ECONOMIC RESEARCH CENTERDISCUSSION PAPER
E-Series

No.E10-2

Multiple Equilibria arising from theDonor’s Aid Policy in Economic
Development
byHikaru Ogawa
Koji Kitaura
Sayaka Yakita

August 2010

ECONOMIC RESEARCH CENTERGRADUATE SCHOOL OF ECONOMICSNAGOYA UNIVERSITY

Multiple Equilibria arising from theDonor’s Aid Policy in Economic
Development
Hikaru OGAWA
School of Economics, Nagoya University
Furocho Chikusaku, Nagoya 464-8601, Japanemail: ogawa@soec.nagoya-u.ac.jp

Koji KITAURA
Department of Civil Engineering, Gifu University
1-1 Yanagido, Gifu 501-1193, Japanemail: kkitaura@gifu-u.ac.jp

Sayaka YAKITA
School of Economics, Nagoya University
Furocho Chikusaku, Nagoya 464-8601, Japan
Tel.:+81-52-789-2379, Fax:+81-52-789-4924
email: yakita.sayaka@b.mbox.nagoya-u.ac.jp1Abstract
This paper presents a neoclassical growth model comprising education and child labor with a focus on developing and aid-receiving countries to demonstrate cyclical growth and bifurcation in economic development. Numerous studies have explained the bifurcation in termsof the internal aﬀairs of the recipient country, such as technology inproduction, subsistence minimum in consumption, and liquidity constraint in investment. The main argument of this paper is that the aid
allocation policy employed by the donor countries, thereby the motiveof the aid-providers, leads to divaricated and cyclical development in
the recipient country.

(Key words) Aid allocation policy, Multiple equilibria, Cyclical growth, Economic development(JEL Classification) F35, O11, O38

2

1

Introduction

Developed countries have made a large fiscal transfer to developing countries
to aid their economic takeoﬀ. The impact of foreign aid from the donors
to the recipient countries varies from country to country, however. Thesevariations could be primarily explained by a particular set of circumstancesof the recipient. The empirical study of Burnside and Dollar (2000) stirs ourinterest in good policies in recipient countries. They find that development
aid contributes to economic growth when the recipient country has a good
policy environment, but it has a less beneficial eﬀect on development if therecipient country is not well governed. This result has been reexamined bymany researchers to foster better understanding of aid eﬀectiveness [Collier
and Dollar (2002), Hansen and Tarp (2001), Easterly et al. (2004), Clemens
et al. (2004), and Dollar and Levin (2006)].
The persistent diﬀerences in growth rates among less-developed countries
have also been explained by theoretical researchers. One of the contributory explanations involves the existence of the threshold eﬀect arising froma discontinuity in technology, as formalized by Azariadis and Drazen (1990).
When the production technology in the receiving country is a step function
with a jump at some critical level of physical/human capital, the economy
exhibits bifurcation; this leads to an environment where stagnant countries
and countries succeeding in economic takeoﬀ coexist1 . This argument calls
for a bifurcation mechanism on a technological feature in receiving countries.
Other factors causing bifurcation in economic growth in most of the preceding theoretical studies have been, for instance, the existence of subsistence
minimum in consumption, liquidity constraint in investment, and nature of1

It is, of course, true that the discontinuity in technology is not strictly required, as
Azariadis and Drazen (1990, p.509) states. In fact, what is actually required is a shift
from decreasing to increasing returns-to-scale technology at any level of state variables.
Though we do not have much studies, we should take a notice of a proof against the ideaof poverty trap induced by the equilibrium multiplicity. Using a simple growth model inwhich poverty traps can arise due to either low saving or low technology at low levels ofdevelopment, Kraay and Raddatz (2007) do not find much evidence of the existence ofpoverty traps based on these mechanisms.

