Introduction

Model

Model Mechanisms

Dynamics

Conclusion

Structural Change in an Open Economy
Kei-Mu Yi
Federal Reserve Bank of Minneapolis
Jing Zhang
University of Michigan

May 28, 20121

1The views expressed here are those of the authors are are not necessarily reflective of views of the Federal

Reserve Bank of Minneapolis or the Federal Reserve System.

Introduction

Model

Model Mechanisms

Dynamics

Structural Change

Share of employment (16 advanced nations)
Sector

1870

1960

1987

AgricultureServices
Manufacturing

0.49
0.24
0.27

0.17
0.44
0.39

0.06
0.63
0.30

Source: Maddison (1991)

Agriculture share declines over time.
Services share rises over time.
Manufacturing share first rises and then declines over time.

Conclusion

Introduction

Model

Model Mechanisms

Dynamics

Conclusion

Global integration, Structural Change
World’s economies increasingly interlinked via trade.
In past 30-40 years many emerging market countries haveglobalized

Manufacturing labor shares are declining in developed nations,and rising (although not permanently) in emerging market
countries.
Trade with emerging markets has been blamed for declining
manufacturing employment in developed countries.

In most countries, manufacturing has the highest productivity
growth.

Introduction

Model

Model Mechanisms

Dynamics

Conclusion

U.S. and South Korea Manufacturing Employment Share
3025United States

Percent

2015South Korea
10501870 1880 1890 1900 1910 1920 1930 1940 1950 1960 1970 1980 1990 2000
Year

Labor Productivity Growth (1970-2005)
Country
U.S.
South Korea

Agriculture

Manufacturing

Services

1.5%
4.9%

3.8%
7.0%

0.7%
1.7%

Introduction

Model

Model Mechanisms

Dynamics

South Korea’s Manufacturing Net Exports As Share of GDP

Conclusion

Introduction

Model

Model Mechanisms

Dynamics

Manufacturing Trade and Employment
Figure: Manufacturing Net Exports and Manufacturing Employment

Change in Manu
ufacturing Labor Share, 1962‐2005,
Percentage Points

25%20%
15%

TWN
THA

10%BOL

5%‐5%

IDN
CRI

MEX
IND

0%MYS
KOR

BRA
COL PHL
PER

VEN

PRT
ITA
JPN
CHL
ESP
CAN

‐10%
FRA
NZL
USA
AUS

‐15%

FIN

BEL
AUT DEN
NLD
ARG
NOR
ISL
GER SWE
CHE

‐20%

GBR

‐25%
‐15%

‐10%

‐5%

0%

5%

10%

15%

20%

25%

Change in Manufacturing Net Exports/GDP, 1962‐2005, Percentage Points

30%

Conclusion

Introduction

Model

Model Mechanisms

Dynamics

Conclusion

Services Employment and Tradelist = β0 + β1 tradeit + β2 gdppcit + γi + iti: country; t: period
list : services employment sharetradeit : exports+imports as a share of GDP
gdppcit : GDP per capita in 2005 international dollars
Table: Trade and Services Labor SharetradeitFixed Effectagdppcit

β0R2Obs

0.67

379

0.0801

1.23e-5

0.369(0.0289)(1.12e-6)(0.0251)

Introduction

Model

Model Mechanisms

Dynamics

Key Question

What is the effect of international trade on the process ofstructural change?

Conclusion

Introduction

Model

Model Mechanisms

Dynamics

Conclusion

Our Approach

We develop a two-country, three-sector model with inter- andintra-sector Ricardian tradeIntroduction

Model

Model Mechanisms

Dynamics

Conclusion

Our Approach

We develop a two-country, three-sector model with inter- andintra-sector Ricardian trade
We study the channels by which trade affects structuralchange:Introduction

Model

Model Mechanisms

Dynamics

Conclusion

Our Approach

We develop a two-country, three-sector model with inter- andintra-sector Ricardian trade
We study the channels by which trade affects structuralchange:Trade delinks sectoral production and sectoral expenditure:Closed: labor share = expenditure share
Open: labor share = expenditure share + net export share

Introduction

Model

Model Mechanisms

Dynamics

Conclusion

Our Approach

We develop a two-country, three-sector model with inter- andintra-sector Ricardian trade
We study the channels by which trade affects structuralchange:Trade delinks sectoral production and sectoral expenditure:
Closed: labor share = expenditure share
Open: labor share = expenditure share + net export share

