value added trade: a tale of two concepts - robert stehrer the
TRANSCRIPT
OverviewConceptsNet trade
A tale of two concepts
Value added trade: A tale of two conceptsRobert Stehrer
The Vienna Institute for International Economic Studies (wiiw)
Version: 2012-12-09
December 10-11, 2012 - CompNet workshop
ECB Frankfurt, Germany.
Robert Stehrer, wiiw CompNet Frankfurt
OverviewConceptsNet trade
A tale of two concepts
Overview
• Two concepts of value added ”flows”
? Value added in trade? Trade in value added? But: terminology is used differently
• ”Net trade” in value added
? Total? Bilateral
• Comparison to other related concepts
Robert Stehrer, wiiw CompNet Frankfurt
OverviewConceptsNet trade
A tale of two concepts
Multi-national accounting and indicators of production fragmentation
• Narrow and broad offshoring measure (Feenstra and Hanson, 1999)
• Vertical specialization (Hummels et al., 2001)
• Foreign and domestic value added content of exports (...)
• Value added exports (Johnson and Noguera, 2012)
• Decomposition of value added exports (Koopman et al., 2010; Stehrer, 2012b)
• Trade balances in VA terms (Stehrer, 2012a)
• Factor content of trade with traded intermediates (Trefler and Zhu, 2010)
• Global value chain approach (Timmer et al., 2012)
• International upstreamness/downstreamness, Distance to consumer (Antras etal. 2012; Fally, 2012)
• Average propagation length (Dietzenbacher, 2007)
Robert Stehrer, wiiw CompNet Frankfurt
OverviewConceptsNet trade
A tale of two concepts
A tale of two concepts
• Two concepts of value added ”flows” across countries
∗ Domestic and foreign value added embodied in a country’s gross
exports/imports:
? Akin to Hummels et al. (2001) VS1 measure (in VA terms rather than gross output terms)
? Consideration from supply side (where inputs are sourced from)
∗ Value added created in one country due to consumption in other
countries:
? Consideration from demand side (value added created for consumption abroad)
• Concepts are closely tied to each other
• Provides insights in estimating bilateral value added flows and double counting
Robert Stehrer, wiiw CompNet Frankfurt
OverviewConceptsNet trade
A tale of two concepts
Concepts
Net trade in gross terms
NXrs = Xrs −Mrs = Xrs −Xsr
NXr = Xr −Mr =∑s
Xrs −∑s
Mrs =∑s
Xrs −∑s
Xsr
Robert Stehrer, wiiw CompNet Frankfurt
OverviewConceptsNet trade
A tale of two concepts
Domestic and foreign value added content of exports and imports(Value Added in trade - VAiT)Domestic and foreign value added embodied in a country’s exports and imports
Other terminology: ...
DomVAiXr = (vr )′(I− A)−1xr
