ACCOUNTING OF VALUE ADDED IN INTERNATIONAL TRADE

Accounting of Value Added in International Trade
Kirill Muradov
National Research University Higher School of Economics, 26, Shabolovka Street, Moscow, 119049, Russian Federation E-mail: kmuradov@hse.ru
Gross exports accounting is a novel sub-area of research that seeks to allocate the value added in gross trade flows to its true country and sector of origin and country or sector of destination. Various frameworks have been recently proposed to perform such decompositions. This paper presents another effort to generalise the accounting framework so that it may be easily interpreted, customised and implemented in matrix computation software. The principal contribution is therefore a relatively simple way to derive the formulae for the decomposition of cumulative value added flows embodied in international trade. The underlying accounting approach is found to be largely similar to that of [Koop-man et al., 2012; Stehrer, 2013], but the block matrix formulation allows the user to simultaneously decompose all bilateral flows at the country and/or sectoral level. The refined framework is applied to describe Russia's export performance from the global value chain perspective using the data from the World Input-Output Database (WIOD) for 2000 and 2010. According to the findings, the countries that directly receive most of Russia's exports are not exactly those that use most of Russia's value added. Russia's mining sector is found to be an intrinsic part of a complex downstream value chain where it indirectly contributes value to partner exports.
Key words: gross exports accounting; value added in trade; global value chains; inter-country input-output tables.
JEL Classification: D57, F15.
1. Introduction
For some time, simple concepts and measurements have not sufficed to describe and explain the patterns of international trade. The fragmentation of production in the late 20th and early 21st century, which some analysts consider as significant as the 19th century industrial revolution [Baldwin, 2011], led to a sustained increase in the trade of intermediate goods and
Kirill Muradov - Candidate of Sciences (PhD), Head of International Educational and Research Programmes, International Institute of Statistical Education.
Received: June 2014/Accepted: October 2014.
services. It is more common nowadays that a particular product purchased for final use is the result of interactions within an inter-industry network where a multitude of producers acquire inputs from one another and add value on each subsequent production stage. Likewise, a raw material or primary input may have to virtually travel along a complex chain of industrial interactions until it is finally consumed or invested as part of a much more sophisticated product. As these interactions span across multiple borders, they are treated as global value chains or global supply chains - a term which has become representative of, if not synonymous to, the international trade [Park et al., 2013].
Case studies have shown that the traditional gross trade statistics give a misleading picture of who produces what and for whom» (an expression from [Daudin et al., 2009]) and how the benefits from trade in the form of value added or job creation are allocated. This is perhaps most manifest in the technology-intensive industries that typically outsource many operations and rely on cross-border supplies of parts and components. In the often cited case of Apple's iPhone, the assembling and exporting economy (China) was found to directly contribute only 2% of the retail price in the destination market (U.S.), while Apple's own contribution was thought to be around 58% [Kraemer et al., 2011]. Interestingly, this is also typical for labour-intensive industries. A cost breakdown of a jacket manufactured in China and sold in the U.S. attributes only 5% to China and 86% to the U.S. [Low, 2013]. A considerable body of similar case studies based on micro data (see an overview in [Ali-Yrkko, Rouvinen, 2013]) provide useful insights but not a comprehensive solution to the issue of identifying value added in gross trade flows. For the latter, economists and statisticians now employ inter-country input-output (ICIO) tables that link flows of goods and services for intermediate and final use between industries and countries in a consistent framework originally proposed by [Leontief, 1936] and refined by [Isard, 1951; Moses, 1955; Leontief, Strout, 1963] and others. The input-output model is capable of capturing the infinite series of interactions among suppliers and consumers along the whole value chain1.
The application of input-output techniques to international trade analyses eventually led to the emergence of a novel sub-area of research - tracing value added in trade, or gross exports accounting. The core objective is to separate net value added flows from gross trade flows as is usually done in national accounting (e.g. for GDP estimates) and to identify the origin and destination of value added in international trade. Various frameworks have been recently proposed to measure value added in trade, and the most influential contributions include [Daudin et al., 2009; Johnson, Noguera, 2012; Koopman et al., 2010, 2012; Stehrer, 2012, 2013; Wang et al., 2013]. Many of the proposed concepts have been utilised by the OECD and WTO. They jointly introduced a Trade in Value Added» database2 in 2013 as a stepping stone in the production of alternatively measured trade statistics.
Gross exports accounting benefits from continuous methodological advances. This paper presents another effort to generalise the accounting framework so that it may be easily interpreted, customised and implemented in matrix computation software. The principal con-
1 [Murray, Lenzen, 2013] is a useful non-technical introduction to the multi-regional (including inter-country) input-output analysis, while the special issue of Economic Systems Research, 2013, vol. 25, no 1 offers a more scholarly discussion.
2 OECD-WTO Trade in Value Added (TiVA), available at: http://stats.oecd.org/Index.aspx? DataSetCode= TIVA_OECD_WTO
tribution of this paper is therefore a relatively simple way to derive the formulae for the decomposition of cumulative value added flows embodied in international trade. The underlying accounting approach is found to be largely similar to that of [Koopman et al., 2012; Stehrer, 2013], but the block matrix formulation allows the user to simultaneously decompose all bilateral flows at the country and/or sectoral level. This leads to a discussion of the implicit and explicit sector aggregation options and an explicit derivation - for the first time, to the author's knowledge - of two matrices that account for the inter-sectoral transfer of value added in the production process of both exporting and the partner country's side.
The proposed framework is applied to quantify Russia's trade performance from the global value chain perspective. The results highlight the unobserved indirect links behind Russia's integration into the global economy. It appears that the countries that directly receive most of Russia's exports are not exactly those that use most of Russia's value added. Russia's mining sector is found to be an intrinsic part of a complex downstream value chain where it indirectly contributes value to partner exports, but the links to the final demand can also be traced.
The paper is organised as follows. Section 2 briefly overviews the frameworks proposed so far and puts this paper in the context of the ongoing research. Section 3 explains the derivation of the formulae to capture value added in international trade and a generalisation of [Koopman et al., 2012; Stehrer, 2013] framework. Section 4 applies some of the derived formulae to real world production and trade data and briefly discusses the results. Finally, Section 5 concludes.
2. Overview of the existing frameworks for the gross exports accounting
Renewed interest in ICIO analysis, partly reinforced by the release of new global IO databases3, has been fuelling the discussion on the gross exports accounting and tracing value added in international trade. A number of frameworks have been recently proposed, and most studies refer to [Hummels et al., 1999] as the point of departure.
Hummels and his co-authors did not provide a method for the complete decomposition of gross trade flows, but proposed first measures of vertical specialisation (VS) in trade that have effectively become building blocks for the subsequent research efforts and are still widely used for global value chains analysis4. These measures, known as VS and VS1 can be described for any single country as follows: (1) VS accounts for the import content of a country's exports, or how much foreign value added is required to produce a unit of direct exports?»; (2) VS1 accounts for a country's domestic value added in partner exports, or how much domestic value added is required to produce partner countries' exports, per unit of direct exports of the country in focus?»
VS depicts a country as a recipient of foreign value added to be further processed for exports, or its relative position with respect to the upstream value chain. VS1 depicts a country as
3 See the special issue of Economic Systems Research, 2013, vol. 25, no 1 for an overview.
4 Examples include [OECD, 2013a; OECD, WTO, UNCTAD, 2013; UNCTAD, 2013]. Note that the measures of vertical specialisation appear in those publications under different names, e.g. backward/ forward participation» or upstream/downstream component».
a supplier of domestic value added to be used in partner exports, or its relative position with respect to the downstream value chain. VS therefore relates to the backward perspective and VS1 to the forward perspective in global value chain analysis.
[Daudin et al., 2009] proposed an additional measure that is in fact a subset of VS1: domestic value added used in partner exports that ultimately returns home in final products. They call it VS1* and developed an ICIO for their computations to correct the inaccuracies in the measures derived by [Hummels et al., 1999] from single-country IO tables.
[Johnson, Noguera, 2012]5 are usually credited with the introduction of a consistent multi-country framework for the computation of the value added content of bilateral trade, or value added exports», that describes value added produced in a source country and finally absorbed in a destination country. They proposed a ratio of value added exports to gross exports at the sector and aggregate levels called the VAX ratio as a way to address the double-counting» problem and measure the intensity of production sharing. Johnson and Noguera generalised the computation procedures in an ICIO setting. Their contribution is also intimately related to the measurement of the factor content of trade as in [Trefler, Zhu, 2010].
[Koopman et al., 2010] developed a framework that was in many respects similar to that of Johnson and Noguera but shifted the focus of their analysis to the complete decomposition of gross exports. Their effort integrated previous literature on vertical specialisation with newer literature on value added content of trade. In brief, the core contribution of [Koopman et al., 2010] is: (1) a consistent and relatively simple method of computation of true VS and VS1 values in an inter-country setting, and (2) a decomposition that attributes all value added in a country's exports to its sources and destinations. [Koopman et al., 2010] proposed a breakdown of gross exports into three basic components: domestic value added destined for direct importing partners or third countries, domestic value added that returns home from abroad, and foreign value added. A more detailed breakdown splits these three basic components into seven more detailed components.
[Koopman et al., 2012] provided a unified framework that breaks up a country's gross exports into the sum of various components that are similar to their 2010 results. They show that the value added exports, VS, VS1, and VS1* are linear combinations of these components. Their new generalised version of the gross exports accounting equation contained nine terms. Though not explicitly observed (but recognised in [Wang et al., 2013]), the 2012 version of Koopman and his co-authors' gross exports decomposition contained a conceptual deviation from the 2010 version. The 2010 paper focused on breaking down direct gross exports into value added components, whereas the 2012 paper focused on capturing both direct and indirect value added flows normalised with respect to gross exports. This is an important distinction between the two inter-related frameworks that will become apparent in the later sections of this paper.
This is also a point where interpretation becomes critical to understand the distinctive features of the existing frameworks. [Stehrer, 2012] drew a borderline between the concepts of trade in value added» and value added in trade» that was rather helpful to structure readers' thoughts about the subject. In bilateral trade relations, the first concept - trade in value added» - accounts for the value added of one country directly and indirectly contained in final consumption of another country. VAX, proposed by [Johnson, Noguera, 2012], is a good exam-
5 First draft manuscript of Johnson and Noguera dates back to 2008.
ple of the application of this concept. The second concept - value added in trade» - calculates the value added contained in gross trade flows between two countries. Examples include VS and VS1. The two concepts address different questions and may be used for different purposes. For trade policy which usually applies to gross trade flows, the results of value added in trade» may be more enlightening. For global value chain analysis, trade in value added» may be a more relevant concept. [Stehrer, 2012] also carefully studied the properties of bilateral and overall trade balances in net and gross terms.
[Stehrer, 2013] applied the framework of [Koopman et al., 2012] at the bilateral level. This allowed for a detailed account of the relationships between the two concepts from [Stehrer, 2012] and the role of third countries in bilateral value added trade. Many results in the present paper are identical to those in [Stehrer, 2013], while the derivation of the relevant formulae offers certain improvements and extends to the bilateral sectoral level.
A number of recent studies review and elaborate the frameworks mentioned so far for specific analytical purposes. [Meng et al., 2012] apply trade in value added» and value added in trade» concepts to measure the progress of regional economic integration through cross-border value chains. They make useful observations on the calculation of trade in value added» at the sectoral level for their alternative version of the revealed comparative advantage indicator. [Kuroiwa, 2014] applies the framework of [Koopman et al., 2012] to derive a gross exports accounting equation for the special case of IDE-JETRO's Asian Input-Output Tables, which, unlike the global ICIO tables, contain exogenous vectors of imports from and exports to the rest of the world. He then uses the equation to assess the technological intensity of China's exports. [Kuboniwa, 2014a, 2014b, 2014c] develops a theoretical discussion on the relationship between trade balances in value added and gross terms building on many of the previously discussed concepts.
In sum, complete frameworks for gross exports accounting combine both trade in value added» and value added in trade» concepts. However, the exact combination varies. It is important to discern two types of such frameworks for a clearer understanding of their applications.
The first type builds on [Koopman et al., 2010] and decomposes direct exports into value added terms. A normalisation with respect to total gross exports is common and each component will be bound between 0 and 100%. [Wang et al., 2013] provide the most complete generalisation of such framework up to date with a breakdown of gross exports into sixteen components at the bilateral sectoral level.
The second type of frameworks builds on [Koopman et al., 2012] and in fact decomposes direct and indirect flows of value added, not exactly gross exports, into value added components. A normalisation with respect to gross exports is possible, but some components may well exceed 100% at the sectoral and bilateral level. A normalisation with respect to total exported value added is more natural and will bind the components between 0 and 100%. It is this type of decomposition that this paper intends to further generalise. It is suggested that this type be better described as cumulative value added accounting» rather than gross exports accounting» of type one.
It appears that there is no single framework that would offer all-in-one solution for all analytical purposes. Each type of decomposition has its own advantages and can be best applied in certain situations but can yield less useful results in other. A researcher or data user has therefore to carefully consider the purpose of the analysis to select proper application. Be-
sides, as in many input-output based applications, meaningful economic interpretation of the proposed formulations is key to their proper use for specific analysis.
3. Refined generalised framework for cumulative value added accounting
This section introduces the notation and the minimal matrix setup» which is thought to be one of the distinctive features of the proposed generalised accounting framework. This paper does not discuss a simplified representation of a two- or three-country world. Instead, the starting point is the general case of K countries and N sectors. The setup is thought to be convenient for both reader's understanding and the implementation in matrix computation software6. Moreover, there are only five core matrices and a number of common matrix operators that are required for decompositions of cross-border flows of value added. The concepts of value added at origin» and value added at destination» are proposed for a better understanding of implicit and explicit aggregation options. This is followed by the derivation of the basic accounting relationship» and various algebraic manipulations to provide basic and itemised decompositions of value added in exports. The basic accounting relationship» is also used for a surprisingly compact proof of the equality of total (i.e. aggregated across partner countries) trade balances in gross and value added terms and for a concise decomposition of the bilateral trade balances. The final part of this section discusses how the proposed framework can be customised to identify the final destination of value added at the product or sector level.
3.1. Concepts, notations and the minimal matrix setup
For the purpose of a holistic value chain analysis, the global economy is modeled by a global input-output table where each product flow is attributed to a selling industry/country and purchasing industry/country for intermediate use or purchasing country for final use. There are also primary inputs to production or value added that is also allocated to a purchasing industry/country. The matrix representation of the global ICIO table for K countries and N economic sectors appears as follows:
Z =


