Ogura “the objective function of government controlled banks in a financial crisis”, j banking and finance (2018)

Accepted Manuscript

The Objective Function of Government-Controlled Banks in a
Financial Crisis
Yoshiaki Ogura
PII:
DOI:
Reference:

S0378-4266(18)30022-0
10.1016/j.jbankfin.2018.01.015
JBF 5291

To appear in:

Journal of Banking and Finance

Received date:
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Accepted date:

21 October 2016
15 January 2018
27 January 2018

Please cite this article as: Yoshiaki Ogura, The Objective Function of Government-Controlled Banks in
a Financial Crisis, Journal of Banking and Finance (2018), doi: 10.1016/j.jbankfin.2018.01.015

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Highlights
• GCBs increased lending to SMEs with a weaker main-bank relationship
in the financial crisis.

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• This is consistent with the welfare maximization by GCBs rather than the
profit maximization.

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Abstract

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The Objective Function of Government-Controlled Banks
in a Financial Crisis

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We present evidence that government-controlled banks (GCBs) significantly increased their
lending to small and medium-sized enterprises (SMEs) whose main bank was a large bank in the
2008–09 financial crisis. Further analyses show that the weak relationship between large banks
and SMEs is a major cause for this phenomenon. The mixed Cournot oligopoly model with
relationship banking, where profit-maximizing private banks and a welfare-maximizing GCB
coexist, shows that this finding is consistent with the welfare maximization by a GCB rather
than its own profit maximization.

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JEL Classification: G21; H44
Keywords: government-controlled banks, mixed oligopoly, relationship banking, small business
financing

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Introduction

The existing literature on government-controlled banks (GCBs) has presented mixed judgments
on the banks’ contribution to economic efficiency. The seminal empirical study by La Porta et al.
(2002) shows international evidence of the underperformance of GCBs. Several subsequent studies

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show evidence that such inefficiency mainly comes from the political constraint or the political
capture (e.g., Sapienza, 2004; Din¸c, 2005),1 and that a privatization significantly improves the
efficiency (Bertrand et al., 2007). On the other hand, recent studies show evidence of the benefits
of GCBs, such as mitigating the credit constraint against SMEs (Behr et al., 2013; Lin et al.,

2014; Sekino and Watanabe, 2014) and the less procyclicality of their lending (Micco and Panizza,

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2006; Brei and Schclarek, 2013; Cull and Per´ıa, 2013; Coleman and Feler, 2015; Behr et al., 2017),2
especially in countries with good governance (Bertay et al., 2015). Moreover, macroeconomic
analyses theoretically predict the possibility of welfare improvement via counter-cyclical policy
lending to firms in a model with a financial friction (e.g., Gertler and Karadi, 2011; Martin and

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Ventura, 2016). However, it remains an open empirical question whether the lending behavior of
GCBs improves welfare.

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This interesting and important issue boils down to the question of which is the actual objective
function of GCBs among various alternatives, such as their own profits, the social welfare, or some

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other political interests. To figure out an empirical strategy to detect their objective function, first
we applied a mixed Cournot oligopoly model (Fraja and Delbono, 1989; Ide and Hayashi, 1992;

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Matsumura, 1998) to the loan market for a firm. The standard mixed-oligopoly model assumes
a public firm, which maximizes the social welfare, and multiple profit-maximizing private firms.
We introduce an additional twist of the asymmetry among profit-maximizing private banks to

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take into account relationship banking, which is a widely accepted phenomenon in small business
financing (for the list of the existing studies, see, e.g., Degryse et al., 2009). Namely, we assume a
credit market with a GCB, a main bank providing a differentiated service based on its information
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More recently, Pereira and Maia-Filho (2015) find a slower transmission of the monetary policy to the interest
rates of GCBs. Illueca et al. (2014) and Iannotta et al. (2013) provide evidence of excess risk-taking by governmentcontrolled banks.
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Brei and Schclarek (2015) theoretically explain that this phenomenon is due to the differences between private
banks and public banks in terms of the objective functions and the funding sources.

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advantage, and another private bank without such an advantage.
We consider two cases; first, the case where the GCB maximizes the social welfare, which is
defined by the sum of the profits of all banks and the surplus for the borrowing firm; second, the
case where the GCB is a profit maximizer, like a private non-main bank. We find that, in response
to the increased loan demand, the welfare-maximizing GCB increases its lending more for firms

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with a weak relationship with its main bank, in the sense that the extent of differentiation of the

main bank is lower and that the main-bank loan demand is more price-elastic. This is because
the GCB is less willing to interrupt a lending relationship between a firm and its main bank if
it provides a differentiated service that is more valuable for the firm and contributes more to the

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social welfare. In contrast, a profit-maximizing GCB never adjusts its lending according to the
strength of the main-bank relationship. This result suggests that we can detect whether a GCB is
a profit maximizer or a welfare maximizer by examining whether it increases lending more to firms
with a weaker main-bank relationship in response to a surge in loan demand.
The microdata provided by the Small and Medium Enterprise Unit of the Japan Finance Cor-

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poration (JFC), one of the major GCBs for SMEs, enables us to conduct this empirical test. The
dataset contains information on the annual financial statements and other basic characteristics of

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each past and current borrower, as well as outstanding loan amounts from the SME Unit of JFC
and private banks up to the four largest lenders. The most desirable feature of the data is that it

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contains the identifier of these private banks so that we can match the bank information.
We focus on the dataset from 2007 to 2011 before and after the 2008-09 financial crisis severely

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affected the Japanese economy through the sharp reduction of exports to the USA and Europe in the
accounting period ending in 2009. The benefits of using the Japanese dataset are threefold. First,

