ISSN 1833-4474

Remittances for Economic Development: the Investment

Perspective
Thanh Le
School of Economics
The University of Queensland
St. Lucia, QLD 4072, Australia
Tel: 61-7-3346 7053; Fax: 61-7-3365 7299
Email: t.le2@uq.edu.au
This version: June 2011
Based on the economic theory of the family, this paper constructs a model of
remittances where the migrant, besides sending money to his family, also invests in
his home country. The investment is looked after by a family member in return for
some monetary compensation. The model focuses on two different cases: state-
contingent transfers (transfers are tied to investment outcomes) and fixed transfers
(transfers are mainly of altruistic motive). As the migrant derives utilities from
consumption, his consumption-investment decision is driven by preferences and future
investment prospects. The transfers are to increase with both business encouraging
and income compensatory effects.
JEL classification: D31, J61, O15, O16.
Keywords: remittances, investment, financial development, income transfer.

1

Remittances for Economic Development: the Investment
Perspective
Thanh Le
School of Economics
The University of Queensland
St. Lucia, QLD 4072, Australia
Tel: 61-7-3346 7053; Fax: 61-7-3365 7299
Email: t.le2@uq.edu.au
This version: June 2011
Abstract
Based on the economic theory of the family, this paper constructs a model of remittances
where the migrant, besides sending money to his family, also invests in his home country. The
investment is looked after by a family member in return for some monetary compensation. The
model focuses on two different cases: state-contingent transfers (transfers are tied to
investment outcomes) and fixed transfers (transfers are mainly of altruistic motive). As the
migrant derives utilities from consumption, his consumption-investment decision is driven by
preferences and future investment prospects. The transfers are to increase with both business
encouraging and income compensatory effects.
JEL classification: D31, J61, O15, O16.
Keywords: remittances, investment, financial development, income transfer.


2

1. Introduction
Recently, there has been a substantial increase in remittance flows from developed countries
to developing countries. An estimate by the World Bank (2007) indicates that total
remittances to developing economies amounted up to $240 billion in 2007 from $31.2 billion
in 1990. The actual numbers are surely much larger given the fact that official statistics miss
informal inflows. This information suggests that remittances are potentially a good source of
finance for economic development, especially for the poorest countries.
There is a considerable debate on the role of remittances to economic development process of
developing countries. Remittance supporters posit that remittances help improve recipients
standard of living and encourage households investment in education and healthcare.
Remittances are also necessary for financing imports and investment. However, the negative
view of remittances indicates that remittances can fuel inflation and reduce recipients
incentive to work which are obviously harmful for growth. Empirical studies on the economic
impact of remittances also produce mixed results (see, for example, Glytsos, 2002; Leon-
Ledesma and Piracha, 2004; Chami et al., 2005).
This paper contributes to the above mentioned debate over the economic impact of
remittances by constructing a theoretical model in which remittances act like a capital inflow
besides an income transfer from overseas. The model is set up based on the economic theory
of the family
1
where the relationship between a migrant and his family back home is
characterized by both altruism (as suggested by Johnson and Whitelaw, 1974) and business
(as pointed by Lucas and Stark, 1985).
2
The relationship is altruistic in the sense that the
migrant cares about his family and makes his utility dependent on the family members utility.

1
There is a big literature on the economic theory of family, especially on the aspect of private income transfers
such as Bernheim et al. (1985), Cox (1987), and Chami (1998).
2
For simplicity, the migrants family back home is assumed to consist of only one member.
3

