Lecture 6 Advanced topics in international trade The ...The Vertical Fragmentation of Production JulienMartin(IRES-UCLouvain) IsabelleMéjean(EcolePolytechnique,CREST,CEPR) APE-ENSAE,December7th

Lecture 6Advanced topics in international trade

The Vertical Fragmentation of Production

Julien Martin (IRES-UCLouvain)Isabelle Méjean (Ecole Polytechnique, CREST, CEPR)

www.julienmartin.eu

APE-ENSAE, December 7th 2012

Martin, J. & Méjean, I. (2012) () Fragmentation of production 2012 1 / 32

Outline

Outline

• Introduction: Definitions, Example, and Research Questions

• Measuring international fragmentationHummels, Ishii, Yi 2001; Johnson, Noguera 2012; Johnson,Noguerra 2012 bis

• Measuring the upstreamness of productionFally 2011; Antras, Chor 2011; Antras, Chor, Fally, Hillberry 2012

• Conclusion


Introduction

• Firms may decide to buy inputs from a supplier: outsourcing• They may choose to produce inputs in a foreign country:offshoring/vertical integration. This induces intra-firmtrade between related parties.

• They may prefer buying intermediate inputs to a foreignsupplier: foreign outsourcing

Firms and countries are specialized in different stages of production.1

The facilitation of international trade has enhanced the global divisionof production sequences. The phenomenon as been called verticalspecialization by Balassa and Findlay, slicing up the value chainby Krugman, fragmentation, production sharing...

1Costinot, Vogel, and Wang (2012) notice this is reminiscent to the division ofoperations, all performed by distinct hands - Adam Smith 1776.


Introduction

GDP and Exports: Conceptually Different

• GDP Singapore 2004: $133 billion

• Total exports Singapore 2004: $202 billion

⇒ value vs value-added


Introduction�� !�"��#$%��&��'��(�)�� $*+��*%�&��'��,�-��$ ��. ��* ��/��0��1��23��3��4�5��6�7�18��9�:�#*+$;��$*+<�=*��$>�&��'�� ?�*; $�$*#; ��*�@�?��@A��(B�71CD��E��F�5��2G3�"$H;$�� #�I �$�$#9Figure: Antras, 2012. Grossman-Hart (1986) Goes Global.


Introduction

Research questions

• Intermediate inputs: two thirds of international trade.This raises several questions. Topics relatively unexplored until 2-3years.

• Is production more fragmented?• Figures on trade flows and trade balances do not account for interna-tional fragmentation. Why not considering the value-added contentof trade flows rather than their gross value?

• What are the determinants of international fragmentation (JohnsonNoguera 2012, Yi 2003)?

• Are countries specializing in specific stages of the global production(Antras, Chor, Fally, Hillbery, 2012)?

• Is the trade collapse during the Great crisis due to global fragmenta-tion?

⇒ To answer, we need a measure of fragmentation of production


J&N 2012

Measuring vertical specialization

• Hummels, Ishii, and Yi (HIY; JIE 2001) ⇒ first paper measuring the leveland evolution of vertical specialization in world trade. They measure theimported input content of exports. This methodology implicitly assumes thatcountries’ exports are entirely absorbed by the final demand abroad.

• Johnson & Noguera (JIE 2012) ⇒ improve HIY methodology to allow fortwo-way trade in intermediates (intermediates produced in A, exported toB, used to produce another intermediate, exported from B to A).

• Johnson & Noguera (2012 bis) generalize HIY, we focus on it in this lecture


J&N 2012

Johnson Noguera (2012)

• S sectors, N countries, 1 variety by sector-country• Production, sector s, country i : qi (s)

• Production is directed to both final and intermediate consumption,both at home and abroad

• Final consumption, produced in country i , consumed in j : qcij(s)

• Intermediate consumption sector s, used in sector t: qmij (s, t)

• Market clearing for quantities produced by country i , sector s:

qi (s) =∑

j

qcij(s) +

∑s

∑j

qmij (s, t)

• Expressed at current prices:

yi (s) =∑

j

cij(s) +∑

s

∑j

mij(s, t)

• Exports from i to j in sector s: xij(s) = cij(s) +∑

s mij(s, t)


J&N 2012

Johnson Noguera (2012) - Algebra

• S × 1 vector of production, in country i : yi

• S × 1 vector of demand, in country j for goods from i : cij

• Aij : S × S IO matrix, with elements Aij(s, t) = mij(s, t)/yj(t)

→ inputs from sector s country i used by j to produce 1 unit of t• Total use of inputs from i by j : Aijyj

• One further writes:

A ≡

A11 A12 ... A1NA21 A22 ... A2N...

