne the ntersecton between value added and gross trade flows at the blateral level. The two solutons anchor value added flows ether to the country of producton or to the country of fnal absorpton, whch we call the source-based and 1 Koopman et al. (2014) provde a decomposton of the total gross exports of a country nto value added exports and sx other components that are double counted n nternatonal trade statstcs. ECB Workng Paper 1695, July

6 the snk-based approach, respectvely (dscussed n detal n the Methodology secton and n Fgure 2). Ths paper contrbutes conceptually to the lterature on double countng by dentfyng the trade flow n whch value added s actually recorded for the frst tme n nternatonal trade statstcs. In comparson to other decompostons suggested n the lterature, we show that Koopman et al. (2014) mplctly use a varaton of the source-based vew when dentfyng value added exports n gross trade flows, but that ther subdvson of value added exports s to some extent arbtrary and not based on the number of nternatonal border crossngs. Fgure 1: Illustraton of the dfference between value added and gross trade balances. Stylsed global producton network. Country 1 shps domestc value added worth 1 USD embedded n fnal goods to country 2 and domestc value added worth 1 USD n ntermedate goods to country 3. Country 3 then adds 3 USD of domestc value added and shps fnal goods worth 4 USD (contanng 1 USD of value added of country 1 and 3 USD of country 3) to country 2 for fnal consumpton. In ths case, the blateral gross trade balances between the countres are NX 12 = 1, NX 13 = 1 and NX 32 = 4. The value added balances dffer from the gross trade balances due to ntermedates trade: NVAX 12 = 2, NVAX 13 = 0 and NVAX 32 = 3. A second conceptual contrbuton s that we dentfy a range of categorcally dfferent components of value added that consttute the dfference between blateral value added and gross trade balances, whch are ndependent of the methodologcal choce above. We fnd two quanttes that explan the lon s share of the dfference between gross and value added balances (other quanttes lke double countng and reflecton are less mportant as shown below): (a) foregn value added absorbed by the two tradng partners and (b) fnal demand n countres other than the two tradng partners. The latter means that n a world of nternatonal producton sharng the blateral trade balance between two countres s to some degree a functon of demand n the rest of the world. 2 The dfferences between the two quanttes are of consderable mportance, snce - due to data avalablty - a majorty of analyses currently stll focuses on gross trade flows. For example, whle both quanttes n our decomposton may or may not be affected by blateral exchange rate movements 3, domestc demand adjustments and trade shocks n thrd countres mpact each of them dfferently. A decrease n domestc demand leads to an adjustment of the porton of the trade balance capturng foregn value added absorbed by the two trade partners, whereas by defnton t wll have no effect on the part of the trade balance whch s due to demand 2 For example, consder the blateral trade balance between Germany and France. To satsfy demand n Chna, Germany exports fnal goods drectly to Chnese frms and costumers. In order to produce these goods Germany needs to mport a part of the requred ntermedates from France thereby pushng Germany more towards a trade defct wth France. Smlarly, France also mports some ntermedates from Germany n order to produce goods whch are meant for fnal consumpton and nvestment n Chna, whch pushes the German trade balance wth France more towards a trade surplus. The magntude and the sgn of the net effect depend on the level and sectoral composton of external demand and the relatve poston n the value chan of the two countres. 3 Dependng on whether t s more approprate to measure prce compettveness n terms of goods or n tasks (Bems and Johnson, 2012; Bayoum et al., 2013). ECB Workng Paper 1695, July

7 n thrd countres. Therefore, a completely balanced blateral gross trade poston s unlkely to be a good benchmark for assessng demand or prce adjustments. Furthermore, ths part of the trade balance may also occasonally be subject to volatlty dervng from demand shocks n thrd countres that are ndependent of developments n the economes of the two trade partners. Pror to the fnancal crss there has been a substantal buld-up n European trade mbalances. Partcular attenton has been pad to mbalances wth other EU countres and especally wth those countres wth large current account defcts that were heavly affected by the fnancal crss and the ensung soveregn debt crss (Berger and Ntsch, 2010; European Commsson, 2010). We therefore apply our decomposton framework to the development of ntra-eu27 trade balances from 1995 to We show that a major part of the dfference, an average of 32% over the sample perod, between ntra-eu value added and gross blateral balances s due to foregn value added consumed 4 by the respectve tradng partner. However, a szable share of ntra-eu blateral trade balances s due to demand n countres other than the two tradng partners. The latter accounted for 25% of the total varance of ntra-eu gross blateral trade balances n 2011, whch s a consderable rse from 3% n A structural decomposton analyss ndcates that ths evoluton was especally due to the rsng mportance of producton fragmentaton n the European Unon whle the change n global demand was the second most mportant factor. The rest of the paper s structured as follows. Secton 2 descrbes our decomposton framework and defnes the two approaches that assgn value added flows to gross trade balances and dscusses the relaton of our decomposton framework to the prevous lterature. Secton 3 presents our emprcal results and Secton 4 concludes. 2 Methodology In ths secton we frst provde a short remnder of how blateral gross and value added trade balances are calculated and, second, we present our decomposton framework, whch can account for the dfferences between these two concepts. In the nterest of space and readablty, ths secton focuses on the case of three countres wthout loss of generalty. The generalsaton to the N-country case and techncal detals of the dervaton are presented n the appendx. 2.1 Blateral balances n gross and value added terms A key fndng of the lterature on global value chans s that blateral trade balances n gross terms dffer from those n value added terms, whle aggregate trade balances are the same n both cases. A global nput-output table allows for the calculaton of blateral value added exports (Johnson and Noguera, 2012). Value added exports between country 1 and country 2 (VAX 12 ) 5 are defned as the value added of country 1, whch s ultmately absorbed n fnal demand by country 2. In the case of three countres, 4 We use the terms consumpton and absorpton n fnal demand nterchangeably. When usng the term consumpton we refer to all fnal demand categores specfed n WIOD ncludng fnal consumpton expendture by households, fnal consumpton expendture by non-proft organsatons servng households, fnal consumpton expendture by the government, gross fxed captal formaton and changes n nventores and valuables. 5 Note that the acronym VAX n ths artcle, whch stands for value added exports, should not be confused wth the VAX-rato (Johnson and Noguera, 2012), whch denotes the rato of value added to gross exports of a country. ECB Workng Paper 1695, July

8 ths s computed n the followng way: l ( ) 11 l 12 l 13 VAX 12 = v l 21 l 22 l 23 l 31 l 32 l 33 f 12 f 22 f 32 = v1 l 11 f 12 + v 1 l 12 f 22 + v 1 l 13 f 32 (1) where v s the value added coeffcent of country of the value added vector v, l j refers to the th row, jth column element 6 of the Leontef nverse L = (I A) 1, A s the global nput-output coeffcent matrx and f j denotes fnal goods flows from country to country j. Value added mports of country 1 from 2 are equal to the value added exports of country 2 to 1. Hence, the value added trade balance of country 1 wth 2 (NVAX 12 ) s the dfference between ther respectve blateral value added exports: NVAX 12 = VAX 12 VAX 21 ( = v 1 l 11 f 12 + v 1 l 12 f 22 + v 1 l 13 f 32) (v 2 l 21 f 11 + v 2 l 22 f 21 + v 2 l 23 f 31) Smlarly, the gross trade balance between country 1 and 2 (NX 12 ) can be expressed as the dfference between ther respectve blateral gross exports: NX 12 = e 12 e 21 = f 12 + z 12 f 21 z 21 = f 12 + a 12 x 2 f 21 a 21 x 1 (2) where e j denotes gross exports from country to j, z j s the flow of ntermedates between and j, whch equals the share of ntermedates of country n producton of country j (a j of the global nput-output matrx A) multpled by the level of gross output n country j (x j ). At ths stage, t s also worth hghlghtng the specfc assumptons and man lmtatons of our study that are assocated wth ts relance on global nput-output tables and whch are shared by the lterature on value added trade as a whole. These lmtatons nclude a proportonalty assumpton used to assgn ntermedate nput flows to the producton of dfferent domestc sectors (Puzzello, 2012). In addton, n the process of preparng global nput-output tables changes have to be made n order to balance the global coeffcent matrx and n some cases methodologcal dscrepances exst n the underlyng natonal accounts concepts between dfferent countres (Detzenbacher et al., 2013). Furthermore, nput-output tables n general assume a fxed nput structure and a constant returns to scale producton functon (Mller and Blar, 2009). However, t should be noted that some of these lmtatons are less relevant for an ex-post analyss of trade flows and when data s avalable, as n our case, for more than a sngle year. 2.2 Decomposton framework To gude the reader through ths secton, we provde a bref outlne of our decomposton framework and a summary of the man deas. The purpose of the decomposton proposed here s to elucdate the dfferences between gross and value added trade balances. To dentfy meanngful categores n blateral gross trade flows we use two smple crtera: (a) the orgn of the value added embedded n gross trade flows and (b) the country, whch ultmately absorbs the value added n ts fnal demand. 6 l j s an S S matrx f the number of sector S s greater than one. ECB Workng Paper 1695, July

9 Accordngly, n a frst step all gross trade flows are expressed as a functon of fnal demand n accordance wth a demand drven Leontef model and are broken down by the orgn of ther value added content. Second, a crucal step s to dentfy the ntersecton between blateral gross and value added exports. The key queston that arses n ths regard s to whch blateral gross trade flow value added exports should be assgned f the embedded value added crosses nternatonal borders multple tmes. It turns out that the soluton to ths problem s a matter of defnton and therefore to some extent arbtrary. We consder two extreme cases takng the perspectve of (1) the country, n whch the value added orgnates (source-based approach) and (2) the country, whch ultmately absorbs the value added n fnal demand (snk-based approach). Whle nfntely many other allocatons are possble n theory, the two cases consdered are arguably the most parsmonous and they allow us to assess the senstvty of our results to ths methodologcal choce. Our preferred soluton s the source-based approach snce t entals an ntutve defnton of double counted value added based on the number of border crossngs. In the source-based approach a value added export s assgned to the gross trade flow, n whch t leaves the producng country for the very frst tme, whereas t s labeled as double counted n case t has crossed nternatonal borders (and hence has been counted as value added exports) prevously. In accordance wth the aforementoned defntons, blateral gross trade balances are decomposed nto sx components explaned n more detal below: a) the ntersecton wth the respectve value added trade balance, value added of one of the two tradng partners that s b) double counted or c) reflected back va thrd countres for consumpton n the country of orgn, d) foregn value added consumed by the respectve tradng partner, e) domestc and f) foregn value added ultmately absorbed n fnal demand of thrd countres. 2.3 Blateral exports and value added components Blateral gross exports from country 1 to country 2, as shown n equaton (2), are a functon of both demand n country 2 for fnal goods of country 1 and gross output of country 2, x 2 : e 12 = f 12 + a 12 x 2 (3) As outlned above, n a frst step, gross exports are expressed as a functon of fnal demand of the country that ultmately absorbs the fnal goods and servces n ts fnal demand. In order to do so, we note that the gross output of country 2, x 2, s endogenous n a demand-drven Leontef system,.e. gross output can be expressed as a functon of fnal demand n all countres n the world x 2 = l 21 (f 11 + f 12 + f 13 ) + l 22 (f 21 + f 22 + f 23 ) + l 23 (f 31 + f 32 + f 33) (4) In a second step, gross exports are broken down by the orgn of ther value added content. We note that the dentty v (I A) 1 = v L = ι holds whch follows from frst prncples 7 and consequently n 7 The output x j of a one sector economy j s smply the sum of ts nputs z j from all countres C and the value added w j generated n country j. C x j = z j + w j =1 or n vector notaton x = ι Z + w (5) ECB Workng Paper 1695, July