"Zn Z12 Zik" fii fl2 * f!k" X1
Z21 Z22 ' Z2k , F = f21 f 22 f2k , x = X2
Zki Zk2 ' Zkk_ fk1 fk2 fkk_ Xk_

Henceforth, indices r and s denote, respectively, the selling and purchasing countries, and indices i and j denote the selling and purchasing sectors in each country (r and i therefore correspond to rows, s and j correspond to columns). In the block matrices above, each block
6 Section 3 in [Muradov, 2014] discusses the derivation of the formulae in much more detail.
element Zre is an N x N matrix of intermediate demand of the purchasing country s from the selling country r, fre is an N x 1 vector of final demand of s from r, Vs is a 1 x N vector of value added used by country s, and xr is an N x 1 vector of total output of country r. So, Z is a global KN x KN matrix of intermediate demand, F is a KN x K matrix of final demand, x is a KN x 1 column vector of total output, and v is a 1 x KN row vector of value added7. The fundamental accounting identities imply that the supply of intermediate and final products equals total output, Zi + Fi = x, and the use of intermediate and primary inputs equals total input (outlays) that must also be equal to total output, iZ + v = x', where i is an appropriately sized summation vector.
The generalised framework in this paper will mostly work with a minimal setup» of only five basic matrices. One of those is F and four other matrices are described below.
Define a KN x KN diagonal matrix of value added coefficients:
V =
"c,1
0
c,2
0 0
0
c,k
where each block vc s is an N x N diagonalised vector of value added coefficients, vc , = . In
xJ

matrix notation, Vc = vx
Two KN x K matrices are required to represent total gross exports and bilateral gross exports:
Etoi =
e1 0 0 e.
00
0
em -
0
21
c2k
In Etot, each Nx1 block element er is equal to the sum of the international sales for in-
termediate and final use over all trading partners, etotr = ^ Zrsin + ^ frs. In Ebil, each N x 1
s^ r
block element ere only accounts for the bilateral flows, eMrs = Zrsin + frs, r * s, and in is an N x 1 vector of ones for the summation across sectors.
0
0
e
e
12
1k
0
0
0
e
e
e
k
k1
k2
7 Value added is usually assumed to be immobile across borders. Overcoming this limitation and accounting for the income flows, beyond trade flows, is an important part of OECD and WTO joint efforts, see [OECD, WTO, 2012].
Next, find the inter-country version of the Leontief inverse which is key to the demand-driven input-output analysis:
(I - A)-1 =
I - Ai -A
A

