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Structural Transformation and Unbalanced Trade in theU.S.
Ricardo Reyes-Heroles
Princeton
April 10, 2013
Ricardo Reyes-Heroles (Princeton) Structural Change and Unbalanced Trade April 10, 2013 1 / 33
Introduction
Two salient features of U.S. economy over past half-century:1 Increase in international trade, unbalanced trade �ows.2 Speci�c sectoral trends in output and labor across agriculture, industryand services ! Structural change (SC):
Question:I What is the quantitative importance of international trade on thestructure of the U.S. economy over the past half-century?
Ricardo Reyes-Heroles (Princeton) Structural Change and Unbalanced Trade April 10, 2013 2 / 33
IntroductionMotivation
Traditional closed economy models of SC cannot explain certaincharacteristics of the data [Buera and Kaboski (2008)].
I Consider two country calibrated international trade model [Yi, Zhangand Uy (2013)].
Quantitative importance of declining costs and "unbalanced trade" inthe U.S.
I Exogenous trade imbalances.
Structure of the economy shapes long term evolution of aggregatevolatility [Gabaix and Carvalho (2011)] ! importance of Domarweights (ratio of sectoral gross output to total value added) asmeasures of sectoral economic activity.
I Intersectoral linkages ) implications on aggregate volatility.
Ricardo Reyes-Heroles (Princeton) Structural Change and Unbalanced Trade April 10, 2013 3 / 33
IntroductionMethodology and Main Results
Use a general equilibrium model of international trade and SC thatincludes trade in intermediate inputs, sectoral linkages andunbalanced trade.
I Asses quantitative importance of changes in trade costs and tradede�cits on SC in the U.S. economy over the period 1970-2000.
Calibrate and simulate model to generate time series.1 Trade imbalances are important in order for the mechanisms in themodel to �t salient features of data ! Acceleration in service sector.
2 Without sectoral linkages ! income e¤ects generated by trade de�citsare ampli�ed.
Ricardo Reyes-Heroles (Princeton) Structural Change and Unbalanced Trade April 10, 2013 4 / 33
IntroductionMotivating Evidence: Value Added Shares and Domar Weights
1970 1980 1990 20000.01
0.02
0.03
0.04
0.05
0.06
0.07
0.08
0.09Agriculture
1970 1980 1990 20000.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8Manufacturing
1970 1980 1990 2000
0.7
0.8
0.9
1
1.1
1.2
1.3
1.4Services
Value AddedDomar Weight
Trade
Ricardo Reyes-Heroles (Princeton) Structural Change and Unbalanced Trade April 10, 2013 5 / 33
Related Literature
Structural change in a closed economy:I Baumol (1967); Ngai and Pissarides (2007); Buera and Kaboski (2008,2011, 2012).
I Kongsamut, Rebelo and Xie (2001); Caselli and Coleman (2001);
Quantitative GE international trade models:I Eaton and Kortum (2002); Álvarez and Lucas (2007); Caliendo andParro (2012), Eaton, Kortum, Neiman and Romalis (2010).
Structural change in an open economy:I Matsuyama (1991); Coleman (2007); Matsuyama (2009); Yi, Zhangand Uy (2013).
Intermediate inputs and GDP volatility:I Gabaix and Carvalho (2011); Caselli, Koren, Lisicky and Tenreyro(2011).
Ricardo Reyes-Heroles (Princeton) Structural Change and Unbalanced Trade April 10, 2013 6 / 33
The Model
Builds on Yi et al. (2013) and Caliendo and Parro (2011).
Two countries: US and the rest of the world (ROW),i 2 fUS ,Rg � N.Three sectors in each country: j 2 fa,m, sg � J.Agriculture (a) and manufacturing (m) sectors consist of a continuumof tradable goods z j 2 [0, 1], j 2 fa,mg.Single non-tradable good in the service sector: s � zm .One factor of production, labor in i , Li .
Ricardo Reyes-Heroles (Princeton) Structural Change and Unbalanced Trade April 10, 2013 7 / 33
The ModelPreferences
Representative household purchases �nal goods, Cij , subject to abudget constraint.
Period utility of the household:
U =�
γ1εiia (Cia�C ia)
εi�1εi + γ
1εiim (Cim�C im)
εi�1εi + γ
1εiis (Cis�C is )
εi�1εi
� εiεi�1
where γia,γim ,γia > 0, γia + γim + γia = 1 and εi > 0.
Elasticity of substitution: ε < 1) complementarities.
Budget constraint of the household:
piaCia + pimCim + pisCis = wiLi + Ti
I wiLi : labor income; Ti : lump-sum transfers.