Trade allows countries to specialize, affecting net export shares
Trade changes relative prices, affecting expenditure shares

Introduction

Model

Model Mechanisms

Dynamics

Conclusion

Our Approach

We develop a two-country, three-sector model with inter- andintra-sector Ricardian trade
We study the channels by which trade affects structuralchange:Trade delinks sectoral production and sectoral expenditure:
Closed: labor share = expenditure share
Open: labor share = expenditure share + net export share

Trade allows countries to specialize, affecting net export shares
Trade changes relative prices, affecting expenditure shares

We demonstrate two ways in which open economy cangenerate hump pattern in manufacturing employment

Introduction

Model

Model Mechanisms

Dynamics

Conclusion

Related Research

Models of structural change:
Closed-economy models: Kongsamut, Rebelo and Xie (2001)
and Ngai and Pissarides (2007)
Open economy models:Matsuyama (2009): an example with Ricardian framework
Coleman (2007): model in which large emerging market
country integrates with rest of world

Models of Ricardian trade: Eaton and Kortum (2002)

Introduction

Model

Model Mechanisms

Two Groups of Theories of Structural Change

Non-homothetic preferences:
Engel (1895)
Kongsamut et. al (2001)

Sector-biased productivity growth:
Baumol (1967)
Ngai and Pissarides (2007)

Closed economy frameworks

Dynamics

Conclusion

Introduction

Model

Model Mechanisms

Dynamics

Model Set Up

Two countries
Three sectors: agriculture, manufacturing, services
Agriculture and manufactured goods are tradable
Services are nontradable

One factor: labor with exogenous supply
Mobile across sectors, but immobile across countries

Productivity growth differs across sectors and countries
Free trade: based on Ricardian comparative advantage

Conclusion

Introduction

Model

Model Mechanisms

Dynamics

Conclusion

Technologies

Services: a single good Yist = Aist List
Agriculture and manufacturing: a continuum of goods
yimt (z) = Aimt (z)Limt (z)z ∈ [0, 1]

yiat (z) = Aiat (z)Liat (z)z ∈ [0, 1]

A is distributed as Fréchet: Fiqt (z) = exp(−Tiqt z −θ )Goods are combined to yield composite goods for consumption

Introduction

Model

Model Mechanisms

Dynamics

PricesPerfect competition in goods and factor markets
Service good price: Pist = Awistit
Agricultural good price:


w2t
w1t
,
A1at (z) A2at (z)

w1t
w2t
,A1mt (z) A2mt (z)piat (z) = min

Manufacturing good price:pimt (z) = minConclusion

Introduction

Model

Model Mechanisms

Dynamics

Conclusion

Preferences

Tradable sector composite goods: elasticity of substitution η
η−1η
R1Ciqt = ( 0 ciqt (z) η dz) η−1

Intratemporal utility: elasticity of substitution 
−1

−1

−1



Cit = (ωa Ciat + ωm Cimt + ωs Cist ) −1
P∞ t
Intertemporal utility:t=0 β U(Cit )Budget constraint (period-by-period):
Pit Cit = Piat Ciat + Pimt Cimt + Pist Cist = wit LitIntroduction

Model

Model Mechanisms

Dynamics

Expenditure Shares

Expenditure share:
Xiqt =Piqt Ciqt= ωq
wit Lit

Piqt
Pit

1−

Aggregate price: 11−
1− 1− 1−
Pit = ωa Piat+ ωm
Pimt + ωs Pist

Sectoral composite good price:Z 1
Piqt =piqt (z)
0

η
η−1

 η−1
ηdz

Conclusion

Introduction

Model

Model Mechanisms

Dynamics

Market Clearing Conditions
Labor markets:
R1
R1
Lit = List + 0 Limt (z)dz + 0 Liat (z)dz,i = {1, 2}Services good markets:
Yist = Cist ,i = {1, 2}

Agriculture goods markets:
P2P2
i=1 yiat (z) =i=1 ciat (z)∀z ∈ [0, 1]

Manufacturing goods markets:
P2P2
i=1 yimt (z) =i=1 cimt (z)∀z ∈ [0, 1]

Conclusion

Introduction

Model

Model Mechanisms

Dynamics

Conclusion

Open-Economy Equilibrium

A competitive equilibrium is a sequence of goods and factor prices{piat (z), pimt (z), Piat , Pimt , Pist , Pit , wit }∞t=0 and allocations{liat (z), limt (z), Liat , Limt , List , yiat (z), yimt (z), Yist , ciat (z),cimt (z), Ciat , Cimt , Cist , Cit }∞t=0 for z ∈ [0, 1] and i = 1, 2, suchthat given prices, the allocations solve the firms’ maximization
problems and the household’s maximization problem, and satisfy
the market clearing conditions.

