trade,migrationandregionalincomedifferences: evidencefromchina ·...
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Introduction Model Quantitative Analysis Conclusion Appendix
Trade, Migration and Regional Income Differences:Evidence from China
Trevor TombeUniversity of Calgary
Xiaodong ZhuUniversity of Toronto and SAIF
Department of Economics, Yale
October 7, 2014
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Introduction Model Quantitative Analysis Conclusion Appendix
Motivation
• Aggregate gains from trade widely studied• What about spatial distribution of gains from trade?
• Aggregate and spatial effects of trade liberalization depend oncosts to internal trade and factor movements• How large are internal trade and migration costs? Do they differ
across space? ... change through time? .. interact with each other?
• To answer these questions, we develop a model and apply it toa useful setting (China)• Significant recent liberalizations (internal and external)• Large inter-province worker flows (40M in 2005; 86M in 2010)• Massive internal income differences
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Introduction Model Quantitative Analysis Conclusion Appendix
Related Literature• International trade with multi-region countries:
• Henderson (1982), Rauch (1991), Bond (1993), Courant andDeardorff (1993), Krugman and Livas Elizondo (1996), Matsuyama(1999), and Venables and Limao (2002)
• Costly Internal Trade (no labour frictions):• Ramondo et al. (2011); Allen and Arkolakis (2012); Cosar and
Fajgelbaum (2012); Caliendo et. al. (2014); Redding (2014);Fajgelbaum and Redding (2014); Tombe and Winter (2014)
• Trade Induced Labour Reallocation (no internal trade):• Kambourov (2009); Artuc et al. (2010); Menezes-Filho and
Muendler (2011); Cosar (2013); Dix-Carneiro (2014)
• Commuting Decisions:• Ahlfeldt, Redding, Sturm, and Wolf (2012)
• Occupational Choice:• Cortes and Gallipoli (2014)
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Introduction Model Quantitative Analysis Conclusion Appendix
This Paper
• Build unique dataset for China: 2000/02 – 2005/07
• We develop a general equilibrium model of internal andexternal trade with goods and factor market frictions• We introduce factor mobility frictions: model migration decisions
(Artuc et al., 2008; Ahlfeldt et al., 2012; Redding, 2014; Cortes andGallipoli, 2014)
• Measure and quantify the effect of (1) international tradeliberalization, (2) internal trade liberalization, (3) factormarket liberalization, (4) productivity change on:• Welfare — aggregate and regional• Migration — between provinces• Income Differences — between provinces
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Introduction Model Quantitative Analysis Conclusion Appendix
Data (in brief)
• Migration: 2000 and 2005 census data• From 2005 census, we can identify for each province those who have
immigrated between 2000 and 2005• Individual earnings data (2005 only) will prove important
• Trade Flows: Extended regional I/O tables 2002 and 2007• Information on international trade for each province and bilateral
trade for each pair of provinces (2002) or regions (2007)• Province-level gross output and total expenditures
• Real Income: Price and GDP data• Nominal GDP by provinces• Province-specific price levels• 1990 common basket price levels + provincial CPI changes
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Introduction Model Quantitative Analysis Conclusion Appendix
Visualizing Key Features of the Data
Figure: The Geography of China
Hainan
Anhui
Zhejiang
Jiangxi
Jiangsu
Jilin
Qinghai
Fujian
Heilongjiang
Henan
Hebei
Hunan
Hubei
Xinjiang
Tibet
Gansu
Guangxi
Guizhou
Liaoning
Inner Mongol
Ningxia
Beijing
Shanghai
Shanxi
Shandong
Shaanxi
Sichuan
Tianjin
Yunnan
Guangdong
Table5 / 36
Introduction Model Quantitative Analysis Conclusion Appendix
Visualizing Key Features of the Data
Figure: Output per Capita (90th/10th ∼ 7)
Hainan
Anhui
Zhejiang
Jiangxi
Jiangsu
Jilin
Qinghai
Fujian
Heilongjiang
Henan
Hebei
Hunan
Hubei
Xinjiang
Tibet
Gansu
Guangxi
Guizhou
Liaoning
Inner Mongol
Ningxia
Beijing
Shanghai
Shanxi
Shandong
Shaanxi
Sichuan
Tianjin
Yunnan
Guangdong
Table 6 / 36
Introduction Model Quantitative Analysis Conclusion Appendix
Visualizing Key Features of the Data
Figure: Home-Share of Spending (90th=0.86, 10th=0.62 )
Hainan
Anhui
Zhejiang
Jiangxi
Jiangsu
Jilin
Qinghai
Fujian
Heilongjiang
Henan
Hebei
