value added trade: a tale of two concepts - robert stehrer the

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



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




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)





• 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




Concepts

Net trade in gross terms

NXrs = Xrs −Mrs = Xrs −Xsr

NXr = Xr −Mr =∑s

Xrs −∑s

Mrs =∑s

Xrs −∑s

Xsr




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




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)




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




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




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





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





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)




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




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





On (bilateral) net trade in gross and value added terms




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




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




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




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




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





A tale of two concepts? A decomposition




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





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




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




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




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




Selected results on double counting

Decomposition for world, by yearin % of gross exports

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�� !� #�!" $#!& %! �!# �!$ #!% &!� ##!& ��!" !& ��!" ��!"

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��'��()��

*+,�� -��'�� '��()��





Decomposition for selected countries, 2007in % of gross exports

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�+� �'!) &(! &'!% !% (! '!( '! �&!& " !$ ")!� ''! '$!% ")!�

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5�6�� 7��89��

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Source: WIOD; author’s calculationsRobert Stehrer, wiiw CompNet Frankfurt



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




(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.

• Hummels, D., J. Ishii, and K.M. Yi (2001), The Nature and Growth of Vertical Specialization in WorldTrade, Journal of International Economics, 54(1).

• Johnson, R.C. and G. Noguera (2012), Accounting for Intermediates: Production Sharing and Trade inValue Added, Journal of International Economics, 87, 105-111.

• Koopman, R.,W. Powers, Z.Wang, and S.-J.Wei (2010). Give credit where credit is due: Tracing valueadded in global production chains. NBER Working Paper 16426.

• Los, B., Dietzenbacher, E., Stehrer, R., Timmer, M. and De Vries, G. (2012), ”Trade performance ininternationally fragmented production networks: Concepts and measures”, WIOD Working Paper No 11.

• Meng, B., Fang, Y. and Yamano, N. (2012), ”Measuring global value chains and regional economicintegration: an international input-Output approach”, IDE Discussion Paper No 362, July 2012.

• OECD - WTO (2012), Trade in Value-Added: Concepts, Methodologies and Challenges, www.oecd.org.

• Stehrer, R. (2012a), Trade in Value Added and the Value Added in Trade, wiiw Working Paper No. 81,Vienna.

• Stehrer, R. (2012b), A Note on Double-Counting in Bilateral (Value Added) Trade, wiiw Working Paper,forthcoming.

• Trefler, D. and S. Zhu (2010). The structure of factor content predictions. The Journal of InternationalEconomics 82, 195207.

• Timmer, M., B. Los, R. Stehrer and G. deVries (2012), Fragmentation, Incomes and Jobs. An analysis ofEuropean competitiveness, in preparation.


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