Trade with Correlation Nelson Lind1 1 Emory 2 UC
Natalia Ramondo2 University
San Diego and NBER
November 28, 2017
A Ricardian Model
Micro to Macro
Application
Ricardo 101 Qbicycles
Similar (High Correlation)
Qbicycles
Different (Low Correlation)
Qapples
Qapples
Insights: I1: Technological differences across countries lead to trade. I2: Gains are higher when trade occurs with more dissimilar partners.
A Ricardian Model
Micro to Macro
Application
Fr´echet 101 Eaton and Kortum (2002, EK) capture I1 but not I2. §
Independent Fr´echet ´ ÿ ¯ PrmaxtZ1 , . . . , ZN u ď zs “ exp ´ Ti z ´θ . i
§
Heterogeneity in θ breaks Fr´echet.
We drop independence in order to capture I2. §
Dependent Fr´echet ´ ¯ PrmaxtZ1 , . . . , ZN u ď zs “ exp ´ G pT1 , . . . , TN qz ´θ .
§
Heterogeneity via G maintains Fr´echet.
A Ricardian Model
Micro to Macro
Application
Fr´echet 101 Eaton and Kortum (2002, EK) capture I1 but not I2. §
Independent Fr´echet ´ ÿ ¯ PrmaxtZ1 , . . . , ZN u ď zs “ exp ´ Ti z ´θ . i
§
Heterogeneity in θ breaks Fr´echet.
We drop independence in order to capture I2. §
Dependent Fr´echet ´ ¯ PrmaxtZ1 , . . . , ZN u ď zs “ exp ´ G pT1 , . . . , TN qz ´θ .
§
Heterogeneity via G maintains Fr´echet.
A Ricardian Model
Micro to Macro
Application
Putting Ricardo’s Second Insight To Work 1
Representation Technological structure ô productivity a Fr´echet process
2
Gains from trade capture I2 ˆ GTd “
3
˙´ 1
θ
Aggregation §
4
πdd Gdd
Macro correlation related to micro structure
Application §
Estimate multi-sectoral model via two step OLS procedure
§
Countries specialized in low-correlation sectors have 40% higher gains.
A Ricardian Model
Micro to Macro
Application
Putting Ricardo’s Second Insight To Work 1
Representation Technological structure ô productivity a Fr´echet process
2
Gains from trade capture I2 ˆ GTd “
3
˙´ 1
θ
Aggregation §
4
πdd Gdd
Macro correlation related to micro structure
Application §
Estimate multi-sectoral model via two step OLS procedure
§
Countries specialized in low-correlation sectors have 40% higher gains.
A Ricardian Model
Micro to Macro
Application
Putting Ricardo’s Second Insight To Work 1
Representation Technological structure ô productivity a Fr´echet process
2
Gains from trade capture I2 ˆ GTd “
3
˙´ 1
θ
Aggregation §
4
πdd Gdd
Macro correlation related to micro structure
Application §
Estimate multi-sectoral model via two step OLS procedure
§
Countries specialized in low-correlation sectors have 40% higher gains.
A Ricardian Model
Micro to Macro
Application
Literature Interpret macro substitution patterns: loCES omoon
Ă
Arkolakis et al. (2012)
GEV lo omoon McFadden (1978)
Ă
Invertible loooomoooon Adao et al. (2017)
Multi-sector EK models: §
Costinot et al. (2012), Costinot and Rodr`ıguez-Clare (2014), Caliendo and Parro (2015), Ossa (2015), Levchenko and Zhang (2016)
Non-Linear/Non-CES gravity: §
Caron et al. (2014), Lashkari and Mestieri (2016), Brooks and Pujolas (2017), Bas et al. (2017)
A Ricardian Model
Micro to Macro
Application
Ricardian Model N countries §
d “ destination
§
o “ origin
Common CES preferences for varieties v P r0, 1s ˆ Xd pv q “
Pd pv q Pd
˙1´σ
ˆż 1 Xd
where
Pd pv q1´σ
Pd “
1 ˙ 1´σ
0
Heterogenous and stochastic production possibilities across origins
A Ricardian Model
Micro to Macro
Structure of Technology
Collection i “ 1, 2, . . . of technologies for producing v .
Constant returns in labor: Yiod pv q “ Z¯i pv qAiod pv qLiod pv q
§
Z¯i pv q “ global productivity of technology i
§
Aiod pv q “ bilateral applicability of technology i
Application
A Ricardian Model
Micro to Macro
Application
Assumptions
A1.
