Strategic Remittances, Asymmetric Information, and Efficiency Wages
Akira Shimada
Faculty of Economics, Nagasaki University

Abstract
By assuming an economy that consists of labour-sending and labour-receiving countries, weinvestigate whether immigrants can actually improve their welfare by strategic remittances underasymmetric information, when wages are determined according to the efficiency wage hypothesis.
For this purpose, we assume two types of workers in the sending country: workers with high effort
and high productivity, and workers with low effort and low productivity. We also assume that
information on effort and productivity of individual immigrants is symmetric between immigrants
and firms in the receiving country if only one kind of worker in the sending country migrates,
whereas such information is asymmetric if both kinds of workers migrate simultaneously. We
show that there are cases in which both kinds of workers have incentives for migration andstrategic remittances, and thereby, neither of them can obtain higher wages. Therefore, incentives
for migration and remittances may prevent both types of immigrants from improving their welfare.
This result is in marked contrast with that by Stark (1995), which assumed that wages are
determined according to productivity. It showed that only skilled immigrants have incentives for
migration and strategic remittances and thereby they can realize higher wages. Our results suggest
whether immigrants can improve their welfare depends on how their wages are determined.

JEL Classification: D82; F22; F24; J24; J61

Keywords: Strategic Remittances; Immigrants; Symmetric information; Asymmetric information;
Efficiency wages
01. Introduction
This paper discusses how immigrant welfare is related to immigrant incentives for strategic
remittances under asymmetric information, and investigates whether incentives for migration andstrategic remittances always lead to higher immigrant welfare when wages are determinedaccording to the efficiency wage hypothesis. We assume an economy that consists oflabour-sending and labour-receiving countries. We also assume that there are two kinds of workers
in the sending country: workers with high effort and high productivity, and workers with low
effort and low productivity. We show that there exist cases in which both kinds of workers
simultaneously have incentives to migrate and to send remittances strategically, and as a result
neither of them can realize higher welfare. In other words, migration and strategic remittances
may lower immigrant welfare.
Workers’ remittances, i.e. current transfers by migrants who are employed in, and considered as
residents of, the countries that host them, have been growing rapidly around the world.1 They
have been increasing for over three decades, from US$6 billion in the early 1970s, to US$50
billion in the mid-1990s, to US$180 billion in 2006 (Chami et al. 2008, IMF 2008).
In response to this development, concern has grown regarding what causes remittances and how
they are used.2 One of the main debates on these problems is about whether remittances are madefor investment and development purposes, or for consumption and non-development purposes.

1

Other categories in the balance of payments that are highlighted when compiling statistics onremittances are employee compensation and migrants’ transfers. According to Chami et al. (2008),
workers’ remittances most closely conform to the notion that researchers and policy makers havein mind when discussing remittance flows.
2

Lucas and Stark (1985) is a representative study that tried to find motivations for remittances.
1Some empirical studies favour the former argument. They find that a significant part ofremittances is devoted to investment, in order to improve the life of the immigrant families or theirown life after they return to their home countries.3 Other empirical studies are in favour of thelatter argument. According to their findings, most remittances are spent on consumption, and for
purposes that are not directly related to the development of the immigrant home countries.4
This debate is likely to remain inconclusive since the arguments made by each author dependon the region and the period under study. In addition, it is not easy for us to distinguish investment
spending from consumption spending, and investment does not always lead to the development
and consumption sometimes contributes to the development.5 Accordingly, we cannot easily

3

According to Durand et al. (1996), migrants in America do not engage in unrestrained consumer

spending. Rather, these immigrants do what they can to improve their own and their families’ wellbeing, given their social and economic constraints. Taylor (1999) argued that a number of
empirical studies from diverse regions support the new economics of labour migration hypothesis,that migration and remittances may set in motion a development dynamic, by easing capital andrisk constraints faced by households in an imperfect market environment, and creating income
growth linkages. Woodruff and Zenteno (2001) found that remittances are responsible for almost
20% of the capital invested in microenterprises throughout urban Mexico.
4

Massey and Parrado (1994) found that most of the money sent by Mexican migrants in America

to their home country is spent on consumption. According to the study on Turkish migrants by
Koc and Onan (2004), migrant savings are generally used to satisfy basic consumption needs.
Semyonov and Gorodzeisky (2008) revealed, by data drawn from four major labour-sending areasin the Philippines, that remittances are used mostly for consumption purposes.
5

For example, spending on foodstuffs is usually considered to be consumption. However, a more2

divide motives for remittances distinctively into investment and development purposes andconsumption and non-development purposes.
This paper focuses instead on a theoretical issue regarding the strategic motive for remittances
under asymmetric information, as discussed by Stark (1995). 6 He explained immigrant
remittances not by investment or consumption purposes, but by the strategic motive.
Stark (1995) assumed a two-country economy consisting of a labour-sending country and alabour-receiving country. There are two kinds of workers in the sending country. Skilled workers
are those who have high productivity. Some of them migrate to the receiving country, where they
are called skilled immigrants. Unskilled workers are those who have low productivity. Some ofthem migrate to the receiving country, where they are called unskilled immigrants. Firms in thesending country are perfectly aware of the individual productivities of workers, but firms in thereceiving country are not necessarily perfectly aware of the individual productivities ofimmigrants.
When only skilled (unskilled) workers migrate to the receiving country, firms in the receiving
country know perfectly that all immigrants are skilled (unskilled). Accordingly, in the receiving
country, information on the individual productivities of immigrants is symmetric between
immigrants and firms. In this case, immigrant wages are determined to be equal to their actual
productivities. Therefore, whatever productivity workers have, workers in the sending country
experience no gains and no losses by migrating to the receiving country.