It is also business-like because the migrant makes investment in his home country and asks
the family member to look after the investment project on his behalf. In return, the migrant
offers the family member some monetary transfer. In this framework, remittances include two
different flows: a capital flow and an income transfer flow. As a result, remittances are not
only compensatory but also business motivated. To make it more general, this paper
differentiates two different situations. In the first situation, the migrant ties the transfer to the
outcome of the investment project. This creates an incentive for the recipient to exert more
managerial effort. In the second situation, the migrant makes a transfer simply based on his
altruistic motive.
The results of the model can be summarized as follows. Despite having different settings, the
two above mentioned situations yield qualitatively close findings. They both reveal that
remittances are not only a pure income transfer which help increase consumption at home but
also an important source of finance for economic development through investment channel.
Here, remittances increase with business encouraging as well as income compensatory
motives. In particular, the migrant will invest more in his home country if the expected gain
from making extra investment is high enough. He will send more monetary payment home if
his income is higher, when his family member is poor, or when he wants to encourage his
relative to exert more effort in managing his investment project. The family member will act
more positively on the migrants project when she cares more about the migrant and when the
promised monetary rewards are higher.
Generally, this paper is well placed into the literature on remittances. It is linked to the theory
on altruistic motivations for remittances (e.g. Johnson and Whitelaw, 1974; Chami et al.,
2005) as well as the theory on self-interested remittances as a means of business (e.g. Lucas
and Stark, 1985). Although not study here, this paper recognizes the theory that considers the
family as a source of insurance company that provides members with protection from any
4

income shocks (Poirine, 1997; Ilahi and Jafarey, 1999) or a bank that finances the migration
of the members (Stark, 1991; Agerwal and Horowitz, 2002; Gubert, 2002).
3
By modeling
explicitly financial development as a factor that encourages investment from remittance flow,
this paper also fits well in the literature on financial market and economic development (e.g.
Giuliano and Ruiz-Arranz, 2005; Mundaca, 2009).
The rest of this paper is structured as follows. Section 2 sets up the theoretical model on
remittances and investment motives. Section 3 documents some implications and further
discussions on the results of the model in Section 2. Section 4 ends the paper with some
concluding remarks.
2. Theoretical models for analyzing remittances
Consider an economy which consists of a large number of identical two-person families that
live for two periods.
4
In each family, one person has already migrated to a foreign country at
the beginning of the first period. He earns an exogenous income y
m
in that foreign country.
The other member of the family remains in the home country. She works in the domestic
labor market and earns an exogenous income y

. In the first period, the migrant makes an

investment I in his home country
5
and asks the family member at home to take care of this
investment.
6
Assume that the investment outcome is subject to uncertainty. For simplicity,
there are only two possible outcomes for this investment, either high outcome I
h
=
0
h
I, 0
h
> 1 with probability p or low outcome I
I
= 0
I
I, u < 0
I
< 1 with probability

3
Rapoport and Docquier (2005) provide a comprehensive review on the economics of remittances.
4
This is a simplified assumption that does not affect the model results. The game can be allowed to play
repeatedly.
5
Of course, there is always an option of investing overseas. However, dealing with this option is beyond the
scope of this paper.
6
Unlike the model by Chami et al. (2005) where the migrant send remittances home as a pure altruistic transfer,
in this current model, the migrant is allowed to invest in his home country from overseas. This is a crucial
assumption that makes this paper distinct from other papers in the literature which commonly assume an
altruistic motive for remittances.
5

(1 p). Here, the probability of high investment outcome occurring is dependent on the
favorable conditions in the financial market o (such as more investment opportunities or low
risks) as well as the effort level c in managing the investment project of the family member
at home. Assume p(o, c) is an increasing and concave function of its two arguments,
p
i
(. ) > u, p
ii
(. ) < u.
7
In the second period, the migrant makes a transfer to the family
member at home (from now on this family member is referred to as the recipient). This paper
focuses its analysis on two different practical situations: investment state-contingent transfers
and fixed transfers.
2.1. State-contingent transfers
It can be imagined as there exists an implicit agreement between the migrant and the
recipient, for example, an implicit agreement between a brother and a sister, in which the
brother working overseas seeks for helps from his sister at home in managing the investment
project and offers her some monetary rewards in return. As the migrant is away, he does not
know or observe his sisters effort level directly. However, he can see the outcome of the
investment project at the end of the first period which depends on his sisters effort. The
migrant is then assumed to tie the monetary rewards to the investment results. If the project is
successful, the migrant transfers a large amount of money back home I
h
to the recipient. If it
is not successful, only a small amount of money I
I
is transferred.
8
Both of these amounts are
known to the recipient ex ante.
The migrant derives utility from his consumption which is equal to y
m
I in the first period
and equal to either y
m
+I
h
I
h

or y
m
+I
I
I
I
depending on whether the investment
project is successful or not in the second period. His expected utility is:

