1. Characterizing Global Value Chains: Production Length and Upstreamness
Measures of Participation in Global Value Chains and Global Business Cycles
NBER Working Paper No
Characterizing Global Value Chains: Production Length and Upstreamness
NBER Working Paper No
Zhi Wang
UIBE & George Mason University
Shang-Jin Wei
Columbia University and NBER
Xinding Yu UIBE
Kunfu Zhu UIBE
4th Aug, 2017
UIBE, Beijing

2. Presentation outline Motivations
Measures of GVC Participation, Length and Position
Decompose GDP and final goods production by country/industry to identify GVC related and unrelated production activities
Intuition behind the derivation of these indexes
Estimation Results
Why these new GVC indexes are better?
Has GVC become longer or shorter over time？
Can these new indexes help to quantify the roles of GVC in the economic shocks of recent global financial crisis
Conclusion

3. Measures of Participation in Global Value Chains and Global Business Cycles
Introduction
To provide a framework to decompose production activities into different types.
Pure domestic
Traditional final goods trade
Simple production sharing (only 1 border crossing)
Complex production sharing (at least 2 border crossings)
Use ICIO table to classify the factor embedded in various products into GVC and non-GVC activities based on whether they cross national borders for production or not.
Forward linkage: Producer’s perspective
Backward linkage: User’s perspective
To propose a set of GVC participation indexes.

4. Outline Accounting Framework Numerical Results
Application: Economic Growth and GVC Participation

5. Accounting Framework
Consider a world economy with G countries and N sectors

6. Gross outputs X can be split into intermediate and final products：
𝐴𝑋+𝑌=𝑋
𝑋=𝐵𝑌
𝐵=(𝐼−𝐴 ) −1 is the (Global) Leontief inverse matrix j
GN×GN
𝑽 𝑩 𝒀 i
Value added from a source country-sector i used in the production of final goods and services in country-sector j

7. Decomposition of value-added and final goods production based on Leontief insights
When N=G=2
Decompose GDP by sector; forward linkage based
Decompose final goods production by VA source; backward Linkage based

8. 𝑽 𝑩 𝒀 = 𝑉 𝐿 𝑌 𝐷 + 𝑉 𝐿 𝑌 𝐹 + 𝑉 𝐿 𝐴 𝐹 𝐿 𝑌 𝐷 + 𝑉 𝐿 𝐴 𝐹 (𝐵 𝑌 −𝐿 𝑌 𝐷 )
𝑽 𝑩 𝒀 = 𝑉 𝐿 𝑌 𝐷 + 𝑉 𝐿 𝑌 𝐹 + 𝑉 𝐿 𝐴 𝐹 𝐿 𝑌 𝐷 + 𝑉 𝐿 𝐴 𝐹 (𝐵 𝑌 −𝐿 𝑌 𝐷 )
Pure Domestic: 𝑉 𝐿 𝑌 𝐷 , Value added that is domestically produced and consumed.
Traditional Final Goods Trade: 𝑉 𝐿 𝑌 𝐹 , Value-added that is embodied in exports/imports of intermediate goods and services.
Simple GVC: 𝑉 𝐿 𝐴 𝐹 𝐿 𝑌 𝐷 , Simple cross country production sharing activities, with only 1 border crossing.
Complex GVC: 𝑉 𝐿 𝐴 𝐹 (𝐵 𝑌 −𝐿 𝑌 𝐷 ), Complex cross country production sharing activities, with at least 2 border crossings.

9. GVC Participation Ratio:
𝑽 𝑩 𝒀 = 𝑉 𝐿 𝑌 𝐷 + 𝑉 𝐿 𝑌 𝐹 + 𝑉 𝐿 𝐴 𝐹 𝐿 𝑌 𝐷 + 𝑉 𝐿 𝐴 𝐹 (𝐵 𝑌 −𝐿 𝑌 𝐷 )
Summing up along the row direction: Decompose value-added generated from each country-sector pair in terms of where it goes.
Figure 1a Decomposition of GDP
— Which types of production and trade are Global Value Chain activities?
Forward Linkage
GVC Participation Ratio:
𝑉_𝐺𝑉𝐶 𝑉

