Global Value Chains: Spiders and SnakesStanford Department Seminar
Pol Antras
Harvard University
November 18, 2016
Pol Antras (Harvard University) Global Value Chains: Spiders and Snakes November 18, 2016 1 / 44
Introduction
Three Major Developments
Three major developments in the world economy in the last 30 years:
1 Information and communication technology (ICT) revolution
2 Deepening of trade liberalization and continuing transportation costreduction
3 Political developments expanding the reach of globalization
An implication: Gradual disintegration of production across borders
Topology of GVCs: Spiders and Snakes (Baldwin and Venables, 2013)
Pol Antras (Harvard University) Global Value Chains: Spiders and Snakes November 18, 2016 2 / 44
Introduction
A Spider: Boeing’s Dreamliner
Pol Antras (Harvard University) Global Value Chains: Spiders and Snakes November 18, 2016 3 / 44
Introduction
A Snake: Manufacturing a Chip
Pol Antras (Harvard University) Global Value Chains: Spiders and Snakes November 18, 2016 4 / 44
Introduction
A Snake: Manufacturing a Chip
Pol Antras (Harvard University) Global Value Chains: Spiders and Snakes November 18, 2016 4 / 44
Introduction
A Snake: Manufacturing a Chip
Pol Antras (Harvard University) Global Value Chains: Spiders and Snakes November 18, 2016 4 / 44
Introduction
A Snake: Manufacturing a Chip
Pol Antras (Harvard University) Global Value Chains: Spiders and Snakes November 18, 2016 4 / 44
Introduction
Why Should We Care?
Does it matter that about two-thirds of world trade is in intermediateinputs instead of final goods?
Does it matter that trade relationships are often initiated byimporters seeking to procure inputs from foreign suppliers?
Current workhorse trade models focus on the extensive and intensivemargin decisions of exporters selling finished products worldwide
Is this without loss of generality?
Pol Antras (Harvard University) Global Value Chains: Spiders and Snakes November 18, 2016 5 / 44
Introduction
Road Map
Today I want to highlight some novel features that arise whenanalyzing and estimating multi-country global sourcing models
1 Spiders: Overview of Antras, Fort and Tintelnot (2016)
2 Snakes: Preview of ongoing work with Alonso de Gortari
Pol Antras (Harvard University) Global Value Chains: Spiders and Snakes November 18, 2016 6 / 44
Spiders: Antras, Fort and Tintelnot (2016)
Spiders: Antras, Fort and Tintelnot (2016)
Pol Antras (Harvard University) Global Value Chains: Spiders and Snakes November 18, 2016 7 / 44
Spiders: Antras, Fort and Tintelnot (2016) Motivation
The Margins of Trade
Suppose that your interpret world trade flows (or U.S. imports morenarrowly) as the legs of spiders
Firms make decisions of where (extensive margin) to source inputsfrom and how much (intensive margin) to buy of each input
Fact: Extensive margin accounts for most of the cross-countryvariation in U.S. imports
Fact: Superior performance (size, labor productivity, TFP) ofimporters
Pol Antras (Harvard University) Global Value Chains: Spiders and Snakes November 18, 2016 7 / 44
Spiders: Antras, Fort and Tintelnot (2016) Motivation
Superior Performance of Importers
02
46
Pre
miu
m
1 3 5 7 9 11 13 15 17 19 21 23 25Minimum number of countries from which firm sources
Premium 95% CI
Pol Antras (Harvard University) Global Value Chains: Spiders and Snakes November 18, 2016 8 / 44
Spiders: Antras, Fort and Tintelnot (2016) Motivation
Challenges for a Multi-Country Global Sourcing Model
In canonical models of exporting, firms assumed to have constantmarginal costs unaffected by trade decisions
Easy to handle various margins of trade
But importing inputs naturally affects the marginal cost of the firm!
Import entry decisions are thus interdependent across markets
Interdependencies across markets complicate the firm’s decision
Which countries should a firm invest in importing from?
From which particular country should each input be bought?
How much of each input should be purchased?
