ISSN (Print) 0473-453X

Discussion Paper No. 1248

ISSN (Online) 2435-0982

INTERGENERATIONAL MOBILITY
AND STUDENT LOANS

Ryota Nakano

July 2024

The Institute of Social and Economic Research
Osaka University
6-1 Mihogaoka, Ibaraki, Osaka 567-0047, Japan

Intergenerational mobility and student loans *Ryota Nakano†
July 2024

Abstract
The decision of whether and how much to borrow from the credit market in order toﬁnance education costs depends crucially on parental investment in education. This study
constructs a simple two-period overlapping generations model incorporating both educational investment from parents and educational borrowing. The analysis shows that in
the case where educational investment from parents and educational borrowing are substitutive, the relaxation of the borrowing constraint improves intergenerational mobility.
In the complementary case, the relaxation of the borrowing constraint may impair intergenerational mobility. Implications differ depending on whether the relationship between
parental investments and borrowings is substitutive or complementary.
Keywords: Educational borrowing, Intergenerational mobility, Education
JEL Classiﬁcation Numbers: I22, I24, J62* I would like to thank Tatsuro Iwaisako, Kohei Okada and the participants at the Japanese Economic Association 2024 Spring Meeting for helpful comments and suggestions. I gratefully acknowledges the ﬁnancial supportof the Joint Usage/Research Centers at the Institute of Social and Economic Research (ISER) and Grants-in-Aid
for Scientiﬁc Research (20H5631). All remaining errors are my own.
†
Graduate School of Economics, Osaka University, 1-7, Machikaneyama, Toyonaka, Osaka, 560-0043,
JAPAN; e-mail address:r.nakano1028@gmail.com

1

Introduction
As a measure of equality of opportunity, researches have paid attention to intergenerational

mobility since the seminar paper by Becker and Tomes (1979). Intergenerational mobility
relates to other fundamental concerns, such as income inequality, social welfare, and economic
efﬁciency, for economists and policymakers. A large body of the empirical literature showsthat the relationship between intergenerational mobility and income inequality is negatively
correlated, which is referred to as the “Great Gatsby Curve” (Blanden, 2013; Corak, 2013,
and references therein). Intergenerational mobility matters because if an individual’s income
is fully determined by her/his family background, income and wealth inequality will persist.
If economic status were determined by birth, people would never make an effort to climb thesocial ladder. It leads to not only a lower competitiveness of society but also to a decline ineconomic efﬁciency.
Education is an important factor of intergenerational mobility, as it provides a viable pathway for climbing the social ladder. Recent empirical research emphasizes that educational
inequality expands in developed countries. Blanden et al. (2023) has explored the “Educational Great Gatsby Curve,” which shows the relationship between educational achievements
and income inequality, and the relationship between educational attainments and income inequality.1 Blanden et al. (2023) has reported that educational attainment does not seem to bepositively correlated with income inequality. However, educational achievement is positively
correlated with income inequality. These observations imply that expanding income inequality
does not necessarily lead to an enlargement of educational attainment gap between the richand the poor. Income inequality may lead to expansions of the gap of educational achievement
between the rich and the poor. What causes the difference behind the observations might beaffordability of higher education. Owing to the lack of money, children from low-income families cannot afford to undergo higher education, even if they are academically capable and eager
to continue their studies. To ﬁll in the gap regarding economic background, school loans andscholarships provided by government are prevalent in developed countries. Despite govern1

In Blanden et al. (2023), educational achievements and attainments are measured by years of schooling andtest scores, respectively.

