Discussion Papers In Economics
And Business

Product Market Competition and Financial
Market Screening
Yuichiro Matsumoto
Discussion Paper 17-14

Graduate School of Economics andOsaka School of International Public Policy (OSIPP)
Osaka University, Toyonaka, Osaka 560-0043, JAPANProduct Market Competition and Financial
Market Screening
Yuichiro Matsumoto
Discussion Paper 17-14

June 2017

Graduate School of Economics andOsaka School of International Public Policy (OSIPP)
Osaka University, Toyonaka, Osaka 560-0043, JAPANProduct Market Competition and Financial
Market Screening∗
Yuichiro Matsumoto†

Abstract
How are the financial market and the product market interrelated? Product market selection affects the default rate and screening incentive of financial intermediaries. In contrast to previous studies, bad screening technology
implies a low interest rate and a low default rate: i.e. intermediaries are successfully repaid more often when the country has a bad screening technology. When a country has an underdeveloped financial market, then the product market is also inefficient. This product market inefficiency means thatthe selection effect of the market is weak. In this case, many entrepreneurs
successfully enter the market. Financially underdeveloped countries sufferfrom low productivity not only for inefficient screening technology but also
for weak product market selection.
Many firms in financially developed countries tend to choose exports,
merely because firms in such countries are more productive. Financiallydeveloped countries have a comparative advantage in a financially dependent
sector.

JEL Classification Codes: E22; E44; F12; O11; O16; O31
Keywords: Financial Development; Default Rate; Firm Heterogeneity; Selection;
International Trade∗†I thank the seminar participants at Osaka University.
Graduate School of Economics, Osaka University: E-mail: u847103e@ecs.osaka-u.ac.jp1

1

Introduction

The condition of the product market affects a project’s profitability and severe
competition increases the default rate. How are the financial market and the product market interrelated? Financial intermediaries decide on the severity at which
they screen a borrower’s ability.1 Intermediaries lend money to entrepreneurs whoneed money to invent new products. When the product market is competitive, theborrower often cannot repay money; i.e., product market conditions determine thedefault rate. Many questions exist related to this market condition. How does financial development affect product market competition? Does weak competition
in a developing country affect the screening decision of intermediaries?
When a country has bad screening technology, it has a low interest rate anda high entry rate, in contrast to the assumption taken by previous studies such as
King and Levine (1993), Laeven et al. (2015), and Sunaga (2016). A country’s
bad screening technology weakens its product market selection. Weak selection
produces a low default rate. Why is this result different from that of previous
studies? Previous studies considered the case in which screening efforts directly
affect the default rate; this study considers the case in which screening efforts
indirectly affect the default rate by increasing the entrant’s expected productivity.
Good screening technology increases an entrepreneur’s productivity, but this alsomeans that the productivity of their rival is also increasing. In this sense, thisresult indicates a general equilibrium effect.
This result has two implications for economic development. First, an uncompetitive product market is a byproduct of a weak financial market. When a country
has bad screening technology, not only this technology itself but also weak product market competition reduces entrants productivity. For example, India suffersfrom too many small enterprises (Nageswaran and Natarajan (2016)). This uncompetitive product market can result from an underdeveloped financial market.
Second, the default risk is not a good indicator for inefficiency despite the common view. Financial underdevelopment weakens product market competition andfacilitates product market entry.
Interactions between product market selection and financial markets also affect firms export decisions. Firms in financially developed countries are produc1

In this paper, intermediaries screen an entrepreneur’s ability before lending. This type ofscreening is called ex ante screening. See also Aghion and Howitt (2009), who classified thefinancial screening model into an ex ante or ex post screening model. In contrast to ex ante screening, ex post screening is done after lending and intends to prevent the borrower from engaging inopportunistic behavior.

2

tive because of efficient screening of financial markets and a competitive productmarket. Because firms in such countries are productive, they tend to export, andmany exporters exist in financially developed countries.2
Somewhat unexpectedly, intermediaries screening decisions do not dependon product market conditions except for the funds required for lending. Productmarket competition only affects the interest rate, which is high when the productmarket is competitive because the default rate is high.

1.1 Literature
Intermediaries affect economic development by selecting able entrepreneurs. Thiseconomic development mechanism is explained by King and Levine (1993) and
Laeven et al. (2015), and Sunaga (2016). However, these studies do not consider
how product market competition affects financial markets. In their model, screening determines the default rate. It is natural to consider that the default rate is not
only determined by financial market efficiency but also depends on the productmarket. In the previous studies mentioned, this channel is omitted. I use the Melitz(2003) type of heterogeneous firm model to construct a model with this property.
The Melitz (2003) model has the following specification. Entrepreneurs pay fixed
costs to invent a new product before productivity is revealed. Entrepreneurs must
pay an additional fixed cost after productivity is revealed when they establish afirm to enter the product market. Otherwise, they do not enter the product market―there is product market selection. The default rate is not only determined byscreening efficiency but also by the severity of the product market selection.
The heterogeneous firm model is used to analyze many problems: Helpman
et al. (2004), Nocke and Yeaple (2007), and Nocke and Yeaple (2008) for analyzing FDI; Baldwin and Okubo (2006) for analyzing economic geography; Baldwin
and Robert-Nicoud (2008) and Naito (2016) for analyzing economic growth ; andEgger and Kreickemeier (2009) and Helpman et al. (2010) for analyzing the relationship between trade liberalization and wage inequality.3
Many papers empirically examined the heterogeneous firm model. Roberts
and Tybout (1997) showed that the fixed cost to engage in exports is substantial.
This fixed cost has a significant role for the heterogeneous firm model because it
2

Manova (2013) showed that the liquidity constraint of the exporter is important to explain therelationship between financial development and trade; however, this concept is out of the scope of
this paper.
3
See also Baldwin (2005) and Baldwin and Forslid (2010).

