Journal of Macroeconomics 33 (2011) 819–827

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Journal of Macroeconomics

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Multiple equilibria arising from donor’s aid policyin economic development

Koji Kitaura a, Hikaru Ogawa b, Sayaka Yakita b,⇑a Faculty of Economics, Tezukayama University, 7-1-1 Tezukayama, Nara 631-8501, Japanb School of Economics, Nagoya University, Furocho Chikusaku, Nagoya 464-8601, Japan

a r t i c l e i n f o

Article history:Received 3 June 2010Accepted 7 September 2011Available online 21 September 2011

JEL classification:F35O11O38

Keywords:Aid allocationFungibilityMultiple equilibriaCyclical growthEconomic development

0164-0704/$ - see front matter � 2011 Elsevier Incdoi:10.1016/j.jmacro.2011.09.003

⇑ Corresponding author. Tel.: +81 52 789 2379; faE-mail addresses: kkitaura@tezukayama-u.ac.jp (

1 See, for example, Collier and Dollar (2002), Hans2 It is, of course, true that the discontinuity in techn

shift from decreasing to increasing returns-to-scale t

a b s t r a c t

This paper presents a neoclassical growth model comprising education and child labor witha focus on developing and aid-receiving countries to demonstrate cyclical growth andbifurcation in economic development. The appearance of multiple equilibria has often beenattributed to the internal affairs of recipient countries, such as technology in production,subsistence minimum in consumption, and liquidity constraints in investment. The mainargument of this paper is that the aid allocation policy employed by donor countries,thereby the motive of aid-providers, leads to divaricated and cyclical development in therecipient countries.

� 2011 Elsevier Inc. All rights reserved.

1. Introduction

Developed countries have repeatedly made large fiscal transfers to developing countries in order to aid their economictakeoff. The impact of foreign aid from donors to recipient countries varies across countries. These variations can primarilybe explained by a set of particular circumstances in the recipient countries. The empirical study of Burnside and Dollar(2000) has piqued our interest in good policies in the recipient countries. The study found that the contribution of develop-ment aid to economic growth is more in countries that have a good policy environment than in those that are not well gov-erned. This result has been reexamined by many researchers in order to develop a better understanding of aid effectiveness.1

The persistent differences in growth rates of less-developed countries have also been explained by theoretical research-ers. One of the contributory explanations is the existence of a threshold effect arising from discontinuity in the use of tech-nology, as shown by Azariadis and Drazen (1990). When production technology in an aid-receiving country is a step functionwith a jump at some critical level of physical/human capital, the economy exhibits bifurcation; this leads to an environmentwhere stagnant countries and countries succeeding in economic takeoff coexist.2 This argument calls for a bifurcation mech-anism on the technological features of aid-receiving countries. The other factors causing bifurcation in economic growth, as

. All rights reserved.

x: +81 52 789 4924.K. Kitaura), ogawa@soec.nagoya-u.ac.jp (H. Ogawa), yakita.sayaka@b.mbox.nagoya-u.ac.jp (S. Yakita).en and Tarp (2001), Easterly et al. (2004), Clemens et al. (2004) and Dollar and Levine (2006).ology is not strictly required, as stated by Azariadis and Drazen (1990, p.509). In fact, what is required is aechnology at any level of state variables.

820 K. Kitaura et al. / Journal of Macroeconomics 33 (2011) 819–827

shown in most of the preceding theoretical studies, are the existence of a subsistence minimum in consumption, liquidity con-straints in investment, and the nature of increasing returns in production; moreover, all of these factors are based on the inter-nal affairs of the target countries, i.e., their preferences, technology, and market conditions.3

This paper aims to spark an interest in the possibility that bifurcation in economic development is generated not only bythe internal conditions of the recipient countries but also by aid policy of donor countries. Specifically, the feature that dif-ferentiates our model from those of other related studies is the reasoning behind our model that multiplicity and cyclicalgrowth are caused by the form of foreign aid allocation employed by the donor countries.4 This bifurcation can be observedeven among countries that have the same technology, preferences, and market structure. The form of foreign aid considered inthis paper is not unusual; we simply assume that the donor provides developing countries with assistance under a co-financeregime to stimulate human capital accumulation until the recipient country’s economic standard reaches the benchmark level,after which the donor ceases to support the recipient and the developing country is no longer on the list of aid recipients.