1mental interventions, the gap remains signiﬁcant. Costs and credit constraints may partly drivethese differences (Blanden et al., 2023).
Motivated by the aforementioned idea, the ﬁrst aim of the present paper is to examine how
individuals decide the amount of educational borrowing, considering both parental investment
and their abilities. This study constructs a simple two-period overlapping generations (OLG)
model incorporating both educational investment from parents and educational borrowing. In
the ﬁrst period of life, individuals make the decision of how much to borrow for educational
purposes while facing the credit constraint, after observing parental investments and their abilities. In line with Fan and Stark (2008), Cremer et al. (2010), and Fan and Zhang (2013), we
assume that whether an individual receives high wage or low wage depends on the probability. The second aim is to clarify the impact of the borrowing constraints on intergenerational
mobility.
The analysis shows that in the case where educational investment from parents and educational borrowing are substitutive, the relaxation of the borrowing constraint improves intergenerational mobility. In the case where educational investment from parents and educationalborrowing are complementary, however, the relaxation of the borrowing constraint may impair
intergenerational mobility. Implications differ depending on whether the relationship between
parental investments and borrowings is substitutive or complementary.
Intergenerational mobility has been studied across various theoretical frameworks. In Owen
and Weil (1998) and Garcia-Penalosa and Wälde (2000), children receive bequests from parents and decide whether to take education. They assume that due to the market imperfections,individuals cannot borrow to ﬁnance the education cost. In Hendel et al. (2005), individuals
can borrow when they decide to undergo education if the ﬁxed educational cost exceeds theirreceived bequests. Educational borrowings in their setting can be interpreted as substitutes foreducational investment from parents. However, dynamic complementarities for educational
investments have been pointed out by Cunha et al. (2006), Cunha and Heckman (2008), andCunha et al. (2010). In the present model, we can consider both the substitutability and complementarity of educational investments. In addition, individuals can choose the amount ofborrowing unlike in the existing literature.

2

Student loans serve as a mechanism for mitigating educational inequality. However, due
to credit market imperfections, such as a lack of appropriate collateral and income risks, theamount of borrowing tends to be smaller than the optimal level. Friedman (1962) suggests
the income-contingent ﬁnancing of students’ investment in human capital. Several countries
have already introduced income-contingent repayment programs. Australia started the Higher
Education Contribution Scheme (HECS) in 1989, which was later followed by other countries,
including Canada, Chile, New Zealand, the UK, and the US.2 Several studies have analyzed
income-contingent loan (hereafter, ICL) in theoretical frameworks. Eckwert and Zilcha (2010)
examine how the precision of such screening information affects investment in education, human capital formation, and economic welfare. Del Rey and Racionero (2010) also analyze fourtypes of educational schemes and show that an ICL with risk-pooling can induce the optimallevel of participation. Eckwert and Zilcha (2012) consider separately three different forms ofgovernment intervention in the market for education loans: unrestricted access to credit markets, unrestricted insurance loans, and restricted insurance loans. The third regime stimulates
investment in education and economic growth compared with the ﬁrst regime. Eckwert andZilcha (2017) consider the case in which income-contingent education ﬁnance coexists withcompetitive credit markets. They show that funding diversity leads to overinvestment due toadverse selection. These papers have explored the ideal system for educational funding in termsof the amount of investment, welfare, and income inequality. It is essential to examine the impact of the introduction of ICLs on intergenerational mobility. However, none of the literature
on ICL examines its effect on intergenerational mobility. The present paper analyzes the impact
of ICLs on intergenerational mobility in Section 4.
Some papers have analyzed educational borrowing constraint employing growth model withhuman capital accumulation. Kitaura (2012) constructs a three-period-lived OLG model inwhich individuals ﬁnance their educational expenditures by borrowing. He shows that if theelasticity of human capital to educational expenditure is great enough, the relationship between
the tightness of the constraints and the growth rate is inverted U-shaped when the constraints
are binding. Miyazaki (2016) examines how the burden of student loans affects young peo2

See Lleras (2004), Chapman (2006), and Lochner and Monge-Naranjo (2016) for details.

3

ple’s decisions. He shows a case in which the GDP growth rate decreases as the borrowing
constraints are relaxed, whereas the growth rate of GDP per capita still increases. These papers
especially focus on the impact of the tightness of the credit market for educational investment
on economic growth, whereas the present paper aims to examine the effect on intergenerational
mobility.
The remainder of this paper is organized as follows: Section 2 explains the model. Section
3 examines the impact on intergenerational mobility. Section 4 introduces the ICL regime in
the baseline model and compares the results with those in the baseline regime. Finally, Section
5 concludes the paper.

