Discussion Papers In Economics
And Business

Trade impacts on skill formation: welfare improvements
accompanied by rises in inequality

Yasuhiro Sato Kazuhiro Yamamoto

Discussion Paper 07-12

Graduate School of Economics andOsaka School of International Public Policy (OSIPP)
Osaka University, Toyonaka, Osaka 560-0043, JAPAN

Trade impacts on skill formation: welfare improvements
accompanied by rises in inequality

Yasuhiro Sato Kazuhiro Yamamoto

Discussion Paper 07-12
April 2007

この研究は「大学院経済学研究科・経済学部記念事業」
基金より援助を受けた、記して感謝する。

Graduate School of Economics andOsaka School of International Public Policy (OSIPP)
Osaka University, Toyonaka, Osaka 560-0043, JAPAN

Trade impacts on skill formation: welfare improvements
accompanied by rises in inequality
Yasuhiro Sato

Kazuhiro Yamamoto yApril 9, 2007

Abstract
In this paper, we focus on the skill formation when considering the trade impacts
on labor markets. Although workers are identical as unskilled labor, they di¤er intheir productivity as skilled. Workers become skilled by incurring the training costs.
Introducing the above settings into a trade model with monopolistic competition, weshow that trade opening enhances skill formation. This is because trade enriches thevarieties of di¤erentiated goods and raises the utility of a worker for a given income.
This e¤ect works stronger for the skilled than for the unskilled although it makes all
agents better o¤, leading to higher skill formation. However, it may be accompanied
by rises in the real wage disparity between skilled and unskilled workers and by risesin the skilled wage inequality. Finally, we examine the possible e¤ects of foreign direct
investment on the labor market structure as well.

JEL Classi…cation: F12, F16, F23, J24, J31
Keywords: trade, skill formation, monopolistic competition, wage inequality, FDI

Graduate School of Environmental Studies,
Nagoya University (Japan).
E-mail:ysato@info.human.nagoya-u.ac.jpyGraduate School of Economics, Osaka University, (Japan); E-mail: yamamoto@econ.osaka-u.ac.jp1

1

Introduction

During the past two decades, the volume of trade has risen than ever before. In fact, theworld merchandise trade volume index for manufactures (1950=100) rose from 2929 in
1995 to 5454 in 2005 (WTO [35]). This indicates that the trade has come to play a more
and more important role in the current economy, which is also convinced by the world
wide proliferation of Regional Trade Agreements (RTAs).1 Moreover, trade now occupies
a signi…cant share in the world economic activities: World Bank [33] reported that exportsof goods and services account for 24.6 percent of world GDP in 2000.
This trend has prospered the analysis of trade e¤ects on various economic activities.
Especially, in the face of the new established facts regarding di¤erences in …rms’performances in the trade environment (see Bernard and Jensen [9][10], among others), impactsof trade in the presence of heterogeneous …rms have been intensively studied by papers
such as Melitz [28], Helpman et al [20], and Antras and Helpman [4].23 These papers developed monopolistic competition models with heterogeneous …rms, and shed light on the
trade impacts on the industrial structure and …rms. In their models, workers are identicaland their focus is not on worker heterogeneity but on di¤erences in the …rm level productivity. However, it is also a traditionally-well-known fact that workers are heterogeneous.
Then, it would be worth asking how trade could interact with labor markets when workers
are heterogenous.
Regarding the labor market, rises in the percentage of skilled labor have been observedin many developed countries during the past few decades. For instance, from 1983 to 2002,
the U. S. manufacturing sector has experienced 37 percent increases in employment in highskill occupations regardless of its contraction during that period (Federal Reserve Bank of
New York [13]). This trend is also con…rmed by Barro and Lee [7] In parallel,.increases in(real) wage gap between skilled and unskilled workers and rises in wage dispersion withingroups (residual inequality) have been distinct. Acemoglu [1] reported that during the past
two decades, the college wage premium in the United States has increased at almost twice.
Lemieux [24] provided empirical evidences on rising wage dispersion (variance) regarding
workers with higher education. Many researches such as Baldwin and Cain [6], Berman
et al [8], Bloom and Brender [11], Katz and Autor [21] supported these …ndings in manyof the older industrial economies of Europe and the United States. These trends wereobserved also in Hong Kong, Korea, Singapore, Taiwan (Fields [15]) and Mexico (Hansonand Harrison [18]).
Whereas possible explanations for these trends have been widely investigated fromthe viewpoint of skill-biased technological progress (see Acemoglu [1]), there is still roomfor exploring other possible causes.4 In fact, some researchers have considered trade asa signi…cant candidate. Richardson [31] (p. 36) surveyed the empirical studies and concluded regarding the impacts of trade on wage disparity as ”...Taken together, they[recent
empirical contributions] suggest to me an important role for trade, close to or larger thanits 10-15 percent share of U.S. output: not tiny, but not overwhelming either...” Also,
Feenstra [14] enumerated more recent studies that support this view. Given the drastic
increases of trade during the past decade, it would be safe to consider trade as one of the1