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the financial crisis was an exogenous shock to Japanese banking and industrial sectors. The banking
sector was barely affected by the shock, while the shock had a deep impact on the performance and
financing behavior of the industrial sectors, especially the exporting sectors. Second, we observed
a clear surge in the demand for bank loans in the accounting period ending in 2009 (for typical
Japanese firms, the end of the accounting year is in March). The survey of large banks conducted
by the Bank of Japan clearly shows this (Figure 1). This is because of the temporary shutdown
of the commercial paper and bond markets (Uchino, 2013) and the precautionary motivations in
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response to the disastrous drop in corporate earnings in the exporting sector, as shown in Section 3.
These points ensure the theoretical assumption of the exogenous loan demand shift for our empirical
hypothesis. Third, the dataset enables us to construct a three-way panel dataset by firm, year,
and lender. This three-way panel data enables us to fully control for the unobservable time-varying
firm characteristics, such as the magnitude of a demand shock and other credit characteristics by

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introducing the firm-by-year cross fixed effect. In the context of this study, both the intensity
of a main-bank relationship and the lending attitude of GCBs are correlated with unobservable
firm characteristics. The estimated correlation between the lending attitude of GCBs and the

intensity of main-bank relationship can be biased due to these unobservables, if we cannot control

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for them perfectly. The firm-by-year cross fixed effect minimize this problem and provide a clear
identification, as proposed by Gan (2007) and subsequent studies.

From the regression using the three-way panel data to control for the firm-by-year cross fixed
effect, we find that the GCBs increased their lending to SMEs whose main bank is a large bank,
which operates nationwide and internationally, in the crisis period of two years after September

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2008, while they decreased lending for other SMEs. On the other hand, we also find that a main
bank decreased lending in the crisis period if it is a large bank, whereas it increased if it is a regional

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bank. Thus, GCBs filled in the loan supply shortage of large main banks.
Since we control for unobservable time-varying firm characteristics as mentioned above, this

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result is less likely to be driven by unobservable firm characteristics, such that a large main bank
obtains negative private information and reduces lending to an SME while a GCB without it keep

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lending, or that a GCB increases its lending because of positive private information while a main

bank without it reduces lending.

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Further analyses with more explicit relationship measures, such as the main-bank loan or deposit
share, a dummy variable indicating that a firm switched main banks before the crisis, or the number
of lenders before the crisis, show that this result is driven by the weak relationship between large
banks and SMEs, which has been recognized in the existing literature (e.g., Cole et al., 2004;
Berger et al., 2005; Uchida et al., 2008; Ogura and Uchida, 2014). This is consistent with the
welfare-maximizing behavior in the above theoretical prediction.
The remaining part of this paper is organized as follows. We describe the source of our dataset in
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Section 2. The financial condition and financing behavior of Japanese SMEs in the 2008-09 financial
crisis are described in Sections 3 and 4. A theoretical model to derive an empirical strategy to detect
the objective function of the GCB is presented in Section 5. The hypothesis for the statistical test,
the data description, the specification for the estimation, and the result of the test are presented

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in Section 6. Section 7 presents the conclusion and the limitation of our analysis.

Data

The dataset for this study is the internal credit information on borrowers at the Small and Medium
Enterprise (SME) Unit of the Japan Finance Corporation (JFC). JFC is a 100% government-

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owned and government-controlled lending institution that provides subsidized long-term loans to
SMEs; microcorporations including start-up firms and farmers; and individuals. It also provides
reinsurance for the public guarantee system for SME loans. JFC does not take deposits and is
financed mostly by borrowing from the Japanese government and partially by issuing bonds with
or without government guarantees. It has a nationwide branch network of 152 branches (March

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2009). The SME Unit is the business unit focusing on loans to SMEs. The total outstanding loan
amount of this unit was about 5.2 trillion JPY in March 2009. The asset size is close to that of

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larger regional banks. The unit was called the Japan Finance Corporation for Small and Medium
Enterprise (JASME) before its merger with other units in October 2008.

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The internal credit information of the SME unit includes the annual financial statement information and other basic characteristics of each borrowing firm, such as the industrial classification,

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the year of establishment, and the location of the JFC branch that transacts with the firm, as

well as the internal credit rating. The most notable feature of the dataset is that it contains the

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outstanding loan amount provided by JFC and other private and government-owned institutions.
The names of lenders can be identified for the largest four lenders to match the financial and other
information of each lender. JFC identifies a main bank of each firm based on information such as
deposit share and loan share. This information enables us to examine what types of firms became
more dependent on GCB lending in the crisis and evaluate the economic efficiency of GCB lending.
We use the observations from calendar years 2007 to 2011, from right before the outbreak of the
crisis to several years after. The dataset covers not only firms with a current positive amount of loan
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outstanding from JFC but also those without this for several years before starting a transaction or
after closing a transaction with JFC. The number of firm-year observations is 230,587. From the
original sample, we drop firms whose main bank is a JA bank (agricultural cooperative), a JF marine
bank (fishery cooperative), a GCB (739 observations), or a Shinkumi bank (3,298 observations),
which is a smaller credit cooperative, since the data of their characteristics are not fully available.

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We drop 14,454 observations whose borrow/asset is greater than one to avoid the effect of firms
under a bankruptcy procedure in all of the estimations. Finally, we drop 64,514 observations for
which any item required for the preliminary regression in Section 4 is not available. The remaining
147,582 observations are the baseline sample for our analysis.

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The industrial composition of the borrowers at the SME Unit of JFC tilted more toward the
manufacturing sector than did the population, which was measured by the 2009 Economic Census
(Table 1). Table 3 shows the descriptive statistics of the variables to be used for the regressions
later. The definition of each variable is listed in Table 2. The median of the main-bank share of
loans is about 38% and that of deposits are about 66%. The median of the loan share of GCBs is

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about 35%, somewhat lower than that of the main bank. The number of lenders other than JFC
is three on average. The minimum is one, i.e., each firm has a relationship with at least one bank

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other than JFC. This is because JFC does not provide checking, savings, or settlement services.
The median of the asset size is 780 million JPY. The Credit Risk Database (CRD), which is closer

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to the population of the SMEs with access to the loan market, indicates that the median asset size
was 85 million JPY in 2003 (Table 1.4 on p.21 in Shikano, 2008). Thus, our dataset focuses on

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larger firms among the SMEs.