2

Model
Consider a two-period OLG model. The population of each generation is constant andassumed to be one. Each individual lives for two periods. In the ﬁrst period, an individual
decides the amount of educational borrowing to fund their own education. Education increases
the probability of acquiring a high level of human capital as we will comprehensively explain
below. In the second period, an individual supplies effective labour and allocates earned wage
to consumption, educational investment for their children, and repayment of educational borrowings. Individuals differ in their ability. Each generation consists of high and low abilities.
The difference in ability affects the likelihood of acquiring a high level of human capital. Such
attribution is random, and the fraction of individuals with high ability is λ ∈ (0, 1).
We assume a small open economy with a constant returns to scale technology. The grossrate of return on capital Rt is exogenously given. The capital-efﬁciency unit of labour ratio
is fully determined by Rt , so the wage rate per efﬁciency unit of labour w̄t is also given. We
assume that both rates are constant along time, Rt = R > 0 and w̄t = w̄ for all t. The
number of efﬁciency units of labour supplied by a worker born in period t − 1 depends on her
level of human capital hi , which is determined by the probability. If an individual succeeds ineducation, she becomes a skilled worker and supplies hs efﬁciency units of labour. The level4

of human capital is given by the following function: h if she succeeds in education
hi =

s



 hu if she fails in education(1)

where hs > hu . As the wage per efﬁciency unit is constant, we deﬁne the total wage as follows:
wi ≡ w̄hi .

(2)Whether each individual acquires a high level of human capital or not is determined by theprobability P (aj , bji , eji ) = aj π(bji , eji ). The probability depends on innate ability aj , educational expenditure by borrowing bji , and parental investment eij . The function π(bji , eji ) satisﬁes
πb > 0, πe > 0, πbb < 0, and πee < 0, where πk denotes the partial derivative with respect to k.
The probability is an increasing function of educational borrowings, educational investmentsfrom parents, and innate ability. This is also a concave function with respect to educationalborrowing and educational investment from parents.

2.1 Individuals
An individual draws utility from consumption and educational investments for their children. For tractability, an individual of generation t with ability j and type i parent maximizes
the following quasi-linear utility function:jUi,t= cji,t + γi ln eji,t ,(3)where γi denotes the preference over educational investment for their children and is assumed
that γs > γu . The assumption reﬂects that wealthier families tend to place greater emphasis on5their children’s education than poorer families. Individuals face three constraints:
cji,t + Rbji,t−1 + eji,t ≤ wij ,(4)Rbji,t−1 ≤ θwu ,(5)0 ≤ bji,t−1 .

(6)

The ﬁrst is budget constraint in the second period of life. The second is the borrowing constraintof educational borrowing, where θ ∈ (0, 1) denotes the tightness of credit constraint. An
individual has access to the credit market and can borrow for educational purposes. We consider
a situation where an individual can borrow up to a certain proportion of the minimum wage
in the next period. This ensures that the lender never incurs a loss. The third is non-negative
constraint for educational borrowing. The amount of educational borrowing cannot be negative.
In other words, individual cannot lend money for others.
We solve the maximization problem backwards. First, we derive the optimal allocationin adulthood given the amount of educational borrowing. Then, we solve the maximization
problem in childhood, which determines the amount of educational borrowing. From (3) and(4), ﬁrst-order conditions yield optimal consumption and educational investment:
cji,t = wi − Rbji,t−1 − γi ,(7)eji,t = γi .

(8)Since we assume that γs > γu , it follows that skilled parents invest more than unskilled parents,
but the amount of educational investment neither depend on their own abilities or those of theirchildren.
In the ﬁrst period of life, individuals choose the amount of educational borrowing to maximize the expected indirect utility. Substituting (7) and (8) into (3), we obtain the expected6indirect utility function:
Vt,ij = P (aj , bji,t−1 , ei,t )Us,t (bji,t−1 ) + [1 − P (aj , bji,t−1 , ei,t )]Uu,t (bji,t−1 )= aj π(bji,t−1 , ei,t )Ω + (wu − γu − Rbji,t−1 + γu ln γu ),(9)where Ω ≡ (ws − wu ) − (γs − γu ) + (γs ln γs − γu ln γu ). The optimal educational borrowing
satisﬁes the following equation:aj πb (bji,t−1 , ei,t )Ω ≥ R.

(10)

When the credit constraint is binding or the optimal educational borrowing is zero, inequality
holds. It is clear that the optimal educational borrowing is time independent. In the following,
we omit the time subscript.