In 2006, there exist 211 RTAs, and among them, 194 were concluded after 1980 (WTO [34]).
Mannase and Turrini [25] considered a model in which heterogeneity of …rms arises from the di¤erencein the skill of entrepreneurs and obtained similar results regarding industrial changes due to trade openness
to those shown in Melitz [28].
3
For recent surveys, see Baldwin [5], Greenaway and Kneller [16] and Helpman [19].
4Skill-biased technical progress raises the demand for skilled labor and skilled worker wages.
22

important factors that a¤ect the skill composition and the wage structure.
The conventional wisdom in the trade theory suggests that the skilled-unskilled wage
gap in developed countries increased since international trade with relatively skill-scarcedeveloping countries raised the relative price of skill-intensive goods and the demand forskilled labor in developed countries (the Stolper-Samuelson e¤ect). More recently, Acemoglu [2] suggested that international trade, via the Stolper-Samuelson e¤ect, enhances
the skill-biased technical change (i.e., technological progress in the skill intensive sector)
and raises the demand for skilled labor, which can account for increases in the wage gap.5
However, most evidences in the United States suggest a declining or constant relative
price of skill-intensive goods between the early 1970’s and mid-1990’s in which the shareof imports from developing countries in the United States GDP increased over fourfold(see, Lawrence and Slaughter [23], and Sachs and Shatz [32]). In addition, Berman etal [8] showed empirically that recent rapid increases in demand for skilled labor in the
United States manufacturing sector are mainly attributed to the within industry changes,
not to the between industry changes. These evidences are not fully consistent with the
Stolper-Samuelson e¤ect, inducing us to look for other candidates.
Given the current importance of trade between developed countries, it would be natural to seek for a channel through which trade between developed countries a¤ects the
skill composition and the wage structure. Yeaple [36] went into this direction by adopting
a monopolistic competition model of trade. He focused on the interaction among monopolistic competition, workers’ skill heterogeneity, and …rms’ technological choice, andshowed that a reduction in trade cost bene…ts …rms that choose relatively more skill-biased
technology, which increases the share of such …rms accompanied by rises in wage rate forhigh skilled workers. However, Yeaple [36] assumed the exogenous distribution of skilledlabor and hence, the skill formation was out of the scope of his analysis.
By contrast, our primary focus is on the role of skill formation in the environment
where developed countries trade with each other. In this paper, we present a trade modelwith monopolistic competition a la Dixit and Stiglitz [12] and skill formation. In our model,
although workers are identical as unskilled labor, their productivity as skilled labor di¤ers
from worker to worker, i.e., they are vertically heterogeneous. If a worker trains herself,
she becomes skilled. Thus, we embeds vertical labor heterogeneity within Krugman [22]model of trade under monopolistic competition and increasing returns.6
Using this model, we will show that trade opening raises the skilled worker ratio,
the skilled-unskilled real wage gap, and the wage dispersion of skilled workers (residual
inequality). In our model, trade allows people to consume wider varieties of goods andlowers the price index of consumption goods, which leads to higher welfare (real wage) of
all agents. However, it raises the real skilled wage more than the real unskilled wage. This
induces even less productive workers to become skilled, which enlarges the wage dispersion
among skilled workers. Thus, our model shows that trade induces skill formation and raises
the wage gap without the Stolper-Samuelson e¤ect and the skill-biased technical progress.
In this sense, we presents a new channel (i.e., skill formation) through which international
trade a¤ects the wage structure. These results show that the trade improves the welfare
of all people although it may worsen inequality. We also study the e¤ects of changes in
5
In relation to this, Matsuyama [27] pointed out that if transportation sector’s technology is skill
intensive, technical progress in this sector enlarges the trade amounts and raises the wage gap.
6
Amiti and Pissarides [3] constructed a trade model with monopolistic competition, horizontally heterogeneous workers, and skill formation. They examined the relationship between skill mismatch parameterand the agglomeration of …rms. They showed that decreases in transportation costs and skill mismatch
parameter induces skill formation and agglomeration of …rms.

