Decomposition of value added in gross exports: a critical review

Enrique Feás (Universidad de Alcalá, Alcalá de Henares, Spain and Real Instituto Elcano, Madrid, Spain)

Applied Economic Analysis

ISSN: 2632-7627

Article publication date: 28 August 2023

Issue publication date: 10 November 2023

948

Abstract

Purpose

The purpose of this paper is to settle the methodological debate on the decomposition of value added in gross exports, proposing a standard, exposing the drawbacks of the alternatives and quantifying the differences.

Design/methodology/approach

This paper systematizes the analytical framework and assesses and quantifies the various methodologies and its main differences.

Findings

The decomposition method of Borin and Mancini (2023), using a source-based approach and an exporting country perspective, should be considered as the standard for decomposing the value added in gross exports. This study finds that alternative approaches and perspectives are methodologically inferior, and that tailored perspectives do not provide an increase in accuracy that compensates their drawbacks.

Originality/value

This paper’s contribution is fourfold: it rejects the alleged equivalence between approaches and perspectives, defending the superiority of a particular method, approach and perspective; it gives quantitative examples of the differences between them; it proves that the drawbacks of tailored perspectives do not compensate their alleged accuracy (as they do not result in big quantitative differences with the standard perspective); and it argues that no valid standard decomposition can forego the calculation of value added exported, which requires the expression of exports in terms of final demand.

Keywords

Citation

Feás, E. (2023), "Decomposition of value added in gross exports: a critical review", Applied Economic Analysis, Vol. 31 No. 93, pp. 182-198. https://doi.org/10.1108/AEA-11-2022-0300

Publisher

:

Emerald Publishing Limited

Copyright © 2023, Enrique Feás.

License

Published in Applied Economic Analysis. Published by Emerald Publishing Limited. This article is published under the Creative Commons Attribution (CC BY 4.0) licence. Anyone may reproduce, distribute, translate and create derivative works of this article (for both commercial and non-commercial purposes), subject to full attribution to the original publication and authors. The full terms of this licence maybe seen at http://creativecommons.org/licences/by/4.0/legalcode


1. Introduction

Since the 1990s, the world has witnessed a rapid expansion of international trade, powered by the rise of global value chains (GVC). A vast literature has analyzed the drivers of firms’ decision to fragment their production internationally, including declining transport, information and communication costs, the sharp increase in technological progress and lower political and economic barriers to trade and capital flows (Amador and Cabral, 2016; Baldwin, 2016; World Bank, 2019). The financial crisis, the COVID pandemic and geopolitical tensions have contained the expansion of GVC, as efficiency gains must now be weighed against various risks, but there is not yet evidence of a clear reshoring trend (Baldwin, 2022).

The fragmentation of production entails an increased role of intermediate products in global trade: between 1995 and 2018 exports of intermediate products represented, on average, 58% of total exports (with 60% for goods and 53% for services) [1]. As a result, statistics expressed in terms of value added (that can considerably differ from gross values) might be more accurate to reflect the reality of globalization, especially for complex goods and services.

However, statistical systems have not been able to catch up with the rhythm of globalization. Trade in national accounts is calculated in terms of value added, but with no geographical breakdown. Customs statistics only provide sectoral and geographical breakdown for goods, but details for services are scarce. They also fail to consider the multiple times that intermediate products cross the border.

The need for statistical tools that measure not only economic interrelations between countries but also between industries in different countries led in the mid-2010s to the development of fully fledged international input–output tables (IOTs) [2] and a parallel debate in the economic literature of how to decompose value added in gross exports, with contributions of Daudin et al. (2011), Johnson and Noguera (2012), Foster-McGregor and Stehrer (2013), Koopman et al. (2014), Wang et al. (2013), Los et al. (2016), Los and Timmer (2018), Nagengast and Stehrer (2016), Johnson (2018), Arto et al. (2019), Miroudot and Ye (2017, 2021) and Borin and Mancini (2017, 2023). Multiple approaches and perspectives have been proposed, not always in a clear manner.

Our aim is to settle the debate in the literature and propose a standard of decomposition of value added in exports using a specific method, approach and perspective, filtering out variations proposed in the literature that are only marginally relevant. For that, after presenting in Section 2 a general analytical standard framework, in Section 3 we will highlight the drawbacks of other alternatives and provide some final arguments. In Section 4, we will quantify the differences in methods, approaches and perspectives and consider sectoral aspects frequently overlooked, before summarizing our conclusions in Section 5.

2. A standard for the decomposition of value added in gross exports

We will consider a traditional international IOT framework with s = 1…G countries, r = 1G partner countries and i = 1…N sectors. Let Z be the intermediate input matrix (dimension GN × GN), Y the final demand matrix (GN × G), VA the value added matrix (1 × GN) and X the production matrix (GN × 1). Submatrices are defined for each country s (and sometimes partner r). The standard demand model, dated back to Leontief (1936), can be expressed as AX + Y = X, where A = Z/X, establishing a relation between production and final demand:

(1) X=(IA)1Y=BY

The global inverse Leontief matrix B represents the increase in production X induced by an increase in final demand Y. Each element Bsr reflects the production effort of country s to satisfy a simultaneous increase of one unit in the final demand of all sectors in country r.

