Tullio Gregori Università degli Studi di Trieste, P.le Europa 1, Trieste Italy (

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1 Tullio Gregori Università degli Studi di Trieste, P.le Europa 1, Trieste Italy ( International Value Added Trade: a subsystem approah Abstrat The struture of international trade has hanged dramatially in reent deades with the emergene of supply hains that span multiple ountries. The growth of these hains is posing new hallenges to studies of ountries ompetitiveness and the analysis of international trade based on the onept of vertial integration has trigged attention from both the empirial and theoretial perspetive. A growing applied literature, that embraes the Leontief model, has produed a large body of interesting results, omplementing the standard gross flow analyses. Value Added in Trade measures value added embodied in gross trade flows, while Trade in Value Added aounts for value added of one ountry diretly and indiretly embodied in final onsumption of another ountry. Suh a task has been performed without using the devie of representing world interindustry relationships via vertially integrated setors or subsystems. Subsystems allow us to split the eonomi system into ideal self-suffiient setors, whih produe a single final ommodity with all their neessary intermediate inputs. In this paper, I fill this gap showing how this approah provides additional information that an shed light on the proess of international prodution fragmentation. Keywords: Value added in trade, Trade in value added, Vertial integrated setors, Subsystems. DAFT 1

2 1. Introdution Over the past deades, world trade has grown faster than both world output and manufaturing value added. Atually, trade as a share of global output has tripled sine the 1950s. From the steam revolution till the mid or late 1980s, globalization was mostly about falling trade osts; this was globalisation s first unbundling (Baldwin, 2013, p. 166). edution in transation osts and better international environment and institutions fostered an unpreedented globalization. Current and apital aount liberalizations failitated trade beyond arm s-length operations opening the way to large foreign diret investment in developing and new aession ountries too. However, the simple ommuniation tehnology available until the mid-1980s fored most of manufaturing proesses to be loated within the same area. Proximity was essential to oordinating and all the stages of prodution had to be inside a single fatory or industrial distrit. Most of the neessary ompetenies had to exist domestially. The digital revolution of the 1980s has entirely hanged the piture. It allows supply hains to be inreasingly slied up into smaller and smaller omponents. This proess has been alled in the literature with a wide range of names, inluding fragmentation, outsouring, offshoring, prodution disintegration or reloation, international produt sharing or segmentation, intra-produt speialization, multi-stage prodution, to quote a few. All of them indiate that many inputs are outsoured to speialized subontrators that are loated abroad. Nowadays, several produts and servies are no longer produed within a single ountry but made in global supply hains. Intra and inter industry trade aounts for a large part of trade growth, signaling the importane of suh a phenomenon defined as the seond wave of global unbundling (Baldwin, 2013). The inreasing fragmentation is hanging the nature of international labor division and it has radially transformed the landsape worldwide. International ompetition is no longer a ountry to ountry but a setor to setor or even a produt to produt ontest. Within this piture, it is generally believed standard trade figures that measure the value of imports and exports do not reflet any more what is really happening (Daudin et al., 2011, Timmer et. al., 2013, Amador and Di Mauro, 2015). Furthermore, it undermines the onventional indiators of ompetiveness and openness. Gross export is no longer a useful measure as flows are appraised on their market value when they ross borders. When these goods ontain a large share of imported inputs, their market value an be very large with respet to loal ommodities. This is the likely reason why some ountries exhibit exessive export-to-gdp ratio exeeding even 100% as in Singapore, Luxemburg, Malta and Estonia. This ratio and the share in world export market are the very first statistial indiator used to assess the importane of international trade in a ountry, but they tend to overestimate the ompetitiveness of eonomies that rely heavily on imported raw materials and intermediate inputs. To overome these issues the onepts of Trade in Value Added (VAiT) and Value Added in Trade (TiVA) have been put forward (Esaith and Inomata, 2011, Johnson and Noguera, 2012, Foster-MGregor and Stehrer, 2013, Koopman et al. 2014). The former aounts for the value added of one ountry diretly and indiretly ontained in final onsumption of another nation. The latter alulates value added ontained in gross trade flows. However, the national inome aounting identity states the ountry s trade defiit or surplus must be the same and equal to the gross one (Benedetto 2012, Stehrer, 2012, Kuboniwa 2014). Bilateral TiVA is defined as the ountry s valued added indued by the destination ountry s final demand, exluding intermediate imports, while VAiT is the ountry s origin value added indued by its gross export to the destination ountry, inluding exports of intermediate ommodities. Atually, they are equivalent when VAiT is measured by the value added ontent of trade as proposed by Trefler and Zhu (2010). This literature shows there are large and growing differenes between gross and value added exports, around 25%, quite heterogeneous aross ountries and bilateral partners (Johnson, 2014). Several 2

