DBJ Discussion Paper Series, No.0903

How Does the Stability of Loan Relations
Depend on its Duration?
Evidence from Firm- and Bank-Level Data
Daisuke Miyakawa(Research Institute of Capital Formation,
Development Bank of Japan)

July

2009

Discussion Papers are a series of preliminary materials in their draft form. No quotations,reproductions or circulations should be made without the written consent of the authors inorder to protect the tentative characters of these papers. Any opinions, findings, conclusions or
recommendations expressed in these papers are those of the authors and do not reflect theviews of the Institute.

How Does the Stability of Loan Relation
Depend on its Duration?
Evidence from Firm- and Bank-Level Data
Daisuke Miyakaway
July 2009

Abstract
This paper empirically studies the stability of loan relations between Japaneselisted …rms and banks. By using a unique data set for Japanese bank loan market, …rst, we estimate the hazard function for the loan relations through nonparametric duration models. Then, with considering empirical …ndings that bankloan relations are systematically governed by the characteristics of …rms, banks, andmatches, the stability of relations is formally examined through semi-parametricand parametric duration analyses. The results support the existence of relationspeci…c capital discussed in the theoretical literature.
Key words: Bank loan relation; Stability; Duration analysis
JEL Classi…cation: G21, G32, C41

I thank Hugo Hopenhayn, Andy Atkeson, Lee Ohanian, Daniel Ackerberg, Isabelle Perrigne, Christian Hellwig, Pierre-Olivier Weill, Pierre-Yves Yanni, Shogo Hamasaki, Junichi Nakamura, KeiichiroOda, Pramuan Bunkanwanicha and seminar participants at UCLA Monetary Economics Proseminar,
Industrial Organization Proseminar, and DBJ Applied Economics Workshop for useful comments andsuggestions.
yResearch Institute of Capital Formation, Development Bank of Japan, 1-9-3 Otemachi Chiyoda-ku,
Tokyo, 100-0004 JAPAN. E-mail: damiyak@dbj.jp.

11

Introduction

Bank loans are one of the most important long-term …nancing sources in many countries(see Freixas and Rochet (2008) for a comprehensive survey). In fact, during the early 80s
in Japan, long-term bank loans comprised over 90% of the corporate’s total long-term
debt1 . While this ratio decreased during the 1980-1990s, it is still more than 70% as of2000 (see Figure-1 ).23
The dominant presence of bank loans in the liability of …rms has encouraged various
empirical studies regarding the determinants of loan relations. The existing empiricalstudies, however, focus almost exclusively on the determinants of the "number of banks"
in a …rm’s liability while implicitly assuming that banks in a loan relations with a …rm
are homogeneous. Yet, in the data, we observe many …rms repeatedly borrowing fromthe same banks, and in many cases, there is a "dominant" bank that accounts for alarge share of the …rm’s total liability. To illustrate, Figure-2 plots the number of banksfrom which a …rm borrows a long-term loan (horizontal axis) and the loan concentrationof the …rm’s long-term bank loan structure (vertical axis).4 For a given number ofbanks, we can clearly see a large dispersion of loan concentration. While there are some…rms exhibiting very ‡at loan share structures (i.e., the …rms locating close to the lower
envelop of the scatter plot), a number of …rms hold highly asymmetric loan relations.
Furthermore, in order to see whether such asymmetric loan shares have any stability ornot, Table-1 also shows the implied Markov transition matrix for the loan share of eachbank in each …rm’s loan portfolio (computed from our data set detailed below). The
large numbers on the diagonal elements roughly imply that the loan shares for each bankhas some persistence, and the loan relations are somewhat stable.5 This could provide
us some predictions that bank loan shares are both stable and asymmetric. The current
literature, however, has not considered these features in analyzing the determinants ofloan relations.
In this paper, we study the stability of loan relations between Japanese listed …rms andbanks, and its determinants by using a unique data set for the Japanese bank loan market.
Our paper complements the existing literature by incorporating the heterogeneous andstable nature of loan relations into the analysis. In our view, the asymmetric and stableloan share structure re‡ects various characteristics speci…c to each …rm and bank, along
1

Total long-term debt is de…ned as the sum of long-term bank loans and corporate bonds, both ofwhich have original maturities longer than one year.
2
This is the average of all the Japanese listed …rms (excluding the emerging markets like JASDAQ).
Note that we condition the data with a criteria that each …rm is operating over the sample period
1982-1999.
3
All the …gures and the tables are in the appendix.
4
The loan concentration is computed as the Her…ndahl index of each …rm’s long-term loan sharevector in 1999. A …rm’s loan Her…ndahl index is de…ned as a squared sum of long-term loan shares ofeach bank lending to the …rm. In this scatter plot, we use …rms belonging to all the industries.
5
This has been predicted in a few empirical literature (e.g., Tachibanaki and Taki (1991)). Other
existing papers (e.g., Horiuchi (1994)) also use various descriptive statistics to claim that this is a concretefeature.

2

with some relation-speci…c capital that makes loans not perfectly substitutable6 . This
"relation-speci…c" capital is a distinct feature of bank …nancing. For example, this typeof capital typically does not exist in the transaction-based …nancing in capital markets(i.e., bond and/or equity issuance).7 We conduct a duration analysis to examine thestability of bank loan relations. The results support the existence of relation-speci…ccapital, which gives rise to the stability of loan relations, as discussed in theoretical
literature. This is a relatively new perspective for the characterization of bank loan
relations.8
We also discuss the implications of having a "mainbank" status for the loan structure.910 Suppose a bank has a certain amount of shares of a …rm. This might extend the…rm’s credit availability from the bank, which in turn may improve the …rm’s outcome.
Alternatively, the existence of such a mainbank may send a good signal to other banks
and this can also improve credit availability. Thus, each bank’s position as a shareholder
may a¤ect the …rm’s loan structure and we are interested in investigating this issue.
This paper is structured as follows. Section 2 brie‡y surveys the related literature.
As a starting point, section 3 demonstrates a non-parametric estimation for a duration
model so as to study a potential shape of hazard function. Then, section 4 studies
the heterogeneous nature of loan relations and studies its determinants, which gives us
some ideas for the determinants of the stability. Section 5 uses semi-parametric andparametric duration models for the nature of the stability and its determinants. Section
6 compares our empirical results with existing studies and discusses some technical issues.
Section 7 concludes and presents future research questions.

2

Related Literature

As discussed in Ogawa et al. (2007), the existing theoretical literature regarding a …rm’s
optimal loan relations have focused exclusively on analyzing the optimal number of banks.
They summarize that the key determinants of the bank number are (i) transaction costswith banks (Bris and Welch (2005); Diamond (1984); Bolton and Scharfstein (1996)),(ii) interbank competition (Broecker (1990)), (iii) the severity of the hold-up problem(Sharpe (1990), Rajan (1992)), (iv) aggregate shocks (Detrangiache et al. (2000)), (v)the severity of the soft-budget constraint problem (Bris and Welch (2005); Bolton and
6

For example, Freixas and Rochet (2008) surveys various models explaining how the relationshipbetween two parties becomes a valuable asset through dealing with each other. Lummer and McConnel(1989) also documents a progressive transmission of privileged information to lenders.
7
We are not claiming that these relations associated with the capital market does not contain any
relationship-capital. Yasuda (2005) is one recent study that extends this view to the corporate-bondunderwriting. However, this type of capital is less important or not practical in capital markets.
8
See Ongena and Smith (2001) as one reference.
9
Mainbank is de…ned, for example, as a bank owning a major position as a share holder and loan
holder (Aoki and Patrick (1994)).
10
In Japan, banks are allowed to hold up to 5% of a …rm’s stock. Most European countries have
similar rules but this is prohibited in the U.S.