3affects product market selection. Pavcnik (2002) showed that resources are reallocated from less to more productive producers after trade liberalization. Eaton
et al. (2011) showed that productivity is positively correlated with a firm’s export
decision, which is consistent with the prediction of the heterogeneous firm model4
Previous studies have confirmed that product market selection changes theproperty of the model; for example, Chaney (2008) used the heterogeneous firmmodel to analyze the gravity equation and obtained results that differed from thoseof the Krugman model. The results of this paper also depend on the existence ofadditional fixed costs and the entry decision: product differentiability does notaffect equilibrium screening efforts only if there is product market selection; trade
costs affect interest rates only if there is product market selection; and high fixed
costs decrease the productivity of entrants only if there is product market selection.
Many papers also examined the relationship between financial markets andproduct markets. Manova (2013) and Chaney (2016) analyzed how financial markets affect export decisions. If the financial institution in a country is functioning
well, firms in a financially vulnerable sector in this country export more than firms
in other countries. Benabou (1996), Benabou (2002), Buera and Shin (2013),
Banerjee and Moll (2010) and Moll (2014) explained how the distribution of productivity is determined in a borrowing constrained economy.

1.2 Contents
Section 2 describes the basic structure of the model. Section 3 describes the properties of the model without product market selection. Although the case withproduct market selection is more realistic, it is useful to examine the case without
product market selection: without analyzing this case, how product market selection affects the outcome is unknown. Section 4 analyzes the case with productmarket selection, and the determination of the screening effort and the interest rateis shown. Although the product market determines the default rate, the screening
effort is not related to the condition of this market. As previously mentioned, bad
screening technology means low interest rates. This effect exists only if countries trade goods internationally and are asymmetric. When countries do not trade
goods, screening technology does not affect the default rate.

4

See also Tybout (2003), Redding (2011) and Bernard et al. (2012).

4

2

Model

There are two countries and Lj units of homogeneous households in countryj ∈ {1, 2}. Each household inelastically supplies one unit of labor and obtains
wage income. According to Helpman and Krugman (1985), sector A is homogeneous goods sector: goods in this sector can be traded without trade costs andmarginal productivity is one regardless of country. Sector M is a monopolisticcompetitive market, and a monopolistic competitive firm produces goods differentiated as variety v.
Households in country j maximize utility Uj :maximize Uj = (1 − β) log Y0 + β log Yij∑∫
subject to
pj (v)yj (v) = Ij
i=1,2

∫

v∈Ωij
ρ−1

ρ

yj (v) ρ ) ρ−1 = Yj(
Ωjpij (v) is the price of variety v goods produced by country i and that are sold tocountry j. yij (v) is the quantity of goods produced by country i and sold to households in country j. Yj is a sectoral aggregate of differentiated goods in country j
consumed by households. ρ is the elasticity of substitution across differentiatedgoods. Ωij is the set of variety v goods produced by country i and sold to country
j. Ij is the income of country j. From the first-order conditions, demand functionof goods yij (v) is obtained:yj (v) =pj (v)−ρ
βIj
Pj 1−ρ(1)∫1
Pj (v) ≡ ( Ωj pj (v)1−ρ ) 1−ρ is the price index in country j. Additionally, goodsin all sectors are assumed to be produced in all country. Wage rate in country jequals 1 when good A is taken as numeraire. In this case, Ij equals Lj .

2.1

Firm’s production decision

Variety v produced in country i and sold to country j has the following production
function:yij (v) = ψ(v)lij (v)5ψ(v) is labor productivity, and lij (v) is labor input. Firms maximize the operating
profit πij (v) of market j:
maximize πij (v) = pij (v)yij (v) − (1 + τij )lij (v)subject to yij (v) = ψ(v)lij (v)yij (v) =pij (v)−ρ
βLj
Pij1−ρ

(2)
(3)
(1)

τij indicates iceberg trade costs. If firms sell goods to foreign markets, theymust pay costs proportional to the value of the goods: τij > 0 if i ̸= j and τii = 0.
From the first-order condition of this problem, I obtain an equilibrium markup:
pij (v) =ρ 1 + τij
ρ − 1 ψ(v)Combining this equation with (3), I obtain the equilibrium operating profit:
ψ(v) ρ−1
πij (ψ(v)) = Aj ()
1 + τij

(4)

L

ρ 1−ρ
j
) P 1−ρ
Aj ≡ ρ1 ( ρ−1is the demand for goods in country j. Equation (4) implies
ij

that operating profit elasticity to productivity is ρ − 1. Operating profit is more
responsive to productivity when goods are more differentiated.

2.2

Firms’entry decisionFirms in country i must invest Fid units of fixed beachhead costs to enter thedomestic market and Fix units of fixed beachhead costs to enter the foreign market. These fixed costs have interpretations. According to Blanchard and Giavazzi(2003) one can interpret these fixed costs to enter the market as a proxy for market
regulations. Alternatively, according to Lee and Mukoyama (2012) these costs canbe viewed as the cost to build a plant. The net profits from entering each market
can be written as follows:
πid (ψ(v)) = max{πii (ψ(v)) − Fid , 0}
πix (ψ(v)) = max{πij (ψ(v)) − Fix , 0}6i ̸= j(5)

i ∈ {1, 2} is the home country of the firm producing variety v, and j is thefirms’foreign country. Combining these equations with equation (4), entry cutoffs ψid and ψix are defined:
Fid = πd (ψid ) = Ai (ψid )ρ−1
ψix ρ−1
Fix = πx (ψix ) = Aj ()
1 + τij(6)

As depicted in Figure 1, firms with productivity ψ enter the domestic market if
and only if ψ ≥ ψid , and firms enter the foreign market if and only if ψ ≥ ψix . As
depicted in Figure 2, a low Ai can be interpreted as strong market selection: if Ai
is decreasing, less productive firms do not enter the market.
πit (ψ)∑dx
j πij (ψ) − Fi − Fi

πii (ψ) − Fid

0
ψid

ρ−1

ψix ρ−1ψ ρ−1Figure 1: Productivity and entry decision.
The high demand factor Aj weakens market selection. Weak market selection
reduces the productivity of entrants. As is shown in section 4, demand Ai is highif country i has bad technology.
7πii (ψ) = Ai ψ ρ−1 − Fid

0
ψid

ρ−1

ψ ρ−1

Figure 2: Demand of domestic market and productivity of entrants.
Firms’total net profit πit (ψ) can be written as follows:πit (ψ) ≡ πid (ψ) + πix (ψ)(7)

If the total net profit is not positive, firms do not enter the product market.

