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: arne.nagengast@bundesbank.de 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