nutritious diet makes workers healthier and more productive. In this case, consumption will leadto the development.
6

The issues related to international migration under asymmetric information are also treated by

Katz and Stark (1986, 1987, 1989) and Stark (1991, part 4).
3

On the other hand, when skilled and unskilled workers migrate to the receiving country
simultaneously, firms in the receiving country are not perfectly aware of the individual
productivities of immigrants. Accordingly, in the receiving country, information on the individual
productivities of immigrants is asymmetric between immigrants and firms. In this case, firms set
immigrant wages at the average of skilled and unskilled immigrant productivities. This is because
firms in the receiving country cannot distinguish skilled immigrants from unskilled immigrants.
As a result, under asymmetric information, skilled immigrants are paid less than theirproductivity, whereas unskilled immigrants are paid more than their productivity. In other words,
skilled immigrants lose, whereas unskilled immigrants gain.
In such circumstances, skilled immigrants may try to dissuade unskilled workers from
migrating to the receiving country since, in this way, information in the receiving country will
become symmetric, and thereby skilled workers will be paid wages that correspond to their actual
productivity. For this purpose, skilled workers may migrate to the receiving country, and may sendpart of their wages to unskilled workers for strategic reasons: to make them stay in the sending
country.
On the other hand, even in the same circumstance, unskilled immigrants have no incentives tosend strategic remittances. This is because, as explained already, due to the asymmetry of
information, they are paid higher wages than their actual productivity if they are with skilled
immigrants. Their wages would be reduced to those that conform to their actual productivity ifthey had dissuaded skilled workers from migrating to the receiving country by making strategic
remittances to them.
Therefore, in Stark’s (1995) model, there is no possibility that both skilled and unskilledworkers in the sending country simultaneously have incentives to migrate to the receiving country
and to make remittances strategically.
4Stark’s analysis is very interesting, in that remittances are made only to satisfy immigrantpresent pecuniary interests. The reasons for remittances are not directly related either to present or
future gains to immigrant families arising from investment or consumption, or to future gains forthe immigrants themselves arising from investment.
In his analysis, as mentioned, wages are set equivalent to the actual productivity of workers
under symmetric information, and it is natural to assume that wages are determined by the averageof different immigrant productivities under asymmetric information. However, how wages andemployment are determined is not modelled formally. Accordingly, it is not necessarily clear
whether workers are maximizing their utilities, or whether firms are maximizing their profits.
In this paper, we adopt the efficiency wage hypothesis to model the labour market formally. We
assume explicitly that firms determine wages in such a manner as to maximize their profits, evenunder asymmetric information.
By doing so, we try to show that there are cases in which skilled and unskilled workers
simultaneously have incentives for migration and strategic remittances. In such cases, neither
skilled nor unskilled immigrants can earn higher wages than those under asymmetric information,
since both types of workers migrate to the receiving country simultaneously, and as a result
information becomes asymmetric between immigrants and firms. Therefore, under efficiency
wages, incentives for strategic remittances themselves can prevent all immigrants from improving
their welfare.
The remainder of this paper is organized as follows: Section 2 models a two-country economy.
Section 3 determines immigrant wages under asymmetric information and symmetric information.
Section 4 examines whether incentives for strategic remittances always increase immigrant
welfare. Section 5 presents concluding comments.

5

2. The ModelIn this section, we model an economy that consists of labour-sending and labour-receiving
countries in which wages are determined according to the efficiency wage hypothesis.
We assume that there are two types of workers in the sending country: workers with high effort
and high productivity, and workers with low effort and low productivity. Workers of one type aresubstitutes for workers of another type as factors of production. Both types of workers are notvoluntarily unemployed in the sending country. Since both types of workers in the sending
country can obtain higher wages by migrating to the receiving country and being employed there,some of workers of each type are willing to migrate to the receiving country. However, even if
workers migrate to the receiving country, they exert the same level of effort and productivity there
as they do in the sending country.7 All native workers in the receiving country exert the samelevel of effort and productivity. They are assumed not to migrate. In both countries wages are
determined according to the efficiency wage hypothesis. We assume that, due to insufficientlabour availability in the receiving country, it accepts immigrants. The two countries are connected
through labour migration. They may also be related through remittances from workers of one typewho are native to the sending country and migrated to the receiving country to workers of anothertype who remain in the sending country.
Workers in the sending country whose effort and productivity are high, exert effort as much aseH if they do not shirk, and their per capita effective labour is also equal to eH , which isassumed to be a constant. Workers in the sending country whose effort and productivity are low

7

Of course this is a simplifying assumption. In general, effort and productivity depend on theplace where labour is supplied. Workers may exert high effort and high productivity in thereceiving country if the working conditions there are better than in the sending country.
6exert effort as much as eL if they do not shirk, and their per capita effective labour is also equal
to eL , which is assumed to be a constant.
In the sending country, there is no asymmetry of information on workers’ effort andproductivity between workers and firms, in the sense that firms are perfectly aware of effort andproductivity of individual workers, and they can distinguish workers with high effort and highproductivity from workers with low effort and low productivity.8 As a result, workers withdifferent levels of effort and productivity are always treated as different inputs by firms in thesending country.
The firms in the sending country produce goods according to the following production function:

A* (eH MH* + eL ML* )a , A* > 0, 1 > a* > 0,*

where A* is a constant, M H* is employment of workers with high effort and high productivity
in the sending country, and M L* is employment of workers with low effort and low productivity
in the sending country. Physical capital is fixed and does not appear explicitly in the production
function.
The profits of the firms in the sending country π * are defined as follows:π * ≡ A* (eH M H* + eL M L* ) a − wH* M H* − wL* M L* ,*where wH* is wages for workers with high effort and high productivity employed in the sending
country, and wL* is wages for workers with low effort and low productivity employed in thesending country. Throughout the analysis the product price in the sending country is assumed to
be one.
Demand functions for workers are derived in a manner such that, the profits of the firms in thesending country are maximized.