A12 I-A
22


A

A
-A
I-A
-1
L11 L12 LT1 Lii
L, L
L1 L
L
= L.
Ars blocks are N x N technical coefficient matrices that relate intermediate inputs to total
zj
V /v1
output aJj = (so A = Zx ). Leontief inverse L is a KN x KN multiplier matrix that allows xJ
total output to be expressed as a function of final demand: x = Ax + Fi = (I A)-1Fi = LFi.
This completes the setup for the derivation of the basic value added accounting formulae in this paper. It is indeed minimal and only consists of five matrices: Vc, L, F, Etot and Em. One more matrix, X , that is the diagonalised total output, will occasionally feature the interim formulations but will eventually disappear from the final ones.
In addition to the usual matrix summation and multiplication, the framework will also require using the following operators:
A
- extracting a block-diagonal matrix from a block matrix or creating a blockdiagonal matrix from a vector;
V
- extracting a matrix with off-diagonal block elements from a block matrix;
0 - block-element by block-element multiplication, known as Hadamard product in case of element-by-element multiplication;
' - transposition of a block matrix.
These four operators should be applied block-wise to the KN x KN L matrix and KN x K F, Etot and Em matrices and x vector. This is an essential pre-requisite for all further manipulations with block matrices throughout this paper. The operators that handle diagonal and off-
A V
diagonal block elements, and , may apply to a single matrix, or an expression in square
brackets, or both. For example, in
V
V V
VLF
diagonal block elements are first removed from L
and F. Vc, L and F are then multiplied and, finally, diagonal block elements are removed from the result.
There is an implicit aggregation concept that defines the dimension of results and therefore needs clarifying. For the larger part of the paper (incl. subsections 3.2-3.5), the default dimension is KN x K or [country/sector] x country that may be reasonably called value added at origin». It corresponds to the dimension of the F, Etot and Em matrices and attributes each aggregated flow destined for country s to each sector i in country r which sources value added.
So the recipient sectors j on the partner countries' side are implicitly aggregated. A reverse concept is value added at destination» which assigns aggregated value added from country r to product of sector j somehow used by country s. This is equal to the K x KN or coun-tryx[country/sector] dimension. In other words, the KN x K aggregation focuses on value added creation whereas K x KN focuses on value added capture. Finally, the full KN x KN or [country/sector] x [country/sector] dimension is feasible to trace both value added creation and capture. An extension to the KN x KN and K x KN dimensions is explored in subsection 3.6. Meanwhile, Fig. 1 illustrates the distinction between the two concepts which is essential for the proper interpretation of the formulations below.
Note that the application of the value added at destination» concept requires that the matrices F, Etot and Em be redefined in KN x KN and the minimal» initial setup be extended to include an additional matrix constructed from Z. Throughout algebraic manipulations, some matrices may therefore have to be redefined in dimensions other that the above. In such cases, for clarity, the new dimension is specified by a subscript, e.g. Z(kvv x k or F(kvv x bv>
Value added at origin
Origin of value added Destination of value added
Country s: imports/use
Country r: exports/production, N sectors (/) Sector /1 value added flow from /1
Sector /2 value added flow from /2
Sector in value added flow from in
Value added at destination
Origin of value added Destination of value added
Country s: imports/use, products of N sectors (j)
Product of sector j1 Product of sector j2 Product of sector jn
Country r: exports/production value added flow in j1 value added flow in j2 value added flow in jn
Fig. 1. Illustration of the value added at origin and value added at destination concepts
3.2. The basic accounting relationship
Note that, by definition of gross exports:
(1) Ebil - Etot = F + Z(KNxK) - X(KNxK),
where Z(KNxK) is the Z matrix condensed to the KN x K dimension (aggregated across the
partner country s' sectors), and X(KNxK)) is a KN x K block-diagonalised vector of total output
arranged in a similar way, to conform with the Etot and Em matrix dimensions. The resulting matrix on both sides of (1) has bilateral trade flows in the off-diagonal block elements and total exports with the negative sign in the diagonal block elements.
Using that Z(
(KNxK)
= Ai
(KNxK)
, rewrite the right part of the equation as follows:
F X(KNxK) + Z(KNxK) = F X(KNxK) + Ax(KNxK) = F (l A)(KNxK) = F L
(KNxK)
Then multiply both sides of (1), including the rewritten right side, by the value added multiplier matrix VcL :
VCL ( - Etot) = VcL (F - U1Xx(KNxK)). A simple rearrangement gives: (2) yXEM = VcLF + VcLE
tot VcX(KNxK).
And the zoom-in view» on this equation is given below8:
L1tet1 Vc,lX L"et2 L Vc,lZ L"e t=1 t=1 t=1
K K K
Vc,2^ L2tet1 Vc,2^ L2tet2 L Vc,2^ L2te
t=1
K
t=1
K
t=1
K
Vc,kZ Lktet1 Vc,kZ Lktet2 L Vc,kZ Lk
Vd L1tft1 Vd L1tft
t=1 t=1
KK
Vc,2^ L2tft1 Vc,2 ^ L2tft2 t=1 t=1
Vc,1L11e1 Vc,1L12e2 L Vc,1L1kek
Vc,2L21e1 Vc,2L22e2
Vc,2L2kek
Vc,kLk1e1 Vc,kLk2e2 ' " Vc,kLkkek
Vc,A 0
0 4,2*2
00
Vc,kxk
Vd Lf t=1
t=1
K
Vc,kZ Lktft1 Vc Lktft2 Vc,kZ L
ktftk
Each of the matrices above deserves a stand-alone interpretation. VcLEbi1 can be
treated as a bilateral value added in trade matrix». Each element in this matrix corresponds to both direct and indirect flows of value added that originates in sector i of country r and lands» in country s to satisfy aggregate (intermediate plus final) demand in country s. Usually, the VcLEbil matrix does not feature the value added in trade» calculations and does not explicitly appear in any of the existing frameworks. However, this matrix is useful to estimate the domestic value added embodied in direct and indirect gross trade flows. Note that the columns of VcLEbi1 (and of Em) sum to the total imports of country s and the rows of VcLEbi1 sum to the domestic value added in total gross exports of country r, sectoral or aggregated.
tk
+
K
K
e
t=1
t=1
t=1
t=1
t=1
t=1
+
8 Zoom-in view», or a representation of a block matrix contents, is limited to the equation (2) here. [Muradov, 2014] provides zoom-in views» and additional descriptions of most of the matrices featuring the proposed framework.
The VcLF matrix is much more familiar as it is equal to Johnson and Noguera's bilateral value added exports» matrix used for their derivation of the VAX measure. So it can be called the trade in value added» matrix. Each element here represents both direct and indirect flows of value added that originates in sector i of country r and ends up» in country s to satisfy its final demand. The rows of VcLF sum to the total value added (sectoral or aggregated) produced in country r. The columns of VcLF sum to the total value added absorbed in country s.
VcLEtoi is the value added in total trade» matrix. [Koopman et al., 2010] proposed to use it for the computation of the multilateral VS and VS1 measures, as the column sums of the off-diagonal elements give VS and the row sums of the off-diagonal (aggregated) elements give VS1 in monetary terms. Note also that the columns of VcLEtoi (and of Etot) sum to the total exports of country s and its rows sum to the total exports of country r's value added (sectoral or aggregated) in gross trade flows.
VcX(KNxK) is a block-diagonal matrix of sectoral value added.
As the primary interest here is international trade, it is legitimate to consider the offdiagonal block elements only from equation (2). VcX(KNxK) then disappears from the basic accounting relationship since it only has the diagonal block elements:
(3) [VcLEM ]=[VcLF]f[VcLEtof ].
The right side of equation (3) can be recognised as the sum of multilateral VAX and VS1 measures in monetary terms. This basic accounting relationship implies a straightforward interpretation: the value added that originates in sector i of country r and lands» in country s via direct and indirect trade flows is equal to the value added that ends up» in the final demand of
V
country s plus the value added that is re-exported by country s to third countries. [VcLF] is
therefore a net term and [VcLEtoJ = Vc L Etoi is a double-counted term. This gives a basic decomposition of the bilateral value added in total trade into two components that can be expressed as its shares. Recall that the default dimension of the resulting matrices is KN x K.
In just three steps, equation (3) can be rearranged to express gross bilateral exports as a sum of value added components. First, note that the bilateral value added in trade matrix» can be decomposed into two matrices that represent direct and indirect bilateral flows of value added
A V
in trade: VcLEM = Vc L Ebil + Vc L Ebil. Then equation (3) may be rearranged as follows:
V
(4) Vc L Ebil = [VcLF]+ Vc L Etoi - l~Vc L Ebil
where Vc L EM is the matrix of domestic value added in direct bilateral exports and Vc L EM is the matrix of domestic value added exported indirectly from sector i in country r to country s.
V
The second step involves the construction of a KN x K matrix of foreign value added in
direct bilateral exports,
Vc(NxKN) L
Ebil , where Vc(NxKN) = tVc,1 Vc,2 L Vc,k] and Vc,s are N x N diagonalised vectors of the value added coefficients as in previous formulations.
A
V A
Vc(NxKN) L Ebil is analogous to Vc L Ebil, but captures all value added other than domestic in
direct bilateral trade flows.
The sum of domestic and foreign value added in direct exports is equal to the total gross exports (provided that v = x' i'Z ), but this only holds for the aggregated gross exports. As is known, sectoral value added in exports is not equal to sectoral gross exports because of the inter-sectoral transfer of value added throughout the production process. So in the KNxK or
[country/sector] x country dimension, the sum of Vc L Ebil and
Vc(NxKN) L
EM will not yield
gross sectoral exports. For example, the exports of manufactured products may embody value added created in the agriculture or services sectors. The value added originating in manufacturing tends to be less than the gross exports of manufacturing, and the value added originating in services tends to exceed the observed gross exports of services. To attain an identity with gross exports at the sectoral level, the third step requires that a correcting term be constructed to account for the difference between gross sectoral exports and sectoral value added in exports:
Ebil
Vc L Ebil +
Vc(NxKN) L
E
<bil
= Ebil [Vc(NxKN)L]Ebil = I [Vc(NxKN)L] I Ebil
This is the matrix of the inter-sectoral transfer of value added on the exporting countries' side. As is known from the existing input-output accounts, sectoral value added is usually less than total inputs minus intermediate purchases because of international trade and transport margins, import duties and statistical discrepancies. In matrix terms, the equality
i'VcL = i' or v = x' i'Z does not hold. For exhaustive accuracy, [Vc(AixA3V)L]j EM may be replaced with I [i'VcL][Vc(vx^v)L]] Em . See [Muradov, 2014] for an extended discussion of
the computation and interpretation of this matrix.
Finally, add the matrix of foreign value added in direct bilateral exports and the correcting term to both sides of equation (4) to obtain the equation for gross sectoral exports:
(S) Ebil = [VcLF]+ VcLEft

