TCER Working Paper Series

Long-term interest rates and bank loan supply: Evidence from firm-bank loan-level
data
Arito Ono
Kosuke Aoki
Shinichi Nishioka
Kohei Shintani
Yosuke Yasui
February 2018
Working Paper E-119
http://tcer.or.jp/wp/pdf/e119.pdf

TOKYO CENTER FOR ECONOMIC RESEARCH
1-7-10-703 Iidabashi, Chiyoda-ku, Tokyo 102-0072, Japan©2018 by Arito Ono, Kosuke Aoki, Shinichi Nishioka, Kohei Shintani and Yosuke Yasui.
All rights reserved. Short sections of text, not to exceed two paragraphs, may be quoted without explicit
permission provided that full credit, including ©notice, is given to the source.

Abstract
Based on a mean-variance model of bank portfolio selection subject to the value-at-risk
constraint, we make predictions on transmission channels through which lower
long-term interest rates increase bank loan supply: the portfolio balance channel, thebank balance sheet channel, and the risk-taking channel. Using a firm-bank loan-level
panel dataset for Japan, we find evidence of the presence of these channels. First, anunanticipated reduction in long-term rates increased bank loan supply. Second, banks
that enjoyed larger capital gains on their bond holdings increased loan supply. Further,
this effect was stronger for loans to smaller, more leveraged, and less creditworthy firms.

Arito Ono
TCER
andChuo University
Faculty of Commerce
742–1 Higashinakano, Hachioji, Tokyo
192–0393, Japana-ono@tamacc.chuo-u.ac.jp

Kosuke Aoki
TCER
andUniversity of Tokyo
Department of Economics

Shinichi Nishioka
Bank of Japan
International Department

Kohei Shintani
Bank of Japan
Financial System and Bank Examination
Departmentkaoki@e.u-tokyo.ac.jp

shinichi.nishioka@boj.or.jp
kouhei.shintani@boj.or.jp

Yosuke Yasui
Japan Research Institute, Limited
Economics Department
yosuke.yasui@gmail.com

Long-term interest rates and bank loan supply:
Evidence from firm-bank loan-level data†
Arito Ono‡
Faculty of Commerce, Chuo University
Email: a-ono@tamacc.chuo-u.ac.jp
Kosuke Aoki
Department of Economics, University of Tokyo
Email: kaoki@e.u-tokyo.ac.jp
Shinichi Nishioka
International Department, Bank of Japan
Email: shinichi.nishioka@boj.or.jp
Kohei Shintani
Financial System and Bank Examination Department, Bank of Japan
Email: kouhei.shintani@boj.or.jp
Yosuke Yasui
Economics Department, Japan Research Institute, Limited
Email: yosuke.yasui@gmail.com
February 2018†

The authors thank Sumit Agarwal, Koichi Ando, Lamont Black, Luisa Carpinelli, Robert
Deckle, Hikaru Fukanuma, Masazumi Hattori, Makoto Hazama, Takeo Hoshi (discussant),
Kaoru Hosono (discussant), Ben Iverson (discussant), Seisaku Kameda, Marco
Macchiavelli, Daisuke Miyakawa, Junichi Nakamura, Koji Nakamura, Kazuo Ogawa,
Masanori Orihara, Lev Ratnovski, Andrew Rose, Toshitaka Sekine, Etsuro Shioji(discussant), Shigenori Shiratsuka, Hajime Tomura, Daisuke Tsuruta, Hirofumi Uchida,
Kenichi Ueda, Iichiro Uesugi, Nobuyoshi Yamori, Toshinao Yoshiba, seminar participantsat the Research Institute of Capital Formation of the Development Bank of Japan, theResearch Institute of Economy, Trade, and Industry, and participants of the 4th ABFER
Annual Conference, the 5th MoFiR Workshop on Banking, 2016 Japanese Economic
Association Spring Meeting, and the 18th TCER Macro Conference for valuable comments.
The authors are also grateful to TEIKOKU DATABANK, LTD. for collaborating in theconstruction of the dataset used for the analysis. Aoki gratefully acknowledges financial
support from the Center for Advanced Research in Finance (CARF, University of Tokyo)
and the JSPS Grant-in-Aid for Scientific Research No. 25380223, while Ono gratefully
acknowledges financial support through the JSPS Grants-in-Aid for Scientific Research
Nos. 25220502 and 15H06619. The views expressed in this paper are ours and do notnecessarily reflect those of the Bank of Japan or any of the institutions with which we areaffiliated.
‡
Corresponding author: Faculty of Commerce, Chuo University, 742–1 Higashinakano,Hachioji, Tokyo 192–0393, Japan. Email: a-ono@tamacc.chuo-u.ac.jp1

Long-term interest rates and bank loan supply:
Evidence from firm-bank loan-level data

Abstract
Based on a mean-variance model of bank portfolio selection subject to thevalue-at-risk constraint, we make predictions on transmission channels throughwhich lower long-term interest rates increase bank loan supply: the portfolio
balance channel, the bank balance sheet channel, and the risk-taking channel.
Using a firm-bank loan-level panel dataset for Japan, we find evidence of thepresence of these channels. First, an unanticipated reduction in long-term rates
increased bank loan supply. Second, banks that enjoyed larger capital gains on
their bond holdings increased loan supply. Further, this effect was stronger forloans to smaller, more leveraged, and less creditworthy firms.