3

Scharfstein (1996)), and (vi) the type of business activity (Von Rheinbaben and Ruckes(1998)).
As with these theoretical studies, existing empirical studies have also taken a somewhat narrow perspective by analyzing this issue by only considering the number of banks
a …rm borrows from. For example, Ogawa et al. (2007) …nds that the …rm’s size, solvability, liquidity, and availability of alternative …nancing determine this number. The
negative correlation between the …rm’s pro…tability and number of banks has been established in a number of papers (see Degryse and Ongena (2001); Harho¤ and Korting(1998); Foglia et al. (1998); Gordon and Schmid (2000); and Machauer and Weber(1999)). However, Weinstein and Yafeh (1998) and a few other papers claim the opposite. Also, some studies establish a negative correlation between the number of banks
and interest rates, a proxy for risk (see Peterson and Rajan (1994); Degryse and Van
Cayseele (2000); Angelini et al. (1998); Machauer and Weber (1999)).
There are a few empirical papers referring to the multiple and heterogeneous bankloan relations. For example, Peterson and Rajan (1994) mentions that small U.S. …rms
have a very asymmetric bank loan structure. Similarly, Elsas (2005) documents thatbanks holding a very close relationship with medium-sized German …rms contributes, on
average, 44% of the …rm’s debt …nancing.11 In particular, Elsas (2005) examines whatcharacteristics of borrowers and lenders determine the incidence of haubank relationships
by using the self assessments of German universal banks. Our motivation is to supplement these casual …ndings by using more objective variables. Speci…cally, we consider
the share of the top lender and the duration of loan relations.12
Most of the existing theoretical studies for dynamic bank loan relations (e.g., Rajan(1992), Boot and Thakor (1994)) take the view that longer loan relations can mitigate
the information asymmetry between …rms and banks more e¤ectively. This implies that
longer loan relations are less likely to break up.1314 In the context of the duration model,
these theoretical studies predict that the hazard ratio of the loan relation exhibits thenegative duration dependency.
Contrary to this simple theoretic prediction, the results in the empirical literatureare somewhat controversial. Onegena and Smith (2001), a paper most closely related toours, examines such a theoretical prediction by applying the duration model to a panel
data for Norwegian bank loan market from 1979 to 1995 and …nds that such a theoreticalprediction is not necessarily supported by their data.15 They actually emphasize the11

Those banks are called as hausbanks in Germany and mainbanks in Japan. We will get back to thede…nitions of those banks later in this paper.
12
Obviously, an asymmetric loan share structure at a speci…c moment could just be a due to luck.
Hence, such objective items cannot be perfect either.
13
The duration is also called a "spell" in the literature. Following the literature, we use this terminology from this section.
14
This is a reason that the pricing pattern in Rajan (1992)’s model exhibits a similar dynamics toswitching cost models.
15
The data consists of matches between banks and Norwegian listed …rms. In their data set, thenumber of observed matches is around 100 to 150. This small number of matches partially re‡ects thefact that the data set does not contain a complete list of bank loan relations for each …rm (i.e., it only4

presence of a "positive" duration dependency of the hazard ratio in bank relations, which
is opposite to the theoretical prediction. They also examine …rms’characteristics as explanatory variables for the hazard function and establish that smaller, higher-levered,and higher-growth …rms, which are presumably exposed to a larger information asymmetry and can get a larger bene…t from a longer relation, tend to have shorter relationships.
They conjecture that these two results potentially re‡ect the …rms’anxiety to be trappedin a relation with the incumbent banks, which are presumably seeking some monopolistic
rent. We intends to revisit their study by using a larger data set in the Japanese bankloan market. The information in our data allows us to study the hazard ratio of therelationship as a function of the length of spell and some relation-speci…c factors alongwith other …rms’and banks’characteristics studied in Ongena and Smith (2001). Farinha and Santos (2002) is another related paper that applies the duration model to thedata in Portugal from 1980 to 1996. They are interested in how switching from a single
relationship to multiple relationships happens. Their main …nding is that the likelihoodof having switching from a single to multiple relations becomes higher as the duration ofa single relation becomes longer. Similar to Ongena and Smith (2001), they conjecturethat these results suggest that …rms are concerned about hold-up problems arising froman exclusive loan relation.

3

Stability of Loan Relation

In the introduction, we attempt to overview the stability of the loan relations through aMarkov Transition Matrix. Unfortunately, one caveat of the implied transition matrix
comes from the fact that we are using the data of outstanding "long-term" bank loans.
In fact, the large number in the diagonal elements might simply re‡ect the nature of
the long-term loan. One alternative way to examine the persistency of the loan sharestructure is a dynamic panel regression. Unfortunately, aside from the usual technicalproblems associated with the estimation of a dynamic panel, we have the exactly sameproblem as in the discussion of the implied transition matrix. Considering this point,
we employ duration models in this section to study the stability of loan relations.
The duration model allows us to explicitly analyze how the length of loan relations
between …rms and banks a¤ect the marginal stability of their loan relations. If thelonger loan relation helps the parties to accumulate some relation-speci…c capital, which
we expect to be the case, the hazard rate of the loan relation is decreasing as the duration
becomes longer. The goal of this section is to see whether or not our data exhibits sucha negative duration dependency of the hazard rate. The duration dependency gives us
an indirect evidence for the stability of loan structure.
Several existing literature has provided a view that a relationship between two parties
becomes more and more valuable for both sides over its duration, which might result in
lower costs and/or improved qualities of services (Freixas and Rochet (2008)). Following
contains the names of top 4 banks in a very subjective de…nition).

5this view, we conjecture the positive correlation between the duration of relations andthe stability of the relation16 .
Note that there exist similar examples in the context of employment, business alliance,and various …nancial transactions. In this paper, we are especially interested in how
valuable such an "intangible asset" is in the context of bank loan relations. Such a
discussion is also motivated by the fact that governments are sometimes concerned about
the survival of …rms that hold a close and exclusive loan relationship with failed banks.
The study of the relationship-capital allows us to see the implications of bank closuresfor …rm survival or growth.

3.1

Structure of Duration Model

3.1.1

Model

In this section, we summarize the basic structure of the duration model.17 The spell
T is de…ned as the duration of time passing before the occurrence of a certain random
event. In our case, the random event is a break-up of a loan relation between a …rm anda bank. The distribution of the spell can be summarized by a survivor function S (t),which denotes a probability that the event has not happened yet as of t.
S (t)

Pr (T

t)

The survivor function can be used to further de…ne the hazard function (t). This
represents a probability that the event happens in the next instantaneous moment conditional on that the event has not happened yet as of t.
8f (t)Pr(t+ >T tjT t)>= d lndtS(t) = S(t)< (t) lim
!0

where
>
: f (t) : Density associated with the distribution of spells

The goal of the duration model is to estimate the hazard function and the survivor
function while considering the e¤ects of some covariates.18 Suppose x and = f ; gdenote the vector of the covariates and the model parameter, respectively. Then, the16

Several papers have attempted to establish the existence of relationship banking (see James (1987),
Peterson and Rajan (1994), Berger and Udell (1995, 2006)). Most of these studies simply regress
the credit availability of each …rms on the existence of the relationship-lender by controlling for various
covariates. The duration analysis employed in this paper aims at revisiting this question from a di¤erent
perspective.
17
For more detailed discussion about the duration model, see Kiefer (1988).
18
By construction, a hazard function has the equivalent information to the corresponding survivor
function.

6

survivor function takes the following structure.
S (t; x; )Pr (Tt; x; )The proportional hazard model, which is one of the most widely used model speci…cation, assumes the hazard function (t; x; ) takes a multiplicative form consisting of(i) a component depending only on the duration 0 (t; ) and (ii) the other component
exclusively capturing the e¤ects of the covariates (x; ).
(t; x; )lim Pr(t+ >T tjT t;x; ) =
!0

0 (t;

) (x; )

If there is no censoring problem (discussed below) and we can somehow specify thefunctional forms for 0 (t; ) and (x; ), it is possible to estimate = f ; g by using
MLE with the data f(ti ; xi )g.19
8= arg max fln L ( )g
>
>
>
>
where
>
<
n
L ( ) = f (ti ; xi ; ) ; f (ti ; xi ; ) = (ti ; xi ; ) S (ti ; xi ; )
i=1
>
>
>
Rt
>
>
: S (ti ; xi ; ) = exp(s; xi ; ) ds
0

Note that all the objects in the likelihood function can be expressed as fairly simple
objects under some simpli…cation assumptions for 0 (t) and (x; ). For example, if
we assume the Weibull distribution for the spell 0 (t; ) =t 1 and use a standard
speci…cation (x; ) = exp ( 0 x), we have S (t; x; ) = exp f t exp ( 0 x)g.

