Download Trade Liberalization’s Impact upon Economic Development: Experiences from Asymmetric Countries:

Trade Liberalization’s Impact upon Economic Development in
an Endogenous Growth Framework: Experiences from
Asymmetric Countries
Xin Zheng*
In the context of a continually changing and reforming world economy, trade
liberalisation plays a vital role in reshaping the economy, and its impact upon
economic development has been studied from various perspectives.
However, different backgrounds, assumptions, methodologies and intentions
have led to various results, making the effects of trade liberalisation a
controversial topic. This paper tests the hypothesis that the effects of
bilateral trade liberalisation between two asymmetric countries are highly
associated with the extent of international technology spill-over, relative
market size, product variety and financial openness. The methodologies
consist of an endogenous growth model and the time series data analysis of
economic indicators obtained from a pool of frequently traded and
economically integrated countries. The analysis finds that higher and
broader international technology spill-over helps to shrink the development
gap between two asymmetric countries; the sizes and openness of trading
partners’ markets influence trading activities’ profitability; diversification of
export and import products reduces the trade liberalisation risk; financial
openness in an effective manner enables trading countries to optimise
export and import structure. These findings shed light on policy makers
about the design of a mutually beneficial trade liberalisation agreement
between two asymmetric countries. The paper concludes that trade policy
formulation should take into account the degree of international technology
spill-over, exploitation of potential market, diversification and optimisation of
export and import structure.
Introduction
The world economy evolves with increasing uncertainties. For the half century, developed and
developing countries have experienced asymmetric productivity growth, demand expansion,
commodity price inflation, world trade promotion and production chain improvements. The
prosperity then was weakened by the global financial crisis with decline in economic growth, rise
in unemployment rate and shrinking world trade. And now the world economy is recovering with
a series of continuing transformation.
*SID: 310035767, Master of Philosophy in Economics (Master by Research), School of Economics, Faculty of Arts
and Social Sciences, The University of Sydney, Australia
Among the long term transformation, there is trade liberalisation in terms of removing quotas,
lowering tariffs, releasing the restrictions of capital flows and flexibilizing the exchange rates.
However, the effects of trade liberalization concerning methodologies and strength of evidence
have always been a controversial topic in the academia.
Some scholars advocated trade liberalisation. Banks (2003) generalised the multiple benefits of
trade liberalisation from the perspective of developed countries. He claimed that trade
liberalisation stimulated productivity and enhanced the economy’s flexibility to shocks.
Specifically, consumers benefited in terms of lower prices and greater variety; competitive
industries gained from reduced input costs and higher consumer purchasing power; Nation-wide
economic infrastructure reaped increased flexibility and dynamism through reforms pushed by
imported competition. Dun and Mtti (2004) elucidated that developing countries profited through
augmentation of domestic comparative advantages, realisation of specification and economics of
scale.
While others pointed out the negative effects of trade liberalisation. Mahdi (2009) argued that
trade liberalisation deteriorated those developing countries which relied on fragile exports in
terms of raw materials and imports of manufactures since trade liberalisation widened the price
gap between primary products and high technology products. Page (2005) revealed that complete
trade liberalisation induced developing countries to suffer from the loss of trade preference for
some special commodities with developed countries and this loss was not negligible.
Literature Review
The driving forces of trade liberalisation’s impacts upon asymmetric economies are heatedly
debated worldwide under endogenous frameworks with various specifications.
Some scholars highlighted the role of international technology spill-over as determinants of trade
liberalisation’s influence. Marconi (2007) established a general equilibrium endogenous growth
model driven by knowledge accumulation and innovations, and his model consisted of two
asymmetric countries. He concluded that under the assumption of no production variety over-lap,
the convergence of long-run growth rates between the two countries is independent of
international technology spill-over; however, under the assumption of initial production variety
over-lap, international technology spill-over generated by trade liberalisation tends to polarise
innovations between the two countries. Czap (2006) initially examined the relationship between
total factor productivity and trade volumes through a Malmquist estimation procedure, then
investigated the threshold of trade liberalisation’s effects upon economic growth through learning
by doing models. He identified that high trade volumes contributed to the improvement in total
factor productivity and summarised that the extent of knowledge spill-over affected the gains
from trade liberalisation.
Some researchers emphasised the importance of market size and product variety. Sara (2008)
formulated the market equilibrium conditions for a model consisting of North-South countries
under a free trade agreement and derived the Nash equilibrium tariffs after endogenizing the free
trade agreement. She revealed that trade liberalization’s influence hinged upon the extent of
asymmetry in market size and vertical differences in production. Bergés (2007) constructed the
long term time series of commodity exports in terms of real value, volume and market prices
before and after free trade agreements between Latin American countries and the United States.
He found that export growth in the developing countries could only be achieved if the free trade
agreement was implemented with improved market access to the developed country and export
structure diversification.
Some argued that the effects of trade liberalisation were associated with financial openness. Han
(2010) maintained that financial openness influenced the transformation of trade product structure
from traditional products to technology-intensified products through efficient allocation of
financial resources. Baldwin and Forslid (2000) discovered that financial openness endogenized
the mark up between borrowers and savers, and this in cooperation with trade liberalisation
exerted pro-growth effect upon the economy.
Others claimed that the benefits of trade liberalisation sprang from the transparent trade regime.
Winters (2004) insisted that trade liberalisation promoted institutional development and
streamlined trade administration process, hence released more resources for other economic
development tasks. Helble, Shepherd and Wilson (2007) demonstrated that improving
transparency in terms of predictability and simplification reduced transaction costs, expanded
trade collaboration and increased economic integration.
Endogenous Growth Model
Market Structure
The endogenous growth theory combines neoclassical growth theory with the research and
development sector, where technological products are produced through intentional investments
in the research and development sector. This theoretic economy consists of two asymmetric
countries in terms of a developed country and a developing country. Each country has three
sectors: final product sector, intermediate product sector, research and development product
sector, and research development product sector belongs to final product sector. Homogeneous
production applies to each sector within each country. Wages are homogenous across each
country. Each country’s trade policy settings are reflected in its trade parameters. The notation for
the countries are i = D (Developed), Dg (Developing). The model distinguishes between the rivalnatured human capital (H) and non-rival-natured technology (A). Several simplifications are
applied here to emphasize on the core analysis: Labour supply is stable, constant and equals
labour demand; total stock of human capital is stable, constant and equals human capital demand;
perfect technology spill-over across sectors within each country.
Final Product Sector’s Incumbents
Final product sector exhibits perfect competitive market structure since final products are rival
and excludable. In final product sector, the developed country employs capital-intensive
production function in terms of technology ( AD ), effective physical capital ( q D K D ), human
capital ( HYD ), labour ( LYD ) and the whole set of intermediate products ( MD ), while the
developing country adopts labour-intensive production function in terms of human capital ( HYg ),
effective labour ( uq Dg LYDg ) and the whole set of intermediate products ( MDg ). M enter the
production function where each intermediate product exhibits symmetric position with constant
elasticity of substitution in an addictively separable fashion. Human capital is measured as
cumulative effects of education and training; labour is measured as the number of working people;
intermediate products are measured as intermediate goods.