Value added VA can also be considered as a vectorial proportion V of the production X (V = VA/X), and expressed for country s in terms of global demand:

(2) VAs=VsXs=VsjGrGBsjYjr

Equation (2) can be broken down into value added produced and absorbed in s and value added produced in s and absorbed abroad:

(3) VAs=VsjGBsjYjs+VsjGrsGBsjYjr

The second term in (3) is usually referred to as value added exported VAXs (Johnson and Noguera, 2012).

The resulting vector (of dimension 1 × G), however, does not reflect for each partner r the value added of s exported to r, but only the value added absorbed in r. Although the sum for all partners, i.e. the total value added of s absorbed anywhere, is equal to the total VAX anywhere, a correct bilateral measure of VAXsr should show the value added of s exported to r regardless of where this value added is eventually absorbed, requiring therefore a different calculation method.

We know that the matrix product VB is a linear combination by columns, reflecting the percentage of value added induced both by domestic inputs and by imported inputs. For country s:

(4) tGVtBts=VsBss+tsGVtBts=ι
where ι is a vector of one of dimension 1 × N. Multiplying the above expression by the vector of total exports of country s Es, we obtain the basic decomposition of the value added in gross exports into two elements: the domestic content (DC) in value added and the foreign content (FC) in value added:

For simplicity, we have not considered the sectoral point of view. If we wanted to keep a sectoral breakdown from the point of view of sector of origin of value added, Vs should be diagonalized as Vs^. This is the case when analyzing the value added induced by final demand VBY. However, the analysis of value added induced by gross exports VBE normally follows an exporting sector point of view, requiring a full diagonalization of VsBsŝ and VsBsŝ.

The delimitation of value added in (5) has two shortcomings: there are exports of value added that are not really value added, and there are exports of value added that are not really exports.

On the one hand, “false” value added stems from the existence of double counting, which occurs because exports include both final and intermediate goods, and the latter often cross the border several times. For example, if Spain exports steel to the UK for the manufacturing of engines later reimported by Spain and incorporated into exported vehicles, the steel exports would be counted twice. The steel in vehicles would not real value added, but reexport of already-computed domestic value added (DVA), so it should be deducted as double counting.

On the other hand, “false” exports result from the fact that a part of total exports returns to the exporting country to be absorbed internally. For example, if Spain exports automotive components to Germany for the manufacturing of a vehicle later imported into Spain, the components will indeed constitute value added, but cannot be considered exports. This returned value added is called “reflection” as per Koopman et al. (2014).

Therefore, the first term in (5), the DC in value added, should be decomposed into “pure” DVA and domestic double counting (DDC, or reexported DVA); in turn, “pure” DVA should be broken down into value added actually exported (VAX) and reflection (REF, or reimported DVA), as shown in Figure 1.

This reasoning is equally applicable, in the double counting part, for the foreign value added (FVA) content (FC). A part of the FC incorporated in the manufacturing of exports might later be reimported and reexported and should be recorded as foreign double counting (FDC), different from the “pure” FVA.

To define “double counting,” we must set a spatial perimeter, so that every item that exits that perimeter more than once will be considered as double counting. The most logical is the territorial border of the exporting country, because it is the one used in traditional concepts of value added such as GDP [3].

When defining that perimeter, we should consider that the global Leontief inverse matrix B incorporates, by definition, the value added generated in successive demand cycles of intermediate goods, thus incurring in double counting for those goods.

If we want to isolate the DVA of a certain country s, considering the items that exit the border only once (to avoid double counting), we must use a coefficient matrix that excludes the export of intermediate goods of s. The coefficient matrix A that includes only domestic and imported inputs from country s is called extraction matrix of s:

(6) As=[A11A11A1sA1GA21A22A2sA2G000Ass000AG1AG2AGsVGG] 

From this matrix, we derive a global Leontief inverse matrix with extraction of country s Bs=(IAs)1, reflecting the induced effect in global production by global demand if country s could receive inputs from other countries, but not provide them.

The extraction matrix of s As should not be confused with the domestic coefficient matrix Ad, which includes neither exports nor imports of inputs by any country (i.e. only domestic inputs). The resulting inverse matrices are also different: in the first case, we would have a global inverse extraction matrix of s Bs, whereas in the second case we would have a block diagonal matrix L of local Leontief inverse matrices, where each submatrix Lss = (I − Ass)−1 shows the induced effect of the own inputs of s, as if it did not have access to foreign markets. The difference between the domestic global Leontief inverse matrix Bss and the local Leontief inverse Lss would be the additional impulse derived from country s’s integration into global value chains.

