Effects of Globalization on Educational Choice andUnemployment under Search Friction
Chihiro INABA
Noritsugu NAKANISHI
February 2022
Discussion Paper No. 2205

GRADUATE SCHOOL OF ECONOMICS
KOBE UNIVERSITYROKKO, KOBE, JAPAN

Eﬀects of Globalization on Educational Choice
and Unemployment under Search Friction
Chihiro INABA∗

Noritsugu NAKANISHI†

February, 2022

Abstract
Trade liberalization increases the import of foreign goods fosters thepenetration of foreign firms into the local markets and makes local markets more competitive. To survive the severer competition, local firms must
improve the qualities of production factor,goods and employ more highly
skilled workers more. An increase in the demand for skilled workers encourages workers to pursue higher education. Despite that the world economy has witnessed the trend of freer international transactions in decades,
However, the recent trend of the employment of highly educated workers isseems stagnant in many countries, in particular, in developed countries globally. Although trade liberalization enhances the demand for skilled workers,
it may does not necessarily contribute to increasing an improvement of theiremployment.
I analyze how trade liberalization aﬀects the local employment of bothskilled workers, and unskilled workers, occupational choices by workers,
and the wage inequality between skilled and unskilled workers. If Whenfirms a firm start to production enters the market, they it must has to employ
one unit of skilled worker labor to develop its own variety of the diﬀerentiated good in advance of actual production and some unskilled workers.
The abilities of Each skilled workers has are heterogeneous ability, so thatthe ex post productivities of firms are become diﬀerent heterogeneous ex
post. The unskilled workers, whose abilities are homogeneous, are used forthe production of the good. However, due to search friction, matches between firms and to unskilled and skilled workers (either skilled or unskilled)∗

Corresponding author. Kansaigaidai University. Email: chihiro.inaba01@gmail.com
Graduate School of Economics, Kobe University. Nakanishi acknowledges the financial support from the Japan Society for the Promotion of Science: Grant-in-Aid for Scientific Research(A), No.16H02016.
†1

are not always successful. With this knowledge, knowing all this, workers
choose make their educational choices: and either to remain to be unskilledworkers or to get educated to be skilled workers learn skills. Trade liberalization changes aﬀects the wage rates of unskilled and skilled workers andthe successful probability of successful matching, which may encourage unskilled workers to learn skill but increase the number of the skilled workers
after trade liberalization. Therefore, the unemployment rate of the skilledworkers may increase after globalization.

1

Introduction

The volume of world trade increased after World War II, and globalization increased rapidly through various free trade agreements. Simultaneously, the levelof education also increased in many developed countries. In Japan, for example,
the university enrollment rate was approximately 15 % in the 1950s, increased to
51% in 2013. The main reason for the increase in the university enrollment rateis the improvement of household incomes. Recently, the trend of globalization
promotes firms to demand well-educated workers to survive severe competition
by foreign firms. Some firms requires people with the communication skills tonegotiate with the foreign companies. Others require those with a high education
to advance ahead of the market competition. Many countries introduce foreign
language course work in compulsory education and invite foreign engineers andbusinessmen to attend to these courses. Consequently, trade liberalization accelerates the popularization of higher education.
How do the trend of globalization and the popularization of higher educationaﬀect the domestic labor market? The results of basic survey of Japanese schools
show that the university advancement rate has increased in Japan, but the employment rate is flattening out. Furthermore, the employment rate of those who
graduated from higher education professional schools is also not increasing. Not
only Japan, but other OECD countries face the similar situation. In Korea, only
about 60 % of young people who graduated from university can get a job.1 The

1Han, H. (2016) Envious of Japanese young people whose employment markets have been
opened widely = South Korea, Korean Joongang Daily translated by Japanese, Retrieved from
November 22, 2016 from http://japanese.joins.com/article/593/213593.html.

2

university enrollment rate is 70% in Korea, which is higher than Japan in 20102 .
Moreover, jobless rate for young people is 12.5% in 2016. In the United States,
Associated Press (AP) reported that 1 in 2 (53%) new graduates are jobless orunderemployed or underemployed in 20123 . Although the university enrollment
rate is 74%, many young people faces the problem of unemployment.
Consequently, the recent trend of globalization and popularization of higher
education does not always get good eﬀects on the local labor market. This article
considers the relationship between popularization of higher education and the employment rate from the aspect of international trade. In particular, we investigates
how globalization aﬀects various types of jobs and the unemployment rate (andthe employment rate). There are two symmetric countries that produce diﬀerentiated goods with labor. We consider two types of labor: skilled and unskilledworkers. Unskilled workers are used for the production of the diﬀerentiated good.
Skilled workers have heterogeneous abilities, and a firm must employ one skilledworker to start a business. The ability of the hired skilled labor also determines
the firm’s productivity. Therefore, the firm that succeeds in hiring a skilled worker
with a higher ability realizes a higher productivity. As we assumed the abilities ofthe skilled workers are distributed over a certain range, firm’s productivity varies
according to the distribution of the abilities of the hired skilled workers. In otherwords, the firms in the market become heterogeneous ex post, which is similar to
Melitz’s (2003) model.
We introduce information asymmetry between firms and workers in the bothskilled and unskilled labor market. To find a skilled worker and some unskilledworkers, the firm has to pay a search cost and it can randomly meet the workers. After matching, the firm and the skilled worker negotiate the skilled wage. If
the negotiation between a firm and a skilled worker succeeds, the firm can start
producing the diﬀerentiated goods, and workers earn the higher negotiated wage
income. On the other hand, we assume that the unskilled labor wage is competitively determined, where the unskilled labor demand of the firms equals to the2OECD (2012) Education at a Glance 2012.
Yen, H. (2012, April 24) 1 in 2 new graduates are jobless or underemployed AssociatedPress Retrieved November 22th, 2016 from https://www.yahoo.com/news/1-2-graduates-joblessunderemployed-140300522.html.
33

