Discussion Papers In Economics
And Business

A Schumpeterian Growth Model with Financial Intermediaries

Miho Sunaga

Discussion Paper 15-19

Graduate School of Economics andOsaka School of International Public Policy (OSIPP)
Osaka University, Toyonaka, Osaka 560-0043, JAPANA Schumpeterian Growth Model with Financial Intermediaries

Miho Sunaga

Discussion Paper 15-19

June 2015

Graduate School of Economics andOsaka School of International Public Policy (OSIPP)
Osaka University, Toyonaka, Osaka 560-0043, JAPANA Schumpeterian Growth Model with Financial Intermediaries ∗Miho Sunaga†

Abstract
This study introduces ﬁnancial intermediaries into the Schumpeterian growth model
developed by Aghion, Howitt, and Mayer-Foulkes (2005). They collect deposits fromhouseholds, provide funds for entrepreneurial projects, and monitor the entrepreneurs.
I consider an economy with moral hazard problems: entrepreneurs can hide the result ofa successful innovation and thereby avoid repaying ﬁnancial intermediaries if the latterdo not monitor entrepreneurial performance. I analyze the eﬀects of ﬁnancial intermediaries’ activities on technological progress and economic growth in such an economy. I
show that ﬁnancial intermediaries need to monitor entrepreneurs in an economy where
the legal protection of creditors is not strong enough. Such monitoring can resolve themoral hazard problem; however, it does not always promote technological innovation,
because it could increase the cost of entrepreneurial innovation and thus reduce theamount invested for innovation. I also examine how monitoring by ﬁnancial intermediaries aﬀects the welfare of individuals through the stringency of ﬁnancial markets.

Keywords: Economic growth, Innovation, Financial intermediaries, Monitoring
JEL Classiﬁcation Numbers: G21, O16, O41∗

I would like to thank Koichi Futagami, Tatsuro Iwaisako, Shingo Ishiguro, Katsuya Takii and participantsof the Japanese Economic Association Spring Meeting 2014 at Doshisha University for their helpful comments
and suggestions.
†
Graduate School of Economics, Osaka University, 1-7 Machikaneyama, Toyonaka, Osaka 560-0043, Japan.
E-mail: pge014sm@student.econ.osaka-u.ac.jp

1

Introduction

The idea that the ﬁnancial sector plays an important role in economic growth is traced
back to Schumpeter (1911). He argues that the following services of ﬁnancial intermediaries
are essential for technological innovation and economic development: mobilizing savings,
evaluating projects, managing risk, monitoring managers, and facilitating transactions. Hisargument has induced many studies, especially empirical ones, on ﬁnance and growth. For
instance, Goldsmith (1969) and King and Levine (1993a) study the empirical link between
ﬁnancial development and economic growth.1 Levine (2005) surveys theoretical and empirical studies on ﬁnance and economic growth. He indicates that the functions provided by theﬁnancial system may inﬂuence savings and investment decisions and thus economic growth.2
This study focuses on one of the ﬁnancial functions, that is, monitoring entrepreneurial performance.3 Monitoring of entrepreneurs by ﬁnancial intermediaries can resolve the moral
hazard problem where entrepreneurs hide the result of a successful innovation and thereby
avoid repaying the ﬁnancial intermediaries. Several studies examine this ﬁnancial function,
but many of them are static and not suitable for analyzing the eﬀects of ﬁnancial interme-1King and Levine (1993a) build on Goldsmith (1969). They use data on 80 countries over the 1960–1989

period, whereas Goldsmith (1969) uses data on about 35 countries over the period 1860–1963. Moreover,King and Levine (1993a) construct additional measures of the level of ﬁnancial development.
2
Levine (2005) indicates the following functions provided by the ﬁnancial system: (i) production of ex
ante information about possible investments, (ii) monitoring of investments and the implications of corporate
governance, (iii) trading, diversiﬁcation, and management of risk, (iv) mobilization and pooling of savings,
and (v) exchange of goods and services. Laeven, Levine, and Michalopoulos (2009, 2015) and Greenwood andJovanovic (1990) focus on function (i) and analyze the eﬀects of the ﬁnancial system on economic growth.
King and Levine (1993a, 1993b) and Acemoglu and Zilibotti (1997) study the eﬀect of ﬁnancial systems ontechnological change and economic growth from functions (iii),(iv), and (v).
3This study focuses on only ex ante monitoring, and not on corporate governance. As for corporate
governance, Bencivenga and Smith (1993) show that the activities of ﬁnancial intermediaries that improve
corporate governance boost economic growth.

1diaries on economic growth in the long run.4 Thus, I develop a Schumpeterian endogenous
growth model where ﬁnancial intermediaries monitor investments and their monitoring may
aﬀect economic growth in an economy with moral hazard problems.
I consider an economy with asymmetric information; borrowers have an incentive to cheat
because lenders cannot observe their activities once the lenders supply them funds. I introduce ﬁnancial intermediaries who can monitor the activities of entrepreneurs in a multisector Schumpeterian growth model with asymmetric information. Aghion, Howitt, andMayer-Foulkes (2005) introduce imperfect credit markets based on asymmetric information
in a multi-sector Schumpeterian growth model. However, their model does not focus on
the activities of ﬁnancial intermediaries. Thus, this study provides a model of monitoringby ﬁnancial intermediaries in contrast to Aghion, Howitt, and Mayer-Foulkes’ (2005) model
where there is no ﬁnancial intermediaries.
The goal of this study is to develop a simple Schumpeterian growth model with ﬁnancial intermediaries who collect deposits from households, provide funds for entrepreneurial
projects, and monitor the borrowers, and to analyze the eﬀects of activities of the ﬁnancial
intermediaries on technological innovation and economic growth in an economy with moral
hazard problems.
My model is based on Aghion, Howitt, and Mayer-Foulkes (2005), which considers an
economy with asymmetric information where borrowers do not repay their obligations but
pay a cost to hide their true revenues, as in Bernanke and Gertler (1989).5 In this study,
I construct a model with moral hazard problems induced by entrepreneurs, following theidea of a hidden cost in Aghion et al. (2005). Moreover, I incorporate the idea of a private
beneﬁt, as in Holmström and Tirole (1997). In Holmström and Tirole (1997), a moral hazard
4Boyd and Smith (1994) consider how a debt contract can lower the monitoring costs, but their framework

is static. Diamond (1984) and Holmström and Tirole (1997) focus on the link between the level of monitored
ﬁnance and the level of investment, but their frameworks are also static.
5
The cost is called a hidden cost in Bernanke and Gertler (1989); it is taken as the degree of creditor
protection in Aghion, Howitt, and Mayer-Foulkes (2005).

