Measuring what matters in value-added trade

Abstract

The spread of global value chains (GVCs) has given rise to new statistical tools, the inter-country input–output tables, and new analytical frameworks aimed at properly identifying production linkages between and within economies. However, several important questions remain unaddressed. This paper proposes a new toolkit for value-added accounting of trade flows at the aggregate, bilateral, and sectoral levels. The paper shows how different empirical issues require distinct accounting perspectives and maps these methodologies onto the economic questions they are best suited to address. We provide novel accounting perspectives that allow us to properly address important empirical issues. With respect to other accounting methodologies previously proposed in the literature, we offer more accurate or, in some cases, more exhaustive value-added decompositions of trade flows (e.g. by covering both domestic and foreign value-added). In addition, the paper gathers a significant amount of the related literature under one comprehensive framework.

Keywords:

• Trade in value-added
• global value chains
• inter-country input-output tables

JEL Classifications:

• E16
• F1
• F14
• F15

Acknowledgments

We would like to thank Robert Johnson for the valuable advice, as well as Pol Antràs, Pao-Li Chang, F. Paolo Conteduca, Gaaitzen De Vries, Stefano Federico, Alberto Felettigh, Aaditya Mattoo, Daria Taglioni, Giovanni Veronese and the WDR 2020 team for their insightful comments. The views expressed in this paper are solely those of the authors and do not necessarily reflect those of the Bank of Italy. The usual disclaimer applies.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Notes

1 A decomposition of bilateral trade flows based on an exporter perspective was originally proposed in Borin and Mancini (2017).

2 As we discuss in Section 3, this accounting perspective can also be used for other purposes such as to single out the portion of trade that is related to GVC activities (see Hummels et al. (2001), Borin and Mancini (2015), and Antràs and Chor (2022)).

3 We include the source and sink decompositions based on a ‘world perspective’ as derived in Borin and Mancini (2017) to have a complete mapping with other contributions in the literature that follow this approach (Koopman et al., 2014; Miroudot & Ye, 2021; Wang et al., 2013). However, we argue that the exports' decompositions based on this perspective do not provide any economically meaningful information in addition to what we obtain through the other perspectives. See Appendix E for further details.

4 It is important to highlight that in the TiVA database the different components are labeled ‘domestic (foreign) value-added content.’ Conversely, following Koopman et al. (2014), we refer to the same components as ‘domestic (foreign) content,’ while the ‘domestic (foreign) value-added’ in our wording indicates the ‘net’ part of the ‘domestic/foreign content’ (i.e. the units of value-added that are not double counted). See also the decomposition scheme by Koopman et al. (2014) in Appendix D.

5 Other methodologies which also use an exporting country-level perspective for the domestic component – Koopman et al. (2014), Wang et al. (2013), Nagengast and Stehrer (2016), and Miroudot and Ye (2021) – take a different approach for the foreign content of exports: a certain item is considered value-added only the first (or the last) time it crosses a foreign border, whereas all the other times it crosses any foreign border it is classified as double counted. We can label this approach a ‘world-level perspective,’ since all trade flows – not only the exports of a single country – are considered to single out the units of value-added that are exported multiple times. In other words, with the exporting ‘country-level perspective,’ a certain unit of value-added is accounted for as foreign value-added only once in the total exports of a country, whereas the ‘world-level perspective’ requires it to be accounted for as foreign value-added only once in total world exports. See Appendix E for a thorough discussion.

6 Part of the intermediate goods exported by country s ($\sum _{j\ne s}^G{\mathbf{\text{A}}}_{sj}{\mathbf{\text{x}}}_j$) are later re-imported by s itself and enter again its exports, generating in this sense a double-counted item in a source-based framework. In particular, we are interested in the intermediate goods shipped abroad that re-enter in the exports from s to r, following any possible production pattern ($\sum _{j\ne s}^G{\mathbf{\text{A}}}_{sj}{\mathbf{\text{x}}}_j^{(\to {\mathbf{\text{e}}}_{sr})}$). This can be computed as: $\sum _{j\ne s}^G{\mathbf{\text{A}}}_{sj}{\mathbf{\text{B}}}_{js}{\mathbf{\text{e}}}_{sr}$.

