International Migration of Labor, Efficiency Wages, and Monetary Policies
Akira Shimada
Faculty of Economics, Nagasaki University

Abstract
Assuming a symmetric two-country economy with labor migration and efficiency wages, weinvestigate which of the two regimes, non-cooperation or inter-government cooperation, isadvantageous. We show that not only the utility of the policy authority but also that of theworkers is higher under inter-government cooperation than under non-cooperation, provided
that migration flows are sufficiently sensitive to changes in real-consumption wage differentials.
Our result is in contrast to the one derived by Agiomirgianakis (1998); according to him, in a
two-country economy with labor migration and labor unions, only the policy authority can attainthe higher utility under inter-government cooperation.

JEL Classification: F42, F22, J4, F41

Keywords: Monetary policy games; International migration of labor; Efficiency wages;
Two-country economy

0I. Introduction
This paper is concerned with monetary policy games in a two-country economy that ischaracterized by international labor migration and efficiency wages, and it attempts to show thatinter-government cooperation in the monetary field may prove to be advantageous not only tothe policy authority but also to the workers.
International monetary cooperation has become one of the crucial issues for many
governments since they have to take into consideration policy interdependence among countries,
which has increased not only due to the growing amount of international trade of goods andinternational flow of financial capital but also due to the growing mobility of labor acrossborders.
Needless to say, the question regarding whether or not the policy authorities should cooperate
in the monetary field is not new. Several authors, including Hamada (1976) and Rogoff (1985)
as early contributors, have analyzed this problem. However, various studies on this issue havenot paid sufficient attention to the mobility of labor.
Agiomirgianakis (1998) analyzed this problem by utilizing a symmetric two-country
macroeconomic model.1 His analysis was different from the previous analyses on this issue,

1

Although there are various other approaches to analyze international migration of labor, it ismost appropriate to utilize open macroeconomic models since the effects of labor migration are
not limited to those on the specific markets belonging to labor-sending and labor-receiving
countries and extend to all sectors of these countries’ economies. Accordingly, several studies(Agiomirgianakis, 1996, 1999, 2000; Agiomirgianakis and Zervoyianni, 2001; Shimada, 2003)
utilized either the two-country or small open economic models to investigate the consequences1since he assumed the labor migration between two countries due to the differences inreal-consumption wages (nominal wages divided by the consumer price index).
He demonstrated that under the possibility of international migration, inter-government
cooperation may prove to be advantageous. In particular, he revealed that the utility of thepolicy authority is likely to be higher under inter-government cooperation than under
non-cooperation, whereas the utility of workers does not differ across regimes.
In order to obtain this result, he modeled labor markets by assuming the existence of labor
unions. Nominal wages and employment are determined through negotiations between thelabor union and the firm in the same manner as is assumed in the monopoly union model(Dunlop, 1944; Oswald, 1985).
However, in reality, labor unions are not always influential in the determination of nominal
wages and employment. Even so, labor unions are exogenous factors. Their existence andobjectives can be derived from the workers’ rational behavior.
Therefore, in this paper, a labor market is modeled by efficiency wages instead of labor
unions, and embedded into a symmetric two-country macroeconomic model with labor
migration in order to infer as to which of the two regimes, non-cooperation or inter-government
cooperation in the monetary field, is advantageous to the policy authority and to the workers.2

of labor migration.
2

Assuming a dual labor market with efficiency wages, Carter (1999) analyzed the problem ofillegal migration, and Müller (2003) investigated the effects of migration on a small open
economy. Although their studies dealt with international migration under the assumption ofefficiency wages, they did not utilize open macroeconomic models.