7
An example for such a function is p(c) = Ao
1
2
,
c
1
2
,
where A > u is a constant.
8
For a simple case, I
I
is very much like an altruistic transfer while I
h
is business related transfer.
6

E(u
m
) = u(y
m
I) +pu(y
m
+I
h
I
h
) +(1 p)u(y
m
+I
I
I
I
) +[E(u

) (1)
where u < [ < 1 is the discount factor for his relative utility. Here, the migrant not only
cares about the outcome of his investment project at home but is also altruistic towards his
sister. As a result, his utility depends on the recipients utility u

. The utility function is

assumed to be increasing, concave, and twice differentiable u
i
(. ) > u, u
ii
(. ) < u. The
migrant benefits more if his investment is more profitable so I
h
I
h
> I
I
I
I
. In other
words, he extracts more surpluses if the investment is successful.
The recipient also derives utility from consumption. Her expected utility is:
E(u

) = u(y

) +p(c)u(y

+I
h
) +|1 p(c)]u(y

+I
I
) :(c) (2)
where :(c) denotes disutility of effort expended on the migrants investment project and
:
i
(c) > u, :"(c) > u.
For simplicity of notation, define u
mh
u(y
m
+I
h
I
h
), u
mI
u(y
m
+I
I
I
I
), u
h

u(y

+I
h
), u
I
u(y

+I
I
). Here, u
mh
> u
mI
, u
h
> u
I
but u
mh
i
< u
mI
i
, u
h
i
< u
I
i

according to the assumption on the increasing and concave utility function.
The model can be solved by backward induction. First, the recipient chooses her effort level
that maximizes her expected utility given her labor income and the monetary reward
contingent on the outcome of the investment project that she manages. The migrant then
makes a decision on the investment and the transfer based on the realization of the investment
project.
The first order condition for the recipients choice of effort is:
7

L(0
r
)
c
= p(c)|u
h
u
I
] :(c) = u (3)
This equation states that the marginal benefit (in utility term) of exerting effort is equal to the
marginal disutility of expending that effort level. Solving the equation implicitly delivers
c

= c(y

, I
h
, I
I
). This leads to the following proposition.
Proposition 1.
c

r
< u,
c

1
h
> u,
c

1
l
< u,
c

m
= u.
Proof. See Appendix.
That is, the recipients effort decreases with her income. As the monetary rewards are known
to both parties ex ante, raising the rewards of high investment outcome or reducing the
transfer of low investment outcome would increase the recipients effort (the business
encouraging effect). The commitment of transferring a positive amount when investment
outcome is low creates a disincentive for effort since it provides more certainty of income
whereas the transfer in high investment outcome case creates more incentives for inducing
higher effort. In addition, it can be seen that
c

r
=
c

1
h
+
c

1
l
which implies that an increase
in the recipients income is equivalent to an increase in transfers in both states of investment.
It costs more for the migrant if he wants the recipient to exert an extra amount of effort. In
other words, the disincentive effect exceeds the incentive effect of positive transfers. The
recipients optimal effort is found to be independent from the migrants income as under this
incentive scheme, the recipient is more concerned about how much money she can get from
the migrant (the monetary rewards) rather than the migrants income.
As for the migrant, he chooses the investment level as well as the amounts of transfer to be
made, I
h
and I
I
, that corresponds to the investment project outcomes, I
h
and I
I
, respectively
in order to maximize his expected utility. The first order conditions are:
8