It is worth highlighting that for each country s we will have a full global extraction matrix Bs (dimension GN × GN), but only one local Lss matrix (dimension N × N). At the same time, the submatrix Bsss of Bs coincides [4] with the local Leontief matrix Lss, i.e.:

(7) Bsss=Lss

We can now separate the components of pure value added from the double counting. From expression (5), it can be proved (Borin and Mancini, 2023, p. 10) that the production induced by country s can be expressed as the sum of the production induced by its own inputs and the production induced by the exchange of inputs with the rest of the world:

(8) Bss=Bsss+(BssBsss)=Bsss+BsssjsGAsjBjs

Substituting equation (8) in equation (5), we have: or, using the equivalence of equation (8):

After separating DVA from double counting, we must identify what part of exports will end up reimported and absorbed by s. To distinguish where an item is ultimately absorbed, we need to express equation (10) in terms of final demand. Following Borin and Mancini (2023), we can expand the DVA value VsLssEsr into:

(11) DVAsr=VsLss(Ysr+AsrLrrYrr+AsrLrrjrYrj+AsrLrrjrArjklBjkYkl)

From (11) we can disaggregate the third and fourth terms to obtain the value added effectively exported by s (VAX) and the reflection. The VAX will be the items that, once fully processed as final goods, do not return to s:

(12) VAXsr=VsLss(Ysr+AsrLrrYrr+AsrLrrjr,sYrj+AsrLrrjrArjklsBjkYkl)

Borin and Mancini (2023) call the two first terms in equation (16) “directly absorbed value added exported” or DAVAX, the value added of s which is both exported and directly absorbed as final goods in country r without the participation of productive systems of third countries.

The reflection (REF) will be the items that, once fully processed as final goods, eventually return to s:

(13) REFsr=VsLss(AsrLrrYrs+AsrLrrjrArjkBjkYks)

Note that the bilateral VAXsr in equation (12) now reflects the value added of s exported to r regardless of where this value added is eventually absorbed (and excluding double counting or value added returning to s).

DDC would consequently be:

(14) DDCsr=tsVt(BtsBtss)Esr=VsLssjsAsjBjsEsr

FVA can also be expanded in terms of final demand, obtaining a similar expression to that of equation (11) with Btss terms (that exclude intermediate inputs provided by s):

(15) FVAsr=tsVtBtss(Ysr+AsrLrrYrr+AsrLrrjrYrj+AsrLrrjrArjklBjkYkl)
with FDC being:
(16) FDCsr=tsVt(BjsBtss)Esr=tsVtBtssjrAsjBjsEsr

The abovementioned decomposition, proposed by Borin and Mancini (2023), provides a consistent framework that can also be used for the calculation of bilateral GVC-related indicators. Thus, the concept of DAVAX allows us to define the GVC-related flows (GVCsr) as the export flows not directly absorbed by the importer, i.e. Esr − DAVAXsr. These flows cross at least two international borders, i.e. they are reexported at least once before being absorbed in final demand, what can be considered as a sufficient condition to be part of an international production network (Borin and Mancini, 2023, p. 13).

From these GVC-related flows, and following the efforts of Hummels et al. (2001), Daudin et al. (2011), Koopman et al. (2014) and Wang et al. (2013), bilateral versions of traditional indicators of vertical specialization can be obtained, both for backward linkages (VS) and for forward linkages (VS1), the latter as the difference between GVCsr and VS.

3. Methodological limitations of other approaches and perspectives

If we define “approach” as the sequential perimeter of what to consider as value added and “perspective” as the spatial perimeter of what to record as value added, we could say that, so far, we have followed a source-based approach and an exporting country perspective. We will now show how other approaches and perspectives are methodologically inferior.

3.1 Source-based versus sink-based approach

In a source-based approach, a domestic item is considered “domestic value added” the first time it is exported, and a foreign item is considered “foreign value added” the first time it is reexported (the rest being recorded as double counting). But we could also devise a sink-based approach, by which a domestic item is considered “domestic value added” the last time it is exported, and a foreign item is considered “foreign value added” the last time it is reexported (the rest being recorded as double counting). This distinction was initially introduced by Nagengast and Stehrer (2016), and implies the use of the global matrix B for the linkage effects (as all successive rounds of exports of intermediates should be included in the value added until the final shipment). However, this might require some adjustments in the definition of exports in terms of absorption.

Although this approach could be acceptable, and in fact has been proposed as an alternative by Nagengast and Stehrer (2016), Los and Timmer (2018), Borin and Mancini (2023) or Miroudot and Ye (2021), we think that it is inferior to the source-based approach.

To understand why, let us suppose a world with three countries, A, B and C. Country A exports $1 of VA to B, which later comes back as $2 (with $1 of additional value added). Then country A incorporates an additional $1 and exports to C for a total amount of $3. The decomposition of those flows from a source- and sink-based approach is reflected in Table 1:

In a source-based approach, exports from A to B would record DVA for $1; exports from A to C would also record DVA for $1 (new VA) plus $1 of double-counted DVA (the VA of A previously processed in B) plus $1 of FVA (VA from B). From the point of view of information, exports from A to B do not show that the VA exported to B will be later reexported, but data of exports from A to C clearly reflect the sourcing of VA.