v v r
Vc L Ebil + Vc(NxKN) L Ebil + I
v
I [yc(NxKN)l]| Ebil



v

An aggregation to the K x K or countryxcountry dimension will drop the correcting term. Construct a sector-wise aggregation matrix Sn:
S =
i 0 0 i
00
where i are N x 1 summation vectors. Aggregate with respect to the exporting sectors. Since the columns of the value added multiplier matrix VcL theoretically add up to one, the last term in (5) becomes zero:
(6)
s;em = s; [VCLF]+ s;ycLEtoi - s;
V V
VcLEbii +s; Vc(VxKV) L
E
bill
which translates the basic relationship (3) into a decomposition of bilateral gross exports at the country level, in a way largely similar to [Koopman et al., 2012; Stehrer, 2013]. The components can now be expressed as ratios (rather than shares) to gross exports and some of these ratios may well exceed 1. This formulation also links various measures known from the literature on gross exports accounting or vertical specialisation in their monetary form: the first term on the right side is the bilateral VAX measure, the second is VS1, and the fourth is VS. The third term may be treated as a reversed VS1» because it represents the exporter's value added that flows from third countries to partners, i.e. in a direction that is opposite to VS1. So these four measures from (6) add up to the aggregate gross exports:
GROSS (BILATERAL) EXPORTS = VAX + VS1 - reversed VS1» + VS
3.3. The itemised accounting of the bilateral value added flows
It is possible to split the [VcLF] and [VcLEtoi] terms from the basic accounting relationship (3) into various components. The former can be expressed as follows:
(7)
[VcLF] =
A A
VcLF + VcLF +
c c
V V A A
VLF- VLF
A V V A
= VLF+ VLF+
V
VV
V LF
The resulting terms on the right side need careful interpretation. The first term VcLF captures the value added that originates in sector i of country r and is embodied in products
V A
made in country r for final demand in country s. The second term V. L F captures the value added that originates in sector i of country r and is embodied in products made in country s for
V
A
V
V
V
final demand in country s. The third term
V
V V
VLF
captures the value added that originates in
sector i of country r and is embodied in products made in third countries for final demand in country s. The principal distinction between these terms is therefore in the place where intermediate products are transformed into final products: in the exporting country r, partner coun-
A V
try s or third countries. Note that only the first term VcLF is in fact an export flow of final products while two other terms represent exports of intermediates that are finally absorbed in the partner country.
r V l V
Another manipulation will discern two components in [VcLEtotJ = Vc L Etot:
(8)
VcLEtoi = VcLo E'M +
Vc L Etot - VcLo E'M
The first term, Vc Lo E'bil, is a matrix of value added that originates in sector i of the exporting country r and returns home via gross exports from the partner country s (reflected value added»). Note, again, that ° and ' signify, respectively, block-by-block multiplication and block-by block transposition. Within block elements, normal matrix multiplication rules hold.
The second term in (8),
V LEt t - V Lo E'
c tot c bii
, is a matrix of value added that originates in
sector i of the exporting country r and is re-exported by partner country s to third countries (redirected value added»).
Finally, compile a new equation for a more profound decomposition of bilateral domestic value added in trade flows from (3), (7) and (8):
(9)
[VcLEbii ] = VcLF+ VcLF+
V V
VLF
+ VLo E'bii +
Vc L Etot - VcLo E'bii
The corresponding equation for gross exports is as follows:
A V VA
Ebii = VCLF+ V.LF+
(10)
V VV

V LF
+ VcLo E'bii +
VcLEot - VcLo Ebii

VcLEbii
Vc(NxKN) L
Ebii + I 1 - Iyc(NxKN)l] I Ebii
The last term in (10), again, accounts for the inter-sectoral transfer of value added from the sector of origin throughout the production process on the exporting country's side. The sector-wise aggregation to the K x K or country x country dimension will remove this term:
V
V
+
A
+
(11)
V VA
SX,=s;ycLF+ s;ycLF+ s;
- S'
V VV

V V
VcLEbil +s; Vc(NxKN) L
VcLF
Eb1.
+ S';VcLo E'bil + s;
VcLEo - VcLo E'bii
Equation (11) yields the results that are identical to those in [Stehrer, 2013] (see equation 9), and the only difference is that in the latter study, double counted terms are split into
V V V r V -.
the final and intermediate components, using that Ebil = F+ Z(KNxK) = F+ [Ax^^ J.
The above derivation of the gross exports accounting equation reveals that it is in fact a result of the decomposition of cumulative value added not direct exports flows. That's the reason why bilateral trade between the partner country and third countries - captured by
V
V V
VLF
VcLE^ - VcLo Eb
bil
and
VcLE
bil
appears in this formula for bilateral gross
exports which may first seem counter-intuitive. This is also the reason why the range of individual components in (10) and (11) expressed as the ratios to gross exports is not confined to 0-100%, so a normalisation with respect to gross exports will give ratios rather than shares. As noted in section 2, for a decomposition of direct bilateral exports into detailed value added components that are bound between 0 and 100% one should use the framework developed in [Wang et al., 2013].
Lastly, note that the difference between
V LE,t- V LoE'
c tot c bil
and
V LE
'bil
gives
the balance of trade in the exporting country's value added between the partner country and third countries. The next subsection will reveal that the difference between these terms equals zero after aggregating across partner countries.
V

V
V
3.4. Aggregation across partner countries: the decomposition of value added in total exports9
As noted earlier, the row sums of VcLEbil, or the aggregation across partner countries, equal domestic value added in total gross exports of country r, inclusive of reflected value added given by the diagonal block elements. Removing the reflected value added results in
V
[VcLEbil]. At the sectoral level, the aggregation of this matrix leads to a decomposition of value added that originates in sector i of country r and is sent to all partner countries via direct and
9 The proposed framework also allows for an aggregation across exporting countries, i.e. a decomposition of value added in total imports. As this is less relevant to the scope of this paper, the decomposition of value added in total imports is not discussed here, but the interested reader may refer to the subsection 3.5 in [Muradov, 2014].
indirect exports. Below, the aggregation results are shown for both the basic accounting equation (3) and the itemised version (9):
(12) [VcLEM]i = [VcLF]i + [VCLE Ji,
(13) [VcLEji = VcLFi + VcLFi +
V
V V
V.LF
+
VLo E
<bil
+
VcLEtoi - VcLo Ebii
where i is a K x 1 summation vector. The interpretation of the individual terms is similar to (3) and (9), with respect to all trading partners. Pre-multiplication by the sector-wise aggregation matrix S' will yield a country level decomposition.
The same type of aggregation applies to equations (5) and (10) to express total sectoral gross exports as the sum of the value added components. However, the aggregation at the country level, based on equations (6) and (11), is of particular interest. The condensed form is:
(14) S'Aili = S'n [VcLF]i + s;vc L E oi - S And the itemised form is given by:
VcLE
bil
i+s;
Vc(NxKN) L
Ebiii.
SEbii i = s;VcLFi + s;VcLFi + s;
(15)
V V V
VcLF i + S'; VcLo E'bii
+
+S'
V LE,t- V LoE'
c tot c bil
V V
i - S'; VcLEbii i + S'; Vc(NxKN) L
E
bil
The fifth term in the above equation S n
VcLEtot- VcLoE'bii
is country r's value
added re-exported by partner country s to third countries. The sixth term S^
VcLEbii
is
country r's value added indirectly exported via third countries to partner country s. At the aggregate country level, these terms equal each other, hence the balance of trade in exporting country r's value added among all partners is zero (for an explicit proof, see [Muradov, 2014]). Equation (14) may also be rewritten in terms of the measures known from the literature on trade in value added and vertical specialisation:
V

V
V

V
GROSS (TOTAL) EXPORTS = VAX + VS1* + VS.
3.5. A note on total and bilateral trade balances
Recall that the columns of VcLEtoi sum to the total exports of country s (and also value added in total exports, provided again that i'VcL = i' or v = x' i'Z) whereas the columns of VcLEM sum to the total imports (also value added in total imports) of s. Also note that the diagonal block elements which are the only elements in the columns of Vc:x(KNxK) can be interpreted as the sum of the value added generated in country s by both domestic and foreign final demand (which is equal to the sum across the rows of VcLF). And the columns of VcLF sum
to the total value added absorbed in country s. Then the basic equation (2) can be simply rearranged in the 1xK dimension to show:
or
(16)
i'VcLEtot i'VcLEbil = i'VcX(KNxK) i'^LF,
i,Etot iE bil = ^VcX ( KNx K) iVcLF
The left side of the equation (16) is a difference between total gross exports and total gross imports of country s, or a 1 x K vector of trade balances in gross terms. Likewise, the right side gives the difference between total value added generated and total value added absorbed in country s, i.e. a 1 x K vector of trade balances in value added terms. This completes the proof of the equality of trade balances in gross and net terms and succinctly confirms the earlier results of [Stehrer, 2012, 2013; Kuboniwa, 2014b, 2014c].
Bilateral trade balances in the K x K matrix form can be calculated as differences between relevant bilateral matrices and their transposes. For gross trade balances this can be expressed as:
/
(17) S'/jEm - bu ) = - Ebin
Using (2) and (6) gross trade balance can be decomposed into various components:
SXi, - (S'Ebi7)' = [SXLF - ((VcLF) 1 + kvcLEtoi - (S'VcLEtoi)'