8This is not true for firms in the receiving country.
7

wH* = eH A*a* (eH M H* + eL M L* ) a −1.

(1H)

wL* = eL A*a* (eH M H* + eL M L* ) a −1.

(1L)

*

*

As mentioned already, we determine wages according to the efficiency wage hypothesis of
Shapiro and Stiglitz (1984). In particular, wages for workers with effort ei , where i = H , L, inthe sending country, are determined so as to prevent shirking by these workers.
We represent the expected lifetime utility of a representative worker with effort ei who is
employed and shirks in the sending country, by VE*Si ,rVE*iS = wi* + ( β + ρ )(VU*i − VE*iS ),where β is the separation rate, which is defined as a ratio of separation of employed workers
with effort ei in the sending country due to reasons other than shirking to the number of
employed workers with effort ei in the sending country, ρ is the detection rate, which is a
probability for an employed worker with effort ei in the sending country of being detected andfired by firms in the sending country due to shirking, and r is the discount rate. The separation
rate, the detection rate and the discount rate are assumed to be the same for both types of workers
and even after migration, and they do not change throughout the analysis. The first term on theright-hand side represents the instantaneous utility under shirking. The second term represents thechanges in the expected lifetime utility arising from being unemployed due to shirking, or forreasons other than shirking.9 VU*i is the expected lifetime utility of a representative unemployedworker in the sending country with effort ei , which is given by

rVU*i = α i (VE*iS − VU*i ),where αi is the accession rate for unemployed workers with effort ei , which is defined as the9This equation corresponds to Equation (1) in Shapiro and Stiglitz (1984), i.e. it is thefundamental asset equation for a shirker.
8ratio of new hires of unemployed with effort ei in the sending country to the number of theunemployed with effort ei in the sending country. Unemployment benefits are assumed to be 0
to simplify the analysis. The right-hand side represents the changes in the expected lifetime utility
arising from being reemployed.10 In steady state, the accession rate α i is determined to equalize
the number of workers with effort ei who flow into unemployment in the sending country to thenumber of workers with effort ei who flow out of unemployment in the sending country. We
also represent the expected lifetime utility of a representative worker with effort ei who is,
employed, and does not shirk, in the sending country, by VE*Ni
rVE*iN = wi* − ei + β (VU*i − VE*iN ).
The first and second terms on the right-hand side represent the instantaneous utility under
non-shirking, and the third term represents the changes in the expected lifetime utility arising frombeing unemployed for reasons other than shirking.11
When workers in the sending country do not migrate to the receiving country, steady state
wages for workers with effort ei in the sending country that satisfy their respective non-shirking
conditions VE*iN = VE*iS are derived as follows:
W ( M H* , M H* ) ≡ 1 + [{M H* ( M H* − M H* )}β + r ] ρ ,W ( M L* , M L* ) ≡ 1 + [{M L* ( M L* − M L* )}β + r ] ρ ,where M H* is the number of workers with high effort and high productivity who are initiallyendowed in the sending country, and M L* is the number of workers with low effort and low
productivity who are initially endowed in the sending country. They are given exogenously. These

10

This equation corresponds to Equation (6) in Shapiro and Stiglitz (1984).

11This equation corresponds to Equation (2) in Shapiro and Stiglitz (1984), i.e. it is thefundamental asset equation for a non-shirker.
9equations can be rewritten as follows:
wH* = eHW ( M H* , M H* ), M H* ≤ M H* ,(2H)wL* = eLW ( M L* , M L* ), M L* ≤ M L* ,(2L)

where ∂wi* ∂M i* > 0 and ∂wi* ∂M i* < 0 for i = H , L.
We assume that the initial endowments of workers in the sending country do no differ between
the two types, i.e. M H* = M L* ( ≡ M * ).
Under this assumptions, from the equilibrium conditions of the labour markets in the sending
country, which are provided by Equations (1H) and (2H) and Equations (1L) and (2L), theemployment of workers with high effort and high productivity and the employment of workers
with low effort and low productivity are derived to be the same, i.e. M H* = M L* (≡ M * ) to satisfy,

A*a* (eH + eL ) a −1 M **a * −1= W ( M * , M * ).

(3)

By substituting M * , which satisfies Equation (3), into Equations (2H) and (2L), equilibrium
wages for workers with high effort and high productivity in the sending country when none ofthese workers migrate and equilibrium wages for workers with low effort and low productivity inthe sending country when none of these workers migrate are determined as follows:

12

wH* = eHW ( M * , M * ).

(4H)

wL* = eLW ( M * , M * ).

(4L)12In the following sections, we deal with cases in which some of workers in the sending country

migrate to the receiving country. In such cases, equilibrium wages in the sending country are
different from Equations (4H) and (4L) because the number of workers of each type remaining inthe sending country is smaller than M *. However, to determine the amount of remittances
needed to dissuade workers in the sending country from migration, we have to know how muchmoney they can earn in the sending country when none of them migrate.
10