2.3

Financial intermediaries

Entrepreneurs need to pay Fir units of money to produce a new variety. Similar
to beachhead costs, this fixed cost has many interpretations: Lee and Mukoyama(2012) and Arkolakis et al. (2008) interpreted this fixed cost as R&D cost. To pay
this cost, an entrepreneur must borrow from a financial intermediary. Althoughanother interpretation is possible, this interpretation is followed for clarity.
The potential productivity of an entrepreneur in country i is follows a Pareto
distribution:ψ(8)
Gi (ψ) = 1 − ( min )−kψi
The slope parameter satisfies k > (ρ − 1). After paying the screening costS ≡ θ(ψif )γ , both the financial intermediary and the entrepreneur know whether
8or not the entrepreneur’s productivity is higher than ψif ; before screening, even
if the entrepreneur does not know the productivity. Intuitively, the entrepreneur
may know the properties of the goods she wants to produce but does not know
their profitability. Previous studies made this assumption. In Laeven et al. (2015)
and Sunaga (2016), the entrepreneur is heterogeneous only on the probability ofsuccess, in contrast to this study. Helpman et al. (2010) worked with screening
technology similar to that of this study.
The intermediary and the entrepreneur randomly match each other. After
matching, the intermediary decides on whether or not to screen the entrepreneur.
If the intermediary decides not to screen the matched entrepreneur, the match is
dissolved. If the intermediary decides to screen, it offers financial contract R̂(ψ)
conditional on ψ before screening. The financial contract must satisfy the limited
liability constraint. That is, the entrepreneur cannot pledge a repayment higher
than the net profit: R̂(ψ) ≤ πit (ψ) for all ψ. Because the payoff from this contract
is nonnegative, the entrepreneur always accepts any offer that satisfies limited liability. To maximize their profits, intermediaries offer the contract R̂(ψ) = πi (ψ).
After screening, they know whether or not the productivity of the entrepreneur ishigher than ψif . The conditional distribution of productivity—productivity ψ ishigher than ψif —is also distributed according to a Pareto distribution:5G(ψ|ψ ≥ ψif ) = 1 − (

ψ
ψif

)−k

(9)

If the entrepreneur passes the screening test, the intermediary lends Fir unitsof money; otherwise, the match is dissolved. Otherwise, he lends money to theentrepreneur. After investing Fir units of money, the profitability of the invention
is revealed.
The expected profit of the intermediary before screening Πfi can be written as
follows:
Πfi (ψif ) = (E[πit (ψ)|ψ ≥ ψif ] − Fir )Prob(ψ ≥ ψif ) − Si(10)(E[πit (ψ)|ψ ≥ ψif ] − Fir ) is the gross return from lending after knowing thatthe productivity is higher than ψif . Prob(ψ ≥ ψif ) is the probability that theentrepreneur is more productive than ψif .
5

In general, the conditional probability of a Pareto distribution has the following property:
Prob[ψ ≥ b|ψ ≥ a] = ( ab )−k for all a ≤ b.

9

It is useful to consider the screening costs per lending contract S̃i :S̃i ≡S
Prob(ψ ≥ ψif )(11)= θi (ψimin )−k (ψif )γ+k
Using (11), (10) can be rewritten:
Πfi (ψif ) = (E[πit (ψ) − Fir |ψ ≥ ψif ] − S̃i )Prob(ψ ≥ ψif )(12)Intermediaries’profits Πi are determined in equilibrium. If Πfi is positive,
more contracts emerge and more entrepreneurs enter the market, which reduces
the price index Pi , the profits of firms πit (ψ), and the profits of the intermediaryΠfi . If Πfi is negative, the financial intermediary does not screen the entrepreneur
and does not lent. It increases Pi , πit (ψ) and Πfi . Hence, Πfi must be zero inequilibrium:
E[πit (ψ) − Fir |ψ ≥ ψif ] − S̃i = 0
(13)
∂Πf

The first-order condition of intermediary ∂ψfi can be calculated as follows:
i

∂Πfi
∂ψif

= {E[πit (ψ) − Fir |ψ ≥ ψif ] − S̃i }+ Prob(ψ ≥ ψi )

∂
∂ψif

∂
∂ψif

Prob(ψ ≥ ψif ){E[πit (ψ) − Fir |ψ ≥ ψif ] − S̃i }=0
Using the zero profit condition (13), this equation can be rewritten to a moreconvenient form:
ϵE[πit (ψ)|ψ ≥ ψif ] = (γ + k)S̃i∂ log E[π t (ψ)|ψ≥ψ f ]iiis the repayment elasticity. Substituting this equation for theϵ≡∂ log ψifzero profit condition (13), the following equation is obtained:(γ+k− 1)S̃i = Firϵ(14)

As is described in the following sections, ϵ changes according to whether or
not product market selection exists—product market selection changes the decision of the intermediary.
10

The interest rate Ri is defined as the expected return from a successful entrepreneur:E[πit (ψ)|ψ ≥ ψid ]
Ri =
(15)
Fir
From this equation and the zero profit condition, the following equation is
obtained:
Ri Prob(ψ ≥ ψid |ψ ≥ ψif ) = Fir + Si
Ri is high when the intermediaries screen the entrepreneur more intensively ormarket selection is strong. Prob(ψ ≥ ψid |ψ ≥ ψif ) indicates the entry rate.
1 − Prob(ψ ≥ ψid |ψ ≥ ψif ) can be viewed as the default rate.

