Clemens Fuest

Ariell Reshef
email: ariell.reshef@psemail.eu

Gianluca Santoni
email: gianluca.santoni@cepii.fr

Pol Antras

Lorenzo Caliendo

Cosimo Beverelli

Davin Chor

Alonso De Gortari

Sébastien Jean

Lionel Fontagné

Thierry Mayer

Guy Michaels

Thomas Piketty

Frank Pisch

Lorenzo Rotunno

Thierry Verdier

Vincent Vicard

Ekaterina Zhuravskaya

Are Your Labor Shares Set in Beijing? The View through the Lens of Global Value Chains

Keywords: E250, F140, F150, F160, F660, J000 labor share, global value chains, upstreamness

We study the evolution of labor shares in 1995-2014, while taking into account international trade based on value added concepts. Declines in labor shares accelerate in 2001-2007, concurrently with global value chain (GVC) integration, after which there is no trend for both. We develop a gravity-based instrument for GVC integration and find that the acceleration in the decline in labor shares is caused by increased intensity of forward GVC integration. The integration of China into GVCs has a disproportionally large effect through this mechanism. Declines in labor shares are shouldered mostly by less skilled workers in fabrication functions. Relatively capital abundant countries integrate more into forward GVCs linkages, which is associated with greater upstreamness within GVCs and increases in capital intensity. Forward GVC integration is associated with international vertical integration of both upstream intermediate input production and of offshoring of downstream assembly.

Introduction

The decline in labor shares in recent decades in many advanced economies has both caught the attention of academics and generated concern of policy makers. Apart from having important implications for economic modeling, the interest in declining labor shares fundamentally stems from its implications for income inequality. 1 Just like labor income, capital income accrues to people, but the ownership of capital is concentrated in the hands of relatively few; moreover, capital ownership among capital owners-and thus capital income-is more concentrated than human capital and labor income among workers.2 A smaller share of value added paid to labor implies that income inequality among people rises. This is particularly acute given relatively weak productivity growth in recent times. 3Figure 1 illustrates that while declines in labor shares started in the 1980s, this evolution accelerated markedly in 2001-2007, when global value chain (GVC) integration accelerated as well.

Both labor shares and forward GVC integration level-o¤ after 2007. 4 We argue that countries and industries that integrated forward di¤erentially more saw greater declines in their labor shares.

More o¤shoring of downstream tasks (including …nal assembly), as well as increases in exports of upstream intermediate inputs for use in foreign downstream production, both lower labor shares. This e¤ect has large explanatory power in 2001-2007, and in particular for China's trading partners.

Signi…cant increases in international integration imply that studying the evolution of factor shares from a closed economy perspective-as does most of this literature (see Grossman and Ober…eld (2021))-is bound to miss some of the underlying mechanisms. While there is a large literature that studies labor market e¤ects of trade integration, recent work illustrates that standard gross trade sales statistics can be misleading, and that this has become particularly acute since China joined the World Trade Organization in 2001 and its subsequent increase of global production sharing. 5 While [START_REF] Freeman | Are your wages set in Beijing?[END_REF] asked "Are your wages set in Beijing?", the deepening of production sharing across international borders requires a di¤erent data approach in order to answer such questions. 6 Labor share Forward GVC integration

Notes. The displayed series are year …xed e¤ects from a regression of either labor shares or forward GVC integration on year …xed e¤ects and country …xed e¤ects, weighted by real GDP. Forward GVC Participation is exports of intermediate inputs in value added terms as a share of GDP. The sample for labor shares includes 39 countries that correspond to the WIOD 2013 release sample of countries, and the year …xed e¤ects are adjusted by the weighted (by GDP) average in 1995. The labor share series encompasses compensation of employees and labor income of self-employed; the latter is based on part of mixed income. For China the labor share includes only compensation of employees. Source: Penn World Tables mark 9.1; see [START_REF] Feenstra | The Next Generation of the Penn World Table[END_REF] for documentation on labor shares. The sample for forward GVC integration in 1995-2014 includes 39 countries that correspond to the WIOD 2013 release sample of countries. Data for 1995-2007 are from WIOD 2013 release. Data for 2007-2014 are from WIOD 2016 release, and the year …xed e¤ects are adjusted by the weighted (by GDP) average in 2007 from the WIOD 2013 release. Data for 1970-1995 are from [START_REF] Johnson | Accounting for intermediates: Production sharing and trade in value added[END_REF], and the year …xed e¤ects are adjusted by the weighted (by of Heckscher-Ohlin trade theory hold much better when using value added trade data versus gross trade values. [START_REF] Timmer | Functional specialisation in trade[END_REF] show that revealed comparative advantage indices based on gross trade statistics deviate signi…cantly from those based on and trade in value added, which are more sensible. [START_REF] Jakubik | The "China shock" revisited: Insights from value added trade ‡ows[END_REF] use data on trade in value added to revisit the estimates in [START_REF] Autor | The China Syndrome: Local Labor Market E¤ects of Import Competition in the United States[END_REF] of the e¤ect of imports from China on local labor markets in the U.S.-and …nd signi…cantly weaker e¤ects. Using gross instead of value added export data is also one of the the conceptual ‡aws underlying the so-called [START_REF] Leontief | Domestic production and foreign trade; the American capital position re-examined[END_REF] paradox. See [START_REF] Johnson | Five facts about value-added exports and implications for macroeconomics and trade research[END_REF] for a portrait of di¤erences between gross trade and value added trade ‡ows, as well as several implications. [START_REF] Koopman | Estimating domestic content in exports when processing trade is pervasive[END_REF] and [START_REF] Kee | Domestic Value Added in Exports: Theory and Firm Evidence from China[END_REF] demonstrate the consequences of the rise of China for mis-representation of gross trade data. [START_REF] Johnson | Five facts about value-added exports and implications for macroeconomics and trade research[END_REF] provides a survey of these issues. 6 As noted in the conclusion of [START_REF] Grossman | Trading tasks: A simple theory of o¤shoring[END_REF]: "...almost all current goods' trade data pertain to gross ‡ows rather than to value added. The globalization of production processes mandates a new approach to trade data collection, one that records international transactions, much like domestic transactions have been recorded for many years." GDP) average in 1995 from the WIOD 2013 release. Compared to the sample of 39 countries, the sample from [START_REF] Johnson | Accounting for intermediates: Production sharing and trade in value added[END_REF] excludes Bulgaria, Cyprus, Czech Rep., Estonia, Lithuania, Luxembourg, Latvia, Malta, Russian Federation, Slovakia, Slovenia, Taiwan; these countries account for 2.8% of GDP of the 39 countries in the WIOD sample.

We study the timing and mechanisms that govern the relationship between labor shares and globalization using country and industry panel data from the World Input-Output Database (WIOD) in 1995-2014. This allows us to account for international integration in value added terms, the same concept in which labor shares are measured. While we …nd that increases in forward foreign GVC integration lowers labor shares, other dimensions of globalization (exports and imports of …nal goods and imports of inputs) do not a¤ect labor shares signi…cantly.

We estimate that the declines of labor shares are driven by forward GVC deepening only in 2001-2007, coinciding with China's accession to the WTO in 2001. Moreover, China's integration into GVCs during this period has a larger e¤ect on its trading partners than other countries with their corresponding trading partners. This is consistent with China attracting assembly tasks and importing intermediate inputs from its trading partners in 2001-2007. This relationship disappears after 2007, when China's integration into GVCs slows down, along with that of the rest of the world (Figure 1). Indeed, [START_REF] Chor | Growing Like China: Firm Performance and Global Production Line Position[END_REF] …nd that the upstreamness of imports by Chinese …rms stops increasing after 2007.

In order to make causal inferences we develop an instrument based on a structural gravity relationship. The main threat to identi…cation in our regressions is if supply shocks increase an industry's exports and at the same time a¤ect its labor share-for example, biased technological change, di¤erential declines in the rental rate of capital, or changes in imported input costs.

Structural gravity attributes variation in exports to variation in source country supply factors, destination country factors (which are determined by all source countries, in addition to the speci…c destination), and bilateral trade barriers. We estimate these factors and construct an instrument for GVC integration that is orthogonal to changes in supply factors. The internal validity of our regressions is bolstered by saturating them with …xed e¤ects. Since the regressions are panels of long di¤erences, adding …xed e¤ects absorbs trends in economy and industry-wide variables. This strategy (including the instrument) addresses most of the concerns for identi…cation that Grossman and Ober…eld (2021) raise for studying the evolution of labor shares.

We then ask whether di¤erences in factor endowments can help interpret the results. [START_REF] Sposi | Trade Integration, Global Value Chains, and Capital Accumulation[END_REF] extend the model of [START_REF] Antràs | On the geography of global value chains[END_REF] to include Heckscher-Ohlin forces that operate within value chains. They assume that upstream stages of production are more capital intensive (which we document, especially in GVCs). When separating the geographical location of di¤erent stages of production is possible, declines in trade barriers cause relocation of relatively capital-intensive upstream stages to relatively capital abundant countries. 7 We …nd evidence that is consistent with this prediction: relative capital abundance predicts both the capital intensity and the volume of exports of intermediate inputs, and these associations strengthen over time. Related to this, we show that increases in the upstreamness of production are associated with reductions in labor shares, and that only the foreign-driven part of upstreamness accounts for this relationship. 8We then show that forward GVC-driven reductions in labor shares are shouldered mostly by labor in fabrication tasks, and to a lesser extent by management and marketing. In contrast, it is not driven by reductions in payments to labor engaged in research and development (R&D). This is consistent with the idea that selling …nal goods requires more interaction with consumers and more management control of production processes compared to producing intermediate inputs further up the value chain. It is also consistent with some degree of knowledge transfer that is involved in forward GVC integration, as argued by [START_REF] Baldwin | The Great Convergence: Information Technology and the New Globalization[END_REF].

Finally, we examine brie ‡y the roles of o¤shoring of assembly and multinational enterprises (MNEs). We …nd that o¤shoring of assembly of hitherto exported …nal goods, while contributing to the patterns we uncover, is not the main mechanism driving the results. Greater intensity of exports of intermediate inputs lowers labor shares, whether or not is it done for the purpose of this kind of o¤shoring. We …nd that MNEs are associated with forward GVC integration both in o¤shoring downward assembly, as well as in o¤shoring upstream input production.

Before turning to positioning our work within the literature, we wish to stress an underemphasized fact: more than the entire drop in overall labor shares and cross-country variation therein is shouldered by unskilled labor. Labor shares decline on average 2.5 percent points in 1995-2007, with signi…cant variation across countries summarized by a coe¢ cient of variation of 1:37 (using GDP in 1995 as weights). In contrast, the share of skilled labor in GDP concurrently increased by 4.25 percent points with a much smaller coe¢ cient of variation of 0.36 (data from EU KLEMS). Consistent with this, we …nd that most of the GVC-induced declines in labor shares are shouldered by labor in fabrication tasks, which is less skilled than labor engaged in management, marketing and R&D. Our …nding of a negative association between GVC integration and labor shares while skilled labor shares increase is reminiscent of, inter alia, [START_REF] Richardson | Income inequality and trade: how to think, what to conclude[END_REF] and especially [START_REF] Wood | How Trade Hurt Unskilled Workers[END_REF]. Consistent with this, [START_REF] Timmer | Fragmentation, incomes and jobs: an analysis of European competitiveness[END_REF] …nd that the rise of GVCs is associated with a shift towards skilled labor employment within total employment in 1995-2008. The rest of the paper is organized as follows. We position our work in the relevant literature in Section 2. Section 3 describes the data and methodology. Section 4 describes changes in factor shares and in GVC integration. In Section 5 we investigate the role of GVC deepening in explaining declines in labor shares, as well as several mechanisms. We o¤er concluding remarks in Section 6.

2 Relationship to the literature Our paper contributes to a large body of work that studies the determinants of labor shares. Since most countries have experienced declines in labor shares, it is plausible that the cause is common to all. One such common trend is globalization. While most previous research focuses on the United States and other developed economies, e.g., [START_REF] Blanchard | The medium run[END_REF], [START_REF] Elsby | The decline of the US labor share[END_REF], [START_REF] Rognlie | Deciphering the fall and rise in the net capital share: accumulation or scarcity?[END_REF], and pays little attention to international economic integration-Harrison (2005) studies the evolution of labor shares in a panel of countries, including less developed ones, and investigates, inter alia, the role of trade openness (aggregate gross imports + exports divided by GDP). [START_REF] Elsby | The decline of the US labor share[END_REF] suggest that o¤shoring may have contributed to the decline of the labor share in the United States, but do not study this beyond simple correlations. [START_REF] Böckerman | Globalization, creative destruction, and labour share change: evidence on the determinants and mechanisms from longitudinal plant-level data[END_REF] and [START_REF] Panon | Labor Share, Foreign Demand and Superstar Exporters[END_REF] study the role of exporters in accounting for the evolution of labor shares in Finnish and French manufacturing, respectively. [START_REF] Weinberger | Openness and Factor Shares: Is Globalization Always Bad for Labor?[END_REF] study the e¤ect of capital goods import liberalization in India, and …nd that this actually increased …rm-level labor shares, probably by increasing quality of capital equipment while lowering its e¤ective price. Compared to these papers, we stress the role of GVC integration and exporting of intermediate inputs, using value added trade data.

The closest paper to ours is chapter 3 in International Monetary Fund (2017). In contrast to our work, that paper does not distinguish the impact of forward from backward GVC integration (it aggregates them) on labor shares, and does not control for other forms of trade, e.g., in …nal goods in regression analysis. In addition, we identify causal e¤ects by distinguishing the period in which GVC integration accelerated, and we use gravity-based instruments in order to overcome bias due to confounding factors. We also study the mechanisms underlying the relationship between GVCs and labor shares in greater detail. 9 As discussed above, we …nd support for an Heckscher-Ohlin mechanism that operates within value chains, as suggested in the model of [START_REF] Sposi | Trade Integration, Global Value Chains, and Capital Accumulation[END_REF]. For example, [START_REF] Aichele | Where is the value added? Trade liberalization and production networks[END_REF] …nd in their calibrated model that reductions in trade costs vis a vis China that are associated with signi…cant reductions in domestic value added shares for China's trading partners. Our …ndings are consistent with this, and add that those declines in domestic value added are accounted for more by labor compensation than capital.

Another common trend, that has been proposed as an explanation for declines in labor shares by [START_REF] Karabarbounis | The global decline of the labor share[END_REF], is the widespread decline in the price of investment. This may have caused a shift in expenditures towards capital if the elasticity of substitution between capital and labor were greater than unity, as [START_REF] Karabarbounis | The global decline of the labor share[END_REF] estimate. 10 Indeed, they document that in countries and industries where the decline in investment goods'prices were deeper, labor shares dropped more. However, [START_REF] Glover | Can capital deepening explain the global decline in labor's share?[END_REF] demonstrate how the estimator of the elasticity of substitution in [START_REF] Karabarbounis | The global decline of the labor share[END_REF] is biased upwards; using a corrected estimator, they estimate an elasticity comfortably below unity. Ober…eld and Raval (2014), using di¤erent econometric methodology, also estimate that the elasticity of substitution between labor and capital is less than unity. 11 Results in Bergholt, Furlanetto, and Faccioli-Ma¤ei (forthcoming) also point toward strong capital-labor complementarity in US data. These …ndings weaken the argument on the importance of the decline in the price of investment in contributing to the decline in the labor share. We control for declines in the price of investment in our regressions, and …nd no evidence for this mechanism in our data. 12 Variation in labor shares may also be related to endogenous directed technological change as proposed by [START_REF] Kennedy | Induced bias in innovation and the theory of distribution[END_REF] and [START_REF] Acemoglu | Labor-and capital-augmenting technical change[END_REF], where the decline in the relative price of capital leads to innovation that corrects initial changes in factors'income shares. [START_REF] Acemoglu | The race between man and machine: Implications of technology for growth, factor shares, and employment[END_REF] discuss the possible implications of technological change and robotization, and vom Lehn (2018) discusses how this manifests across occupations. Bergholt, Furlanetto, and Faccioli-Ma¤ei (forthcoming) …nd an important role for automation in US data. [START_REF] Bentolila | Explaining movements in the labor share[END_REF] study variations in labor shares in OECD countries and show how they are linked to technological change, prices of imported materials and labor market frictions. Grossman, Helpman, Ober…eld, and Sampson (2017) show that in a growth model with endogenous human capital accumulation, the decline in productivity growth can lead to declines in labor shares. More generally, biased technological progress can explain both variation in exporting and in labor shares, as we show below. In our analysis we develop a gravity model-based instrument that helps identifying the role of forward GVC integration separately from domestic technological change and changes in prices 1 0 [START_REF] Harrigan | Techies, Trade, and Skill-Biased Productivity[END_REF] …nd an elasticity between labor, capital and materials greater than 1 using French administrative …rm-level data. When the elasticity of substitution between labor and capital is greater than unity and when factor markets are competitive, then a lower relative price of capital causes an increase in the share of expenditures on capital due to strong substitution towards capital usage. This explanation can also capture embodied technological change (computers, robots, etc.), as argued in [START_REF] Martinez | Automation, Growth and Factor Shares[END_REF]. See also [START_REF] Graetz | Robots at work[END_REF].

1 1 [START_REF] Karabarbounis | The global decline of the labor share[END_REF] consider the aggregate economy elasticity of substitution, while Ober…eld and Raval (2014) consider only the elasticity in manufacturing. It is possible that the two di¤er markedly, as shown in [START_REF] Reshef | Is Technological Change Biased Towards the Unskilled in Services? An Empirical Investigation[END_REF].

1 2 In a previous version of this paper we showed that in the presence of capital-skill complementarity the relationship between the price of investment or the rental rate of capital and labor shares may not even be monotone. of inputs, inter alia imported intermediate inputs. 13 Recent work studies the evolution of the labor share at the …rm or establishment level, usually in manufacturing. [START_REF] Kyyrä | The micro-level dynamics of declining labour share: lessons from the Finnish great leap[END_REF] and [START_REF] Autor | The fall of the labor share and the rise of superstar …rms[END_REF] consider the role of …rm size distribution and increases in market share concentration in accounting for changes in labor shares, while [START_REF] Kehrig | The micro-level anatomy of the labor share decline[END_REF] assigns a much smaller role for changes in concentration in US manufacturing establishments, and [START_REF] Mertens | Micro-mechanisms behind declining labour shares: Market power, production processes, and global competition[END_REF] attributes most of the decline in the labor share in German manufacturing to production process transformation, rather than …rm concentration. [START_REF] Stansbury | The Declining Worker Power Hypothesis: An Explanation for the Recent Evolution of the American Economy[END_REF] argue that declines in rent sharing with labor, due to declines in "labor power", can help explain both the decline in labor shares and the decline in the NAIRU in the United States. [START_REF] Brooks | Exploitation of Labor? Classical Monopsony Power and Labor's Share[END_REF] argue that employers' monopsony power in China and India lowers labor shares there, and that this e¤ect has declined over time. Our sample covers mostly developed, mid-income and transition economies, but also important developing and emerging economies (e.g., India and China), and we perform our analysis both at the industry and country levels.