More than 70% of our sample firms chose regional banks3 as their main bank (Table 4). Regional

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banks operate within a single or a couple of adjacent prefectures. The remaining 30% chose large
banks, which have a nationwide branch network and operate nationwide or internationally.4 Large

banks have features clearly different from those of other types of banks. First, the main-bank shares
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Regional banks include both the member banks of the Regional Banks Association of Japan and the Second
Association of Regional Banks, and cooperative banks, such as Shinkin and Shinkumi banks. The asset size of the
banks in the two regional bank associations ranges from 0.2 to 11.6 trillion JPY as of March 2009. The asset size of
cooperative banks is smaller, and ranges from 0.004 to 3.9 trillion JPY as of March 2009.
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Large banks include city banks (Mitsubishi UFJ, Sumitomo-Mitsui, Mizuho, Mizuho Corporate, Risona, Saitama
Risona, Shinsei, and Aozora) and trust banks (Mitsubishi UFJ Trust, Mizuho Trust, Chuo-Mitsui Trust, and Sumitomo Trust). The asset size ranges from 6.1 to 149 trillion JPY as of March 2009.

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of deposits and loans are significantly lower when the main bank is a large bank than otherwise
(Panels (a) and (b), Figure 2). Second, firms switch their main banks more frequently when their
main bank is a large bank than otherwise (Table 5). The probability that a firm had switched
main banks from the previous year is higher by at least 1% for larger banks. The difference was
at a maximum in 2010, the later stage of the financial crisis. Third, the ratio of SME loans over

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total loans of large banks is significantly lower than that for other types of banks (Panel (c), Figure
2).5 The difference is about 10-17%. The gap significantly widened in 2009, in the midst of the
crisis, and has remained wide since then, as large banks decreased the SME ratio considerably,
while regional banks slightly increased the SME ratio. In contrast to the decline of large banks in

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SME lending, the share of the GCBs for firms whose main bank was a large bank kept increasing
in 2008 (Panel (d), Figure 2). These figures and table suggest that large banks maintain a weaker
relationship with SMEs than regional banks do, even if they are recognized as a main bank by the
firm or other lenders.

Table 6 shows a comparison of the characteristics of those firms whose main bank was a large

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bank and others in the crisis period of two years from September 2008. The main-bank share of
loans and deposits decreased significantly more for firms whose main bank was a large bank, and

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the loan share of GCBs increased more for them. In terms of creditworthiness, the firms whose
main bank is a large bank had assets twice as large as the other firms. The JFC credit rating for

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them was significantly higher than that for others, whereas the damage to the credit rating, sales,

interest coverage ratio (∆credit rating, ∆ln(sales), and ∆int.cover) were more severe for the former

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group of firms. This is because the weight of exporters such as the manufacturing sector is larger
for the clientele of large banks than that of regional banks or cooperative banks. In short, those

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whose main bank was a large bank were larger and more creditworthy, but they were affected more
severely by the temporary shock of the global financial crisis.
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Cooperative banks are allowed to lend to individuals and SMEs only by regulation.

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3

Corporate Finance of Japanese SMEs in the 2008-09 Financial
Crisis

3.1

Loan demand increased sharply in 2009

The dataset shows that the 2008-09 financial crisis severely affected the Japanese SME loan market

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with a short lag through the plummeting export to the USA and Europe. Panel (a) of Figure 3 is
the plot of the sector average of the ratio of EBITDA over total assets, which is calculated from the
microdata provided by JFC and is normalized to 100 in 2007 for all sectors. Clearly, the earnings
of Japanese SME exporters in the electronics, transportation equipment (including auto makers
and their suppliers), and other manufacturing sectors dropped by more than 50% from 2008 to

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2009. These exporters increased their cash holdings in response to this serious crisis, probably with
a precautionary motivation (Panel (b) in Figure 3) despite the fact that the cash flow from their
usual operation had dramatically contracted. The increased cash holdings were mainly financed
by bank loans as is indicated by the sharp increase in the ratio of loans over assets in the export

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sectors (Panel (c) in Figure 3).

Banks responded differently by type

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The response of each individual bank varies by bank type. Figure 4 shows the average annual

change in loans from each lender to each firm. The values are normalized by the total asset of each

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firm in the previous year. GCBs for SMEs including all units of JFC and the Shoko Chukin Bank,6
another GCB for SMEs, increased their lending sharply in 2009 and kept increasing it until 2011 as

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a result of the reinforcement of the safety-net lending for SMEs by the government through these
GCBs. Regional banks also increased their lending in 2009 but decreased it in 2010. In contrast,

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large banks never increased their lending even in 2009, although the speed of reduction slowed in
2009. This stark contrast between regional banks and large banks is likely to stem from the fact
that the relationships of a large bank with SMEs are weaker than those of a regional bank, as shown
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The JFC SME Unit accounts for about 70%, JFC other units account for about 10%, and the Shoko Chukin
Bank accounts for about 20% of observations in each year in our sample (Table 8). The influence of the government
is somewhat smaller for the Shoko Chukin Bank than for JFC. The government holds 46.46% (March 2009) of the
share of the Shoko Chukin Bank, and the remainders are widely held by various private entities, including financial
institutions. The bank is mostly financed by deposits and bank debentures (the latter is until 2012). Its board
includes several members sent from the government. It has a nationwide branch network of 93 branches. The amount
of outstanding loans is 9.2 trillion JPY, which is larger than that for the SME Unit of JFC (March 2009).

