1. The multilateral nature of balterial trade in the age of global value chains (Work in progress)
Fei Wang, Zhi Wang and Kunfu Zhu
University of International Business and Economics
Shang-Jin Wei
Columbia Business School and NBER
Global Value Chain Training and Research Workshop
University of International Economics and Business
Beijing, July 29-August 4, 2018

2. Bilateral Trade Imbalance

3. Motivation
Most economists agree that balance of trade is not a good measure of the effect of a country’s trade policy (Lawrence, 2018) and balances of bilateral trade should not be the focus of national policy due to the multilateral nature of international trade (Bergsten, 2006).
However, as the bilateral trade balance is frequently headline news and a regular topic in the trade policy debate around the world, an analytical framework that is able to reveal the multilateral characters of bilateral trade in the age of global value chains, would help the public and policy makers to better understand the deeply rooted multilateral nature of many bilateral trade issues such as the role of exchange rate in current account adjustment.
Understand the roles of third countries may play in balterial trade balance between two trading partners also help us to better understand the limited role of trade protection policies is able to achieve and the unintended results it may induce in the age of global value chains.

4. The Trade Balance of USA-China and the appreciation of RMB, 2004-2017

5. How to measure third country effect in balterial trade?
The earlier study of such issues started with Hummels, Ishii and Yi (HIY, 2001). They propose using foreign value-added embodied in imported intermediate imports to export production as a measure of vertical specialization (VS) , the first measure of foreign production factor’s role in a country’s export production.
A framework that extends HIY to multilateral setting, tracing value added and double counted items in aggregate gross trade flows is proposed by Koopman, Wang and Wei (KWW, 2014). Wang, Wei, and Zhu (2014) extend the KWW method, provides an accounting framework that resembles in spirit that of KWW (2014) at the bilateral, sector, and bilateral sector levels. For this reason, we might label the overall accounting framework as KWWZ method.

6. The Major Contribution of Gross Trade Accounting method proposed by KWWZ
Bridge two most important statistics (GDP in national account and Gross trade in custom statistics) and demonstrate the first time in the literature that the components of gross trade beyond DVA have specific types of relationships with GDP statistics.
Domestic value-added absorbed abroad (VAX): home country’s GDP used to satisfy foreign demand, factor content embodied in gross exports crosses national borders at least once;
Domestic value added returned and eventually consumed at home (RDV): not part of a country's exports of value-added, but account for part of the country's GDP, factor content crosses national borders at least twice; (1)+(2) = DVA: GDP in exports
Foreign value added in exports (FVA), part of other countries’ GDP, embodied factor content also crosses national borders at least twice;
Double counted terms due to intermediate goods being traded back and forth that cross border multiple times (PDC), counts no country’s GDP as it is the factor content that has already been counted by at least one of the three components above and crosses national borders at least three times.

7. The Major Contribution of Gross Trade Accounting proposed by KWWZ
By identifying which parts of the gross trade transactions are double counted relative to GDP statistics and what the sources of double counting are, the KWW (and WWZ) method provides a way to correctly interpret gross trade transactions in value-added terms (relative to GDP) and offers a set of summary statistics that quantitatively measure what and how much is double counted for each bilateral/sector trade flow.
All measures of trade in value-added and vertical specialization in the literature, such as the “vertical specialization” measure proposed by Hummels, Ishii and Yi (2001) and “import content of exports” proposed by the National Research Council (2006) can be expressed as linear combinations of various components of the KWW decomposition.

8. Economic interpretation Relation to GDP statistics
The roles of third countries in bilateral trade can be measures by 3 of the 8 detailed components
Core KWW decomposition
Detailed
items
Economic interpretation
Relation to GDP statistics
# of border crossing
VAX_G
Value added exports
DVA_DIR
Domestic VA in production of exports that finally absorbed by trading partner
Home GDP satisfies final demand in partner country
At least once
DVA_IND
Domestic VA in production of exports that finally absorbed by third countries
Home’s GDP satisfies final demand in third countries
 At least twice
RDV_G
Returned DVA
Domestic VA first exported but finally returned home and consumed there
Home’s GDP satisfies own domestic final demand through international trade
FVA
Foreign value added
MVA
Trading partner’s VA used in production of exports that return to and absorbed by partner
Partner’s GDP satisfies final demand in partner country
OVA
Third countries’ VA used in production of exports that finally absorbed by partner
Third countries’ GDP satisfies final demand in partner country
PDC
Pure double counting
ODC
Pure double counting in gross exports sourced from third countries
Non country’s GDP
At least three times
DDC
Pure double counting in gross exports sourced from home
MDC
Pure double counting in gross exports sourced from partner

