Download I. Introduction - Editorial Express

Intra-industry Trade and Industry Distribution of Productivity:
A Cournot-Ricardo Approach
April, 2009
E. Young Song*
Department of Economics
Sogang University
*
Department of Economics, Sogang University, C. P. O. Box 1142, Korea
Tel: +82-2-705-8696, Fax: +82-2-705-8180, E-mail: [email protected]
Intra-industry Trade and Industry Distribution of Productivity:
A Cournot-Ricardo Approach
E. Young Song*
Sogang University
Abstract
This paper constructs a Cournot-Ricardo model of trade by incorporating Cournot competition
in a Ricardian trade model. In this model, the share of intra-industry trade in bilateral trade volume
decreases as trading partners become more different in terms of the industry distribution of labor
productivity.
We show that this relationship is a special case of a more general relationship: the share of
intra-industry is decreasing in a specialization index. This specialization index turns out to be
equal to the difference in the industry distribution of productivity in the case of our CournotRicardo model, while it is given by the difference in capital-labor in the well-known case of
monopolistic competition.
As both technologies and factor endowments would be important in shaping specialization
patterns in the real world, we conjecture that the share of intra-industry trade is decreasing in two
measures of specialization: the difference in the industry distribution of productivity and the
difference in capital-ratio. Our OLS estimations strongly support this conjecture. In fixed effects
regressions, both measures lose significance in the entire sample, but the industry distribution of
productivity is significant in explaining trade between high income countries.
Key words: Intra-industry trade; specialization; Cournot; labor productivity; industry distribution
JEL classification: F11, F12
*
Department of Economics, Sogang University, C. P. O. Box 1142, Korea
Tel: +82-2-705-8696, Fax: +82-2-705-8180, E-mail: [email protected]
1
I. Introduction
The monopolistic competition model of trade, founded by Dixit and Norman (1980),
Krugman (1979) and Lancaster (1979), dominates economists’ way of thinking on intra-industry
trade. The dominance is equally true in empirical arena. The finding of Helpman and Krugman
(1985) that the monopolistic competition model implies an inverse relationship between the
share of intra-industry trade and the difference in relative factor endowments set the stage for
theory-based empirical research on intra-industry trade. Helpman (1987), Hummels and
Levinsohn (1995) and many others tested this implication. These studies found somewhat mixed
results, but they succeeded in placing the Chamberlinian perspective on the center stage of
empirical research on intra-industry trade.
Davis (1995) challenged the monopolistic competition model as an exclusive tool for
understanding intra-industry trade. He showed that by introducing cross-country productivity
differences in a Heckscher-Ohlin world, one can easily generate intra-industry trade. This
Ricardo-Heckscher-Ohlin model also predicts that intra-industry will be high between countries
with similar factor endowments.
In a partial equilibrium framework, we can find another important approach to intra-industry
trade. Brander (1981), and Brander and Krugman (1983) showed that international Cournot
competition in segmented markets generate intra-industry trade. Bernhofen (1998) finds a good
fit between the Cournotian model and the pattern of intra-industry trade observed in
petrochemical industries.
This paper extends the Cournotian model to a general equilibrium theory. We merge the
model of Brander (1981) with the Ricardian model of Dornbusch, Fischer and Samuelson (1977).
2
