Policy Research Working Paper 9785 Countries and Sectors in Global Value Chains Alessandro Borin Michele Mancini Daria Taglioni Development Economics Development Research Group September 2021 Policy Research Working Paper 9785 Abstract Production of goods and services has increasingly globalized leads to a considerable underestimation of the involvement since the 1970s, but how to measure this phenomenon is in global value chain activity by some industries—especially still the object of academic debate. The concepts of back- services—and countries. Moreover, the paper shows that ward and forward global value chain participation, which the standard way of measuring participation, which dis- quantify the extent to which countries are exposed to foreign tinguishes between backward and forward linkages, leads supply and demand shocks, are likely to be mismeasured. to overstating backward integration. This in turn is the Furthermore, the customary practice in the literature of sole source of a false empirical regularity, whereby coun- quantifying global value chain participation as a proportion tries and the global economy are viewed as systematically of gross trade flows leads to neglect of some important more integrated backward than forward. If this were true, features of global value chain participation. This paper pro- it would be expected that the global economy would be poses a novel, comprehensive way to measure global value structurally more exposed to supply shocks than demand chain participation using inter-country input-output link- shocks. Instead, the analysis finds that activities that are ages in trade and output. The analysis finds that measuring both integrated backward and forward represent the most global value chain participation as relative to trade flows sizable share of global value chain–related production. This paper is a product of the Development Research Group, Development Economics. It is part of a larger effort by the World Bank to provide open access to its research and make a contribution to development policy discussions around the world. Policy Research Working Papers are also posted on the Web at http://www.worldbank.org/prwp. The authors may be contacted at dtaglioni@worldbank.org. The Policy Research Working Paper Series disseminates the findings of work in progress to encourage the exchange of ideas about development issues. An objective of the series is to get the findings out quickly, even if the presentations are less than fully polished. The papers carry the names of the authors and should be cited accordingly. The findings, interpretations, and conclusions expressed in this paper are entirely those of the authors. They do not necessarily represent the views of the International Bank for Reconstruction and Development/World Bank and its affiliated organizations, or those of the Executive Directors of the World Bank or the governments they represent. Produced by the Research Support Team Countries and Sectors in Global Value Chains Alessandro Borin Michele Mancini Daria Taglioni∗ Keywords : trade in value-added; global value chains; inter-country input-output tables. JEL classification : E16, F1, F14, F15. ∗ Borin: Alessandro.Borin@bancaditalia.it, Bank of Italy; Mancini: Michele.Mancini@bancaditalia.it, Bank of Italy and European Central Bank; Taglioni: dtaglioni@worldbank.org, The World Bank. This paper was started as part of the World Bank’s World Development Report 2020 "Global Value Chains: Trading for Development" project. The broad set of measures discussed in the paper is available on the World Integrated Trade Solutions (WITS) platform: the dataset is available here and the data visualiza- tions here. Furthermore, readers interested in computing their own measures of global value chain trade by origin and destination using also user-provided input output tables are referred to the icio module in Stata by Belotti et al. (2021). The study team is grateful for support from the World Bank’s Knowledge for Change Program (KCP). The views expressed are those of the authors and do not necessarily reflect those of the World Bank, its Executive Directors, or the countries they represent nor those of the European Central Bank or the Bank of Italy. 1 Introduction Production of goods and services has increasingly globalized since the 1970s, but how to measure this phenomenon is still the object of academic debate. The main challenge lies in measuring where value is added in a GVC, where it comes from, and where it flows to. Ideally, data that trace firm-to-firm transactions both within and across countries should be used, since it is not countries or industries that engage in value chain production but rather firms. Using a firm-level approach to GVC participation however is severely constrained by data availability. According to Bems and Kikkawa (2021) only one country in the world - Belgium - allows to obtain comparable data on firm-level trade and the complementary census information on firm-to-firm domestic transactions needed for a fully-fledged measurement of GVC participation. It is equally hard to disentangle the foreign input content of a firm’s exports from the foreign content of overall production (Kee and Tang, 2016 attempted to do so using processing trade in China). Even when a firm is identified as an exporter of intermediate inputs (instead of final goods), it is almost impossible to establish whether those inputs are fully absorbed in the importing country or whether they are reexported to third markets by the importing firms after having added value to them. Finally, without linking customs data across countries, it is very hard to establish the nature of the GVC link. Given the difficulties in using a firm-level approach to measuring many important aspects of GVC participation, a large body of work has focused on combining information from customs offices with national input-output tables. The most widely used are the World Input-Output Database (WIOD; Timmer et al., 2015), a collaborative project led by researchers at the University of Groenigen; the Trade in Value Added (TiVA) database compiled by the Organization for Economic Cooperation and Development (OECD); and the EORA global supply chain database (Lenzen et al., 2013), constructed by a team of researchers at the University of Sydney. Despite their limitations,1 such global input- output databases can be used to devise ways of measuring the extent to which production processes have globalized in recent years, how countries and sectors participate in GVCs, and several features of GVC linkages consistent with what Antràs (2020) calls the broad view of GVC participation.2 Building on global input-output tables, a sufficient condition for considering trade 1 Global input-output tables have two main limitations. First, because they rely on aggregated input- output data, the resulting sectoral disaggregation of GVC flows is coarse. They therefore miss a lot of GVC activity within the broadly defined sectors. For example, one can compute the origin of fabricated metal products in the production of motor vehicles in the United States but cannot infer where more specific components such as tires, car engines, or windshield wipers originate. Second, in constructing the tables, researchers are forced to impose strong assumptions to back out some bilateral intermediate input trade flows that cannot be readily read from either customs data or national IO tables, leading to statistically relevant aggregation biases (De Gortari, 2019; Bems and Kikkawa, 2021). 2 In Antràs (2020), broad view of GVC participation a global value chain or GVC consists of a series of stages involved in producing a product or service that is sold to consumers, with each stage adding value, and with at least two stages being produced in different countries 2 as GVC-related is that it crosses at least two borders (Hummels et al. 2001; Borin and Mancini, 2015; Antràs, 2020). This can be seen as the sum of two natural measures of cross-border linkages, i.e. backward GVC participation and forward GVC participation, which broadly speaking trace how much imports are embedded in a country’s exports and how much of a country’s own production is absorbed by demand from the global markets. According to the definition, all what is bought from abroad and exported constitutes a backward linkage and all what is exported for consumption in third markets is a forward linkage: • Backward GVC participation, in which a country’s exports embody inputs previously imported from abroad. In this case, GVC participation is considered backward as the intermediates used in exports come from previous production stages. • Forward GVC participation, in which a country’s production or exports are not fully absorbed in the importing country and instead are embodied in the importing country’s exports to third countries. This type of GVC participation is considered forward because the domestic firm is at the early stage of production of goods exported by a trade partner or by third countries. The first bias that this paper studies is generated when the distinction between backward participation and forward participation is assumed