2

This paper demonstrates that not only the utility of the policy authority but also that of theworkers is higher in the inter-government cooperative regime than in the non-cooperative
regime, provided that migration flows are sufficiently sensitive to the changes inreal-consumption wage differentials. In other words, in a symmetric two-country economy
with labor migration and efficiency wages, inter-government cooperation may prove to beadvantageous to the policy authority and to the workers.
The result that inter-government cooperation may prove to be advantageous to the policy
authority can be explained as follows: Since, in the inter-government cooperative regime,
policy authorities take into consideration the fact that the influence of a domestic monetary
expansion for reducing unemployment via an induced fall in the effective labor force will be
offset by an equal expansion abroad, they do not increase the money stocks in order to reduce
unemployment, even if the sensitivity of migration flows is large and the domestic monetary
expansion seems to be effective in reducing unemployment. This suggests that money stocks
are independent of the sensitivity of migration flows, thereby making unemployment and theconsumer price index independent of the sensitivity of migration flows in the inter-government
cooperative regime. On the other hand, in the non-cooperative regime, policy authorities do
not consider the fact that the influence of a country’s monetary expansion will be offset byanother country’s monetary expansion, and thus they unilaterally increase the money stocks in
an attempt to reduce unemployment through the reduction in the effective labor force. Thissuggests that, in contrast to the inter-government cooperative regime, the money stocks in the
non-cooperative regime depend on the sensitivity of migration flows, and they increase withincreases in the sensitivity of migration flows.

Consequently, in comparison to theinter-government regime, larger money stocks are observed in the non-cooperative regime for3the sufficiently large sensitivity of migration flows. The larger money stocks under the
non-cooperative regime reduce unemployment, which leads to a higher utility for the policy
authority. On the hand, they lead to an increase in the consumer price index, which makes theutility for the policy authority lower. In case of sufficiently large sensitivity of migration flows,
the latter negative effects outweigh the former positive effects, suggesting lower utility for thepolicy authority in the non-cooperative regime than in the inter-government cooperative regime.
Therefore, inter-government cooperation is advantageous to the policy authority in case of thesufficiently large sensitivity of migration flows.
The result that inter-government cooperation may also prove to be advantageous to theworkers can be explained as follows: Since the utility of workers decreases with increases in
the consumer price index, larger money stocks result in a lower utility for the workers under
non-cooperation. On the other hand, although the consumer price index is also dependent on
nominal wages, they take the same values in both the regimes. This is because the firm’s
wage-setting under the non-shirk condition and the workers’ utility maximization do differ
across regimes. Therefore, in case of sufficiently large sensitivity of migration flows, the utility
for the workers in the non-cooperative regime is lower than that in the inter-government
cooperative regime, implying that inter-government cooperation is advantageous to the workers.
The result shown in this paper implies that inter-government cooperation in the monetary
field appears to be preferable to non-cooperation in interdependent economies characterized byinternational migration and efficiency wages.
The result shown in this paper is in contrast to that shown by Agiomirgianakis (1998), since,in his model, inter-government cooperation may prove to be advantageous only to the policy
authority. However, this paper’s result is consistent with his argument that international4migration of labor changes the nature of monetary policy games played by monetary authorities
in interdependent economies.
The paper is organized as follows: Section II presents a symmetric two-country
macroeconomic model with labor migration and efficiency wages. A firm in each country is
assumed to be unable to detect shirking by workers perfectly and set nominal wages in order toprevent shirking.

Sections III and IV deal with the non-cooperative regime and theinter-government cooperative regime, respectively. Section V compares the utilities of thepolicy authority and the workers under the two regimes. Section VI includes the concludingcomments.

II. The Model
A two-country economy is assumed—each country has a single non-competitive labormarket and nominal wages are determined to prevent workers from shirking. Home andforeign countries are symmetric in their economic structures and are interdependent throughinternational trade of goods and international migration of labor. In each country, there areworkers, a firm, and a policy authority. Workers are not organized in labor unions.
Workers are assumed to migrate between home and foreign countries.

Accordingly,

effective labor force in the home country increases in comparison to its initial labor endowment,
if workers in the foreign country migrate to the home country, and it decreases if workers in thehome country migrate to the foreign country.
A firm in each country demands labor for producing a single kind of product. Since the firmcannot perfectly detect shirking by workers, it sets nominal wages in order to prevent shirking,treating workers’ effort and the money stock as given. Workers, on the other hand, attempt to5

maximize their utilities by manipulating their effort, treating the firm’s wage-setting and themoney stock as given.
Each country’s product is not only demanded in the same country but also in the other country
and is exported there.

The products of the home and foreign countries are imperfect

substitutes.
It is assumed that each country has its own money market and that money is the only financial
asset held by its residents.
The model is summarized by Equations (1)-(7). Structural equations in this paper are thesame as those employed by Jensen (1993), Zervoyianni (1997), Agiomirgianakis (1998), andShimada (2004). Variables are expressed in logs unless otherwise defined. Variables without
the asterisk represent the home country and variables with the asterisk represent 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 ≡ ex + p* − p.