Hunan
Hubei
Xinjiang
Tibet
Gansu
Guangxi
Guizhou
Liaoning
Inner Mongol
Ningxia
Beijing
Shanghai
Shanxi
Shandong
Shaanxi
Sichuan
Tianjin
Yunnan
Guangdong
Table 7 / 36
Introduction Model Quantitative Analysis Conclusion Appendix
Visualizing Key Features of the Data
Figure: Migrant Worker Shares (90th=0.2, 10th=0.006)
Hainan
Anhui
Zhejiang
Jiangxi
Jiangsu
Jilin
Qinghai
Fujian
Heilongjiang
Henan
Hebei
Hunan
Hubei
Xinjiang
Tibet
Gansu
Guangxi
Guizhou
Liaoning
Inner Mongol
Ningxia
Beijing
Shanghai
Shanxi
Shandong
Shaanxi
Sichuan
Tianjin
Yunnan
Guangdong
Table 8 / 36
Introduction Model Quantitative Analysis Conclusion Appendix
Table: Migrant Characteristics (from Census Data)
1990 2000 2005
Total Migrants 32.7 M 130.6 M 165.4 MInter-Provincial Migrants 10.5 M 35.8 M 53 M
Inter-Provincial Migrant Workers 2 M 28 M 40 M
(a) Migrant Stock
EmployedAll Inter-Provincial Inter-Provincial
Migrants Migrants Migrants
Number 165.4 M 53 M 40 MReason for Migrating
Work 45% 73% 91%Family 30% 21% 6%
Education 6% 2% 2%Other 18% 4% 0.3%
Other CharacteristicsWith Children 30% 28% 27%
Agricultural Hukou 62% 83% 86%Male 50% 53% 57%
(b) Characteristics of Migrant Stock (Census 2005)9 / 36
Introduction Model Quantitative Analysis Conclusion Appendix
Migration Costs
Wide variety of very large costs to live outside one’s Hukou region:• Lack of employment contracts (no provision of benets or otherlegal rights; reform 2007)
• Difficult to find housing (couldn’t rent an apartment in Beijinguntil 2005)
• Unregistered migrants detained/deported (until 2003,following a death)
• Limited health insurance access• Children attend school barred or expensive fees (can be 20% ofincome)
• Other (more standard) costs:• communication with and travel to home province• language/ethnic dierences
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Introduction Model Quantitative Analysis Conclusion Appendix
Internal Trade Barriers
Pre-2001:• Strong local protectionism and high internal trade barriers inthe 1980s and 1990s (Young, 2000; Poncet, 2003)
• The degree of local market protection is positively associatedwith the size of the state sector in the region
Post-2001:• Downsizing the state-owned sector• State council’s directive about eliminating local marketprotection in 2001
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Introduction Model Quantitative Analysis Conclusion Appendix
Main Results
• Welfare gains are, by far, largest for domestic reforms(especially internal trade cost reductions)
• Trade flows respond very little to changes in migration costs
• Internal migration responds very little to changes in trade costs
• Internal (not external) liberalization lowers income differences
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Model
Introduction Model Quantitative Analysis Conclusion Appendix
Regions and Preferences
• N + 1 regions: N within China + rest of the world• Endowments:
• L0n initial Hukou registrants
• Each of whom differ in productivity (more on this later)
• Sn fixed land used for housing and production
• Representative H.H. Objective:• Maximize utility per effective-worker
un = cαn s1−αun
subject toPncn + rnsun ≤ vn
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Introduction Model Quantitative Analysis Conclusion Appendix
Production
• Final Good: composite of a continuum of intermediates
Yn =
(ˆ 1
0yn(j)(σ−1)/σdj
)σ/(σ−1)• Elasticity of substitution σ > 1• Final goods are consumed (C ) and used in production as
inputs (Q); market clearing ⇒ Yn = Cn + Qn
• Tradable Intermediates: y produced with CRS technologyusing effective-labour (H), land (SY ), and inputs (Q)
yn(j) = ϕn(j)Hn(j)βSYn(j)ηQn(j)1−β−η
• TFP ϕ differs across firms; as in Eaton and Kortum (2002)
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Introduction Model Quantitative Analysis Conclusion Appendix
Prices and Trade Patterns• Iceberg trade costs τni + perfect competition ⇒
pni (ϕ) = τniMCi (ϕ) ∝ τniwβi r
ηi P
1−β−ηi /ϕ
• With TFP ϕ distributed Frechet: Fi (ϕ) = e−Tiϕ−θ, fraction of
region n spending allocated to goods produced in region i is
πni =Ti
(τniw
βi r
ηi P
1−β−ηi
)−θ∑N+1
k=1 Tk
(τnkw
βk r
ηkP
1−β−ηk
)−θ• Aggregate price index in region n (for tradables)
Pn ∝
[N+1∑k=1
Tk
(τnkw
βk r
ηkP
1−β−ηk
)−θ]−1/θ• Finally, market clearing for land ⇒ rn ∝ wnHn/Sn
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Introduction Model Quantitative Analysis Conclusion Appendix