ForVAiXr = (v−r )′(I− A)−1xr
DomVAiMr = (vr )′(I− A)−1mr
ForVAiMr = (v−r )′(I− A)−1mr
DirForVAiMr = trace(
(v̂−r )′(I− A)−1m̂r)
• Expressed as a share of exports in gross terms (or imports)
• By definition: X = DVAiX + FVAiX
• Akin to Hummels et al. (2001) VS measure
Robert Stehrer, wiiw CompNet Frankfurt
OverviewConceptsNet trade
A tale of two concepts
Consider country 1
Value added content of exports
VAiX1 = v̂Lx̂1
v1l11x1∗ v1l120 v1l130v2l21x1∗ v2l220 v2l230v3l31x1∗ v3l320 v3l330
=
VAiX1∗(1) 0 0
VAiX1∗(2) 0 0
VAiX1∗(3) 0 0
Value added content of imports from 2 and 3
VAiM1 = v̂Lm̂1
v1l110 v1l12x21 v1l13x31
v2l210 v2l22x21 v2l23x31
v3l310 v3l32x21 v3l33x31
=
0 VAiX21(1) VAiX31(1)
0 VAiX21(2) VAiX31(2)
0 VAiX21(3) VAiX31(3)
Robert Stehrer, wiiw CompNet Frankfurt
OverviewConceptsNet trade
A tale of two concepts
This concept is closely related to VS measures (e.g. Hummels et al., 2001) - theimport content of exports:
FVAiXr = (v−r )′Lxr =∑s,s 6=r
(vs)′Lsrxr∗ in % of gross (=value added) exports
Relates to HIY VS1 measure (based on world IO table):
VS2r = (1−r )′Lxr =∑s,s 6=r
1′Lsrxr∗ in % of gross output needed for exports
If based on domestic and import IO tables:
VS1r =∑s,s 6=r
1′Asr L̃rrxr∗ in % of gross exports
Robert Stehrer, wiiw CompNet Frankfurt
OverviewConceptsNet trade
A tale of two concepts
Resulting measures are quite similarComparison of three indicators, 2007
0.30
0.40
0.50
0.60
0.70
VS1 (HIY) VS2 FVAiX
0.00
0.10
0.20
RU
S
BR
A
US
A
AU
S
JPN
IDN
GB
R
IND
CA
N
ITA
CH
N
FR
A
RO
U
DE
U
CY
P
GR
C
ES
P
TU
R
ZR
OW
ME
X
LVA
PR
T
LTU
SW
E
FIN
PO
L
AU
T
KO
R
NLD
DN
K
EST
IRL
SV
N
BE
L
BG
R
MLT
CZ
E
TW
N
SV
K
HU
N
LUX
Source: WIOD; author’s calculations
Robert Stehrer, wiiw CompNet Frankfurt
OverviewConceptsNet trade
A tale of two concepts
Evolution of vertical specialisation (VS2), 1995 and 2007
20.0
25.0
30.0
35.0
40.0
45.0
50.0
1995 2007
0.0
5.0
10.0
15.0
20.0
BRA
RUS
JPN
AUS
USA
IDN
CHN
IND
GBR
ITA
TUR
FRA
KOR
ROU
DEU
GRC
LVA
CYP
CAN
ESP
PRT
POL
FIN
SWE
LTU
ROW
AUT
NLD
BGR
MEX
DNK
EST
IRL
TWN
BEL
CZE
SVN
LUX
SVK
HUN
Source: WIOD; author’s calculations
Robert Stehrer, wiiw CompNet Frankfurt
OverviewConceptsNet trade
A tale of two concepts
Sourcing structure of foreign content of exports, 1995 and 2007
40%
50%
60%
70%
80%
90%
100%
ASIA BRIIAT CHN EU12 EU15 NAFTA ROW
0%
10%
20%
30%
40%
1995 2009 1995 2009
EU-12 EU-15
Source: WIOD; author’s calculations
Robert Stehrer, wiiw CompNet Frankfurt
OverviewConceptsNet trade
A tale of two concepts
Trade in value added (TiVA)Value added created in a country due to final consumption elsewhere
Other terminology: ...