From this Cournot-Ricardo model, we derive a new determinant of intra-industry trade: the
industry distribution of labor productivity. The model implies that the share of intra-industry
trade in bilateral trade volume increases as the industry distribution of labor productivity
becomes more similar between trading partners.
We try to understand this finding in a larger theoretical framework. We derive a general
relationship that the share of intra-industry trade is decreasing in a specialization index, and is
increasing in bilateral trade volume relative to the product of partner incomes. We go on to show
that the specialization index turns out to be equal to the difference in the industry distribution of
labor productivity in the case of the Cournot-Ricardo model. We also demonstrate that the
famous prediction of the monopolistic competition model is a special case of the general
relationship that we found: in the case of monopolistic competition, the specialization index is
given by the difference in capital-labor ratio. The industry distributions of productivity or relative
factor endowments affect the share of intra-industry trade because they determine the degree of
specialization between trading partners.
We put these theoretical observations to a test. Using production and trade data compiled by
Nicita and Olarreaga (2006), we find that the degree of specialization indeed has a strong
negative effect on the share of intra-industry trade. This relationship holds well in both OLS and
fixed effects models. We also investigate the relationship between the share of intra-industry and
two measures of specialization: the difference in the industry distribution of productivity and the
difference in capital-labor ratio. In OLS estimations, we find that both measures have strong
negative effects on intra-industry trade. In fixed effects models, however, the relationship
becomes fragile. Still, we find that the industry distribution of productivity is significant in
3
explaining trade between high income countries.
The paper is organized as follows. Section II constructs the Cournot-Ricardo model. Section
III makes some theoretical observations. Section IV conducts empirical investigations. Section
IV concludes.
II. A Cournot-Ricardo Model.
The specifications for technologies and preferences are the same as in the Ricardian model of
trade with a continuum of goods by Dornbusch, Fischer and Samuelson (1977-henceforth, the
DFS model).
Two countries produce a continuum of goods indexed on the unit interval [0, 1]. Labor alone
is used to produce goods. Unit labor requirements for good z in the home and in the foreign
country are given by a(z) and a*(z). We index goods such that home country comparative
advantage diminishes as z increases. Defining relative unit labor requirements as
a*(z)
A(z)  a(z) ,
(1)
A(z) is decreasing in z.
Labor is perfectly mobile between industries. We use w and w* to denote the competitive
wages in the home and in the foreign country.  expresses the relative wage of the home country,
w/w*.
The two countries are populated by consumers with identical Cobb-Douglas tastes. Denoting
the expenditure share of good z by b(z), the demand for good z in each country is determined by
the following equations.
4
b(z) Y
q(z) = p(z) ,
b(z) Y*
q*(z) = p*(z) ,
(2)
1
with 
b(z) dz = 1.
0
q(z) and q*(z) are the demand for good z in the home and the foreign country. p(z) and p*(z) are
the price of good z in the home and the foreign country. Y and Y* are the income levels of the
two countries.
The DFS model assumes that each industry is perfectly competitive. With costless trade, each
good is supplied solely by the country with a lower unit cost. Thus we have no intra-industry
trade.
Instead we assume that each industry is a Cournot duopoly composed of a home firm and a
