Discussion Papers In Economics
And Business
Educational funds and economic growth:private versus public funds
Kohei Okada

Discussion Paper 19-07

May 2019

Graduate School of Economics
Osaka University, Toyonaka, Osaka 560-0043, JAPANEducational funds and economic growth:private versus public funds∗
Kohei Okada†

Abstract
This study constructs an overlapping generations model in order to examine the relationshipbetween education and R&D activities. Using this model, we analyze the eﬀect of individuals’
borrowing of educational funds on economic growth. We first consider the benchmark case inwhich individuals borrow educational funds at a market interest rate. We next consider that
individuals borrow educational funds from a government at a constant rate of interest. If thepolicy interest rate is too low, the number of skilled workers increases, but economic growth is
not achieved in the long run, because an increase in the demand for educational funds owing to
the low policy interest rate crowds out funds for R&D investment and hinders economic growth.
In addition, this study examines welfare and intergenerational inequality. When the government
lowers the policy interest rate, the current generation’s welfare level increases. However, future
generations’ welfare levels will decrease. This study shows that the government faces a trade-oﬀ
between the current generation’s welfare and future generations’ welfare.
Keywords: Education policy, Occupational choice, Intergenerational inequality, R&D
JEL Classification Numbers: I22, I24, H52, O10∗
I would like to thank Koichi Futagami, Tetsuo Ono, Tatsuro Iwaisako, Takeo Hori, Masashi Tanaka, Miho Sunaga,
and Takaaki Morimoto for their helpful comments and suggestions. In addition, I thank participants of the 2017
Japanese Economic Association Spring Meeting held at Ritsumeikan University, and the 49th Economic Theory and
Policy Workshop held at Tokyo Institute of Technology for their helpful comments and suggestions. I acknowledge financial support from the Grant-in-Aid for JSPS Fellows of the Japan Society for the Promotion of Science
No.JP18J15399†
Graduate school of economics, Osaka unversity. Address: 1-7 Machikaneyama, Toyonaka, Osaka 560-0043, Japan.
Phone: +81-6-6850-5232. E-mail: sge005ok@student.econ.osaka-u.ac.jp

1

120
CanadaGross enrollment ratio (%)

100

Germany
Finland

80

FranceUnited Kingdom

60

Ireland
Iceland

40

Italy
Japan

20

Korea, Rep.
Luxembourg01971 1976 1981 1986 1991 1996 2001 2006 2011 2016
Year

United States

Figure 1: Gross enrollment ratio trends of Canada, Germany, Finland, France, the United Kingdom,
Ireland, Iceland, Italy, Japan, Korea, Luxembourg, and the United States

1

Introduction

Economic development has been achieved in many countries, bringing an increase in the number ofpeople who receive higher education. In this process, governments have adopted various educational
policies. Figure 1 shows that the gross enrollment ratios of Canada, Germany, Finland, France, theUnited Kingdom, Ireland, Iceland, Italy, Japan, Korea, Luxembourg, and the United States haveincreased. Figure 1 confirms that people receiving higher education in developed countries haveincreased1 . For example, in the United States, the gross enrollment ratio, which was about 47% in
1971, has been around 90% since 2010.
On the other hand, let us focus on the R&D activity because it is quite important factor for
economic growth. We can divide twelve countries mentioned above into two types. First typeis Type A countries whose R&D expenditure tends to increase and R&D would be undertaken
actively. Type A countries include Germany, France, United Kingdom, Italy, Japan, and UnitedStates. Second type is Type B countries whose R&D expenditure tends to decrease and R&D
would not be undertaken actively. Type B countries include Canada, Finland, Ireland, Iceland, andLuxembourg. Figure 2 shows the trends of average R&D expenditure of Type A countries and TypeB countries. From Figure 2, we can find that average R&D expenditure of Type A countries tends
to increase. For example, in Korea, the R&D expenditure, which was about 2.26% of GDP in 1996,
1

Autor et al. (1995) empirically show this trend.

2

3

R&D expenditure (% of GDP)

2.5
2
1.5

Type A countries
Type B countries

1
0.5
01996 1998 2000 2002 2004 2006 2008 2010 2012 2014 2016
Year

Figure 2: Trends of average R&D expenditure of Type A and Type B countries
has been around 4.24% since 2016. On the other hand, we can find that average R&D expenditureof Type B countries tends to decrease. For example, in Canada, the R&D expenditure, which was
about 2.02% of GDP in 2001, has been around 1.61% since 2016.
In order to do so, this study focuses on the eﬀect of borrowing educational funds on R&D
activity. In developed countries, many people who receive education borrow funds as scholarships
to pay for their education expenses. According to “Education at a glance 2014” (2014) publishedby the OECD, many students receive scholarships in OECD countries. In particular, in Europe
and the United States, almost 80% of students receives scholarships. In addition, such scholarshipprojects are led by their governments, and significant financial resources are needed to promote
the scholarship projects. Thus, governments raise financial resources. For example, in Japan, most
students who receive scholarships do so by borrowing in the form of a student loan from the Japan
Student Services Organization (JASSO)2 The total rental amount of the Japan Student Services
Organization was 5 billion dollars in 2003, which increased to 18.3 billion dollars in 2016. The
Japan Student Services Organization’s budget for financial year 2017 was 1.95 billion dollars, ofwhich 6.9 billion dollars was covered by repayment from borrowers. The Japanese government
covers a part of the remaining budget by raising funds, such as government loans and Fiscal Loan
2

The Japan Student Services Organization (JASSO) is an independent administrative corporation establishedunder the Ministry of Education, Culture, Sports, Science and Technology. JASSO mainly administers scholarshipprograms in Japan.