to fully characterize engage- ment in GVCs. The concepts of backward and forward participation are important, since exposure to foreign economic forces depends on the absolute and relative importance of forward and backward linkages in GVCs.3 The empirical regularity we are primarily concerned about is that GVC participation encompasses many activities that are linked simultaneously backward and forward to entities abroad. This is what is known as the I2E (import to export) in the Baldwin and Lopez-Gonzales (2015) terminology. To see the measurement bias originating from assuming away this empirical fact consider a simple world economy made of four countries and one product (Table 1). In this example, countries 1-3 collaborate to produce P, a product that is fully exported to country 4, where consumption takes place. Country 1 uses domestic resources (K, L) to produce intermediate good N1 which then exports to Country 2 for a value of 50. Country 2 combines N1 with domestic input N2 to produce semi-finished good S1. This is subsequently exported to Country 3, where it is further processed and re-exported for consumption to Country 4 as final good P. In this simplified world, the domestic value added (DVA) generated in each country is given by subtracting Imports from Sales. Total world exports are equal to a value of 230. Based on the definition of Hummels et al. (2001), whereby crossing at least two 3 High exposure to forward linkages in GVCs increases the ability of the domestic economy to grow on the back of growing foreign demand, but it also increases the risk of external demand shocks. High exposure to backward linkages in GVCs allows a more efficient use of domestic resources, and easier access to foreign inputs, technology, and know-how, but it also increases the risk of imported supply shocks. 3 Table 1: Illustrative example: the global value chain of hypothetical product P What is produced? Imports Sales Exports DVA Consumption Country 1 Intermediate good N1 0 50 50 50 0 Country 2 Intermediate good S1 50 80 80 30 0 Country 3 Final product P 80 100 100 20 0 Country 4 No production 100 0 0 0 100 borders is a sufficient condition for a trade flow to be considered GVC-related, exports of the traditional type amount to a value of 20. This is the value added generated in Country 3, which is one step away from the location of consumption (Country 4). The remaining value of 210 is GVC-related, since it crosses at least two borders before reaching the final consumer. A framework that characterizes GVC cross-border linkages using the forward ver- sus backward distinction leads to decompose exports from each country as in Table 2. From this decomposition it appears that GVC backward integration is larger than GVC forward integration for each country in our simplified world economy, except for Country 1 that by construction does not import any goods. Interestingly, backward integration is also greater than forward integration at the world aggregate level: forward integration is equal to a value of 80, while backward integration is equal to a value of 130. Table 2: Decomposition of Export Flows Imports Sales Exports DVA Export Decomposition: non-GVC GVC-related Forward Backward Country 1 0 50 50 50 0 50 0 Country 2 50 80 80 30 0 30 50 Country 3 80 100 100 20 20 0 80 Country 4 100 0 0 0 0 0 0 Total 230 230 230 100 20 80 130 The simplified example reflects similar results from actual global datasets of country- sector GVC participation measures: backward linkages are systematically higher than forward linkages, and forward and backward participation do not balance out at global level (Figure 1). Since there is no reason grounded in theory predicting that backward integration can be systematically larger than forward integration, and since at the global level the two need to balance out, for the same reason that world imports are equal to world exports, we conclude that there is a bias in the GVC decomposition. Accordingly in this paper we show that for a more accurate representation of the GVC phenomenon, we should allow for three distinct modes of participation: pure forward participation for the activities at the beginning of the value chain, pure backward participation for the activities at the end of the chain, and two-sided or intermediate participation for activities neither at the beginning nor at the end of the chain. 4 Figure 1: GVC Backward and Forward Participation at the global level (share of total trade) Source: own elaboration based on WIOD. The second improvement that we propose is to measure GVC participation as a proportion of output, which allows to take the viewpoint of the producing sector. Taking the viewpoint of the producing sector - and not only the one of the exporting sector - allows to improve our understanding of GVC participation in two opposite cases. First, it allows to capture otherwise unobserved indirect participation, e.g. of those sectors and countries whose production feeds into GVCs despite a limited direct involvement in cross-border trade. This is the case for example of many professional services that are often supplied predominantly as inputs to manufacturing sectors that participate directly to GVCs. Failure to capture the full extent of their involvement in GVCs leads to underestimate severely also total services GVC participation (See Figure 2). Second, it allows to identify those cases in which a country’s exposure to GVCs is limited because trade constitute a small share of overall domestic output. This for example was the case of China at the beginning of the process of trade liberalization. In the late 1980s and early 1990s Chinese exporting firms, mainly located in Special Economic Zones where highly involved in global value chain production, but the bulk of the economic activity was still generally domestically oriented. Computing GVC participation relative to output on top of GVC participation relative to trade would have indicated that the domestic economy was relatively insulated from foreign shocks despite its export sector was heavily reliant on GVCs. Our paper studies systematically these measurement issues at the macro-level us- ing an accounting framework. As it is customary in the related literature, we propose a representation of GVC participation that uses global input-output data at the country- industry level of aggregation. Due to the nature of the data, our proposed framework 5 Figure 2: Exporter versus producer perspective in measuring GVC participation GVC-Trade GVC-Output (as % of total output) (as % of total output) Source: Our elaborations on data from EORA and ADB MRIO remains subject to the limitations of homogeneity, proportionality and aggregation dis- cussed by De Gortari (2019), Antràs and Chor (2021) and Bems and Kikkawa (2021) among others. The reader is warned however that such biases cannot be solved in most empirical work, given the unavailability of globally representative micro-data that trace firm-to-firm transactions both within and across countries. Since the original contributions on conceptualizing vertical integration (Hummels et al 2001) and measuring countries’ value added in gross trade (Koopman et al. 2014), there has been a rapidly expanding demand for measures of GVC participation. This paper responds to this demand. It is the first to propose a comprehensive method to measure GVC participation at the country-sector level using Inter-Country Input-Output (ICIO) linkages in both trade and output and to develop the relative measures from all the main sources of ICIO data. The basic building block is a computational device proposed initially by Borin and Mancini (2015, 2019) and discussed in the survey by Antràs and Chor (2021). Specifically, this computational device consists in identifying traditional trade (or non-GVC trade) as gross trade flows that cross just one border. Flows that cross more than one border are considered GVC-related, instead. The current paper also applies the rationale originally developed for trade flows to measuring GVC-related output. By identifying the portion of both output and trade that are related to GVC activities, the paper points out some important biases that originate from neglecting the producer perspective in favor of the exporter perspective. An additional original contribution of the paper is to break down the measures of GVC-related trade and output in three additive terms, i.e. a backward component corresponding to the activities at the beginning of the chain, a forward component corresponding to the activities at the end of the chain, and an intermediate component – two-sided – for all activities encompassing both sourcing and selling intermediates. The measures proposed present two desirable features: i) they are bounded between 0 and 1, facilitating comparisons across different data points; and ii) 6 they are additive at any level of aggregation/disaggregation of trade flows, thus data can be summed up and partitioned at any level along both the geographical and the sectoral dimension. In so doing, the methodology and indicators proposed by this paper offer a summary and yet comprehensive system of measures on countries and sectors engagement in GVC activities. The reminder of the paper is structured as follows. Section 2 describes the method- ology of decomposing GVC-related trade participation in three measures: pure backward participation, pure forward participation, and two-sided or intermediate participation. Section 3 generalizes these results beyond trade, i.e. GVC-related value-added, GVC- related final goods production, and GVC-related output. Section 4 shows that our pro- posed decomposition matters empirically, showing the measures applied to country-wide, sector-specific examples. Finally Section 5 concludes. Annex A illustrates the notation and provides some basic accounting relationships used in the paper. Finally, Annex B illustrates how to retrieve the broad set of measures discussed in the paper and made available on the World Integrated Trade Solutions (WITS) platform. 