3

increasing returns in production2 . All of these are based on internal aﬀairs,i.e., preference, technology, and market conditions in the target country [seethe excellent survey by Azariadis and Stachurski, 2004].
The aim of this paper is to arouse interests in the possibility that thebifurcation in economic development is not only generated by the internal
conditions, but is arose from the donor-side. Specifically, the feature, which
diﬀerentiates our model from other related studies, is the reason that themultiplicity and cyclical growth is caused by the form of foreign aid allocation the donor employs3 . The form of foreign aid considered in this paper
is not odd; we simply assume that the donor provides developing countries
with assistance under a co-finance regime to stimulate human capital accumulation until the recipient’s economic standard reaches the benchmark
level. However, after the recipient exceeds this benchmark, the donor ceases
to support it, so that the developing country is no longer on the list of aid
recipients.
In this paper, the donor’s aid policy is not only characterized by the
benchmark level, but also aid allocation between various types of public
spending. This standpoint is based on the evidences that suggest the importance of eﬀective aid allocation among various types of public spending in
the recipient country4 . In our model, two types of policy options are considered; one is education aid to improve the quality of public education, andthe other is cash transfer to ensure poor families with schooling-age children
2See, for instance, Galor and Zeria (1993), Galor and Weil (2000), Hazan and Berdugo(2002), Tabata (2003), and Moav (2005).
3
Although few studies have depicted the relationship between the donor’s aid policy
and growth path in economic development, a study by Dalgaard (2008) deserves attention.
Using the model of Arrow and Kurz (1970), Dalgaard succeeds in showing that the foreign
aid policy may cause cyclical growth. While Dalgaard does not consider the allocation offoreign aid in alleviating poverty, our results argue that the aid allocation rule employedby donor countries, thereby the motive of aid provider, causes not only cyclical growth,
but also multiple equilibrium in the recipient countries, which has not been mentioned.
4
For instance, Hansen and Tarp (2001) point out that the aid-growth relationshipdepends not only on the level of aid, but also on the aid allocation. World Bank (1998)
argues that the decision on aid allocation would have a greater impact on poverty reduction
if it were targeted the poorest countries.

4

go to school. This approach enables us to examine how the allocation rule
determined by the donor aﬀects the economic development in the recipient
countries.
Employing various styles of foreign aid modeling, this paper presents
a neoclassical growth model with aid allocation policy to argue that thepersistent diﬀerences among developing countries are created by the donor’s
choice on the benchmark level and the aid allocation. This bifurcation can beobserved even among countries with the same technology, preferences, andmarket structure.
The rest of this paper is organized as follows. Section 2 presents themodel. Section 3 examines the growth paths and steady states. Section 4
discusses the validity of the main results by assuming alternative forms offoreign aid. Finally, Section 5 concludes the paper.

2

Model

We employ a three-periods-overlapping-generations model in a small open
economy. In our analysis, there exist individuals who live for three-periods
and a recipient government that receives support from the developed countries until it reaches a certain level of development. The subscript t(=
1, 2, · · · ) denotes the time.

2.1

Individuals

All individuals live for three periods and are endowed with one unit of time inboth the first and second periods of their life. In the first period (childhood),
they spend their time not only in schooling to acquire human capital, butalso by working as child laborers. In the second period (parenthood), theywork, plan their family, and rear children. Finally, they retire in the third
period.
Individuals are considered to inherit the human capital of their parents.
Further, they attend school to acquire human capital. The function of humancapital accumulation is given as5ηht = eαt−1 Et−1
hγt−1 .

(1)

It is assumed that the human capital of the individual born at time t − 1
depends on the schooling time, et−1 , quality of public education, Et−1 , andhuman capital of their parent, ht−1 . Note that human capital is accumulated
both by the schooling time and public expenditure for education, both ofwhich are considered to be complementary. The lifetime utility of the individual of generation t, born in period t − 1, is assumed to be log-linear, andis given by the form

Ut = (1 − β) ln ct+1 + β ln nt ht+1 ,(2)

where β is the preference parameter for children. The utility of the individuals of generation t depends on the consumption in the third period, ct+1 ,the number of children they rear, nt , and the level of human capital of theirchildren, ht+1 .
In the second period of life, as parents, individuals decide how to allocate
the endowed time of unit one to their children between schooling and working
as child laborers. Assuming that the working ability of children is inferior
to that of parents (0 < θ < 1), the provision of eﬃcient labor by a child isexpressed as (1 − et )θht , where 1 − et and θ represents the time devoted toworking and the working ability of the child respectively5 . Moreover, parents
decide their own time allocation of unit one between working and childrearing. We denote the rearing time per child as z; then, the time devoted torearing nt children is znt , while that devoted to working is 1 − znt . Since weassume that individuals consume only in the third period of their life, theysave all of their income in the second period. Thus, the budget constraintsof the individuals born at t − 1 are given as
5

Hazan and Berdugo (2002) and Chakraborty and Das (2005) also assume that the
productivity of child labor is relatively low.

