Migration Decisions, Remittances, and Altruism
Akira Shimada
Faculty of Economics, Nagasaki University
Abstract
We can easily infer that remittances by the migrant will be large if he is very altruistic. However,remittances that an individual household expects to receive, i.e. expected remittances, will not benecessarily large even if the migrant is very altruistic since they depend not only on remittances by
the migrant, who has already moved to the host county, but also on how likely it is that ahousehold member, a potential migrant, actually migrates, and such a probability can be affectedby altruism. Previous studies focused mainly on the effects of altruism on remittances by the
migrant. However, what actually matter to the household are not remittances by the migrant, but
expected remittances, because a potential migrant does not necessarily migrate to the host country.
In this study, we investigate the effects of altruism on migration decisions by the potential migrant,
as well as on remittances by the migrant, to make clear the effects of altruism on expected
remittances. We show that if there are no migration costs, the potential migrant always migrates,and expected remittances, that are equal to remittances by the migrant in this case, are positively
related to altruism. However, if migration incurs costs, the potential migrant does not necessarily
migrate, and the potential migrant who is very altruistic is less likely to migrate. Accordingly,
expected remittances do not necessarily increase with the degree of altruism. In particular,
altruism may have negative impacts on expected remittances.

JEL Classification: D64; F22; F24; J61
Keywords: Migration decisions; Migration costs; Remittances; Altruism

Email address for correspondence: shimada@nagasaki-u.ac.jp
1

1 Introduction
In this study, we discuss how altruism affects migration decisions of the potential migrant andremittances by the migrant, and try to make clear the effects of altruism on remittances that anindividual household expects to receive.
Remittances have been increasing very rapidly, and they are contributing to many developing
countries by alleviating poverty and developing their economies (World Bank 2006; Chami et al.
2008). Accordingly, these countries are trying to increase remittances.1
Various hypotheses, including altruism, self-interest, co-insurance between migrants andhouseholds, and repayment of a loan from the family, have been put forward to explain why
migrants send remittances (Lucas and Stark 1985; Stark 1995; Rapoport and Docquier 2006; Ruiz
and Vargas-Silva 2009). Most of these are not mutually exclusive.
Among them, altruism is considered a major incentive, especially in countries where family ties
are strong (Cai 2003), although there are a lot of controversies on the role of altruism, and any
single motive cannot explain why migrants send remittances. We can easily understand that if ahousehold member who has already migrated to the host country and is working there is morealtruistic, remittances sent to other household members will be larger.
However, even if a potential migrant who is a household member is altruistic, other household
members will receive no remittances if he does not migrate. This suggests that remittances that anindividual household expects to receive from its member in abroad, i.e. expected remittances, do

1Reducing the remittance fees seems to be most effective for this purpose. However, it is not soeasy to manipulate them. Shimada (2010) discussed how the remittance-receiving countries canincrease its amount without manipulating the sending and receiving fees, and without affecting theinterests of agents involved in sending and receiving remittances.
2matter to other household members and that expected remittances depend not only on remittancesthat will be made by the migrant, who is already in the host country, but also on how likely ahousehold member still in the home country is to move to the host country.
Previous studies on altruism and remittances focused mainly on the effects of altruism on
remittances by the migrant who has already moved to and is working in the host country. Results
are mixed; however, a large number of studies attempted to show how altruism affects the amountof migrants’ remittances (Secondi 1997; Agarwal and Horowitz 2002; Cai 2003).
On the other hand, studies on the effects of altruism on migration decisions, more precisely, themigration probability of the potential migrant, have been relatively neglected. However, Tcha
(1995a) showed that strong altruism of the parent towards her children makes household
migration more likely. Similarly, Tcha (1995b) derived that the more altruistic the parent istowards her children, the more likely the family is to migrate to the higher income area. Tcha
(1996) tested the effects of altruism on migration decisions by using aggregated data from theUnited States and Korea. These studies suggest that altruism can also have effects on migration
decisions.
Accordingly, we can infer that altruism affects expected remittances, which is defined to be themigration probability of the potential migrant  remittances by the migrant, both through its
effects on remittances and through its effects on migration decisions.
Therefore, we explicitly take the effects of altruism on remittances by the migrant and on
migration decisions by the potential migrant into account in order to make clear how altruism
changes expected remittances to an individual household. No major attempt seems to have yet
been made to examine the effects of altruism on migration decisions by the potential migrant andon remittances by the migrant simultaneously in the same model.
We find that if there are no migration costs, the potential migrant always decides to migrate3whatever the degree of his altruism. Moreover, as the potential migrant becomes more altruistic oras the income difference between the host and home countries becomes larger, he sends larger
remittances to other household members after migration. In this sense, with no migration costs,
altruism has positive effects on expected remittances. On the other hand, if there are migration
costs, the potential migrant does not necessarily decide to migrate, and a very altruistic potential
migrant is less likely to migrate. Due to these effects, expected remittances do not necessarily
increase with the degree of altruism. In particular, when the income difference is sufficiently large,other household members receive smaller remittances if the potential migrant is very altruistic.
Therefore, with migration costs, altruism does not necessarily have positive impacts on expected
remittances. It may have negative effects on expected remittances.
The remainder of this paper is organized as follows. Section 2 first models a representative
household that includes a potential migrant and assumes that migration can be done without costs.
We then discuss how altruism affects remittances by the migrant, migration decisions by thepotential migrant, and thereby expected remittances. Section 3 assumes that migration requires
costs and investigates the effects of altruism. Section 4 presents concluding remarks.