3

Funds, to the value of 13.8 billion dollars. The remainder is financed through private borrowing by
the JASSO of 3.37 billion dollars. Therefore, the Japanese government procures significant funds
for the scholarship project. In the United States, as in Japan, agencies called Aﬃliate Computing
Services provide student loans; the total loan amount increased from about 45.5 billion dollars in2003 to 100 billion dollars in 2011. In this study, we analyze macroeconomic trends taking into
account scholarship projects operated by a government. This study examines how this expansionof demand for funds aﬀects supplies of funds for other sectors.
We construct an overlapping generations model in which economic growth is induced by expanding the variety of goods by R&D activities. In addition, we introduce a mechanism for anindividual to borrow educational funds. If an individual receives education, he or she becomes askilled worker. Skilled workers earn more income than do unskilled workers who do not receive
education. However, skilled workers must borrow educational funds to pay educational costs. In
this study, we analyze the following two cases. The first case is (1) a private funds regime in which
individuals borrow educational funds at a market interest rate in the financial market. The secondcase is (2) a public funds regime in which individuals borrow educational funds from a government
at a constant interest rate. We show a condition by which the economy can grow over time in
the private funds regime and also in the public funds regime. In the private funds regime, theeconomy can grow over time if the skill premium and R&D productivity are suﬃciently high. In
the public funds regime, if the policy interest rate is too low, expansion of demand for educational
funds crowds out funds for R&D activities. Therefore, overly fast expansion of skilled workers caninterrupt economic growth.
Furthermore, this study conducts welfare analysis and examines intergenerational inequality. If
the government lowers the policy interest rate, it has two eﬀects on the economy. One is a positiveeﬀect on the welfare level. A reduction in the policy interest rate increases the number of skilledworkers. It increases individuals’ disposable income. The other is a negative eﬀect on welfare. If
the increase in the demand for educational funds reduces the supply of funds for R&D, it decreases
the future generations’ income. Therefore, it has a negative eﬀect on the welfare level of future
generations. When the government lowers the policy interest rate, the current generation’s welfare
is increased by the positive eﬀect. However, future generations’ welfare is reduced by the negativeeﬀect. This study shows that the government faces a trade-oﬀ between the current generation’s
4welfare and future generations’ welfare.
This study is related to much research on economic growth and education. Boldrin and Montes(2005) analyze the relationship between education funds and economic growth. However, they
focus only on accumulation of physical capital and human capital, and do not take account of
R&D activities. On the other hand, the present study considers that the demand for funds forpaying educational expenses crowds out the supply of funds to the R&D sector and that economic
growth may not be achieved over the long run. Dalgaard and Kreiner (2001) and Strulik (2005)
analyze the relationship between R&D investment and human capital accumulation. However,these studies do not consider financial markets for education expenses. Acemoglu (1998) and Galorand Moav (2000) focus on an increase in the number of workers with higher education along withtechnological progress after World War II. they argue that this increase is caused by skill-biased
technological change. However, these studies do not analyze the relationship between financial
markets for educational funds and economic growth. Grossmann (2007) analyzes the impact of
R&D subsidy policy and educational policy on R&D and economic growth. His research and thepresent study both analyze the eﬀect of the government’s educational policy on R&D and economic
growth. However, Grossmann (2007) does not analyze the government’s scholarship policy suchthat individuals borrow the educational funds from a government. Morimoto (2017) analyzes therelationship between R&D subsidy policy and occupational choice. He finds the existence of an
optimal R&D subsidy rate. In addition, he analyzes the relationship between R&D subsidy policy
and intergenerational inequality. However, he focuses only on the R&D subsidy policy.
The rest of this paper is organized as follows. Section 2 shows the basic structure of the model,
Section 3 analyzes the equilibrium and dynamics. Section 4 examines welfare and intergenerational
inequality. The conclusion is described in Section 5.

2

The model

2.1

Individuals

Time is discrete and denoted by t = 0, 1, 2, · · · . Each individual lives three periods (youth, adulthood, and old age). The population size of each generation is normalized to one. In the first periodof their lives (youth), individuals decide whether to receive education or not. If they receive edu5

cation, they have to borrow funds to pay the cost of education. However, they can work as skilledworkers when they reach adulthood. If they do not receive education, they do not need to borrow.
However, they become unskilled workers. In the second period of their lives (adulthood), individuals work and obtain wage income according to their skill. Individuals who borrow funds in youth
have to repay it from their income in this period. In the public funds regime, all individuals pay alump-sum tax. Individuals save the remaining income. We assume for simplicity that individuals do
not consume in the first and second periods. In the final period of their lives (old age), individuals
obtain a subsidy from the government and consume their total wealth. We also assume that eachindividual does not have any bequest motives for their children.
When young, if individuals do not receive education, they become unskilled workers and supply
one unit of labor. On the other and, skilled workers who receive education can supply h(> 1)
unit of labor. If an individual wants to obtain education, he or she must pay the educational
cost depending on his or her ability θ. Each individual’s ability is randomly given by the uniform
distribution defined over [0, 1]; that is, the distribution function of ability is F (θ) = θ and thedensity function is f (θ) = 1. Furthermore, we assume that an individual whose ability is θ has topay γθ as the educational cost. This assumption means that the lower ability an individual has, themore educational cost he or she has to pay.
Each individual chooses to become a skilled worker if and only if his or her disposable income
as a skilled worker is higher than that as an unskilled worker. Therefore, if the following conditionis satisfied, an individual whose ability is θ chooses to become a skilled worker.
γ≥ wt × 1,θRγθ≥≡ θ̂t−1 ,wt (h − 1)

wt h − R→(1)where R and θ̂t−1 are the gross rate of interest of educational loan and the threshold of ability,
respectively. Individuals whose ability is above (under) this threshold become skilled (unskilled)workers.
We consider two cases in the following analyses. One is that individuals borrow from an asset market (private funds). The other is that they borrow from the government (public funds).

6

Therefore, R is defined as

R≡




R

if individuals borrow from the asset market (private funds),



RB

if individuals borrow from the government (public funds),t

where Rt and RB are the gross rate of market interest and the gross rate of policy interest set by
the government, respectively.

2.2

Final goods sector

Final goods Yt are allocated to consumption, production of intermediate goods, R&D activities, andinvestment in education. The final goods are treated as a numeraire. The final goods are producedby competitive firms using the following production function:

Yt = Ht1−α∫ At

xt (j)α dj,(2)0

where Ht is human capital devoted to production and xt (j) is intermediate goods j ∈ [1, At ]. At
denotes the variety of intermediate goods. In this economy, human capital is used only in the final
goods sector. Human capital is given by the sum of unskilled workers’ labor supply and skilledworkers’ labor supply, that is,∫ θ̂t−1
Ht =∫ 1

hd = h − (h − 1)θ̂t−1 .

1dθ +
0

(3)

θ̂t−1

Given the wage rate wt and the price of intermediate goods pt (j), the profit-maximizing conditions
with respect to Ht and xt (j) arept (j) = αHt1−α xt (j)α−1 ,∫ At
wt = (1 − α)Ht−αxt (j)α dj.