Prices and Trade Patterns• Iceberg trade costs τni + perfect competition ⇒
pni (ϕ) = τniMCi (ϕ) ∝ τniwβi r
ηi P
1−β−ηi /ϕ
• With TFP ϕ distributed Frechet: Fi (ϕ) = e−Tiϕ−θ, fraction of
region n spending allocated to goods produced in region i is
πni =Ti
(τniw
βi r
ηi P
1−β−ηi
)−θ∑N+1
k=1 Tk
(τnkw
βk r
ηkP
1−β−ηk
)−θ
• Aggregate price index in region n (for tradables)
Pn ∝
[N+1∑k=1
Tk
(τnkw
βk r
ηkP
1−β−ηk
)−θ]−1/θ• Finally, market clearing for land ⇒ rn ∝ wnHn/Sn
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Introduction Model Quantitative Analysis Conclusion Appendix
Prices and Trade Patterns• Iceberg trade costs τni + perfect competition ⇒
pni (ϕ) = τniMCi (ϕ) ∝ τniwβi r
ηi P
1−β−ηi /ϕ
• With TFP ϕ distributed Frechet: Fi (ϕ) = e−Tiϕ−θ, fraction of
region n spending allocated to goods produced in region i is
πni =Ti
(τniw
βi r
ηi P
1−β−ηi
)−θ∑N+1
k=1 Tk
(τnkw
βk r
ηkP
1−β−ηk
)−θ• Aggregate price index in region n (for tradables)
Pn ∝
[N+1∑k=1
Tk
(τnkw
βk r
ηkP
1−β−ηk
)−θ]−1/θ• Finally, market clearing for land ⇒ rn ∝ wnHn/Sn
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Introduction Model Quantitative Analysis Conclusion Appendix
Regional Income
• Nominal Income (Expenditures) per Effective Worker:
vn =wn︸ ︷︷ ︸
Labour Income+ (1− α)vn + ηwn/β︸ ︷︷ ︸
Spending on Land
=
(β + η
αβ
)wn
• Total expenditures: Xn = vnHn
• Real Income per Effective Worker (vn/Pαn r1−αn ):
Vn ∝T
αθ(β+η)n︸ ︷︷ ︸
Technology
· π− αθ(β+η)
nn︸ ︷︷ ︸Market Access
· (Sn/Hn)η+(1−α)ββ+η︸ ︷︷ ︸
Land / effective worker
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Introduction Model Quantitative Analysis Conclusion Appendix
Regional Income
• Nominal Income (Expenditures) per Effective Worker:
vn =wn︸ ︷︷ ︸
Labour Income+ (1− α)vn + ηwn/β︸ ︷︷ ︸
Spending on Land
=
(β + η
αβ
)wn
• Total expenditures: Xn = vnHn
• Real Income per Effective Worker (vn/Pαn r1−αn ):
Vn ∝T
αθ(β+η)n︸ ︷︷ ︸
Technology
· π− αθ(β+η)
nn︸ ︷︷ ︸Market Access
· (Sn/Hn)η+(1−α)ββ+η︸ ︷︷ ︸
Land / effective worker
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Introduction Model Quantitative Analysis Conclusion Appendix
Inter-Provincial Migration
• Real Income per Effective Worker: Vi in region i
• Worker Productivity: different across region• Denote the effective labour units by z• Effective labour is i.i.d. across individuals and locations
• Real Cost of Migration: share time/income lost, 1− µni
• Rule: Migrate from n to i iff µniziVi = maxk=1,...,N {µnkzkVk}
• If z follows a Frechet distribution Fz(x) = e−(
xγ
)−κ, then
share of region n registered workers that move to region i is
mni =(Viµni )
κ∑Nk=1 (Vkµnk)κ
Gravity Evidence
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Introduction Model Quantitative Analysis Conclusion Appendix
Expected Income and Aggregate Welfare
Proposition 2: If worker productivities zi are distributed Frechet withmean 1 and variance parameter κ, and agents are able to migratebetween regions at cost µij , then the expected real income net ofmigration costs for workers from region i is
V 0i = Vim
−1/κii ,
and aggregate average real income (welfare) is therefore
W =N∑i=1
λ0i Vim
−1/κii ,
where λ0i =
L0i∑N
j=1 L0j
is region i ’s registration share.
Proof: See paper. Intuition: max {µnkzkVk} ∼ Frechet(κ,Vnm
−1/κnn
)
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Introduction Model Quantitative Analysis Conclusion Appendix
Eq’m Effective Labour in Each Region• Workers in Region n: Ln =
∑Ni=1minL
0i
• Analogous to Eaton-Kortum, where πni is both (1) share ofgoods and (2) share of spending, we can show mni is both1. Share of workers registered in n that work in region i2. Share of income earned by all workers registered in n from those
workers working in region i
• Effective Workers in Region n:
HnVn =N∑i=1
minL0i Vim
−1/κii
⇒ Hn =N∑i=1
(µinm
− 1κ
in
)minL
0i
• Useful with data on real GDP (HiVi ), migration (mni ,mnn),and hukou registrations (L0n) → solves for Vi , then Hi
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Introduction Model Quantitative Analysis Conclusion Appendix
Eq’m Effective Labour in Each Region• Workers in Region n: Ln =
∑Ni=1minL
0i
• Analogous to Eaton-Kortum, where πni is both (1) share ofgoods and (2) share of spending, we can show mni is both1. Share of workers registered in n that work in region i2. Share of income earned by all workers registered in n from those
workers working in region i
• Effective Workers in Region n:
HnVn =N∑i=1