(1)
(2)

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

(3)
(4)
(5)
(6)

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

(7)*Equation (1) presents the production functions of the firms in the home and foreign countries,
where y represents output, l represents the employment level, and a is a constant not
expressed in the log. Equation (2) presents the labor demand functions of the firms in thehome and foreign countries, where w represents nominal wages and p represents the
product price. They are derived from profit maximization of the firm in each country.
Equation (3) defines the real exchange rate z , where ex is the nominal exchange rate (home6currency price of foreign currency). Equation (4) presents the equilibrium condition of the
trade balances of the home and foreign countries, where b is a constant not expressed in thelog. The effects of the real exchange rates on the trade balance are assumed to be stronger thanthose of the difference in the national product of the two countries on the trade balance, so thatb is greater than 1.3 We define the home (foreign) country’s consumer price index q ( q * )as a weighted average of the price of the home (foreign) country’s product and the price of theforeign (home) country’s product in term of the home (foreign) currency, giving rise toEquation (5), where c is a constant not expressed in the log.4 Home and foreign countries’
real-consumption wages wc and wc* are given by Equation (6). Equation (7) presents theequilibrium conditions of the money markets in the home and foreign countries, where mdenotes the money stock. The policy authorities manipulate the money stocks.
An assumption is made in keeping with Agiomirgianakis (1998) that workers migrate
between the two countries due to real-consumption wages differentials. For example, if thereal-consumption wages in the home country are higher than those in the foreign country, thenworkers native to the foreign country migrate to the home country by d ( wc − wc* ) , where d ,which is a positive constant not expressed in the log, measures the sensitivity of migration flows
to changes in the real-consumption wage differentials.

3

See Shimada (2004), footnote 3, for the economic interpretation of b.

4

The home country’s consumer price index is P1− c ( EXP* )c and the foreign country’s

consumer price index is

P* ≡ exp p*.

P*1− c ( P EX )c ,where

P ≡ exp p,

EX ≡ exp ex,andResidents of the home (foreign) country are assumed to have a preference forthe goods produced in the home (foreign) country so that 0 < c < 1 2 .

7

Assumptions on international migration of labor lead to the following definitions of the homecountry’s effective labor force l f and the foreign country’s effective labor force l f * :l f ≡ l + d ( wc − wc* ),
l

*f

(8.1)

≡ l + d ( w − wc ), l = l ,
*

*
c

*

(8.2)

where l , which is a positive constant, denotes the domestic labor force in the absence of
migration, i.e., the initial labor endowment.
Through appropriate substitutions, the model of Equations (1)-(7) can be solved for l , l * ,y, y * , p, p* , z , q, q* , wc , wc* as functions of w, w* , m, m*. 5

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

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


(9.1)
(9.2)
(9.3)
(9.4)
(9.5)
(9.6)
(9.7)
(9.8)
(9.9)
(9.10)(9.11)

This paper assumes that a firm in each country cannot perfectly observe whether the workers
are shirking or not. Accordingly, as mentioned above, it sets nominal wages in a manner thatprevents shirking (Shapiro and Stiglitz, 1984). Given nominal wages, employed workers ineach country choose their effort level to maximize their expected lifetime utility.

5

See Shimada (2004) pp. 91–92 for the economic interpretation of Equations (9.1)-(9.11).

8

Since workers are not organized in labor unions, employed workers have no concern for thenumber of workers employed. They are only interested in their wages. If a representative
employed worker in each country does not shirk, his instantaneous utility can be measured byreal-consumption wages less effort. On the other hand, if he shirks, his instantaneous utility ismeasured by real-consumption wages. However, in such a case, he is detected and fired at theprobability ρ , 0 < ρ < 1.

The probability ρ is assumed to be the same for the twocountries. In addition, some of the employed workers in each country might separate fromjobs, even if they are not fired on the grounds of shirking. The separation rate, which is definedas the ratio of separations due to reasons other than shirking to the number of employed workers,
is given by β , 0 ≤ β < 1.