(4)
(5)

0

2.3

Intermediate goods sector

There is a number of diﬀerentiated intermediate goods. A single firm produces each intermediate
good j ∈ [0, At ] and can supply a diﬀerentiated good monopolistically. The monopoly is protected7

by perfect patent protection. Each monopolistic firm produces one unit of an intermediate good byusing one unit of final goods. The producer of intermediate good j maximizes the following profit,
πxt (j) = pt (j)xt (j) − xt (j),subject to the inverse demand function of the final goods sector (4). From the profit-maximization
condition, the price of intermediate goods j ispt (j) =

1
.
α

(6)

Hence, all intermediate goods have the same price. Therefore, the firm-specific index j in thediﬀerentiated goods sector can be dropped. By substituting this into demand function (4), we
obtain the output level of intermediate goods:
2

xt = α 1−α Ht .

(7)

Thus, the profit of each intermediate good firm is given by
1+απxt = (1 − α)α 1−α Ht .

2.4

(8)

R&D sector

In this economy, R&D firms also use the final goods to invent new intermediate goods. Afterinvention, the firms sell a blueprint of a new intermediate good to an entrepreneur in the intermediate
goods sector. R&D firms use η unit of the final goods to invent one unit of new intermediate goods.
We suppose that there are no spillover eﬀects from the accumulated intermediate goods that havebeen invented. Free entry into R&D races leads to the following zero-profit condition:
vt ≤ η

with equality if

8∆At > 0.

(9)The value of vt is equal to the present value of future profits given by

vt−1 =

∞
∑

πxT
.
T
Π R
T =t τ =t τAfter some manipulations, we can obtain the following no-arbitrage condition.

Rt =vt + πxt
.
vt−1

(10)

Each individual saves at the gross rate of market interest Rt determined by (10). Moreover, if an
individual borrows funds from the asset market, he or she faces this market interest rate.

3

Equilibrium

In this section, we consider the private funds regime and the public funds regime. Regardless of thecharacteristics of these two regimes, from (2) and (7), the following holds;
2αYt = α 1−α At Ht .

(11)

From (5) and (7), the wage rate wt is
2α

wt = (1 − α)α 1−α At .

3.1

(12)

(1) Private funds regime

We first consider the private funds regime in which individuals who need educational funds borrowfrom the asset market. The interest rate is determined by the no-arbitrage condition (10). By using(1), (3), (8), (9), and (12), the no-arbitrage condition (10) becomes
1+α[η + (1 − α)α 1−α h]AtRt =≡ RtM .
αγ + ηAt

9(13)

Here, note that

∂RtM
∂At

1+α
1−α

h]αγ
= [η+(1−α)α> 0. From (1) and (13), the threshold of ability θ̂t−1(αγ+ηAt )2

becomes1+α[η + (1 − α)α 1−α h]γθ̂t−1 =

2α(1 − α)α 1−α (h − 1)(αγ + ηAt ).

This shows that when At decreases, θ̂t−1 increases. Because θ ∈ [0, 1], this determines the lower
bound of At . The lower bound A becomes
1+αA=[η + (1 − α)α 1−α ]γ2α(1 − α)α 1−α η(h − 1)

.

(14)

When At < A, θ̂t−1 = 1. Thus, θ̂t−1 becomesθ̂t−1 =

1+α[η+(1−α)α 1−α h]γ
2αAt ≥ A,if(1−α)α 1−α (h−1)(αγ+ηAt )



1

(15)
if

At < A.

When At < A, all individuals become unskilled workers. Therefore, no educational loans are
made. Consequently, the asset market equilibrium condition is given by∫ 1
wt dθ = vt At + vt ∆At .

(16)

0

The left-hand side of (16) is unskilled workers’ saving. The right-hand side of (16) is investment inassets. By using (9) and (12), we can rewrite (16) as follows:2α(1 − α)α 1−α At =|{z}
≡S1M (At )ηAt+1| {z }.

(17)≡D1M (At+1 )Let us denote the left-hand side of (17) as S1M (At ) and the right-hand side of (17) as D1M (At+1 ).
When At ≥ A, some individuals receive education and become skilled workers. The individuals
who receive education access the asset market to obtain educational funds. Unlike the public funds
regime, individuals’ demand for educational funds directly aﬀects the asset market. Therefore, the10asset market equilibrium condition is given by∫ θ̂t−1∫ 1
wt dθ +

0γ
(wt h − RtM )dθ =∫ 1γdθ + vt At + vt ∆At .
θ̂t θ

θ

θ̂t−1

(18)

The left-hand side of (18) is the sum of unskilled workers’ saving and skilled workers’ saving. The
right-hand side of (18) is the sum of demand for education funds and investment in assets. By using(9), (12), (13), and (14), we can rewrite (18) as follows:(1 − α)α
|

2α
1−α

{
}
1+α
2α
(1 − α)α 1−α (h − 1)(αγ + ηAt )[η + (1 − α)α 1−α h]γAt
log
+1
hAt −
1+α
αγ + ηAt[η + (1 − α)α 1−α h]γ{z}≡S2M (At )2α= γ log(1 − α)α 1−α (h − 1)(αγ + ηAt+1 )1+α[η + (1 − α)α 1−α h]γ{z|+ ηAt+1 .

(19)}≡D2M (At+1 )Let us define the left-hand side of (19) as S2M (At ) and the right-hand side of (19) as D2M (At+1 ).
Now, the following lemma holds.
Lemma 1∂S2M (At )∂ 2 S2M (At )∂D2M (At+1 )∂ 2 D2M (At+1 )
>
0,
>
0,
< 0 hold.
>
0,
and
2
∂At
∂At+1
∂At
∂A2t+1

Proof. See Appendix A.
We next assume the following with respect to the R&D productivity parameter.
Assumption 1 R&D productivity parameter η satisfies the following condition
2αη < (1 − α)α 1−α .

(A1)Assumption 1 means that R&D productivity is suﬃciently high. Under Assumption 1, S2M (A) >D2M (A) holds. Because two cases exist, we can draw phase diagrams that describe the dynamics.
One is that (i) S2M (At ) and D2M (At+1 ) have no intersection point. The other is that (ii) S2M (At ) andD2M (At+1 ) have two intersection points. Figure 3 represents the dynamics of case (i). In this case,the economy continues to grow in the long run. From (15), the threshold of ability θ̂t−1 decreases
and the enrollment rate continues to rise over time. Figure 4 represents the dynamics of case (ii).
In this case, if the initial technology level A0 is too low (A0 < A∗1 ), the economy converges to A∗1
11

!!! (!! )!!! (!!!! )!!! (!! )!!! (!!!! )0!

!! !!!!

!!

Figure 3: Phase diagram of case (i)!!! (!! )!!! (!!!! )!!! (!! )!!! (!!!! )
0

! !!