Pol Antras (Harvard University) Global Value Chains: Spiders and Snakes November 18, 2016 9 / 44
Spiders: Antras, Fort and Tintelnot (2016) Contribution
Main Contributions of Antras, Fort and Tintelnot (2016)
Develop a quantifiable multi-country sourcing model
Characterization of intensive and extensive margins of global sourcing
Eaton-Kortum (2002) and multi-country Melitz (2003) are special cases
Develop methodology to solve firm’s problem with interdependencies
Apply theoretical insights and IO algorithm to estimate model
Counterfactual analysis of shock to China’s sourcing potential
Study effects of shocks to global sourcing
Distinguish net vs. gross changes in sourcing / employment
Reduced-form evidence consistent with these predictions
Pol Antras (Harvard University) Global Value Chains: Spiders and Snakes November 18, 2016 10 / 44
Spiders: Antras, Fort and Tintelnot (2016) Environment
Environment
J countries
Measure of Lj consumers / workers
Preferences: Dixit-Stiglitz over manufacturing varieties, elasticity ofsubstitution σ > 1 (later introduce non-manufacturing sector)
Final good sector produces these varieties:
Measure Nj of heterogeneous firms (pinned down by free entry)Firms characterized by core productivity ϕMonopolistic competitionNon-tradable final output
Intermediate good sector
Each firm uses a unit measure of intermediate inputs (next slide)
Trade cost τij to import from country j by country i
Perfect competition =⇒ Marginal-cost pricing of inputs
Pol Antras (Harvard University) Global Value Chains: Spiders and Snakes November 18, 2016 11 / 44
Spiders: Antras, Fort and Tintelnot (2016) Environment
Production Technology
Marginal cost of final good producer ϕ based in i is:
ci
({j (v)}1
v=0 , ϕ)=
1
ϕ
1∫0
(pi (v , j(v)))1−ρ dv
1/(1−ρ)
Pol Antras (Harvard University) Global Value Chains: Spiders and Snakes November 18, 2016 12 / 44
Spiders: Antras, Fort and Tintelnot (2016) Environment
Production Technology
Marginal cost of final good producer ϕ based in i is:
ci
({j (v)}1
v=0 , ϕ)=
1
ϕ
1∫0
(τij(v )aj(v ) (v)wj(v )
)1−ρdv
1/(1−ρ)
Pol Antras (Harvard University) Global Value Chains: Spiders and Snakes November 18, 2016 12 / 44
Spiders: Antras, Fort and Tintelnot (2016) Environment
Production Technology
Marginal cost of final good producer ϕ based in i is:
ci
({j (v)}1
v=0 , ϕ)=
1
ϕ
1∫0
(τij(v )aj(v ) (v)wj(v )
)1−ρdv
1/(1−ρ)
Tricky to characterize equilibrium in terms of aj ’s
Pol Antras (Harvard University) Global Value Chains: Spiders and Snakes November 18, 2016 12 / 44
Spiders: Antras, Fort and Tintelnot (2016) Environment
Production Technology
Marginal cost of final good producer ϕ based in i is:
ci
({j (v)}1
v=0 , ϕ)=
1
ϕ
1∫0
(τij(v )aj(v ) (v)wj(v )
)1−ρdv
1/(1−ρ)
Tricky to characterize equilibrium in terms of aj ’s
Productivity 1/aj (v) for a given location j drawn from Frechetdistribution:
Pr(aj (v) ≥ a) = e−Tjaθ, with Tj > 0.
Pol Antras (Harvard University) Global Value Chains: Spiders and Snakes November 18, 2016 12 / 44
Spiders: Antras, Fort and Tintelnot (2016) Environment
Production Technology
Marginal cost of final good producer ϕ based in i is:
ci
({j (v)}1
v=0 , ϕ)=
1
ϕ
1∫0
(τij(v )aj(v ) (v)wj(v )
)1−ρdv
1/(1−ρ)
Tricky to characterize equilibrium in terms of aj ’s
Productivity 1/aj (v) for a given location j drawn from Frechetdistribution:
Pr(aj (v) ≥ a) = e−Tjaθ, with Tj > 0.