2

problem exists in that borrowers can obtain a private beneﬁt by not managing their project
diligently. They show that in an economy with the moral hazard problem, the monitoringlevel can aﬀect aggregate production and alleviate the moral hazard; however, their model isstatic and thus cannot analyze the eﬀects of monitoring on economic growth in the long run.
Therefore, one of the contributions of this study is examining a similar issue in a dynamic
framework, that is, lower monitoring cost; in other words, this study examines whether higher
monitoring technology of ﬁnancial intermediaries can accelerate economic growth by lowering
the cost of raising funds for entrepreneurs. I also show that in an economy where the legal
protection of creditors is suﬃciently high, ﬁnancial intermediaries do not have to monitor
entrepreneurs, and the equilibrium level of innovation in this economy is the same as in theeconomy with no moral hazard problems.6
The rest of the paper is organized as follows. Section 2 presents the basic structure of
the model. In Section 3, I ﬁrst consider an economy without moral hazard problems as thebenchmark, and then an economy with moral hazard problems. The section analyzes the link
between legal protection of the creditor and the role of ﬁnancial intermediaries. The eﬀects
of ﬁnancial intermediaries’ monitoring on economic growth are also analyzed. Section 4shows the results of Section 3 graphically and provides their implications. Section 5 performs
welfare analyses. Concluding remarks are oﬀered in Section 6.

2

The Model

2.1

Environment

I develop a discrete-time multi-sector Schumpeterian growth model where ﬁnancial intermediaries collect deposits from households, provide funds for entrepreneurial projects, and6

One of the studies examining the legal system and ﬁnancial development is La Porta et al. (2000);

the study takes the view that diﬀerences in the legal system are the fundamental source of international
diﬀerences in ﬁnancial development.

3monitor the entrepreneurs. The model has the same basic structure as Aghion, Howitt, andMayer-Foulkes’ (2005) Schumpeterian growth model in a discrete-time framework, exceptthat the monitoring activities of ﬁnancial intermediaries is incorporated. Aghion, Howitt,
and Mayer-Foulkes (2005) consider a ﬁnancial market, but they do not consider the activities
of ﬁnancial intermediaries. I assume a small open economy consisting of a continuum of
individuals: households, entrepreneurs, and ﬁnancial intermediaries.7 Each individual lives
for two periods.
Households are endowed with one unit of labor, which is inelastically supplied to the ﬁnal
goods sector in the ﬁrst period. They have a ﬁxed population size L, which is normalized to 1;
save by having deposits with ﬁnancial intermediaries in the ﬁrst period; and consume the ﬁnal
goods in both periods. I give a more detailed explanation of household behavior in Section
2.6. Entrepreneurs are born with entrepreneurial ideas in the ﬁrst period. However, only one
entrepreneur’s idea per sector has a positive probability of producing a successful innovationand improving the production technology in the second period. In each intermediate goods
sector, the entrepreneur who has such an innovative idea can raise funds for investment inthe ﬁrst period. Entrepreneurs who can successfully innovate have an advantage over those
who cannot, in that they can produce an intermediate good at a lower cost compared to theothers. Thus, successful entrepreneurs can earn monopolistic proﬁts in the second period.
Financial intermediaries collect deposits from households and provide funds for innovative
activities in the ﬁrst period. There is a moral hazard problem in that entrepreneurs can makethe following decisions after availing funds from the ﬁnancial intermediaries: ﬁrst, whether to
use all the funds obtained from ﬁnancial intermediaries for investment or not; second, whether
to repay the ﬁnancial intermediaries or not.8 Thus, ﬁnancial intermediaries must monitor the
7

In Aghion, Howitt, and Mayer-Foulkes (2005), there are m countries. They focus on the process oftechnology transfer; however, I focus on the eﬀect of the ﬁnancial intermediaries’ monitoring on growthrather than the eﬀect of technological transfer on growth.
8
Entrepreneurs can hide their revenue by paying a certain cost. This cost is called a hidden cost in
Bernanke and Gertler (1989).

4

entrepreneurs and thereby alleviate the moral hazard problem. In the following subsections,
I consider in detail the ﬁnal goods sector, the intermediate goods sector, households, and theﬁnancial sector respectively.

2.2

Final Goods Sector

Final goods, Zt , are produced from labor and a continuum of specialized intermediate goods
according to the following production function:∫ 1
α ∈ (0, 1),αA1−αi,t xi,t di,1−αZt = L(1)0

where xi,t is the input for intermediate good i in period t, and Ai,t is the level of technologyof the intermediate goods sector i in period t. L represents labor supply, which is normalized
to 1. The ﬁnal good, Zt , is used for both consumption and as an input for the production ofintermediate goods.
I use the ﬁnal good as the numeraire. The ﬁnal good is produced under perfect competition.
Thus, the price of each intermediate good, pi,t , is equal to its marginal product:(pi,t = α

2.3

Ai,t
xi,t

)1−α
.