Table I. Comparison of Theoretic Models
Human Capital Endogenous
Growth Model (Lucas,1988)
Human Capital Endogenous
Technology Endogenous Growth Model
Growth Model (Marconi, 2007)
(Zheng, 2011)
Final Product Sector: Production Function
Final Product Sector:
Final Product Sector:
Production Function
Production Function
𝐘𝐭 =
𝐀𝐭 𝐊 𝐛𝐭
𝐮𝐪𝐭 𝐋𝐭
𝟏−𝐛
𝛄
𝐪𝐚
Y = K φ Ly 1−α
constant Technology level; 𝐊 𝐭 is
Xij
production; 𝐪𝐭 is labour augmenting
Corporate R&D Sector:
technological factor 𝐮𝐪𝐭 𝐋𝐭 stands for
Hj = β K LHj
Developing country:
N Dg
YDg =
α Dg β Dg
ADg HYDg
K Dg
1
K=
N
𝛄
product sector; 𝐪𝐚 represents
Intermediate Product Sector:
N
MDj = ADj · LMDj , where j=1, 2, 3 ···ND
Hj
j=1
MMDgj = ADgj · LMDgj , Where j=1, 2, 3 ···NDg
Research and Development Product Sector
Hj = H = K
𝐀𝐭 > 𝟎
γH =
𝐋𝐭 = 𝐋𝟎 𝐞𝐧𝐭
𝐔 𝐜𝟏 , 𝐜𝟐 = 𝛂𝟏 𝐜𝟏
+ 𝛂𝟐 𝐜𝟐
∞
Ut =
e−ρ
H
= βLHj
H
τ−t
N Dg
𝐊𝐭 =
𝛄
𝐮𝐪𝐭 𝐋𝐭 𝟏−𝐛 𝐪𝐚
Developed Country: UD t =
∞
t
e−λ D
Developing Country: UDg t =
∞
t
e−λ Dg
log c τ dτ
t
c
∞
Ly + NLx + N LH + f + ψN = L
𝐪𝐭 = 𝛅𝐪𝐭 𝟏 − 𝐮
t
∞
C+ψwN= wL+Nπ
CWorld = YWorld
A Dgj
N Dg
S−t
S−t
ln⁡CD s
ds
ln⁡ CDg s
ds
Subject to:
Labour Market Clearing Condition
− 𝐜𝐭 𝐋𝐭
j=1
Consumer Utility Function:
Subject to:
𝐀 𝐭 𝐊 𝐛𝐭
ND
ADgj = ηDgj · ADg · HADgj · LADgj , ADg =
Euler Equation: c = r − ρ
Subject to:
ND
A
j=1 Dj
ADj = ηDj · AD · HADj · LADj , AD =
Consumer Utility Function:
−𝛒 −𝟏/𝛒
MDgj 1−α Dg −β Dg −γ Dg
Where qDg stands for labour augmenting technological factor
In symmetric equilibrium:
Human capital;
−𝛒
uqDg LYDg
γ Dg
j=1
the total effective workforce in final
Consumer Utility Function:
MDj 1−α D −β D −γ D
Where qD stands for capital augmenting technological factor
Xj = Hj LXj
And its Sub-Sector
γ
D
LYD
j=1
Intermediate Product Sector:
working hours workers spent on
βD
YD = AD HYDD qD K D
α
j=1
physical capital; u is the fraction of
externalities from average
ND
α
N
Where 𝐘𝐭 is the output; 𝐀𝐭 is the
Developed country:
t
e−r D (s−t) · CD s
∞
ds ≤
t
e−r Dg (s−t) · (CDg s ) ds ≤
e−r D (s−t) · (WD s + R D s ) ds
∞
t
e−r Dg (s−t) · (WDg s + R Dg s ) ds
Steady State:
Steady State:
Steady State:
𝐪𝐭
=𝛅 𝟏−𝐮 =𝐯
𝐪𝐭
𝐜𝐭 𝐤 𝐭
𝟏−𝛄−𝐛 𝐯
=
=
=Ӽ
𝐜𝐭 𝐤 𝐭
𝟏−𝐛
𝐂𝐭 𝐊 𝐭
𝟏−𝛄−𝐛 𝐯
=
=
+𝐧=Ӽ
+𝐧
𝐂𝐭 𝐤 𝐭
𝟏−𝐛
1
rE =
ψ
LX
LH w
rR&𝐷 = β − β
+
N
N w
1 − α LX
LH
w
−
+f +
α
N
N
w
LH LX
N
r=ρ+ α+φ β
+ + 1−α
N LX
N
L
ζ LX LH
N
=
+
+f+ψ
N α2 N
N
N
rAD =
rADg =
wD AD HAD ηD · LMDi · AD · HADi ηD · LADi · HADi
−
−
+
+
wD AD HAD
ADi
ND
wDg ADg HADg ηDg · LMDgi · ADg · HADgi
ηDg · LADgi · HADgi
−
−
+
+
wDg ADg HADg
ADgi
NDg
rSD =
rSDg =
βD
L
ADi
· MD −
+ fD
1 − βD
ND
ηD · AD · HADi
FD
βDg
LMDg
ADgi
·
−
+ fDg
1 − βDg
NDg
ηDg · ADg · HADgi
FDg
Returns to Scale:
Returns to Scale:
Returns to Scale:
When 𝐪𝐭 = 𝐪𝐚 , 2+γ―b>2-b>1
φ+1>1
2 + βD > 1, 2 + γDg > 1
+
WD
WD
+
WDg
WDg
Below are the asymmetric function specifications, where for the developed country, I choose
the capital augmenting form; for the developing country
ND
YD =
α
AD HYDD
qD KD
βD
γD
LYD
MDj 1−α D −β D −γ D
1
j=1
N Dg
α
β
Dg
YDg = ADg HYDg
K DgDg
u q Dg LYDg
γ Dg
MDgj 1−α Dg −β Dg −γ Dg
(2)
j=1
Where YD and YDg are the final products of the developed and the developing countries; αD
and αDg are the elasticities of YD and YDg with respect to HYD and HYDg respectively; βD is
elasticity of YD with respect to q D K D , 0< βD <1; βDg is the elasticity of YDg with respect to
K YDg , 0< βDg <1; γD is the elasticity of YD with respect to LYD , 0<γD <1; γDg is the elasticity
of YDg with respect to u q Dg LYDg , 0<γDg <1; 1 − αD − βD − γD and 1 − αDg − βDg − γDg are
the elasticities of YD and YDg with respect to MDj and MDgj ; ND is the number of intermediate
products that the developed country produces and NDg is the number of intermediate products
that the developing country produces; return of scale in (1): 1 + αD + βD + βD + γD + 1 −
αD − βD − γD = 2 + βD > 1; return of scale in (2): 1 + αDg + βDg + γDg + γDg + 1 − αDg −
βDg − γDg = 2 + γDg > 1; The final product sectors exhibit increasing returns to scale with
respect to the whole combination of inputs.
Intermediate Product Sector
Intermediate product sector features monopolistically competitive market structure with
constant returns to scale, and each firm occupies a negligible market share. Intermediate
products are produced using a combination of technology (A) and labour (LM ). Assume all
intermediate products are perfect substitutes. Below are the production functions.
MDj = ADj · LMDj
(3)
Where j=1, 2, 3 ···ND .
MMDgj = ADgj · LMDgj
Where j=1, 2, 3 ···NDg .
(4)
Research and Development Product Sector
Research and Development product sector is a subsector of intermediate product sector, and it
produces technology A to be used as an input in intermediate product sector of the developing
country, and as an input in both final product sector and intermediate product sector of the
developed country. Below are the technology evolution formulas.
ADj = ηDj · AD · HADj · LADj ,
j = 1, 2, 3 ··· ND
(5)
ADgj = ηDgj · ADg · HADgj · LADgj ,
j = 1, 2, 3 ··· NDg
(6)
AD =
ADg =
ND
j=1 ADj
ND
N Dg
j=1
ADgj
NDg
(7)
(8)
Where ηD > 0 and ηDg > 0 are the developed and the developing countries’ research and
development sectors’ productivity parameters; HAD and HADg are developed and developing
countries’ human capital devoted to the research and development sector; LAD and LADg are
developed and developing countries’ labour devoted to the research and development sector; AD
and ADg are developed and developing countries’ common technology, which are defined as the
arithmetic average of firm-specific technology.
Denote PA as the price per unit technology, WH as the rental price per unit human capital. The
market clearing price per unit technology can be found when the rental price per unit technology
equals the marginal product of human capital. Under the assumption of labour mobility within
each country, labour wages are homogenous whin each country.
WLD = WLDj = PAD · ηDj · AD · HADj
(11)
WLDg = WLDgj = PADg · ηDgj · ADg · HADgj
(12)
Define PMDj and PMDgj as the prices of intermediate products in developed and developing
countries respectively. The following illustrates the intermediate products’ aggregate demand
derived from final product sectors’ profit maximisation.
ND
α
maxM D AD HYDD
βD
qD K D
γ
ND
MDj 1−α D −β D −γ D −
D
LYD
j=1
MDj · PMDj
j=1
N Dg
α
β
Dg
ADg HYDg
K DgDg u q Dg LYDg
maxM Dg
(13)
N Dg
γ Dg
MDgj 1−α Dg −β Dg −γ Dg −
MDgj · PMDgj
j=1
(14)
j=1
Differentiate the above with respect to each Mj and obtain the inverse demand functions.
α
PMDj = 1 − αD − βD − γD · AD HYDD
qD KD
α
βD
γ
D
LYD
· MDj −α D −β D −γ D
β
Dg
PMDgj = 1 − αDg − βDg − γDg · ADg HYDg
K DgDg u q Dg LYDg
γ Dg
(15)
· MDgj −α Dg −β Dg −γ Dg
(16)
Intermediate product sectors maximise their profits.