2 Migration Decisions and Remittances with No Migration Costs
In this section we assume no migration costs and determine the amount of remittances thepotential migrant would send to his household in the home country after he migrated to the hostcountry. We also discuss whether the potential migrant will have an incentive for migration to thehost county or not, i.e. migration decisions (migration probabilities) when migration does not
require any costs. Combining these results, we calculate expected remittances, and try to find how
they are related to altruism when there are no migration costs.
We focus on a representative household whose members are assumed to be altruistic with each4other. We first consider the case where a member of the household, who is the only potential
migrant, has already chosen to migrate to the host country, and is now working in that country. A
representative migrant earns income by WM in the host country, and he may send part of his
income as remittances to his household in the home country altruistically by R , 0  R  WM .
Migrant’s income WM is exogenously given and assumed to be a constant. The migrant
determines the amount of remittances to maximize his utility. The migrant spends the rest of hisearned income WM  R in the host country, and his direct utility is ln(WM  R) . Following
Poirine (2006), we specify utility functions to obtain practical solutions. A representative
household, except the migrant, earns income by WH in the home country, and receives
remittances from the migrant. The household’s earned income is exogenously given and assumed
to be a constant. The household in the home country spends their earned income and remittances,and their direct utility is ln(WH  R) .
The utility of the migrant U M depends not only on his own direct utility but also on the utilityof other household members U H . Similarly, the utility of the household except the migrant
depends not only on their own direct utility but also on the utility of the migrant. We assume thatthe degree of altruism does not differ between the migrant and other household members. This is a
simplifying assumption. In the first chapter of Stark (1995), each individual has different degreesof altruism towards the other individual.

U M  (1   ) ln(WM  R)  U H ,U H  (1   ) ln(WH  R)   U M ,where  , 0    1, measures the degree of altruism of all household members.

These equations can be solved as,

U M  (1   ) ln(WM  R)   ln(WH  R)( U Mmigration ) ,U H  (1   ) ln(WH  R)   ln(WM  R) ,5

(1)

where    (1   ) . The larger  is, the larger  is. In other words, the more altruistic the
migrant is, the larger weight is put on the direct utility of other household members.
Assuming that WM  kWH , where k is a constant and k  1, i.e. income that can be earned in
the host country is k times as large as income that can be earned in the home country, we
differentiate the migrant’s utility with respect to remittances in order to determine their optimal
amount.
dU Mmigration
11
(  k  1)WH .
 R 
dR(kWH  R)(WH  R) 1 Accordingly, if   1 k , then dU Mmigration dR  0 . In this case, the migrant’s utility can be
maximized by not sending any remittances. In other words, the optimal amount of remittances by
the migrant is,R  1 k  0 .

(2a)

On the other hand, if   1 k , then the migrant sends remittances to maximize his utility. In
particular, the optimal amount of remittances by the migrant is,R  1 k  (1   ) 1 (  k  1)WH .

(2b)

These results suggest that even if the potential migrant moved to the host country, he would notnecessarily send remittances. Whether he will send remittances or not, and how much he will send
depend on the degree of altruism and the income difference. In particular, the more altruistic thepotential migrant is or the larger the income difference is, the more likely the potential migrant is
to send remittances after migration, since   1 k is more likely to happen. Remittances, if hesends the positive amount, are larger as he is more altruistic or as the income difference is larger,
i.e. dR  1 k d  0, dR  1 k dk  0.
By substituting Equation (2a) into Equation (1), the migrant’s utility in the case of   1 k isderived as,

6

U Mmigration  1 k  ln WH 1ln k .
1 (3a)Similarly, by substituting Equation (2b) into Equation (1), the migrant’s utility in the case of  1 k is derived as,
U Mmigration  1 k 