Both types of workers in the sending country can obtain higher wages by migrating to thereceiving country and being employed there. Accordingly, among the same type of workers,
s* M * , where 0 < s* < 1, are willing to migrate to the receiving country. 13 They are notvoluntarily unemployed in the receiving country.
As for the patterns of migration from the sending to receiving countries, there are two
possibilities. One possibility is that workers of different types migrate to the receiving country at
the same time. Another possibility is that workers of one type migrate to the receiving country, andworkers of another type do not migrate, but stay in the sending country.
When workers of different types migrate to the receiving country simultaneously, we assume
that firms in the receiving country are not perfectly aware of effort and productivity of individual
immigrants, and that they cannot distinguish immigrants with high effort and high productivity
from immigrants with low effort and low productivity. In this case, asymmetry of information
prevails between immigrants and firms in the receiving country with regard to effort andproductivity of individual immigrants. As a result, firms in the receiving country have noalternative but to treat all immigrants, even with different levels of effort and productivity, as thesame input. In such a case, immigrant wages that satisfy their non-shirking condition do notnecessarily correspond to their actual effort and productivity.
On the other hand, when only workers of the same type migrate to the receiving country, firms

13

Even if wages are higher in the receiving country and employment probability does not differ

across immigrants, not all workers in the sending country will migrate to the receiving country
since, for example, migration costs differ among workers. Some workers may have experiences ofliving abroad. It will be easy for such workers to migrate than those who have no experiences ofliving abroad.
11

in the receiving country have perfect information on effort and productivity of individual
immigrants. Accordingly, there is no asymmetry of information between immigrants and firms
with regard to effort and productivity of individual immigrants. As a result, in this case immigrant
wages are determined in a manner that reflects their actual effort and productivity. However, forthis case to happen, workers of another type have to be provided with some incentives to stay inthe sending country because, as the analysis by Stark (1995) shows, some of them may be able toearn higher wages by moving to the receiving country and finding a job there.

3. Immigrant Wages in the Receiving Country under Asymmetric Information and under
Symmetric Information

In this section, we determine immigrant wages in the receiving country in the case in which
both types of worker in the sending country migrate to the receiving country simultaneously, andtherefore information on effort and productivity of individual immigrants is asymmetric between
immigrants and firms in the receiving country; and in the case in which only workers of the same
type migrate, and information is therefore symmetric.
First, we deal with a case in which both types of workers migrate to the receiving country
simultaneously. In this case, workers in the sending country migrate to the receiving country by
2 s * M * . As already assumed, firms in the receiving country do not know whether an individual

immigrant has high effort and high productivity or low effort and low productivity. As aconsequence, firms treat all immigrants as the same input.
In order to employ immigrants, firms have to set their effort and productivity at a certain level.
This is because firms cannot determine immigrant employment and wages without assuming theireffort and productivity.
Firms in the receiving country set immigrant effort and productivity to eH or eL to maximize
profits. They do not choose other values for immigrant effort and productivity. This can be12explained as follows: If firms consider immigrant effort and productivity to be lower than eL anddetermine their wages accordingly, all immigrants will shirk. Even in this case firms pay wages,
but nothing is produced. If firms consider immigrant effort to be between eL and eH , anddetermine their wages accordingly, immigrants with e H will shirk and immigrants with eL will
be overpaid.14 Firms can produce the same amount of output at lower cost if they assume
immigrant effort and productivity to be eL . If firms consider immigrant effort to be higher thaneH and determine their wages accordingly, no immigrants will shirk, but all of them will be
overpaid.15 Firms can produce the same amount of output at lower cost if they assume immigrant
effort and productivity to be eH .
In one case, in which firms in the receiving country take immigrant effort and productivity to behigh and determine immigrant wages accordingly, we assume that the production function takes
the following form:~~~
N Ha1 (eH τ H M H + eLτ L M H ) a 2 , a1 , a2 > 0, a1 + a2 < 1, 0 < τ L ,τ H < 1, τ H + τ L = 1,~~
where N H , M H are the numbers of native workers and immigrants employed in this case, τ H

is the ratio of employed immigrants with high effort and high productivity among all employed
immigrants, which is a constant and given independently of how firms assume immigrant effort
and productivity; and τ L is the ratio of employed immigrants with low effort and low
productivity among all employed immigrants, which is also a constant and given independently of
how firms assume immigrant effort and productivity. Per capita effective labour of native workers

14

Even if immigrants with eL are overpaid, their effort and productivity do not increase, andproduction does not increase.
15

Even if all immigrants are overpaid, their effort and productivity do not increase, andproduction does not increase.
13

in the receiving country is one. Although employed immigrants with low effort and low
productivity are overpaid, as already assumed, their effort and productivity remain unchanged. No
employed immigrants shirk in this case. Accordingly, the total effective input of immigrants is~~
eHτ H M H + eLτ L M H . As expressed by the production function, native workers and immigrants are

assumed to be complements as factors of production, in the sense that the marginal product of one
input is positively related to the employment of the other input. As in the sending country, physicalcapital is fixed and does not appear explicitly in the production function. Accordingly, the profits
of firms in this case are defined as follows:
~1

~

~

~

~

~ N −w~ M ,π~H ≡ N Ha (eHτ H M H + eLτ L M H ) a − w
N
H
M
H
2

H

H

~
~
where w
N H is native worker wages in this case and wM H is immigrant wages in this case.

Throughout the analysis, the product price in the receiving country is assumed to be one.
Firms demand native workers and immigrants in such a manner as to maximize profits. We
have already assumed that there are insufficient native workers in the receiving country.16
Accordingly, it would be better for us to assume that the initial endowment of native workers in~~
the receiving country N is not large, so that ∂π~H ∂N H > 0 for N H ≤ N . Consequently,
native worker employment is determined to be (1 − v) N , where v, 0 < v < 1, is the ratio of
native workers who prefer to be voluntarily unemployed among native workers initially existent in~
the receiving country. On one hand, we assume that firms can choose M H , such that~~
∂π~H ∂M H = 0 for M H ≤ 2 s * M * . Under these assumptions, firms demand immigrants in the16

If a country does not have enough skilled labour, it will try to accept skilled immigrants.