The separation rate β is assumed to be the same for the twocountries.
The expected lifetime utility of a representative employed shirker in the home country VES
is,rVES = wc + ( β + ρ )(VU − VES ),(10)

where r is the discount rate, which is assumed to be the same for two countries and VU is the
expected lifetime utility of a representative unemployed worker in the home country. Equation(10) can be rewritten as,
VES =wc + ( β + ρ )VU.
r+β +ρ

(10’)

On the other hand, the expected lifetime utility of a representative employed non-shirker inthe home country VEN is,rVEN = wc − ln e + β (VU − VEN ),(11)

where e, which is not expressed in the log, is effort of a representative employed non-shirker

9in the home country. Since employed non-shirkers exert a positive level of effort to someextent but cannot do so infinitely, the effort level of a representative employed non-shirker in thehome and foreign countries is assumed to lie between its minimum e min , e min > 1, and its
maximum e max , i.e., e min ≤ e, e* ≤ e max , where e* is effort of a representative employednon-shirker in the foreign country. Equation (11) can be rewritten as,
VEN =wc − ln e + βVU
.
r+β

(11’)

The employed workers in the home country may or may not shirk based on a comparison of
VEN and VES .

In order to prevent them from shirking, the firm in a home country has to set

nominal wages that are sufficiently high to ensure VEN ≥ VES .

However, because there is no

reason for the firm in a home country to pay more than what is essential to eliminate shirking, it
will set nominal wages such that VEN = VES (≡ VE ).

The following is obtained by substituting

Equations (10’) and (11’) into this condition:
wc = rVU + (r + β + ρ )

ln e
.
ρ

(12)

VU is, in turn, given by,W 
rVU = ln  + α (VE − VU ),Q
where W is the unemployment benefit in the home country, which is a constant not expressedin the log, Q ≡ exp q, and α , 0 ≤ α < 1, is the accession rate, the ratio of new hires in thehome country to the number of workers unemployed in the home country. The foreign country
is assumed to have the same accession rate as the one in the home country.
In order to simplify the analysis, this paper assumes that there are no separations or accessions

10

in the home and foreign countries, i.e., β = α = 0. 6

This paper also assumes that

W = W * = 1, where W * is the unemployment benefit in the foreign country, which is not
expressed in the log. Substituting these assumptions into Equation (12) and the equation for
VU , nominal wages in the home country become,r
w = 1 +  ln e.
ρ

(13.1)

Equation (13.1) shows that nominal wages in the home country increase with increases in effortof the employed workers in the home country and decrease with increases in the detection
probability.
The expected lifetime utility of a representative employed worker in the home country under
the non-shirk condition will take the form of,
VE = −

q ln e+.
rρ(14.1)

Equation (14.1) says that under the non-shirk condition, the expected lifetime utility of arepresentative employed worker in the home country decreases with increases in the homecountry’s consumer price index.7
By the same argument, nominal wages in the foreign country and the expected lifetime utilityof a representative employed worker in the foreign country are obtained under the non-shirk

6

Carter (1998) made a similar assumption. He assumed that workers in the high-wage sector

do not quit nor are they separated from their job.
7

This relation will be used to compare the utilities of the employed workers under two regimes

in Section V.

11condition as follows:r
w* = 1 +  ln e* ,ρ*q ln e*VE* = − +.
rρ

(13.2)(14.2)

According to Equations (13.1), (13.2), (14.1), and (14.2), nominal wages and the expected
lifetime utility of a representative employed worker are symmetric between the home andforeign countries.
The policy authority in each country attempts to attain full employment and the consumer
price index target, which is assumed to be 0. The utility function of the home country’s policy*
authority VPA and the utility function of the foreign country’s policy authority VPA
are of theforms,
VPA = −(l − l f ) 2 − hq 2 , h > 0,*VPA
= −(l * − l * f ) 2 − hq*2 ,(15.1)(15.2)

where h, which is a constant not expressed in the log, reflects the relative weight assigned by
the policy authorities to employment as against the consumer price index. Equations (15.1)
and (15.2) imply that policy authorities dislike deviations of actual levels of employment fromthe effective labor forces and changes in the consumer price index. These objectives areaccomplished by the manipulation of the money stocks.8

III. Non-Cooperation
This section deals with the non-cooperative regime where the policy authorities in the homeand foreign countries behave independently and the money stock, unemployment, and the8

Policy authorities are assumed to be able to control the money stocks perfectly.