minL0i Vim
−1/κii
⇒ Hn =N∑i=1
(µinm
− 1κ
in
)minL
0i
• Useful with data on real GDP (HiVi ), migration (mni ,mnn),and hukou registrations (L0n) → solves for Vi , then Hi
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Introduction Model Quantitative Analysis Conclusion Appendix
Eq’m Effective Labour in Each Region• Workers in Region n: Ln =
∑Ni=1minL
0i
• Analogous to Eaton-Kortum, where πni is both (1) share ofgoods and (2) share of spending, we can show mni is both1. Share of workers registered in n that work in region i2. Share of income earned by all workers registered in n from those
workers working in region i
• Effective Workers in Region n:
HnVn =N∑i=1
minL0i Vim
−1/κii
⇒ Hn =N∑i=1
(µinm
− 1κ
in
)minL
0i
• Useful with data on real GDP (HiVi ), migration (mni ,mnn),and hukou registrations (L0n) → solves for Vi , then Hi
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Quantitative Analysis
Introduction Model Quantitative Analysis Conclusion Appendix
The Equilibrium Conditions• Trade balance: vnHn =
∑N+1i=1 πinviHi
• Trade flows: πni ∝ PθnTi
(τniw
βi r
ηi P
1−β−ηi
)−θ
• Final good price: P−θn ∝∑N+1
i=1 Ti
(τniw
βi r
ηi P
1−β−ηi
)−θ• Land rental price: rn ∝ wnHn/Sn
• Real income: Vn ∝ wn/Pαn r
1−αn
• Migration flows: mni = (Viµni )κ∑N
k=1(Vkµnk )κ
• Migrant real incomes: HnVn ∝∑N
i=1minL0i Vim
−1/κii
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Introduction Model Quantitative Analysis Conclusion Appendix
The Equilibrium Conditions• Trade balance: vnHn =
∑N+1i=1 πinviHi
• Trade flows: πni ∝ PθnTi
(τniw
βi r
ηi P
1−β−ηi
)−θ• Final good price: P−θn ∝
∑N+1i=1 Ti
(τniw
βi r
ηi P
1−β−ηi
)−θ• Land rental price: rn ∝ wnHn/Sn
• Real income: Vn ∝ wn/Pαn r
1−αn
• Migration flows: mni = (Viµni )κ∑N
k=1(Vkµnk )κ
• Migrant real incomes: HnVn ∝∑N
i=1minL0i Vim
−1/κii
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Introduction Model Quantitative Analysis Conclusion Appendix
The Equilibrium Conditions• Trade balance: vnHn =
∑N+1i=1 πinviHi
• Trade flows: πni ∝ PθnTi
(τniw
βi r
ηi P
1−β−ηi
)−θ• Final good price: P−θn ∝
∑N+1i=1 Ti
(τniw
βi r
ηi P
1−β−ηi
)−θ• Land rental price: rn ∝ wnHn/Sn
• Real income: Vn ∝ wn/Pαn r
1−αn
• Migration flows: mni = (Viµni )κ∑N
k=1(Vkµnk )κ
• Migrant real incomes: HnVn ∝∑N
i=1minL0i Vim
−1/κii
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Introduction Model Quantitative Analysis Conclusion Appendix
The Equilibrium Conditions• Trade balance: vnHn =
∑N+1i=1 πinviHi
• Trade flows: πni ∝ PθnTi
(τniw
βi r
ηi P
1−β−ηi
)−θ• Final good price: P−θn ∝
∑N+1i=1 Ti
(τniw
βi r
ηi P
1−β−ηi
)−θ• Land rental price: rn ∝ wnHn/Sn
• Real income: Vn ∝ wn/Pαn r
1−αn
• Migration flows: mni = (Viµni )κ∑N
k=1(Vkµnk )κ
• Migrant real incomes: HnVn ∝∑N
i=1minL0i Vim
−1/κii
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Introduction Model Quantitative Analysis Conclusion Appendix
The Equilibrium Conditions• Trade balance: vnHn =
∑N+1i=1 πinviHi
• Trade flows: πni ∝ PθnTi
(τniw
βi r
ηi P
1−β−ηi
)−θ• Final good price: P−θn =∝
∑N+1i=1 Ti
(τniw
βi r
ηi P
1−β−ηi
)−θ• Land price: rn ∝ wnHn/Sn
• Real income: Vn ∝ wn/Pαn r
1−αn
• Migration flows: mni = (Viµni )κ∑N
k=1(Vkµnk )κ
• Migrant real incomes: HnVn ∝∑N
i=1minL0i Vim
−1/κii
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Introduction Model Quantitative Analysis Conclusion Appendix
Exact-Hat Algebra (Dekle et al., 2008)• Solving for relative changes eases the analysis
rn ∝ wnHn/Sn
⇒ rn = wnHn
• Another (less trivial) example:
P−θn =
∑N+1i=1 T
′i
(τ′niw
′βi r′ηi P
′1−β−ηi
)−θ∑N+1
i=1 Ti
(τniw
βi r
ηi P
1−β−ηi
)−θ=
∑N+1i=1 Ti
(τni w
βi r
ηi P
1−β−ηi
)−θTi
(τniw
βi r
ηi P
1−β−ηi
)−θ∑N+1
i=1 Ti
(τniw
βi r
ηi P
1−β−ηi
)−θ≡
N+1∑i=1
Ti
(τni w
βi r
ηi P
1−β−ηi
)−θπni
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Introduction Model Quantitative Analysis Conclusion Appendix
Exact-Hat Algebra (Dekle et al., 2008) Data: πni
Model mapping F :(τni , Tn, µni
)→(Vn,m′ni , π
′ni
), given (πni , Ln,mni ,Xn, L0n)
Our strategy: infer(τni , Tn, µni
)from F−1
(Vn,m′ni , π
′ni
)
wnHnXn =N+1∑i=1
π′inwi HiXi , (1)
π′ni = Pθn πni Ti
(τni w
β+ηi P1−β−η
iˆLηi
)−θ, (2)
P−θn =N+1∑i=1
πni Ti
(τni w
β+ηi P1−β−η
iˆLηi
)−θ, (3)
Vn =wn
Pαn r1−αn
=wα
n
Pαn H1−αn
, (4)
m′in =min
(Vnµin
)κ∑N
k=1 mik
(Vk µik
)κ , (5)
H ′nV′n =
N∑i=1
m′in L0i V ′i m′ii−1/κ
. (6)
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Introduction Model Quantitative Analysis Conclusion Appendix
Calibrating the Model