Data and methodology

The main source of data is the World Input-Output Database (WIOD). We outline the main features here and relegate other details to Appendix B. We use the WIOD 2013 release to compute statistics over the pre-2008 …nancial crisis period of 1995-2007. Along with detailed Input-Output tables for 40 countries and 35 industries (of which 14 are in manufacturing, ISIC rev. 3), the 2013 release also provides Socio-Economic Accounts with data on employment, labor compensation and capital stocks, all by country and industry. WIOD 2013 uses the 1993 System of National Accounts (SNA). We also use the more recent 2016 WIOD release, covering 43 countries and 56 industries (of which 14 are in manufacturing, ISIC rev. 4) to compute statistics for 2007-2014. WIOD 2016 uses the 2008 SNA. 14 In both datasets the labor share includes compensation of employees and labor income of self-employed (part of "mixed income"). 15 The labor shares from the WIOD data 1 3 Declines in labor shares have been also related to structural change [START_REF] Ngai | Structural change in a multisector model of growth[END_REF], [START_REF] Buera | The rise of the service economy[END_REF], [START_REF] Mcadam | Medium run redux[END_REF]), the di¤erence between capital returns and output growth [START_REF] Piketty | Capital in the Twenty-…rst Century[END_REF]), deregulation of labor markets [START_REF] Blanchard | Macroeconomic e¤ects of regulation and deregulation in goods and labor markets[END_REF]), deregulation of bank branching in the U.S. (Weinberger and Leblebicioglu (forthcoming)), to dynamics in real estate values [START_REF] Gutiérrez | Revisiting the Global Decline of the Labour Share[END_REF]), and to fertility and immigration (d'Albis, Boubtane, and Coulibaly (2021)). [START_REF] Bengtsson | What determines the capital share over the long run of history?[END_REF] study the institutional determinants of the long run evolution of labor shares in a closed economy context. For business cycle properties of the labor share see [START_REF] Mcadam | Medium run redux[END_REF], [START_REF] Young | Labor's share ‡uctuations, biased technical change, and the business cycle[END_REF]Mućk, McAdam, and[START_REF] Mu Ćk | Will the "True" Labor Share Stand Up? An Applied Survey on Labor Share Measures[END_REF].

1 4 For WIOD 2013 release documentation see [START_REF] Timmer | An illustrated user guide to the world input-output database: the case of global automotive production[END_REF]. For WIOD 2016 release documentation see [START_REF] Timmer | Fragmentation, incomes and jobs: an analysis of European competitiveness[END_REF]. See http://www.wiod.org/home for further details on WIOD country coverage and data availability.

1 5 WIOD 2013 release reports data until 2011, but the incidence of missing values for labor shares in the Socio-Economic Accounts increases signi…cantly after 2009. This is not an issue in WIOD 2016. In both datasets and in all years, the input-output matrices do not have missing values. Changes in the System of National Accounts preclude merging data from the two WIOD releases. However, for comparability of within-sample trends we reclassify WIOD 2016 release data to conform with the 2013 release in two dimensions. First, we allocate countries that appear in the 2016 release but not in the 2013 release to the "Rest of World" (ROW) category. Second, since the sectors in the 2016 release are more disaggregate, we aggregate them to the same level of the 2013 release. 16 The correlation across the two WIOD releases in 2007 for labor shares and forward GVC integration is over 0.85, and the trends in the overlapping years (2000)(2001)(2002)(2003)(2004)(2005)(2006)(2007)(2008)(2009)(2010)(2011) are remarkably similar. 17 We drop Poland from the analysis because it is an extreme outlier in 1995, and thus creates unreasonable variation over time for that country.

Forward GVC integration

We measure forward GVC integration as payments to domestic factors that are generated by downstream foreign industries. This is driven by more than just direct exports of intermediate inputs and services to businesses, as it takes into account the entire network of GVCs, where value can "travel" across several borders (e.g., purchases from buyers of my output, etc.). 18 We rely on the standard methodology of [START_REF] Leontief | Quantitative input and output relations in the economic systems of the United States[END_REF], applied to an international setting.

Gross output for any industry located in any country is the sum of intermediate input demand from all other industries located in all other countries, plus production of …nal goods. In matrix notation, this is X = AX + Y , where X is the vector of gross outputs, AX is intermediate demand and Y is …nal good production; A is the matrix of technical coe¢ cients. 19 Rearranging leads to X = (I A) 1 Y = BY , where B = (I A) 1 is the Leontief (inverse) matrix, which takes into account the indirect production linkages across industries. The matrix B summarizes all value chains, be they domestic or global. 20 It is useful to de…ne …nal good production Y as a diagonal 1 6 The sectoral reclassi…cation is important for comparability of changes over time across the two WIOD releases because the increase in the number of industries in WIOD 2016 is due to splitting industries into relatively upstream and relatively downstream industries.

1 7 Table A1 and Table A2 in the appendix report country-level labor shares and skilled labor shares in 1995, 2007 and 2014.

1 8 See [START_REF] Hummels | The nature and growth of vertical specialization in world trade[END_REF] and [START_REF] Yi | Can vertical specialization explain the growth of world trade?[END_REF] on the increasing importance of vertical specialization and integration in world trade.

1 9 A typical entry of the A matrix a od ij indicates the value of input from industry i located in country o that is needed to produce one dollar worth of good j in country d.

2 0 A typical entry of the B matrix b od ij indicates the value of production in industry i located in country o that is required in order to satisfy one unit of …nal demand for product j in country d, while taking into account direct and indirect intermediate demand from all other using industries. matrix, with the corresponding values on the diagonal and zeros elsewhere, implying that X is a matrix as well.

By pre-multiplying gross output terms (in US dollars) by a diagonal matrix of value added to gross output ratios (intensities) one obtains V X = V BY . The left hand side, V X, is industry value added produced and the right hand side, V BY , is demand for …nal goods in value added terms. 21 Each element of the V BY matrix contains all payments to factors that are employed in sector i in origin country o that contribute to the production of …nal goods in sector j in destination country 22 This follows the GVC income approach, which is theoretically consistent. 23 Figure 1 illustrates that the weighted average f orward increases by 2.84 percent points in 1995-2007. All but one country (Latvia) in our sample exhibit increases in this period, to varying degrees. Figure 1 also illustrates that f orward leveled o¤ after 2007, which is a consequence of much more modest increases in some countries, and some reductions in others. 24

Upstreamness

Forward GVC integration manifests in a concurrent increase in "upstreamness", de…ned as the average number of production stages between production in a particular industry in a given country and …nal good demand, across all possible value chains (domestic and global). [START_REF] Antràs | On the measurement of upstreamness and downstreamness in global value chains[END_REF] use the following measure of upstreamness

U r i = 1 Y r i X r i + 2 P s P j a rs ij Y s j X r i + 3 P s P j P t P k a rs ij a st jk Y t k X r i + ::: ; (1)
where, as above, Y is …nal demand, X denotes gross output, and a rs ij are technical coe¢ cients, denoting the amount of output of industry i located in country r that is required to produce one unit of output of industry j located in country s. [START_REF] Miller | Output upstreamness and input downstreamness of industries/countries in world production[END_REF] show that (1) is equal to the row-sum of the inverse [START_REF] Ghosh | Input-output approach in an allocation system[END_REF] matrix G (which is related to the Leontief inverse B matrix), U = G , where is a column vector of ones. 25 This is useful, because it permits to easily separate the part of upstreamness that is accounted for by domestic linkages and foreign ones:

U = U D + U F : (2)
Here U D = G D , where G D is a block-diagonal matrix using only domestic demand. The foreign

part is U D = [G G D ] = G F .
In Figure 2 we illustrate that global upstreamness increases, as in [START_REF] Antràs | On the measurement of upstreamness and downstreamness in global value chains[END_REF], that the increase in U is entirely driven by U F , as in [START_REF] Miller | Output upstreamness and input downstreamness of industries/countries in world production[END_REF], and in addition, that most of this takes place in 2001-2007.

Antràs, [START_REF] Antràs | Measuring the upstreamness of production and trade ‡ows[END_REF] show that upstreamness is negatively correlated with labor shares in a cross section of U.S. manufacturing industries. We replicate this …nding using the WIOD data in Section 5.6 below, which is an assumption in the model of [START_REF] Sposi | Trade Integration, Global Value Chains, and Capital Accumulation[END_REF]. We also show that this correlation holds within industries over time: industries that increase their upstreamness-and in particular foreign-driven upstreamness-exhibit declining labor shares. This is consistent with the mechanism in [START_REF] Sposi | Trade Integration, Global Value Chains, and Capital Accumulation[END_REF], where in response to a reduction in the cost of geographical production fragmentation, the relatively capital abundant country specializes in more upstream and capital intensive steps in the value chain. Notes. The displayed series are year …xed e¤ects from a regression of either country-level upstreamness (U ct ), its domestic (U D ct ) and foreign (U F ct ) components, or their natural logarithms (ln U ct , ln U D ct , ln U F ct ) on year …xed e¤ects and country …xed e¤ects, weighted by real GDP in 1995. Country-level upstreamness indices are computed as the weighted average of industry values from (2) (using value added as weights), and U ct = U D ct + U F ct . The sample includes 39 countries that correspond to the WIOD 2013 release, which is also the source of the data.

4 Accounting for sources of change in labor shares

Composition versus within-industry intensities

We split value added into labor and capital payments, as follows V L BY + V K BY = V BY , where V f are diagonal matrices of factor shares in output. 26 Computing factor shares is straightforward. We split factor payments into the part that arises from payments by domestic …nal goods producers, and payments by foreign …nal goods producers. The domestic contribution is the block-diagonal part of V f BY . The contribution of foreign industries is the o¤-block-diagonal part of V f BY , and is akin to numerator of f orward de…ned above, di¤erentiated by factor f . We decompose changes in factor shares into changes in within-industry intensities where factors are located V f , and industry composition, determined by demands for …nal goods in destination markets Y and the network of GVCs B. The change in V f BY (indeed, of any three conformable matrices) from period 1 to period 2 can be written as

V f 2 B 2 Y 2 V f 1 B 1 Y 1 = (V f BY ) = ( V f )B 1 Y 1 + V f 1 ( B)Y 1 + V f 1 B 1 ( Y ) +V f 1 ( B)( Y ) + ( V f )B 1 ( Y ) + ( V f )( B)Y 1 +( V f )( B)( Y ) : (3)
where denotes the element-by-element change operator. 27 While other decompositions of changes exist, (3) o¤ers a natural way to contemplate counterfactual scenarios, where we consider the exclusive role of each component of V f BY , while …xing other components to their values in the initial period (technically, setting changes in all other dimensions to zero). Considering changes in BY together is methodologically desirable, because the same data are used to construct both B and Y . Once we perform these decompositions for V f BY , we compute the corresponding factor shares.

Before turning to the results of the decomposition we wish to ‡ag an important caveat to analyzing changes in V f BY : factor shares in any industry in any country are invariant to the using industries, or to whether the using industry is domestic or foreign. It is well-known that within industries exporters are more capital and skill intensive; this may bias our analysis of the role of GVC integration in the evolution of labor shares. 28 Table 1 reports the results of the decomposition of factor shares using (3) for 1995-2007. Panel A reports this for the entire economy, while Panel B focuses on manufacturing industries, which follow similar patterns but in greater magnitudes. 29 Columns 1-4 report the shares of income accruing to capital and labor from domestic industries and from foreign industries. All other columns are derived from these. Column 5 reports the overall labor share in GDP. Column 6 reports the share in GDP arising from all international sources (this is the f orward concept, displayed in Figure 1).

Columns 7 and 8 report labor shares in payments by domestic and foreign industries, respectively.

All numbers are weighted averages across countries using GDP in 1995 as weights. V BY 1995 ). 30 Changes in industry composition due to B alone account for 0.47 percent points, and changes due to Y account for 0.44 percent points. Together, (BY ) accounts for 0.87 percent points decline in the labor share-which is 35 percent of the change. In manufacturing the split is 37 percent for within-industry changes and 40 percent for composition. 31 Both within industry changes in factor intensities and changes in industry composition account 2 9 Although all factors in Panel B are employed in manufacturing, services industries, both domestic or foreign, can also be a source of income for manufacturing.

3 0 Within-industry changes can be signi…cantly driven by changes in …rm composition, which are associated with globalization. This can be seen by juxtaposing the 4-digit SIC industry level analysis of U.S. manufacturing in [START_REF] Berman | Changes in the Demand for Skilled Labor Within U.S. Manufacturing: Evidence from the Annual Survey of Manufactures[END_REF] with the analysis of the plant level data that underlies the 4-digit SIC industries in [START_REF] Bernard | Exporters, Skill Upgrading, and the Wage Gap[END_REF]. Virtually all …rm level evidence indicates that exporting …rms are signi…cantly more capital and skill intensive (see, for example, [START_REF] Bernard | Firms in International Trade[END_REF] for the U.S., [START_REF] Harrigan | Skill Biased Heterogeneous Firms, Trade Liberalization and the Skill Premium[END_REF] in Chile). Therefore, variations in …rm composition due to trade liberalization can also lower labor shares within-industries. See also [START_REF] Kehrig | The micro-level anatomy of the labor share decline[END_REF] for an establishment-level anatomy of the decline in the labor share with in U.S. manufacturing.

3 1 [START_REF] Karabarbounis | The global decline of the labor share[END_REF] and International Monetary Fund (2017) …nd a smaller role for industry composition. There are at least two reasons for this. The …rst is that they use industry value added shares to aggregate industry-level value added labor shares. This can generate misleading results on the role of composition, because it does not take into account changes in composition due to sourcing decisions. The second reason for di¤erences in results is variation in data sources, measurement, and level of aggregation. International Monetary Fund (2017) use only 10 industries, which mechanically causes more variation to occur within industries compared to our data, which include 35 industries. In the limit, if there is only one industry, all of the variation is within this single industry. The sample of countries is also di¤erent across studies. [START_REF] Karabarbounis | The global decline of the labor share[END_REF] consider value added shares in corporate income, while we consider the entire economy.

for the evolution of labor shares. This informs the empirical investigation in Section 5, and leads us to study determinants of changes of labor shares both at the industry and at the national levels. 32

Complex GVCs and foreign sources of demand

We study the relative importance of foreign value chains captured in B, and of foreign demand for …nal goods Y . We start by decomposing B using Stone's additive decomposition (see Appendix E for details):

B = I + (B d I) + B x + B g : (4)
Here I captures the direct e¤ect of demand, while the other components capture indirect linkages:

B d I
V f ( B)Y = V f ( B d )Y + V f ( B x )Y + V f ( B g )Y : (5)
Final goods production can be written as

Y = Y d + Y f ; (6)
where Y d is domestic demand by the country producing the …nal goods and Y f is foreign demand for …nal goods. Both Y d and Y f include demand for domestically-produced goods and for imports.

Using (6) we can write

V f B( Y ) = V f B( Y d ) + V f B( Y f ) ; (7)
which allocates demands to production via B and then to factor payments via V f .

Table 2 displays the results of the analysis for labor shares (V f = V L ) in 1995-2007 for the entire economy level and separately for manufacturing. The four "Total"rows in columns 1-3 report labor shares in GDP that are paid by domestic industries, foreign industries, and overall in 1995; these are the same numbers in columns 2, 4 and 5 in Table 1. The "Total" rows in columns 4-6 report the changes in the same concepts. The rows above the "Total" rows indicate the contributions of sub-components of either B or Y to their levels and changes in the corresponding columns.

We start with the Stone decomposition of B in levels. Overall, most payments to labor in 1995 are generated due to domestic linkages (91% for all industries and 80% in manufacturing). Almost all of labor payments originating in domestic industries occurs via to domestic linkages (B d ), while most of the demand from foreign industries occurs due to bilateral trade linkages (B x ) (roughly 84%). Complex GVCs (B g ) originate mostly from foreign industries; return loop value chains are much less important. These …ndings are consistent with [START_REF] Miroudot | Made in the world?[END_REF].

The novel …ndings are the contributions to changes, using (5). Column (6) of contributing to an increase in labor payments due to domestic demand for foreign …nal goods. The latter is due to domestic industries supplying labor intensive inputs to foreign industries. The changes in manufacturing are larger, and overall in the same direction as the entire economy.

Table 2 delivers two messages. The …rst is that shifts towards more complex GVCs account for an important part of the decline in labor shares. The second is that the greater reliance on foreign sources of income demand, including how domestic demand for …nal goods is supplied by foreign production, contribute to lower labor shares. 34

Explaining changes in labor shares

In this section we study the role of forward GVC integration and juxtapose it with other explanations. We start with …tting the following industry-by-country regression in a panel of changes

LS ic;t = 1 F W D ic;t + 2 BACK ic;t + 3 EXP ic;t + 4 IM P ic;t + 5 ln q c;t + …xed e¤ects + " ic;t ; (8)
where LS ic is the change in labor share in industry i located in country c. The …rst four variables on the right hand side of (8) capture dimensions of globalization:

F W D ic = f orward ic =V A ic is
the share of exports of intermediate inputs in value added, i.e., forward foreign GVC intensity (the industry-country equivalent of the country-level variable examined in Section 3.1); BACK ic = f oreign_inputs ic =inputs ic is the share of imported inputs in total input purchases, i.e., backward foreign GVC intensity; EXP ic = y c ic =V A ic is export intensity of …nal goods in value added (y c ic is …nal demand for industry i in country c from other countries c); and IM P ic = y c i; c =absorption i;c is import intensity of …nal goods in total absorption (y c i; c is demand of country c for …nal goods i produced in other countries c; and absorption i;c is given by local production plus imports minus exports of …nal good i in country c: y i;c + y c i; c y c i;c ). Finally, q c is the relative price of capital equipment investment (only country-level variation). 35 36 We estimate versions of (8) for manufacturing industries and then for all strictly private sector industries in 1995-2014. 37 While we expect GVC deepening to a¤ect manufacturing, GVCs should a¤ect services and other non-traded sectors through input linkages. We split the sample into three periods: 1995-2001, 2001-2007 and 2007-2014. The split is determined by the timing of changes in the rate of decline of the labor share, which are evident in Figure 1. In the Appendix G we present a procedure that identi…es 2001 as a natural split for the 1995-2007 sub-sample. The second split is mandated by the fact that cover the period before 2007 and the period after 2007 with di¤erent releases of the WIOD (see discussion in Section 3).