Introduction

Model

Model Mechanisms

Dynamics

Closed Economy Equilibrium

Sectoral labor share = sectoral expenditure share
lqt =Lqt
wt LqtPqt Cqt=== Xqt
Lt
wt Lt
Pt Ct

Expenditure share:Xqt = ωqPqt
Pt

1−Prices: Pqt = Awqtt , where Aqt = Tqt1/θ /γ.

Conclusion

Introduction

ModelModel Mechanisms

Dynamics

Closed Economy Dynamics

L̂qt = X̂qt = (1 − ) P̂qt − (Xat P̂at + Xmt P̂mt + Xst P̂st )= ( − 1) Âqt − (Xat Âat + Xmt Âmt + Xst Âst ) = 1: no structural change < 1: labor moves from the highest productivity growth
sector to the lowest productivity growth sector
 > 1: labor moves from the lowest productuviity growth
sector to the highest productivity growth sector

ConclusionIntroduction

Model

Model Mechanisms

Dynamics

Conclusion

Key Implications of Closed Economy

Preferences play a major role in labor allocation across sectors.
Structural change does not occur if the elasticity ofsubstitution equals one.
With elasticity of substitution less than one:
The high productivity growth sectors experience declining
relative prices, expenditure shares and labor shares.
Labor moves from the most productive sector to the least
productive sector.

Introduction

Model

Model Mechanisms

Dynamics

Key Ingredients of Open Economy
Trade based on comparative advantage (Ricardian)
Assume country 1 has a comparative advantage inmanufacturing.
That is, under free trade,
A1mt
A1at>.
A2mt
A2at

Under free trade, the LOOP holds: p1qt (z) = p2qt (z).
Tradable composite good prices are equalized acrosscountries: P1qt = P2qt .

Conclusion

Introduction

Model

Model Mechanisms

Dynamics

Open Economy: Prices

Under Fréchet distribution (and free trade):Piqt =wit
Aiqt

Piqt
1
wit = Aiqt

Services price: Pwistit = A1ist

−θ1++wjt
Ajqt

wjt Aiqt
wit Ajqt

−θ − θ1−θ − θ1Conclusion

Introduction

Model

Model Mechanisms

Dynamics

Prices in Open vs. Closed Economy

Piatwitand Pwimt
are lower in open economy
itPistwit

is the same

Pitwitis lower in open economy
Welfare is higher in open economy

Pist
P1at
P2mt
Pit rises, P1t and P2t declines in open economy
P1mt
P1at is higher in the open economy

Conclusion

Introduction

Model

Model Mechanisms

Dynamics

Conclusion

Expenditure Shares in Open vs. Closed Economy

Relative prices and the elasticity of substitution play key rolein determining expenditure shares Xiqt .
With elasticity less than one, in both countries in open
economy,services expenditure shares are higher;
expenditure share of the sector with comparative disadvantage
is lower;
expenditure share of the sector with comparative advantage isambiguous.

Introduction

Model

Model Mechanisms

Dynamics

Conclusion

Open Economy: Intra-Sector Trade
In addition to (sectoral) expenditure shares, another share matters:
the share of sectoral spending that is on imports:
Share of country 1’s expenditure on sector q goods fromcountry 2 (under free trade):

π12qt =1(w2t /A2qt )−θ=−θ−θ
w/A1qt −θ1t(w2t /A2qt ) + (w1t /A1qt )1+()
w2t /A2qt

π12qt rises as w2t /A2qt decreases relative to w1t /A1qt
The rise is larger with larger θ (a low productivity dispersion)Comparative advantage implies π12mt < π12at

Introduction

Model

Model Mechanisms

Dynamics

Conclusion

Open Economy: Inter-Sector Trade

Putting together these two shares:
Manufacturing net exports of country 1 as share of its GDP:N1mt =π21mt X2mt w2t L2t− π12mt X1mtw1t L1tComparative advantage implies N1mt > 0 and N1at < 0.
The net export ratio of the sector with comparative advantage ispositive in each country.