10 the three-country case v 1 l 11 + v 2 l 21 + v 3 l 31 1 v 1 l 12 + v 2 l 22 + v 3 l 32 = 1 v 1 l 13 + v 2 l 23 + v 3 l 33 1 (6) Substtutng x 2 n equaton (3) by (4) and multplyng the resultng expresson by the frst lne of equaton (6) 8 yelds: e 12 = v 1 l 11 f 12 + v 2 l 21 f 12 + v 3 l 31 f 12 + v 1 l 11 a 12[ l 21 (f 11 + f 12 + f 13 ) + l 22 (f 21 + f 22 + f 23 ) + l 23 (f 31 + f 32 + f 33 ) ] + v 2 l 21 a 12[ l 21 (f 11 + f 12 + f 13 ) + l 22 (f 21 + f 22 + f 23 ) + l 23 (f 31 + f 32 + f 33 ) ] + v 3 l 31 a 12[ l 21 (f 11 + f 12 + f 13 ) + l 22 (f 21 + f 22 + f 23 ) + l 23 (f 31 + f 32 + f 33 ) ] In order to dentfy meanngful categores n blateral gross trade flows we use (a) the orgn of the value added embedded n gross trade flows and (b) the country, whch ultmately absorbs the value added n ts fnal demand. Accordngly, we apply the label v r..f.s to the terms n e 12, where r ndcates the country of orgn of the value added and s denotes the country, n whch the value added s eventually consumed, ndependent of the path the value added takes n between whch can cross borders multple tmes: e 12 = v 1 l 11 a 12 v 1..f.1 l 2 f 1 + v 1 l 11 f 12 + v 1 l 11 a 12 l 2 f 2 + v 1 l 11 a 12 l 2 f 3 v 1..f.2 v 1..f.3 + v 2 l 21 a 12 l 2 f 1 + v 2 l 21 f 12 + v 2 l 21 a 12 l 2 f 2 + v 2 l 21 a 12 l 2 f 3 v 2..f.1 v 2..f.2 v 2..f.3 + v 3 l 31 a 12 l 2 f 1 + v 3 l 31 f 12 + v 1 l 11 a 12 l 2 f 2 + v 3 l 31 a 12 l 2 f 3 v 3..f.1 v 3..f.2 v 3..f.3 Before presentng our trade balance decomposton, we need to clarfy the relaton between domestc value added absorbed n fnal demand by country 2 (v 1..f.2 ) and value added exports from country 1 to 2 (VAX 12 ). Phrasng the queston dfferently, we need to determne how to dstrbute VAX 12 to blateral gross trade flows between countres. To llustrate the problem, let s consder the frst term, v 1 l 11 f 12, n the expresson for VAX 12 n equaton (1). It s mportant to note that the coeffcent l 11 descrbes The global nput-output coeffcent matrx can be obtaned by scalng the row entres of the nput matrx Z by the total output of the respectve country: A = Zˆx 1, where ˆx denotes the dagonal matrx created from vector x. Smlarly, the value added coeffcent vector can be obtaned by scalng the value added generated n a partcular country by ts total output: v = wˆx 1. Substtutng Z = Aˆx and postmultplyng by ˆx 1 n equaton (5) yelds or x ˆx 1 = ι Aˆxˆx w ˆx ι = ι A + v whch can be re-wrtten as v (I A) 1 = ι to yeld the expresson used n the man text. Note that ths dervaton was adopted from Mller and Blar (2009) wth mnor modfcatons n notaton. 8 The left-hand sde of the expresson s unchanged snce all entres of the vector n equaton (6) are equal to one. ECB Workng Paper 1695, July

11 all possble ways that value added from country 1 can take to travel embedded n ntermedate goods through nternatonal producton networks back to country 1 (see Appendx A.1). A smlar argument holds for the other two terms n Equaton (1). Ths means that n the presence of nternatonal producton sharng a certan proporton of value added n VAX 12 passes - embedded n ntermedates - through gross trade flows between any two countres n the world. Ths mples that t s recorded several tmes n nternatonal trade statstcs. At least n theory, t s concevable to assgn these portons of VAX 12 to the respectve blateral flows. 9 In the followng, we consder two extreme cases. Frst, we take the perspectve of the country, n whch the value added orgnates (source-based approach) and, second, we consder the country whch ultmately absorbs the value added n ts fnal demand as a reference pont (snk-based approach). Whle t s concevable to attrbute value added exports of country 1 to 2 to gross trade flows between thrd countres, ths would be theoretcally unappealng and the two cases consdered n ths text are arguably the most parsmonous. In the source-based approach (for a numercal example see Fgure 2a and Secton 2.6), we assgn only that porton of v 1..f.2 to VAX 12 whch leaves the country for the frst tme n fnal goods or n the form of ntermedate goods for further processng abroad, whch we denote by VAX* 12. The remander of v 1..f.2 has by defnton been re-mported by 1 after processng abroad and hence has crossed nternatonal borders at least twce, whch we denote by DBC for double countng. To mplement ths mathematcally the entry of the Leontef nverse l 11 s splt nto a porton that represents ntra-country processng, I + a 11 + a 11 a 11 + a 11 a 11 a = (1 a 11 ) 1 (.e. every possble way of gong from country 1 to country 1 wthout leavng the country) captured by the domestc Leontef nverse, and the remander l 11 (1 a 11 ) 1, whch has crossed nternatonal borders at least twce. v 1..f.2 = v 1 l 11 f 12 + v 1 l 11 a 12 l 2 f 2 = v 1 (1 a 11 ) 1 f 12 + v 1 (1 a 11 ) 1 a 12 l 2 f 2 VAX* 12 + v 1 (l 11 (1 a 11 ) 1 )f 12 + v 1 (l 11 (1 a 11 ) 1 )a 12 l 2 f 2 DBC Smlarly, we can consder gross exports between country 1 and 3, e 13, whch also nclude a term v 1..f.2 that can be splt nto VAX* 12 and DBC. Note that n the source-based approach VAX* j terms appear only n blateral gross exports of country,.e. the value added producng country. Therefore, n the source-based approach, summng VAX* j terms across all blateral mports of country j,.e. the value added absorbng country, n general does not yeld value added mports from country. In Appendx A.5 we prove that the sum of all VAX* 12 terms n e 12 and e 13 equals the value added exports from country 1 to 2, VAX For example, n the stylsed producton chan depcted n Fgure 3a domestc value added of country 1 travels embedded n ntermedates va country 2 and 3 to country 4 where t s absorbed n fnal demand, and hence counts as value added exports from country 1 to 4, VAX 14. At least n theory, the value added trade worth 1 USD of country 1 could be assgned to the gross trade flow between country 2 and 3, even though ths nvolves nether the country that generated nor consumes the value added. ECB Workng Paper 1695, July

12 In the snk-based approach (for a numercal example see Fgure 2b and Secton 2.6), nstead of consderng the producng country we take the absorbng country as a reference pont. In ths case, we assgn value added exports to the gross trade flow, n whch value added last enters the country of fnal demand. Hence, we allocate only that porton of v 1..f.2 to VAX 12 whch never leaves country 2 agan before beng absorbed n fnal demand. The remander of v 1..f.2 wll once agan be flagged as havng been double counted. Domestc value added n fnal goods exports between country 1 and 2 s drectly consumed n country 2 so t s unambguously assgned to VAX* 12. For ntermedate goods the stuaton s slghtly more complcated. The porton of country 1 s value added whch s drectly used n the producton of fnal goods mmedately consumed n country 2 s allocated to VAX* 12. The remander leaves country 2 agan embedded n ntermedates even though t eventually re-enters 2 agan for fnal absorpton. The part of country 1 s value added that never leaves country 2 agan before beng consumed, can be expressed mathematcally as 1 + a 22 + a 22 a 22 + a 22 a 22 a = (1 a 22 ) 1 nstead of usng l 22. v 1..f.2 = v 1 l 11 f 12 + v 1 l 11 a 12 l 22 f 22 + v 1 l 11 a 12 = v 1 l 11 f 12 + v 1 l 11 a 12 (1 a 22 ) 1 f 22 VAX* 12 l 2 f v 1 l 11 a 12 (l 22 (1 a 22 ) 1 )f 22 + v 1 l 11 a 12 l 2 f 2 2 DBC Smlarly, we can consder the gross exports between country 3 and 2, e 32, whch also nclude a term v 1..f.2 that can be splt nto VAX* 12 and DBC. Note that n contrast to the source-based approach VAX* j terms appear only n blateral gross mports of country j,.e. the value added absorbng country. Therefore, n the snk-based approach, summng VAX* j terms across all blateral exports of country,.e. the value added producng country, n general does not yeld value added exports of country. Agan, n Appendx A.5 we prove that the sum of the VAX* 12 terms n e 12 and e 32 equals the value added mports of country 2 from 1, VAM 21, and hence the value added exports from country 1 to 2, VAX 12. Arguments can be found aganst and n favour of ether one of the source- and the snk-based approach. We lean slghtly towards the source-based approach snce t entals an ntutve defnton of value added that s double counted based on the number of border crossngs. In the nterest of space, we focus on the source-based approach n the man text and present the snk-based decomposton and ts results n the appendx. 2.4 Relaton to alternatve decomposton approaches Several decompostons of gross trade flows have recently been suggested n the lterature (Daudn et al., 2011; Johnson and Noguera, 2012; Koopman et al., 2014; Foster-McGregor and Stehrer, 2013). However, none of these nvestgates the relaton between blateral gross and value added trade n general and blateral gross and value added trade balances n partcular. Whle Johnson and Noguera (2012) relate value added balances to gross trade balances n terms of dfferences n blateral value added to export ratos, ther analyss leaves unexplaned why these ratos dffer between countres n the frst place. The ECB Workng Paper 1695, July

