Reducing the Inflow of Unskilled Foreign Workers
Akira Shimada
Faculty of Economics, Nagasaki University

Abstract
This paper investigates the effects of minimum wages on the inflow of unskilled foreign workers
in a two-country macroeconomic model. We assume that all workers are unskilled and bothcountries’ labor markets are competitive. In this model, workers move from a country of lower
expected real-consumption wages (nominal wages divided by the consumer price index andmultiplied by the probability of employment) to a country of higher wages. This paper showsthat, in cases where minimum wages are not introduced, workers move from a country with alarger domestic labor force (initial labor endowment) to a country with a smaller one. If minimum wages are introduced into a country with a smaller domestic labor force, such migration canlikely be reduced. This results from the fact that a country with a smaller domestic labor force,by increasing its minimum wages, decreases its expected real-consumption wages because decreases in the employment probability will be larger than increases in real-consumption wages.

JEL Classification: F41; F22; J38

Keywords: International migration of unskilled labor; Minimum wages; Two-country macroeconomic model01. Introduction
Today most workers moving among countries are unskilled workers migrating from developing
countries to developed countries. Many developed countries are now experiencing large inflows
of unskilled foreign workers. It is reasonable for unskilled workers to migrate, since working
conditions in their home countries are inferior to those in developed countries. However, many
developed countries, including Japan where about 80% of foreign workers are estimated to be
unskilled, are reluctant to accept unskilled foreign workers, while encouraging skilled foreign
workers’ immigration.1 This is because the large inflow of unskilled foreign workers likely helps
to preserve low-wage industries and hinder the improvement of working conditions and laborproductivity.2 For these reasons, many developed countries are trying to reduce the inflow of
unskilled foreign workers mainly by implementing immigration control laws and government
regulations. However, such laws and regulations are not always effective in reducing the inflow
of unskilled foreign workers, since, as we said earlier, seeking better working conditions is rational behavior, which is difficult to control. Accordingly, we need to investigate this problem interms of economics and have to find a way to reduce the inflow of unskilled foreign workers
considering the rationality of their behavior.
International migration of labor is strongly connected with open macroeconomies. It has
close relations to markets in macroeconomies, exchange rates and policy authorities’ behavior.
However, it has not been sufficiently analyzed in the context of open macroeconomic frameworks
except by Agiomirgianakis (1998). Since unskilled foreign workers’ inflow is one of the mostserious migration problems and we are trying to reduce it by governmental economic policies, weneed to employ open macroeconomic models for the analysis.
Therefore we focus in this paper on the reduction of unskilled foreign workers’ inflow in an
open macroeconomic model. In particular, we explore the effectiveness of policy authorities’
manipulation of minimum wages. For this purpose, we assume a two-country economy with

1

Ministry of Health, Labour and Welfare of Japan (2002).

2

In Japan, the government formally takes the position not to accept unskilled foreign workers.

Actually, many unskilled foreign workers continue to enter Japan as foreign students or foreign
trainees.
1different initial labor endowments and workers migrating between two countries because ofdifferences in expected real-consumption wages, that is, nominal wages divided by the consumer
price index and multiplied by the employment probability.
Our analysis shows that unskilled workers migrate from a foreign country with a larger domestic labor force (initial labor endowment) to a home country with a smaller one if there are no
minimum wages. This is because the home country with a smaller domestic labor force hashigher nominal wages and a lower consumer price index, which implies that it has higher expected real-consumption wages. And unskilled workers are assumed to migrate from a country
with lower expected real-consumption wages to a country with higher ones. If minimum wages
are introduced into the home country with a smaller domestic labor force, the home country can
reduce unskilled workers’ migration from the foreign country with a larger domestic labor force byincreasing home country’s minimum wages. This is because, by increasing minimum wages, thehome country with a smaller domestic labor force reduces its employment probability and increases its real-consumption wages, and the former effects are stronger than the latter effects.
In what follows, we first set out a two-country economic framework with different domestic
labor forces between two countries and assume factors initiating international migration of labor.
We then examine how unskilled workers migrate between two countries without introducing
minimum wages and we also examine the effects of minimum wages on unskilled workers’ migration. We finish the paper with a discussion of the implications of our findings.