Ricardo Reyes-Heroles (Princeton) Structural Change and Unbalanced Trade April 10, 2013 8 / 33
The ModelTechnologies
Technology for tradable good z j 2 [0, 1] in sectors j 2 fa,mg:
qij�z j�= x ji
�z j��θj
hl ji�z j�iβji
"∏k2J
mk ,ji�z j� αk ,ji
#1�βji
.
Technology in service sector:
Qis = Ais [Lis ]βsi
"∏k2J
Mk ,si
αk ,si
#1�βsi
,
I x ji�z j�: inverse e¢ ciency of producing good z j in country i .
I βsi � 0: share of value added in services in country i .I αk ,ji � 0: share of intermediates from sector k for production of z j ,
∑k2J αk ,ji = 1.I Ais : exogenous productivity.
Ricardo Reyes-Heroles (Princeton) Structural Change and Unbalanced Trade April 10, 2013 9 / 33
The ModelTechnologies (Tradables) and Trade Costs
Tradable sectors j 2 fa,mg:I Inverse e¢ ciency in country i and sector j distributed exponential withparameter T ji � 0:
Pr[x ji � x ] = Fji (x) = 1� e
T ji x , for any x � 0.
Two types of trade costs: κih =�1+ τjih
�d jih.
I d jih � 1: iceberg costs; and ad valorem tari¤: τjih .
Ricardo Reyes-Heroles (Princeton) Structural Change and Unbalanced Trade April 10, 2013 10 / 33
The ModelTechnologies: Non-tradable Aggregate
Tradable goods aggregated into an "nontradable aggregate good" Qij .
I Purchase as intermediate input mj ,ki
�x ji
�or �nal consumption goods,
Cij .
Aggregation:
pijqij = mins ji (x
j )
Zpji�x j�s ji�x j�
φj�x j�dx j
s.t.
"ZRN+
s ji�x j� ηj�1
ηj φj�x j�dx j# ηj
ηj�1
� Qij .
Ricardo Reyes-Heroles (Princeton) Structural Change and Unbalanced Trade April 10, 2013 11 / 33
EquilibriumPrices
Cost of an input bundle:
c ji = Bijwβjii
hpia αa,ji pim αm,ji pis αs ,ji
i(1�βji ), (1)
where pij : price of an intermediate input.I (i) Cost varies across sectors, and (ii) direct e¤ects of changes in prices(sectoral linkages)
Price in i of tradable x jh produced in h: pjih
�x jh�= x jh
θj
c jhκjih.
Prices of goods actually paid in country i :
pji�x j�= min
npjii�x ji�, pjih
�x jh�o, for j 2 fa,mg and pis =
csiAis.
I Assume distribution of productivities is independent across goods,sectors and countries.
Ricardo Reyes-Heroles (Princeton) Structural Change and Unbalanced Trade April 10, 2013 12 / 33
EquilibriumPrices and Trade Shares
Sectoral prices:
pij = Bj Φji�θj
, (2)
where
Φji =
�T jh�c jhκjih
�� 1θj + T ji
�c ji�� 1
θj�.
Trade shares: for j 2 fa,mg and πsih = 0.
πjih =T jh�c jhκjih
�� 1θj
T jh�c jhκjih
�� 1θj + T ji
�c ji�� 1
θj=T jh�c jhκjih
�� 1θj
Φji
. (3)
Ricardo Reyes-Heroles (Princeton) Structural Change and Unbalanced Trade April 10, 2013 13 / 33
EquilibriumMarket Clearing
Trade is unbalanced sector by sector. Let Ni denote net exports ofcountry i and Xij = pijqij .
I De�ne Wij =πjii1+τjii
+πjih1+τjih
for j 2 fa,mg.
World market clearing:
∑j2JWijXij +Ni = ∑
j2J∑h
πjhi
1+ τjhiXhj , or NUS +NR = 0. (4)
Domestic market clearing:
Xij = ∑k2J
αj ,ki
�1� βki
�(WikXik +Nik ) + pij Cij + γij
�pijpi
�1�εi
Ii , (5)
where Ii = wiLi �Ni �∑j pij Cij .
Exogenous aggregate trade de�cit, endogenous sectoral trade de�cits.Ricardo Reyes-Heroles (Princeton) Structural Change and Unbalanced Trade April 10, 2013 14 / 33
Structural Transformation and Trade
Let Yij = Xij +Nij . Then, VA shares are:
VASi ,j = βjiXijwiLi
+ βjiNijwiLi
where DWi ,j is the Domar weight in country i and sector j .
Ricardo Reyes-Heroles (Princeton) Structural Change and Unbalanced Trade April 10, 2013 15 / 33
CounterfactualsFor any x and future value x 0, de�ne x = x 0
x , and Aij = (Tji )�θj :
(Xij )0 = ∑
k2Jαj ,ki
�1� βki
� �(Wik )
0 (Xik )0 + (Nik )
0�+(pij )0 Cij +γij
(pij )
0
(pi )0
!1�εi
(Ii )0 .