.... . .

...AN1 AN2 ... ANN

; y ≡

y1y2...

yN

; cj ≡

c1jc2j...

cNj


J&N 2012

Johnson Noguera (2012) - Algebra

• The global market clearing condition writes:

y = Ay +∑

j

cj or y =∑

j

(I − A)−1cj

• with (I − A)−1 =∑+∞

k=0 Ak

• In words: total consumption is the direct output absorbed + the outpoutused to produce a final good + the output used to build the intermediateused to build a final good + ...

• We can define the quantity from country i consumed in j , either directly(exports of final goods or exports of inputs used to produce "domestic" finalgoods) or through exports from third countries incorporating inputs fromcountry i

y1jy2j...

yNj

≡ (I − A)−1cj


J&N 2012

Johnson Noguera (2012) - Definitions

• The value added to output ratio for sector t country i is:

ri (t) = 1−∑

j

∑s

Aji(s, t)

Def .1 country i ’s value added absorbed in country j is:

vaij =∑

s

vaij(s) =∑

s

ri (s)yij(s)

Def .2 the sector level bilateral value added to exports ratio is:

vaij(s)/xij(s)

Def .2 the aggregate bilateral value added to exports ratio is:

vaij/ιxij

where ι is a 1× S vector of ones


J&N 2012

Johnson Noguera (2012) - Example

• 1 sector, 3 countries: the US (1), China (2), Japan (3)• China imports inputs from the US and Japan• China exports the final good (say an iPad) to the US only• US and Japan export only intermediate goods• The production can be represented as:

y1y2y3

≡α11 α12 0

0 α22 00 α32 α33

y1y2y3

+

c11c22 + c21

c33

→ in the US, part of the production is used to produce the intermediate good, part is

used by China to produce good 2, and the last part is consumed by US consumers

→ in China, part of the production is used to produce the final good, the rest isconsumed in China and in the US

→ in Japan, part of the production is used to produce the intermediate good, partis used by China to produce good 2, and the last part is consumed by Japaneses


J&N 2012

Johnson Noguera (2012) - Example

• This yields to the following system:

y1 =1

1− α11c11 +

α12

(1− α11)(1− α22)c21︸︷︷︸

y11

+α12

(1− α11)(1− α22)c22︸︷︷︸

y12

y2 =1

1− α22c21︸︷︷︸

y21

+1

1− α22c22︸︷︷︸

y22

y3 =1

1− α33c33︸︷︷︸

y33

+α32

(1− α33)(1− α22)c22︸︷︷︸

y32

+α32

(1− α33)(1− α22)c21︸︷︷︸

y31

• Trade and VA balances:

tb12 = x12 − x21 and vab12 = (1− α11)y12 − (1− α12 − α22 − α32)y21

• After simple computations: tb12 + α32y21 = vab12

⇒ The value added deficit between the US and China is smaller than thetrade deficit : China’s trade contains Japanese content


J&N 2012

Johnson Noguera (2012) - Data

• GTAP 7.1 database• Info on balance of payment statistics (World Bank / IMF)• Info on Bilateral trade (COMTRADE)• Info on: Input-Output tables (national sources)• 57 sectors, 94 countries, in 2004

• Drawback 1: IO data are not bilateral ⇒ proportionality assumptions (madefor IO domestic/imports too)

• Drawback 2: The input content of domestic production and exports issupposed to be the same


J&N 2012

Johnson Noguera (2012) - Results

• First compute the multilateral value added to exports ratio⇒ large variations across countries: does it reflect the sector specialization of

countries or differences in the VAX ratio within sectors, between countries?⇒ Mainly the composition of exports, but rich countries tend to export with

higher VAX ratio in manufacturing industries

• Then, they compute the bilateral value added export ratio⇒ a given exporter has very different VAX for a given sector, depending on the

partners (income differences and geography explain part of this variation)