JEL classifications: E44, E52, G11, G21
Keywords: monetary policy, bank loan, portfolio balance channel, bankbalance sheet channel, risk-taking channel, value-at-risk constraint2

1. Introduction
Since the onset of the recent global financial crisis, central banks around theworld have initiated unconventional monetary policies to stimulate economic
activity and prevent deflation. One of the objectives of unconventionalmonetary policy is to reduce long-term interest rates, and a number of studies
provide empirical evidence that unconventional monetary policy in advanced
countries had the intended effect of lowering long-term interest rates (e.g.,
Fukunaga et al. 2015, Gagnon et al. 2011, Krishnamurthy and VissingJorgensen 2011). It is not well understood, however, how banks’ lending
behavior is affected by the decline in long-term interest rates brought about by
those policy measures. In particular, while there is some evidence that
unconventional monetary policy and/or lower long-term interest rates have led
institutional investors to rebalance their portfolios towards riskier assets(Carpenter et al. 2015, Joyce et al. 2014), the evidence on bank loan supply islimited.
Against this background, the present study aims to provide simple but
strong evidence that the decline in long-term interest rates has indeed stimulated3

bank loan supply. To do so, we construct a unique and massive firm-bank loanlevel panel dataset for Japan covering the period 2002–2014, which makes it
possible to address the identification challenge that the effect of long-term
interest rates on loan supply needs to be disentangled from the effect on loan
demand by controlling for time-varying unobserved firm heterogeneity with
firm-year fixed effects.
More specifically, we first construct a simple mean-variance model ofbank portfolio selection subject to the value-at-risk (VaR) constraint, in which
the VaR constraint is similar to that in Adrian and Shin (2011). We consider abank that invests in two kinds of assets: loans and government bonds (“bonds”
hereafter), taking the prices of those assets as given. Our simple framework
predicts that a change in the price of bonds (i.e., long-term interest rates) affects
bank loan supply via three transmission channels. The first channel is what weshall call the “portfolio balance channel.” Specifically, we argue that the effectof a reduction in long-term interest rates on loan supply depends on the tradeoff between the “substitution effect” and the “income effect.” The substitution
effect means that, in response to the decline in long-term interest rates, a bank4

subject to the VaR constraint will increase its loan supply because the decrease
in income from bond holdings makes it more profitable for the bank to holdloans. In contrast, the income effect means that the bank will reduce its loan
supply because under the VaR constraint the decrease in income from bondholdings makes it costlier than before for the bank to hold loans. In sum, theeffect of lower long-term interest rates on loan supply depends on the relative
size of these two opposing effects, and a lower interest rate increases loan supply
if the substitution effect is larger than the income effect. The second channel isthe bank balance sheet channel. When interest rates fall and bond prices go up,a bank’s net worth increases through the capital gains on the bonds that it holds.
The stronger balance sheet allows the bank to increase its loan supply. We callthis the “net worth effect.” The third channel we examine is the risk-taking
channel, which is closely related to the bank balance sheet channel (net worth
effect). We extend our analytical framework to distinguish risky loans and safeloans, and our model predicts that in response to an increase in its net worth abank will increase the supply of risky loans more than that of safe loans.
Based on this framework, we empirically examine whether these5effects were at work in banks’ lending behavior to Japanese firms during theperiod 2002–2014. More specifically, to examine the net worth effect (bankbalance sheet channel), we analyze the cross-bank variation in bank net worth
caused by changes in long-term interest rates, which are the same across banks,
and banks’ interest rate risk exposure (i.e., bond holdings), which differs acrossbanks. In order to identify shifts in bank loan supply we use firm-bank matchlevel loan data, which allow us to identify multiple loans to the same firm in thesame year by different banks. Using such data and controlling for firm-year
fixed effects to take firms’ unobservable loan demand into account, we examine
the relationship between changes in individual firms’ loans from different banks
and shocks to the net worth of these banks. In addition, to examine the risktaking channel, we investigate whether the bank net worth effect is stronger forloans to riskier firms.
Regarding the income effect and the substitution effect (portfolio
balance channel), we examine how unanticipated changes in long-term interest
rates affect bank loan supply. Because changes in long-term interest rates arecommon across banks, we cannot empirically identify cross-bank variations in6the income and substitution effects. However, the rich panel data set used in thisstudy allows us to examine which of these two opposing effects is dominant for
all banks together while controlling for various time-varying firm and bankcharacteristics and time-invariant firm and bank fixed effects that might affectindividual bank loan supply. In addition, we examine whether the portfolio
balance channel is stronger for banks facing higher loan interest rates than thosefacing lower loan rates by interacting changes in long-term interest rates withbank-specific loan interest rates. Because this interaction term differs acrossbanks, the additional analysis allows us to examine the heterogeneity amongbanks regarding the portfolio balance channel while controlling for firm-year
fixed effects that take firms’ unobservable loan demand into account.
We obtain the following empirical results. First, we find thatunanticipated reductions in long-term interest rates increased bank loan supply,
which suggests that the substitution effect is indeed larger than the income effect.
Our estimation shows that a 1 percentage point reduction in long-term interest
rates raises the growth rate of a bank’s loan supply by 1.6 percentage points.
Second, banks that enjoyed larger capital gains on their bond holdings

7significantly increased their loan supply, which provides evidence that the bankbalance sheet channel (net worth effect) plays a role. Based on our estimation
result, a one standard deviation increase in a bank’s capital due to capital gains
relative to its total assets (equivalent to a 0.18 percentage point increase in theratio of bank capital to total assets) raises the growth rate of a bank’s loan supply
by 0.8 percentage points. Given that the mean of the loan growth rate during theobservation period was −5.2 percent, the substitution effect (net of the income
effect) and the net worth effect are of modest but not negligible economic
significance. Further empirical investigations we conduct show that the bankbalance sheet channel is stronger with regard to loans to smaller, more leveraged,
and less creditworthy firms, which suggests the existence of the risk-taking
channel.
This study is closely related to the following two strands of literature.
First, a growing number of theoretical and empirical studies examine thetransmission channels of monetary policy, highlighting channels other than thestandard interest rate channel. For instance, theoretical models developed by,among others, Bernanke and Gertler (1989) and Kiyotaki and Moore (1997),