Parameter Value Target
η 0.1 Land’s share of gross output1− β − η 0.6 Intermediate’s share of output1− α 0.13 Housing’s share of expenditureLi Data National Employment Levelπij Data Bilateral Trade SharesXn Model-Implied Initial Eq’m GDPθ 4 Elasticity of Trade
Details to Follow
τni Pair Specific Bilateral Trade Sharesκ 2.21 Ex-Post Income Dispersionµni Pair Specific Migration and Real Income GapsTn Region Specific Real Income Data
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Introduction Model Quantitative Analysis Conclusion Appendix
Estimating Trade Costs• Flexible trade costs index (Head and Ries, 2001; Novy, 2013)
• Recall: πni ∝ PθnTi
(τniw
βi r
ηi P
1−β−ηi
)−θ• ⇒ ln
(πniπnn
)= ln
(PθnTi
(τniw
βi rηi P
1−β−ηi
)−θPθnTn
(wβn rηn P
1−β−ηn
)−θ)≡ Sn−Si−θln(τni )
• ⇒ ln(πniπnn
)+ ln
(πinπii
)= −θ [ln (τni ) + ln (τin)]
• The Head-Reis Index: τni ≡√τniτin =
(πnnπiiπniπin
)1/2θ• Notice: it’s symmetric (τni = τin)• We modify the index to incorporate region-specific costs• i.e. an exporter-specific cost ti implies
τni = τni√
ti/tn
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Introduction Model Quantitative Analysis Conclusion Appendix
Estimating Trade Costs• Flexible trade costs index (Head and Ries, 2001; Novy, 2013)
• Recall: πni ∝ PθnTi
(τniw
βi r
ηi P
1−β−ηi
)−θ• ⇒ ln
(πniπnn
)= ln
(PθnTi
(τniw
βi rηi P
1−β−ηi
)−θPθnTn
(wβn rηn P
1−β−ηn
)−θ)≡ Sn−Si−θln(τni )
• ⇒ ln(πniπnn
)+ ln
(πinπii
)= −θ [ln (τni ) + ln (τin)]
• The Head-Reis Index: τni ≡√τniτin =
(πnnπiiπniπin
)1/2θ• Notice: it’s symmetric (τni = τin)• We modify the index to incorporate region-specific costs• i.e. an exporter-specific cost ti implies
τni = τni√
ti/tn
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Introduction Model Quantitative Analysis Conclusion Appendix
Estimating Trade Costs• Flexible trade costs index (Head and Ries, 2001; Novy, 2013)
• Recall: πni ∝ PθnTi
(τniw
βi r
ηi P
1−β−ηi
)−θ• ⇒ ln
(πniπnn
)= ln
(PθnTi
(τniw
βi rηi P
1−β−ηi
)−θPθnTn
(wβn rηn P
1−β−ηn
)−θ)≡ Sn−Si−θln(τni )
• ⇒ ln(πniπnn
)+ ln
(πinπii
)= −θ [ln (τni ) + ln (τin)]
• The Head-Reis Index: τni ≡√τniτin =
(πnnπiiπniπin
)1/2θ• Notice: it’s symmetric (τni = τin)• We modify the index to incorporate region-specific costs• i.e. an exporter-specific cost ti implies
τni = τni√ti/tn
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Introduction Model Quantitative Analysis Conclusion Appendix
Estimating Trade Cost Asymmetries• If asymmetries are export costs, then τni = dni ti• Waugh (2010): asymmetries are exporter-specific
• Tombe and Winter (2014) show this is also true within countries
• Models imply ln (πni/πnn) = Si − Sn − θln (τni ); so, estimate
ln
(πniπnn
)= ρni + ιn + ηi + εni ,
where ρni is a directionless pair-effect such that ρni = ρin, and ιnand ηi are importer- and exporter-effects
• As the exporter effect is ηi = Si − θln (ti ) and the importereffect is ιn = −Sn, we infer export costs as
tn = e−(ιn+ηn)/θ
Export Cost Estimates
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Introduction Model Quantitative Analysis Conclusion Appendix
Relative Change in Trade Costs
Table: % Change in Trade Costs(τ2007ni /τ2002
ni
)Source i
Importer n NE B&T N Cst C Cst S Cst Cntrl NW SW WLDNE -11.8 -16.7 -23.5 -24.7 -23 -18 -18.5 -27.7B&T -14.2 -15 -15.5 -13.8 -23.9 -25.7 -18.5 -26.9N Cst -5.7 -1 -1 -11.2 -20.7 -22.6 -20.7 -20.3C Cst -16.4 -5.2 -4.5 -11.2 -15.9 -17.9 -12.4 -19.1S Cst -18.4 -4 -15.1 -12 -20.7 -24.7 -20.8 -10.6Cntrl -6.6 -5.2 -15.1 -6.7 -11.2 -19.1 -16.8 -27.9NW -4 -10.6 -20 -12 -18.6 -21.9 -17.8 -37.8SW -3.8 -1.2 -17.5 -5.4 -13.8 -19.1 -17.2 -27.7WLD -3.8 -0.2 -6.5 -1.6 9.7 -21 -29.4 -18.5
Distance, not ρni By Sector
25 / 36
Introduction Model Quantitative Analysis Conclusion Appendix
Calibrating the Model
Parameter Value Target
η 0.1 Land’s share of gross output1− β − η 0.6 Intermediate’s share of output1− α 0.13 Housing’s share of expenditureLi Data National Employment Levelπij Data Bilateral Trade SharesXn Model-Implied Initial Eq’m GDPθ 4 Elasticity of Trade
Details to Follow
τni Pair Specific Bilateral Trade Sharesκ 2.21 Ex-Post Income Dispersionµni Pair Specific Migration and Real Income GapsTn Region Specific Real Income Data
25 / 36
Introduction Model Quantitative Analysis Conclusion Appendix
Heterogeneity of Labour Productivity, κ
• Variation in the ex-post wage distribution given by a simplefunction of this paramtere (Cortes and Gallipoli, 2014)