10. 𝑽 𝑩 𝒀 = 𝑉 𝐿 𝑌 𝐷 + 𝑉 𝐿 𝑌 𝐹 + 𝑉 𝐿 𝐴 𝐹 𝐿 𝑌 𝐷 + 𝑉 𝐿 𝐴 𝐹 (𝐵 𝑌 −𝐿 𝑌 𝐷 )
𝑽 𝑩 𝒀 = 𝑉 𝐿 𝑌 𝐷 + 𝑉 𝐿 𝑌 𝐹 + 𝑉 𝐿 𝐴 𝐹 𝐿 𝑌 𝐷 + 𝑉 𝐿 𝐴 𝐹 (𝐵 𝑌 −𝐿 𝑌 𝐷 )
Summing up along the column direction: Decompose country-sector final goods production in terms of where the value added comes from.
Figure 1b Decomposition final goods production
— Which part of final goods production and trade belong to GVCs?
Backward Linkage
GVC Participation Ratio:
𝑌_𝐺𝑉𝐶 𝑌

11. Decomposition of GDP by country/industries Which types of value-added production and trade activities belong to GVC?
Complex cross country
production sharing
A country/sector’s total
value-added
(GDP by industry)
In production of value added in final goods exports directly
2-V_RT
In production of final products to domestic market directly
1-V_D
In intermediates that finally return to home countries
3b.V_GVC_D=RDV_F
In production of value-added in intermediate exports
3-V_GVC
In intermediates indirectly absorbed by importing country or re-exported to third countries
3c.V_GVC_F
In intermediates directly absorbed by direct importers
3a-V_GVC_R
Simple cross country
VAX(J&N) =2+ 3c=
Production for foreign demand ;
1+3b =Production for domestic demand.
DVA(KWW) = = GDP in exports ; 1 . 1 ≥2

12. Decompose final goods production by country/sector Which part of final goods production and trade activities belong to GVCs?
Production of final goods by country/sector
Domestic VA in final product exports
2-Y_RT
Domestic VA consumed in domestic market directly
1-Y_D
Domestic VA in intermediates imports that re-exported
3b. Y_GVC_D
Domestic and foreign VA in intermediate inputs
3-Y_GVC
Foreign VA in intermediate trade
3c. Y_GVC_F
Partner VA in intermediate imports consumed directly by
Source country
3a-Y_GVC_R
FVA(Los, Timmer and Vries)=3a+3c
DVA = 1+2+3b 1 1 ≥2
Shallow cross country
production sharing
Deeper cross country
production sharing

13. Returned Value Added as share of total GVC related activities
The relative sizes of parts R, D, and F may reflect the differences of roles in the GVCs for different countries.
For example, GVC_D, “returned DVA” accounts for a relatively larger proportion in the US, as the US is controlling both ends (design and sales) of the value chain.

14. Figure 3 Forward/Backward Participation Indexes, 2000 to 2014
Numerical Results
Country Level
Figure 3 Forward/Backward Participation Indexes, 2000 to 2014

15. Figure 4 GVC participation Indexes, Country Level，2014

16. Sectoral Level

17. Figure 5 GVC participation Indexes, Sectoral Level, 2014

18. Table 3 Sectoral Level Participation Indexes, Forward/Backward Linkage
Country-Sector Level
Table 3 Sectoral Level Participation Indexes, Forward/Backward Linkage

20. Advantages of the new “GVC Participation Index”
Correcting a bias in traditional indexes
Traditional VS/VS1 ratio use gross exports as the denominator may lead to an upward bias at the bilateral/sectoral level.
Table 4 Comparison between Traditional and New Measures in US sectors, 2014

21. The upward bias is more pronounced for utility and service sectors, as a large proportion of their value added is exported indirectly

22. Differentiating “simple” and “complex” GVC participation
The “simple” and “complex” parts of GVC participation are different in size and the trend of change

23. Application: Economic Growth and GVC Participation
Figure 9 Changing Trends of Different Types of Production Activities
as a Share of Global GDP (2000–2014)   

24. during the global business cycle, global level (2000–2014)
Figure 10 Nominal growth rates of different value added creation activities
during the global business cycle, global level (2000–2014)

25. These facts suggest a possible link between the expansion and recession of aggregate economic activities and the share of GVC trade in total production activities.
A number of recent papers have suggested that joining GVCs can improve economic growth
—— Baldwin and Yan, 2014; OECD, 2014; IMF, 2015, World Bank, 2016
However, none of these studies decomposes trade into traditional trade, and simple and complex GVC activities.