12consumer price index under non-cooperation are determined.
The employed workers in the home country will choose their effort in order to maximize theexpected lifetime utility of a representative employed worker, treating e* , m and m* asgiven, i.e., they will solve,max −eq ln e, subject to (9.8), ∂e* ∂e = 0, ∂m ∂e = 0 and ∂m* ∂e = 0. 9+
rρThis gives us the optimal effort level of the employed workers in the home country ~e.
e max , if
e~ =  min e , if

(1 − a + ac b)(1 + r ρ ) > 1,
(1 − a + ac b)(1 + r ρ ) < 1.

(16.1)

Equation (16.1) suggests that if increases in the utility of the employed workers due to increases
in their effort and in the real-consumption wages are larger (smaller) than decreases in the utility
due to increases in their effort, they maximize their utility by exerting maximum (minimum)
effort.
The optimal effort level of the employed workers in the foreign country ~e * is obtained in asimilar manner.
e max , if
e~* =  min e , if

(1 − a + ac b)(1 + r ρ ) > 1,
(1 − a + ac b)(1 + r ρ ) < 1.

(16.2)

Equations (16.1), (16.2), (13.1) and (13.2) suggest that the optimal effort level and nominal
wages do not differ across countries.

9

As mentioned above, since the workers are not unionized, the utility of the employed workers

does not depend on the number of the employed workers. Accordingly, the employedworkers’ objective function can be presented by the utility of a representative employed worker.

13

The policy authority in the home country will set the money stock in order to maximize its
utility, treating e, e* , and m* as given, i.e., it will solve,
max VPA subject to (9.1), (8.1), and (9.8), ∂e ∂m = 0, ∂e* ∂m = 0 , and ∂m* ∂m = 0. 10mThis gives us the condition,
2ac 
ac f(l − l ) + h1 − a + q = 0.
1 + d 1 − a +
b 
b 




(17.1)

The foreign country’s policy authority maximizes its utility in a similar manner, giving rise to
the condition,
2ac  * * fac  *
(l − l ) + h1 − a + q = 0.
1 + d 1 − a +
b 
b 




(17.2)

Equations (17.1), (17.2), and w = w* suggest m = m*.

From this relation and Equations(17.1), (9.1), (8.1), (9.8), (13.1), and (16.1), the money stock is determined as follows:m = m* ={1 + d (1 − a + 2ac b) − ah(1 − a + ac b)}(1 + r ρ ) ln ~e + h(1 − a + ac b)a ln a
1 + d (1 − a + 2ac b) + h(1 − a )(1 − a + ac b)(≡ m NC ). 11(18)

According to Equation (18), the money stock in the non-cooperative regime depends on thesensitivity of migration flows to changes in real-consumption wage differentials. In the
non-cooperative regime, the policy authorities do not take into consideration the fact that the
influence of a domestic monetary expansion for reducing unemployment via the induced fall in

10

Equation (13.1) and ∂e ∂m = 0 imply that ∂w ∂m = 0, and Equation (13.2) and∂e* ∂m = 0 imply that ∂w* ∂m = 0.
11l = l * = ln a is assumed throughout the analysis.

14the effective labor force will be offset by an equal expansion abroad. Accordingly, the policy
authorities unilaterally increase the money stock in order to induce migration flows and thereby
to reduce unemployment. This implies that the money stock is dependent on the sensitivity of
migration flows.

Since policy authorities utilize migration flows to attain their policy

objectives, macroeconomic interdependence through migration flows is operative in the
non-cooperative regime, as pointed out by Agiomirgianakis (1998).
From Equations (9.1), (8.1), (13.1), (16.1), and (18), unemployment is derived. Equation(17.1) and unemployment give us the consumer price index.
h(1 − a + ac b){−(1 + r ρ ) ln ~e + a ln a}l − l f = l* − l* f =(≡ [l − l f ]NC ).
1 + d (1 − a + 2ac b) + h(1 − a)(1 − a + ac b){1 + d (1 − a + 2ac b)}{−(1 + r ρ ) ln e~ + a ln a}(≡ q NC ).
q = q* = −1 + d (1 − a + 2ac b) + h(1 − a )(1 − a + ac b)

(19)
(20)

Equations (19) and (20) suggest that the utilities for the policy authority and the employedworkers depend on the sensitivity of migration flows.