For each po, dq, Aiod pv q is iid across pi, v q.
A2. For each v , tZ¯i pv qθ ui“1,2,... is a Poisson process with intensity measure g ´2 dg that is independent of ttAiod pv quN o,d“1 ui“1,2,... .
Remark A2 implies that Z¯i pv q has a Pareto tail with shape θ.
A Ricardian Model
Micro to Macro
Application
Productivity as a Fr´echet Process (Lemma 1) Effective productivity A˚od pv q “ max Z¯i pv qAiod pv q i“1,2,...
is a θ-Fr´echet process on po, dq if and only if there exists technologies with global productivity and bilateral applicability such that A1 and A2 hold. Effective productivity distribution across origins: «
ˆ
PrA˚1d pv q ď a1 , . . . , A˚Nd pv q ď aN s “ exp ´E max
o“1,...,N
Aiod pv q ao
Proof. Apply spectral representation theorem for max-stable processes. (De Haan, 1984; Penrose, 1992; Schlather, 2002)
˙θ ff
A Ricardian Model
Micro to Macro
Application
Interpreting the Productivity Process
Origin productivity and iceberg trade costs: Ao ” ErAioo pv qθ s1{θ
and τod ”
Ao . ErAiod pv qθ s1{θ
Correlation function: Aiod pv qθ xo G px1 , . . . , xN q “ E max o“1,...,N ErAiod pv qθ s „
d
A Ricardian Model
Micro to Macro
Parameterizing the Distribution
PrA˚1d pv q ď a1 , . . . , A˚Nd pv q ď aN s #
«ˆ ˙ ˆ ˙ ff+ a1 ´θ aN ´θ “ exp ´G τ1d , . . . , τNd A1 AN d
Application
A Ricardian Model
Micro to Macro
Application
Joint Distribution of Prices (Proposition 1) Competition ùñ price equals lowest marginal cost. Pod pv q “ min
i“1,2,...
Wo ¯ Zi pv qAiod pv q
Competitiveness of o in d: ˆ Φod ”
τod Wo Ao
˙´θ
Implied joint distribution of prices: ” ´ ¯ı θ PrP1d pv q ě p1 , . . . , PNd pv q ě pN s “ exp ´G d Φ1d p1θ , . . . , ΦNd pN
A Ricardian Model
Micro to Macro
Application
Trade Shares (Proposition 2) Let A1 and A2 hold. Suppose that markets are perfectly competitive. Then: The share of expenditure by country d on goods from country o is πod “
Φod God 1d , . . . , ΦNd q
G d pΦ
where
God ” God pΦ1d , . . . , ΦNd q .
The price index in country d is 1
Pd “ γG d pΦ1d , . . . , ΦNd q´ θ where γ “ Γ
1 ` θ`1´σ ˘ 1´σ
θ
.
A Ricardian Model
Micro to Macro
Application
Gains From Trade (Proposition 4) Let A1 and A2 hold. Suppose that markets are perfectly competitive. Then the gains from trade relative to Autarky are Wd {Pd GTd ” “ pWd {Pd qAutarky
ˆ
πdd Gdd
˙´ 1
θ
.
Independence ùñ Gdd “ 1 ùñ Arkolakis et al. (2012) Calculating πdd {Gdd only requires bilateral expenditure shares: ˆ ˙ πod d π1d πNd πod “ G ,..., for o “ 1, . . . , N God o G1d GNd
A Ricardian Model
Micro to Macro
Application
Example: Three Country Nested CES Country 1 and country 2 are technological peers with correlation ρ. ¯ ´ 1{p1´ρq 1{p1´ρq 1´ρ G d px1 , x2 , x3 q “ x1 ` x2 ` x3 For country 3, G33 “ 1 so ´1
GT3 “ π33θ . For countries 1 and 2 « GTd “
ff´ 1
θ
πdd ´
πdd π1d `π2d
¯ρ
looooomooooon πdd {Gdd
.