We report regressions with increasingly demanding combinations of …xed e¤ects that absorb time, country and industry trends in labour shares. Our most demanding speci…cations of (8) include country-industry …xed e¤ects (with and without time …xed e¤ects), which absorb any trends within these units, e.g., within-industry and country trends in use of housing [START_REF] Gutiérrez | Revisiting the Global Decline of the Labour Share[END_REF]). We report robust standard errors clustered by country and by industry (two-way clusters), to accommodate the fact that q c varies only by country [START_REF] Moulton | An illustration of a pitfall in estimating the e¤ects of aggregate variables on micro units[END_REF]), and to account for any cross-country correlations in the errors across industries [START_REF] Cameron | Robust inference with multiway clustering[END_REF]).

We estimate (8) by weighted least squares (WLS) with V A ic in 1995 as weights (choosing di¤erent years for weights changes little the results). This gives the regression coe¢ cients an aggregate interpretation. 38 We also estimate versions of ( 8) at the country level, in order to address country-level labor shares directly. The di¤erence between the two speci…cations is that the latter also allows for impacts on industry composition. We develop an instrument to address concerns for identi…cation, as described below, and apply it both at the country-industry and at the country levels.

Baseline WLS estimates

Table 3 presents the baseline results. We start with speci…cations without any …xed e¤ects, and then increase the saturation of the model up to inducing country-industry and period …xed e¤ects.

Overall, only the coe¢ cient to F W D is statistically signi…cant across all speci…cations. Moreover, the magnitude is stable across speci…cations, which considerably alleviates concerns for endogeneity caused by omitted variables. The coe¢ cient to BACK is negative, but not precisely estimated and is smaller than that to F W D, implying a more limited role for o¤shoring in reductions in labor shares.

The largest e¤ect for manufacturing industries is found in the most demanding speci…cation in column 7; it implies that a one percent faster increase in forward foreign GVC integration is associated with 0.43 percent point faster decline the labor share. Perhaps not surprisingly, the e¤ect is smaller when considering all private sector industries, at 0.28. These are economically large e¤ects. A manufacturing industry in a given country at the third quartile of F W D sees its labor share drop by 2 percent points more than an industry at the …rst quartile, which is a …fth of the inter-quartile range for LS (10 percent points). The equivalent computation for all private sector industries gives about half as much explanatory power. 39

Baseline W2SLS estimates

The results above imply a strong relationship between increases in forward GVC integration and declines in labor shares. Here we address concerns for causal interpretation of this relationship.

While WLS may be biased due to omitted variables despite the high saturation of …xed e¤ects, the main concern for endogeneity arises from unobserved biased technological change, or from di¤erential reductions in the rental rate of capital. To make this concrete, suppose that the value added production function in some industry is

Y = [ ( K K) + (1 ) ( L L) ] 1= ; 1;
where K and L capture capital and labor augmenting technological change, respectively. Then cost minimization in competitive factor markets implies that the labor share can be written as

LS = 1 ( K =r) 1 ; ( 9
)
where r is the rental rate of capital and = 1= ( 1) is the elasticity of substitution between capital and labor. An increase in K or reduction in r will make the industry more competitive and it will export more, and at the same time have a direct e¤ect on LS unless = 1 (similar arguments can be made for changes in L and wages). We do not take a stand on whether is above or below unity, which implies a di¤erent direction of bias for the estimator of ( 8). Bias would similarly arise in the context of a gross output production function if intermediate inputs are not equally complementary to capital and labor, and their price declines due to, e.g., importing of intermediate inputs.

In order to deal with such concerns we construct an instrument based on structural gravity that is inspired by [START_REF] Aichele | Where is the value added? Trade liberalization and production networks[END_REF]. We start with the technical coe¢ cients matrix

A = [a dj ci ],
where c is a source country, d is a destination country, and i and j denote industries. The data underlying A are ‡ows of intermediate inputs. We use tools from structural gravity to construct changes in A that are not in ‡uenced by changes in the source country and industry, thus eliminating technological change, but allowing for changes in destination and bilateral forces. We use this to construct changes in B = (I A) 1 and in value added ‡ows V BY that are orthogonal to the direct e¤ects of technological change or input prices.

Denote by dj

i the overall (not source country-speci…c) share of intermediate input i in gross production of industry j in destination country d. It follows that P c a dj ci = dj i , so that P c a dj ci = dj i = 1. Therefore, input import shares are given by dj ci = a dj ci = dj i . We model these along the lines of [START_REF] Eaton | Technology, geography, and trade[END_REF],

dj ci = T j ci C i ci dj ci i P c 0 i T j c 0 i =C c 0 i i dj c 0 i i = expf ln T j ci C i ci | {z } j ci + [ ln X c 0 i T j c 0 i =C c 0 i i dj c 0 i i ] | {z } dj i + dj ci i | {z } dj ci g ; (10)
where T denotes the level of technology, denotes bilateral trade barriers, the unit cost terms C may include inputs (both domestic and imported) and domestic primary factors, as in [START_REF] Caliendo | Estimates of the Trade and Welfare E¤ects of NAFTA[END_REF], and we allow di¤erent elasticities by industry. Note that we also allow the technology to di¤er depending on the using industry. We estimate (10) by PPML in …ve cross 1995, 2001, 2007, 2007 0 and 2014, where 2007 0 denotes data from WIOD 2016: 40

sections in periods t =
dj ci = e (t) j ci + (t) dj i + (t) dj ci : (11)
Using the estimates we can construct

Source : b T (t) j ci b C (t) i ci = e b (t) j ci Destination : X c 0 b T (t) j c 0 i b C (t) i c 0 i [b (t) dj ci ] i = b (t) dj i = e b (t) dj i Bilateral : [b (t) dj ci ] i = e b (t) dj ci :
For each period t (except for 1995) we build e dj ci (t) by replacing the period t source elements by those estimated in period t 1. In doing so, we also replace for each destination country d and industry

j the corresponding b T (t) j ci b C (t) i ci element inside b (t) dj i with b T (t 1) j ci b C (t 1) i
ci (which makes it vary also by source country c, e (t) dj ci ). Once this is done we recover e a dj ci (t) = e dj ci (t) dj i , where dj i are data, and build e A (t). We use this to build e

B (t) = [I e A (t)] 1 and V (t) e B (t) Y (t) from
which we compute F W D (t) using the same methodology as above. Our instrument is

Z ci;t = F W D (t) ci F W D (t 1) ci : (12)
The changes Z ci;t are driven by variation in demand and variation in bilateral trade barriers, and are orthogonal to variation in source country c and industry i supply shocks, which may be directly correlated with labor shares.

Table 4 reports the results of estimating (8) by weighted 2SLS (W2SLS), using ( 12) as an instrument. We report here only the results using the most saturated model, and relegate results of speci…cations with fewer …xed e¤ects to Table A8 in the appendix, as they deliver a similar message. In columns 1 and 4 we repeat the baseline WLS results from Table 3, column 7. Columns 2 and 5 reports the W2SLS estimates, including …rst stage statistics, and columns 3 and 6 report the …rst stage regressions. The W2SLS estimates of the coe¢ cients to F W D are negative and much larger than the WLS estimates in absolute value. This is consistent with upward bias in the WLS estimates in Table 3, which can arise from three reasons. First, classic measurement error would bias the estimator of the coe¢ cient to F W D towards zero. Second, measurement error in value added alone would bias the estimator of the coe¢ cient to F W D towards 1 (it is in the denominator of both F W D and LS). Third, unmeasured capital-augmenting technological change (an increase in K ) or changes in the rental rate of capital r (despite controlling for ln q at the country level) would tend to increase the labor share if the elasticity of substitution between capital and labor is smaller than 1, while boosting exports. 41 In order to asses the importance of potential violations of the exclusion restriction, we applied the Local-to-Zero (LTZ) approximation of [START_REF] Conley | Plausibly exogenous[END_REF]. We use this methodology to compute con…dence intervals for the coe¢ cient to F W D that take into account uncertainty about the validity of the exclusion restriction for Z. We …rst estimate by WLS a version of ( 8) that includes the instrument ( 12), and we store the standard error of the coe¢ cient to the instrument, b , denoted b b . We then use the LTZ approximation to construct con…dence intervals for the W2SLS coe¢ cient to F W D using di¤erent multiples of b b -1, 10, 25 and 50-and two distribution functions for -normal and uniform. The con…dence intervals do not include zero even at 50 times b b . This indicates that even if the instrument is not strictly exogenous, it is strong enough to justify small violations of the exclusion restriction, and is thus useful for inference. 42 We are checked whether outliers drive our results. We therefore repeatedly estimated (8), each time dropping a country, and industry, or a country-industry pair. The point estimates are not sensitive to these sample restrictions. We only …nd for a handful of c-i pairs that omitting them changes the point estimate signi…cantly. Even in these cases the point estimates remain negative and statistically signi…cant. We report these in Appendix H.

In a previous version of this paper we built an instrument for F W D by applying the gravity methodology described in (10) directly to bilateral value added ‡ows, V BY . These yielded similar qualitative W2SLS results. The gravity model does not apply to value added ‡ows, because V BY ‡ows cannot be decomposed into source, destination and bilateral components that are log-linearly separable. GVCs are in ‡uenced by all countries' productivities and costs and all bilateral trade barriers-potentially more than once, with di¤erent elasticities and in nonlinear ways. Nevertheless, the in ‡uence of source and destination countries and industries remains important. It is reassuring, therefore, that by removing the source country and industry variation in this setting we obtain similar results.

The role of China

After establishing that the negative relationship between labor shares and forward GVC integration is causal in Table 4 we turn to the role of China in driving them. We show that the e¤ect of forward [START_REF] Conley | Plausibly exogenous[END_REF] for a discussion of this last point and of the LTZ approximation in general. Results for the WLS estimates of (8) that include the instrument (12), as well as the con…dence intervals that use the LTZ approximation are reported in the appendix in Table A10 andTable A11, respectively. GVC integration on reductions in labor shares is concentrated in 2001-2007, the period starting with China's accession to the WTO, in which its integration into GVCs accelerated, and in which the decline in labor shares accelerates (Figure 1). Moreover, we …nd particularly strong e¤ects when China is on the importing side.

4 1 @LS=@ K = ( 1) r 1 2 K > 0 if < 1. 4 2 See Section III.C in
We report the results in Table 5, using the most saturated model; results from speci…cations with fewer …xed e¤ects deliver the same message. 43 In columns 1 and 6 we repeat the baseline WLS results from Table 3,column 7 The results are similar when we add all other private sector industries, with the only di¤erence being that we also estimate an equally strong e¤ect of China in 1995-2001.

Country-level regressions

The decompositions results in Table 1 imply that both within-industry changes and change in industry composition account for reductions in labor shares, and in equal measure. In order to take into account both margins, we estimate (8) at the country level.

We report the results in Table 6. Columns 1-4 report WLS estimates of (8) using value added in 1995 as weights, with di¤erent con…gurations of …xed e¤ects. We report robust standard errors clustered by country. Overall, the results resemble those in Table 4, and the coe¢ cients are larger for both manufacturing and for the entire economy. While the estimates are precise in all speci…cations in columns 1-4 in manufacturing, including both country and period …xed e¤ects reduces precision for the entire economy, although the point estimate changes little.

In addition, we estimate (8) by W2SLS using the same instrument (12) aggregated up to manufacturing or the entire economy, reported in Table 6 in column 5, with …rst stage regressions reported in column 6. We report only the speci…cation with country …xed e¤ects. Di¤erent con…gurations of …xed e¤ects yield similar results, and are reported in Table A9 in the appendix, but as with WLS, using both country and period …xed e¤ects for the entire economy yields an imprecisely estimated coe¢ cient to F W D-but not in manufacturing. As with the W2SLS regressions at the country-industry panel, the instrument is not weak and the estimated coe¢ cient to F W D is larger compared to WLS. We discuss above in Section 5.2 potential explanations for this larger e¤ect. 44 In unreported regressions we estimate that for manufacturing the e¤ect of F W D is concentrated in 2001-2007, with a greater e¤ect for F W D when China is the importer-similar to the results discussed in Section 5.3 and reported in Table 5 (and with larger coe¢ cients). However, when estimating the same speci…cations for the entire economy, the coe¢ cients to F W D across periods and destinations are much less precisely estimated.

Overall, the results at the country level corroborate those at the country-industry level.

The role of endowments

In this section we ask whether the patterns of forward GVC integration are associated with relative factor abundance (RKA). If relatively upstream production is more capital intensive (we corroborate this in Section 5.6), then Heckscher-Ohlin logic would imply that as trade barriers decline and GVCs rise, upstream activities should be attracted to relatively capital abundant countries. These countries should, therefore, export more intermediate inputs that are relatively capital intensive to less capital abundant countries, where labor-intensive downstream stages take place. This is the mechanism underlying the model in [START_REF] Sposi | Trade Integration, Global Value Chains, and Capital Accumulation[END_REF].

In order to explore these ideas empirically we start by estimating the following regression

(V K BY ) od (V L BY ) od GDP o = RKA od + 0 gravity od + o + d + " od ; (13
RKA od = ln E K o E K o + E K d ln E L o E L o + E L d ;
where E f i are expenditures on factor f 2 fK; Lg in country i 2 fo; dg. The coe¢ cient of interest is , and given the discussion above, we expect a positive relationship. We control for standard bilateral control variables in gravity od : log distance, and indicators for a common border, colonial ties, common language, free trade agreements, and common currency. 45 We also include in (13) origin and destination …xed e¤ects to control for overall attractiveness of o for capital intensive production, and overall tendency of d to produce …nal goods with capital intensive inputs structure (the source of income ‡owing from d to o). The results in Table 5 indicate that the e¤ects of forward GVC integration are present only in 2001-2007, so we study these e¤ects only in that period. We estimate (13) by OLS in two cross sections, in 2001 and in 2007. We report robust two-way clustered standard errors at the country o and country d level.

We report the results in columns 1 and 2 of Table 7. We …nd that greater RKA is associated with greater capital intensity of exports of intermediate inputs from o to d, and that this association has strengthened a bit from 2001 to 2007. Since we include both source and destination …xed e¤ects, this result is not driven by overall abundances per se.

We now turn to discuss the volume of these exports. We estimate gravity regressions

V BY od = expf RKA od + 0 gravity od + o + d g + " od ; (14)
where We interpret this strengthening of the e¤ect of RKA on both the volume and the capital intensity of forward GVC integration as a consequence of reductions in barriers to the geographical spread of GVCs, in line with the predictions in [START_REF] Sposi | Trade Integration, Global Value Chains, and Capital Accumulation[END_REF].

V
Finally, we investigate whether the e¤ect of RKA is di¤erent for direct exports, V B x Y od , com-

pared to indirect exports of intermediate inputs, V B g Y od , where V BY od = V B x Y od + V B g Y od for
o 6 = d (see (4) above). We see in columns 5 and 6 of Table 7 a stronger association of RKA with direct exports of intermediate goods, V B x Y od , which is reasonable given the bilateral nature of RKA od (and, similarly, stronger e¤ects of distance and common language), versus the more complex and indirect GVCs involved in V B g Y od . 46 Overall, the results in Table 7 imply that the pattern of expansion of forward GVC integration is responsive to factor endowments. Relatively capital abundant countries tend to integrate forward, increasing the capital intensity of their exports of intermediate inputs, which contributes to lower labor shares.

Changes in positioning within GVCs: upstreamness

Industries and countries that increased the intensity of supplying intermediate inputs to foreign industries have seen their labor share decline. This is consistent with the idea that production that is more upstream, i.e. farther away from …nal goods production or …nal assembly is less labor intensive. It is also the key assumption in [START_REF] Sposi | Trade Integration, Global Value Chains, and Capital Accumulation[END_REF]. Here we investigate this assumption.

We …t two sets of regressions using data in 2001-2007, the period in which the relationship between forward GVC integration and labor shares is strongest. First we …t country by industry by year panel regressions. Then we …t cross section long di¤erence regressions of changes from 2001 to 2007. The dependent variable is labor shares and the explanatory variables are either upstreamness (1) or its domestic and foreign components (2) (in levels or in changes). We also control for downstreamness, which is computed in an analogous way as upstreamness, except that it pertains to distance from the …rst stage of production. This control is important since, as Antràs and Chor (2018) demonstrate, upstreamness and downstreamness are positively correlated, and together they indicate the overall position of an industry within its average value chain. We use di¤erent sets of …xed e¤ects (FEs) in the panel regressions in order to illustrate di¤erent sources of variation. We report robust standard errors clustered both by country and by industry.

We report the results in Table 8. We start with manufacturing industries. Column 1, with only year …xed e¤ects, demonstrates that upstreamness (U ) is associated with lower labor shares in the cross section-but this is not precisely estimated. This is consistent with Antràs, Chor, Fally, and Hillberry (2012), who document a similar negative correlation in a cross section of U.S. manufacturing industries. Since we control for downstreamness, this implies that length (or fragmentation) of value chains per se is not strongly associated with labor shares. In columns 2 and 3 we …nd that this association is stronger over time within countries and industries. In column 4 we …nd that the domestic component of upstreamness (U D ) is associated with lower labor shares in the cross section. In contrast, in columns 5 and 6 we see that increases in the foreign component of upstreamness (U F ) are associated with decreases in labor shares over time, not changes in the domestic component. These results are corroborated in columns 7 and 8 using long di¤erences, where we see that the association between upstreamness and declines in labor shares is driven by the foreign component. When we turn to the results for all private sector industries we …nd similar patterns. The only substantive di¤erence is that we …nd a signi…cant positive association between increases domestic upstreamness and changes in labor shares in column 8.