3

trade environment and e¤ects of Foreign Direct Investment (FDI), and prove that FDI, if…rms prefer it to export, enhances skill formation and may raise inequality.
This paper is organized as follows. In section 2, we present a basic model and analyze
the autarky economy. Section 3 analyzes the case of trade opening and compare the resultswith those in the autarky economy. In section 4, we consider the e¤ects of FDI. Section 5
concludes the paper.

2

Setup of the model

In this section, we introduce the basic structure of the model and explore its equilibrium.
In doing so, we …rst construct a closed economy model, and will extend it to an open
economy model in the next section.

2.1

Consumption

Consider a country in which there is a continuum of (immobile) workers of which measureis one. Each worker is endowed with one unit of time that can be spent on working.
Workers are either skilled or unskilled. Skilled and unskilled workers di¤er in the following
two points. First, workers must train themselves in order to become skilled by incurring
the …xed training cost c (> 0) in terms of utility. Second, as we will see in detail later,when workers work as skilled, they are heterogeneous in productivity, which is denoted byb. Each worker is assumed to have an identical utility function of the CES form:
Uu =
and
Us =

Z
Z

1=

q( ) d;if the worker is unskilled,2
1=

q( ) dc;

if the worker is skilled.

2

where is the index of di¤erentiated goods and the measure of the set
represents themass of available goods. q( ) is the consumption of good .
is a positive constantsatisfying 0 < < 1. This implies that the di¤erentiated goods are substitutes and thatthe elasticity of substitution between two di¤erentiated goods is = 1=(1) > 1. Let
ws and wu denote the skilled and unskilled wage rate, respectively. The wage income Ii isgiven as: Is = bws and Iu = wu . The demands and utility level are given asIip( ) P 1
Iu
;
P
Is
c:
P

q( ) =
Uu =
Us =

;

i = s; u;(1)p( ) is the price of variety , and P is the price index de…ned as
P =

Z

1=(1

p( )1
2

4

d

)

:

(2)

2.2

Production

We assume that the unskilled labor is the numeraire. Thus the unskilled wage income isequal to one: wu = 1. Di¤erentiated goods are produced in a monopolistic competitivemarket. Each …rm supplies one variety and in order to begin production, it must employ
one unit of skilled labor in e¢ ciency units. The payment for skilled labor ws represents
the …xed cost for production. For the production of one unit of output, units of unskilledlabor are necessary. Hence, the marginal cost is described by , which is also normalized
to be one for the expositional simplicity. The pro…t maximizing pricing behavior of a …rm
is to set a price equal to
p=
:
(3)
1
Note here that all …rms set the equal price under the constant markup pricing rule. Therefore, the price index (2) becomes
P = n1=(1

)

p;

(4)

where n is the number of varieties (i.e., the number of …rms). As seen in standard monopolistic competition models a la Dixit and Stiglitz [12], larger number of varieties leads tolower price index, which improves the indirect utility of workers for a given income level.
Using (3) and (4), the pro…t of a …rm becomes
= (p
=

AI
n

1)

AI
p P1

ws

ws :

AI describes the aggregate income. We assume the free entry and exit of …rms, which
drives the …rm’s pro…t to zero:
AI
:
(5)
ws =
n