In a sink-based approach, exports from A to B would only record double-counted DVA for $1 (VA absorbed abroad); exports from A to C would record $2 of DVA ($1 previously processed in A plus an additional $1), plus another $1 of FVA (VA from B). From the point of view of information, data of exports from A to B correctly reflect that the VA of A will not be absorbed in B, and data of exports from A to C show that the VA of A is absorbed in C but not that half of that VA required previous processing abroad.

Therefore, the sink-based approach misrepresents the economic importance of global value chains. In the example, by looking at the source-based data, policymakers can correctly infer not only the importance of the economic relations between A and B and between A and C, but also that flows from A to C require an active economic exchange with third countries (B, in this case); however, by looking only at the sink-based data, policymakers might wrongly deduce that flows between A to C just need direct imports from B (the FVA, 1 in both cases), and not that those imports are processed goods which initially came from A. Thus, the decision, for instance, to replace B by D as provider of inputs could have unintended economic consequences for A. In other words, by putting the focus on where the absorption takes place, the sink-based approach underestimates the importance of global value chains and the economic interdependence with the rest of the world, therefore, devaluating the rich information contained in IOTs.

This does not mean, of course, that a sink-based approach might not be useful for specific economic analyses, e.g. to study the relationship between production and final demand (Borin and Mancini, 2023, p. 5), but it should not be put on an equal footing with the source-based approach which, despite its limitations, offers a more balanced picture of today’s economic interdependence.

On the contrary, it is important to mention that, even though the sink-based approach uses mainly matrix B instead of L for the calculation of most terms of value added (as international processing is considered value added until the “ultimate shipment”), the use of the extraction matrix is eventually unavoidable. This is because, when trying to isolate the last time that all items from s are exported to r, we need to distinguish, within the exports of intermediates of s that are processed in r and reexported as intermediates to be processed in third countries, which part is absorbed elsewhere without going again through s. This problem can only be solved algebraically (see Supplementary Data) by using the inverse matrix with extraction of the exports of intermediates from s, i.e. matrix Bs (Borin and Mancini, 2023, p. 15).

3.2 Exporting country perspective vs alternative perspectives

As for the perspective or spatial perimeter, the logical choice is the country perspective (including here any group of countries acting as a block) but we can define alternative perspectives by altering the extraction matrix A to be considered. A bilateral perspective would make zero not all exports of intermediates of s, but only the intermediates exported to country r, a sector perspective would make zero the exports of intermediates of s in sector i for all countries, and a sector-bilateral perspective would make zero the exports of intermediates of s to r for sector i. These alternatives thus narrow down the concept of double counting.

The use of targeted perspectives has been defended by some authors (Los and Timmer, 2018) as a more accurate form of assessing the value added (e.g. the GDP) exposed to a given trade flow but it has some drawbacks form a theoretical and practical point of view:

  • No additivity. Although targeted perspectives only marginally change the formulation of equation (9), for bilateral perspectives BsssLss and equation (10) would not hold anymore, and sectoral perspectives would require the export matrix Esr to be adjusted [5]. The advantage of an exporting country perspective is that it keeps a consistent accounting approach for different levels of aggregation of trade flows, so the sum of indicators on a bilateral, sector and sector–bilateral level coincide with the aggregated ones. This is not the case for tailored accounting perspectives. Additivity, however, seems a logical requirement for standard indicators, as inconsistency across different levels of aggregation would discourage its use.

  • No relation with global value chain indicators. As we saw above, the exporting country perspective allows a clear identification of global value chain–related flows, through the concept of DVA directly absorbed by the importing partner (DAVAX), needed to compute the GVC-related trade (as all exports not directly absorbed by importer) that has become the standard measure in the literature to quantify GVCs and GVC participation (Antràs and Chor, 2022). DAVAX, however, is not available in tailored perspectives.

  • Computing burden. As we have seen, the use of an exporting country perspective requires the calculation of G global inverse extraction matrices, one per country. With tailored perspectives the required number of extraction matrices becomes difficult to handle. If we wanted to calculate value added indicators for all countries in a single year in a database like the 2021 version of the OECD TiVA, instead of the 67 inverse extraction matrices for the country perspectives we would require 4,422 in a bilateral perspective, 3,015 in a sectoral perspective and almost 200,000 in a sector–bilateral perspective. Of course, this argument would be debatable if the differences between indicators were considerable but, as we will see in Section 4.2, this is not the case.

The concept of “world” perspective, which extends the concept of double counting, presents more problems. Unlike the country perspective, which considers double counting all flows that exit the exporter’s border more than once, the world perspective considers double counting all flows that cross any border more than once. Therefore, the applicable coefficient matrix would be the domestic coefficient matrix Ad. In this case, Bsss would still be equal to Lss, but Btss would become zero, so FVA would also be zero and all FC would be FDC (Miroudot and Ye, 2021, p. 77). We disagree here with Borin and Mancini (2023, app. E), who present a formulation of FVA and FDC with world perspective that deviates from the extraction matrix-based framework.