foreign firm. As in Brander (1981), we assume that the home and the foreign market for each
good z are segmented, and each firm makes distinct quantity decisions for each market. Given the
unit-elastic demand curve in (2), it is easy to show that the following conditions should hold in
equilibrium.
p(z) = p*(z) = w a(z) + w* a*(z),
(3)
w* a*(z)
s(z) = w a(z) + w* a*(z) =
(4)
A(z)
.
A(z) + 
The price of a good is identical in two countries and is determined by the sum of the duopolists’
unit costs. The market share of the home firm is given by s(z), which is increasing in the home
country’s relative productivity A(z) and is decreasing in its relative wage . With the demand
curves in (2), then the world supply of good z by the home firm is given by
5
s(z) (q(z) + q*(z)) = s(z)
b(z) (Y + Y*)
.
p(z)
(5)
Likewise, the world supply of good z by the foreign firm is equal to
(1 - s(z)) (q(z) + q*(z)) = (1 - s(z))
b(z) (Y + Y*)
.
p(z)
(6)
Let us define E[s] as the mean of s(z) over goods, where the density is given by the
expenditure share of a good b(z).
1
 s( z)b( z)dz .
E[s] 
0
To clear the home labor market, the labor supply L must be equal to the sum of the home firms’
labor demand across industries.
L=
1
 a( z)s( z)(q( z)  q * ( z))dz
0
1
=  s( z )(1  s ( z ))b( z )dz
0
Y Y *
.
w
(7)
Similarly, for the foreign country,
1
L* = 
 a*(z) (1-s(z)) (q(z) + q*(z)) dz
0
1
=  s( z )(1  s ( z ))b( z )dz
0
Y Y *
.
w*
(8)
Dividing (8) by (7),
w
L*
 = w* = L .
(9)
The relative wage is determined by the ratio of labor endowments. Then using equation (4), we
can express the market share of the home country in each industry as a function of the two
parameters: comparative advantage and relative labor endowment.
6
A(z)
L/a(z)
s(z) = A(z) + L*/L = L/a(z) + L*/a*(z) .
(10)
The income level of the home country is equal to the total expenditure on domestically
produced goods. Thus
Y=
1
 s( z)b( z)(Y  Y *)dz = E[s] (Y+Y*).
(11)
0
Thus, the mean market share E[s] also equals the share of home GDP in world GDP.
By construction, we have intra-industry trade in every industry. Each country supplies a
fraction of each other’s market and cross-hauling occurs in every industry. Note that the size of
the foreign market is equal to b(z) Y*. As the home firm supplies the fraction s(z) of this market,
the exports of the home country in industry z is given by
x(z) = s(z) b(z) Y* = s(z) b(z) (1-E[s]) (Y+Y*).
(12)
Likewise, the imports of the home country in industry z is given by
m(z) = (1-s(z)) b(z) Y = (1-s(z)) b(z) E[s] (Y+Y*).
(13)
The net export of good z is then equal to
x(z)-m(z) = (s(z) - E[s]) b(z) (Y+Y*).
(14)
Thus in an industry where the home country is more competitive than in the average market, it
becomes a net exporter. Recall that s(z) is increasing in A(z). Thus the ratio of net export to the
market size increases as the comparative advantage of the home country increases. Our CournotRicardo model preserves the basic Ricardian flavor.
Using three equations above, we can calculate the Grubel-Lloyd index of intra-industry trade,
7
1
 x( z)  m( z) dz
GL = 1 
 ( x( z)  m( z))dz
0
1
= 1
E[ s[ z ]  E ( s) ]
.
2 E[ s](1  E[ s])
(15)
0
Note that E[s(z)-E[s]] is the mean absolute deviation of market shares from the national mean.
The intensity of intra-industry between two countries decreases as the dispersion of market shares
across industries increases. To link the dispersion index to the parameters of the model, let us
denote the home labor productivity in industry z by z) (= 1/a(z)) and the foreign counterpart by
z) (= 1/a*(z)). We first linearize equation (4) in terms of z) and z) around their
respective means E[ and E[Thenwe substitute the linearized function s(z) into equation
(15) and obtain the following equation.
1  ( z)  * ( z)
GL  1  E[