3

Product Market without Selection

In this section, the case without product market selection is addressed: Fid =Fix = 0 and ψif = ψid = ψix . All firms enter the market. Hence, the expected total
operating profit can be calculated using (4):E[πif (ψ)|ψ ≥ ψif ] =∑Ajk(ψ f )ρs −1
k − (ρ − 1) j (1 + τij )ρ−1 i(16)This equation implies the elasticity of repayment ϵ is ρ − 1. The equilibrium
screening efforts is obtained using (11) and (14):1S̃i = k+γ
Fir
−1
ρ−1

(17)

Proposition 1. a) Product differentiation—high ρ—is positively correlated withscreening efforts:
∂ψi
>0
∂ρ

∂Si
>0
∂ρ

∂ S̃i
>0
∂ρ

b) R&D cost is positively correlated with screening efforts:
∂ψi
>0
∂Fir

∂Si
>0
∂Fir

11

∂ S̃i
>0
∂Fir

c) Screening inefficiency implies a less productive entrant and higher individual
screening cost Si . However, total screening cost per lending S̃i is not changed:
∂ψi
∂Si
<0
>0
∂θi
∂θi
d) Screening effort is not related to trade cost:
∂Si
∂ S̃i
∂ψif
=
=
∂τjk ∂τij ∂τij

∂ S̃i
=0
∂θi

i, j, k ∈ {1, 2}

When the product market is highly differentiated, intermediaries screen more
intensively because the expected profit is more sensitive to screening efforts inthese sectors. Although this result is intuitive, it is not obtained if there is product market selection: see section 4. When R&D costs are high, intermediaries
should lend more money. They screen the entrepreneur more intensively. Anotherinterpretation of this result is the quality-quantity substitution—if the cost of producing one variety of goods is high, it is profitable to produce the variety withhigher quality rather than producing greater variety. These relationships remain
valid even with product market selection described in the following section. But
ψif cannot be interpreted as the productivity of entrants in the case of the following
section. When the screening technology is inefficient, the intermediary must pay
a higher screening cost and endure a less efficient borrower. However, the total
screening cost to produce one variety S̃i is not changed because it must adjust
to satisfy the zero profit condition. Many variables are not related to screening
efforts: the equilibrium screening efforts depends only on limited variables. This
result remains valid even when considering product market selection, as describedin the following section.
The interest rate (15) depends only on product differentiation from the zeroprofit condition (13) and equilibrium screening (17):Ri = 1 + (
=1+(

S̃i
)
Fir
1
)
k+γ
−1
ρ−1

(18)

Proposition 2. a) The interest rate is positively correlated with product differentiation:
∂Ri
>0
∂ρ
12

b) The interest rate is not relate to R&D costs, screening inefficiency, and trade
costs:
∂Ri
∂Ri
∂Ri
∂Ri
=
=
=
=0
r
∂Fi
∂θi
∂τij
∂τji

i ̸= jA highly differentiated market implies that the intermediary screens the entrepreneur more intensively. To compensate for this screening cost, additional
money must be repaid, which increases the interest rate . Other variables do notaffect the interest rate: for example, the interest rate of an efficient country is notdifferent from that of an inefficient country. This insensitivity result does not holdwhen there is product market selection(see section 4).
The effect of financial development to welfare is derived. Demand Ai is used
as a measure of welfare: Ai is positively correlated with the price index Pi and a
low Ai indicates a high level of welfare. From (11), (17), and (13), I obtain thefollowing equation:∑

Aj ϕij (ψif )ρ−1 =j1r
ρ−1 Fi1 − k+γ

ϕij ≡ (1 + τij )1−ρ indicates market openness: it is low when trade costs are high.
This equation can be rewritten into a more convenient form using (11) and (17):

ρ−1

ρ−1

A1 + ϕ12 A2 = F̃1r

(19)

ϕ21 A1 + A2 = F̃2r

(20)
ρ−1

− 1} k+γ −1 θiγ+k (ψimin )− γ+k (ρ−1) (Fir )1− γ+k means R&D inefficiency.
F̃ir ≡ { k+γρ−1F̃ir is high if the screening technology is inefficient and R&D costs are high. Theseequations can be solved diagrammatically—see Figure 3 and 4.
Previous studies, including Venables (1987), Melitz and Ottaviano (2008), and
Demidova (2008), obtained similar results. Even if financial market screening exists, these results remain valid. If one country becomes more efficient, the welfareof the other country is decreasing. This result is reminiscent of the home market
effect: aggregate demand externality deprives a less efficient market of firms. If
one country becomes more efficient, the welfare of this country is increasing as is
expected.
The more liberalized country endures lower welfare. Firms in a country witha low trade barrier are at a disadvantage: they need to pay higher trade costs thanfirms in a country with a high trade barrier. Fewer firms enter the market in a
k

13

A2
F̃1r
ϕ12

F̃2r

0

F̃1r

F̃2r
ϕ21

A1

Figure 3: Technological improvement in the home country increases welfare in
the home country, and decreases welfare in the foreign country.

14

A2

F̃1r
ϕ12

F̃2r

0

F̃1r

F̃2r
ϕ21

A1

Figure 4: Unilateral trade liberalization of the home country decreases the welfareof the home country, and increases the welfare of the foreign country.