(2)

Intermediate Goods Sector

For each intermediate goods sector i, an entrepreneur born in period t-1 can successfully
innovate and produce an intermediate good in the next period, t. Let µi,t be the probability
that an entrepreneur successfully innovates. Then, the level of technology of intermediate
goods sector i in period t, Ai,t , becomes




 At
with probability µi,t ,
Ai,t =

Ai,t−1 with probability 1 − µi,t (3)where At is the world technology frontier. I assume that At > Ai,t−1 for all i, t. The worldtechnology frontier grows at a constant rate g > 0.
5

If an entrepreneur can successfully innovate, she will produce an intermediate good withtechnology that can transform one unit of the ﬁnal good into one unit of intermediate good.
This entrepreneur is called a successful innovator. Entrepreneurs who do not innovate canproduce an intermediate good but incur a higher cost of production. They need χ units of
the ﬁnal good to produce one unit of the intermediate good. I assume that α1 > χ > 1.
In all intermediate goods sectors, there exists an unlimited number of entrepreneurs—thecompetitive fringe—capable of producing the intermediate good at the unit cost of χ. Then,each successful innovator does not charge more than χ in equilibrium in order to preventthe competitive fringe from entering the intermediate goods market. Thus, each successful
innovator charges χ and can enjoy the cost-of-production advantage.9
Each successful innovator becomes a monopoly in her intermediate goods sector. She
charges a price equal to the unit cost of the competitive fringe, χ, and earns monopoly
proﬁts for one period.10 In the intermediate goods sector where innovation is unsuccessful,production will occur under perfect competition, and so the price will be equal to the unit
cost of the competitive fringe, χ, and the unsuccessful innovators earns zero proﬁt. Thus, ineach intermediate goods sector, the price of the intermediate good pi,t becomes
pi,t = χ, ∀i.

(4)From (4) and (2), the quantity demanded for intermediate good i becomes1( ) 1−ααxi,t =
Ai,t , ∀i.
χ

9

(5)

The condition for innovators to enjoy the cost of production advantage is the following limit-price con-straint: pi,t ≤ χ
10In the absence of a competitive fringe, when α1 < χ, each successful innovator charges a price equal to α1 .
However, when α1 > χ > 1, each successful innovator is forced to charge the limit price χ in order to prevent
entry by the fringe, as in Aghion, Howitt, and Mayer-Foulkes (2005) and Aghion and Howitt (2009, chapter
4).

6

Thus, the proﬁt of entrepreneurs in the intermediate goods sector i, πi,t , can be given by

( ) 1


pi,t xi,t − xi,t = (χ − 1) α 1−α Ai,t = πAt , if successful,χ
πi,t =(6)
pi,t xi,t − χxi,t = 0, if unsuccessful,where π = (χ − 1)

2.4

1( ) 1−ααχ)(and χ ∈ 1, α1 . 11

Aggregate Behavior

This subsection aggregates economic activities. I deﬁne the average level of technologicalproductivity, At , as

∫ 1
At =

Ai,t di.

(7)0

Substituting (5) and (7) into production function (1), the aggregate output becomesα( ) 1−α
α
Zt =
At .
χ

(8)

Since perfect competition prevails in the ﬁnal goods sector, the wage rate, wt , is equal to themarginal product of labor in producing the ﬁnal good, and is proportional to At :α( ) 1−ααwt = (1 − α)Zt = δAt , where δ = (1 − α)
.
χ

(9)

In equilibrium, the probability of successful innovation is the same across sectors: µi,t = µt
for all i. Therefore, the law of motion of average productivity becomes
At = µt At + (1 − µt )At−1 .

(10)Equation (10) reveals that the average technological productivity of an economy in period t
is a weighted average of the µt sectors that implement the world frontier technology, At , andthe 1 − µt sectors that use the average technology in period t-1, At−1 .
I deﬁne technology gap as the distance from the world technology frontier:12
at ≡
11
12

At
.
At

(11)

Note that Ai,t = At if innovation is successful, from (3).
The deﬁnition of ”technology gap” is the same as that in Acemoglu, Aghion, and Zilibotti (2006), Aghion,

Howitt, and Myer-Foulkes (2005), and Laeven, Levine, and Michalopoulos (2009, 2015).

7

This deﬁnition implies that as at approaches 1, the economy’s average technology, At , isclosed to the world technology frontier, At .13 From (10) and (11), the technology gap evolves
according to(
at = µt +1 − µt1+g)
at−1 ,(12)

where g is the growth rate of the world frontier technology, At .

2.5

Financial Intermediaries

Financial intermediaries are born with endowment ω f > 0 in period t-1. Their net worthff
in period t-1, Nt−1
, is equal to their endowment, ω f . In other words, Nt−1
= ω f obtains

in period t-1. It is assumed that ω f is not enough to provide funds for the entrepreneurs
and monitor them, and so ﬁnancial intermediaries need to collect deposits from households.
After they collect deposits from the households, they invest their own net worth as well as thedeposits received by providing funds for the entrepreneurs who have a positive probability ofinnovation or by holding risk-free assets.14 Thus, their balance sheet condition can be givenbyfLft−1 + Bt−1 = Dt−1 + Nt−1,

(13)where Lft−1 is the amount of funds lent to the entrepreneurs in period t-1, Bt−1 is the amountfof risk-free asset holdings, Dt−1 is the amount of deposits received in period t-1, and Nt−1
istheir own net worth. If the ﬁnancial intermediaries provide funds Lft−1 for the entrepreneursin period t-1, the successful innovators pay them µt Rtf Lft−1 in period t.15 If the ﬁnancial
intermediaries hold risk-free assets Bt−1 in period t-1, they would have (1 + r)Bt−1 assets inperiod t.

13
14

Note that at ∈ [0, 1].
I assume a small open economy, and so ﬁnancial intermediaries can invest abroad at the rate of return,r, which is given.
15
Note that µt is the proportion of sectors where innovation is successful and ﬁnancial intermediaries agree
not to claim payment if the entrepreneurs, that is, the borrowers, fail to innovate.

8

Since the ﬁnancial market and world capital market are eﬃcient, ﬁnancial intermediaries
would require that the expected return rate on funds provided to entrepreneurs be equal to
the return rate on their risk-free asset holdings in case there is no moral hazard problem.
Thus, the no-arbitrage condition in an economy with no moral hazard problem can be givenbyµt Rtf = 1 + r.