However, in actual economies, it is not easy to accept skilled immigrants as much as needed.
Under such a circumstance, in order to increase production, the country will accept immigrantsthat are complements to skilled native workers.
14

following manner:~ a 2 −1
~ = (1 − v) a1 N a1 (e τ + e τ ) a 2 a M
w
.
MH
H H
L L
H
2

(5)

On the other hand, steady state wages for immigrants, which satisfy their non-shriking
condition when firms take their effort to be high, are~**~ = e W (MwMHH
H 2 , s M ),(6)

where the separation rate, the detection rate and the discount rate for immigrants are assumed tobe the same as those in the sending country.
Utilizing Equations (5) and (6), immigrant employment is determined to satisfy the following
condition:~~(1 − v ) a1 N a1 (eHτ H + eLτ L ) a 2 a2 M Ha 2 −1 = eHW ( M H 2 , s * M * ).

(7)~
By substituting M H , which satisfies Equation (7), into Equation (6), we can derive immigrant

wages in the case in which firms take their effort and productivity to be high.
In the other case, in which firms in the receiving country take immigrant effort and productivity
to be low and determine immigrant wages accordingly, we assume that the production function
takes the following form:~~
N La1 (eLτ L M L ) a 2 ,~~where N L , M L are the numbers of native workers and immigrants employed in this case. Since,~in this case, immigrants with high effort shirk, the total effective input of immigrants is eLτ L M L .

Accordingly, the profits of firms in this case are defined as follows:
~1

~

~

~

~ N −w~ M ,π~L ≡ N La (eLτ L M L ) a − w
N
L
M
L
2

L

L

~
~
where w
N L is native worker wages in this case and wM L is immigrant wages in this case.

Native worker employment is the same as in the case where immigrant effort and productivity~~
are taken to be high, and M L is determined to satisfy ∂π~L ∂M L = 0. Firms demand

immigrants in the following manner:15

~ a 2 −1~ = (1 − v) a1 N a1 (e τ ) a 2 a M
w
.
ML
L L
L
2

(8)

On the other hand, steady state wages for immigrants that satisfy their non-shriking condition
when firms take their effort to be low are,~**~ = e W (Mw
MLL
L 2 , s M ).

(9)

Utilizing Equations (8) and (9), immigrant employment is determined to satisfy the following
condition:~~(1 − v ) a1 N a1 (eLτ L ) a 2 a2 M La 2 −1 = eLW ( M L 2 , s * M * ).

(10)~
By substituting M L , which satisfies Equation (10), into Equation (9), we can derive immigrant

wages in the case where firms take their effort to be low.
In the former case, where immigrant effort and productivity is taken to be high by firms, bothtypes of immigrants are exerting their effort, but immigrants with low effort and low productivity
are overpaid. Whereas, in the latter case, in which firms take immigrant effort and productivity to
be low, immigrants with low effort and low productivity are paid corresponding to their actual
effort and productivity, but immigrants with high effort and high productivity are not exerting theirefforts. Since we cannot determine a priori in which case firms can obtain higher profits, we must
examine both cases.
We now turn to another situation, in which only workers of the same type migrate to thereceiving country. In this case, the number of immigrants is s*M *. As already assumed, undersymmetric information, firms in the receiving country are perfectly aware of effort andproductivity of individual immigrants.
If only workers with high effort and high productivity migrate, the production function of firms
in the receiving country is
N Ha1 (eH M H ) a 2 ,where N H , M H are the numbers of native workers and immigrants employed in this case. The
16

total effective input of immigrants is eH M H since immigrants do not shirk.
Firms demand native workers and immigrants in such a way as to maximize profits:π H ≡ N Ha (eH M H ) a − wN N H − wM M H ,
1

2

H

H

where wN H is native worker wages in this case and wM H is immigrant wages in this case. They
are employed to satisfy N H = (1 − v) N and ∂π H ∂M H = 0 .
Therefore, in the case in which only the workers with high effort and high productivity migrate,
immigrants are demanded in the following manner:wM H = (1 − v) a1 N a1 eHa2 a2 M Ha 2 −1.

(11)

On the other hand, their steady state wages that satisfy their non-shriking condition are

wM H = eHW ( M H , s*M * ).

(12)

Utilizing Equations (11) and (12), immigrant employment is determined to satisfy the following
condition:(1 − v) a1 N a1 eHa 2 a2 M Ha 2 −1 = eHW ( M H , s*M * ).

(13)

By substituting M H , which satisfies Equation (13), into Equation (12), we can derive
immigrant wages in the case in which all of them are with high effort and high productivity.
Similarly, if only workers with low effort and low productivity migrate, their steady state wages
that satisfy their non-shirking condition are

wM L = eLW ( M L , s*M * ),(14)

where wM L , M L are immigrant wages and employment in this case. Immigrant employment inthis case is determined to satisfy the following condition:(1 − v) a1 N a1 eLa 2 a2 M La 2 −1 = eLW ( M L , s*M * ).

(15)

By substituting M L , which satisfies Equation (15), into Equation (14), we can derive
immigrant wages in the case in which all of them are with low effort and low productivity.
Summarizing the results derived in this section, under asymmetric information, immigrant17

wages are determined to satisfy Equations (6) and (7) or Equations (9) and (10). Under symmetric
information, wages for immigrants with high effort and high productivity are determined to satisfy
Equations (12) and (13), and wages for immigrants with low effort and low productivity are
determined to satisfy Equations (14) and (15).