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in extant empirical studies (e.g., Uchida et al., 2008; Ogura and Uchida, 2014) and the tables and
figures in the previous section. As if to fill in this gap, GCBs increased lending more extensively
for firms whose main bank was a large bank after 2009.
A quick guess suggests that this difference between large main banks and regional main banks
is due to exposure to the negative shock of the financial crisis. However, the financial indicators of

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these banks in the period show that the Japanese banking sector was not seriously affected by the
overseas shock. For example, Figure 5 is the plot of the average risk-adjusted capital ratio of each
type of bank. The figure indicates that the damage to the capital ratio in 2009 was quite limited,
even for large banks that had more exposure to foreign assets although the size of the reduction

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was larger for large banks than that for the other types of banks. The capital ratio of large banks
quickly recovered in 2010. The movement of large banks is mainly driven by the denominator of
the capital ratio, the amount of total loans. The total loans of city banks, which consists of the
major part of large banks, increased by 4.6% from March 2008 to March 2009, whereas it decreased
3.7% in the next year (Source: Bank of Japan). The sharp increase in the capital ratio of large

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banks in 2010 is also due to the capital increases by massive seasoned equity offerings (SEO) in

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response to the expected reinforcement of the regulatory requirement for capital.7

Preliminary Regression Analysis: Share of the Main Bank and
GCBs

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To check whether the casual observation that the share of GCBs increased for firms whose main

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bank was a large bank after 2009 was neither driven by the deteriorated financial soundness of main
banks nor the characteristics of the clientele of each type of bank, we regress the GCBs’ share to

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bank-type dummies and various firm and main-bank characteristics.
The precise specification for this preliminary regression is
ln(GCB f or SM Es shareit ) = β0 + β1 · M B largeit + β2 · M B largeit · crisist
+β3 · M B largeit · post − crisist + δ Xit + µi +
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it ,

(1)

For example, Mizuho Financial Group raised capital of 516 billon JPY on July 24, 2009, and 729.17 billion JPY
on July 22, 2010 by SEO. Mitsubishi UFJ Financial Group raised capital of 1 trillion JPY on December 22, 2009,
and Sumitomo Mitsui Banking Corporation raised 827.4 billion JPY on June 22, 2009, by SEO.

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where i is the index for each firm, t = {2007, · · · , 2011}, and βs, γs and a column vector δ are
coefficients to be estimated. Xit is a column vector of control variables including main-bank characteristics, firm characteristics, crisis dummies, and the interaction term of the year dummies and
sector dummies. Main-bank characteristics consist of the financial soundness or risk-taking capacity of each bank, such as capital ratio, ROA, and non-performing loan ratio. Firm characteristics

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include those related to the creditworthiness of each firm. The details of the variable definition and
the descriptive statistics are listed in Tables 2 and 3, respectively. θt is the year fixed effect. µi
is the firm fixed effect.

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is the error term. ln(GCB f or SM Es shareit ) is a logit-transformed

share of GCBs for SMEs in the loan for firm i in year t (see Table 2 for details). M B largeit is

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a dummy variable, which equals one if the main bank of firm i in year t is a large bank. crisis
is a dummy variable, which is equal to one if the observation is reported in the crisis period from
September 2008 to August 2010. post-crisis is a dummy variable to indicate the post-crisis period
from September 2010 to the end of the sample period, December 2011.

We also estimate a model in which the dependent variable is replaced with the logit-transformed

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loan share of the main bank, ln(M B loan share), or the ratio of total borrowing over total asset

borrowing in the crisis.

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of each firm, borrow/asset to look at the change in the main-bank share and the change in total

The regression result is listed in Table 7. Column (1) is the list of estimated coefficients and

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the firm cluster robust standard errors when we regress the logit-transformed GCB share. The
base category includes firms whose main bank is a regional bank including a cooperative bank.

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The estimated coefficient for the dummy variable crisis is negative and significant. This indicates
that the GCB dependence of those whose main bank is a regional bank or a cooperative bank kept

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decreasing in the crisis period. In contrast, the estimated coefficients of the interaction terms of
M B large and the crisis-phase dummies are positive and significant, i.e., those whose main bank
is a large bank increased its dependence on GCBs in the crisis period, relative to those whose main
bank is a regional bank.
Column (2) in Table 7 shows the result when we regress the logit-transformed main-bank share.
The estimated coefficient of M B large is deeply negative and significant. This point shows that the
main-bank share is smaller when the main bank is a large bank, given the same firm characteristics
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and the same financial soundness of the main bank. Thus, the relationship between large banks
and SMEs is weaker than that between regional banks and SMEs. The estimated coefficients of
MB large×crisis and MB large×post-crisis are negative and significant. This indicates that the
share of large main banks kept decreasing in the financial crisis.
Column (3) in Table 7 shows the result when we regress the ratio of total borrowing over total

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assets of each firm. The estimated coefficients of the interaction terms of M B large with the crisis
and the post-crisis dummies are negative and significant. This means that a firm borrowed less when
its main bank was a large bank than otherwise, despite having the same level of creditworthiness.
These results suggest that large banks decreased their lending to SMEs relative to regional banks,

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and in place of large banks, the GCBs filled the need for funds. However, we cannot fully control for
unobservable and time-varying firm characteristics in these preliminary regressions. We introduce
a cross fixed effect of firm × year by making use of the three-way panel data of the firm, year, and
bank level to address this problem sharply in the full analysis.

The control variables also show interesting results. Main-bank characteristics in Columns (2)

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and (3) show that the main-bank share and total borrowing reduce when the main bank suffers
from a higher non-performing loan ratio. However, the effect of the capital adequacy ratio of the

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main bank, which is adjusted by subtracting the minimum requirement for the credit risk, on the
main-bank share is opposite: the main-bank share is smaller for those with a main bank with a

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higher capital ratio. As for the firm characteristics, firms with a higher credit rating have a higher
share of GCBs, a lower share of main banks, and lower borrowing. Perhaps this captures the

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reverse causality, i.e., those with less debt are rated higher. On the other hand, the improvement in
credit rating increases the main-bank share and total borrowing, while it reduces the dependence

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on GCBs. Larger firms, which are presumably more creditworthy, depend less on GCBs. Those
with more tangible assets that are pledgeable as collateral are more dependent on their main bank
and have a higher dependence on borrowing.