2.2 Optimal educational borrowing
As we do not specify the functional form of the probability of acquiring a high level ofhuman capital, we cannot derive the solutions for optimal educational borrowings in an explicit
form. Based on some assumptions regarding the probability function, we can compare theamount of educational borrowings among individuals using (10). The introduction of parental
investment in eduction inﬂuences the decision that their children make in the ﬁrst period oflife. The relationship between educational investments from parents and educational borrowing
plays a crucial role in determining the extent to which individuals borrow in childhood.
Educational investments from parents and educational borrowings are relatively substitutive if the cross partial derivative with respect to educational investments from parents andeducational borrowing is negative, that is, πbe < 0. If educational investments from parents
are assumed to be the expenditure for university or college tuition, educational borrowings are
viewed as potential substitutes for parental ﬁnancial contributions. Ultimately, children are notrequired to borrow money if their parents fully cover tuition. In this case, a larger parental
investment decreases the amount of educational borrowing. Educational borrowings of wealth-7ier students are less than those of poorer students. There are two candidates of order in thesubstitutive case:bls < bhs < blu < bhuor bls < blu < bhs < bhu .

The magnitudes of bhs and blu depend on the functional form of probability of acquiring a highlevel of human capital. Figure 1 shows how the amount of borrowing is determined. The
downward-sloping curves represent the left-hand side of (10).

R
bls

bhs

blu

bhu

b

Figure 1: Optimal educational borrowing. In the substitutive case, there are two candidates
regarding the order of the amount borrowing for education. We show the ﬁrst case in thisﬁgure. As we have seen (10), the marginal cost of borrowing remains constant. The marginal
beneﬁt of borrowing is decreasing in the amount of borrowing. If the interior solution exists, it
is depicted in ﬁgures.
Parental investment does not affect the amount of educational borrowing if πbe = 0. The
amount of borrowing for education is irrelevant to the amount of educational investment fromparents. Children who have same ability borrow the same amount in this case, so we obtainbls = blu < bhs = bhu .

Educational investment from parents and educational borrowing are relatively complementary if πbe > 0. The dynamic complementarity of educational investments has been reported
by Cunha et al. (2006), Cunha and Heckman (2007), and Cunha et al. (2010). In these papers,
the introduction of dynamic complementarity explains a variety of ﬁndings established in thechild development and child intervention literature. If educational investments from parents
are assumed to be expenditures for education at early stages, educational borrowings for higher
education can be considered as complementary inputs. A larger ei,t−1 increases the amount of8

educational borrowing. There are two candidates of order in this case:blu < bhu < bls < bhs ,or

blu < bls < bhu < bhs .

The order of bhu and bls is indeterminate unless the functional form of the probability is speciﬁed.

3

Intergenerational mobility
Following Iyigun (1999) and Fan and Zhang (2013), we deﬁne intergenerational mobility

as the odds ratio by
M≡

Pul + Puh
∈ [0, 1].
Psl + Psh

(11)

If M is equal to one, equality of opportunity is achieved. Children of any parents have an
equal opportunity to acquire a high level of human capital. If M is equal to zero, the economy
is unfair in terms of equality of opportunity. Only children who have skilled parents have achance to acquire a high level of human capital.
To analyze the impact of changes in the tightness of the borrowing constraint on intergenerational mobility, we consider the case in which the borrowing constraint is initially binding
for all individuals. In this case, individuals choose the same constant amount of borrowing b̄
regardless of the substitutability of investments discussed above. As Psh > Puh and Psl > Pul , itfollows that M < 1. In the following subsections, we examine the impact on intergenerational
mobility where the tightness θ decreases.

3.1 Substitutive case
Proposition 1. In the case where educational investment from parents and educational borrowing are substitutive, the relaxation of the borrowing constraint increases intergenerational
mobility.
Proof. From (5), it follows that b̄ = θwu /R. We can consider intergenerational mobility as a9

function of θ, that is, M (θ). Differentiating M (θ) with respect to θ, we obtain∂M (θ)
1=∂θ(Psl + Psh )2

[(

∂Pul
∂Puh
+
∂θ
∂θ

)

(
(Psl + Psh ) − (Pul + Puh )∂Psl ∂Psh
+
∂θ
∂θ

)]
.