Country-specific fixed cost of offshoring wi fij
Pol Antras (Harvard University) Global Value Chains: Spiders and Snakes November 18, 2016 12 / 44
Spiders: Antras, Fort and Tintelnot (2016) Environment
Firm’s problem
Firm chooses:
Sourcing strategy Ji (ϕ) ⊆ {1, ..., J}Source country j(v) ∈ Ji (ϕ) for each intermediate v
Quantity of each input j(v) purchases
Price of final good
Sourcing strategy thus determines set of countries from which firmcan buy inputs
Pol Antras (Harvard University) Global Value Chains: Spiders and Snakes November 18, 2016 13 / 44
Spiders: Antras, Fort and Tintelnot (2016) Firm Behavior
Firm Behavior Conditional on Sourcing Strategy
Share of intermediate input purchases sourced from any country j :
χij (ϕ) =Tj (τijwj )
−θ
Θi (ϕ)if j ∈ Ji (ϕ)
Sourcing potential of country j (for firms in i): Tj (τijwj )−θ
Sourcing capability of firm ϕ in i :
Θi (ϕ) ≡ ∑k∈Ji (ϕ)
Tk (τikwk)−θ
Marginal cost:
ci (ϕ) =1
ϕ(γΘi (ϕ))−1/θ
Pol Antras (Harvard University) Global Value Chains: Spiders and Snakes November 18, 2016 14 / 44
Spiders: Antras, Fort and Tintelnot (2016) Firm Behavior
Optimal Sourcing Strategy
Profit Function:
maxIij∈{0,1}Jj=1
ϕσ−1
(γ
J
∑j=1
IijTj (τijwj )−θ
)(σ−1)/θ
Bi − wi
J
∑j=1
Iij fij
Pol Antras (Harvard University) Global Value Chains: Spiders and Snakes November 18, 2016 15 / 44
Spiders: Antras, Fort and Tintelnot (2016) Firm Behavior
Optimal Sourcing Strategy
Profit Function:
maxIij∈{0,1}Jj=1
ϕσ−1
(γ
J
∑j=1
IijTj (τijwj )−θ
)(σ−1)/θ
Bi − wi
J
∑j=1
Iij fij
Proposition 1. The solution Iij (ϕ) ∈ {0, 1}Jj=1 to the optimalsourcing problem is such that:
(a) a firm’s sourcing capability Θi (ϕ) =J
∑j=1
Iij (ϕ)Tj (τijwj )−θ
is nondecreasing in ϕ;
(b) if (σ− 1) /θ ≥ 1, then Ji (ϕL) ⊆ Ji (ϕH) for ϕH ≥ ϕL,where Ji (ϕ) = {j : Iij (ϕ) = 1} .
Pol Antras (Harvard University) Global Value Chains: Spiders and Snakes November 18, 2016 15 / 44
Spiders: Antras, Fort and Tintelnot (2016) Firm Behavior
Optimal Sourcing Strategy
Profit Function:
maxIij∈{0,1}Jj=1
ϕσ−1
(γ
J
∑j=1
IijTj (τijwj )−θ
)(σ−1)/θ
Bi − wi
J
∑j=1
Iij fij
Proposition 2. Define the mapping Vj (ϕ, J) taking a value ofone whenever including country j in the sourcing strategy J
raises firm-level profits πi (ϕ, J) , and taking a value of zerootherwise. Then, whenever (σ− 1) /θ ≥ 1,Vj (ϕ, J′) ≥ Vj (ϕ, J) for J ⊆ J′.
This result will be instrumental for reducing the dimensionalityof the optimal sourcing problem
Pol Antras (Harvard University) Global Value Chains: Spiders and Snakes November 18, 2016 15 / 44
Spiders: Antras, Fort and Tintelnot (2016) Firm Behavior
Interdependencies in Firm Sourcing Decisions
Proposition 3. Holding constant the the market demand level Bi ,whenever (σ− 1) /θ ≥ 1, an increase in the sourcing potential
Tj (τijwj )−θ or a reduction in the fixed cost fj of any country j ,
(weakly) increases the input purchases by firms in i not only from j ,but also from all other countries.
Corollary. There may exist complementarities between domestic andforeign sourcing
Pol Antras (Harvard University) Global Value Chains: Spiders and Snakes November 18, 2016 16 / 44
Spiders: Antras, Fort and Tintelnot (2016) Structural Estimation
Structural Estimation
Pol Antras (Harvard University) Global Value Chains: Spiders and Snakes November 18, 2016 17 / 44
Spiders: Antras, Fort and Tintelnot (2016) Structural Estimation
Data
2007 data from the U.S. Census BureauEconomic CensusesImport transactions data
Sample is all manufacturing firms (around 250,000 firms)Include firms with non-manufacturing activity23% of employment and 38% of sales65% of (non-mining) importsA quarter of these firms imports
Structural EstimationLimit analysis to countries with 200+ U.S. importers66 countries and the U.S.