∑j2J(Wij )
0 (Xij )0 + (Ni )
0 = ∑j2J
∑h
�πjhi
�0�1+ τjhi
�0 (Xhj )0 .
pij =
24∑h
πjhi
"κjih c
jh
Ahj
#� 1θj35θj
.
�πjih
�0= πjih
"c jhphj
κjihAhj
#�θj
Ricardo Reyes-Heroles (Princeton) Structural Change and Unbalanced Trade April 10, 2013 16 / 33
Taking the Model to the DataData
Construct an aggregate of countries that form a single union thattrades with the U.S., call it the rest of the world (ROW): group of 24countries. trade �ows
Period: 1970 to 2000.
Aggregate data: EU KLEMS, GGDC-10, and APO (AsianProductivity Organization).
Bilateral trade �ows: NBER-UN dataset on bilateral trade �ows.
Input-Output tables: OECD STAN database
Ricardo Reyes-Heroles (Princeton) Structural Change and Unbalanced Trade April 10, 2013 17 / 33
Taking the Model to the DataParameters: Levels
Table 1: Model�s ParametersParameters Calibration Method
βji Data
αj ,ki Input-Output tables
γji Data and model [Herrendorf, Rogerson & Valentiniyi (2013)]Cij Data and model [Herrendorf, Rogerson & Valentiniyi (2013)]ε Data and model [Herrendorf, Rogerson & Valentiniyi (2013)]θj Eaton et al. (2010)
Calibration
Ricardo Reyes-Heroles (Princeton) Structural Change and Unbalanced Trade April 10, 2013 18 / 33
Taking the Model to the DataShocks [Eaton et al. (2010)]
Table 2: Model�s ShocksShocks Method
τjih Data tari¤s
d jih Model and data [Eaton et al. (2010)] trade frictions
Aji Model and data [Eaton et al. (2010)] productivity
d jih =
πjih
πjhh
!�θj pjhpji
!�1\(1+ τih)
�1
Aji =�
πjii
�θj
w βi(pai )
γaai (1�βai ) (pmi )γami (1�βai ) (psi )
γasi (1�βai )
pji
Ricardo Reyes-Heroles (Princeton) Structural Change and Unbalanced Trade April 10, 2013 19 / 33
Model�s FitTrade Shares: U.S.
1970 1980 1990 20000.04
0.05
0.06
0.07
0.08
0.09
0.1Agriculture
1970 1980 1990 20000.04
0.06
0.08
0.1
0.12
0.14
0.16
0.18
0.2
0.22Manufacturing
DataBaseline
DataBaseline
Ricardo Reyes-Heroles (Princeton) Structural Change and Unbalanced Trade April 10, 2013 20 / 33
Model�s FitValue added (VA) shares
1970 1980 1990 20000
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8Value Added Shares
1970 1980 1990 20000.19
0.2
0.21
0.22
0.23
0.24
0.25
0.26
0.27
0.28
0.29Manufacturing
1970 1980 1990 20000.69
0.7
0.71
0.72
0.73
0.74
0.75
0.76
0.77
0.78
0.79Services
DataManufacturing
DataServices
Ricardo Reyes-Heroles (Princeton) Structural Change and Unbalanced Trade April 10, 2013 21 / 33
Model�s FitDomar weights
1970 1980 1990 20000
0.2
0.4
0.6
0.8
1
1.2
1.4Domar Weights
1970 1980 1990 20000.45
0.5
0.55
0.6
0.65
0.7
0.75Manufacturing
1970 1980 1990 20001.06
1.08
1.1
1.12
1.14
1.16
1.18
1.2
1.22Services
DataBaseline
DataBaseline
Ricardo Reyes-Heroles (Princeton) Structural Change and Unbalanced Trade April 10, 2013 22 / 33
Results: Balanced TradeValue added shares
1970 1980 1990 20000.19
0.2
0.21
0.22
0.23
0.24
0.25
0.26
0.27
0.28
0.29Manufacturing
1970 1980 1990 20000.69
0.7
0.71
0.72
0.73
0.74
0.75
0.76
0.77
0.78
0.79Services
BaselineBalanced Trade
BaselineBalanced Trade
Ricardo Reyes-Heroles (Princeton) Structural Change and Unbalanced Trade April 10, 2013 23 / 33
Results: Balanced TradeDomar weights
1970 1980 1990 20000.45
0.5
0.55
0.6
0.65
0.7
0.75Manufacturing
1970 1980 1990 20001.06
1.08
1.1
1.12
1.14
1.16
1.18
1.2
1.22Services
BaselineBalanced Trade
BaselineBalanced Trade
Ricardo Reyes-Heroles (Princeton) Structural Change and Unbalanced Trade April 10, 2013 24 / 33
Results: No Sectoral LinkagesValue added shares
1970 1980 1990 20000.19
0.2
0.21
0.22
0.23
0.24
0.25
0.26
0.27
0.28Manufacturing
1970 1980 1990 20000.7
0.71
0.72
0.73
0.74
0.75
0.76
0.77
0.78
0.79Services
NL BaselineNL BalancedBaselineBalanced
NL BaselineNL BalancedBaselineBalanced
Ricardo Reyes-Heroles (Princeton) Structural Change and Unbalanced Trade April 10, 2013 25 / 33
Results
Table 2: Results (MSE)Agriculture Manufacturing Services
BaselineValue added shares 0.007679 0.015338 0.018341Domar weights 0.017784 0.045363 0.022496
Balanced TradeValue added shares 0.008313 0.019373 0.023990Domar weights 0.019670 0.055576 0.031702
No LinkagesValue added shares 0.006599 0.015761 0.017698Domar weights 0.015231 0.047414 0.020623
No Linkages and Balanced TradeValue added shares 0.007277 0.021990 0.021990Domar weights 0.017276 0.062762 0.033837
Ricardo Reyes-Heroles (Princeton) Structural Change and Unbalanced Trade April 10, 2013 26 / 33
Now What?