15

country with a low trade barrier, leading to a high price index of a country with a
low trade barrier.
Equations (19) and (20) can also be solved using algebra:
Ai =F̃ir − ϕij F̃jr
1 − ϕij ϕjii ̸= j(21)

Openness is assumed to be sufficiently low to ensure a positive price index:
i.e. F̃ir − ϕij F̃jr > 0. Using (21), the following result is obtained:
Proposition 3. a) If inefficiency in country 1 is increasing, demand A1 of thiscountry is increasing; however, that of the other country A2 is decreasing.
∂A1

∂A1

∂ F̃1

∂ F̃2r>0>rb) Unilateral trade liberalization of a country hurts this country, and benefits theforeign country:
∂A1
∂A1
>0>
∂ϕ21
∂ϕ12
c) Suppose that ϕ = ϕ12 = ϕ21 . Bilateral trade liberalization increases the welfare of both countries.
∂A1
<0
∂ϕ
∂A1

∂A1
> 0 from (21).
∂ϕ21
F̃1r
∂ F̃2
The differentiation of A1 with respect to ϕ12 can be described as follows:

Proof. It is straightforward to show

>0>

∂A2

and
r

∂A1
ϕ21 F̃1r − F̃2r=
<0
∂ϕ12 (1 − ϕ12 ϕ21 )2
Inequality is derived from F̃2r − ϕ21 F̃1r > 0.
The effect of bilateral liberalization can be obtained as follows:∂A1 2ϕF̃1r − (1 + ϕ2 )F̃2r=∂ϕ(1 − ϕ2 )2∂A1
ϕ + ϕ−1F̃ ris positive if and only if F̃1r <. However, this inequality is incom2∂ϕ2
patible with F̃ir − ϕij F̃jr > 0.
16

4

Product Market with Selection

In this section, the following assumption is taken as in the standard heterogeneous
firm model:
Assumption 1. a) Some potential firms do not enter the market and some domestic
firms do not export:i, j, k ∈ {1, 2}

ψif < ψjd < ψkx

The expected repayment can be written as a function of the entry rate Prob(ψ ≥ψ |ψ ≥ ψ f ) because π d (ψ) is zero if ψ is lower than ψid :d

E[πit (ψ)|ψ ≥ ψif ] = E[(πid (ψ) + πix (ψ) − F r )|ψ ≥ ψid ]Prob(ψ ≥ ψ d |ψ ≥ ψ f )Repayment elasticity ϵ is k in this case. (14) and ϵ = k imply the following
equation:kS̃i = Fir
(22)γThis equation is similar to but slightly different from (17): this equation does
not include ρ—screening efforts do not depend on product differentiation. Using
this equation, the following results were obtained:
Proposition 4. a) Product differentiation is not related to screening efforts:
∂ψif
∂Si
∂ S̃i
=
=
=0
∂ρ
∂ρ
∂ρ

(23)

b) R&D cost is positively correlated with screening efforts:
∂ψif
>0
∂Fir

∂Si
>0
∂Fir

∂ S̃i
>0
∂Fir

c) Screening inefficiency implies a lower screening threshold and a higher individual screening cost Si . However, screening cost per lending S̃i is not changed:
∂ψif
<0
∂θi

∂Si
>0
∂θi

∂ S̃i
=0
∂θi

d) Screening effort is not relate to physical capital cost and trade cost:
∂ψif
∂ψif
∂ψif
=
=0
=
∂Fjd ∂Fjx ∂τjk
17

i, j, k ∈ {1, 2}

Product differentiation does not affect screening efforts, in contrast to the previous section. Screening efforts do not change the total net profit π t but onlychange the probability of entry. This produces an insensitivity to the elasticity
of substitution. Except for ρ, the implication of this proposition is same as theprevious section: only the amount of money that the intermediary must lend Fir
affects screening efforts. It is unexpected that the product market condition does
not affect the screening decision. Product market regulation, as represented by ahigh Fid , does not affect the screening decision even if it affects entry severity. Additionally, other variables representing the product market condition do not affectscreening.6
The interest rate and the entry rate are analyzed. The interest rate is intimately
related to the entry rate. The following equation can be obtained from (13), (15),and (22):k(24)
Ri Prob(ψ ≥ ψid |ψ ≥ ψif ) = (1 + )γThis equation implies that the interest rate and the entry rate move in opposite
directions. If the entry rate is low, intermediaries offer a high interest rate. Before
analyzing interest rate, the expected operating profit is calculated using (6):kAi (ψid )−k − F dk − (ρ − 1)
Fid
=
k
−1
ρ−1
E[πix (ψ)|ψ ≥ ψid ] = E[π x (ψ)|ψ ≥ ψ x ]Prob(ψ ≥ ψix |ψ ≥ ψid )E[πid (ψ)|ψ ≥ ψid ] =

=

6

Fix
ψx
( id )−k
ψi
k
−1
ρ−1

This result does not depend on the special functional form in this paper. For instance, consider∂ log Prob(ψ≥ψid |ψ≥ψif ).
∂ log ψifi
ϵp (ψif )From the zero profit condition and first-order condition, the following is obtained: S̃ ϵ (ψf ) F .
s
i
log S
the following non constant elasticity case: ϵ(ψif ) ≡ ∂∂log
and ϵp (ψif ) ≡ψfWhen this equation has a unique solution, equilibrium screening does not depend on the productmarket condition.

18

Substituting these equations for (15), I obtain the interest rate:
E[πit (ψ)|ψ ≥ ψid ]
Fir
x
1
1
d
x ψi −k
=
{F
+
F
(
) }
i
Fir i
ψid
k
−1
ρ−1

Ri =

i=
̸ j

(25)

This equation is slightly cumbersome. I analyze the symmetric country case before analyzing the general asymmetric case.