6

st = nt (1 − et )θht + (1 − znt )ht (1 − τ ) + Rt ,ct+1 = st (1 + r̄),

(3)
(4)

where st is the saving, τ is the income tax rate, and r̄ is the world interest
rate. The right-hand side of (3) is the income in the second period of their life;
this comprises the income from child labor after considering the taxed adult’slabor income and cash transfer, Rt . The wage per unit of human capital isnormalized to one because we implicitly assume that the production function
is linear in human capital.

2.2

Government

The government in the recipient country provides both public education andcash transfer to its citizens. It is financed by income tax revenue and foreign
aid. The government receives foreign aid, Ft , from the foreign country until
the recipient country reaches a certain level of development. The benchmark
level is exogenous for the recipient country and, in any case, is determined by
the donor who in turn refers to criteria such as the world standard level. We
begin by describing the formula for foreign aid in its simplest form, deferring
the discussion of various extensions. The form of foreign aid is assumed to bea type of a matching grant aimed at stimulating human capital development,
as shown below:

Ft = f (ht )ht ,wheref (ht ) =(f > 0, if ht < h̄0,
if ht ≥ h̄.

(5)This equation shows that the foreign aid received by the country depends on
its level of human capital. When the level of human capital in the recipient7

country is relatively low, i.e., less than a benchmark level, h̄t , foreign aid will
be provided. Since human capital accumulates with time, foreign aid will
not be provided after the human capital reaches a benchmark level, h̄t 6 .
Given the level of foreign aid that it receives, the recipient country at time
t allocates foreign aid as a part of the financial source for public education,
Et , and cash transfer to the residents, Rt . In addition, the revenue fromincome tax is also allocated for public education and cash transfer. That is,since public education and cash transfer are co-financed both by domestic
income tax revenue and foreign aid, the government’s budget constraints for
public education and cash transfer are given by7

Et = pτ (1 − znt )ht + qFt ,Rt = (1 − p)τ (1 − znt )ht + (1 − q)Ft ,

(6)
(7)

where p denotes the share of tax revenue allocated to public education, andq is the ear-marked by the donor for the public education.
In the following analysis, we assume that p and q are exogenous to therecipient economy, and that they are fixed at a certain level. The assumption that the foreign aid allocation is exogenous to recipient can be related
to the notion of foreign aid ownership and fungibility. The former has been
applied to describe the environment in which the donor and/or the recipient
has a responsibility for the design of development program [Ole (2001)]. The
assumption made in our model suggests that the donor has a full ownership in foreign aid allocation in recipient countries. The full ownership by
6

Although we cannot denote the in-depth rule of foreign aid in individual countries,
the aid policy rule of DAC in OECD is helpful. It creates a list of ODA recipients by
categorizing them into four groups based on their income levels. Within the list, if theincome level of a certain country consistently exceeds the maximum level for three years,
that country graduates from the list. Twenty-five countries had graduated from this listby 2003. See OECD (2009).
7
A first attempt to introduce co-financing foreign aid transfer is made by Chatterjee
et al.(2003). They investigate the link between foreign aid, growth and welfare using an
endogenous growth model with public capital accumulation. Moreover, in the same setting,
Chatterjee and Turnovsky (2006) examine the recipient government’s intertemporal fiscal
balance introducing endogenous labor supply.