4. Strategic Remittances

In this section, we show that there are cases in which both types of workers in the sending
country have incentives for migration and strategic remittances simultaneously, and that, as aresult, neither of these workers can improve their welfare.
First, we consider the case in which firms in the receiving country can obtain higher profits byassuming high effort and high productivity for immigrants under asymmetric information. In this~ .
case, as shown by Equations (6) and (7), immigrant wages are w
MH~
Let us assume that w
M H are higher than wM H . If this is so, the right-hand side of Equation(7) must be larger than the right-hand side of Equation (13), i.e.
~eH W ( M H 2 , s*M * ) > eH W ( M H , s*M * ).
~This suggests that M H 2 > M H . At the same time, the left-hand side of Equation (7) also mustbe larger than the left-hand side of Equation (13), i.e.
~
(1 − v ) a1 N a1 (eHτ H + eLτ L ) a 2 a2 M Ha 2 −1 > (1 − v ) a1 N a1 eHa 2 a2 M Ha 2 −1.

~
We can rewrite this as {τ H + (eL eH )τ L }a2 (1− a2 ) > M H M H . Since {τ H + (eL eH )τ L }a 2 (1− a 2 )
< 1,

~
~
~
M H M H < 1. However, this contradicts M H 2 > M H , since M H M H < 1 implies~~~
M H < M H , whereas M H 2 > M H implies M H > M H . Therefore, in the case where firms

take immigrant effort and productivity to be high, immigrants with high effort and highproductivity can obtain higher wages when only these workers migrate to the receiving country,
i.e.
18

~ .
wM H > w
MHThis suggests that workers with high effort and high productivity in the sending country can earnhigher wages in the receiving country if they are able to prevent the migration of workers with low
effort and low productivity. In this way, they are able to make information symmetric between
themselves and firms in the receiving country.
~
Let us also assume that w
M H are higher than wM L . If this is so, the right-hand side ofEquation (7) must be larger than the right-hand side of Equation (15), i.e.
~eH W ( M H 2 , s * M * ) > eLW ( M L , s * M * ).
~If the difference between eH and eL is sufficiently small, M H 2 > M L . At the same time, theleft-hand side of Equation (7) must also be larger than the left-hand side of Equation (15), i.e.
~
(1 − v ) a1 N a1 (eHτ H + eLτ L ) a 2 a2 M Ha 2 −1 > (1 − v ) a1 N a1 eLa 2 a2 M La 2 −1.

~
We can rewrite this as {(eH eL )τ H + τ L }a2 (1− a 2 ) > M H M L . If a2 is sufficiently small,~{(eH eL )τ H + τ L }a 2 (1− a 2 ) is approximately equal to one. In such a case, M H M L is likely to be~smaller than one. However, this contradicts M H 2 > M L . Therefore, in this case again,

immigrants with low effort and low productivity are likely to obtain higher wages when only theseworkers migrate to the receiving country, i.e.
~ .
wM L > w
MHThis suggests that workers with low effort and low productivity in the sending country are likely
to earn higher wages in the receiving country if they can prevent the migration of workers withhigh effort and high productivity. In this way, they can make information symmetric between
themselves and firms in the receiving country.
Summarizing the results derived in the case in which firms in the receiving country take
immigrant effort and productivity to be high under asymmetric information, it is possible that not
only for immigrants with high effort and high productivity, but also for immigrants with low effort
19and low productivity, to obtain higher wages under symmetric information, i.e.
~ .
wM H , wM L > w
MH

(16)

Equation (16) is in contrast to the relation derived by Stark (1995). In his model, as mentioned
already, only skilled workers can obtain higher wages under symmetric information. Equation (16)suggests that workers of one type may be able to realize higher wages in the receiving country ifthey can make workers of another type stay in the sending country.
We now turn to another case, in which firms in the receiving country can obtain higher profits
by assuming low effort and low productivity for immigrants under asymmetric information. In this~ .
case, as shown by Equations (9) and (10), immigrant wages are w
ML~
Let us assume that w
M L are higher than wM H . If this is so, the right-hand side of Equation(10) must be larger than the right-hand side of Equation (13), i.e.
~eLW ( M L 2 , s * M * ) > eHW ( M H , s * M * ).
~This suggests that M L 2 > M H . At the same time, the left-hand side of Equation (10) must also

be larger than the left-hand side of Equation (13), i.e.
~
(1 − v ) a1 N a1 (eLτ L ) a 2 a2 M La 2 −1 > (1 − v) a1 N a1 eHa 2 a2 M Ha 2 −1.
~~
We can rewrite this as (eLτ L eH ) a 2 (1− a 2 ) > M L M H . Since (eLτ L eH ) a 2 (1− a 2 ) < 1, M L M H~< 1. However, this contradicts M L 2 > M H . Therefore, in the case in which firms take

immigrant effort and productivity to be low, immigrants with high effort and high productivity canobtain higher wages when only these workers migrate to the receiving country, i.e.
~ .
wM H > w
ML

This suggests that workers with high effort and high productivity in the sending country can earnhigher wages in the receiving country if they are able to prevent the migration of workers with low
effort and low productivity. In this way, they are able to make information symmetric between
themselves and firms in the receiving country.
20

~
Let us also assume that w
M L are higher than wM L . If this is so, the right-hand side ofEquation (10) must be larger than the right-hand side of Equation (15), i.e.
~eLW ( M L 2 , s * M * ) > eLW ( M L , s * M * ).
~This suggests that M L 2 > M L . At the same time, the left-hand side of Equation (10) must belarger than the left-hand side of Equation (15), i.e.
~
(1 − v ) a1 N a1 (eLτ L ) a 2 a2 M La 2 −1 > (1 − v) a1 N a1 eLa 2 a2 M La 2 −1.
~~
We can rewrite this as τ La 2 (1− a 2 ) > M L M L . Since τ La 2 (1− a 2 ) < 1, M L M L < 1. However, this~contradicts M L 2 > M L . Therefore, in this case too, immigrants with low effort and low

productivity can obtain higher wages when only these workers migrate to the receiving country,i.e.
~ .
wM L > w
ML

