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Part 1: Neoclassical Trade Theory
Session A
Preliminaries: Two-SectorModels
Feenstra (Ch 1)
Trade & Investment Larry D. Qiu 2
Introduction
Analysis beginning from the equilibrium in a
single economy
Get familiar with the two basic international
trade models and the standard analysis
Trade & Investment Larry D. Qiu 3
1. The Ricardian Model
Trade & Investment Larry D. Qiu 4
Outline of the Ricardian model and
results.
The environment: labor, technology difference,
Question: Whats the pattern of trade?
Result: Comparative advantage determines thepattern of trade.
Home
Good 1
Good 2
Foreign
Good 1
Good 2
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The 2x1 model
Two goods: i
One factor: labor, L in Home and L* in Foreign
Technology:
Productivity:
Prices:
Labor is perfectly mobile b/w industries within each
country, but immobile b/w countries
*
productionofunitperneededlaborofunit
i
i
a
a
*
1and
1
ii aa
*
2
1* andpricerelative,, pp
pppp
ii =
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Analysis 1: Autarky equilibrium
Social planners problem: utility maximization:
Def: Production possibility set (PPS) and
production possibility frontier (PPF):
(1)s.t.),(max 221121, 21 Lyayayyuyy +
2y
1y
2/ aL
1/ aL
Uay2
ay1
A
2
1
2
1
a
a
u
u=
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A1: Perfect competition
Zero profit condition
Normalize
Then,
2
1
2
1
2
2
1
1 and,aa
pp
ap
apwap ii ===
12=p
22
and1
a
LwLI
aw ===
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Analysis 2: International trade
H has comparative advantage in producing
good 1
Then,
Assumption: free trade and no transport costs
Question: what is the equilibrium p at which
world demand equals world supply?
Let us first use graphic analysis
*
2
*1
2
1
a
a
a
a
*app
At point A
A
B
Def: industry 1 (2) is labor
(capital) intensive
At point B: reverse
FIR: factor intensities change at different factor prices
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Question: which
(w,r) (factor prices)for Home?
Answer: endowment
matters. Therefore,
we need to analyze
(1.6) (full
employment) as
well.
),(11 rwCp =
),(22 rwCp =
Ar
Aw
Br
Bw
r
w
A
B
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Graphic analysis of (1.6)
Suppose A is the solution to (1.5). Then we have
),(),,( AAiKiKAA
iLiL rwaarwaa ==
K
LLa2 La1
Ka2
Ka1
Producing
one unit of
each good
K
LLa2 La1
Ka2
Ka1
Producing 21 , yy
)( 2,22 KLaay
)( 1,11 KLaay
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What is the total endowment required to produce
21 and yy
AK
K
LA
L
?
A
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If are produced, A is the total factors
needed. In reverse, if the country has endowment A,there is a unique which will be produced.
This is how (1.6) is solved.
What if the countrys endowment is outside the cone
(next slide)?
Answer: only one good will be produced (with factor
prices being adjusted to satisfy (1.6)).
Def: Cone of diversification
21 and yy
21 and yy
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K
L
Cone of diversification
A
C
D
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Graphic analysis of (1.6)
Suppose B is the solution to (1.5). Then we have
),(),,( BBiKiKBB
iLiL rwaarwaa ==
1 in A
2 in A
2 in B1 in B
Note: there is no
overlappingK
L
K
L
B
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K
L
Diversificationcone B
Diversification
cone A
Result: If H is a labor (capital) abundant country, A (B) is
the solution, with low (high) wage and high (low) rental
B
B
A
A
K
L
K
L>
A: labor abundant
B: capital abundant
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Trade & Investment Larry D. Qiu 29
Case 2: No FIR (Factor Price Equalization)
Two iso-cost curves
from (1.5) No FIR: Factor
intensities do not
change
determine
, using
which in (1.6) to
determine
),(11 rwCp =
),(22 rwCp =
Ew
Er
r
w
E),( EE rw
and iKiL aa
21 and yy
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EK
K
LE
L
E
Factor Price Equalization Theorem: Suppose 2 countries
have free trade, identical technologies, but different
endowments. If both countries are diversified and FIR does not
occur, then the factor prices (w,r) are equalized across these
countries.