Overall, the results show that increases in upstreamness that are driven by exports of intermediate inputs to foreign industries are negatively associated with labor shares. As industries re-position farther away from …nal good production and assembly, they require less labor and more capital.

Changes in functional specialization

In this section we ask what types of labor tasks account for the declines in labor shares documented above. We draw on data from Timmer, Miroudot, and de Vries ( 2019), that allows splitting labor income into four categories of functional specialization: management (M GT ), research and development (R&D), fabrication (F AB), and marketing (M KT ). This allows us to write

LS ic = M GT ic + R&D ic + F AB ic + M KT ic :
Inspection of the occupational classi…cations that underlie the four functions reveals that they are particularly meaningful in manufacturing, but less so in non-manufacturing industries. For example, outside of manufacturing the marketing category is very heterogeneous, resembling a residual of the other, more consistently de…ned functions.

As above, we focus on the period in which the association between labor shares and forward GVC integration is strongest. Thus, we …t the following long di¤erence regressions in 2001-2007, both in manufacturing and in all private sector industries:

F U N CT ION ic = D U D ic + F U F ic + D ic + …xed e¤ects + " ic ; (15)
and

F U N CT ION ic = 1 F W D ic + 2 OF F ic + 3 EXP ic + 4 IM P ic + 1 ln q c + …xed e¤ects + " ic ; (16)
where F U N CT ION 2 fM GT; R&D; F AB; M KT g, D ic is the measure of downstreamness in industry i and country c. We weigh regressions by value added in 2001 and cluster standard errors by country and by industry. In order to ease the exposition of ( 16), we report only estimates of 1 ; other coe¢ cients are not precisely or robustly estimated, and imply much weaker e¤ects. 47 We estimate ( 15) and ( 16) with no …xed e¤ects, country e¤ects and industry e¤ects; results using both country and industry …xed e¤ects are not precisely estimated, which is not surprising given the very demanding speci…cation (only one cross section of changes). Since all variables are in changes, the coe¢ cients are comparable across all speci…cations.

We report the results in Table 9. Across all speci…cations, we …nd that U F and F W D are negatively associated with M GT , M KT and-to a much greater extent-with F AB.

One reason for the larger e¤ect on fabrication tasks is that increases in upstreamness and GVC integration are driven by o¤shoring of assembly. Expenditure on management, design, marketing and post-sales services also decline as we move up the value chain, away from …nal good production.

Our interpretation of this is that selling …nal goods requires more interaction with consumers and more management control of production processes compared to producing intermediate inputs further up the value chain. More generally, as [START_REF] Baldwin | The Great Convergence: Information Technology and the New Globalization[END_REF] argues, moving production stages within a value chain across borders requires moving some management and marketing together with fabrication tasks, because GVC integration involves technology transfer to where production activities are relocated. 48 In contrast, we do not …nd any e¤ect of forward GVC integration on the share of labor expenditures in R&D. This is what we would expect to …nd if forward GVC integration is associated with multinationals o¤shoring assembly, where parents perform almost all of the R&D for the multinational, a pattern that is well documented by several sources. 49 A corollary of these …ndings is that R&D becomes more intensive within labor in industries that integrate forward into foreign GVCs. Interestingly, when estimating (15) in the sample with all private sector industries (but not in manufacturing) we …nd a positive association between changes in downstreamness D with R&D. Together with the results on upstreamness, this implies that R&D becomes more intensive in industries that increase the overall length of the value chains they participate in. However, the association of downstreamness with R&D is not strong enough to increase labor shares signi…cantly, as seen in Table 8. 50 Overall, forward GVC integration and greater upstreamness are associated with declines in labor shares because they require less expenditure on fabrication, management and marketing labor activities.

O¤shoring of assembly of exports of …nal goods

We start by asking whether the e¤ect of an increase in the export intensity of intermediate inputs is due to o¤shoring of assembly of …nal goods that would have otherwise been exported. O¤shoring of assembly of …nal goods that would have been consumed domestically is controlled for by IM P .

The …rst stage regressions in Table 4 do not reveal any correlation between IM P and F W D.

We compute a modi…ed version of F W D, denoted F W D , in which we subtract exports of …nal goods from value added in the denominator of F W D. O¤shoring of assembly may increase the numerator of F W D if domestic inputs are shipped to foreign assembly sites. At the same time, it may reduce the denominator if it causes fewer exports of …nal (assembled) goods. If o¤shoring of labor-intensive assembly of hitherto exported …nal goods is an important mechanism, then F W D should have a smaller e¤ect on the reduction in labor shares. The results in columns 5 and 10 of Table 5 imply that, compared to the baseline results for F W D in columns 1 and 6, there is a slightly weaker association F W D with labor shares in manufacturing, but a slightly stronger association in all private sector industries. 51 The coe¢ cient to EXP (changes in exports of …nal goods intensity) increases dramatically in columns 5 and 10. This is because the numerator is precisely the part that is deducted from the denominator of F W D .

In unreported regressions we tried to detect a di¤erent e¤ect of F W D through two channels:

value added bilateral exports of intermediate inputs that cross borders only once and are absorbed in the direct destination country-versus when it is embodied in exports of the destination country, i.e. complex GVCs that cross borders more than once. Due to the high collinearity, we could not separately identify these e¤ects. In our data 75 percent of F W D accrues to value that crosses borders only once, on average. 52 We conclude that o¤shoring of assembly of …nal goods exports is one mechanism through which forward GVC integration lowers labor shares, although probably not the most important one.

Multinationals and cross-border capital ownership

Given their importance in the world economy, we now study the role of multinational enterprises (MNEs) in forward GVC integration. 53 By exploiting the bilateral and directional nature of GVC integration and cross-border ownership we can shed light on the nature of this relationship. To the extent that the returns to capital (or pro…ts) of a¢ liates of MNEs are repatriated to the country of origin, this has implications for labor shares in national income (compared to domestic product) and, therefore, inequality across individuals.

We estimate the following gravity equation in a cross section in 2007: We report the results in Table 10. In columns 1-3 we see that cross-border MNE activity in both directions is associated with exports of intermediate inputs, and the di¤erence in the strength of the association is small. This implies that both types of vertical international integration play a role in fostering forward GVC integration: o¤shoring of upstream input production and of downstream assembly. This dovetails with our results in Table 5, where we did not …nd signi…cant di¤erences for the e¤ect of forward GVC integration on labor shares once we excluded assembly o¤shoring.

V BY od =
We also investigate whether the these associations are di¤erent for direct exports, V B x Y od , compared to indirect exports of intermediate inputs, V B g Y od , where

V BY od = V B x Y od + V B g Y od
for o 6 = d (see (4) above). We see in columns 4-6 and 7-9 of labor activities. The increase in foreign forward GVC integration and in upstreamness all but halt after 2007, when labor shares cease to decline, on average. Since skilled labor shares increase while the overall labor share declines, this implies that unskilled labor shoulders the decreases in payments to labor, which is consistent with the greater drop in fabrication compared to other labor activities.

We show that the rise in forward GVC integration is associated with di¤erences in relative capital abundances, and with cross-border MNE presence.

Concerns for the social costs of GVC integration, and on labor in particular, have recently been aired by The White House (2021); our paper illustrates that some of these concerns are not misplaced. First, to the extent that inequality is a concern, and given that redistribution of the gains from globalization is far from perfect (and potentially very costly), our …ndings on the e¤ect of globalization on lowering labor shares raise concerns about the costs of further economic integration. Second, our …ndings on MNE activity imply that studying the e¤ects of globalization on income distribution through the evolution of labor shares should take into account a national product approach, rather than rely solely on domestic production approach. This is because MNEs own (most of) the capital installed in their foreign a¢ liates, and thus a large part of the income ‡ows due to GVC integration do not accrue where production takes place, but to the owners of capital involved in production.

One important caveat of our study is that we do not identify the underlying forces that drive globalization (for example, reductions in man-made trade barriers, or technological forces). Nevertheless, whatever the underlying causal forces, we demonstrate that they operate through forward foreign GVC integration. In addition, since we do not observe …rms, we cannot study whether One major caveat in using these data arises from the proportionality assumptions in constructing WIOD. Value added shares within industry gross output and factor expenditure shares within value added are the same within an industry and country, regardless of the using industry and country or …nal consumption destination. For example, this means that the WIOD data do not allow the value added intensity in gross output to depend on the use of output (downstream industries or consumption, domestic or foreign). de Gortari (2017) demonstrates that the latter can have signi…cant quantitative implications for measures of economic integration between the U.S. and Mexico. In contrast, [START_REF] Puzzello | A proportionality assumption and measurement biases in the factor content of trade[END_REF] …nds that similar proportionality assumptions lead to small bias in factor content of trade.

Figure A2 depicts a schematic outline for the structure of the WIOD for the exemplary case of 3 countries and 2 sectors. See http://www.wiod.org/home for further details on the country coverage and data availability. 2 is total demand for …nal goods in country t for good 2 sourced from country r. The WIOD distinguishes among …ve …nal demand use categories. In order to conserve on space, these …ve categories are not displayed in the Figure A2 (the categories are: …nal consumption expenditure by households, …nal consumption expenditure by non-pro…t organizations, …nal consumption expenditure by government, gross …xed capital formation and changes in inventories and valuables). Furthermore, X is a vector of total gross outputs for industries by location (indicated by the row). Total intermediate consumption for an industry i located in a country c (indicated by the column) A c i is the sum of all A elements within a column. Value added V c i of an industry i located in a country c (indicated by the column) is obtained by deducting A c i from the corresponding total gross output entry X c i for that industry i and country c (indicated by the row).

Summing all Y elements gives global consumption of …nal goods. From the expenditure approach to national accounting this is also global GDP.

B.2 Value added computations

Value added computations are based on Timmer, Los, Stehrer, and de Vries (2013), which is rooted in the seminal work of [START_REF] Leontief | Quantitative input and output relations in the economic systems of the United States[END_REF]. The goal is to decompose the value of …nal goods production (i.e., …nal demand) according to the industry and location where the value added originated. Conversely, one can also compute the allocation of payments to primary factors (capital and labor) according to the industries where these value added payments originate. Technically, the computation relies on a diagonal matrix of …nal demand Y , the Leontief inverse matrix B, as well as a diagonal matrix of direct value added coe¢ cients per sector, V . All these are obtained from the values depicted in the Figure A2 above.

The elements of the diagonal matrix of …nal goods demand Y are obtained by a row-wise summation of the "Y -area" in Figure A2 across all countries (and use categories; see above for details):

Y c i = X k Y ck i :
The elements of the diagonal matrix of value added coe¢ cients V are obtained by subtracting the entire intermediate consumption of a sector (column sum in the input-output matrix A) from the sectoral gross output and dividing this by the gross output of the sector

v c i = X c i P k;j A kc ji X c i :
The Leontief inverse matrix is B = (I A) 1 , where A is the matrix containing all sub-elements equal to

a sr ij = A sr ij X r j
and I is the identity matrix. We compute the B matrix in a few steps. In the …rst, we derive the input-output coe¢ cients, a sr ij . We obtain these coe¢ cients by dividing each cell in the A region in Figure A2 along a column by the gross output X of the respective column sector. This gives the matrix A. A typical element a sr ij of A indicates the amount of output from industry i located in source country s (indicated by the row) that is needed to sustain the production of one unit of output in industry j in destination country r (indicated by the column). In the second step we compute an auxiliary matrix by subtracting the A matrix of input-output coe¢ cients from an identity matrix I. Finally, we invert the auxiliary matrix to obtain the required Leontief matrix B. A typical element b sr ij of B indicates the amount of output from industry i located in source country s (indicated by the row) that is needed to sustain the production of one unit of …nal demand of product j in destination country r (indicated by the column).

In order to obtain the gross output needed to sustain …nal demand we multiply BY . In order to get the corresponding concept in value added terms, we pre-multiply BY by the diagonal matrix V with elements V c i on the diagonal (appropriately ordered) to get V BY . For illustration, an example of the matrix V BY for the case of three countries and two industries is

v s 1 b ss 11 y s 1 v s 1 b ss 12 y s 2 v s 1 b sr 11 y r 1 v s 1 b sr 12 y r 2 v s 1 b st 11 y t 1 v s 1 b st 12 y t 2 v s 2 b ss 21 y s 1 v s 2 b ss 22 y s 2 v s 2 b sr 21 y r 1 v s 2 b sr 22 y r 2 v s 2 b st 21 y t 1 v s 2 b st 22 y t 2 v r 1 b rs 11 y s 1 v r 1 b rs 12 y s 2 v r 1 b rr 11 y r 1 v r 1 b rs 12 y r 2 v r 1 b rt 11 y t 1 v r 1 b rt 12 y t 2 v r 2 b rs 21 y s 1 v r 2 b rs 22 y s 2 v r 2 b rr 21 y r 1 v r 2 b rr 22 y r 2 v r 2 b rt 21 y t 1 v r 2 b rt 22 y t 2 v t 1 b ts 11 y s 1 v t 1 b ts 12 y s 2 v t 1 b tr 11 y r 1 v t 1 b ts 12 y r 2 v t 1 b tt 11 y t 1 v t 1 b tt 12 y t 2 v t 2 b ts 21 y s 1 v t 2 b ts 22 y s 2 v t 2 b tr 21 y r 1 v t 2 b rr 22 y r 2 v t 2 b tt 21 y t 1 v t 2 b tt 22 y t 2 3 7 7 7 7 7 7 5 : (18)
The elements of the V BY matrix can be interpreted in two ways. First, the values of the matrix along a column indicate backward linkages of production. The sum within a column is the value added that an industry located in a country generates in order to satisfy demand for …nal goods that it produces. Values within a column denote the value contribution of all industries and countries (given by the row) to the production of another industry located in a country (given by the column). For example, v r 1 b rs 12 y s 2 indicates the value added of sector 1 located in country r that is supplied in order to produce …nal goods of industry 2 in country s. By summing across all rows within a column one obtains the total value of …nal goods production y s 2 , which is also …nal demand for industry 2 located in country s, no matter where this is sold around the world (i.e., no matter where demands arises from). For example,

P i;k v k i b ks i2 y s 2 = F D s 2 = y s 2
. Summing all y s j across columns j within a country s does not give the GDP of country s because trade may not be balanced (if trade were balanced, then this sum does give GDP of country s). However, summing all y s j across all j and s gives global GDP.

The second interpretation considers the values of the V BY matrix within a row, indicating the forward linkages of production. In this interpretation values indicate how payments to primary factors employed in a country-industry (given by the row) are "…nanced" by production of …nal goods (in terms of value added) of other industries and countries (given by the columns). Thus, in the context of forward linkages, v r 1 b rs 12 y s 2 is the part of GDP paid to factors employed in industry 1 in country r by production of …nal goods in industry 2 of country s. The sum across all columns within a row is thus equal to the country-industry's value added of the considered row, for example, P j;k v r 1 b rk 1j y k j = V A r 1 . Therefore, summing the industry rows for a given country gives GDP of that country, for example

P i V A r i =GDP r .

B.3 Foreign value added shares

We compute two foreign value added shares. The …rst is foreign value added shares in …nal goods production based on the backward perspective. These are payments to factors located in foreign countries. This is calculated by summing within a column entries across rows of all industries located in foreign countries:

backward c i = P s6 =c P j v s j b sc ji y c i P s P j v s j b sc ji y c i = P s6 =c P j v s j b sc ji y c i y c i :
Using the example in ( 18), the foreign value added (not share thereof) in production of sector 1 in country s, is the sum of v s 1 b ss 11 y s 1 , v s 2 b ss 21 y s 1 , v t 1 b ts 11 y s 1 and v t 2 b ts 21 y s 1 . The second foreign value added share concept entails shares in factor payments (value added) paid by foreign industries, based on the forward perspective. This is calculated by summing within a row entries across columns of all industries located in foreign countries:

f orward c i = P s6 =c P j v c i b cs ij y s j P s P j v c i b cs ij y s j = P s6 =c P j v c i b cs ij y s j va c i
Using the example in (18), the foreign value added (not share thereof) in factor payments of sector 1 in country s, is the sum of v s 1 b sr 11 y r 1 , v s 1 b sr 12 y r 2 , v s 1 b st 11 y t 1 and v s 1 b st 12 y t 2 . The denominator in this case is equal to value added of industry 1 in country s, va s 1 .

B.4 Production factors computations

As described in Timmer, Erumban, Los, Stehrer, and de Vries (2014), the methodology described above can also be applied to decompose the value of …nal goods production according to capital and labor. The only di¤erence consists the use of a di¤erent vector of coe¢ cients. The calculations above transform gross outputs X = BY into value added by pre-multiplying by the diagonal matrix V . Instead, we only need to pre-multiply X by a di¤erent diagonal matrix, one that transforms gross outputs into factor payments.

In order to derive this it is necessary to divide sector level data on capital and labor compensation by sectoral output

v c f;i = F c i X c i ;
where F and f denote payments and the share of payments to a particular factor. Thus, v c f;i is the gross output share of factor f . Values for F c i are given by the Socio-Economic Accounts in the WIOD. Pre-multiplying BY by a diagonal matrix V f with elements v c f;i on the diagonal gives a matrix of factor shares in production, V f BY , which can be read like the V BY matrix above, only in terms of payments to factor f . The decomposition of the …nal goods'value into to capital, highand less-skilled labor incomes requires three di¤erent matrices.

C Backward GVC integration

Each element of the V BY matrix contains all payments to factors that are employed in sector i in origin country o that contribute to the production of sector j in destination country d: (vby) A3 and Table A4 in the appendix report country-level backward GVC integration using WIOD [START_REF] Reshef | Is Technological Change Biased Towards the Unskilled in Services? An Empirical Investigation[END_REF]and WIOD 2016, respectively, in 1995, 2007and 2014. . The global trend in backward GVC integration is similar to that of forward GVC integration (exhibited in Figure 1), because the numerators use the same global trade in inputs in value added terms. However, forward and backward di¤er at the country and industry level, due to di¤erences across industries and countries in the tendency to import inputs or to export inputs from and to other industries, respectively.