unskilled labor supply. Workers can choose whether to take an education at the
beginning of the period. Unskilled workers enter the labor force without education, while the income of the unskilled workers is independent of their ability.
When unskilled workers pursue an education with education cost, they can realize
their ability and become skilled workers. If the skilled workers are successfully
employed, they earn a more proportionately higher income. Comparing with theunskilled and skilled income, which depend on workers own ability, workers decide whether to be unskilled and skilled.
Our model have two ability cutoﬀs: educational cutoﬀ and production cutoﬀ. Educational cutoﬀ is a ability boundary between skilled worker and unskilledworker. A person with ability above educational cutoﬀ becomes a skilled labor,
and otherwise the person works as an unskilled labor. Educational cutoﬀ is determined by educational choice, where a worker with educational cutoﬀ is indifferent between being skilled and unskilled. On the other hand, production cutoﬀ
is determined by firm’s free entry, which is familiar with Melitz (2003)’s cutoﬀ
productivity. If a firm matches with a skilled worker who has a ability above production cutoﬀ, the firm can continue operation with a positive profit. However,firms which employ a skilled worker below production cutoﬀ ability face the negative profit and exit the market. Therefore, the skilled workers have two reasonsof unemployment: search friction and ability below production cutoﬀ. First, since
the matching with skilled worker and firm is stochastic, some skilled workers fails
to meet a firm. This type of unemployment is common to search and matchingmodel of Pissarides (2000). Secondly, due to free entry, skilled workers withlower ability than productivity cutoﬀ must be unemployed even if they are able tomeet firm. Since the skilled workers’ ability is distributed over education cutoﬀ,
the skilled workers between education cutoﬀ and productivity cutoﬀ are certainly
unemployed.
We consider international trade between two symmetric countries; additionally, there are ice-berg costs for exporting the diﬀerentiated goods to the foreigncountry. Trade liberalization raises demand of the diﬀerentiated goods, and the
profit of the goods increases. Since the profit is distributed to a firm and skilledworkers through negotiation, the increase in profit leads to an increase in the bargaining wage rate. The increase in the profit of the firms attracts the potential
4

firm to enter the search for the skilled workers. Therefore, the demand of theskilled worker increases. The increase of the bargaining wage rate and the demand for skilled workers increases the incentive to become the skilled worker.
However, these changes raise the total income of a country, and the value of unskilled workers also increases. The eﬀect of globalization is ambiguous on educational choices. However, we find it possible that globalization may increaseskilled unemployment.
Our study relates to the literature of international trade with the labor-searchmodel. Davis (1998) and Davidson and Matusz (2004) introduced incompletenessof labor market into neoclassical trade model and investigated the eﬀect of tradepattern and unemployment. Recently, researches introducing incompleteness oflabor market into monopolistic competition model has increased. For example,
Helpman and Itskhoki (2009), Helpman et al. (2010a,b), Egger and Kreickemeier(2009, 2012), and Ferlbermayr et al. (2010) investigated the eﬀects of globalization on local unemployment. They showed that there are two contradictory eﬀects
international trade on the labor market. First, globalization increases the average productivity of the industry through the selection of low-productivity firms,
which increases employment. Secondly, since an increase in the average productivity means an increase in the eﬀective firms, the rise in employment is not muchgreater than the increase in production. Consequently, the employment contracts.
However, their model does not determine the firm’s productivity in the labor market. In their model, the lottery determines the productivity of a firm. A firm withrelatively high productivity negotiates with skilled workers, whereas another firmwith relatively low productivity exits from the market. Although the entry andexit of a firm depend on the productivity lottery and labor matching, productivity
and the industry structure are not aﬀected as much by labor matching.
This article also relates to the choice between skilled and unskilled workers.
Furusawa et al. (2021), Falvey et al. (2010), and Danziger (2017) introduce theendogenous decision of skilled and unskilled workers. Furusawa et al. (2021)
assumes that the firm’s productivity is depends on the ability of the skilled workers. Trade liberalization raises the profit of the firm with well-skilled workers andexpands the income inequality between unskilled and skilled labor. Falvey et al.
(2010) and Danziger (2017) assume that workers have heterogeneous ability but
5they do not realize their ability unless education. They have concluded that trade
increases the demand for educated workers and induces workers more schoolingdecisions. However, Furusawa et al. (2021), Falvey et al. (2010), and Daniziger(2017) assume full employment, so that they do not consider eﬀect of trade liberalization on unemployment problem.
Zenou (2008) introduced the labor search model into the skilled labor market
and investigated the worker’s job choices between skilled and unskilled workers.
Some may argue that the unemployment problem with the unskilled workers ismore important than that of skilled workers . However, Zenou noted that the lawsof regarding skilled workers are stricter and that their position is more aﬀected bypolicy change than that of unskilled workers. Because we focus on the relationship between the popularization of higher education and the low employment rateof highly skilled workers, it is reasonable to consider the unemployment problemof skilled workers. Zenou addresses this problem only with a partial equilibrium
and in an autarky economy and considers only the unemployment of the skilledworker. It is important to consider not only the unemployment problem of theskilled labor but the unemployment of the unskilled labor. Therefore, we introduce the unemployment the unskilled labor and consider the eﬀect of globalization.
The remainder of the paper is organized as follows. Section 2 explains thebase of the model and the equilibrium under autarky. Section 3 analyzes the eﬀectof globalization. Section 4 concludes with a summary and a discussion of future
research.

2

The Model

2.1

Preference

The diﬀerentiated good consists of a continuum of varieties; the set of diﬀerentiated varieties is denoted by Ω. We assume a CES utility function:
[∫
u=

x(ω)
ω∈Ω

6

σ−1
σ

σ
] σ−1
,
dω

(1)

where x(ω) denotes the consumption level of variety ω ∈ Ω and σ > 1 denotes
the elasticity of substitution. Normalizing the total nominal expenditure on thediﬀerentiated good equal to unity, we obtain the following demand function foreach diﬀerentiated variety: for ω ∈ Ω,x(ω) =

p(ω)−σ,P1−σ(2)

where p(ω) denotes the price of variety ω ∈ Ω and P is the price index of thediﬀerentiated good defined as follows:
[∫
P≡

2.2

1−σ

p(ω)
ω∈Ω

1
] 1−σ
dω
.

(3)

Distributions of Potential and Realized Abilities

There is a continuum of potential workers; the measure of them is denoted by
N. Every potential worker shares an equal basic ability to serve as an unskilledworker. At the same time, each worker has its own “potential educated ability”
that makes it possible for the worker to serve as a skilled worker. The potential
educated ability of a worker, however, is realized only after the worker gets educated by incurring the cost of education. Potential workers can always enter theunskilled labor market without any additional cost of education. In contrast, if potential workers want to enter the skilled labor market (seeking for higher skilled
wage rates), they have to pay the costs of education to realize their educated abilities.
The potential educated abilities are distributed over the range of nonnegative
reals: R+ . The cumulative distribution function of the potential educated ability
is denoted by G : R+ → [0, 1]. The corresponding density function is denoted by
g : R+ → R+ . Not all potential workers want to get educated. In other words, thedistribution G (or g) is not necessarily realized on the whole domain.
Suppose, for the moment, that there is a lower boundary α > 0 of the potential
educated ability such that every worker with the potential educated ability α lower
than α chooses not to be educated, while every worker with the potential educatedability α no less than α chooses to get educated. Then, given the educational7

choices by the potential workers, we obtain the distribution of the realized educated abilities. The distribution function of the realized educated abilities, denoted
by F : R+ → [0, 1], becomes as follows:G(α) − G( α )





1 − G( α )F(α) ≡ 0if α ≥ α,(4)if α < α.