2.3

Skill formation

To keep things simple, we assume that an unskilled worker can become skilled by incurring
once he/she takes training. Each worker is endowed with one unit of time that can bespent on working. However, workers are heterogeneous in productivity b when working
as skilled. b represents the skilled labor supply in e¢ ciency units, which determines thewage income of each skilled worker as bws . As unskilled, workers supply one unit of laborand obtain the wage income of 1. We assume that the distribution of b is given by the
distribution function G(b). G(b) is assumed to be de…ned over (0; 1) and continuouslydi¤erentiable, implying that the density function g(b) is continuous.
Each worker compares the (indirect) utility when he/she becomes skilled with thatwhen unskilled, and chooses to be skilled if the former is larger than the latter. Therefore,
there is a cuto¤ level of productivity br , under which the utility of being skilled (see (1))
is equal to the utility of being unskilled. br is determined by the arbitrage behavior ofworkers, which is given by1
br ws= + c:(6)PP
We call this as the skill formation condition.
Because the number of total workers is normalized to one, 1 G(br ) workers are skilled
and G(br ) workers are unskilled. Because b represents the productivity of a skilled worker,
5

R1

br bg(b)db describes the total skilled labor supply.

Also, one unit of skilled labor being
necessary for the production of one variety, the number of varieties n is given by
Z 1
dn(br )
bg(b)db;n = n(br )= br g(br ) < 0;
(7)
dbr
br
where n(br ) is positive for br 2 (0; 1). As the skilled worker ratio increases, the number ofvarieties available in the economy rises. Substituting (7) into (4), we have
P = n(br )1=(1

)

p;

dP
pn(br ) =(1=dbr
1) dn(b )=db
r
r

> 0:

(8)

Using (3) and (8), (6) can be rewritten as
ws =

2.4

1
1+
br

c
1

n(br )1=(1

)

:

(9)

Equilibrium and its e¢ ciency property

Aggregate income AI is given as
AI = ws

Z 1

bg(b)db + wu G(br )br= ws n(br ) + G(br ).
Substituting this into (5) and solving it with respect to ws , we obtainws =(G(br ):
1) n(br )(10)

An equilibrium is summarized by a pair (bar ; wsa ) that satis…es (9) and (10). The superscripta represents the variables are related to the closed economy (autarky) case.
In the br ws plane, the zero pro…t condition (10) is increasing in br and goes to in…nity(zero) as br approaches one (zero). When the skilled labor supply is small, the economy hasless varieties, which yields higher revenue for each …rm. Free entry drives the pro…t of each…rm to zero, implying that the skilled wage rate is high. Hence, the zero-pro…t condition
is depicted as an upward-sloping curve. In the skill formation condition (9), when br
converges to zero, the arbitrage of workers requires that the skilled wage must goes up to
in…nity. When br converges to one, no variety is available and the price index increases toin…nity, which extinguishes the relative attractiveness of being skilled for a given skilled
wage rate. Thus, in order for the skill formation condition to be satis…ed, the skilled wage
must also rise to in…nity. In fact, because limbr !0 n(br ) > 0 and limbr !1 n(br ) = 0, we caneasily see that the skill formation condition diverges to in…nity as br goes to either zero orone.
Now de…ne as
RHS of (9)RHS of (5)=(1)n(br ) + cn(br )(br G(br )

6

2)=(

1)

:

Therefore, if

> 2,
lim

br !1

= 0 < 1;

which implies that RHS of (5) is larger than RHS of (9) in the neighborhood of br = 1.
From the above arguments, we know that (9) and (5) have at least one intersection in the
br ws plane when > 2 (see Figure 1 for the illustration).
[Please insert Figure 1 around here]
Summarizing the above arguments, we obtain the following proposition:7
Proposition 1 The model has an interior equilibrium when

> 2.

Hereafter, we assume this inequality holds, which is consistent with the markup rateestimated by Hall [17].8 As becomes smaller, the monopoly power of each …rm getsstronger and the price p goes up (see (3)). This induces more and more workers to become
skilled, and all workers become skilled when comes very close to one. In order for themodel to have an interior solution, the …rm’s monopoly power must not be such strong.
Before moving the analysis of trade, it is worth examining the welfare properties of theskill formation in this model. In this paper, we adopt the Benthamite welfare function asa welfare criterion:
Z 1
bws
1
W =
c g(b)db + G(br )
(11)
P
P
br
G(br )=c [1 G(br )] ;(1)P
where we used (10). Note here that the skilled worker fraction increases as br decreases.
Di¤erentiating (11) with respect to br and evaluating it at an equilibrium (substituting(6) and (10) into it), we havedW=
dbr equilibriumcg(br )
< 0:(
1)