ND
maxM D
ND
MDj · PMDj − δD · μD ·
MDj
j=1
j=1
ND
= maxM D
ND
MDj · 1 − αD − βD − γD ·
α
AD HYDD
qD K D
βD
γD
LYD
−α D −β D −γ D
· MDj
− δD · μD ·
j=1
ND
ND
= maxM D
1 − αD − βD − γD · AD ·
α
HYDD
qD K D
βD
γD
LYD
· MDj
1−α D −β D −γ D
− δD · μD ·
j=1
N Dg
maxM Dg
MDj
j=1
MDj
(17)
j=1
N Dg
MDgj · PMDgj − δDg · μDg ·
j=1
MDgj
j=1
N Dg
= maxM Dg
N Dg
MDgj · 1 − αDg − βDg − γDg ·
α Dg
ADg HYDg
β
K DgDg
u qDg LYDg
γ Dg
· MDgj
−α Dg −β Dg −γ Dg
− δDg · μDg ·
j=1
N Dg
= maxM Dg
MDgj
j=1
N Dg
1 − αDg − βDg − γDg ·
α Dg
ADg HYDg
β
K DgDg
u qDg LYDg
γ Dg
· MDgj
1−α Dg −β Dg −γ Dg
j=1
− δDg · μDg ·
MDgj
j=1
Each country’s common technology is available across the sectors within the country. Larger
common technology leads to higher productivity. Assume firms are homogenous across each
country. ADj =AD and ADgj =ADg .
g A D = g A Dj =
g A Dg = g A Dgj =
ADj AD
=
= ηD · HADj · LADj
ADj AD
ADgj ADg
=
= ηDg · HADgj · LADgj
ADgj ADg
(18)
The model distinguishes between exhaustive rival input human capital (H) and non-rival input
technology (A), the partial excludability of technology allows technology spill-over across the
two countries.
The firms also have fixed amounts of management cost fD and fDg in developed and developing
countries respectively.
Final Product Market’s Foreign Entrants
Final product market permits free trade between the two asymmetric countries. Hence new
foreign entrants enter the market whenever profitable opportunities arise. Once they enter the
market, they incur zero import tax from the trading country, take the same product price in local
market, benefit from and contribute to the general stock of technology in local market through
A=
N
j=1 A j
N
, use the same labour and human capital from their own country. However, entrance
into local market requires initial establishment cost FD · WD (Developed country enters
developing country’s market) or FDg · WDg (Developing country enters developed country’s
market), which is treated as a sunk cost in this model. Hence foreign entrants will only enter the
market if the discounted present value of production’s future cash flows VD or VDg is bigger than
the corresponding sunk costs, equivalently, VD > FD · WD or VDg > FDg · WDg .
Consumers
Both countries’ consumers exhibit identical logarithmic preferences:
Developed country’s consumers’ utility function:
∞
UD t =
e−λ D
S−t
t
ln⁡CD s
ds
(19)
Developing country’s consumers’ utility function:
∞
UDg t =
t
e−λ Dg
S−t
ln⁡ CDg s
ds
(20)
Where CD and CDg are consumption of final products in developed and developing countries
respectively. λ is the subjective discount rate of time preference.
Each country’s consumers maximize their utility with respect to their inter-temporal budget
constraints.
∞
t
∞
t
e−r D (s−t) · CD s
∞
ds ≤
t
e−r Dg (s−t) · (CDg s ) ds ≤
Where DD s = e−
s
r
t D
v dv
e−r D (s−t) · (WD s + R D s ) ds
∞
t
(21)
e−r Dg (s−t) · (WDg s + R Dg s ) ds
and DDg s = e−
s
r
t Dg
v dv
(22)
are the discount factors for developed
Dg
and developing countries respectively; CDD s and CD s
are the developed country’s
Dg
consumptions of domestic goods and imports from the developing country; PDD and PD are the
prices of developed country’s domestic goods and imports from the developing country;
Dg
D
CDg s and CDg
s are the developing country’s consumptions of domestic products and imports
Dg
from the developed country; PDD and PD are the prices of developing country’s domestic products
and imports from the developed country; WD s and WDg s are the wages of developed and
developing countries, assuming labour wages are homogenous within each country; R D s and
R Dg s are capital gains of developed and developing countries.
Maximise the consumers’ utilities and obtain the following Euler equations:
CD
= rD − λD
CD
(23)
CDg
= rDg − λDg
CDg
(24)
Equilibrium with free final goods trade and no intermediate goods trade
Domestic Incumbents
Here final goods are freely traded and intermediate goods are not traded. Each country produces
final products using domestic intermediate products.
Assume symmetry across domestic intermediate goods sector, MDi = MD and MDgi = MDg .
Hence,
ND
YD =
α
AD HYDD
γD
qD K D β D LYD
α
MDj 1−α D −β D −γ D = AD HYDD qD K D
βD
γ
D
LYD
· ND · MD 1−α D −β D −γ D
j=1
= AD · HYD α D · qD K D
βD
γ
D
· ND α D +β D +γ D · LYD
· N D · MD
1−α D −β D −γ D
(25)
N Dg
YDg =
α Dg
ADg HYDg
β Dg
K Dg
u qDg LYDg
γ Dg
MDgj 1−α Dg −β Dg −γ Dg
j=1
= ADg ·
α Dg
HYDg
·
β Dg
K Dg
α Dg
· u qDg LYDg
γ Dg
· NDg · MDg 1−α Dg −β Dg −γ Dg
β Dg
= ADg · HYDg · K Dg · NDg α Dg +β Dg +γ Dg · u q Dg LYDg
γ Dg
· NDg · MDg
1−α Dg −β Dg −γ Dg
(26)
For the developed country, the final product production function exhibits constant return to the
combination of human capital HYD , effective physical capital qD K D , labour LYD and total amount
of intermediate products ND · MD , and displays overall increasing return to scale due to
technology spill-over in terms of AD and intermediate products specialisation in terms of
ND α D +β D +γ D . For the developing country, the final product production function exhibits constant
return to the combination of human capital HYDg , physical capital K Dg , effective labour u q Dg LYDg ,
and total amount of intermediate products NDg · MDg , and displays overall increasing return to
scale due to technology spill-over in terms of ADg and intermediate products specialisation in
terms of NDg α Dg +β Dg +γ Dg .
Perfect competitive market structure and economic participants’ profit maximisation behaviour
lead to marginal product of labour equals wage and marginal product of intermediate goods
equals the price per unit of intermediate good.
ND
α
WD = γD AD HYDD
qD KD
βD
γ −1
MDj 1−α D −β D −γ D = γD ·
D
LYD
j=1
YD
LYD
(27)
N Dg
α
β
Dg
WDg = γDg ADg HYDg
K DgDg u q Dg
γ Dg
LYDg γ Dg −1
MDgj 1−α Dg −β Dg −γ Dg = γDg ·
j=1
YDg
LYDg
(28)
The following are the inverse demand functions for the intermediate products.
α
PMD = PMDj = 1 − αD − βD − γD · AD HYDD
qD KD
α
β
βD
γ
D
LYD
· MDj −α D −β D −γ D
Dg
PMDg = PMDgj = 1 − αDg − βDg − γDg · ADg HYDg
K DgDg u qDg LYDg
γ Dg
· MDgj −α Dg −β Dg −γ Dg
(29)
(30)
Alternatively, based on the Dixit and Stiglitz monopolistically competitive model (Dixit and
Stiglitz, 1977), below are the downward sloping demand functions for the intermediate products
derive from above (See Appendix I).
α
1 − αD − βD − γD AD HYDD q D K D
PMDi
MD = MDj =
= 1 − αD − βD − γD · YD ·
MDg = MDgj =
1 − αDg − βDg −
1
D +β D +γ D
γ
D
LYD
1
α D +β D +γ D
1
−
α D +β D +γ D
PMDj
1
1−
ND
α D +β D +γ D
j=1 PMDj
α Dg
γDg ADg HYDg
β
K DgDg
u q Dg LYDg
31
γ Dg
1
α Dg +β Dg +γ Dg
PMDgj
= 1 − αDg − βDg − γDg · YDg ·
Where − α
βD
and − α
1
Dg
+β Dg +γ Dg
1
−
α Dg +β Dg +γ Dg
PMDgj
1
1−
N Dg
α Dg +β Dg +γ Dg
P
j=1 MDgj
(32)
are the elasticities of intermediate products demand with
respect to the intermediate product prices for the developed and developing countries respectively.
Profits in the intermediate product sectors are:
πDj = MDj · PMDj − LMDj + LADj + fD · WD
(33)
πDgj = MDgj · PMDgj − LMDgj + LADgj + fDg · WDg
(34)
Each country maximises the present discounted value of its profit:
∞
max Present Value πMDj t =
t
MDj s · PMDj s − LMDj s · WD s − LADj s + fD · WD s
· e−r
∞
max Present Value πMDgj t =
t
MDgj s · PMDgj s − LMDgj s · WDg s − LADgj s + fDg · WDg s
s−t
· ds (35)
· e−r
s−t
· ds (36)
Subject to the constraints of intermediate products: intermediate product technology (3) and (4),
general technology (5) and (6), intermediate product demand (31) and (32)
From (3) and (4), I obtain LMDj =
M Dj
A Dj
and LMDgj =
M Dgj
A Dgj
, then I plug the values into (35) and (36).