9. An example of trade decomposition5 1 2 3 4 6 7
Chinese Steel
Japanese
Auto industry
Chinese Consumer
AUS Iron Ore
Consumer US
Japan R&D
China
Re-exports
DVA_DIR: 1-2, DVA_IND: 1-3, RDV_G: 1-4, DDC: 1-5;
MVA: 6-1-2, MDC: 6-1-3/4/5;
OVA: 7-1-2, ODC: 7-1-3/4/5.

10. Preliminary: Inter-Country Input-Output Table
Outputs
Inputs
Intermediate Uses
Final Uses
Total Outputs
Country 1
Country 2 ⋯
Country G 1 2 G
Intermediate Inputs
Z11
Z12
Z1G
Y11
Y12
Y1G X1
Z21
Z22
Z2G
Y21
Y22
Y2G X2 ⋮ ⋱
ZG1
ZG2
ZGG
YG1
YG2
YGG XG
Value Added
VA1
VA2
VAG
𝑿=𝑨𝑿+𝒀
𝑿= (𝑰−𝑨) −𝟏 𝒀
Total Inputs

11. Matrix partition: diagonal and off-diagonal
Y F = 0 ⋯ Y 1g ⋮ ⋱ ⋮ Y g1 ⋯ 0
𝐴 𝐷 = 𝐴 𝐴 ⋯ ⋯ ⋮ ⋮ ⋱ ⋮ ⋯ 𝐴 𝑔𝑔 and 𝐴 𝐹 =𝐴− 𝐴 𝐷
are GN by GN domestic and imported input coefficient matrix respectively
𝑌 𝐷 =𝑌− 𝑌 𝐹

12. Additional Notations
B=(I−A ) −1 :GN by GN global Leontief inverse matrix;
L=(𝐼− 𝐴 D ) −1 : GN by GN local Leontief inverse matrix;
B D = B 11 ⋯ 0 ⋮ ⋱ ⋮ 0 ⋯ B gg ， B F = 0 ⋯ B 1g ⋮ ⋱ ⋮ B g1 ⋯ 0 , X = X 1 ⋯ 0 ⋮ ⋱ ⋮ 0 ⋯ X g
Bs are GN by GN diagonal and off diagonal matrix;
X is a GN by G diagonal block matrix of total outputs.
E:𝐺𝑁 𝑏𝑦 𝐺 𝑚𝑎𝑡𝑟𝑖𝑥 𝑜𝑓 𝑏𝑖𝑎𝑙𝑒𝑟𝑖𝑎𝑙 𝑔𝑟𝑜𝑠𝑠 𝑒𝑥𝑝𝑜𝑟𝑡𝑠
E = Y F + A F L Y D is the exports directly consumed by trade partner without further boarder crossing.
V : GN by GN diagonal matrix of direct value-added coefficients;
Y, 𝑌 𝐷 and 𝑌 𝐹 : GN by G diagonal matrix of final consumption;

13. Local Leontief Inverse Matrices: an analytical tool to isolate pure domestic production
Production and use balance, or the row balance condition: X=f(Y)
𝑋=𝐴 X +𝑌= 𝐴 𝐷 X + 𝑌 𝐷 + 𝐴 𝐹 X +𝑌 𝐹 = 𝐴 𝐷 X + 𝑌 𝐷 +𝐸
=(𝐼− 𝐴 𝐷 ) −1 𝑌 𝐷 +(𝐼− 𝐴 𝐷 ) −1 𝐸 (1)
=𝐿 𝑌 𝐷 +𝐿𝐸 =𝐿 𝑌 𝐷 +𝐿 𝑌 𝐹 +𝐿 𝐴 𝐹 X
Where superscript “D” represents diagonals, “F” represents off diagonals
𝐸= 𝐴 𝐹 X +𝑌 𝐹 = Y F + A F L Y D + A F LE= E + A F LE
=(I− A F L ) −1 E = E + A F L(I− A F L ) −1 E = E + A F B E (2)
Value-added multiplier
V B= V B D + V B F = V L+ V B D −L + V B F (3)