8

donor would be partly justified by applying the argument of Hjertholm andWhite (2001), which suggests that, as the donors have a comparative advantage in allocating resources eﬃciently, they tend to dominate the foreign
aid programs in developing countries, so that they are reluctant to allow therecipients more than a limited role.
The assumption is also based on the condition that the foreign aid is notfungible. As Healey and Klillick (2001) pointed out, if the aid resources are
fungible, donors can do little without domestic ownership8 .

2.3

Optimization

The problem faced by adult individuals at time t is to choose consumption,
ct+1 , number of children, nt , and the children’s schooling time, et , such that
their lifetime utility is maximized. From (1)-(4), the first-order conditions
for the individuals are derived as
1−β
μt
=
,
ct+1
1 + r̄
β:= μt [zht (1 − τ ) − (1 − et )θht ],nt
αβ:= μt θnt ht ,etct+1 :

(8)

nt

(9)

et

(10)

where μt is the Lagrange multiplier. Equation (9) means that the marginalutility of having an additional child is equal to the net marginal cost ofchildren, which is the cost of rearing a child minus the child labor income.
Equation (10) shows that the marginal utility of schooling is equal to themarginal cost, which is the marginal return on child labor.
From (8)—(10), we can represent the demand functions of nt and et as

8

See Pack and Pack (1993), Feyzioglu et al. (1998), Chatterjee et al.(2007) and Kitaura(2009) for the fungibility problem. See also McGillivray and Morrissey (2001) which
reviews the studies focusing on the fungibility problem.

9

β(1 − α)[(1 − τ )ht + Rt ],[z(1 − τ ) − θ]ht
α[z(1 − τ ) − θ]=.
θ(1 − α)

nt =

(11)

et

(12)

Since the schooling time of the child cannot be negative, we assume here thatz(1 − τ ) > θ, where the working ability of the child as compared to an adultis suﬃciently small. Since (7) holds, (11) can be rewritten asn∗ =β(1 − α)[(1 − τ ) + f (1 − q) + τ (1 − p)].
z(1 − τ ) + βτ z(1 − α)(1 − p) − θ(13)Using (6) and (13), the expenditure for public education can be derived as∙

Et = pτµzβ(1 − α)[(1 − τ ) + f (1 − q) + τ (1 − p)]1−z(1 − τ ) + βτ z(1 − α)(1 − p) − θ¶¸+ f q ht . (14)Substituting (12) and (14) into (1), the human capital accumulation can bederived as

ht+1 = Aα (Bf + C)η hη+γ
,
t

(15)

where
α(1 − τ − Θ),Θ(1 − α)q(1 − τ − Θ) + βτ (1 − α)(q − p),B ≡1 − τ − Θ + βτ (1 − α)(1 − p)pτ [1 − τ − Θ − β(1 − τ )(1 − α)],C ≡1 − τ − Θ + βτ (1 − α)(1 − p)
A ≡

(16)
(17)
(18)

and Θ = θz −1 . The form of (15) depends on the sign of A, B, and C. Owing
to the assumption that the schooling time of child is positive, 1 − τ − Θ > 0,
the sign of A is positive. It implies that the denominators of B and C are
10

positive. However, the signs of B and C cannot be determined because thesign of the numerators in B and C are ambiguous. Since ht+1 = ht in thesteady-state, the steady-state level of human capital, ĥ∗ , is derived from (15)
as9
η

α

ĥ∗ = A 1−η−γ (Bf + C) 1−η−γ .

3Analysis

3.1

Preliminary Consideration(19)

In this section, we analyze how the benchmark level of human capital aﬀects
the bifurcation of economic development. For our analysis, we will specify
the form of (15), and assume that the sign of C is positive. Since the sign ofthe denominator in C is always positive, assuming that C > 0 is equivalent
to assuming that the sign of the numerator in C is positive; that is,

1 − τ − Θ > β(1 − τ )(1 − α).

(20)Moreover, the form of human capital accumulation depends on the sign of
B. To determine this sign, let us denote the numerator of B as Bn ,Bn ≡ q(1 − τ − Θ) + βτ (1 − α)(q − p).

(21)(21) can be modified to 1 − τ − Θ = (Bn − βτ (1 − α)(q − p))/q, and bycombining with (20), we have

Bn > qβ(1 − τ )(1 − α) + βτ (1 − α)(q − p) = β(1 − α)(q − τ p).