2 GVC-related trade In this section we take the view of an exporting sector, showing how to detect within any trade flow the amount of it that can be traced back to global value chains. Consider a standard Inter-Country Input-Output (ICIO) model with G countries and N sectors. Appendix A gives an exhaustive definition of the notation and, for this reason, here we only mention that Esr is the N × 1 vector of exports of country s to country r, Xs is the N × 1 vector of gross output produced by country s, Ysr is the N × 1 vector of final goods and services produced by country s and absorbed in country r, A is the GN ×GN global matrix of input coefficients, B is the global Leontief inverse matrix for the entire inter-country model, L is the local Leontief inverse matrix, taking into account only the domestic chains, and Vs is the 1 × N vector that incorporates the value-added shares embedded in each unit of gross output produced by country s. Lastly, given a generic 1 × N or N × 1 vector W, W is its N × N diagonal form. It is convenient to start from the identification of the simplest form of trade between countries, by tracing the amount of value that crosses just once the border between the exporter and the importer. It consists of the value of final goods produced entirely at home and consumed abroad and of the value of the intermediate inputs that are (entirely) produced at home and used by the importing country to produce final goods for its internal market. In more formal terms, the simplest form of trade between country s and r is the Directly Absorbed Value-Added exports: DAVAXsr = Vs Lss Ysr + Vs Lss Asr Lrr Yrr , (1) 7 The vector DAVAXsr identifies, for each country s n ∈ N sector of exports, the ‘traditional’ type of exports to country r, as opposed to the international shipments that take place under the global sharing of production (‘GVC-related trade’). In other words, the ‘GVC-related trade’ includes all the traded items that cross at least two international borders, i.e. that are re-exported at least once before being absorbed in final demand. This can be considered as a sufficient condition for an exported good to be part of an international production network.4 The ‘GVC-related trade’ can be measured simply by excluding from country s gross exports to country r the domestic value-added exported by each sector n that is absorbed directly by country r, i.e. the bilateral partner (DAVAXsr ): GVCsr = Esr − DAVAXsr .5 (2) This GVC indicator presents two desirable features: i ) once divided by exports, i.e. GVCsr Esr , it is bounded between 0 and 1, since it traces within the trade flow the share of it related to GVC activity; ii ) it is additive at any level of aggregation/disaggregation of trade flows; thus, data can be summed at any level – total country exports/world exports/world sector exports/country groups and so on – in order to obtain the proper GVC participation measures at the desired level of aggregation. For instance, the GVC share of the total exports of country s, for each sector n, will be G G GVCXs = GVCsr Esr , (3) r=s r=s while at the world level we have: G G G G GVCXworld = GVCsr Esr . (4) s r=s s r=s Total GVC-related trade for any country s is obtained summing across the exports of each sector n, as G r=s uN GVCsr GV CXs = G G . (5) s r=s uN Esr where uN is the 1 × N unit row vector. 4 In principle, also value-added produced in completion stages of the production process, even if it crosses only one border, should be labeled as GVC. However, this part cannot be singled out using standard ICIO tables and, indeed, it is not considered by any other measure of GVC trade in the literature. 5 This broad definition is completely in line with Borin and Mancini (2017, 2019). However its sub- components differ. More specifically, here the pure forward participation corresponds to what they label as forward participation. Instead, the sum of pure backward and two-sided participation equals their backward participation. See below for further discussion. 8 In the same way, world trade related to GVC is G G s r=s uN GVCsr GV CX = G G . (6) s r=s uN Esr It should be noted that the overall GVC participation encompasses three different types of GVC linkages, i.e. purely forward, purely backward, and intermediate ones. In fact, a sector of export n might be engaged in GVC activities at the end of the chain, relying on imported inputs to export goods and services that are not further re-exported by the partner (pure backward participation). Alternatively, it might participate closer to the origin of the chain, exporting value-added that has been generated within the domestic chains – without any border crossing – to partners which, in turn, re-exports it to other markets (pure forward participation). Finally, the sector might be located in a more central position of the chain, therefore using imported inputs to produce its own exports, further re-exported by the partner (two-sided participation). In the rest of the section, we provide a precise measure of the share of exports related to ‘pure forward’, ‘two-sided’ and ‘pure backward’ linkages. The pure forward participation is simply the difference between the entire domestic value-added that is exported (Vs Lss Esr ) and the one that is directly absorbed by the importer,6 i.e. the DAVAXsr GVCP ureF orwsr = Vs Lss Esr − DAVAXsr .7 (7) The rest of the GVC-related trade is given by the sum of the pure backward participation and the intermediate participation. This is what Hummels et al. (2001) call vertical specialization, i.e. the import content of exports G uN Ats Lss Esr .8 (8) t=s 6 It should be noted that Borin and Mancini (2017, 2019) label what here is defined as pure forward participation simply as forward. In fact, in this paper we refine their classification considering a broader sufficient condition to define the total forward participation, i.e. the supply of intermediate inputs for foreign exporters. In turn, the necessary condition to have a pure forward participation is that intermediate inputs for foreign exporters have to originate in the domestic economy, as in equation (7). 7 For some empirical application, it could be convenient to trace also the market where the value-added is ultimately absorbed, following Borin and Mancini (2019): G G G G GVCP ureF orwsr = Vs Lss Asr Lrr ( Yrj + Arj Bjk Ykl ). j =r j =r k l=s 8 Borin and Mancini (2019) show that Hummels et al. (2001) import content of exports might be expressed in a more convenient way to trace also the origin of the imported inputs. In this way, import content of exports is given by the sum of the entire foreign content in a country’s exports and the domestic double counting, i.e. the domestic inputs that are first exported and then imported again by the country 9 The total import content of exports might be broken down into two very different terms, namely the import content of country s’s exports absorbed by the importing country r and the import content of country s’ exports re-exported by r. The former measures ‘pure’ backward participation, since the chain ends just after the exporting activity. The latter, instead, traces the GVC activities that are more in an intermediate position, as goods and services are further re-exported beyond the bilateral partner, i.e. two-sided participation.9 Operationally, we first express bilateral exports Esr as the sum of exports of final goods and intermediates that are absorbed by the partner without crossing any other border and intermediates that are further re-exported by the partner, G Esr = (Ysr + Asr Lrr Yrr ) + Asr Lrr Erj . (9) j =r Then, we substitute this result back in in the import content of exports (8). Pure backward participation is given by the imported inputs embedded in the exports to final markets10 G GVCP ureBacksr = uN Ats Lss (Ysr + Asr Lrr Yrr ) . (11) t=s Instead, two-sided participation is given by the imported inputs embedded in the to produce other exports G G Vs Lss Asj Bjs Esr + Vt Bts Esr . j =s t=s 9 Borin and Mancini (2017, 2019) consider the entire import content of export as a measure of GVC backward participation. In fact, a sufficient condition to define backward participation is the use of imported intermediates to produce exports. In this work we refine this definition, adding a necessary condition for pure backward participation, i.e. the use of imported intermediates to produce exports to final destinations. In other terms, we label as two-sided participation the imported intermediates used to produce exports that are further re-exported. While it would be correct to account them in the engagement in backward activities, as in Borin and Mancini (2017, 2019), it is true that they also meets the sufficient condition to be considered as forward participation, i.e. the supply of intermediates for foreign exporters. 