In this paper, the donor country’s aid policy is characterized not only by a benchmark level but also by the type of aidallocation among various areas of public spending. This approach is based on data that indicates the importance of effectiveaid allocation among various types of public spending for economic growth in the recipient country.5 In our model, we haveconsidered two types of policy options: one is education aid to improve the quality of public education, and the other is cashtransfers to poor families. It is natural to have a stake in aid for education because the sectoral composition of aid has changedquite dramatically since the early 1990s. The most notable change is in the share of aid devoted to education, which rose fromapproximately 5.9% during 1990–1992 to approximately 8.2% during 2002–2004, whereas the share of non-educational aid andgeneral budget support decreased from approximately 12.5% to approximately 7.5% (Thiele et al., 2007). The decomposition ofaid enables us to examine how the allocation of aid between productive and non-productive spending affects the economicdevelopment of the recipient country.

The rest of this paper is organized as follows. Section 2 introduces the basic model, and Section 3 presents the optimiza-tion problem. The growth paths and steady states are examined in Section 4. Section 5 concludes the paper.

2. Model

2.1. Individuals

We employ a three-periods-overlapping-generations model in a small open economy. In our analysis, there exist individ-uals who live for three-periods and a recipient government that receives support from developed countries until it reaches acertain level of development. All individuals in the recipient country live for three periods and are endowed with one unit oftime in both the first and second periods of their lives. In the first period (childhood), they spend their time in schooling inorder to acquire human capital and working as child laborers. In the second period (parenthood), they work, plan their fam-ilies, and rear children. Finally, they retire in the third period.

Individuals are considered to inherit human capital from their parents. Further, they attend school to acquire human cap-ital. The function of human capital accumulation is given as

3 Seepresent

4 Althis notewnot conthe aid

5 For(1998)

6 Althg + c < 1

ht ¼ eat�1Eg

t�1hct�1; ð1Þ

where the subscript t(=1,2, . . .) denotes the period. In (1), a, g, and c are the parameters which fit the confines of [0,1].6 It isassumed that human capital of the individuals born at time t � 1 depends on the schooling time, et�1, the level of public edu-cation, Et�1, and the human capital of their parents, ht�1. Note that human capital is accumulated both through schooling timeand public expenditure for education.

The lifetime utility of an individual of generation t, born in period t � 1, is assumed to be log-linear, and is given by theform

Ut ¼ ð1� bÞ ln ctþ1 þ b ln nthtþ1; ð2Þ

where b(>0) is the preference parameter for children. The utility of the individuals of generation t depends on the consump-tion in the third period, ct+1, the number of children they rear, nt, and the level of human capital of their children, ht+1.

In the second period of life, as parents, individuals decide on how to allocate the endowed time of unit one to theirchildren between schooling and working as child laborers. Assuming that the working ability of children is inferior to thatof parents, the provision of efficient labor by a child is expressed as (1 � et)hht, where 1 � et and h(0 < h < 1) represents the

, for example, Galor and Zeria (1993), Galor and Weil (2000), Hazan and Berdugo (2002), Tabata (2003), and Moav (2005). See also the excellent surveyed by Azariadis and Stachurski (2004).ough few studies have depicted the relationship between the donor’s aid policy and growth path in economic development, a study by Dalgaard (2008)orthy. Using the model of Arrow and Kurz (1970), Dalgaard succeeds in showing that foreign aid policy may cause cyclical growth. While Dalgaard does

sider the allocation of foreign aid in alleviating poverty, our results argue that the aid allocation rule employed by donor countries, thereby the motive ofprovider, causes not only cyclical growth but also multiple equilibrium in the recipient countries, which has not been mentioned previously.example, Hansen and Tarp (2001) point out that the aid-growth relationship depends not only on the level of aid but also on aid allocation. World Bankargues that the decision on aid allocation would have a greater impact on poverty reduction if it were targeted at the poorest countries.ough Glomm and Kaganovich (2003, 2008) assume that g = c, we relax this condition in this model. The restriction that is required in our model is, as will be found later.