26. ΔlnVAict = β0 + β1×V-Shareict + β2×Wct + β3× Zit + γt + δc + uict
ΔlnVAict: The change of sectoral GDP in industry i of Country c;
V-Shareict: The share of different types of value added creation activities (D, RT, Simple GVC and Complex GVC) in sectoral GDP;
Wct and Zit: Country and sectoral level control variables;
γt and δc: Year and country fixed effects.

27. Table 6 Benchmark Regression Results
(ΔlnVAict = β0 + β1×VShareict + uict)

28. Regression Results with Year and Country Fixed Effects

32. Conclusion
In this paper we propose a production activity accounting framework based on whether factor content crosses national borders for production or not.
We show that a set of GVC participation indexes built on such framework have more desirable properties than the existing ones in the literature.
Complex GVC was the most important driving force for globalization and co-moves strongly with the growth of global GDP, both in booms and in recessions.

33. The concept of production Length
Characterizing Global Value Chains: Production Length and Upstreamness
The concept of production Length
The average production stage between primary inputs to final products, it is the average times that value-added created by production factors employed in a country/sector has been counted as gross output in the whole economy.
Other industry
Other industry
First count
Second count
Third count
Primary input (capital, labor, land)
Gross output of Cotton
Gross output of textile
Gross output of appeals
Consumer
Other intermediate inputs
Other intermediate inputs
Other intermediate inputs
It measures gross outputs induced by one unit of value added created in a particular sector, or the footprints of each sector’s value added in the economy as a whole.

34. The intuition and derivation of total production length measure in sequential production process DVA generated in the sequential production process and its length
First stage: directly embodied in final products. DVA is measured as 𝛿 𝑖𝑗 𝑣 𝑖 𝑦 𝑗 , length of the production chain is 1, output is also 𝛿 𝑖𝑗 𝑣 𝑖 𝑦 𝑗 . If i and j are the same, 𝛿 𝑖𝑗 equals 1, otherwise it equals 0;
Second stage: embodied in its gross output that is used as intermediate input in the production of sector j final products. DVA is measured as 𝑣 𝑖 𝑎 𝑖𝑗 𝑦 𝑗 , the length of the production chain is 2, induced output equals 2 𝑣 𝑖 𝑎 𝑖𝑗 𝑦 𝑗 , which account value-added 𝑣 𝑖 𝑎 𝑖𝑗 𝑦 𝑗 as output twice, once for sector i, once for sector j .
Third stage: embodied in its gross output that is used as intermediates in all sectors to produce their gross outputs which are used as intermediates to produce sector j final products. DVA is measured as 𝑣 𝑖 𝑘 𝑛 𝑎 𝑖𝑘 𝑎 𝑘𝑗 𝑦 𝑗 , the length of the production chain is 3, and the induced output is 3 𝑣 𝑖 𝑘 𝑛 𝑎 𝑖𝑘 𝑎 𝑘𝑗 𝑦 𝑗 . The same value-added originally produced from sector i is counted as output three times in sector i, k and j respectively;
The same goes for the succeeding stages. Generalizing the above process to include all rounds of value-added produced in sector i directly and indirectly embodied in sector j final products, DVA and its induced outputs are measure as:
𝛿 𝑖𝑗 𝑣 𝑖 𝑦 𝑗 + 𝑣 𝑖 𝑎 𝑖𝑗 𝑦 𝑗 + 𝑣 𝑖 𝑘 𝑛 𝑎 𝑖𝑘 𝑎 𝑘𝑗 𝑦 𝑗 +…= 𝑣 𝑖 𝑏 𝑖𝑗 𝑦 𝑗 𝛿 𝑖𝑗 = 1, 𝑖=𝑗 0, 𝑖≠𝑗

35. The measurement of total production Length
Production length between primary input of sector i and final products of sector j
Total gross output induced by value-added of sector i
generated from the production
of final products in sector j
Value-added of sector i
generated from the production
of final products in sector j
When value added is used as input in a production stage, either as primary input or intermediate inputs, it will be count as output where it is used. Therefore, the length of a production chain is the times of value added counted as output in the production chain, from the first time it is used as primary input until it absorbed by a final product.