!!∗

!∗! !!

!! !!!!

Figure 4: Phase diagram of case (ii)and cannot continue to grow in the long run. From (15), the threshold of ability θ̂t−1 and theenrollment rate become constant in the long run. On the other hand, if the initial technology levelA0 is suﬃciently high (A0 > A∗2 ), the economy continues to grow in the long run and the enrollment
rate rises. If the initial technology level A0 is at a middle level (A∗1 < A0 < A∗2 ), the economy does
not grow from the initial level because R&D does not take place3 .
We investigate whether case (i) or case (ii) occurs. For this purpose, let us define ψ(A) as

3
Following previous researches, we assume that the technology level dose not diminish and At dose not decrease.
When A∗1 < A0 < A∗2 , we can find that S2M (A0 ) < D2M (A0 ) from Figure 4. Considering that At dose not decrease(i.e. A1 = A0 ) and (19) is derived from vt = η, (9) has to hold with inequality (i.e. v0 < η) to satisfy the asset market
equilibrium condition (S2M (A0 ) = D2M (A1 )).

12ψ(A) ≡ D2M (A) − S2M (A), that is,
ψ(A) ≡ D2M (A) − S2M (A)2α= γ log(1 − α)α 1−α (h − 1)[η + (1 − α)α

1+α
1−α

2α

+ γ log(αγ + ηA) + ηA − (1 − α)α 1−α hA

h]γ
{
}
2α
h]γA
[η + (1 − α)α(1 − α)α 1−α (h − 1)
+ γ log(αγ + ηA) + 1
+
log
1+α
αγ + ηA[η + (1 − α)α 1−α h]γ1+α1−αDiﬀerentiating ψ(A) with respect to A, we obtain
1+α

2α
γη
[η + (1 − α)α 1−α h]αγ 2
ψ (A) =+ η − (1 − α)α 1−α h +αγ + ηA(αγ + ηA)2
{
}
1+α
2α
(1 − α)α 1−α (h − 1)(αγ + ηA)[η + (1 − α)α 1−α h]γηA
× log
+1 +
.
1+α
(αγ + ηA)2
[η + (1 − α)α 1−α h]γ

′

(20)

The value of A that maximizes ψ(A) is determined from equation ϕ′ (A) = 0. Let us denote themaximizer as Â. Substituting Â into ψ(A), we examine whether ψ(Â) takes a positive value or
not. However, because it is diﬃcult to explore the condition analytically, we conduct a numericalanalysis. By setting α = 0.2 and γ = 1, we can draw Figure 5 to show how the pair of parameters(h, η) determines the two cases.
Figure 5 shows that case (i) occurs if h and η are suﬃciently low. If the skill premium h is
high, an individual’s incentive to become a skilled worker is high. Then, an individual’s higher
incentive increases the number of skilled workers, which increases demand for educational funds.
The larger demand of educational funds crowds out investments for R&D. The supply of funds for
R&D activities decreases, and then, long-run economic growth is not attained. On the other hand,
if R&D productivity is high (η is low), long-run economic growth can be attained, because R&D
firms invent actively. We can show the following proposition
Proposition 1 Under Assumption 1, if h and η are suﬃciently low, case (i) occurs. Then, theeconomy continues to grow in the long run and the enrollment rate rises over time.
Proof. See Appendix B.

13

(ii)

0.35

0.3

0.25

!

0.2

0.15

(i)

0.1

0.05

0

0

1

2

3

4

5

6

7

8

9

10

ℎ

Figure 5: Parameter region of (h, η) for case (i) or (ii)

!-1

!

!+1

youth

adulthood

old agesubsidytax
government

government
repayment
old ageadulthood

loan
youth

Figure 6: Government policy for each generation

14

3.2

(2) Public funds regime

We consider the public funds regime in which each individual borrows from the government. In thiscase, the government lends the funds to individuals who need to borrow at policy interest rate RB .
We assume that individuals cannot invest the funds borrowed from the government in the asset
market instead of paying education fees. The government collects a lump-sum tax Tt from each
adult and uses the tax revenue to lend funds to young individuals who want to receive education.
Thus, the following holds:
∫ 1

∫ 1

γ
dθ.
θ̂t θ

Tt dθ =
0(21)

Furthermore, the government receives RB γθ repayment from individuals who borrowed funds inyouth and return the revenue to each old as subsidy Gt . Thus, the following relationship holds:∫ 1γ
RB dθ =
θ
θ̂t−1

∫ 1
Gt dθ.

(22)0

We next consider the asset market. We first derive the threshold of ability between skilledworkers and unskilled workers in the equilibrium. From (1) and (12), the threshold of ability θ̂t−1
becomesθ̂t−1 =RB γ
2α(1 − α)α 1−α (h − 1)At.

This shows that when At decreases, θ̂t−1 increases. Because θ ∈ [0, 1], this determines the lower
bound of At as follows:

A=

RB γ
2α

(1 − α)α 1−α (h − 1)

.

(23)

Thus, θ̂t−1 becomesθ̂t−1 =

RB γ
2α
1−α
(h−1)At(1−α)α



1

if

(24)
if

15

At ≥ A,At < A.

From (1), (3), (8), (9), (10), and (12), the gross market interest rate Rt is given by
1+α(1 − α)α 1−α h RB αγ−≡ RtG .
Rt = 1 +
η
ηAt

(25)

To analyze a situation in which individuals borrow educational funds from the government, we
assume that if the government changes the policy interest rate at time t, the government sets alower policy interest rate than the market interest rate determined by (25)4 .
When At < A, all individuals become unskilled workers. Therefore, there is no borrowing of
educational funds. In this case, the asset market equilibrium condition is also given by (17).
On the other hand, when At ≥ A, some individuals receive education and become skilled workers.
Therefore, the government’s lending policy is undertaken. The asset market equilibrium conditionis given by∫ θ̂t−1(wt − Tt )dθ +

∫ 1 (

0

wt h − R B

θ̂t−1

)
γ
− Tt dθ = vt At + vt ∆At .
θ

(26)

The left-hand side of (26) is the sum of unskilled workers’ saving and skilled workers’ saving. The
right-hand side of (26) is investment in assets. By using (9), (12), (21), and (24), we can rewrite(26) as follows:[(1 − α)α

2α
1−α

|

]
2α
(1 − α)α 1−α (h − 1)AthAt − RB γ log
+1
RB γ
{z
}
≡S2G (At )2α(1 − α)α 1−α (h − 1)At+1= γ log+ ηAt+1 .
RB γ
|
{z
}

(27)

≡D2G (At+1 )Let us define the left-hand side of (27) as S2G (At ) and the right-hand side of (27) as D2G (At+1 ). We
can show that the following lemma holds, as for S2G (At ) and D2G (At+1 ).
Lemma 2

∂S2G (At )∂ 2 S2G (At )∂D2G (At+1 )∂ 2 D2G (At+1 )< 0 hold.
> 0, ∂A> 0, ∂A> 0, and2∂At∂A2t+1t+1tProof. See Appendix C.
1+α
1−α

h]At
The government sets RB < RtG . From this relationship and (25), we obtain RB < [η+(1−α)α= RtM . This
αγ+ηAtresult means that the government sets a lower policy interest rate than the market interest rate of the private funds
regime.
4

16

!!! (!! )!!! (!!!! )!!! (!! )!!! (!!!! )0!