K. Kitaura et al. / Journal of Macroeconomics 33 (2011) 819–827 821

time devoted to working and the working ability of the child, respectively.7 Moreover, parents decide on their own timeallocation of one unit between working and child rearing. If we denote the rearing time per child as z, the time devotedto rearing nt children will be z nt, and that devoted to working will be 1 � z nt. Since we assume that individuals consumeonly in the third period of their life, they save all of their income in the second period. Thus, the budget constraints of indi-viduals born at t � 1 are given as

7 Hazlabor.

8 The9 Her

the reci(2010).

10 Althrecipienmaximu

11 Anwelfarerecipien

st ¼ ntð1� etÞhht þ ð1� zntÞhtð1� sÞ þ Rt ; ð3Þctþ1 ¼ ð1þ rÞst; ð4Þ

where st denotes the saving, s the income tax rate, and r the world interest rate, which is given exogenously.8 The right-handside of (3) is the income in the second period of their life; this comprises the income from child labor, adult labor, and cashtransfer, Rt, which is provided by the government. We assume that the government cannot tax unlawful income gained fromchild labor. (4) represents the budget balance in the third period, indicating that consumption in the retirement period is fi-nanced by saving in the prior period.

2.2. Government

The government in the recipient country provides both public education, Et, and cash transfer, Rt, to its citizens. It is fi-nanced by income tax revenue and foreign aid. The government receives foreign aid, Ft, from donor countries until the re-cipient country reaches a certain level of development. The benchmark level, measured by the level of human capital inthe recipient country, is exogenous for the recipient country and, in any case, determined by the donor country that in turnrefers to criteria such as the world standard level. The simplest form of foreign aid is assumed to be a type of matching grantaimed at stimulating human capital development, as shown below:9

Ft ¼ f ðhtÞht ; where f ðhtÞ ¼f > 0 if ht <

�h

0 if ht P �h

(: ð5Þ

This equation shows that the foreign aid received by a country depends on its level of human capital. When the level ofhuman capital in the recipient country is relatively low, i.e., lesser than the benchmark level, �h, foreign aid will be pro-vided. Since human capital accumulates with time, foreign aid will not be provided once it reaches the benchmark level,�h.10

Given the level of foreign aid, the recipient country at time t allocates the aid as part of the financial source for publiceducation, Et, and cash transfer to the residents, Rt. In addition, revenue from income tax is also allocated for publiceducation and cash transfer. In other words, since public education and cash transfer are co-financed by domestic in-come tax revenue and foreign aid, the government’s budget constraints for public education and cash transfer are givenby11

Et ¼ psð1� zntÞht þ qFt; ð6ÞRt ¼ ð1� pÞsð1� zntÞht þ ð1� qÞFt ; ð7Þ

where p denotes the share of tax revenue allocated to public education and q denotes the share earmarked by the donor forpublic education. Here, we consider the education expenditure as a productive public investment and avoid taking up otherproductive spending, such as infrastructural and agricultural development. This approach enables us to figure out the effectof aid for productive education in a developing country by contrasting it with the aid for non-productive cash transfer. Inorder to focus on the aid policies represented by q and �h, in the following analysis we assume that the policy variables inthe recipient country, s and p, are exogenous.

an and Berdugo (2002) and Chakraborty and Das (2005) also assume that the productivity of child labor is relatively lower than the productivity of adult

wage per unit of human capital is normalized to one because we implicitly assume that the production function is linear in human capital.e, we discuss the effects of foreign aid on the basis of a model wherein the level of foreign aid is determined according to the level of human capital inpient country. An alternative form of foreign aid that depends on the income level of adults in the recipient country is also discussed in Kitaura et al.

ough 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 ODAts by categorizing them into four groups based on their income levels. Within the list, if the income level of a certain country consistently exceeds them level for 3 years, that country graduates from the list. Twenty-five countries had graduated from this list by 2003. See OECD (2009).

attempt to introduce co-financing foreign aid transfer is made by Chatterjee et al. (2003). They investigate the link between foreign aid, growth andusing an endogenous growth model with public capital accumulation. Moreover, in the same setting, Chatterjee and Turnovsky (2006) examine thet government’s intertemporal fiscal balance introducing endogenous labor supply.