0
m
I
= u
m
i
+pu
mh
i
0
h
+(1 p)u
mI
i
0
I
= u (4)
L(0
m
)
1
h
= p
i
(c

)
c

1
h
|(u
mh
u
mI
) +[(u
h
u
I
)] +p(c

)([u
h
i
u
mh
i
)
[:
i
(c

)
c

1
h
= u (5)
L(0
m
)
1
l
= p
i
(c

)
c

1
l
|(u
mh
u
mI
) +[(u
h
u
I
)] +|1 p(c

)]([u
I
i
u
mI
i
)
[:
i
(c

)
c

1
l
= u (6)
It should be noted that the derivation in equation (4) uses the assumptions that I
h
= 0
h
I and
I
I
= 0
I
I. The equation implies that investment is future consumption. At optimal, the utility
cost of making investment in the first period is equal to the expected utility gain of that
investment in the second period. Solving the equation implicitly delivers the optimal
investment level I

. It would be interesting to examine how a change in financial market

conditions, captured by o, or a change in the migrants income, y
m
, would affect this
investment level. As a result, the two following propositions are made.
Proposition 2.
I

u
> u if
u
ml
|
u
mh
|
<
0
h
0
l
.
Proof. See Appendix.
Here,
u
ml
|
u
mh
|
reflects the marginal rate of change or the cost in terms of utility between two
states of investment profitable and lost. By contrast,
0
h
0
l
indicates the premium or the surplus
in monetary terms between these two states. The result implies that when the financial market
condition becomes more favorable (represented by an increase in o), the migrant will increase
9

his investment back home if the expected monetary gain outweighs the expected utility loss
resulting from such an investment increase. However, when the cost is more than the gain, he
will very likely cut down the investment level. His investment decision will be indifferent if
the expected cost is equal to the expected gain.
The intuition is as follows. An increase in o raises the probability of successful investment as
the financial market now becomes healthier, contains lower risks, and provides more
investment opportunities. This creates both an income effect and a substitution effect. The
income effect tends to induce higher investment as well as higher consumption to the migrant.
However, the substitution effect tends to make the migrant to move away from investment
and more into consumption. Whether the optimal level of investment is higher or lower with
an increase in the level of financial development depends which effect actually dominates the
other.
Proposition 3.
I

m
> u if u
m
ii
< p0
h
u
mh
ii
+(1 p)0
I
u
mI
ii
.
Proof. See Appendix.
The result signifies the trade-off between current consumption and future consumption in
which investment plays a role as the cost to the current consumption but the return to future
consumption (in terms of utility). As soon as the loss in marginal utility of current
consumption is smaller than the expected gain in marginal utility of future consumption, the
migrant will increase the investment level to his home country when his income is higher.
This can also be explained on the ground of income effect and substitution effect as what was
provided after Proposition 2.
10

With respect to the migrants decision on monetary rewards, rearranging equations (5) and (6)
gives:
[
c

1
h
|p
i
(c

)(u
h
u
I
) :
i
(c

)] +p
i
(c

)
c

1
h
(u
mh
u
mI
) +p(c

)([u
h
i

u
mh
i
) = u (5)
[
c

1
l
|p
i
(c

)(u
h
u
I
) :
i
(c

)] +p
i
(c

)
c

1
l
(u
mh
u
mI
) +|1 p(c

)]([u
I
i

u
mI
i
) = u (6)
In both equations, the first term reflects the (indirect) impact of the recipients choice of effort
on the migrants utility and is equal to zero according to (3). The second term reflects the
increase in the migrants utility due to an extra effort from the recipient. The third term shows
the trade-off in terms of utility of consumption between the migrant and the recipient due to
additional transfer. Solving (5) implicitly yields I
h

= I
h
(y
m
, y

, I
h
, I
I
). Similarly, solving
(6) implicitly yields I
I

= I
I
(y
m
, y

, I
h
, I
I
).
Proposition 4.
1
h

I
h
> u,
1
h

I
l
< u,
1
h

m
< oi > u,
1
h

r
< u,
1
h

[
> u
And
1
l

I
h
< u,
1
l

I
l
> u,
1
l

m
> u,
1
l

r
< u,
1
l

[
> u.
Proof. See Appendix.
Results obtained indicate that the amount transferred increases with the investment outcome
surplus (represented by the difference between I
h
and I
I
) but does not necessarily increase
with the migrants income. The migrants reaction to changes in investment outcomes reflect
the fact that he intends for remittances to reward the recipients efforts (the business
encouraging effect). Here, remittances are meant to be used mainly for the case of better
11