(22)(22) implies that Bn is always greater than β(1 − α)(q − τ p), and the sign of
Bn , which is crucial for determining the sign of B, can be either positive or
9This is stable equilibrium because 0 < (∂ht+1 /∂ht )|ht =ĥ∗ = η + γ < 1.

11

negative depending on the relative level of q and τ p. When q ≥ τ p, i.e., in
the case where the share of income tax revenue allocated for public educationis relatively large, Bn is always positive. However, when q < τ p, it does not
exclude the possibility of Bn , and therefore B, from being negative10 . Thisoccurs when q is so small that it does not exceed τ p.
The sign of B is crucial for our analysis in order to determine the benchmark level of foreign aid. We will show that in the case of B < 0, the donor
must set the benchmark level h̄ eﬀectively; otherwise, multiple steady-state
equilibria may emerge. Specifically, our analysis in subsection 3.2 focuses on
the case of B < 0, where multiple equilibria are observed. In contrast, if
q is larger than τ p, such that it satisfies B > 0, a dynamic property arises
wherein human capital always converges to a unique steady-state equilibrium in the country, irrespective of how high or low the benchmark level h̄ is.
In addition, an alternative property of dynamics arises wherein the country
experiences cyclical growth.
In the following analysis, note that(η + γ)Aα (Bf + C)η
∂ht+1
=
> 0,
∂ht
ht1−η−γ(1 − η − γ)(η + γ)Aα (Bf + C)η
∂ 2 ht+1
=
−
<0
∂h2t
h2−η−γt
for both B < 0 and B > 0. Further, note that when the human capital of
the recipient country reaches the benchmark level h̄, f (h) equals zero. Thismeans that the recipient country will no longer receive any foreign aid, andtherefore, (15) will become,
ht+1 = Aα (C)η hη+γ
t
10

(23)

The share of income tax revenue devoted to public education does not necessarily haveto be zero for B to be negative. The discussion in the case of B < 0 still holds; at least q issmall enough not to exceed τ p. This is likely to hold when the foreign aid is mainly spenton cash transfer rather than on public education, and the income tax revenue is mainly
spent on public education rather than on cash transfer.

12where public education is financed solely by the income tax revenue generated
within the country. Denoting the steady-state level of human capital whenηαf (h) = 0 as h̃∗ , we have h̃∗ = A 1−η−γ C 1−η−γ .

3.2

Case B < 0 (q < τ p)

When B < 0 (q < τ p), the accumulation of human capital according to (23)
is faster than that of (15) because Bf + C < C. Furthermore, it is clearthat ĥ∗ < h̃∗ ; this means that when f > 0, the steady state level of humancapital is smaller than that when f = 0. The intuition of this result is asfollows. An increase in the share of cash transfers raises fertility rate anddecreases the labor supply, since the rearing time per child is constant. This
would reduce the human capital in the recipient country. That is, the level ofhuman capital decreases with the provision of foreign aid. This is the pointsuggested by Dalgaard (2008), which shows that, as the transfer is made in
cash, the donor will be faced with the Samaritan’s dilemma; An increase in
the cash transfer reduces the human capital investment, and that it induces
the recipient economy to fall into poverty trap.
Since the human capital accumulation is faster when accumulation occurs
according to (23), and the steady state level of human capital (h̃∗ ) is greaterthan ĥ∗ , we can depict both functions as shown in Figure 1.
Figures 1-a and 1-c depict the case when human capital converges to aunique equilibrium. In contrast, Figure 1-b shows the case when multiple
equilibria emerge. In Figure 1-a, we show the case ĥ∗ < h̃∗ < h̄, where
the benchmark level of human capital is set substantially high. In this case,human capital converges to a steady state level ĥ∗ regardless of the initialhuman capital h0 . Figure 1-b shows the case when the benchmark level h̄ isset between the steady state levels of both f > 0 and f = 0, i.e., ĥ∗ < h̄ < h̃∗ .
In this case, there exists a possibility of multiple equilibria wherein the initiallevel of human capital plays a crucial role. If an economy has a relatively
low level of initial human capital, i.e., h0 < h̄, it will converge to a low levelof human capital, ĥ∗ . On the other hand, in an economy wherein the initiallevel of human capital is relatively high, human capital will converge to h̃∗ .
13Therefore, in this case, developing countries, which are usually considered tohave a relatively low level of initial human capital, tend to converge to a low
steady state. Figure 1-c displays the third case, where the benchmark level ofhuman capital is substantially low, i.e., h̄ < ĥ∗ < h̃∗ . When benchmark levelof human capital is set at a relatively low level, human capital will converge
to h∗ = h̃∗ , irrespective of the level of initial human capital.