822 K. Kitaura et al. / Journal of Macroeconomics 33 (2011) 819–827

3. Optimization

3.1. Individuals in the recipient country

A problem faced by adult individuals at time t is to decide on level of consumption, ct+1, number of children, nt, and thechildren’s schooling time, et, so as to maximize their lifetime utility, given the quality of public education, Et, and the amountof cash transfer, Rt. Using (1)–(4), we derive the demand for ct+1,nt, and et as

12 Thi13 See

McGilli

ctþ1 ¼ ð1� bÞ½ð1� sÞht þ Rt �; ð8Þ

nt ¼bð1� aÞ½ð1� sÞht þ Rt �½zð1� sÞ � h�ht

; ð9Þ

et ¼a½zð1� sÞ � h�

hð1� aÞ ; ð10Þ

respectively. Since the schooling time of a child cannot be negative, we assume that z(1 � s) P h. Substituting (5) and (7) into(9), we have

n� ¼ bð1� aÞ½1� spþ f ð1� qÞ�zð1� sÞ � hþ bszð1� aÞð1� pÞ : ð11Þ

Using (5), (6) and (11), the expenditure for public education is obtained as

Et ¼ ps zð1� sÞ � h� zbð1� aÞ½f ð1� qÞ þ 1� s�zð1� sÞ � hþ bszð1� aÞð1� pÞ

� �þ fq

� �ht : ð12Þ

Substituting (10) and (12) into (1), human capital accumulation can be described by

htþ1 ¼ AaðBf þ CÞghgþct ; ð13Þ

where

A � að1� s�HÞHð1� aÞ ; ð14Þ

B � qð1� s�HÞ þ bsð1� aÞðq� pÞ1� s�Hþ bsð1� aÞð1� pÞ ; ð15Þ

C � ps½ð1� sÞ½1� bð1� aÞ� �H�1� s�Hþ bsð1� aÞð1� pÞ ; ð16Þ

and H � hz�1. Since ht+1 = ht in the steady state, the steady-state level of human capital, h�, is derived as12

h� ¼ Aa

1�g�cðBf þ CÞg

1�g�c: ð17Þ

3.2. Donor

Our model describes an environment wherein the donor countries have the responsibility to design the development pro-grams of the recipient countries and have full ownership and control of the foreign aid allocation. Full ownership by the do-nors is partially justified by applying the argument of Hjertholm and White (2001), which suggests that donors have acomparative advantage in allocating resources efficiently and therefore tend to dominate the foreign aid programs in devel-oping countries; thus, they permit the recipient countries to only play a very limited role.

Alesina and Dollar (2000) among others provide considerable evidence that the pattern and effects of foreign aid are dic-tated by political and strategic considerations of the donor countries. Although many suppositions can be made regarding adonor country’s objectives, we assume that a rational and benevolent donor would aim to increase the steady-state humancapital of the recipient country; i.e., the donor attempts to maximize (17) with respect to q.

In examining the effect of donor-leading aid policies on the economic development of recipient countries, we encounterthe fungibility problem, which offsets the positive impact of foreign aid.13 When the foreign aid is not fungible, the govern-ment of the recipient country has no means of circumventing the goals of the donors to serve their own interests, and thus, theaid is used as per the wishes of the donor. As we will find later, in our model, the donor country directs the recipient to spendthe aid money on public education because the donor is assumed to aim at increasing the human capital of the recipient coun-try. However, the recipient country may not accede to the donor’s plan and may tend to divert the aid to other ends. Owing to

s is a stable equilibrium because 0 < ð@htþ1=@htÞjht¼h� ¼ gþ c < 1.Pack and Pack (1993), Feyzioglu et al. (1998), Healey and Killick (2001), Chatterjee et al. (2007) and Kitaura (2009) for the fungibility problem. See also

vray and Morrissey (2004), which reviews the studies focusing on the fungibility problem.