3 indies and deomposition tehniques have been proposed to address these differenes (Koopman et al. 2014), international fragmentation (Los et al. 2015) or the great trade ollapse (Nagengast and Stehrer, 2016). Value added international trade has never been addressed with the devie of representing world interindustry relationships via vertially integrated setors or subsystems as suggested by Sraffa (1960) and Pasinetti (1973). The method of the subsystems is a way to subdivide a natural system into as many parts as there ommodities in its net produt, in suh a way that eah part forms a smaller self-replaing system the net produt of whih onsist of only one kind of ommodity (Sraffa, 1960, p. 89). The analysis is no longer arried out in terms of industries or branhes only, but in terms of vertially integrated setors. Industry-subsystems tables show both gross and net (value added) inputs required diretly and indiretly to support atual final demand in all the ountries. It is also possible to introdue an operator that allows us to relassify any variable linked to prodution from branhes to subsystems and to attribute the value of this variable to eah final ommodity, observing the industries of origin thereof (Momigliano and Sinisalo, 1984, p. 260). In this paper I adopt the value added perspetive, but we an use fator ontent too (Montresor and Vittui Marzetti, 2011, Garbellini and Wikiermann, 2014). The present paper is organized as follows. Setion 2 gives on overview of the standard measure of VAiT and TiVA. In setion 3 I introdue the Sraffian approah and modify it in order to fit into the international trade framework. Setion 4 presents a simple numerial example and setion 5 onludes and illustrates sope for future researh. 2. Standard measures of value added trade We assume there are ountries eah of whih produes n ommodities. We adopt the standard notation in multiregional analysis (Miller and Blair, 2006) so that denote the value flow of goods from setor i in ountry to setor j in region s. Just as the order of subsripts is from to with respet to setors, the order of supersripts indiates from to with respet to geographi loations. The world s s industry-by-industry flow matrix is Z Z z ij. Define the overall (N 1) output and final demand vetors as x and y, whose (N 1) ountry omponents are and. Input oeffiients are obtained from normalizing the industry olumns ˆ 1 x s z ij y A Z x. This yields the standard World Input Output model: where: i x y f (1) I A 1 B i x A A A B B B x x A A A B B B 1 1 x A A A B B B, A 1, B 1, and the overall final demand vetor is obtained by the following ountry aggregation: 3

4 y y y y y y y y y 1 y y y y 1 1 f f f Johnson and Noguera (2012) fous on the vetor of output used both diretly and indiretly to produe final goods absorbed in ountry : with x q 1 a different way: or q 1 I A f (2). Atually, as suggested by Koopman et al. (2014), we an arrange the Leontief model in q q q B B B y y y q q q B B B y y y q q q B B B y y y q q q I A f f f (4) 1 (3) Q I A F (4bis) where both the gross output deomposition Q and final demand matries F are (N ). In (3) and are (N 1) gross output and final demand vetors produed in ountry and absorbed in s. Of ourse, q q s1 s s y y. Let N s1 v u I - A, where u N is the (1 N) unit vetor 1, and ˆv q s s y the (N N) diagonal matrix with diret value-added oeffiients along the diagonal. Then, we obtain the value-added prodution matrix: g g 1g g vˆ B y vˆ B y vˆ 0 0 q q q g 1 g g g1 2 2g g 0 ˆ 0 ˆ ˆ ˆ v q q q v B y v g1 B y g1 vbf ˆ g g1 v q q q g g vˆ ˆ B y v g1 B y g1 (5) whose blok elements in the diagonal give eah ountry s prodution of value added absorbed at home, while off diagonal blok elements show value added produed in ountry and absorbed abroad. The rows 1 In the following, I will drop subsript of the unit vetor that onforms ase by ase. 4