].
2 E ( ) E ( *)
(16)
Equation (16) is the key result of this paper. The intensity of intra-industry trade increases as the
distribution of (z)/E[ across industries matches more closely with that of (z)/E[. In
other words, intra-industry trade will be intense between countries that have similar industry
distributions of labor productivity (relative to the national mean).
III. Some Theoretical Observations
In this section, we make some theoretical observations and try to understand the results of
the previous section from a larger perspective.
Let us use the following notations. Xijk is the value of good k shipped from country i to
country j. Xij is the value of all goods shipped from country i to country j. Yik is the value of good
8
k produced in country i, and Yi is the value of all goods produced in country i. We use YW to
denote the world production,  Yi. Using these notations, we present the following propositions.
i
[Proposition 1]
The world is composed of two countries i and j. They trade with each other with zero costs and
trade is balanced. Consumers have identical homothetic preferences.
Then
IIT 
GRAV
,
SPEC
(17)
where
1
IIT 
and GL = 1 
1  GL
GRAV =
SPEC =
X ij
Yi Y j YW
1
2
 X ijk  X kji
X ij  X ji
,
,
 ik   kj ,  ik 
k
k
Yi k
.
Yi
The proof is in the appendix. GL is the Grubel-Lloyd index of intra-industry trade. IIT stands
for intra-industry trade. It increases from 1 to infinity as GL goes from 0 to 1. GRAV, which
stands for gravity, is the ratio of bilateral trade to the product of partner incomes (scaled by world
income). Let us call this ratio the gravity coefficient. It is well-known that the gravity coefficient
is equal to unity in a world where the simple or ‘frictionless’ gravity equation holds. With trade
frictions, the coefficient falls below unity. SPEC is an index of specialization between trading
9
partners. This index takes the minimum value of zero when two countries have an identical
industry structure, and the maximum value of unity when there is complete specialization.
Krugman (1991) employs the same index in his study on economic geography. Now it is widely
used as an index of specialization between two regions.
Proposition 1 states that given the volume of trade (relative to the product of partner
incomes), the share of intra-industry trade in bilateral trade is decreasing in the degree of
specialization between trading partners. It is important to understand that this relationship holds
as an accounting identity under the hypotheses of Proposition 1. No economic theory has been
used to derive the equation, and no causal chain is presumed among three variables.
However, specific theories impose restrictions on these variables. For example, the
following proposition can be derived from the model of the previous section.
[Proposition 2]
In the Cournot-Ricardo model of section II,
SPEC 
1  ( z)  * ( z)
E[