13 decomposton that s most smlar to our contrbuton s the work by Koopman et al. (2014) (henceforth KWW), who decompose gross exports - albet at the aggregate level - nto value added exports and terms that are double counted n nternatonal trade statstcs. The mplct defnton of value added exports n the decomposton by KWW s worth clarfyng n the lght of our blateral decomposton framework ntroduced here. In KWW all value added trade flows are assgned to the exportng country and the remander of the gross trade flows between countres s labeled as double counted. Hence, KWW n prncple endorse the source-based approach. However, value-added exports are then further subdvded nto (1) domestc value added n drect fnal goods exports (v s C r s lss f sr ), (2) domestc value added n ntermedates exports absorbed by drect mporters (v s C r s lsr f rr ) and (3) domestc value added n ntermedates re-exported to thrd countres n ntermedate goods (v s C r s C t s,r lsr f rt ). Note that ths subdvson s not based on how often value added crosses nternatonal borders, but on the dstncton between fnal and ntermedate goods, and a somewhat ambguous partton of ntermedate exports. Our decomposton framework suggests two refnements to the subdvson of value added exports. Frst, the dvson nto fnal and ntermedate goods exports s to a certan degree arbtrary snce the frst term nvolves both ntermedate and fnal goods flows. In (1) l ss descrbes all possble ways that domestc value added can travel through nternatonal producton networks back to country s (see dscusson above and Appendx A.1). Hence, a certan share of the domestc value added n (1) s ntally exported n ntermedates before t s ncluded n fnal goods exports of s and shpped off to country r for absorpton n fnal demand. Only v s (I a ss ) 1 f sr leaves country s for the very frst tme n fnal goods that are absorbed n country r and therefore should be consdered to be part of (1). The remander v s (l ss (I a ss ) 1 )f sr crosses nternatonal borders at least twce n ntermedates before beng absorbed n fnal demand and hence s more approprately subsumed n category (3) whch captures domestc value added n ntermedates that s re-exported to thrd countres n ntermedate goods. Second, not all ntermedates n (2) are absorbed by ther drect mporter snce the Leontef nverse l sr descrbes all possble ways that value added can flow between country s and country r nvolvng thrd countres, whch s not n general equvalent to a sr,.e. drect sourcng of ntermedates by country r from country s. In the followng l sr wll be substtuted by three terms. As a frst step only value added should be consdered that has not left country s for processng abroad prevously. In order to do so, once agan, the term (I a ss ) 1 should be used. In a second step, we are only nterested n that part of domestc value added, whch s drectly shpped from country s to r for whch we use the nternatonal sourcng coeffcent a sr denotng the share of total nputs of country r that comes from country s. Fnally, we exclusvely want to consder value added that does not leave country r agan (snce ths would mply that value added crosses nternatonal borders at least twce n ntermedates before beng absorbed n fnal demand and hence ths part would be more approprately allocated to category (3)). In order to do so we choose (I a rr ) 1 whch allows for ntra-country processng. In summary, the term l sr s substtuted by (I a ss ) 1 a sr (I a rr ) Once agan, the remander v s (l sr (I a ss ) 1 a sr (I a rr ) 1 )f rr crosses nternatonal borders multple 10 Another way to derve ths expresson s from the defnton of the matrx nverse (see Appendx A.4). Equaton (12) states that l 12 = (1 a 11 ) 1 (a 12 l 22 + a 13 l 32 ) for the three-country case. The generalsaton to the N-country case of ths expresson s l sr = (1 a ss ) 1 ( t s ast l tr ). Note that n ths expresson only (1 a ss ) 1 a sr l rr descrbes drect mports of ntermedates of country r from s. In order to exclude value added leavng country r for addtonal processng abroad, once agan, l rr needs to be substtuted by (1 a rr ) 1. Collectng terms and substtutng l sr n v s l sr f rr one arrves at v s (I a ss ) 1 a sr (I a rr ) 1 f rr as before. ECB Workng Paper 1695, July

14 tmes and s assgned to category (3). In summary, for a consstent decomposton wth the sourcebased approach as defned above (.e. based on the number of nternatonal border crossngs) and the labels suggested by KWW, t would be approprate to decompose value added exports as follows: (1) v s C r s (I ass ) 1 f sr, (2) v s C r s (I ass ) 1 a sr (I a rr ) 1 f rr and (3) v s C r s (lss (I a ss ) 1 )f sr + v s C r s (lsr (I a ss ) 1 a sr (I a rr ) 1 )f rr + v s C r s C t s,r lsr f rt. Hence, (1) descrbes value added that leaves country s for the very frst tme n fnal goods exports, (2) captures domestc value added n ntermedates that s absorbed mmedately by drect mporters wthout beng re-exported for further processng and (3) collects all the domestc value added terms that cross nternatonal borders several tmes before beng ncorporated n domestc fnal goods or fnal goods of other countres and before beng absorbed n fnal demand abroad. Note that value added n terms (1) and (2) crosses nternatonal borders only once before beng absorbed n fnal demand, whereas value added n term (3) crosses nternatonal borders multple tmes and therefore leads to double countng n nternatonal trade statstcs. Whle the two decompostons dffer conceptually from each other, how mportant the dfferences are quanttatvely s an emprcal queston. Table 1 shows the subdvson of value added exports accordng to KWW and our alternatve subdvson based on the frst nternatonal border crossng denoted by KWW* for the top ten value added exporters n 2011 n bllon USD. The KWW* subdvson assgns the share of (1) domestc value added n drect fnal goods exports and (2) domestc value added n ntermedates exports absorbed by drect mporters that crosses nternatonal borders more than once to the thrd category (3*). Therefore (1) and (2) n the KWW decomposton are always larger than (1*) and (2*) n the KWW* decomposton, and (3) s always smaller than (3*). For example, Chna exported domestc value added worth 744 bllon USD n fnal goods exports, 8 bllon USD of whch were orgnally exported as ntermedates by Chna. Snce ths part was re-mported by Chna after processng abroad, t crossed nternatonal borders several tmes and was hence added to the thrd category (3*). Chna exported 676 bllon USD worth of domestc value added n ntermedates whch was ncluded and consumed n fnal goods n the same country. Domestc value added worth 128 bllon USD of ths amount crossed nternatonal borders more than once and was added to the thrd category (3*). In general, for domestc value added n drect fnal goods exports the dfference between the two decompostons (cf. (1) vs. (1*)) s quanttatvely relatvely mnor snce only a small porton of domestc value added s re-mported by the country of producton. For domestc value added n ntermedates exports absorbed by drect mporters, however, the dfference between the two decompostons (cf. (2) vs. (2*)) s quanttatvely non-neglgble. Ths s because domestc value added n ntermedate goods often crosses nternatonal borders more than once before beng absorbed n fnal demand. The revsed decomposton KWW* takes multple border crossngs nto account and therefore yelds a consderably larger value of domestc value added n ntermedates re-exported to thrd countres n ntermedate goods. In general, whether to choose the KWW or the KWW* decomposton depends on the partcular research or polcy queston under consderaton. If the nterest les n categorsng value added flows accordng to dfferences n fnal absorpton, KWW could be used snce the KWW decomposton splts value added exports nto three categores accordng to whch country s nvolved n producng the fnal good before consumpton f sr, f rr and f rt, where s s the country that produces the value added, r s a drect tradng partner of s and t s a thrd country. In ECB Workng Paper 1695, July

15 our case, KWW* s preferable snce t accurately dentfes the part of the value added that leads to double countng n nternatonal trade flows. KWW KWW* countres (1) (2) (3) (1*) (2*) (3*) DV n drect fnal goods exports DV n ntermedates exports absorbed by drect mporters DV n ntermedates re-exported to thrd countres n ntermedate goods DV n drect fnal goods exports DV n ntermedates exports absorbed by drect mporters DV n ntermedates re-exported to thrd countres n ntermedate goods VAX CHN , 574 USA , 455 DEU , 112 JPN GBR FRA RUS ITA CAN KOR world 4, 414 7, 400 1, 510 4,370 5, 839 3, , 325 Table 1: Comparson between the KWW and KWW* decomposton. Subdvson of value added exports (column 8) accordng to KWW (column 2-4) and our adjusted subdvson denoted by KWW* (column 4-7) for the top ten value added exporters n 2011 n bllon USD. (Devatons between the totals of the two subdvsons are due to roundng.) 2.5 Decomposton of blateral gross trade balances (source-based approach) Ths brngs us back to apply the source-based decomposton approach above to blateral trade balances (see Appendx A.2 for the snk-based approach). Usng the defnton of a blateral trade balance n gross ECB Workng Paper 1695, July

16 terms and nsertng the respectve expressons yelds: NX 12 = e 12 e 21 = v 1 (I a 11 ) 1 f 12 + v 1 (I a 11 ) 1 a 12 l 2 f 2 v 2 (I a 22 ) 1 f 21 v 2 (I a 22 ) 1 a 21 NVAX* 12 (e 12 ) l 1 f 1 NVAX* 12 (e 21 ) + v 1 (l 11 (I a 11 ) 1 )f 12 + v 1 (l 11 (I a 11 ) 1 )a 12 l 2 f 2 + v 2 l 21 a 12 l 2 f 1 DBC (e 12 ) v 2 (l 22 (I a 22 ) 1 )f 21 v 2 (l 22 (I a 22 ) 1 )a 21 DBC (e 21 ) + v 2 l 21 f 12 + v 1 l 11 a 12 l 2 f 1 + v 2 l 21 a 12 REFL (e 12 ) l 1 f 1 v 1 l 12 a 21 l 2 f 2 v 1 l 12 f 21 v 1 l 12 a 21 + v 3 l 31 f 12 + v 3 l 31 a 12 l 2 (f 1 + f 2 ) v 3 l 32 f 21 v 3 l 32 a 21 FVA tp (e 12 ) + v 1 l 11 a 12 l 2 f 3 + v 2 l 21 a 12 DVA 3rd (e 12 ) + v 3 l 31 a 12 l 2 f 3 v 3 l 32 a 21 FVA 3rd (e 12 ) DBC (e 12 ) l 1 f 2 DBC (e 21 ) l 1 f 1 v 2 l 22 a 21 l 1 f 2 l 1 (f 1 + f 2 ) l 2 f 3 v 2 l 22 a 21 l 1 f 3 FVA 3rd (e 21 ) FVA tp (e 21 ) l 1 f 3 v 1 l 12 a 21 REFL (e 21 ) l 1 f 3 DVA 3rd (e 21 ) where ndvdual terms come wth a label ndcatng whether they belong to e 12 or e 21 and have been grouped nto the followng categores. NVAX* 12 s the subset of NVAX 12 that s part of the blateral gross trade balance between country 1 and 2 as descrbed above. DBC refers to the double countng terms dentfed prevously and, n addton, value added of the respectve tradng partner that s double counted,.e. j vj..f. (e j ), where j {1, 2} and (e j ) denotes the approprate blateral gross trade flow. REFL s value added of one of the two trade partners that s reflected back va thrd countres and eventually consumed n the country of producton,.e. v..f., where {1, 2}. FVA tp s foregn value added consumed by one of the two tradng partners,.e. k vk..f., where {1, 2} and k {3} n the three country case. DVA 3rd s value added of one of the two tradng partners ultmately absorbed n a thrd country,.e. k v..f.k, where {1, 2} and k {3} n the three country case. FVA 3rd s foregn value added ultmately absorbed n a a thrd country,.e. k l vk..f.l, where k {3} and l {3} n the three country case. Please refer to the appendx A.3 for the generalsaton of the source-based decomposton to the N-country case. Note that n the results secton we group DBC and REFL together as a resdual term, and we combne DVA 3rd and FVA 3rd to capture any mbalance between the two drect tradng partners that s due to demand n thrd countres. Snce we are nterested n the dfferences between gross and value added trade (7) ECB Workng Paper 1695, July