5 ˆvBF of sum to the total value added, while the olumns add up to the total value added absorbed in a given ountry. Value added exports from ountry to s and worldwide are: s g gs e = vˆ B y (6) VA g1 g gs e = vˆ B y (7) VA s g1 Similarly, ountry imports value added produed in ountry s and worldwide: s s sg g VA g1 e = vˆ B y (8) s sg gs m = vˆ y (9) VA B s g1 Country bilateral value added trade balane with ountry s is: s g gs s sg g ˆ ˆ VA B B g1 g1 Finally, we an figure out ountry gross exports to ountry s: t = u v y u v y. (10) and bilateral gross trade balane: It is easy to hek that: s s s s eg A x y (11) s s s s A x y A x t =u u +y. (12) s s G s s VA G s1 s1 t t (13) Kuboniwa (2014) alls it the fundamental theorem, but (13) simply reaffirms the national inome aounting identity, as GDP minus domesti demand is equal to gross net trade. However, setoral trade balanes in value added an differ from those in gross terms even if (13) implies the overall sum is equal to zero: s1 s s tva t G 0 (14) Following Stehrer (2012) we an embrae a different approah to figure out value added exports and imports to and from all other ountries: e VA B B y y 0 y y B B 0 0 vˆ 0 y y y y B B y y 0 y y (15) 5

6 B B y B B m ˆ ˆ 0 ˆ ˆ VA v v v v y 1 B B y It is easy to hek (16) and (7) are equivalent sine: (16) 1s y s e v B v B v B v B v B (17) 2s 1 g gs g gs ˆ ˆ ˆ y s ˆ ˆ VA y y g1 s s g1 Atually, Stehrer (2012) deems speial value added and final demand vetors: s y s v D 0 0 v, ve v v 0 v v (18) f f f f f (19) E suh that v v v, y f f. Nagengast and Stehrer (2016) all value added exports as: D E E VAX DB E eva = v f u (20) that is value added of ountry whih is absorbed in final demand abroad. Similarly, we an define imports and trade balane in ompat form: VAM = v Bf u m (21) E VA t e m v Bf v Bf v x vbf GDP u f NX (22) VA VA VA D E E D Eq. (22) states the national inome aounting identity one more. With this notation, bilateral value added and net value exports an be written as: s s s s s u e v Bf, t v Bf v B f (23) N VA D VA D D The latter equals a ountry s net exports in gross terms as in (10). The former an be obtained by (6) too. Los et al. (2015) adopt a similar approah to identify vetors of value added involved by a value hain as they deem ˆvBFu. They onsider a partiular final demand matrix F in whih only the ells in the row representing final demand for the ountry-industry (i,j) have their atual values and all other final demand is set to 0. Los et al. (2015, p. 88). This implies Fu is a vetor with a single positive element, whih is obtained by adding domesti and foreign final demand for (i,j) s produts. 6