(14)

I consider the following moral hazard problem. Entrepreneurs who are provided with funds
may cheat the ﬁnancial intermediaries by not repaying the loan once they successfully innovate. This moral hazard problem can be resolved if ﬁnancial intermediaries monitor theentrepreneurs; however, it costs mLft−1 to monitor entrepreneurs when the ﬁnancial intermediaries lend them Lft−1 .16
Let ρ = {0, 1} be the probability that ﬁnancial intermediaries can obtain repayment. If the
ﬁnancial intermediaries monitor the borrowers, they obtain repayment with the probability
ρ = 1. Otherwise, they obtain repayment with the probability 0.
If ﬁnancial intermediaries monitor the borrowers, since both the ﬁnancial market and world
capital market are eﬃcient, the markets would require that the expected return rate on funds)(
ρµt Rtf Lft−1 −Lft−1 −mLft−1, be equal to the return rate on theprovided for the entrepreneurs,
Lft−1
(
)
−Bt−1
risk-free asset holdings, (1+r)BBt−1. In equilibrium, ρ = 1 if ﬁnancial intermediaries
t−1
monitor the borrowers. Thus, the no-arbitrage condition in an economy with the moral
hazard problem and ﬁnancial intermediaries’ monitoring can be given byµt Rtf = 1 + r + m.

(15)

Because of perfect competition between ﬁnancial intermediaries, the following zero-proﬁt
conditions hold:µt Rtf Lft−1 + (1 + r)Bt−1 − Rtd Dt−1 = 0, if no monitoring,
16

(16)

I assume that if ﬁnancial intermediaries monitor the entrepreneurs, the entrepreneurs who successfully

innovate are forced to repay them.

9µt Rtf Lft−1 + (1 + r)(

Bt−1 − mLft−1)− Rtd Dt−1 = 0, if monitoring.

(17)

If ﬁnancial intermediaries decide to monitor the entrepreneurs in period t-1, they have toborrow the monitoring cost, mLft−1 , in the world capital market in period t-1, and repay(1 + r)mLft−1 in period t.17
If the ﬁnancial intermediaries do not monitor the entrepreneurs, the balance sheet condition(13), the no-arbitrage condition (14), and the zero-proﬁt condition (16) yield the following
gross return for deposits, Rtd :(Nf
Rtd = (1 + r) 1 + t−1
Dt−1

)
.

(18)

If the ﬁnancial intermediaries do monitor the entrepreneurs, the balance sheet condition (13),the no-arbitrage condition (15), and the zero-proﬁt condition (17) yield the following gross
return for deposits, Rtd :(Nf
Rtd = (1 + r) 1 + t−1
Dt−1

)

(
− rm

Lft−1
Dt−1

)
.

(19)

Lf

:18
Assume the following rule of the lending to net worth ratio, Nt−1
f
t−1

Lft−1
1+r
> f .
rm
Nt−1

2.6

(20)

Households

The economy is populated by a ﬁxed number L of identical households, and L is normalized
to 1. The households live for two periods, and are endowed with one unit of labor, which issupplied inelastically in the ﬁrst period. The households consume the ﬁnal goods in the ﬁrst
and second periods, with the following utility function:y
U = ln Ct−1
+ β ln Cto ,
17
18

(21)

Since I assume a small open economy, the risk-free rate, r, is exogenous.
Under rule (20), the return for deposits determined by (19) is larger than 1 + r, which is the return on

risk-free asset holdings. Then, households can save only by having deposits with ﬁnancial intermediaries,
whether or not the ﬁnancial intermediaries monitor the entrepreneurs. For the derivation of (19) and (20),see Appendix A.

10ywhere Ct−1
and Cto denote the consumption of the ﬁnal goods in the ﬁrst and second periods

respectively, and β ∈ (0, 1) is the discount factor.19 They save by having deposits Dt−1 withﬁnancial intermediaries, who pay them a certain gross return Rtd .20 Each household born inyperiod t-1 can choose to consume in the ﬁrst and second periods, Ct−1
and Cto , respectively,

and have deposit Dt−1 to maximize the above utility function subject to the following budget
constraints:yCt−1+ Dt−1 = wt−1 ,(22)

Cto = Rtd Dt−1 .

(23)

The ﬁrst-order condition of the household’s maximization problem is(
Dt−1 =

β1+β)wt−1 .

(24)

At−1 .

(25)

Using (9), I can rewrite (24) as(
Dt−1 =

3

βδ
1+β

)

Innovation

The probability of an entrepreneur successfully innovating in period t, µt , depends on theamount of funds invested in innovation during period t-1 :21
Ni,t−1 = (θµi,t )γ At .

(26)

Here, Ni,t−1 is the amount of funds invested in innovation during period t-1 : that is, thedemand for funds; θ is a parameter reﬂecting the institutional and other characteristics thataﬀect the cost of innovation at every level of technology; and γ is the inverse of the R&D
19
20

The utility function is speciﬁed to be of log-utility type, since it is tractable for analyses.
In equilibrium, Rtd > 1 + r, implying that the households cannot access the world capital market and cansave only by having deposits.
21
Formulation (26) is based on Laeven, Levine, and Michalopoulos(2009, 2015).

11

investment elasticity with γ > 1.22 Function (26) implies that the higher the world technology
frontier, At , the more diﬃcult it is to innovate, as in Aghion, Howitt, and Mayer-Foulkes(2005).

3.1

Equilibrium Innovation without Moral Hazard

In this subsection, I consider an economy that has no moral hazard problems. To put itin another way, all the entrepreneurs in this economy decide not to privately use the funds
borrowed from ﬁnancial intermediaries and therefore repay the ﬁnancial intermediaries.23
In this economy, each entrepreneur whose idea has a positive probability of successful
innovation chooses the amount of R&D investment Ni,t−1 to maximize her expected proﬁts
Πei,t in intermediate goods sector i:max Πei,t = βµi,tNi,t−1where(

πAt − Rtf Ni,t−1

)
,

( )(
)1
1
Ni,t−1 γ.
µi,t =
θ
At

(27)

(28)

The ﬁrst term in the parentheses in (27), πAt , gives the monopolistic proﬁts of producing
an intermediate good. The second term, Rtf Ni,t−1 , gives the amount that she has to pay theﬁnancial intermediary. The corresponding ﬁrst-order condition yields(

Ni,t−1
At

)

(
=

π
1+γ

)(

1
Rtf

)
.