7 We discuss this point more extensively in Section 4.1, where we propose an alternative decomposition of gross exports that generalizes to an n-country context the approach suggested by Johnson (2018).

8 The ${\mathbf{\text{VAXIM}}}_{sr}$ indicator, as any other measure based on an exporting country-level perspective can be summed across bilateral importing partners to obtain an aggregate indicator for the exporting country s. Then, the ${\mathbf{\text{VAXIM}}}_{sr}$ can be particularly useful, for instance, when we are interested in decomposing the overall trade balance of a country by its bilateral positions. When the analysis focuses exclusively on a given bilateral relation, it might be more appropriate to resort to the approach presented in Section 4.1.

9 We have already discussed the differences with the ${\mathbf{\text{DAVAX}}}_{sr}$ indicator. The mismeasurement in Koopman et al. (2014) as compared to the ${\mathbf{\text{VAXIM}}}_{sr}$ can be precisely gauged by considering the decomposition of bilateral exports in Equation D.2 in Appendix D. Koopman et al. (2014) allocate the second term of their decomposition to the bilateral importers' final demand; in reality, only sub-items 2a and 2b of Equation D.2 can be defined as such (while sub-item 2c is not). Conversely, part of the third term (3c) should also be classified as ‘direct importers’ final absorption', instead of third countries'.

10 These components are computed in exactly the same way in the source-based breakdown and sink-based one.

11 For example in Nagengast and Stehrer (2016) the domestic value-added absorbed in third countries is calculated as ${\mathbf{\text{v}}}_s{\mathbf{\text{B}}}_{ss}{\mathbf{\text{A}}}_{sr}{\mathbf{\text{B}}}_{rr}\sum _{j\ne s,r}{\mathbf{\text{y}}}_{rj}$. The simultaneous application of the ${\mathbf{\text{B}}}_{ss}$ Leontief inverse matrix and the ${\mathbf{\text{B}}}_{rr}$ one, leads to a double counting of the same value-added.

12 In both the decompositions the domestic content of exports (i.e. the sum of the domestic value-added and the domestic double counted) corresponds to those defined by Koopman et al. (2010).

13 Depending on the choice between the source and the sink based decomposition, the ‘value-added’ is attributed to a certain export flow or to another.

14 In Section 4.2 we present a decomposition based on a pure sectoral-bilateral perspective which means that a certain unit of value-added is considered as double counted only when it is exported multiple times to the same partner within the same sector. In this framework, the additivity property does not hold, but these alternative measures may be very useful when addressing some specific issues such as trade policy analysis.