7 Another strand of literature fouses on trade in fators. Following Trefler and Zuh (2010), the ontent of value added as ontained in a ountry s gross exports and imports ( Value Added in Trade ) is given by: with e v B v B v B 1 vˆ B vˆ B vˆ B e e e e g 1 v ˆ B vˆ B vˆ B 1 1 vˆ B e vˆ B e vˆ B e eg 1 1 ˆ 11 1 ˆ G ˆ vˆ B e ˆ ˆ G v B eg v B eg g g 1 1 G vˆ B ˆ ˆ G v B G v B G G G G g eg e G. However, Kuboniwa (2014) proves, in a G = 3 system, the output transfer equation implied in (24) admit a unique output solution, whih is the same as in (1). This author also suggests the same holds for the general model, as his empirial analysis indeed shows. Hene, value added in trade and trade in value added are equivalent measures. In the following setion, I will show how to expand the TiVA framework in order to assess whih final ommodities are atually exported in value added terms. (24) 3. A Sraffian approah Sraffa (1960) defines a subsystem as gross prodution needed to supply final demand to a single industry. Hene, we an rewrite (1) by onsidering a diagonal matrix of final demand, say ŷ, instead of the olumn vetor y. The orresponding (N N) prodution matrix of vertially integrated setors is: 1 ˆ ˆ X I A y = Β y. (25) Sine eah entry in the Leontief inverse measures impat in domesti output due to a unit hange in final demand, any olumn in vertially integrated setor prodution matrix depits output ativated by a single omponent of final demand. There is a vertially integrated setor for eah ommodity produed in every ountry. If ŷ is formed by a zero olumn vetor but one deviating element equal to one, as in Los et al. (2015), than any olumn in X is simply a multi-setor output multiplier, as eah b s ij speifies how muh setor i in ountry must produe in order to get one unit of the j-th final demand absorbed in ountry s. In other words, if we set standard Type 1 multiplier (Shnabl, 1995). On the other hand, for any final demand vetor, eq. (25) allows to get a useful deomposition of total prodution ativated by a ountry s final demand bundle, sine eah olumn of the matrix X represents prodution needed, diretly and indiretly, to satisfy final demand for the orresponding industry. It is interesting to notie that olumns of X omprise subsystems of the eonomy, while rows show how output by a single setor is distributed to satisfy all final demand items. Momigliano and Sinisalo (1982) introdued the S-operator. This operator is obtained dividing the matrix X row by row by the orresponding total output: ŷ = I, we obtain a deomposition by vertially integrated setor of the 1 xˆ y ˆ. (26) 1 S I A 7

8 Therefore the S-operator is simply norming the prodution matrix X and eah row of S adds up to one, showing the proportions of the ativity of eah branh whih omes under the various subsystems (Momigliano and Sinisalo, 1982, p. 281). Columns represent a subsystem in terms of setoral output shares diretly and indiretly needed to sustain final demand for the orresponding ommodity. The S-operator relassifies any magnitude from setors to subsystems. However, we are not allowed to figure out olumn sums beause values are not homogenous. To overome this problem we an premultiply (26) by an appropriate diagonal matrix suh as : vˆ B yˆ vˆ B yˆ vˆ B yˆ s 1 V v ˆ ˆ ij v I A y vˆ B yˆ vˆ B yˆ vˆ B yˆ v B yˆ v B yˆ v B yˆ ˆv ˆ ˆ ˆ. (27) The resulting matrix V offers a new arrangement of net world flows. Eah entry, say v s, shows the amount of value added required, both diretly and indiretly, from setor i in ountry in order to satisfy final demand absorbed in setor j of ountry s. Sine all entries are in homogeneous units (i.e. value added), we an sum entries in every row or olumn. Summation along rows gives setoral value added, i.e. payments to prodution fators, while the sum of entries in a olumn is equal to final demand. We an also figure out a net bakward linkage indiator that allows us to identify key setors when eonomy-wide output generated by final demand in j is larger than the amount of j s output that is generated by all the other industries final demands. So industry j an be said to be more important for the others than the others are for industry j, and j would thus be identified as a key setor by this measure (Miller and Blair, 2009, p. 559). Atually, we are not using gross output, as suggested by these authors, but value added: N s T vkj ujvu 1 1 s k NM j T N uv u s j v jk s1 k1 where u j is a (N 1) zero vetor but one entry equal to one in orrespondene of setor j in ountry. It has been observed a net multiplier for industry j that is larger than one an be shown to indiate that the final demand in j generates more value added in other industries than all the other industries final demands do generate value added in industry j.1 Hene, in terms of generating value added, industry j an be said to be more important for the others than the others are for industry j (Dietzenbaher, 2005, p ). If this ratio is larger than one setor j in ountry will absorb more value added from other industries than the value added it provides to the other subsystems. We an use this index to identify setors at the end of the global supply hains sine a subsystem produes final goods by definition. The larger its value the relatively loser setor j in ountry is to final demand, and vieversa. The overall sum of all the entries in the value added matrix is, of ourse, world GDP: ij (28) 8