3.2

Discussion

Before estimating the duration model, we discuss some technical issues.
3.2.1

Censoring Problem and the Adjustments

One typical problem associated with the duration data is censoring. Figure-3 illustrates
four major cases of censoring. The straight lines correspond to observed spells while thedashed lines represent unobserved spells. For example, we can observe the beginningof the spell for observation-2 but do not have information about the end of these spells.
All we know is that the spell has survived at the end of the observation period.
If all of our observations are non-censored (i.e., observation-1), we can simply apply
19

ti and xi denote the length of completed spell for i-th observation and the set of (potentially timevarying) explanatory variables for the i-th observation, respectively.

7the MLE explained above to the data. However, the existence of censoring requires us
to make adjustments.
Right-Censoring For right-censoring, the adjustment is well established and straightforward (Kiefer (1988)). The idea is to treat the right-censored observations as survivors at the end of the observation period. In order to use the information that theright-censored observations have survived at this timing, we can simply use a Tobit-typeadjustment to the likelihood function.
8
n
R
R
R
>
L
(
)
=
ff (ti ; xi ; )gdi fS (ti ; xi ; )g1 di
>
>
i=1
<
where
>
>
1 if i-th observation is not right-censored
>
: dR
i =
0 if i-th observation is right-censored

We use this adjustment for our data.20 Note that if we are only considering rightcensoring, nonparametric estimation for the survivor function (e.g., Kaplan and Meier(1958)) can easily be done.
Left-Censoring The adjustment for left-censoring is less straightforward. One simple
way to deal with this problem is to discard the left-censored observation, which has often
been employed in empirical literature.21 Ongena and Smith (2001) employs this strategy
and discusses the possibility that their estimation for the duration is overestimated.22
We follow the existing literature and simply discard the left-censored observations in thispaper.
3.2.2

Determination of the spell

Ongena and Smith (2001) de…nes the duration of relationships to be the number ofconsecutive years for which a …rm lists each bank as primary banks23 . In our data set,
determining the beginning and end of the relationship in itself is an issue. In particular,considering that we can only capture the match between banks and …rms through theoutstanding loan amount, we need to be careful about such determinations. Note thateven if a bank-…rm pair does not have a positive outstanding loan in a speci…c year,
it does not necessarily mean that the relationship broke since it could be that the …rm
simply did not have …nancing needs that year. Considering this point, we employ thecriteria that the end of match is de…ned as an observation of zero outstanding loans in
20

Ongena and Smith (2001) is also using this adjustment.
Heckman and Singer (1984) shows that this method leads to ine¢ cient but consistent estimators.
22
Amemiya (1999) proposes a likelihood function for the left-censored data.
23
In Norway, listed …rms are obliged to report its primary bank relationships (up to 4 banks) in its
report to the Oslo Stock Exchange.
21

8

5 consecutive years. We assume that the absence of the loan provision for such a long
period can be recognized as a termination of their relationship.24
3.2.3

Heterogeneity in Loan Maturity

Our data set does not contain the detailed information about each loan contract but
only the sum of long-term loan amounts from one bank to one …rm. Considering thatour de…nition of the duration is potentially a¤ected by the maturity of each loan, it isbetter to control the heterogeneity in loan maturity. One way to control this e¤ect is
to include (i) …rm’s short-/long-term bank loan ratios for each incumbent bank and (ii)bank’s type (e.g. long-term loan bank & trust bank dummy versus other banks dummyetc.) as explanatory variables. These terms can partly capture the heterogeneity on theloan maturity. Due to the limited availability of short-term bank loan amounts from abank to a …rm, we cannot use (i).25 We employ (ii) in the later discussion.

3.3

Data

We construct a …rm- and bank-level data set for the Japanese long-term bank loan
market.26 The …rst data source is DBJ Corporate Financial Databank, which storesthe loan amounts from each bank to each …rm and each …rm’s …nancial characteristics.
The second data source is the …nancial statement of each bank provided by the Japanese
Banker’s Association, which stores each bank’s …nancial characteristics. Following theliterature, we exclude …rms in utility, realty, construction, retail, and wholesale industries.
Then, we merge these two large data sets and construct a balanced panel data from 1982
to 1999. As a result of this balancing, the data set consists of 1518 …rms and 148
banks. We construct this balanced panel data in order to exclude the demographice¤ect associated with the entry and exit of …rms. As far as we know, this combined
data set has never been used to analyze bank loan relations. Figure-4 illustrates the
structure of the data.
The unique feature of this data set is that it contains the outstanding loan amountfrom each Japanese bank to each listed …rm, as well as the …nancial characteristics ofeach …rm. In comparison, Ongena and Smith (2001) uses a data set with a similar
structure but contains only the name of at most three banks associated with each …rm.
The complete information about …rms’loan structure and bank’s information in our data
set allows us to characterize each …rm’s bank …nancing structure in a much more precise
24

Precisely speaking, this …ve-year rule a¤ects the starting date of each spell since we need to observeat least …ve-year blank before each spell starts. Instead, we treat all the fresh spells over the sample
period as starting from the date we observe the initiation of relationships. We think this does not makea serious problem with considering that the estimated results under di¤erent criteria for spell are similar
to the current …ve-year rule.
25
Short-term loan data is only available for 1998 and 1999 in our current data set.
26
Throughout the paper, we use the standard de…nition for long-term loans; that is, loans with original
maturities longer than 1 year.

9

way than existing studies.
We have some remarks about our data set. First, in order to capture the status ofloan relations between a bank and a …rm, it might be better to use short-term lending
information. This is because a positive outstanding loan at a speci…c year does notnecessarily imply that there was an active …rm-bank loan relation in that year–it may
just re‡ect a past transaction. Thus, using short-term loan data would decrease our
exposure to this problem. However, our current data set only contains short-term loan
data for 1998 and 1999, and thus, we need to rely on the long-term loan data (i.e.,maturity greater than 1 year as of lending/borrowing)27 . Nonetheless, we think thatthe provision of such long-term loan implies a close relationship between the …rm andbank. In this paper, we exclusively focus on the long-term loan information based on
this perspective. Second, we ignore all other transactions between …rms and banks(e.g., payment transaction, bond/equity underwriting, provision of credit line, businessconsulting, debt guarantee, factoring, and bill discount) that might also represent the…rm-bank relation. Because of the limitation of our data set, we cannot account for allof these transactions. Since loan provision is the most important activity for the relation
between …rms and banks, we believe that our approach is permissible.
From the data set detailed above, we can construct the duration data for each match
between a given …rm and a given bank. As already mentioned, each spell is assumed
to end if we observe zero outstanding loans in 5 consecutive years. We discard theleft-censored observations while the right-censoring is adjusted through the method explained in Kiefer (1988).28 Figure-5 illustrates the data structure and the number ofobservations. We use sample-1 and -2 for our duration analysis. Figure-6 presents the
distribution of the spells based on these two samples. We can see that the distribution
is highly skewed but it contains a certain number of observations over the long duration.