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Model for the Welfare Evaluation of GCBs

To understand the welfare effect of such lending behavior by GCBs theoretically, and to clarify a
relevant hypothesis, we construct a model based on the mixed Cournot oligopoly model (e.g., Fraja
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and Delbono, 1989; Ide and Hayashi, 1992; Matsumura, 1998), in which private banks and a GCB
exist. Our new twist added to the standard model is the assumption that the service provided by
a main bank is differentiated to a various extent. By this addition, we can conduct a comparative
statics with respect to the strength of relationship between a bank and a firm. By using this model,
we elucidate the difference between the supply function of a GCB that maximizes its own profit

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and that of the one maximizing the social welfare consisting of the total borrower’s profit and the
total lender’s profit. From this theoretical analysis, we derive a statistical hypothesis for detecting
the objective function of GCBs; either social welfare or their own economic profit.

5.1

Setup

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We consider the case where a main bank, a non-main bank, and a GCB are potential lenders for a
firm. We assume that the firm prefers loans from its main bank to those from others. This sort of
brand loyalty would be generated by the borrower’s expectation that the main bank is willing to
provide additional loans in a flexible manner when the firm is under temporary financial distress

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(Chemmanur and Fulghieri, 1994; Din¸c, 2000; Bolton et al., 2016) or the expectation of additional
services, such as more effective advising and monitoring, based on proprietary information at the

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main bank generated from a long-term relationship (Boot and Thakor, 2000; Yafeh and Yosha,
2001). We assume that the loans from non-main banks and from the GCB are homogeneous services.

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Firms expect that these additional benefits will improve their corporate value. To formulate this
assumption into an analytical model, we assume the following loan demand function of a firm,

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which can be derived from the profit maximization problem of each firm, which is not explicitly

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modeled here.

Lm = α − δβRm + γR−m ,

(2)

L−m = α − βR−m + γδRm ,

(3)

where Lm is the amount of a loan from the main bank and L−m is the amount of loans from a

non-main bank or a GCB, i.e., L−m ≡ Lo + Lg , where Lo is a loan amount from an outside bank
and Lg is a loan amount from a GCB. Rm is the gross interest rate of the loan from the main bank,
and R−m is that of the loan from other banks. The interest rate is identical for loans from a non12


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main bank and from a GCB, since these loans are homogeneous. The other letters are exogenous
parameters. We assume
γ/β < δ < 1.

(4)

The first inequality is a standard assumption, which means that a loan demand for a bank is more

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elastic with respect to the rate quoted by the bank than the rate of the other banks. δ is the
key parameter to describe the brand loyalty for the main bank loan, or the strength of bank–firm
relationship. This parameter indicates that loan demand is less price-elastic for a main bank than
other banks and that the negative demand impact of an increased interest rate is smaller for a

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main bank than for a non-main bank or a GCB, which supplies non-differentiated services. This
inelasticity gives a larger loan share and a larger profit for the main bank.
We consider a mixed-oligopoly loan market, where a GCB, which may maximize the social
welfare, and private banks, which engage in asymmetric Cournot competition,8 are operating. By
solving the above simultaneous equations of demand functions with respect to each interest rate,

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we obtain the following inverse demand functions,

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Rm = K(a − bLm − cL−m ),

R−m = a − bL−m − cL−m ,

(5)
(6)

b/c > K > 1, b > c.

(7)

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where K ≡ 1/δ, a ≡ α/(β 2 − γ 2 ), b ≡ β/(β 2 − γ 2 ), and c ≡ γ/(β 2 − γ 2 ). Assumption (4) implies

K is an indicator of the strength of the main-bank relationship of each firm in the sense that the

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higher K indicates stronger firm loyalty to its main bank or lower price elasticity of demand for
the main-bank loan.
We assume that the firm defaults on all loans with a probability of 1 − p ∈ (0, 1) to take into

account the credit risk. The firm does not yield anything, and so the profit of the firm and the
repayment from the firm are zero in the default case. The funding cost or an opportunity cost for
8
An empirical study about the Japanese banking sector by Uchida and Tsutsui (2005) does not reject the possibility
that large banks are competing in a Cournot manner. There is no clear consensus whether the Cournot model is a
good approximation for lending competition, but we use this setup for the tractability of the model.

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lending to this firm is r, which is common to all types of banks. To ensure that the main bank
provides a strictly positive loan in the Nash equilibrium, we assume that
ap − r > 0.

5.2.1

Equilibrium
Welfare-maximizing GCBs

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5.2

(8)

First, we consider the Nash equilibrium in the case where the GCB sets its amount of lending to
this firm so as to maximize the social welfare in the market for lending to this firm, i.e., the sum
of the firm profit and the total profit of all banks.

max
Lm

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The profit maximization problem for the main bank is

pK(a − bLm − cL−m )Lm − rLm .

That for the non-main private bank is
max

p(a − b(Lo + Lg ) − cLm )Lo − rLo ,

(10)

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Lo

(9)

Lm

K(a − bl − cL−m )dl + p

max p
Lg

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The welfare maximization problem for the policy bank is

0

Lo +Lg

(a − bl − cLm )dl − r(Lm + Lo + Lg ).

0

(11)

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The first term is the firm profit from the loan from a main bank, the second term is the firm profit
from the loans from a non-main bank and the GCB, and the last term is the total funding cost for

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the banking sector.

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The FOCs for each of these problems are
pK(a − 2bLm − c(Lo + Lg )) − r = 0,

(12)

−pbLo + p(a − bL−m − cLm ) − r = 0,

(13)

−(1 + K)pcLm + pa − pbL−m − r = 0.

(14)

The second-order condition for the maximization is satisfied since the differentiation of the left-hand

side of each of these FOCs is negative.

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Solving this system of equations with respect to Lm , Lo , and Lg gives the equilibrium supply
of loans by each type of banks as follows:
b(apK − r)
ap − r
−c ,
2
− (1 + K)c } (ap − r)K
Kc(ap − r)
b(apK − r)
Lo =
−c ,
2
2
bp{2b − (1 + K)c } (ap − r)K
Kc2
ap − r
b(apK − r)
2b
+
Lg = max 0,
− c(1 + 2K)
p{2b2 − (1 + K)c2 }
b

(ap − r)K

(15)

p{2b2

(16)
.