9 uvu' GDP u vˆ B yˆ u' yˆ vˆ B vˆ B vˆ B 0 0 u ' = uyˆ u' 1 vˆ B vˆ B vˆ B 0 0 yˆ 1 u vˆ B vˆ B vˆ B 0 yˆ 0 (29) as olumn sums in the left hand matrix are still equal to one. Sine row sums of the S-operator are meaningless, an resort to V as an alternative. Atually, Momigliano and Sinisalo (1982) propose to divide eah ell by the total of the orrespondent olumn: Entry rs ij C = V(uV ) 1 (30) is the share aounted by setor i in ountry r in the total value added required by subsystem j of ountry s in order to produe the output needed to satisfy that final demand. The C-operator allows to unover ommodities whose prodution required a substantial ontribution by several setors suggesting that outsouring is at work. It is also interesting to notie these matries are invariant to relative prie hanges. In ase of the value added matrix, we an see that: ˆ ˆ ˆ ˆ ˆ vˆ v pˆ pˆ pˆ pˆ v (31) V I A y I A y I A y where values with a bar indiate physial quantities (ampa, 1982, Momigliano and Sinisalo, 1982). Finally, the S-operator does not depend on setoral labor produtivities, while the C-operator on final demand strutures (Montresor and Mazzetti, 2011). ˆ s ˆ s Even if v B y shows value added flows from setors in ountry embodied in final demand of ountry s, it does not orrespond to bilateral net trade as we an hek in the numerial example provided in the next setion. Atually, value added deliveries to another ountry do not fulfill the basi properties for VAiT: First, adding up a ountry s bilateral trade surpluses or defiits over all partner ountries should result in this ountry s overall trade surplus or defiit. Seond, a ountry s bilateral trade surplus (defiit) with another ountry must this other ountry s bilateral defiit (surplus), i.e. it s mirrored (Stehrer, 2012, p. 2). Similarly, value added produed in and inluded in foreign final demand, i.e. v ˆ s ˆ s B y, is not equal to net exports worldwide, nor v s s ˆ B yˆ is total imports. In order to assess s s net trade in ountry (with respet to the world) let s onsider (22) within this approah: vˆ B yˆ ' F NX GDP uf u u uf u ' ˆ ˆ ˆ ˆ ˆ ˆ ˆ ˆ ˆ ˆ ˆ ˆ DB E EB B E EB DB B = u v f v f u' u v f v y u ' u v y v f u ' (32) where u F is a ( 1) vetor with all zero entries but the ones orresponding to ountry. The last right hand side in (32) explains why the value added matrix annot be used to detet VAiT sine v ˆ y ˆ has zero D B 9

10 entries but flows from setors in ountry as in V. These figures are not exports as they inlude value added reated by domesti demand too. Hene, we have to orret it by. The latter generates also imports and the differene is the net trade matrix whose entries depit value added flows due to foreign final demand pushing exports and domesti final demand ativating imports. Atually, the net value added trade matrix is given diretly by ˆ ˆ ˆ ˆ vdbfe vebf that show exports in the first item and imports in the last one. The net value added trade matrix is also equal to ˆ ˆ vbf ˆ ˆ E veby. The first one an be oneived as worldwide value added due to foreign final demand. ows orresponding to ountry are still exports embodied in all final demand items and the sum of these entries is equal to VAiT or TiVA. As above, row sums give foreign final demand. It is obvious that within global hains foreign setors provide part of the value added needed to satisfy them and we have to orret these flows by, that is value added reated outside ountry due to total final demand. v ˆ vˆ Bfˆ B E y ˆ A numerial example In order to assess the approah introdued in the previous setion, let s onsider a system omprised by three ountries in eah of whih three setors (say Agriulture, Manufaturing, and Servies) provide differentiated ommodities. Maro data for these ountries are presented in Table 1. Domesti demand, i.e. household and publi onsumption plus gross apital formation, is always equal to 300, while GDP may differ by about 10%. International trade is balaning in the last ountry, while the prodution defiit in the first nation is mathed by a trade surplus in the seond one. However, international trade is sizable in all of them as export propensities, import penetration, and openness ratios show. Table 1 Maro data Value added Domesti demand Export Import Net export Export prop. Import penetr. Openness atio % 72% 148% % 82% 159% % 76% 152% tot % 77% 153% These aggregate data are derived from the world Input Output table presented below. In the first ountry all the setors have an idential value added and quite similar gross output. In ountry 2, manufaturing is the prevailing industry, while tertiary is the leader in the last nation. Value added oeffiients ranges from 37% to 53%. Final demand is larger where there is a likely omparative advantage, while intermediate demand is relevant for manufaturing and the servie setors. Table 2 World Input Output table a 1 m 1 s 1 a 2 m 2 s 2 a 3 m 3 s 3 tot. f 1 f 2 f 3 y a m