realization of investment output at which the recipient exerts a higher level of effort.
However, the transfers decrease with the recipients income (the income compensatory
effect). This implies that besides providing more incentives for the recipient to expend higher
effort (the business related motive), remittances can also be compensatory (the altruistic
motive). This argument is further strengthened by the results that the transfers are shown to
increase with the migrants degree of altruism towards the recipient.
2.2. Fixed transfers
By contrast to the first situation just exposed, now assume that the migrant transfers to the
recipient a fixed amount of money regardless of the outcome of the investment project. The
reason why the migrant does not tie the money rewards to the investment outcome in this case
because he knows that the recipient also cares about him (that is why it may not be necessary
to have such an incentive scheme as before). The relationship between the migrant and his
relative can now be imagined in a most natural way as the one between a son (the migrant)
and his parent (the recipient). As a result, there exists mutual (two-sided) altruism between the
two individuals.
The expected utility for the migrant is as follows:
E(u
m
) = u(y
m
I) +pu(y
m
+I
h
I) +(1 p)u(y
m
+I
I
I) +[
m
E(u

) (7)
where u < [
m
< 1 is the discount factor for the migrant which reflects his degree of altruism
towards his parent.
The expected utility for the recipient now becomes:
12

E(u

) = u(y

) +u(y

+I) :(c) +[

E(u
m
) (8)
where u < [

< 1 denotes the discount factor for the recipient which also reflects her
degree of altruism towards her son.
For simplicity of notation, define u
mh
u(y
m
+I
h
I), u
mI
u(y
m
+I
I
I). Solving
this system of equations gives:
E(u
m
) =
1
1-[
m
[
r
|u(y
m
I) +pu
mh
+(1 p)u
mI
+[
m
u(y

) +[
m
u(y

+I)
[
m
:(c)] (9)
E(u

) =
1
1-[
m
[
r
|u(y

) +u(y

+I) :(c) +[

u(y
m
I) +[

pu
mh
+
[

(1 p)u
mI
] (10)
Again, the model can be solved by backward induction in which the recipient chooses her
effort level to maximize her expected utility given the amount of money to be received and
her labor income; the migrant chooses his levels of investment and transfer to maximize his
expected utility. The first order condition for the recipients decision on effort level to expend
is:
L(0
r
)
c
=
1
1-[
m
[
r
|:
i
(c) +[

p
i
(c)(u
mh
u
mI
)] = u (11)
The interpretation of this equation is as the following. While expending some extra effort acts
as disutility, :
i
(c), it raises the recipients utility by increasing the chance of the migrant
getting utility surplus.
Proposition 5.
c

m
< u,
c

r
= u,
c

1
> u,
c

[
r
> u.
13

Proof. See Appendix.
It can be seen that the impact of changes in incomes of both agents on the recipients effort
are different from the incentive transfer case. The first difference is that the recipients effort
now decreases with the migrants income. This might be because the marginal increase in the
migrants utility is less than the recipients disutility from exerting extra effort. The second
difference is that the recipients decision on exerting effort is invariant to her own income.
This is because in this case, the recipient cares about the migrants well-being. A change in
her income does not change her altruism towards the migrant.
The conditions also say that an increase in the transfer raises the recipients effort level
because monetary compensation offers her more incentive to exert effort (business
encouragement). This effect is the same as in the case of state-contingent transfers. Another
interesting result is the recipient will work harder on the investment project if she is more
altruistic towards the migrant. This result makes sense as both agents are altruistic to each
other.
As for the migrant, his strategic move is to choose the level of investment to be made as well
as the amount of remittances to be transferred back home such that his utility is maximized.
The first order conditions are given by:
L(u
m
)
I
=
1
1-[
m
[
r
|u
m
i
+pu
mh
i
0
h
+(1 p)u
mI
i
0
I
] = u (12)
L(0
m
)
1
=
1
1-[
m
[
r
|pu
mh
i
(1 p)u
mI
i
+[
m
u
i
(y