D Proof of decomposition equation (3)

The change in the product V X (indeed, of any two conformable matrices) can be written as

(V X) = V X 1 + V 1 X + V X : (19)
To see this, start with

V X = V 2 X 2 V 1 X 1 :
Add and subtract V 2 X 1 and rearrange to get

V X = V 2 X 2 V 1 X 1 + (V 2 X 1 V 2 X 1 ) = V 2 (X 2 X 1 ) + (V 2 V 1 ) X 1 = V X 1 + V 2 X :
Now add and subtract V 1 X and rearrange to get

V X = V X 1 + V 2 X + (V 1 X V 1 X) = V X 1 + V 1 X + V 2 X V 1 X = V X 1 + V 1 X + (V 2 V 1 ) X = V X 1 + V 1 X + V X :
Applying the same algebra in ( 19) to X = (BY ) and plugging this back into (19) yields ( 3).

E Stone' s additive decomposition

This is based on [START_REF] Miller | Input-Output Analysis, Foundations and Extensions[END_REF], pages 285-290, originally from [START_REF] Stone | Input-Output and National Accounts[END_REF]. Consider e A, an n n matrix. Start with

X = AX + Y and subtract e AX X e AX = AX e AX + Y =) (I e A)X = (A e A)X + Y to get X = (I e A) 1 (A e A)X + (I e A) 1 Y De…ne A (I e A) 1 (A e A)
and write

X = A X + (I e A) 1 Y (20)
Pre-multiply by A to get

A X = (A ) 2 X + A (I e A) 1 Y (21)
and use ( 21) in ( 20) to get

X = (A ) 2 X + A (I e A) 1 Y + (I e A) 1 Y = (A ) 2 X + (I + A )(I e A) 1 Y
Now solve again for X to get

X = [I (A ) 2 )] 1 | {z } M 3 (I + A ) | {z } M 2 (I e A) 1 | {z } M 1 Y (22)
Stone' s additive decomposition starts with X = M 3 M 2 M 1 Y in ( 22) and arrives at:

X = IY + (M 1 I) | {z } Y f M 1 + (M 2 I) M 1 | {z } Y f M 2 + (M 3 I) M 2 M 1 | {z } Y f M 3 (23)
Here is the derivation of (23) starting with ( 22):

B = M 1 M 2 M 3 = M 2 M 1 + M 1 M 2 M 3 M 2 M 1 = M 2 M 1 + (M 3 I) M 2 M 1 = M 1 + M 2 M 1 M 1 + (M 3 I) M 2 M 1 = M 1 + (M 2 I) M 1 + (M 3 I) M 2 M 1 = I + (M 1 I) + (M 2 I) M 1 + (M 3 I) M 2 M 1
In the context of international analysis, e A = A d is the matrix of diagonal (or block-diagonal, if industries are not aggregated) elements such that

A d = 2 6 6 6 4 A 11 0 0 0 0 A 22 0 0 0 0 . . . 0 0 0 0 A nn 3 7 7 7 5
and

A f = 2 6 6 6 6 4 0 A 12 A 1n A 21 0 . . . . . . . . . A n 1;n A n1
A n;n 1 0 3 7 7 7 7 5

:

Then B d = I A d 1 = 2 6 6 6 4 (I A 11 ) 1 0 0 0 0 (I A 22 ) 1 0 0 0 0 . . . 0 0 0 0 (I A nn ) 1
Using these in A gives

A = I A d 1 A f = B d A f = 2 6 6 6 4 (I A 11 ) 1 0 0 0 0 (I A 22 ) 1 0 0 0 0 . . . 0 0 0 0 (I A nn ) 1 3
0 (I A 11 ) 1 A 12 (I A 11 ) 1 A 1n (I A 22 ) 1 A 21 0 . . . . . . . . . (I A n 1;n 1 ) 1 A n 1;n (I A nn ) 1 A n1 (I A nn ) 1 A n;n 1 0 3 7 7 7 7 5
and also the related M 2 matrix M 2 = I + A . The typical o¤-diagonal (i; j) i6 =j element of A (and also of M 2 ) is (I A ii ) 1 A ij ; it captures demand for factors in i that originate from intermediate inputs demand in production in j that cross borders from j to i once. Now consider

(A ) 2 = 2 4 X l6 =i;j (I A ii ) 1 A il (I A ll ) 1 A lj 3 5 i;j which has a typical (i; j) element P l6 =i;j (I A ii ) 1 A il (I A ll ) 1 A lj .
This captures demand for factors in i that originate from intermediate inputs demand in production in j that cross borders twice from j to i. The …rst matrix on the right A lj gives demand from j's industries in l. The second matrix (I A ll ) 1 calculates the output that needs to be produced in l in order to satisfy the demand from j. The third matrix A il gives the implication of this for demand from i's industries. And the fourth matrix (I A ii ) 1 calculates the output that needs to be produced in i in order to satisfy the demand from l.

Applying the above to Stone's additive decomposition gives

X = IY + [B d I] | {z } Y f M 1 + B d A f B d | {z } Y f M 2 + (B B d B d A f B d ) | {z } Y f M 3 : If we consider e A = A f , we have M 1 = B f = I A f 1
Here B f captures total demand for output (including the initial injection of direct demand from Y ) due to value chains that always cross borders. For example, B f includes chains like A ij A jk A kl A lm :::, where i 6 = j, j 6 = k, k 6 = l, l 6 = m:::, but it is possible to have, for example, i = k. Thus domestic feedbacks are possible in B f . Here f M 1 = B f I in Stone's additive decomposition nets out the direct e¤ect of the initial injection by deducting I. However, f M 2 = B f A d B f does not have a clear interpretation, despite clearly capturing some of the possible value chains. Similarly for f M 3 . However, we can say that f M 2 + f M 3 gives the remainder of output that is induced by demand after taking into account the direct injection and f M 1 . In the main text equation ( 4) reads

B = I + (B d I) + B d A f B d | {z } B x + (B B d B d A f B d ) | {z } B g

:

Here I captures the direct e¤ect of demand on output. Next, B d I captures output that is induced by all strictly domestic indirect linkages. To see this, note that

B d = (I A d ) 1 , To see this, note that B d = (I A d ) 1
, where A d is the matrix of block diagonal elements from A, capturing only domestic linkages. Next, B x captures output that is induced by all strictly bilateral trade in intermediate inputs that cross borders only once (exports from the standpoint of the producing country). To see this, note that A f = A A d , i.e. the o¤-block-diagonal elements of A. B x takes all domestic output requirements (the …rst B d on the right), computes the implied international demand for intermediate inputs captured in A f , and then the implied total domestic requirements in the producing country (the second B d on the left). Finally, B g captures all other types of linkages, essentially net interregional feedback e¤ects (net of strictly direct intra-and direct international e¤ects captured B d and B x , respectively). I.e., B g captures the e¤ect of complex global value chains: output that is induced by combining both domestic and foreign linkages, that may cross borders more than once, and that may include return e¤ects.

F Price of investment in capital equipment

We use data from the Penn World Tables mark 9.0 (PWT, see [START_REF] Feenstra | The Next Generation of the Penn World Table[END_REF]) and from the United States' Bureau of Economic Analysis (BEA), applying the same methodology as in [START_REF] Karabarbounis | The global decline of the labor share[END_REF] with updated data (their sample ends in 2010).

For each country c in year t we divide the investment price index (P inv ct ) by the consumption price index (P con ct ), both in terms of their corresponding PPP US prices (from PWT data). This means that P inv ct =P con ct is the relative price of investment in terms of that of the United States'ratio in PPP. In order to convert this to the relative price from the domestic standpoint we divide P inv ct =P con ct by P inv U SA;t =P con U SA;t and then multiply by the ratio of the price index for private …xed investment (P pf i U SA;t ) to the personal consumption expenditures price index (P pce U SA;t ) (the latter from BEA data). In the regressions we use log di¤erences in the resulting q ct = (P inv ct =P con ct )=(P inv U SA;t =P con U SA;t ) (P pf i U SA;t =P pce U SA;t ). The weighted average decline in q c in 1995-2007 is roughly 12%, or 1% per year, while the weighted average decline in 2007-2014 is roughly 15%, or 2% per year-twice the annual rate in the previous period. Figure A3

and

2007 LS ic = 1 2007 F W D ic + 2 2007 BACK ic + 3 2007 EXP ic + 4 2007 IM P ic + 1 2007 ln q c + …xed e¤ects + " ic ; ( 25
)
where 1995 denotes changes from 1995 to year , and 2007 denotes changes from year to 2007, for = 1996; 1997; :::2006. The results (available upon request) imply that the coe¢ cient to F W D is small and imprecisely estimated in (24) unless > 2001; the coe¢ cient to F W D is large and precisely estimated in (25) when 2001. Regressions like ( 24) and ( 25) using data aggregated to the country level deliver a similar message.

H Outlier analysis

In order to check for the in ‡uence of outliers we repeatedly estimated (8), each time dropping a country, an industry, or a country-industry pair. The point estimates are not very sensitive to these sample restrictions. We report in Figure A4 and Figure A5 the coe¢ cient to F W D when we estimate (8) while dropping one country-industry observation at a time, together with the 95% con…dence intervals. In manufacturing industries (Figure A4) in ‡uential observations are: USA in "Food, beverages and tobacco"(15t16), "Electrical and optical equipment"(30t33), "Transport equipment"(34t35); Japan in "Basic metals and fabricated metals"(27t28), "Electrical and optical equipment"(30t33), "Transport equipment"(34t35); Germany in "Transport equipment"(34t35). In all private sector industries (Figure A5) in ‡uential observations are: Japan in "Transport equipment" (34t35), China in "Agriculture, hunting, forestry and fhishing", (AtB), Great Britain in "Financial intermediation" (J). GDP andin Manufacturing Value Added, 1995-2007 Notes. Panel A reports decompositions of changes in factor shares in GDP, while Panel B reports decompositions of changes in factor shares within manufacturing industries' value added. Columns 1-4 report the shares of income accruing to capital and labor from domestic industries and from foreign industries. Column 5 reports the overall labor share (columns 2 + 4). Column 6 reports the share of income accruing from serving foreign industries. The split between domestic and foreign industries is given by different entries within rows in VfBY.

The contribution of foreign industries to factor shares is given by the forward concept defined in the text. The contribution of domestic industries is given by the complement of the forward concept. The rows labeled "Levels" report levels in 1995 and in 2007. Rows labeled as "Changes" report true and counterfactual changes. All numbers are weighted averages using GDP in 1995 as weights. Notes. The dependent variable is changes in country-industry specific labor shares in three periods: 1995-2001, 2001-2007, 2007-2014. Δ forward is the change in intermediate inputs exports intensity in value added (forward GVC integration), Δ backward is the change in importing of intermediate inputs intensity in total input purchases, Δ exports of final goods is the change in export intensity of final goods in value added, and Δ imports of final goods is the change in import intensity of final goods in domestic absorption. Δ log relative price of investment is the country-level log change in investment prices. All regressions are weighted by value added in 1995 as weights. A constant is always included but not reported. Robust standard errors in parentheses are computed by two-way clustering by country and by industry. *** p<0.01, ** p<0.05, * p<0.1. : 1995-2001, 2001-2007, 2007-2014. Δ forward is the change in intermediate inputs exports intensity in value added (forward GVC integration). In columns 2 and 7 we split Δ forward by period; in columns 3 and 8 we split by shipments to China and the Rest of the World (RoW); and in columns 4 and 9 we split by both period and destination of shipments (China, RoW). In columns 5 and 10 Δ forward net of assembly offshoring is the change in intermediate inputs exports intensity in value added that excludes exports of final goods; we drop the bottom and top percentiles of this variable to avoid extreme outliers that are driven by deducting exports of final goods from value added in the denominator. Δ backward is the change in offshoring of intermediate inputs intensity in total input purchases, Δ exports of final goods is the change in export intensity of final goods in value added, and Δ imports of final goods is the change in import intensity of final goods in domestic absorption. Δ log relative price of investment is the countrylevel log change in investment prices. All regressions are weighted by value added in 1995 as weights. A constant is always included but not reported. Robust standard errors in parentheses are computed by two-way clustering by country and by industry. *** p<0.01, ** p<0.05, * p<0.1.

Manufacturing industries Private sector industries

Dependent variable: Notes. Panel A reports decompositions of changes in factor shares in GDP, while Panel B reports decompositions of changes in factor shares within manufacturing industries' value added. Columns 1-4 report the shares of income accruing to capital and labor from domestic industries and from foreign industries. Column 5 reports the overall labor share (columns 2 + 4). Column 6 reports the share of income accruing from serving foreign industries. The split between domestic and foreign industries is given by different entries within rows in VfBY.

Δ forward intensity (1) (2) (3) (4) (5) (6)
The contribution of foreign industries to factor shares is given by the forward concept defined in the text. The contribution of domestic industries is given by the complement of the forward concept. The rows labeled "Levels" report levels in 2007 and in 2014. Rows labeled as "Changes" report true and counterfactual changes. All numbers are weighted averages using GDP in 2007 as weights. Source: authors' calculations based on WIOD 2016 release. : 1995-2001, 2001-2007, 2007-2014 : 1995-2001, 2001-2007, 2007-2014 [START_REF] Conley | Plausibly exogenous[END_REF]. The Null hypothesis is that the instrument ΔZ is excluded from the second stage, structural equation, i.e., it's coefficient in this equation is zero. The "local to zero" (LTZ) approximation takes into account uncertainty about whether the true value of this coefficient is zero. The table reports confidence intervals for the endogenous variable ΔFWD in the second stage regression that apply the LTZ approximation with different distributional assumptions and different variances of the value of the coefficient to ΔZ in the structural equation. These variances are multiples of the variance of the coefficient to ΔZ in Table A10.

Multiples of the variance of the coefficient to ΔZ in Table A10 (

Figure

  Figure 1. Labor Shares and Forward GVC Participation

  exhibit virtually identical trends at the country level as those from the Penn World Tables used to construct Figure 1. In Appendix A, we show that di¤erent concepts of the labor share exhibit very similar trajectories, in particular the 2001-2007 acceleration in the decline in labor shares and the change in trajectory after 2007.

Figure

  Figure 2. Upstreamness and its components

  . In columns 2 and 7 we interact F W D with period …xed e¤ects and …nd that the e¤ect is present only in 2001-2007. In columns 3 and 8 we split F W D into the part which is imported by China and another part that is imported by the rest of the world (RoW). The coe¢ cient to F W D to China is large and precisely estimated, while the coe¢ cient to F W D to RoW is smaller and not statistically signi…cant at conventional levels of signi…cance. In columns 4 and 9 we interact F W D to China and to RoW with period …xed e¤ects. In manufacturing we …nd that the e¤ect of both F W D to China and to RoW are precisely estimated only in2001-2007.

  GVC deepening accounts for declines in labor shares by changing the composition of …rms-along the lines[START_REF] Harrigan | Skill Biased Heterogeneous Firms, Trade Liberalization and the Skill Premium[END_REF],[START_REF] Autor | The fall of the labor share and the rise of superstar …rms[END_REF] and De Loecker and Eeckhout (2018)-or by changes within …rms. Understanding the role of …rms in GVC integration and changes in labor shares is an important task for future research.

Figure

  Figure A1: Di¤erent Labor Share Concepts in the Penn World Tables

Figure A2 :

 A2 Figure A2: Schematic Outline of a World Input-Output Table

  displays histograms of percent changes in the investment price in1995-2007 and in 2007-2014.

FigureG

  Figure A3: Percent Changes in the Investment Price

Figure

  Figure A4: Manufacturing Industries

  . Δ forward is the change in intermediate inputs exports intensity in value added (forward GVC integration). The instrument Δ Z is constructed by eliminating home-country and industry sources of variation from Δ forward in a gravity relationship; see text for complete details. Δ backward is the change in importing of intermediate inputs intensity in total input purchases, Δ exports of final goods is the change in export intensity of final goods in value added, and Δ imports of final goods is the change in import intensity of final goods in domestic absorption. Δ log relative price of investment is the country-level log change in investment prices. All regressions are weighted by value added in 1995 as weights. A constant is always included but not reported. Robust standard errors in parentheses are computed by two-way clustering by country and by industry. *** p<0.01, ** p<0.05, * p<0.1.

  Notes. The dependent variables are changes in labor income shares in value added of four categories of "functional specialization": management (MGT), R&D, fabrication (FAB), and marketing (MKT). Overall labor shares are the sum of shares over these four categories. Changes for all variables are computed for 2001-2007. The first two lines in each panel reoprt coefficients from regressions where foreign and domestic upstreamness are included. The third line reports the coefficient to Δ forward, the change in intermediate inputs export and GVC intensity, from regressions where the other explanatory variables are the change in offshoring of intermediate inputs intensity in total input purchases (Δ offshoring), the change in export intensity of final goods in value added (Δ exports of final goods), the change in import intensity of final goods in total absorption (Δ imports of final goods), and the country-level log change in investment prices (Δ log relative price of investment, normalized: mean=0, S.D.=1). Regressions estimated by weighted least squares with value added in 2001 as weights. Robust standard errors in parentheses are computed by two-way clustering by country and by industry. *** p<0.01, ** p<0.05, * p<0.1.

  od ij summarizes payments to primary factors employed in country o in industry i due to exports (in value added terms) of intermediate inputs. We de…ne forward foreign GVC integration for an industry i in country o as the share of exports of intermediate inputs in value added terms in value added: f orward o i =

	d: (vby) od ij . Then concept at the country level is f orward o = P d6 =o P j (vby) P d6 =o P d6 =o (vby)	P	j (vby) od ij =	P d	P j (vby) od ij . The equivalent

od =GDP o , where vby od = P i P j (vby) od ij and GDP o = P d (vby) od .

Table 1

 1

	reveals several facts. First, on average, the increase of 2.45 percent points in capital
	shares is driven both by domestic industries (0.87 pp), and even more so by payments from foreign
	industries (1.57 pp). In manufacturing industries the increase of 4.04 percent points in capital
	shares is almost entirely driven by payments from foreign industries (3.81 pp). The overall decline in
	labor shares is driven by domestic industries (-3.72 pp), where the increase in payments from foreign
	industries (+1.27 pp) is far from enough to compensate for this decline (similarly, in manufacturing).
	Thus, the decline in labor shares is associated with a shift towards foreign sources of income (2.84
	pp overall, and 7.13 pp in manufacturing).
	Changes in industry composition account for a large part of the decline of labor shares. Of the
	overall average decline of 2.45 percent points in labor share, 1.06 percent points-or 43 percent of
	the actual change-are accounted for by within-industry changes in factor shares (V 2007 B 1995 Y 1995

  captures the e¤ect of all strictly domestic input-output linkages, B x captures bilateral exports of intermediate inputs that cross borders only once, and B g captures complex global value chains that cross borders more than once, including "return loops". 33 Equation (4) allows us to write

Table 1

 1

	implies

  BY od is the value added of exports of intermediate inputs from origin country o used in

destination country d for …nal good production. The other variables are as in (13). We estimate (

14

) by PPML, and report robust two-way clustered standard errors at the country o and country

d level.