4.1

Symmetric country

When two countries is symmetric, the export entry rate Prob(ψ ≥ ψ x |ψ ≥ ψ d )takes the following simple form from (6):Prob(ψ ≥ ψix |ψ ≥ ψid ) = (xkψ x −k
−k F
)
=
(1
+
τ
)
(
)− ρ−1dd
ψF

Substituting this equation for (25), I can rewrite the equilibrium interest rate:
R=

1
k
−1
ρ−1

x
1
k
d
x
−k F
{F
+
F
(1
+
τ
)
(
)− ρ−1 }rdFFCombining this equation with (24), I obtain the following proposition:
Proposition 5. a) The interest rate is negatively correlated to trade costs τ and
F x:
∂
∂R
<0<
Prob(ψ ≥ ψ d |ψ ≥ ψ f )
∂τ
∂τ
∂R
∂
<0<
Prob(ψ ≥ ψ d |ψ ≥ ψ f )
x
x
∂F
∂F
b) The interest rate is negatively correlated to the R&D cost:∂R∂<0<
Prob(ψ ≥ ψ d |ψ ≥ ψ f )
r
∂F
∂F r

19

c) The interest rate is positively correlated to the domestic entry cost:
∂
∂R
>
0
>
Prob(ψ ≥ ψ d |ψ ≥ ψ f )
∂F d
∂F d
d) The interest rate is not related to screening inefficiency:∂R∂=
Prob(ψ ≥ ψ d |ψ ≥ ψ f ) = 0∂θ∂θThe entry rate’s movement is similar to standard Melitz model. High trade
costs and high R&D costs lead product market less competitive. A less competitive market implies a high entry rate. If the domestic entry cost is increasing, entry
becomes difficult.
Screening inefficiency does not affect the interest rate. Although inefficient
screening technology reduces the entry rate by reducing the entrepreneur’s productivity, it also increases the entry rate by weakening product market competition. In the symmetric country case, these two forces cancel out each other. As issubsequently shown, screening technology affects product market selection whencountries are asymmetric.
I analyze the productivity of entrant ψ d :Proposition 6. a) For x = F d , F x , τ , the productivity of the entrant is increasing
if and only if the entry rate is decreasing:∂Prob(ψ ≥ ψ d |ψ ≥ ψ f )∂ψ d> 0 ⇐⇒<0∂x∂xb) The productivity of the entrant is decreasing if R&D cost is increasing:
∂ψ d
<0
∂F r

(26)

(27)

f

Proof. Part a is evident from ∂ψ= 0. From (11), (22), (25) and (24), I obtain∂xthese equations:∂ log ψ f=1
∂ log F r
∂ log R
∂ log ψ d
∂ log ψ f
−1=
= ks (−)∂ log F r
∂ log F r ∂ log F r(ks + γ)

d

log ψ
1
= γ+k
− k1 < 0
From these equations, I obtain ∂∂ log
Fr

Although the intermediary screens more severely when R&D costs are high,the productivity of the entrant is decreasing. The screening effect is weaker thanthe product market selection.
20

4.2

Asymmetric Country

Using the entry cutoff (6), the export cutoff can be written as a function of thedomestic cutoff:
1
Fix ρ−1
ψix
=
(1
+
τ
)(
)
(28)
ij
ψjd
Fjd
I eliminate the export cutoff from (25) using this equation:
Ri =

1
k
−1
ρs − 1

ψjd −k
1
k
d ρ−1
d
)
+
ϕ̂
(F
{F
(
) }
ij
j
Fir i
ψid

i ̸= j(29)kϕ̂ij ≡ (1 + τij )−k (Fix )1− ρ−1 indicates the openness of country j as in section 3.
Combining this equation with (24), I obtain the following equation:k

F1d (ψ1d )−k + ϕ̂12 (F2d ) ρ−1 (ψ2d )−k = F̂1r
ϕ̂21 (F1d )
k

k
ρ−1

(ψ1d )−k + F2d (ψ2d )−k = F̂2r

(30)
(31)

k
F̂ir ≡ θiγ+k ( ρ−1− 1)( γk )− γ+k (Fir )1− ρ−1 indicates R&D inefficiency: F̂ir is high if
R&D cost is high and screening inefficiency is high. When openness is assumed tobe sufficiently low, the slope of equation (30) is steeper than that of equation (31).
This restriction ensures a diagrammatic analysis. The technological improvementof the home country—i.e. F̂1r is decreasing—decreases the productivity of domestic entrants ψ1d and increases the productivity of foreign entrants ψ2d as depicted in
Figure 5. The unilateral trade liberalization of the home country increases the productivity of domestic entrants ψ1d and decreases productivity of foreign entrants ψ1
as depicted in Figure 6.
The solution to equations (30) and (31) has the following form:kkF̂1r − ϕ̂12 (F2d ) ρ−1 −1 F̂2r
k

(ψ1d )−k =F1d − ϕ̂12 ϕ̂21 (F1d ) ρ−1 (F2d ) ρ−1 −1
k

k

(32)

Openness is assumed to be sufficiently low:7

7This assumption is slightly different from the assumption used for Figure 5 and 6. This paper
primarily works with algebraic solutions. The diagrams are used only for pedagogical purposes.

21

(ψ2d )−k
F̂1r
ϕ12

F̃2r

0

F̂1r

F̃2r
ϕ21

k
ˆ F d ρ−1phi
12 2

(ψ1d )−kFigure 5: Technological improvement and cutoff22

(ψ2d )−k

F̂1r
ϕ12

F̃2r

0

F̂1r

F̃2r
ϕ21

k
ˆ F d ρ−1phi
12 2

(ψ1d )−kFigure 6: Unilateral trade liberalization and cutoff.