The corresponding density function, denoted by f : R+ → R+ , is


g(α)



 1 − G( α ) if α ≥ α,f (α) ≡ 0if α < α.

(5)It should be noted that both the distribution function F and the density function
f depend upon the lower boundary α, which, in turn, depends upon the workers’
educational choices. In a later section, we will show that there exists such a lower
boundary of the potential educated ability as described above.

2.3

Matching Technology

Suppose, for the moment, there are H skilled workers and L unskilled workers inthis economy. We denote the measure of unemployed skilled workers by uH andthat of unemployed unskilled workers by uL . In turn, firms want to hire certain
amounts of skilled workers and unskilled workers and, therefore, post their vacancies to each of the labor markets. The total vacancy posted by the firms for theskilled labor is denoted by vH and that for the unskilled labor by vL .
Both the skilled and unskilled labor markets are not perfect. We adopt theframework of the search-matching labor market friction model developed by Pissarides (2000). The labor market frictions are represented by the following matching functions, through which firms and workers are matched randomly: for i =H, L,
Mi (ui , vi ).
The matching function represents the flow rate of realized matches between firms
and workers. We assume that the matching technology is increasing and exhibits8

constant-returns-to-scale (CRS). In each of the markets, when the number of unemployed workers increases, it becomes easier for the firms to be matched withworkers. Similarly, an increase in the vacancies makes it easier for workers to findtheir jobs. If both the number of unemployed workers and the number of vacancies increase proportionally, the number of the matched pairs also increases at thesame proportion.
For i = H, L, let θi ≡ vi /ui be the ratio of the numbers of the unmatched firms
and the unemployed workers, which is called the labor market tightness. Consider
the unskilled labor market. The probability of successful matching for a firm canbe written as a function m of the labor market tightness θL :m(θL ) ≡ML (vL , uL )= ML (vL /vL , uL /vL ) = ML (1, 1/θL ).
vL(6)

The second equality follows from the CRS matching technology. Since ML isincreasing in its arguments, m is decreasing in θL . Similarly, the probability ofsuccessful matching for a worker can be written as a function of θH as follows:θL m(θL ) ≡ML (vL , uL ) ML (vL , uL )/vL ML (1, 1/θL )==.
uL
uL /vL
1/θL(7)

It is easy to verify that θL m(θL ) is increasing in θL . From a single firm’s point ofview, an increase in the labor market tightness means an increase in the numberof competitors in search of workers and, therefore, induces a lower probability ofsuccessful matching. In contrast, from a single worker’s point of view, an increasein the labor market tightness means an increase in the number of job oﬀers andinduces a higher probability of successful matching.
Similar to the unskilled labor market, the probabilities of successful matchingin the skilled labor market for a single firm and that for a single worker can be
written as functions of the labor market tightness θH :MH (vH , uH )= MH (1, 1/θH ),vH
MH (vH , uH ) MH (1, 1/θH )θH n(θH ) ≡
=
.
uH
1/θH
n(θH ) ≡[for a firm](8)[for a worker](9)

We can show that n(θH ) is decreasing in θH and θH n(θH ) is increasing in θH .4
Sometimes, the Inada-like conditions are required: limθ→+∞ m(θ) = limθ→+∞ n(θ) = 0 andlimθ→+0 m(θ) = limθ→+0 nθ) = +∞
4

9

2.4

Behavior of a Firm

There is a huge pool of potential firms, which are homogeneous ex ante. Eachpotential firm is contemplating entering the market of the diﬀerentiated good. To
enter the market, each firm has to pay a fixed entry cost once and for all.5 In
addition, when a firm enters the market, it has to hire one unit of skilled labor inorder to develop its own diﬀerentiated variety. The ability of the skilled labor hiredby a firm also determines the firm’s productivity. Therefore, the firm that succeeds
in hiring a skilled worker with a higher ability can realize a higher productivity.
As we assumed the abilities of the skilled workers are distributed over a certain
range, the productivity of firms varies according to the distribution of the abilitiesof the hired skilled workers. In other words, the firms in the market become
heterogeneous ex post.
Suppose that a firm has succeeded both in the entry and in the employmentof a skilled worker with the educated ability α. To produce the diﬀerentiatedvariety developed by the skilled worker, the firm has to employ a certain numberof unskilled workers. We assume that the input-coeﬃcient of unskilled labor of a
firm is equal to the inverse of the skilled worker’s ability employed by the firm,that is, 1/α. Accordingly, to produce x(ω) units of the diﬀerentiated variety ω,
the firm needs to employ ℓ = x(ω)/α units of unskilled workers; equivalently, if
the firm employs ℓ units of unskilled workers, it can produce x(ω) = ℓα units ofvariety ω. Given the demand function for a certain variety ω (i.e., Eq. (2)), thetotal revenue accruing to the firm when it employs ℓ units of unskilled workers
becomes a function R of ℓ and α as follows:
σ−1

R(ℓ, α) ≡ [ℓαP] σ .

(10)Strictly speaking, R depends upon the price index P, but we omit P from theexpression of R for simplicity.
Consider an operating firm matched with ℓ units of unskilled workers6 and acertain skilled worker whose educated ability being α. In each period, the firm
and the employed workers are hit by two independent idiosyncratic shocks: (i)56

We will discuss the nature of the fixed entry cost more in detail later.
We identify ℓ with the number of jobs conducted by the unskilled workers in this firm10

with probability sH , the matched pair of the firm and the skilled worker breaks up
and, then, the firm leaves the market immediately and the skilled worker becomes
unemployed; (ii) with probability χ, each job is destroyed because of some matchspecific shocks, in other words, χ portion of ℓ unskilled workers (i.e., χℓ workers)
are fired due to these shocks. For each of the employed unskilled workers, theprobability of losing his/her job is sL ≡ 1 − (1 − sH )(1 − χ) = sH + χ − sH χ, which
we call the rate of job separation.
Optimal vacancy postingIn each period, taking the unskilled wage rate wL

as given, each firm decides the optimal number of vacancy posting. Let J(ℓ, α)
be the optimal value function of a firm with productivity α who employs ℓ units
of unskilled workers (at the beginning of a period). The dynamic programming
problem of the firm is formulated as follows:1[R(ℓt , α) − wL ℓt − cL kt − wH + (1 − sH )J(ℓt+1 , α)]1+rs.t. ℓt+1 = (1 − χ)ℓt + m(θL )kt .