15 As for any other case in which the perspective coincides with the considered trade flow, there is no distinction between a source- and sink-based approach. Although Equation 16(16) ${\mathbf{\text{u}}}_N{\mathbf{\text{e}}}_{sr}=\stackrel{\begin{array}{c}\mathrm{d}\mathrm{o}\mathrm{m}\mathrm{e}\mathrm{s}\mathrm{t}\mathrm{i}\mathrm{c}\\ \mathrm{c}\mathrm{o}\mathrm{n}\mathrm{t}\mathrm{e}\mathrm{n}\mathrm{t}\left({\mathbf{\text{DC}}}_{sr}\right)\end{array}}{\overbrace{\underset{\begin{array}{c}\mathrm{b}\mathrm{i}\mathrm{l}\mathrm{a}\mathrm{t}\mathrm{e}\mathrm{r}\mathrm{a}\mathrm{l}\\ \mathrm{p}\mathrm{e}\mathrm{r}\mathrm{s}\mathrm{p}\mathrm{e}\mathrm{c}\mathrm{t}\mathrm{i}\mathrm{v}\mathrm{e}\\ {\mathbf{\text{DVA}}}_{\mathrm{s}\mathrm{r}}^{\ast }\end{array}}{\underbrace{\phantom{\sum _{t\ne s}^G}{\mathbf{\text{v}}}_s{\mathbf{\text{B}}}_{ss}^{\text{⧸}sr}{\mathbf{\text{e}}}_{sr}}}+\underset{\begin{array}{c}\mathrm{b}\mathrm{i}\mathrm{l}\mathrm{a}\mathrm{t}\mathrm{e}\mathrm{r}\mathrm{a}\mathrm{l}\\ \mathrm{p}\mathrm{e}\mathrm{r}\mathrm{s}\mathrm{p}\mathrm{e}\mathrm{c}\mathrm{t}\mathrm{i}\mathrm{v}\mathrm{e}\\ {\mathbf{\text{DDC}}}_{sr}^{\ast }\end{array}}{\underbrace{{\mathbf{\text{v}}}_s{\mathbf{\text{B}}}_{ss}^{\text{⧸}sr}\phantom{\sum _{j\ne s}}{\mathbf{\text{A}}}_{sr}{\mathbf{\text{B}}}_{rs}{\mathbf{\text{e}}}_{sr}}}}}+\stackrel{\begin{array}{c}\mathrm{f}\mathrm{o}\mathrm{r}\mathrm{e}\mathrm{i}\mathrm{g}\mathrm{n}\\ \mathrm{c}\mathrm{o}\mathrm{n}\mathrm{t}\mathrm{e}\mathrm{n}\mathrm{t}\left({\mathbf{\text{FC}}}_{sr}\right)\end{array}}{\overbrace{\underset{\begin{array}{c}\mathrm{b}\mathrm{i}\mathrm{l}\mathrm{a}\mathrm{t}\mathrm{e}\mathrm{r}\mathrm{a}\mathrm{l}\\ \mathrm{p}\mathrm{e}\mathrm{r}\mathrm{s}\mathrm{p}\mathrm{e}\mathrm{c}\mathrm{t}\mathrm{i}\mathrm{v}\mathrm{e}\\ {\mathbf{\text{FVA}}}_{sr}^{\ast }\end{array}}{\underbrace{\sum _{t\ne s}^G{\mathbf{\text{v}}}_t{\mathbf{\text{B}}}_{ts}^{\text{⧸}sr}{\mathbf{\text{e}}}_{sr}}}+\underset{\begin{array}{c}\mathrm{b}\mathrm{i}\mathrm{l}\mathrm{a}\mathrm{t}\mathrm{e}\mathrm{r}\mathrm{a}\mathrm{l}\\ \mathrm{p}\mathrm{e}\mathrm{r}\mathrm{s}\mathrm{p}\mathrm{e}\mathrm{c}\mathrm{t}\mathrm{i}\mathrm{v}\mathrm{e}\\ {\mathbf{\text{FDC}}}_{sr}^{\ast }\end{array}}{\underbrace{\sum _{t\ne s}^G{\mathbf{\text{v}}}_t{\mathbf{\text{B}}}_{ts}^{\text{⧸}sr}\phantom{\sum _{j\ne s}}{\mathbf{\text{A}}}_{sr}{\mathbf{\text{B}}}_{rs}{\mathbf{\text{e}}}_{sr}}}}}.$(16) was obtained proceeding as for the derivation of the source-based decomposition of Section 3.2.1, we could have obtained the same result by exploiting a sink-based algebra, as in Section 3.2.2.

16 The decomposition by sector of export, instead, is not univocal even in the bilateral-level perspective and will change depending on whether we employ a source-based or a sink-based approach. However, in this context, we do not consider this type of breakdown particularly meaningful from an economic standpoint. It is more useful to analyze the case in which a specific exporting sector, within a bilateral relationship, is the focus of the analysis.

17 In this perspective, a certain unit of value-added is considered ‘double counted’ only when it is re-exported by the same country and sector.

18 See also Chen et al. (2018) for an application on Brexit of a regional extension of the Los et al. (2016) bilateral decomposition. Since this decomposition does not cover foreign value-added it would not be suited to assess other countries exposure as we do in this section. Another work on Brexit applying the aforementioned decomposition is Ijtsma et al. (2018).