F
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Effects of goods price changes on factor
price
Comparative statics on the zero profit condition (1.5)
dradwadrr
Cdw
w
Cdp iKiL
iii +=
+
=
1,, iKiLiKiL =+=== i
iK
i
iL
C
wa
C
wa
x
dxx
Denote
Percentage change cost share
=
=
2
1
1L2L
1K2K
2K2L
1K1L
2
1
||
1
p
p
r
w
r
w
p
p
Then
1K2K2L1L|| ==where
(1.7)
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Suppose industry 1 is labor intensive
2
2
1
1
K
L
K
L
a
a
a
a>
Also suppose the relative price of good 1 increases
Then 0|| >
Then
02
1 >p
pd
0 21 >= ppp
Then, from (1.7), we have
221
2122211221
1
12
2111122112
)()(
||
)()(
||
pppppp
r
pppppp
w
LL
LLLLL
KK
KKKKK
+=
=
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Trade & Investment Larry D. Qiu 33
Stopler-Samuelson Theorem
An increase in the relative price of a good will
increase the real return to the factor usedintensively in that good, and reduce the real return
to the other factor.
Intuition:
Definition: magnification effect
Implications: income redistribution
rppw 21 >>>
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Graphic analysis of SST
),(' 11 rwCp =
),(11 rwCp =
),(22 rwCp =
0r
0w
'r
'ww
r
0but0Suppose 21 => pp
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Effects of endowment changes on output
Comparative statics on the full employment condition
(1.6)
1,1,, 2K1K2L1LiKiL =+=+== K
ay
L
ay iKiiLiDenote
=
=
K
L
y
y
y
y
K
L
||
1
1L1K
2L2K
2
1
2
1
2K1K
2L1L
Then
2L2K1K1L|| ==where
(1.8)
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Suppose industry 1 is labor intensive
2
2
1
1
K
L
K
L
a
a
a
a>
Also suppose
Then 0|| >
0and0 => KL
Then, from (1.8), we have
0||
and0
||
12
21 >=
LyL
Ly KK
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Trade & Investment Larry D. Qiu 37
Rybczynski Theorem
An increase in a factor endowment will increase
output of industry using it intensively, anddecrease the output of the other industry.
Intuition (see next slide):
Implications: Dutch disease
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K
L
(L,K) (L,K)
),( 22 KL aa
),( 11 KL aa
),( 222 KL aay
),( 111 KL aay
),(' 222 KL aay
),(' 111 KL aay
Graphic analysis of the
Rybczynski Theorem
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Conclusion
Ricardian model
2x2 model (the preliminary H-O model), with fixed
output prices: derive a set of results Provide tools to prove the theorems and intuitions,
for further study.
Part 1: Neoclassical Trade Theory
Session B
The Heckscher-Ohlin ModelFeenstra (Ch 2)
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Introduction
The environment: endowment difference.
Questions:
Pattern of trade?
Gains from trade?
Do data support the theory (next part)?
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The Heckscher-Ohlin Theory
The HOS model
Keep the same assumptions as in the 2x2 modelin Ch 1 (two countries with identical technology,
identical demand (homothetic taste), free trade in
goods, no FIR, etc), but prices are determined
endogenously in international trade between two
countries: 2x2x2 model.
The Theorem
Each country will export the good that uses itsabundant factor intensively.
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Analysis/Proof
Strategy:
Focusing on the case in which good 1 is labor
intensive, home is labor abundant, moreover
Procedure: autarky
Methodology: graphic analysis
KKLLK
L
K
L
a
a
a
a
K
L
K
L >=>> **,*
*,
2
2
1
1
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Analysis
Autarky equilibrium
at home (slope):
What is ?
We prove
by contradiction
(next slide).
a
aa
p
pp
2
1=
apaa
pp >
Indifference curve
PPF
Budget line
GDP line
Home
1y
2y
A
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Trade & Investment Larry D. Qiu 45
1y
2y
Homothetic taste
fixed share of income
spent on each good
F in point C
A
C
Rybcynzski Theorem
F should produce at
at point like B, not
C.