1
1 k
1 k
ln
WH 
ln
WH .
1  1 
1  1 (3b)

We next deal with the case where the potential migrant has already chosen not to migrate, and is
now working in the home country. In this case, we assume that the potential migrant earns thesame income as the rest of his household, i.e. WH . Since he does not send remittances, his direct
utility is ln WH . Other household members do not receive remittances, so that their direct utility isalso ln WH .
Accordingly, the utility of the potential migrant and the utility of other household members canbe represented as,
U M  (1   ) ln WH   U H ,U H  (1   ) ln WH  U M .
From these equations we find that the potential migrant and other household members have thesame utility.
U M  ln WM ( U Mnon  migration ) .

(4)

U H  ln WH .
The potential migrant determines whether to migrate by comparing the utility attainable bymigration and working in the host country with that attainable by remaining and working in thehome country. If   1 k , then from Equations (3a) and (4), the gain for the potential migrant by
migrating to the host country U Mmigration  U Mnon  migration is,7

U Mmigration  U Mnon  migration 

1ln k ( Uˆ M  1 k ) ,
1 

(5a)

where ln k  Uˆ M  1 k  k (1  k )1 ln k . Since Uˆ M  1 k  0 , the potential migrant with any degreeof altruism (   1 k ) attains the higher utility by migrating to the host country if migration does
not incur any costs. Moreover, the gain for the potential migrant due to migration is larger, the lessaltruistic the migrant is and the larger the income difference is ( dUˆ M  1 k d  0 ,dUˆ M  1 k dk  0 ). In a similar manner, if   1 k , then from Equations (3b) and (4), the gain
for the potential migrant is,
U Mmigration  U Mnon  migration 



1
1
ln

ln
 ln(1  k )( Uˆ M  1 k ) ,1  1  1  1 

(5b)where k (1  k )1 ln k  Uˆ M  1 k  ln(1  k )  ln 2 . Since dUˆ M  1 k d  0 and limUˆ M  1 k  0 , 1Uˆ M  1 k  0 . Accordingly, in this case as well, if there are no migration costs, the potential
migrant with any degree of altruism (   1 k ) attains the higher utility by migration, and thegain is larger, the less altruistic the migrant is and the larger the income difference is( dUˆ M  1 k d  0 , dUˆ M  1 k dk  0 ).
The gain for the potential migrant described by Equations (5a) and (5b) can be shown as Fig. 1.
All curves are downward-sloping and above the horizontal axis for the different values of k ,suggesting that the gain arising from migration decreases with the degree of altruism, but isalways positive. The curve with the large k lies above the curve with the small k .
Therefore, with no migration costs, the potential migrant with any degree of altruism has anincentive for migration and decides to migrate.2 Moreover, the less altruistic potential migrant has

2

Being different from the assumption made in the text, if the host country’s income is smaller

than the home country’s income, i.e. k  1 , then the gain is always negative, i.e. Uˆ M  1 k ,8

a stronger incentive since the gain is larger. This is contrasted with the effects of altruism on
remittances made by the migrant (see Equations 2a and 2b). To explain the reason intuitively, analtruistic potential migrant sends larger remittances after migration. This lowers the utility derived
from migration, and thereby reduces the gain from migration.
Accordingly, if there are no migration costs, the migration probability is one for any potential
migrant, and thereby, expected remittances are always equal to remittances by the migrant. Thissuggests that the household expects to receive no remittances if   1 k and that expected
remittances are larger as the potential migrant is more altruistic if   1 k . Accordingly, we
conclude that expected remittances are monotonically increasing with the degree of altruism.
Fig. 2 shows how expected remittances, which can be described by Equations (2a) and (2b)when there are no migration costs, are related to the degree of altruism and income differences.
Until  reaches 1 k , all curves are on the horizontal axis. After that, they become
upward-sloping. The curve with the large k lies above the curve with the small k .
To summarize results derived in this section, if there are no migration costs, the potential
migrant with any degree of altruism always decides to migrate. However, the migrant does notnecessarily send remittances. In particular, he does not send any remittances if he is less altruistic.
Remittances, if any positive amount is sent, are larger as the migrant is more altruistic. With nomigration costs, since the migration probability is one for any potential migrant, expected
remittances are always equal to remittances. This suggests that if the potential migrant is altruistic,Uˆ M  1 k  0 . Accordingly, if the host country’s income is smaller than the home country’s
income, no potential migrant has an incentive for migration, and no one decides to migrate.
Although this appears to be rather trivial, this is not an assumption on the migration decision of
the potential migrant, but the result derived from the utility maximization of the potential migrant.
9

expected remittances are larger. Therefore, without migration costs, altruism has positive effects
on expected remittances.