K. Kitaura et al. / Journal of Macroeconomics 33 (2011) 819–827 823

informational asymmetry between the donor and recipient country, the recipient may spend only a small part of the aid on pub-lic education, and the rest is distributed as cash transfer. This case can be interpreted as a case where the foreign aid is fungible.

In this subsection, we classify our analysis into two parts: non-fungible aid and fungible aid policies.Non-fungible aid. When f > 0, the maximization of the level of human capital in the steady state, represented by (17), with

respect to q gives q = 1, since @h�=@q > 0 for all q 2 [0,1]. This strategy is easily understood as human capital accumulation ispromoted by education. Thus, the donor country focuses the aid on public education. Substituting q = 1 into (15), we haveB = 1. The process of human capital accumulation and human capital in the steady state are given by the following equations:

htþ1 ¼ Aaðf þ CÞghgþct ; ð18Þ

h� ¼ Aa

1�g�cðf þ CÞg

1�g�c; ð19Þ

respectively. The form of (18) depends on the sign of A and C. Owing to the assumption that the schooling time of a child ispositive, 1 � s �H P 0, the sign of A and the denominator of C are always positive (see (14) and (16)). However, the sign of Ccannot be determined because the sign of the numerators in C is ambiguous. For our analysis, however, we assume that(1 � s)(1 � b(1 � a)) > H, which ensures that C is positive.

Fungible aid. When the aid is not allocated as intended by the donor, it is not necessarily that the aid, in effect, is allocatedas q = 1. In fact, 0 6 q < 1 generally holds for the recipient country. In this case, the process of human capital accumulationand human capital in the steady state can be represented by (13) and (17).

4. Steady state

4.1. Preliminary consideration

In this section, we analyze how the benchmark level of human capital, �h, affects bifurcation in economic development.From (13), we find that

@htþ1

@ht¼ ðgþ cÞAaðBf þ CÞg

h1�g�ct

> 0;

@2htþ1

@h2t

¼ �ð1� g� cÞðgþ cÞAaðBf þ CÞg

h2�g�ct

< 0:

Further, note that when human capital of the recipient country reaches the benchmark level, �h, the recipient country ceasesto receive foreign aid; i.e., f = 0. Therefore, when ht P �h, (18) becomes

htþ1 ¼ AaCghgþct ; ð20Þ

where public education is financed solely by income tax revenue generated within the country. Denoting the steady-statelevel of human capital when f = 0 as ~h�, we have ~h� ¼ A

a1�g�cC

g1�g�c.

4.2. Non-fungible aid (q = 1)

Here, we have three different cases: two involve a unique steady state and one involves the possibility that human capitaldoes not converge to a steady state. Accumulation of human capital according to (18) is faster than that according to (20)because f > 0. Furthermore, it is clear that h� > ~h�, suggesting that the steady-state level of human capital when f > 0 is great-er than that when f = 0. Using these properties, the process of human capital accumulation is depicted in Fig. 1.

Fig. 1a and b depict the case where human capital converges to a unique equilibrium. In contrast, Fig. 1c shows the casewhere human capital does not converge and the steady state cannot be achieved. In Fig. 1a, where ~h� < h� < �h, the bench-mark level of human capital is set substantially high. In this case, human capital converges to a high steady-state level, de-noted by h�, regardless of the initial human capital. Fig. 1b displays the case where the donor country sets the benchmarklevel of human capital at a considerably low level, i.e., �h 6 ~h� < h�. In this case, human capital will converge to a low level,~h�.

Fig. 1c shows the third case where the benchmark level �h is set between the possible steady-state levels, i.e., ~h� < �h 6 h�.In this case, there is a possibility that the steady state cannot be achieved and the aid-receiving country experiences cyclicaldevelopment. The intuition behind this result is as follows: If the level of human capital in the recipient country is lower thanthe benchmark level, the government of the recipient country will receive foreign aid and will use it to provide public edu-cation. An increase in the earmarked aid for public education affects human capital in the following two ways: First, an in-crease in foreign aid results in a drop in fertility rate, nt (see (11)), and an increase in labor supply, 1 � z nt. Second, anincrease in foreign aid leads to an improvement in the quality of public education (see (12)). Thus, the level of human capitalwill increase with a provision of foreign aid. When the level of human capital exceeds the benchmark level, the donor coun-try will cease to provide foreign aid. As a result, educational expenditure in the recipient country is reduced and, therefore,the level of human capital falls below the benchmark level. Thus, the recipient country again receives foreign aid, leading tocyclical growth.

a b

cFig. 1. Evolutions of the per capita human capital under non-fungible aid.