11 s a m s a m s tot va x Table 3 and 4 show gross and net trade flows. The latter are from the TiVA approah. It is interesting to notie how net trade flows between ountry 1 and 3 are whimsial, while gross trade is signifiant. The first ountry is selling its agriultural output worldwide, and importing both manufatured goods and servies. The opposite holds in ountry 2, while the last one is balaning agriultural imports with exports in seondary. Trade flows are quite large in all the nations, with a total VAiT that is half of world GDP. Table 3 Gross trade flows EXP A M S tot. IMP A M S tot tot tot EXP tot. NX tot tot tot Table 4 Value added flows EXP A M S tot. IMP A M S tot tot tot EXP tot. NX tot tot tot

12 Table 5 displays the value added matrix. Sums along olumns are setoral value added, while summations along rows provide final demand. The overall total is world GDP. Net multipliers are figure out in the last olumn. They are larger the one in all the primary setors, and the maximum is ahieved in the first ase. This primary setor of ountry 1 is selling only 20% of its gross output as intermediate demand and the net multiplier is revealing it is quite lose to final demand. Intermediate demand shares are large but below 50% in the agriulture and manufaturing of the seond ountry, where net multiplier are still above one. We annot state the net multipliers is onveying the same information as diret sales yet, as it inludes indiret effets too. Take the servie setor in ountry 1 where intermediate demand is slightly less than the final one, but the net multiplier is below one. Table 5 The V matrix a 1 m 1 s 1 a 2 m 2 s 2 a 3 m 3 s 3 va NM a m s a m s a m s y ows in matrix V indiate how payments to prodution fators are inluded in all the final demand items. For instane, summing up all the entries onerning ountries but 1 final demands. i.e T u V V u, we get value added delivered by the first nation and inluded in other final demand items. This figure an shed light on how muh other ountries an indiretly ativate prodution in the first nation, but does not onern exports, as its value is 35 only and muh less than VAX. By the same token, T u V V u is not VAM (it is equal to 74), nor the differene is net trade in value added. Nevertheless, these figures are important as they an signal how a ountry partiipate in global value hains. It is immediate to hek olumn shares are the S-operator. In the first ountry most of agriultural value added is absorbed by its own final demand (86.3%), while this share is smaller in tertiary (62.8%) and muh less in manufaturing (55.1%). Atually, all setors, but manufaturing in ountry 3, are largely ativated by their own final demand. Not all the industries are foused in loal markets yet. For instane, manufaturing value added of the last ountry is spread worldwide, with a sizeable quota in seondary final demand of ountry 2. Table 6 the S-operator 12