3 Migration Decisions and Remittances with Migration Costs

This section turns to the case where there are migration costs, and examines the effects ofaltruism on migration decisions and remittances in that situation to find how altruism affects
expected remittances.
If migration incurs costs, the potential migrant will decide whether to migrate by comparing thegain due to migration and its costs.
We denote the migration cost by C and assume that C is distributed uniformly between
ln k ( lim Uˆ M  1 k ) and ln(1  k )  ln 2 ( limUˆ M  1 k ) . This assumption is to exclude trivial
 0

 1

cases. If the migration cost is larger than ln k , then the potential migrant never decides to migrate,
and thereby expected remittances are zero. If it is smaller than ln(1  k )  ln 2 , then the potential
migrant always decides to migrate, and thereby expected remittances are equal to remittances,being the same as in the case where there are no migration costs.
When   1 k , the potential migrant will migrate to the host country if,C1
ln k ( Uˆ M  1 k ) .
1 

Accordingly, the migration probability MP  1 k is expressed as follows: 1MP  1 k  
ln k  ln(1  k )  ln 2{ln k  ln(1  k )  ln 2}1 .
1  
(6a)Equation (6a) suggests that a less altruistic potential migrant is more likely to migrate( dMP  1 k d  0 ). This occurs because the net gain for the potential migrant due to migration
Uˆ M  1 k  C is more likely to be positive if he is less altruistic. Accordingly, altruism seems to10have negative impacts on expected remittances through decreases in the migration probability.
However, as Equation (2a) shows, when   1 k , even if the potential migrant moved to the hostcountry, he would not send any remittances. Accordingly, when   1 k , the household cannot
expect to receive any remittances. In other words, expected remittances are,
MP  1 k  R  1 k  0 .

(7a)Therefore, in this case, altruism does not have any effects on expected remittances.
When   1 k , the potential migrant will migrate to the host country if,
C

1
1


ln

ln
 ln(1  k )( Uˆ M  1 k ) ,1  1  1  1 

and the migration probability MP  1 k is expressed as follows:
 1

1


MP  1 k  ln
ln
 ln 2 {ln k  ln(1  k )  ln 2}1 .
1  1  1  1 

(6b)Equation (6b) also suggests that a less altruistic potential migrant is more likely to migrate( dMP  1 k d  0 ). Moreover, as Equation (2b) indicates, remittances are positive when  1 k . Accordingly, the household expects to receive the positive amount of remittances. In
particular, expected remittances are,
 1



1
MP  1 k  R  1 k  ln
ln
 ln 2 {ln k  ln(1  k )  ln 2}1
1  1  1  1  (1   ) 1 ( k  1)WH .

(7b)

Therefore, in this case, altruism will have some effects on expected remittances.
Fig. 3 shows the migration probability described by Equations (6a) and (6b) for the different
values of k . All curves are downward-sloping. The curve with the large k lies below the curvewith the small k , suggesting that the potential migrant is less likely to migrate as the hostcountry’s income becomes larger. Accordingly, the effects of the income difference on the11migration probability when there are migration costs are opposite to the effects of the income
difference on an incentive for migration when there are no migration costs (see Equations 5a and5b).
Fig. 4 shows how expected remittances described by Equations (7a) and (7b) change with thedegree of altruism. For any income difference, expected remittances are zero at the lower degreeof altruism. After  exceeded 1 k , they first increase with the degree of altruism, and then takethe maximum value at a certain degree of altruism. After that, they decrease.
The relationship between expected remittances and altruism depends on the income difference.
According to Fig. 4, expected remittances are the same or larger for any degree of altruism if theincome difference is larger. However, if the income difference is large, expected remittances arelikely to be positive for most of the degree of altruism, and take the largest value at the lower
degree of altruism. On the other hand, if the income difference is small, expected remittances arelikely to zero for most of the degree of altruism, and take the largest value at the higher degree of
altruism. In Fig. 4 expected remittances take the largest values at   0.3 if k  10 ,   0.4 if
k  5 , and   0.65 if k  2 .