14. Revised KWWZ gross trade flow decomposition to study third country effect
E= V L E + V L A F B E + V B D −L E+ V B F E + V B F A F LE
(4)
u E sr = V s L ss E sr DVA_DIRa + V s L ss A sr t≠s G B rt E tr DVA_DIRb + V s L ss A sr t≠s G B rt u≠s,r G E tu DVA_IND
+ V s L ss A sr t≠s G B rt E ts RDV_G + V s t≠s G B st A ts L ss E sr DDC
+ V r B rs E sr MVA + V r B rs A sr L rr E r MDC + t≠s,r G V t B ts E sr OVA + t≠s,r G V t B ts A sr L rr E r ODC
Where E sr = Y sr + A sr L rr Y rr
(5)
DVA_DIRa is home DVA directly absorbed by partner.
DVA_DIRb is home DVA indirectly absorbed by partner.
RDV_G, DVA_DIRb, DDC, MVA and MDC are all loop effects in the two trading partners

15. How to measure the multilateral factor or third country effect in balterial trade Need analyze more detailed DVA items to find how final demand in third countries impact balterial trade between two trading partners
u 𝐷𝑉𝐴 sr = V s L ss E sr DVA_DIRa + V s L ss A sr t≠s G B rt E tr DVA_DIRb + V s L ss A sr t≠s G B rt u≠s,r G E tu DVA_IND + V s L ss A sr t≠s G B rt E ts RDV_G
E tu = Y tu + A tu L uu Y uu
DAV_IND to gross trade ratio can be used to measure how important the partner country as a transfer planform for the home country’s DVA absorbed in third countries. Not only determined by the production sharing arrangement between the home and partner country; but also driven by final demand in third countries.
(6)

16. How to measure the multilateral factor or third country effect in balterial trade Need analyze detailed components in VS to find how the supply capacities in third countries impact balterial trade between two trading partners
u 𝑉𝑆 sr = V s t≠s G B st A ts L ss E sr DDC + V r B rs E sr MVA + V r B rs A sr L rr E r MDC t≠s,r G V t B ts E sr OVA + t≠s,r G V t B ts A sr L rr E r ODC
(7)
OVA to gross trade ratio can be used to measure how important third countries play in the home country’s export production. Not only drive by final demand in partner country, but also determined by the production sharing arrangement between the home and third countries.
ODC to gross trade ratio can be used to measure how complex the third country effect. It is independent to any countries final demand, and determined by production technology and the production arrangement among home, partner and third countries.

17. What cause the deviation between balance of bilateral trade in gross and in value-added terms?
u E sr − E rs −u[DVA_ G sr −DVA_ G rs ]
=u[ VS sr − VS rs ]
(8)
Proposition
In bilateral trade, only and only if VS embodied in the two way trade equal each other, Balance of Trade (BOT) in gross term and value-added term are the same. The larger the difference of VS between trading partners, the bigger the deviation VA BOT from gross BOT.

18. Multilateral Nature of US-China balterial Trade: Gross Trade
Third country transfer played important role, but decline in recent years

19. Multilateral Nature of US-China balterial Trade: Manufacture
Third country transfer played important role, but decline in recent years

20. Growth of US-China trade in manufacturing products and contribution of third country effects
Period
Trade Value
Contribution of DVA_DIR
Contribution of DVA_IND
Contribution of RDV+DDC+MC
Contribution of OC
US exports to China
10.0
44.2
21.2
17.6
17.1
35.0
40.8
28.9
14.1
16.2
52.7
59.4
15.2
9.7
15.7
China Exports to US
38.5
43.6
3.8
7.0
45.5
183.7
51.2
5.8
5.1
37.9
159.7
57.2
8.9
5.5
28.3
US net imports from China
28.5
43.5
-2.3
3.3
55.5
148.7
53.7
0.3
3.0
43.0
107.0
56.2
3.5
34.6