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Lm =

(17)

Lm and Lo are positive under assumptions (7) and (8). The latter term of RHS of (17) can be
negative. We assume that Lg equals zero in this case.

The impact of the demand shock, which is expressed by the increase in a, the upward shift of

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the demand curve, on the supply by the GCB is
dLg
(2 − c/b)(b − cK)
=
da

2b2 − (1 + K)c2

(18)

if Lg > 0, or zero if Lg = 0. This derivative is always positive under assumptions (7) and (8). The
effect of the strength of the main-bank relationship on this response is

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d2 Lg
c(b − c)(2b + c)
=−
< 0.
dKda
(b − cK)(2b2 − (1 + K)c2 )

(19)

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This is negative under assumptions (7) and (8). It means that the GCB supplies larger amounts to a
firm whose main-bank relationship is weak and supplies less to a firm whose main-bank relationship

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is strong in response to the increase in the loan demand of the firm. This is because the welfaremaximizing government bank takes into account the fact that a unit of loans from the main bank

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generates more benefits for the firm than does a unit of loans from the other banks, including the

government bank, because of the additional benefit from relationship banking by the main bank.

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This effect is captured by the first term in the LHS of the FOC for the GCB (14). As K gets larger
and the loans from the main bank Lm get larger due to the increase in demand, the marginal social
welfare of a unit of loans by the GCB decreases. Thus, the GCB is less willing to provide a loan to
those with higher K, i.e., those with a strong relationship with their main bank.
5.2.2

Profit-maximizing GCB

Now we consider the case where the GCB behaves in the same way as the non-main bank as a
Cournot competitor. The GCB solves the same maximization problem as that of the non-main
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private bank in this case. The FOC for the GCB is given by
−pbLg + p(a − bL−m − cLm ) − r = 0.

(20)

Solving the system of Eqs. (12), (13), and (20) gives the equilibrium loan supply of each type of
banks, {Lg , Lm , Lo }, as follows:

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(3b − 2c)(apK − r) + 2cr(K − 1)
,
2pK(3b2 − c2 )
K(ap − r)(b − c) − 1/2cr(K − 1)
Lg = Lo = max 0,
.
pK(3b2 − c2 )

Lm =

(21)
(22)

Lm is positive under assumptions (7) and (8). In this case, the effect of the positive loan demand

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shock, which is expressed by the increase in a, on the loan supply of the GCB Lg is
dLg
b−c
= 2
da
3b − c2

(23)

if Lg is positive or zero if Lg is zero. The effect of the intensity of the main-bank relationship on
this response is

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d2 Lg
= 0.
dKda

(24)

of the borrowing firm.

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Namely, the GCB does not adjust its supply according to the intensity of the main-bank relationship

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The following proposition is a summary of the results in this section.

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Proposition (Welfare Maximizing vs. Profit Maximizing). In response to a demand increase, a
welfare-maximizing government-controlled bank (GCB) increases lending more for a firm with a

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weaker relationship with its main bank. Lending by a profit-maximizing GCB is independent of the
strength of the relationship between a firm and its main bank.
This proposition suggests that we can identify whether the government bank is trying to max-

imize the social welfare by examining the negative correlation between the supply of GCB lending
and the strength of the main-bank relationship of the borrower under a surge of loan demand like
that in the Japanese loan market in the crisis period from September 2008 to August 2010, as
mentioned in Section 3.1. Thus, the hypothesis to be tested is as follows.
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Hypothesis. Loan amounts from GCBs increased more for firms whose main bank was a large
bank in response to the loan demand surge in the financial crisis.
If we find that the above hypothesis is not supported by our dataset, it means that Japanese
GCBs are not maximizing the social welfare.

Hypothesis Test: Are GCBs maximizing the social welfare or
their profits?

6.1

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Measure for the strength of the bank-firm relationship

To test the above proposition, we need a good proxy measure for the strength of the main-bank

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relationship.

Our primary proxy measure is a dummy variable to indicate a main bank is a large bank,
M B large. Many existing studies suggest that the information on whether the main bank is a large
bank can work as a proxy for the weakness of a main-bank relationship. The theory suggests that
a large bank with a more centralized lending-decision mechanism is not competent in utilizing the

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soft information that is required for relationship banking (e.g., Stein, 2002), and several empirical
studies show supportive evidence of this (e.g., Cole et al., 2004; Berger et al., 2005; Uchida et al.,

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2008; Ogura and Uchida, 2014). Typical large banks in Japan are city banks and trust banks,
which have a nationwide branch network and operate nationwide or internationally. The weakness

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of the relationships of large banks with SMEs is also consistent with the significantly lower mainbank share when the main bank is a large bank in Figure 2 and with the higher probability of a

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main-bank switch at large banks in Table 5.
We also use the measures, which is more explicit and focused. The first ones are the loan share

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and the deposit share of the main bank as of 2007, M B loan share and M B deposit share. The
higher values of them indicate the stronger main-bank relationship. The second one is the dummy
variable, which equals one if a firm switched main banks in the pre-crisis period or zero otherwise,
M B switch. It indicates a stronger relationship if this variable equals zero. The last one is the
maximum number of lenders except for GCBs in the pre-crisis period, #lenders. The larger value
of it indicates a weaker main-bank relationship.

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6.2

Identification strategy

Our test strategy is to look at the difference in differences (DID). To put it more precisely, we
tested the statistical significance of the difference between the response of GCB lending to firms
with a strong main bank relationship and to those without one after the loan demand surge in the

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2008-09 financial crisis. We argue that the loan demand surge in the crisis period was an exogenous
shock to the Japanese credit market, given that it was mainly propagated from the USA and the
EU to Japan through the exporting sector, as discussed in Section 3.1.