],
2 E ( ) E ( *)
(18)
GRAV = 1.
(19)
The proof is simple. By equation (5), the value of good z produced in the home country is
equal to p( z ) s( z )(q( z )  q * ( z ))  s( z )b( z )(Y  Y *) . By equation (11), the GDP of the home
country is equal to E ( s )(Y  Y *) . Thus the share of good z in home GDP is given by
s( z )b( z ) / E ( z ) .
Similarly,
the
share
of
good
z
in
foreign
GDP
is
given
by
(1  s( z ))b( z ) /(1  E ( z )) . The absolute value of the difference, summed (integrated) over all
10
goods, and divided by 2 is our specialization index SPEC. It is easy to show that this is equal to
E[ s[ z]  E(s) ] / 2E[s](1  E[s]) . From the linear approximation that we used to derive equation
(16), equation (18) immediately follows. To calculate the total exports of the home country, we
integrate x(z) in equation (12) over all goods.
1
X   s( z )b( z )Y * dz  E ( s)Y * 
0
YY *
.
Y Y *
(20)
Thus GRAV is equal to 1.1
Now we can see that equation (16) is a special case of proposition 1. With the gravity
coefficient fixed to unity, the Grubel-Lloyd index must be equal to one minus the specialization
index, which in the Cournot-Ricardo model, is given by the difference in the industry distribution
of labor productivity. We now turn to a well-known case.
[Proposition 3]
The world is composed of two countries i and j that produce two goods using capital K and labor
L. Two countries have identical technologies and trade is costless. If trade equalizes factor prices,
SPEC = c
ki  k j
yi y j
,
(21)
where ki  K i / Li , yi  Yi / Li and c is a constant that depends on the prices of two goods. K i
and Li are capital and labor endowments of country i.
The proof is in the appendix. Proposition 3 is interesting as it reveals the influential theory
of intra-industry trade by Helpman and Krugman (1985) as a special case of proposition 1. From
1
This demonstrates that contrary to the popular belief, specialization is not necessary for the gravity equation to
hold. In a different paper, we extend this observation and derive the general condition for the gravity equation.
11
the monopolistic competition framework, they derive the prediction that the share of intraindustry trade in bilateral trade volume increases as countries get more similar in their capitallabor ratios. To see the link with proposition 1, suppose that two goods produced in proposition 3
are product differentiated and subject to economies of scale as in the monopolistic competition
model. Then we can easily show that the simple gravity condition holds and GRAV is equal to
unity. By Proposition 1
IIT 
1 yi y j
c ki  k j
(22)
As the difference in capital-labor ratio between trading partners decreases, IIT increases. Thus
the inverse relationship between intra-industry trade and the difference in capital-labor ratio is a
special case of proposition 1. In addition, we obtain the exact functional form for the
relationship, which previous studies fail to provide. Furthermore, proposition 3 suggests an
important control variable for this relationship: the product of per-capita incomes. Researchers
on intra-industry trade repeatedly observed that intra-industry trade between low income
countries is low even though they have similar capital-labor ratios. Thus they included the
average level of development of trading partners in their regressions and found that this variable
positively influences intra-industry trade.2 The product of per-capital incomes can be thought as a
variable representing the average level of development.
IV. Empirical Results
In this section, we put our propositions to a test. We construct two regression equations. The
first one is based on proposition 1. Taking the natural logarithm of equation (17) and adding
2
See Greeway and Milner (1986)
12
country and time subscripts and an error term, we obtain the following regression equation.
log IITijt   0  1 log SPECijt   2 log GRAVijt   ijt .
(23)
If all the conditions of proposition 1 are satisfied, regression equation (23) with 1 =  and 2 =
1 will have a perfect fit. The error term arises because these conditions are violated in actual data.
The most important violation is that we are living in a multi-country world and trade barriers
exist among these countries. This will make country i trade more or less with country j than with
other countries in the world, and proposition 1 will not hold exactly. Furthermore, preferences
are neither identical nor homothetic, and there are heavy measurement errors in all these
variables. What we would like to check is if proposition 1 still explain a significant part of the
world despite all these violations.
Our second regression equation comes from propositions 2 and 3. In the Cournot-Ricardo
model, the degree of specialization is given by the difference in the industry distribution of labor
productivity. To match with data, we use the following discrete version of the index.
1
k
 k*
PRODIF  E[