21. Multilateral Nature of US-China balterial Trade: ICT Products
Third country transfer played important role, but decline in recent years

22. Growth of US-China trade in ICT products and contribution from each component
Period
Trade Value
Contribution of DVA_DIR
Contribution of DVA_IND
Contribution of RDV+DDC+MC
Contribution of OC
US Exports to China
3.8
45.3
17.0
15.3
22.4
8.6
27.9
39.2
10.5
11.1
55.8
28.4
15.6
0.2
China Exports to US
12.2
18.4
3.2
11.3
67.0
76.6
34.2
4.4
7.3
54.2
72.1
52.1
7.1
33.8
US net imports from China
8.5
6.5
-2.9
9.6
86.7
68.0
35.0
0.0
5.3
59.7
61.0
51.4
5.5
39.9

23. The increasing of US net imports from China and contribution of multilateral effects
Period
Net Imports
Contribution of DVA_DIR
Contribution of DVA_IND
Contribution of RDV+DDC+MC
Contribution of OC
All Sectors
35.1
53.8
-1.6
1.6
46.3
172.6
62.2
-1.3
37.5
106.9
60.1
4.4
2.2
33.3
Manufacture
28.5
43.5
-2.3
3.3
55.5
148.7
53.7
0.3
3.0
43.0
107.0
56.2
5.8
3.5
34.6
ICT
8.5
6.5
-2.9
9.6
86.7
68.0
35.0
0.0
5.3
59.7
61.0
51.4
3.2
5.5
39.9

24. Value-added structure of US net imports from China, billion US dollars, 2014 Role of third countries in bilateral trade
Sectors
TEXP
DVA_dir
DVA_ind
RDV
MC+DDC OC
(1) =
(2a)
(2b)
(3)
(4)
(5)
All sectors
Value
335.2
202.8
0.5
-9.7
15.7
125.8
Share
100
60.5
0.2
-2.9
4.6
37.5
Manufacture
301.6
160.5
5.4
-6.1
15.9
126
53.2
1.8
-2.0
5.2
41.8
ICT sector
141.2
56.3
1.7
-2.7
10.7
75.1
39.9
1.2
-1.9
7.6
53.1
Data source: Author computed from OECD ICIO Table with processing trade in China and Mexico

25. Value-added structure of US-China bilateral trade in ICT products, 2014
OVA+ODC is the largest portion of China’s exports. China need use upstream inputs from third countries; DVA_IND is the largest portion of US exports , which are US ICT products imported by China used as inputs to produce China’s ITC exports for third country markets (US exports through China).

26. Change value-added structure of US-China Net imports in ICT products 1995-2014
The difference of value-added structure in China exports to US and US exports to China are the fundamental factor of US-China trade imbalance in ICT products

27. What we can learn from the decomposition
The results not only reveal the misleading nature of balance of trade computed from gross trade statistics but also the sources of the error.
Based on the value added method, in 2014, US-China bilateral balance of manufacturing trade is only about 55% of what is indicated by the gross trade data. Domestic value-added absorbed by importing countries (US here) only took 53% (column 2a) of the total gross imbalance;
US actually ran surplus in terms (3): there are more US value-added in US exports to China re-export by China back to US than Chinese value added in China export to US re-export by US back to China, indicating that US intermediate exports producers are located more upstream in various GVCs than Chinese firms;
The rest came from third country effects:
42% due to Chinese exports to the US using more value-added from third countries than that in US exports to China (column 5+6);
4.1% due to Chinese exports to the US including more US value added than Chinese value-added embodied in US exports to China (column 4);
1.1% due to more double counting in China’s exports to the US than that in US exports to China (column 7), indicating Chinese value-added has more border crossing than US value-added before they reach their final consumers.