2. The Model
We consider a two-country economic model where home and foreign countries are almost symmetric in their economic structures. They are interdependent through international trade ofgoods and international migration of labor. In each country, there are unskilled workers, a firm
and a policy authority. The model, however, disregards skilled workers and labor unions.
Each country’s labor market is perfectly competitive in a case where minimum wages are notintroduced. In such a case, each country’s nominal wages and employment levels are determined to equate its demand for and supply of labor.
Workers can move between the two countries. In a case where workers born in a foreigncountry migrate to a home country, the home country’s labor force consists of workers born in2

home and foreign countries. In another case where workers born in the home country migrate to
the foreign country, the foreign country’s labor force consists of workers born in foreign and homecountries.
In each country, a firm demands labor to produce a single kind of product. Home country’s
product (Foreign country’s product) is not only demanded in the home country (the foreign country) but also in the foreign country (the home country), and is exported there. Home and foreigncountries’ products are imperfect substitutes.
We assume that each country has its money market and money is the only financial asset heldby its domestic residents.
The model is summarized by Equations (1)-(7). Structural equations of this paper are thesame as ones employed by Jensen (1993), Zervoyianni (1997), Agiomirgianakis (1998) and Shimada (1999, 2000, 2002a, 2002b). Variables are expressed in logs unless otherwise defined.
Variables without stars refer to the home country and variables with stars refer to the foreigncountry.

y = al , y * = al * , 0 < a < 1.
1
1
1
1
( w − p) +ln a, l * = −( w* − p * ) +
ln a.
l=−
1− a
1− a
1− a
1− a
z ≡ e + p * − p.

(1)y − y = bz , b > 0.
q ≡ p + cz, q * ≡ p * − cz, 0 < c < 1 2.
wc ≡ w − q, wc* ≡ w * − q * .

(4)

m = p + y, m = p + y .

(7)

*

*

*

(2)
(3)
(5)
(6)

*

Eq. (1) is the production functions of home and foreign countries’ firms, where y is output of thehome country’s firm (the home country’s national product), y is output of the foreign country’s*

firm (the foreign country’s national product), l is the home country’s employment level, l * isthe foreign country’s employment level, and a is a constant not expressed in the log. Eq. (2) isthe labor demand functions of home and foreign countries’ firms, where w is the home country’s
nominal wage, w* is the foreign country’s nominal wage, p is the home country’s product price
and p

*

is the foreign country’s product price. They are derived from the profit maximization ofeach country’s firm. Eq. (3) is the definition of the real exchange rate z , where e is thenominal exchange rate measured as units of home country’s currency per unit of foreign country’s
currency. Eq. (4) is the equilibrium condition of both countries’ trade balances, where b is a3

constant not expressed in the log. If the real exchange rate (the difference in the two countries’
national product) has stronger effects on the trade balance than the difference in the two countries’ national product (the real exchange rate), then b is larger (smaller) than 1.3 Eq. (5) isdefinitions of the home country’s consumer price index q and the foreign country’s consumer
price index q , where c is a constant not expressed in the log.4 Eq. (6) is definitions of home*country’s real-consumption wages wc and foreign country’s real-consumption wages wc* . Eq.
(7) is the equilibrium conditions of home and foreign countries’ money markets, where m is thehome country’s money stock and m * is the foreign country’s money stock. We assume eachcountry’s policy authority does not manipulate its money stock, which implies m and m are*constants throughout the analysis.5
In this paper workers are assumed to migrate because of differences in expected
real-consumption wages between two countries. Assuming workers in each country have thesame employment opportunity, in other words, native and foreign workers in the same country
have the same employment probability, if home country’s expected real-consumption wages

l − l f + wc are higher than foreign country’s expected real-consumption wages l * − l * f + wc* ,thenworkers

born

in

the

3 Home country’s trade balance

foreigncountry

migrate

to

the

home

countryby

TB and foreign country’s trade balance TB * are defined as,

TB = −TB * = α1 z − α 2 ( y − y * ), α 1 ,α 2 > 0,
where α1 and α 2 are constants not expressed in logs. The equilibrium of both countries’ tradebalance requires,y − y* = (α1 α 2 ) z .
Replacing α 1 α 2 with b , we get Eq. (4).