Contradiction!
aapp =Suppose
aapp
B
But should it be ? It must beaaaa
pppp >< or aa pp >
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Where is the free trade equilibrium price p? Prove
Z(p)D(p)S(p) excess demand for good 1 at home
Z*(p)
D*(p)
S*(p)
excess demand for good 1 abroad Z(p)+Z*(p) excess demand for good 1 in the world
Since Z(pa) = 0, Z*(pa) > 0
Z(pa)+Z*( pa) > 0
also Z(pa*) < 0, Z*(pa*) > 0
Z(pa*) +Z*(pa*) > 0
Then by continuity of the excess demand functions, there must
be a price p, with such that Z(p)+Z*(p) = 0
),( aa ppp
),(
aa ppp
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Welfare and gains from trade?
Whats the welfare implication of the HO
theorem?
The abundant factor in each country gains fromtrade, and the scarce factor loses.
Proof: and the SST.
Gains from trade?
),( aa ppp
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Gains from trade for
each country
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Part 1: Neoclassical Trade Theory
Session C
Ricardian Model with a
Continuum of GoodsDornbusch, Fisher and Samuelson (AER, 1977)
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Introduction
Continuum of goods vs. many discrete
commodities: simplification The distinguishing feature: a cut-off point
which determines imported and exported
goods
Tariffs and transport costs: a range of
commodities not traded
Useful framework for other applications
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The model and issues
What is the pattern of trade?
Is every product traded?
How is pattern of trade affected by a change
in country size, technology progress, demand
shift, and unilateral transfer?
Home Foreign
Technology
a(z)
Technology
a*(z)
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The model: Supply side
Discrete commodity case Constant unit labor requirement
Arrangement
Comparative advantages?
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A continuum of goods
Relative unit labor requirement (decreasing in
z)
Comparative advantages? Competitiveness:
H produces z iff
].1,0[for z
Relative wageRelative costs
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Define
Then, H and F efficiently produce
Relative price of z, produced at H, to z, also
produced at H
Relative price of z, produced at H, to z,
produced at F
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In summary of the supply side: we use the
relative wage
To determine the borderline commodity,which gives indication of pattern of production
To determine the relative price structure,
because the we have known which countries
produce which goods.
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The model: Demand side
Cobb-Douglas demand
Constant expenditure share (prove for 2 good
case)
Identical tastes between two countries
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The fraction of income spent on the goods
produced by H
The fraction of income spent on the goods
produced by H
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Equilibrium relative wages and
specialization
What are the equilibrium conditions?
Hs labor market: income equals expenditure
The schedule starts at zero and approaches infinity as
approaches unity. It is a representation of the demandside: arise in results in a rise in relative wage
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The previous condition is also a trade balance
condition
Another condition (supply side): the
specialization condition
zzA ~at)(=
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Equilibrium relative
prices?
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Comparative statics
The importance of comparative statics in
economic analysis Based on Fig 1, we can see that the unique
equilibrium is determined jointly by tastes,
technology, and relative size. Hence we can
do comparative statics analysis with regard to
these changes.
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Relative size:
Intuition?
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Technical progress:
How?
A uniform
proportionalreduction in Fs unit
labor requirement
Intuition: loss in
comparative
advantages
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Demand shifts:
How?
A shift from high z
commoditiestoward low z
commodities
Intuition
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Transport costs and nontraded goods
Samuelsons iceberg transport cost: a
fraction of the good arrives: g=g(z)
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Supply side
Therefore H exports z iff
F exports z iff
Then, for any given
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Demand side
Let be the fraction of H income spent on Hs goods.
Similarly, . Then,
The trade balance condition
And so the unique solution for relative wage as a
function of exogenous variables: relative size and
transport costs
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Other applications
Tariffs
Exchange rates
Etc, e.g.,
Copeland and Taylor, Trade and transboundary
pollution,AER 1995
Eaton and Kortum, Technology, Geography, and
Trade, Econometrica, 70, 2002.