23

Assumption 2.
kkϕ̂ij (Fjd ) ρ−1 −1ρ−11>F̂ir > ϕij (Fjd ) ρ−1 −1 F̂jrki ̸= jUsing (32), the following proposition is obtained:
Proposition 7. a) R&D inefficiency in the home country is negatively correlatedwith domestic cutoff and is positively correlated with export cutoff. R&D inefficiency in the foreign country has the opposite effect from that of the domestic andthe export cutoffs:
∂ψ1d

∂ψ1d

∂ F̂1
∂ψ1x

∂ F̂2r∂ψ1x<0<
r∂ F̂1r>0>∂ F̂2rb) The domestic entry cost of each country is positively correlated with the domestic cutoff of each country. The domestic entry cost of the home country is
positively correlated with the export cutoff of the home country; the domestic entry cost of the foreign country is negatively correlated with the export cutoff of thehome country:
∂ψ1d
>0
∂F1d
∂ψ1d
>0
∂F2d
∂ψ1x
<0
∂F1d
∂ψ1x
<0
∂F2d
c) The openness of the home country is negatively correlated with the domestic
cutoff. The openness of the foreign country has an opposite effect from that ofdomestic cutoff:
∂ψ1d
∂ψ1d
<0<
∂ ϕ̂21∂ ϕ̂1224

Proof. See appendix.
The welfare implication of technical change and trade liberalization is similar
to that of the previous section:
Corollary 1. a) R&D inefficiency and high domestic entry cost decrease the welfare of this country and increase the welfare of the foreign country:
∂A1

>0>
r

∂A1

∂ F̂1
∂ F̂2r
∂A1
∂A1
>0>
d
∂F1
∂F2d
b) A country’s unilateral trade liberalization decreases the welfare of this country
and increases the welfare of the foreign country:∂A1∂ ϕ̂21>0>∂A1∂ ϕ̂12

Proof. For x = F̂jr , ϕ̂jk , the log differentiation of Fid = Ai (ψid )ρ−1 implies thatAi and ψid move in the opposite direction:∂ log Ai
∂ log ψid
= (1 − ρ)∂x∂x
ψx

For Fjd , the log differentiation of Fix = Aj ( 1+τi ij )ρ−1 implies that Ai and ψjx movein the opposite direction:∂ log Ai
∂ log ψix
=
(1
−
ρ
)
s
∂Fjd
∂Fjd
Combining these two equations with proposition 7 shows that the above proposition is correct.
Inefficient technology in the home country implies low welfare in this country.
Inefficient technology in the foreign country implies high welfare in the homecountry: inefficient technology in the foreign country allows the home country to
specialize in differentiated sectors. Firms in a country with high openness must
pay high trade costs. In this country, fewer firms enter the market.
25

Using corollary 1, the results of proposition 7 can be interpreted as follows.
The productivity of entrant ψ1d is low if openness ϕ̂21 is high: selection is weakin a highly open market. The R&D inefficiency of the home country increases
its demand. The home country’s high demand reduces the productivity of the entrants as depicted in Figure 2. The R&D inefficiency of the foreign country has the
opposite effect and domestic entry cost has a more nuanced effect. If the domestic entry cost of the home country increases, it indirectly weakens the selection
since it increases the demand of the home country but it directly strengthens theselection because entry is more costly. Moreover, direct effect dominates in thismodel.
From proposition 7 and equation (24), the following proposition is obtained:
Proposition 8. a) R&D inefficiency in the home country decreases the interest
rate and increases the entry rate of the home country; R&D inefficiency in thehome country increases the interest rate and decreases the entry rate of the foreigncountry:∂R1∂ F̂1r<0<∂∂ F̂1r

∂R1

∂

∂ F̂2

∂ F̂2r>0>rProb[ψ ≥ ψ1d |ψ ≥ ψ1f ]Prob[ψ ≥ ψ1d |ψ ≥ ψ1f ]b) Unilateral trade liberalization decreases the interest rate and increases theentry rate of this country, and increases the interest rate and decreases the entry
rate of the foreign country:∂R1∂ ϕ̂21∂R1∂ ϕ̂12<0<>0>∂∂ ϕ̂21∂∂ ϕ̂12

Prob[ψ ≥ ψ1d |ψ ≥ ψ1f ]Prob[ψ ≥ ψ1d |ψ ≥ ψ1f ]c) The home country’s high domestic entry cost increases the interest rate and decreases the entry rate of this country, and decreases the interest rate and increases
the entry rate of the foreign country.
∂
∂R1
>0>
Prob[ψ ≥ ψ1d |ψ ≥ ψ1f ]
d
∂F1
∂F1d
∂R1
∂
<0<
Prob[ψ ≥ ψ1d |ψ ≥ ψ1f ]
d
∂F1
∂F2d
26

∂
Proof. For x = ϕ̂jk , Fjd , F̂2r , it is straightforward to show the sign of ∂x
Prob(ψ ≥fd
ψi |ψ ≥ ψi ) because the screening threshold does not depend on x:∂∂ψid
Prob(ψ ≥ ψid |ψ ≥ ψif ) > 0 ⇐⇒
<0
∂x
∂x
1
From (24), the sign of ∂R
is also obtained. For F̂1r , R1 is a decreasing function:
∂x

∂R1

=−
r

∂ F̂1

1

1
k
ψ2d −k
d
d ρ−1
{F
+
ϕ̂
(F
)
(
) }
12
2
(F1r )2 1
ψ1d

k
−1
ρ−1
1
1
k
∂ ψ2d −k
d ρ−1
+
)
( ) }
{
ϕ̂
(F
12
2
(F1r )k∂ F̂1r ψ1d
−1
ρ−1
<0

From proposition 7 the second term is negative. 0 < ∂ F̂∂ r Prob(ψ ≥ ψid |ψ ≥ ψif )1
is satisfied from (24).
In contrast to the symmetric country case, inefficient screening technology has
a positive effect on the entry rate. A country’s inefficient screening technology
makes this country less competitive than the foreign country. This effect works
only through international trade: when countries do not trade, the interest rate
1 Fid
Ri = kr does not depend on θi . These observations imply that this effect− 1 Fiρ−1
is driven by international trade.
When Fid and Fix are interpreted as a proxy for product market regulation,
product market regulation affects the default rate. Domestic market regulations
increase the default rate; foreign market regulation decreases default rate which
does not depend on regulations for domestic firms or exporters.
The export entry rate Prob(ψ ≥ ψix |ψ ≥ ψid ) can also be calculable fromproposition 7:
Proposition 9. R&D inefficiency of the home country is negatively correlatedwith its export entry rate of home country; R&D inefficiency of foreign country is
positively correlated to export entry rate of the home country:∂∂ F̂1rProb[ψ ≥ ψ1x |ψ ≥ ψ1d ] < 0 <27∂∂ F̂2rProb[ψ ≥ ψ1x |ψ ≥ ψ1d ]This proposition shows that many firms in the financially developed country
engage in export activities. This finding reflects the concept that financially developed countries have a comparative advantage for differentiated sector. Thisis roughly consistent with Beck (2002) and Beck (2003).8 Firms in financiallydeveloped countries tend to export more than firms in financially underdeveloped
countries because firms in developed countries are more productive. Screening increases firms productivity and the competitive product market selects productive
firms. These two sources of productivity gain enables firms to export.