36. Measure of Production Lengths in Matrix Notation
Measure of Domestic Value added
𝑉 𝑌 + 𝑉 𝐴 𝑌 + 𝑉 𝐴𝐴 𝑌 = 𝑉 𝐼+𝐴+𝐴𝐴+… 𝑌
= 𝑉 (𝐼−𝐴 ) −1 𝑌 = 𝑉 𝐵 𝑌
Measure of DVA induced gross output
𝑉 𝑌 +2 𝑉 𝐴 𝑌 +3 𝑉 𝐴𝐴 𝑌 = 𝑉 (𝐼+2𝐴+3𝐴𝐴+…) 𝑌
= 𝑉 𝐵+𝐴𝐵+𝐴𝐴𝐵+… 𝑌 = 𝑉 𝐵𝐵 𝑌
Production lengths in matrix notation
PL𝑣𝑦= 𝑉 𝐵𝐵 𝑌 𝑉 𝐵 𝑌

37. Using the shares of sector value added in GDP as weights, aggregate over all i and j, we obtain average production length of the world economy as a whole:
PL𝑤= 𝑢 𝑉 𝐵𝐵 𝑌 𝑢 𝑢 𝑉 𝐵 𝑌 u = 𝑉𝐵𝐵𝑌 𝑉𝐵𝑌 = 𝑢𝐵𝑌 𝑢𝑌 = 𝑢𝑋 𝐺𝐷𝑃
It indicates that the average length of the production chain in whole economy equals the ratio of total gross outputs to GDP, which is an index of complexity of the production process in the economy, i.e., the higher this ratio, the more complex the production system in the economy.

38. Forward-Linkage Production Length, Country-Sector Level, 2014

39. Backward-Linkage Production Length, Country-Sector Level, 2014

40. Changes of Major Segments of Production Length for Major Economies
Forward-Linkage

41. Changes of Major Segments of Production Length for Major Economies
Backward-Linkage

42. Changes of Major Segments of Production Length
Sectoral Level
Forward-Linkage

43. Changes of Major Segments of Production Length
Sectoral Level
Backward-Linkage

44. Can production length measure directly infer production line position?
Production lengths based on forward and backward linkage are equal each other at the global level because the accounting identity of global final demand always sums to global value- added. However, they may not equal each other at the country or country/sector level due to international trade and cross border production activities.
What is the relation between production length measure and production line position? Can production length measure be used directly to infer “upstreamness” or “downstreamness” of a country or a country/sector pair? Current literature is not clear on such important questions and often uses production length to infer production line position directly.

45. Forward Linkage Production Length
𝑃𝐿𝑣_𝐺𝑉𝐶= 𝑋𝑣_𝐺𝑉𝐶 𝑉_𝐺𝑉𝐶
Backward Linkage Production Length
𝑃𝐿𝑦_𝐺𝑉𝐶= 𝑋𝑦_𝐺𝑉𝐶 𝑌_𝐺𝑉𝐶
The average production line position in a global value chain can be defined as the ratio of the two production lengths：
𝐺𝑉𝐶𝑃𝑠= 𝑃𝐿𝑣_𝐺𝑉𝐶 𝑃𝐿𝑦_𝐺𝑉𝐶 ′

46. Production Position Index
Country Level Position Index, 2014
Country
Production Position Index
TPL
GVC Position Index
PL_GVC
(Forward / Backward)
Forward
Backward
RUS
1.226
2.503
2.041
AUS
1.048
4.865
4.645
NLD
1.125
2.270
2.017
1.036
4.688
4.525
1.091
2.212
2.027
BEL
1.018
3.977
3.905
SWE
1.065
2.034
1.911
1.016
4.091
4.027
DEU
1.043
2.054
1.970
FRA
1.013
4.170
4.114
CAN
1.017
2.004
1.972
BRA
1.011
4.410
4.361
GBR
1.946
1.922
JPN
4.608
4.560
1.003
2.140
2.134
1.005
4.096
4.077
IDN
1.001
2.094
2.091
1.002
3.976
3.968
0.992
1.844
1.859
ESP
4.243
4.275
ITA
0.985
1.985
2.015
0.989
4.330
4.376
USA
0.984
1.785
1.814
4.391
4.441
KOR
0.979
2.348
2.399
0.986
4.066
4.122
1.874
1.915
TUR
0.975
4.238
4.347
CHN
0.976
2.891
2.963
MEX
0.967
3.838
3.970
0.965
1.890
1.958
0.962
4.625
4.810
1.857
1.925
0.961
4.136
4.304
0.957
2.059
0.950
3.923
4.130
IND
0.934
1.813
1.942
0.945
5.322
5.634
0.930
1.704
1.833
0.937
4.190
4.472