IV. Inter-government Cooperation
This section deals with the inter-government cooperative regime where the policy authorities
in the home and foreign countries behave cooperatively and the money stock, unemployment,
and the consumer price index under inter-government cooperation are determined.
Since the employed workers in the two countries behave independently and the employedworkers do not cooperate with the policy authority in each country, they solve the same
maximization problems as those under non-cooperation. Accordingly, the optimal effort levelof the employed workers in the home country is given by Equation (16.1), and the optimal effort
level of the employed workers in the foreign country is given by Equation (16.2).

15

Since the policy authorities in the two countries cooperate with each other, they will set theirmoney stocks such that they maximize the sum of their utilities, treating e and e* as given,
i.e., they will solve,*max
VPA + VPA,*m ,msubject to (9.1), (8.1), (9.8), (9.2), (8.2), (9.9), ∂e ∂m = 0, ∂e* ∂m = 0, ∂e ∂m = 0 and ∂e* ∂m* = 0.
*This gives us the following conditions:
ac 
ac *
1 + d (1 − a + 2ac b)
d (1 − a + 2ac b) * * f(l − l f ) +(l − l ),1 − a +  q − q = −
b 
b
h
h

(21.1)acac d (1 − a + 2ac b)
1 + d (1 − a + 2ac b) * * f− q + 1 − a +  q * =(l − l f ) −(l − l ).
b
b 
h
h

(21.2)
Equations (21.1), (21.2), and w = w* suggest m = m*.

From this relation and Equations(21.1), (9.1), (8.1), (9.8), (13.1), and (16.1), the money stock is determined as follows:m = m* ={1 − ah(1 − a)}(1 + r ρ ) ln ~e + h(1 − a)a ln a(≡ m IGC ).
2
1 + h(1 − a)(22)

According to Equation (22), in contrast to the non-cooperative regime, the money stock underinter-government cooperation does not depend on the sensitivity of migration flows to changes
in real-consumption wage differentials. In the inter-government cooperative regime, the policy
authorities are aware of the fact that the influence of a domestic monetary expansion for
reducing unemployment via the induced fall in the effective labor force will be offset by anequal expansion abroad. Accordingly, the policy authorities do not use the monetary policies
to order to induce migration flows and thereby to reduce unemployment. This suggests that themoney stock is independent of the sensitivity of migration flows. Since policy authorities do
not utilize migration flows to accomplish their policy objectives, macroeconomic
interdependence through migration flows is not operative in the inter-government cooperative16

regime, as pointed out by Agiomirgianakis (1998).
Unemployment is derived from Equations (9.1), (8.1), (13.1), (16.1), and (22). Equation(21.1) and unemployment give us the consumer price index.
h(1 − a ){−(1 + r ρ ) ln e~ + a ln a}(≡ [l − l f ]IGC ).
l − l f = l* − l* f =2
1 + h(1 − a)~− (1 + r ρ ) ln e + a ln a(≡ q IGC ).
q = q* = −2
1 + h(1 − a)

(23)
(24)

Equations (23) and (24) suggest that the utilities for the policy authority and the employedworkers are independent of the sensitivity of migration flows.

V. Comparison of the Two Regimes
This section compares the utilities of the policy authority and the employed workers under
non-cooperation and inter-government cooperation and shows which of the two regimes isadvantageous to the policy authority and to the workers.
For this purpose, a special case where migration flows are sufficiently sensitive to changes inreal-consumption wage differentials is considered, i.e., we take up the case where d is
sufficiently large.
The money stock in the non-cooperative regime for the sufficiently large sensitivity of
migration flows is approximated by taking the limit of m NC .
r
~ NC ).
lim m NC = 1 +  ln e~ (≡ m
d →∞
 ρ
A comparison of the money stocks under the two regimes for the sufficiently large sensitivityof migration flows reveals that,~ NC > m IGC .
m(25)

According to Equation (25), the monetary policy is more expansionary in the non-cooperative17

regime than in the inter-government cooperative regime, provided that the sensitivity of
migration flows is sufficiently large.