• Ex-post income is r.v. Z = max {µnkzkVk}, which is Frechet
• CDF given by Pr(Z < x) ≡ Fi (x) = e−(x/[∑N
j=1(cijVj)κ]1/κ
)−κ
• Log income is therefore ∼Gumbel, with s.d. π/(κ√6)
• Census 2005 has individual earnings data; the average standarddeviation within origin-destination pairs implies κ ≈ 2.21• Controlling for age, occupation, hukou location, marital status,
industry, gender, education, etc... implies κ ≈ 2.85
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Introduction Model Quantitative Analysis Conclusion Appendix
Migration Costs• As with trade, µni = (mni/mnn)1/κ (Vn/Vi )
0 0.05 0.1 0.15 0.2 0.250
40
80
120
160
200
Disposable Income Net of Migration Costs, in 2000
Fre
quen
cy
(a) Histogram of cni
0 1 2 3 4 5 6 7 80
20
40
60
80
100
120
140
"Disposable" Income Share
Fre
qu
ency
(b) Histogram of cnizi
• Average migration cost: 89.6% of income• Average migration costs for migrants: 9.6% of income• Average change in migration costs, 2000-2005: µni = 1.14
Example: To Beijing
27 / 36
Introduction Model Quantitative Analysis Conclusion Appendix
Calibrating the Model
Parameter Value Target
η 0.1 Land’s share of gross output1− β − η 0.6 Intermediate’s share of output1− α 0.13 Housing’s share of expenditureLi Data National Employment Levelπij Data Bilateral Trade SharesXn Model-Implied Initial Eq’m GDPθ 4 Elasticity of Trade
Details to Follow
τni Pair Specific Bilateral Trade Sharesκ 2.21 Ex-Post Income Dispersionµni Pair Specific Migration and Real Income GapsTn Region Specific Real Income Data
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Introduction Model Quantitative Analysis Conclusion Appendix
Infer Productivity Changes from Real Income Growth
0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.50.7
0.8
0.9
1
1.1
1.2
1.3
1.4
1.5
Relative Real Income Change, Data from 2002−07
Rela
tive R
eal In
com
e C
hange, M
odel
(c) Real Income, when Tn = 1
−20
0
20
40
60
80
100
120
Inner M
ongolia
Shandong
Henan
Shanxi
Shannxi
Tia
njin
Jiangsu
Jiangxi
Shanghai
Hebei
Hunan
Sic
huan
Guangxi
Guiz
hou
Jilin
Zhejia
ng
Hubei
Heilo
ngjia
ng
Nin
gxi
aFujia
nG
ansu
Lia
onin
gQ
inghai
Yunnan
Guangdong
Beiji
ng
Xin
jiang
Anhui
Chongqin
gH
ain
an
% C
ha
ng
e in
(A
dju
ste
d)
Pro
du
ctivity P
ara
me
ter
(d) Required Change in Tα
θ(β+η)n
Notes: Compares the model-implied change in each province’s real income Vn whenunderlying productivity is constant to real income changes measured in data. Both areexpressed relative to the mean. In order for the model implies real income changesto match data, we require changes in underlying productivity draws Tn. The impliedproductivity change in display in the right panel, adjusted as T
α/θ(β+η)n .
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Introduction Model Quantitative Analysis Conclusion Appendix
Counterfactual Exercises
• We run a variety of counterfactuals
1. Internal Trade: τni for i , n 6= N + 1 only2. External Trade: τni for i , n = N + 1 only3. All Trade: τni for all pairs4. Migration: µni for all pairs5. All Domestic: Internal Trade + Migration6. Everything
• We then repeat all of the above with Tn changes
• Changes in outcomes of interest• Internal and external trade• Stock of migrants• Income differences (variance of log-income)• Aggregate welfare
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Introduction Model Quantitative Analysis Conclusion Appendix
Counterfactual Aggregate Outcomes
Change in TradeMeasured Cost GDP Ratio (p.p.) Migrant Income AggregateReduction of Internal External Stock Differences Welfare
Internal Trade 38.7 -2.7 -1.8% -3.6% 7.3%
External Trade -3.1 17.9 0.8% 2.1% 2.5%
All Trade 34.2 13.7 -0.9% -1.5% 9.6%
Migration 0.0 0.1 37.1% -8.9% 0.4%
All Domestic 38.7 -2.6 33.1% -11.9% 7.7%
Everything 34.1 13.8 34.2% -10.2% 10.1%
Data (2002-07) 17 12 18.5% -0.1% –
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Introduction Model Quantitative Analysis Conclusion Appendix
Lower Migration Costs: Employment and Real Income
0 0.5 1 1.5 2 2.5 3−10
−5
0
5
10
15
20
Beijing
Shanghai
Guangdong
Inner Mongolia
Initial Real Income, Relative to Mean
% C
hange in L
abour
Forc
e
(e) Employment
0 0.5 1 1.5 2 2.5 3−15
−10
−5
0
5
10
15
20
25
Beijing
Shanghai
Guangdong
Inner Mongolia
Initial Real Income, Relative to Mean
% C
hange in R
eal In
com
e
(f) Real Income
Notes: Displays the percentage change in employment Ln and real income Vn by provincein response to lower inter-provincial migration costs.