It is clear, then, that the origin of most discrepancies in the literature on the decomposition of value added in gross exports lays in the use of different versions of the matrix B. The multiplicity of approaches and perspectives has not helped clarify the framework, but rather the opposite: the attempt to include all possibilities, even those that might have economic sense only in very specific cases, has delayed the consolidation of a valid and consistent method.

3.3 Time to settle the debate

We believe that the state of the debate is already reap for assessing the advantages and shortcomings of the main methodological contributions in the economic literature.

We must start by acknowledging the importance of the seminal contribution of Koopman et al. (2014). They present the first framework for decomposing the value added in gross exports, setting the bases for the methodological debate, and should be given credit for providing the first definitions of DVA and FVA, and the concepts of reflection and double counting. However, their method has shown some methodological limitations and internal inconsistencies:

  • They only propose a decomposition method for aggregated exports but fail to decompose the value added in bilateral exports.

  • Although they consistently use the global Leontief inverse B (therefore implicitly adopting a sink-based approach), some terms are not correctly calculated from a sink-based approach, as pointed out by Borin and Mancini (2023).

  • They use a country perspective for DVA, but a world perspective for FVA.

Wang et al. (2013) overcome some of the limitations of Koopman et al. (2014), proposing a framework to decompose the value added in bilateral gross exports. However, they also show some limitations:

  • They do not use a consistent approach for their decomposition, using the source-based approach for most terms of the DVA (with the local Leontief inverse L) but incorrectly including the global Leontief inverse B in some cases, therefore, incorporating some double-counted items.

  • They also follow a different perspective for DVA and FVA, as they replicate the framework of Koopman et al. (2014). Miroudot and Ye (2021) prove that they use a variation of the world perspective for the FC.

Nagengast and Stehrer (2016) are the first to introduce the distinction between the source-based and the sink-based approach. They are particularly interested in the bilateral trade balances, and they develop a specific decomposition for that purpose. However, despite acknowledging the importance of considering as value added only the flows that have “not left country s for processing abroad previously” (Nagengast and Stehrer, 2016, p. 1285), and therefore the need to use the local Leontief inverse matrix L, they eventually fail to use it systematically and end up incurring in double counting. They also calculate the FVA with the global Leontief inverse matrix B and avoid dealing with sectoral issues.

Los and Timmer (2018) realize that using the global Leontief inverse matrix B in the basic decomposition leads to inconsistencies, as exports of intermediates produce double counting. They propose for the first time the use of extraction matrices to delimitate exports from a country perspective. Their only shortcoming is that they limit their analysis to the DVA and forget to mention the need of a similar approach for the FVA.

It is Borin and Mancini (2023) who, for the first time, propose a general framework for both DC and FC using extraction matrices and lay out a complete decomposition of value added in exports using a consistent approach and perspective for both. They distinguish two sequential scopes or approaches (source- and sink-based) and a long list of spatial scopes or perspectives (world, country, bilateral and sector–bilateral). By doing that, they attempt to present all previous decompositions as particular cases of their general framework, even while pointing out some of the abovementioned inconsistencies. Unfortunately, this catch-all strategy does not help clarify what the most appropriate framework would be.

Miroudot and Ye (2021) take a step forward and defend the use of the source-based approach and the country perspective, and they even provide a more elegant formulation of the general Borin and Mancini (2023) decomposition: where Bs is the global Leontief inverse with extraction of s and Bsss its submatrix (Miroudot and Ye call them B* and Bss*, respectively), B is the ordinary global Leontief inverse and As (AI for Miroudot and Ye) is AAs. Their formulation remains valid for several perspectives and in the basic source-based approach and country-perspective is equivalent to the formulation of Borin and Mancini (2023) in (9).

However, Miroudot and Ye (2021) refuse to further decompose their framework in terms of final demand, evading the thorny issue of assessing the consistency of the source- and sink-based approaches. They merely say that having two approaches does not make sense because the DVA and the FVA already “have a certain origin and destination,” i.e. the origin and destination of gross exports (Miroudot and Ye, 2021, p. 69). For them, using subcomponents leads to a problematic definition of temporal sequence (source/sink) and should be avoided.

This is, from our point of view, unacceptable, given that a breakdown in terms of demand is essential for at least three reasons:

  1. To distinguish between the value added generated by final exports and intermediate exports, the latter being only correctly expressed for a certain level of final demand, as pointed out by Wang et al. (2013, p. 10)

  2. To calculate the key indicator for trade in value added, the VAX. Without decomposing the DVA in terms of final demand, there can be no VAX, and without VAX a big part of the interest of the decomposition of the value added in gross export disappears. Segregating the VAX from the reflection and the double counting is part of the essence of the decomposition problem, and undertaking that task inevitably requires assumptions.