10 The country of origin of the imported inputs might be traced separating foreign content from domestic double counting, G GVCP ureBacksr = Vs Lss Asj Bjs (Ysr + Asr Lrr Yrr ) j =s G + Vt Bts (Ysr + Asr Lrr Yrr ) . (10) t=s 10 re-exports of the bilateral partner11 G G GVCT woSidesr = uN Ats Lss Asr Lrr Erj . (13) t=s j =r Since GVCP ureBacksr traces backward linkages up to country s’s exports to the final market, it mirrors GVCP ureF orwsr , which measures forward linkages on-wards from the origin of the chain, i.e. country s itself. Instead, the intermediate participation meets the sufficient condition that define a broad measure of backward participation – since it encompasses the use of imported inputs for the country’s exports – and also a broad measure of forward participation – as it also encompasses the exports of inputs that are further re-exported by the bilateral partner. However, it does not meet the necessary condition for pure backward participation – use of imported inputs for the country’s exports to final markets – nor the one for pure forward participation – exports of inputs produced with domestic value-added that are further re-exported by the bilateral partner. Depending on the empirical application, it could be useful to consider broad measures of participation instead of pure ones. These are precisely defined by the sufficient conditions highlighted above, and can be computed simply aggregating the intermediate mode of participation to one of the two pure modes. Finally, the GVC-related trade within the export flow from s to r for any sector n might be expressed as the sum of these three components: GVCsr = GVCP ureF orwsr + GVCP ureBacksr + GVCT woSidesr . (14) The forward, backward and two-sided participation might also be computed for any level of aggregation, as for the overall indicator of ‘GVC-related trade’ (see equations 3 to 6). Furthermore, at the aggregate level, i.e. summing across exporters s, importers r and sectors n, the ‘GVC pure backward-related trade’ is equal to the ‘GVC pure forward- 11 As for the pure forward and pure backward participation, the country of origin of the imported inputs and the country of final absorption might be traced as G G G G GVCT woSidesr = Vs Lss Asj Bjs Asr Lrr Yrj + Arj Bjk Ykl j =s j =r k l=s G G G G + Vt Bts Asr Lrr Yrj + Arj Bjk Ykl , (12) t=s j =r k l=s 11 related trade’: G G uN GVCP ureBacksr = uN GVCP ureF orwsr . (15) s,r=s s,r=s Lastly, a natural measure of the type of participation in GVC at any level of aggregation can be straightforwardly obtained as the difference between pure forward and pure backward participation divided by the overall GVC participation. For instance, for each n exporting sector within the trade flow from s to r: Psr = (GVCP ureF orwsr − GVCP ureBacksr ) GVCsr . (16) The vector Psr measures the ‘forwardness’ of country s exports to country r, for each sector, and each of its elements is bounded between -1 and 1. At the country-level, i.e. summing across sectors and bilateral partners, we have: G G r=s uN GVCP ureF orwsr − r =s uN GVCP ureBacksr Ps = G . (17) r=s uN GVCsr At the global level, P is equal to zero, given the relation in equation (15): G Ps = 0. (18) s Thus, any index different from zero at any level of aggregation might be interpreted as a deviation from the world aggregate average. 2.1 Comparison with other indices of GVC-trade participation The GVC-related trade indicator proposed above is not the first measure based on ICIO tables that has been developed to gauge the relevance of GVCs in international ship- ments. The ‘vertical specialization’ index (VS) of Hummels et al. (2001), measuring the import content of country’s exports, is probably one of the first and most popular of these measures: G VSsr = uN Ats (I − Ass )−1 Esr Esr . (19) t=s However, as pointed out by the authors themselves, it is a partial measure of participation in global value chains, as also shown in Figure 3, where VSsr , computed at the global level, lies well below the total GVC-trade. Indeed, it can be shown that Hummels et al.’s (2001) vertical specialization VSsr corresponds precisely to the sum of pure backward and two-sided GVC participation as reported in equations (11) and (13). 12 In addition, equations (10) and (12) generalize the VSsr indicator, providing information both on the very origin of the value and on its final destination. In order to take forward linkages into account, Hummels et al. (2001) also suggest considering the exports of intermediate products that are later further processed and re- exported (they label it VS1). However, they do not propose a precise formulation of this measure, since it can be implemented only in a fully-fledged ICIO framework that was not available at the time of writing. Thus, the ‘forward’ component of GVC-trade in equation (7) can be considered as the first correct implementation of the VS1 indicator suggested by Hummels et al. (2001). Therefore, our overall GVC-trade indicator can be seen as the implementation and generalization of Hummels et al. (2001) insights: GVCsr = GVCP ureF orwsr + GVCP ureBacksr + GVCT woSidesr . (20) VS1sr VSsr Notably, at the country level, GVCP ureF orws differs from the version of the VS1s index proposed by Koopman et al. (2014) – and recently reported also by Aslam et al. (2017) – since they compute it by aggregating the content of a country’s production embedded in other countries’ exports (i.e. Vs r=s Bsr Er∗ ). While the GVCP ureF orw index is a portion of country s’s exports (like VS), this does not necessarily hold true for the measure proposed by Koopman et al. (2014). Suppose, for instance, that a certain intermediate component exported by country s later undergoes other processing phases in different countries; the original component will be double-counted several times in the summation of country s’s content in other countries’ exports. The discrepancy between the original value of goods exported by s and the related amount that enters in Koopman et al.’s (2014) indicator increases with the relative ‘upstreamness’ of country s’s produc- tion. This is a feature that refers to the relative positioning of a country in GVCs and that has been specifically addressed in the literature through proper tools.12 Moreover, this positioning does not directly influence the V S indicator which is commonly used as the ‘backward’-participation counterpart of the V S 1 indicator proposed by Koopman et al. (2014).13 Conversely, the GVCP ureF orw of equation (7) measures the share of a country’s exports related to forward GVC linkages in a way that is consistent with how the GVCP ureBack (i.e. VS) measures the portion that is related to backward GVC connections. 12 Indicators of relative upstreamness/downstreamness in GVCs have been proposed by Fally, 2012; Antràs et al., 2012; Wang et al., 2017, among others. See Antràs and Chor (2019) for a comprehensive discussion. 13 The VSs index does not vary with the number of borders crossed by a certain item before being imported by country s. In other words, the relative ‘downstreamness’ of country s does not influence the VSs indicator in the same way as its relative ‘upstreamness’ influences the VS1s indicator in the formulation of Koopman et al. (2014). 13 Figure 3: Comparison among different GVC measures. Finally, other studies have measured a country’s GVC-trade participation by iden- tifying the export components that are later re-exported by the direct importer, as we propose here (see, among others, Rahman and Zhao, 2013; Cappariello and Felettigh, 2015; Ahmed et al., 2017; Altomonte et al., 2018). However, these contributions rely on the decomposition of gross exports of Koopman et al. (2014) or, alternatively, on that of Wang et al. (2013). The problem, discussed in detail in Borin and Mancini (2019), is that these methodologies do not properly allocate countries’ exports between the share that is directly absorbed by importers and the one that is re-exported abroad. Thus, the resulting measures of GVC participation are also imprecise. In some cases the complement of the Johnson and Noguera (2012) value-added exports to gross exports ratio (VAX) has been interpreted as a measure of the share of trade involved in GVCs (see the red line in Figure 3). Although the change over time of this indicator tends to be closely related to the variation in international fragmentation of production —especially at the world level, see Johnson and Noguera (2017)— in level terms, it underestimates to a quite large extent the weight of GVCs in trade. As compared to the GVC-related trade index of equation (4), the underestimation is given by the difference between VAX and DAVAX divided by gross exports, as shown also in Antràs and Chor (2021).14 2.2 Regional GVC-related trade The total GVC-related trade as reported in equation (14) can be broken down to distin- guish between intra-regional and extra-regional value chain participation. The same holds 14 This comes from the fact that only a subportion of VAX is not GVC-related, and this is precisely the DAVAX. 