These facts suggest that even if the potential migrant is very altruistic, the household cannot
necessarily expect to receive larger remittances. When the income difference is very small,
expected remittances are likely to remain to be zero even if the potential migrant is very altruistic.
For example, if the host country’s income is only 1.1 times as large as the home country’s income,
expected remittances are zero until the degree of altruism exceeds about 0.9, indicating that
expected remittances can be the same for most of the degree of altruism. In other words, altruism
has no effects on expected remittances. On the other hand, when the income difference is verylarge, expected remittances are likely to decrease as the potential migrant becomes more altruistic.
For example, if the host country’s income is 100 times as large as the home country’s income,12

expected remittances decrease as the potential migrant becomes more altruistic if the degree of
altruism is larger than only about 0.19. This suggests that given the large income difference,
expected remittances to the household with the higher degree of altruism can be smaller than thoseto the household with the lower degree of altruism. In other words, altruism has negative effects
on expected remittances.
Therefore, if we take into account of the effects of altruism on migration decisions of thepotential migrant as well as on remittances by the migrant when migration incurs costs, altruism
does not necessarily increase the amount of remittances that the household expects to receive. It
may not change expected remittances, or it may decrease expected remittances.
To summarize the results derived in this section, if there are migration costs, the potential
migrant does not necessarily decide to migrate, and altruism is not always effective for thehousehold in the home country to receive larger remittances.

4 Concluding Remarks

We found that altruism has positive impacts on expected remittances through increases inremittances by the migrant working in the host country. We also found that altruism has negative
impacts on expected remittances through decreases in migration probabilities of the potential
migrant who is considering whether to migrate to the home country when there are migration
costs. Combining these effects, we derived the result that expected remittances to an individual
household do not increase monotonically with the degree of altruism. Altruism may have negative
impacts on expected remittances when migration requires costs.
Our results suggest that an individual household cannot necessarily expect to receive large(small) remittances because household members are very (less) altruistic with each other. Many
studies found that altruism alone cannot explain remittances by the migrant. On the other hand,13according to our results, altruism alone affects remittances that the household expects to receive invarious manners.

Acknowledgements

This paper was presented at the 9th International Conference of the European Economics andFinance Society held in Athens, June 2010. I am grateful to George M. Agiomirgianakis and otherparticipants for their valuable comments. Needless to say, any remaining errors are my
responsibility.

14

References

Agarwal, R. and A. W. Horowitz. (2002). “Are International Remittances Altruism or
Insurance? Evidence from Guyana Using Multiple-Migrant Households.” World
Development 30: 2033-2044.
Cai, Q. (2003). “Migrant Remittances and Family Ties: A Case Study in China.” International
Journal of Population Geography 9: 471-483.
Chami, R., A. Barajas, T. Cosimano, C. Fullenkamp, M. Gapen, and P. Montiel. (2008).
Macroeconomic Consequences of Remittances. Occasional Paper (International MonetaryFund) No. 259.
Lucas, R. E. B. and O. Stark. (1985). “Motivations to Remit: Evidence from Botswana.”
Journal of Political Economy 93: 901-918.
Poirine, B. (2006). “Remittances Sent by a Growing Altruistic Diaspora: How Do They
Grow Over Time?” Asia Pacific Viewpoint 47: 93-108.
Rapoport, H. and F. Docquier. (2006). The Economics of Migrants’ Remittances. In Handbook of
the Economics of Giving, Altruism and Reciprocity: Applications, ed. S.-C. Kolm and J. M.
Ythier, 1135-1198, Amsterdam: Elsevier Science B. V.
Ruiz, I. and C. Vargas-Silva. (2009). “To Send, or Not to Send: That is the Question. A Review of
the Literature on Workers’ Remittances.” Journal of Business Strategies 26: 65-90.
Secondi, G. (1997). “Private Monetary Transfers in Rural China: Are Families Altruistic?”
Journal of Development Studies 33: 487-511.
Shimada, A. (2010). “The Transfer of the Remittance Fee from the Migrant to the Household.”
Journal of Economic Integration 25: 613-625.
Stark, O. (1995). Altruism and Beyond. Cambridge: Cambridge University Press.
Tcha, M. (1995a). “Altruism, Household Size and Migration.” Economics Letters 49: 441-445.
15

Tcha, M. (1995b). “Altruism, Conflict, and the Migration Decision.” International Regional
Science Review 18: 289-312.
Tcha, M. (1996). “Altruism and Migration: Evidence from Korea and the United States.”
Economic Development and Cultural Change 44: 858-878.
World Bank. (2006). Global Economic Prospects: Economic Implications of Remittances andMigration. Washington, DC: World Bank.

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Fig. 1 Gain for the Potential MigrantFig. 2 Expected Remittances with No Migration Costs

Note: The home country’s income is assumed to be one.

17

Fig. 3 Migration Probability with Migration Costs

Fig. 4 Expected Remittances with Migration Costs

Note: The home country’s income is assumed to be one.

18