From (5) and (6), I derive the increases in Hamilton values due to one unit changes in the
corresponding state variables ADj and ADgj : ADj = ηD · AD · HADj · LADj and ADgj = ηDg · ADg ·
HADgj · LADg j .
Based on Hamiltonian optimal control theory, below are present value Hamiltonian (PVH) at time
t:
+∞
PVHMDj (t) =
÷∞
PVHMDgj t =
e−r MD
s−t
·
·
PMDgj s −
t
e−r MDg
s−t
t
PMDj (s) −
WD
· MDj − LADj (s) + fD · WD + Q Dj · ηD · AD · HADj · LADj
ADj
· ds (37)
WDg
· MDgj − LADgj s + fDg · WDg + Q Dgj · ηDg · ADg · HADgj · LADgj
ADgj
· ds (38)
Where ADj and ADgj are the technology state variables; LADj , LADgj and PMDj , PMDgj are the control
variables; QDj and QDgj are the co-state variables representing the shadow values at time t of
increasing a unit of state variable technology ADj and ADgj at time s.
α
From (31) and (32), I obtain: MD = MDj =
1−α D −β D −γ D A D H YDD
P MDj
1
−
α Dg +β Dg +γ Dg
P MDgj
1
1−
N Dg
α Dg +β Dg +γ Dg
P
j=1
MDgj
MDg = MDgj = 1 − αDg − βDg − γDg · YDg ·
1
γ
q D K D β D L YDD α D +β D +γ D
and
, and plug them into (37) and
(38) respectively, then derive the following:
PMDj −
WD
· MDj − LADj + fD · WD + Q Dj · ηD · AD · HADj · LADj
ADj
α
= PMDj
WD
−
·
AD
1 − αD − βD − γD AD HYDD
PMDj
= PMDj
WD
−
·
AD
α
γD AD HYDD
1 − αD − βD −
qD K D
βD
qD K D
βD
γ
D
LYD
1
α D +β D +γ D
1
γ D α D +β D +γ D
LYD
− LADj + fD · WD + QDj · ηD · AD · HADj · LADj
·
1
1
α D +β D +γ D
PMDj
− LADj + fD · WD + QDj · ηD
· AD · HADj · LADj
PMDgj −
(39)
WDg
· MDgj − LADgj + fDg · WDg + QDgj · ηDg · ADg · HADgj · LADgj
ADgj
= PMDgj
WDg
−
·
ADgj
α
β
Dg
1 − αDg − βDg − γDg ADg HYDg
K DgDg u qDg LYDg
γ Dg
1
α Dg +β Dg +γ Dg
− LADgj + fDg · WDg + QDgj · ηDg · ADg
PMDgj
· HADgj · LADgj
= PMDgj
WDg
−
·
ADgj
1 − αDg −
α Dg
βDg − γDg ADg HYDg
β
K DgDg
u qDg LYDg
1
γ Dg α Dg +β Dg +γ Dg
· WDg + QDgj · ηDg · ADg · HADgj · LADgj
·
1
PMDgj
1
α Dg +β Dg +γ Dg
− LADgj + fDg
(40)
Based on the first order conditions for the maximisation of (39) and (40) with respect to PMDj and
PMDgj respectively (see Appendix II), I obtain the optimal prices:
PMDi = PMD =
1
WD
·
1 − βD ADi
PMDgi = PMDg =
(41)
WDg
1
·
1 − βDg ADgi
(42)
Based on the first order conditions for the maximisation of (39) and (40) with respect to MDi and
MDgi respectively (see Appendix II), I obtain the optimal prices:
WD = QDi · ηD · AD · HADi
⟹ Q Di
=
WD
ηD · AD · HADi
WDg = QDgi · ηDg · ADg · HADgi ⟹ QDgi =
Where
∂A
ηD · AD · HADi = ∂L Di =
∂ η Dg ·A Dg ·H ADgi ·L ADgi
∂L ADgi
ηDg
(43)
WDg
· ADg · HADgi
∂ η D ·A D ·H ADi ·L ADi
,
∂L ADi
ADi
(44)
and
∂A Dgi
ηDg · ADg · HADgi = ∂L
ADi
=
are the marginal product values of labour in research and development
sector.
The optimal behaviour for each country is to invest in research and development sector up to the
point where the shadow value of the innovation equals its marginal product value of labour in
research and development sector.
Research and development sector makes optimal production plan according to marginal net return
of technology rA equals the difference between existing technology gross return and the cost of
developing new technology.
∂PVHMDi ∂πDi
QDi ∂πDi 1
=
= rADi · QDi − QDi ⟹ rADi =
+
·
∂ADi
∂ADi
QDi ∂ADi QDi
(45)
∂PVHMDgi
∂πDgi
QDgi ∂πDgi
1
=
= rADgi · QDgi − QDgi ⟹ rADgi =
+
·
∂ADgi
∂ADgi
QDgi ∂ADgi QDgi
(46)
(45) and (46) imply that the returns on technology equal the growth rate of technology’s shadow
value plus marginal profit of technology per unit of technology’s shadow value.
1
From (43) and (44), I obtain: Q
Di
=
η D ·A D ·H ADi
WD
and
1
Q Dgi
=
η Dg ·A Dg ·H ADgi
W Dg
,
From (37) and (38), I obtain:
Q Dgi ·η Dg ·H ADgi ·L ADgi
N Dg
∂π Di
∂A Di
WD
=A
Di
2
· MDi +
Q Di ·η D ·H ADi ·L ADi
and
ND
∂π Dgi
∂A Dgi
W Dg
=A
Dgi
2
· MDgi +
,
From (3) and (4), I obtain: MDi = ADi · LMDi and MMDgi = ADgi · LMDgi ,
Hence, I derive:
rADi =
QDi
WD
QDi · ηD · HADi · LADi ηD · AD · HADi
+
· MDi +
·
2
QDi
ND
WD
ADi
rADgi =
=
QDi
WD
QDi · ηD · HADi · LADi ηD · AD · HADi
+
· ADi · LMDi +
·
2
QDi
ND
WD
ADi
=
QDi ηD · LMDi · AD · HADi
WD · ηD · HADi · LADi ηD · AD · HADi
+
+
·
QDi
ADi
ηD · AD · HADi · ND
WD
=
QDi ηD · LMDi · AD · HADi
ηD · LADi · HADi
+
+
QDi
ADi
ND
QDgi
WDg
QDgi · ηDg · HADgi · LADgi
+
· ADgi · LMDgi +
2
QDgi
NDg
ADgi
=
(47)
·
ηDg · ADg · HADg
WDg
QDgi ηDg · LMDgi · ADg · HADgi
ηDg · LADgi · HADgi
+
+
QDgi
ADgi
NDg
(48)
Assume technology is symmetric across sectors and human capital is symmetric across research
and development sector within each country. Then from (43) and (44), I obtain: QD = QDi =
WD
η D ·A D ·H ADi
=η
WD
D ·A D ·H AD
and QDg = QDgi = η
W Dg
Dg ·A Dg ·H ADgi
=η
W Dg
Dg ·A Dg ·H ADg
, and I derive:
QD QDi wD AD HAD
=
=
−
−
QD QDi wD AD HAD
(49)
QDg QDgi wDg ADg HADg
=
=
−
−
QDg QDgi wDg ADg HADg
(50)
Plug (49) and (50) into (47) and (48), in equilibrium, the return of technology should be equal
across each intermediate product sector’s research and development sector within each country to
rule out arbitrage.
rAD = rADi =
wD AD HAD ηD · LMDi · AD · HADi
ηD · LADi · HADi
−
−
+
+
wD AD HAD
ADi
ND
(47)
rADg = rADgi =
wDg ADg HADg ηDg · LMDgi · ADg · HADgi
ηDg · LADgi · HADgi
−
−
+
+
wDg ADg HADg
ADgi
NDg
(48)
The return in research and development sector is an increasing function of human capital devoted
to research and development sector HA , general technology stock A, labour LA and LM devoted to
research and development sector and intermediate products sector respectively; growth rate of
w
wage w . The reasons behind the phenomenon are: more inputs into the production generate more
output; higher general stock of knowledge stimulates technology growth through technology
spill-over across sectors within each country; higher growth rate in wages induces reducing input
cost through research and development sector become more profitable.
The return in research and development sector is a decreasing function of growth rate of
A
technology stock A , sector-specific technology Ai , the number of existing intermediate product
market incumbents N, growth rate of human capital
HA
HA
devoted to research and development
sector. The underlying intuitions are: the marginal product of an input decreases as the input
increases while holding the quantities of its complementary inputs constant, more market
incumbents lead to more competition which tends to reduce returns.