A Ricardian Model
Micro to Macro
Application
General Framework: Micro to Macro (In Paper) Introduce standard micro-foundations §
Correlated preferences (Anderson, 1979)
§
Monopolistic competition with heterogenous firms (Melitz, 2003)
§
Global value chains (Antr`as et al., 2017)
Expenditure shares on products with characteristic m πmod “
d pΨ ~ 1d , . . . , Ψ ~ Nd q Ψmod Hmo ~ 1d , . . . , Ψ ~ Nd q H d pΨ
Result: aggregation over m ùñ macro correlation function πod
Φod God pΦ1d , . . . , ΦNd q “ G d pΦ1d , . . . , ΦNd q
with
Φod
ˆ ˙ Wo ´θ “ τod Ao
A Ricardian Model
Micro to Macro
Application
Example: Cross-Nested CES Macro correlation function M ÿ
G d px1 , . . . , xN q “
˜
m“1
N ÿ
¸1´ρm pωmod xo q1{p1´ρm q
o“1
Expenditure shares ˆ πmod “
Pmod Pmd
˙´
θ 1´ρm
ˆ ˙ Pmd ´θ γ Pd
with ˜ Pmod “ pωmod Φod q
´1{θ
,
Pmd “
N ÿ o“1
θ ´ 1´ρ
Pmod
m
¸´ 1´ρm
˜
θ
,
and
Pd “ γ
M ÿ m“1
¸´ 1
θ
´θ Pmd
A Ricardian Model
Micro to Macro
Application
Application: Sectoral Model
Interpret latent dimension m as sector s. ˆ πsod “
Psod Psd
˙´
θ 1´ρs
˙ ˆ Psd ´θ γ Pd
Implied gains and correlation correction ˆř GTd “
πsdd Gdd s
˙´ 1
ř
θ
where
Gdd “ ř
πsdd ř p o πsod qρs
s 1´ρs s πsdd
A Ricardian Model
Micro to Macro
Application
Two Step OLS Assumption: ln τsod “ lnp1 ` tsod q ` δ 1 Geood ` usod 1
Use variation over o to estimate σs ”
θ 1´ρs
ln πsod “ αso ` βsd ´ σs lnp1 ` tsod q ´ σs δ 1 Geood ` sod 2
Use variation over s to estimate 1{θ ln ysod “ aso ` bd ` δ 1 Geood `
1 ln xsd ` usod θ
where ysod ”
1 1 ` tsod
ˆ
π ř sod o πsod
˙´
1 σs
“
1 Psod 1 ` tsod Psd
ˆ and
xsd ”
ÿ o
πsod “
Psd γPd
˙´θ
A Ricardian Model
Micro to Macro
Application
Macro Counterfactual Data: §
Trade flows and freight costs from Adao et al. (2017)
§
Gravity covariates from CEPII
Pool estimation over years.
σs estimates
θ estimate
! Infer sectoral correlations, ρs “ max 0, 1 ´ Calculate GTd and Gdd .
θ σs
) .
A Ricardian Model
Micro to Macro
Application
Gains From Trade in 2006 Level SVK
Gains From Trade 1.05 1.075
HUN
LTU
Percent Difference in Gains From Trade −10 0 10 20 30
1.1
40
Percent Difference
BLX SVN BGR BAL NLD TWN CZE AUT DNK
IRL
ROU PRT SWEPOL GRC DEU FIN CAN
TUR JPN IDN RUS ESP ITA IND FRA CAN KOR GBR POL USABRA DEU AUS FIN GRC
BGR NLD
PRT
SVN BLX
BAL
ROU
AUT DNK
SVK TWN
SWE
HUN
CZE
MEX CHN
IRL
1
−20
1.025
ESP KOR TUR FRA MEXGBR ITA IDN RUS IND AUS CHN USA JPN BRA
LTU
.6
.65
.7
.75 .8 .85 Self Trade Share
Black: GTdCN “ p
ř s
1´ρs πsdd
.9
`ř o
πsod
.95
˘ρs
1
.6
.65
.7
.75 .8 .85 Self Trade Share
.9
.95
ř 1 q´ θ . Red: GTdCES “ p s πsdd q´1{ε for ε “ 5.
Percent difference calculated as 100 ˆ
GTdCN ´GTdCES GTdCES ´1
More Years: Level
.
More Years: Precent Difference
1
A Ricardian Model
Micro to Macro
What Explains Heterogeneity? Balassa revealed comparative advantage (RCA) index: ř ř Xsodt { sdt Xsodt d ř RCAsot “ ř od Xsodt { sod Xsodt
RCA-weighted correlation index: ρRCA “ dt
ÿ s
RCAsdt ρs ř s RCAsdt
High RCAsdt in high correlation sectors ùñ high ρRCA dt .