J(ℓt , α) = max
kt

(11)
(12)

The FOC for the maximization of the RHS of Eq. (11) iscL∂J(ℓt+1 , α)
= (1 − sH ).
m(θL )∂ℓ
Applying the Envelope Theorem to Eqs. (11) and (12), we obtain[]∂J(ℓt , α)1 ∂R(ℓt , α)∂J(ℓt+1 , α)=
− wL + (1 − χ)(1 − sH )
.
∂ℓ
1+r
∂ℓ
∂ℓ

(13)

(14)

In the steady state where ℓt = ℓt+1 = ℓ for all t, we have ∂J(ℓt , α)/∂ℓ =∂J(ℓt+1 , α)/∂ℓ = ∂J(ℓ, α)/∂ℓ. Therefore, by substituting Eq. (13) into Eq. (14),
we obtain(r + sL )cL∂R(ℓ, α)= wL +.
(15)∂ℓ(1 − sH )m(θL )Taking account of the definition of R(ℓ, α), we can solve the above equation for ℓ,which can be regarded as a function of α:
(
)σ [
]−σ
σ−1
(r + sL )cLℓ(α) =wL +Pσ−1 ασ−1
σ(1 − sH )m(θL )
(
)σ
σ−1
=
A−σ Pσ−1 ασ−1 ,
σ
11

(16)

where(r + sL )cL.
(17)(1 − sH )m(θL )Because the RHS depends negatively upon the unskilled wage rate wL , then ℓ(α)
A ≡ wL +can be regarded as the firm’s demand function for unskilled workers.7 The equation of motion, Eq. (12), in the steady state implies k = χℓ/m(θL ). Then, the optimal vacancy posting of the firm with productivity α, denoted by k(α), becomes
proportional to ℓ(α):k(α) =
Value of a firmχℓ(α).
m(θL )(18)

Substituting Eq. (16) and Eq. (18) into Eq. (11), we can solve it

for J(ℓ(α), α), which is the “value” of a firm. As can be easily seen from Eq. (11),the value of a firm depends not only on the firm’s productivity α but also on theskilled wage rate wH . For the ease of subsequent analysis, we shall write the valueof a firm as a function Jˆ of the firm’s productivity α and the skilled wage rate wH :1
[R(ℓ(α), α) − wL ℓ(α) − cL k(α) − wH ]r + sH
[
{
}
]
1
cL χ
=
R(ℓ(α), α) − wL +ℓ(α) − wH
r + sHm(θL )

ˆ wH ) =
J(α,

(19)

Note that Eq. (19) only considers the value of operating firms. The firms pay
vacancy costs for simultaneously searching ℓ’s unskilled workers and have wait
one period to recruit their workers. In this period, they can be hit by a destruction shock, with probability sH till starting production, so that they never start
producing. Using Eq. (19), we define the value of the entering firm, Π(α, wH ) as
ˆ wH ) − cL ℓ(α)
Π(α, wH ) ≡ (1 − sH ) J(α,m(θL )[](r + sL )cL
1 − sHR(ℓ(α), α) − wL ℓ(α) −ℓ(α) − wH=
r + sH(1 − sH )m(θ)(20)

Obviously, Π is increasing in α, but decreasing in wH . For the convenience of thesubsequent analysis, let us define{}σ−11 (σ − 1)Pπ(α) ≡ασ−1σσA7

We omit the explicit indication of the dependence of ℓ(α) on wL .

12

Then, Eq. (20) can be simplified toΠ(α, wH ) =2.5

1 − sH[π(α) − wH ] .
r + sH(21)

Unskilled Labor Market Equilibrium

Let Z be the measure of firms operating in the market. Then, the number of unskilled workers employed at the beginning of each period, denoted by Le , becomes
(
)σ
∫ +∞
σ−1
Le = Zf (α)ℓ(α)dα = Z
A−σ Pσ−1 α̃σ−1 ,σ0where α̃ denotes the average productivity of the operating firms:
1
1
[
[∫ +∞
] σ−1
] σ−1
∫ +∞
1
σ−1
σ−1
≡
.
α̃ ≡
f (α)α dαg(α)α dα1 − G( α ) α0(22)

It should be noted that α̃ depends upon the lower boundary α of the realized educated abilities, which plays important roles in our analysis later.
Let L be the measure of unskilled workers. By the definition of the matching technology, the number of successful (i.e., matched) unskilled workers isθL m(θL )L. Therefore, in equilibrium, we must have
Le = θL m(θL )L,which can be solved for the unskilled wage rate:8
(
)[
] σ1
σ−1
Z
(r + sL )cL
σ−1
σ−1
wL =
P σ α̃ σ −.
σ
θL m(θL )L(1 − sH )m(θL )(23)

Using Eq. (23) and (16), we can rewrite π(α) as{}
1 θL m(θL )LP σ−1.
π(α) =ασZ α̃
The total vacancy for unskilled workers, vL , is the sum of the vacancies offirms:

8

∫ +∞

∫ +∞
χ
vL = Zf (α)k(α)dα =·Zf (α)ℓ(α)dαm(θL )00χχ· Le =· θL m(θL )L = χθL L=
m(θL )m(θL )The derivation of Eq. (23) is relegated to an appendix.

13

The measure of unemployed unskilled workers is uL and that of employed unskilled workers is L − uL . In each period, θL m(θL )uL units of unemployed unskilled workers get their jobs through the matching technology and, at the sametime, sL (L − uL ) units of employed unskilled workers lose their jobs due to theidiosyncratic shocks. In the steady state, we must have θL m(θL )uL = sL (L − uL ),implyingsL L.
θL m(θL ) + sL
The tightness of the unskilled labor market, θL , is defined as the ratio of vL and uL .
uL =Therefore, we have
θL ≡

vL
=(
uL

χθL L
)
sL L
θL m(θL ) + sL⇔

θL m(θL ) =

1−χ
· sL
χ

(24)

In equilibrium, the probability that an unemployed unskilled worker is matchedwith a firm and gets his/her job is solely determined by the exogenous probabilitiesof the idiosyncratic shocks.