14 for its sub-components, i.e. pure forward, pure backward and two-sided participation in equations (7), (11) and (13). Given a country s, member of a region K , intra-regional value-chain participation, IRVCs,K for each exporting sector n is defined as the sum of the import content of inputs sourced directly from a regional member that are exported to final markets (pure backward) or to partners that re-exports it (two-sided), and domestic value-added re- exported by a regional member (pure forward). In formal terms, G G IRVCP ureBacks,K = uN Ats Lss (Ysr + Asr Lrr Yrr ) (21) t∈K,t=s r=s G G G IRVCT woSides,K = uN Ats Lss Asr Lrr Erj . (22) t∈K,t=s r=s j =r G G IRVCP ureF orws,K = Vs Lss Esr − DAVAXsr , (23) r∈K,r=s r∈K,r=s Extra-regional value-chain participation with countries outside region K , ERVCs,K /, is the difference between the total GVC participation and the intra-regional one: / = GVCis − IRVCis,K ERVCis,K (24) for i = P ureF orw, P ureBack, Interm. 3 A more general view on GVC participation In the previous section we showed how to precisely single out the amount of a sector’s gross trade that stems from countries’ participation in global production sharing. This allows to assess how import and export dynamics are driven by the evolution of GVCs. Nevertheless, in order to gauge the overall degree of involvement of a specific sector we cannot limit the analysis to trade flows. In some countries the exporting sectors might be deeply integrated in GVCs, but they might account only for a small fraction of the whole economic activity. It was the case, for instance, of China at the beginning of the opening up process in the late ‘80s and early ‘90s, when the exporting firms, mainly located in the Special Economic Zones, where highly involved in the international production chains, while the remaining part of the economic activity was still generally domestically oriented. Moreover, regarding the sectoral participation in GVCs, it is necessary to take into account that some industries might be indirectly but heavily involved in international production networks despite their limited export activity (e.g. often services are supplied as inputs to manufacturing sectors that directly participate to GVCs). 15 A more general assessment of the amount of productions of each sector that is related to GVCs is retrieved taking into account the entire supply chain in which a sector participates to, regardless of its involvement in export activities. Similarly as for the identification of GVC-related trade, we identify three salient moments that matters to define a supply chain, namely the contribution provided by a sector to the production stages at its very beginning, in an intermediate position, and at the very end of it. Here the emphasis to define the mode of participation is on the sector of production, not on the sector of exports, as in Section 2. Therefore, the activities related to the creation of value-added that will be exported by any sector and then re-exported by the partner are the most purely forward ones, the very first link of a chain. Those related to the assembly of the final goods or services are instead the most purely backward related, as they represents the last link of a chain. Even final goods that are not exported fall into this case, if they are assembled using inputs that have previously crossed at least two borders. In between we find all the activities that encompass both buying and selling of inputs, therefore representing an intermediate type of participation, not purely forward nor backward but two-sided. In the following sections we define three indices of GVC participation based on the framework provided above. In Section 3.1 we present the GVC-related value-added, a measure of purely forward engagement in GVC, traced in the sector of its origin. In Section 3.2 we compute the GVC-related final goods and services, a measure of purely backward participation, traced at the very end of the chain, in the sector of final completion. Finally, in Section 3.3 we provide a comprehensive breakdown of total output, showing how to trace not only GVC-related value-added and final goods and services – the origin and the end of the chain – but also a more central mode of participation, consisting of all the inputs that are bought and sold by a sector in the intermediate links of the global supply chain. It turns out that this intermediate mode of participation, overlooked by the literature, is by far the most relevant in the data. 3.1 GVC-related value-added The portion of value-added related to GVC corresponds to value-added originated in a specific sector, exported directly or after further domestic processing stages, and re- exported by the bilateral partner. This mode of participation is purely forward, as goods and services are sold onwards from the origin. It is obtained subtracting from total value- added of a sector the portion that is never exported and the one that cross just one border, following Borin and Mancini (2015) and Wang et al. (2017), i.e. G G G GVCV s A = Vs Bsj Yjk − Vs Lss Yss + Ysr + Asr Lrr Yrr (25) j,k r=s r=s 16 It should be noted that at the country level this is precisely the GVC-related trade forward G G 15 participation in equation (7), since Vs j,k Bsj Yjk − Vs Lss Yss = Vs Lss r=s Esr . Instead, at the sectoral level GVC-forward participation in exports and GVC-related value-added do differ. The former traces the engagement in GVC activities of a particular exporting sector, which might not be the origin of the value-added. Instead, the latter looks at the direct and indirect connections with international production networks of the sector that is the origin of the value-added and might not even export at all. At the country level, summing across the n sectors, the share of value-added related to GVC activities is VA uN GVCV s A GVCP ureF orws GV CXs = = , (26) uN VAs uN VAs while at the world level G G uN s GVCVs A uN s GVCP ureF orws GV CX V A = G = , (27) uN s VAs uN G s VAs It should be noted that at the global level, while the overall GVC-related trade (GV CX in equation 6) takes into account also the length and the complexity of the GVCs, GVC-related value-added does not. In fact, when the same item (i.e. value added component) is re-exported many times along the value chain by different countries, the GVC share of gross trade will automatically increase as compared to the non-GVC portion. Instead, the GVC-related value-added indicator is not directly affected by the fact that a certain item crosses just two or many borders. 3.2 GVC-related final goods production Following the usual rationale, we consider as GVC-related those final goods and services productions that crossed at least two borders, as in Wang et al. (2017). This is traced in the sector that completes the final goods and services, as it is the very last link of a chain, purely backward integrated. Operationally, we need to subtract from total final goods production what is imported by the bilateral partner and absorbed in the domestic econ- omy and what is produced only exploiting domestic value chains, before being absorbed by the domestic or foreign demand: G G G GVCY s = Ysz − Vj Ljj Ajs Lss Yss − Vs Lss Ysz (28) z j =s z Again, at the country level, summing across the n sectors, the share of final goods 15 In other words, domestic value-added in exports, which is given by the GVC pure forward participation and the traditional trade, is equal to the total domestic value-added minus the domestic value-added in final goods that has never crossed a single border. 17 related to GVC activities is Y uN GVCYs GV CXs = G , (29) z uN Ysz while at the world level G uN s GVCY s GV CX Y = G , (30) uN s,z Ysz Obviously, at the global level, summing across countries and sectors, final goods production related to GVC is equal to the value-added related to GVC activities: G G uN GVCV s A = uN GVCY s . (31) s s In the next Section we show that this property can be exploited to obtain an index of the degree of relative participation in GVC-output. 