In a case where the real exchange rates havestronger effects on the trade balance than the difference in the two countries’ national product,

α1 is larger than α 2 implying b is larger than 1. In another case where the difference in thetwo countries’ national product has stronger effects on the trade balance than the real exchange
rate, α 2 is larger than α1 implying b is smaller than 1.
4Home country’s price index not expressed in the log is P

index not expressed in the log is P

*1− c

1− c

( EP * ) c and foreign country’s price( P E )c , where P ≡ exp p, E ≡ exp e and P* ≡ exp p*.

5 In this paper, policy authorities’ role is limited to manipulating minimum wages.

4

See section 3.

d{l − l f + wc − (l * − l * f + wc* )}, where l f is the home country’s effective labor force, l * f is theforeign country’s effective labor force and d is a positive constant not expressed in the log. On
the other hand, if foreign country’s expected real-consumption wages are higher than homecountry’s expected real-consumption wages, then workers born in the home country migrate to
the foreign country by d{l − l**f+ wc* − (l − l f + wc )} .

Assumptions on international migration of labor lead to the following definitions of the homecountry’s effective labor force l and the foreign country’s effective labor force l
f

*f

.

l f ≡ l + d{l − l f + wc − (l * − l * f + wc* )},(8.1)

l * f ≡ l * + d{l * − l * f + wc* − (l − l f + wc )},(8.2)

where l is the home country’s domestic labor force in the absence of international migration oflabor (the home country’s initial labor endowment) and l * is the foreign country’s domestic labor
force in the absence of international migration of labor (the foreign country’s initial labor endowment).

This paper, being different from Shimada (1999, 2000, 2002b), assumes that l issmaller than l .6 Two countries’ economic structures are symmetrical except for the difference*in their domestic labor forces.
Through appropriate substitutions, Eqs. (1)-(7) can be solved for l , l , y , y , p , p , z ,***q , q* , wc , wc* as functions of w , w* , m , m* .

l = m − w + ln a.
l * = m * − w* + ln a.
y = a (m − w) + a ln a.
y * = a(m * − w* ) + a ln a.
p = (1 − a )m + aw − a ln a.
p * = (1 − a)m * + aw* − a ln a.
az = {m − w − (m * − w* )}.
b
ac 
ac

q =  − a + ( m − w) + m − (m* − w* ) − a ln a.
b 
b

ac 
ac

q * =  − a + (m* − w* ) + m* − (m − w) − a ln a.
b 
b


(9.1)
(9.2)
(9.3)
(9.4)
(9.5)
(9.6)
(9.7)
(9.8)
(9.9)

6 Shimada (2001) explicitly introduced capital stock and labor into the model as factors of pro-duction and investigated cases where two countries have different capital stocks and where twocountries have different domestic labor forces in the absence of international migration of labor.
5

ac 
ac

wc = 1 − a + ( w − m) − ( w* − m* ) + a ln a.
b 
b

ac 
ac

wc* = 1 − a + ( w* − m* ) − ( w − m) + a ln a.
b b(9.10)(9.11)