28. Multilateral Nature of Germany-US balterial Trade: Total
Germany also important base for US MNE
affiliates export to rest of the world, especially
other EU countries

29. Multilateral Nature of Germany-US balterial Trade: Motor Vehicles
Third country effects play increasingly important role in US net auto imports from Germany

30. Value-added Structure of US net imports from Germany, 2014
Sectors
TEXP
DVA_dir
DVA_ind
RDV
MC+DDC OC
(1) =
(2a)
(2b)
(3)
(4)
(5)
All sectors
Value
40.6
30.0
-8.1
-2.2
2.6
18.1
Share
100
74.0
-19.9
-5.4
6.6
44.7
Manufacture
54.8
34.7
0.5
-0.8
2.4 18
63.2
0.9
-1.5
4.5
32.9
Motor vehicles sector
26.4
16.9
1.3
-0.1
0.8
7.5
64.1
5.0
-0.4
3.1
28.2
Data source: Author computed from OECD ICIO Table without considering processing trade

31. Change value-added structure of US net imports from Germany 1995-2014

32. Change role of third countries on US-Germany trade balance in ICT products 1995-2014
增加一个DVA_IND占比高的部门

33. Change role of third countries on US-Japan bilateral trade in Auto and Auto part 1995-2014
The difference of value-added structure in China exports to US and US exports to China are the fundamental factor of US-China trade imbalance in ICT products

34. What we can learn from the decomposition
US-China balterial trade is not special. Similar pattern also can be observed in US-Germany and many other bilateral trade routes;
A special feature of US net imports from Germany is that there is much larger portion of US intermediate goods export to Germany were re- exported back to US or to third countries than that in US imports from Germany (Column 2b and 3), in these two portions US actually ran a large surplus, especially in services sectors, further demonstrating the complex composition and offsetting factors inside gross net trade flows.
Both supply capacity and final demand in third countries increased their impacts on the balance of trade of auto between US and Japan in recent years.
This implies that net bilateral imports no longer be a uniform measure for import penetration as the time when final good trade dominate, since its value-added structure can vary significantly across country/sector and bilateral routes in the age of global value chains.
This also implies that any bilateral trade policy change will have a third country effect that policy maker can not overlook.

35. Value-added structure of US-Mexico bilateral trade 2014

36. Value-added structure of US-Canada bilateral trade 2014

37. Value-added structure of UK-Ireland bilateral trade
2014

38. VA structure of UK-France bilateral trade
2014

39. The country source of third country effect (supply side) in US net imports from China, Germany and Japan; 2014
Exports Sector
Net Imports
(Billions USD)
OVA (%)
Value Source Countries of the Multi Effect
High income (%)
Upper middle income (%)
Lower middle income (%)
(1)
Share in (1)
(2)
Share in (2)
(3)
(4)
(5)
USA Net Imports from Germany
Manufacture
54.81
32.88
79.80
11.19
9.02
LTI
-1.25
-17.01
45.48
30.43
24.09
MTI
-1.30
-34.37
135.22
-39.61
4.39
HTI
57.35
30.28
76.67
13.42
9.91
USA Net Imports from Japan
30.59
19.66
29.86
38.30
31.84
-16.56
15.08
55.50
27.86
16.64
-0.94
23.03
100.11
51.58
-51.68
48.09
18.16
38.85
35.18
25.97
USA Net Imports from China
301.59
41.76
70.92
11.09
17.99
53.60
26.01
56.51
15.90
27.59
34.87
25.98
59.38
13.92
26.70
213.12
48.30
72.90
10.28
16.82
需不需要考虑价值来源部门？

40. The country sources of OVA (third country supply):
For Germany, mainly from high income countries, about 80%, while 10% from high and low middle countries each;
For China, about 70% from high income countries and the percentage increase as technology intensity increase, least from countries in the same income group at about 10%,
Japan is different, about 40% from middle high income countries, each 30% from high and middle low income countries.