17 balances, we also ntroduce the addtonal term CORR (for value added correcton). CORR denotes value added produced by one of the two trade partners that s absorbed n fnal demand by the respectve trade partner, whch s part of the value added trade balance, but does not fgure n the balance n gross terms: CORR = NVAX* 12 NVAX 12 (8) Ths term reflects value added that s part of other blateral gross trade balances (of the exportng country n the source-based approach and of the mportng country n the snk-based approach). 2.6 Examples Ths secton provdes some stylsed examples of the dfferent categores n the decomposton of blateral gross trade balances and the value added correcton factor, CORR, descrbed n the prevous secton n order to help buld ntuton. Frst, consder the three country example already referred to n the ntroducton (Fgure 1), n whch country 1 shps domestc value added worth 1 USD embedded n fnal goods to country 2 and domestc value added worth 1 USD n ntermedate goods to country 3. Country 3 then adds 3 USD of domestc value added and shps fnal goods worth 4 USD (contanng 1 USD of value added of country 1 and and 3 USD of country 3) to country 2 for fnal consumpton. In ths case, the blateral gross trade balances between the countres are NX 12 = 1, NX 13 = 1 and NX 32 = 4. The value added balances dffer from the gross trade balances due to ntermedates trade: NVAX 12 = 2, NVAX 13 = 0 and NVAX 32 = 3. Our decomposton framework allows the allocaton of blateral value added trade to gross trade flows. Consder the value added exports of country 1, whch produces a total of 2 USD of value added that are ultmately absorbed n fnal demand n country 2. To whch blateral gross trade flow n ths three country world should the value added exports of country 1 be assgned? The answer dffers n the source-based and the snk-based approach. In the source-based approach, value added trade s assgned to the very frst trade flow n whch t leaves the country of producton (Fgure 2a). In our example, domestc value added of country 1 worth 1 USD leaves country 1 for the frst tme n ntermedate goods exports to country 3, and 1 USD of value added exports s accordngly assgned to the gross trade balance between country 1 and 3, NX 13. Note that we do so even though the value added wll eventually be absorbed n fnal demand n country 2 (and hence s part of the value added exports of country 1 to country 2, VAX 12, and also the value added trade balance between country 1 and country 2, NVAX 12 ). Smlarly, domestc value added of country 1 worth 1 USD leaves country 1 for the frst tme embedded n fnal goods exports to country 2, and 1 USD of value added exports s accordngly assgned to the gross trade balance between country 1 and 2, NX 12. Note that ths porton of value added of country 1 s also consumed by country 2, and therefore t s part of the value added exports of country 1 to country 2, VAX 12, and the ther value added trade balance, NVAX 12. Snce ths fracton of value added of country 1 s part of both the value added and the gross trade balance between country 1 and 2, t represents the ntersecton between the two concepts and accordngly we label t NVAX* 12. As mentoned above not all of the value added trade balance between country 1 and country 2 (NVAX 12 = 2) s contaned n ther respectve gross trade balance (NVAX* 12 = 1). 1 USD was exported n ntermedates to country 3 for further processng ECB Workng Paper 1695, July

18 Fgure 2: Illustraton of the dfference between source-based and snk-based allocatons of value added. a) Source-based approach. The source-based approach assgns the value added exports of country 1 to country 2 to the gross trade flow, n whch the value added leaves the country of producton, country 1, for the frst tme. In ths case, 1 USD of value added s assgned to the gross trade flow between country 1 and 2, and 1 USD of value added s assgned to the gross trade flow between country 1 and 3. b) Snkbased approach. The snk-based approach assgns the value added mports of country 2 from country 1 to the gross trade flow, n whch the value added last enters the country of consumpton, country 2. In ths case, 1 USD of value added s assgned to the gross trade flow between country 1 and 2, and 1 USD of value added s assgned to the gross trade flow between country 2 and 3. before fnal absorpton n country 2. In order to keep track of ths part of the value added balance that enters other blateral gross trade balances, we compute the dfference between the ntersecton of value added and gross trade balance, and the value added balance tself, whch we label CORR for value added correcton factor (CORR=NVAX* 12 - NVAX 12 = 1 2 = 1). In the snk-based approach, value added trade s assgned to the very last trade flow n whch t enters the country of fnal absorpton (Fgure 2b). In our example, domestc value added of country 1 worth 1 USD enters country 2 n fnal goods, that are mmedately consumed, from country 3, and 1 USD of the value added mports of country 3 from country 1 s accordngly assgned to the gross trade balance between country 2 and 3, NX 23. Note that we do so even though the value added does not orgnate n country 3 (and s part of the value added mports of country 2 from country 1, VAM 21, and also the value added trade balance between country 1 and country 2, NVAX 12 ). Smlarly, domestc value added of country 1 worth 1 USD enters country 2 n fnal goods, whch are mmedately absorbed n fnal demand, from country 1. Note that ths porton of value added of country 1 s assgned to the same gross trade balance n both the source-based and n the snk-based approach. Therefore, as n the source-based approach, ths fracton of value added of country 1 s part of both the value added and the gross trade balance between country 1 and 2, t represents the ntersecton between the two concepts and accordngly we label t NVAX* 12. Agan, the value added trade balance between country 1 and country 2 (NVAX 12 = 2) s not a subset of ther respectve gross trade balance (NVAX* 12 = 1). 1 USD of value added of country 1 s assgned to the gross trade balance between country 2 and 3. As before, we compute the dfference between the ntersecton of value added and gross trade balance, and the value added balance tself (CORR=NVAX* 12 - NVAX 12 = 1 2 = 1). Although n ths smple example the correcton factor turns out to be the same n both the source-based and n the snk-based approach, ths s not true n general. The followng examples are ndependent of whether the source- or the snk-based ECB Workng Paper 1695, July

19 approach s chosen (wth the excepton of the example for the double countng term). Foregn value added consumed by the respectve tradng partner (FVA tp ): Country 3 has a gross trade surplus of 4 USD wth country 2. 3 USD of the gross trade balance s value added of country 3 that s absorbed n country 2,.e. NVAX 32 (Fgure 1). The remander of 1 USD of the gross trade balance s value added of country 1 that country 3 mported n ntermedates, whch s ultmately absorbed by the drect tradng partner, country 2. Ths counts as foregn value added absorbed by one of the two tradng partners,.e. FVA tp. In summary, the gross trade balance between country 3 and 2 can be decomposed nto NX 32 = NVAX 32 + FVA tp = = 4. Domestc value added ultmately absorbed n fnal demand of thrd countres (DVA 3rd ): Country 1 has a gross trade surplus of 1 USD wth country 3 (Fgure 1). In value added terms, however, trade between the two countres s completely balanced snce nether country consumes any value added of the other. The dfference between gross and value added balances arses because country 1 shps 1 USD worth of ntermedate goods to country 3, whch are ultmately deemed for consumpton n a thrd country (n ths case country 2). Snce the value added n ntermedate goods orgnates n one of the two tradng partners, t s labeled domestc value added ultmately absorbed n fnal demand n a thrd country. In summary, NX 13 = DVA 3rd = 1. Foregn value added ultmately absorbed n fnal demand of thrd countres (FVA 3rd ): For ths category an example wth a longer producton chan s necessary. Consder a world wth four countres formng a sequental producton chan (Fgure 3a), n whch country 1 shps ntermedate goods of 1 USD to country 2. Country 2 then adds 2 USD of domestc value added to those ntermedate goods and exports them to country 3 for further processng. Country 3 n turn adds another 3 USD of domestc value added and shps everythng of as fnal goods worth 6 USD (contanng 1 USD of value added of country 1, 2 USD of value added of country 2 and 3 USD of value added of country 3) to country 4 for fnal consumpton. Country 2 has a gross trade surplus of 3 USD wth country 3, but balanced trade n value added terms snce nether country consumes any value added of the other. The dfference between gross and value added balances arses, on the one hand, due to domestc value added of country 2 worth 2 USD that s shpped off to country 3 for fnal absorpton n country 4 (DVA 3rd, see (d) above). In addton, country 2 exports 1 USD of foregn value added (of country 1) to country 3 that s also deemed for fnal absorpton n country 4 and therefore should be adequately labeled FVA 3rd. In summary, NX 23 = DVA 3rd + FVA 3rd = = 3. Value added of one of the two tradng partners that s reflected back va thrd countres for consumpton n the country of orgn (REFL): In order to llustrate the reflecton term 12 consder a three country example (Fgure 3b), n whch country 1 exports 1 USD of domestc value added n ntermedates to country 2. Country 2 adds 2 USD of domestc value added and shps 3 USD worth of ntermedates to country 3. Country 3 then adds another 3 USD of value added and shps 6 USD of fnal goods (contanng 1 USD of value added of country 1, 2 USD of value added of country 2 and 3 USD of value added of country 3) to country 1. Country 1 has a gross trade surplus of 1 USD wth country 2, but balanced trade n value added terms. The dfference arses from domestc value added worth 1 USD that s exported to country 2, whch re-enters country 1 for fnal consumpton after processng n country 3. Essentally, 12 For ease of exposton only the second term of the reflecton expresson n equaton (7) s consdered. ECB Workng Paper 1695, July