Value added exports (VAX) - J&N (2012) - are defined as
VAXr = (vr )′(I− A)−1f−r
Analogously, the value added imports (VAM) can be defined as
VAMr = (v−r )′(I− A)−1f r
• Expressed relative to gross exports (VAX ratio; Johnson and Noguera, 2012)
Robert Stehrer, wiiw CompNet Frankfurt
OverviewConceptsNet trade
A tale of two concepts
Consider country 1
Value added created in 1 due to final consumption (domestic andimported) in 2 and 3
VAXr = (v1 0 0)L
0 + f 12 + f 13
0 + f 22 + f 23
0 + f 23 + f 33
Value added created in 2 and 3 due to final consumption (domestic andimported) in 1
VAMr = (0 v2 v3)L
f 11 + 0 + 0f 21 + 0 + 0f 31 + 0 + 0
Robert Stehrer, wiiw CompNet Frankfurt
OverviewConceptsNet trade
A tale of two concepts
A comparison
40.0
50.0
60.0
70.0
80.0
90.0
100.0
Domestic value added content of exports (DVAiX) Value added exports (TiVAx)
0.0
10.0
20.0
30.0
40.0
RU
S
BR
A
AU
S
IDN
JPN
GB
R
US
A
IND
CA
N
ITA
CH
N
RO
U
CY
P
FR
A
GR
C
WO
RLD
TU
R
DE
U
ME
X
ES
P
LVA
PR
T
LTU
SW
E
FIN
PO
L
AU
T
ZR
OW
KO
R
NLD
DN
K
ES
T
IRL
SV
N
BE
L
BG
R
MLT
TW
N
CZ
E
SV
K
HU
N
LUX
Source: WIOD; author’s calculations
Robert Stehrer, wiiw CompNet Frankfurt
OverviewConceptsNet trade
A tale of two concepts
On (bilateral) net trade in gross and value added terms
Robert Stehrer, wiiw CompNet Frankfurt
OverviewConceptsNet trade
A tale of two concepts
Net trade(For details see Stehrer, 2012a)
NXr = Xr −Mr
NTiVAr = VAXr −VAMr
NVAiTr = (DomVAiXr + ForVAiXr ) − (DomVAiMr + ForVAiMr )
NXr = NTiVAr = NVAiTr
NVAiTr = v′Lt = 1′(I− A)(I− A)−1t = 1′t = NXr with t =
x1∗
−x21
−x31
NTiVAr = vrLf−r − v−rLfr
= vrLf−r + vrLfr − vrLfr − v−rLfr
= vrLf − vLfr
= vry − 1′fr
= y r − 1′fr
= NXr
Robert Stehrer, wiiw CompNet Frankfurt
OverviewConceptsNet trade
A tale of two concepts
y r = 1′
f rr
fsr
ftr
+
trs + trt
−tsr−ttr
= 1′
f rr + trs + trt
fsr − fsr − zsr
ftr − ftr − ztr
= 1′
f rr + f rs + f rt
00
+
zrs + zrt
−zsr−ztr
Robert Stehrer, wiiw CompNet Frankfurt
OverviewConceptsNet trade
A tale of two concepts
Bilateral:NXrs 6= NTiVArs
For VAiT concept not straightforward how to define bilateral net trade:
NVAiT12 = v̂Lt̂12 =
v1l11t12 −v1l12t21 0v2l21t12 −v2l22t21 0v3l31t12 −v3l32t21 0
Under conditions - ”symmetry” and ”adding-up” - that
NVAiTrs = −NVAiTsr and∑s
NVAiTrs = NVAiTr
it holds that∑s
NXrs =∑s
NVAiTrs =∑s
NTiVArs 6=∑s
DirNVAiTrs
Robert Stehrer, wiiw CompNet Frankfurt
OverviewConceptsNet trade
A tale of two concepts
Results2005, bn US-$
TWNKORJPNRUS
BRAIDNAUSTUR
ZROW
INDCANMEX
EU−27
USA
CHNRUS
JPN
INDKORBRAIDNTWNMEX
TURCANAUS
USA
ZROW
AUSIDN
INDBRACANTURCHNRUSMEX KOR
ZROW
EU−27
TWN
USA
CHN
EU−27
CANZROW
JPN
MEXINDTWN
BRAKORIDNTUR
RUS
AUS
−50
0
50
100
150
−50
0
50
100
150
0
20
40
60
−150
−100
−50
0
−50 0 50 100 150 −50 0 50 100 150
0 20 40 60 −150 −100 −50 0
CHN EU27
JPN USA
Trade in value added
Value added in trade
Robert Stehrer, wiiw CompNet Frankfurt
OverviewConceptsNet trade
A tale of two concepts
Trade balances
• A countries trade balance in VA terms equals trade balance in grosstrade