(29)

Equation (29) implies that any increase in the cost of raising funds, Rtf , reduces the R&D
investment, Ni,t−1 . Because of (28), Equation (29) can be rewritten as follows:( )() γ1 ( ) γ11π1.
µi,t =
θ
1+γ
Rtf
22

(30)

This assumption, γ > 1, implies that the marginal productivity of investment on innovation gradually

decreases.
23
In this subsection, I consider a perfect ﬁnancial market where entrepreneurs can borrow unlimited quantities from ﬁnancial intermediaries.

12f
In equilibrium, the cost of raising funds becomes the same across sectors: Ri,t
= Rtf for all i.

Thus, the probability of innovation becomes the same across sectors: µi,t = µt for all i. The
equilibrium return for lending, Rf ∗ , is determined so as to satisfy the no-arbitrage condition(14) and the entrepreneur’s optimization condition (30). Thus, I obtain
R

f∗

( γ
) 1
θ (1 + γ) γ−1
=
.
βγ π

(31)

By substituting Rf ∗ into optimization conditions (29) and (30), I obtain the equilibrium∗
amount of R&D investment Nt−1
and the equilibrium probability of successful innovation µ∗

as follows:

(

γ
) γ−1
βπ
=
,
θ(1 + γ)
1
(
) γ−1
βπ
∗
,
µ =
θγ (1 + γ)

∗
Nt−1
At

)

(

(32)
(33)

where it is assumed that βπ < (1 + γ)θγ in order to ensure that µ∗ ∈ (0, 1). In equilibrium,
the entrepreneur’s proﬁts, Πe∗t , can be written as(Πe∗t = βπβπγθ (1 + γ)

1
) γ−1

(
At

γ
1+γ

)

(
∗

= βπµ At

γ
1+γ

)
.

(34)

From (33) and (12), the technology gap in this economy with no moral hazard evolves
according to(∗

at = µ +1 − µ∗
1+g)
at−1 ≡ H1 (at−1 ),(35)

where at converges in the long run to the steady state:
a∗ =

3.2

(1 + g)µ∗∈ (0, 1).
g + µ∗(36)

Equilibrium Innovation with Moral Hazard

In this subsection, I describe an economy that has moral hazard problems. Assume that after
the entrepreneurs are provided with funds for R&D investment by ﬁnancial intermediaries,
they can decide whether to use all the funds, Lft−1 , for investment, or whether to privately use

13

a part of the funds, qLft−1 , q ∈ (0, 1).24 Speciﬁcally, if their innovation is unsuccessful, theyobtain the funds left for themselves, qLft−1 , in period t.25 If their innovation is successful,they use the funds left for themselves in period t-1, qLft−1 , to hide the result of their successful
innovation. In this economy, I assume that entrepreneurs can hide the result of a successful
innovation and avoid repaying the ﬁnancial intermediaries in period t if they can pay thecost for it, qLft−1 . Hereafter, I call this cost a hidden cost.26 I assume that parameter q is
given by the legal system for creditor protection.
Assume that the credit market is perfect. Now, the following equation must hold in equi∗. Let N̂t−1 be the amount of investment when entrepreneurs privately
librium: Lft−1 = Nt−1∗
use a part of the funds, that is, N̂t−1 = (1 − q)Nt−1. Furthermore, let µ̂t be the probability ofsuccessful innovation when they invest N̂t−1 in period t-1. Then, the incentive compatibility
constraint that induces the entrepreneurs to be honest is given by∗β (1 − µ̂t ) qNt−1+ β µ̂t πAt ≤ Πe∗
t .

(37)

The right-hand side of (37) is equal to Equation (34), which gives the entrepreneurs’ expected
proﬁts in equilibrium when there is no moral hazard problem and they use all the funds forinvestment. The left-hand side of (37) is the entrepreneurs’ expected proﬁts when they do
not use all the funds for investment in period t-1. The ﬁrst term on the left-hand side of (37)
implies the entrepreneurs’ expected beneﬁt when their innovation is unsuccessful in periodt,27 while the second term of the left-hand side of (37) implies the entrepreneurs’ expected
beneﬁt when their innovation is successful and they earn monopolistic proﬁts but do not
24

When entrepreneurs privately use a part of the funds, the amount of investments decrease. From (26),the probability of successful innovation when they privately use a part of the funds is lower than that when
they use all the funds for investments.
25
This assumption of private beneﬁt is based on Holmström and Tirole (1997).
26
This assumption of a hidden cost is based on Bernanke and Gertler (1989) and Aghion, Howitt, andMayer-Foulkes (2005).
27
Note that β is a discount factor, (1 − µ̂t ) is the probability of unsuccessful innovation when the amount∗of investment is N̂t−1 , and qNt−1
is a private beneﬁt.

14

repay the ﬁnancial intermediaries in period t.28
From (26), (32), (33), and (34), Equation (37) can be rewritten as()
11
q 1 − (1 − q) γ µ∗ β + (1 − q) γ (1 + γ) ≤ γ.

(IC)(IC) is satisﬁed when q is close to 1, because γ > 1 and β < 1.29 When q is close to 1,
entrepreneurs can divert a larger part of funds, but since the hidden cost is high, they lose
the incentive to divert. An increase in q has two eﬀects: one, it increases the private beneﬁt
the entrepreneurs obtain when their innovation is unsuccessful, and two, it increases thehidden cost to be dishonest when their innovation is successful. Since entrepreneurs use alarge part of funds privately and the quantities of investment decrease when q is close to 1,
the probability of successful innovation decreases. Therefore, the latter eﬀect is larger than
the former eﬀect and they lose the incentive to use funds privately when q is close to 1. The
following proposition summarizes the above results.
Proposition 1 The case in which legal protection is suﬃciently high:If the degree of creditor protection is suﬃciently high, that is, the hidden cost q is close
to 1, ﬁnancial intermediaries do not need to monitor the entrepreneurs since the incentive
constraint is satisﬁed. The equilibrium in this case is the same as that in the economy with nomoral hazard problem. Consequently, if the degree of creditor protection is suﬃciently high,that is, the hidden cost q is close to 1, the amount of investment, the probability of successful
innovation, the dynamics of technology gap, and the steady state of the technology gap in the28

Note that µ̂t is the probability of successful innovation when the amount of investment is N̂t−1 and πAt

represents the monopolistic proﬁts given by (6).
29
When q is close to 1, the left-hand side of (IC) is close to β and the right-hand side of (IC) is γ. Notethat γ > 1 and β < 1. Now, the incentive compatibility condition is satisﬁed when q is close to 1. On theother hand, when q is close to 0, the left-hand side of (IC) is close to 1+γ and the right-hand side of (IC) is γ.
Because the left-side of (IC) is strictly larger than the right-hand side, the incentive compatibility condition
is not satisﬁed when q is close to 0.