8

show that a positive shock to a borrower’s net worth mitigates the financial
frictions between the borrower and its lenders, and hence increases borrowing(firm balance sheet channel). In a similar vein, Adrian and Shin (2011), Gertler
and Karadi (2011), Holmstrom and Tirole (1997), and Stein (1998) show that apositive shock to a financial intermediary’s net worth alleviates the financial
frictions between the financial intermediary and its depositors, which results in
the increase in its lending capacity (bank balance sheet channel) and therebalancing of its portfolio towards riskier assets (risk-taking channel). While
there are a number of empirical studies that provide evidence of the bankbalance sheet channel as a transmission channel of monetary policy, most ofthese employ either aggregate data (e.g., Bernanke and Blinder 1992) or banklevel data (e.g., Hosono 2006, Kashyap and Stein 2000), which cannot clearly
disentangle the effects of monetary policy on loan supply and loan demand.
Against this background, recent studies, including Hosono and Miyakawa(2014) and Jiménez et al. (2012), have used firm-bank loan-level data to identify
the effect of bank net worth induced by a change in monetary policy on loan
supply. Other studies using firm-bank loan-level data to identify the effect of9monetary policy on banks’ risk-taking include Ioannidou et al. (2015), Jiménez
et al. (2014), and Paligorova and Santos (2017).1
Another recent strand of the literature investigates the effect of
unconventional monetary policy on asset prices and how the induced changes
in asset prices affect investors’ portfolios. As mentioned earlier, a number of
empirical studies find that unconventional monetary policy reduces long-term
interest rates (e.g., Fukunaga et al. 2015, Gagnon et al. 2011, Krishnamurthy
and Vissing-Jorgensen 2011). In addition to the standard interest rate channel
that works through changes in loan demand, lower long-term interest rates maylead investors to shift their portfolios toward assets other than long-term
government bonds and boost the price of those others assets; this is the so-called“portfolio balance channel” (Joyce et al. 2014). Carpenter et al. (2015) and
Joyce et al. (2014) respectively find evidence that institutional investors shifted
their portfolios away from government bonds towards riskier assets in responseto the Federal Reserve’s asset purchases program and the Bank of England’s

1

To distinguish bank loan supply shocks from loan demand shocks, a growing number of
empirical studies have been using firm-bank loan-level data. Examples include the studies
by Khwaja and Mian (2008) and Schnabl (2012) on the supply-side impact of international
financial crises, and Duchin and Sosyura (2014) and Giannetti and Simonov (2013) on theeffect of public capital injections to banks during crises.

10quantitative easing (QE).2 From a theoretical perspective, the portfolio balancechannel may also apply to banks; however, as far as we are aware, there are few
empirical studies on this issue, likely because in many countries government
bonds make up only a small share of banks’ assets. However, as will be seen
below, this is not the case for Japan, where the share of government bonds inbanks’ portfolios has grown, while that of bank loans has stagnated.
This study is placed at the intersection of these two strands of literature.3
The key contribution of the study is that it examines different transmission
channels of unconventional monetary policy simultaneously in a simple
framework. As mentioned above, previous studies have examined the portfolio
balance channel, the bank balance sheet channel, and the risk-taking channel ofmonetary policy independently. As far as we are aware, this is the first study to
examine these channels concurrently by employing Japan’s unique institutional

2

Foley-Fisher et al. (2016) find evidence that the demand for riskier corporate debt byinsurance companies increased in response to the Federal Reserve’s maturity extension
program.
3Note, however, that the portfolio balance channel in the present study is slightly different
from that discussed in the literature on unconventional monetary policy. For example, theportfolio balance channel in Joyce et al. (2014) relies on the existence of the so-called“preferred-habitat” of different investors that may have peculiar investment motives otherthan expected return and risk, while the portfolio balance channel in the present study relieson the net effect of the substitution and income effects on banks’ portfolio selection under
the VaR constraint.

11

setting, in which banks play a major role in corporate finance as well as ingovernment bond markets.
Note, however, that instead of focusing on the effect of monetary policy
on bank loan supply, the present study focuses on the effect of long-term interest
rates on bank loan supply. There are two reasons for doing so. First, there is aconsensus that monetary policy affects real activity through its effects on longterm interest rates, even though the particular mechanisms through which
unconventional monetary policy affects long-term interest rates remains a
subject of debate.4 As will be shown in our simple model in Section 3, banks
determine their portfolio composition given the expected return of assets (loans
and bonds in our model). For the sake of simplicity, we make no a priori
assumptions on the transmission mechanism of monetary policy to long-term
interest rates. Instead, we take changes in long-term interest rates as our pointof departure and examine whether we find any evidence of the portfolio balance

4

There are a number of theoretical and empirical studies that discuss whether
unconventional monetary policies such as quantitative easing (QE) and the Large-Scale
Asset Purchase Program (LSAP) affect long-term interest rates. For instance, Eggertsson
and Woodford (2003) theoretically argue that under certain conditions a central bank’s asset
purchases are irrelevant beyond their effect on private agents’ expectations about the future
course of monetary policy (signaling effects). In contrast, Krishnamurthy and VissingJorgensen (2013) highlight the role of the scarcity channel, in which the purchase ofgovernment bonds by central banks indeed affects bond prices (long-term interest rates).

12

channel. Simultaneously, we examine whether we find evidence of the bankbalance sheet channel, since changes in long-term interest rates bring about
capital gains or losses. Second, if we were to focus on monetary policy rather
than long-term interest rates, it would be much harder – if not impossible – todisentangle the monetary policy stance and economic conditions.5 In addition,
if a change in monetary policy and/or long-term interest rates is anticipated,
there is a possibility of reverse causality, as banks and firms may well adjust
their lending or borrowing prior to the change (Khawaja and Mian 2008). Thus,in order to examine the effect of long-term interest rates on bank loan supply,
we need to single out exogenous and unanticipated changes in long-term rates
that are orthogonal to banks’ lending behavior to avoid the endogeneity problem.
To do so, we employ long-term forward interest rates as a proxy for the expected
return on bonds, since changes in forward rates reflects unanticipatedcomponent of expected return on bonds, and are less likely to be affected by

5

Previous studies examining the impact of monetary policy on loan supply rely on settings
where monetary policy tends to be relatively independent of economic conditions. For
example, Jiménez et al. (2012), focusing on Spain, argue that the monetary policy of the
ECB has been fairly exogenous for countries on the European periphery such as Spain,
while Ioannidou et al. (2015) use observations for Bolivia, a country that has beencharacterized by a high level of dollarization and for which, as a result, monetary policy isessentially set by the Federal Reserve. Obviously, the situation in Japan is quite different,so that the strategies employed in these studies would not work in our setting.