∗ As reflects a country’s savings
∗ However, in bilateral terms this is different
∗ Trade balances by factors of production
US bilateral trade deficits (in bn US-$) Trade balances by factor (in bn US-$)
-160
-140
-120
-100
-80
-60
-40
-20
0
20
EU
27
Ch
ina
Ro
W
Ca
na
da
Jap
an
Me
xic
o
Ind
ia
Taiw
an
Ko
rea
Ru
ssia
Bra
zil
Ind
on
esi
a
Tu
rke
y
Au
stra
lia
Gross terms VA terms
-600.0
-400.0
-200.0
0.0
200.0
400.0
Capital High Medium Low
-160
-140
EU
27
Ch
ina
Ro
W
Ca
na
da
Jap
an
Me
xic
o
Ind
ia
Taiw
an
Ko
rea
Ru
ssia
Bra
zil
Ind
on
esi
a
Tu
rke
y
Au
stra
lia
-800.0
-600.0
USA EU27 China
Source: WIOD; author’s calculations
Robert Stehrer, wiiw CompNet Frankfurt
OverviewConceptsNet trade
A tale of two concepts
A tale of two concepts? A decomposition
Robert Stehrer, wiiw CompNet Frankfurt
OverviewConceptsNet trade
A tale of two concepts
A comparison
40.0
50.0
60.0
70.0
80.0
90.0
100.0
Domestic value added content of exports (DVAiX) Value added exports (TiVAx)
0.0
10.0
20.0
30.0
40.0
RU
S
BR
A
AU
S
IDN
JPN
GB
R
US
A
IND
CA
N
ITA
CH
N
RO
U
CY
P
FR
A
GR
C
WO
RLD
TU
R
DE
U
ME
X
ES
P
LVA
PR
T
LTU
SW
E
FIN
PO
L
AU
T
ZR
OW
KO
R
NLD
DN
K
ES
T
IRL
SV
N
BE
L
BG
R
MLT
TW
N
CZ
E
SV
K
HU
N
LUX
Source: WIOD; author’s calculations
Robert Stehrer, wiiw CompNet Frankfurt
OverviewConceptsNet trade
A tale of two concepts
Decomposition of a country’s gross exports into VA components(For details see Stehrer, 2012a)
• Applying decomposition method of Koopman et al. (2010) at bilateral level
• 2 countries, aggregate level
Using VAiT concept:
VA(e12) = VA(a12x2 + f 12) = v1l11f 12 + v2l21f 12 + v1l11a12x2 + v2l21a12x2
Applying property of inverse matrices (XX−1 = I)
VA(e12) = v1l11f 12 + v1l12f 22︸ ︷︷ ︸VAX12
+ v1l12f 21 + v1l12a21x1︸ ︷︷ ︸DVAiM12︸ ︷︷ ︸
DVAiX12
+ v2l21f 12 + v2l21a12x2︸ ︷︷ ︸FVAiX12
Robert Stehrer, wiiw CompNet Frankfurt
OverviewConceptsNet trade
A tale of two concepts
VA(e12) = v1l11f 12 + v1l12f 22︸ ︷︷ ︸VAX12
+ v1l12f 21 + v1l12a21x1︸ ︷︷ ︸DVAiM12︸ ︷︷ ︸
DVAiX12
+ v2l21f 12 + v2l21a12x2︸ ︷︷ ︸FVAiX12
VA(e21) = v2l21f 11 + v2l22f 21︸ ︷︷ ︸VAX21
+ v2l21f 12 + v2l21a12x2︸ ︷︷ ︸DVAiM21︸ ︷︷ ︸
DVAiX21
+ v1l12f 21 + v1l12a21x1︸ ︷︷ ︸FVAiX21
• Note: DVAiM12 = FVAiX21 and DVAiM21 = FVAiX12
• DVAiM and FVAiX are double-counted in trade statistics
• For GDP only FVAiX is double-counted
• Difference in VAiT and TiVA concept is whether or not DVAiM (”returned VA”)is included or not
• Net trade: NTiVA = VAX12-VAX21=NX
Robert Stehrer, wiiw CompNet Frankfurt
OverviewConceptsNet trade
A tale of two concepts
This generalizes to 3 (and more) countries
VA(e12) = v1 l11f 12 + v1 l12f 22 + v1 l13f 32︸ ︷︷ ︸VAX12
+ v1 l12f 21 + v1 l12a21x1︸ ︷︷ ︸DVAiM12
+ v2 l21f 12 + v2 l21a12x2︸ ︷︷ ︸FVAiX12(2)
+ v3 l31f 12 + v3 l31a12x2︸ ︷︷ ︸FVAiX12(3)︸ ︷︷ ︸
FVAiX12
+(v1 l12f 23 + v1 l12a23x3)− (v1 l13f 32 + v1 l13a32x2)
• Additional terms (capturing third-country value added trade flows) cancel outwhen summing over partner countries
• Similar when calculating bilateral and total net trade