Application
A Ricardian Model
Micro to Macro
Application
.55
RCA-Induced Correlation Heterogeneity in 2006 SWE FIN DEU
RCA−Weighted Correlation Index .25 .35 .45
IRL
JPN
CZE AUT TWN HUN SVK
KOR GBR FRA ITA POL CAN ESP
SVN BALDNK
BLX
NLD
PRT ROU
MEX
USA CHN AUS BRA
GRC
LTU
IDNRUS IND TUR
.15
BGR
.6
.65
.7
.75 .8 .85 Self Trade Share
RCA-weighted correlation index, ρRCA “ dt
ř s
.9
.95
1
sdt ρs řRCA , across countries in 2006. RCAsdt s
More Years
A Ricardian Model
Micro to Macro
Application
RCA-Weighted Correlation Index from 1995 to 2006 Baltic Republics
1995
2000 Year
2005
.5 RCA−Weighted Correlation Index .3 .35 .4 .45 .25
RCA−Weighted Correlation Index .3 .35 .4 .45
.5
China
.25
.25
RCA−Weighted Correlation Index .3 .35 .4 .45
.5
Brazil
1995
2005
2005
2005
.5 .25
RCA−Weighted Correlation Index .3 .35 .4 .45
.5 RCA−Weighted Correlation Index .3 .35 .4 .45 2000 Year
2000 Year
United States
.25
RCA−Weighted Correlation Index .3 .35 .4 .45 .25 1995
1995
Korea
.5
Indonesia
2000 Year
1995
2000 Year
2005
1995
2000 Year
2005
More Countries Baltic Republics are Estonia, Latvia, and Lithuania.
A Ricardian Model
Micro to Macro
Application
Comparative Advantage and Gains From Trade ln Gddt ρRCA dt ln πddt Country Effects Year Effects Obs. R2
ln GTdt
-.079
-.139
-.031
-.054
(.007)˚˚
(.014)˚˚
(.003)˚˚
(.005)˚˚
.445
.454
-.217
-.213
(.005)˚˚
(.009)˚˚
(.002)˚˚
(.004)˚˚
444 .947
X X 444 .995
444 .961
X X 444 .996
High correlation index associated with lower gains from trade. Changes in RCAsdt ùñ heterogeneous and evolving GTdt .
A Ricardian Model
Micro to Macro
Application
Conclusion Putting Ricardo’s second insight to work §
Technological structure ô productivity a Fr´echet process
§
Micro estimates ùñ correlation function ùñ macro counterfactuals
§
Application: gains from trade hinge on correlation structure
Potential applications §
Multinational firms, sub-national trade, global value chains
§
Any environment using Fr´echet tools (selection in GE)
New questions §
Trade policy implications? (Costinot et al., 2015, 2016)
§
Relate macro patterns to micro fundamentals? (Hanson et al., 2015)
Estimates
Gains From Trade
%∆ Gains
Correlation Heterogeneity
References
Back
−10
Sectoral Elasticity 0 10
20
Estimates of Sectoral Elasticities
Correlation Dynamics
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
Sector
OLS estimates (pooled across years) of σs from differenced sectoral gravity equation ∆ ln πsodt “ ∆d βsdt ´ σs ∆d lnp1 ` tsodt q ´ σs δ 1 ∆d Geood ` ∆d sodt for difference between d “ AUS and d “ USA.
Estimates
Gains From Trade
%∆ Gains
Estimate of θ « 2.56
1{θ Share Border Log Distance Year Effects Year-Covariate Interactions Obs. R2
Correlation Heterogeneity
Correlation Dynamics
References
Back
(1) .393
∆d ysodt (2) .391
(3) .391
(.032)˚˚
(.032)˚˚
(.032)˚˚
-.909
-.909
-.828
(.051)˚˚
(.051)˚˚
(.178)˚˚
.049
.049
.070
(.021)˚
(.021)˚
(.073)
X
X X 5589 .114
5589 .113
5589 .114
Pooled OLS estimates of 1{θ from differenced gravity equation ÿ 1 ∆d ysodt “ ∆d βdt ` δ 1 ∆d Geood ` ∆d ln πsod ` ∆d usodt θ o for difference between d “ AUS and d “ USA.