],
2 E ( ) E ( * )
(24)
where  k denotes labor productivity in industry k. In the monopolistic competition model, the
degree of specialization is determined by the difference in capital-labor ratio scaled by the
product of per-capita incomes.
KDIF 
ki  k j
yi y j
.
(25)
We do not view two theories as mutually exclusive. Both the industry distribution of technology
and relative factor endowments would influence the formation of specialization among countries.
13
So we let them compete in the following regression equation.
log IITijt   0  1 log PRODIFijt   2 log KDIFijt  3 log GRAVijt   ijt .
(26)
We do not force GRAV to take the value of unity as implied by the theory, because in the real
world, trade barriers would be sure to reduce gravity.
The data that we use come from Nicita and Olarreaga (2006). They provide data on outputs
and the number of employees in 28 manufacturing industries (ISIC 3 digit level) for 100
countries. From the data, we can calculate output share and labor productivity by industry for
each country, and hence SPEC and PRODIF for each country pair. They also report bilateral
trade flows at ISIC 3digit level. The data well suit our purpose as they follow the same industry
classification as productivity data. From these, we calculate the gravity and Grubel-Lloyd index
for each country pair. Data on capital stock and GDP per worker are obtained from the Penn
World Table version 6.2. We used the perpetual inventory method to create data on capital stock
from investment flows. From this data set, we construct KDIF for each country pair. We will also
use variables that are frequently used in the estimation of gravity equations: distance and
dummies for common language, common border, island, landlock, colony and regional trade
agreement. These variables come from Rose (2004).
To construct SPEC and PRODIF, we should observe output shares and labor productivities in
all industries of trading partners. Thus a large number of missing values in output data severely
restrict the size of the panel. To lessen this restriction, we dropped four industries that seem to
generate too many missing values. 3 The availability of data on capital stock puts a further
3
These industries are tobacco (314), other petro and coal products (354), petro refineries (353) and pottery, china,
earthware (361).
14
restriction on the size of the panel. Due to these problems, almost all low incomes countries drop
out of the sample.
The data span years from 1976 to 2001, though observations are very thin at the front and
rear end. Capital stock slowly changes over time and contains many measurement errors caused
by inaccurate investment data and time-to-build. We have a similar problem with productivity
data as technology slowly changes and labor hoarding over business cycles can contaminate
productivity figures. For this reason, we focus on medium-term relationship between intraindustry and specialization, and use quadrennial observations. Dropping the thin ends, we choose
years 1978, 1982, 1986, 1990, 1994 and 1998.
Table 1: Means of Major Variables
Trade Partners
North-North
North-South
South-South
Total
GL
0.36
SPEC
0.27
GRAV
0.18
PRODIF
0.13
KDIF(104)
0.38
(0.18)
(0.10)
(0.31)
(0.05)
(0.40)
0.20
0.34
0.16
0.18
2.47
(0.12)
(0.08)
(0.33)
(0.06)
(1.37)
0.36
0.26
0.83
0.23
1.20
(0.16)
(0.07)
(0.81)
(0.07)
(1.18)
0.32
0.29
0.18
0.14
0.96
(0.18)
(0.10)
(0.33)
(0.06)
(1.22)
Obs.
843
321
15
1,179
N = 428
T = 2.8
The numbers in the parentheses are standard deviations.
Table 1 reports summary statistics for major variables. The total number of observations is
1,179. The number of country pairs included is 428 and the average number of observations per
15
country pair is 2.8. The panel is unbalanced. The table also divides observations into three
income groups. Using the World Bank’s classification, we define a high or upper middle income
country as a North country and a lower middle and low income country as a South country. 843
observations (72 %) are from North-North trade, and 321 (27 %) from North-South trade. Southsouth trade is almost ignored in the sample.
The means of major variables are reported in the table. As expected, the Grubel-Lloyd index
is higher in North-North trade than in North-South trade. The measures of specialization, SPEC,
PRODIF and KDIF, are higher in North-South trade than in North-South trade. The gravity
coefficient is slightly higher in North-North trade than in North-South trade. The numbers in the
parentheses report standard deviations. We see a significant amount of variations in variables.
However, most of them come from variations between trading partners. Despite using
quadrennial data, time-series variations within trading partners are very limited, and more than
85 % of total variations come from between variations for all variables in the table. Combined
with a small number of observations per country pair, this feature of data makes fixed effects
estimation challenging.
Table 2: Correlations
log IIT
1.00
log SPEC
log SPEC
-0.53
1.00
log GRAV
0.30
0.12
1.00
log PRODIF
-0.40
0.58
0.08
1.00
log KDIF
-0.40
0.44
-0.04
0.40
log IIT
log GRAV
16
log PRODIF
log KDIF
1.00
Table 2 reports correlations among major variables. All variables now are logarithmic. In the
first column, we can see that the correlation between IIT and SPEC is negative, and that between
IIT and GRAV is positive, supporting proposition 1. In the second column, we observe that SPEC
is positively correlated both with PRODIF and with KDIF, as implied by propositions 2 and 3. In
the third and fourth column, we see that GRAV is not correlated with PRODIF or KDIF, but
PRODIF and KDIF are positively correlated.
17
Table 3: Intra-industry Trade, Specialization and Gravity
log IIT
(1)
(2)
(3)
OLS
OLS
Fixed Effects
log SPEC






