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

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