This is because, as mentioned above, in the

non-cooperative regime, the policy authorities increase the money stock in an attempt to reduce
unemployment. Moreover, the money stock becomes larger with increases in the sensitivity of
migration flows ( ∂m NC ∂d > 0 ). In contrast, in the inter-government cooperative regime, as
mentioned in the previous section, the money stock is independent of the sensitivity of migration
flows.12
In the non-cooperative regime, unemployment decreases while the consumer price index
increases as the migration flows become more sensitive ( ∂[l − l f ]NC ∂d > 0, ∂q NC ∂d > 0 ).
This is because the larger sensitivity of migration flows renders the monetary expansion more
effective in reducing unemployment, and a larger money stock results in an increase in the
consumer price index (see Equation 9.8).

On the other hand, in the inter-government

cooperative regime, the unemployment and the consumer price index are independent of thesensitivity of migration flows (see Equations 23 and 24).
Accordingly, in case of sufficiently large sensitivity of migration flows, unemployment is
lower

under

non-cooperation

than

under

inter-government

cooperation,i.e.,lim[l − l f ]NC > [l − l f ]IGC , leading to a higher utility for the policy authority in thed →∞non-cooperative regime, while the consumer price index is higher under non-cooperation than12

If we do not assume migration, monetary policies become more expansionary under
IGC

inter-government cooperation than under non-cooperation, i.e., m

> mNC

d =0

. This is theresult by Rogoff (1985). Accordingly, international migration changes the ranking of themoney stocks under the two regimes.

18

under inter-government cooperation, i.e., lim q NC > q IGC , leading to a lower utility for thed →∞policy authority in the non-cooperative regime.
Since the latter negative effects dominate the former positive effects, the utility for the policy
authority in the inter-government cooperative regime is higher than that in the non-cooperative
IGC
regime, i.e., VPA> VPANC , provided that the sensitivity of the migration flows is sufficiently

large.13 In other words, inter-government cooperation may prove to be advantageous to thepolicy authority. This result is the same as the one derived by Agiomirgianakis (1998).
Substituting Equations (9.8) and (9.9) into Equations (14.1) and (14.2), respectively, theexpected lifetime utility of the employed workers can be expressed as,
VE = VE* = −(1 − a )m + aw − a ln a ln ~
e
+
.
r
ρ

Since nominal wages and effort do not differ across regimes, the above equation suggests thatthe expected lifetime utility of the employed workers decreases with increases in the moneystock. Therefore, using Equation (25), we can derive the result that the expected lifetime utility

13

If we do not assume migration, the smaller money stock makes unemployment higher under

non-cooperation than under inter-government cooperation, leading to a lower policy authority’s
utility in the non-cooperative regime, whereas it makes the consumer price index lower under
non-cooperation than under inter-government cooperation, leading to a higher policy authority’s
utility in the non-cooperative regime. Since the former negative effects dominate the latter
positive effects, the policy authority’s utility is higher in the inter-government regime than in the
IGC
non-cooperative regime, i.e., VPA> VPANCd =0.

This suggests that international migration does

not change the ranking of the policy authority’s utilities under the two regimes.

19

of the employed workers in the inter-government cooperative regime is higher than that in the
non-cooperative regime, i.e., VEIGC > VENC , provided that the sensitivity of the migration flows
is sufficiently large. 14

In other words, inter-government cooperation may prove to beadvantageous to the employed workers.
Inter-government cooperation may also prove to be advantageous to the unemployed workers.
This is because the larger money stock under non-cooperation makes the consumer price index
higher, leading to the lower expected lifetime utility of a representative unemployed worker
under non-cooperation, i.e., VUIGC > VUNC .

Therefore, inter-government cooperation may

prove to be advantageous to all workers.
This result is different from the one derived by Agiomirgianakis (1998). In his model,
wages are determined by the negotiations between the firm and the labor union, and the labor
union’s utility takes the same value in the two regimes.15
Results derived from the comparison of the utilities of the policy authority and the workers in
the two regimes can be summarized as follows: Inter-government cooperation may prove to be

14

Since, as mentioned already, under the assumption of no migration, the money stock is larger

in the inter-government cooperative regime than in the non-cooperative regime, the expected
lifetime utility of the employed workers is higher in the non-cooperation regime than in theinter-government cooperative regime, i.e., VENC

d =0

> VEIGC .