Proposition 2 The equilibrium level of skilled worker fraction is ine¢ ciently low.
Although skill formation by one worker enables other people to consume another varietyof goods, this e¤ect is not recognized by workers who decide whether or not to become
skilled, which implies that the skill formation has a positive externality. As indicated by
the conventional wisdom, this leads to the under-supply of skilled workers. This resultand (11) can be referred to when we consider the e¤ects of trade or FDI on the national
welfare.
7

The condition > 2 assures only that at least one interior equilibrium exisits and does not imply theuniqueness of it.
8
Hall [17] showed that many industries of the United States have the markup rate =(1) between
1.5 to 3 (see Table 5). Given his warning regarding overestimation (see p.939), this range of the markup
rate is consistent with our assumption.

7

3

Trade, skill formation and the (skilled) wage structure

Now assume that the economy is open and consider a world (or a trade bloc) that iscomposed of 1 + m countries whose economies are of the type that was described in theprevious section. We assume that the di¤erentiated goods are traded with the standard
iceberg trade cost. Hence, T > 1 units of a good must be shipped in order for one unit
to arrive at destination.9 This modi…cation dose not changes the number of varieties (7)produced in one country. Here, we consider a symmetric equilibrium in which all countries
have the same number of varieties, the same price index, and the same skilled worker share.
In this open economy, the price index (2) becomes
P = n(br )p1

1=(11 + mT 1

)

:

(12)

Using (7), (3) and (12), the skill formation condition (6) can be written as
ws =

1
br

1+

c
1

1=(1

n(br ) 1 + mT 1

)

:

(13)

The pro…t of a …rm now becomes
= (p

1)

(1 + mT 1
p P1

)AI

ws ;

(14)

leading to the fact that the pricing behavior of …rms and zero pro…t condition are unalteredand are given by (3) and (10), respectively. An equilibrium is summarized by a pairX(bXr ; ws ) that satisfy (10) and (13). The superscript X represents the case of trading
economy.
The closed economy equilibrium is described by (9) and (10) whereas the open economy
equilibrium is determined by (13) and (10). Since the zero pro…t condition is the same fortwo cases, the di¤erence in the result comes from the di¤erence in the locus of the skill
formation condition. Simple comparison between (9) and (13) shows that in the br ws
plane, trade opening shifts the skill formation condition downward as described in Figure
2.
[Please insert Figure 2 around here]
We can see from this …gure that the trade opening enhances the skill formation. Under
trade, people can consume wider varieties of di¤erentiated goods and enjoy lower priceindex than under autarky. This implies that people enjoy higher utilities from the same
income under trade than under autarky. Hence, trade increases the relative importance of
nominal income to training disutility, leading to the downward shift of the skill formation
condition as described in Figure 2. Because the incentive to be skilled and obtain higher
income gets stronger, more workers train themselves to become skilled. Thus, proliferationof trade (WTO [35]; World Bank [33]) and skill formation (Federal Reserve Bank of New
York [13]; Barro and Lee [7]) can proceed in the same direction.
This result has a signi…cant welfare implication. Because the price index declines, theutility of unskilled rises by trade opening. Among skilled workers, some become skilled
9

We can introduce the …xed costs of export as in Melitz [28] without changing any results. For the
expositional simplicity, we assume no …xed costs of export, which implies …rms always choose to export.

8

after trade opening whereas others are already skilled under autarky. Declines in the priceindex implies rises in the utility of already skilled workers. From (6), we can see that theutility of marginal worker (i.e., a worker with productivity br ), and hence, the utility of
new skilled workers also increases. Thus, trade opening pro…ts all people. Of course, thenational welfare also rises: because the zero-pro…t condition is unaltered by trade, (11) still
applies to the economy under trade. And larger utility of unskilled and marginal workers
under trade than under autarky readily veri…es that trade raises the national welfare. The
following proposition summarizes the above arguments.
Proposition 3 Trade opening enhances the skill formation (i.e., lowers br and raises the
skilled worker fraction 1 G(br )), and raises the utility of all workers.
Moreover, production structure also changes. Smaller br implies increases in the number of varieties produced in one country (see (7)). It also leads to decreases in the output
per …rm:
output per …rm =G(br );n(br )br g(br ) [n(br ) + G(br )]d(output per …rm)
=
> 0:
dbr
n(br )2