  3. To calculate the reflection (REF), which should be a tool to perfect the national statistics of value added. If a country exports an item and this item eventually returns to the country to be reexported (with additional value added incorporated), the income elements of the value added (compensation of employees and gross operating surplus) should only appear once as true value added.

To reinforce their position, Miroudot and Ye (2021) point out that, in any case, the definition of double counting as the value added that has crossed the country’s border “more than once” makes economic sense, but not statistical sense, because the input–output framework “cannot tell us how many times the added value has crossed borders,” because “there are many paths through which the added value can reach the final consumers and these are unknown” (Miroudot and Ye, 2021, p. 70). They follow Los and Timmer (2018) affirming that the input–output matrix has collapsed the different stages of production and any definition of “double counting” requires specific assumptions that do not have to be met.

Although this consideration has a trace of truth, we think it is just one of the multiple statistical limitations of the international input–output model, not more problematic than the production or the proportionality assumptions [6]. True, any international IOT is a simplified version of reality, but this is not enough reason to claim the impossibility of finding a “simple formula for calculating foreign value added” nor for the “lack of consensus in (…) what the meaning of ‘physical border’ is in terms of available statistics.” Once theoretical assumptions have been made (and those regarding the source-based approach are perfectly acceptable), decomposition methods should only be assessed in terms of methodological consistency.

4. Quantifying alternative decompositions

The complexity of the current input–output databases and the computational burden of implementing the different methodologies has undoubtedly hindered the practical implications of using a specific one. We will now quantify the differences between methods, approaches and perspectives, using the 2021 edition of the OECD Inter-Country Input–Output Tables (OECD, 2021a) and the software exvatools (Feás, 2023) [7].

4.1 Approaches

Table 2 shows a comparative decomposition of the value added in Spain’s gross exports according to the source- and sink-based methodologies of Borin and Mancini (2023), Koopman et al. (2014) and Wang et al. (2013), abbreviated here as BM, KWW and WWZ, respectively.

We can see that:

  • The total DC and total FC are equivalent, regardless of the decomposition method or the breakdown level.

  • The three methods are also equivalent aggregating for all countries and all sectors, as differences are compensated in the aggregation process; a mathematical proof appears in Borin and Mancini (2023).

  • When considering sectoral exports only, differences appear, but are relatively reduced for DVA, VAX, REF and DDC. They are bigger, however, for FVA and FDC, as the method of Wang et al. (2013) has a different perspective for FC (with a wider concept of double counting).

  • The biggest differences appear when we consider bilateral exports (here EU and non-EU), because that is where most methodological discrepancies appear. Note one exception: the REF, where the Borin and Mancini (2023)-source and the Wang et al. (2013) decompositions coincide, although there are differences in its internal components.

It is interesting to break down these elements, at least for the value added exported, into that induced by final goods and induced by intermediate goods, as seen in Table 3.

4.2 Perspectives

As discussed in Section 3.2, tailored perspectives are not only less consistent than the exporter perspective, but they are extremely unpractical. To additionally prove our point, we can make a comparison of the difference between the exporting sector perspective and the bilateral, sector and sector–bilateral perspective for the main indicators. We will use the 2021 edition of the OECD TiVA database (ICIO Inter-Country Input-Output tables) for the year 2018, including all countries in the bilateral and sectoral perspective, a sample of 23 (representing 75% of all exports) for the sectoral–bilateral perspective. We will also group the 45 sectors of the database in 29 for the sector and sector–bilateral perspective (see Supplementary Data for details).

We will calculate the global inverse extraction matrices and produce the basic indicators (including VAX and REF) for the bilateral, sector and sector–bilateral perspective and compare them with their equivalent in the exporting country perspective. To make differences comparable, we will express them as a percentage of the total respective exports, and calculate the mean, the median and a selection of percentiles. Results are shown in Table 4:

As we can see, tailored perspectives reduce the value of the DDC and therefore increase the DVA for a given DC. For the DVA or VAX, the difference represents only 0.23% of sector–bilateral exports, 0.14% of bilateral exports and 0.11% of bilateral exports when compared with the exporting country perspective. Deviations over 0.5% of exports only occur on the tails of the distribution, and the highest deviations (amounting to 1.1%) happen only in the sector–bilateral perspective in the 1% tails. Practically all the difference is absorbed by the VAX, and the reflection practically remains unaltered. Kernel density distributions for the data are shown in the online Supplementary Data.

Therefore, we can conclude that using the exporting sector perspective instead of tailored perspectives is not only methodologically sounder, more consistent and compatible with useful indicators of global value chain trade but it also incurs in a really small cost in terms of accuracy.

4.3 Other considerations: sector of origin vs exporting sector

It is also interesting to note the frequently overlooked impact of the sectoral point of view, i.e. the type of diagonalization of the product VB, on VAX. In most decompositions, VAX is calculated using an exporting sector point of view ( VsBsŝ), whereas the VAX of Johnson and Noguera, equivalent to the OECD indicator FFD_DVA (“Domestic value added embodied in foreign final demand”), uses a sector of origin of value added point of view ( VsBsŝ) (OECD, 2021b, p. 37). Figure 2 shows that, between 1995 and 2018, world VAX with an exporting sector point of view (Borin and Mancini) was on average a 48% bigger in manufacturing and a 33% smaller in services than with an origin point of view (OECD) due to servicification, i.e. the intensive use of services as inputs for the manufacturing sector. These differences would disappear if we calculated the decomposition using an origin perspective, and only bilateral differences would remain.