!! !!!!

!!

Figure 7: Phase diagram of case (iii)
We make Assumption 1 also in the public funds regime. Under Assumption 1, S2G (A) > D2G (A)holds. Because two cases can exist, we can draw phase diagrams that describe the dynamics. One
is that (iii) S2G (At ) and D2G (At+1 ) have no intersection point. The other is that (iv) S2G (At ) andD2G (At+1 ) have two intersection points. Figure 7 represents the dynamics of case (iii). In this case,the economy continues to grow in the long run. From (24), the threshold of ability θ̂t−1 decreases
and the enrollment rate also continues to rise over time. Figure 8 represents the dynamics of case(iv). In this case, if the initial technology level A0 is too low (A0 < A∗∗1 ), the economy converges toA∗∗
1 and cannot continue to grow in the long run. From (24), the threshold of ability θ̂t−1 and theenrollment rate become constant in the long run. On the other hand, if the initial technology levelA0 is too high (A0 > A∗∗2 ), the economy continues to grow in the long run and the enrollment rate∗∗
rises. If the initial technology level A0 is at a middle level (A∗∗
1 < A0 < A2 ), the economy does not

grow from the initial level because R&D dose not taken place ((9) holds with inequality).
Proposition 2 Under Assumption 1, given h and η, a unique policy interest rate R̂B > 0 exists
satisfying the following:(1) When RB > R̂B (the policy interest rate is high), case (iii) is obtained. Then, the economy
continues to grow in the long run and the enrollment rate rises.
(2) When RB < R̂B (the policy interest rate is low), case (iv) is obtained. If the level of initialtechnology A0 is suﬃciently low, economic growth and the rise of the enrollment rate finallystops in the long run.
17

!!! (!! )!!! (!!!! )!!! (!! )!!! (!!!! )
0

! !!

!!∗∗

!∗∗
! !!

!! !!!!

Figure 8: Phase diagram of case (iv)
Proof. See Appendix D.
If the level of technology At rises, the wage rate wt also rises. The increase of the wage rate
wt decreases the threshold of ability θ̂t−1 . Therefore, the number of skilled workers increases. On
the other hand, if the wage income increases, individuals save more. This saving finances R&D
activities. If the policy interest rate RB is too low, expansion of demand for educational funds
crowds out funds for R&D activities more. Therefore, overly fast expansion of skilled workers
interrupts economic growth.
Proposition 3 Under Assumption 1, if the skill premium of skilled workers h is high and/or R&D
productivity is low (η is high), then, R̂B is high. Therefore, the government has to set the policy
interest rate suﬃciently high to achieve the long-run economic growth.
Proof. See Appendix E.
If the skill premium h is high, an individual’s incentive to become a skilled worker is high. Then,the individual’s higher incentive increases the number of skilled workers. The increase of skilledworkers increases demand for educational funds, which crowds out investment in R&D activities.
Therefore, if the government does not set a higher policy interest rate, the supply of funds for R&D
firms decreases and economic growth is not sustained. On the other hand, if R&D productivity ishigh (η is low), the economy can grow in the long run regardless of the lower policy interest rate,
because R&D firms invent actively.
Last, we compare the private and public funds regimes. Suppose the government adopts an
18

education policy by which it lends funds to individuals who receive education at time t and At < A∗∗
1 .
From Proposition 1, if h and η are suﬃciently low, case (i) in which the economy continues to growoccurs in the private funds regime. Under this h and η, there is a policy interest rate thresholdR̂B that distinguishes between case (iii) in which the economy continues to grow in the long run
and case (iv) in which the economy cannot grow in the long run if At < A∗∗
1 from Proposition 2.
If the government sets a higher interest rate, RB , than R̂B at time t, case (iii) occurs, in which
the economy continues to grow in the long run. On the other hand, if the government sets a lower
interest rate, RB , than R̂B , case (iv) occurs, in which the economy cannot grow in the long run if
At < A∗∗
1 . Therefore, long-run economic growth may be hindered by the government educational
policy that sets too low a rate of policy interest.

4

Welfare and intergenerational inequality

In this section, we consider welfare and intergenerational inequality. In this economy, all individuals
obtain utility from consumption when old. Therefore, we define the welfare levels of this economy
at time t as the sum of consumption of old individuals at time t. The welfare levels of the private
funds regime is

UtM =



2α

RM (1 − α)α 1−α A
t+1
M S M (A )
Rt+1
t
2

t

if
if

At < A,(28)

At ≥ AThe welfare levels of the public funds regime is5

UtG =



2α

G (1 − α)α 1−α A
Rt+1
t

if

∫


G S G (A ) − (RG − R ) 1 γ dθ
Rt+1
t
B
2
t+1
θ̂t θ

if

At < A,(29)

At ≥ A.

Suppose the government changes the policy interest rate at time 0. Figures 9 and 10 are the resultsof the numerical calculation under the following parameter setting: h = 1.5, α = 0.2, γ = 2,
and η = 0.3055. Figure 9 shows the eﬀect of changes in the policy interest rate RB at time 0 on

5

The detailed calculation method of the welfare levels is described in Appendix F.