We see in columns 3 and 4 of Table

7

that greater RKA is strongly associated with greater exports of intermediate goods, and that this association, too, has strengthened from 2001 to 2007.

  exp arcsinh(af f iliates od ) + arcsinh(af f iliates do ) + 0 gravity od + o + d +" od ; BY od is income accruing to primary factors in country o due to exports of intermediate inputs for …nal goods production in country d. Here af f iliates od is the number of a¢ liates located in o with parents in (owned by) d; af f iliates do is the number of a¢ liates located in d with parents in (owned by) o; and arcsinh(x) = ln[x + (1 + x 2 ) 1=2 )] is the inverse hyperbolic sine transformation, which approximates the logarithmic function but allows for zeros (other functional forms, e.g., ln(1 + x), yield similar results). Thus, captures the degree to which exports of intermediate inputs are associated with foreign-owned upstream input production; and captures the degree to which exports of intermediate inputs are associated with foreign-owned downstream assembly activity. The data on a¢ liates are averages in 1996-2001, and taken from Ramondo, Rodríguez-[START_REF] Ramondo | Multinational production: Data and stylized facts[END_REF]. Using other measures of cross-border ownership intensities such as FDI stocks and a¢ liate sales yield, qualitatively, the same results.54 The variables in gravity od are described in the previous section, and we include origin and destination …xed e¤ects to control for unobserved factors that may determine overall attractiveness of a location for input or …nal good production, and overall MNE prowess. We estimate (17) by PPML, and report robust two-way clustered standard errors at the country o and country d level.

	where V
	(17)

  Table 10 a stronger association with direct exports of intermediate goods, V B x Y od , which is reasonable given the bilateral nature the cross-border ownership indicators (other gravity variables has similar correlations as in Table9).55 In this paper we studied the evolution of labor shares in a sample of 39 countries, both developed and less developed, in 1995-2014. Our main message is that deepening of forward foreign GVC integration caused declines in labor shares, especially in 2001-2007, after China's accession to the WTO and until the trade collapse of 2008. This is driven by increases in exporting-in value added terms-of intermediate inputs which tend to be more capital intensive. It manifests in an increase in industry upstreamness, and in a shift away from fabrication, as well as marketing and management

	6 Concluding remarks

  od ij summarizes payments to foreign primary factors due to imports (in value added terms) of intermediate inputs used in industry j located in country d. De…ne backward foreign GVC integration for an industry j in country d as the share of imports of intermediate inputs in value added terms in input use: backward d j =

	od ij . Then ij . The equivalent i (vby) od P P P o P i (vby) od P ij = P o6 =d i (vby) P concept at the country level is backward d = P o6 =d P P o6 =d P i j (vby) od ij = o i P j (vby) od ij . Table

Table 1 :

 1 Decomposition of Changes in Labor Shares in

	34t35-JPN	AtB-CHN	J-GBR
	95% CI	Estimate

Table 2 :

 2 Sources of Compositional Changes in Payments to LaborNotes. Panel A reports decompositions of levels and changes in labor shares in GDP, while Panel B reports decomposition of levels and changes in labor shares within manufacturing industries' value added. The four "Total" rows in columns 1-3 report labor shares in GDP that are paid by domestic industries, foreign industries, and overall in 1995; these are the same numbers in columns 2, 4 and 5 in Table1. The "Total" rows in columns 4-6 report the changes in the same concepts. The rows above the "Total" rows indicate the contributions of sub-components of either B or Y to levels in columns 1-3 or to changes in columns 4-6. All numbers are weighted averages using GDP in 1995 as weights. Source: authors' calculations based on WIOD 2013 release.

	Source: authors'

Table 3 .

 3 Changes in Labor Shares and Forward GVC Integration in 1995-2014

	Dependent variable: Δ labor share

Table 4 .

 4 Changes in Labor Shares and Forward GVC Integration in 1995-2014: W2SLS Manufacturing industries Private sector industries Notes. The dependent variable is changes in country-industry specific labor shares in three periods: 1995-2001, 2001-2007, 2007-2014. Δ forward is the change in intermediate inputs exports intensity in value added (forward GVC integration). The instrument Δ Z is constructed by eliminating home-country and industry sources of variation from Δ forward in a gravity relationship; see text for complete details. Δ backward is the change in importing of intermediate inputs intensity in total input purchases, Δ exports of final goods is the change in export intensity of final goods in value added, and Δ imports of final goods is the change in import intensity of final goods in domestic absorption. Δ log relative price of investment is the country-level log change in investment prices. All regressions are weighted by value added in 1995 as weights. A constant is always included but not reported. Robust standard errors in parentheses are computed by two-way clustering by country and by industry. *** p<0.01, ** p<0.05, * p<0.1.

	Δ labor share	Δ labor share

Table 5 .

 5 Changes in Labor Shares and Forward GVC Integration in 1995-2014: period splits, China and assembly offshoring Dependent variable: Δ labor share Notes. The dependent variable is changes in country-industry specific labor shares in three periods

Table 6 .

 6 Changes in Labor Shares and Forward GVC Integration in 1995-2014: Country level regressions A. Manufacturing industries B. Private sector industriesNotes. The dependent variable is changes in country-level labor shares in three periods:1995-2001, 2001-2007, 2007-2014. Δ forward is the change in intermediate inputs exports intensity in value added (forward GVC integration). The instrument Δ Z is constructed by eliminating home-country and industry sources of variation from Δ forward in a based on a gravity relationship; see text for complete details. Δ backward is the change in importing of intermediate inputs intensity in total input purchases, Δ exports of final goods is the change in export intensity of final goods in GDP, and Δ imports of final goods is the change in import intensity of final goods in domestic absorption. Δ log relative price of investment is the country-level log change in investment prices. All regressions are weighted by value added in 1995 as weights. A constant is always included but not reported. Robust standard errors in parentheses are clustered by country.Notes. The dependent variables in all columns pertain to (value added) income accruing to primary factors located in origin country o due to exports of intermediate inputs that are part of GVCs that end in final good production in destination country d. In columns 1-2 it is income accruing to capital located in o minus income accruing to labor in o, as a share of GDP in o; in columns 3-4 it is the total income flow of this type; in column 5 it is income due to direct bilateral exports of intermediate inputs [V(Bx)Y]; in column 6 it is income due to flows that pass through at least one other country, not o and not d, i.e., complex GVCs [V(Bg)Y]. Income flows calculated from WIOD 2013. Relative capital abundance of o relative to d is described in the text. All regressions estimated on 1,482 observations (=39*38, where 39 is the number of countries in our sample), and include origin and destination fixed effects. Robust standard errors in parentheses are computed by two-way clustering by origin and by destination. *** p<0.01, ** p<0.05, * p<0.1. ) report long difference regressions, where the dependent and explanatory variables are changes between 2001 and 2007. The explanatory variables are upstreamness and its domestic and foreign components, with variation that is commensurate with the dependent variable. All regressions estimated by weighted least squares with value added in 2001 as weights. Robust standard errors in parentheses are computed by two-way clustering by country and by industry. *** p<0.01, ** p<0.05, * p<0.1. Standardized, "beta" coefficients reported in brackets. Overall labor shares are the sum of shares over these four categories. Changes for all variables are computed for 2001-2007. The first three lines in each panel reoprt coefficients from regressions where foreign and domestic upstreamness are included, as well as downstreamness. The fourth line reports the coefficient to Δ forward, the change in intermediate inputs export and GVC intensity, from regressions where the other explanatory variables are the change in offshoring of intermediate inputs intensity in total input purchases (Δ offshoring), the change in export intensity of final goods in value added (Δ exports of final goods), the change in import intensity of final goods in total absorption (Δ imports of final goods), and the country-level log change in investment prices (Δ log relative price of investment). Regressions estimated by weighted least squares with value added in 2001 as weights. Robust standard errors in parentheses are computed by two-way clustering by country and by industry. *** p<0.01, ** p<0.05, * p<0.1.

	W2SLS	1st stage

Table 10 .

 10 Multinationals and forward GVC integration Notes. The dependent variables are all (value added) income accruing to primary factors located in origin country o due to exports of intermediate inputs that are part of GVCs that end in final good production in destination country d. In columns 1-3 it is the total income flow of this type; in columns 4-6 it is income due to direct bilateral exports of intermediate inputs [V(Bx)Y]; in columns 7-9 it is income due to flows that pass through at least one other country, not o and not d, i.e., complex GVCs [V(Bg)Y]. Income flows calculated from WIOD 2013 release in 2007. The number of affiliates are averages in 1996-2001 from Ramondo, Rodriguez-Clare and Tintelnot (2015), and other variables from the CEPII gravity dataset. The arcsinh(x) = ln[x + (1+x^2)^0.5] is the inverse hyperbolic sine function that approximates , All regressions are estimated on 1122 observations (=34*33, where 34 is the number of countries in this sample after merging the data on the number of affiliates) using PPML, and include origin and destination fixed effects. Robust standard errors in parentheses are computed by two-way clustering by origin and by destination. *** p<0.01, ** p<0.05, * p<0.1.

	Forward GVC integration	Direct bilateral exports of intermediate inputs	Complex global value chains
	VBY(o,d) = V(Bx)Y(o,d) + V[Bg]Y(o,d)	V(Bx)Y(o,d)	V(Bg)Y(o,d)

Table A2 :

 A2 LaborShares and High Skill Labor Shares, 2007-2014 Notes. Weighted averages using GDP in 2007 as weights. Source: authors' calculations based on WIOD 2016 release (labor shares) and EU KLEMS 2017 release (high skill labor shares).

	Table A3: Forward and Backward Linkages, 1995-2007 Table A4: Forward and Backward Linkages, 2007-2014
							Backward Linkages: Foreign Value Backward Linkages: Foreign Value
		Labor Shares in GDP Forward Linkages: Foreign Value Forward Linkages: Foreign Value K income from L income from	High Skill Labor Shares in GDP Added Share in Domestic Industries Added Share in Domestic Industries K income from L income from L income	Income from
				added Share in GDP added Share in GDP domestic domestic	foreign	VA VA foreign	(domestic +	GDP in foreign
	Country Country	1995 2007	2007 2014 industries	Change Change industries	1995 2007 industries	2007 2014 industries	Change Change foreign)	2007 industries
	AUS AUS		13.2 14.0	(1)	15.0 14.8	1.8 0.9 (2)	(3)	10.5 9.6	10.3 9.6 (4)	-0.2 0.0 (5)	(6)
	AUT BEL BGR AUT Levels BEL VBY 2007 BGR VBY 2014		16.0 24.3 15.8 20.6 24.8 17.7	38.4 37.4	23.3 26.8 23.2 21.0 26.1 25.1	7.3 2.5 7.5 0.4 1.3 50.7 7.4 51.1	5.3 5.2	14.9 23.2 21.1 18.1 22.4 28.4	20.3 26.1 32.0 19.0 27.4 5.7 26.8 6.3	5.4 2.8 11.0 0.9 56.38 5.0 -1.6 57.41	10.96 11.56
	BRA CAN CHN CYP CZE DEU DNK BRA CAN Changes CHN V2014*B2007*Y2007 -VBY 2007 CYP V2007*B2014*Y2007 -VBY 2007 CZE V2007*B2007*Y2014 -VBY 2007 DEU V2007*B2014*Y2014 -VBY 2007 DNK VBY 2014 -VBY 2007	5.2 18.7 8.7 7.3 22.3 11.0 13.2 7.8 17.7 11.9 18.6 23.0 17.6 18.4	-1.04 -0.26 -0.19 -0.11 -1.01	8.5 18.7 14.2 10.1 26.2 19.6 19.2 7.5 17.9 9.2 21.1 26.8 18.2 18.6	3.3 0.0 5.5 2.8 3.8 8.6 6.0 -0.3 0.2 -2.8 1.03 2.6 -0.08 3.8 -0.84 0.7 -0.50 0.2 0.41	-0.29 0.28 0.34 0.25 -0.02	5.1 14.6 11.2 17.8 23.7 9.2 13.6 7.8 13.6 15.2 17.9 25.8 13.9 21.1	7.6 13.9 16.5 17.9 30.0 15.1 19.8 8.9 15.0 10.5 0.30 17.3 0.06 29.6 0.68 15.0 0.35 21.1 0.62	2.5 -0.7 5.3 0.1 6.3 5.9 6.2 1.0 1.5 1.33 -4.8 -0.02 -0.6 -0.16 3.8 -0.15 1.1 0.0 1.03	0.01 0.34 1.03 0.60 0.60
	ESP ESP		7.7 9.7		9.7 10.5	2.0 0.9		11.0 14.5	15.1 13.2	4.1 -1.3
	EST EST		23.3 24.5 K income from 24.6 29.2	1.3 4.7 L income from	28.7 24.1 K income from	26.0 27.3 L income from	-2.8 3.2 L income	Income from
	FIN FIN		20.3 19.2	22.7 17.7 domestic	2.4 -1.5 domestic	14.8 17.3 foreign	18.7 18.1 foreign	3.9 0.8 (domestic +	foreign
	FRA FRA		10.2 10.6	10.3 11.7 industries	0.1 1.1 industries	9.7 12.3 industries	12.1 13.8 industries	2.4 1.6 foreign)	industries
	GBR GBR		13.4 12.9	(1)	14.5 13.8	1.2 0.9 (2)	(3)	12.3 12.2	12.3 12.6 (4)	0.0 0.4 (5)	(6)
	GRC GRC		3.4 9.1		8.7 11.6	5.4 2.5		10.9 13.1	15.3 12.6	4.4 -0.6
	HUN IDN HUN VBY 2007 IDN VBY 2014		16.5 13.5 22.1 18.1	37.5 35.5	24.8 19.1 26.5 14.8	8.3 5.6 4.3 39.4 -3.3 39.6	11.0 11.0	22.8 13.1 32.0 13.8	32.3 14.3 34.2 12.1 14.3 13.9	9.5 1.2 51.51 2.2 0.5 53.52	23.07 24.84
	IND IND		5.8 10.1		9.5 7.3	3.7 -2.8		7.9 13.9	14.5 11.7	6.6 -2.3
	IRL ITA JPN KOR LTU LUX IRL ITA V2014*B2007*Y2007 -VBY 2007 JPN V2007*B2014*Y2007 -VBY 2007 KOR V2007*B2007*Y2014 -VBY 2007 LTU V2007*B2014*Y2014 -VBY 2007 LUX VBY 2014 -VBY 2007	23.0 9.9 5.2 13.4 18.0 43.1 27.7 10.9 8.0 15.2 20.0 45.0	-1.87 -0.64 -0.59 -0.42 -2.03	31.5 11.4 9.6 18.1 20.9 48.1 33.4 11.4 7.8 19.5 27.1 45.3	8.5 1.5 4.4 4.7 2.9 5.0 5.7 0.5 1.84 -0.2 -0.16 4.3 -2.01 7.1 -1.38 0.3 0.25	-0.84 0.87 0.82 0.89 0.01	28.4 11.3 3.7 15.3 23.6 25.0 30.0 12.9 8.3 17.9 19.5 47.3	32.1 14.4 8.1 19.3 21.5 40.0 37.1 12.4 0.87 10.3 -0.08 20.9 1.78 21.8 0.90 51.6 1.76	3.7 3.1 4.4 4.0 -2.1 15.0 7.1 2.71 -0.4 -0.24 2.0 -0.23 3.0 -0.48 2.3 4.3 2.01	0.03 0.79 2.61 1.80 1.77
	LVA LVA		22.0 17.7		17.8 24.0	-4.1 6.2		20.7 20.5	22.1 21.2	1.4 0.6
	MEX MEX		12.1 9.7		12.7 10.9	0.6 1.2		13.2 14.1	13.7 15.2	0.5 1.1
	MLT MLT		19.5 26.8		28.2 22.9	8.6 -3.9		28.9 41.2	30.1 44.7	1.2 3.6
	NLD NLD		21.5 23.0		23.3 31.8	1.8 8.9		20.3 17.8	21.8 22.0	1.5 4.1
	PRT POL		9.4 16.2		12.3 20.2	2.9 3.9		16.5 19.3	17.0 20.2	0.5 0.9
	ROU PRT		11.9 11.9		14.5 15.1	2.6 3.2		15.9 15.7	19.5 16.7	3.7 1.0
	RUS ROU		19.8 14.0		23.1 20.2	3.4 6.2		7.5 17.6	8.0 20.5	0.6 2.9
	SVK RUS		27.0 23.8		26.9 24.1	0.0 0.2		23.4 7.7	32.1 8.7	8.7 1.0
	SVN SVK		16.8 23.1		22.3 25.8	5.5 2.7		21.8 31.1	26.6 31.8	4.8 0.7
	SWE SVN		18.8 22.2		22.8 26.0	4.0 3.8		15.8 23.6	19.4 22.8	3.6 -0.7
	TUR SWE		4.5 20.8		6.4 20.0	1.9 -0.8		9.4 17.5	14.5 15.7	5.1 -1.8
	TWN TUR		17.0 10.3		28.7 12.3	11.7 2.0		20.1 14.4	22.2 15.4	2.1 1.0
	USA USA		6.0 5.1		6.2 5.9	0.2 0.8		5.1 6.2	7.1 6.4	2.1 0.3
	Average Average		15.1 17.4		18.8 19.3	3.7 1.9		15.9 18.7	19.5 19.8	3.5 1.1
	Weighted average Weighted average		8.9 10.9		11.7 11.5	2.8 0.6		8.1 11.2	11.3 11.5	3.1 0.4
	Notes. Weighted averages using GDP in 1995 as weights. Source: authors' calculations based on WIOD Notes. Weighted averages using GDP in 2007 as weights. Source: authors' calculations based on WIOD
	2013 release. 2017 release.

Table A5 :

 A5 Decomposition of Changes in Labor Shares in GDP and in Manufacturing Value Added, 2007-2014 Panel A reports decompositions of levels and changes in labor shares in GDP, while Panel B reports decomposition of levels and changes in labor shares within manufacturing industries' value added. The four "Total" rows in columns 1-3 report labor shares in GDP that are paid by domestic industries, foreign industries, and overall in 2007; these are the same numbers in columns 2, 4 and 5 in TableA5. The "Total" rows in columns 4-6 report the changes in the same concepts. The rows above the "Total" rows indicate the contributions of sub-components of either B or Y to levels in columns 1-3 or to changes in columns 4-6. Source: authors' calculations based on WIOD 2013 release.