• Thus, at aggregate level same results as for TiVA concept
• When applying again property of inverse matrices, this results inX=DVAiX+FVAiX
Robert Stehrer, wiiw CompNet Frankfurt
OverviewConceptsNet trade
A tale of two concepts
Relationship to VAiT concept
VA(e12) + VA(e13) = v1 l11f 12︸ ︷︷ ︸DVAiFDX12
+ v1 l11a12x2︸ ︷︷ ︸DVAiIIX12︸ ︷︷ ︸
DVAiX12
+ v1 l11f 13︸ ︷︷ ︸DVAiFDX13
+ v1 l11a13x3︸ ︷︷ ︸DVAiIIX13︸ ︷︷ ︸
DVAiX13
+
v2 l21f 12 + v2 l21a12x2︸ ︷︷ ︸FVAiX12(2)
+ v3 l31f 12 + v3 l31a12x2︸ ︷︷ ︸FVAiX12(3)︸ ︷︷ ︸
FVAiX12
+
v3 l31f 13 + v3 l31a13x3︸ ︷︷ ︸FVAiX13(3)
+ v2 l21f 13 + v2 l21a13x3︸ ︷︷ ︸FVAiX13(2)︸ ︷︷ ︸
FVAiX12
= DVAiX1 + FVAiX
1
• Summing up and applying property of inverse matrices again results in VAiT
concept
• Justifies to use total (i.e. intermediates and final goods) exports
• Special case: An oil-exporting country would also export ’domestic value added’
• This approach allows to computationally cheaper decomposition
Robert Stehrer, wiiw CompNet Frankfurt
OverviewConceptsNet trade
A tale of two concepts
Selected results on double counting
Decomposition for world, by yearin % of gross exports
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��������'������������()����
*+,����� -���������������'��������� ������'������������()����
Source: WIOD; author’s calculations
Robert Stehrer, wiiw CompNet Frankfurt
OverviewConceptsNet trade
A tale of two concepts
Decomposition for selected countries, 2007in % of gross exports
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Source: WIOD; author’s calculationsRobert Stehrer, wiiw CompNet Frankfurt
OverviewConceptsNet trade
A tale of two concepts
Summary
• Two concepts of ”value added trade” considered
• Different concepts - different interpretations - similar outcomes
∗ Supply side considerations (VS)
∗ Demand side
• Net trade positions are unchanged in aggregate, but not bilateral
• Decomposition yields further insights
∗ Relation between supply and demand concepts
∗ For bilateral considerations
∗ Computational methods
Robert Stehrer, wiiw CompNet Frankfurt
OverviewConceptsNet trade
A tale of two concepts
(Related) References
• Antras, P., D. Chor, T. Fally and R. Hillberry (2012), Measuring Upstreamness of Production and TradeFlows, NBER Working Papers 17819.
• Daudin, G., Rifflart, C. and Schweisguth., D. (2011), ”Who Produces for Whom in the World Economy?”,Canadian Journal of Economics 44(4):1409-1538, November.
• Dietzenbacher E., and Romero, I. (2007), ”Production chains in an interregional framework: identificationby means of average propagation lengths”, International Regional Science Review, 362-383.
• Feenstra, R.C. and G.H. Hanson, 1999. The impact of outsourcing and high-technology capital on wages:Estimates for the United States, 1979-1990. Quarterly Journal of Economics, 114, 907-941.
• Fally, T. (2012), On the Fragmentation of Production in the US, University of Colorado-Boulder, July 2012.
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Robert Stehrer, wiiw CompNet Frankfurt