The numerator is the aggregate output in one country, and the denominator is the numberof …rms in one country.
Proposition 4 Trade opening increases the number of varieties produced in one country,
and lowers the output per …rm.
The cost of hiring an unskilled worker (i.e., nominal unskilled wage = 1) becomes highrelatively to the cost of hiring a skilled worker (ws ) , inducing more …rms to enter the
economy but to produce less, thus leading …rms to a more intensive "large-item, small-scale
production."
Although the utility, and hence the real wage of already and new skilled workers rises
with trade opening, the average real wage of skilled workers may or may not increase.
This is because the productivity of new skilled workers is lower than that of alreadyskilled workers. Hence, although trade raises the new skilled workers by inducing them tobecome skilled, it may change the wage structure in a way in which the average skilled real
wage may decline. Hereafter, we examine what changes in the wage structure accompanies
the trade opening.
The average productivity among skilled workers is
Z 1
g(b)
Bs =
b
db:
(15)
1
G(br )
brDi¤erentiating this with respect to br yields
dBs
=
dbr
>
= 0:

br g(br )g(br )+n(br )G(br ) [1 G(br )]2
Z 1
br g(br )g(br )+br g(b)db
1 G(br ) [1 G(br )]2 br
1

9

(16)

Hence, trade opening, via declines in br , reduces the average productivity among skilledworkers, and hence the average nominal wage of skilled workers Bs ws .10 New goods being
available, the price index P also declines (i.e., P X < P a ), which is con…rmed by thefollowing two facts: (i) the price index under trade P X is lower than the price index underautarky P a for a given br , (ii) P declines as br decreases.11 These declines in the priceindex may raise the average real wage Bs ws =P of skilled workers. Whether or not thisis true depends on the type of distribution G(br ) we consider. In the remaining of thissection, as a benchmark, we specify G(br ) as the uniform distribution and demonstratethat trade opening in fact raises the average real wage of skilled workers. Note here thatthe real wage 1=P of unskilled workers rises irrespective of type of G(br ).
Under the uniform distribution, the average real skilled wage can be rewritten as
Bs ws
1
=
P
2

1+

1
br

c+

1
P

;

which implies that12
BsX wsX
Bsa wsa> 0:
PX
Pa
Hence, trade opening raises the average real wage of skilled workers. This is not theend of the story. We can further examine whether or not the skilled-unskilled wage gap
W G = Bs ws =P 1=P enlarges. Simple calculations show that
W GX

W Ga =
>
=

1
2
1
2

1
bX
r
1
1+ a
br
1
1
PX
Pa
1+

1
1
1
1
1+ a
PX
PX
2
br
1
1
1
1
X
a
X
P
P
P
Pa
1
1
1+ a
1 > 0.
2
br
c+

c+

1
Pa

+

1
Pa

From this, we can readily see that whereas trade opening bene…ts unskilled workers, skilledworkers enjoy trade bene…ts more than do unskilled workers. These rises in wage gap giveless productive workers to become skilled, which reduces the average productivity.
Proposition 5 Trade opening raises the skilled-unskilled real wage gap.
The next question is how this a¤ects the inequality. In this paper, our focus is on
the skilled workers and we over-simpli…ed the features of unskilled workers, which makes
us to hesitate to refer to the overall income inequality. Hence, we examine only the
income inequality among skilled workers. Lemieux [23] showed the trends in the residual
inequality (i.e., wage inequality unexplained by observed characteristics, which measures
the inequality within groups) in the United States over the past three decades by examining
the variance of the residual computed from the estimated wage equation. His results
showed that the rises in residual inequality arose from rising wage dispersion for groups
with higher education and increasing in the share of groups with higher education (that had
10This is the consequence of the constant mark-up pricing shown in (3). If we use a model with the
pro-competitive e¤ect in which trade raises the good price, the average nominal wage of skilled workers
may increase. See Ottaviano et al [30] for an example of a monopolistic competition model with the
pro-competitive e¤ect.
11
See (8) and (12).
12aX
Notice that we already know that bX< P a.
r < br and P