13

current economic conditions than changes in spot interest rates or changes inmonetary policy.
The remainder of the paper is organized as follows. Section 2 briefly
describes developments in monetary policy and bank portfolios in Japan in the
2000s. Section 3 then presents our simple mean-variance model of bankportfolio selection subject to the VaR constraint, which provides empiricalpredictions. Next, Section 4 explains our data and sample selection, theempirical strategy we employ, and the variables, while Section 5 presents theempirical results. Finally, Section 6 concludes and discusses topics for future
research.
2. Developments in monetary policy and bank portfolios in Japan
As mentioned, we use a firm-bank matched loan-level dataset that covers not
only large listed firms but also unlisted small and medium-sized enterprises(SMEs) and spans the period from 2002 to 2014. The period covered by ourdata includes not only periods of monetary easing through unconventional
policies but also a period, in the mid-2000s, when the Bank of Japan exited fromquantitative easing, so that there are sufficient cyclical fluctuations in long-term

14interest rates. In addition, given that Japan has a predominantly bank-based
financial system, bank lending plays a prominent role in the provision of funds
especially to SMEs that find it difficult to raise funds in capital markets, so thatJapan provides a good case study of the impact of interest rates on bank loan
supply. To provide some background for our analysis, this section briefly
discusses developments in Japan’s monetary policy, interest rates, and banks’
asset portfolios in the 2000s using aggregate data.6
Following the collapse of the dot-com bubble in 2000, the BOJ
embarked on its QE policy in March 2001, which set bank reserves as the policy
target and introduced forward guidance using the Consumer Price Index as the
instrument to tell the public under what conditions the BOJ would exit from
QE.7 QE effectively lowered the short-term policy rate to zero. At the sametime, the amount of JGBs held by the Bank of Japan increased substantially andlong-term interest rates declined. The BOJ ended QE in March 2006 and raised
the policy target rate to 0.25% in July of the same year. Following the Great

6

Associated figures are provided in the Online Appendix A.
Specifically, in its policy statement on March 19, 2001, the BOJ announced that the QE
will stay in place until the inflation rate measured by the CPI (excluding perishables) is
expected to stabilize at more than zero percent.
715

Recession, the BOJ started “Comprehensive Monetary Easing” in October 2010.
Under Comprehensive Monetary Easing, the BOJ purchased a variety of assets
including exchange-traded funds (ETFs) and Japan real estate investment trusts(J-REITs) as well as JGBs. In April 2013, the BOJ introduced “Quantitative andQualitative Monetary Easing (QQE),” under which it started purchasing
massive amounts of JGBs including bonds with longer remaining maturities toincrease the monetary base. QQE resulted in zero short-term rates and lower
long-term rates.
Against this background, the ratio of Japanese banks’ bond holdings tototal loans outstanding increased in the 2000s until the BOJ started QQE, whichsuggests that Japanese banks increased their exposure to interest rate risk. The
loan growth rate was mostly sluggish except for the mid-2000s and after 2012,
while the loan interest rate has been steadily declining except for a brief period
in the mid-2000s. Sluggish loan growth and declining loan interest rates suggestthat loan developments were largely driven by demand factors and that it isimportant to control for loan demand factors in identifying supply factors.8
8

It is also important to control for supply factors other than those we focus below. In
particular, during the period this study focuses on, Japanese banks struggled with resolving
massive non-performing loans, especially in the early 2000s, which may have affected their16

3. Theoretical model
To derive theoretical predictions on the effect of long-term interest rates on banklending, we construct a simple model of bank portfolio selection. Consider abank that has net worth. The bank originates loans, and obtains funds from deposits

and invests in bonds. Thus, its profit function and balance

sheet constraint are defined as
(1)
s. t.
where

(2)
,

denotes the bank’s profit and, andrespectively represent

the interest rate of loans, bonds, and deposits. We assume that the bank takes
those interest rates as given and thatandare stochastic variables. The

mean and standard deviation ofandare given by

,

,

and

, respectively. Combining equations (1) and (2) yields(3)
We assume that the bank is risk averse and maximizes its expected

profit while minimizing the volatility of its profit. More specifically, the bank’sloan supply. Regarding the effect of the bad loan problem on bank loan supply in Japan,see, for instance, Peek and Rosengren (2000) and Watanabe (2007).

17

optimization problem is given by
Max

E

γ
Var
2

(4)

where γ is the parameter for relative risk aversion, which is assumed to bestrictly positive. We also assume that the correlation between
zero.

and

is

We assume that the bank is subject to the VaR constraint. Under the

VaR constraint, the bank will build its portfolio (loans and bonds) such that it
would not be insolvent unless a considerable stress event materializes. Moreprecisely, we assume that the VaR constraint is given by0
where the strictly positive parameter(5)

represents the largest magnitude of thestress in terms of the volatility of bank assets (loans and bonds) under which thebank is solvent, andandrespectively

represent the loss (negative spread) if the stress event materializes. Arranging
inequality (5), we have
5 ’
Inequality (5)’ shows that the bank should hold sufficient net worth (right-handside) to absorb losses from loans and bonds under the stress event (left-hand18side) when constructing its optimal portfolio