Reduced form evidence on interdependenciesBalanced panel of manufacturing firms in 1997 and 2007UN Comtrade data; 1997 BEA Input-Output tables
Pol Antras (Harvard University) Global Value Chains: Spiders and Snakes November 18, 2016 17 / 44
Spiders: Antras, Fort and Tintelnot (2016) Structural Estimation
Some Firm-level Import Statistics
Count of distinct source locations and products imported by a firm
Mean Std. Dev. 25th Ptile Median 95th Ptile
Country Count 3.26 5.09 1 2 11Product Count 11.91 48.89 1 3 41
Although extreme, the continuum of inputs assumption helps a lot
Pol Antras (Harvard University) Global Value Chains: Spiders and Snakes November 18, 2016 18 / 44
Spiders: Antras, Fort and Tintelnot (2016) Structural Estimation
Overview of Estimation
Step 1: Back out sourcing potential from firm-level input shares
Recovered from country fixed effects in normalized share regressions
Step 2: Estimate demand elasticity and productivity dispersion
Project fixed effect on human-capital adjusted labor cost
Step 3: Estimate fixed costs of sourcing and residual demand
Simulated method of moments + Jia’s (2008) algorithm
J,, fijn −1 ∑
j1
j∈JTj ijwj
−−1/
B − ∑j∈J
fijn
Step 1 Step 2Step 3
Pol Antras (Harvard University) Global Value Chains: Spiders and Snakes November 18, 2016 19 / 44
Spiders: Antras, Fort and Tintelnot (2016) Structural Estimation
Sourcing Potential vs. Fixed Cost Estimates
10−3
10−2
10−1.9
10−1.8
10−1.7
10−1.6
10−1.5
10−1.4
10−1.3
10−1.2
CAN
MEX
GTM
SLV
HND
CRI
PAN
DOM
TTO
COL
VENECU
PER
CHL
BRA
ARG
SWE
NOR
FINDNK
GBRIRLNLD
BEL
LUX
FRA
DEU
AUT
CZESVK
HUN
CHE
POL
RUS
UKR
ESPPRT
ITA
SVN
GRC
ROMBGR
TUR
ISR
SAU
ARE
IND
PAK
BGD
LKA
THA
VNM
MYS
SGP
IDN
PHL
MAC
CHN
KOR
HKG
TWN
JPN
AUS
NZL
EGY
ZAF
Sourcing Potential
Med
ian
Fix
ed C
ost
Pol Antras (Harvard University) Global Value Chains: Spiders and Snakes November 18, 2016 20 / 44
Spiders: Antras, Fort and Tintelnot (2016) Counterfactual
Counterfactual: China Shock
Negative shock to China’s sourcing potential to match 1997 share ofChina importers (38% of its 2007 level)
Resolve for equilibrium price index and mass of new firms
Calculate impact from going back to 2007 sourcing potential values
Compare baseline model predictions to models with alternativeparameter values that imply:
Universal importing
Independent entry decisions
Common fixed costs
Pol Antras (Harvard University) Global Value Chains: Spiders and Snakes November 18, 2016 21 / 44
Spiders: Antras, Fort and Tintelnot (2016) Counterfactual
Baseline Results
Chinese Change sourcing Change Sourcing Shareimport status from US from other countries of firms
Entrants 1.008 1.015 0.066Continuers 1.002 1.002 0.019Others 0.994 0.986 0.915
Aggregate sourcing from the U.S. is reduced by 0.60 percent
For every 10 domestic manufacturing jobs destroyed, 2 new jobs arecreated (and we do not allow for exports!)
Manufacturing price index falls by 0.2%.
Pol Antras (Harvard University) Global Value Chains: Spiders and Snakes November 18, 2016 22 / 44
Spiders: Antras, Fort and Tintelnot (2016) Reduced-Form Evidence
Reduced-Form Comparison to the Data
Model predicts increased domestic and third market sourcing byChina importers
∆yn = β0 + βCh∆Chinan + εn
∆Chinan =ImportsChn2007−ImportsChn1997
(ImportsChn2007+ImportsChi1997)/2
∆yn is 1997 to 2007 change in firm n’s:
log domestic inputsDHS growth rate of non-China importslog number of non-China source countries
OLS estimates clearly problematic =⇒ use IV strategy similar toAutor, Dorn and Hanson (2013) but on the input side
Pol Antras (Harvard University) Global Value Chains: Spiders and Snakes November 18, 2016 23 / 44
Spiders: Antras, Fort and Tintelnot (2016) Reduced-Form Evidence
Estimates of the China Shock on Firm Sourcing
Dependent variable is change from 1997 to 2007 in firm n:
Domestic No. of Foreign Domestic No. of Foreigninputs countries inputs inputs countries inputs
OLS IV
China, DHS 0.084*** 0.255*** 0.360*** 0.934*** 0.553*** 0.654***(0.012) (0.007) (0.013) (0.258) (0.080) (0.197)
Constant 0.069*** 0.144*** 0.315*** -0.064 0.097*** 0.269***(0.023) (0.013) (0.026) (0.047) (0.017) (0.044)
Adj. R2 0.00 0.11 0.05N 127,400 127,400 127,400 127,400 127,400 127,400
First Stage Statistics Coeff (se) 2.691*** (0.504) KP Fstat 28.51
Notes: All variables are changes or growth rates from 1997 to 2007. Standard errors are in parenthe-ses and clustered by 439 NAICS industries. N rounded for disclosure avoidance.