3.3

Case B > 0 (q > τ p)

When B > 0 (q > τ p), we have three diﬀerent cases; one of these involves thepossibility that human capital does not converge to a steady state. Note thatwhen B > 0, the speed of human capital accumulation according to (15) isfaster than that of (23), and ĥ∗ > h̃∗ . Figure 2 shows the case where humancapital convergence does not occur and the steady state cannot be achieved11 .
This can be achieved when the benchmark level, h̄, is set between h̃∗ and ĥ∗ .
The intuition behind the result is as follows. If the level of human capital in
the recipient country is smaller than the benchmark level, the government of
the recipient country will receive foreign aid. When q > τ p, the government
will then use it to provide public education. An increase in the ear-marked
aid for the public education aﬀects human capital in the following two ways.
First, an increase in q drops the fertility rate, nt (see (13)), and increases
the labor supply, 1 − znt . Second, a higher q leads to improve the qualityof public education (see (14)). Thus, the level of human capital will increase
with the provision of foreign aid. When the level of human capital exceeds thebenchmark level, the donor country’s government ceases to provide foreign
aid. As a result, educational expenditure by the recipient may reduce, andIn the case that ĥ∗ > h̃∗ , high steady state equilibrium is possible. This can happen
when the benchmark level, h̄, is set at a relatively high level, h̄ > ĥ∗ . Human capitalconverges to ĥ∗ regardless of its initial level. In another case, the benchmark level ofhuman capital is set at a relatively low level, h̄ < h̃∗ . Here, human capital converges to aunique steady state, h̃∗ , regardless of its initial level. Although both cases converge to aunique steady state equilibrium, the equilibrium for the latter is lower than that for theformer. Therefore, when the economy is in a situation such that B > 0, it is preferable toset a relatively high benchmark level of human capital in order to achieve a higher steadystate equilibrium.
11

14

therefore, the level of human capital will become lower than the benchmark
level. Thus, the recipient country will again receive foreign aid, leading tocyclical growth.
We summarize our main results focusing on multiple equilibria and cyclical growth as follows.
Proposition. When hˆ∗ < h̄ < h˜∗ , multiple equilibria emerge if q < τ p;otherwise, the economy experiences cyclical growth.

4Remarks on the alternative form of foreignaid

In the previous section, we discussed the eﬀects of foreign aid on the basis ofa model wherein the level of foreign aid is determined according to the levelof human capital in the recipient country. Here, we analyze and employ analternative form of foreign aid that depends on the income level of adults in
the recipient country.
Let us assume that foreign aid takes the form Ft = f (1−znt )ht , where (5)holds. Then, the budget constraints for public education and cash transfer
are given as

Et = pτ (1 − znt )ht + qf (1 − znt )ht ,Rt = (1 − znt )ht [(1 − p)τ + (1 − q)f ].