∗∗

,

∗∗

so as to satisfy theinequality. The bank solves the maximization problem (4) subject to inequality(5)’.
The comparative statics for the effect of a decrease in bond returns
on the optimal amount of loans∗∗

are shown analytically in the Online

Appendix B. Here, we only provide the intuition behind the results. Inequality(5)’ is analogous to a budget constraint in a standard consumption choice model,
where the effects of a price change for one good can be decomposed into asubstitution effect and an income effect. In our case, the substitution effectmeans that a decrease in

makes it relatively costly for the bank to invest in∗∗bonds and the bank hence increases
decrease in. The income effect means that adecreases income from government bonds, which tightens the

VaR constraint and hence reduces∗∗. The bank thus reduces

satisfy inequality (7)’. In sum, the effect of a decrease in∗∗on

in order to∗∗depends

on the relative impacts of the substitution effect and the income effect.9
The effect of an increase in

on

9

∗∗

is straightforward: a larger

These effects do not exist without the VaR constraint. That is, when the expected returnof bonds falls, the bank only reduces its amounts of bonds (and hence deposits) and does
not change the amount of loans. For more details, see Appendix B.

19makes inequality (7)’ less binding and hence the bank increases∗∗. Although

our simple static model abstracts from how changes in bond interest rates affectbanks’ net worth, in practice, when bond interest rates fall (and hence the priceof bonds increases), banks’ net worth increases as a result of the increase in thevalue of their bond holdings. This increase in the value of banks’ bond holdings
can be interpreted as an increase in. This net worth effect corresponds to thebank balance sheet channel in the literature (e.g., Gertler and Karadi 2011,
Holmstrom and Tirole 1997, Stein 1998).
Finally, in order to examine whether a bank will increase its holdingsof risky assets more than of safe assets in response to a positive net worth shock(the risk taking channel), we extend our analysis to a three-asset case: safe loans,risky loans, and bonds. We assume that the return on risky loans has a higher
mean and higher standard deviation than safe loans, while the Sharpe ratio ofrisky loans is lower than that of safe loans. The last assumption on the Sharpe
ratio implies that loans are considered as risky if they do not offer sufficient
excess return to compensate for their return volatility and is in line with theexisting literature on the risk taking channel of monetary policy, which finds

20that risky loans offer a lower risk premium (see, for instance, Ioannidou et al.
2015 and Paligorova and Santos 2017). Details of the model as well as thecomparative statics for the effect of an increase in bank net worth on the amountof risky loans relative to safe loans are shown in the Online Appendix B. The
comparative statics show that when a bank’s net worth increases, the bankincreases risky loans more than safe loans. Thus, an increase in bank net worth
induces more bank risk-taking.
4. Data, empirical strategy, and variables
4.1. Data and sample selection
To construct our firm-bank matched loan-level data, we use the database
compiled by TEIKOKU DATABANK, LTD. (TDB). The TDB database, whichis the main source of our dataset, contains information on listed and unlisted
firms in Japan, including their characteristics (e.g., ownership structure, creditscores, etc.), their financial statements, and up to 15 financial institutions thateach firm transacts with. Regarding financial institutions that a firm transacts
with, the TDB database contains information on their identities and whether thebank is the main bank of a firm. The definition of the main bank is somewhat

21subjective in that it is identified by each firm. In addition, and most importantly
for our analysis, the TDB database allows us to identify the amount of loans
outstanding provided by each bank that each firm transacts with. These firmbank loan-level data are available for the period 2002–2014, although thenumber of observations for 2014 is much smaller than for the other years. Most
variables in the TDB database are revised yearly, so that we use annual data forour panel.
We restrict our sample to firms for which data on (i) the total loans
outstanding, (ii) the amount of loans outstanding from at least two banks, and(iii) the TDB credit score are available in the TDB database.10 For the reason
explained below, we exclude from our sample firms that obtained loans fromonly one bank. Based on these sample selection criteria, we have 48,975 firms
in total.
In addition to the TDB database, we use Nikkei Financial Quest, banks’financial statements compiled by the Japanese Bankers Association, and banks’
annual reports to obtain bank-level data. Macroeconomic variables are obtained
10

The TDB credit score rates firms based on their business history, capital structure, size,
profitability, funding status, CEO, and vitality. The score takes a value between 1 and 100,with a higher score representing a better rating.

22

from Nikkei Financial Quest. Regarding banks, we restrict our sample todeposit-taking financial institutions that mainly focus on commercial banking.
To be more specific, our sample banks consist of city banks, regional banks,
second-tier regional banks, and Shinkin banks. 11 Regarding mergers andacquisitions (M&A), we treat merged banks as distinct institutions from theentities that were merged. Based on this procedure, we end up with observations
on 408 banks in total.
Using the firm and bank data described above, we construct anunbalanced firm-bank matched loan-level panel that covers the period 2002–
2014. The total number of individual firm-bank loan observations for the entire
period is 379,989.
4.2. Empirical strategy
4.2.1 Main estimations
The advantage of firm-bank matched loan-level panel data is that such data
make it possible to disentangle credit supply shocks from credit demand shocks
and identify the bank balance sheet channel. For this reason, such data have11

We exclude long-term credit banks and trust banks, which are somewhat different fromcommercial banks. For a detailed description of the type of banks in Japan, see Uchida andUdell (2010).