Pol Antras (Harvard University) Global Value Chains: Spiders and Snakes November 18, 2016 24 / 44
Snakes: Antras and de Gortari (2016)
Snakes: Antras and de Gortari (2016)
Pol Antras (Harvard University) Global Value Chains: Spiders and Snakes November 18, 2016 25 / 44
Snakes: Antras and de Gortari (2016)
A Snake: Manufacturing a Chip
Pol Antras (Harvard University) Global Value Chains: Spiders and Snakes November 18, 2016 25 / 44
Snakes: Antras and de Gortari (2016) The Role of Trade Costs
Sequential Production and Trade Costs
Consider optimal location of production for the different stages in asequential GVC
Without trade frictions ≈ model with spiders
Conditional on a set of sourcing locations, minimize each input’ssourcing cost independently
With trade frictions, matters become trickier
Location of a stage takes into account upstream and downstreamlocations
Where is the good coming from? Where is it going to?
Need to solve jointly for the optimal path of production
Pol Antras (Harvard University) Global Value Chains: Spiders and Snakes November 18, 2016 25 / 44
Snakes: Antras and de Gortari (2016) Our Contribution
Main Contributions of Antras and de Gortari (2016)
Develop a general-equilibrium model of GVCs with a generalgeography of trade costs across countries
1 Characterize the optimality of a centrality-downstreamness nexus
Consistent with evidence from Factory Asia
2 Develop tools to solve the problem in high-dimensional environments
Reformulate problem so it is solvable with DP and LP techniques
Illustrate transition from domestic to regional to global value chains
Pol Antras (Harvard University) Global Value Chains: Spiders and Snakes November 18, 2016 26 / 44
Snakes: Antras and de Gortari (2016) Our Contribution
Main Contributions of Antras and de Gortari (2016)
Develop a general-equilibrium model of GVCs with a generalgeography of trade costs across countries
1 Characterize the optimality of a centrality-downstreamness nexus
Consistent with evidence from Factory Asia
2 Develop tools to solve the problem in high-dimensional environments
Reformulate problem so it is solvable with DP and LP techniques
Illustrate transition from domestic to regional to global value chains
3 Develop a tractable multi-stage variant of the Eaton-Kortum (2002)framework for an arbitrary number of countries and sequential stages
Facilitates quantitative analysis using world I-O tables
Pol Antras (Harvard University) Global Value Chains: Spiders and Snakes November 18, 2016 26 / 44
Snakes: Antras and de Gortari (2016) General Environment
Model: General Environment
Pol Antras (Harvard University) Global Value Chains: Spiders and Snakes November 18, 2016 27 / 44
Snakes: Antras and de Gortari (2016) General Environment
Environment
There are J countries (indexed by i or j) where consumers deriveutility from consuming a set of final-good varieties (indexed by z)
Consumer goods produced combining N stages (indexed by n) thatneed to be performed sequentially using a unique factor (labor)
The last stage N can be interpreted as assembly
Countries can in principle differ in their:
Labor productivity: unit labor requirements ain (z)
Geography: J × J matrix of iceberg trade coefficients τij proportionalto value of good being shipped
Size: each country i is populated by Li consumers, each inelasticallysupplying one unit of labor
Pol Antras (Harvard University) Global Value Chains: Spiders and Snakes November 18, 2016 27 / 44
Snakes: Antras and de Gortari (2016) General Environment
Sequential Production Technology
Stage n technology for good z :
yni (z) = f nz
(Lni (z)
ani (z), cn−1
i (z)
)for all n, i , z ,
where
cni (z) =J
∑j=1
δnji (z) ynj (z)
τji, for all n, i , z ,
with some initial vector of c0i ’s.