(12)

When πbe < 0 holds, then ∂Puj /∂θ > ∂Psj /∂θ, so we obtain
(

∂Pul
∂Puh
+
∂θ
∂θ

)

(
(Psl + Psh ) > (Pul + Puh )∂Psl ∂Psh
+
∂θ
∂θ

)
.

(13)

When (13) holds, ∂M (θ)/∂θ > 0. Once the interior solutions achieve, individuals do notchange the amount of borrowing any longer. It means that ∂Pij /∂θ will be zero at some point.
In either order of educational borrowings, (13) holds even after some individuals achieve theiroptimal amount. Thus, (13) holds for all θ.
The intuition is as follows. Children with wealthy parents require smaller amount of educational borrowing than those with poor parents due to the substitutability. As we have seen in
Section 2.2, the interior solutions of poor children are larger than those of wealthy children. An
increase in the tightness of the borrowing constraint from a sufﬁciently small value increases
the amount of educational borrowing for both wealthy and poor children. The marginal beneﬁtof increasing educational borrowing for poor children is higher than that for wealthy children.
It leads to increase intergenerational mobility. Once the interior solutions are achieved, children no longer change their decisions, even if the borrowing constraint continues to be relaxed.
As the tightness of the borrowing constraint relaxes, wealthy children achieve their optimallevel of educational borrowing faster than poor children. Even after wealthy children achieve
their optimal level, poor children can increase their possibilities until they achieve their optimal
amount. Overall, the beneﬁt from a continued increase in the tightness for poor children is
greater than that for wealthy children.

3.2 No correlation case
Proposition 2. In the case where there is no correlation between educational investment fromparents and educational borrowings, the relaxation of the borrowing constraint increases in-10

tergenerational mobility.
Proof. When πbe = 0 holds, ∂Puj /∂θ = ∂Psj /∂θ always holds. Therefore, (13) can be rewrittenby (Psl + Psh ) ≥ (Pul + Puh ). It holds for all θ because M ≤ 1.
Children with same abilities have the same amount of educational borrowing because theleft-hand side of (10) coincides for both types of children. The marginal beneﬁt of borrowing
for both types of children coincides as well. In turn, changes in the tightness of the credit
market affect the decisions of both children in a same manner. The remaining mechanism of
increasing intergenerational mobility is the same as the substitutive case.

3.3 Complementary case
Figure 2 illustrates how individuals decide the amount of borrowing in the complementarycase. First, we consider the case in which blu < bhu < bls < bhs holds, as shown in the left graphin Figure 2. In the region where θ is larger than θ′ , intergenerational mobility is a decreasing
function of θ. In the shaded region, an increase in the tightness of the borrowing constraint onlychanges the educational borrowing of children with skilled parents. The educational borrowing of children with skilled parents continues to increase until the amount reaches the interior
solution. The numerator of (11) remains constant, but that of the denominator still increases,
and thus, intergenerational mobility declines. Both educational borrowings change in the remaining region as the tightness of the borrowing constraint increases. Both the numerator anddenominator of (11) increase, and therefore, the effect on mobility is ambiguous. Next, weconsider the case in which blu < bls < bhu < bhs holds, as shown in the right graph in Figure 2.
In the region where θ is larger than θ′′ , mobility is a decreasing function of θ. In the rest of theregion, the effect on mobility is ambiguous.

3.4 The effect of the expansion of the wage gap
An expansion of the wage gap plays a crucial role when children decide the amount ofborrowing. A natural question is how expansions of the wage gap inﬂuence children’s decisionsof educational borrowing. Intuitively, an increase in the wage gap motivates children to borrow11θ ′ wuRθ ′′ wu
R

R

R
blu

bhu

bls

bhs

b

blu

bls

bhu

b

bhs

Figure 2: Complementary case. In the shaded region, intergenerational mobility is a decreasing
function of θ. The impact on intergenerational mobility in the remaining region is ambiguous.
more, as the marginal beneﬁt of borrowing rises. However, both wealthy and poor children are
motivated to increase their borrowing. Thus, the overall effect on intergenerational mobility isunclear.
This subsection examines the effect of changes in the wage gap between skilled and unskilled wages, deﬁned as ŵ ≡ ws −wu .34 Assume that all agents achieve their interior solutions.
Differentiating M with respect to ŵ, we obtain∂M (ŵ)1=l∂ ŵ
(Ps + Psh )2