Introduction

ModelModel Mechanisms

Dynamics

Open Economy: Labor Allocation
Services labor share: list = List /Lit = Xist
Manufacturing labor share of country i:limt =Limt= Ximt + Nimt
Lit

Direct contribution of trade: Nimt
Country 1 has a comparative advantage in manufacturing
N1mt > 0 and N2mt < 0Indirect contribution of trade: Ximt

Similarly for agriculture labor shareConclusion

Introduction

ModelModel Mechanisms

Dynamics

Conclusion

Labor Dynamics
Growth in manufacturing labor share:l̂1mt =X1mt
N1mt
X̂1mt +N̂1mt
l1mt
l1mt

First term: the expenditure effectSecond term: the trade or net export effectPositive growth in manufacturing net export share contributes
positively to labor share.
To focus on trade effect, consider case with elasticity ofsubstitution across sectors = 1; hence, X̂1mt = 0

Introduction

Model

Model Mechanisms

Impact of Trade on Structural Change

Dynamics

Conclusion

Introduction

Model

Model Mechanisms

Dynamics

Conclusion

Productivity Growth and Hump Pattern in Manufacturing
ANecessary condition for N̂1mt > 0: Âmt > Âat , (Aqt = A1qt)
2qt
Under free trade, manufacturing labor share equation:
wt L1t + L2t
l1mt = ωm π11m
wt L1tπ11m = π21m : specialization term
Reciprocal of GDP share: country-size term

As manufacturing productivity grows, specialization term
contributes positively to manufacturing labor share, while
country-size term contributes negatively.
Each country buys more of its manufactured goods fromcountry 1 (e.g., South Korea).
If Âat > 0, country 1 relative wage grows, country 2 (e.g.,United States) purchasing power falls. Country 1 needs lesslabor to meet country 2 demand.

Introduction

Model

Model Mechanisms

Dynamics

Conclusion

Productivity Growth and Hump Pattern in Manufacturing

Initially, specialization term is dominant.
Eventually, country-size term dominates.
Once manufacturing becomes close to completely specialized,
employment growth from specialization effect becomes small.
In limiting case, country 2 buys all its manufactured goods
from country 1, but country 2 has zero mass, so the global
economy is effectively just country 1.
Country 1 employment share declines until it equals
expenditure share.

Introduction

ModelModel Mechanisms

Dynamics

Conclusion

Structural Change in Open Economy: Example 1

 = 0.5
ωa = 1/3

Preferencesσ ∗ = 1.0
ωm = 1/3

ωs = 1/3

L10 = 1

Labor Endowment
L20 = 10L̂1t = L̂1t = 1.0

Sectoral Productivitiesθ = 4.0
A1a0 = 1.0
A2a0 = A1a0 (L20 /L10 )1/θÂ1at = 1.01
Â2at = 1.02