10higher wage dispersion than does groups with lower education). For the sake of comparing
our results to the results of Lemieux [23], We employ the coe¢ cient of variation as anindex of skilled wage dispersion. The coe¢ cient of variation CVs is de…ned as the ratio of
the standard deviation Ss to the mean Bs ws =P :
CVs =

Ss
;
Bs ws =P

(bws

ws )2

where Ss is given as
1
Ss =
P

Z 1
br

1=2

g(b)
db
1 G(br ):After some (tedious) calculations, we have
CVs =

( R1

2
br b g(b)db
Bs2 [1 G(br )]

1

)1=2

:

#1=2

:

(17)

Under the Pareto distribution, (17) can be rewritten as"

4 1 + br + b2r
CVs =3(1 + br )2

1

Di¤erentiating this with respect to br , we …nd
dCVs
=
dbr

2(1 br )< 0:
3CVs (1 + br )3

As shown in (16), trade opening induces less productive workers to become skilled andhence, raises the skilled wage dispersion:
Proposition 6 Trade opening enlarges the wage dispersion among skilled workers.
This result is consistent with the empirical …ndings of Lemieux [23], indicating that trade
can play an important role in enhancing skill formation and in raising the residual inequality.
A few comments are in order. First, inequalities between skilled and unskilled oramong skilled workers may themselves be seen as a social problem. We don’t aim to argue
the pros and cons of this view. However, it would be worth mentioning that behind thetrends of rising inequality, people may become better o¤ via trade.
Second, here, we consider only the inequality between skilled and unskilled and thatamong skilled workers, and not the total income inequality. Here, the e¤ect on the total
income inequality is determined by the above mentioned e¤ect regarding two inequalities
and the e¤ect on skill composition of workers. The former ampli…es the total inequality.
However, since more workers get skilled, the latter reduces the total inequality because it
increases the ratio of people with higher income. Since the overall e¤ect on total inequality
heavily depends on the speci…cation and parameters of the model including the distributionfunction G(b), we just uncovered the possible channels through which trade may havee¤ects on inequality and don’t conclude about the overall e¤ect on the total inequality.
Once the economy is open, the trade environment a¤ects the skill formation. An
increase in the number m of trading countries and a decline in the trade cost T both shift
11the skill formation condition downward, leading to decreases in bX
r and increases in theskilled worker fraction. It also lowers the price index, and hence, raises the real wage
disparity and makes all people better o¤. Moreover, smaller bX
r deepens the large-item,
small-scale production.
Proposition 7 An increase in the number m of trading countries or a decline in the trade
cost T enhances skill formation and has similar e¤ ects on the market structure to trade
opening.

4

Trade versus FDI

Zeile [37] showed that in 1994, 42.7 percent of the total trade volume of U.S. goods imports
took place within the boundaries of multinational …rms, with the share being 36.3 percent
for U.S. exports of goods. Also, from 1986 to1999, international trade has grown fasterthan GDP, and the growth of foreign direct investment (FDI) has been higher than international trade (Markusen [26]). In 2003, total inward and outward of FDI for the OECD
countries amounted to 384.4 billion and 576.3 billion U.S. dollars, respectively (OECD[29]). These evidences con…rm us that the importance of multinational …rms has increased
recently and they are now the key players in the world economy. Moreover, Markusen [26]pointed out that skilled labor endowments are strongly and positively related to FDI.
Therefore, it is worth …guring out how FDI could interact with skill formation. Thissection do this by comparing the case of export to the case of FDI.
Assume that …rms can supply goods to foreign countries via FDI as well. In that case,they face no trade cost (T = 1) but have to bear …xed investment (fI ). This alters theprice index (2) as
1=(1 )
P = np1 (1 + m):
(18)
The number of varieties in each country n is given byn = n(br )=(1 + mfI ):From this and (12), the worker’s arbitrage condition (6) becomes:
(
1=(1
1
c
1+m
ws =
1+
n(br )br1
1 + mfI

)

)

(19)

The pro…t of a …rm under FDI is given as
= (p

1)

(1 + m)AI
p P1(1 + mfI )ws :(20)