[(

∂Puh
∂Pul
+
∂ ŵ
∂ ŵ

)

(
(Psl + Psh ) − (Pul + Puh )∂Psl ∂Psh
+
∂ ŵ
∂ ŵ

)]
. (14)))((
We compare ∂Pul /∂ ŵ + ∂Puh /∂ ŵ with ∂Psl /∂ ŵ + ∂Psh /∂ ŵ to evaluate whether (14) is
positive. Because the interior solutions satisfy (10) with equality, we can obtain the condition
where (14) is positive as follows:
−1
−1
−1
−1
[al πbb (bl∗+ [ah πbb (bh∗> [ah πbb (bl∗+ [ah πbb (bh∗u , eu )]u , eu )]s , es )]s , es )](15)[aj πbb (bj∗i , ei )] represents the slope of the left-hand side of (10) evaluated at each optimal value.
It can be interpreted as the sensitivity in response to changes in the wage gap. If (15) holds, themarginal increase in optimal borrowing for children who have unskilled parents is larger than3

An increase in wage gap ensures from three reasons: an increase in ws , a decrease in wu , or both. The sourceof the wage gap does not affect the result because individuals decide the amount of borrowing based on the wage
gap itself, not the source of the wage gap.
4
An introduction of the subsidy for repayment can be considered in the model. However, its effect on intergenerational mobility is the same as an increase in wage gap. The decrease in the RHS of (10) due to the subsidy
is equal to the increase in the LHS of (10). Individuals recognize the increase in the wage gap as being equivalent
to the subsidy for repayment.

12

that for wealthy children when the wage gap rises. In other words, children who have unskilledparents are more responsive to the change in the wage gap.
Proposition 3. If poor children are more responsive to changes in the wage gap than wealthy
children, increases in the wage gap improve intergenerational mobility.

4

Income-contingent loan
Several countries have adopted the income-contingent repayment schemes for educationalloans. Switching from the conventional credit market regime to ICL regime, the incentive forborrowers may have changed. Borrowers know that regardless of how much they borrow inchildhood, they are not obligated to repay as long as they fail in education and earn a lower
wage in adulthood.5 Thus, the introduction of ICLs may have different implications of intergenerational mobility.
This section examines the impact of the ICL on intergenerational mobility. Consider thefollowing simple ICL scheme for tractability. If an individual succeeds and becomes a skilledworker, her repayment will be the sum of borrowing and interest, Rbt−1 . If an individual fails
and becomes a unskilled worker, she will repay nothing.6 To balance total borrowing andrepayment in the economy, the government imposes a lump-sum tax T for every agent. Only
successful individuals repay their borrowing in the second period.
The budget constraints of borrowers in the second period are rewritten as follows:
cju + euj + T ≤ wu ,(16)

cjs + Rbjs + ejs + T ≤ ws .

(17)

5

One may concern about moral hazard and adverse selection. In the present setting, moral hazard and adverse
selection problems do not arise. Gary-Bobo and Trannoy (2015) examine optimal school loan contract undermoral hazard and adverse selection.
6
This simpliﬁcation does not seem to be realistic. However, students who use the HECS in Australia do nothave to repay if their income is below a certain level.

13

The optimal condition for educational borrowing is7
aj πb (bji , ei )(Ω − Rbji ) = aj π(bji , ei )R.

(18)

Let b̃ji and b̂ji denote the interior solution in market loan regime and in the ICL regime, respectively. To compare the amount of borrowing in market loan regime with that of the ICL regime,
we deﬁne the following function:G(bji ) ≡)πb (bji , ei ) (Ω − Rbji − R.
jπ(bi , ei )(19)

Substituting the optimal amount of borrowing in the market loan regime into (19), we obtain

G(b̃ji ) =

{
}
R
j
j
Ω[1
−
π(
b̃
,
e
)]
−
R
b̃
i
i
i .
aj Ωπ(b̃ji , ei )(20)

When (20) is positive, we conﬁrm that b̃ji < b̂ji because G(b̂ji ) = 0. We can rewrite condition(20) as follows:[1 − aj π(b̃ji , ei )](Ω − Rb̃ji ) > aj π(b̃ji , ei )Rb̃ji .