Estimates
Gains From Trade
%∆ Gains
Correlation Heterogeneity
Correlation Dynamics
1.1
Gains From Trade in 1996: GTd versus GTdCES
Gains From Trade 1.05 1.075
BLX IRL
LTU BAL NLD SVN SVK
BGR
1.025
HUN DNK CZE AUT TWN CANPRT SWE FINROU GBR GRC MEX KOR DEU POL TUR ESP FRA IDN ITA RUS AUS
1
IND CHN USA BRA JPN
.6
.65
.7
.75 .8 .85 Self Trade Share
.95
` ˘ρs ‰´ θ1 1´ρs ř . s πsdd o πsod ř “ p s πsdd q´1{ε for ε “ 5.
Black data: GTd “ Red line: GTdCES
.9
“ř
1
References
Estimates
Gains From Trade
%∆ Gains
Correlation Heterogeneity
Correlation Dynamics
Gains From Trade 1.05 1.075
1.1
Gains From Trade in 1998: GTd versus GTdCES
IRL
BLX LTU BAL SVN SVK NLD HUN
BGR
1.025
AUT IDN CAN DNK CZE TWN PRT SWE ROU POL FIN GRC MEX KOR DEU ESP GBR RUS FRA TUR ITA AUS
1
IND USA CHN BRA JPN
.6
.65
.7
.75 .8 .85 Self Trade Share
.95
` ˘ρs ‰´ θ1 1´ρs ř . s πsdd o πsod ř “ p s πsdd q´1{ε for ε “ 5.
Black data: GTd “ Red line: GTdCES
.9
“ř
1
References
Estimates
Gains From Trade
%∆ Gains
Correlation Heterogeneity
Correlation Dynamics
1.1
Gains From Trade in 2000: GTd versus GTdCES
IRL
BLX
Gains From Trade 1.05 1.075
LTU HUN
SVK BGR SVN NLD BAL CZEAUT DNK TWN CANPRT ROU SWE GRC
1.025
IDN FIN DEU ESP POL KOR MEX FRA RUS GBRITA TUR AUS
1
IND CHN USA BRA JPN
.6
.65
.7
.75 .8 .85 Self Trade Share
.95
` ˘ρs ‰´ θ1 1´ρs ř . s πsdd o πsod ř “ p s πsdd q´1{ε for ε “ 5.
Black data: GTd “ Red line: GTdCES
.9
“ř
1
References
Estimates
Gains From Trade
%∆ Gains
Correlation Heterogeneity
Correlation Dynamics
1.1
Gains From Trade in 2002: GTd versus GTdCES
BLX
Gains From Trade 1.05 1.075
IRL
SVK
LTU
BGR SVN BAL HUN NLD AUT CZE DNK ROU TWN CAN PRT GRC SWE
IND CHN BRA USA JPN
1
1.025
POL DEU FIN ESP IDN RUS KOR GBR FRA MEX TUR ITA AUS
.6
.65
.7
.75 .8 .85 Self Trade Share
.95
` ˘ρs ‰´ θ1 1´ρs ř . s πsdd o πsod ř “ p s πsdd q´1{ε for ε “ 5.
Black data: GTd “ Red line: GTdCES
.9
“ř
1
References
Estimates
Gains From Trade
%∆ Gains
Correlation Heterogeneity
Correlation Dynamics
1.1
Gains From Trade in 2004: GTd versus GTdCES
Gains From Trade 1.05 1.075
SVKBLX BGR LTU SVN
IRL
HUN NLD CZE BAL TWNAUT
ROU DNK
1.025
PRT POL CAN GRC SWE DEU FIN KOR IDN ESP MEX TUR GBR FRA RUS ITA IND AUS CHN
1
USA BRA JPN
.6
.65
.7
.75 .8 .85 Self Trade Share
.95
` ˘ρs ‰´ θ1 1´ρs ř . s πsdd o πsod ř “ p s πsdd q´1{ε for ε “ 5.
Black data: GTd “ Red line: GTdCES
.9
“ř
1
References
Estimates
Gains From Trade
%∆ Gains
Correlation Heterogeneity
Correlation Dynamics
1.1
Gains From Trade in 2006: GTd versus GTdCES SVK
Gains From Trade 1.05 1.075
HUN
Back
LTU BLX SVN BGR BAL NLD TWN CZE AUT DNK
IRL
ROU PRT SWEPOL GRC DEU FIN CAN
1
1.025
ESP KOR TUR FRA MEXGBR ITA IDN RUS IND AUS CHN USA JPN BRA
.6
.65
.7
.75 .8 .85 Self Trade Share
.95
` ˘ρs ‰´ θ1 1´ρs ř . s πsdd o πsod ř “ p s πsdd q´1{ε for ε “ 5.