(24)
(25)

Since individuals’ decisions are made according to the policy variables Et and
Rt , the demand functions for nt and et are determined in the same manneras in (11) and (12). From (11) and (25), we haven∗∗ =β(1 − α)[1 − τ + (1 − p)τ + (1 − q)f ].
z(1 − τ ) + βz(1 − α)[(1 − p)τ + (1 − q)f ] − θ(26)Substituting (26) into (24), we get the expenditure for public education as
15

Et =

(1 − τ )[1 − β(1 − α)] − Θht (pτ + f q),(1 − τ ) + β(1 − α)[(1 − p)τ + (1 − q)f ] − Θ(27)Then, from (12) and (27), the human capital accumulation can be derived
as ht+1 = eαt Etη hγt = Aα Dη hη+γ
, where A is given as (16) andt

D =(1 − τ )[1 − β(1 − α)] − Θ(pτ + f q).
(1 − τ ) + β(1 − α)[(1 − p)τ + (1 − q)f ] − Θ(28)Note that f has no impact on A, while D is a function of f . This meansthat to clarify the eﬀect of f on the form of human capital accumulation, we
need to derive ∂D/∂f using (28). This can be derived as[(1 − τ )[1 − β(1 − α)] − Θ][q(1 − τ − Θ) + βτ (1 − α)(q − p)]∂D. (29)=∂f[(1 − τ ) + β(1 − α)[(1 − p)τ + (1 − q)f ] − Θ]2
From the assumption that et > 0, the sign of the denominator in (29) isalways positive. Moreover, when we assume that C > 0, we have 1 − τ −Θ − β(1 − τ )(1 − α) > 0, and hence, the sign of the first square bracket
in the numerator is positive. Thus, the sign of (29) depends on the sign ofq(1 − τ − Θ) + βτ (1 − α)(q − p). This means that the sign of D is determinedaccording to the relative magnitudes of q and p; this is essentially the same
argument as that discussed in the previous section.

5

Conclusion

In this paper, we have formulated a neoclassical growth model comprising
education, child labor, and cash transfer, with a focus on developing andaid-receiving countries. While numerous preceding studies have explained
the bifurcation in terms of internal aﬀairs, the main argument of this paper
is that the aid allocation policy employed by donor countries, thereby the
motive of aid providers, leads to divaricated and cyclical growth in economic
development.
16

This analysis is important for several reasons. First, empirical researchers
may wish to test how the changes in the critical income level of aid policy affect the growth paths in developing countries. This paper oﬀers a simple but
basic model to associate the donor’s policy on critical income level with economic development. Second, researchers in applied work require additional
reasons for explaining the various growth paths that we observe in economic
development. The present work is also useful because it formally incorporates critical factors in developing countries, e.g., fertility, cash transfer, andchildren’s labor-education trade-oﬀ. This enables us to examine the impact
of internal policies related to these factors on the growth path of economic
development.
Furthermore, since our main interest is to present a simple model showingthat the foreign aid policy employed by donor countries causes divaricatedand cyclical growth in economic development, we simply assume that the
government policies are fixed; The current model consider neither the objectives nor strategic behaviors of the donor country, although Alesina andDollar (2000) among others shows considerable evidence supporting that thepattern of aid is dictated by the political and strategic considerations of thedonor. The extension of the present model, which is left for future investigation, to the one that considers endogenous policy choices could provide
insightful implications on the optimal policies adopted in both the donor andrecipient countries.

Acknowledgements
An earlier version of this paper was presented at the 2009 ACE International
Conference held in Hong Kong. The authors would like to thank Segnana
Maria Luigia for her helpful comments. The second author has been supported by grants from the JSPS Grant-in-Aid for Scientific Research (B) andthe Zengin Foundation for Studies on Economics and Finance.

17

References
Alesina, A., and Dollar, D. (2000), Who Gives Foreign Aid to Whom and
Why?, Journal of Economic Growth 5, 33-63.
Arrow, K.J., and Kurz, M. (1970), Public Investment, the Rate of Return,and Fiscal Policy, Johns Hopkins Press.
Azariadis, C., and Drazen, A. (1990), Threshold Externalities in Economic
Development, Quarterly Journal of Economics 105, 501-526.
Azariadis, C., and Stachurski, J. (2004), Poverty Traps. In: Aghion, Durlauf(Eds.), Handbook of Economic Growth.
Burnside, C., and Dollar, D. (2000), Aid, Polices, and Growth, American
Economic Review 90, 847-868.
Chakraborty, S., and Das, M. (2005), Mortality, Fertility and Child Labor,
Economics Letters 86, 273-278.
Chatterjee, S., Sakoulis,G., and Turnovsky, S. J. (2003), Unilateral Capital
Transfers, Public Investment, and Economic Growth, European Economic Review, 47, 1077-1103.
Chatterjee, S., and Turnovsky, S. J. (2006), Foreign Aid and Economic
Growth: The Role of Flexible Labor Supply, Journal of Development
Economics, 84, 507-533.
Chatterjee, S., Giuliano, P., and Kaya, I. (2007), Where Has All the MoneyGone? Foreign Aid and the Quest for Growth, IEA Discussion paper
2858.
Clemens, M.A., Radelet, S., and Bhavnani, R. (2004), Counting Chickens
When They Hatch: The Short Term Eﬀect of Aid on Growth, Working
Paper No. 44, Center for Global Development.