20 Fgure 3: Illustraton of dfferent categores n the decomposton of blateral gross trade balances. a) Example for FVA 3rd. Country 1 shps ntermedate goods of 1 USD to country 2. Country 2 then adds 2 USD of domestc value added to those ntermedate goods and exports them to country 3 for further processng. Country 3 n turn adds another 3 USD of domestc value added and shps everythng of as fnal goods worth 6 USD (contanng 1 USD of value added of country 1, 2 USD of value added of country 2 and 3 USD of value added of country 3) to country 4 for fnal consumpton. b) Example for the reflecton term, REFL. Country 1 exports 1 USD of domestc value added n ntermedates to country 2. Country 2 adds 2 USD of domestc value added and shps 3 USD worth of ntermedates to country 3. Country 3 then adds another 3 USD of value added and shps 6 USD of fnal goods (contanng 1 USD of value added of country 1, 2 USD of value added of country 2 and 3 USD of value added of country 3) to country 1. c) Example for the double countng term, DBC. As b) but nstead of country 3 exportng the fnal good worth 6 USD to country 1, suppose that country 3 exports an ntermedate good worth 6 USD (contanng 1 USD of value added of country 1, 2 USD of value added of country 2 and 3 USD of value added of country 3) to country 1 for further processng. Country 1 then adds 3 USD of value added and shps a fnal good worth 9 USD to country 2 for fnal consumpton (contanng a total of 4 USD of value added of country 1). the value added s reflected back to the country of ntal producton va a thrd country. In summary, NX 12 = REFL = 1. Value added of one of the two tradng partners that s double counted: Consder the same three country example as before wth one small modfcaton that llustrates the double countng term for the source-based approach 13 (Fgure 3c). Instead of country 3 exportng the fnal good worth 6 USD to country 1, suppose that country 3 exports an ntermedate good worth 6 USD (contanng 1 USD of value added of country 1, 2 USD of value added of country 2 and 3 USD of value added of country 3) to country 1 for further processng. Country 1 then adds 3 USD of value added and shps a fnal good worth 13 For ease of exposton only the thrd term of the double countng expresson n equaton (7) s consdered. ECB Workng Paper 1695, July

21 9 USD to country 2 for fnal consumpton (contanng a total of 4 USD of value added of country 1). The gross trade balance of country 1 wth country 2 s now equal to 10 USD (1 USD n ntermedate goods and 9 USD n fnal goods). The value added surplus, however, s only equal to 4 USD. The frst factor that accounts for the dscrepancy s foregn value added worth 5 USD (2 USD of country 2 and 3 USD of country 3) deemed for fnal consumpton by the drect tradng partner, country 2 (labeled FVA tp ). The remander, 1 USD, s domestc value added that has been counted twce once n ntermedate goods and then agan n fnal goods exports. In summary, NX 12 = NVAX 12 + FVA tp + REFL = = Decomposng blateral trade balances In the followng sectons we focus on the most mportant results usng the source-based approach whle the dfferences between the source- and the snk-based approach are presented n the appendx (see Appendx A.7). None of our man fndngs s senstve to the partcular decomposton approach employed. 14 Results are based on the World Input Output Database (WIOD) Selected results for ndvdual country pars n mllon USD (1) (2) (3) (4) (5) (6) (7) gross trade balance value added trade balance value added n gross trade balance value added correcton: (3)-(2) foregn value added (trade partner demand) domestc and foregn value added (3rd country demand) resdual NLD-DEU 43, , , 131 3, , , DEU-FRA 39, , , 461 5, 500 9, 946 5, 599 1, 092 NLD-BEL 23, 990 4, 230 3, , GBR-IRL 22, 504 3, 472 3, , , NLD-ITA 22, , , 118 2, 048 6, 864 4, n % of gross trade balance NLD-DEU DEU-FRA NLD-BEL GBR-IRL NLD-ITA Table 2: Decomposton of the fve largest blateral trade balances between EU27 countres n (Devatons from totals and 100 % are due to roundng.) Table 2 shows the fve largest gross blateral trade balances between EU27 countres n 2011 and the components derved usng the source-based decomposton framework outlned above. In general, the composton of gross trade balances s farly heterogeneous across country pars, although some frst patterns become apparent. As documented prevously, value added balances dffer markedly from 14 By defnton the only dfference that can arse are shfts between the contrbutons of the part of the value added balance that overlaps wth the blateral gross trade balance and double countng terms. In the appendx (see Appendx A.7) we show that for these two categores the quanttatve dfferences between the two approaches are relatvely mnor. 15 See ECB Workng Paper 1695, July

22 balances n gross terms. For example, whle the Netherlands reported a trade surplus of 44 bllon USD wth Germany, the value added balance between the two countres was 67% lower and stood at 14.4 bllon USD. Our decomposton framework dsentangles the two concepts and quantfes the factors that contrbute to ther dfferences. For most country pars 16 the value added contaned n the gross blateral balance (column 3) s smaller than the value added balance (column 2), whle the remander appears n the gross blateral balances of other countres (column 4). Foregn value added consumed by the respectve tradng partner makes up a substantal share of the dfference between gross and value added concepts for most of the trade balances consdered. Another mportant factor that emerges s demand n countres other than the two trade partners, whch, for example, makes up a szable porton of 28% of the gross blateral trade balance between the Netherlands and Germany. The resdual, whch s composed of trade that s double counted and domestc value added that s reflected back va thrd countres for domestc consumpton, does not play a sgnfcant role n any of the fve blateral trade balances under consderaton. NLD-DEU DEU-FRA top 5 demand countres mllon USD % of 3rd country demand % of gross trade balance top 5 demand countres mllon USD % of 3rd country demand % of gross trade balance ROW 4, ROW 3, USA 1, ESP 1, CHN 1, AUT FRA ITA AUT BEL Table 3: Thrd country demand decomposton of the NLD-DEU and DEU-FRA gross trade balance n 2011 by demand country. Gven the mportance of demand n thrd countres n explanng the dfference between value added and gross trade balances, Table 3 provdes a further breakdown of whch countres matter for the thrd country demand effect n the gross trade balance between the Netherlands and Germany as well as Germany and France. Demand n countres not further specfed n WIOD explan about 10% of both gross trade balances. Both fnal demand n the Unted States and Chna are responsble for 3% of the trade surplus of the Netherlands vs-à-vs Germany whle France and Austra each contrbute another 2%. Germany s trade surplus wth France s partally due to demand n Span (3%), Italy (2%) and Belgum (1%), whle demand n Austra actually leads to a small reducton (2%) of ts surplus. Demand n other countres not lsted n Table 3 account for the remander of the thrd country effect. A pont that s worth hghlghtng s that blateral value added balances do not necessarly have to be () smaller, but can also be () larger n absolute terms than gross trade balances. Furthermore, the trade balance can also reverse ts sgn, whch means that a country could go, for example, from () a trade surplus n gross terms to a trade defct n value added terms, and (v) n some rarer cases ths value added trade defct could also be larger n absolute terms than ts gross trade surplus. Whch partcular 16 Note that the value added n the gross trade balance between the UK and Ireland s greater than the value added trade balance. Whle the value added n gross exports to a partcular country s by defnton equal to or smaller than the value added exports to that country, t s evdent that the same does not hold for a blateral trade balance, whch s the dfference between the blateral exports of the two countres. ECB Workng Paper 1695, July

23 n mllon USD (1) (2) (3) (4) (5) (6) (7) gross trade balance value added trade balance value added n gross trade balance value added correcton: (3)-(2) foregn value added (trade partner demand) domestc and foregn value added (3rd country demand) resdual () NLD-DEU 43, , , 131 3, , , () NLD-GBR 6, , 771 8, 135 2, , , () GBR-LUX 19, , (v) SWE-DNK n % of gross trade balance () NLD-DEU () NLD-GBR () GBR-LUX (v) SWE-DNK Table 4: Decomposton of greatest dfferences between gross and value added blateral balances n (Devatons from totals and 100% are due to roundng.) case apples to a gven country par depends on the sgn and magntude of the value added trade balance and the remanng components of the decomposton. Table 4 shows the decomposton of the greatest dfferences between gross and value added blateral balances between EU27 countres n 2011 for the four dfferent cases descrbed above. 17 () The value added balance between the Netherlands and Germany shows the largest reducton relatve to the gross trade balance wthout changng ts sgn, and the factors that contrbute to the dfference were already dscussed above. () The value added trade surplus between the Netherlands and the UK s actually larger than the surplus measured n gross terms. Ths s due to consderable Dutch value added flows enterng the UK va thrd countres (column 4) and because the UK provdes more ntermedates to the Netherlands destned for consumpton n thrd countres (column 6), whch s not offset by the large foregn value added surplus of the Netherlands wth the UK (column 5). () The UK has a large trade surplus wth Luxembourg n gross terms, yet a small trade defct n value added terms. Ths s manly due to demand n countres other than the UK and Luxembourg (column 6),.e. because the UK provdes a large volume of domestc and foregn ntermedates to Luxembourg that are eventually consumed n other countres. (v) Fnally, the Swedsh value added balance wth Denmark changes ts sgn and s larger n absolute terms than ts gross trade balance. In ths case, a combnaton of foregn value added (column 5) and demand n thrd countres (column 6) explans the dfference. 3.2 Decomposton of ntra-eu27 trade mbalances Although these country-specfc results hghlght the mportance of the varous factors drvng the dfferences between gross and value added trade balances, we am at a broader vew of these patterns across EU27 countres (the results for EMU17 countres are presented n Appendx A.6). In gross terms ntra-eu27 trade mbalances ncreased substantally between 1995 and 2008 (Fgure 4a) as measured by 17 () value added balance smaller n absolute terms than and same sgn as gross trade balance; () value added balance larger n absolute terms than and same sgn as gross trade balance; () value added balance smaller n absolute terms than and dfferent sgn as gross trade balance; (v) value added balance larger n absolute terms than and dfferent sgn as gross trade balance. Note that for () and () the trade mbalance n gross terms s exacerbated,.e. appears larger than t actually s, whle for () and (v) t s attenuated,.e. appears smaller than t actually s. ECB Workng Paper 1695, July