Substituting labor demand functions (Eq. 2) into production functions (Eq. 1), we obtain aggregate supply functions that positively relate the product price to output in each country. As
money stocks increase, the curves equilibrating money markets (Eq. 7) shift upward to the right,
resulting in increases in output and product prices (see Eqs. 9.3-9.6). Increases in nominal
wages shift the aggregate supply curves upward to the left, causing decreases in output andincreases in product prices (see Eqs. 9.3-9.6). Since each country’s output is an increasing
function of each country’s employment level, the employment levels increase as we increase
money stocks and decrease as we increase nominal wages (see Eqs. 9.1 and 9.2).
Increases in the home country’s money stock and/or decreases in home country’s nominal
wages decrease home country’s net exports by increasing home country’s output. Decreases in
the foreign country’s money stock and/or increases in foreign country’s nominal wages increase
foreign country’s net exports by decreasing foreign country’s output. To keep the equilibrium ofboth countries’ trade balances, real exchange rates have to depreciate, in other words, z has toincrease (see Eq. 9.7).
Increases in the home country’s money stock not only increase the home country’s productprice, but also increase the foreign country’s product price expressed in terms of home country’s
currency by increasing home country’s output and depreciating real exchange rates (increasingz ). Accordingly increases in the home country’s money stock lead to increases in the homecountry’s consumer price index (see Eq. 9.8). On the other hand, decreases in home country’s
nominal wages decrease the home country’s product price, while they increase the foreign country’s product price expressed in terms of home country’s currency by increasing home country’s
output and depreciating real exchange rates. Accordingly effects of home country’s nominal
wages on the home country’s consumer price index are ambiguous (see Eq. 9.8).
Increases in the foreign country’s money stock and/or decreases in foreign country’s nominal
wages decrease the foreign country’s product price expressed in terms of home country’s currency
by increasing foreign country’s output and appreciating real exchange rates (decreasing z ).
Accordingly increases in the foreign country’s money stock and/or decreases in foreign country’s
6nominal wages lead to decreases in the home country’s consumer price index (see Eq. 9.8).
Therefore increases in the home country’s money stock, decreases in the foreign country’s
money stock and/or increases in foreign country’s nominal wages bring about decreases in homecountry’s real-consumption wages by increasing the home country’s consumer price index (see Eq.
9.10).
Increases in home country’s nominal wages increase home country’s real-consumption wages
directly. They also increase home country’s real-consumption wages by appreciating real exchange rates (decreasing z ) and decreasing the home country’s consumer price index. On the
other

hand,

increases

in

home

country’s

nominalwages

decreasehomecountry’s

real-consumption wages by increasing the home country’s product price and the home country’s
consumer price index. Since the former two effects are stronger than the latter effects, increases
in home country’s nominal wages lead to increases in home country’s real-consumption wages(see Eq. 9.10).
We can explain Eqs. (9.9) and (9.11) in the same way as we do Eqs. (9.8) and (9.10).

3. Minimum Wages and International Migration of LaborThis section first tries to show that in the absence of minimum wages, workers in the foreigncountry with a larger domestic labor force migrate to the home country with a smaller one, thenintroduces minimum wages into the home country and investigate its effects on migration offoreign country’s workers to the home country.
In the case where minimum wages are not introduced, all of the effective labor force are employed in each country, consequently Eqs. (8.1) and (8.2) are rewritten as,l f ≡ l + d ( wc − wc* ),(8.1’)≡ l + d ( w − wc ).

(8.2’)

l

*f

*

*
c

From the equilibrium condition of the home country’s labor market l = l f , the equilibrium
condition of the foreign country’s labor market l * = l * f and Eqs. (9.1), (9.2), (9.10), (9.11), we getfollowing equations.


2ac 
2ac  *
*(m − w) − d 1 − a +(m − w ) = l − ln a.
1 + d 1 − a +
b 
b 




2ac 
2ac  ***− d 1 − a +(m − w) + 1 + d 1 − a +(m − w ) = l − ln a.
b 
b 



7

(10)
(11)

Substituting m − w and m* − w* solved from Eqs. (10) and (11) into Eqs. (9.10), (9.11), (8.1’) and(8.2’)，we get both countries’ effective labor forces in the absence of minimum wages.
−1