log GRAV





log Distance




Language




Border




Island




Landlock




Colony




13 RTA dummies
X
O
X
R2



Obs.






Year dummies are included in all regressions. Language(= 0, 1), Border= 0, 1), Island(= 0, 1, 2),
Landlock(= 0, 1, 2) , Colony(=0, 1) are dummy variables. The numbers in the parentheses are tratios.
The R2 of fixed effects regressions are from within regressions. T denotes the average number of
observations per country pair.
* : significant at 1%.
** : significant at 5%.
18
Table 4: Determinants of Intra-industry Trade: Productivity vs. Factor Proportion
log IIT
(4)
(5)
OLS
(6)
OLS

Fixed Effects
 

 



log KDIF






log GRAV





log Distance




Language




Border




Island




Landlock




Colony




13 RTA dummies
X
O
X
R2



Obs.






log PRODIF

Year dummies are included in all regressions. Language(= 0, 1), Border= 0, 1), Island(= 0, 1, 2),
Landlock(= 0, 1, 2) , Colony(=0, 1) are dummy variables. The numbers in the parentheses are tratios.
The R2 of fixed effects regressions are from within regressions. T denotes the average number of
observations per country pair.
* : significant at 1%.
** : significant at 5%.
19
Table 3 reports the results of estimating equation (23). In all regressions, we included year
dummies to control for time effects. In regression (1), we use an OLS estimation. The estimated
coefficient on SPEC is which is greater than the theoretical value of , but is significant at
1%. The coefficient on GRAV is positive, but far smaller than unity implied by proposition 1.
However, it still is significant at 1%. In regression (2), we replace GRAV with variables
frequently used in estimating gravity equations. In regressing gravity equations, these variables
are inserted as proxies for transportation costs and other trade barriers. It is well known that they
are highly significant in explaining variations of GRAV across trading partners. For example, in a
typical analysis, GRAV decreases as distance between trading partners increases, and increases
when trading partners share a common language or a common border. It has also been noted by
many researchers that one of these variables, distance between trading partners, has a significant
negative effect on intra-industry trade. This observation is particularly important to us because
the negative correlation between IIT and SPEC might have been driven by the common factor of
distance, or some other variables. A shorter distance between trading partners may increase the
intensity of intra-industry and decrease the difference in industry structure at the same time,
because of more similar climate conditions or consumer tastes. So we control for these effects by
adding gravity variables in the regression equation. Regression 2 reports the results. As expected,
intra-industry trade decreases with distance and increases with a common language. However,
the coefficient on SPEC still is significantly negative, though its absolute value has shrunk a
little.
However, there may be omitted variables other than these gravity variables whose variations
across trading partners cause a spurious correlation between IIT and SPEC. To eliminate their
20
influence and extract a time-series relationship between IIT and SPEC, we estimate a fixed
effects model in regression (3). As we can see, SPEC still has a significant negative effect on IIT.
However, the coefficient on GRAV has a wrong sign, and is significant at 5% at that. This
puzzling relationship between IIT and GRAV is observed in all fixed effects estimations below.
Having found that the predictions of proposition 1, especially the negative correlation between
intra-industry and specialization, are born out by production and trade data, we now turn to our
main interests: propositions 2 and 3. In table 4, we put PRODIF and KDIF instead of SPEC, and
let them compete in the same regression. Regression (4) reports an OLS estimation results. The
estimation confirms both propositions 2 and 3. The estimation coefficient on PRODIF is
negative and significant at 1%, as that on KDIF is. In regression (5), as in regression (2), we
replace GRAV with gravity variables. As before, intra-industry trade decreases with distance, and
increases with a common language. It is interesting to note that a common border enhances intraindustry trade, but having an island economy as a trading partner diminishes intra-industry trade.
The coefficients on PRODIF and KDIF still are negative and significant at 1%. In regression (6),
we estimate a fixed effects model. Here, the coefficient on PRODIF is not significant any more,
and the coefficient on KDIF becomes zero. Measurement errors in calculating productivity and
capital per worker might be the source of weak correlations. The lack of within variations
combined with a small number of observations (less than 3 per country pair) might be another.
To probe the matter further, in Table 5, we run fixed effects regressions in two subsamples:
North-North trade and North-South trade. (The South-South sample is dropped because of a
small number of observations.) In regression (7), we report estimation results for North-North
trade (trade between high or upper middle income countries). The negative coefficient on
21
Table 5: Determinants of Intra-industry Trade in North-North and North-South Trade
log IIT
(7)
(8)
(9)
Fixed Effects
Fixed Effects
Fixed Effects
North-North
North-South
High Income






log KDIF






log GRAV






R2



Obs.