18Collier, P., and Dollar, D. (2002), Aid Allocation and Poverty Reduction,
European Economic Review 46(8), 1475-1500.
Dalgaard, C.J. (2008), Donor Policy Rules and Aid Eﬀectiveness, Journalof Economic Dynamics and Control 32, 1895-1920.
Dollar, D., and Levine, R. (2006), The Increasing Selectivity of Foreign Aid,
1984-2003, World Development 34(12), 2034-2046.
Easterly, W., Levine, R., and Roodman, D. (2004), Aid, Policies, and
Growth: Comment, American Economic Review 94(3), 774-780.
Feyzioglu, T., Swaroop, V., and Zhu, M. (1998), A Panel Data Analysisof the Fungibility of Foreign Aid. World Bank Economic Review, 12,
29-58.
Galor, O., and Weil, D.N. (2000), Population, Technology and Growth:
From Malthusian Stagnation to the Demographic Transition and Beyond, American Economic Review 90, 806-828.
Galor, O., and Zeria, J. (1993), Income Distribution and Macroeconomics,
Review of Economic Studies 60, 35-52.
Hansen, H., and Tarp, F. (2001), Aid and Growth Regressions, Journal of
Development Economics 64, 547-570.
Hazan, M., and Berdugo, B. (2002), Child Labour, Fertility, and Economic
Growth, Economic Journal 112, 810-828.
Healey, J., and Killick, T. (2001), Using Aid to Reduce Poverty, in Tarp,
F., and Hjertholm, P. (eds), Foreign Aid and Development: Lessons
Learnt and Directions for the Future, New York: Routledge.
Hjertholm, P., and White, H. (2001), Foreign Aid in Historical Perspective:
Background and Trend, in Tarp, F., and Hjertholm, P. (eds), Foreign
Aid and Development: Lessons Learnt and Directions for the Future,
New York: Routledge.
19

Kitaura, K. (2009), Child Labor, Education Aid, and Economic Growth,
Journal of Macroeconomics 31, 614-620.
Kraay, A., and Raddatz, C. (2007), Poverty Traps, Aid, and Growth, Journal of Development Economics 82, 315-347.
McGillivray, M., and Morrissey, O. (2004), Fiscal Eﬀects of Aid, in Fiscal
Policy for Development: Poverty, Reconstruction and Growth, ed. by
T. Addison, and A. Roe, pp.72-96. Palgrave Macmillan, Basingstoke,
Hampshire, United Kingdom.
Moav, O. (2005), Cheap Children and the Persistence of Poverty, Economic
Journal 115, 88-110.
OECD (2009), Aid for Trade at a Glance 2009: Maintaining Momentum,
OECD, Paris.
Ole, M. A. (2001), Sector Programme Assistance, in Tarp, F., and Hjertholm,P. (eds), Foreign Aid and Development: Lessons Learnt and Directions
for the Future, New York: Routledge.
Pack, H., and Pack, J. (1993), Foreign Aid and the Question of Fungibility,
Review of Economics and Statistics, 75, 258-265.
Tabata, K. (2003), Inverted U-shaped Fertility Dynamics, the Poverty Trap
and Growth, Economics Letters 81, 241-248.
World Bank (1998), Assessing Aid: What Works, What Doesn’t, and Why.
Washington, DC: The World Bank.

20

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21

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