Matsuyama, Beyond Icebergs: Toward A Theory
of Biased Globalization (forthcoming), Review of
Economic Studies
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Part 1: Neoclassical Trade Theory
Session C
Technology transfer, FDI andinternational trade: A Ricardian
approachCheng, Qiu and Tan (JDE, 2004)
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Introduction
An application of the continuum of goods
model to technology transfer via FDI Explore the implications on
Division of labor between local firms and MNEs;
NorthSouth wage gaps;
Regional and aggregate welfare;
Government incentives to promote or discourage
technology transfer via MNEs;
Pattern of product cycles.
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Features and contributions
FDI arise due to technological differences
between two regions (as opposed to marketentry, etc)
Perfect competition (as opposed to
oligopolistic competition)
FDI and technology transfer requires specific
resources consisting of expatriate managers
and technicians
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A continuum Ricardian trade model with
technology transfer
Goods and technology
South L, North L*
South a(z), North a*(z), z in [0, 1]
For simplification: a*(z)=1
Assumption: a(z)>1 and is increasing in z
Normalization: Southern wage rate =1
Notation: Northern wage rate w*>1.
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Trade & Investment Larry D. Qiu 73
Technology transfer:
Efficiency loss, expatriates wage Unit cost of producing z by MNEs in the South
Preferences: a continuum version of Cobb-
Douglas utility function
Welfare
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Equilibrium without technology transfer
We have the standard DFS model, in which
the equilibrium consists of and isdetermined by
Hence,
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Equilibrium with technology transfer
Good z is produced by
For given w*
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How to determine w*?
World income
Goods market equilibrium condition
Demand for expatriates
Substituting T to get Y
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The equilibrium is determined by
Then, we can conduct comparative statics
analysis to get some results/propositions
below
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And more results
Part 2: Empirical Tests of Trade
Patterns and Flows
(A)
Leontief ParadoxFeenstra (Ch 2)
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Introduction
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Leontief Paradox
It is a presumption that the US is capital-abundant but
yet it exports labor intensive goods. Leontief rejects the null hypothesis (H-O theory): Is the
theory wrong?
Three possibilities to explain the paradox: Assumptions are not realistic
Data problem
Methodology is wrong
Note (1) capital stock vs. capital flow
(2) Use US technology for both import and export
An half-century debate
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HOV Model and Leamers Test
Vanek (1968): Extension to include many
countries, many goods and many factors, theMxN model. And consumption difference.
Essence of the HOV model
State the relationship between endowmentand pattern of trade in factor services.
The HOV theorem:
A country exports factor k services if its
endowment of factor k relative to the worldendowment exceeds its share of world GDP.
Trade & Investment Larry D. Qiu 83
The HOV model
=
=
=
i
i
i
i
i
i
KK
LL
D
DD
y
yy
aa
aaA
2
1
2
1
21
21Let Technology matrix
Output vector for country i
Demand/consumption vector for country i
is the net export (of goods) vector for country i
is the factor content of trade
then, country i exports labor services
then, country i exports capital services
Then
ii
iii
ATF
DyT
=
=
0
0
>
>i
K
i
L
F
FIf
If
Trade & Investment Larry D. Qiu 84
The HOV theorem
wiiiiVsVATF ==
w
ii
w
i
K
i
Li
D
Ds
VVVV
VV
=
+=
= 21,
whereEndowment vectors
Share of world consumption
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Trade & Investment Larry D. Qiu 85
Leamers test (1980)
There is no paradox!: US K/L ratio in production exceedsthat in consumption
Why?
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Explanations: Leamer vs Leontief
What is source of the paradox?
It must be the methodology problem, because Leamerused the same data and assumptions.
Where did Leontief go wrong?
Leontief had performed the wrong test! (Leamer): we
should not compare the K/L ratios in the export and
import. Why?
There are more than 2 factors
Trade is not balanced: US is a net exporter of both
capital and labor services Leontief calculated only production, Leamer calculated
both production and consumption
Trade & Investment Larry D. Qiu 87
No paradox for the US, but what about
other countries?