41. The Geographic Sources of Third Country Effects in Global Trade
Emerging economies play increasing role in third country effect, especially China, increased 5 times.
While the share contributed US, Japan and Gemerny declined from 40% in 1995 to less than 30% in 2014

42. Summary and Conclusion
National income accounts record domestic output in value added terms but standard trade statistics record trade in gross terms. Our method is the first one in the literature to reveal the significant role that third countries have played in balterial trade relations in the age of global value chains that has been masked by official trade statistics.
We apply KWWZ gross trade accounting framework and revise the decomposition by regroup the detailed items in their original decomposition formula to make it suitable to measure the role of multiterminal factor in bilateral trade. Apply our method to most recent version of OECD ICIO table, we show that net bilateral imports no longer be a uniform measure for import penetration and trade shocks as the time when final good trade dominate, since its value- added structure can vary significantly across country/sector and bilateral routes in the age of global value chains. Because the multileral nature of modern trade, the goal of trade policies should not be focus on bilateral trade balances but instead on eliminating trade barriers along GVCs, including what behind national borders.

43. The roles of third countries in bilateral trade can be measures by 3 of the 8 detailed components
DAV_IND to gross trade ratio is used to measure how important the partner country as a transfer planform for the home country’s DVA absorbed in third countries. Not only determined by the production sharing arrangement between the home and partner country; but also driven by final demand in third countries.
OVA to gross trade ratio is used to measure how important third countries play in the home country’s export production. Not only drive by final demand in partner country, but also determined by the production sharing arrangement between the home and third countries.
ODC to gross trade ratio is used to measure how complex the third country effect. It is independent to any countries final demand, and determined by production technology and the production arrangement among home, partner and third countries.

44. Thank you for your attention!
Zhi Wang, Professor and Dean, Research Institute of Global Value Chain, University of International Business Economics
Research Professor and Senior Policy Research Fellow, Schar School of Policy and Government, George Mason University
Website:
UIBE GVC indictor database:
When use this database, please make a Reference to: UIBE GVC Index Team, “Data files structure of the UIBE GVC index system”
Any questions and suggestions about UIBE GVC Index, please contact GVC index team at UIBE.
Contact: team leader, Professor Fei Wang;
The 2017 GVC development report:
and-analyzing-the-impact-of-gvcs-on-economic-development
The discussion of the 2017 GVC development report at Brookings

45. Major Reference
Koopman, R., Wang, Z., Wei, S.J. (2014). Tracing Value-Added and Double Counting in Gross Exports. American Economic Review, 104(2),
Lawrence, Z. Robert (2018) “Five Reasons Why the Focus on Trade Deficits Is Misleading” Policy Brief, 18-6, Peterson Institute of International Economics.
Los, B., M. P. Timmer, and G. J. de Vries (2016): “Tracing Value-Added and Double Counting in Gross Exports: Comment,” The American Economic Review, 106, 1958–1966.
Wang, Z., Wei, S.J., Zhu, K. (2013). Quantifying international production sharing at the bilateral and sector levels. NBER Working Paper No
Leontief, W. (1936). Quantitative input and output relations in the economic system of the United States. The Review of Economic and Statistics, 18,
Trade in Value-Added — Developing New Measures of Cross Border Trade, co- edited with Aaditya Mattoo and Shangjin Wei, CEPR/World Bank, April added-developing-new-measures-cross-border-trade

46. Change role of third countries in US net imports from Germany 1995-2014
目前线有点多，仅保留第三方影响的线?

47. Value-added structure of UK-Gemerny bilateral trade 2014

48. Apply KWWZ method to analyze third country effects in balterial trade
(1)+(2)
Domestic VA absorbed by direct importer
(DVA_DIR)
(5)
Pure double counting from domestic sources
(DDC)
(6)+(7)
Importer content in gross
exports
(MVA+MDC)
(8)+(9)
Other countries content in gross
(OVA+ODC)
(0)
Gross exports
(goods and services)
(E)
(1)+(2)+(3)
Domestic value-added absorbed abroad
(VAX_G)
(6)+(8)
Foreign value-added
(FVA)
(4)
Domestic value-added first exported then returned home
(RDV_B)
(5)+(7)+(9)
Pure double counted terms
(PDC)
Vertical Specialization (VS)
Domestic Value-added (DVA)
Regroup detailed
items based on issue at hand
(3)
Domestic VA absorbed by other countries
(DVA_IND)
E can be at country-sector, country aggregate, bilateral -sector or bilateral aggregate;
both DVA and RDV are based on backward industrial linkages