3.4

Univariate Analysis

Table-2 shows the summary statistics of our data set for 1999. The …rst group ofvariables (L-Share, L-Amount, TOPL-Share, and TOPL-Amount) are taken for eachmatch. L-Share and L-Amount represents the bank’s share in a …rm’s total long-termbank loan and its loan amount conditional of those two numbers are strictly greater thanzero, respectively.29 Similarly, TOPL-Share and TOPL-Share stands for the top lender’sshare in a …rm’s total long-term bank loan and its loan amount.
The second (BankNum, F-TBLT, F-Size, F-ROA, F-LR, F-LEV, F-STLT, F-BTD)
and the third groups of variables (B-Size, B-ROA, B-CTA, B-TETA, B-IHI ) are taken
for each …rm or bank. BankNum represents the number of banks a …rm is borrowing
from. F-TBLT is the amount of a …rm’s total long-term bank loan. F-Size is …rm size,
27

We are currently constructing a similar data set for short-term bank loans in Japan.
Again, we treat all the fresh spells over the sample period as starting from the date we observe theinitiation of relationships.
29
In this sense, the average of those numbers are conditional means.
28

10represented by the …rm’s total asset. Each …rm’s pro…tability is measured by F-ROA
computed from the …rm’s EBITDA divided by its total asset where EBITDA denotes
the earning before interest payment, tax payment, depreciation, and amotization. Each…rm’s liquidity asset-to-liquidity liability ratio F-LR is used to measure a …rm’s liquidity.
F-LEV and F-STLT are used for measuring a …rm’s leverage and debt maturity.30 The
variables for banks (B-Size, B-ROA, B-CTA, B-TETA, B-IHI ) are de…ned in a similar
fashion. Note that B-Size is measured by the total loan assets (not simply by total
assets), liquidity is measured by the cash-to-total asset ratio B-CTA, and B-TETA isused to denote the total equity-to-total asset ratio, a proxy for …nancial stability.
One unique feature of our analysis is that we compute the industry concentrationof each bank’s loan portfolio, denoted B-IHI. This represents the industry Her…ndahl
index for each bank’s loan portfolio. Note that this index represents each bank’s industry
concentration only for listed …rms and not for each bank’s overall portfolio. Nonetheless,we think that this index is still useful to characterize the degree of specialization of eachbank.
The last variable (MKT-LOAN ) in the table represents the market size of the bankloan market, which is computed by the simple sum of all banks’loan assets.
From these summary statistics, we can obtain a rough impression that the top lender’sshare (0:47) is asymmetrically high on average, compared to other lenders if we consider
the average number of banks (9:8 banks). Also, we can …nd a high dispersion in the
distribution of loan shares. As we brie‡y observed in Figure-2, each banks’loan sharesare asymmetric. In the later subsection, we use the top lender’s loan share as one
representation of the asymmetric loan share structure.

3.5

Non-Parametric Estimation Results

In this section, we show our estimation results based on a non-parametric estimation
method. The bene…t of this method is that we do not need to assume any speci…cfunctional form for the hazard function.
First, Kaplan-Meier’s estimator de…ned below gives us an estimated survivor function.
Figure-7 depicts this non-parametrically estimated survivor function where two dashedlines represent 95% con…dence intervals.
8
t
>
nj dj
>
: Kaplan-Meier’s estimator for survivor function
Sb (t) =
>
>
nj
j=0
<
where
>
>
nj : Number of observations that have not failed or censored at the beginning of j>>
: d : Number of failures occurring to these observations during jj30

F-STLT represented the ratio of short-term debt to the long-term debt.
the debts including bank loans and other debts (e.g., corporate bond).

11

For F-STLT, we use all

Then, we can use the de…nition of the hazard function to compute the hazard function.
Figure-8 depicts this non-parametrically estimated hazard function with a polynomial
approximation.
nob (t) =
ln Sb (t) ln Sb (t 1)

Alternatively, we can use Nelson-Aalen’s estimator for a cumulative hazard function(de…ned below). Then, we can approximate the hazard function by using a Gaussian
kernel with a speci…c bandwidth. Figure-9 depicts the estimated hazard function withthe approximated hazard function smoothed by Gaussian kernel with bandwidth 2.
X djb (t) =H
: Nelson-Aalen’s estimator for cumulative hazard functionnj
jjtj t

The downward sloping parts of these two estimated hazard functions imply the negative duration dependency of the hazard ratio. We also …nd a positive duration dependency over relatively shorter durations, which potentially re‡ects the nature of thesample. Since all the duration is measured solely by the outstanding long-term loan, it
is possible for the duration to increase for the …rst few years. Presumably, the samples
are simply paying back the debt over the …rst few years without borrowing again. An
important …nding is that we still have a negative duration dependency for the sample
with a longer duration than 5 years.

4

A Detour: Asymmetry of Loan ShareThe non-parametric method demonstrated in the previous section cannot control covariates. In order to proceed to semi-parametric and parametric duration models, we study
the determinants of heterogenous bank loan relations in this section. As a proxy for theheterogeneity of loan relations, we use the top lender’s loan share for each …rm. If sucha share is high, the …rm is considered as having a highly heterogeneous and asymmetricloan relations.

4.1

Preliminary Discussion

In order to empirically establish the determinants of the top lender’s share, we can use
the established determinants for the number of banks in the existing literature. First, we
can conjecture that a larger …rm tends to have a top lender with a smaller share, which
is a widely accepted empirical fact. Second, we examine the impact of a …rm’s risk as apotential determinant of the top lender’s loan share. This re‡ects the view establishedin the existing literature (Peterson and Rajan (1994); Degryse and Van Cayseele (2000);
Angelini et al. (1998); Machauer and Weber (1999)). Third, considering that a certain
number of empirical studies have established that …rms with high pro…tability tend to be12

…nanced with a more concentrated loan structure (e.g., Gordon and Schmid (1996); Foglia
et al. (1998); Harho¤ and Korting (1998); Machauer and Weber (1999); Degryse andOngena (2001); Farinha and Santos (2002)), we use …rms’pro…tability as one potential
determinant of the top lender’s loan share.

4.2

Firm SizeFirst, we check our conjecture that a larger …rm has a less asymmetric loan share structure, which implies a smaller likelihood for a larger …rm to have a top lender with a very
high loan share. For example, the existence of a …xed transaction cost induces a small…rm to use a limited number of banks (Diamond (1984)). The same argument holds
when banks have some …xed cost for screening and/or monitoring. In order to coverthese costs, the top lender’s loan share may need to be high for small …rms. Anotherpossibility is that if the geographical distance is important for the implementation of
screening and/or monitoring, larger …rms (with many subsidies and projects) might needto deal with a wide range of banks located in various regions (Hauswald and Marquez(2005)). Alternatively, the existence of lending limits of each bank can also account for
the negative correlation between …rm size and top lender’s loan share.
4.2.1

Firm’s Assets

In order to examine this conjecture, Figure-10 depicts the likelihood of having a top
lender with at least a certain level of loan share (i.e., 50%, 70%, and 90%) over di¤erent
levels of …rm size.31 Apparently, larger …rms are more likely to have a top lender whichholds a higher loan share. From these results, we can conjecture that there is a negative
correlation between the top lender’s share and the …rm’s total size. This will be examined
more formally in a later section.
4.2.2

Firm’s Debt

As another proxy for …rm size, we can use the size of total debt.32 This number can also
be interpreted as the asset size …nanced by debt. Figure-11 illustrates the likelihood of
having a top lender with at least a certain level of loan share (i.e., 50%, 70%, and 90%)
over the long-term bank loan size.33 Figure-12 repeats the same illustration for total
long-term debt (i.e., bank loan and other long-term debt). Both graphs indicate theclear negative dependency of the top lender’s loan share over …rm size.
31

We set the horizontal axis by thirty bins of the log of asset size.
Firm’s indebtedness might be recognized as a proxy for risk. However, since the size of debt itself
does not represent the risk, we use leverage to represent the risk in the later discussion.
33
For this …gure, we set the horizontal axis by thirty bins of the log of long-term bank loan size.
32

13

4.3

Firm’s Leverage

Second, as a proxy of a …rm’s risk, we use a …rm’s leverage. As Bolton and Scharfstein(1996) carefully models, banks may try to keep their loan share for risky …rms at a certain(low) level. This re‡ects the banks anxiety about being locked-in to the loan relation.
Their model demonstrates how such a dispersed loan share structure prevents a …rms
from strategically defaulting. Alternatively, the negative correlation between a …rm’s
riskiness and its top lender’s loan share can be interpreted as a re‡ection of each bank’s
optimal portfolio choice as modeled in Pyle (1971) or Hart and Ja¤ee (1974). In theirmodels, each bank solves a standard optimal portfolio choice problem. As long as there
is some correlation among the repayments of each …rm, banks try to diversify the risk bychoosing the appropriate sizes of loans for each …rm.
Figure-13 depicts the likelihood of having a top lender with a certain level of loan
share over …rm leverage.3435 Apparently, …rms with a lower leverage, which is presumably
associated with lower risk, are more likely to have a top lender with a high loan share.
Although there is a spike over the very high leverage, the overall tendency implies thatthe top lender’s share negatively depends on a …rm’s total size.