824 K. Kitaura et al. / Journal of Macroeconomics 33 (2011) 819–827

We summarize our main results for the case where aid is not fungible as follows:

Proposition 1. Assume that q = 1, and thereby B = 1 > 0. When the donor sets �h at a sufficiently high level to satisfy ~h� < h� < �h,the equilibrium converges to a high steady-state level of human capital. In contrast, when it sets �h at a sufficiently low level,�h 6 ~h� < h�, the equilibrium converges to a low steady state. Otherwise, when ~h� < �h 6 h�, the recipient country experiencescyclical development.

4.3. Fungible aid (q < 1)

When q < 1, the sign of B is crucial for our analysis. The results obtained in Proposition 1 still hold if q P sp, which impliesthat B P 0 will always hold. However, when q < sp, it does not exclude the possibility that B becomes negative. When B < 0,the accumulation of human capital according to (20) is faster than that according to (18). Furthermore, it is clear that h� < ~h�,suggesting that the steady-state level of human capital when f > 0 is smaller than that when f = 0.

The intuition of this property is simple: From (11), an increase in f increases the fertility rate and decreases the labor sup-ply of adult, since the rearing time per child is constant. A reduction in adult labor reduces the tax revenue, thereby reducingthe expenditure on public education when q < ps (from (12)). This reduces the human capital in the recipient country. There-fore, in this case, the donor faces a dilemma: An increase in aid reduces the investment for human capital accumulation,which in turn induces the recipient’s economy to fall into a poverty trap with abundant child labor.14

Since human capital accumulation according to (20) is faster than that according to (18) and ~h� > h�, then the situationshown in Fig. 2 arises. Fig. 2a and b depict the case where human capital converges to a unique equilibrium. In contrast,Fig. 2c shows the case where multiple equilibria emerge. Fig. 2a depicts the case where the benchmark level of human capitalis set substantially high, i.e., h� < ~h� 6 �h. In this case, human capital converges to a steady-state level, h�, regardless of theinitial human capital. Fig. 2b represents the case where the benchmark level of human capital is substantially low, i.e.,�h 6 h� < ~h�. In this case, the human capital will converge to ~h�. Fig. 2c shows the case where the benchmark level, �h, isset between the steady-state levels; i.e., h� < �h < ~h�. In this case, there is a possibility of multiple equilibria wherein the

14 In a somewhat different context without foreign aid, Azarnert (2008) derives a similar result in the sense that income security raises the fertility andreduces the spending on education, thereby reducing the investment in human capital, which creates the poverty trap.

a

c

b

Fig. 2. Evolutions of the per capita human capital under fungible aid.

K. Kitaura et al. / Journal of Macroeconomics 33 (2011) 819–827 825

initial level of human capital plays a crucial role. If an economy has a relatively low level of initial human capital, i.e., h0 <�h,

it will converge to a low level of human capital, h�. On the other hand, in an economy where the initial level of human capitalis relatively high, the human capital converges to ~h�. Therefore, in this case, the developing countries, which are usually con-sidered to have a relatively low level of initial human capital, tend to converge to a low steady state. Focusing on the case ofB < 0, which may occur when q < 1, we obtain the following result:

Proposition 2. Assume that B < 0. When the donor sets �h at a sufficiently high level to satisfy h� < ~h� 6 �h, the equilibriumconverges to a low steady-state level of human capital. In contrast, when it sets �h at a sufficiently low level, �h 6 h� < ~h�, theequilibrium converges to a high steady state. Otherwise, when h� < �h < ~h�, multiple equilibria may arise in the steady state.