A1m0 = 1.0
A2m0 = A1m0 (L20 /L10 )1/θÂ1mt = 1.02
Â2mt = 1.01

A1s0 = 1.0
A2s0 = A1s0 (L20 /L10 )1/θÂ1st = 1.0
Â2st = 1.0

Introduction

ModelModel Mechanisms

Dynamics

Conclusion

Structural Change in Country 1

Figure: Employment Shares, Closed and Open
0.7

0.7

0.7

0.6

0.6

0.5

0.5

0.4

0.4

0.4

0.3

0.3

0.3

0.2

0.2

0.2

0.1

0.1

0.6

Exp & labor share, closed
Exp share, open
Labor share, open

0.5

0020406080(a) Agriculture

100

000.1
20406080(b) Manufacturing10000204060(c) Services

80100

Introduction

Model

Model Mechanisms

Dynamics

Conclusion

Structural Change in Country 2

Figure: Employment Shares, Closed and Open
0.5

0.5

0.5

0.4

0.4

0.3

0.3

0.3

0.2

0.2

0.2

0.4

0.1
0Exp & labor share, closed
Exp share, open
Labor share, open

20406080(a) Agriculture

1000.1020406080(b) Manufacturing1000.10204060(c) Services

80100

Introduction

Model

Model Mechanisms

Dynamics

Conclusion

Import Shares

Figure: Import Shares
1.1

0.25

0.2

10.15

Agriculture
Manufacturing0.90.10.8

0.7
00.05204060(a) Country 180

10000204060(b) Country 280100

Introduction

Model

Model Mechanisms

Dynamics

Conclusion

Wages, Prices, and Welfare

Figure: Wages, Prices, and Welfare
1.1

3

1

2.5

0.9

1.6
1 Open2 Open1&2 Closed

1.4
1.2

20.8

1 Open2 Open1 Closed
2 Closed

1
1.5

0.7
0.6

0.8
1 Open2 Open

10.5
0.4
00.6

0.5

204060(a) Wages

80

100

000.4

204060(b) Prices80

100

0.2
0204060(c) Welfare

80100

IntroductionModel

Model Mechanisms

Dynamics

Structural Change and Trade Costs
Introduce iceberg trade costs
Prices:i− θ1h−θ−θPiqt = (wit /Aiqt ) + (τqt wjt /Ajqt )Import shares:
πijqt =(τqt wjt /Ajqt )−θ.
(τqt wjt /Ajqt )−θ + (wit /Aiqt )−θDecline in τqt affects Piqt and πijqt like increase in Ajqt

Decline in trade costs can also generate structural change,even in absence of biased sectoral productivity growth

Conclusion

Introduction

Model

Model Mechanisms

Dynamics

Conclusion

Trade Costs and Hump Pattern in Manufacturing
Suppose country 1 has comparative advantage inmanufacturing and is small relative to country 2.
Productivity levels are constant over time

As trade costs decline, specialization increases (manufacturing
net export surplus grows) and country 1 relative wage rises
Initially, specialization effect dominates country-size effect, so
manufacturing labor share in country 1 rises
Eventually, country 1 labor used to satisfy country 2
manufacturing demand declines, so manufacturing labor sharein country 1 falls

Introduction

Model

Model MechanismsDynamics

Structural Change in Open Economy: Example 2

 = 0.5
ωa = 1/3Preferencesσ ∗ = 1.0
ωm = 1/3

ωs = 1/3

L10 = 1Labor Endowment
L20 = 10L̂1t = L̂1t = 1.0

Sectoral Productivitiesθ = 4.0
A1a0 = 1.5
A2a0 = 2.0(L20 /L10 )1/θÂ1at = 1.0
Â2at = 1.0

A1m0 = 2.0
A2m0 = 1.5(L20 /L10 )1/θÂ1mt = 1.0
Â2mt = 1.0

τq0 = 2.5

Trade Costs
τqt − 1 declines at 3% per period

A1s0 = 1.0
A2s0 = 1.0(L20 /L10 )1/θÂ1st = 1.0Â2st = 1.0

Conclusion

Introduction

Model

Model Mechanisms

Dynamics

Conclusion

Structural Change in Country 1

Figure: Employment Shares, Closed and Open
0.4

0.6

0.6

0.5

0.5

0.4

0.4

0.3

0.3

0.2

0.2

0.1

0.1

0.3

0.2

Exp & labor share, closed
Exp share, open
Labor share, open

0.1

00102030(a) Agriculture

400102030(b) Manufacturing

4000102030(c) Services

40

Introduction

Model

Model Mechanisms

Dynamics

Conclusion

Conclusion
International trade provides environment in which sectoral
output and sectoral expenditure need not be equalWith neoclassical trade, comparative advantage interacts with
global sectoral demand to determine patterns of expenditure,trade, production, and employment
We study structural change in an open economy with modelthat highlights these themes
Model yields rich insights and can potentially better explain
patterns in data
Extending model to include non-homothetic preferences,intermediate goods, and trade costs does not alter the main
implications
Companion project: quantitative assessment

Introduction

Model

Model Mechanisms

Dynamics

Conclusion

Accounting: the U.S.

Year

lmt

Xmt

Nmt

Xmt + Nmt

1970

25.6%

27.9%

-1.1%

26.8%

2000

14.5%

21.6%

-4.8%

16.8%

Change-11.1%

-6.3%

-3.7%

-10.0%The direct trade effect accounts for one third of the decline in
US manufacturing labor share.

Introduction

Model

Model Mechanisms

Dynamics

Conclusion

Accounting: the U.K.

Yearlmt

Xmt

Nmt

Xmt + Nmt

1970

34.6%

31.0%

2.4%

33.4%

2000

16.8%

22.9%

-7.8%

15.1%

Change-17.8%-8.1%-10.2%-18.3%The direct trade effect accounts for more than one half of thedecline in British manufacturing labor share.

Introduction

Model

Model Mechanisms

Dynamics

Conclusion

Manufacturing Labor Share and Income
40353025201510USKorea

UKJapan5005000

10000

15000

20000

25000

30000

35000

40000