13 a1 m1 s1 a2 m2 s2 a3 m3 s3 a m s a m s a m s As stated above, we annot perform row sum in table 6, but we an use the C-operator as an alternative. These shares are informative. Values along the diagonal indiate the weight of eah branh within its subsystem. They are all, but seondary in ountry 3, larger than 50% showing the importane of self-ativation. Spillovers may be important too. For instane, sa sm 11.4% reveals that agriultural and manufaturing final demand in ountry 1 is ativating loal servie providers a lot. We an notie that, even if all these industries are trade oriented, only about 25% of ativities used in prodution ome from outside the ountry. This share drops to 15% in the servie setor of ountry 3. Table 7 the C-operator a1 m1 s1 a2 m2 s2 a3 m3 s3 a m s a m s a m s The V matrix, S and C operators are extremely useful to address subsystem ompositions, disentangle strutural hanges and see whih ommodities are boosting prodution. They are not linked with exports and imports in value added yet. To address foreign trade we must resort to the NVAT matrix and its deompositions. Table 8 presents value added trade flows for the first ountry, where imports have a negative sign. Sums along eah row are VAiT or TiVA (ompare with table 4) and the overall value is also the gross trade balane that is a defiit of 30 units. Let s take the first setor. Agriultural gross exports add up to 99 units, 76 of whih are delivered as final demand. VAiT is only 50 and tables 8 and 9 show whih omponents of are ativating these net exports. Atually, most of it is still inluded in its own produts, as we an see from table 9. If agriulture is produing tomatoes only, about 82% of primary value added exports is due to tomatoes bought by foreign families. However, value added exports are also 13

14 in other foreign final demand items, suh as goods (tomato saue) and servies (restaurants serving tomato salads or pasta with tomato saue) produed domestially or abroad. Figures along this row are not large, but findings are ase dependent. As we an see from the third rows in tables 8 and 9, value added servie exports are mostly inluded in other items, as only about one third is due to its own foreign final demand. Notieably a larger share is due to the other domesti items, that is foreign final demand for loal agriultural produt (8.7 units, i.e. 29%) and manufatured goods (4.5 units or 15%). Table 8 NVAT matrix for ountry 1 a1 m1 s1 a2 m2 s2 a3 m3 s3 VAiT a m s a m s a m s tot Table 9 VAiT shares for ountry 1 a1 m1 s1 a2 m2 s2 a3 m3 s3 tot. a m s a m s a m s Final demand ativates prodution in all the setors. Table 8 shows how to sustain a foreign final demand of 76 units, domesti manufaturing ontributes with exports equal to 7.4 units and servies with 8.7. Atually, all the entries in the first olumn of the ˆ ˆ vbf E desribe the subsystem onneted with the foreign final demand for primary produts. As the C-operator is invariant to hanges in final demand, the struture is the same. However, this is not the fous of our analysis, as we are not interested in spillovers. In order to dislose net trades we have to turn to imported value added. This is due to domesti final demand. Let s onsider the primary setor again. Domesti final onsumers buy 68 units. To produe this 14