f
v ( v ^ v v
S'nVcLEbil S'nVcLEbil + S'n Vc(NxKN) L Ebil S'n Vc(NxKN) L Ebil
V y1 -- --
The matrix of bilateral balances of value added in gross trade can be computed as: (18) SXLE^ (SXLE J = SXLE^ E^L'VS
or in the decomposed form,
s;vclem -(s;vclem )= s;vclf -((vlf) + s;ycLEtoi -(s;ycLEtoi )
Finally, the matrix of bilateral balances of trade in value added is:
(19)
svclf-((vClf) = svClf - F'L'VcSn.
It is therefore evident that these three types of bilateral trade balances for a pair of countries are not equal unless under very special conditions. For example, the gross trade balance (22) equals the balance of trade in value added (24) only if the sum of respective elements in the matrices of bilateral balances of domestic re-exported value added, domestic re-directed value added and foreign value added is zero.
3.6. Extension to the KN x KN and K x KN dimensions and value added at destination»
The discussion has so far focused on the decomposition of value added flows that originate in sector i of exporting country r and end up» or land» in partner country s. It therefore attributed all value added component flows to their country/sector of origin. An extension to the KN x KN dimension and aggregation to the K x KN dimension would capture all value added created in country r embodied in products of sector j consumed or re-exported by partner country s. Such change of perspective is not a trivial exercise and requires an extension to the minimal» initial setup.
Decompositions of value added at destination rather than at origin have been suggested on an ad hoc basis in the literature on trade in value added. [Koopman et al., 2010] propose to aggregate across exporting country sectors and disaggregate the partner country sectors in a matrix similar to the value added in total trade» VcLEtoi matrix in this paper. They treat it as a sectoral measure of value-added trade in global value chains» (see formula 12 in [Koopman et al., 2010] for the two-country case). [Meng et al., 2012] briefly discuss similar type of disag-gregation applied to their sectoral trade in value added» measure that they use to derive alternative, TiVA-based version of revealed comparative advantage indicators (equations 12-13 in [Meng et al., 2012]).
This paper makes a systematic effort to sort out the implicit aggregation in previously used measures in a block matrix environment. First, convert F, x^wxA), Etot and Em matrices from the KN x K to the KN x KN dimension:
l(KNxKN) '
f11 fl2 * f1k
f21 f 22 f2k
f f
k1 ''
k2
kk_
(KN xKN)
xx1 0
0 xX 2 00
k
E
tot(KNxKN) '
ej 0 0 e2
00
Ebil(KNxKN)
21

12
k2
b1k
c2k
0
The above conversion of F, Etot and Em and x is for computational purpose only, to keep the sectoral dimension of results, and does not involve a meaningful interpretation.
Now Z, F(bv*hv), Etot(KmKN), Em(kw*kn) and X(KNxKN) are all KN x KN matrices. Owing to the
above specification, all blocks in F(kn*kn), Etot{KN»KN), Em(kw*kw) and X(KVxKV) contain either diagonal elements only or zeros except Z where blocks contain nonnegative values in all or many of the elements. For the equation (1) to hold in KN x KN dimension, one more term is required to offset the presence of the off-diagonal elements in each block of Z:
Z* =
Z11 Z1: Z21 Z
'22
Zk1 Z
k2
Z1 Z
2k
Z
kk