Accordingly, internationalmigration changes the ranking of the employed workers’ expected lifetime utilities under thetwo regimes.
15

See Agiomirgianakis (1998) p.200 for the equality of the labor union’s utility under the two

regimes.

20

advantageous not only to the policy authority but also to the workers, provided that the workers
migrate between two countries, and in each country, nominal wages are determined by theefficiency wage hypothesis.

VI. Conclusions
Using a symmetric two-country macroeconomic model with international migration andefficiency wages, the utilities of the policy authority and the workers in the non-cooperative andinter-government cooperative regimes were compared, and inter-government cooperation was
found to be advantageous not only to the policy authority but also to the workers if migration
flows are sufficiently sensitive to changes in real-consumption wage differentials.16
Although this result is different from that derived by Agiomirgianakis (1998), it is inagreement with his argument that international migration of labor alters the nature of monetary
policy games played by monetary authorities in interdependent economies.
This paper’s result suggests that inter-government cooperation appears to be compatible with
open economies that are characterized by migration and efficiency wages.

Acknowledgements
I am deeply indebted to George M. Agiomirgianakis for providing many encouraging

16

This result does not directly imply that the monetary union may prove to be advantageous to

the policy authority and to the workers, since, even under inter-government cooperation, two
independent monetary authorities are being assumed. However, it seems very interesting to
examine the case of a single monetary authority.

21

comments and helpful suggestions. This paper was presented at the 4th annual meeting of theEuropean Economics and Finance Society. I am grateful to the participants at the conference
for helpful comments and valuable suggestions. Of course, any shortcomings of the paper are
my responsibility.

22References
Agiomirgianakis, G. M. (1996), International Macroeconomic Interdependence andInternational Migration of Labour, International Journal of Finance and Economics, 1,
133-147.
Agiomirgianakis, G. M. (1998), Monetary Policy Games and International Migration of Labor
in Interdependent Economies, Journal of Macroeconomics, 20, 243-266.
Agiomirgianakis, G. M. (1999), The Macroeconomics of Open Economies under Labor
Mobility, Ashgate, Aldershot.
Agiomirgianakis, G. M. (2000), Monetary Policy Games and International Migration in a Small
Open Economy, Review of International Economics, 8, 698-711.
Agiomirgianakis, G. M. and Zervoyianni, A. (2001), Macroeconomic Equilibrium with Illegal
Immigration.” Economic Modelling 18: 181-202.
Carter, T. J. (1998), Policy in a Two-Sector Efficiency Wage Model: Substituting Good Jobs for
Bad, Journal of Post Keynesian Economics, 20, 445-461.
Carter, T. J. (1999), Illegal Immigration in an Efficiency Wage Model, Journal of International
Economics, 49, 385-401.
Dunlop, J. T. (1944), Wage Determination under Trade Unions. New York: Macmillan.
Hamada, K. (1976), A Strategic Analysis of Monetary Interdependence, Journal of Political
Economy, 85, 677-700.
Jensen, H. (1993), International Monetary Policy Cooperation in Economies with Centralized
Wage Setting, Open Economies Review 4, 269-285.
Müller, T. (2003), Migration Policy in a Small Open Economy with a Dual Labor Market,
Review of International Economics, 11, 130-143.

23

Oswald, A. J. (1985), The Economic Theory of Trade Unions: An Introductory Survey,
Scandinavian Journal of Economics, 87, 160-193.
Rogoff, K. (1985), Can International Monetary Cooperation be Counterproductive? Journal ofInternational Economics, 18, 199-217.
Shapiro, C. and Stiglitz, J. E. (1984), Equilibrium Unemployment as a Worker Discipline
Device, American Economic Review, 74, 433-444.
Shimada, A. (2003), Kokusai rodo ido no makurokeizaigaku bunseki (Macroeconomic Analysis
of International Migration of Labor, Gogensha, Tokyo.
Shimada, A. (2004), Reducing the Inflow of Unskilled Foreign Workers, South-Eastern Europe
Journal of Economics, 2, 85-96.
Zervoyianni, A. (1997), Monetary Policy Games and Coalitions in a Two-Country Modelwith Unionised Wage Setting, Oxford Economic Papers, 49, 57-76.

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