23been widely used in studies examining the bank balance sheet channel in thecontext of monetary policy (Hosono and Miyakawa 2014, Ioannidou et al. 2015,
Jiménez et al. 2012; 2014, Paligorova and Santos (2017)), financial crises(Khwaja and Mian 2008, Schnabl 2012), and public capital injections to banks
during a crisis (Duchin and Sosyura 2014, Giannetti and Simonov 2013). In thecontext of our study, the aim is to investigate the impact of changes in long-term
interest rates on bank loan supply employing the model presented in Section 3.
Specifically, in our analysis we focus on exogenous changes in banks’ net worth
brought about by changes in the prices of bonds that banks are holding.
Suppose that changes in loans to firm i by bank j (, ) aredetermined by macroeconomic shocks such as changes in long-term interest
rates ( ∆), bank-specific loan supply shocks such as capitalgains/losses due to changes in the value of bond holdings reflecting changes ininterest rates (( __), and firm-specific loan demand shocks) such as an increase in sales growth. That is:

∆

,

∆

_

_
If

_

,

is unobservable, OLS regression yields biased estimates of24

. However, if we observe a change in loans to the same firm by another bank,j’, we can write a similar equation:
∆

,

∆

_

_

′

,

Differencing the above two equations yields
∆

,

∆

,

,

, ′

Thus, firm-specific demand shocks are eliminated when we difference thechanges in loan amounts to the same firm provided by different banks and we
obtain an unbiased estimate ofwhich captures the effect of bank-specificloan supply shocks. Note that for us to be able to estimate the above equation,a firm needs to have lending relationships with at least two banks. This is thereason that we exclude from our sample firms that obtained loans from only one
bank.
Specifically, we estimate the following three types of regression
equations:
∆

, ,
∆

1
(6)
,

,
, ,

25

∆

, ,
_
,

,

1

(7)

,
, ,

∆

, ,
_
,

,

1

(8)
,

, ,

In equation (6), we control for the bank-level fixed effectlevel fixed effectand the firm-

to capture bank- and firm-specific time-invariant factors.

In addition, we control for time-variant covariates, namely macroeconomic
conditions (characteristics (,), bank characteristics (,), and firm). We employ a one-year lag for all independent

variables to avoid possible endogeneity problems. Next, in equation (7), we
additionally include the year fixed effect. While this specification takes

time-variant unobservable macroeconomic factors into account, including year
fixed effects means that we cannot estimate the impact of changes in long-term
interest rates, ∆, and other macroeconomic variables. Finally,equation (8) incorporates the firm-year fixed effect,, which captures

time-variant firm-level unobservable factors such as firm-specific loan demandthat may not be fully captured by variables included in,inequations (6) and (7). In terms of the interpretation of our results, the coefficient

26

on ∆

in equation (6) indicates whether higher long-term interest

rates increase bank loan supply (through the income effect) or decrease it(through the substitution effect). Meanwhile, the impact of capital gains/losses
on bank bond holdings on loan supply,_, is included in all three

specifications, but our preferred specification is equation (8), where the firmyear fixed effect,, , takes unobservable time-variant firm heterogeneity

into account. The results of main estimations are presented in Section 5.1.
The empirical investigation on the bank balance sheet channel usedhere follows the identification strategy employed by Hosono and Miyakawa(2014) and Jiménez et al. (2012), who also used firm-bank loan-level panel data.
However, our approach differs from theirs in that we use a different proxy forbank net worth shocks, namely capital gains accruing to banks through theirinterest rate risk exposure (_), while the other two studies use

the interaction term between the variable which represents the monetary policy
stance (e.g., short-term interest rates) and banks’ net worth level prior to changes
in monetary policy. While the interaction term used in these studies may
indirectly measure the magnitude of the bank net worth effect brought about by27monetary policy shocks, we think capital gains accruing to banks through theirinterest rate exposures provide a much more direct measurement. Our approach
is similar to that in studies examining the effect of public capital injections onbank loan supply, in that, just like those studies, we also directly examine theimpact of additional net worth accruing to banks.
4.2.2 Cross-term estimations
As noted above, we cannot estimate the impact of changes in long-term interest
rates, ∆, on bank loan supply using our preferred specification,

equation (8), which controls for the firm-year fixed effect. However, we can
examine whether the strength of the portfolio balance channel differs acrossbanks by interacting ∆with a bank characteristics variable while

incorporating firm-year fixed effects, as in Hosono and Miyakawa (2014) andJiménez et al. (2012). Therefore, we estimate the following equation:∆, j, t

∆

1
,
,

1

,
,

1
(9)

, ,

The coefficient on the interaction term ∆measuresthe relative strength of the portfolio balance channel for banks with certain
characteristics. The characteristic that we focus on is changes in bank-specific28

loan interest rates, which allows us to examine whether the strength of theportfolio balance channel differs across banks. We expect that the substitution
effect from bonds to loans is stronger for banks facing higher expected returns
on loans so thatis negative. The results are presented in Section 5.2.

In a similar vein, and more importantly, we examine the risk-taking_

channel by interactingwith firm characteristics variables that

represent firms’ riskiness. That is, we estimate the following equation:
∆

, ,
_
,
,

,
1
, ,

1
,

(10)

.

As proxies for firms’ riskiness, we use firms’ size, leverage, and credit score.
The results are presented in Section 5.3.
4.3. Variables
Definitions of the dependent and independent variables used in the estimation
are presented in Table 1, while Table 2 provides their summary statistics. The
dependent variable is ∆, which represents the percentage change inloans to firm i by bank j in year

from year

the log-difference between year

and

29

1 and is obtained by taking

1. We define loans as the sum of

short-term loans, long-term loans, and bills discounted in the TDB dataset. The
mean of ∆is −5.2 percent, while the median is −3.5 percent (Table 2).