Foreign Entrants
Foreign entrants finance their initial establishment through issuing securities in the domestic
market, assume the returns of the securities are:
rSD =
πD VD
+
(The security return of developed country ′ s investment in developing country ) (51)
VD VD
rSDg =
πDg VDg
+
(The security return of developing country ′ s investment in developed country) (52)
VDg VDg
Substitute (41), (5), (3) and (42), (6), (4) into (33) and (34) respectively, also assume symmetry in
labour allocation across intermediate sectors in terms of LMDi =
L MD
ND
and LMDgi =
L MDg
N Dg
, I obtain:
πDi = MDi ·
1
WD
ADi
·
− LMDi +
+ fD · WD
1 − βD ADi
ηD · AD · HADi
= ADi · LMDi ·
1
WD
ADi
·
− LMDi · WD −
+ fD · WD
1 − βD ADi
ηD · AD · HADi
=
βD
ADi
· LMDi −
+ fD
1 − βD
ηD · AD · HADi
=
βD
LMD
ADi
·
−
+ fD
1 − βD
ND
ηD · AD · HADi
πDgi = MDgi ·
· WD
· WD (53)
WDg
ADgi
1
·
− LMDgi +
+ fDg · WDg
1 − βDg ADgi
ηDg · ADg · HADgi
βDg
LMDg
ADgi
·
−
+ fDg
1 − βDg
NDg
ηDg · ADg · HADgi
=
· WDg
(54)
Plug (51) and (52) into (49) and (50) respectively, and I derive:
rSD
πD VD
=
+
=
VD VD
=
rSDg
πDg VDg
=
+
=
VDg VDg
=
βD
L
A
· NMD − η · A Di· H
+ fD
1 − βD
D
D
D
ADi
· WD
+
FD · WD
βD
L
A
· NMD − η · A Di· H
+ fD
1 − βD
D
D
D
ADi
FD
+
WD
WD
βDg
LMDg
ADgi
· N − η ·A ·H
+ fDg
1 − βDg
Dg
Dg
Dg
ADgi
· WDg
FDg · WDg
βDg
LMDg
ADgi
· N − η ·A ·H
+ fDg
1 − βDg
Dg
Dg
Dg
ADgi
FDg
WD
WD
+
+
WDg
WDg
WDg
WDg
The entrant’s return is negatively correlated with the initial establishment cost F, entrant country’s
sector-specific technology growth, fixed input cost f, the number of incumbents; while positively
correlated with entrant country’s wage growth rate,
In equilibrium, the return on incumbents’ research and development equals the return on entrants’
investment security. The similarity between the two returns is that they are both decreasing
A
A
functions of technology growth A in their home country. In the r― A two dimensional space with r
on the vertical line and
A
A
on the horizontal line, In final product sector, the existence of
equilibrium requires the intersection of incumbents’ research and development return rA as a
A
function of A and entrants’ investment security return rs ; the stability of equilibrium requires that
rA > rS above the equilibrium point and rA < rS below the equilibrium point. The evolution
towards equilibrium is jointly determined by incumbents’ impact upon rA , entrants’ impact upon
rS and the number of market competitors. Hence,
1
HA
∂r A
>
A
∂
A
∂r S
A
∂
A
1
⟹ −1 > − η·H
AF
1
= − η·H
AF
⟹η<
, this indicates that
Resources Allocation and Market Clearing
Labour resource allocation:
ND
LD = LYD + LAD +
LMDi
i=1
N Dg
LDg = LYDg + LADg +
LMDgi
i=1
Human capital allocation:
HD = HYD + HAD
HDg = HYDg + HADg
Market clearing of consumption goods:
CD + CDg = YD + YDg
Long-run Dynamics and Convergence
The long-run dynamics reflects the interaction among research and development product sector,
intermediate product sector, incumbents and entrants in the final product sector. The research and
development product sector, as a core subsector of the intermediate product sector, generates rates
of returns rA based on intermediate products sectors’ intentional profit-maximizing investments in
technology input production. The intermediate product sector creates rate of return r through
intermediate product profits maximisation behaviour, and this rate is also used as the general cash
flow discount factor throughout the whole paper. Assume trade is balanced in each country and
all the domestic final products are consumed either by domestic or foreign consumers. Below
illustrates the transitional dynamics towards the long run equilibrium,
Research and development product sector:
rAD = rADi =
rADg = rADgi =
wD AD HAD ηD · LMDi · AD · HADi
ηD · LADi · HADi
−
−
+
+
wD AD HAD
ADi
ND
wDg ADg HADg ηDg · LMDgi · ADg · HADgi
ηDg · LADgi · HADgi
−
−
+
+
wDg ADg HADg
ADgi
NDg
Intermediate product sector and incumbents in final product sector (Derivation refers to Appendix
III). Under the assumption of free capital flows among sectors within the country and nonexistence of arbitrary opportunities, the rate of returns between intermediate product sector and
incumbents in final product sector should be the same.
rD = λD + δ · ηD · HAD · LAD + γ ·
rDg = λDg + αDg ·
KD
HYD
LYD ND
LMD
+ αD ·
+ βD ·
+
+ 1 − βD · ηD · HAD · LAD +
KD
HYD
LYD ND
LMD
HYDg
LYDg NDg
LMDg
+ βDg ·
+
+ 1 − βDg · ηDg · HADg · LADg +
HYDg
LYDg NDg
LMDg
New entrants in final product sector:
Developing country’s entrant into the developed country’s final product market:
rSD =
βD
L
A
· NMD − η · A Di· H
+ fD
1 − βD
D
D
D
ADi
FD
+
WD
WD
Developed country’s entrant into the developing country’s final product market:
rSDg =
βDg
LMDg
ADgi
· N − η ·A ·H
+ fDg
1 − βDg
Dg
Dg
Dg
ADgi
FDg
+
WDg
WDg
Empirical Analysis between two Asymmetric Countries:
The United States and China
Statistics Summary
Table II. Statistical Summary of the Variables from Q1 1992 to Q4 2010 with Quarterly
frequency (The beginning year 1992 is chosen due to the availability of China GDP quarterly
data)
Summary
Statistics
Mean
Standard
Deviation
Skewness
Kurtosis
Range
Minimum
Maximum
Observations
U.S.Trade Balance
China-U.S.
with
U.S.
China
U.S.Exports U.S.Imports
U.S.-China
U.S. GDP
U.S.
China. GDP
China
Exchange
China=U.S.Export
GDP
GDP
to China
to China
Trade
(Billion
Inflation (100 Million
Inflation Rate (Chinese
s to China-U.S.
Growth
Growth
(Million
(Million U.S.
Liberalization
U.S.Dollars)
Rate Chinese Yuan)
Rate Yuan to One
Imports to China
Rate
Rate
U.S.Dollars)
Dollars)
Indexes
U.S. Dollar)
(Million
U.S.Dollars)
7.7504
1.18% 2.51% 86688.9235 35.80% 4.65%
7.7504
7876.6737 38644.8658
-30768.19211
26.9775
0.9074
0.0067
0.0115
83057.0231
0.6800 0.0646
0.9074
6437.5776
29305.3906
23201.99821
11.2245
0.5924
-1.3581
3.2560
5.4676
8.7236
76
3.4805
-1.3590
0.0384
-0.0137
0.0247
76
2.7239
3.1590
-0.8254 1.9515
-0.9810
1.7770
-0.6865 1.5834
0.0645 395227.6717 2.0157 0.2907
-0.0143 5974.3283 -0.7784 -0.0217
0.0502 401202.0000 1.2373 0.2690
76
76
76
76
0.5924
-1.3581
3.2560
5.4676
8.7236
76
0.4723
-0.9793
1.1500
0.6599
27355.6000 98788.2000
1619.9000
5048.1000
28975.5000 103836.3000
76
76
-1.045699083
-0.600719874
78728.6
-82156.8
-3428.2
76
-1.6716
-0.2736
32.0000
8.0700
40.0700
75
Source: U.S. Census Bureau; National Bureau of Statistics of China; U.S. Financial Forecast Centre;
the U.S. Federal Reserve System; World Trade Organization (WTO)
Note: U.S.-China Trade Liberalization Indexes is measured as a linear combination form of Simple
Average MFN Applied, Duty free MFN Applied, Non ad valorem duties MFN Applied and Duties > 15 %
MFN Applied. And the linear form is selected according to statistical methodology and previous
literature. Higher number indicates higher level of trade liberalisation. There is a structural break at
Q1 2002, because China’s WTO accession date is 11 December 2001.
Unit―Root Tests
The Dickey-Fuller (DF) unit root test and the Augmented Dickey-Fuller (ADF) unit root test
are conducted to identify the order of integration, the results are listed in Table III.