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Introduction Model Quantitative Analysis Conclusion Appendix
Lower Migration Costs: Trade Volumes
0 0.5 1 1.5 2 2.5 3−3
−2
−1
0
1
2
3
4
Beijing
ShanghaiGuangdong
Inner Mongolia
Initial Real Income, Relative to Mean
% C
ha
ng
e in
Tra
de
Vo
lum
e (
Imp
ort
s+
Exp
ort
s)
(g) International Trade
0 0.5 1 1.5 2 2.5 3−3
−2
−1
0
1
2
3
4
Beijing
ShanghaiGuangdong
Inner Mongolia
Initial Real Income, Relative to Mean
% C
ha
ng
e in
Tra
de
Vo
lum
e (
Imp
ort
s+
Exp
ort
s)
(h) Internal Trade
Notes: Displays the percentage change in trade volumes, both internationally and inter-nally, for each provinces resulting from lower migration costs. Aggregate trade changeslittle, but there is substantial variation across provinces. Coastal regions trade moremore as a result of lower internal migration costs; interior regions trade less.
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Introduction Model Quantitative Analysis Conclusion Appendix
Distributional Effects on Real Income Differences
0 0.5 1 1.5 2 2.5 3−10
−5
0
5
10
15
20
25
Beijing
ShanghaiGuangdong
Jilin
Initial Real Income, Relative to Mean
% C
hange in R
eal In
com
e
(i) Internal Trade
0 0.5 1 1.5 2 2.5 3−10
−5
0
5
10
15
20
25
Beijing
Shanghai
Guangdong
Tianjin
Inner Mongolia
Initial Real Income, Relative to Mean
% C
hange in R
eal In
com
e
(j) International Trade
Notes: Displays the percentage change in real incomes for each provinces resulting fromselected counterfactual.
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Introduction Model Quantitative Analysis Conclusion Appendix
Distributional Effects on Real Income Differences
0 0.5 1 1.5 2 2.5 3−15
−10
−5
0
5
10
15
20
25
Beijing
Shanghai
Guangdong
Inner Mongolia
Initial Real Income, Relative to Mean
% C
hange in R
eal In
com
e
(k) Migration Costs
0 0.5 1 1.5 2 2.5 3−10
−5
0
5
10
15
20
25
Beijing
Shanghai
Guangdong
Tianjin
Inner Mongolia
Initial Real Income, Relative to Mean
% C
hange in R
eal In
com
e
(l) Infernal Reforms
Notes: Displays the percentage change in real incomes for each provinces resulting fromselected counterfactual.
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Introduction Model Quantitative Analysis Conclusion Appendix
... with Productivity Changes
p.p. Change in Regional Marginal PriorChange in Trade/GDP Ratio Migrant Income Aggregate Welfare Welfare
Productivity and ... Internal External Stock Variance Welfare Change Change
Productivity Only -1.1 -4.6 -9.3% 11.5% 40.3% – –
Internal Trade 36.8 -6.9 -12.3% 6.2% 50.2% 7.1% 7.3%
External Trade -3.8 11.4 -8.3% 13.1% 43.3% 2.2% 2.5%
All Trade 32.9 7.9 -11.2% 8.0% 53.1% 9.2% 9.6%
Migration -1.1 -4.6 22.4% 3.1% 40.8% 0.4% 0.4%
Internal Reform 36.8 -6.8 17.2% -1.5% 50.7% 7.5% 7.7%
Everything 32.8 7.9 18.5% -0.1% 53.7% 9.5% 10.1%
Data (2002-07) 17 12 18.5% -0.1% – – –
35 / 36
Introduction Model Quantitative Analysis Conclusion Appendix
Conclusion
• We develop a general equilibrium model of internal-externaltrade with partial factor mobility• Highly tractable; eas to implement quantitative exercises• Useful for “measure” magnitude of trade and migration costs
• We apply the model to China and quantify the impacts oftrade liberalization and migration on aggregate welfare andregional income differences
• Domestic reforms substantially more important than externalliberalization• Lower migration and trade costs are complementary policies
• Opening up is important for China, but not because of goodstrade
36 / 36
Introduction Model Quantitative Analysis Conclusion Appendix
Cross-Province Differences Back
Summary Metric Across Province
Importer Mean Median p90 p10 90/10 Ratio
Real GDP per Capita 1 0.67 2.64 0.37 7.14Exports per Capita 1 0.17 2.08 0.03 69.33
Home Share 0.74 0.76 0.86 0.62 1.39Migration Share 0.06 0.02 0.2 0.006 31.67
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Introduction Model Quantitative Analysis Conclusion Appendix
Migration and Gravity Back