+I)] = u (13)
As the condition in equation (12) is similar to that of equation (6), its interpretation follows
what is given to equation (6). Therefore, in this case, the migrant is expected to behave
exactly the same as in the case of state-contingent transfers in forming his investment
14

decision. His investment responses to a change in the level of financial development and his
income level are the same as what discussed under propositions 2 and 3 above.
Equation (13) indicates that the migrants utility is maximized when the cost (in utility terms)
of additional transfer, reflected by the first two terms inside the bracket, is equal to the benefit
(in terms of utility) of it which is reflected by the last term inside the bracket. While the utility
cost is a direct effect as the migrants consumption falls, the utility benefit is an indirect effect
as the migrant derives utility from the recipients extra consumption.
Proposition 6.
1

m
> u,
1

r
< u,
1

[
m
> u,
1

I
h
> u,
1

I
l
> u.
Proof. See Appendix.
That is, similar to the previous case of state-contingent transfers, the migrants transfer
increases with his degree of altruism and the investment outcome surplus but decreases with
the recipients income (due to income compensatory effect). The only difference lies in the
result that the transfer increases with the migrants income while it is not clearly the case
under the incentive scheme. The reason is that the migrant is more altruistic towards the
recipient in this case so he will send more money home when he earns higher income
overseas. Again, the obtained results show that remittances may contain both business
encouraging and income compensatory effects.
3. Some implications and further discussions
The above theoretical consideration has been concerned with a model of investment
remittances which examines two different practical situations of migrant-recipient
relationship. Although the settings of these two cases are different, the results obtained are
15

qualitatively the same. They both point out several important implications regarding the
causes and effects of remittances:
(i) The migrant sends more money home when his earnings are higher.
(ii) The recipient tends to receive more income transfer from overseas when her income is
lower (income compensatory effect).
(iii) The migrants decision on the division of income between consumption and
investment is driven by intertemporal preferences and information about future
investment prospective. More specifically, he will invest more in his home country if
the expected gain from such an activity is high enough.
(iv) Remittance transfer increases with successful investment outcomes as monetary
rewards to the recipient for taking care of the migrants investment project at home
(business encouraging effect). It also increases with the migrants degree of altruism
towards the recipient.
(v) The recipient tends to exert more managerial effort on the investment project when
her income is low, when more financial rewards through remittances are promised in
advance (business encouraging effect), or when she is more altruistic towards the
migrant.
It can be seen that results in (i) and (ii) are fairly general. They reflect the altruistic motive. The
predictions in (iii), (iv), and (v) are consistent with both investment-business hypothesis and the
altruistic hypothesis. While the altruistic motive is clear and receives a fair amount of attention
in the literature, the business oriented motive is generally new and worth examining further.
So far, the model in the paper has been assuming that the recipients incentive to exert effort
is independent financial development in affecting the probability of success in making
16

investment. The parameter o is meant to capture the favorable financial market condition.
9
If
c is unchanged, an increase in o will lead to an increase in p(o, c) as there are more good
opportunities for doing business
10
and, hence, the expected returns on investment will be
higher. This is an incentive for the migrant to invest in his home country from overseas and it
is expected that there will be more remittances devoted to investment.
11
However, one may
argue that the increase in o is not totally free of charge as there might be a moral hazard
problem involved: the recipient might not exert as much effort as previously (c may be
lower). Whether p(o, c) increases or decreases will depend on the relative change in
magnitudes of o and c. As a result, the investment outcome and, hence, total investment out
of remittances, will also be subject to this relative change. This creates a puzzle on the role of
financial market development in extracting investment from remittances. Examining this issue
will open an important new research project.
4. Conclusions
This paper has developed a model which allows it to examine the motivation for sending
remittances. Remittances are made both due to altruistic and business doing motivations. It is
shown that remittances not only compensate the recipients for unfavorable economic
conditions but also serve as an important flow of capital as well as monetary rewards for
investment managerial efforts. From macroeconomic stance, this creates two opposing effects
of remittances in the relationship with home countrys income level. While the compensatory