15 amount, the primary setor needs foreign intermediate inputs and negative entries in the first olumn show value added imports from foreign branhes taking into aount all the diret and indued effets. Goods produed by foreign industries are somehow important as, to sustain 68 units of domesti final demand, manufaturing provides about 10 units of value added from ountry 2 and 3. Total import is equal to 17 units and this sum is balaning the domesti omponents. The first olumn in table 8 disloses net trade onneted with agriultural produts in the first nation. On one side, positive entries show value added exported by domesti industries, i.e. due to foreign demand for loal agriultural produts. A foreign final demand of 76 units has generated exports by 57, with a 75% ratio. On the other side, a domesti final demand of 68 units reates value added imports by 17 units, with a 25% ratio. The overall value is 40.1 units that is the trade surplus due to the different soures of agriultural final demand. The servie setor example is intriguing. Gross output is 170 with a value added equal to 90. Very little is sold to foreign final onsumers (16 units) and its final demand is weakly ativating domesti output and value added exports. The latter are whimsial in agriulture. Nonetheless, the third row of table 8 shows this setor is exporting muh more, as value added exports total 30 units, while gross exports are equal to 22. This is due to foreigners, who like other domesti ommodities, suh as tomatoes, that absorb servies a lot. Hene, tertiary appear muh more ompetitive on VAiT basis than on standard measures. This is not a omplete piture yet, sine a large domesti final demand (70) requires inputs and value added imports (15.2). The overall balane, between exports due to foreign final demand and imports generated by the domesti one, is slightly negative (-2.7). Finally, eah row in table 9 shows the struture of value added imports too. For instane, value added imports from manufaturing in ountry 2 are mostly due to its own final demand (70%), while this share is muh smaller for similar imports from ountry 3 (about 17%). Maybe the latter is produing omponents that are spread in almost all final demand items, while the former mostly ars that are diretly sold to final onsumers in ountry 1. Empirial analyses will dislose suh ases. 4. Conlusions Global Value Chains are probably the most prominent feature of the reent globalization wave. These vertial supply linkages are posing new hallenges to analyses of international trade and ountries ompetitiveness as intermediates move aross borders several times before being assembled into final goods. Double ounting of trade may severely bias standard trade statistis. An example an shed some light on this point. The firm Burberry sends perfume bottles from Frane to Shanghai to be deorated with a Sottish pattern before bringing them bak to be sold on the Frenh market. Standard trade statistis suggest that Frane is exporting perfume bottles to China and China is exporting perfume bottles to Frane. Yet Frane does not export anything for Chinese onsumption, as the perfume bottles are onsumed in Frane. China simply exports deoration for Frenh onsumption. Suppose the pigments used for the deoration of the perfume bottles are imported by China from Japan. This Japan-China trade flow does not mean that China onsumes Japanese produts, as the final onsumer is in Frane. Unravelling these long supply hains is impossible using simply trade statistis (Daudin, 2011, p. 1404). Several ase studies have motivated the growing literature on global hains. These ase study fae obvious limitations, as the partiular omponents of a produt under onsideration are themselves made of other omponents and so on. At the end, it is far from being easy to trae bak a produt to the ultimate produer: there is no simple answer to who makes the ipod or where it is made. The ipod, like many other produts, is made in several ountries by dozens of ompanies, with eah stage of prodution ontributing a different amount to the final value (Varian 2007). 15

16 Two measures are ommonly used to address these issues: Trade in Value Added and Value Added in Trade. TiVa answers the question: how muh value added of other ountries is ontained in the onsumption of the ountry under examination?, while VAiT is takling the question: How muh of foreign value added does the gross exports of a ountry embody? (Stehrer, 2012). Kuboniwa (2014) proves the equivalene theorem between TiVA and VAiT in terms of fator (value-added) ontent of trade as proposed by Trefler and Zhu (2014). As value added generated in a setor an be inluded in any kind of ommodity, it is natural to wonder what the soure of this output is. This problem an be easily solved adopting the Sraffian onept of vertially integrated setors or subsystems. They allow us to split the eonomi system into ideal self-suffiient setors, whih produe a single final ommodity with all their neessary intermediate inputs. This way I an provide an answer to Varian s question about who is atually making the ipod and how it is ontributing to the trade balane too. The Value added matrix has been already used in several analyses onerning outsouring and deindustrialization at the national level. Furthermore, World Input Output tables have been used to derive the distribution of value added by all ountries involved in the prodution hain of a partiular final good (Los et al. 2015). Unfortunately, the latter does onsider bakwards effets only, while the former is not oherent with standard international trade framework as neither value added inluded in foreign ommodities is exports in value added nor foreign value added in domesti final demand orresponds to value added imports. However, adapting the methodology devised by Stehrer among others I formulate a new matrix, alled NVAT, whih shows value added bilateral trades distinguishing between exports and imports. The former is due to external final demand about all final ommodities. The latter is linked with domesti demand that requires not only foreign intermediate inputs but foreign value added too. In the ase of a Ferrari, whose last stage of prodution is in Maranello, Italy, an export is arried out when the ar is sold outside Italy. Positive entries in NVAT show value added generates by these sales pinpointing the ontribution of all the Italian industries diretly and indiretly involved in Ferrari s omponents. However, some Italian ustomers buy Ferraris, whose making require foreign inputs and valued added too. Negative entries in NVAT show imported valued added. The overall sum is the valued added trade balane onerning these bilateral flows. NVAT fulfils the identity between the sum total of a ountry s value-added trade balanes and gross trade balanes (net gross exports or net exports) and may be an important tool to assess international ompetitiveness. 16

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