2ac 
2ac 
*l = l + d 1 − a +1 + 2d 1 − a + (−l + l ).
b
b





(12.1)

f

−1

l

*f

2ac 
2ac *= l + d 1 − a +1 + 2d 1 − a + (−l + l ).
b 
b 



(12.2)*

Eqs. (12.1) and (12.2) show that l f is larger than l and l * f is smaller than l * under theassumption of l < l * . This implies that workers born in the foreign country migrate to thehome country. We can explain this result as follows. The smaller initial labor endowment of
the home country makes its employment level and output smaller than those of the foreign country. This implies that home country’s nominal wages are higher than those of the foreign country. Since z < 0 , the home country’s consumer price index is lower than the foreign country’s
consumer price index, if the product prices do not differ between two countries. On the other
hand, the home country’s product price is higher than the foreign country’s product price. Since
the former two effects are stronger than the latter effects, home country’s real-consumption
wages are higher than those of the foreign country.7,8 Therefore it is rational for many of theforeign country’s workers to migrate to the home country.

We have shown that the home country faces with the inflow of unskilled workers from the

From Eqs. (9.10), (9.11), (9.1) and (9.2), the difference in real-consumption wages between two
countries is,7

wc − wc* = −(1 − a + 2ac b)(l − l * ).
Prior to the initiation of migration, wc is higher than wc since l − l = l − l
*

8

*

*

and l < l .
*In this paper migration does not equalize real-consumption wages between two countries. We

can explain this as follows. Let us assume that real-consumption wages are equalized by migration. Equilibrium conditions of labor markets,l + d (wc − wc* ) = m − w + ln a,
l * + d (wc* − wc ) = m* − w* + ln a,
imply that two countries have different nominal wages, since l < l . However, if nominal wages*

are different, real-consumption wages take different values between two countries according toEqs. (9.10) and (9.11).
8

foreign country. Let us investigate whether the home country’s policy authority can reduce theinflow by manipulating its minimum wages. For this purpose, we assume two things. One
assumption is that the home country’s policy authority determines the value of the minimum
wage wmin to be equal to or higher than the nominal wage that equates the demand for andsupply of home country’s labor. Another assumption is that the home country’s firm sets its
nominal wages to be equal to or higher than minimum wages. Under these assumptions, thehome country’s employment level is determined by the labor demand of the home country’s firm.9
Since all of the foreign country’s effective labor force are employed and not all of the homecountry’s effective labor force are employed, Eqs. (8.1) and (8.2) are rewritten as,l f = l + d (l − l f + wc − wc* ),l*f(8.1’’)= l + d {w − (l − l + wc )}.
**c(8.2’’)f

From Eqs. (8.1’’), (9.1), (9.10) and (9.11), if the home country’s firm sets its nominal wages
equally to minimum wages, the home country’s effective labor force becomes,

lf =

1
2ac 
2ac  *d dd *ln a +l−(m − w ).
1 − a +(m − wmin ) +− a +
1+ d
1+ d 
1+ d
1+ d 
b 
b 

(13)

Substitution of Eqs. (9.11), (9.1), (13) and (9.10) into Eq. (8.2’’) and the equilibrium condition of theforeign country’s labor market l * = l * f give us,

m* − w* + ln a2ac 2ac  *
d 
d 
d
d
*
ln a +l−= l* +
− a +
( m − wmin ) −1 − a +(m − w ).
1+ d
1+ d
1+ d 
1+ d 
b 
b 

(14)

Substituting m* − w* solved as a function of m − wmin into the right-hand sides of Eqs. (13) and(14), we get both countries’ effective labor forces in the case where minimum wages are introduced
into the home country.
−1

d 
d 
2ac  
2ac 
2ac 
2ac  * *l =l +
1 − a +  − l + l −  − a +(m − wmin ) −  − a + ln a +  − a +
l .
1 +
b  
bb
1+ d  1+ d 
b  





f

(15.1)−1

l*f = l * −d d 
2ac  
2ac 
2ac 
2ac  * *
1 − a +  − l + l −  − a +(m − wmin ) −  − a + ln a +  − a +
l .
1 +
b  
bb
1+ d  1+ d 
b  