19the welfare levels of the current generation6 . According to Figure 9, the lower policy interest rateincreases the welfare levels of the current generation. Figure 10 shows how changes of policy interest
rate RB at time 0 aﬀect the welfare levels of each individual before the 10th generation. As shownin Figure 10, the government can raise the welfare levels of the 0th to 4th generations by setting thepolicy interest rate lower. However, when the government lowers the policy interest rate, the welfare
level of individuals after the 5th generation declines. By the results of the numerical calculation,R̂B = 0.8. If the government sets RB lower than 0.8, case (iv) is obtained. Then, economic growth
finally stops in the long run.
Decreases in the policy interest rate have two eﬀects on welfare levels. The first eﬀect is positiveon all generations’ welfare levels. Suppose that the government lowers the policy interest rate attime 0. From (1), the enrollment rate of young individuals (1 − θ̂t ) increases after time 0. The
rise of the enrollment rate increases the number of skilled workers who earn more income than dounskilled workers. Therefore, the welfare level, which is the sum of consumption of all individuals
in the same generation, increases. In addition, from (25), the decrease in the policy interest rateincreases the market interest rate. When the market interest rate rises, individuals’ savings receipts
increase. Therefore, their consumption levels in old age increase and their welfare levels can be
improved.
On the other hand, the second eﬀect is negative. Suppose that the government lowers the rate
policy interest at time 0. Then, the enrollment rate is raised and the demand for educational funds
increases by the first eﬀect. The expansion of demand for educational funds crowds out funds for
R&D activities. When the level of R&D activities decreases, the rate of economic growth declines
and the future technical level falls. Then, the wage rate and the market interest rate decline in
the future from (12) and (25). Therefore, future generations’ income and consumption decline.
This outcome reduces the future generations’ welfare levels. If individuals of the current generation
earn lower income, they invest less. Then, R&D becomes more inactive and the technology levelof the next generation decreases. The lower technology level reduces the next generation’s income.
Therefore, the impact of the negative eﬀect gradually enlarges through the generations.
6
The reason the old people’s welfare level is not shown in Figure 9 is that the welfare level of the old at time 0 is
not aﬀected by the policy change. The enrollment rate of the old (1 − θ̂−2 ) and the market interest rate faced by theold R0 is not aﬀected by the policy interest rate change at time 0. Therefore, the welfare level of the old at time 0 is
not aﬀected by the policy change.

20

adult

young

18
16
14

walfare

12
10
8
6
4
2

0

0.2

0.4

0.6

0.8

1

1.2

1.4

Rb

Figure 9: Relationship between policy interest rate and current generation welfare: The verticalline shows the welfare levels of young generation or adult generation at time 0. The horizontal line
shows the policy interest rate.
The lower policy interest rate leads to the higher welfare levels of the current generation, as
shown in Figure 9, because the positive eﬀect is greater than the negative eﬀect. As shown in
Figure10, when the government sets a low policy interest rate, the welfare levels of the 0th to 4th
generation increase, because the positive eﬀect is greater than the negative eﬀect. However, thewelfare levels of individuals after the 5th generation decline, because the negative eﬀect is greaterthan the positive eﬀect. The government faces a trade-oﬀ between improving the welfare of thecurrent generation and increasing the welfare of future generations.

5

Conclusion

We introduced borrowing educational funds by individuals into an endogenous growth model of avariety-expansion type R&D. Using this model, we analyzed the eﬀect of individual’s borrowing
of educational funds on economic growth. When individuals access the asset market directly andborrow educational funds at a market interest rate (private funds regime), if the skilled worker’s
skill premium and R&D firms’ productivity are low, economic growth cannot be achieved in thelong run. When individuals borrow educational funds from the government with a fixed interest21

Rb=0.8

Rb=1

Rb=1.2Market15
14
13

Welfare

12
11
10
9
8
7
6

0

1

2

3

4

5

6

7

8

9

10

Time

Figure 10: Relationship between policy interest rate and intergenerational inequality: The verticalline shows the welfare levels of young generation or adult generation at time 0. The horizontal line
shows time.
rate set by the government (public funds regime), if the policy interest rate is too low, expansion ofdemand for educational funds crowd out funds for R&D activities. Therefore, overly fast expansionof skilled workers interrupts economic growth. In addition, we suggest that even though long-run
economic growth is attained when the individual borrows from the financial market, the economy
cannot grow in the long run because of the government’s excessive education policy. In addition, we
examined welfare and intergenerational inequality. If the government lowers the policy interest rateon educational fund lending, it has both a positive eﬀect and a negative eﬀect on the economy. Whenthe government lowers the policy interest rate of educational fund lending, the current generation’s
welfare increases by the positive eﬀect. However, future generations’ welfare will decrease by theindirect negative eﬀect. This study showed that the government faces a trade-oﬀ between thecurrent generation’s welfare and future generations’ welfare.

22

Appendix
Appendix A：Proof of Lemma 1
From (14), we obtain1+ααγ + ηA =[η + (1 − α)α 1−α h]γ2α(1 − α)α 1−α (h − 1)

.

(30)

We also obtain
1+α

2α∂S2M (At )[η + (1 − α)α 1−α h]αγ 2= (1 − α)α 1−α h −∂At(αγ + ηAt )2

{

}

2α

log

(1 − α)α 1−α (h − 1)(αγ + ηAt )1+α[η + (1 − α)α 1−α h]γ

+1

1+α

η
[η + (1 − α)α 1−α h]γAt×−(αγ + ηAtαγ + ηAt
1+α= (1 − α)α

and

2α
1−α

[η + (1 − α)α 1−α h]αγ 2h−(αγ + ηAt )2{}2α(1 − α)α 1−α (h − 1)(αγ + ηAt )× log+ αγ + ηAt
1+α[η + (1 − α)α 1−α h]γ∂ 2 S2M (At )is calculated as follows
∂A2t
1+α

∂ 2 S2M (At )2[η + (1 − α)α 1−α h]γη=(αγ + ηAt )3
∂A2t

{

}

2α

αγ log(1 − α)α 1−α (h − 1)(αγ + ηAt )1+α[η + (1 − α)α 1−α h]γ)+η+ αγ + ηAt

1+α
(
αγη
[η + (1 − α)α 1−α h]γ−2(αγ + ηAt )αγ + ηAt}{1+α2α[η + (1 − α)α 1−α h]γη(1 − α)α 1−α (h − 1)(αγ + ηAt )=2αγ log+ ηAt .
1+α(αγ + ηAt )3[η + (1 − α)α 1−α h]γ2α1−α (h−1)(αγ+ηAt )1+α[η+(1−α)α 1−α h]γ

From this equation, if 2αγ log (1−α)α
A=

(31)

1−α
[η+(1−α)α 1+α h]γ2α(1−α)α 1−α η(h−1)

22 (At )
> 0 holds. Considering At ≥≥ 0, ∂ S∂A
2t, after some manipulations, we obtain the following inequality,
2α2αγ log(1 − α)α 1−α (h − 1)(αγ + ηAt )1+α[η + (1 − α)α 1−α h]γ

