Appendix A: The Translog GVC Production Function
In this Appendix we show how the expression for the wage bill share provided by the translog model (see equation 4 in the main text) can be derived as a log-linear approximation of the solution to a cost-minimization problem. We prove the relationship between the estimated coefficients and the price elasticities as given in (6) and discuss how to interpret the coefficient on the time trend in terms of biased technical change. For notational simplicity we leave out the quasi-fixed capital stock K.
Conditional on the level of output Y and time t, the short-run variable cost function is defined as: system of first-order conditions for cost minimization is given by:
𝐹𝐿(𝑁𝐿, 𝑁𝑀, 𝑁𝐻; 𝑡) pair of labour inputs the marginal rate of technical substitution should be equal to their relative prices. Log-linearization of the first-order conditions gives the following expressions:
(
35 We write the solution to this system of equations as:
(
The first matrix on the right-hand side is the inverse of the coefficient matrix in (A.5) and its elements consist of price elasticities 𝜂𝐸𝐷 = 𝜕 ln 𝑁𝐸⁄𝜕 ln 𝑊𝐷 and output elasticities 𝜂𝐸𝑌 =
We can directly compare this expression to that of the wage bill share implied by the translog model in equation (4). From this we can conclude the following. First, the price elasticity 𝜂𝐸𝐷 can be indeed inferred from the 𝛾𝐸𝐷coefficients according to the expressions given in (6). For example, we see that 𝛾𝐸𝐸 = (1 + 𝜂𝐸𝐸− 𝑠𝐸)𝑠𝐸 so that 𝜂𝐸𝐸 = 𝛾𝐸𝐸⁄𝑠𝐸+ 𝑠𝐸− 1. Second, the rate of technical progress 𝜕 ln 𝐹 𝜕𝑡⁄ only affects the cost shares if the production technology is non-homothetic so that 𝜃𝐸𝑌 ≠ 0. Assuming constant returns to scale, what matters is how
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technical change alters the marginal rate of technical substitution between pairs of labour inputs
𝜕 ln[𝐹𝐸⁄𝐹𝐷] 𝜕𝑡⁄ . If it leaves this ratio unchanged, then technical change is said to be Hicks-neutral and cost shares remain unaffected. If it does not, then there is bias in technical change according to the definition put forward by Acemoglu (2002). The time trend 𝛿𝐸𝑇 in equation (4) then captures the term in square bracket in equation (A.8), which is price-elasticity-weighted average of the bilateral bias terms. Hence, it shows whether “on average” labour with education E gains in productivity from technical change relative to the other labour types.
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Appendix B: Derivation of GVC Cost Shares and Factor Prices
Wage bill shares and factor prices in GVCs are two key variables in our framework. They are not directly observable in primary data and we will construct a synthetic dataset by mapping final goods to value added by labour with different levels of education in any country in the world. This ex-post accounting framework is based on backward tracing through the value chain of final products to identify the sources of value added as in Los, Timmer and de Vries (2015).
More formally, consider a world with C countries and I industries. This means that in total there are 𝐶 × 𝐼 country-industry pairs. The world input-output tables give for any country-industry pair i its gross output in each year 𝑦𝑖𝑡, the amount it sells to country-industry j for intermediate use 𝑧𝑖𝑡𝑗, and the amount it sells for final use worldwide 𝑓𝑖𝑡. By definition total output equals total sales in each year t:
𝑦𝑖𝑡 = ∑ 𝑧𝑖𝑡𝑗
𝑗
+ 𝑓𝑖𝑡
(B.1) We define the so-called technical coefficients of the input-output system as 𝑎𝑖𝑗𝑡 = 𝑧𝑖𝑡𝑗⁄𝑦𝑗𝑡, so that (B.1) can be written as:
𝑦𝑖𝑡 = ∑ 𝑎𝑖𝑗𝑡𝑦𝑗𝑡
𝑗
+ 𝑓𝑖𝑡
(B.2) In matrix notation this is represented by 𝐲𝑡 = 𝐀𝑡𝐲𝑡+ 𝐟𝑡, where 𝐀𝑡 is the matrix for which 𝑎𝑖𝑗𝑡 is the element in row i and column j. The solution to this system of equations is given by (see e.g. Miller and Blair 2009):
𝐲𝑡= 𝐁𝑡𝐟𝑡, (B.3)
with 𝐁𝑡 = (𝐈 − 𝐀𝑡)−1 the Leontief Inverse (Leontief 1953). The element 𝑏𝑖𝑗𝑡 in row j and column i gives the amount of output from country-industry j required to produce one dollar’s worth of output for final use by country-industry i in year t. From the Socio-Economic Accounts we obtain for each country-industry the total hours worked by labour with education E in country-industry j in each year t, ℎ𝑗𝑡𝐸, and its hourly wage 𝑤𝑗𝑡𝐸.