	Table A6: Sources of Compositional Changes in Payments to Labor
				mean	Std.Err.	p25	p50	p75	IQR
	A. All sectors, percent in GDP A. All sectors A. Manufacturing industries (N = 1532)
	Δ labor share		2007, Percent in GDP 0.001 0.084		-0.052	-0.002	Δ2007-2014 0.049	0.100
	Δ forward intensity	Income from	Income from 0.031	0.048		0.002	Income from 0.025	Income from 0.050	0.048
	-to China	domestic	foreign 0.010		Domestic + 0.016 0.001	domestic 0.005	foreign 0.013	Domestic + 0.012
	-to RoW	industries	industries 0.021		foreign 0.041	0.001	industries 0.017	industries 0.040	foreign 0.039
	-net of assembly offshoring	(1)	(2) 0.044		0.069	(3)	0.006	(4) 0.032	(5) 0.078	(6) 0.071
	-absorbed in destination		0.032		0.053		0.002	0.022	0.063	0.062
	Value chains -re-exported			0.012		0.023		0.001	0.009	0.022	0.021
	Domestic (Bd) Δ backward intensity		50.54	0 0.011		50.54 0.026	-0.001	-0.09 0.008	0 0.020	-0.09 0.021
	Bilateral trade (Bx) Δ exports of final goods intensity 0	4.43 0.009		0.041	4.43	-0.001	0 0.004	0.01 0.018	0.01 0.019
	Complex GVCs (Bg) Δ imports of final goods intensity 0.14	1.27 0.046		0.234	1.41	0.006	0.01 0.036	0.05 0.085	0.06 0.080
	Total (B) Δ log relative price of investment 50.68	5.71 -0.067		56.38 0.143	-0.158	-0.08 -0.072	0.06 0.004	-0.02 0.163
	Sources of demand B. All private sector industries (N = 3270)
	Domestic (Yd) Δ labor share B. Manufacturing inductries, percent in value added 46.60 0.000 4.46 Foreign (Yf) 4.08 1.24 Δ forward intensity 0.016		51.06 0.070 5.32 0.038	-0.033 -0.001	-0.71 -0.001 -0.13 0.007	0.69 0.035 -0.01 0.026	0.068 -0.02 -0.14 0.027
	Total (Y) -to China		50.68	5.71 0.005		56.38 0.010	0.000	-0.84 0.002	0.68 0.005	-0.16 0.005
	-to RoW			0.011		0.034		-0.002	0.004	0.019	0.021
	Levels Changes Value chains Domestic (Bd) Bilateral trade (Bx) Complex GVCs (Bg) Total (B) Sources of demand Domestic (Yd) Foreign (Yf) Total (Y) -net of assembly offshoring Income from domestic industries (1) 39.04 0 0.35 39.39 28.63 10.76 39.39 2007, Percent in GDP Income from foreign industries Domestic + foreign (2) (3) 0 39.04 9.34 9.34 2.78 3.13 12.12 51.51 9.02 37.65 3.09 13.86 12.12 51.51 0.020 0.048 -0.001 -absorbed in destination 0.014 0.038 -0.001 -re-exported 0.005 0.014 0.000 Δ backward intensity 0.011 0.023 0.000 Δ exports of final goods intensity 0.003 0.023 0.000 Δ imports of final goods intensity 0.015 0.179 0.000 Δ log relative price of investment -0.064 0.139 -0.116 Δ labor share -0.006 0.057 -0.052 Δ forward intensity 0.031 0.035 0.014 Δ backward intensity 0.012 0.015 0.008 Δ exports of final goods intensity 0.009 0.024 0.003 Δ imports of final goods intensity 0.047 0.045 0.032 Δ log relative price of investment -0.067 0.143 -0.158 Δ labor share -0.006 0.028 -0.021 Δ forward intensity 0.012 0.020 0.002 Notes. B. Manufacturing Δ backward intensity 0.012 0.014 0.004	Income from domestic industries (4) -0.17 0 0.01 -0.16 -1.27 -0.74 -2.01 0.009 0.005 0.002 0.008 0.000 0.001 -0.080 -0.005 0.027 0.013 0.009 0.051 -0.072 -0.013 0.008 0.012	Income from foreign industries (5) 0 -0.06 -0.02 -0.08 1.74 0.04 1.78 Δ2007-2014 0.029 0.021 0.008 0.020 0.004 0.014 0.004 0.031 0.049 0.023 0.015 0.073 0.004 0.012 0.014 0.023	Domestic + foreign (6) -0.17 -0.06 -0.01 -0.24 0.47 -0.70 -0.23 0.030 0.022 0.008 0.020 0.004 0.014 0.120 0.082 0.036 0.015 0.012 0.041 0.163 0.033 0.013 0.020
	Δ exports of final goods intensity	0.002		0.010		-0.002	0.001	0.008	0.010
	Δ imports of final goods intensity	0.006		0.012		-0.005	0.007	0.012	0.016
	Δ log relative price of investment	-0.064		0.139		-0.116	-0.080	0.004	0.120

Table A7 .

 A7 Descriptive statistics, 1995Descriptive statistics, -2014 Notes. Statistics are for changes in country-industry specific variables (panels A and B) or in country specific variables (panels C and D), in three periods:1995-2001, 2001-2007, 2007-2014. Δ labor shares is the change in labor compensation ratio in value added. Δ forward is the change in intermediate inputs exports intensity in value added (forward GVC integration). Δ forward net of assembly offshoring is the change in intermediate inputs exports intensity in value added that excludes exports of final goods. Δ forward absorbed in destination is the part of Δ forward net of assembly offshoring value added that cross borders only once and is absorbed in the direct destination country. Δ forward re-exported is the part of Δ forward net of assembly offshoring value added that is embodied in exports of the destination country, i.e. complex GVCs that cross borders more than once. Δ backward is the change in importing of intermediate inputs intensity in total input purchases, Δ exports of final goods is the change in export intensity of final goods in value added, and Δ imports of final goods is the change in import intensity of final goods in domestic absorption. Δ log relative price of investment is the country-level log change in investment prices. IQR = p75-p25 is the inter-quartoile range. The dependent variable is changes in country-industry specific labor shares in three periods

							Dependent variable in W2SLS: Δ labor share
		(1)	(2)	(3)	(4)	(5)	(6)	(7)	(8)	(9)	(10)	(11)	(12)	(13)	(14)
	A. Manufacturing industries
		W2SLS	1st stage	W2SLS	1st stage	W2SLS	1st stage	W2SLS	1st stage	W2SLS	1st stage	W2SLS	1st stage	W2SLS	1st stage
	Δ forward intensity	-1.212***		-0.929***		-1.117***		-1.294**		-1.193***		-0.919***		-1.018***
		(0.402)		(0.272)		(0.352)		(0.431)		(0.358)		(0.108)		(0.140)
	Δ backward intensity	-0.469	-0.369**	-0.423*	-0.388***	-0.530*	-0.446***	-0.552	-0.392***	-0.605*	-0.452*** -0.517** -0.441***	-0.566	-0.424***
		(0.299)	(0.124)	(0.206)	(0.126)	(0.290)	(0.088)	(0.342)	(0.125)	(0.328)	(0.082)	(0.224)	(0.085)	(0.338)	(0.105)
	Δ exports of final goods intensity	0.169	0.108	0.178**	0.120*	0.136	0.060	0.275*	0.156**	0.225*	0.093	0.233***	0.079	0.258**	0.120
		(0.122)	(0.067)	(0.070)	(0.056)	(0.091)	(0.056)	(0.131)	(0.069)	(0.110)	(0.057)	(0.076)	(0.052)	(0.100)	(0.073)
	Δ imports of final goods intensity	0.026	0.014	0.023	0.015*	0.018	0.007	0.023	0.013	0.015	0.006	0.016	0.007	0.026	0.007*
		(0.024)	(0.009)	(0.020)	(0.008)	(0.017)	(0.006)	(0.023)	(0.008)	(0.015)	(0.005)	(0.013)	(0.005)	(0.015)	(0.004)
	Δ log relative price of investment	0.033	0.095**	0.062	0.114***	0.004	0.070**	0.029	0.088**	0.003	0.067**	0.043	0.076**	0.050	0.074**
		(0.058)	(0.035)	(0.062)	(0.032)	(0.067)	(0.028)	(0.060)	(0.033)	(0.067)	(0.027)	(0.075)	(0.026)	(0.076)	(0.026)
	Δ Z		0.049***		0.055***		0.056***		0.048***		0.055***		0.077***		0.076***
			(0.008)		(0.011)		(0.009)		(0.008)		(0.009)		(0.010)		(0.010)
	Fixed effects	-	-	Per	Per	Cty	Cty	Ind	Ind	Cty, Ind	Cty, Ind Cty, Ind, Per Cty, Ind, Per Cty-Ind, Per Cty-Ind, Per
	Observations	1,532	1,532	1,532	1,532	1,532	1,532	1,532	1,532	1,532	1,532	1,532	1,532	1,532	1,532
	R-squared		0.198		0.214		0.400		0.275		0.457		0.478		0.589
	Kleibergen-Paap F statistic	39.67		24.85		38.62		38.64		36.74		55.56		53.24
	B. All private sector industries
		W2SLS	1st stage	W2SLS	1st stage	W2SLS	1st stage	W2SLS	1st stage	W2SLS	1st stage	W2SLS	1st stage	W2SLS	1st stage
	Δ forward intensity	-1.116***		-0.536***		-1.086***		-1.241***		-1.212***		-0.772***		-0.832***
		(0.212)		(0.082)		(0.215)		(0.262)		(0.241)		(0.129)		(0.216)
	Δ backward intensity	-0.421*** -0.319*** -0.242*** -0.306*** -0.484*** -0.403*** -0.420** -0.302*** -0.482** -0.387*** -0.336** -0.364*** -0.331** -0.293***
		(0.152)	(0.091)	(0.075)	(0.091)	(0.165)	(0.088)	(0.170)	(0.089)	(0.184)	(0.078)	(0.130)	(0.077)	(0.128)	(0.081)
	Δ exports of final goods intensity	0.389**	0.305***	0.202	0.288***	0.340**	0.279***	0.419*	0.283***	0.372*	0.257***	0.258	0.221***	0.310	0.241**
		(0.173)	(0.089)	(0.125)	(0.085)	(0.161)	(0.078)	(0.222)	(0.097)	(0.203)	(0.087)	(0.165)	(0.079)	(0.202)	(0.091)
	Δ imports of final goods intensity	0.024	0.014	0.016	0.014	0.019	0.011	0.019	0.010	0.015	0.007	0.012	0.008*	0.017*	0.008**
		(0.016)	(0.009)	(0.010)	(0.009)	(0.014)	(0.007)	(0.013)	(0.006)	(0.011)	(0.004)	(0.008)	(0.004)	(0.008)	(0.003)
	Δ log relative price of investment	0.020	0.054**	0.021	0.068***	0.023	0.048**	0.023	0.053***	0.025	0.047**	0.043	0.054***	0.045	0.051***
		(0.031)	(0.020)	(0.029)	(0.019)	(0.038)	(0.018)	(0.033)	(0.019)	(0.038)	(0.017)	(0.041)	(0.019)	(0.045)	(0.018)
	Δ Z C. Manufacturing (N = 117)		0.028*** (0.006)		0.041*** (0.006)		0.031*** (0.007)		0.026*** (0.006)		0.030*** (0.007)		0.056*** (0.008)		0.054*** (0.008)
	Fixed effects	-	-	Per	Per	Cty	Cty	Ind	Ind	Cty, Ind	Cty, Ind Cty, Ind, Per Cty, Ind, Per Cty-Ind, Per Cty-Ind, Per
	Observations	3,270	3,270	3,270	3,270	3,270	3,270	3,270	3,270	3,270	3,270	3,270	3,270	3,241	3,241
	R-squared		0.156		0.174		0.273		0.251		0.358		0.386		0.518
	Kleibergen-Paap F statistic	21.15		44.80		18.59		20.19		18.98		49.03		43.33
	Notes.
	D. Entire economy (N = 117)

Table A8 .

 A8 Changes in Labor Shares and Forward GVC Integration in 1995-2014, W2SLS

		(1)	(2)	(3)	(4)	(5)	(6)	(7)	(8)
		W2SLS	1st stage	W2SLS	1st stage	W2SLS	1st stage	W2SLS	1st stage
	Δ forward intensity	-1.130***		-0.077		-1.140**		-0.265
		(0.402)		(0.986)		(0.420)		(1.350)
	Δ backward intensity	-0.559	-0.118	-0.348	-0.414	-0.503	-0.104	-0.533	-0.197
		(0.608)	(0.381)	(0.606)	(0.372)	(0.682)	(0.313)	(0.607)	(0.345)
	Δ exports of final goods intensity	0.098	0.393	-0.393	0.631**	-0.089	0.410	-0.347	0.503*
		(0.525)	(0.239)	(0.731)	(0.236)	(0.563)	(0.260)	(0.686)	(0.274)
	Δ imports of final goods intensity	0.429*	0.181**	0.313	0.174**	0.277	0.004	0.338	0.047
		(0.252)	(0.070)	(0.272)	(0.069)	(0.241)	(0.101)	(0.230)	(0.109)
	Δ log relative price of investment	-0.010	0.058*	-0.014	0.065**	0.008	0.048*	0.020	0.058**
		(0.053)	(0.034)	(0.061)	(0.028)	(0.074)	(0.029)	(0.105)	(0.026)
	Δ Z		0.050***		0.020		0.055***		0.034
			(0.011)		(0.016)		(0.013)		(0.021)
	Fixed effects	-	-	Per	Per	Cty	Cty	Cty, Per	Cty, Per
	Observations	117	117	117	117	117	117	117	117
	R-squared		0.365		0.427		0.640		0.652
	Kleibergen-Paap F statistic	19.35		1.638		17.23		2.621
		W2SLS	1st stage	W2SLS	1st stage	W2SLS	1st stage	W2SLS	1st stage
	Δ forward intensity	-0.936		1.369		-1.113		2.617
		(0.696)		(2.074)		(0.781)		(6.481)
	Δ backward intensity	0.025	-0.039	0.276	-0.168	0.246	0.057	0.137	-0.053
		(0.225)	(0.116)	(0.599)	(0.181)	(0.417)	(0.149)	(0.895)	(0.213)
	Δ exports of final goods intensity	-0.237	0.836***	-2.283	0.903***	-0.507	0.915***	-4.009	0.994***
		(0.613)	(0.284)	(1.794)	(0.280)	(0.743)	(0.278)	(6.297)	(0.276)
	Δ imports of final goods intensity	0.315	0.329	-0.435	0.452	-0.056	0.115	-0.770	0.278
		(0.415)	(0.228)	(1.140)	(0.274)	(0.406)	(0.282)	(2.100)	(0.324)
	Δ log relative price of investment	0.008	0.017	-0.016	0.025**	0.040	0.021	-0.040	0.029**
		(0.024)	(0.015)	(0.060)	(0.012)	(0.032)	(0.016)	(0.192)	(0.013)
	Δ Z		0.021***		0.015		0.021***		0.013
			(0.006)		(0.010)		(0.007)		(0.019)
	FEs	-	-	Per	Per	Cty	Cty	Cty, Per	Cty, Per
	Observations	117	117	117	117	117	117	117	117
	R-squared		0.423		0.451		0.607		0.626
	Kleibergen-Paap F statistic	14.49		2.545		10.21		0.473

Table A9 .

 A9 Changes in Labor Shares and Forward GVC Integration in 1995-2014: Country level regressions, W2SLS A. Manufacturing industries Dependent variable in W2SLS: Δ labor share B. All industries Notes. The dependent variable is changes in country-level labor shares in three periods

Table A10 .

 A10 . Δ forward is the change in intermediate inputs exports intensity in value added (forward GVC integration). The instrument Δ Z is constructed by eliminating home-country and industry sources of variation from Δ forward in a based on a gravity relationship; see text for complete details. Δ backward is the change in importing of intermediate inputs intensity in total input purchases, Δ exports of final goods is the change in export intensity of final goods in GDP, and Δ imports of final goods is the change in import intensity of final goods in domestic absorption. Δ log relative price of investment is the country-level log change in investment prices. All regressions are weighted by value added in 1995 as weights. A constant is always included but not reported. Robust standard errors in parentheses are clustered by country. *** p<0.01, ** p<0.05, * p<0.1. "Structural equation" used for the "local to zero" approximation of[START_REF] Conley | Plausibly exogenous[END_REF] Dependent variable: Δ labor shareManufacturing industriesPrivate sector industries Notes. The dependent variable is changes in country-industry specific labor shares in three periods:1995-2001, 2001- 2007, 2007-2014. Δ forward is the change in intermediate inputs exports intensity in value added (forward GVC integration). ΔZ is the instrument, here added to the second stage equation, constructed by eliminating home-country and industry sources of variation from Δ forward in a gravity relationship; see text for complete details. Δ backward is the change in importing of intermediate inputs intensity in total input purchases, Δ exports of final goods is the change in export intensity of final goods in value added, and Δ imports of final goods is the change in import intensity of final goods in domestic absorption. Δ log relative price of investment is the country-level log change in investment prices. All regressions are weighted by value added in 1995 as weights. A constant is always included but not reported. Robust standard errors in parentheses are computed by two-way clustering by country and by industry. *** p<0.01, ** p<0.05, * p<0.1.

	Sample	Distribution			1	1 0	2 5	5 0
	Δ forward intensity Manufacturing Uniform Δ backward intensity Normal	Lower Bound Upper Bound Lower Bound Upper Bound	WLS -0.367*** -1.521 (0.108) -0.485 -0.268 -1.513 (0.306) -0.511	-1.551 -0.531 -1.531 -0.504	WLS -1.607 -0.258** -0.580 (0.108) -1.606 -0.151 (0.150) -0.433	-1.696 -0.624 -1.780 -0.260
	Δ exports of final goods intensity Private sector Uniform Δ imports of final goods intensity Normal Δ log relative price of investment	Lower Bound Upper Bound Lower Bound Upper Bound	0.153 (0.100) 0.023 (0.013) 0.003	-1.255 -0.422 -1.244 -0.405	-1.262 -0.413 -1.234 -0.406	0.142 -1.292 (0.126) -0.438 0.013* -1.250 (0.007) 0.014 -0.416	-1.315 -0.456 -1.297 -0.362
				(0.079)			(0.046)
	ΔZ			-0.043*			-0.025**
				(0.023)			(0.010)
	Fixed effects: Cty-Ind, Period		Yes			Yes
	Observations			1,459			3,086
	R-squared			0.311			0.315

Table A11 .