2.6

Skilled Labor Market

Before entering the diﬀerentiated good market, each potential firm has to hire askilled worker to develop its own diﬀerentiated variety. The potential firm has
to pay a search cost to post a vacancy for a skilled worker. Once a firm and askilled worker have been matched through the matching mechanizm at the skilledlabor market, they negotiate on the wage rate for the skilled worker. We adopt theframework of a generalized Nash bargaining to examine the negotiation between
the matched pair of a firm and a skilled worker.
2.6.1

Skilled Wage Negotiation

Suppose that a firm is matched with a skilled worker of ability α. First, consider
the firm’s payoﬀ from the negotiation. If the pair reaches an agreement on theskilled wage rate wH , the firm obtain the value Π(α, wH ) as defined in Eq. (20).
If, on the other hand, the negotiation fails, the firm has to leave the market andreceive nothing; the firm’s reservation payoﬀ is zero. Therefore, the firm’s net
gain from the negotiation is Π(α, wH ) − 0.
14

Next, consider the skilled worker’s payoﬀ. Let WH be the skilled worker’s
benefit from being employed by the firm (i.e., the value of employment) and let U H
be the value of remaining to be unemployed (i.e., the value of unemployment). If
the negotiation ends up with the skilled wage rate wH , the skilled worker receives
wH in each period. At the same time, the skilled worker knows that he or she faces
the possibility of being fired due to the idiosyncratic shocks with the probabilityof sH in each period. In other words, the state of the skilled worker changes fromthe employed to the unemployed with the probability of sH ; the “capital loss” dueto the idiosyncratic shocks is sH (U H − WH ). Therefore, in the steady state, WH canbe defined as the discounted sum of wH + sH [U H − WH ] over time:
WH ≡

+∞
∑
wH + sH [U H − WH ](1 + r)tt=1=

wH − sH [WH − U H ].
r

By solving the above equation for WH , we obtainWH =1[wH + sH U H ] .
r + sH(25)

At this stage of the negotiation, the skilled worker regards the value of unemployment, U H , as being independent of the skilled wage rate under consideration.
That is, if the skilled worker succeeds in raising the wage rate by one unit in thenegotiation, then he or she thinks that the value of employment, WH , increases by
the amount of 1/(r + sH ). The skilled worker’s net gain from the negotiation is
WH − U H .
The Nash bargaining over the skilled wage rate is described by the following
maximization problem of the generalized Nash product:max [WH − U H ]β [Π(α, wH )]1−β ,
wH

(26)

where β (0 < β < 1) represents the relative bargaining power of the skilled worker.
Taking account of Eq. (21) and Eq. (25), the FOC for the above maximization withrespect to wH isβΠ(α, wH ) = (1 − sH )(1 − β)[WH − U H ],(27)

which is equivalent toβ[π(α) − wH ] = (1 − β)[wH − rU H ].
15

(28)

Solving it for wH yields
wH = βπ(α) + (1 − β)rU H= β [π(α) − rU H ] + rU H .

(29)Here, rU H is the amortized value of unemployment and, hence, it can be seen as
the reservation wage rate for the skilled worker. If the skilled worker accepts thejob with the negotiated wage rate wH , the pair of the firm and the skilled worker
will be able to create the total surplus of π(α) in each period. Then, the diﬀerence between π(α) and rU H represents the net surplus for the pair. Accordingly,
Eq. (29) means that the skilled worker receives the β-fraction of the net surplus in
addition to the reservation wage rate. One important thing to be noted is that thenegotiated skilled wage rate wH depends on both the ability of the skilled worker(i.e, α) and the reservation wage rate (i.e, rU H ); with a slight abuse of notation,
we write this relation as wH (α, rU H ). By substituting this into Eq. (20), we canwrite the value of a firm as a function of α and rU H :Π◦ (α, rU H ) ≡ Π(α, wH (α, rU H )).
2.6.2

(30)

Entry of Firms

Consider a potential firm contemplating the entry to the market. The firm is
randomly matched with a skilled worker with the probability n(θH ) through thematching mechanizm as defined in Eq. (8). However, not every matched firm canoperate in the market. Remember that for a firm, the ability of the matched skilledworker determines the firm’s productivity. As shown by Melitz (2003), there is a
production cutoﬀ level of productivity, denoted by α∗ , below which the value ofthe firm is negative. If a firm is matched with a skilled worker with the ability
lower than α∗ , the firm exits immediately from the market, avoiding a negative
profit. Hence, the combined probability of a successful matching and starting
business becomes n(θH )[1 − G(α∗ )].
Let V be the value of vacancy (i.e., the value of non-entry) and Π be the valueof a firm.9 When a potential firm posts a vacancy, it has to pay the search cost of
The variable Π here is not a function, but signifies a simple number. The reader should not be
confused.
916

cH . In each period, the firm can move from the non-operation (i.e., outside of themarket) to the market operation (i.e., inside of the market) with the probability ofn(θH )[1 − G(α∗ )]. Then, the value of vacancy satisfies the following relation:rV = −cH + n(θH )[1 − G(α∗ )][Π − V].

(31)

Free entry in the supply of vacancies implies V = 0. Then, in the steady state, we
have

cH
(32)
n(θH )[1 − G(α∗ )]In turn, consider an unemployed skilled worker. In each period, an unemΠ=ployed skilled worker receives an unemployment insurance b and, in a unit time,
he or she can move from the unemployed situation to the employed situation withthe probability θH n(θH ) through the matching mechanizm. Then, the value of unemployment, U H , satisfies
rU H = b + θH n(θH )[WH − U H ].

(33)

By replacing Π◦ (α, rU H ) in Eq. (27) with Π in Eq. (32) and substituting Eq. (33)
into Eq. (27), we obtain10
rU H = b +βcH θH(1 − β)(1 − sH )[1 − G(α∗ )](34)

Substituting Eq. (34) into Eq. (29), we obtain the Wage Determination equation:
]
[
cH θH
wH (α) = b + β π(α) − b +(35)(1 − sH )[1 − G(α∗ )]Combining Eq. (21), Eq. (32) and Eq. (35), we obtain the Job Creation equation:
1 − sHcH[π(α) − wH (α)] =r + sHn(θH )[1 − G(α∗ )]

2.7

(36)

Product Market Equilibrium

To solve the value of the production cutoﬀ, α∗ , and the ratio of vacancy and unemployment, θH , we consider the market equilibrium condition for the diﬀerentiated10

Whatever the actual value of a firm in Eq. (27) is, it has to satisfy the transition equation
Eq. (31). This justifies the replacement of Π◦ (α, rU H ) in Eq. (27) with Π in Eq. (32).