Table III. DF-ADF Unit Root Tests
Variable
U.S. GDP (Billion U.S.Dollars)
U.S. GDP Growth Rate
Log (U.S.GDP)
U.S.Inflation Rate
China. GDP
(100 Million Chinese Yuan)
China GDP Growth Rate
Log (China GDP)
China Inflation Rate
China-U.S. Exchange Rate
(Chinese Yuan to One U.S. Dollar)
Test for Unit Root ADF Unit Root Test Statistics
in
Intercept Intercept+Trend
Level
0.0909
-2.3286
First Difference -4.7278
-4.6924
Level
-5.0123
-5.4152
First Difference -13.1354
-13.0406
Level
-1.8415
-0.5797
First Difference -4.9844
-5.3525
Level
-2.6276
-2.5603
First Difference -5.9965
-5.8952
Level
3.8999
1.8499
Concludion
(10% Level of
I(1): Integrated of Order 1
I(0): Stationary
I(0): Stationary
I(0): Stationary
I(1): Integrated of Order 1
I(0): Stationary
I(1): Integrated of Order 1
I(0): Stationary
I(1): Integrated of Order 1
First Difference
-2.7192
-4.4050
I(0): Stationary
Level
First Difference
Level
First Difference
Level
First Difference
-8.5194
-6.0029
3.8999
-2.7192
-1.1697
-3.6291
-8.3712
-5.9831
1.8499
-4.4050
-1.4254
-3.6799
I(0): Stationary
I(0): Stationary
I(1): Integrated of Order 1
I(0): Stationary
I(1): Integrated of Order 1
I(0): Stationary
Level
-2.5832
-2.6515
I(1): Integrated of Order 1
First Difference
-8.3041
-8.7269
I(0): Stationary
-1.5185
-2.1374
-9.0050
2.4922
-2.7096
1.7098
-5.0410
-1.4103
-9.4627
-3.1058
-2.8499
-9.0690
0.4045
-3.7290
-1.1547
-5.3404
-0.9031
-9.5143
I(2): Integrated of Order 2
I(1): Integrated of Order 1
I(0): Stationary
I(1): Integrated of Order 1
I(0): Stationary
I(1): Integrated of Order 1
I(0): Stationary
I(1): Integrated of Order 1
I(0): Stationary
U.S.Trade Balance with China
Level
=U.S.Exports to China-U.S. Imports to China First Difference
(Million U.S.Dollars)
Second Difference
Level
U.S. Exports to China
First Difference
Level
U.S. Imports from China
First Difference
Level
U.S.-China Trade Liberalisation Indexes
First Difference
Data Analysis Software: Eviews
The ADF unit roots tests suggest that variables U.S.GDP, Log(USGDP), U.S. Inflation Rate,
China GDP, Log(China GDP), China Inflation Rate, Exchange Rate, U.S. Exports to China,
U.S. Imports to China and Trade Liberalisation are both integrated of order 1. Compared with
U.S.GDP and China GDP, Log(USGDP) and Log(China GDP) are easier to interpret since
their first difference values stand for GDP growth rates. Hence, I choose D(Log(USGDP),
D(U.S. Inflation Rate), D(Log(China GDP), D(China Inflation Rate), D(Exchange Rate),
D(U.S. Exports to China), D(U.S. Imports from China) and D(Trade Liberalisation) to do
further research.
Co-integration Analysis
Based on the results of unit root tests, co-integration analysis is conducted to determine
whether a linear combination of I(1) variables are co-integrated. The first step is to specify the
lag structure of the vector auto-regressions model (VAR). Two relationships are tested: the
impacts of Trade Liberalisation upon U.S. Imports from China and Log(USGDP); the impact
of Trade Liberalisation upon U.S. Exports to China and Log(China GDP). Based Johansen
Co-integration test (Appendix IV), both Trace test and Maximum Eigenvalue test indicate the
number of co-integrating vectors r=6 for the first relationship and the number of cointegrating vectors r=3 for the second relationship. Hence, there exist corresponding long-run
linear relationships among the two set of variables. The outputs of vector auto-regressions
(VAR) suggest the following long run relationships:
Table IV. The impacts of Trade liberalisation upon Log (USGDP)
DLOGUSGDP
1.0000
DUSINFLATIO DUSIMPORTS DLOGCHINA DEXCHANGE DTRADELIBE
NRATE
FROMCHINA
GDP
RATE
RALISATION
0.886739
(0.56488)
[ 1.56979]
{ 0.0606 }
372352.6
(198364.)
[ 1.87712]
{ 0.0324 }
-15.19199
(13.9035)
[-1.09268]
{ 0.1392 }
35.52485
(19.5004)
[ 1.82175]
{ 0.0365 }
28.48987
(58.9889)
[ 0.48297]
{ 0.3153 }
Standard errors in ( ), t-statistics in [ ] and p-value in { }
According to the table, in the long run, the U.S. GDP growth rate is positively correlated the
magnitude of trade liberalisation between U.S. and China although not significantly (Pvalue=0.3153), and it is also positively correlated with U.S. Imports from China significantly
(P-value=0.0324).
The long-run equilibrium estimation:
DLOGUSGDP = 0.8867 DUSINFLATIONRATE + 372352.6 DUSIMPORTSFROMCHINA - 15.1920
DLOGCHINAGDP + 35.5249 DEXCHANGERATE + 28.4899 DTRADELIBERALISATION
Table V. The impacts of Trade liberalisation upon Log (China GDP)
DLOGCHINA DCHINAINFL DTRADELIBE
DUSEXPORT DEXCHANGE
DLOGUSGDP
GDP
ATIONRATE RALISATION
STOCHINA
RATE
1
-0.003209
(0.00755)
[-0.42472]
{ 0.3362 }
0.258323
(0.49135)
[ 0.52575]
{ 0.3004 }
-0.001044
(0.00118)
[-0.88683]
{ 0.1892 }
83.41516
(630.051)
[ 0.13239]
{ 0.4475 }
0.223721
(0.16352)
[ 1.36819]
{ 0.0879 }
Standard errors in ( ), t-statistics in [ ] and p-value in { }
According to the table, in the long run, the U.S. GDP growth rate is positively correlated the
magnitude of trade liberalisation between U.S. and China although not significantly (Pvalue=0.3004), and it is also positively correlated with U.S. Imports from China although not
significantly (P-value=0.4475).
The long-run equilibrium estimation:
DLOGCHINAGDP = -0.0032 DCHINAINFLATIONRATE + 0.2583 DTRADELIBERALISATION 0.0010 DLOGUSGDP + 83.4152 DUSEXPORTSTOCHINA + 0.2237 DEXCHANGERATE
The Error-Correction Model
Table VI. The Error Correction Model Estimation
The impacts of Trade liberalisation upon Log (USGDP):
Dependent Variable: ∆Log(USGDP)
Independent Variables
Estimates
Intercept
0.0050
DUSINFLATIONRATE
0.1227
DUSIMPORTSFROMCHINA
0.0001
DLOGCHINAGDP
0.0010
DEXCHANGERATE
0.0010
DTRADELIBERALISATION
0.0001
Error Correction (-1)
-0.0245
t-ratios
14.4019
3.7735
0.3787
0.8439
1.9045
0.2930
-1.3827
P-values
0.0000
0.0003
0.7061
0.4017
0.2776
0.7704
0.1713
The error correction coefficient is -0.0245, has a small magnitude and correct sign, although
not statistically significant. Hence, the speed of convergence to equilibrium is quite slow.
The impacts of Trade liberalisation upon Log (China GDP):
Dependent Variable: ∆Log(China GDP)
Independent Variables
Estimates
Intercept
0.0240
DCHINAINFLATIONRATE
1.1208
DTRADELIBERALISATION
-0.0503
DLOGUSGDP
-1.2077
DUSEXPORTSTOCHINA
0.0001
DEXCHANGERATE
-0.0552
Error Correction (-1)
-1.1009
t-ratios
0.4425
0.7295
-2.0107
-0.1294
3.8210
-0.7181
-9.6907
P-values
0.6595
0.4682
0.0483
0.8974
0.0003
0.4751
0.0000
Note: The model diagnostic tests including model misspecification test, no serial correlation
test, heteroscedasticity test and normality tests are conducted to ensure these above models
are the best fit.
The error correction coefficient is -1.1009, has a moderate magnitude and correct sign, and
statistically significant. This reveals a moderate speed of convergence to equilibrium.
Conclusions
This paper tests the hypothesis that the effects of bilateral trade liberalisation between two
asymmetric countries are highly associated with the extent of international technology spillover, relative market size, product variety and financial openness.
The methodologies consist of an endogenous growth model and the time series data analysis
of economic indicators obtained from a pool of frequently traded and economically integrated
countries.