The main independent variables are the change in the expected rate of
return on long-term bonds, ∆, and bank-specific capitalgains/losses as a result of changes in interest rates on bonds that banks havebeen holding,_. As a proxy for ∆, we use thedifference between 10-year forward interest rates, calculated in the following
manner. We consider two forward rates: the forward rate observed in year
1 for 10-year bonds starting in year , and the forward rate observed in year
2 for the same 10-year bonds starting in year

. We then take thedifference between the two. If we denote the forward rate as
where subscript

,

10 ,

is the year in which the forward contract is concluded andis the year in which the forward contract is executed, ∆isdefined as:∆
Thus, ∆,

10

captures the change between year

30

,

10
2 and year1

in the expected return of the same 10-year bonds.12 Note that we use not thechange in spot rates but the change in forward rates. Using forward rates enable
us to correctly identify unanticipated changes in the expected returns on bonds,
while

spot

rates

may

well

be

contaminatedbycontemporaneous

macroeconomic conditions that affect banks’ lending behavior simultaneously.
If they are indeed contaminated, the use of spot rates might result in a biased
estimates of the portfolio balance channel. Table 2 shows that the mean of∆is −0.35 percentage points, while the median is −0.45

percentage points. Based on the model in Section 3, we expect that thecoefficient on ∆is negative if the substitution effect is larger than

the income effect.
We calculate the bank-specific capital gains/losses stemming frombanks’ exposure to interest rate risk via the holding of bonds with various
maturities as follows:∑ ∆_where ∆____

is the change in the spot interest rate in year

12

To be precise, we use 10-year implied forward rates, which are calculated from spot rates
of various maturities observed in different years, based on the assumption that term
structure is explained by expectation theory.

31

and

represents the maturity of various spot rates, 13

represents a bank’s holdings of bonds with maturity_

is a bank’s total assets in year_

in year

1 , and1, which are used to expresschanges in the value of bond holdings relative to the bank’s assets.14 Table 2
shows that the mean of_is 0.04 percent, while the median is

0.08 percent. Based on the model in Section 3, the coefficient on_

should take a positive value if the net worth effect is present.
Figure 1 shows developments in the key variables of interest during theperiod 2002–2014. As can be seen in Figure 1(a), the median of ∆wasnegative and fairly stable during this period, although loans contracted at a fasterrate during the period 2002–2004 when Japanese banks were reducing massive
non-performing loans and again in 2009 and 2010 in the midst of the Great

13

Banks disclose their bond holdings for each maturity based on the following categories:
less than 1 year, 1–5 years, 5–10 years, and 10 years or more. Thus, to calculate_, we use the median value of each category for the spot rate and maturity;that is, we use
0.5, 3, 7.5, and 12 years respectively.
14
One may argue that bank-specific capital gains/losses also arise through banks’ holdingof stocks if, for example, there is a negative correlation between bond prices and stock
prices as predicted by the discounted cash flow model, so that lower long-term interest rates
boost stock prices. Lower long-term interest rates may also increase bank net worth throughthe changes in the fair value of loans and deposits, which are usually recorded on a bookvalue basis, if the effective maturity (i.e., the time interval for changes in interest rates) ofloans is longer than that of deposits. However, we do not have reliable data on thecorrelation of the prices of bonds and stocks held by each bank. Nor do we have data on
the effective maturity of bank loans and deposits. Thus we abstract from these changes
when calculating_.

32

Recession. Unanticipated changes in the forward rate, ∆, weremostly negative, except in 2005 and 2006 (Figure 1(b)). Finally, the median ofbanks’ capital gains on the bonds that it holds,_, was positive in

2002–2003 and 2008-2013 (Figure 1(c)).
We also use the following time-variant covariates that may affect∆. Regarding macroeconomic variables, the most important variable forour analysis is the expected rate of return of loans. We use the annual change in
the average contract interest rate on new loans and bills discounted publishedby the Bank of Japan (∆). Based on the prediction of our model in

Section 3, we expect the coefficient on ∆addition to ∆to be positive. In, we use the nominal GDP growth rate (∆the annual percentage change of the Tokyo Stock Price Index (∆

) and
).

As for variables representing bank characteristics, we use the bankcapital-asset ratio, which is the bank net worth over total assets (employ

_

_

). We

as a proxy for banks’ lending capacity. As mentioned above,

the financial strength of Japanese banks was weak in the early 2000s due to thenon-performing loan problem, which may have weakened loan supply. Further,33

to take into account that the effect of bank net worth on bank loan supply may
be non-linear we also include the square of this term (we use the bank liquidity ratio (

_

_

_

). In addition,), the bank return on assets (bank size as measured by the logarithm of total assets (

_

_

),

), and a dummy

variable that is equal to one if a bank is the main bank of a borrowing firm andzero otherwise (_).

Regarding firm characteristics, we use the firm capital-asset ratio( _), the liquidity ratio ( _( _∆), the return on assets ( _), sales growth), firm size as measured by the logarithm of total assets ( _firm age (in logarithm,_),), and the logarithm of the number of banks

that a firm transacts with ( _).

To deal with possible outliers in the TDB dataset, we winsorize thefollowing firm-level variables at the upper and lower 0.5 percentiles: ∆
_

,

_

,

_

, and

_∆

,

.

5. Results
In this section, we present our estimation results. Section 5.1 presents the main
results on the portfolio balance channel and the bank balance sheet channel.

34Section 5.2 examines the relative strength of the portfolio balance channel
among banks. Section 5.3 presents the estimation results on the risk-taking
channel.
5.1. Main results: Portfolio balance channel and bank balance sheet channel
Table 3 presents the main results of our empirical analysis. Columns (i), (ii) and(iii) respectively correspond to empirical specifications (8), (9), and (10) in
Section 4.2, with the rows reporting the estimated coefficients andheteroskedasticity-robust standard errors clustered at the bank level.
Starting with the results in column (i), we find that the coefficient on∆, representing unexpected changes in the long-term forward rate,is negative and significant. The estimated coefficient implies that a 100-basis
point decrease in the long-term forward rate increases firms’ loan growth rateby 1.6 percentage points. This result suggests that the substitution effect is larger
than the income effect. Further, consistent with the theoretical model, thecoefficient on ∆coefficient on

is significantly positive. Turning to the_, which measures the net worth effect, this ispositive and significant. The estimated coefficient implies that a one standard