A GVC is identified by the product that is finalised in a particular country. We denote this by subscript z. To produce one dollar of final output z, the required working hour by labour E in
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country industry j is given by 𝑏𝑗𝑧𝑡(ℎ𝑗𝑡𝐸⁄𝑦𝑗𝑡), with a payment of 𝑏𝑗𝑧𝑡(ℎ𝑗𝑡𝐸⁄𝑦𝑗𝑡)𝑤𝑗𝑡𝐸. Hence, total working hours of labour E in producing one dollar of final output z is given by ∑𝑗𝑏𝑗𝑧𝑡(ℎ𝑗𝑡𝐸⁄𝑦𝑗𝑡), and similarly the total wage paid to labour E is ∑𝑗𝑏𝑗𝑧𝑡(ℎ𝑗𝑡𝐸⁄𝑦𝑗𝑡)𝑤𝑗𝑡𝐸.
We can then derive our main variables of interest for each GVC, which are wage bill shares in the GVC:
𝑠𝑧𝑡𝐸 = ∑ 𝑏𝑗 𝑗𝑧𝑡(ℎ𝑗𝑡𝐸⁄𝑦𝑗𝑡)𝑤𝑗𝑡𝐸
∑ ∑ 𝑏𝐷 𝑗 𝑗𝑧𝑡(ℎ𝑗𝑡𝐷⁄𝑦𝑗𝑡)𝑤𝑗𝑡𝐷, (B.4)
and average GVC wages:
𝑊𝑧𝑡𝐸 = ∑ 𝑏𝑗𝑧𝑡(ℎ𝑗𝑡𝐸⁄𝑦𝑗𝑡)
∑ 𝑏𝑗 𝑗𝑧𝑡(ℎ𝑗𝑡𝐸⁄𝑦𝑗𝑡)𝑤𝑗𝑡𝐸
𝑗
. (B.4)
In the last expression, the weight on right-hand side is the share of country-industry j in total employment of labour E within GVC z.
Note that in the main text we replace the GVC index z by pc, which captures the product p and country of completion c.
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Appendix C: Data Sources
The data for this study is taken from the World Input-Output Database (WIOD), which is freely available at www.wiod.org. It has been specifically constructed for the analysis of global value chains, see Timmer et al. (2015). It provides world input-output tables for each year since 1995, covering 40 countries and regions, including all 27 countries of the European Union (as of 1 January 2007) and 13 other major economies in the world (see Table C.1). In addition, an estimate for the remaining non-covered part of the world economy is provided such that the value-added decomposition of final output is complete. It contains data for 35 sectors covering the overall economy, including agriculture, mining, construction, utilities, oil, 13 manufacturing industries and 17 services industries (see Table C.2).
Table C.1: Countries and Regions Covered in the World Input-Output Database (WIOD)
High-income Economies Other Economies
Australia Brazil
Austria Bulgaria
Belgium China (Mainland)
Canada Cyprus
Denmark Czech Republic
Finland Estonia
France Hungary
Germany India
Greece Indonesia
Ireland Latvia
Italy Lithuania
Japan Malta
Luxembourg Mexico
Netherlands Poland
Portugal Romania
South Korea Russian Federation
Spain Slovak Republic
Sweden Slovenia
Taiwan, China Turkey
United Kingdom Rest-of-World region
United States
Notes: List of countries and regions covered in the WIOD, November 2013 release.