9
This condition may include any good policy that enhances the likelihood of successful investment such as
regulatory policy, macroeconomic conditions, and institutions, etc. These factors are generally correlated with
financial development. By financial development this paper refers to the development of the financial sector per
se as well as infrastructure that supports that system.
10
This is one positive aspect of financial development. Other aspects include better insurance against shocks and
better diversifying rate of return risks, etc.
11
One may argue that the lack of financial development leads to high returns to capital for those who can access
it and remittances may be sent back to take advantage of business opportunities that local financing is unable to
take advantage of. This may be true for some particular cases. However, when the financial system is
underdeveloped, there are often high risks associated with these high returns. In the end, on average, the risk
adjusted returns may not be as high as they first appear to be.
17

effect results in a negative relationship with income growth which is consistent with the
literature, the business encouraging effect is positive since it stimulates remittances for
investment purposes. This is a novel aspect of the paper. This aspect makes remittances a
potentially important source of finance for economic development. It highlights the role of
financial development in mobilizing investment for productive activities from this source of
finance.
The lesson to learn is that in countries where there is an effective financial system in place,
the business encouraging effect may dominate the compensatory effect and remittances have a
net positive contribution to economic development. Remittances and financial development
can be complementary and they may interact to promote growth. Testing this hypothesis will
surely enrich the literature. From economic policy point of view, countries should aim to
improve the local conditions (i.e. infrastructure, legal framework, etc.) in general and the local
financial system in particular. This will attract more remittances from overseas for productive
activities and allow recipient countries to optimize the potential benefits of remittances.
Appendix - Mathematical proofs of propositions
In the proofs that follow, conclusions on directions of inequalities are reached based on the
standard assumptions made on the utility and probability functions, specifically: u
i
(. ) >
u, u
ii
(. ) < u; :
i
(. ) > u, :
ii
(. ) < u; and p
i
(. ) > u, p
ii
(. ) < u.
Proof of Proposition 1
Using the condition specified in (3), it can be derived as follows:
oc

oy

=
p
i
(c

)(u
I
i
u
h
i
)
p
ii
(c

)(u
h
u
I
) :
ii
(c

)
< u
18

oc

oI
h
=
p
i
(c

)u
h
i
p
ii
(c

)(u
h
u
I
) :
ii
(c

)
> u
oc

oI
I
=
p(c

)u
I
i
p
ii
(c

)(u
h
u
I
) :
ii
(c

)
< u
oc

oy
m
= u
Proof of Proposition 2
Differentiating (4) with respect to o and then rearranging gives:
oI

oo
=
p
i
(o)(u
mI
i
0
I
u
mh
i
0
h
)
u
m
ii
+p(o)u
mh
ii
0
h
2
+|1 p(o)]u
mI
ii
0
I
2

Given that the denominator is always negative, the sign of this derivative is determined by the
sign of the term u
mI
i
0
I
u
mh
i
0
h
or, by rearranging, the sign of the term
u
ml
|
u
mh
|

0
h
0
l
. Hence,
I

u
> u if
u
ml
|
u
mh
|
<
0
h
0
l
.
Proof of Proposition 3
From (4) it can be derived the following:
oI

oy
m
=
u
m
ii
p0
h
u
mh
ii
(1 p)0
I
u
mI
ii
u
m
ii
+p0
h
2
u
mh
ii
+(1 p)0
I
2
u
mI
ii