23

(32)

≥0

Therefore, when At ≥ A,

∂ 2 S2M (At )∂S2M (At )>0holds.
We
examine
the
sign
of
2
∂At ; when At = A, the∂Atfollowing holds
1+α2α∂ 2 S2M (At )[η + (1 − α)α 1−α h]αγ 21−α h −=(1−α)α(αγ + ηA)2
∂A2t
At =A
{
}
2α
(1 − α)α 1−α (h − 1)(αγ + ηA)
× log+ αγ + ηA .
1+α
[η + (1 − α)α 1−α h]γ

From (30), we obtain
2α

2α∂S2M (At )γ[(1 − α)α1+α 1 − αh][(1 − α)α 1−α (h − 1)]2
= (1 − α)α 1−α h −
1+α
∂At
At =A
{γ[η + (1 − α)α 1−α h]}2






1+α
1+α


2α

(1 − α)α 1−α (h − 1)γ[η + (1 − α)α 1−α h] γ[η + (1 − α)α 1−α h] +× αγ log
1+α
2α
2α



γ[η + (1 − α)α 1−α h](1 − α)α 1−α (h − 1) (1 − α)α 1−α (h − 1) 


|

{z
}

=0

= (1 − α)α

2α
1−α

> 0.

(33)

∂ 2 S2M (At )∂S M (A )> 0, 2∂At t > 0 holds when At ≥ A.
∂A2t
∂D2M (At+1 )We obtain ∂A
as follows:
t+1

Considering∂D2M (At+1 )
γη
=
+η >0
∂At+1
αγ + ηAt+1
and also obtain(34)∂ 2 D2M (At+1 )as follows:∂A2t+1γη 2∂ 2 D2M (At+1 )=−< 0.
(αγ + ηAt+1 )2∂A2t+1(35)

Appendix B：Proof of Proposition 1
From Assumption 1, D2M (A) < S2M (A) holds. Therefore, ψ(A) ≡ D2M (A) − S2M (A) < 0 holds. In
addition, From Lemma 1, ψ(A) is a concave function with respect to A. Therefore, ψ ′ (A) < 0 is a24

! ! (!! )!! (!!!! )0!

!! !!!!

!!

0!

!(!) = ! ! (!) − ! ! (!)

Figure 1125

suﬃcient condition for case (i) to occur. From (20), we obtain
1+α

2α
γη
[η + (1 − α)α 1−α h]αγ 2+ η − (1 − α)α 1−α h +ψ (A) =αγ + ηA(αγ + ηA)2
{
}
1+α
2α
(1 − α)α 1−α (h − 1)(αγ + ηA)[η + (1 − α)α 1−α h]γηA
× log
+1 +
1+α
(αγ + ηA)2
[η + (1 − α)α 1−α h]γ
[
]
2α
2α
[
] (1 − α)α 1−α1−α h − η
2α
(h
−
1)
(1
−
α)α
= 2η + (1 − α)α 1−α (h − 1 + α)−1+α2α2η + (1 − α)α 1−α (h − 1 + α)
η + (1 − α)α 1−α h′(36)We define the following functions to examine the sign of ψ ′ (A).
2α

Λ(η, h) ≡(1 − α)α 1−α (h − 1)
1+α

η + (1 − α)α 1−α h

,

(37)

2α

Ω(η, h) ≡(1 − α)α 1−α h − η2α2η + (1 − α)α 1−α (h − 1 + α)

.

(38)

We can obtain the following:
2α2α∂Ω(η, h)[2η + (1 − α)α 1−α (h − 1 + α)] + 2[(1 − α)α 1−α h − η]
<0
=−
2α
∂η
[2η + (1 − α)α 1−α (h − 1 + α)]2(39)

∂ 2 Ω(η, h)
2
>0
=
2α
2
∂η
[2η + (1 − α)α 1−α (h − 1 + α)]4

(40)

2α

Λ(0, h) =(1 − α)α 1−α h
2α(1 − α)α 1−α (h − 1 + α)
h
=
h−1+α

(41)

2α

Ω(0, h) =(1 − α)α 1−α (h − 1)1+α

(1 − α)α 1−α h
h−1
=
.
αh

(42)

We define ĥ as h when equality Ω(0, h) = Λ(0, h) holds.

26

!(!, 0)1!

!(!, 0)

1

0

1−!

ℎ

ℎ!

1

!(!, 0) > !(!, 0)

Figure 12

According to Figure 12, when h < ĥ, Ω(0) > Λ(0) holds. Now, we draw the relationship between(37) and (38) in Figure 13.

!(0, ℎ)!(!, ℎ)!(0, ℎ)−(1 − !)!

!!!
!!!

ℎ

(!, ℎ)!̂0!!

(1 − !)! !!!ℎ

!

!!

−

(1 − !)! !!! (ℎ − 1 + !)2

(i)Figure 13

We define η̂ such that Ω(η, h) = Λ(η, h) holds. According to Figure 13, when η ≤ η̂, case (i)occurs. Therefore, when h ≤ ĥ and η ≤ η̂ holds, case (i) occurs.

27Appendix C：Proof of Lemma 2∂S2G (At )is given by∂At
2α∂S2G (At )RB γ= (1 − α)α 1−α h −
.
∂At
At

(43)

When At ≥ A, we show the following:
2α∂S2G (At )RB γ= (1 − α)α 1−α h −
∂At
At
2α
RB γ
> (1 − α)α 1−α (h − 1) −
A
( t
)
2α
RB γ
(1 − α)α 1−α (h − 1)
At −
=
2α
At
(1 − α)α 1−α (h − 1)2α

(1 − α)α 1−α (h − 1)
(At − A) ≥ 0.
=
At

(44)

∂ 2 S2G (At )is calculated as∂A2t

We obtainThus,∂ 2 S2G (At )
RB γ
=
> 0.
2
∂At
A2t

(45)

∂D2G (At+1 )γ=+ η > 0.
∂At+1
At+1

(46)

∂ 2 D2G (At+1 )γ= − 2 < 0.
2
∂At+1
At+1

(47)

∂D2G (At+1 )as follows:∂At+1∂ 2 D2G (At+1 )becomes∂A2t+128

Appendix D：Proof of Proposition 2
We investigate conditions in which case (iii) occurs. Let us define ψ(A) as ψ(A) ≡ D2G (A) − S2G (A),that is,ψ(A) ≡ D2G (A) − S2G (A)2α= (1 + RB )γ log A − [(1 − α)α 1−α h − η]A + RB γ
− (1 + RB )γ log

RB γ
2α

(1 − α)α 1−α (h − 1)

.