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Table C.2: Sectors in the World Input-Output Database (WIOD)
Code Sector Name
AtB Agriculture, Hunting, Forestry and Fishing C Mining and Quarrying
⋆ 15t16 Food, Beverages and Tobacco
⋆ 17t18 Textiles and Textile Products
⋆ 19 Leather, Leather Products and Footwear
⋆ 20 Wood and Products of Wood and Cork
⋆ 21t22 Pulp, Paper, Printing and Publishing 23 Coke, Refined Petroleum and Nuclear Fuel
⋆ 24 Chemicals and Chemical Products
⋆ 25 Rubber and Plastics
⋆ 26 Other Non-Metallic Mineral
⋆ 27t28 Basic Metals and Fabricated Metal
⋆ 29 Machinery, Not elsewhere classified
⋆ 30t33 Electrical and Optical Equipment
⋆ 34t35 Transport Equipment
⋆ 36t37 Manufacturing, Not elsewhere classified; Recycling E Electricity, Gas and Water Supply
F Construction
50 Sale and Repair of Motor Vehicles and Motorcycles; Retail Sale of Fuel 51 Wholesale Trade, Except of Motor Vehicles and Motorcycles
52 Retail Trade and Repair, Except of Motor Vehicles and Motorcycles H Hotels and Restaurants
71t74 Renting of Machinery & Equipment and Other Business Activities L Public Administration and Defence; Compulsory Social Security
M Education
N Health and Social Work
O Other Community, Social and Personal Services P Private Households with Employed Persons
Notes: List of sectors covered in the WIOD (November 2013 release) by ISIC revision 3 industry code.
Each of these sectors can potentially contribute to a GVC. In this study we focus on GVCs of manufacturing products, that is final output of manufacturing industries indicated by ⋆.
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Apart from the input-output tables, an important input into our analysis is information on quantities and prices of labour and capital used in production. We briefly describe the methods and sources used in this construction. For a full discussion, see Erumban et al. (2012).
A. Wages and Employment by Educational Attainment Levels
Data on wages and employment by skill types are not part of the core set of national accounts statistics reported by National Statistical Institutes; at best only data on total hours worked and wages by industry are included. Therefore, additional material has been collected from employment and labour force statistics. For each country covered, a choice was made of the best statistical source for consistent wage and employment data at the industry level. In most countries this was the labour force survey (LFS). In most cases this needed to be combined with an earnings surveys as information wages are often not included in the LFS. In other instances, an establishment survey, social-security database, industry or population census was used. Care has been taken to arrive at series which are time consistent, as most employment surveys are not designed to track developments over time, and breaks in methodology or coverage frequently occur. For most countries data on hours worked was taken from the EU KLEMS database (O’Mahony and Timmer 2009), revised and updated. For countries not in EU KLEMS new sources have been used which are described in the detailed country notes (Erumban et al.
2012).
Labour compensation of self-employed is not registered in the National Accounts, which as emphasized by Angrist and Krueger (1999) leads to an understatement of labour's share. This is particularly important for less advanced economies that typically feature a large share of self-employed workers in industries like agriculture, trade, business and personal services.
Imputations have been made. For advanced countries, the compensation per hour of self-employed is assumed equal to the compensation per hour of employees. For emerging countries this assumption is not plausible as a large part of informal workers earns much less than the average wage of low-educated workers. Instead, additional information was used which differs by country (Erumban et al. 2012).
In the WIOD-SEA three skill types of labour are being distinguished, based on the level of educational attainment of the worker. Three types of workers are identified following the International Standard Classification of Education (ISCED). Low-educated (ISCED categories 0, 1 and 2) roughly corresponds to less than secondary schooling. Middle-educated (3 and 4)
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means secondary schooling and above, including professional qualifications, but below college degree. High-educated (5 and 6) includes those with a college degree and above.
Typically, data on wages is scarcer than for number of workers, both in terms of industry coverage and time such that imputations have to be made. For each country relative wages for at least one year in the period 1995--2007 are available which ensures that country-specific skill premia are reflected in the data. For most countries there are at least three observations across the period such that changes in skill premia over time are reflected. Wages for years in between are linearly interpolated. The level of industry detail also varies across countries and depends crucially on the sample sizes of the surveys on which the estimates are based. If needed, shares of aggregate sectors were applied to more detailed underlying industries. Details on various country-specifics can be found in Erumban et al. (2012).