4.4

Firm’s Pro…tability

Third, we examine the correlation between the …rm’s pro…tability and the top lender’sloan share. Pro…tability is an well established determinant for the optimal number ofbanks in the existing literature (Degryse and Ongena (2001); Harho¤ and Korting (1998);
Foglia et al. (1998); Gordon and Schmid (2000); Machauer and Weber (1999)). Ourconjecture is that there is a positive correlation between a …rm’s pro…tability and its top
lender’s loan share. Again, Figure-14 depicts the likelihood of having a top lender witha certain level of loan share over …rm pro…tability.36
Unlike the theoretical prediction, the pro…tability does not seem to a¤ect the likelihood of having a top lender with a certain level of loan share. In order to see themarginal e¤ect of the …rm’s pro…tability to the top lender’s loan share more precisely, we
might need to appropriately control covariates. This point is examined formally below.
34

We set the horizontal axis by eighteen bins of the leverage.
Note that interest rates associated with each loan from one bank to one …rm or the averaged interest
rate for the total outstanding loan of one …rms can be interpreted a more direct measure of each …rm’s
risk. Unfortunately, due to the limitation of our data, we cannot use the interest rate as a proxy forrisk.
36
We set the horizontal axis by thirty bins of the …rm’s ROA.
35

14

4.5

Panel Regression

4.5.1

Heterogeneous Loan Relations

For the graphical illustrations demonstrated so far, we have only used …rm-speci…c characteristics as the potential determinants of the loan structure. In this section, we additionally incorporate bank-speci…c characteristics and an aggregate factor to the analysis.
We run a panel regression using a top lender’s loan share as a dependent variable while
using the characteristics of each …rm and its top lender, and an aggregate factor as explanatory variables. For this regression, we set each match between a …rm and its top
lender as a group. Since a …rm might change its top lender for di¤erent years, our data
inevitably takes the form of an unbalanced panel data.
For model selection, pooling estimate is rejected from Breusch-Pagan test and randome¤ect estimation survives. Then, Hausman-test rejects the null hypothesis that the
random-e¤ect estimation is not correlated with regressors. As a result of these standard
test procedure for model selection, we choose the …xed-e¤ect model. Table-3 summarizes
the estimation results.
First, our estimation result supports the three conjectures raised in the previous
section. Both …rm size and leverage have negative coe¢ cients for the top lender’s loan
share. Moreover, …rm pro…tability has a positive e¤ect on the top lender’s loan share inthis panel regression, which is consistent with the results of the existing theoretical andempirical studies. Other than these three items, …rm’s liquidity has a positive e¤ect on
the top lender’s loan share. This is somewhat consistent with the result established in
Detrangiache et al. (2000), which argues that a liquidity shock to banks a¤ect the optimal
number of banks. Our result implies that …rms with higher liquidity are more likely tochoose the banks with higher loan shares. Firm’s reliance on bank loan compared toother …nancing channels also has a negative e¤ect on the top lender’s loan share. This canbe interpreted as one illustration of Bolton and Scharfstein (1996)’s argument explained
above.
Second, bank size also has a positive e¤ect on the top lender’s loan share while thepro…tability, liquidity and …nancial stability have no signi…cant e¤ects. This contradicts
the result in Detrangiache et al. (2000). This may re‡ect the fact that Japanese…rms were not concerned about bank failures since the Japanese banking sector was
highly protected until the 1980s. Another interesting result is that the bank’s industry
specialization index has a positive e¤ect on the top lender’s loan share, which implies
that the industry specialization of each lender actually a¤ects the loan structure.37
Third, from the aggregate view point, we can con…rm that the size of loan marketa¤ects the top lender’s loan share negatively. One interpretation would be that the larger
availability of funds in the market, which can be accompanied with a higher interbank
competition, reduces the relationship-lending as demonstrated in Rajan (1992). Lastly,
37

This point is discussed theoretically in Boot and Thakor (2000) and empirically examined in, forexample, Degryse and Ongena (2001).

15

…rms are more likely to concentrate the loan relation during a boom (i.e., 1980s). Thisis consistent with the result of, for example, Detrangiache et al. (2000).
Bank’s Status as a Shareholder In Japan and many European countries, banks areallowed to hold non-…nancial company’s stocks as a large shareholder. This simultaneous
position as a lender and a shareholder is sometimes called as a mainbank relation.38 In
this section, we study the impact of this mainbank status to the top lender’s loan share.
We use the following three de…nitions of the mainbank relation: (i) the top lenderis also the top shareholder, (ii) the top lender is among the top three shareholders, and(iii) the top lender is among the top ten shareholders. Table-4 summarizes the panel
regression based on de…nition (i). We are interested in the coe¢ cient of the dummy
variable taking one if the top lender satis…es de…nition (i). As the table shows, wecannot reject that the coe¢ cient is zero for any of the de…nitions (see Table-4 to Table6 ).
Presumably, the mainbank status has several di¤erent e¤ects on the top lender’s loan
share. First, the status as an important shareholder might induce the top lender toprovide a larger credit availability which leads to a larger share. Second, contrarily,
excess exposure to one …rm induces its mainbank to reduce the loan share. Third,
the existence of the mainbank might send a preferable signal about the …rm to other
lenders, which in turn extends the credit availability from other banks. The current
panel regression roughly con…rms that non of these forces are dominant.

4.6

Summary

In this section, we have illustrated how the observed heterogenous loan relations re‡ects …rm-speci…c characteristics, bank-speci…c characteristics, aggregate variables, andrelation-speci…c characteristics (i.e., the incumbent loan share). These casual observations are veri…ed through a panel regression.
We have con…rmed that (i) smaller, pro…table, less risky …rms with less reliance onbank loans are more likely to have a top lender with a larger loan share, (ii) larger bankswith higher specialization are more likely to have a higher loan share as a top lender,and (iii) loan market size has a negative impact on top lender’s share. These results areused to study semi-parametric and parametric duration models in the next section.

5

Stability of Loan Relation in Parametric Models

Using the …ndings we obtained in the previous section, we estimate parametric duration
models in this section. First, we apply Cox’s semi-parametric estimation method. Note38

For the intensive discussion about Japanese mainbank system, see Aoki and Patrick (1994) and Aoki
and Saxonhouse (2000).

16

that we do not need to put any restrictions on the functional form for the baseline hazard
function. By using the estimators, we can back out the hazard function graphically. This
gives us some ideas for the model selection in parametric duration models, the results ofwhich we discuss in the last section.
5.0.1

Semi-parametric Estimation

The negative duration dependency observed in the non-parametric estimation might re‡ect the characteristics of …rms and banks. For example, …rms with low pro…tability
might …nd it di¢ cult to …nance their project through the capital market and may needto rely more on bank loan …nance for a long period. The non-parametric estimation
demonstrated above cannot distinguish such e¤ects of covariates from the pure duratione¤ect. Cox’s partial likelihood model (Cox (1972)) is useful to extract this duratione¤ect while controlling other characteristics.3940
Figure-15 depicts the estimated baseline hazard function h0 (t) and Table-7 summarizes the estimation results associated with the covariates. First, Figure-15 shows the
positive duration dependency for the shorter durations and the negative dependency ofthe duration for longer durations. These results have the same implication as in the
non-parametric estimation. Second, several characteristics of …rms and banks a¤ect the
duration. The estimated coe¢ cients imply that …rms with higher pro…tability, higher
liquidity, and higher leverage tend to terminate loan relations in shorter periods. Furthermore, banks with smaller size, higher pro…tability, higher liquidity, and lower …nancial
stability tend to terminate loan relations in shorter periods.
Figure-16 and Table-8 repeat the same estimation for the mode with the specialization
matching index, which is the multiplication of each bank’s industry specialization index(B-SPI ) and the dummy variable taking one if a …rm’s industry is in the top threeindustries a bank is exposed to.41 The important result is that such a specialization
matching leads to a longer loan relations. Even after controlling for all these factors,
we can still observe a negative duration dependency over the relatively longer duration(e.g., longer than 7 years). This supports our conjecture about the relationship-capital.
39

This method is called a semi-parametric estimation since we still do not need to specify any functional
form for the baseline hazard function.
40
For this estimation, we use the characteristics of …rms and banks, and one match-speci…c variablemeasured at the end of the previous year to the actual matching. In this sense, we estimate the duration
model with time-invariant covariates.
41
a variable B-SPI as a proxy for each bank’s industry specialization: B-SPI for Bank b
P We2 de…ne2k
SP Ibt1 where J is the total number of …rms, Jk is the total numbers of …rms in Industryk Jk =Jkk, and SP Ibt 1 is the ratio of (i) the probability that two …rms from Industry-k pool are borrowing
from Bank-b and the probability that two …rms in ALL industries pool are borrowing from Bank-b.
Intuitively, this variable represents how likely the …rms in a speci…c industry are borrowing from a givenbank b.