24 a 6 5 SD ntra EU27 blateral trade balances gross value added b Varance decomposton [bllon USD] [%] value added correcton value added n gross trade balance resdual foregn value added 3rd country demand Fgure 4: Development of ntra-eu27 blateral trade balances and ther components. a) Standard devaton of ntra-eu27 blateral trade balances n gross and value added terms. b) Varance decomposton of ntra-eu27 blateral gross trade balances. the standard devaton of the blateral trade balances between all EU27 countres 18. The great trade collapse led to a substantal reducton n the mbalance measure n 2009, whle blateral mbalances have rebounded snce and almost reached ther pre-crss level n A smlar trend s observed when consderng mbalances n value added terms. However, n the past decade there has been a growng dvergence between the measure n gross and value added terms wth the ncrease n the latter beng much weaker. We apply a varance decomposton of ntra-eu blateral gross trade balances n order to assess the mportance of ndvdual components of the trade balance and to account for the dvergent development of gross and value added balances over tme. 19 Fgure 4b shows that ntra-eu gross trade balances have become less representatve of value added trade balances over tme. In 1995 the trade balance n value added terms (value added n gross trade balance + value added correcton) accounted for 69% of the gross trade balance, whle n 2011 ts share was down to only 49%. Ths trend was n partcular due to a rsng mportance of demand n thrd countres, whch ncreased from 3% n 1995 to 25% n Foregn value added drectly consumed by one of the two tradng partners determned the major part of the dfference between gross and value added concepts, although ts mportance has remaned relatvely constant accountng for an average of 32% of the varance n the perod under consderaton. Smlarly, the part of the value added trade balance not ncluded n the gross trade balance (value added correcton) has not changed apprecably snce 1995 and on average was equvalent to about 9% of the gross trade balance. The overall conclusons reman unchanged when consderng the sample of euro area countres, 18 A total of = 702 blateral trade balances or 351 country pars were consdered,.e. two trade balances - one defct and one surplus - for each par of countres. 19 The overall varance of gross trade balances s decomposed nto var( x ) = var(x ) + cov(x, x j ) j where x refers to the -th component that consttutes the trade balance. The contrbuton of component x s then computed as φ(x ) = var(x ) + j cov(x, x j ) var( x ).e. the contrbuton of the covarance term of x and x j s equally splt between components and j. ECB Workng Paper 1695, July

25 .e. EMU17 nstead of EU27 countres (see Appendx A.6). a Varance decomposton 3rd country demand (1995) v A f trade partner demand b Varance decomposton 3rd country demand varance 0.5 x covarance trade partner demand varance [%] 10 [%] Fgure 5: Accountng for changes n the thrd country demand effect. a) Structural decomposton analyss of ntra-eu27 blateral gross trade balances decomposng the shft n the thrd country demand effect relatve to the reference year 1995 nto changes of fnal demand ( f), nternatonal producton sharng ( A) and value added content ( v). b) Varance decomposton of ntra-eu27 blateral gross trade balances nto varance and covarance components of thrd country and trade partner demand. (Whte lne - overall thrd country demand contrbuton.) To shed lght on the drvng forces behnd the ncrease n the thrd country demand effect over tme two addtonal analyses are performed. Frst, we used a structural decomposton analyss (Detzenbacher and Los, 1998; Mller and Blar, 2009) 20 of the thrd country demand effect n order to gan further nsghts nto what determned ts change over tme. The structural decomposton analyss provdes a breakdown of the shft n the thrd country demand effect nto changes of fnal demand ( f), nternatonal producton sharng ( a and l) and value added content ( v). Fgure 5a ndcates that relatve to the reference year 1995 ntensfed nternatonal producton sharng contrbuted roughly two thrds (+15.5pp) to the larger promnence of the thrd country demand effect, whle changes n fnal demand were responsble for most of the remander (+9pp). 21 The sectoral value added content of exports - whch, for example, s reduced when frms outsource the generaton of value added to other sectors - had a neglgble mpact (-0.5pp). Second, we splt the gross trade balance nto trade partner and thrd country demand shares and 20 Structural decomposton analyss provdes an addtve decomposton of a matrx product y of n-terms nto contrbutons of ts ndvdual factors x y = 1 2 ( x 1)[(x x 0 n) + (x x 1 n)] [x0 1 ( x 2)(x x1 n ) + x1 1 ( x 2)(x x0 n )] [(x x0 n 2 )( x n 1)x 1 n + (x x1 n 2 )( x n 1)x 0 n ] [(x x 0 n 1) + (x x 1 n 1)]( x n) where superscrpts ndcate data for dfferent years (t = 0, 1). 21 Note that the changng contrbuton of 3rd country demand n 1995 s due to two effects. Frst, whle the varance of the thrd country demand effect n 1995 remaned constant over tme, the overall varance of ntra-eu blateral balances ncreased and hence one would expect the former s relatve contrbuton to declne. Second, the covarance terms between 3rd country demand n 1995 and all the other components does change over tme. Ths generates a second source of varaton n 3rd country demand n 1995, snce half of the covarance terms are assgned to thrd country demand effect n ECB Workng Paper 1695, July

26 repeated the varance decomposton exercse from before consderng both the varance and covarance terms that contrbute to the overall magntude of the thrd country demand effect. Fgure 5b suggests that the rsng mportance of demand n thrd countres for ntra-eu blateral balances was due to both an ncrease n the magntude - the varance - of the thrd country demand effect (from 11.1% n 1995 to 20.7% n 2011) and a stronger algnment - a postve covarance - between the thrd country demand effect and the remander of the trade balance (from -7.7% n 1995 to 4.6% n 2011). The ncrease n the covarance term means that countres runnng a classc trade defct (.e. mportng more from ther trade partner than they are exportng to them) were also more lkely to move relatvely more downstream n nternatonal producton chans (.e. mportng more ntermedates from ther trade partners than they were exportng to them n order to satsfy fnal demand n thrd countres). a 30 Varance decomposton b 10 Change between 1995 and [%] [%] RoW BRA,MEX USA Chna IDN,IND,JPN,KOR,TWN Rest EU EMU trade partner Fgure 6: Contrbutons of ndvdual countres to ntra-european mbalances. a) Varance decomposton of ntra-eu27 gross trade balances between 1995 and 2011 by country of fnal demand. b) Dfference of ndvdual country and regonal contrbutons between 2011 and (Whte lne - overall thrd country demand contrbuton.) To further characterse the thrd country demand effect we consder an addtonal varance decomposton whch dentfes the contrbutons of ndvdual countres to ntra-european mbalances. Fgure 6a provdes a breakdown of ntra-eu27 blateral trade balances by demand for both domestc and foregn value added n dfferent countres and regons. EU27 and n partcular EMU countres other than the tradng partners were on average responsble for 5% of blateral mbalances. The US wth 3% was the sngle most mportant country n 2011, whle Chna accounted for 1% of the varance. Demand n Indonesa, Inda, Japan, Korea and Tawan together, as well as Brazl and Mexco combned contrbuted about 1% each. The remander of 13% was due to demand n the rest of the world. The large dsperson of contrbutons across countres shows that - whle the cumulatve thrd country demand effect was a non-neglgble 25% - any sngle country had only a relatvely mnor mpact on the average blateral trade balance n the EU. Fgure 6b shows that partcularly demand n other EU countres, the US and the rest of the world had a larger mpact on ntra-eu mbalances n 2011 than n 1995, whereas the sgnfcance of drect trade partners declned sharply. Demand n other countres only margnally ncreased n mportance. It s worth hghlghtng that due to the changes that occurred n the past decade about ECB Workng Paper 1695, July

27 one ffth of ntra-eu27 trade balances n 2011 was due to demand n non-eu countres. Ths suggests that ntra-european trade mbalances were overstated whle those wth countres outsde the European Unon were slghtly underestmated. Indeed, the value added trade balance vs-á-vs the European Unon as a whole was smaller (and therefore the one wth non-european countres larger) than the gross trade balance for 21 of the 27 countres. A smlar result holds for the euro area for whch the value added trade balance of ndvdual countres wth the EMU aggregate was smaller than the gross trade balance for 15 out of 17 countres. Ths fndng makes t undesrable to assess ntra-eu (ntra-emu) mbalances n terms of gross trade flows snce a szeable share of these are n fact trade mbalances wth countres outsde of the European Unon (euro area) and they wll by defnton be unaffected by adjustment of domestc demand wthn the European Unon (euro area). 4 Concludng remarks The ntensfcaton of nternatonal producton sharng has been a defnng feature of the nternatonal economy n the recent decade. The avalablty of global nput-output tables (Detzenbacher et al., 2013) has sparked a growng lterature on global value chans that has ncreasngly allowed to frame trade n value added terms (Foster-McGregor and Stehrer, 2013; Tmmer et al., 2013; Johnson and Noguera, 2012). Elucdatng the relaton between the gross and value added concepts, and partcularly what accounts for ther dfferences, s a crucal step for nterpretng and fully comprehendng value added measures of trade. The prevous lterature has often hghlghted the numercal dfferences between gross and value added flows, but n the absence of a framework that relates the two concepts has left unexplaned what consttutes ther dspartes. 22 Ths paper contrbutes to ths lterature by provdng a novel decomposton of blateral trade balances that accounts for the dfferences between gross and value added concepts. A caveat whch turns out to be nherent n the subject matter s that the queston regardng the relaton between value added and gross trade flows s theoretcally ll-defned, and that the answer necessarly has to be a matter of what we defne value added flows to be. A frst conceptual contrbuton s that we are, to the best of our knowledge, the frst to descrbe ths problem and to dscuss the two most parsmonous solutons to t, whch determne the ntersecton between value added and gross trade flows at the blateral level. A second conceptual contrbuton s that we dentfy a range of categorcally dfferent components of value added that consttute the dfference between blateral value added and gross trade balances, whch are ndependent of the methodologcal choce above. We provde a novel dstncton between (foregn) value added that s due to demand of the drect tradng partner, and (domestc and foregn) value added that s due to demand n thrd countres. Whle both are ultmately the results of trade n ntermedates, the dfference between these two categores proves to be mportant from a polcy perspectve as demand n thrd countres s by defnton unaffected by domestc demand n the two tradng partners, whch s often one of the man targets for current account adjustments. In an applcaton of our decomposton framework to ntra-european trade mbalances we show that gross trade balances have become ncreas- 22 Wth the excepton of (Koopman et al., 2014), who decompose gross exports nto value added exports and double counted terms at the aggregate level. ECB Workng Paper 1695, July