The analysis finds that higher level of trade liberalisation and international technology spillover help to shrink the development gap between two asymmetric countries; the effects are
reflected more adequately in the long run equilibrium than in the short run dynamics; the sizes
and openness of trading partners’ markets influence trading activities’ profitability;
diversification of export and import products reduces the trade liberalisation risk; financial
openness in an effective manner enables trading countries to optimise export and import
structure.
These findings shed light on policy makers about the design of a mutually beneficial trade
liberalisation agreement between two asymmetric countries. Thus, the conclusion is that trade
policy formulation should take into account the degree of international technology spill-over,
exploitation of potential market, diversification and optimisation of export and import
structure.
Reference
BERGÉS, A. R. 2007. Trade Liberalization and Market Access: Analyzing Dominican Export
Performance during the Twentieth Century.
CZAP, H. J. 2006. Three essays on technological spillovers, innovation, and economic growth
DUN, R. M. A. J. H. M. 2004. International Economics.
HELBLE, M. S., BEN & WILSON, JOHN S 2007. Transparency, trade costs, and regional
integration in the Asia Pacific.
MAHDI, S. T. 2009. Trade Liberalization and Poverty Reduction in Developing Countries: The
Case of Africa.
MARCONI, D. 2007. Endogenous Growth and Trade Liberalization between Asymmetric
Countries.
PAGE, S. 2005. Special and Differential Treatment of Developing Countries in the World
Trade Organization.
RICHARD E. BALDWIN, R. F., PHILIPPE MARTIN 2000. Economic geography and public policy.
WINTERS, L. A. 2004. Trade Liberalisation and Economic Performance: An Overview The
Economic Journal, 114.
MD = MDi =
Appendix I: derivation of the demand functions for intermediate
products
α
1 − αD − βD − γD AD HYDD
PMDi
=
βD
qD K D
α
1 − αD − βD − γD AD HYDD
γ
D
LYD
qD K D
α
= 1 − αD − βD − γD · AD HYDD
1
α D +β D +γ D
βD
qD K D
γ
D
LYD
βD
=
α
1 − αD − βD − γD AD HYDD
1−(α D +β D +γ D )
1+
α D +β D +γ D
γ
D
LYD
·
α
AD HYDD
qD K D
βD
γ
α D +β D +γ D +1−(α D +β D +γ D )
α D +β D +γ D
γ
D
LYD
1
−
α +β D +γ D
PMDiD
1
−
α +β D +γ D
α
1 − αD − βD − γD AD HYDD
qD K D
βD
γ
D
LYD
1−(α D +β D +γ D )
α D +β D +γ D
j=1
1
−
α +β D +γ D
· PMDiD
α
qD K D
ND
j=1
MDj 1−α D −β D −γ D
1 − αD − βD − γD AD HYDD
MDj 1−α D −β D −γ D
D
LYD
βD
· PMDiD
ND
= 1 − αD − βD − γD
qD K D
βD
γ
D
LYD
1−(α D +β D +γ D )
α D +β D +γ D
1
−
α +β D +γ D
PMDiD
= 1 − αD − βD − γD · YD ·
α
1 − αD − βD − γD AD HYDD
qD K D
βD
γ
D
LYD
1−(α D +β D +γ D )
−
α D +β D +γ D
·
ND
i=1
MDi
− α D +β D +γ D
1
−
α +β D +γ D
PMDiD
= 1 − αD − βD − γD · YD ·
ND
j=1
1
−
α +β D +γ D
= 1 − αD − βD − γD · YD ·
α
1 − αD − βD − γD AD HYDD
PMDiD
1
1−
ND
α D +β D +γ D
P
i=1 MDi
qD K D
βD
γ
D
LYD
· MDj −α D −β D −γ D
1
1−
α D +β D +γ D
1−α D −β D −γ D
−
α D +β D +γ D
1
−
α +β D +γ D
PMDiD
α
MDg = MDgi =
=
=
β
Dg
1 − αDg − βDg − γDg ADg HYDg
K DgDg u qDg LYDg
γ Dg
1
α Dg +β Dg +γ Dg
PMDgi
1 − αDg − βDg −
α Dg
γDg ADg HYDg
β
K DgDg
1 − αDg − βDg −
α Dg
γDg ADg HYDg
β
K DgDg
= 1 − αDg − βDg − γDg ·
α Dg
ADg HYDg
u qDg LYDg
u qDg LYDg
β
K DgDg
γ Dg
α Dg +β Dg +γ Dg +1−(α Dg +β Dg +γ Dg )
α Dg +β Dg +γ Dg
γ Dg
1−(α Dg +β Dg +γ Dg )
1+
α Dg +β Dg +γ Dg
u qDg LYDg
γ Dg
·
−
α
· PMDgiDg
1 − αDg − βDg −
−
α
PMDgiDg
1
+β Dg +γ Dg
1
+β Dg +γ Dg
α Dg
γDg ADg HYDg
β
K DgDg
u qDg LYDg
γ Dg
1−(α Dg +β Dg +γ Dg )
α Dg +β Dg +γ Dg
−
α
· PMDgiDg
1
+β Dg +γ Dg
= 1 − αDg − βDg
α
N Dg
− γDg
α
β
Dg
ADg HYDg
K DgDg u qDg LYDg
γ Dg
MDgj 1−α Dg −β Dg −γ Dg
N Dg
j=1
j=1
−
α
PMDgiDg
= 1 − αDg − βDg − γDg · YDg ·
1 − αDg − βDg −
α Dg
γDg ADg HYDg
β
K DgDg
u qDg LYDg
γ Dg
γ Dg
1−(α Dg +β Dg +γ Dg )
α Dg +β Dg +γ Dg
N Dg
j=1
α
−
α
PMDgiDg
N Dg
j=1
β
Dg
1 − αDg − βDg − γDg ADg HYDg
K DgDg u qDg LYDg
1
+β Dg +γ Dg
1
1−
α Dg +β Dg +γ Dg
PMDgj
−
α
· PMDgiDg
1
+β Dg +γ Dg
MDgj 1−α Dg −β Dg −γ Dg
1
+β Dg +γ Dg
1−(α Dg +β Dg +γ Dg )
−
α D g +β Dg +γ Dg
·
N Dg
i=1
MDgi
− α Dg +β Dg +γ Dg
1
−
α Dg +β Dg +γ Dg
PMDgi
= 1 − αDg − βDg − γDg · YDg ·
= 1 − αDg − βDg − γDg · YDg ·
β
Dg
1 − αDg − βDg − γDg ADg HYDg
K DgDg u qDg LYDg
γ Dg
· MDgj 1−α Dg −β Dg −γ Dg
1
1−
α Dg +β Dg +γ Dg
1−α Dg −β Dg −γ Dg
−
α Dg +β Dg +γ Dg
Appendix II: derivation of the first order conditions for
the maximisation of the present value Hamiltonian
The developed country:
∂
W
PMDj − D ·
AD
1 − αD − βD −
α
γD AD HYDD
βD
qD K
D
1
αD +βD +γD
γD
LYD
1
αD +βD +γD
1
·
PMDj
− LADj + fD · WD + QDj · ηD · AD · HADj · LADj
∂PMDj
α
=
1 − αD − βD − γD AD HYDD
α
·
1 − αD − βD − γD AD HYDD
=
1 − αD − βD −
qD K
βD
D
qD K
1
αD +βD +γD
γD
LYD
D
qD K
α
γD AD HYDD
βD
1
αD +βD +γD
γ
D
LYD
βD
D
· PMDj
1
αD +βD +γD
γD
LYD
1
αD +βD +γD
−
· PMDj
−
1
αD + βD + γD
· PMDj −
WD
AD
1
−1
αD +βD +γD
−
· PMDj
1
αD +βD +γD
−
· 1−
1
αD + βD + γD · PMDj
· PMDj −
=0
1
Since
1 − αD − βD −
α
γD AD HYDD
1−
qD K
βD
D
αD +βD +γD
γD
LYD
1
αD + βD + γD · PMDj
1
αD + βD + γD · PMDj
1
αD + βD + γD
−
1 − αD + βD + γD
αD + βD + γD
PMDj =
∂
PMDi −
WD
·
ADi
1 − βD · HYD α D · LYD β D
· PMDj
· PMDj −
· PMDj −
WD
AD
WD
AD
=
≠0, I obtain:
=0
=1
αD + βD + γD · PMDj · A D
=1
WD
αD + βD + γD · PMDj · A D
1 − αD + βD + γD
· PMDi
1
−
βD
·
WD
AD
− LADi + fD · WD + Q Di · ηD · A D · HADi · LADi
∂LADi
= −WD + Q Di · ηD · AD · HADi = 0
WD = Q Di · ηD · AD · HADi
The developing country:
αD +βD +γD
WD
1
1
βD
1
−
WD
AD
∂
PMDgi −
WDg
·
ADgi
1
β Dg
1 − βDg · HYDg α Dg · LYDg β Dg
1
−
β Dg
· PMDgi
− LADgi + fDg · WDg + Q Dgi · ηDg · ADg · HADgi · LADgi
∂PMDgi
1
=
· PMDgi
Since
β Dg
1 − βDg · HYDg α Dg · LYDg β Dg
1
−
−1
β Dg
=
1 − βDg · HYDg
1 − βDg · HYDg α Dg · LYDg β Dg
1−
1
−
β Dg
· PMDgi
αDg
1
β Dg
· LYDg
1
β Dg
β Dg
· PMDgi
−
1
β Dg
−
WDg
1
· PMDgi −
·
βDg
ADgi
· 1−
WDg
1
· PMDgi −
βDg · PMDgi
ADgi
≠0, I obtain:
WDg
1
· PMDgi −
βDg · PMDgi
ADgi
βDg
1
−
β Dg
· PMDgi
1 − βDg · HYDg α Dg · LYDg β Dg
WDg
1
· PMDgi −
· PMDgi
ADgi
=0
=1
WDg
1
−
=1
βDg βDg · PMDgi · ADgi
1 − βDg
WDg
=
βDg
βDg · PMDgi · ADgi
PMDgi =
∂
PMDgi
WDg
−
·
A Dgi
1 − βDg · HYDg
α Dg
· LYDg
β Dg
1
β Dg
· PMDgi
WDg
1
·
1 − βDg ADgi
1
−
β Dg
− LADgi + fDg · WDg + Q Dgi · ηDg · A Dg · HADgi · LADgi
∂LADi
= −WDg + Q Dgi · ηDg · ADg · HADgi = 0
WDg = Q Dgi · ηDg · ADg · HADgi
=0
1
β Dg
Appendix III: The Derivation of Rates of Returns in Intermediate
Product Sectors and Incumbents in Final Product Sectors
Assume trade is balanced in each country and all the domestic final products are
consumed either by domestic or foreign consumers.