5. Conclusions

This article has made a critical analysis of the literature on the decomposition of value added in exports.

We have reviewed the methodological inconsistencies in the literature before Borin and Mancini (2023), and seen that the use of multiple approaches and perspective for very specific cases should not hide the general validity of the source-based approach and the exporting perspective, which should be considered the standard for decomposing value added in exports.

Alternative approaches like the sink-based, or alternative perspectives like the world, bilateral, sector or sector–bilateral (using tailor-made extraction matrices), though theoretically possible and useful for very specific analyses, do not deserve the same status, and seem more a gentle way of rescuing the validity of the pioneering works in the literature of value added in exports than an indispensable methodological tool.

We have proven the methodological superiority of the source-based approach with exporting perspective and given quantitative examples of the differences between alternative methods, approaches and perspectives. We have also shown that the drawbacks of tailored perspectives do not compensate their alleged accuracy (as they do not result in big quantitative differences with the standard perspective); and we have stated that any valid standard decomposition requires the calculation of the VAX, so the expression of exports in terms of final demand is always a must.

We believe that the methodologic debate is ripe enough so that the bilateral VAX with a source-based approach and an exporting perspective becomes an integral part of the available and widely used statistical indicators for the analysis of globalization.

Figures

Decomposition of value added in gross exports

Figure 1.

Decomposition of value added in gross exports

World VAX in manufacturing and business services using a sector of origin vs an exporting sector point of view (millions of US$)

Figure 2.

World VAX in manufacturing and business services using a sector of origin vs an exporting sector point of view (millions of US$)

Source- and sink-based approaches

Component Source-based Sink-based
A→B A→C A→B A→C
DVA 1 1 0 2
DDC 0 1 1 0
FVA 0 1 0 1
Gross exports 1 3 1 3

Source: Author, based on Borin and Mancini (2019)

Comparative decomposition of value added in Spain’s gross exports according to different methodologies (US$ million, 2018)

World EU-27 Extra EU-27
Sector VA comp. BM source BM sink WWZ/KWW* BM source BM sink WWZ BM source BM sink WWZ
Total EXGR 467,540 467,540 467,540 250,831 250,831 250,831 216,709 216,709 216.709
DC 356,208 356,208 356,208 191,214 191,214 191,214 164,994 164,994 164.994
DVA 355,100 355,100 355,100 190,593 190,293 190,436 164,507 164,807 164.664
VAX 351,947 351,947 351,947 188,086 187,786 187,929 163,860 164,160 164.018
REF 3,153 3,153 3,153 2,507 2,506 2,507 646 647 646
DDC 1,108 1,108 1,108 620 921 778 488 187 330
FC 111,333 111,333 111,333 59,618 59,618 59,618 51,715 51,715 51.715
FVA 110,888 110,888 86,710 59,367 59,250 42,729 51,521 51,637 43.982
FDC 445 445 24,623 251 367 16,889 194 77 7.733
Goods EXGR 257,516 257,516 257,516 142,148 142,148 142,148 115,368 115,368 115.368
DC 171,410 171,410 171,410 95,535 95,535 95,535 75,875 75,875 75.875
DVA 170,510 170,680 170,575 95,022 94,921 94,955 75,488 75,759 75.620
VAX 168,529 168,696 168,594 93,437 93,334 93,369 75,092 75,362 75.224
REF 1,981 1,984 1,981 1,585 1,587 1,585 396 397 396
DDC 900 730 836 513 614 581 387 116 255
FC 86,106 86,106 86,106 46,613 46,613 46,613 39,493 39,493 39.493
FVA 85,738 85,712 65,587 46,402 46,287 32,491 39,336 39,425 33.096
DDC 368 394 20,519 211 326 14,122 157 68 6.397
Services EXGR 210,024 210,024 210,024 108,683 108,683 108,683 101,341 101,341 101.341
DC 184,797 184,797 184,797 95,678 95,678 95,678 89,119 89,119 89.119
DVA 184,590 184,420 184,525 95,571 95,371 95,481 89,019 89,048 89.044
VAX 183,418 183,250 183,353 94,650 94,452 94,560 88,768 88,798 88.793
REF 1,172 1,169 1,172 921 919 921 251 250 251
DDC 207 378 272 107 307 197 100 71 75
FC 25,227 25,227 25,227 13,005 13,005 13,005 12,222 12,222 12.222
FVA 25,150 25,176 21,123 12,965 12,963 10,237 12,185 12,213 10.886
FDC 77 51 4,104 40 41 2,767 37 10 1.336
Note:

*The aggregate (total) decomposition of WWZ matches that of KWW for all the specified components