3.3 GVC-related output We now develop a more comprehensive framework to trace different modes of GVC par- ticipation within output, taking the view of a sector of production. We show that this encompasses the GVC activities traced in value-added and final goods, but also all the ex- changes of inputs within the intermediates stages of production that are related to GVCs. This is crucial since GVC-related value-added and final goods provide just a partial repre- sentation of countries’ and sectors’ engagement in GVCs. The former looks only at purely forward linkages, traced in the very first link of a chain, i.e. the sector of origin of the value-added. The latter considers only purely backward linkages, measured in the very last link of a chain, i.e. the sector of completion of final goods and services. At the end of the section we will discuss the advantages of assessing GVC participation considering the entire chain. Following the same rationale as in the case of GVC participation traced in trade flows we define as GVC-related the output of a sector that crosses more than one border. First, we decompose the total output of a specific sector in terms of i ) imported intermediates, ii ) domestic intermediates and iii ) value added: G G Xs = Vj Ljj k=j Ajk Bks Xs + Vs Lss Ass Xs + Vs Xs (32) j Then, we trace in each one of the terms above the share that is related to GVC activities, i.e. that crosses at least two borders. Starting from imported inputs, we note that only those coming directly from the 18 partner – bought by country s sector n directly from abroad or indirectly, from other domestic sectors after many processing stages within the domestic value chain – and not re-exported cannot be considered as related to GVC. The reason is that only these imported inputs cross just one border. The rest, directly or indirectly bought by the sector through domestic and foreign value chains, crosses at least two borders, either before the domestic absorption or considering also their re-export. Thus, GVC-related imported inputs is G G G GVCImpInp s = Vj Ljj k=j Ajk Bks Xs − Vj Ljj Ajs Lss Lss Yss (33) j j =s It should be noted that the only portion of GVC imported inputs not sold to other sectors, i.e. at the end of the chain, is the one purchased by the sector of completion of the final good. Indeed, this is the only share of total output that is purely related to backward participation in GVC. In other words, it represents the very last link of a chain, since it encompasses i ) the inputs that have crossed more than one border that are embedded in final goods and services produced in country s by the sector and absorbed in s itself; and ii ) the inputs that have crossed one border and are embedded in final goods and services produced in s by the sector and exported by the same sector to the final market. Therefore, starting from (33), pure backward GVC related-output is obtained substituting final production to output in the two terms: G G G X G GVCP ureBacks = Vj Ljj k=j Ajk Bks Ysz − Vj Ljj Ajs Lss Yss (34) j z j =s X is equal to GVC-related final Despite the different formulation, GVCP ureBacks goods production, i.e. GVCY s reported in equation (28). 16 Lastly, the part of GVC-related imported inputs that is not pure backward par- ticipation might be considered as an intermediate type of participation in GVCs, i.e. two-sided, as imported inputs are bought directly or indirectly by the sector (backward) but are sold to other sectors (forward): GVCT woSideImpInp s = GVCImpInp s X − GVCP ureBacks (35) The same strategy to compute GVC-related output might be applied to the second component, i.e. domestic inputs. These inputs originate in country s and are bought directly or indirectly through domestic chains by the sector (Vs Lss Ass Xs ). We can 16 Proof available upon request. 19 focus on just two sub-components of domestic inputs, namely domestic inputs sold to G other countries by the sector ( r=s Asr Xr ) and domestic inputs sold to other domestic G sectors and embedded in exports later on ( r=s Ass Lss Asr Xr ). To encompass GVC participation, we need to be sure that inputs are further re-exported by the bilateral partner, thus crossing at least two borders. This can be achieved substituting total gross output of country r, Xr , with the total gross output of r that is re-exported, or, in other terms, not directly absorbed, Xexp r = Xr − Lrr Yrr . It should also be noted that GVC- related domestic inputs embraces both backward and forward inter-linkages. In fact, these inputs are bought within domestic chains (backward component) but also sold to other domestic sectors or directly exported (forward component). Therefore, GVC-related domestic inputs represents an intermediate mode of GVC participation: G GVCT woSideDomInp s = Vs Lss Ass (Asr Xexp r + Ass Lss Asr Xexp r ) (36) r=s Finally, we consider the last component of output, i.e. value-added, and trace the part of it related to GVC following the same rationale applied to domestic inputs. The only difference is that the sector producing value-added identifies the very first link of a supply chains, i.e. it’s actual origin. Thus, it might be considered as a measure of pure forward participation in GVCs: G X GVCP ureF orws = Vs (Asr Xexp r + Ass Lss Asr Xexp r ). (37) r =s Not surprisingly, despite the different formulation, GVC pure forward participa- tion measured in output is equal to GVC-related value-added, i.e. GVCV s A reported in equation (25).17 Summing up, as for the GVC-related trade presented in Section 2, GVC-related output can be broken down in three components: pure backward participation, i.e. im- ported inputs embedded by the sector in final goods; pure forward participation, i.e. value-added sold by the sector of origin abroad or domestically and incorporated in ex- ports later on; domestic inputs and imported inputs not embedded in final goods, i.e. a two-sided type of GVC participation that is simultaneously backward and forward related, since it consists of inputs that are first bought and then sold by the sector: GVCX X X X s = GVCP ureBacks + GVCP ureF orws + GVCT woSides (38) 17 Proof available upon request. 20 where GVCT woSideX ImpInp + GVCT woSideDomInp . s = GVCT woSides s As for the other indices of GVC participation, results at the country level, i.e. summing across the n sectors, might be obtained thanks to the additive property of these measures: X uN GVCX s GV CXs = , (39) u N Xs while at the world level uN Gs GVCs X GV CX X = , (40) uN Gs Xs Analogously, GVCX s sub-indices can be aggregated to national and global level: X uN GVCiXs GV CiXs = , (41) uN Xs while at the world level uN G X s GVCis GV CiX V A = G , (42) uN s Xs where i = P ureF orw, T woSide, P ureBack . In addition, the value of output that never crosses a border, i.e. purely domestic, is obtained as the sum of the domestic inputs and value-added that are not exported at all: DomX s = Vs Lss Ass Lss Yss + Vs Lss Yss . (43) Finally, output related to traditional trade, i.e. crossing only one border before being absorbed by final demand, can be computed as: TradX X X s = Xs − Doms − GVCs . (44) As for the indicator of ‘GVC-related trade’, at the global level, i.e. summing across all countries, the ‘GVC pure-backward-related output’ will be equal to the ‘GVC pure-forward-related output’: G G GVCP ureF orws = GVCP ureBacks . (45) s s Therefore, a natural measure of the type of participation in output of countries and sectors in GVC can be straightforwardly obtained as PX X X s = GVCP ureF orws − GVCP ureBacks GVCX s . (46) The vector PX s measures the ‘forwardness’ of the n sectors in country s in terms 21 of their total output, and is bounded between -1 and 1. At the country level, summing across the sectors, we have X uN GVCP ureF orws − uN GVCP ureBacks Ps = . (47) uN GVCs In addition, it is equal to 0 at the aggregate level, given the relation in equation (45). It should be clear now why GVCX is a much more general indicator with respect to GVCY = GVCP ureBack X and GVCV A = GVCP ureF orwX .Not considering as part of the GVC participation the inputs exchanged in the intermediate stages of a production chain leads to largely understate the actual engagement in GVCs of countries and sectors. In fact, the total value of the inputs sold and bought during the intermediate stages of global supply chains represents more than half of the total output related to GVCs, as shown in Section 4. Another drawback of relying only on GVCV A or GVCY is the inaccurate mode of GVC participation that can be inferred from them once they are expressed as a share of total value-added and total final goods and services production, respectively, as in Wang et al. (2017). Suppose, for instance, that a sector produces only final goods (total value of 100), with imported inputs related to GVCs (75), adding a very small amount of value- added (25), which is in turn completely GVC-related. The share of value-added related to GVCs with respect to total value-added, i.e. GV CX V A in equation (26), will be equal to 100%, while the share of final goods production related to GVCs with respect to total final goods production, i.e. GV CX Y in equation (29), will be 75%. This might lead to the incorrect conclusion that the sector is mostly integrated in GVCs with forward linkages, even if it participates in GVCs especially in the completion of final products, at the end of a chain. Instead, the index of ‘forwardness’ based on GVC-related output, X , will correctly indicate a higher backward participation compared to forward, i.e. Ps −0.50 = (25 − 75)/(25 + 75). The reason is that it traces, within the total GVC-output,18 the amount of it that is related to pure backward or pure forward participation, and it does not depend on the scale of value-added or final goods production. In addition, since it is equal to zero at the global level, the actual position of a country or a sector with respect to the average (i.e. zero) is immediately evident. 