(15.2)
Before examining the effects of manipulation of minimum wages, let us consider a special case9

The profit of the home country’s firm does not change if the home country’s employment level isdetermined by the labor demand of the home country’s firm.
9where the home country’s policy authority determines the value of minimum wage to be equal to
the nominal wage that equates the demand for and supply of home country’s labor. In this case,if the home country’s firm sets its nominal wages equally to minimum wages, all of the effective
labor force are employed in both countries. In such a case, Eqs. (15.1) and (15.2) coincide with
Eqs. (12.1) and (12.2) respectively and workers born in the foreign country migrate to the homecountry.
We then raise home country’s minimum wages from the equilibrium nominal wage. According to Eq. (15.1), its effects on the home country’s effective labor force are ambiguous. However,if b > 1 , then increases in home country’s minimum wages decrease the home country’s effective
labor force.10 This result can be explained as follows. As we increase home country’s minimum
wages, the employment probability in the home country l − lfdecreases, although the differ-ence in real-consumption wages between two countries wc − wc increases.11 If b > 1 , then the*former effects are stronger than the latter effects, which implies home country’s expected
real-consumption wages become smaller as we increase home country’s minimum wages.
Therefore in the case of b > 1 , fewer unskilled workers migrate from the foreign country to thehome country as home country’s minimum wages increase.12
On the other hand, if b < 1 , then the increases in home country’s minimum wages increase
the home country’s effective labor force and decrease the foreign country’s effective labor force.
This result implies that in the case of b < 1 , more unskilled workers migrate from the foreigncountry to the home country as home country’s minimum wages increase.
Results derived above are summarized as follows. If b > 1 , then the home country can
reduce unskilled workers’ migration from the foreign country by increasing home country’s minimum wages. On the other hand, if b < 1 , increasing home country’s minimum wages urges
unskilled workers’ migration from the foreign country.

10

dl f dwmin = d (1 + d )−1{1 + d (1 + d )−1(1 − a + 2ac b)}−1(−a + 2ac b). If b > 1 , then dl f dwmin < 0 .

11d (l − l f ) dwmin = −{1 + d (1 + d )−1 (1 − a + 2ac b)}−1{2d (1 + d )−1 (1 − a + 2ac b) + d (1 + d )−1} < 0.

d ( wc − wc* ) dwmin = {1 + d (1 + d ) −1 (1 − a + 2ac b)}−1 (1 + 2d )(1 + d ) −1 (1 − a + 2ac b) > 0.
12

If the home country’s policy authority continues to increase its minimum wages, it will soon

happen that workers born in the home country will migrate to the foreign country.
10Whether b is larger than 1 or not, that is, whether the real exchange rates have stronger
effects on the trade balance than the difference in two countries’ national product or not is anempirical problem. However, according to Agiomirgianakis (1998, footnote 9), for most countries
empirical evidence suggests that the real exchange rates have stronger effects and this allows us
to conclude b > 1 . Therefore it is very likely by increasing home country’s minimum wages, thehome country can reduce the inflow of unskilled workers from the foreign country.

4. Conclusions
Many developed countries are now suffering from the inflow of unskilled foreign workers.
However, it is difficult for these countries to prevent it only by immigration control laws andgovernment regulations, since it is rational for unskilled foreign workers to migrate to countries
where they can get better working conditions. Using an open macroeconomic framework, thispaper tried to find a way to reduce the inflow of unskilled foreign workers by considering therationality of their behavior. This paper showed that it is very likely a home country with asmaller domestic labor force can reduce the unskilled worker’s inflow from a foreign country witha larger one by increasing home country’s minimum wages. Our result suggests that if weabstract the negative effects of minimum wages on domestic unskilled workers, we can effectively
reduce the inflow of unskilled foreign workers by appealing to the rationality of workers as well as
using immigration control laws and government regulations.

11References
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