M [Z^i] [Z21i] [Z22i]
Zki]
[Z2ki]
[Zk1i] [Zk2i] L [Zkki]
Then the equation (1) in KN x KN dimension is as follows:
(20)
Ebil(KNxKN) Etot(KNxKN) = F(KNxKN) + Z *(KNxKN) Z
The same manipulation applies as in subsection 3.2, and the difference is that one more term appears on the right side:
(21)
VcLEbil(KNxKN) = VcLF(KNxKN) + VcLEtot(KNxKN) Vc:X(KNxKN) VcLZ
The last term accounts for the inter-sectoral transfer of value added embodied in intermediate products on their way from the sector of origin i to the sector of destination j. So, this is the inter-sectoral transfer of value added on the partner countries' side.
Finally, removing the diagonal block elements yields the basic accounting relationship in the KN x KN or full [country/sector] x [country/sector] dimension:
(22) [VcLEbil(KNxKN)]- [VcLF(KNxKN)]+ [VcLEtot(KNxKN)] [VcLZ1
0
0
0
0
k
All subsequent equations for the value added or gross exports accounting as in subsections 3.2-3.4 in the KN x KN dimension should include the last term from (22). In the first two matrices on the right side of the equation (22), each element should be interpreted as the value
added originating in sector i of country r embodied in product of sector j used by country s for domestic consumption or re-exports. The last term accounts for the re-allocation of value added originating in sector i of country r resulting from the inter-sectoral flows of intermediates for which country s is responsible. Appendix D in [Muradov, 2014] explores the properties of this matrix in more detail.
Pre-multiplication of (22) and any derivative equation by the sector-wise aggregation matrix S'n will condense the results to the K x KN or country x [country/sector] dimension:
(23) S [VcLEbil(KNxKN)] = S/J VcLF(KNxKN)]+ S/j [VcLEto<KNxKN)]- VcLZ ]
where each element in any resulting matrix should be interpreted as the value added originating from (all sectors of) country r embodied in product of sector j used by country s for domestic consumption or re-exports. Again, the re-allocation term accounts for the inter-sectoral value added flows on the partner countries' side. Note that the aggregation of (22) and (23) across recipient country's sectors, respectively, to the KN x K and K x K dimensions, i.e. post multiplication by Sn, will make the last term equal to zero.
One should also note that a transformation of (22) into a gross exports accounting equation in the KN x KN dimension will have no meaningful interpretation because of the presence of zeroes in the off-diagonal elements of each block in Em(v*v> However, an aggregated version in K x KN dimension can be interpreted in terms of the total value added components embodied in products received at the partner side.
This completes the discussion of the generalised framework proposed in this paper for the accounting of value added in international trade.
4. Application and selected results: Russia in global value chains
For an application of the proposed value added accounting framework, this section focuses on Russia's global and bilateral exports. Previous studies have revealed an extremely high content of domestic value added in Russia's gross exports. As an upstream natural resource producer, Russia was found to have a large share of its domestic value added absorbed by direct importers, delivered via intermediate rather than final products. A significant portion of Russia's intermediate exports were also used by other countries to produce their intermediate goods exports [Koopman et al., 2010, 2012; OECD 2013b].
In conventional analysis of international trade, exports and exporters of energy and other natural resources are often isolated or neglected. However, a brief discussion below shows that the natural resource exporters like Russia may be an interesting case for the analysis of global value chains. In particular, Russia's case will show how the value added generated in a resource-extracting sector is circulated through partner and third countries' trade, or downstream value chain.
The formulae derived through the previous section are tested here with the data from the World Input-Output Database (WIOD). The WIOD database contains a series of national and inter-country supply, use and input-output tables supplemented by sets of socio-economic and environmental indicators for the period from 1995 to 2011. The data covers 27 European
Union member states, 13 other major non-European economies plus estimates for the rest of the world and discerns 35 industries based on NACE revision 1 which corresponds to ISIC revision 310.
The results are estimates that necessarily reflect the assumptions that the WIOD compilers had to make in the process of creating and balancing their ICIO tables, including Russia's input-output tables11.
4.1. Russia's global and bilateral exports: does the accounting approach matter?
As follows from the previous section, three concepts may be applied to measure total and bilateral trade flows:
gross exports» - that is usual gross trade statistics,
value added in exports» - that is gross trade flows reallocated to the countries of origin of value added contained therein, and
exports of value added» - that is gross trade flows reallocated to the countries of origin of value added with the double-counted flows removed.
V V
This involves computing three vectors, S^E^-/, S'n [VcLEbilJi and S'n [VcLF]i, and - for
cross-country comparison - the shares of each element with respect to the column sums. Note that the reflected exports (diagonal elements in the respective matrices) are not accounted for, to conform with the basic accounting relationship (3). Accounting for the reflected exports may be important for such country as the United States, but does not affect the order of the results.
Using these three concepts and WIOD data for 2010, Table 1 ranks world top 20 exporters. Change of concept affects the relative importance of most countries in the global trade, though the differences are not dramatic. China overtook the United States as the largest exporter in terms of gross exports (10,9% vs. 10,2% of global exports), but lacked behind the United States as the country of origin of value added embodied in those exports (11,1% vs. 11,9%). Finally, China and the United States performed almost equally well in generating net value added for consumption abroad (11,7% of global traded value added, but China actually led with a negligible 0,02% advantage).
In Table 1, moving from the gross exports to domestic value added in exports measurement means removing foreign value added in national exports and adding domestic value added in partner exports (less those that return home). In the language of the literature on vertical specialisation, this means subtracting VS and adding VS1 (again, corrected for reflected exports). So net (indirect) exporters of value added - those who indirectly supply more domestic value added than directly receive foreign value added - usually raise to higher ranks. In 2010, Russia is the 11th global exporter in gross terms and 6th in terms of domestic value added in exports with the total exports indicator raised by 42%, or from 2,3 to 3,6% of the global ex-
10 For more information on the WIOD project, see [Timmer, 2012; Dietzenbacher et al., 2013] and the WIOD website www.wiod.org.
11 The only supply and use table officially available to the WIOD project for Russia was dated 1995. For a discussion of the issues related to the use of this table for the modelling of a consistent time series of Russia's supply and use tables, see [Baranov et al., 2014].
ports. Similarly, Australia climbs up from the 17th to 12th position and its contribution to the global exports raises from 1,7 to 2,2%. The opposite examples are most notably given by Belgium and Chinese Taipei.
Table 1.
Twenty largest global exporters in 2010 and three measurement options (million US$ and percentage of total world exports, current prices)
Gross exports Domestic value added in all exports Exports of domestic value added
No. Exporter US$ mln % No. Exporter US$ mln % No. Exporter US$ mln %
1 China 1743486 10,9 1 United States 1767249 11,9 1 China 1300561 11,7
2 United States 1634458 10,2 2 China 1645795 11,1 2 United States 1298542 11,7
3 Germany 1391739 8,7 3 Germany 1195077 8,0 3 Germany 903105 8,1
4 Japan 835356 5,2 4 Japan 918590 6,2 4 Japan 690182 6,2
5 United Kingdom 617535 3,9 5 United Kingdom 620217 4,2 5 United Kingdom 452148 4,1
6 France 609074 3,8 6 Russia 528076 3,6 6 France 394262 3,6
7 Korea 519545 3,2 7 France 513184 3,5 7 Italy 346051 3,1
8 Italy 514168 3,2 8 Italy 444477 3,0 8 Canada 337358 3,0
9 Netherlands 468328 2,9 9 Canada 422439 2,8 9 Russia 330619 3,0
10 Canada 449279 2,8 10 Korea 386228 2,6 10 Korea 287267 2,6
11 Russia 371743 2,3 11 Netherlands 352855 2,4 11 Netherlands 258148 2,3
12 Belgium 322585 2,0 12 Australia 323310 2,2 12 Australia 229948 2,1
13 Spain 322167 2,0 13 Spain 276740 1,9 13 India 220449 2,0
14 Chinese Taipei 311633 1,9 14 India 275697 1,9 14 Spain 212852 1,9
15 India 308576 1,9 15 Brazil 248603 1,7 15 Mexico 185057 1,7
16 Mexico 286285 1,8 16 Mexico 231554 1,6 16 Brazil 183369 1,7
17 Australia 273733 1,7 17 Chinese Taipei 222378 1,5 17 Belgium 161346 1,5
18 Brazil 232982 1,5 18 Belgium 221631 1,5 18 Chinese Taipei 155067 1,4
19 Sweden 212123 1,3 19 Indonesia 199799 1,3 19 Indonesia 145827 1,3
20 Ireland 197741 1,2 20 Sweden 177034 1,2 20 Sweden 130802 1,2
Note: the Rest of the World is dropped from the list of exporters. Source: WIOD database, author's calculations.
Moving further right in the table, from domestic value added in exports to exports of domestic value added means removing the domestic value added that circulates through the downstream value chain via intermediate products and is therefore double counted. Then net exporters of value added would typically step back or, at best, retain their ranks. In 2010, Russia being the 6th largest country in terms of domestic value added in exports (contribution 3,6%) becomes the 9th exporter of net value added (contribution 3,0%). Australia remains to be the 12th largest exporter with a slightly lower contribution in terms of net value added (2,2% turns to 2,1%).
In Table 2, same measurement concepts are applied to Russia's bilateral exports. The three approaches to identify the largest export partners yield three different results: the principal export market in gross terms is Italy (8,8%), the principal destination for Russia's value added embodied in gross exports is China (7,0%), and the most important final destination for Russia's value added is the United States (9,6%). The differences as we will see in more detail below stem from the relative position of Russia's trading partners as absorbers or re-exporters of value added.
Table 2.
Russia's ten largest trade (export) partners in gross and value added terms, 2010 (million US$ and percentage of Russia's total exports, current prices)
Gross exports Domestic value added in all exports Exports of domestic value added
No. Partner US$ mln % No. Partner US$ mln % No. Partner US$ mln %
1 Italy 32783 8,8 1 China 37078 7,0 1 United States 31735 9,6
2 China 24188 6,5 2 United States 36873 7,0 2 China 26515 8,0
3 Germany 19459 5,2 3 Italy 36678 6,9 3 Italy 25290 7,6
4 United States 18206 4,9 4 Germany 35010 6,6 4 Germany 20833 6,3
5 Netherlands 16826 4,5 5 France 25315 4,8 5 France 17655 5,3
6 France 16773 4,5 6 Japan 21859 4,1 6 Japan 17260 5,2
7 Japan 14975 4,0 7 Netherlands 20236 3,8 7 United Kingdom 10302 3,1
8 Poland 11813 3,2 8 Korea 14212 2,7 8 Spain 8275 2,5
9 Finland 9369 2,5 9 United Kingdom 14147 2,7 9 Poland 7817 2,4
10 Korea 8496 2,3 10 Poland 13601 2,6 10 Korea 7535 2,3
Note: the Rest of the World is dropped from the list of exporters. Source: WIOD database, author's calculations.
A remarkable finding from Table 2 is that the importance of the United States as an export destination for Russia is much higher than revealed by the traditional trade statistics. In
2010, 4,9% of Russia's gross exports were directly sent to the United States, but the share of total exported value added from Russia that eventually ended up in the United States was 9,6% which effectively made the United States the largest consumer of the value added of Russian origin. Similarly, China accounted for 6,5% of Russia's gross exports and 8,0% of its exported value added. The EU members were collectively the largest market for Russia's exports in gross terms (43,4%) and contributed somewhat lower share to the final use of its value added (40,6%). Apparently, the integration into global value chains allowed Russia to serve distant markets via intermediate supply to the closer European neighbours.
4.2. Understanding the basic components of Russia's value added flows
The basic accounting relationship (3) links together two concepts from Tables 1 and 2 -
V
domestic value added in exports» (S^ [VcLEM]i) and exports of domestic value added»
V
(SI [VcLF]i) - and relates the difference between the two to the domestic value added reV
exported by trading partners (S^ [VcLEtoi]i), which is hereafter referred to as the re-exported value added» for brevity. This term statistically captures cumulative double counted flows of value added that circulate across borders and are largely responsible for the growth of global value chains. It is also known as VS1 [Hummels et al., 1999], or an indicator of forward participation» in global value chains (various OECD publications), or downstream component» [UNCTAD, 2013]. Application of the accounting relationship (3) allows one to see which of the two components - exports of value added for final demand or for re-exports - and to what extent is responsible for cumulative value added in global exports that can be attributed to a single country. Figure 2 reports the results as the ratios to gross exports in 2000 and 2010, partly isolating the effect of different years' prices. Top 20 exporters are ranked according to the value added to total gross exports ratios.
It appears that six countries in the WIOD database - the United States, Japan, United Kingdom, Russia, Australia and Brazil - have total domestic value added circulating in global exports that is equal or exceeds their total gross exports. By the way, China is quite close to assume this pattern if it beefs up its downstream value added exports. Note that the United States, Japan and United Kingdom have relatively stable ratios of domestic value added in global exports to total gross exports. Visible changes, if any, e.g. decline in Japan's ratio in 2000-2010 by 0.04, mostly correspond to the respective change in its final», or absorbed» component. Meanwhile, Brazil, Australia and Russia experienced an increase in their ratios through 2000-2010, respectively by 0,07, 0,14 and 0,19. The source of the increase was the re-exported» component which rose by 0,06 in Brazil, by 0,11 in Australia and by 0,16 in Russia. This effectively discerns a group of the upstream suppliers of services in global value chains (United States, Japan, United Kingdom) and a group of the upstream suppliers of natural resources (Russia, Australia, Brazil).
Russia stands out for the extremely high contribution of both value added that ends up in final demand and the value added that is further re-exported, if the domestic gross exports is used as a benchmark. The re-exported component expressed as the ratio to gross exports shows the magnitude and growth rate that is unparalleled in the WIOD database. However, the
use of other databases with superior country coverage, e.g. OECD - WTO TiVA database built on the OECD ICIO system, would reveal similar pattern for such resource-rich countries as Norway, Saudi Arabia and Chile.
Russian Federation Japan United States Australia China United Kingdom Italy Germany Austria France Sweden Spain Denmark Korea Canada Mexico Chinese Taipei Netherlands Belgium Ireland
2000
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0,00 0,20 0,40 0,60
0,80
1,00
1,20
1,40 1,60
^ Exports of domestic value added / total gross exports Re-exported domestic value added / total gross exports Note: the Rest of the World is dropped from the list of exporters.
Fig. 2. The basic decomposition of value added flows, ratio to total gross exports Source: WIOD database, author's calculations.
4.3. The anatomy of Russia's value added in gross exports
Equation (11) offers the itemised decomposition of the bilateral value added flows normalised to the bilateral gross exports. This is particularly useful to see the indirect trade in a country's value added among its trade partners, that is not a direct component of gross exports and cannot be observed in simple versions of value added accounting.
Table 3 relates each component bilateral value added flow to Russia's gross exports to top 20 destinations (ranked as of 2010) in 2000 and 2010. The last two rows summarise the results for total Russia's gross exports. Note that in column F, the values are negative which is required so that all components sum up to gross exports as in equation (11). Yet the sum of the values in columns A through G does not equal 1 because value added is usually somewhat less than total output minus intermediate demand.
Two trends can be clearly discerned: (1) a decline of the relative importance of the direct deliveries of final products to nearly all principal export markets, and (2) significant rise of the indirect trade in Russia's value added among its partners which is in fact double-counted from the value chain perspective. In 2000, only two countries - the United States and United Kingdom - were heavily involved in trading value added that ultimately originated from Russia. In 2010, Germany and Spain joined, each indirectly receiving Russia's value added equivalent to more than 0,9 of the direct gross exports from Russia while Belgium received 1,95! For China, France, Japan, Korea, Sweden, Turkey this measure exceeded 0,5. In 2010, many of the largest Russia's export partners have negative balance of trade in Russia's value added with third countries which explains why they earn higher profile as destinations for Russia's value added when the indirect flows are explicitly accounted for. Italy and the Netherlands are notable exceptions: they indirectly re-export more Russia's value added than they receive.
The last rows in Table 3 confirm that the amount of total Russia's value added that direct partners re-export to third countries equals total Russia's value added that direct partners indirectly receive via third countries. These two components can be summed to cancel each other. This may be treated as partner balance in trading Russia's value added that is zero at the aggregate country level.
Table 3.
Bilateral flows of Russia's domestic value added, decomposed and normalised to gross exports to twenty largest export destinations, an itemised decomposition
Partner Year Gross ex- Value added flows, ratios to gross exports
ports, US$ mln (current prices) Domestic, in final products Domestic, in final and intermediate products (double-counted) Foreign
A B C D E F G
Italy 2000 8507 0,03 0,69 0,07 0,00 0,28 -0,20 0,08
2010 32783 0,01 0,69 0,07 0,01 0,34 -0,20 0,04
China 2000 3008 0,04 0,77 0,07 0,00 0,25 -0,31 0,13
2010 24188 0,03 0,97 0,10 0,01 0,43 -0,64 0,05
Continues
Partner Year Gross ex- Value added flows, ratios to gross exports
ports, US$ mln (current prices) Domestic, in final products Domestic, in final and intermediate products (double-counted) Foreign
A B C D E F G
Germany 2000 16447 0,19 0,49 0,10 0,00 0,34 -0,25 0,09
2010 19459 0,13 0,61 0,33 0,02 0,71 -0,91 0,05
United States 2000 3844 0,12 1,14 0,57 0,00 0,28 -1,30 0,14
2010 18206 0,08 1,22 0,45 0,00 0,28 -1,14 0,05
Netherlands 2000 2165 0,03 0,39 0,15 0,00 0,78 -0,50 0,09
2010 16826 0,02 0,22 0,08 0,00 0,87 -0,29 0,04
France 2000 5304 0,03 0,70 0,15 0,00 0,40 -0,42 0,09
2010 16773 0,06 0,77 0,22 0,01 0,45 -0,61 0,04
Japan 2000 2915 0,19 0,75 0,18 0,00 0,20 -0,48 0,11
2010 14975 0,07 0,90 0,18 0,00 0,30 -0,56 0,05
Poland 2000 4069 0,02 0,67 0,04 0,01 0,27 -0,15 0,09
2010 11813 0,02 0,58 0,07 0,02 0,47 -0,24 0,04
Finland 2000 3263 0,06 0,39 0,02 0,01 0,46 -0,07 0,09
2010 9369 0,02 0,40 0,04 0,02 0,54 -0,12 0,05
Korea 2000 1761 0,08 0,56 0,08 0,00 0,44 -0,31 0,10
2010 8496 0,07 0,68 0,14 0,01 0,77 -0,77 0,05
Hungary 2000 2228 0,01 0,61 0,04 0,01 0,37 -0,16 0,09
2010 6521 0,04 0,51 0,06 0,01 0,49 -0,21 0,04
Spain 2000 2593 0,03 0,73 0,17 0,00 0,41 -0,47 0,09
2010 6513 0,07 0,86 0,34 0,00 0,59 -0,96 0,04
United Kingdom 2000 1884 0,12 0,90 0,53 0,00 0,50 -1,19 0,10
2010 5777 0,10 0,96 0,72 0,01 0,66 -1,56 0,05
Sweden 2000 683 0,11 0,68 0,42 0,00 0,82 -1,16 0,09
2010 5615 0,04 0,28 0,21 0,00 0,95 -0,58 0,04
Greece 2000 1457 0,06 0,70 0,08 0,00 0,26 -0,23 0,09
2010 5378 0,05 0,75 0,10 0,00 0,23 -0,22 0,04
Lithuania 2000 1378 0,11 0,37 0,03 0,02 0,39 -0,06 0,09
2010 5119 0,07 0,34 0,07 0,01 0,54 -0,12 0,04
Turkey 2000 2542 0,04 0,80 0,07 0,00 0,18 -0,24 0,11
2010 4325 0,16 0,70 0,20 0,01 0,32 -0,53 0,06
Continues
Partner Year Gross ex- Value added flows, ratios to gross exports
ports, US$ mln (current prices) Domestic, in final products Domestic, in final and intermediate products (double-counted) Foreign
A B C D E F G
Slovak Republic 2000 2174 0,03 0,34 0,02 0,06 0,49 -0,07 0,08
2010 3596 0,03 0,45 0,07 0,02 0,56 -0,21 0,04
Bulgaria 2000 1674 0,03 0,36 0,01 0,02 0,50 -0,05 0,08
2010 3338 0,02 0,42 0,04 0,04 0,53 -0,14 0,04
Belgium 2000 717 0,11 0,55 0,51 0,01 1,36 -1,69 0,11
2010 2973 0,08 0,64 0,46 0,01 1,63 -1,95 0,05
TOTAL (all partners) 2000 2010 98757 371743 0,13 0,08 0,60 0,65 0,13 0,17 0,01 0,01 0,37 0,52 -0,37 -0,52 0,10 0,05
Note: A - direct, in final products, absorbed by partners;
B - direct, in intermediate products, processed and absorbed by partners;
C - indirect, in intermediate products, processed by third countries and absorbed by partners;
D - reflected, in final and intermediate products (double-counted);
E - re-exported to third countries, in final and intermediate products (double-counted);
F - indirect via third countries, in final and intermediate products (double-counted);
G - foreign, in final and intermediate products. Russia's partners are ranked according to bilateral gross exports in 2010. The Rest of the World is excluded.
Source: WIOD database, author's calculations.
4.4. Discovering the sectoral origin of value added in Russia's exports
V V V
The basic accounting equation in the KN x K dimension [VcLEM] = [VcLF]+ [VcLEtoi] uncovers sector detail behind the aggregated results. Figure 3 shows the contribution of top 10 Russia's sectors to the total domestic value added in exports in 2000 and 2010, and the breakdown discerns the value added for final demand and for re-exports.
Both graphs for 2000 and 2010 show the prevalence in terms of value added in exports of a few sectors that generate trade and transport margins. However, it is Mining and quarrying» that is clearly responsible for an expansion of Russia's value added flows to the downstream value chain through 2000s. And the re-exported component of the value added created in this sector was growing faster than the finally absorbed one. The manufacturing sectors other than fuel production had their relative value added in exports shrunk through this period.
2000
W/////////////MWA : : : :~1 - . I
7ZZZZZZZZEZ3. '''' ^
'/////
777
777
22
_
-1-1-1-1-1
0,0 0,1 0,2 0,3 0,4 0,5 2010
'///////////////////////////////- :::::: "~1
///////////////. . -I
'///--
// I
77