To conduct this DID analysis, we use the three-way panel data of the annual change in the
amount of outstanding loans from each bank at the end of each accounting period of each firm,

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which was normalized by the total asset of the firm in the previous year (∆loan/asset). A notable
benefit of estimating the model with the three-way panel data is that we can introduce the firm×year
cross fixed effect to control for the heterogeneous magnitude of a loan demand shock and other
time-varying unobservable individual firm factors, such as profitability, growth opportunity, and
creditworthiness, since we have multiple observations for each firm-year cell. Thanks to this cross

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fixed effect, we can eliminate the endogeneity problem due to the potential correlation between

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the choice of a main bank and the lending attitude of a main bank through an time-varying and
unobservable firm characteristics. For example, an under-performing firm might be willing to
contact an under-performing bank with an inferior monitoring ability. This correlation resulting

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from an unobservable firm factor makes difficult to tell apart the effect of the bank-firm relationship
from the firm factor as pointed out by Gan (2007). The cross fixed effect enables us to control for

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the latter factor more sharply and to extract the former effect. In our context, the elimination of
the time-varying unobservable firm factor by the cross fixed effect minimizes the possibility that

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the difference in the lending behaviors of GCBs and large banks are driven by the unobservable
firm factors. Likewise, we can introduce the lender×year fixed effect to control for the unobservable
time-varying characteristics of each lender, such as the financial soundness of each lender.
The three-way panel data is obtained by transforming the original dataset described in Section
2 from the firm-year level panel to the firm-year-lender level panel data. After this transformation,
we obtain 900,635 firm-year-lender observations for which ∆loan/asset is available. We drop the

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entire observation of a firm whose ∆loan/asset is in the top 1% or the bottom 1% in any of the
years from 2007 to 2011 (69,154 observations). We also drop 112,369 observations which are the
only observation within a firm-year cell and cannot control for the firm-year fixed effect. The
resulting 831,481 observations are our baseline sample for the three-way panel regression.9
As noted in the data description, our dataset includes the amount of outstanding loans from a

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bank to a firm in each year for the largest four lenders and the SME Unit of JFC. If the number of
lenders other than the SME Unit of JFC exceeds four, the outstanding loans of the fourth largest
lender and other smaller lenders including the unknown lenders, are summed up and classified as
loans from miscellaneous “Other institutions.” The composition of the types of lenders in each year

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is listed in Table 8. Regional banks, including cooperative banks, account for the largest part of
the dataset, about 44%. GCBs for SMEs, including the SME Unit and the Micro Corporation and
Individual Unit of JFC, and the Shoko Chukin Bank account for the next largest part, about 35%.
Large banks account for about 19%. The class “Other institutions,” which is the mixture of the
fourth largest and smaller lenders, and the other GCBs, including the Development Bank of Japan,

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account for a very small part of our observations.

Table 9 shows the descriptive statistics of the annual change in loan outstanding from a bank to

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a firm in a year, which is normalized by the total asset of the firm in the previous year, ∆loan/asset.
The mean and median of ∆loan/asset are around zero. Figure 4 is the plot of the sample mean of

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∆loan/asset by each class of lenders. Clearly, the loans by GCBs to SMEs kept increasing from
2009 to 2011. The increase in GCB loans to SMEs increased more precipitously when the main

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bank of a firm was a large bank than otherwise. The figure also shows that the loan growth of large
banks is always lower than that of regional banks.

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9
We adjust ∆loan/asset right after each bank merger in the following way (1,291 observations). We treat the
value for each acquired bank, which loses its official bank ID (Kin’yu Kikan code) upon merger, as missing after the
merger. For each acquiring bank, which maintains its official bank ID after merger, we calculate ∆loan/asset on the
consolidated basis, i.e., we set the numerator equals to the difference between the loan from the post-merger bank
and the sum of the loans of pre-merger banks.

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We estimate the following firm×year fixed-effect model by using the three-way panel data.
∆loan/assetijt = β0 + (β1 + β2 · crisist + β3 · post-crisist ) · GCB f or SM Ejt
+ (β4 + β5 · crisist + β6 · post-crisist ) · GCB f or SM Ejt · M B largeit
+ (β7 + β8 · crisist + β9 · post-crisist ) · large bankjt + δ Xijt + ρit +

ijt ,

(25)

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where i is the index of a firm, j is the index of a bank, and t (= 2007, · · · , 2011) is the year. βs and
a column vector δ are the coefficients to be estimated. Xijt is a column vector of control variables.
ρit is the cross fixed effect of firm i and year t.

ijt

variables are listed in Table 2.

is the error term. The definitions of the other

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The most important coefficients for our hypothesis test is β5 . If Japanese GCBs behave as a
welfare maximizer rather than a profit maximizer, they should increase their lending more for firms
whose main-bank relationship is weaker, typically firms whose main bank is a large bank, i.e., β5
is positive and significant. We also tested the hypothesis by replacing M B large with alternative
measures of the strength of a main-bank relationship; i.e., a dummy variable to indicate whether

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a firm has switched main banks in the pre-crisis period, M B switch; the pre-crisis loan share of
the main bank, M B loan share; the pre-crisis deposit share of the main bank, M B deposit share;

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and the number of non-GCB lenders in the pre-crisis period, #lenders. We need to note that the
interpretation of the signs of coefficients is opposite for M B loan share and M B deposit shares,

measures.

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since these variables are increasing in the strength of the relationship as opposed to the other

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The theoretical model suggests that the response to a demand surge differs between a main
bank and a non-main bank, and this difference depends on the strength of the relationship. Thus,

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the most important control variable is a dummy variable to indicate whether a lender is a main
bank, main bank, and its interaction with a dummy variable to indicate whether a lender is a
large bank, large bank. The relationship with non-main banks, which are supposed to be weaker
than that with main banks, also can affect the lending by GCBs, although it is not explicitly
modeled in the theoretical model. We control for this effect by introducing the interaction terms
of GCB f or SM E, N M B large, which is a dummy indicating whether a firm borrowed from a

non-main large bank in the pre-crisis period, and the crisis-phase dummies. Dummies of other
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types of lenders and their interaction terms with crisis-phase dummies are also included in our
estimation model.