 A11 Confidence intervals for ΔFWD obtained using the "local to zero" approximation Notes. Methodlogy follows

Table A12 .

 A12 Functional Specialization,Upstreamness and Forward Foreign GVC Integration, 2001-2007

		1)	(2)	(3)	(4)	(5)	(6)	(7)	(8)	(9)	(10)	(11)	(12)
	A. Manufacturing
	Dependent variable:	Δ MGT	Δ R&D	Δ FAB	Δ MAR	Δ MGT	Δ R&D	Δ FAB	Δ MAR	Δ MGT	Δ R&D	Δ FAB	Δ MAR
	Δ forward intensity	-0.167***	-0.019	-0.398*** -0.141***	-0.181**	-0.007	-0.256*** -0.102***	-0.091***	-0.018	-0.368*	-0.093*
		(0.049)	(0.047)	(0.101)	(0.038)	(0.066)	(0.058)	(0.071)	(0.029)	(0.026)	(0.032)	(0.194)	(0.045)
	Δ backward intensity	-0.153	-0.125	-0.283*	-0.079	-0.181*	-0.128	-0.238	-0.056	-0.024	-0.077	-0.199*	-0.036
		(0.088)	(0.078)	(0.147)	(0.050)	(0.096)	(0.086)	(0.154)	(0.068)	(0.030)	(0.046)	(0.100)	(0.030)
	Δ exports of final goods intensity	0.001	0.014	0.016	0.006	0.004	0.011	0.012	0.006	0.003	0.021***	0.027*	0.008
		(0.006)	(0.009)	(0.014)	(0.010)	(0.008)	(0.007)	(0.011)	(0.011)	(0.005)	(0.007)	(0.014)	(0.008)
	Δ imports of final goods intensity	0.002	-0.021	-0.010	0.013	0.013	-0.016	-0.065**	0.007	-0.010	-0.013	0.002	0.017
		(0.012)	(0.018)	(0.029)	(0.021)	(0.019)	(0.015)	(0.026)	(0.018)	(0.009)	(0.010)	(0.041)	(0.019)
	Δ log relative price of investment	-0.001	-0.023	0.018	0.020	-0.001	-0.025	0.006	0.018
		(0.022)	(0.035)	(0.025)	(0.015)	(0.023)	(0.035)	(0.029)	(0.017)
	Fixed effects	-	-	-	-	I n d	I n d	I n d	I n d	C t y	C t y	C t y	C t y
	Observations	531	531	531	531	531	531	531	531	531	531	531	531
	R-squared	0.090	0.047	0.177	0.106	0.126	0.093	0.373	0.198	0.659	0.491	0.319	0.265
	B. All industries
	Dependent variable:	Δ MGT	Δ R&D	Δ FAB	Δ MAR	Δ MGT	Δ R&D	Δ FAB	Δ MAR	Δ MGT	Δ R&D	Δ FAB	Δ MAR
	Δ forward intensity	-0.147***	0.014	-0.296*** -0.106**	-0.156***	0.015	-0.134***	-0.116*	-0.075***	0.001	-0.386*** -0.108***
		(0.040)	(0.034)	(0.088)	(0.042)	(0.048)	(0.038)	(0.043)	(0.061)	(0.014)	(0.028)	(0.127)	(0.028)
	Δ backward intensity	-0.045	-0.014	-0.212***	-0.052	-0.127	-0.061	-0.116*	-0.133	0.022	0.015	-0.305***	-0.036
		(0.080)	(0.059)	(0.059)	(0.106)	(0.076)	(0.049)	(0.059)	(0.091)	(0.055)	(0.053)	(0.099)	(0.073)
	Δ exports of final goods intensity	-0.001	0.013	-0.006	0.017	0.002	0.007	0.001	0.012	0.001	0.017*	-0.005	0.018
		(0.009)	(0.010)	(0.017)	(0.013)	(0.007)	(0.006)	(0.008)	(0.007)	(0.006)	(0.010)	(0.019)	(0.014)
	Δ imports of final goods intensity	0.001	0.002	0.001	0.002	0.001	0.002	0.002	0.000	-0.002	0.003**	0.001	0.003
		(0.001)	(0.002)	(0.004)	(0.004)	(0.001)	(0.002)	(0.004)	(0.002)	(0.001)	(0.001)	(0.003)	(0.003)
	Δ log relative price of investment	-0.027	-0.017	0.016	0.028*	-0.021	-0.014	0.006	0.040**
		(0.026)	(0.015)	(0.010)	(0.016)	(0.025)	(0.015)	(0.012)	(0.018)
	Fixed effects	-	-	-	-	I n d	I n d	I n d	I n d	C t y	C t y	C t y	C t y
	Observations	1,118	1,118	1,118	1,118	1,118	1,118	1,118	1,118	1,118	1,118	1,118	1,118
	R-squared	0.031	0.023	0.090	0.016	0.064	0.134	0.302	0.115	0.257	0.188	0.134	0.109

Changing shares contradict the …rst of the so-called "Kaldor facts"and lead to rejecting the[START_REF] Kaldor | A model of economic growth[END_REF] model of growth, along with other models that imply the same constancy of shares. Varying shares also have rami…cations for computation of total factor productivity and long run macroeconomic projections.

For example, see[START_REF] Piketty | Capital in the Twenty-…rst Century[END_REF], and up to date statistics from the World Inequality Database, https://wid.world/. This goes beyond the classic "functional inequality"between workers, "capitalists"and "rentiers", due to Adam Smith and David Ricardo.

An additional concern relates to how income inequality a¤ects overall growth and political economy; see, e.g.,[START_REF] Persson | Is inequality harmful for growth?[END_REF],[START_REF] Alesina | Distributive politics and economic growth[END_REF],[START_REF] Alesina | Income distribution, political instability, and investment[END_REF], and more recently[START_REF] Ostry | Inequality and unsustainable growth[END_REF].

In Appendix A we show that di¤erent concepts of the labor share in the Penn World Tables exhibit very similar trajectories, in particular the 2001-2007 acceleration in the decline in labor shares and the change in trajectory after 2007.[START_REF] Gutiérrez | Revisiting the Global Decline of the Labour Share[END_REF] argue that after adjusting for (netting out) the housing sector, labor shares did not decline during 1970-2015 in a set of advanced economies plus China, India, and Russia-except in the US and Canada. However, we do …nd in their data that labor shares declined in 2001-2007-both using their "adjusted corporate sector" and "adjusted business sector" series-in similar magnitudes to our data.

Tre ‡er and Zhu (2010) show that taking into account intermediate inputs helps aligning factor content of trade predictions of the Heckscher-Ohlin model with the data.[START_REF] Ito | Heckscher-Ohlin: Evidence from virtual trade in value added[END_REF] show that predictions

The main insight in[START_REF] Sposi | Trade Integration, Global Value Chains, and Capital Accumulation[END_REF] can be deduced from[START_REF] Helpman | A Simple Theory of International Trade with Multinational Corporations[END_REF] if plants are thought of as downstream and headquarters upstream activities.

Although we do not test this, this mechanism can raise labor shares everywhere if tasks or inputs that are relatively labor un-intensive within capital-abundant countries are o¤shored to labor-abundant countries, in which they are relatively labor intensive, as in[START_REF] Feenstra | Foreign direct investment and relative wages: Evidence from Mexico's maquiladoras[END_REF].

Another di¤erence is that International Monetary Fund (2017) mix several datasets that are based on di¤erent methodologies, whereas we rely on the WIOD for both labor shares and GVC measures.

1 By construction, summing all elements of V BY or of V X gives world GDP, i.e. the value of global expenditures on …nal goods accrues to primary production factors, which is also equal to their income. Summing all elements within the rows that pertain to a country's industries gives that country's GDP; summing all elements within the columns that pertain to a country's industries gives that country's production of …nal goods and services (in value added terms).2 2 TableA3and TableA4in the appendix report country-level forward GVC integration in 1995, 2007 and 2014. An alternative view of GVC deepening is backward linkages, which imply payments to foreign factors by domestic industries though supply of intermediate inputs and services. Since the world is a closed economy (and this is taken into account in the WIOD data), the global (and, therefore, average) forward and backward linkages are the same, although within each country there can be di¤erences between the two. We discuss backward linkages in Appendix C.2

[START_REF] Johnson | Five facts about value-added exports and implications for macroeconomics and trade research[END_REF] reviews di¤erent input-output approaches to study trade in value added. There are two complementary methodologies that describe how value added is traded, either from the consumption or the production perspective. The production perspective allocates the value added in a given location (and industry) of production to …nal goods production via global value chains of intermediate inputs. Since this traces the income generated by production of …nal goods to primary factors thought intermediate input ‡ows it is also named "GVC income" decomposition[START_REF] Timmer | Fragmentation, incomes and jobs: an analysis of European competitiveness[END_REF]).[START_REF] Johnson | Five facts about value-added exports and implications for macroeconomics and trade research[END_REF] acknowledges that by measuring the domestic and foreign content of domestic production, GVC income is conceptually closely tied to the literature on o¤shoring and trade in tasks. The third approach to trade in value added focuses on the decomposition of gross exports.[START_REF] Johnson | Five facts about value-added exports and implications for macroeconomics and trade research[END_REF] argues that the theoretical motivations for a gross export decomposition are "unclear" and that some bilateral export decompositions may also generate inconsistencies, e.g.,[START_REF] Koopman | Estimating domestic content in exports when processing trade is pervasive[END_REF]. For these reasons, the analysis presented in this paper builds on the GVC income approach.

2 4 The slowdown in forward GVC deepening is consistent with[START_REF] Timmer | Fragmentation, incomes and jobs: an analysis of European competitiveness[END_REF], who rely on the same data. On the manifestation of the "so-called" trade collapse from 2008 on value added trade see[START_REF] Bems | Vertical Linkages and the Collapse of Global Trade[END_REF] and[START_REF] Nagengast | The great collapse in value added trade[END_REF].

5 The "inverse Ghosh" matrix G relates changes in gross output across industries to changes in primary factor use in a particular industry, where primary factor use is value added: X = G 0 V . It is related to the Leontief inverse matrix B by the following formula XGX 1 = B. See chapter 12 in[START_REF] Miller | Input-Output Analysis, Foundations and Extensions[END_REF] for more details.

6 See, also[START_REF] Timmer | Slicing up global value chains[END_REF]. 2 7 See Appendix D for proof. 2 8 See, e.g.,[START_REF] Bernard | Firms in International Trade[END_REF] and[START_REF] Harrigan | Skill Biased Heterogeneous Firms, Trade Liberalization and the Skill Premium[END_REF]. Another caveat is that we do not make allowances for capital depreciation. International Monetary Fund (2017) demonstrate that although a¤ecting levels, adjusting for this hardly alters trends in factor shares.

2 We performed the same analysis for factor shares in2007 -2014 (Table A5 in the appendix) (Table A5 in the appendix). The main di¤erences are that labor shares increase by 1 percent points, on average, in contrast to the decline in 1995-2007, and that within-industry changes account for more than all of the increase in labor shares in this period, while composition accounts for small reductions (in the same direction as in 1995-2007).3 3 For example, consider a hypothetical German car door producer that ships doors to Czech Republic, where windows are manufactured and installed in the doors, which get shipped back to Germany and installed in cars that are either purchased domestically or are exported.

4 We performed the same analysis in2007 -2014 (Table A6 (Table A6 in the appendix). The main di¤erence is that in manufacturing changes in both domestic ( B d ) and foreign linkages ( B x and B g ) contribute to declines in labor shares. In addition, changes in foreign demand in 2007-2014 account for small declines in labor shares, not increases as in1995-2007.

5 The data for q are from the Penn World Tables mark 9.0 (PWT, see[START_REF] Feenstra | The Next Generation of the Penn World Table[END_REF]) and from the United States'Bureau of Economic Analysis (BEA), applying the same methodology as in[START_REF] Karabarbounis | The global decline of the labor share[END_REF]. See Appendix F for more details.3 6 In order try to address the relationship between …rm market share concentration and labor shares highlighted in[START_REF] Autor | The fall of the labor share and the rise of superstar …rms[END_REF] we experimented with adding to (8) the log of the number of …rms at the country-by-industry level using data from UNIDO's INDSTAT 2019 edition database (we harmonize the 2-digit ISIC rev. 3 industry de…nition In INDSTAT to match the WIOD 2013 classi…cation). This variable is very weakly correlated with labor shares and adding it does not alter the other coe¢ cients. This is clearly an imperfect indicator of concentration, but we could not …nd other sources to compute industry concentration for so many industries and countries from 1995. For example, Orbis would allow us to do so only from 2004 and only for publicly available …rms.3 7 The private sector excludes the following industries: "Public Admin and Defence; Compulsory Social Security", "Education", "Health and Social Work", "Other Community, Social and Personal Services", "Private Households with Employed Persons".

8 See also[START_REF] Solon | What are we weighting for?[END_REF] on motivation for weighting. 3 9 See descriptive statistics in TableA7. We make sure that our results are not driven by outliers. In unreported results we drop the top and bottom 1% observations of F W D; these yield virtually identical results.

0 In practice, the source and destination …xed e¤ects are identi…ed only up to a constant. We allocate this constant to b (t) dj ci . Since dj ci are shares and we estimate (11) by PPML, this has no consequences for out procedure below.

3 These results are available upon request.

4 Di¤erent speci…cations of the instrument, discussed above in Section

5.2, yield similar results, although they prove to be signi…cantly weaker instruments when aplied to the entire economy, compared to manufacturing.4 5 Data from the CEPII gravity dataset.

6 We also see that membership in the same free trade agreement and sharing a common currency increases V B g Y od but not V B x Y od . This may be associated with the fact that these integration tools are multilateral in nature, fostering a greater "pool" of countries through which intermediate inputs can ‡ow at low costs. The negative association of common border with V B g Y od is mechanical, since V B g Y od necessarily passes through third countries.

7 Full results are available in TableA12in the appendix.

8 Indeed, this technology transfer has been hailed by many economists as one of the largest bene…ts of GVC integration for less developed countries. The point here is that this technology transfer cannot be achieved without some transfer of management and marketing tasks.4 9 For example, about 80% of R&D expenditures by U.S. multinationals in 2014 was performed by parents located in the U.S.; see National Sciences Board (2018), Chapter 4.

0 We also estimated (16) by W2SLS using the instrument (12). Within manufacturing industries we …nd similar results to those in Table8, except that the coe¢ cients are generally larger; as in Table4, the instrument is strong. However, the results are much less precise in the sample of all private sector industries. These results are available upon request.

1 We drop the top and bottom 1 percent of observations in order to eliminate very extreme outliers, which are driven by observations in which exports of …nal goods is most of value added, leading to unrealistic values for the modi…ed F W D.5 2 While the increase in the share of value added that crosses borders more than once within total trade is often portrayed as the hallmark of GVC integration (e.g., Antràs (2021)), it is not as important as a share of production value added.5 3 In 2016 MNEs accounted for about a third of global GDP, two thirds of global exports and 40% of imports of intermediate inputs; see[START_REF] Cadestin | Multinational enterprises and global value chains: New Insights on the trade-investment nexus[END_REF].

4 These results are available upon request. Many of the the observations on cross-border ownership are imputed ("extrapolated"), as described in the data appendix of[START_REF] Ramondo | Multinational production: Data and stylized facts[END_REF]. After merging the data on a¢ liates to our data we are left with 1122 observations, where we lose information on …ve of the 39 countries in our sample: Cyprus, Estonia, Latvia, Malta, Taiwan (1122 = 34 33, compared to 1482 = 39 38).5 5 The results are robust to dropping Ireland and the aggregated Belgium+Luxemburg, which are the only tax havens in our data according to[START_REF] Hines | Fiscal paradise: Foreign tax havens and American business[END_REF].

gratefully acknowledges support from a public grant overseen by the Agence National de la Recherche (ANR), under grant number ANR-16-CE26-0001-01.

Appendix

A Labor share concepts in the Penn World Tables

The Penn World Tables report …ve di¤erent concepts of labor shares. Here we list them, and we denote their labels in the Figure A1 and in brackets: 3. Compensation of employees + labor income of self employed (mixed income), computed by assuming that self-employed workers use labor and capital in the same proportion as the rest of the economy [Employees + Self empl (K/L)].

4. Compensation of employees + labor income of self employed (mixed income), computed by using the aggregate average wage of self-employed [Employees + Self empl (avg wage)].

5. Compensation of employees + value added in agriculture, assuming that all value added in agriculture is labor compensation (on average, it is 90%). This correction is useful for developing countries, where about half of self-employed workers are in agriculture [Employees + Self empl (agric)].

See [START_REF] Feenstra | The Next Generation of the Penn World Table[END_REF] and their online appendix for fuller details. See also Mućk, McAdam, and Growiec (2018) for an overview of di¤erent measures of the labor share.

In Figure A1 we report year …xed e¤ects from regressions of each labor share concept on year …xed e¤ects and country …xed e¤ects, weighted by real GDP. We use data from Penn World Tables 9.1 on all labor shares concepts, dropping all observations that are extrapolated (extrapolated values are set to the …rst or last observed value, so they have no content for the evolution of labor shares). The year …xed e¤ects are adjusted be equal to zero in 1983, the …rst year in which the fourth concept is available. The sample includes 39 countries that correspond to the WIOD 2013 release sample of countries.

Figure A1 demonstrates that all measures of the labor share exhibit similar trends, especially the acceleration in the decline in [START_REF] Hummels | The nature and growth of vertical specialization in world trade[END_REF]-2007. Mućk, McAdam, and Growiec (2018) also show that for the United States, all measures of the labor share exhibit common trends from 2001 and on. This is important for us, because 2001 is the year after which the association of labor shares declines with forward foreign GVC deepening is strongest.

In Figure 1 in the main text all countries'labor shares are the Employees + Self empl (K/L) series, except for China (compensation of employees) and India and Indonesia (compensation of employees + value added in agriculture).