This suggests that workers with low effort and low productivity can also earn higher wages in thereceiving country if they are able to prevent the migration of workers with high effort and highproductivity. In this way, they are able to make information symmetric between themselves andfirms in the receiving country.
Summarizing the results derived in the case where the firms in the receiving country take
immigrant effort and productivity to be low under asymmetric information, it is possible that not
only immigrants with high effort and high productivity, but also immigrants with low effort andlow productivity, can obtain higher wages under symmetric information, i.e.
~ .
wM H , wM L > w
ML

(17)

Equation (17) also contrasts with the relation derived by Stark (1995). Equation (17) suggests thatworkers of one type may be able to realize higher wages in the receiving country if they can makeworkers of another type stay in the sending country.
Whether firms maximize profits by assuming immigrant effort and productivity to be high or to21

be low, workers with high effort and high productivity will try to dissuade workers with low effort
and low productivity from migrating to the receiving country. At the same time, workers with low
effort and low productivity will try to dissuade workers with high effort and high productivity
from migrating to the receiving country.
Strategic remittances may make this possible. In particular, if workers with high effort and highproductivity (workers with low effort and low productivity) earn sufficiently high wages in thereceiving country when they are there alone, workers with high effort and high productivity(workers with low effort and low productivity) may send part of their wages to workers with low
effort and low productivity (workers with high effort and high productivity) to induce them to stayin the sending country.
To explain this possibility more concretely, we show that workers with high effort and highproductivity are likely to prevent the migration of workers with low effort and low productivity,
by making remittances to the latter workers. Wages for the former workers excluding remittances
will be even higher than those earned under asymmetric information.
As Equations (16) and (17) show, the difference between immigrant wages with high effort andhigh productivity under symmetric information and under asymmetric information, i.e.
~ , where i = H , L, is positive. Each employed immigrant with high effort and highwM H − wMiproductivity can earn more by this amount by preventing the migration of potential immigrants
with low effort and low productivity.17 It goes without saying that the number of employed17

Of course, as we mention below, the net gain for an employed immigrant due to prevention of~ since,the migration of workers with low effort and low productivity is smaller than wM H − w
Mito do so, immigrants with high effort and high productivity have to send part of their wages toworkers with low effort and low productivity.
22

immigrants with high effort and high productivity is smaller than the number of those immigrants
existent in the receiving country, i.e. M H < s *M *. However, the difference between immigrant
wages under asymmetric information and wages for workers with low effort and low productivity~ − w* , which is equal to the cost needed to make each potential
in the sending country, i.e. w
MiL
immigrant with low effort and low productivity stay in the sending country, can be positive andsufficiently small for an appropriate choice of A*. Accordingly, the total gain for employed

immigrants with high effort and high productivity due to the prevention of the migration of~ ) M , may be larger
potential immigrants with low effort and low productivity, i.e. ( wM H − w
MiH~ − w* ) s*M *. 18
than its total cost, which is equal to or smaller than ( wMiL~ )M > (w~ − w* ) s*M *.
( wM H − w
Mi
H
Mi
L

(18)

If Equation (18) holds, workers with high effort and high productivity will remit part of theirwages to potential immigrants with low effort and low productivity in the sending country. This isbecause, even if they make remittances, employed immigrants with high effort and high~ − w* ) s*M * M , than those
productivity can earn higher wages, which are equal to wM H − ( wMiLH~ . Accordingly, by migration andearned under asymmetric information, which are equal to w
Miremittances, workers with high effort and high productivity can obtain higher welfare. At the sametime, by receiving remittances, potential immigrants employed in the sending country exerting18~ − w* ) s*M * is the amount of remittances that is necessary in the case in which all(w
MiL

potential immigrants with low effort and low productivity are employed in the sending country
and will be employed in the receiving country. However, all potential immigrants with low effort
and low productivity will not be employed in either country. In case they are employed at thesame probability in the two countries, the amount of money needed to prevent migration will be~ − w* ) s*M *.
smaller than ( wMiL23low effort and low productivity can earn higher wages in the sending country, which are equal tothose earned in the receiving country.19 Accordingly, without migrating, they can attain higher
welfare in the sending country by receiving remittances. Therefore, it is likely that they lose
motivation to migrate.20
All these suggest that under Equation (18), workers with high effort and high productivity have
incentives for both migration and remittances.
We next show that workers with low effort and low productivity are likely to prevent the
migration of workers with high effort and high productivity, by making remittances to the latterworkers. Wages for the former workers excluding remittances will be even higher than thoseearned under asymmetric information.
As Equations (16) and (17) show, the difference between immigrant wages with low effort andlow productivity under symmetric information and under asymmetric information, i.e.
~ , where i = H , L, is positive. Each employed immigrant with low effort and low
wM L − wMiproductivity can earn more by this amount by preventing the migration of potential immigrants

19~ − w*The total earnings of a potential immigrant with low effort and low productivity are w
MiL

if he is not employed in the sending country.
20

By receiving remittances, the total earnings of an employed potential immigrant with low effort~ . Accordingly, without moving to the receiving country, heand low productivity become w
Mi
can earn the same wages in the sending country as he would earn if employed in the receiving
country under asymmetric information. Similarly, by receiving remittances, the total earnings of~ − w* .
an unemployed potential immigrant with low effort and low productivity become w
MiH

Accordingly, without moving to the receiving country, he can earn money without supplying
labour.