17goods. Since firms’ productivities are heterogeneous, we can use the Zero Cutoﬀ
Profit condition and the Free Entry condition as Melitz (2003). First, the cutoﬀ
productivity α∗ are such that Π(α∗D ) = 0 in Eq. (20):
] σ−1
[
σ
1
θ
m(θ
)LP
L
L
π(α∗ ) =(α∗ )σ−1 = wH (α∗ )σ
Z α̃σ−1(37)

Substituting Eq. (37) into Eq. (20) at the average ability α̃, we obtain the following
Zero Cutoﬀ Profit (ZCP) conditions][
1 − sH ( α̃ )σ−1∗wH (α ) − wH (α̃)
Π(α̃) =
r + s H α∗

(38)

Substituting wH (α) in Eq. (37) into Eq. (35), the wage of cutoﬀ ability α∗ is derivedasβcH θH(1 − β)(1 − sH )[1 − G(α∗ )]From Eq. (35) and Eq (39), the wage with average ability, wH (α̃) becomes[ ( )σ−1]{}α̃βcH θHw(α̃) = β ∗+1−β b+α(1 − β)(1 − sH )[1 − G(α∗ )]wH (α∗ ) = b +

(39)

(40)

Using Eq. (40) and the Zero Cutoﬀ Profit in Eq. (38), we obtain a condition which
describes the relationship between the production cutoﬀ productivity α∗ and theratio of vacancy and unemployment θH :{} [( )σ−1](1 − β)(1 − sH )α̃βcH θHcH∗b[1 − G(α )] +
−1 =
(41)
∗
r + sH(1 − β)(1 − sH )αn(θH )
In equilibrium, total expenditure on the diﬀerentiated good equals total revenues of all firms serving the demand in this sector. Note the total expenditure on
the diﬀerentiated good is an numéraire and that there are operation firms with theskilled worker whose ability over α∗ , the expenditure condition is
∫ +∞
g(α)
dα = 1p(α)x(α)
1 − G(α∗ )α∗Using the demand function of the diﬀerentiated goods in Eq. (2) and the optimal
firm size in Eq. (15), we obtain another relationship euqation between α∗ and θH :
∫ +∞
α∗

{
} σ−1
σ
2
θ
m(θ
)LP
g(α)
L
L
− (σ−1)
σ
dα
α̃
ασ−1
=1
1 − G(α∗ )
Z
18

(42)

Given the production productivity α∗ , Eq, (37) determines the price index, P.
Substituting the price index condition in Eq. (37) into the revenue condition in
Eq. (42), we rewrite the revenue condition omitting the price index:
(

1
σ ∗
α

)σ−1 {

βcH θHb+(1 − β)(1 − sH )[1 − G(α∗ )]} ∫ +∞
α∗

ασ−1

g(α)
dα = 1. (43)
1 − G(α∗ )As given α, two equations of Eq. (41) and Eq. (43) determine the production cutoﬀ
productivity α∗ and the ratio of vacancy and unemployment θH .
To analyze the the equilibrium value of α∗ and θH , we assume that workers’
abilities are distributed according to a Pareto distribution11 . Setting the scale parameter of that distribution to unity, the probability density is . The shape parameter γ governs the rate of decay of the distribution. We need to impose γ > σ − 1
to ensure that variance of the scales distribution is finite. Using this Pareto distribution, Eq. (41) and Eq. (43) are modified as{ ( )γ} {( )σ−1}1βcH θHα̃cH(1 − β)(1 − sH )
b ∗ +
−1 =
∗
r + sHα(1 − β)(1 − sH )αn(θH )γ − (σ − 1)βcH θH {α∗ }γ=b+(1 − β)(1 − sH )
σγ

(44)
(45)

Determining the equilibrium of α∗ and θH , we set the below assumptions aroundthe equilibrium of α∗ and θH :12{( )σ−1}α̃n′ (θH )β−<−1n(θH )2 r + sH α∗(46)

When the above assumptions are satisfied, Eq. (44) has a positive relationshipbetween α∗ and θH , and Eq. (45) has a negative relationship between α∗ and θH .
Fig. 1 illustrates the Eq. (44) and Eq. (45).

2.8

Educational choice

A worker with ability α determine whether to get an education at the beginningof the term. Unskilled workers enter the labor force without education, while the11

Bernard et al. (2007), Ghironi and Melitz (2005), and Helpman et al. (2004) assume that firm
productivities are distributed according to Pareto distribution.
12
We explain derivation of the assumptions at Appendix.

19

Figure 1: Determinant of α∗ and θH
income of the unskilled workers is independent of their ability. When unskilledworkers pursue an education with education cost, e, they can realize their ability and become skilled workers. Substituting Eq. (37) into Eq. (35), we obtainwH (α∗ ):{ ( )σ−1}[]αβcH θH (α∗ )γwH (α) = β ∗+1−β b+−eα(1 − β)(1 − sH )Let us consider wL in Eq. (23). Z is the number of firms and equal to the numberof the matched-skilled workers. The flow of the skilled unemployment is uH,t+1 =sH (H − uH,t ) − θH n(θH )uH,t , and at the steady state uH,t+1 = uH , t, so that the numberof the firm isθH n(θH )H
θH n(θH ) + sH
Suppose that the total number of labor is N. Since the workers’ ability is disZ=

tributed according Pareto distribution, the pool of skilled and unskilled labor, H
and L, is calculated as∫ ∞H=
αg(α)dα = α−γ N,
α

L=

∫ α
0

20

αg(α)dα = (1 − α−γ )NUsing Eq. (37) and the value of Z, H, and L, and substituting, we obtain theunskilled wage, wL :{} −γ+σ−1 ∗ −(σ−1)α{α }θH n(θH )γ(σ − 1)χwL ={γ − (σ − 1)}(1 − χ)sL θH n(θH ) + sH
1 − α−γ{}βcH θH (α∗D )γ(r + sL )cL× b+−(1 − β)(1 − sH )(1 − sH )m(θL )If the wage of the worker with α in the skilled labor market, which detects
educational cost, is higher than that of the unskilled labor market, wH (α) − e > wL ,the worker shift to the skilled labor pool from the unskilled labor market. On theother hand, if the wage earned by the skilled labor market is lower that of theunskilled labor market, wH (α) − e < wL , the worker remain in the unskilled labormarket. In equilibrium, there is an educational cutoﬀ ability α, where the expected
wage rate for unskilled worker, wL , has to be equal with the expected income ofskilled worker wH (α) − e. Therefore, the education cutoﬀ, α is determined in thefollowing equation:w(α) − e = wL

(47)

Since wL is decreasing in α and wH (α) is increasing in α, there exists an equilibrium educational cutoﬀ, α.