Applies also to assembly yNi (z) and final-good consumption cNi (z)
Can solve recursively to express final consumption in terms of valueadded in all stages
Pol Antras (Harvard University) Global Value Chains: Spiders and Snakes November 18, 2016 28 / 44
Snakes: Antras and de Gortari (2016) Example
Example: A Symmetric Cobb-Douglas Snake
Assume a Cobb-Douglas technology with a single source ofcomponents at each stage
yn`(n) =
(Ln`(n)
an`(n)
)1/n (cn−1`(n)
)1−1/n; cn−1
`(n)=
yn−1`(n)
τji
This delivers:
yN`(n) =N
∏i=1
(Ln`(n)
an`(n)
)1/N
×(
τ`(n−1)`(n)
)− n−1N
Unless τ`(n−1)`(n) = τ, can no longer minimize costs stage-by-stage
Incentive to reduce trade costs increases as one moves downstream
Pol Antras (Harvard University) Global Value Chains: Spiders and Snakes November 18, 2016 29 / 44
Snakes: Antras and de Gortari (2016) Isolating Trade Costs
Isolating Trade Costs
Pol Antras (Harvard University) Global Value Chains: Spiders and Snakes November 18, 2016 30 / 44
Snakes: Antras and de Gortari (2016) One-to-One Case
One-to-One Assignment with N = J
Consider the case with just one final good and log utility
Lemma 1 (Modified TSP)
In the even case N = J, the optimal one-to-one assignment of stages tocountries seeks to solve
min{`(n)}Nn=1
H (` (1) , ..., ` (N)) =N
∑i=1
ΛiN ln τ`(N)i +N−1
∑n=1
n ln τ`(n)`(n+1),
where Λi = λiLi/J
∑i=1
λiLi .
Connection to Traveling Salesman Problem
But ‘traveling salesman’ is getting increasingly tired
Pol Antras (Harvard University) Global Value Chains: Spiders and Snakes November 18, 2016 30 / 44
Snakes: Antras and de Gortari (2016) One-to-One Case
Optimal Pure Snake in Factory Asia: Production
Pol Antras (Harvard University) Global Value Chains: Spiders and Snakes November 18, 2016 31 / 44
Snakes: Antras and de Gortari (2016) One-to-One Case
‘Empirical Fit’
CHN
HKG
IDN
JPN
KOR
MYS PHLSGP
THA
TWN
VNM
1.7
1.8
1.9
2
2.1
2.2
2.3
2.4
2.5
0 1 2 3 4 5 6 7 8 9 10 11 12
Average Expo
rt Upstreamne
ss (ACFH)
Upstreamness in the Optimal Global Value Chain
Pol Antras (Harvard University) Global Value Chains: Spiders and Snakes November 18, 2016 32 / 44
Snakes: Antras and de Gortari (2016) A Probabilistic Approach
A Probabilistic Approach
Pol Antras (Harvard University) Global Value Chains: Spiders and Snakes November 18, 2016 33 / 44
Snakes: Antras and de Gortari (2016) A Probabilistic Approach
A Multi-Stage Eaton-Kortum Model
Assume preferences are
u
({cNi (z)
}1
z=0
)=
(∫ 1
0
(cNi (z)
)(σ−1)/σdz
)σ/(σ−1)
, σ > 1
Technology features CRS and Ricardian technological differences
yni (z) =
(Lni (z)
ani (z)
)1/n (cn−1i (z)
)1−1/n
If a production chain follows the path {` (1) , ` (2) , ..., ` (N)}, then
log
(Pr
(N
∏n=1
a`(n)n (z) ≥ a
))= −aθ
N
∏n=1
T`(n)
Randomness can be interpreted as uncertainty on compatibility
Pol Antras (Harvard University) Global Value Chains: Spiders and Snakes November 18, 2016 33 / 44
Snakes: Antras and de Gortari (2016) Some Results
Some Results
Likelihood of a particular GVC ending in i is
Pr (` (1) , ` (2) , ..., ` (N) ; i) =
N−1∏n=1
A`(n)
(τ`(n)`(n+1)
)−θn× A`(N)
(τ`(N)i
)−θN
Θi
where Aj = Tj (wj )−θ and Θi is the sum of the numerator over all
possible country permutations
Notice that trade costs again matter more downstream than upstream
Can compute final-good trade shares and intermediate input shares asexplicit functions of Aj ’s and trade costs
Pol Antras (Harvard University) Global Value Chains: Spiders and Snakes November 18, 2016 34 / 44
Snakes: Antras and de Gortari (2016) Centrality and Downstreamness
The Centrality-Downstreamness Nexus
Define the average upstreamness U (`; i) of production of a givencountry ` in value chains that seek to serve consumers in country i :
U (`; i) =N
∑n=1
(N − n+ 1)× Pr (` = ` (n) ; i)
∑Nn′=1 Pr (` = ` (n′) ; i)
Closely related to upstreamness measure in Antras et al. (2012)
If τij = (ρiρj )−1 for i 6= j and τii = ξ (ρiρi )
−1 with ξ < 1:
Proposition (Centrality-Upstreamness Nexus)
The average upstreamness U (`) of a country in global value chains isdecreasing in its centrality ρ (`).