24

with high effort and high productivity.21 It goes without saying that the number of employed
immigrants with low effort and low productivity is smaller than the number of those immigrants
existent in the receiving country, i.e. M L < s*M *. However, since the difference between
immigrant wages under asymmetric information and wages for workers with high effort and high~ − w* , which is equal to the cost needed to makeproductivity in the sending country, i.e. w
MiHeach potential immigrant with high effort and high productivity stay in the sending country, can bepositive and sufficiently small for an appropriate choice of A*. Accordingly, the total gain for
employed immigrants with low effort and low productivity by preventing the migration of~ ) M may be larger than its total
workers with high effort and high productivity, i.e. ( wM L − w
MiL~ − w* ) s*M *. 22
cost, which is equal to or smaller than ( wMiH~ )M > (w~ − w* ) s*M *.
( wM L − w
Mi
L
Mi
H

(19)

If Equation (19) holds, workers with low effort and low productivity will remit part of theirwages to potential immigrants with high effort and high productivity in the sending country. This21

Of course, as we mention below, the net gain for an employed immigrant due to prevention of~ since,the migration of workers with high effort and high productivity is smaller than wM L − w
Mito do so, immigrants with low effort and low productivity have to send part of their wages toworkers with high effort and high productivity.
22~ − w* ) s*M * is the amount of remittances that is necessary in the case in which all(w
MiH

potential immigrants with high effort and high productivity are employed in the sending country
and will be employed in the receiving country. However, all potential immigrants with high effort
and high productivity will not be employed in either country. In case they are employed at thesame probability in the two countries, the amount of money needed to prevent migration will be~ − w* ) s*M *.
smaller than ( wMiH25

is because, even if they make remittances, employed immigrants with low effort and low~ − w* ) s*M * M , than those
productivity can earn higher wages, which are equal to wM L − ( wMiHL~ . Accordingly, by migration andearned under asymmetric information, which are equal to w
Miremittances, workers with low effort and low productivity can obtain higher welfare. At the sametime, by receiving remittances, potential immigrants employed in the sending country exerting
high effort and high productivity can earn higher wages in the sending country, which are equal tothose earned in the receiving country.23 Accordingly, without migrating, they can attain higher
welfare by receiving remittances.24
All these suggest that under Equation (19), workers with low effort and low productivity also
have incentives for both migration and remittances.
As explained already, Equations (18) and (19) hold simultaneously for an appropriate choice of
A* . 25 This suggests that it is possible that not only workers with high effort and high productivity,

23

The total earnings of a potential immigrant with high effort and high productivity are~ − w* if he is not employed in the sending country.
w
Mi
H
24

By receiving remittances, the total earnings of an employed potential immigrant with high

~ . Accordingly, without moving to the receiving country,
effort and high productivity become w
Mihe can earn the same wages in the sending country as he would earn if employed in the receiving
country under asymmetric information. Similarly, by receiving remittances, the total earnings of~ − w* .
an unemployed potential immigrant with high effort and high productivity become w
MiL

Accordingly, without moving to the receiving country, he can earn money without supplying
labour.
25

We have already shown that Equation (16) holds if the difference between eH and eL issufficiently small and a2 is also sufficiently small. Moreover, if the difference between eH and26

but also workers with low effort and low productivity, have incentives for migrating to thereceiving country and making remittances simultaneously.
However, in such a case, since both kinds of workers migrate to the receiving country
simultaneously, information on effort and productivity of individual immigrants becomesasymmetric between immigrants and firms in the receiving country. Since firms do not know
effort and productivity of individual immigrants perfectly, they set immigrant wages to be equal to~ , where i = H , L. As a result, neither immigrants with high effort and high productivity norw
Mi~ . This suggests
immigrants with low effort and low productivity can earn wages higher than w
Mithat incentives for migration and strategic remittances may prevent the improvement of all
immigrant welfare.
This result is in stark contrast with that derived by Stark (1995). As mentioned already, in
Stark’s model, skilled and unskilled immigrants do not, at the same time, have incentives for
migration and remittances. Therefore, there is no possibility at all that incentives for migration andstrategic remittances do more harm than good to all immigrants.
Summarizing the results derived in this section, if we assume efficiency wages and firms
determine wages to maximize their profits then even under asymmetric information, there arecases in which incentives for migration and strategic remittances make it impossible for both
immigrants with high effort and high productivity, and immigrants with low effort and low
productivity, to improve their welfare. Therefore, incentives for migration and remittances prevent
both types of immigrants from improving their welfare. This result is contrasted with the one

eL is sufficiently small, wL* and wH* are approximately equal. Accordingly, by choosing A*

appropriately, we can make the left-hand side of Equation (18) larger than its right-hand side, andthe left-hand side of Equation (19) larger than its right-hand side, simultaneously.
27

derived by Stark (1995).

5. Conclusions

This paper investigated the role of remittances in improving immigrant welfare, assuming a
two-country economy in which wages are determined according to the efficiency wage hypothesis.
In particular, we sought to clarify whether strategic remittances always lead to higher immigrant
welfare under different wage settings.
We demonstrated that, under efficiency wages, it is possible that not only workers with higheffort and high productivity but also workers with low effort and low productivity, have incentives
for migration to the receiving country and making strategic remittances, and, as a result, neither ofthese two types of workers can obtain higher wages than those obtainable under asymmetric
information in the receiving country. Therefore, incentives for migration and strategic remittances
may prevent all immigrants from obtaining higher welfare. Our result contrasts with that of Stark(1995), in which wages are set equal to productivity, and incentives for migration and remittances
can lead to higher welfare of skilled immigrants.
Our results suggest that incentives for strategic remittances do not always improve immigrant
welfare, which depends on how immigrant wages are determined.

28

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