• Last, they compare trade and value added balances


J&N 2012

Johnson Noguera (2012) - Results�� ! "#$#�� !%& �� '()( *�+ � %��%& �� ,�(-. '()( /0(1. *�+ � 10(2. %�� ,3(/.'()( 44(4. %�� 4(�. '()( 00(4. '()( 0�(4.5�� (2. *�+ � 6(1. %�� 6(/. '(7( 6(1.8��9 0(-. 5�� 6(,. 8��9 6(�. 5�� 6(1.:��;��<�� ! =�� !>�� %?��&��( %& �� 5��>�� 1�(3. %?��&��@�� -1(1. %& �� ,4(2. 5�� 32(4.8��9 2(,. 8��9 44(1. '()( 40(4. '()( �(1.'(7( 0(3. '(7( 2(6. 5�� (1. %& �� 0(2.'()( 0(,. '()( 0(,. 8��9 0(1. 8��9 4(6.)��&��+�A�� &�� (�&�� &�� &��+ ��&��A� ��+��&�� &��@�� 9��@�� &�� ()&��@��@��B� ��@��9�&��A@�� A��&� �� (�� A�066�(CDEDFDGDHIJKLMN ONP QLR QKR SNT UML VOM WXL YZR [\M T]L^LRTULQXTMN]CDEDFDGDHIJKLMN ONP QLR QKR SNT UML VOM WXL YZR [\M T]LJNM_WQN]aZ\MXbJKLMN cLPTNbdSSNSbaZ\MXbJKLMN> �@��4�%�� )��)&��A8��e+��f��@��e+��9%@��9g066�h2,Martin, J. & Méjean, I. (2012) () Fragmentation of production 2012 16 / 32

J&N 2012

Johnson Noguera (2012) - Results�� !"#��$ %�# �#� "#� #�� &#� "�� !� ��'#�� (��)��*�� (��*��)��*�� (��+,-./0123,4560/547/580598:54.0;880835459<0=>?/6@0A9,608B6560=CDEF5/690/GHII1JKLFigure: Johnson Noguera, 2012


J&N 2012

Johnson Noguera (2012 bis) - Results�� !"# $%& '()*+$,-.��/+0,&(..+0,1*�203+0,0/41*�2 /+005 6$*(4 44( ��7+..+/840�0+/9:;<=��>�� ?��@��A��A�?�A��B�� !"# $%& '()*+$,-.��/+0,&(..+0,1*�203+0,0/41*�2 /+005 6$*(4 44( ��7+..+/840�0+/9:;<= ��Consistent with HIY (2001): 1970-1990 vertical specialization grew 30% andexplains 30% of world trade growth


ACFH 2012

Measuring the Upstreamness of Production

• We have seen that i) VAX ratios have decreased for almost all coun-tries from 1970, and ii) the VAX ratios are very different betweensectors and between countrie within sectors

• Questions: Do countries specialize in different stages of the produc-tion process? What determines such specialization?

⇒ We need a measure of industry downstreamness to answer those ques-tions: how far is the industry/sector from final demand?

⇒ Antras and Chor (2012) and Fally (2012) propose 2 different measuresof upstreamness

⇒ Antras, Chor, Fally, and Hillberry (2012) show they are equivalentand provide evidence on the determinants of the country level averageupstreamness of exports


ACFH 2012

ACFH 2012 - Measure 1

• Let’s focus on a closed economy• Production can be written as a function of final consumption (cf sl.9):

y(s) = c(s) +∑

t

d(s, t)c(t) +∑

t

∑u

d(s, t)d(s, u)c(t) + ..

• where dst is the amount of good s needed to produce good t• ACFH propose to weight each of the term of this sum by the distancefrom final use (plus one):

U1 = 1× c(s)

y(s)+2×

∑t

d(s, t)c(t)

y(s)+3×

∑t

∑u

d(s, t)d(s, u)c(t)

y(s)+..

• if U1(s) = 1, the entire production is directly consumed. The largerU1, the more upstream is the industry


ACFH 2012

ACFH 2012 - Measure 2

• dstY (t)Y (s) share of s purchased by t. The upstreamness of industry s is:

U2(s) = 1 +N∑

t=1

dstY (t)

Y (s)U2(t)

• Defining the matrix ∆ with dstY (t)Y (s) in entry s, t:

U2 = [I −∆[−1︸︷︷︸N×N

1︸︷︷︸N×1

• The more upstream the industries you serve as an intermediate, themore upstream you are

• It turns out that U1 and U2 are equivalent


ACFH 2012

ACFH 2012 - Open economy

• In an open economy, production writes:

y(s) = c(s) +∑

t

d(s, t)y(t) + x(s)−m(s)