4.4. A numerical example

For further illustration, we provide a simple example wherein cyclical growth and multiple equilibria are produced. As-sume that q = 1.0, a = 0.3, g = 0.2, c = 0.2, b = 0.3, s = 0.1, and f = 0.3. In addition, we set h = 0.07 and z = 0.15, which followDoepke (2004) and de la Croix and Doepke (2004). Then, we have ~h� ¼ 0:1107 and h� ¼ 0:4248; the recipient country expe-riences cyclical development between ~h� ¼ 0:1107 and h� ¼ 0:4248. In order to observe the multiple equilibria in their con-crete form, we set q = 0.01 and use the other parameters listed above. Then, we have the following two equilibria in thesteady state: h� ¼ 0:2168 and ~h� ¼ 0:2332. These values slightly change to h� ¼ 0:2233 and ~h� ¼ 0:2353 when the share ofeducation spending and the tax rate increases, that is, q = 0.10 and s = 0.25.

To summarize, under non-fungible aid (q = 1), the level of human capital enters a cycle between ~h� and h� if the donor sets�h between ~h� and h�. A cyclical growth emerges in a fairly large proportion of cases even though the parameter values aresubtly changed. In contrast, under fungible aid (q = 0.02 < 1), we confirm that there are two steady states, h� ¼ 0:216 and~h� ¼ 0:233 when the donor sets �h between h� and ~h�. The result of multiple equilibria can be widely observed with subtlechanges of the parameters.

5. Conclusion

In this paper, we formulated a neoclassical growth model comprising education, child labor, and cash transfer, with a fo-cus on developing and aid-receiving countries. While numerous preceding studies have explained the bifurcation in

826 K. Kitaura et al. / Journal of Macroeconomics 33 (2011) 819–827

economic development in terms of internal affairs, the main argument of this paper is that the aid allocation policy employedby donor countries, thereby the strategy of aid providers, leads to divaricated and cyclical growth in economic development.A noteworthy feature of this paper is that in describing the donor-recipient relationship, we formally incorporated certaincritical factors of developing countries, such as fungibility, fertility, and children’s labor-education trade-off. This enabledus to examine the impact of internal policies related to these factors on the growth path of economic development.

Although the main argument of this paper was to show the possibility of multiple equilibria and cyclical growth causedby donor countries’ aid policies, which was captured by setting the benchmark level, �h, our results imply that the larger thefraction of aid devoted to education, q, the higher is the possibility of cyclical growth. It goes without saying that the fractionof aid devoted to education is not the only the root factor that causes the cyclical growth or multiple equilibria. Hence, the-oretically, we have not been able to precisely show which country may experience a cyclical growth or multiple equilibria onthe basis of its share of education spending. However, based on the fact that the fraction of aid devoted to education has beenincreasing over time, our results imply that the economy has a tendency to experience cyclical growth, given other factorsconstant.

Before concluding this paper, we will discuss some problems that remain unsolved. First, since our main interest is topresent a simple model showing that the foreign aid policy employed by donor countries causes divaricated and cyclicalgrowth in economic development, we simply assume that the policies in the recipient countries, p and s, are fixed: the cur-rent model considers neither the objectives nor the strategic behaviors of the recipient governments. Incorporation of theendogenous policy choices of the recipient countries could provide insightful information related to the implications ofthe optimal policies adopted. Second, a thorough empirical examination can be conducted on the basis of this model, eventhough we confirm the evolution of cyclical and diverse development using a simple numerical simulation. An importantresearch topic from both academic and practical perspectives would be to test how changes in the critical income level ofaid policies affect the growth paths in developing countries.

Acknowledgements

An earlier version of this paper was presented at the Kyushu University, University of Freiburg, Tokyo Metropolitan Uni-versity, the City University of Hong Kong, Tezukayama University, and WEAI at San Diego. The authors would like to thankKeisuke Osumi, Nobuaki Hori, Toshiki Tamai, Hiroki Arato, Takeo Hori, Akira Momota, Antonio Farfán Vallespin, SegnanaMaria Luigia, and Jinzhuo Zhao for helpful comments. The authors also thank the anonymous referee, who made suggestionsfor which the authors are grateful. The second author has been supported by grants from the JSPS Grant-in-Aid for ScientificResearch (B) and the Zengin Foundation for Studies on Economics and Finance.

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