Black data: GTd “ Red line: GTdCES
.9
“ř
1
References
Estimates
Gains From Trade
%∆ Gains
Correlation Heterogeneity
Correlation Dynamics
Percent Difference in Gains From Trade −10 0 10 20 30
40
Gains From Trade in 1996: GTd versus GTdCES
LTU
BGR BLX BAL SVN NLD
GRC RUS ROU TUR DNK PRT
SVK IRL
JPN IND
ESP BRA POLITA FRA KOR DEUIDN CHN FINGBR AUS USA SWE MEX
HUN AUT CAN
−20
CZE TWN
.6
.65
.7
.75 .8 .85 Self Trade Share
Percent difference calculated as 100 ˆ
.9
.95
GTd ´GTdCES GTdCES ´1
.
1
References
Estimates
Gains From Trade
%∆ Gains
Correlation Heterogeneity
Correlation Dynamics
Percent Difference in Gains From Trade −10 0 10 20 30
40
Gains From Trade in 1998: GTd versus GTdCES
LTU IDN BGR BLX BAL SVN NLD SVK
HUN
ROU RUS GRC TUR
ESP AUT CAN POL KORFRAITA DEU GBR AUS FIN CZE SWE MEX TWN
IND
JPN
BRA CHN USA
−20
IRL
DNK PRT
.6
.65
.7
.75 .8 .85 Self Trade Share
Percent difference calculated as 100 ˆ
.9
.95
GTd ´GTdCES GTdCES ´1
.
1
References
Estimates
Gains From Trade
%∆ Gains
Correlation Heterogeneity
Correlation Dynamics
Percent Difference in Gains From Trade −10 0 10 20 30
40
Gains From Trade in 2000: GTd versus GTdCES
IND LTU IDN
BLX
HUN
JPN
BRA USA CHN
−20
IRL
BGR RUS ROU TUR NLD PRT GRC SVN BAL SVK DNK ESP ITA AUT CAN FRA POL KOR DEU GBR AUS CZE FIN SWE MEX TWN
.6
.65
.7
.75 .8 .85 Self Trade Share
Percent difference calculated as 100 ˆ
.9
.95
GTd ´GTdCES GTdCES ´1
.
1
References
Estimates
Gains From Trade
%∆ Gains
Correlation Heterogeneity
Correlation Dynamics
Percent Difference in Gains From Trade −10 0 10 20 30
40
Gains From Trade in 2002: GTd versus GTdCES
IND BGR LTU IDN RUS TUR
ROU BLX SVK
PRT GRC
SVN NLD BAL AUTDNK
CAN
JPN ESP ITA POL FRA
DEU CZE HUN
SWE
BRA
KOR GBR AUS
USA
FIN MEX
TWN CHN
−20
IRL
.6
.65
.7
.75 .8 .85 Self Trade Share
Percent difference calculated as 100 ˆ
.9
.95
GTd ´GTdCES GTdCES ´1
.
1
References
Estimates
Gains From Trade
%∆ Gains
Correlation Heterogeneity
Correlation Dynamics
Percent Difference in Gains From Trade −10 0 10 20 30
40
Gains From Trade in 2004: GTd versus GTdCES
BGR LTU
IDN ROU NLD
BLX
TUR RUS
PRT GRC
SVN CAN
SVK
IND
BAL AUT DNK POL GBR DEU KOR FIN CZE SWE MEX TWN
JPN BRA
ESP ITA FRA
USA AUS
HUN CHN
−20
IRL
.6
.65
.7
.75 .8 .85 Self Trade Share
Percent difference calculated as 100 ˆ
.9
.95
GTd ´GTdCES GTdCES ´1
.
1
References
Estimates
Gains From Trade
%∆ Gains
Correlation Heterogeneity
Correlation Dynamics
Back
Percent Difference in Gains From Trade −10 0 10 20 30
40
Gains From Trade in 2006: GTd versus GTdCES
LTU
BGR NLD
TUR JPN IDN RUS ROU ESP ITA IND FRA CAN KOR GBR POL USABRA DEU AUS FIN GRC
PRT
SVN BLX
BAL AUT DNK
SVK TWN
SWE
HUN
CZE
MEX CHN
−20
IRL
.6
.65
.7
.75 .8 .85 Self Trade Share
Percent difference calculated as 100 ˆ
.9
.95
GTd ´GTdCES GTdCES ´1
.