Importance of taking into account trade de�cits when trying toexplain structural change in the U.S.
I Endogenize trade imbalances ) Link between trade imbalances andsectoral comparative advantage? [Obstfeld and Rogo¤ (1995)]
Evolution of Domar weights ) Shapes evolution of volatility.I How much of change in volatility can be attributed to unbalancedtrade?
std�ln AaUS
�= 0.010, std
�ln AmUS
�= 0.025, std
�ln AsUS
�= 0.006
I Simple initial approximation from 1981 to 1987:
Change Baseline: �0.00805Change Balanced: �0.00582
Ricardo Reyes-Heroles (Princeton) Structural Change and Unbalanced Trade April 10, 2013 27 / 33
Tari¤s and Unbalanced Trade
1970 1975 1980 1985 1990 1995 20000
0.1
0.2
0.3
0.4
Ta
riffs
1970 1975 1980 1985 1990 1995 20000.03
0.06
0.09
0.12
0.15
Sh
are
s
U .S .
ROW
Exports
Imports
Tari¤s and Trade Share
1970 1975 1980 1985 1990 1995 20005
4
3
2
1
0
1
U.S. Net Exports (share of GDP)
back
Ricardo Reyes-Heroles (Princeton) Structural Change and Unbalanced Trade April 10, 2013 28 / 33
Trade Flows Covered
Table A.1: U.S. Trade Flows Covered byCountries Considered in ROW (%)
Average Min. MaxImports to U.S. 69.2 54.8 77.8Exports from U.S. 72.1 60.1 83.0
back
Ricardo Reyes-Heroles (Princeton) Structural Change and Unbalanced Trade April 10, 2013 29 / 33
Calibration
Table A.2: Model�s ParametersParameters Calibration Values
βji DataβaUS= 0.42βmUS= 0.39βsUS= 0.66
βaR= 0.64βmR= 0.34βsR= 0.58
αj ,ki Input-Output tables I-O
Cij Data and modelCUS ,a= 1008.7CUS ,m= 4697.2CUS .s= �1344.8
CR ,a= 4518.5CR ,m= 1734.2CR ,s= �858.45
γji Data and modelγaUS= 5.8� 10�6γmUS= 0.1464γsUS= 0.8536
γaR= 0.0026γmR= 0.2384γsR= 0.7590
εi Data and model εUS= 0.0101, εR= 0.1139θa, θm Eaton et al. (2011) θa= 1
2 , θm= 1
2
Back
Ricardo Reyes-Heroles (Princeton) Structural Change and Unbalanced Trade April 10, 2013 30 / 33
Tari¤s
back
Ricardo Reyes-Heroles (Princeton) Structural Change and Unbalanced Trade April 10, 2013 31 / 33
Trade Frictions
1970 1980 1990 20001
1.2
1.4
1.6
1.8
2
2.2
2.4
2.6
2.8
3To US from ROW
1970 1980 1990 20001
1.5
2
2.5
3
3.5
4To ROW from US
AgricultureManufacturing
back
Ricardo Reyes-Heroles (Princeton) Structural Change and Unbalanced Trade April 10, 2013 32 / 33
Productivity
1970 1980 1990 20000.85
0.9
0.95
1
1.05
1.1
1.15
1.2
1.25US
1970 1980 1990 20001
1.1
1.2
1.3
1.4
1.5
1.6
1.7
1.8ROW
AgricultureManufacturingServices
back
Ricardo Reyes-Heroles (Princeton) Structural Change and Unbalanced Trade April 10, 2013 33 / 33