Pol Antras (Harvard University) Global Value Chains: Spiders and Snakes November 18, 2016 35 / 44
Snakes: Antras and de Gortari (2016) Empirical Application
Empirical Application
Pol Antras (Harvard University) Global Value Chains: Spiders and Snakes November 18, 2016 36 / 44
Snakes: Antras and de Gortari (2016) Empirical Application
Calibration to World-Input Output Database
We next map our multi-country Ricardian framework to worldInput-Output Tables
World Input Output Database: Released in 2012
35 sectors
40 countries (85% of world GDP) + ROW
Yearly: 1995-2011
Provides information on input and final output flows across countries
Pol Antras (Harvard University) Global Value Chains: Spiders and Snakes November 18, 2016 36 / 44
Snakes: Antras and de Gortari (2016) Empirical Application
Calibration to World-Input Output DatabaseWhat a world IO table should look like
automotive production, illustrating its power in analyses of international productionfragmentation. Section 4 is more general and considers specific measurement issuesthat are important for prudent use of the data, and identifies areas that are most inneed for improvements. The WIOD is meant to serve as a dynamic resource that willbe expanded over time and section 5 considers future developments.
2. WIOD in Comparative Perspective
In this section we first outline the concept of a world input–output table, followed by abrief discussion of the contents of the WIOD compared with other database initia-tives. Through a comparison of value-added export measures based on the variousdatabases we conclude that empirical differences are relatively minor.
WIOD Characteristics
Central in the WIOD is a time-series of world input–output tables. A world input–output table (WIOT) can be regarded as a set of national input–output tables that areconnected with each other by bilateral international trade flows. This is illustrated bythe schematic outline for a WIOT involving three countries in Figure 1. A WIOT pro-vides a comprehensive summary of all transactions in the global economy betweenindustries and final users across countries. The columns in the WIOT contain informa-tion on production processes. When expressed as ratios to gross output, the cells in acolumn provide information on the shares of inputs in total costs. Such a vector of costshares is often referred to as a production technology. Products can be used as inter-mediates by other industries, or as final products by households and governments(consumption) or firms (stocks and gross fixed capital formation). The distribution ofthe output of industries over user categories is indicated in the rows of the table. Animportant accounting identity in the WIOT is that gross output of each industry(given in the last element of each column) is equal to the sum of all uses of the outputfrom that industry (given in the last element of each row).