15

equilibrium with no monitoring are, respectively,
(

∗
Nt−1
At

)

(
=

βπ
θ(1 + γ)

γ
) γ−1

,

(32)

(

1
) γ−1
βπ
µ =
,
θγ (1 + γ)()
1 − µ∗∗
at = µ +at−1 ≡ H1 (at−1 ),
1+g

∗

a∗ =

(1 + g)µ∗∈ (0, 1).
g + µ∗

(33)
(35)
(36)

I next consider the case where the degree of creditor protection is not suﬃciently high,that is, q is close to 0. In order to enable ﬁnancial intermediaries monitor the entrepreneurs,
the following inequality must hold:µt Rtf Lft−1 − mLft−1 ≥ 0.

(38)This inequality implies that ﬁnancial intermediaries have an incentive to monitor when the
return on lending as promised is larger than the cost of monitoring. Thus, inequality (38)is satisﬁed for all m, since the no-arbitrage condition (15) is satisﬁed in equilibrium. The
maximization problem for entrepreneurs under monitoring by ﬁnancial intermediaries is thesame as that under no monitoring by ﬁnancial intermediaries in (27). Thus, in this case, theoptimizing conditions for entrepreneurs are the same as in (29) and (30). In equilibrium, theprobability of innovation is the same across all sectors: µi,t = µt for all i; the no-arbitrage
condition (15) holds; and the entrepreneurs’ optimization condition (30) is satisﬁed. Thus,
ef , in the equilibrium with monitoring can be given by
the return for lending, R
ef = (1 + βm) γ−1
R
γ

( γ
) 1
γ
θ (1 + γ) γ−1= (1 + βm) γ−1 Rf ∗ .
γ
β π

(39)

ef , is higher than that with
Equation (39) implies that this equilibrium return for lending, R
no monitoring, Rf ∗ .30 This result comes from the no-arbitrage condition (15). Moreover, as
ef , increases as well.
the monitoring cost, m, increases, this equilibrium return for lending, R
30

Note that Rf ∗ is given by (31).

16ef into the optimization conditions (29) and (30), I can obtain the equiBy substituting R
et−1 , and the equilibrium probability of successful
librium amount of R&D investment, Ninnovation, µ̃, as follows: 31
(
)
γ
(
) γ−1
∗
et−1
−γ
−γ N
N
βπ
= (1 + βm) γ−1= (1 + βm) γ−1 t−1 ,θ(1 + γ)AtAtµ
e = (1 + βm)

−1
γ−1

(

βπ
θγ (1 + γ)

1
) γ−1

−1

= (1 + βm) γ−1 µ∗ .

(40)

(41)

I obtain the second equality of (40) from (32) and the second equality of (41) from (33). Ine et , isthe equilibrium with monitoring, the entrepreneur’s proﬁts, Πe e = βπ µ̃At
Π
t

(

γ
1+γ

)
.

(42)

From (41) and (12), in the economy with no moral hazard, the technology gap evolves
according to(
at = µ̃ +1 − µ̃
1+g)
at−1 ≡ H2 (at−1 ),(43)

where at converges in the long run to the following steady state:ã =(1 + g)µ̃∈ (0, 1).
g + µ̃

(44)

The following property establishes those of the steady-state technology gap when ﬁnancial
intermediaries monitor the entrepreneurs.
Proposition 2 The technology gap in an economy with monitoring at−1 converges to thesteady state ã, which is always less than a∗ .
Proof. See Appendix C.
Note that monitoring by ﬁnancial intermediaries can enforce repayment when innovation
is successful, but there remains the moral hazard problem that entrepreneurs may privately
use a part of the funds to obtain a private beneﬁt when their innovation is unsuccessful.

31

Since I assume that βπ < (1 + γ)θγ so that µ∗ ∈ (0, 1) and m > 0, I ensure that µe ∈ [0, 1).

17

Nevertheless, in the equilibrium with monitoring, no moral hazard problems arise. The
following proposition summarizes this argument.32
Proposition 3 The case in which legal protection is not suﬃciently high:If the degree of creditor protection is not suﬃciently high, that is, the hidden cost q is close
to 0, monitoring by ﬁnancial intermediaries removes all moral hazard problems. In the equilibrium with monitoring, entrepreneurs have no incentive to privately use a part of the funds
even if the hidden cost q is not suﬃciently high. The equilibrium in this case is not the sameas that in the economy with no moral hazard problem, because the cost of raising funds in theeconomy with monitoring, R̃f , is higher than that in the economy with no monitoring, Rf ∗ .
Consequently, if the degree of creditor protection is not suﬃciently high, that is, the hidden
cost q is close to 0, the amount of investment, the probability of successful innovation, thedynamics of technology gap, and the steady state of the technology gap in the equilibrium with
monitoring are, respectively,
(
)
γ
(
) γ−1
∗
et−1
−γ
−γ N
N
βπ
γ−1
= (1 + βm)= (1 + βm) γ−1 t−1 ,θ(1 + γ)AtAtµ
e = (1 + βm)

−1
γ−1

(

βπ
γ
θ (1 + γ)(
at = µ̃ +ã =1 − µ̃
1+g

1
) γ−1

−1

= (1 + βm) γ−1 µ∗ ,

(40)

(41)

)
at−1 ≡ H2 (at−1 ),(1 + g)µ̃∈ (0, 1).
g + µ̃

(43)(44)

The following lemma establishes the properties of equilibrium innovation in the economy
with monitoring.
Lemma 1 Properties of the equilibrium innovation in the economy with monitoring:32

In Appendix B, I show that when ﬁnancial intermediaries monitor, the incentive constraint is satisﬁed

for all q. Thus, even if the degree of creditor protection is not suﬃciently high, that is, q is close to 0, nomoral hazard problems arise in the equilibrium with monitoring.