1
References
Estimates
Gains From Trade
%∆ Gains
Correlation Heterogeneity
Correlation Dynamics
References
.55
RCA-Induced Correlation Heterogeneity in 1996
RCA−Weighted Correlation Index .25 .35 .45
SWE FIN JPN
DEU IRL SVN
AUT TWN DNK
GBR FRA KOR ITA ESP
CZE CAN BLX
SVK NLD BAL HUN
PRT MEX POL AUS IDN ROUGRC TURRUS
BGR
USA
BRA CHN IND
.15
LTU
.6
.65
.7
.75 .8 .85 Self Trade Share
RCA-weighted correlation index, ρRCA “ dt
ř s
.9
.95
1
sdt ρs řRCA , across countries in 2006. RCAsdt s
Estimates
Gains From Trade
%∆ Gains
Correlation Heterogeneity
Correlation Dynamics
References
.55
RCA-Induced Correlation Heterogeneity in 1998
RCA−Weighted Correlation Index .25 .35 .45
SWE
FIN DEU
IRL SVN
AUT TWN
HUN NLD BLXBALSVK
FRA ITA
KOR ESP POL PRT MEX
AUS
GRC RUS ROU TUR
IDN
BRA CHN IND
BGR
.15
LTU
JPN USA
GBR
DNK CZE CAN
.6
.65
.7
.75 .8 .85 Self Trade Share
RCA-weighted correlation index, ρRCA “ dt
ř s
.9
.95
1
sdt ρs řRCA , across countries in 2006. RCAsdt s
Estimates
Gains From Trade
%∆ Gains
Correlation Heterogeneity
Correlation Dynamics
References
.55
RCA-Induced Correlation Heterogeneity in 2000
RCA−Weighted Correlation Index .25 .35 .45
SWE FIN DEU
IRL
JPN
TWN AUT HUN BLX
SVN CZE BAL SVK NLD
GBR KORFRA ITA ESP
DNK CAN
PRT
POL MEX AUS
ROU GRC
LTU
USA
IDN
BRA CHN
RUS TUR
IND
.15
BGR
.6
.65
.7
.75 .8 .85 Self Trade Share
RCA-weighted correlation index, ρRCA “ dt
ř s
.9
.95
1
sdt ρs řRCA , across countries in 2006. RCAsdt s
Estimates
Gains From Trade
%∆ Gains
Correlation Heterogeneity
Correlation Dynamics
References
.55
RCA-Induced Correlation Heterogeneity in 2002
RCA−Weighted Correlation Index .25 .35 .45
SWE
FIN DEU JPN
TWN AUT
IRL HUN
SVNCZE
BLX
GBR KOR FRA
DNK BAL
SVK
ITA
CAN
ESP POL
NLD PRT
MEX
ROU GRC
LTU
USA
BGR
AUS CHN BRA
RUS IDN IND
.15
TUR
.6
.65
.7
.75 .8 .85 Self Trade Share
RCA-weighted correlation index, ρRCA “ dt
ř s
.9
.95
1
sdt ρs řRCA , across countries in 2006. RCAsdt s
Estimates
Gains From Trade
%∆ Gains
Correlation Heterogeneity
Correlation Dynamics
References
.55
RCA-Induced Correlation Heterogeneity in 2004
SWE FIN
RCA−Weighted Correlation Index .25 .35 .45
DEU IRL
TWNAUT CZE HUN SVN BAL SVK BLX
GBR FRA ITA ESP
DNK CAN POL
NLD
PRT LTU
JPN
KOR
ROU
USA
CHN AUS MEX
GRC
BRA
IDN RUS
BGR
IND
.15
TUR
.6
.65
.7
.75 .8 .85 Self Trade Share
RCA-weighted correlation index, ρRCA “ dt
ř s
.9
.95
1
sdt ρs řRCA , across countries in 2006. RCAsdt s
Estimates
Gains From Trade
%∆ Gains
Correlation Heterogeneity
Correlation Dynamics
Back
.55
RCA-Induced Correlation Heterogeneity in 2006
References
SWE FIN DEU
RCA−Weighted Correlation Index .25 .35 .45
IRL
JPN
CZE AUT TWN HUN SVK
KOR GBR FRA ITA POL CAN ESP
SVN BALDNK
BLX
NLD
PRT ROU
MEX
USA CHN AUS BRA
GRC
LTU
IDNRUS IND TUR
.15
BGR
.6
.65
.7
.75 .8 .85 Self Trade Share
RCA-weighted correlation index, ρRCA “ dt
ř s
.9
.95
1
sdt ρs řRCA , across countries in 2006. RCAsdt s
Estimates
Gains From Trade
%∆ Gains
Correlation Heterogeneity
RCA-Induced Correlations Over Time
Correlation Dynamics
References
Back
AUT
BAL
BGR
BLX
BRA
CAN
CHN
CZE
DEU
DNK
ESP
FIN
FRA
GBR
GRC
HUN
IDN
IND
IRL
ITA
JPN
KOR
LTU
MEX
NLD
POL
PRT
ROU
RUS
SVK
SVN
SWE
TUR
TWN
USA
.2 .3 .4 .5 .2 .3 .4 .5 .2 .3 .4 .5 .2 .3 .4 .5 .2 .3 .4 .5