Sample
log PRODIF
Year dummies are included in all regressions. Language(= 0, 1), Border= 0, 1), Island(= 0, 1, 2),
Landlock(= 0, 1, 2) , Colony(=0, 1) are dummy variables. The numbers in the parentheses are tratios.
The R2 of fixed effects regressions are from within regressions. T denotes the average number of
observations per country pair.
* : significant at 1%.
** : significant at 5%.
PRODIF now becomes significant at 5%. The coefficient on KDIF still is zero and insignificant.
We have similar results when the sample is further restricted to country pairs with high income,
as regression (9) reports. Regression (8) is for South-South trade. Now the coefficient for
PRODIF becomes insignificant, while the coefficient on KDIF is negative and significant at 1 %.
To summarize our fixed effects estimations, the difference in the industry structure of labor
productivity has a significant negative effect on intra-industry trade in North-North trade.
22
However, the effect becomes insignificant in North-South trade, making the overall relationship
between two variables unclear. The opposite results hold for the difference in capital-labor ratio.
The difference in capital-labor ratio seems to have no effect on intra-industry trade in NorthNorth trade, while it shows a significant negative effect on intra-industry trade in North-South
trade. Again, these discordant results make the overall relationship between intra-industry trade
and the difference in capital-labor ratio unclear.
V. Conclusion
The model developed in this paper is highly stylized. The world is composed of two countries
and they compete in a Cournot duopoly in every industry. However, we intend the simple model
merely as an economical way of stating our basic intuition. If the mutual penetration of markets
is a significant source of intra-industry trade, the industry structure of productivity would affect
the degree of specialization, which would, in turn, influence the intensity of intra-industry trade.
The intuition has a theoretical base. The share of intra-industry trade in bilateral trade volume
decreases when the degree of specialization between trading partners increases. The well-known
prediction of the monopolistic competition model, that the share of intra-industry trade is
inversely related to the difference in capital-labor ratio, is one special case. As the difference in
capital-labor ratio increases, it increases the degree of specialization, which is nothing but the
Rybczynski effect. This increase in specialization reduces intra-industry trade. However, capitallabor ratio is just one of the factors that determine the industry structure of an economy. The
industry distribution of productivity would be another, and it would affect intra-industry trade
through its effect on specialization.
23
We confirm these conjectures in production and trade data. Both the difference in the
industry distribution of productivity and the difference in capital-ratio are highly significant in
explaining variations of the Grubel-Lloyd index across country pairs. However, their explanatory
power over variations within a country pair is limited. In a future study, we should probe further
as to what drives these contrasting results.
24
References
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26
APPENDIX
[Proof for Proposition 1]
By the definition of  ik , the following equation holds.
X iik  X ijk   ik Yi .
(A1)
Under the assumptions made, the price of each good is identical in two countries and the
expenditure share of good k is equal to k in both countries. Thus
X iik  X kji   k Yi .
(A2)
X ijk  X kji  (ik   k )Yi ,
(A3)
ik Yi   jk Y j   k YW .
(A4)
From these two equations,
A(4) implies that
ik   k  (ik   jk )
Yj
.
YW
(A5)
Plugging this equation into equation (A3),
X ijk  X kji  (  ik   jk )
YiY j
Yw
.
(A6)
Thus
 X ijk  X kji    ik   jk
k
k
or
27
YiY j
Yw
,
 X ijk  X kji
k
2 X ij
1
 ik   jk

2
.
 k
YiY j
X ij /
Yw
The left-hand side of the equation is the proportion of inter-industry trade in total trade, 1  GL.
The right-hand side is equal to SPEC/GRAV. Thus
1
GRAV

.
1  GL SPEC
■
[Proof for Proposition 3]
Let PX and PZ be the prices of two goods X and Z in a trade equilibrium. Let W and R denote the
wage and the rental rate of capital. Using X i and Zi to denote the production of X and Y in
country i, we can express the full employment condition as
a XK
a
 XL
aZK   X i   K i 
.

aZL   Z i   Li 
(A7)
akv denotes the input of factor v used to produce one unit of good k. With factor price
equalization, two countries have identical a’s. Solving for the outputs of two good,
Xi 
1
(aZL K i  azK Li ) ,

(A8)
where   aZK aZL  aXLaZK .
Using this equation,
 iX 
PX X i
P a k  azK
 X ZL i
.
RK i  WLi
 Rk i  W
(A9)
In a similar way, we can calculate  jX and derive the following equation.
28
iX   jX 
PX aZL ki  azK aZL k j  azK
(

).
 Rk i  W
Rk j  W
(A10)

PX
[( aZL ki  azK )( Rk j  W )  (aZL k j  a zK )( Rk i  W )]
yi y j

PX
(ki  k j )( aZK R  aZLW )
yi y j

PX PZ ki  k j
.

yi y j
The last equality used the zero profit condition that PZ  aZK R  aZLW . Finally, since
 iZ  1   iX ,
SPEC =
P P ki  k j
1
 ik   kj   iX   jX  X Z

2 k  X ,Z

yi y j
■
29
(A11)