18

ef , increases with the• The cost of raising funds in the equilibrium under monitoring, R
monitoring cost, m; that is,
ef
∂R
> 0.
∂m
et−1 , decreases• The equilibrium amount of investment in innovation with monitoring, Nwith the monitoring cost, m; that is,
et−1
∂N
< 0.
∂m
• The probability of innovation in the equilibrium with monitoring, µ̃, decreases with themonitoring cost, m; that is,
∂ µ̃
< 0.
∂m
Proof. The above properties are obtained by diﬀerentiating (39),(40), and (41) with respect
to m.
The following proposition establishes the properties of the steady-state technology gap
when there is monitoring by ﬁnancial intermediaries.
Proposition 4 The economy with monitoring stagnates if the ﬁnancial intermediaries’ monitoring technology is too low:
∂ã
< 0.
∂m
Proof. By diﬀerentiating (44) with respect to µ̃, I obtain(1 + g)g
∂ã
=
> 0.
∂ µ̃
(g + µ)2
This implies that ã is increasing at µ̃. From the lemma, I obtain
∂ µ̃
< 0.
∂m
19

Thus,∂ã ∂ µ̃
< 0.
∂ µ̃ ∂m

Proposition 4 implies that the lower the cost of ﬁnancial intermediaries’ monitoring, thehigher is the steady-state technology gap level, ã. Lemma 1 explains why monitoring by
ﬁnancial intermediaries promotes innovation when the monitoring cost is suﬃciently low.
ef , is also low. ThisFirst, when the monitoring cost, m, is low, the cost of raising funds, R
e , and the probability of successful innovation, µ̃.
boosts the amount demanded for funds, N
When the probability of successful innovation µ̃ is high, the steady-state technology gap level,ã, becomes correspondingly higher. By the deﬁnition of at ,(11), the high level of ã implies
progress of innovation. Thus, Lemma 1 and Proposition 4 exhibit the eﬀect of monitoringby ﬁnancial intermediaries on innovation and economic growth.33

4

Dynamics

This section investigates the properties of the dynamic system. Consider an economy withﬁnancial intermediaries’ monitoring.
The model economy’s technology gap at−1 evolves according to the dynamic system H2 (at−1 )(43) when the degree of creditor protection q is close to 0 and there is ﬁnancial intermediary
monitoring. This dynamic system is illustrated in Figures 1 and 2.
Note that H2 (at−1 ) is a linear function with slope between 0 and 1 and the vertical intercept
is µ̃. Lemma 1 implies that the lower the monitoring cost, m, the higher is the equilibrium
probability of successful innovation, µ̃. From Proposition 4, when µ̃ increases, the verticalintercept of H2 (at−1 ) rises and the slope of H2 (at−1 ) declines. Consequently, when ﬁnancial
intermediaries face a lower monitoring cost, the system H2 (at−1 ) shifts upward in Figure 1,
and the steady state of the technology gap, ã, becomes correspondingly higher. Thus, when33

The relation between monitoring investment and economic growth is discussed in Levine (2005).

20

Figure 1: An economy with lower ﬁnancial intermediaries’ monitoring costﬁnancial intermediaries face a lower monitoring cost, their monitoring can resolve the moral
hazard problem and promote innovation.
On the other hand, Lemma 1 implies that when the monitoring cost is suﬃciently high,monitoring becomes a heavy burden on ﬁnancial intermediaries, and it does not promote
innovation, although it might resolve the moral hazard problem. From Proposition 4, whenµ̃ becomes lower, the vertical intercept of H2 (at−1 ) declines and the slope of H2 (at−1 ) rises.
Consequently, when ﬁnancial intermediaries face a suﬃciently high monitoring cost, the system H2 (at−1 ) shifts downward in Figure 2, and the steady state of the technology gap, ã,
becomes correspondingly lower. This lower steady state of the technology gap does not stemfrom the credit constraints in the model with no ﬁnancial intermediary monitoring. In thisstudy, it stems from the ﬁnancial intermediaries’ monitoring activities.

5

Welfare Eﬀects of Financial Intermediaries’ Monitoring

In the previous section, I showed that increases in monitoring cost impede innovation andeconomic growth. In this section, I examine the welfare eﬀect of ﬁnancial intermediaries’21Figure 2: An economy with higher ﬁnancial intermediaries’ monitoring costmonitoring.
First, consider the welfare eﬀect on households in the economy with monitoring. Households supply one unit of labor at the wage rate wt , which is used to ﬁnance their consumption.
Since perfect competition prevails in the ﬁnal goods sector, the wage rate wt is equal to themarginal product of labor in producing the ﬁnal good. Thus, in the equilibrium, the wage
rate can be given byα( ) 1−αα.
wt = (1 − α)Zt = δat At , , where δ = (1 − α)χ(9)The wage rate increases as the technology gap at increases. From Proposition 4, any increasein monitoring cost lowers the technology gap at , since it leads to stringency in the ﬁnancial
market and so impedes innovation. Hence, increases in monitoring cost lead to lower wage
rates and thus worsen the welfare of households.
In each intermediate goods sector, only one entrepreneur can raise funds from ﬁnancial
intermediaries and invest for innovation. Moreover, the proportion of the sectors where
innovation is successful is µt . Since the successful innovators can earn monopoly proﬁt, πAt ,and the other entrepreneurs earn zero proﬁt, from Equation (6), the proﬁt earned by all the22entrepreneurs in the economy can be shown as