RCA−Weighted Correlation Index
.2 .3 .4 .5
AUS
1995
2000
2005
1995
2000
2005
1995
2000
2005
1995
Year Graphs by Country
2000
2005
1995
2000
2005
1995
2000
2005
Estimates
Gains From Trade
%∆ Gains
Correlation Heterogeneity
Correlation Dynamics
References
R. Adao, A. Costinot, and D. Donaldson. Nonparametric counterfactual predictions in neoclassical models of international trade. The American Economic Review, 107(3):633–689, 2017. J. E. Anderson. A theoretical foundation for the gravity equation. The American Economic Review, 69(1):106–116, 1979. P. Antr` as, A. de Gortari, et al. On the geography of global value chains. Technical report, 2017. C. Arkolakis, A. Costinot, and A. Rodr´ıguez-clare. New trade models, same old gains? The American Economic Review, pages 94–130, 2012. M. Bas, T. Mayer, and M. Thoenig. From micro to macro: Demand, supply, and heterogeneity in the trade elasticity. Journal of International Economics, 108:1–21, 2017. W. Brooks and P. Pujolas. Non linear gravity. 2017. L. Caliendo and F. Parro. Estimates of the trade and welfare effects of nafta. The Review of Economic Studies, 82(1):1–44, 2015. J. Caron, T. Fally, and J. Markusen. International trade puzzles: a solution linking production factors and demand. The Quarterly Journal of Economics, 129(3):1501–1552, 2014. A. Costinot and A. Rodr`ıguez-Clare. Trade theory with numbers: Quantifying the consequences of globalization. Technical Report 4, 2014. A. Costinot, D. Donaldson, and I. Komunjer. What goods do countries trade? a quantitative exploration of ricardo’s ideas. Review of Economic Studies, 79:581–608, 2012. A. Costinot, D. Donaldson, J. Vogel, and I. Werning. Comparative advantage and optimal trade policy. The Quarterly Journal of Economics, 130(2):659–702, 2015. A. Costinot, A. Rodr´ıguez-Clare, and I. Werning. Micro to macro: Optimal trade policy with firm heterogeneity. Mimeo, MIT, 2016. L. De Haan. A spectral representation for max-stable processes. The Annals of Probability, 12(4):1194–1204, 1984. ISSN 00911798. URL http://www.jstor.org/stable/2243357. J. Eaton and S. Kortum. Technology, geography, and trade. Econometrica, pages 1741–1779, 2002. G. H. Hanson, N. Lind, and M.-A. Muendler. The dynamics of comparative advantage. Technical report, National bureau of economic research, 2015. D. Lashkari and M. Mestieri. Gains from trade with heterogeneous income and price elasticities. Mimeo, Harvard University, 2016. A. Levchenko and J. Zhang. The evolution of comparative advantage: Measurement and welfare implications. Journal of Monetary Economics, 78:96–111, 2016.
Estimates
Gains From Trade
%∆ Gains
Correlation Heterogeneity
Correlation Dynamics
References
D. McFadden. Modeling the choice of residential location. Transportation Research Record, (673), 1978. M. J. Melitz. The impact of trade on intra-industry reallocations and aggregate industry productivity. Econometrica, 71(6): 1695–1725, 2003. R. Ossa. Why trade matters after all. 97(2):266–277, 2015. M. D. Penrose. Semi-min-stable processes. The Annals of Probability, 20(3):1450–1463, 1992. ISSN 00911798. URL http://www.jstor.org/stable/2244652. M. Schlather. Models for stationary max-stable random fields. Extremes, 5(1):33–44, 2002.