0,0 0,1 0,2 0,3 0,4 0,5 0 Absorbed value added / total gross exports Re-exported value added / total gross exports
Fig. 3. Russia's domestic value added global flows from ten largest exporting sectors, a basic decomposition
Source: WIOD database, author's calculations.
4.5. Quantifying the role of partners and third countries in trading Russia's value added
Let us focus on the single sector that is critical for Russia's export performance, Mining and quarrying». The application of the equation (10) for the itemised decomposition of the value added originating in this sector in Russia may reveal that the gross export figures disguise the sizable increase in indirect value added flows among Russia's export partners and third countries. Aggregated country-wise in either direction (re-exported from partners to third countries or re-directed from third countries to partners), this value added flow is equal to 0,25 of the total gross exports of Mining and quarrying» in 2000 and 0,50 in 2010. Many top partners are now actively engaged in indirect imports rather than exports of intermediates containing the value added from Russia's mining and quarrying sector. In 2000, among the top
Wholesale Trade Mining and Quarrying Inland Transport Basic Metals and Fabricated Metal Retail Trade; Repair of Household Goods Electricity, Gas and Water Supply Coke, Refined Petroleum and Nuclear Fuel Renting and Other Business Activities Chemicals and Chemical Products Agriculture, Hunting, Forestry and Fishing
Mining and Quarrying Wholesale Trade Inland Transport Basic Metals and Fabricated Metal Coke, Refined Petroleum and Nuclear Fuel Retail Trade; Repair of Household Goods Renting and Other Business Activities Electricity, Gas and Water Supply Chemicals and Chemical Products Other Transport Activities; Travel Agencies
twenty export destinations, four were in fact net indirect importers of the value added of the said origin (i.e. they re-exported less Russia's value added than they indirectly received): Turkey, United Kingdom, China and Austria. In 2010, this status accrued to nine of the top twenty export destinations: China, France, Japan, Germany, the United States, Spain, United Kingdom, Romania and Czech Republic (see [Muradov, 2014] for a graphic illustration).
The matrix representation of the detailed value added components in this paper makes them highly customisable for specific analytical purposes. This is exemplified below in another application not covered in section 3 that will allow one to see how the value added from Russia's Mining and quarrying» sector is embodied in the back-and forth trade among Russia's partners.
First, the bilateral foreign value added in trade» matrix in the KN x K dimension
Vc(NxKN) L
EM is modified to include Russia's value added only. The result is a KN x K matrix
of trade in Russia's sectoral value added among all K countries. Next, extracting the rows sector-wise gives N K x K matrices that depict the bilateral flows of value added originating in Russia's sector i in partner trade. The matrix elements should be normalized, e.g. with respect to sectoral gross exports, for a sensible visualisation.
An example of such visualisation is shown in Fig. 4 that identifies the most important flows of the value added originating in Russia's Mining and quarrying» sector. If 0,3% of the total gross exports of that sector is chosen as a threshold, the dominant flows in 2000 are confined almost entirely to Europe. Many European countries appeared as the net exporters of value added of the said origin and Germany was a trade hub. Germany also re-exported that value added to the United States. By 2010, more countries shifted to the net importer status while the pattern of the value added flows became more complex. The directions of flows are now more diversified and no single hub may be discerned though the Netherlands rather than Germany appear to be at the centre of this network. Finally, East Asia enters the picture and China emerges as the dominant re-exporter if Russia's value added from mining and quarrying to the United States.