CD = YD ⟹ log⁡
(CD ) = log⁡
(YD ) ⟹
CD YD
=
CD YD
CDg = YDg ⟹ log⁡
(CDg ) = log⁡
(YDg ) ⟹
CDg YDg
=
CDg YDg
CD
CD
YD
= rD − λD ⟹ rD = λD +
= λD +
CD
CD
YD
CDg
CDg
YDg
= rDg − λDg ⟹ rDg = λDg +
= λDg +
CDg
CDg
YDg
Assume symmetry across each intermediate product sector within each country.
ND
YD = AD δ · K D γ · HYD α D · LYD β D ·
MDi 1−β D = AD δ · K D γ · HYD α D · LYD β D · ND · MD 1−β D
i=1
⟹
YD
AD
KD
HYD
LYD ND
MD
=δ·
+γ·
+ αD ·
+ βD ·
+
+ 1 − βD ·
YD
AD
KD
HYD
LYD ND
MD
N Dg
YDg = HYDg α Dg · LYDg β Dg ·
MDgi 1−β Dg = HYDg α Dg · LYDg β Dg · NDg · MDg 1−β Dg
i=1
⟹
HYDg
LYDg NDg
MDg
YD
= αDg ·
+ βDg ·
+
+ 1 − βDg ·
YD
HYDg
LYDg NDg
MDg
Then I plugged in the dynamics of YD and YDg , and obtained the following:
rD = λD +
YD
AD
KD
HYD
LYD ND
MD
= λD + δ ·
+γ·
+ αD ·
+ βD ·
+
+ 1 − βD ·
YD
AD
KD
HYD
LYD ND
MD
rDg = λDg +
YDg
HYDg
LYDg NDg
MDg
= λDg + αDg ·
+ βDg ·
+
+ 1 − βDg ·
YDg
HYDg
LYDg NDg
MDg
Since MD = AD · LMD ⟹
MMDg = ADg · LMDg ⟹
MD AD LMD
=
+
MD AD LMD
MDg ADg LMDg
=
+
MDg ADg LMDg
AD
= ηD · HAD · LAD
AD
ADg
= ηDg · HADg · LADg
ADg
Hence,
MD AD LMD
LMD
=
+
= ηD · HAD · LAD +
MD AD LMD
LMD
MDg ADg LMDg
LMDg
=
+
= ηDg · HADg · LADg +
MDg ADg LMDg
LMDg
rD = λD + δ · ηD · HAD · LAD + γ ·
rDg = λDg + αDg ·
KD
HYD
LYD ND
LMD
+ αD ·
+ βD ·
+
+ 1 − βD · ηD · HAD · LAD +
KD
HYD
LYD ND
LMD
HYDg
LYDg NDg
LMDg
+ βDg ·
+
+ 1 − βDg · ηDg · HADg · LADg +
HYDg
LYDg NDg
LMDg
Appendix IV: Johansen Co-integration Test Output
Sample (adjusted): 1993Q1 2010Q4
Included observations: 72 after adjustments
Trend assumption: Linear deterministic trend
Series: DLOGUSGDP DUSINFLATIONRATE DUSIMPORTSFROMCHINA DLOGCHINAGDP DEXCHANGERATE
DTRADELIBERALISATION
Lags interval (in first differences): 1 to 2
Unrestricted Cointegration Rank Test (Trace)
Hypothesized
No. of CE(s)
Eigenvalue
Trace
Statistic
0.05
Critical Value
Prob.**
None *
At most 1 *
At most 2 *
At most 3 *
At most 4 *
At most 5 *
0.987030
0.393116
0.338396
0.321977
0.187042
0.124022
430.9717
118.1211
82.16296
52.42057
24.44329
9.533797
95.75366
69.81889
47.85613
29.79707
15.49471
3.841466
0.0001
0.0000
0.0000
0.0000
0.0017
0.0020
Trace test indicates 6 cointegrating eqn(s) at the 0.05 level
* denotes rejection of the hypothesis at the 0.05 level
**MacKinnon-Haug-Michelis (1999) p-values
Unrestricted Cointegration Rank Test (Maximum Eigenvalue)
Hypothesized
No. of CE(s)
Eigenvalue
Max-Eigen
Statistic
0.05
Critical Value
Prob.**
None *
At most 1 *
At most 2 *
At most 3 *
At most 4 *
At most 5 *
0.987030
0.393116
0.338396
0.321977
0.187042
0.124022
312.8506
35.95812
29.74238
27.97729
14.90949
9.533797
40.07757
33.87687
27.58434
21.13162
14.26460
3.841466
0.0001
0.0278
0.0260
0.0047
0.0395
0.0020
Max-eigenvalue test indicates 6 cointegrating eqn(s) at the 0.05 level
* denotes rejection of the hypothesis at the 0.05 level
**MacKinnon-Haug-Michelis (1999) p-values
Sample (adjusted): 1993Q1 2010Q4
Included observations: 72 after adjustments
Trend assumption: Linear deterministic trend
Series: DLOGCHINAGDP DCHINAINFLATIONRATE DTRADELIBERALISATION DLOGUSGDP
DUSEXPORTSTOCHINA DEXCHANGERATE
Lags interval (in first differences): 1 to 2
Unrestricted Cointegration Rank Test (Trace)
Hypothesized
No. of CE(s)
Eigenvalue
Trace
Statistic
0.05
Critical Value
Prob.**
None *
At most 1 *
At most 2 *
At most 3
At most 4
At most 5
0.992757
0.523989
0.333840
0.234018
0.109773
0.019944
466.5052
111.7124
58.26579
29.01757
9.822613
1.450500
95.75366
69.81889
47.85613
29.79707
15.49471
3.841466
0.0001
0.0000
0.0039
0.0613
0.2946
0.2284
Trace test indicates 3 cointegrating eqn(s) at the 0.05 level
* denotes rejection of the hypothesis at the 0.05 level
**MacKinnon-Haug-Michelis (1999) p-values
Unrestricted Cointegration Rank Test (Maximum Eigenvalue)
Hypothesized
No. of CE(s)
Eigenvalue
Max-Eigen
Statistic
0.05
Critical Value
Prob.**
None *
At most 1 *
At most 2 *
At most 3
At most 4
At most 5
0.992757
0.523989
0.333840
0.234018
0.109773
0.019944
354.7928
53.44665
29.24822
19.19496
8.372113
1.450500
40.07757
33.87687
27.58434
21.13162
14.26460
3.841466
0.0001
0.0001
0.0303
0.0913
0.3421
0.2284
Max-eigenvalue test indicates 3 cointegrating eqn(s) at the 0.05 level
* denotes rejection of the hypothesis at the 0.05 level
**MacKinnon-Haug-Michelis (1999) p-values