• We would like to focus on δst = dstY (t)−x(s,t)+m(s,t)y(s)

• but data on x(s, t) and m(s, t) are not available⇒ assume that the domestic content of production is the same as the

export and import content of production⇒ In such case, the measure of upstreamness remains valid as long as

we consider dst = dsty(s)

y(s)+x(s)−m(s)


ACFH 2012

ACFH 2012 - Data

• Use I-O matrix for the US in 2002 (see BEA website)

• Disaggregated data: 426 industries

• Use additional information on imports, exports, and inventories

• OECD STAN database to compare the rank correlation of industries’upstreamness across countries


ACFH 2012

ACFH 2012 - Results

• Production from 19 industries goes to final use directly (U = 1)

• The more upstream industry is petrochemicals (U = 4.65)

• The average distance from final consumption is 2.

• For manufacturing, most downstream industries are automobile, fur-niture, and footwear; the most upstream are raw materials

• Rank correlation across countries is positive and significant: about0.85 for the US and EU

• Capital intensive industries tend to be more upstream industries


ACFH 2012

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ACFH 2012

ACFH 2012 - Results

• R2 very small

• Most of the results are not

• Financial development seems the most important determinant: coun-tries with a high level of financial developement specialize in down-stream industries. This is also true for manufacturing: not an artefactdue to financial services


ACFH 2012

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ACFH 2012

ACFH 2012 - Results

• R2 are much higher

• GDP per capita has a non linear effect on trade flows depending theupstreamness of the industry

• Complementarity between rule of law and downstreamness

• Complementarity between physical capital and industry upstreamness


ACFH 2012

ACFH 2012 and Fally 2011 - Discussion

• Sectoral measure of distance to final demand⇒ you have the average# of stages to final demand

• Average # of stages in the US: 1.95 in the 70s, 1.65 in 2002 (Fally,2011)

• At fist sight this goes against Johnson & Noguera findings• But, in fact they measure to different things:• JN (2011) measure international fragmentation:⇒ the fact that some stages are produced abroad

• Fally (2011) measures production fragmentation:⇒ if a stage that was produced in the US is now produced in China, no

effect on his measure of fragmentation

→ Fally explains the decrease in US production fragmentation by thegrowing importance of services and shift of production toward indus-tries closer to final demand


Conclusion

Related papers

• Theory: Costinot, Vogel, Wang (REStud 2012): elementary theory of globalsupply chains. Countries that do less mistakes specialize in latter stages ofproduction (where mistake is the most costly)

• Several papers on the role of product fragmentation to explain the greatcrisis. See Bems, Johnson, and Yi (2010): important role of demandspillovers during the crisis

• di Giovanni & Levchenko (2010, AEJ:Macro) and Ng (2010, JIE) show thatpart of international business cycle comovement is due to the internationalfragmentation of production


Conclusion

Some interesting extensions

• Link the change in production fragmentation to the increase in outputvolatility (see Carvalho Gabaix 2012)

• Use those measures to study the transmission of shocks (theory dvd byAcemoglu et al 2012)

• Impact of exchange rate movements on US current account deficit alsodepend on the vertical fragmentation of production across countries (seeMéjean, Rabanal, and Sandri 2011)

• Does international fragmentation occur within firm boundaries? does itdepend on the upstreamness of the production? (Antras & Chor 2012)


Bibliography

Non exhaustive bibliography

Pol Antras & Davin Chor 2012.Organizing the Global Value Chain .harvard mimeo.

Pol Antras & Davin Chor & Fally & Russell Hillberry 2012.A measure of upstreamness of production and trade flows .forthcoming in The American Economic Review P&P.

Fally 2012.On the Fragmentation of Production in the US .mimeo.

Hummels, David & Ishii, Jun & Yi, Kei-Mu, 2001.The nature and growth of vertical specialization in world trade.Journal of International Economics, Elsevier, vol. 54(1), pages 75-96, June..

R. Johnson & G. Noguera 2012.Accounting for Intermediates: Production Sharing and Trade in Value Added .Journal of International Economics, 86 (2).

R. Johnson & G. Noguera 2012.Fragmentation and Trade in Value Added over Four Decades.mimeo.


Documents

Lecture 6 Advanced topics in international trade The ...The Vertical Fragmentation of Production JulienMartin(IRES-UCLouvain) IsabelleMéjean(EcolePolytechnique,CREST,CEPR) APE-ENSAE,December7th