Continues
s United 4
\ States
^ United ^ Kingdom
Spain
2010
Sweden Finland
*
( \ N
Italy China

x. J
| net exporter of value added H net importer of value added
Note: The Rest of the World is excluded.
> 0,5% of gross exports of "Mining and quarrying" sector 0.40.5% of gross exports of "Mining and quarrying" sector 0,3-0.4% of gross exports of "Mining and quarrying" sector
Fig. 4. Circulation of the value added originating in Russia's Mining and Quarrying» sector embodied
in bilateral gross exports
Source: WIOD database, author's calculations.
4.6. Decomposition at destination: quantifying Russia's value added embodied in domestically consumed and re-exported goods and services at partner side
In this subsection, the quest is for the sectors of partner countries that deliver products where Russia's value added is embodied and for the actual use of those products, i.e. final domestic use or re-exports.
The respective row from equation (22) gives the flow of the value added from Mining and Quarrying» in Russia to sectors in other countries where it is embodied for further use. In
particular, the rows in [VcLF( KNxKN)] and VcLE^^^n,] contain estimates of the use of the value added sourced from Russia's Mining and Quarrying» in the products of partner countries' sectors and their sum is equal to the respective row sum in [VcLEM( KNxKN)], or the total value added sourced from Mining and Quarrying». These two terms may be treated as the
demand factors for the generation of value added in the sector considered. Meanwhile, [vcLZ*] explains the individual sectoral deviations between the amount of the value added that left the
origin and the amount that was received at the destination. For example, in 2010, 0,09% of the total value added from Russia's mining and quarrying sector was directly and indirectly sent to partner countries in the form of the products of the construction sector. At the same time, 8,94% of that value added was found embodied in the products of construction for final domestic use worldwide, and 0,10% in the products of construction for re-exports. The difference of
8,95% (the respective entry in [VcLZ*]) flowed from Russia's mining and quarrying to the products of construction indirectly through the products of other sectors in the recipient countries. This means that the use of Construction» products abroad is a significant factor not directly observed and creates demand for the exports from Russia's Mining and Quarrying» sector.
Differentiating value added by sector at destination leads to an alternative decomposition of a country's total value added in both direct and indirect exports. The visualisation of results in KN x KN, or [country/sector] x [country/sector] dimension, even for one country, is quite a complex task, so the figures below narrow the focus, again, to Russia's Mining and Quarrying» exporting sector.
In Fig. 5, the total value added flow from Mining and Quarrying» is aggregated across all partner countries and disaggregated across recipient sectors. This is to show the importance of the inter-sectoral transfer term: the products of Mining and Quarrying» appear as the largest carriers of Russia's value added that originates in that sector (55,3%), but the bulk of it (53,5%) is eventually used in the products of other sectors. Figure 6 exemplifies a decomposition of Russia's value added by products of the partner countries' sectors where it is embodied for domestic final use and re-exports. Inter-sectoral term is dropped for a clearer focus on the use of products in partner countries, or, in other words, the ultimate destination of Russia's value added created in the Mining and Quarrying» sector. This concept is reverse to that in Fig. 3 which discerned the sectoral origin of value added in exports.
Mining and Quarrying Coke, Refined Petroleum and Nuclear Fuel
///////
//////////////////////////////////////////////////A 11
Basic Metals and Fabricated Metal Chemicals and Chemical Products Electrical and Optical Equipment
Transport Equipment Inland Transport Machinery, Nec

ZEZH
EIS
Wholesale Trade, Except of Motor Vehicles
Food, Beverages and Tobacco
I ID
E ZED
in
E ZD
20% -10% 0% 10% 20% 30% 40% 50% 60%
H Re-directed to/from other sectors Domestic final use Re-exports
Fig. 5. Decomposition of the value added from Russia's Mining and Quarrying» sector in gross exports according to the products of partner countries' sectors where it is embodied, including the inter-sectoral transfer term, 2010 (percentage of total)
Source: WIOD database, author's calculations.
As might be expected, the products of Coke, Refined Petroleum and Nuclear Fuel» sector for both domestic use and exports appear as the principal absorbers of the value added created in Mining and Quarrying». Other products contributing to the demand for Russia's value added from Mining and Quarrying» include those of Construction» and Electricity, Gas and Water Supply» for domestic use, Basic Metals and Fabricated Metal», Chemicals and Chemical Products» for exports. Interestingly, the top 10 list also includes such entries as the products of Food, Beverages and Tobacco» and Public Administration and Defence, Compulsory Social Security». One can therefore conclude that in 2010, domestic worldwide use of public administration and defence services worth a dollar helped generate nearly 3 cents of value added in Russia's mining and quarrying.
Coke, Refined Petroleum and Nuclear Fuel Construction Chemicals and Chemical Products Basic Metals and Fabricated Metal Electricity, Gas and Water Supply Electrical and Optical Equipment Transport Equipment Food, Beverages and Tobacco Machinery, Nec
Public Admin and Defence; Compulsory Social Security
................................
...........
"
-1-1-1-1-1-1
0% 5% 10% 15% 20% 25% 30%
Domestic final use IHRe-exports
Fig. 6. Decomposition of the value added from Russia's Mining and Quarrying» sector in gross exports according to the products of partner countries' sectors where it is embodied for final use or re-exports, 2010 (percentage of total)
Source: WIOD database, author's calculations.
An additional partner country breakdown (not shown here) reveals that European economies largely use Russia's value added from Mining and Quarrying» to produce and export fuels. Contrary to European countries, China mostly uses that value added of the Russian origin for domestic construction and exports of electrical and optical equipment. The United States use it for domestically consumed fuels but also for public administration and defence. In other words, every dollar spent in the United States for public administration and defence services generates 0,9 cents of value added in Russia's mining and quarrying sector. This is an intrinsic implication of global value chains that link two seemingly unrelated sectors in two distant countries
5. Conclusion
Gross exports accounting frameworks build on the recent progress in developing global input-output databases to identify the origin and destination of value added behind conventional trade statistics. The decomposition of gross trade flows utilises common value added
concepts, but the exact method may vary. The starting point may be direct bilateral gross exports disentangled into additive value added components, and the results should be useful for trade policy analysis. Or it may be direct and indirect (cumulative) bilateral flows of value added, from the origin to the destination. The results then are thought to be more relevant for global value chain analysis. It is this type of frameworks that this paper intends to generalise and elaborate.
At the core of the technical discussion is an elegant and simple way to derive a basic decomposition of the cumulative value added flows that attribute each flow to the country and sector of origin and to the country and sector of destination. Two basic components include value added that ends up», or is finally absorbed, in partner country and value added that only lands» in partner country to be further re-exported. The first component is in fact a part of a country's GDP that is absorbed (finally used) overseas and can be treated as the ultimate external demand factor that contributes to the GDP. The second component corresponds to the double counted flows of value added that are responsible for inflating gross exports figures and may be treated as an intermediate demand factor. Both components can not be directly observed in gross trade statistics.
There are various ways to split these basic components and obtain more detailed indicators or aggregate those across sectors or countries or both. The matrix representation appears to be highly customisable and adaptable to matrix computation software. The formulations proposed yield results that are mostly identical to those of [Stehrer, 2013] who built his work on [Koopman et al., 2012]. The discussion has also led to the derivation of two matrices of the inter-sectoral transfer of value added for which, respectively, the exporting country and partner country is responsible. These matrices, to the author's knowledge, didn't explicitly feature previous studies. Excluding these two matrices or respective matrix elements from the value added accounting equations at the bilateral sectoral level will make them incomplete. The basic form of the derived accounting relationship is also used to prove in a quick and efficient way that the total trade balances are equal in gross and value added terms.
Applied to real data from the WIOD database, the proposed formulations uncover a great deal of detail intrinsic to the expanding global value chains. Gross trade statistics hide a multitude of indirect linkages that shape countries' export performance. Indirect linkages show how production in one country responds to final or intermediate demand in another country while visible link may appear weak or may not exist at all. Russia seems to be a very good example to test the significance of such indirect links. Exported value added of Russian origin -primarily from the mining and quarrying sector - is then repeatedly used in the downstream value chain, and to a higher extent than for any other country in the WIOD database. This has little effect on the total gross exports or total value added satisfying foreign final demand, but affects Russia's bilateral relations with trade partners. Indirect links shed light on the importance of some partners. For example, flows of Russia's value added that end up in the United States' final domestic consumption are largely not governed by direct trade policies, as those are mostly indirect flows.
* * *
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