Bowen, Leamer, and Sveikauskas (AER, 1987):
Many countries
.,...1;,...1),()( MkCiVsVsignFsign wkii
k
i
k ===
.,...1;,...1;,...1),()( MlMkCiVsVVsVFF wlii
l
w
k
ii
k
i
l
i
k ===>>
Sign test
Rank test
Result? 50% success. FAIL again! No better than flipping a coin.
Implications: HOV model fails to meet the data. Some assumptions of the
model are wrong. Which one?
Trade & Investment Larry D. Qiu 88
Treflers diagnostic test
The assumption of equal technology across
countries is especially bad!
Trefler (JPE, 1993) estimates technologydifference across countries and makes
adjustment:
There is no reason to requires the data to
match the HO model
US is abundant in adjusted labor => Leontief
was right!
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Trade & Investment Larry D. Qiu 89
Conclusions
Tests directly on HO model as Leontief did giveunsatisfactory results.
Empirical studies after Leontief try to improve it Leamer (and others) uses HOV model: factor content
Trefler introduces technology differences
Both technology and endowment differences aremajor determinants of trade patterns
Further research in empirical studies: explainingtech differences Increasing returns to scale
Geography and climate Colonial institutions
Social capital
Part 2: Empirical Tests of Trade
Patterns and Flows(B)
The Case of Missing Trade
Trefler (AER, 1995)
Trade & Investment Larry D. Qiu 91
Motivation of the study
The H-O theorem and the HOV theorem have been
widely accepted in international trade theory.
BUT, the HOV theorem has been repeatedly
rejected, empirically.
In other fields of economics, the poor performance of
a major theory leads to
More careful consideration of the data, and
New theories that can accommodate the anomalies.
But, not for the HOV theorem.
This paper attempts to do both.
Trade & Investment Larry D. Qiu 92
Contribution of the paper
First, it demonstrates that the HOV theorem isrejected because factor service trade departsfrom its endowments-based prediction insystematic and informative way.
Second, it shows that the HOV is rejectedempirically in favor of a modification thatallows for home bias in consumption andinternational technology difference.
Literature Review (omitted)
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Trade & Investment Larry D. Qiu 93
Testing the HOV theorem against
statistical alternative
Sample: 33 countries and 9 factors
Notation: = the factor content of country cs net exports.
= the endowment of factor f in country c.
= the endowment of factor f in the world.
= the consumption share of country c in the world.
HOV equation:
If country c is abundant in factor f (i.e., ),
then it exports the services of factor f (i.e., >0 ).
Result (there are 297 observations): the correlation between
and is 0.28, very poor.
fcF
fcV
fwV
cs
fwcfcfc VsVF =
cfwfc sVV >/
fcF
fcF
fwcfc VsV
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A view through the HOV window
Fig. 1: define
Plot it against
By HOV equation, = 0 (not shown).
At least and should have the same
sign (but only 50%).
The main feature: = 0 (the diagonal), called
the case of the missing trade
)( fwcfcfcfc VsVF =
fwcfc VsV
fc
fcF fwcfc VsV
fcF
Trade & Investment Larry D. Qiu 95 Trade & Investment Larry D. Qiu 96
Fig. 2: the endowment paradox
The left panel of Fig 2: Poor countries tend to have
negative deviations, and rich countries tend to have
positive deviations. (The correlation of the number of
negative deviations per country with per capita GDP
is 0.87).
The right panel of Fig 2: Rich countries tend to be
scarce in most factors, and poor countries tend to be
abundant in all factors. (The correlation with per
capita GDP is 0.89).
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Trade & Investment Larry D. Qiu 97 Trade & Investment Larry D. Qiu 98
Suggestion/indication
The pattern of Fig 2 would occur if rich countries rantrade deficits and poor countries ran trade surpluses.
But if anything, the opposite is true.
Thus, the HOV theorem must have omitted somefactors in the endowment set and for those factors therich countries are abundant.
What are they? It suggests alternative theories(hypotheses).
Alternat ive hypotheses: technology andconsumption.