Source: Author. Data calculated using OECD ICIOT tables (2021 edition) for year 2018

Subdecomposition of value added exports (VAX) in Spain’s gross exports according to different methodologies (US$ million, 2018)

World EU-27 Extra EU-27
Sector VA comp. BM source BM sink WWZ* BM source BM sink WWZ BM source BM sink WWZ*
Total VAX, total 351,947 351,947 351,947 188,086 187,786 187,929 163,860 164,160 164,018
Finals 183,365 183,908 183,908 94,120 94,410 94,410 89,246 89,498 89,498
Interm. 168,581 168,038 168,038 93,967 93,376 93,519 74,615 74,662 74,520
Goods VAX, total 168,529 168,696 168,594 93,437 93,334 93,369 75,092 75,362 75,224
Finals 77,511 77,934 77,934 41,507 41,738 41,738 36,003 36,195 36,195
Interm. 91,018 90,762 90,660 51,929 51,596 51,631 39,089 39,167 39,029
Services VAX, total 183,418 183,250 183,353 94,650 94,452 94,560 88,768 88,798 88,793
Finals 105,854 105,974 105,974 52,612 52,672 52,672 53,242 53,303 53,303
Interm. 77,564 77,276 77,379 42,038 41,781 41,888 35,526 35,496 35,491
Note:

*The aggregate (total) decomposition of WWZ matches that of KWW

Source: Author, using OECD ICIO tables (2021 edition) data for year 2018

Differences in tailored perspectives vs exporting sector perspective (percentage of total respective exports)

Indicator Mean Median 1% 5% 25% 75% 95% 99%
Bilateral
DVA 0.1422 0.0913 0.0031 0.0089 0.0276 0.2098 0.4272 0.8433
VAX 0.1408 0.0909 0.0031 0.0089 0.0276 0.2083 0.4125 0.8221
REF 0.0014 0.0001 0.0000 0.0000 0.0000 0.0005 0.0069 0.0240
DDC −0.1422 −0.0913 −0.8433 −0.4272 −0.2098 −0.0276 −0.0089 −0.0031
FVA 0.0635 0.0323 0.0008 0.0022 0.0089 0.0999 0.2180 0.3231
FDC −0.0635 −0.0323 −0.3231 −0.2180 −0.0999 −0.0089 −0.0022 −0.0008
Sector
DVA 0.1138 0.0655 0.0000 0.0037 0.0224 0.1478 0.3704 0.7508
VAX 0.1121 0.0653 0.0000 0.0037 0.0223 0.1470 0.3675 0.7255
REF 0.0017 0.0001 0.0000 0.0000 0.0000 0.0007 0.0057 0.0280
DDC −0.1138 −0.0655 −0.7508 −0.3704 −0.1478 −0.0224 −0.0037 0.0000
FVA 0.0439 0.0231 0.0000 0.0011 0.0063 0.0614 0.1625 0.2362
FDC −0.0439 −0.0231 −0.2362 −0.1625 −0.0614 −0.0063 −0.0011 0.0000
Sector–bilateral
DVA 0.2296 0.1717 0.0087 0.0363 0.1003 0.2899 0.5989 1.1142
VAX 0.2267 0.1709 0.0087 0.0362 0.0997 0.2879 0.5894 1.0802
REF 0.0030 0.0004 0.0000 0.0000 0.0001 0.0014 0.0115 0.0476
DDC −0.2296 −0.1717 −1.1142 −0.5989 −0.2899 −0.1003 −0.0363 −0.0087
FVA 0.0846 0.0609 0.0004 0.0043 0.0283 0.1182 0.2397 0.3846
FDC −0.0846 −0.0609 −0.3846 −0.2397 −0.1182 −0.0283 −0.0043 −0.0004

Source: Author, using OECD ICIO tables (2021 edition) data for year 2018

Notes

1.

Own calculations with data from the OECD Trade in Value Added (TiVA) database (2021).

2.

The most relevant are the OECD TiVA database (OECD, 2021a), the World Input–Output Database (Timmer et al., 2015), the Eora database (Lenzen et al., 2013) and the ADB Multiregional Input Output database (Asian Development Bank, 2020).

3.

Gross domestic product (GDP) follows a territorial perimeter (VA generated in the physical territory of a specific country, regardless of where productive factors are located), unlike gross national product, which follows a personal perimeter (VA generated by workers or companies with habitual residence in a specific country, regardless of where the VA is generated).

4.

We will see later that this that does not hold in case of some specific alternative perspectives.

5.

A detailed formulation of these alternative perspectives can be seen in Borin and Mancini (2023) or, in a more general way, in Miroudot and Ye (2021).

6.

For a detailed description of the assumptions included in the international IOT framework, see OECD (2018, pp. 9–10).

7.

An alternative would be using the Stata package ICIO (Belotti et al., 2021).

Supplementary data

Supplementary data for this article can be found online.

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Corresponding author

Enrique Feás can be contacted at:efeas@rielcano.org

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