19

As the denominator is negative, the sign of this derivative is dependent on the sign of the
terms in the numerator or u
m
ii
p0
h
u
mh
ii
(1 p)0
I
u
mI
ii
. Therefore,
I

m
> u if u
m
ii
<
p0
h
u
mh
ii
+(1 p)0
I
u
mI
ii
.
Proof of Proposition 4
Differentiating (5) with respect to I
h
and I
I
gives:
oI
h

oI
h
=
p(c

)u
mh
ii
p
i
(c

)
oc

oI
h
u
mh
i
p
i
(c

)
oc

oI
h
u
mh
i
+[p(c

)u
h
ii
+p(c

)u
mh
ii
> u
oI
h

oI
I
=
p
i
(c

)
oc

oI
h
u
mI
i
p
i
(c

)
oc

oI
h
u
mh
i
+[p(c

)u
h
ii
+p(c

)u
mh
ii
< u
oI
h

oy
m
=
p(c

)u
mh
ii
p
i
(c

)
oc

oI
h
(u
mh
i
u
mI
i
)
p
i
(c

)
oc

oI
h
u
mh
i
+[p(c

)u
h
ii
+p(c

)u
mh
ii
<> u
oI
h

oy

=
[p(c

)u
h
ii
p
i
(c

)
oc

oI
h
u
mh
i
+[p(c

)u
h
ii
+p(c

)u
mh
ii
< u
oI
h

o[
=
p(c

)u
h
i
p
i
(c

)
oc

oI
h
u
mh
i
+[p(c

)u
h
ii
+p(c

)u
mh
ii
> u
Similarly, differentiating (6) with respect to I
h
anu I
I
gives:
oI
I

oI
h
=
p
i
(c

)
oc

oI
I
u
mh
i
p
i
(c

)
oc

oI
I
u
mI
i
+[|1 p(c

)]u
I
ii
+|1 p(c

)]u
mI
ii
< u
20

oI
I

oI
I
=
|1 p(c

)]u
mI
ii
+p
i
(c

)
oc

oI
I
u
mI
i
p
i
(c

)
oc

oI
I
u
mI
i
+[|1 p(c

)]u
I
ii
+|1 p(c

)]u
mI
ii
> u
oI
I

oy
m
=
|1 p(c

)]u
mI
ii
p
i
(c

)
oc

oI
I
(u
mh
i
u
mI
i
)
p
i
(c

)
oc

oI
I
u
mI
i
+[|1 p(c

)]u
I
ii
+|1 p(c

)]u
mI
ii
> u
oI
I

oy

=
[|1 p(c

)]u
I
ii
p
i
(c

)
oc

oI
I
u
mI
i
+[|1 p(c

)]u
I
ii
+|1 p(c

)]u
mI
ii
< u
oI
I

o[
=
|1 p(c

)]u
I
i
p
i
(c

)
oc

oI
I
u
mI
i
+[|1 p(c

)]u
I
ii
+|1 p(c

)]u
mI
ii
> u
Proof of Proposition 5
Using condition (11), the following results can be obtained:
oc

oy
m
=
[

p
i
(c

)(u
mI
i
u
mh
i
)
:
ii
(c

) +[

p
ii
(c

)(u
mh
u
mI
)
< u
oc

oy

= u
oc

oI
=
[

p
i
(c

)(u
mh
i
u
mI
i
)
:
ii
(c

) +[

p
ii
(c

)(u
mh
u
mI
)
> u
oc

o[

=
p
i
(c

)(u
mI
u
mh
)
:
ii
(c

) +[

p
ii
(c

)(u
mh
u
mI
)
> u

21

Proof of Proposition 6
From (13), it can be derived the following results:
oI

oy
m
=
pu
mh
ii
+(1 p)u
mI
ii
pu
mh
ii
+(1 p)u
mI
ii
+[
m
u
ii
(y

+I)
> u
oI

oy

=
[
m
u
ii
(y

+I)
pu
mh
ii
+(1 p)u
mI
ii
+[
m
u
ii
(y

+I)
< u
oI

o[
m
=
u
i
(y

+I)
pu
mh
ii
+(1 p)u
mI
ii
+[
m
u
ii
(y

+I)
> u
oI

oI
h
=
pu
mh
ii
pu
mh
ii
+(1 p)u
mI
ii
+[
m
u
ii
(y

+I)
> u
oI

oI
h
=
(1 p)u
mI
ii
pu
mh
ii
+(1 p)u
mI
ii
+[
m
u
ii
(y

+I)
> u
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