(48)

Diﬀerentiating ψ(A) leads to
2α(1 + RB )γ− [(1 − α)α 1−α h − η].
Aψ ′ (A) =This derivative equals zero when A =(1+RB )γ2α(1−α)α 1−α h−η≡ Ã. It is obvious that ψ(A) takes a maximum

value when A = Ã. The maximum value of ψ(A) is{ψ(Ã) = γ}2α(1 + RB ) log(1 − α)α 1−α (h − 1)(1 + RB )2α[(1 − α)α 1−α h − η]RB

−1 .

(49)

We next examine the sign of ψ(Ã). If the following inequality holds, then ψ(Ã) takes a positive
value
2α

(1 + RB ) log(1 − α)α 1−α (h − 1)(1 + RB )2α[(1 − α)α 1−α h − η]RB

− 1 ≥ 0.

This can be rewritten as2α(1 − α)α 1−α (h − 1)(1 + RB )|[(1 − α)α

2α
1−α

{z

h − η]RB1≥ e 1+RB .

(50)

}

≡ϕ(RB ;h,η)1

We define the left-hand side of (50) as ϕ(RB ; h, η). It is obvious that ϕ(RB ; h, η) and e 1+RB are decreasing functions of RB . Moreover, we show that limRB →0 ϕ(RB ; h, η) = ∞, limRB →∞ ϕ(RB ; h, η) =2α(1−α)α 1−α (h−1)2α(1−α)α 1−α h−η11, limRB →−1 e 1+RB = ∞ and limRB →∞ e 1+RB = 1. The following inequality holds un-

29

!

!!

(1 − !)! !!! (ℎ − 1)

! !!!!

1!!

(1 − !)! !!! ℎ − !

!(!! ; ℎ, !)
−1

0

!!

!!!
(!!!)

(!!)

Figure 14: Determination of R̂B
der (A1):2α(1 − α)α 1−α (h − 1)2α

(1 − α)α 1−α h − η

< 1.

(51)

From the preceding arguments, Figure 14 shows the graph of the left-hand side and that of theright-hand side of (50). We define R̂B as the policy interest rate at which (50) holds with equality.
When RB ≤ R̂B , case (iii) is obtained.

Appendix E：Proof of Proposition 3
We investigate the eﬀects of the change of h and η on R̂B . We obtain
2α2α∂ϕ(RB ; h, η)(1 − α)α 1−α (1 + RB )[(1 − α)α 1−α − η]
=
≥0
2α
∂h
[(1 − α)α 1−α h − η]2 RB

(52)

and
2α

(1 − α)α 1−α (h − 1)(1 + RB )∂ϕ(RB ; h, η)
=
≥ 0.
2α
∂η
[(1 − α)α 1−α h − η]2 RB(53)

Therefore, if h or η increases, ϕ(RB ; h, η) shifts, as described in Figure 15. From Figure 15, we findthat R̂B rises if h or η increase.

30

!

!!

(1 − !)! !!! (ℎ − 1)

! !!!!

1!!

(1 − !)! !!! ℎ − !

!(!! ; ℎ, !)
−1

0

!! '!

!!!

!!

Figure 15

Appendix F：Welfare
We consider the welfare of this economy. All individuals obtain utility from consumption when old.
Therefore, we define the welfare levels of this economy at time t as the sum of consumption of old
individuals at time t.

(1) Private funds regime
First, we consider the private funds regime. We define UtM as the welfare levels of this economy.
When At < A, all individuals become unskilled workers. Therefore, aggregate consumption of all
individuals is given by
∫ 1
UtM =

M
Rt+1
wt dθ
0
2α

M
= Rt+1(1 − α)α 1−α At(54)Moreover, when At ≥ A, aggregate consumption of all individuals is given byUtM =∫ θ̂t−1∫ 1
M
Rt+1
wt dθ +

0

(
γ)
M
Rt+1
wt h − RtM
dθ
θ
θ̂t−1

M
= Rt+1S2M (At )

(55)

31

(2) Public funds regime
Next, we consider the public funds regime. We define UtG as the welfare levels of this economy.
When At < A, all individuals become unskilled workers. Therefore, aggregate consumption of all
individuals is given by
∫ 1
UtG =

G
Rt+1
wt dθ
0
2α

G
= Rt+1(1 − α)α 1−α At .

(56)

Moreover, when At ≥ A, aggregate consumption of all individuals is given byUtG =∫ θ̂t−1[ G]
Rt+1 (wt − Tt ) + Gt+1 dθ +0GG
= Rt+1S2G (At ) − (Rt+1− RB )

∫ 1

∫ 1 [
θ̂t−1

(
)
]
G
G γ
Rt+1
wt h − Rt+1
− Tt + Gt+1 dθ
θ

γ
dθ.
θ̂t θ

(57)

Appendix G：Data• Figure 1 and Figure 2 is based on data released by World bank.

References[1] Acemoglu, Daron. “Why do new technologies complement skills? Directed technical change
and wage inequality.” Quarterly Journal of Economics (1998): 1055–1089.
[2] Boldrin, Michele, and Ana Montes. “The intergenerational state education and pensions.” The
Review of Economic Studies 72.3 (2005): 651–664.
[3] Dalgaard, Carl-Johan, and Claus Thustrup Kreiner. “Is declining productivity inevitable?”
Journal of Economic Growth 6.3 (2001): 187–203.
[4] Galor, Oded, and Omer Moav. “Ability-biased technological transition, wage inequality, andeconomic growth.” Quarterly Journal of Economics (2000): 469–497.

32

[5] Grossmann, Volker. “How to promote R&D-based growth? Public education expenditure on
scientists and engineers versus R&D subsidies.” Journal of Macroeconomics 29.4 (2007): 891–
911.
[6] Morimoto, Takaaki. “Occupational choice and entrepreneurship: eﬀects of R&D subsidies on
economic growth.” Journal of Economics (2017): 1–25.
[7] OECD “Education at a glance 2014” (2014).
[8] Rivera-Batiz, Luis A., and Paul M. Romer. “International trade with endogenous technologicalchange.” European Economic Review 35.4 (1991): 971–1001.
[9] Strulik, Holger. “The role of human capital and population growth in R&D‐ based models of
economic growth.” Review of International Economics 13.1 (2005): 129–145.
[10] Japan Student Services Organization “Nihongakuseishienkiko Gaiyo 2016” (2016).

33