3Open Economy

We investigate the eﬀect of globalization on a worker’s job choice and the thenumber of unemployment of a country. There are two symmetric countries withthe same preferences, production technology, number of workers, and characteristics of the labor market. We assume that the systems of the labor market are
independent from each other. Suppose that the firms face fixed market access costf > 0 if they start exporting, and that it costs an ice-berg type tariﬀ, τ ≥ 1, toexporting goods. We denote the index of X, D as exporting and domestic sales.
Operating revenues from sales on a foreign market are equal to pX xX /τ. By symmetry, demands on the domestic and foreign market are given by Eq. (2). Equating
marginal revenues across market yields pX (α) = τpD (α) and xX (α) = τ1−σ xD (α).
Therefore, total revenues of the exporting sales is RX (α) = τσ−1 RD (α).
21Unskilled labor market Considering the total revenue, the optimal employmentof unskilled workers in Eq. (15)(σ−1ℓX = τ

σ−1
ℓD =
σ

)σ

A−σ Pσ−1 ασ−1 τ1−σ

The potential firms, which have not matched any workers yet, consider the expected value of operating both domestic and exporting. Since labor supply, given
as educational cutoﬀ α, is not changed, the wage of unskilled worker becomes
(

σ−1
wL =
σ

)[

] σ1
Z
(r + sL )cLσ−1
σ−1
P σ α̃ σ (1 + τ1−σ ) −.
θL m(θL )L(1 − sH )m(θL )(48)

Substituting wL into the optimal employment, ℓ, we obtain the equilibrium employment of each firm asℓ=θL m(θL )L ( α )σ−1.
Zα̃

Hence, πD (α) and πX (α) are rewritten as() σ−1
1 θL m(θL )LP σ σ−1α ,πD (α) =σ
Z α̃σ−1() σ−1
1 θL m(θL )LP σ σ−1 1−σπX (α) =α τ .
σ
Z α̃σ−1
Since it costs f to export, the value of the firms with an α’s skilled worker ismodified asΠ(α, wH ) ≡1 − sH[πD (α) + πX (α) − f − wH ].
r + sL(49)

Skilled labor market The structure of skilled labor market is also the same in
Section 2.6. The firms entry the market and search a skilled worker with cost ofcH , After matching, they recognize the matched-skilled worker’s ability α. Given
firm’s revenues are increasing in α, there exists a threshold α∗D below which firms
do not take up production. Similarly, firms with a productivity level between α∗D
and α∗X will serve only their domestic market. The firms calculate their actual
profit after recognizing α, and decide whether their activity policy: exit, only
domestic sale, or both domestic and exporting sales. The firms negotiate wH withthe skilled worker, and the wage schedule becomes the same one in Eq. (35).
22

Product Market Equilibrium

At a threshold of α∗D , the value of firms which

only sell their variety in domestic market go to zero, Π(α∗D , wH ) = 0:πD (α∗D ) =() σ−1
1 θL m(θL )LP σ(α∗X )σ−1 = wH (α∗D )
σ−1
σ
Z α̃

(50)

From Eq. (35), the wage of α∗D -ability worker is the same of Eq. (39). On theother hand, the profit of exporting sales is zero at the threshold of α∗X , and we
obtain πX (α∗X ) − f = 0. Therefore, it can be shown that the condition for α∗D and
α∗X :
(
τ

1−σ

)
α∗X
f
∗ =
αD
wH (α∗D ){= f · b+βcH θH(1 − β)(1 − sH )[1 − G(α∗D )]

}−1

(51)

Given α∗D , Eq. (51) determines α∗X . To guarantee α∗X > α∗D , we assumeτσ−1 f > b +βcH θH.
(1 − β)(1 − sH )[1 − G(α∗D )]Notice that πX (α) = τ1−σ πD (α), the wage of α∗X -ability skilled worker is calculatedwith Eq. (35):βcH θHwH (α∗X ) = β[πD (α∗D ) + πX (α∗X ) − f ] + (1 − β)b +(1 − sH )[1 − G(α∗D )]{}βcH θHσ−1= βτ f + (1 − β) b +(1 − β)(1 − sH )[1 − G(α∗D )](52)

Using Eq. (35) and the feature of α∗D and α∗X , we obtain The ZCP condition as[{}]
βcH θH
1 − sHπ(α̃) − f − β[π(α̃) − f ] + (1 − β)b +Π(α̃) =
r + sH(1 − sH )[1 − G(α∗D )](1 − β)(1 − sH )
=
r+s
{


( )σ−1H ( )σ−1}
( )σ−1








α̃
βc
θ
α̃
α̃




H
H
σ−1
× 
+
−
1
+
f
−
1
βτ








 (1 − β)(1 − sH )[1 − G(α∗D )]


 α∗D
α∗X
α∗X
With the ZCP and the free entry condition is given in Eq. (32), so that we obtainthe first condition which describes the relationship between the production cutoﬀ
23

productivity α∗ and the ratio of vacancy and unemployment θH .
( )σ−1{( )σ−1
}




α̃
α̃
βcH θH+ (1 − β) ∗
− 1
b+



 α∗D

αX
(1 − β)(1 − sH )[1 − G(α∗D )]( )σ−1
(r + sH )cH
 σ−1 α̃

+f 
βτ
−
1
=

∗



 (1 − β)(1 − sH )[1 − G(α∗D )]n(θH )
αX

(53)

In equilibrium, total expenditure on the diﬀerentiated good equals total revenues of all firms serving the demand in this sector.
∫ +∞
∫ +∞
g(α)
g(α)
pD (α)xD (α)
dα +pX (α)xX (α)
dα = 1∗
1 − G(αD )1 − G(α∗X )α∗D
α∗XThe price index, P, is determined by Eq. (50). Using the value of P with the expenditure condition gives us the second condition which describes the relationshipbetween α∗D and θH .
}{βcH θHb+(1 − β)(1 − sH )[1 − G(α∗D )]( )σ−1 ∫()σ−1 ∫
 1
1g(α)g(α) 
σ−1
σ−1
 = 1× σ  ∗+αααD
1 − G(α∗D )τα∗D
1 − G(α∗X )
α∗D
α∗X

(54)

For given α, conditions in Eq. (51), (53), and (54) allow to solve α∗D , α∗X , andθH . By symmetry, the three conditions together allow to solve for the cutoﬀs anddemand levels simultaneously. To clarify the later discussion, we assume thatthe workers’ ability follows the Pareto distribution, so that Eq. (53) and Eq. (54)become( )σ−1 { ( )−γ( )σ−1
}




α̃
1
βcH θH α̃+ (1 − β) ∗
− 1
+
b ∗



 α∗D

αX
αD
(1 − β)(1 − sH ))( )−γ 
(
σ−1




1
(r + sH )cH
 σ−1 α̃

−
1
+f ∗
βτ
=


∗




αD
αX
(1 − β)(1 − sH )n(θH )b+βcH θH (α∗D )γγ − (σ − 1)+f =(1 − β)(1 − sH )
γσ

(55)
(56)

Eq. (55) is a decreasing function of θH even if the assumption of Eq. (46) is satisfied. The raise of α∗D decreases Eq.(55) as long as α∗X is larger than α∗D . Therefore,
Eq. (55) has a positive relationship between α∗D and α∗X , such as closed economy.
On the other hand, Eq. (56) always has a negative relationship between α∗D andθH .
24

Trade Liberalization

Trade liberalization (decreasing τ) only aﬀects Eq. (55).