28 ngly less representatve of value added balances. We demonstrate that the major determnant behnd ths ncreasng dscrepancy s the rsng mportance of the part of the trade balance whch s due to demand n countres other than the two drect tradng partners. We use a structural decomposton analyss that allows us to quantfy the relatve contrbutons made by changes n nternatonal producton sharng and fnal demand respectvely, and we fnd that changes n the European dvson of labour account for roughly two thrds of the ncrease. Focusng on the countres behnd the mbalances, we fnd that a szeable share of about one ffth of the varance of ntra-european mbalances n 2011 was due to demand n countres outsde the European Unon. Ths means that the problem of ntra-european mbalances has been overstated n the past, whle trade mbalances wth countres outsde of Europe were larger than nferred from gross trade balances. A smlar result holds for the euro area. Partcularly n a currency unon, t s mportant to establsh wth whom trade mbalances exst snce the burden of adjustment may dffer between trade defcts vs-á-vs member countres and thrd partes (d Mauro and Pappada, 2014). Even though ther lmtatons are wdely acknowledged gross blateral trade balances stll fgure wdely n the economc lterature and polcy debates (Davs and Wensten, 2002; Bahman-Oskooee and Brooks, 1999). Despte some general lmtatons of nput-output models, our paper provdes a strong case for consderng value added nstead of gross blateral trade balances snce a szable porton of gross blateral trade balances s no longer under the nfluence of the drect tradng partners themselves. ECB Workng Paper 1695, July

29 References Antras, P., Chor, D., Fally, T., Hllberry, R., May Measurng the Upstreamness of Producton and Trade Flows. Amercan Economc Revew 102 (3), Bahman-Oskooee, M., Brooks, T., March Blateral J-Curve between US and her Tradng Partners. Revew of World Economcs 135 (1), Bayoum, T., Sato, M., Turunen, J., May Measurng Compettveness: Trade n Goods or Tasks? IMF Workng Papers 13/100, Internatonal Monetary Fund. Bems, R., Johnson, R. C., October Value-Added Exchange Rates. Workng Paper 18498, Natonal Bureau of Economc Research. Berger, H., Ntsch, V., Oct The Euro s Effect on Trade Imbalances. IMF Workng Papers 10/226, Internatonal Monetary Fund. Daudn, G., Rfflart, C., Schwesguth, D., Who Produces for Whom n the World Economy? Canadan Journal of Economcs 44 (4), Davs, D. R., Wensten, D. E., May The Mystery of the Excess Trade (Balances). Amercan Economc Revew 92 (2), d Mauro, F., Pappada, F., Euro Area External Imbalances and the Burden of Adjustment. Journal of Internatonal Money and Fnance. Detzenbacher, E., Los, B., Structural Decomposton Technques: Sense and Senstvty. Economc Systems Research 10 (4), Detzenbacher, E., Los, B., Stehrer, R., Tmmer, M., de Vres, G., The Constructon of World Input-Output Tables n the WIOD Project. Economc Systems Research 25 (1), European Commsson, May Survellance of Intra-Euro-Area Compettveness and Imbalances. European Economy 1, Drectorate General Economc and Monetary Affars (DG ECFIN), European Commsson. Foster-McGregor, N., Stehrer, R., Value Added Content of Trade: A Comprehensve Approach. Economcs Letters 120 (2), Johnson, R. C., Noguera, G., Accountng for Intermedates: Producton Sharng and Trade n Value Added. Journal of Internatonal Economcs 86 (2), Koopman, R., Wang, Z., We, S.-J., Tracng Value-Added and Double Countng n Gross Exports. Amercan Economc Revew 104 (2), Mller, R., Blar, P., Input-Output Analyss: Foundatons and Extensons. Cambrdge Unversty Press. OECD (Ed.), Interconnected Economes: Beneftng from Global Value Chans. OECD Publshng. ECB Workng Paper 1695, July

30 Puzzello, L., A Proportonalty Assumpton and Measurement Bases n the Factor Content of Trade. Journal of Internatonal Economcs 87 (1), Stone, R., The Dsaggregaton of the Household Sector n the Natonal Accounts. In: Pyatt, G., Round, J. I. (Eds.), Socal Accountng Matrces. A Bass for Plannng. The World Bank, Washngton, DC, pp Tmmer, M. P., Los, B., Stehrer, R., de Vres, G. J., Fragmentaton, Incomes and Jobs: An Analyss of European Compettveness. Economc Polcy 28 (76), ECB Workng Paper 1695, July

31 A Appendx A.1 Leontef nverse In the man text t was argued that a coeffcent of the Leontef nverse descrbes all possble ways that value added from a country r travels embedded n ntermedate goods through nternatonal producton networks to country s. In ths secton, we llustrate ths statement mathematcally. Denote the global nput-output matrx by A and the matrx wth the domestc coeffcents by Ã. For the three-country case: a 11 a 12 a 13 a A = a 21 a 22 a 23 Ã = 0 a 22 0 a 31 a 32 a a 33 The Leontef nverses of these two matrces can be wrtten as a geometrc seres,.e. L = I + A + A 2 + A 3 + = (I A) 1 and L = I + Ã + Ã 2 + Ã 3 + = (I Ã) 1 where a 11 a 12 a 13 a 11 a 12 a 13 a1 a 1 a1 a 2 a1 a 3 A 2 = a 21 a 22 a 23 a 21 a 22 a 23 = a2 a 1 a2 a 2 a2 a 3 a 31 a 32 a 33 a 31 a 32 a 33 a3 a 1 a3 a 2 a3 a 3 and A 3 = = a1 a 1 a1 a 2 a1 a 3 a 11 a 12 a 13 a2 a 1 a2 a 2 a2 a 3 a 21 a 22 a 23 a3 a 1 a3 a 2 a3 a 3 a 31 a 32 a 33 j ( a1 a j )a j1 j ( a1 a j )a j2 j ( a1 a j )a j3 j ( a2 a j )a j1 j ( a2 a j )a j2 j ( a2 a j )a j3 j ( a3 a j )a j1 j ( a3 a j )a j2 j ( a3 a j )a j3 A typcal element of the matrx A 3 s a (3)kl = 3 ( 2 a k2 a 23 )a 3l More generally for the matrx A n a typcal element s a (n)kl = n ( ( a k2 a ) ) 23 a a n 1n a nl n ECB Workng Paper 1695, July

32 Therefore, a typcal element of the Leontef nverse can be wrtten usng the expressons derved from the geometrc seres above n l (n)kl = δ kl + a kl + m=2 a (m)kl wth δ kl = 1 for k = l and δ kl = 0 for k l (Kronecker delta). Thus, the entres of the Leontef nverse descrbe all possble ways to go from country k to country l. Note that naturally ths also holds true for the dagonal elements n the matrx wth the domestc coeffcents Ã. For calculatng the part of the value added whch does not leave a country at all one therefore has to take account only of the dagonal elements of the à matrx Thus n matrx notaton lkk = (a kk ) m = (1 a kk ) 1 m=0 L = (I Ã) 1 In the text the Leontef s therefore splt nto L = L + (L L) or l 11 l 12 l 13 l l 11 l 11 l 12 l 13 L = l 21 l 22 l 23 = 0 l l 21 l 22 l 22 l 23 l 31 l 32 l l33 l 31 l 32 l 33 l 33 It s mportant to note that (l kk l kk ) 0 (or a non-negatve matrx n the mult-sectoral case) whch holds by defnton (see also Stone (1985)). ECB Workng Paper 1695, July

33 A.2 Decomposton of blateral gross trade balances (snk-based approach) As mentoned n the text, the correspondng decomposton for the snk-based approach s gven by NX 12 = e 12 e 21 = v 1 l 11 f 12 + v 1 l 11 a 12 (1 a 22 ) 1 f 22 v 2 l 22 f 21 v 2 l 22 a 21 (1 a 11 ) 1 f 11 NVAX* 12 (e 12 ) NVAX* 12 (e 21 ) + v 1 l 11 a 12 (l 22 (1 a 22 ) 1 )f 22 + v 1 l 11 a 12 l 2 f 2 + v 2 l 21 a 12 l 2 f 1 2 DBC (e 12 ) v 2 l 22 a 21 (l 11 (1 a 11 ) 1 )f 11 + v 2 l 22 a 21 l 1 f 1 v 1 l 12 a 21 1 DBC (e 21 ) + v 2 l 21 f 12 + v 1 l 11 a 12 l 2 f 1 + v 2 l 21 a 12 REFL (e 12 ) DBC (e 12 ) l 1 f 2 DBC (e 21 ) l 2 f 2 v 1 l 12 f 21 v 1 l 12 a 21 + v 3 l 31 f 12 + v 3 l 31 a 12 l 2 (f 1 + f 2 ) v 3 l 32 f 21 v 3 l 32 a 21 FVA tp (e 12 ) + v 1 l 11 a 12 l 2 f 3 + v 2 l 21 a 12 DVA 3rd (e 12 ) + v 3 l 31 a 12 l 2 f 3 v 3 l 32 a 21 FVA 3rd (e 12 ) l 1 f 1 v 2 l 22 a 21 l 1 f 2 l 1 (f 1 + f 2 ) l 2 f 3 v 2 l 22 a 21 l 1 f 3 FVA 3rd (e 21 ) FVA tp (e 21 ) l 1 f 3 v 1 l 12 a 21 REFL (e 21 ) l 1 f 3 DVA 3rd (e 21 ) where ndvdual terms were labeled as n the source-based approach. Note that NVAX* 12 and DBC are the only terms that are dfferent from those n the source-based approach. ECB Workng Paper 1695, July

34 A.3 Generalsaton to N-country case The generalsaton of the source- and snk-based approach to the N-country case s acheved by summng the correspondng terms over all trade partners. A.3.1 Source-based approach NX j = e j e j N = v (I a ) 1 f j + v (I a ) 1 a j l jk f kj v j (I a jj ) 1 f j v j (I a jj ) 1 a j k NVAX* j (e j ) NVAX* j (e j ) N k l k f k N N + v (l (I a ) 1 )f j + v (l (I a ) 1 )a j l jk f kj + v j l j a j l jk f k DBC (e j ) DBC (e j ) v j (l jj (I a jj ) 1 )f j v j (l jj (I a jj ) 1 )a j N + v j l j f j + v l a j l jk f k + v j l j a j k k N k k l k f k v l j a j DBC (e j ) DBC (e j ) N k l jk f kj v l j f j v l j a j N k l k f kj REFL (e j ) REFL (e j ) N k l k f k v j l jj a j N k l k f jk N [ N + v k l k f j + v k l k a j l jm (f m + f mj ) ] N [ N v k l kj f j v k l kj a j l m (f m + f mj ) ] k,j + [ v l a j + v j l j a j] N m k,j FVA tp (e j ) FVA tp (e j ) k l jk N m,j f km N + v k l k a j k,j [ v j l jj a j v l j a j] N DVA 3rd (e j ) DVA 3rd (e j ) N N l jm f mn m n,j FVA 3rd (e j ) FVA 3rd (e j ) k l k m N f km m,j N v k l kj a j k,j N N l m f mn m n,j ECB Workng Paper 1695, July