5Conclusion

Combining the heterogeneous firm model with the financial screening model indicates how product markets and financial markets are interrelated. The financial
market has a one-sided influence on the product market. When there is productmarket selection, product market conditions do not affect the decisions of financial
intermediaries: i.e. even if the selection is severe, intermediaries do not change
their screening intensity. However, screening efficiency affects product market
conditions.
In contrast to previous studies, an inefficient financial market decreases thedefault rate, which equals a high entry rate. A high entry rate reduces entrant productivity. Hence, a country with an inefficient financial market suffers from low
productivity not only through inefficient screening but also through weak selection. This effect exists only if countries trade. More concretely, this effect canbe viewed as a byproduct of international specialization. Countries with an inefficient financial market have a comparative disadvantage for differentiated goods.
Hence, only a limited number of entrepreneurs produce a new product in thiscountry, which weakens competition. Weak competition leads entrants to repay.
Paradoxically, an inefficient financial market produces a low default rate. Default
risk is not a good indicator of financial market efficiency. A financially underdeveloped country has an unproductive product market not only as a result of inefficient screening but also because of weak competition. This result is somewhat
8

The caveats exist that are related to Manova (2013), who uses establishment size to control
for selection effect. In contrast to her study, the price index is an appropriate measure of selection
for the results of this paper. From cutoff condition, each cutoff is determined by the price index.
Second, although Manova (2013) uses the price index for her analysis, the price index used in
the empirical studies is not compatible with the index used in this paper. Since wage is used as
numeraire in this paper, a relevant measure is the price index divided by factor prices.

28

paradoxical initially, but is a natural mechanism when appropriately interpreted.

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A

Proof of Proposition 7

I show the results of domestic cutoff before the results of the export cutoff.
∂ψ1d
< 0:
∂ F̂ r1∂ψ1d−k∂ F̂1r=1(F1d − ϕ̂12 ϕ̂21 (F1d ) ρ−1 (F2d ) ρ−1 −1
k

k

>0

∂ψ1d
> 0:
∂ F̂2r∂ψ1d−k∂ F̂2rϕ̂12 (F2d ) ρ−1 −1k=−(F1d − ϕ̂12 ϕ̂21 (F1d ) ρ−1 (F2d ) ρ−1 −1
k

k

<0

∂ψ1d
> 0:
∂F1d
k
1 − ρ−1F1d − ϕ̂12 ϕ̂21 (F1d ) ρ−1 −1 (F2d ) ρ−1 −1∂(ψ1d )−k
=−
<0
k
k
∂F1d
(F1d − ϕ̂12 ϕ̂21 (F1d ) ρ−1 (F2d ) ρ−1 −1 )2kkkϕ̂ij (Fjd ) ρ−1 −1 .
Inequality is derived from assumption 1 > ρ−1
k

∂ψ1d
> 0:
∂F2d

∂(ψ1d )−k∂(F2d ) ρ−1 −1kk=ϕ̂12 (ϕ̂21 (F1d ) ρ−1 F̂1r − F1d F̂2r )(F1d − ϕ̂12 ϕ̂21 (F1d ) ρ−1 (F2d ) ρ−1 −1 )2
k

32

k

<0

k

Last inequality is derived from ϕ̂21 (F1d ) ρ−1 (ψ1d )−k + F2d (ψ2d )−k = F̂2r .
∂ψ1d
> 0:
∂ ϕ̂
12

∂(ψ1d )−k
∂ ϕ̂12(F2d ) ρ−1 −1 F̂2r F1d + ϕ̂21 F̂1r (F1d ) ρ−1 (F2d ) ρ−1 −1
k

=

k

k

(F1d − ϕ̂12 ϕ̂21 (F1d ) ρ−1 (F2d ) ρ−1 −1 )2
k

k

<0

∂ψ1d
< 0:
∂ ϕ̂21∂(ψ1d )−k∂ ϕ̂21F̂1r − ϕ̂12 (F2d ) ρ−1 −1 F̂2r
k=

(F1d − ϕ̂12 ϕ̂21 (F1d ) ρ−1 (F2d ) ρ−1 −1 )2kk∗ (ϕ̂12 (F1d ) ρ−1 (F2d ) ρ−1 −1 ) > 0kk

From equation (6), the following relationship is satisfied:∂ log ψ2d
∂ log A2
= (1 − ρ)∂x∂x∂ log ψ2d
+1>0
= (1 − ρ)∂F2d∂ψ x∂ log A2
= (1 − ρ) 1
∂ x̂
∂ x̂
∂ψ d

x = F̂ir , F1d ,x = F2dx̂ = F̂ir , Fid ,
∂ψ d

∂ψ d

∂ψ d

Combining these two equations with ∂ F̂ 2r < 0 < ∂ F̂ 2r , and ∂ ϕ̂ 2 < 0 < ∂ ϕ̂ 2
12
21
2
1
provide the following results:∂ψ1x∂ F̂1r∂ψ1x∂ F̂1d

>0>
>0>

33

∂ψ1x
∂ F̂2r∂ψ1x∂ F̂2d