We first consider the eﬀect of decreasing ice-berg cost on α∗D , α∗X and θH as given
the education cutoﬀ, α. Fig. 2 draws the change in decreasing τ which shifts
Eq. (55) to right, and trade liberalization increases the production cutoﬀ, α∗X , anddecreases the ratio of vacancy and unemployment, θH . This change has two eﬀects
on unemployment: probability eﬀect and middle class eﬀect. Decreasing θH reduces the matching probability for skilled labor, which increases unemployment.
Larger α∗X expands the range that the skilled workers with relatively lower ability
are unemployed. The decrease in τ makes market competition more severe, andthe firms which matched the lower-ability skilled worker exit from the market,
while trade liberalization increases the operating profit of exporting sales. In results, the number of skilled unemployment increases, especially the lower-skilledworker may be damaged by trade liberalization.

Figure 2: Eﬀect of a reduction of τ on α∗ and θH
Next, we also allow the change of educational choice, α. From Eq. (48), tradeliberalization raises the demand of the unskilled labor because of easier to export
their goods. To solve Eq. (48), let us consider the condition of the price index.
Since we assume that total expenditures are numéraire, the price index must be25

satisfied as(

θL m(θL )LP
Z

) σ−1
σ

α̃

− (σ−1)
σ

2

∫ +∞
α∗X

ασ−1

g(α)
dα = 1.
1 − G(α∗X )Substituting this condition into Eq. (48), we obtain the unskilled wage under international trade:{} −γ+σ−1 ∗ −(σ−1)α{α }γ(σ − 1)χ
θH n(θH )wL ={γ − (σ − 1)}(1 − χ)sL θH n(θH ) + sH
1 − α−γ{∗ γ }βcH θH (αD )(r + sL )cL× b+(1 + τσ−1 ) −.
(1 − β)(1 − sH )(1 − sH )m(θL )(57)

With Eq. (35), (50), and πX (α∗X ) = f , the skilled wage is calculated as
βcH θHwH (α) = β[πD (α) + πX (α) − f ] + (1 − β) +1 − G(α∗D ) ( )σ−1{} ( )σ−1








βcH θH
 α

 α

=
β
+
1
−
β
+
−
1
b
+
f



∗
∗
∗




 αD

 αX

(1 − β)(1 − sH )[1 − G(αD )]{}( )σ−1βcH θH (α∗X )γ
α


1−σ
+ 1 − β= b + (1 − β)(1 − sH ) − f,
(β + τ ) α∗


D
(58)
where we use Eq. (51) and Pareto distribution in the last line. The educational
cutoﬀ, α, determined by Eq. (47), Eq. (57), and Eq. (58).
Trade liberalization aﬀects the determination of θH and α∗D in Eq. (55) andEq. (56), and also changes the educational cutoﬀ, α, thorough the comparison ofwH and wL . To see the eﬀect of trade liberalization on some variables, we define
an implicit function, E(α∗ , θH , α, τ) ≡ wH (α) − e − wL = 0, which is derived by
the educational choice condition. From Eq. (55) and Eq. (56), α∗D and θH can besolved as a function of α and they are aﬀected by τ. α is solved by educational
condition and can be expressed as a function of τ, so that the implicit function canbe modified E(α∗D (α, τ), θH (α, τ), α(τ), τ). By implicit function theory, the eﬀectof decreasing τ on the education cutoﬀ is
∂α∗

∂E
D
+ ∂θ∂EH ∂θ∂τH + ∂E∂α∂α∗ ∂τ
∂τ
=−
.
∗
∂α
∂E
D
∂τ
+ ∂E ∂θH + ∂E∗
∂αD ∂α26∂θH ∂α∂αNote that ∂α∗D /∂τ < 0, ∂θH /∂τ > 0, ∂α∗D /∂α < 0 and ∂θH /∂α < 0 ∂α∗D /∂α > 0from Eq. (55) and Eq. (56). Deceasing in τ gives an ambiguous eﬀect on the
education cutoﬀ, α. If the sign of the above equation is positive, trade liberalization decreases the education cutoﬀ, and the production cutoﬀ, α∗D , also increases
from (55) and Eq. (56). The expand of the range between α and α∗D means thatthe skilled workers with low ability are easy to become unemployment while thenumber of the skilled workers increase. This model cannot solve the total eﬀects
on the unemployment analytically. However, we show the possibility that globalization may increase the number of unemployment. .

4

Conclusion

This article analyzes the eﬀects of globalization on the worker’ choice of jobs andemployment. We assume that search friction exists in the skilled and unskilled labor market and that workers can choose to be skilled or unskilled worker. If a firm
succeeds in matching with a skilled worker, it can start a business and the productivity of the firm depends on the ability whose matched-skilled worker has. Tradeliberalization among two symmetry countries increases the profit of the operating
firms, which raises the entry of firms and the demand for skilled workers. Theseeﬀects attract both skilled and unskilled workers. We obtain ambiguous eﬀects
of globalization on the worker’s education choice. However, we find a possibility where the globalization promotes the popularization of high education and theunemployment of skilled workers. Future research would be to consider heterogeneous countries. Our model assume symmetric countries, but this assumption
does not depict the real world. Since we adopt a search-matching model in thisstudy, it is diﬃcult to consider heterogeneous countries. Although heterogeneous
countries could complicate the model , the implication of heterogeneity gives us
the new insight into the international trade and labor market literature.

27

A

Derivation of Eq. (23)
⇔
⇔
⇔

B

Le = θL m(θL )L
(
)σ
σ−1
Z
A−σ Pσ−1 α̃σ−1 = θL m(θL )L
σ
(
)[
] σ1
σ−1
Z
(r + sL )cLσ−1
σ−1
P σ α̃ σ = wL +σ
θL m(θL )L(1 − sH )m(θL )()σ − 1 σ1 σ−1(r + sL )cLσ−1
wL =B P σ α̃ σ −,σ(1 − sH )m(θL )(59)

Derivation of assumptions for Eq. (45)

Totally diﬀerentiating Eq. 45 with respect to α∗ and θH , we obtain ( )γ+1 {( )σ−1}
{ ( )γ} ( )σ
 ∗
α̃
1
1
1
1 − β 
σ−1
bγ
 dα
−
1
+
(σ
−
1)
b
+
c
θ
α̃
−
H
H
r + sH
α
α∗
α∗
α∗
[ ′
{
}]
n (θH )
1 − β ( α̃ )σ−1
= −−− 1 cH dθHn(θH )2 r + sH α∗
Note that the sign of the left hand side is negative, the sign of the brace for theright hand side must be negative to get the positive relationship between α∗ and θH .
Considering the numerical value of the parameter used by Bernard et al. (2007),
Petrongolo and Pissarides (2001), and Shimer (2001), those assumptions are easy
to be satisfied.

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