Taking the di¤erence in the price index (di¤erence between (8) and (12)) into consideration, we can investigate under which condition …rms prefer FDI to export by comparing(14) with (20). Simple comparison give
under FDI >under export, fI <

T1

1
1 + mT 1(21):

Since (20) again leads to the zero pro…t condition (10), the di¤erence between the locusof (13) and that of (19) generates the di¤erence between skill formation under export and12that under FDI. Comparing these two equations, we can see that (13) locates above (19) i¤(21) holds. Hence, when the …xed skilled labor requirement for FDI is small, FDI enhanceskill formation. In addition, the term 1 T 1= 1 + mT 1
is a decreasing functionof the number of trade partner, m, and transportation cost, T . Hence, when the numberof trade partner countries is small, or transportation costs are high, FDI enhance skill
formation.
Proposition 8 Firms prefer FDI to export i¤ fI < 1 T 1
case, compared to export, FDI enhances the skill formation.

= 1 + mT 1

. In thisThe condition described in Proposition 8 requires that the …xed costs of FDI is small,or transport cost of goods is small, or the number of trading countries small. Amongthese three requirements, the …rst two obviously enable …rms to earn under FDI thanunder export. Regarding the third, if the number of trading countries is large, …rms
must establish plants in many countries, which increases the burden of high …xed costs
under FDI. Hence, the condition described in Proposition 8 is equivalent to require that
it is more pro…table for …rms to achieve FDI than to export goods. Furthermore, higher
pro…ts implies a stronger incentive for …rms to enter the economy, making wider varieties
available for consumers and lowering the price index. As shown in Section 3, a lower priceindex bene…ts skilled workers more than unskilled workers and enhances skill formation.

5

Concluding remarks

In this paper, we uncovered the possible impacts of international trade on the workers’
skill formation and the wage structure. We showed that trade enhances the skill formation,and can raise the inequality between skilled and unskilled workers and that among skilledworkers. The e¤ects of changes in trade environments and of FDI are also examined. Our
study showed that the skill formation can play an important role when we consider the
relationship between trade and labor markets. An interesting implication of our framework
is to shed light on the fact that globalization can bene…t all people via skill formation but
it may worsen inequality.
It is worth mentioning some possible extensions. First, we considered only symmetriccountries. However, trade between countries of di¤erent size should also be investigated,of which importance is suggested by the fact that we often observe RTAs between large
and small countries (such as RTA between the United States and Morocco or that between
Japan and Singapore). Because of the possibility of the home market e¤ect, international
trade may work in favor of skill formation in the large country whereas it may harm skill
formation in the small country. However, there is still some scope that the small country
becomes better o¤ due to the availability of wider range of varieties. Second, multinational…rms should be considered more in detail. We adopted a highly (and perhaps over-)simpli…ed way in the sense all countries and …rms are symmetric, implying that all …rms
choose FDI or any …rms do not choose it. However, in the real world, it may be easier for…rms to establish their plants in some countries than in other countries, or …rms would
combine trade with FDI. In order to obtain full implication related to FDI, we shouldincorporating these more realistic features. Third, incorporating the framework developedin this paper into a model with heterogeneous …rms a la Melitz [28] may give us implications
that can be compared with empirical results regarding trade e¤ects on heterogeneous …rms.
Especially, it would be interesting to explore how the interaction between trade and skill
formation a¤ects the allocations of heterogeneous workers to heterogeneous …rms.
13

.

Acknowledgements
We are grateful to Fukunari Kimura, Kazuo Mino, Kenzo Abe, Kristian Behrens, Koichi
Futagami, Masahisa Fujita, Masahiro Endo, Ryoji Ohdoi, Se-il Mun, Tomoya Mori, Toru
Kikuchi, Toru Naito, Toshiaki Tachibanaki and Yuzo Honda for their helpful comments
and suggestions. Of course, we are responsible for any remaining errors.

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16

ws

Zero profit
condition
Skill formation
condition

wsa

bra

0

unskilled workers

Figure1. Equilibrium

1
skilled workers

brws
Zero profit
condition

wsa
Skill formation
condition

wsX
0

brX

bra

1

Figure 2. Impact of trade on skill formationbr