17

5.0.2

Parametric Estimation

The result in the semi-parametric estimation gives us a conjecture about the appropriate
distribution of the spell.
The Weibull distribution is widely used in the literature. This distribution allows us
to check whether the baseline hazard exhibits a monotonically increasing or decreasing
shape over spells. Since we have already observed the non-monotonic form for thebaseline hazard from the Cox’s method, it is not appropriate to assume the Weibull
distribution. For the same reason, we cannot use the exponential distribution since it only
covers the case that the hazard ration is independent from the duration. One possibility
is the log-logistic distribution, which accounts for (i) the monotonically decreasing hazardand (ii) the hazard increasing initially and decreasing later over the duration.42 Tables-9and -10 summarize this estimation results.
First, the estimated gamma is smaller than 1, which means the hazard increases andthen decreases over the spells. This con…rms our observations in our parametric andsemi-parametric estimations. Second, the estimated coe¢ cients are consistent with theone in the parametric and semi-parametric estimations. Note that we are using theaccelerated failure-time formulation for the current estimation while the proportional
hazards formulation is employed for Cox’s proportional hazard model. Due to thisdi¤erence, the signs of each coe¢ cient must be opposite in these two estimations.

6

Discussion

6.1

Comparison with Existing Studies

Ongena and Smith (2001) emphasizes the positive duration dependency of the hazard
ratio and the estimated coe¢ cients in their duration analysis as a re‡ection of …rms’
concern about the rent extraction of their incumbent banks. They conjecture that …rms
with a higher information asymmetry (e.g., higher leverage) try to terminate the loan
relation in a shorter period since they anticipate that they will be locked in the loan
relation with the incumbent banks.
In our estimation, we have a similar estimated coe¢ cient for …rm’s leverage (i.e.,higher leverages imply shorter durations) but a negative duration dependency. First,
the negative duration dependency established in our semi-parametric estimation over
the relatively longer duration range implies that the accumulation of relationship-capitalhas some value.43 Actually, Ongena and Smith (2001) also …nds the similar patternof the duration dependency through a parametric estimation of log-logistic distribution.
42

See, for example, Cleves et al. (2004) pp. 240-.
For example, Miyakawa (2009) models the emergence of relationship-lending without relying on
asymmetric information. It demonstrates how the sustained loan relation improves the quality ofchosen projects, which originated from the perspective in Hauswald and Marquez (2003).
43

18

In this sense, our result is not necessarily inconsistent with theirs. We would rather
emphasize the …ndings that (i) it takes a certain length of time to establish valuablebank relations and (ii) the duration data is contaminated by the nature of long-termloans. Through a further analysis based on, for example, the short-term bank loandata, we can actually verify this claim more precisely. Second, if we take the view
explained above, the coe¢ cient of …rm’s leverage can be interpreted in a di¤erent way
from Ongena and Smith (2001). In particular, "banks" might try to keep the relation
with these overindebted …rms at a relatively low level since they consider the possibilityof being trapped in the loan relation with them (Bolton and Scharfstein (1996)). Notethat we have already con…rmed in the previous section that …rms with higher leveragetend to have a more dispersed loan structure. This gives us a conjecture that banks
determine the optimal loan share by considering the …rm’s risk while sustaining loan
relations still gives rise to some positive value. The estimated coe¢ cients in our panel
regression and duration analysis are consistent with this story.

6.2

Technical Issues

Note that there are still two potential problems: (i) heterogeneity in loan maturity and(ii) left-censoring problem. We have already discussed how we can potentially deal
with the …rst problem. The second problem can be adjusted, for example, by the way
explained in Amemiya (1999) which proposes a likelihood function for the left-censoreddata. The basic idea is to (i) separately express the likelihoods for the left-censored andnon left-censored observations by using the following entry ratio function to the spell, and(ii) weight each likelihood by the probabilities of having these two types of observations.
e ( t j x; ) = lim Pr(In the spell at

tjNot in the spell at t

;x; )

!0

As Amemiya (1999) and D’Addio and Rosholm (2002) detail, however, we need toknow the shape of e (t j x; ) in order to implement MLE. If we employ the simplest
speci…cation for e (t j x; ) = e (x; ) (i.e., stationary entry ratio), the likelihood function
is known to become quite simple. We can combine this adjustment methods for leftcensored data with the Tobit type adjustment for right-censored data. One remark isthat the stationary entry ratio assumption is convenient but obviously restrictive. We
need to implement a test for the stationarity assumption. We leave this adjustment forleft-censoring as a future research question.

7

Concluding Remarks

This paper studies the determinants of a …rm’s bank …nancing structure. In addition to
the number of banks, which has been exclusively discussed in the existing literature, theasymmetry of each bank’s loan share is examined. By using a unique data set for the19

Japanese bank loan market, we document the heterogenous and somewhat stable loan
share structure, and establish the determinants of the loan relations. We have con…rmedthat (i) smaller, pro…table, less risky …rms with less reliance on bank loans are more likely
to have a top lender with a larger loan share, (ii) larger banks with higher specialization
are more likely to have a higher loan share as a top lender, and (iii) loan market size has
a negative impact on top lender’s share. The stability of bank loan relations are also
examined through a duration analysis. The results support the existence of relationspeci…c capital, at least for a relatively longer duration range, which gives rise to thestability of loan relations as discussed in theoretical literature. We also con…rm that…rms with higher pro…tability, higher liquidity, higher leverage tend to terminate loan
relations in shorter periods. Furthermore, banks with smaller size, higher pro…tability,
higher liquidity, and lower …nancial stability also tend to terminate loan relations inshorter periods.
To conclude, we list several future research questions. First, we advance our analysis
to the data on short-term bank loan relations. The contamination of the data set by thenature of long-term loan relations potentially biases the estimation of duration model.
In order to extract the implication for the value of sustained loan relations and compare
it with the existing literature, we need to …nish such an additional analysis. Second, weneed to re…ne the estimation with a proper treatment for the technical issues discussed inthis paper. For example, the left-censoring problem needs to be adjusted by, for example,
Amemiya (1999)’s method. The heterogeneity in loan maturity is also an important
problem we need to address. Third, other transaction between …nancial institutions
and …rms can be analyzed. Yasuda (2005) empirically studies the relationship basedon bond underwriting services and found somewhat similar result we obtained in thispaper. Fourth, in order to directly establish the value of relationship-capital, it might
be better to use some structural model instead of the reduced form analysis employed inthis paper and other existing studies. In fact, the negative duration dependency itself
cannot completely guarantee the existence of relationship-speci…c capital since it may
just re‡ect an informational captivity. The structural model constructed in Miyakawa(2009) is one model that can be used to go in this direction.