(21)

The left-(right-)hand side of (21) means the expected loss (gain) in the ICL regime, evaluatedat the optimal amount of borrowing in the market loan regime, if an individual fails to becomea skilled worker. An individual needs to repay the loan in exchange for becoming a skilledworker. It can be interpreted as a gain from the failure to become a skilled worker because
she does not have to repay the loan. When the loss is larger than the gain, valued at optimalborrowing in the market loan regime, the shift therefrom to the ICL regime increases the amountof borrowing. When (21) holds, the expected loss of utility is larger than the gain. Individuals
can reduce their expected loss and increase the gain by increasing the borrowing in the ICL
regime.
In addition to the condition, al π(b∗ , eu )(Ωl − Rb∗ ) ≥ T is required because when an individual borrows
nothing, she does not have to pay the lump-sum tax. It means that the expected gain of borrowing is larger thanthe expected amount of the lump-sum tax even if the individual has a lower innate ability. If this condition holds,
the individual will choose a positive amount of borrowing in equilibrium.
714

In contrast, if (21) violates, individuals will reduce the educational borrowing in response to
the change of regime. Intuitively, the shift from the market loan regime to the ICL regime seems
to increase the amount of educational borrowing. However, in the ICL regime, an increase in
the amount of educational borrowing reduces the beneﬁt of becoming a skilled worker because
only skilled workers have the obligation to repay the borrowing. In contrast to the ICL regime,
both skilled and unskilled workers have the obligation to repay the borrowing in the market loan
regime. Therefore, the shift from the market loan regime to the ICL regime might decrease theamount of educational borrowing under some conditions.
Without the speciﬁcation of the probability function, the impact of intergenerational mobility is unclear. To evaluate the impact on intergenerational mobility, we consider two functional
forms. In the ﬁrst case, we assume that Pij (aj , bji , ei ) = aj [1 − (bji + ei )−1 ]. From (10), we canderive the probability where individuals borrow the optimal amount in the market loan regime
as follows:(P̃ij = 1 −

R
aj Ω

) 12
.

(22)

The probability does not depend on the amount of parental investments. Thus, intergenerational
mobility in the market loan regime is 1. From (18), we derive the probability in the ICL regime,(P̂ij = 1 −RΩ + Rei

) 12
.

(23)

In contrast to the market loan regime, the probability does not depend on their abilities. Thus,
intergenerational mobility in the ICL regime is less than 1. In this case, the shift from themarket loan regime to the ICL regime reduces intergenerational mobility. Second, we assume that Pij (aj , bji , ei ) = aj (bji )α e1−α. To ensure the probability Pij < 1, we assume thati−1/α (α−1)/αγi.

bji < aj

From (10) and (18), we derive the optimal amount of borrowings, b̃ji =(aj α/R)1/(1−α) and b̂ji = αΩ/[(1 + α)R]. Substituting optimal borrowings into (11), we obtain
MICL = (γu /γs )1−α and MM L = γu /γs . Because γu < γs , it follows that MICL > MM L .
Thus, the shift from the market loan regime to the ICL regime leads to improved intergenerational mobility in the Cobb-Douglas case.
15

5Conclusion
The decision of whether and how much to borrow for educational costs from the credit

market crucially depends on parental investment in education. In this study, taking parental investment into consideration, we examine how changes in the tightness of the credit market for
educational investment affect the decision of educational borrowing for children. We constructa simple two-period OLG model with both parental investment in education and educationalborrowing. The analyses show that in the case where educational investment from parents
and educational borrowing are substitutive, the relaxation of the borrowing constraint increases
intergenerational mobility. In the case where educational investment from parents and educational borrowings are complementary, however, the relaxation of the borrowing constraint
may decrease intergenerational mobility. In reality, a signiﬁcant number of students borrow
due to the costs associated with higher education. In this context, both forms of educational
investment appear to be substitutive. Thus, the relaxation of the borrowing constraint improvesintergenerational mobility.

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