• Evidence that gravity equations capture commuting decisions(Erlander and Stewart, 1990; Sen and Smith, 1995; Ahlfeldt et al., 2012)
• Inter-provincial migration also consistent with gravity
−1
2−
10
−8
−6
−4
−2
Lo
g(N
orm
aliz
ed
Mig
ratio
n m
ij/m
ii fo
r 2
00
0)
9 10 11 12 13Log(Driving Time, Between Capitals)
(m) Migration vs. Travel Time
−1
2−
10
−8
−6
−4
−2
Lo
g(N
orm
aliz
ed
Mig
ratio
n m
ij/m
ii fo
r 2
00
0)
−3 −2 −1 0 1 2 3Ratio of Real Income per Effective Worker, Log(Vj/Vi)
(n) Migration vs. Income Differences
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Introduction Model Quantitative Analysis Conclusion Appendix
Trade Cost Changes, Using Distance (not ρni) Back
• Capture symmetric effect with bilateral distances dni
ln
(πniπnn
)= δln(dni ) + ιn + ηi + εni
Table: % Change in Trade Costs
SourceImporter NE B&T N Cst C Cst S Cst Cntrl NW SW WLD
NE -9.7 -9.4 -16.0 -20.6 -17.6 -17.3 -12.3 -19.9B&T -16.2 -9.7 -9.4 -11.2 -20.5 -26.7 -14.3 -21.0N Cst -13.3 -6.9 -0.1 -13.9 -22.0 -28.2 -21.6 -19.0C Cst -23.9 -11.6 -5.4 -14.7 -18.1 -24.5 -14.2 -18.5S Cst -22.7 -6.8 -12.4 -8.3 -19.6 -27.9 -19.2 -6.2Cntrl -12.6 -9.2 -13.6 -4.2 -12.5 -23.6 -16.3 -25.4NW -4.9 -9.3 -13.8 -4.2 -14.9 -17.2 -12.3 -31.8SW -10.6 -6.0 -16.6 -3.5 -15.5 -19.6 -22.3 -25.6WLD -13.1 -7.6 -8.1 -2.3 4.6 -23.6 -35.6 -20.7
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Introduction Model Quantitative Analysis Conclusion Appendix
Provincial Export-Cost Estimates Back
−4
0−
20
02
04
0P
rovin
ce
−S
pe
cific
Exp
ort
Co
st,
Ta
riff
−E
qu
iva
len
t %
South
wes
t
Nor
thwes
t
Nor
th C
oast
South
Coa
st
Beijin
g/Tia
njin
Nor
thea
st
Cen
tral C
oast
Cen
tral R
egion
2002 2007
Notes: Displays the tariff-equivalent (in percentage points) region-specific export costs.All expressed relative to the average for the year. A value of 30 for a certain regionimplies it is 30 percent more costly to export from that region to any other, relative tothe export costs for the average region. 40 / 36
Introduction Model Quantitative Analysis Conclusion Appendix
Migration Costs Back
• As with trade, µni = (mni/mnn)1/κ (Vn/Vi )
Figure: Costs of Migrating Into Beijing
Hainan
Anhui
Zhejiang
Jiangxi
Jiangsu
Jilin
Qinghai
Fujian
Heilongjiang
Henan
Hebei
Hunan
Hubei
Xinjiang
Tibet
Gansu
Guangxi
Guizhou
Liaoning
Inner Mongol
Ningxia
Beijing
Shanghai
Shanxi
Shandong
Shaanxi
Sichuan
Tianjin
Yunnan
Guangdong
41 / 36
Introduction Model Quantitative Analysis Conclusion Appendix
Trade Patterns, by Region Back
Table: Expenditure Shares πni , Year 2002
Source
Importer NE B&T N Cst C Cst S Cst Cntrl NW SW WLD
NE 0.879 0.007 0.010 0.008 0.013 0.011 0.008 0.009 0.055
B&T 0.039 0.634 0.094 0.030 0.026 0.033 0.014 0.012 0.119
N Cst 0.018 0.033 0.798 0.034 0.018 0.038 0.009 0.008 0.044
C Cst 0.002 0.002 0.006 0.810 0.015 0.024 0.005 0.005 0.133
S Cst 0.005 0.004 0.005 0.026 0.723 0.019 0.004 0.015 0.198
Cntrl 0.006 0.003 0.011 0.048 0.023 0.878 0.007 0.007 0.018
NW 0.020 0.008 0.021 0.033 0.045 0.036 0.774 0.038 0.026
SW 0.009 0.003 0.004 0.018 0.043 0.014 0.009 0.880 0.020
WLD 0.000 0.000 0.000 0.001 0.002 0.000 0.000 0.000 0.996
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Introduction Model Quantitative Analysis Conclusion Appendix
% Change in Internal Bilateral Costs (2002-07) Back
Summary Metric Across Pairs
Importer Mean Median Min Max
Agriculture -7.33 -6.96 -37.63 31.07Mining -8.92 -8.29 -36.95 29.35
Food and Tobacco -9.99 -13.14 -29.52 7.43Textiles -6.51 -4.53 -45.49 56.12
Wood & Furniture -14.00 -14.82 -48.26 37.93Paper & Printing 3.09 1.88 -21.93 29.40
Chemicals -6.64 -6.96 -19.56 10.16Non-Metallic Min -17.54 -19.89 -36.80 4.61Metal Products -10.59 -9.89 -27.73 5.53
Machinery -14.99 -17.65 -33.71 33.64Transport Equip. 2.29 -7.58 -34.18 76.13Electrical Machi -1.74 -6.59 -24.40 60.12
Other -3.67 -0.55 -49.32 50.53Utilities -0.35 -16.29 -52.22 101.42
Construction -16.78 -36.75 -73.30 111.76Transportation -11.86 -17.64 -42.91 26.58Other Services -10.25 -12.88 -30.60 19.37
43 / 36