47. Production Position Index
Sectoral Level Positions Index, World Average, 2014
Sector
Production Position Index
GVC Position Index
Mining and quarrying
2.221
Electricity and gas supply
1.368
Forestry and logging
1.919
Coke and refined petroleum products
1.285
Financial service activities
1.609
1.228
Activities of head offices, Legal and accounting
1.592
Real estate activities
1.140
Administrative and support service
1.519
1.137
Advertising and market research
1.474
Other service activities
1.134
Postal and courier
1.455
1.126
Support activities for transportation
1.427
Motion picture, video and television programme
1.123
Activities auxiliary to financial services
1.411
Water supply
1.119
Wholesale trade
1.314
Telecommunications
1.105
Accommodation and food service
0.768
Machinery and equipment
0.879
Textiles and leather products
0.766
Computer, electronic and optical products
0.876
Food, beverages and tobacco
0.736
Furniture
Education
0.718
Publishing
0.856
Public administration and defense
0.686
0.846
Other transport equipment
0.666
Electrical equipment
0.816
Motor vehicles, trailers and semi-trailers
0.663
0.803
Human health and social work
0.574
Basic pharmaceutical products
0.795
Construction
0.505
0.779
Extraterritorial organizations and bodies
0.362
Activities of households
0.743

48. Sectoral Level:
A comparison of GVC positions across Economies, 2014

49. Time Trend: Selected Industries
Electrical and Optical Equipment

50. —— Impact of global Financial Crisis
Index application:
participation intensity, production line positions, GVC length, and the economic shocks of the recent global financial crisis
Different Effects of the Same Economic Shock to Different Value Added Creating Activities
—— Impact of global Financial Crisis

51. +β4×GVCPtic + β5×Wic + β6× Zc + γi + uic
Δln(Vaic) = β0 +β1×Positionic + β2×PLv_GVC_Internationalic +β3×PLv_GVC_Domesticic
+β4×GVCPtic + β5×Wic + β6× Zc + γi + uic
(1)
(2)
(3)
(4)
(5)
(6)
(7)
(8)
(9)
Position
8.303**
8.231*
8.633**
8.544**
8.871**
7.744*
7.596*
8.077*
7.931*
(4.223)
(4.992)
(4.162)
(4.254)
(4.211)
(4.455)
(4.403)
(4.508)
(4.476)
International Portion
-9.240**
-7.108
-10.26**
-8.319*
(4.608)
(4.427)
(4.660)
(4.481)
Domestic Portion
3.942***
3.890***
4.112***
4.086***
(1.048)
(1.039)
(1.049)
(1.040)
GVCP (forward)
-26.94***
-26.79***
-25.64***
-20.14***
-18.29***
(3.430)
(5.206)
(3.462)
(3.830)
(3.945)
GVCP (backward)
-0.302
(8.278)
Simple GVCP (forward)
-4.909
-5.483
-0.228
-0.561
(8.348)
(8.354)
(8.400)
(8.426)
Complex GVCP (forward)
-61.26***
-56.95***
-51.20***
-45.72***
(13.41)
(13.33)
(12.77)
(12.51)
Mature（=1）
3.402***
3.125***
3.324***
3.063***
(0.789)
(0.799)
(0.796)
(0.804)
Labor Productivity *
( )
( )
( )
High Skill
-17.02***
-17.27***
-17.82***
-18.02***
(3.707)
(3.692)
(3.770)
(3.751)
Constant
-18.75***
-18.64***
-19.75***
-19.15***
-19.93***
-8.983
-13.40*
-7.893
-11.79
(4.627)
(5.856)
(4.616)
(4.718)
(4.708)
(8.224)
(8.042)
(8.264)
(8.062)
Sector Fixed Effects
YES
Observations
1,379
1,343
1,358
1,322
R-squared
0.229
0.236
0.245
0.251
0.241
0.253
0.258

52. Conclusion Remarks
We have developed a GVC index system that includes three types of indexes:
a production length index for the average number of production stages and complexity of the global value chain;
a participation index for the intensity of a country-sector’s engagement in global value chains; and
a position index for the location of a country sector on a global value chain, or the relative distance of a particular production stage to both ends of a global value chain.
We thus can provide a comprehensive picture of each country/sector pair’s GVC activities from multiple dimensions.
By estimating these indexes according to real world data, we produce a large set of indicators. We hope these indexes could be widely used by both theoretical and empirical economists in advancing studies for economics of global supply chains.

53. Thanks!