35 A.3.2 Snk-based approach NX j = e j e j = v l f j + v l a j (1 a jj ) 1 f jj v j l jj f j v j l jj a j (1 a ) 1 f NVAX* j (e j ) NVAX* j (e j ) N N + v l a j (l jj (1 a jj ) 1 )f jj + v l a j l jk f kj + v j l j a j l jk f k k j DBC (e j ) v j l jj a j (l (1 a ) 1 )f v j l jj a j N k DBC (e j ) N + v j l j f j + v l a j l jk f k + v j l j a j + k N REFL (e j ) N [ N v k l k f j + v k l k a j l jm (f m + f mj ) ] k,j m FVA tp (e j ) + [ v l a j + v j l j a j] N + k l jk N m,j f km N v k l k a j k,j DVA 3rd (e j ) N l jm m N f mn n,j FVA 3rd (e j ) k l k f k v l j a j k DBC (e j ) N k l k f kj DBC (e j ) l jk f kj v l j f j v l j a j N k l k f k v j l jj a j N k l k f jk REFL (e j ) N [ N v k l kj f j v k l kj a j l m (f m + f mj ) ] k,j [ v j l jj a j v l j a j] N k l k m FVA tp (e j ) N m,j f km N v k l kj a j k,j N l m m DVA 3rd (e j ) N f mn n,j FVA 3rd (e j ) ECB Workng Paper 1695, July

36 A.4 Matrx nverse If A s an n-by-n nvertble matrx, there exsts an n-by-n matrx B such that AB = BA = I n (9) and the matrx B s called the matrx nverse of A, denoted by A 1. Ths equaton s sometmes referred to as the property of nverse matrces. From the defnton of the matrx nverse, several denttes can be derved that wll be useful for the proofs n the next secton. Note that, techncally speakng, the source- and snk based approach dffer wth respect to the correspondng denttes whch are appled. A.4.1 Useful denttes (source-based approach) I a 11 a 12 a 13 l 11 l 12 l (I A)(I A) 1 = (I A)L = I = a 21 I a 22 a 23 l 21 l 22 l 23 = (10) a 31 a 32 I a 33 l 31 l 32 l For the source-based approach three of the resultng nne denttes wll be relevant: (1 a 11 )l 11 a 12 l 21 a 13 l 31 = 1 (1 a 11 )l 12 a 12 l 22 a 13 l 32 = 0 (1 a 11 )l 13 a 12 l 23 a 13 l 33 = 0 or solvng for the entry of the Leontef nverse related to output of country 1: l 11 = (1 a 11 ) 1 (1 + a 12 l 21 + a 13 l 31 ) (11) l 12 = (1 a 11 ) 1 (a 12 l 22 + a 13 l 32 ) (12) l 13 = (1 a 11 ) 1 (a 12 l 23 + a 13 l 33 ) (13) A.4.2 Useful denttes (snk-based approach) l 11 l 12 l 13 I a 11 a 12 a (I A) 1 (I A) = L(I A) = I = l 21 l 22 l 23 a 21 I a 22 a 23 = l 31 l 32 l 33 a 31 a 32 I a For the snk-based approach one of the resultng nne denttes wll be relevant: l 11 a 12 + l 12 (I a 22 ) l 13 a 32 = 0 or solvng for l 12 : l 12 = (l 11 a 12 + l 13 a 32 )(1 a 22 ) 1 (14) ECB Workng Paper 1695, July

37 A.5 Proofs A.5.1 Source-based approach In ths secton, we show that the sum of all VAX* 12 terms n e 12 and e 13 equals the value added exports from country 1 to 2, VAX 12. As dscussed n man text, n order to arrve at the VAX* 12 terms we substtute (1 a 11 ) 1 for l 11 n the expresson for v 1..f.2 n the blateral gross exports to country 2 V AX 12 (e 12 ) = v 1 (1 a 11 ) 1 f 12 + v 1 (1 a 11 ) 1 a 12 l 2 f 2 and country 3 In the followng, we need to show that V AX 12 (e 13 ) = v 1 (1 a 11 ) 1 a 13 l 3 f 2 V AX 12 = V AX 12 (e 12 ) + V AX 12 (e 13 ) In order to do so, l 11, l 12 and l 13 s substtuted by (11)-(13) n the expresson for VAX 12 : V AX 12 = v 1 l 11 f 12 + v 1 l 12 f 22 + v 1 l 13 f 32 = v 1 (1 a 11 ) 1 (1 + a 12 l 21 + a 13 l 31 )f 12 + v 1 (1 a 11 ) 1 (a 12 l 22 + a 13 l 32 )f 22 + v 1 (1 a 11 ) 1 (a 12 l 23 + a 13 l 33 )f 32 = v 1 (1 a 11 ) 1 f 12 + v 1 (1 a 11 ) 1 a 12 l 2 f 2 + v 1 (1 a 11 ) 1 a 13 l 3 f 2 = V AX 12 (e 12 ) + V AX 12 (e 13 ) A.5.2 Snk-based approach Here, we show that the sum of all VAX* 12 terms n e 12 and e 32 equals the value added exports from country 1 to 2, VAX 12 and hence the value added mports of country 2 from 1, VAM 21. As dscussed n the descrpton of the snk-based approach, to arrve at the VAX* 12 terms we substtute (1 a 22 ) 1 for l 22 n the expresson for v 1..f.2 n the blateral gross mports of country 2 from country 1 V AX 12 (e 12 ) = v 1 l 11 f 12 + v 1 l 11 a 12 (1 a 22 ) 1 f 22 and from country 3 V AX 12 (e 32 ) = v 1 l 13 a 32 (1 a 22 ) 1 f 22 + v 1 l 13 f 32 ECB Workng Paper 1695, July

38 In the followng, we need to show that V AX 12 = V AX 12 (e 12 ) + V AX 12 (e 32 ) In order to do so, n the expresson for VAX 12 l 12 s substtuted by (14): V AX 12 = v 1 l 11 f 12 + v 1 l 12 f 22 + v 1 l 13 f 32 = v 1 l 11 f 12 + v 1 (l 11 a 12 + l 13 a 32 )(1 a 22 ) 1 f 22 + v 1 l 13 f 32 = v 1 l 11 f 12 + v 1 l 11 a 12 (1 a 22 ) 1 f 22 + v 1 l 13 a 32 (1 a 22 ) 1 f 22 + v 1 l 13 f 32 = V AX 12 (e 12 ) + V AX 12 (e 32 ) ECB Workng Paper 1695, July

39 A.6 Euro area results All decomposton analyses presented n the man text were also performed for the sample of EMU17 countres. The results are qualtatvely very smlar for the euro area subset of EU27 countres and the man conclusons reman unchanged. a 10 SD EMU blateral trade balances gross value added b 100 Varance decomposton 8 80 [bllon USD] [%] value added correcton value added n gross trade balance resdual foregn value added 3rd country demand Fgure 7: Development of ntra-emu17 blateral trade balances and ther components. a) Standard devaton of ntra-emu17 blateral trade balances n gross and value added terms. b) Varance decomposton of ntra-emu17 blateral gross trade balances. a Varance decomposton b Varance decomposton 3rd country demand varance 0.5 x covarance trade partner demand varance [%] 5 [%] rd country demand (1995) v A f trade partner demand Fgure 8: Accountng for changes n the thrd country demand effect. a) Structural decomposton analyss of ntra-emu17 blateral gross trade balances decomposng the shft n the thrd country demand effect relatve to the reference year 1995 nto changes of fnal demand ( f), nternatonal producton sharng ( A) and value added content ( v). b) Varance decomposton of ntra-emu17 blateral gross trade balances nto varance and covarance components of thrd country and trade partner demand. (Whte lne - overall thrd country demand contrbuton.) ECB Workng Paper 1695, July

40 a 30 Varance decomposton b 10 Change between 1995 and [%] [%] RoW BRA,MEX USA Chna IDN,IND,JPN,KOR,TWN Rest EU EMU trade partner Fgure 9: Contrbutons of ndvdual countres to ntra-emu mbalances. a) Varance decomposton of ntra-emu17 gross trade balances between 1995 and 2011 by country of fnal demand. b) Dfference of ndvdual country and regonal contrbutons between 2011 and (Whte lne - overall thrd country demand contrbuton.) ECB Workng Paper 1695, July

41 A.7 Comparson snk- and source-based approach Ths secton presents a short comparson of ndvdual country and varance decomposton results for the snk- and source-based approach. By defnton, the two approaches only dffer wth regards to the contrbutons of double countng terms and the part of the value added balance that concdes wth the blateral gross trade balance. Hence, the results pertanng to foregn value added and demand n thrd countres are unaffected by ths methodologcal choce. Table 5 shows how domestc value added of the two trade partners whch s absorbed by the respectve trade partner (and hence n theory qualfes to be part of the value added balance) s splt nto beng part of the value added balance and a double countng term. In general the double countng term dffers apprecably n the two decompostons. However, n both cases the double countng term s quanttatvely relatvely small n comparson wth the value added n the gross trade balance. Table 6 shows the results of the varance decomposton of ntra-eu27 trade balances for both source- and snk-based decompostons. As before, the contrbuton of the double countng terms s dscernbly dfferent n the two approaches, but the absolute contrbuton s very small n both cases. In the source-based approach, the relatvely small contrbutons of the double countng term reflects the fact that the share of domestc value added that s re-mported for further processng n the country of producton and eventually re-exported for absorpton n fnal demand by the drect trade partner s comparatvely mnor. Smlarly, for the snk-based approach the double countng term s margnal snce the value added of the drect trade partner that s re-exported and later re-mported for absorpton n fnal demand s relatvely small n comparson wth the drect trade partner s value added that s drectly consumed. In concluson, although the two approaches are conceptually very dfferent from each other, the quanttatve dfferences are n general relatvely mnor and do not affect the conclusons drawn n the man text. source-based approach snk-based approach domestc value added absorbed by respectve trade partner value added n gross trade balance double countng value added n gross trade balance double countng n mllon USD NLD-DEU 11, , , DEU-FRA 23, , 461 1, , NLD-BEL 4, 004 3, , GBR-IRL 3, 962 3, , NLD-ITA 11, , , Table 5: Indvdual country results accordng to source- and snk-based decompostons. Domestc value added (of one of the two tradng partners) absorbed by the respectve trade partner s subdvded nto the part of the value added trade balance that concdes wth the blateral gross trade balance and a double countng term accordng to the source- and the snk-based approach. (Devatons from totals are due to roundng.) ECB Workng Paper 1695, July

42 source-based approach snk-based approach domestc value added absorbed by respectve trade partner value added n gross trade balance double countng value added n gross trade balance double countng n % Table 6: Varance decomposton of ntra-eu27 mbalances accordng to source- and snkbased decompostons. (Devatons from totals are due to roundng.) ECB Workng Paper 1695, July