20

Appendix: Table and Figure
Bo r ro w in g- to - ( Bo r ro w in g+ Bo n d) Ratio
1
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
1982

1986

1990

1994

1998

Data source: DBJ Corporate Financial Databank.2

Firm's loan Herfindahl index
.4
.6
.8

1

Figure-1: Long-Term Bank Loan / Total Long-Term Debt

0

8

0

10

20
30
BANKNUM_T

40

Data source: DBJ Corporate Financial Databank
Figure-2: Asymmetric Bank Loan Structure in 1999

21

50

SHARE=0(0, 0.01](0.01, 0.05](0.05, 0.1]
(0.1, 0.2]
(0.2, 0.3]
(0.3, 0.4]
(0.4, 0.5]
(0.5, 1.0)
SHARE=1

1
2
3
4
5
6
7
8
9
10

SHARE=0(0, 0.01]

1
0%
20%
8%
5%
5%
5%
5%
6%
6%
19%

2
14%
70%
9%
0%
0%
0%
0%
0%
0%
0%

(0.01, 0.05]

3
32%
8%
74%
14%
2%
1%
0%
0%
0%
0%

(0.05, 0.1]

(0.1, 0.2]

4
18%
1%
7%
68%
12%
2%
1%
0%
0%
1%

5
17%
0%
1%
10%
72%
17%
4%
2%
2%
1%

(0.2, 0.3]

(0.3, 0.4]

6
8%
0%
0%
1%
7%
65%
17%
6%
2%
1%

7
4%
0%
0%
0%
1%
9%
59%
17%
4%
2%

(0.4, 0.5]

8
3%
0%
0%
0%
0%
1%
10%
55%
10%
1%

(0.5, 1.0)

9
3%
0%
0%
0%
0%
1%
3%
13%
69%
7%

Data source: DBJ Corporate Financial Databank
Table-1: Persistency in Asymmetric Bank Loan Structure

Observation-1

No censoring

Right-censoring

Observation-2

Observation-3

Observation-4

Left-censoring

Left- & Right-censoring

Time

Observation Period

Figure-3: Four Types of Censoring

22

SHARE=1

10
2%
0%
0%
0%
0%
0%
0%
1%
5%
68%

All the Japanese Listed Firms
For t = 1982,… ,1999

Firm-Jx1t

Bank-1

L11t=100

0

…

0

…

0

30

x2t

Bank-2

0

0

…

5

…

100

20

…

…

Lijt=5

0

0

…

…

…

Firm-(J-1)

…

…

…

Firm-j…

…

…

Firm-2…

Firm-1…

(At t)…

Characteristics
Vectorfor Bank

…

yJt

…

yJ-1t

…

…

…

yjt

…

…

…

y2t

…

y1t

…

All the Japanese Banks

Characteristics
Vectorfor Firm

xitBank-i

50

0

xI-1t

Bank-(I-1)

70

40

…

20

…

0

0

xIt

Bank-I

0

30

…

0

…

100

10

Figure-4: Illustration of Data Structure

Observation-1
1540 obs

Non-censored spell

Right-censored spell

Observation-2
2708 obs
Observation-3
4741 obs
Observation-44948 obs

Left-censored spell

5 yrLeft- & Right-censored spell
Observation Period
Time

1994

1982

Figure-5: Data Structure

23

1999

Frequency
400

600

800

Median: 4 Mean: 4.58

0200Upperbound is 12 yr
due to 5 yr criterion

0

5

10
_t

Figure-6: Distribution of Spells

24

15

Variable

De…nition

Avr

Std.

A Bank’s share in
0.15
a Firm’s total long-term bank loan
L-Amount(MU) A Bank’s loan amount for a Firm
1,371
TOPL-ShareTop bank’s share in
0.47
a Firm’s total long-term bank loan
TOPL-Amount (MU) Top bank’s loan amount for a Firm
3,235
BankNum
Number of banks lending to a Firm
9.8
F-TBLT(BU) Firm’s total long-term bank loan
17
F-Size(BU) Firm’s total asset
148
F-ROA
(%)
Firm’s EBITDA / total asset
4.49
F-LR
Firm’s liquidity
1.40
asset / liquidity liability
F-LEV
Firm’s total debt / total asset
0.64
F-STLT
Firm’s short-term debt / long-term debt 2.05
F-BTD
Firm’s long-term
0.80
bank loan / total long-term debt
B-Size(TU) Bank’s total loan asset
22
B-ROA
(%)
Bank’s operational pro…t / total asset
0.35
B-CTA
Bank’s cash / total asset
0.05
B-TETABank’s total equity / total asset
0.05
B-IHI
Bank’s industry specialization
0.003(Her…ndahl Index)
MKT-LOAN(TU) Sum of all banks’total loan asset
493
Data source: DBJ Corporate Financial Databank
Note: 1999 data and exclude the …rms in utility, realty, construction, retail,and wholesale industries

0.18

L-ShareTable-2: Summary Statistics

25

3,346
0.23
6,200
6.7
43
380
4.48
0.83
0.21
4.41
0.29
11
0.33
0.03
0.01
0.005
-

Survivor Function: Non-parametric
0.95
0.85
0.75
0.65
0.55
0.45
1

2

3

4

5

6

7
8
Duration

9

10

11

12

13

Figure-7: Non-parametrically Estimated Survivor Function

Hazard Ratio: Non-parametric
0.09
0.08
0.07
0.06
0.05
0.04
0.03
0.02
0.01
0
1

2

3

4

5

6
7
8
Duration

9

10

11

12

Figure-8: Non-parametrically Estimated Hazard Function

26

13

.02

.04

.06

.08

.1

Smoothed hazard estimate

0

5

10

15

analysis time

Figure-9: Non-parametrically Estimated Hazard Function(Gaussian kernel with bandwidth 2)% of Firms with bank holding a larger loan share
100%
90%
80%
70%
60%
50% Criterion

50%

70% Criterion

40%

90 Criterion

30%
20%
10%
0%
1

3

5

7

9

11

13

15

17

19

21

23

25

27

29

30 Bins of LN(Firm's Total Asset)

Data source: DBJ Corporate Financial Databank
Figure-10: Firm Distribution with a Top Lender with a High Share27

% of Firms having a top lender with a larger loan share
110%

90%

70%

50% Criterion

50%

70% Criterion
90% Criterion

30%

10%

-10%

1

3

5

7

9

11

13

15

17

19

21

23

25

27

29

30 Bins of LN(Firm's Long-Term Bank Loan)

Data source: DBJ Corporate Financial Databank
Figure-11: Firm Distribution with a Top Lender with a High Share% of Firms having a top lender with a larger loan share
110%

90%

70%

50% Criterion

50%

70% Criterion
90% Criterion

30%

10%

-10%

1

3

5

7

9

11

13

15

17

19

21

23

25

27

29

30 Bins of LN(Firm's Long-Term Debt)

Data source: DBJ Corporate Financial Databank
Figure-12: Firm Distribution with a Top Lender with a High Share28

% of Firms having a top lender with a larger loan share
100%
90%
80%
70%
60%
50% Criterion

50%

70% Criterion

40%

90% Criterion

30%
20%
10%
0%
1

2

3

4

5

6

7

8

9 10 11 12 13 14 15 16 17 18

18 Bins of Firm's Leverage

Data source: DBJ Corporate Financial Databank
Figure-13: Firm Distribution with a Top Lender with a High Share% of Firms having a top lender with a larger loan share
100%
90%
80%
70%
60%
50% Criterion

50%

70% Criterion

40%

90% Criterion

30%
20%
10%
0%
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23
30 Bins of Firm's ROA

Data source: DBJ Corporate Financial Databank
Figure-14: Firm Distribution with a Top Lender with a High Share29

TOPL-Share (t)Coe¤t-statF-Size (t-1)-0.0604276-7.95
Number of observations
11811
F-ROA (t-1)
0.1456902
3.33
Number of groups
1941
F-LR (t-1)
0.0219466
4.93
R2 (within)
0.4013
F-LEV (t-1)-0.0970796-4.41
R2 (between)
0.1526
F-STLT (t-1)
3.97E-06
0.04
R2 (overall)
0.1923
F-BTD (t-1)-0.0292974-3.49
F-test all u_i=0 (Pr>F)0
B-Size (t-1)
0.0840175
78.54
Sigma_u0.20648467
B-ROA (t-1)
0.2309756
1.42
Sigma_e0.1390402
B-CTA (t-1)
0.0062733
0.83
rho
0.68803016
B-TETA (t-1)
0.0263379
0.12
Observation per group
B-IHI (t-1)
0.0944128
6.04
Min
1
MKT-LOAN (t-1) -0.0301059-2.46
Average
6.1
1980s Dummy
0.016211
2.62
Max
17
Year
0.0008416
0.9Constant-1.260576-0.75
Note-1: Breusch-Pagan test rejects pooling OLS
Note-2: Hausman test rejects random-e¤ects modelNote-3:and denote signi…cance at the1% and5% from a two-tailed t-test
Table-3: Panel Regression (1982-1999)