Two additional points are worth mentioning. First, in our analysis we excluded data for the year 2003. The reason is that for a number of European countries wages by level of educational attainment data in the EU labour Force Survey was miscoded such that the share of low-educated workers jumped up from 2002 to 2003 and down again from 2003 to 2004. This data was used in the WIOD-SEA as well, and we therefore excluded it in the main analysis.
Including this (erroneous) data would not quantitatively change the main results of this paper however. Second, the WIOD-SEA does not provide data for the rest-of-the-world region. For the 13 manufacturing industries in our analysis we took the labour share from the corresponding industries in China and assumed all labour is low-educated in the RoW region. For the remaining industries the labour share is set equal to zero. The results are robust to this assumption as the RoW region exports few services that are used as intermediates in GVCs of advanced countries. We used relative wages from China to calculate hours worked for corresponding industries in RoW.
B. Capital Stock
The WIOD SEAs contain capital stock series by industry at constant prices. The series cover all fixed assets as defined in the SNA 1993. As for labour, for most countries data was taken from the EU KLEMS database (O’Mahony and Timmer 2009). For other countries, capital stocks have been constructed on the basis of the Perpetual Inventory Method (PIM) in which the capital stock in year t is estimated as the sum of the depreciated capital stock in year 𝑡 − 1 plus real investment in year t. The depreciation rates are industry-specific rates and assumed to be the same for all countries. For many countries long time-series of investments are available
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and there is no need to have information on an initial stock estimate. For countries with no investment data before 1995 (mainly Eastern European countries), industry specific ratios of value added to capital stocks were used of a country at a similar stage of development. For countries for which investment series were available for a number of years before 1995, an initial capital stock for the year in which investment series start was estimated using the Harberger method, which can be written as: 𝐾0 = (𝑖 (𝑔 + 𝑑)⁄ ) × GO, where 𝐾0 is the initial capital stock in constant 1995 prices, GO is gross output by industry in constant 1995 prices, 𝑖 is the investment rate, 𝑔 is the average growth rate of output, and 𝑑 is the total depreciation rate by industry. For the rest-of-the-world region, a ratio of the capital price relative to the US was estimated from the Penn World Tables (Feenstra, Inklaar and Timmer 2015). This was applied to the value added in each industry (which is in US dollars) times the capital share (one minus the labour share) to back out the capital stock in each industry.
Appendix D: Summary Statistics
Table D.1: Descriptive Statistics of the GVC Panel Dataset
Obs Mean St Dev Min Max
Wage bill shares
𝑠𝐿 3,256 0.27 0.13 0.03 0.74
𝑠𝑀 3,256 0.47 0.11 0.16 0.78
𝑠𝐻 3,256 0.26 0.07 0.09 0.54
Average hourly wages
ln(𝑊𝐿) 3,256 1.78 0.45 0.17 2.76
ln(𝑊𝑀) 3,256 2.56 0.40 1.12 3.45
ln(𝑊𝐻) 3,256 3.16 0.38 1.76 4.03
Capital and output levels
ln(𝐾 𝑌⁄ ) 3,256 0.82 0.32 -0.25 2.21
ln(𝑌) 3,256 8.37 1.91 1.81 13.00
Notes: Own calculations based on November 2013 release of World Input-Output Database (WIOD, Timmer et al. 2015). Annual observations for 273 GVCs of manufacturing products. The real capital stock by country and industry in the SEA is given in constant national prices from 1995. We convert these to 1995 US dollars, correcting for differences between countries in the price level of capital formation using data from the Penn World Tables (version 8.0, Feenstra, Inklaar and Timmer 2015). We derive capital ratios by dividing the real capital stock by value added in the corresponding country-industry. Similar as for employment, we account for the capital contributed by each country-industry and aggregate across country-industries within a GVC to measure K. Real output of a chain is obtained by applying the gross output deflator on final output from the country-industry of completion.
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Appendix E: Additional Robustness Checks
This appendix provides additional robustness checks of the main results reported in Table 1 of the main text.