In addition to a national input–output table, imports are broken down according tothe country and industry of origin in a WIOT. This allows one, for example, to tracethe country of origin of the chemicals used in the food industry of country A. Thecombination of national and international flows of products provides a powerful tool
…Country
1Country 1 …Country
MCountry M
Industry Industry1 … …
Industry1 N
Industry N… …
Industry 1…Industry N
……Industry 1…Industry N
Total use
Supply from country-
industries
Country 1
CountryM
Value added by labour and capital
Gross output
Use by country-industries Final use by countries
Figure 1. Schematic Outline of a World Input–Output Table (WIOT)
USER GUIDE TO WORLD INPUT–OUTPUT DATABASE 577
© 2015 John Wiley & Sons LtdFigure: Timmer et al. (2015)
Alonso de Gortari (Harvard University) Empirics of GVCs April 20, 2016 36 / 73
Pol Antras (Harvard University) Global Value Chains: Spiders and Snakes November 18, 2016 37 / 44
Snakes: Antras and de Gortari (2016) Empirical Application
Targeting Final-Good Shares
We target final good shares, which are functions of Aj = Tj (wj )−θ
and ρij = (τij )−θ
Use gravity estimates (Head and Mayer, 2014) to back out trade costs
Distance, contiguity, common language, colonial link, RTAs, commoncurrency
Introduce additional wedge Z that magnifies foreign trade costsrelative to domestic ones
Can use (J − 1)× (J − 1) WIOD final-good shares and labor-marketclearing (or trade balance) to estimate Z , Tj and wj for j = 1, ..., J
We set θ = 5 and N = 3 to match an aggregate gross-output tovalue-added ratio of 2
Pol Antras (Harvard University) Global Value Chains: Spiders and Snakes November 18, 2016 38 / 44
Snakes: Antras and de Gortari (2016) Empirical Application
Fit of the Model
10-8
10-6
10-4
10-2
100
WIOD
10-8
10-6
10-4
10-2
100
Estim
atio
n
Final Consumption Shares: All - LogLog Scale
10-8
10-6
10-4
10-2
100
WIOD
10-8
10-6
10-4
10-2
100
Estim
atio
n
Input Shares: All - LogLog Scale
Pol Antras (Harvard University) Global Value Chains: Spiders and Snakes November 18, 2016 39 / 44
Snakes: Antras and de Gortari (2016) Empirical Application
Counterfactuals
A 50 percent reduction in foreign trade costs (wedge Z )
USA JP
NC
HN
CAN
AUS
RoW MEX IN
DBR
AID
NKO
RTW
NFR
AR
US
ESP
ITA
DEU
GBR TU
RPR
TFI
NPO
LSW
ER
OM
BEL
AUT
GR
CN
LDBG
RC
YP EST
CZE LV
AIR
LSV
KLT
UD
NK
HU
NSV
NLU
XM
LT
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
% o
f Exp
orts
GVC Participation Index
Benchmark50% Fall in Trade Costs
Pol Antras (Harvard University) Global Value Chains: Spiders and Snakes November 18, 2016 40 / 44
Snakes: Antras and de Gortari (2016) Empirical Application
Counterfactuals
A 50 percent reduction in foreign trade costs (wedge Z )
CA
N
Ro
W
ME
X
CH
N
FR
A
AU
S
ES
P
JP
N
BR
A
RU
S
ITA
DE
U
IND
GB
R
IDN
0
0.02
0.04
0.06
0.08
0.1
0.12
% o
f E
xp
ort
sBenchmark Calibration: GVC Participation Index
Benchmark
50% fall in trade costs
Pol Antras (Harvard University) Global Value Chains: Spiders and Snakes November 18, 2016 41 / 44
Snakes: Antras and de Gortari (2016) Empirical Application
Regional versus Non-Regional GVC Integration
As Z falls, GVCs first become more regional and then more global
0.75 1 1.25 1.5Z
0.25
0.26
0.27
0.28
0.29
0.3
Ratio
USA: NAFTA Participation / RoW Participation
Pol Antras (Harvard University) Global Value Chains: Spiders and Snakes November 18, 2016 42 / 44
Snakes: Antras and de Gortari (2016) Empirical Application
Real Income Gains
Autarky Counterfactual: GVC Model vs. Eaton-Kortum with I-O loop
1 1.25 1.5 1.75
N=1 with I-O Loop
1
1.25
1.5
1.75
GV
Cs:
N=
3
Real Income Gains
1.7 1.75 1.8 1.85 1.9 1.95 2 2.05
Log(GDP)-Weighted Trade Cost to RoW
1
2
3
4
5
6
7
Co
rre
ctio
n t
o N
=1
with
I-O
Lo
op
Re
al In
co
me
Correction to Real Income Gains vs Remoteness
Pol Antras (Harvard University) Global Value Chains: Spiders and Snakes November 18, 2016 43 / 44
Snakes: Antras and de Gortari (2016) Conclusions
Conclusions
We have developed frameworks to study how technology andgeography shape the location of production along GVCs
Both for Spiders and for Snakes
Frameworks deliver novel qualitative insights, but can also be used toquantitatively assess the implications of the rise of GVCs
I view this work as a stepping stone for a future analysis of the role ofman-made trade barriers in GVCs
Should countries use policies to place themselves in particularlyappealing segments of global value chains?
What is the optimal shape of those policies?
Pol Antras (Harvard University) Global Value Chains: Spiders and Snakes November 18, 2016 44 / 44