6.3
6.3.1

Results
Main results

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The baseline results of the estimation are listed in Column (1), Table 10. The base category is
regional and cooperative banks. The first three coefficients show that GCBs for SMEs reduced its
lending in the pre-crisis period, but the trend reversed in the crisis. Most of our specifications are
consistent on this point.

The coefficient of GCB f or SM E × crisis × M B large (the row of GCB f or SM E × crisis ×

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relation in Column (1)) is positive and significant at a 1% significance level, i.e., GCB loans in
the crisis increased more for firms whose main bank is a large bank. The coefficient is 0.491. Since
the mean of ∆loan/asset for regional banks in 2009 is 0.44 (Figure 4), the impact is economically
significant. This result supports that GCBs for SMEs behaved as welfare-miximizers rather than

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profit-maximizers. This effect is still significant in the post-crisis period although the magnitude
is smaller than that in the crisis period. This extended effect is mainly because GCBs provide

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long-term loans only by the regulation.

The coefficient of GCB f or SM E × crisis × N M B large is also positive and significant. This

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result means that GCB loans increased more for firms who have borrowed from a non-main large
bank in the pre-crisis period. This result is also consistent with welfare-maximizing GCBs since they

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will increase loans to firms who receive less differentiated services from existing lenders including
non-main banks.

To clarify the change in the lending behavior of each type of main banks and GCBs, we sum-

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marize the marginal effects in Table 11 and Figure 6, which are calculated from the estimates in
Column (1), Table 10. The estimated marginal effects listed in Table 11 indicate the mean change
in ∆loan/asset for each type of banks relative to the mean of regional banks. The first row shows
that GCBs for SMEs reduced its lending in the pre-crisis period relative to regional banks, but they
increased in the crisis and post-crisis periods for firms whose main bank is a large bank (Column
i) while they did not for firms whose main bank is a regional bank or cooperative bank (Column

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ii), which supposedly maintains stronger relationship with SMEs. The second row shows that large
main banks keep reducing their lending (Column iii), whereas regional main banks increased its
lending in the crisis period (Column iv). The difference between them is statistically significant
(Column v). These points are consistent with the lending behavior of a welfare-maximizing GCB,

which increases lending more to firms whose main bank relationship is weaker and less likely to

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obtain additional loans from the main bank.

Columns (2)-(5) show the estimates with alternative measures of main-bank relationships. All
these results are consistent with welfare-maximizing GCBs rather than profit-maximizing. Columns
(2) and (3) are the results when we replace M B large with the loan or deposit share of the main

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bank, M B loan share or M B deposit share. Here, we posit that a main bank with a higher
share have stronger relationship with a firm. GCBs increased lending less for firms whose main
bank loan/deposit share is higher and has a stronger relationship with a main bank. This result
is consistent with the welfare-maximization by GCBs again. The coefficients of the interaction
terms of the main bank dummy (the latter half of the table) indicate a counter-intuitive result that

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those with stronger relationship obtain smaller amount of loans from their main bank in the crisis
period. This is probably because a part of the effect of the main bank share is captured by the

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large-bank dummy in the same way as in the baseline regression in Column (1), which is negative
and significant in the crisis period, since the main bank share negatively correlated with the large

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bank dummy as shown in Table 2.

Columns (4) is the result when we use the dummy indicating whether a firm switched main

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banks in the pre-crisis period as a measure of the strength of the main-bank relationship. We assume
that those has switched main banks should have weaker relationship with their main banks. The

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coefficient of GCB f or SM E × crisis × M B switch (the row of GCB f or SM E × crisis × relation
in Column (4)) is positive and significant in the same magnitude as in Column (1). This is also
consistent with welfare-maximizing GCBs. Among the control variables, main bank × M B switch
has a highly positive coefficient. This is because the loan growth of a main bank has to be higher
for switchers in the pre-crisis period due to the definition of M B switch, i.e., a switch to a new
main bank implies the increase of loans from the new main bank.
Column (5) is the result when we use the number of lenders except for GCBs in the pre-crisis
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period as a measure of the strength of the main-bank relationship. We expect that larger number
of lenders indicates the weak relationship with the main bank. The coefficient of GCB f or SM E ×
crisis × #lenders (the row of GCB f or SM E × crisis × relation in Column (5)) is positive and
significant. The economic significance is also large ∆loan/asset from GCBs for SMEs increases

by 0.537 in the crisis period for a firm with a single lender while it increases by 1.611 for a firm

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with the mean number of lenders, 3. This result is also consistent with the welfare-maximization
by GCBs.
6.3.2

Additional Tests against Alternative Explanations

Financial soundness of a main bank.

The result so far shows that large banks keep reducing

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SME lending and does not their lending despite of the surge of the fund demand. A possible reason
is that they are more severely damaged by the financial crisis than regional banks. To examine
this possibility explicitly, we introduce the interaction term of GCB f or SM E × crisis and the
risk-adjusted capital ratio of a main bank.10 If firms whose main bank is severely damaged turn

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to GCBs, then the coefficient of this interaction term should be negative. The result is, however,
the opposite (Column (1) in Table 12). Thus, the financial soundness of a main bank did not have

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a significant impact on the shift to GCBs. This result is plausible in light of the fact that the
Japanese banking sector was not seriously damaged by the financial crisis, as indicated in Figure

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5. In this specification, the coefficient of the key variable GCB f or SM E × crisis × M B large is
a little smaller than that in the baseline results, but still positive and significant.

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To control for time-varying bank characteristics including unobservable ones, we estimated a
model including bank×year fixed effects as well as firm×year fixed effects. The results are listed

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in Column (2) in Table 12. The coefficient of GCB f or SM E × crisis × M B large is positive
and significant. The estimated magnitude is also similar to the baseline estimation. This result is
consistent with welfare-maximizing GCBs.
Extensive margin vs. intensive margin.

To see whether this shift was concentrated on

those who kept borrowing from a GCB, or on those who started to borrow in the crisis period, i.e.,
10
We drop lending from Shinkumi banks, which are classified into regional banks in the other regressions, and other
institutions since the information of their risk-adjusted capital ratio is not available.

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