Output weighted. One concern is that the measurement error in observations may be heterogeneous across observations, and its variation might be larger for GVCs with smaller output. For example, observations on GVCs where the product is finalised in Luxembourg can have a very small output value and are likely to have higher measurement error. We weight observations with the log of final output in column (2) of Table E.1. This has little effect on the results, although the coefficients on the time trend become somewhat smaller. The results are also robust to leaving out any single country (not reported).
Non-linear trends. In the baseline model biases in technical change are modeled as linear trends, but this might be overly restrictive. For example, Autor, Dorn and Hanson (2015) suggest that the impact of technical change on US labour markets was stronger in the 1990s than in the 2000s. To capture potential non-linearity in technical change in our empirical model, we follow Baltagi and Griffin (1988) who proposed a general index approach in which the time trend t is replaced by year dummies using the first year as a reference. For labour type E, 𝛿𝐸𝑇𝑡 is replaced by ∑12𝑡=2𝜆𝐸𝑡𝑍𝑡 where 𝑍𝑡 are year dummies. The parameter restriction ∑𝐸𝛿𝐸𝑇 = 0 is subsequently replaced by ∑𝐸𝜆𝐸𝑡 = 0 for all t. As shown in column (3) of Table E.1, the cross price coefficient estimates are affected but the associated price elasticities are barely affected (not reported). As before, for each labour type a strong linear trend is found. These are traced out in Figure E.1, cumulating from 1995. Over the 12 year period the cumulative bias is minus 9.32 percentage points for low-educated, and plus 0.95 and 8.36 for middle- and high-educated, respectively. These trends are highly comparable to the baseline. Consequently further results in this paper are reported for the linear bias model only.
Cross-country differences in schooling quality. In the construction of the (average) wages in GVCs we assumed that workers across countries with similar schooling levels have the same productivity. Arguably, this is a reasonable assumption for workers with high school or below which are likely to carry out tasks that require few skills that are acquired through formal schooling. But cross-country differences in the quality of schooling systems are likely to matter more for the productivity of high-educated workers. Even grouping workers by the international standard classification of education (ISCED), as we did, is unlikely to fully correct for this.
Unfortunately, as discussed in the data section, there is no information on international
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differences in quality of schooling systems that we can use. To investigate the possible impact on our results, we adopt an extreme test and assume that cross-country differences in wages for high-educated are completely due to differences in productivity. Put otherwise, we assume (effective) factor price equalisation for high-educated workers across countries, but not for other workers. This is done by imputing the hourly wage for high-educated workers in the US for all countries, such that reallocation of tasks for high-educated workers across countries has no impact on the effective average wage for high-educated work in the GVC.
The results are given in column (4) of Table E.1. We find that the wage coefficients change considerably compared to the baseline results. This volatility is expected as wages are all expressed relative to the high-educated wage. It is thus more relevant to inspect the price elasticities. They are still of the right sign: the elasticities of factor demand in L relative to (𝑊𝐿, 𝑊𝑀, 𝑊𝐻) are given by (−0.693, 0.489, 0.204), for M (0.278, −0.557, 0.280), and for H (0.207, 0.499, −0.706). The factor bias estimates, which are our main variables of interest, are still highly significant for low- and high-educated, and insignificant for middle-educated. The magnitudes are comparable to the baseline results.
Figure E.1: Cumulative Changes in Bias in Technical Change
Notes: Based on regression with non-linear biased technical change reported in column (3) of Table E.1.
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Notes: Estimation of parameters determining wage bill shares in system of equations as given in formulas (8) and (9). Column (1) is the baseline model as in Table 1, in which we assume a linear trend in the biases in technical change, while in column (3) this is replaced by year dummies. In column (2) observations are weighted with the log of final output value of the GVC. Column (4) reports results assuming international effective factor price equalization of high-educated workers, using US wages for all countries. Coefficients are estimated with maximum
Notes: Estimation of parameters determining wage bill shares in system of equations as given in formulas (8) and (9). Column (1) is the baseline model as in Table 1, in which we assume a linear trend in the biases in technical change, while in column (3) this is replaced by year dummies. In column (2) observations are weighted with the log of final output value of the GVC. Column (4) reports results assuming international effective factor price equalization of high-educated workers, using US wages for all countries. Coefficients are estimated with maximum