30

TOPL-Share (t)Coe¤t-statF-Size (t-1)-0.0601683-7.92 Number of observations
11811
F-ROA (t-1)
0.1471617
3..36
Number of groups
1941
F-LR (t-1)
0.0220271
4.95
R2 (within)
0.4014
F-LEV (t-1)-0.0963166-4.37
R2 (between)
0.1521
F-STLT (t-1)
2.95e-06
0.03
R2 (overall)
0.1918F-BTD (t-1)-0.0295199-3.51 F-test all u_i=0 (Pr>F)0
B-Size (t-1)
0.0839932
78.51
Sigma_u0.20652385
B-ROA (t-1)
0.2350157
1.44
Sigma_e0.13903422
B-CTA (t-1)
0.0064047
0.85
rho
0.68813007
B-TETA (t-1)
0.0167272
0.08
Observation per group
B-IHI (t-1)
0.0927898
5.92
Min
1
MKT-LOAN (t-1)-0.0301297-2.46
Average
6.1
1980s Dummy
0.0158594
2.57
Max
17
Year
0.0007966
0.85
Mainbank Dummy -0.0123936-1.36
Constant-1.173964-0.70
Note-1: Breusch-Pagan test rejects pooling OLS
Note-2: Hausman test rejects random-e¤ects modelNote-3:and denote signi…cance at the1% and5% from a two-tailed t-test
Note-4: Mainbank Dummy takes 1 if the top lender is also the top shareholder
Table-4: Panel Regression with Mainbank dummy (Def-(i) 1982-1999)

31

TOPL-Share (t)Coe¤t-statF-Size (t-1)-0.0604778-7.96 Number of observations
11811
F-ROA (t-1)
0.1467597
3.35
Number of groups
1941
F-LR (t-1)
0.0219588
4.93
R2 (within)
0.4013
F-LEV (t-1)-0.0969715-4.40
R2 (between)
0.1530F-STLT (t-1)
3.43e-06
0.04
R2 (overall)
0.1925F-BTD (t-1)-0.0292964-3.49 F-test all u_i=0 (Pr>F)0
B-Size (t-1)
0.0840231
78.53
Sigma_u0.20644123
B-ROA (t-1)
0.2237683
1.37
Sigma_e0.1390457
B-CTA (t-1)
0.0062070.82
rho
0.68792286
B-TETA (t-1)
0.0402669
0.18
Observation per group
B-IHI (t-1)
0.0950287
6.06
Min
1
MKT-LOAN (t-1) -0.0307906-2.50
Average
6.1
1980s Dummy
0.0165386
2.66
Max
17
Year
0.0008964
0.95
Mainbank Dummy 0.0023416
0.47
Constant-1.352153-0.80
Note-1: Breusch-Pagan test rejects pooling OLS
Note-2: Hausman test rejects random-e¤ects modelNote-3:and denote signi…cance at the1% and5% from a two-tailed t-test
Note-4: Mainbank Dummy takes 1 if the top lender is in the top 3 shareholders
Table-5: Panel Regression with Mainbank dummy (Def-(ii) 1982-1999)

32

TOPL-Share (t)Coe¤t-statF-Size (t-1)-0.0603535-7.94 Number of observations
11811
F-ROA (t-1)
0.1432642
3.27
Number of groups
1941
F-LR (t-1)
0.0218654
4.91
R2 (within)
0.4014
F-LEV (t-1)-0.0978993-4.44
R2 (between)
0.1515
F-STLT (t-1)
1.77e-06
0.02
R2 (overall)
0.1917
F-BTD (t-1)-0.0294299-3.50 F-test all u_i=0 (Pr>F)0
B-Size (t-1)
0.084026
78.54
Sigma_u0.20667581
B-ROA (t-1)
0.2715384
1.62
Sigma_e0.13903966
B-CTA (t-1)
0.0065036
0.86
rho
0.6884289
B-TETA (t-1)-0.0357656-0.16
Observation per group
B-IHI (t-1)
0.0935383
5.98
Min
1
MKT-LOAN (t-1) -0.0268402-2.12
Average
6.1
1980s Dummy
0.0152596
2.44
Max
17
Year
0.0006125
0.64
Mainbank Dummy -0.0055998-1.04
Constant-0.8866308-0.52
Note-1: Breusch-Pagan test rejects pooling OLS
Note-2: Hausman test rejects random-e¤ects modelNote-3:and denote signi…cance at the1% and5% from a two-tailed t-test
Note-4: Mainbank Dummy takes 1 if the top lender is in the top 10 shareholders
Table-6: Panel Regression with Mainbank dummy (Def-(iii) 1982-1999)

33

.2

Smoothed hazard function
.4
.6

.8

Cox proportional hazards regression

0

5

10

15

analysis time

Figure-15: Semi-parametrically Estimated Hazard Function

Obs
Cox Proportional Hazard

Hazard Ratio

Std.

= 4070z

F-Size0.999793 0.0173687
-0.01
FROA
25.75275
16.71936
5FLR
1.229482 0.0577113
4.4
FLEV
2.067779 0.4847136
3.1
B-Size0.8045732
0.020627-8.48
BROA
1e+10 1.3e+101
18.47
BCTA
2.749936
1.234649
2.25
BTETA
5.55e-35
1.96e-34-22.38Note-1: Hazard ratio > (<) 1 means the covariate increases (decreases)
the hazard ratio
Note-2:and denote signi…cance at the 1% and from a two-tailed z-test.
Table-7: Semi-parametric Estimation

34

.4

Smoothed hazard function
.6
.8

1

Cox proportional hazards regression

0

5

10

15

analysis time

Figure-16: Semi-parametrically Estimated Hazard Function

Obs
Cox Proportional Hazard

Hazard Ratio

Std.

= 4070z

F-Size1.00323 0.0174764
0.19
FROA
29.59997 19.30651
5.19
FLR
1.239904 0.0584251
4.56
FLEV
2.202717 0.5192203
3.35
B-Size0.7893122 0.0209879
-8.9
BROA
1.56e+98 1.97e+99
17.98
BCTA
2.675354 1.210344
2.18
BTETA
4.9e-35 1.72e-34-22.47
Specialization Match
0.7594184 0.0723587-2.89
Note-1: Hazard ratio > (<) 1 means the covariate increases (decreases)
the hazard ratio
Note-2:and denote signi…cance at the 1% and from a two-tailed z-test.
Table-8: Semi-parametric Estimation

35

Obs
Log-logistic

Coef.

Std.

= 4070z

F-Size
FROA
FLR
FLEV
B-Size
BROA
BCTA
BTETA
Constant

0.008441
0.011006
0.77-1.80794
0.415014-4.36-0.15428
0.030288-5.09-0.43976
0.145138-3.03
0.137026
0.017651
7.76-182.589
10.54746-17.31-0.47157
0.308917-1.53
49.36557
2.289116
21.57-1.81220.485002-3.74
0.446807
0.009242
Note-1: Coe¢ cient > (<) 0 means the covariate increases (decreases)
the failure timeNote-2: < (>) 1 means the log-logistic hazard increases and decreases(monotonically decreases)
Note-3:denotes signi…cance at the 1% from a two-tailed z-test.
Table-9: Parametric Estimation

Obs
Log-logistic

Coef.

Std.

=
z
0.73
-4.38
-5.12
-3.07
7.64
-17.25
-1.5
21.57
0.66
-3.62

F-Size0.008038
0.011025
FROA-1.81946
0.415557
FLR-0.15516
0.030296
FLEV-0.44774
0.145635
B-Size0.135656
0.017764
BROA-182.191
10.55966
BCTA-0.46412
0.308933
BTETA
49.38301
2.289598
Specialization Match
0.000996
0.001506
Constant-1.76991
0.489045
gamma
0.446829
0.009242
Note-1: Coe¢ cient > (<) 0 means the covariate increases (decreases)
the failure timeNote-2: < (>) 1 means the log-logistic hazard increases and decreases(monotonically decreases)
Note-3:denotes signi…cance at the 1% from a two-tailed z-test.
Table-10: Parametric Estimation

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39