4 Empirics: country-sector measures of GVC participation Using the EORA dataset, which covers the period 1990-2015, and the Asian Development Bank MRIOT database (ADB), which covers the period 2007-2019 we are able to construct 18 In this simplified example we considered a sector producing only final goods, thus GVC-related output and GVC-related final goods obviously coincide. However, its conclusions are valid also in more general cases. 22 a series of GVC participation from 1990 to 2019. These data can inform two types of questions. First, they allow to evaluate the extent to which countries/sectors participate in GVC, or in other words, what part of trade and output are involved in GVC. Secondly the allow to assess how countries and sectors participate in GVCs. The question in this second case is whether a given country-sector is mainly a supplier of inputs or a downstream user. Taking the view of both the exporting and producing sectors enriches the charac- terization of GVC involvement and add a layer of complexity that has been overlooked in previous works. Figure 4 and 5 report the quintiles of the distribution of GVC trade (y-axis) and GVC output (x-axis) for manufacturing and services respectively. The bi- variate distributions at the country-sector level are quite disperse, meaning that GVC Output and GVC trade does not fully overlap in terms of information content. However, the information content of GVC output seems to be richer than the one provided by GVC-trade (Table 3), as the coefficient of variation of the former is 3 to 4 times larger than the one of the latter. This holds across sectors at the global level, across countries, and across country-sector. Figure 4: Bivariate density plot of GVC Figure 5: Bivariate density plot of GVC Output and GVC trade, manufacturing, Output and GVC trade, services, EORA EORA 2015. 2015. Table 3: GVC Output and GVC trade coefficients of variation across ICIO sources in 2014. Inter-Country Input Output Table Coefficient of variation ADB-MRIO EORA OECD-TiVA WIOD GVC-trade 0.24 0.23 0.34 0.26 Sector GVC-output 0.72 0.67 0.78 0.67 Ratio 2.99 2.93 2.33 2.63 GVC-trade 0.23 0.24 0.25 0.22 Country GVC-output 0.84 0.70 0.95 0.91 Ratio 3.61 2.87 3.74 4.07 GVC-trade 0.35 0.30 0.43 0.39 Country- GVC-output 1.38 1.09 1.45 1.52 sector Ratio 3.89 3.58 3.40 3.92 Note: 2014 data 23 4.1 What part of a country’s trade and output are involved in GVCs? GVC output is important. Looking only at GVC trade understates the actual extent of GVCs by around 10 trillion USD, as GVC trade amounts to about 5 trillions USD while GVC output amounts to about 15 trillions USD (Figures 6 and 7). Intermediate, or two-sided, participation is the most relevant component of GVC output, accounting for more than 60% of the total GVC participation. Considering only GVC output pure forward (GVC in value added) or pure backward (GVC in final goods) understates the actual extent of GVC participation. The two-sided or mixed participation is less relevant in GVC trade. This is explained by the fact that most exporting sectors and firms engage at the end or at the beginning of the chains. Instead, most producing sectors (GVC output) are characterized by two-sided exposure - import to export or sourcing to sell (see Figures 8-9). Figure 6: GVC Output Participation, USD Figure 7: GVC Trade Participation, USD Figure 8: GVC Output Participation, as Figure 9: GVC Trade Participation, as a share of total output share of total output This evidence is valid not only at the global level, but also at the country-sector level, as shown in Figure 10 and Figure 11, which report the distribution of the different participation modes divided by the total GVC participation. For more than 60% of country-sector pairs the intermediate mode of GVC output participation is the prevalent one, while one third of country-sector pairs has a two-sided participation accounting for 24 more that two thirds of their total GVC participation. Figure 10: Distribution of GVC output Figure 11: Distribution of GVC exports participation modes over total GVC output, participation modes over total GVC exports, WIOD 2014. WIOD 2014. From the point of view of sectors, services participation in GVC is negligible when we look at the share of GVC-trade over output. It is noticeably larger when participation is measured from the viewpoint of GVC output. The reason is that services sectors do not export directly but exploit domestic chains to export indirectly, and when one looks at export only their contribution ends up recorded as exports of a downstream using sector. Meanwhile about one quarter of all manufacturing output is connected to GVC trade (see Figure 12 and Figure 13). Figure 12: GVC Output Participation in Figure 13: GVC Trade Participation Manu- Manufacturing and Services, as share of total facturing and Services, as a share of total out- output. EORA and ADB MRIO. put. EORA and ADB MRIO. At the country level GVC trade and output are clearly correlated, but the country rank is different. Each dot in Figure 14 and Figure 15 is a country among the 30 countries worldwide with the highest real GDP. We highlight those countries whose rank moves by at least 25 positions when we compare GVC output to GVC trade participation. For example, in the left hand panel Germany is ranked 22nd in terms of GVC output participation but 53rd in terms of GVC trade participation, out of a total of 189 countries reported in the EORA dataset. 25 Figure 14: GVC Output Participation vs Trade Participation in Manufacturing, EORA Figure 15: GVC Output Participation vs 2015. Trade Participation in Services, EORA 2015. 4.2 Supplier or user of intermediate inputs? The indices of forwardness discussed in Section 2 and Section 3 are useful to assess the type of engagement of countries in GVCs. Indeed, they are also correlated with relative position, computed as the ratio of upstreamness and downstreamness (see Antràs and Chor, 2019 and Wang et al., 2017). Figure 16 and Figure 17 show that correlation is higher for forwardness in output, more in line with the standard measures of positioning. Figure 16: Forwardness in exports vs Figure 17: Forwardness in output vs position, EORA 2015. position, EORA 2015. Position is computed as the ratio of up- Position is computed as the ratio of up- streamness and downstreamness. streamness and downstreamness. 5 Conclusion This paper identifies two important sources of mismeasurement of GVC participation in country-sector (macro) settings and proposes a methodology and measures that correct for these biases. First, the paper shows that the distinction of participation in backward versus forward leads to a false empirical regularity whereby each country appears system- atically more GVC integrated backward than forward. Instead, separating pure backward 26 and forward participation from intermediate activities, in which both sourcing and selling of inputs takes place, is empirically relevant. The resulting two-sided (or mixed) GVC participation is the largest segment of overall GVC output participation.When backward and forward participation are netted out of the intermediate steps, backward and forward participation balance out at the global level. Second, the paper also shows that GVC participation in services and some manufacturing sectors is severely underestimated when taking the viewpoint of the exporting sector. The services industry accounts for 15 per- cent of total GVC trade, but 30 percent of total GVC output. 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Zhu, 2013. ‘Quantifying International Production Sharing at the Bilateral and Sector Levels.’ NBER Working Paper, No. 19677. Wang, Z., S. Wei, X. Yu and K. Zhu, 2017. ‘Characterizing Global Value Chains: Pro- duction Length and Upstreamness.’ NBER Working Paper Series, 23261. 28 A Notation and basic I-O relations This appendix simply recalls our notation, together with some basic accounting relation- ships. We consider the general case of G countries producing N goods that are interna- tionally traded both as intermediate inputs and as final goods. Thus, Xs = (xs s s 1 x2 · · · xN ) is the N × 1 vector of the gross output of country s and Ys is the N × 1 vector of final goods, which is equal to the final demand for goods produced in s in each country of G destination r: r Ysr . To produce one unit of gross output of good i a country uses a certain amount a of intermediate good j produced at home or imported from other countries. Thus, each unit of gross output can be either consumed as a final good or used as an intermediate good at home or abroad: G Xs = (Asr Xr + Ysr ) r where Asr is the N ×N matrix of coefficients for intermediate inputs produced in s and processed further in r:   asr,11 asr,12 ··· asr,1N  asr,21 asr,22 ··· asr,2N    Asr =  . . .. .   . . . . . . .   asr,N 1 asr,N 2 · · · asr,N N . Using the block matrix notation, the general setting of production and trade with G countries and N goods can be expressed as follows:         X1 A11 A12 ··· A 1G X1 Y11 Y12 ··· Y 1G 1  X2   A21 A22 ··· A2G  X2   Y21 Y22 ··· Y2G  1          . = . . .  .  +  . . .  . (A.1)  .   . . .. .. . .  .    . . .  .   . . . .   . . . .  . .   XG AG1 AG2 · · · AGG XG YG1 YG2 · · · YGG 1 (N G×1) (N G×N G) (N G×1) (N G×G) (G×1) from which it is straightforward to derive the following relationship between gross output and final demand:    −1  G  X1 I − A11 −A12 · · · −A1G r Y 1r G  X2   −A21 I − A22 · · · −A2G Y 2r          r  .  =  . . . . ..     .  . . . .  .  . . . . .         G XG −AG1 −AG2 · · · I − AGG r Y 1G 1 G    B11 B12 · · · B 1N r Y1r G  B21 B22 · · · B 2N   Y2r     r =   . . .. .  .  (A.2)  .. . . . . .  . .    G B G 1 B G2 · · · BGG r Y1G where Bsr denotes the N ×N block of the Leontief inverse matrix in a global IO setting. It indicates how much of country s’s gross output of a certain good is required to produce one unit of country r’s final production. The direct value-added share in each unit of gross output produced by country s is equal to one minus the sum of the direct intermediate input share of all the domestic and foreign suppliers: G Vs = uN (I − Ars ) (A.3) r where uN is the 1×N unit row vector. Thus, the G×GN direct domestic value-added matrix for all countries can be defined as:   V1 0 · · · 0  0 V2 · · · 0    V=  . . .. .   . . . . . . .   0 0 · · · VG while the overall G×GN value-added share matrix is obtained by multiplying the V matrix by the Leontief inverse B:   V1 B11 V1 B12 ··· V 1 B 1G  V2 B21 V2 B22 ··· V 2 B 2G    VB =   . . .. .   . . . . . . .   VG BG1 VG BG2 · · · VG BGG Since the value-added shares of different countries in final goods have to sum to one, the following property holds: G Vt Btr = uN (A.4) t Defining the GN ×G final demand matrix as:   Y11 Y12 ··· Y1G  Y21 Y22 ··· Y2G    Y=  . . .. .   .. . . . . .   YG1 YG2 · · · YGG 2 we can derive the G×G value-added matrix by pairs of source-absorption countries: VA ≡ VBY = G G G   V1 r B1r Yr1 V1 r B 1r Y r 2 ··· V1 r B1r YrG G G G  V2 B2r Yr2 V2 B 2r Y r 2 ··· V2 B2r YrG    r r r = . . .. .  (A.5)   . . . . . . .   G G G VG r BGr YrG VG r BGr YrG · · · VG r BGr YrG 3 B GVC Database on the World Integrated Trade Solutions The broad set of measures discussed in the paper is available on the World Integrated Trade Solutions (WITS) platform: the dataset is available here and the data visualizations here. Data sources Inter-Country Input-Output data has been provisioned from multiple data sources. These are • EORA26 (1990-2015) 199.82 version (eora). Lenzen, M., Moran, D., Kanemoto, K., Geschke, A. 2013. ‘Building Eora: A Global Multi-regional Input-Output Database at High Country and Sector Resolution.’ Economic Systems Research, 25:1, 20-49. Please remember that the Eora MRIO is free for academic (university or grant- funded) work at degree-granting institutions. All other uses require a data license before the results are shared. • WIOD 2016 VERSION (2000-2014) (wiodn) and WIOD 2013 VERSION (1995- 2011) (wiodo). Timmer, M. P., E. Dietzenbacher, B. Los, R. Stehrer and G.J. de Vries, 2015. ‘An Illustrated User Guide to the World Input-Output Database: the Case of Global Automotive Production.’ Review of International Economics. 23: 575-605. • OECD TiVA 2018 VERSION (2005-2015) (tivan) and OECD TiVA 2016 VERSION (1995-2011) (tivao). OECD, Trade in Value Added database, 2018, oe.cd/tiva • ADB MRIO 2021 version (2000;2007-2020) (adb). Asian Development Bank MRIOT Database, mrio.adbx.online The GVC Trade dataset contains measures related to international trade. The unit of observation is the exporting country-importing country-exporting sector-year. The GVC Output dataset contains measures related to gross output. The unit of observa- tion is country-producing sector-year. All data are in millions of US dollars. Variables description GVC Trade dataset GVC-related trade measures the value of goods and services exported by a sector or a country that crosses more than one border. The difference between gross trade and GVC- related trade is defined as Traditional trade, i.e. the value of goods and services that crosses just one border. The Traditional trade can also be divided into Traditional 4 trade in intermediate goods and Traditional trade in final goods. GVC-related trade presents two desirable features: • once expressed as a share of gross trade, it is bounded between 0 and 1; • it is additive at any level of aggregation/disaggregation of trade flows; thus, data can be summed at any level – total country exports/world exports/world sector exports/country groups and so on – in order to obtain the proper GVC participation measures at the desired level of aggregation GVC-related trade is always traced in the exporting sector. The overall GVC-related trade encompasses three different types of GVC linkages. • Pure forward GVC related-trade: value-added in goods and services entirely generated within the domestic chains – without any border crossing – exported by the sector and re-exported further by the partner. The exporting sector is engaged in GVC activities at the origin of the chain. • Two-sided GVC related-trade: imported inputs bought by the exporting sector directly from abroad or indirectly through domestic chains, exported and further re-exported by the partner. The exporting sector is located in a central position of the chain. • Pure backward GVC related-trade: imported inputs bought by the sector directly from abroad or indirectly through domestic chains, exported by the sector to the final market, as intermediates or final goods. The exporting sector is engaged in GVC activities close to the end of the chain. A natural measure of the Type of participation in GVC-related trade (forward- ness) at any level of aggregation can be straightforwardly obtained as the difference between pure forward and pure backward participation as a share of the overall GVC related-trade. This measure is bounded between -1 and 1 and it is equal to zero at the global level. GVC Output dataset GVC-related output is the output of a country or sector that directly or indirectly crosses more than one border. It provides a more general assessment of the amount of productions of each sector that is related to GVCs, since it takes into account the entire supply chain the sector participates to, regardless of its direct involvement in export activities. The GVC-related output shares the same properties of GVC related-trade: 5 • once expressed as the share of output, it is bounded between 0 and 1; • it is additive at any level of aggregation/disaggregation. Within the total output of a country or sector, the amount that never crosses a single border, neither directly or indirectly, is labeled Purely domestic output. Instead, the output that directly or indirectly crosses just one border is labeled Output related to traditional trade, i.e. value-added produced by the sector and sold abroad to the final market, directly by the producing sector or indirectly trough domestic chains. The overall GVC-related output encompasses three different types of GVC linkages. • Pure forward GVC related-output: value-added produced by the sector and sold directly abroad by the sector or indirectly trough domestic chains; then, re- exported by the partner country. In other terms, the GVC-output is traced in the sector where the value-added originates, the very first link of a chain. Pure forward GVC related-output might also be labeled as GVC related-value-added. • Two-sided GVC related-output: domestic inputs bought by the sector within domestic chains and sold directly abroad by the sector or indirectly trough domestic chains, and re-exported by the partner; imported inputs bought directly from abroad by the sector or indirectly trough domestic chains, and sold directly abroad as inputs or indirectly trough domestic chains. In other terms, the GVC-output here is traced in the sector that simultaneously buys and sells intermediate inputs, in a central position of the chain. • Pure backward GVC related-output: imported inputs bought by the sector directly from abroad or indirectly through domestic chains, and embedded in final goods and services production sold to domestic consumers – if inputs crossed more than 1 border before – or to foreign consumers – if inputs crossed only 1 border. In other terms, GVC-output is traced in the sector that completes the final goods or services, the very last link of a chain. Pure backward GVC related-output might also be labeled as GVC related-final goods and services. A natural measure of the Type of participation in GVC-related output (forward- ness) at any level of aggregation can be straightforwardly obtained as the difference between pure forward and pure backward participation as a share of the overall GVC related-output. This measure is bounded between -1 and 1 and it is equal to zero at the global level. Finally, readers interested in computing their own measures of global value chain trade by origin and destination using also user-provided input output tables are referred to the icio module in Stata by Belotti et al. (2021). Please note that in icio backward participation is equal to pure backward + two-sided participation while forward participation corresponds to the pure forward participation described in this paper. 6