(
) 1


 γ βπ) γ−1 πAt , if no monitoring,θ (1+γ)µt πAt =
(
) 1

1

(1 + mβ)− γ−1 γ βπ
) γ−1 πAt , if monitoring.
θ (1+γ)Note that µt = µ∗ =(βπθγ (1+γ)

1
) γ−1

(45)

in an economy without monitoring and µt = µ̃ = (1 +mβ)− γ−1 µ∗ in an economy with monitoring, from Equations (33) and (41). From (45), it is1

obvious that increases in monitoring cost lower the entrepreneurs’ proﬁt. As the eﬀect ofﬁnancial intermediaries’ monitoring on the welfare of households, any increase in monitoring
cost leads to stringency in the ﬁnancial market and worsens the welfare of entrepreneurs.
In summary, although ﬁnancial intermediaries pay a monitoring cost in each period, both
the goods market and the ﬁnancial market take on the burden of monitoring costs and thenany increase in monitoring cost worsens the welfare of households as well as entrepreneurs.34

6

Conclusion

This study developed a Schumpeterian growth model with ﬁnancial intermediaries who monitor the behavior of entrepreneurs in an economy with asymmetric information between ﬁnancial intermediaries and entrepreneurs. The main ﬁndings of my model are as follows: (1)ﬁnancial intermediaries do not need to monitor borrowers if the legal protection of creditors
measured by the amount of hidden cost is high; (2) monitoring by ﬁnancial intermediaries
removes the moral hazard problem but impedes innovation and economic growth if the monitoring cost is too high; (3) a high monitoring cost worsens the welfare of households as wellas entrepreneurs through stringency in the ﬁnancial and goods markets.
Some studies examine the eﬀect of the ﬁnancial system on innovation and economic growth,35
but they do not consider the activities of ﬁnancial intermediaries. The contributions of thisstudy are the introduction of ﬁnancial intermediaries into a simple Schumpeterian growth34
35

Note that ﬁnancial intermediaries live only for two periods and earn zero proﬁts in each period.
I introduced some of these studies in section 1.

23

model and the provision of some implications of the eﬀect of the behavior of ﬁnancial intermediaries on innovation and economic growth. After the recent ﬁnancial crisis, various
governments and institutions, including central banks, discuss the role of ﬁnancial intermediaries and take measures for ﬁnancial intermediaries to boost economic growth. The ﬁndingsof my model will be of some help to these discussions, although I have not included thegovernment or a central bank in my model. This topic is left for future research.

AppendixA

The derivation of Equations (19) and (20)First, balance sheet condition (13) can be rewritten asf
Bt−1 = Dt−1 + Nt−1
− Lft−1 .

(13’)

By substituting (13’) and (15) into (17), I obtainf(1 + r + m)Lft−1 + (1 + r)(Dt−1 + Nt−1
− Lft−1 ) − (1 + r)mLft−1 − Rtd Dt−1 = 0f⇔ mLft−1 + (1 + r)(Dt−1 + Nt−1
) − (1 + r)mLft−1 − Rtd Dt−1 = 0.

Then, I obtain

(

Nf
d
Rt−1
= (1 + r) 1 + t−1
Dt−1

)

(
− rm

Lft−1
Dt−1

)
.

In order to hold 1 + r < Rtd , which is determined by (19), I need
(
)
(
)
f
Lft−1
Nt−1
− rm
>1+r
(1 + r) 1 +
Dt−1
Dt−1
(
⇔ (1 + r)
⇔

f
Nt−1
Dt−1

(

)
> rm

Lf
1+r
> t−1 .
rm
Dt−1

Thus, I assume rule (20).
24

Lft−1
Dt−1

)

(20)

B

Proof of Proposition 2

Proof. In the case with monitoring, the incentive constraint is()
et−1 ≤ Πe e.
et−1 + β µ̂t πAt − R
ef N
β (1 − µ̂t ) q Nt(46)

The right-hand side of (46) is equal to Equation (42), which is the entrepreneurs’ expected
proﬁts in equilibrium with the moral hazard problem when they use all the funds for investment under monitoring. The left-hand side of (46) is the entrepreneurs’ expected proﬁts
when they do not use all the funds for investment in period t-1. The ﬁrst term of theleft-hand side of (46) implies the entrepreneurs’ expected beneﬁt when their innovation is
unsuccessful in period t, whereas the second term implies the entrepreneurs’ expected beneﬁtwhen their innovation is successful and they earn monopolistic proﬁts, repaying the ﬁnancial
intermediaries in period t.36 Equation (46) can be rewritten as()
1
βq 1 − (1 − q) γ µ̃(
) ≤ γ(1 + mβ).
1γ1 − (1 − q)(47)

The left-hand side of (47) is less than 1 since q ∈ (0, 1), γ > 1, and µ̃ < 1. The right-handside of (47) is larger than 1 since γ > 1 and mβ > 1. Thus, I obtain)(1
βq 1 − (1 − q) γ µ̃(
) < 1 < γ(1 + mβ).
1γ1 − (1 − q)
Hence, in the equilibrium with monitoring, incentive constraint (47) is satisﬁed for all q.

36et−1 implies that (1 − µ̂t ) is the probability of unsuccessful
Note that β is a discount factor, (1 − µ̂t ) q N

et−1 is a private beneﬁt, µ̂t is the probability ofinnovation when the amount of investment is N̂t−1 and q N
ef N
et−1 is the cost of
successful innovation when the amount of investment is N̂t−1 , πAt is given by (6), and R
ef is given by (39).
lending, where R

25

C

Proof of the second part of Proposition 3∗

is given by Equation (36).
Proof. ã = (1+g)µ̃
is given by Equation (44) and a∗ = (1+g)µ
g+µ̃
g+µ∗
Subtracting ã from a∗ , I obtain(1 + g)µ∗ (g + µ̃) − (1 + g)µ̃(g + µ∗ )(1 + g)g(µ∗ − µ̃)(1 + g)µ∗ (1 + g)µ̃
−
=
=
> 0.
g + µ∗
g + µ̃
(g + µ∗ )(g + µ̃)(g + µ∗ )(g + µ̃)
The last inequality is obtained by µ∗ > µ̃.

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