35

deviation increase in_, which corresponds to an increase in theratio of bank capital to total assets by 0.18 percentage points, increases bankloan supply by 0.8 percentage points. Compared to the mean of ∆,which is −5.2%, the net worth effect is of modest but not negligible economic
significance.
Next, looking at the other covariates, the results are mostly consistent
with our expectations. Of the remaining macroeconomic control variables,∆

takes a significant positive coefficient, implying that the loan growthrate is higher when the stock market is doing well. As for bank characteristics,
the coefficient on_

is significantly positive while that on

_

_

is

significantly negative, indicating that the effect of bank net worth on loan supply
is non-linear in that the positive marginal effect diminishes as the bank capitalasset ratio increases. Next, the coefficient on_

is positive andsignificant, which suggests that a closer firm-bank relationship has a positiveeffect on the loan growth rate. Finally, all of the firm characteristics variables
we employ have significant coefficients, indicating that the growth rate of loans
from an individual bank is higher the higher a firm’s capital ratio, liquidity ratio,

36

ROA, and sales growth, the smaller and younger a firm, and the smaller thenumber of banks it transacts with.
Next, columns (ii) and (iii) respectively show the estimation resultswith year fixed effects and firm-year fixed effects. Note that the macroeconomic
variables are dropped in column (ii), while the firm characteristics variables aswell as the macroeconomic variables are dropped in column (iii). Thus, wecannot estimate the effect of ∆in these specifications. On theother hand, controlling for unobservable time-variant macroeconomic
conditions and unobservable firm-level characteristics including firms’ loan
demand allows us to more precisely estimate the effect ofloan supply. We find that the coefficient on

_

_

on

is 3.57 in column(ii) and 4.65 in column (iii) compared to 4.60 in column (i). Thus, thecoefficients are of a similar magnitude as that in column (i). However, becauseof larger standard errors_

is significant only at the 10 percent

level in columns (ii) and (iii), which is lower than in column (i). The larger
standard errors in columns (ii) and (iii) suggest that there may exist significant
heterogeneity in firm and bank characteristics that affects the magnitude of the37

effect of changes in bank net worth on loan supply. The role of heterogeneity infirm and bank characteristics is discussed in the following subsections.
5.2. Relative strength of the portfolio balance channel among banks
In this subsection, we investigate whether the portfolio balance channel isstronger for banks facing higher loan interest rates than those facing lower loan
rates by interacting ∆rates (_∆

with changes in bank-specific loan interest).

_∆

represents the yearly change inthe ratio of a bank’s loan interest income to total loans outstanding. We predictthat the substitution effect from bonds to loans is stronger for banks facing
higher expected returns on loans and therefore that the coefficient on∆_∆

is negative.

Column (iv) of Table 3 shows the estimation results. The coefficient on
the interaction term ∆_∆is significantly

negative, which is consistent with our prediction.
5.3. Results on the risk-taking channel
In this subsection, we examine the risk-taking channel. The model in Section 3
implies that a positive bank net worth shock affects banks’ risk taking capacity

38

and that banks’ supply of risky loans increases more than that of safe loans.15
Thus, in response to a bank-specific positive net worth shock stemming frombanks’ exposure to interest rate risk, banks may be more aggressive in extendingloans to riskier firms. To examine this possibility, we use firms’ size, capitalasset ratio, and TDB credit score as proxies for firms’ degree of riskiness. We
assume that smaller firms, more leveraged firms with a lower capital-asset ratio,
and firms with a lower TDB credit score are riskier. We construct a dummy
variable that equals one if a firm’s total assets are smaller than the median,
_ _

_

_ _

_

is

_ _

_

for larger firms. In a similar vein, we construct dummy

variables, and expect that the coefficient on_ __larger

than

that

_ _

and

_

on

_

_
1

that equal one if

the capital-asset ratio and TDB score of a firm is smaller than their sample
median.
Table 4 displays the estimation results. We find significant positive
15

Ioannidou et al. (2015), Jimenetz et al. (2014), and Paligorova and Santos (2017) findevidence for the risk-taking channel of monetary policy. Also see Aoki and Sudo (2012),
who argue that a deterioration in banks’ net worth reduces their risk taking capacity andresults in a rebalancing of banks’ portfolios towards government bonds. Meanwhile,
Duchin and Sosyura (2014) report that U.S. banks that received government assistancefrom the Troubled Asset Relief Program shifted their asset allocation to riskier assets.

39

coefficients for firms that are smaller, have a lower capital-asset ratio, and havea lower TDB score (columns (i), (ii), and (iii)). These results indicate that thebank net worth effect is stronger for loans to riskier firms, and suggest theexistence of the risk-taking channel.
6. Conclusion
Employing a unique and massive firm-bank loan-level panel dataset covering avariety of banks and firms in Japan during the period 2002–2014, this study
investigated the effects of long-term interest rates on bank loan supply to firms.
To disentangle the effects of interest rates on bank loan supply from those onbank loan demand, we incorporated firm-year fixed effects to control for timevarying unobservable loan demand. Our empirical analysis yielded thefollowing results. First, a decrease in long-term interest rates led to an increasein banks’ loan supply, providing evidence for the existence of the portfolio
balance channel, which consists of the net outcome of the substitution effect(the shift from government bonds to loans under the VaR constraint) and theincome effect (slower loan growth due to the decrease in income fromgovernment bonds that tightens the VaR constraint). Second, we find that an40

increase in banks’ net worth as a result of an increase in the value of bondholdings brought about by a decline in long-term interest rates led to an increasein loans to firms, providing evidence for the bank balance sheet channel. Third,
we find that the effect of strengthened bank balance sheet is stronger in the caseof loans to smaller, more leveraged, and less creditworthy firms, providing
evidence for the risk-taking channel.
The analysis in this study raises a number of issues that remain to beaddressed in future research. First, while we provide evidence for the existenceof the portfolio balance sheet channel and the bank balance sheet channel(supply factors), how important they are in quantitative terms relative to demand
factors (such as an increase in loan demand due to lower long-term interest rate)
remains an open question. Our estimation results suggest that the economic
impact of these channels is modest, but in order to gain a better quantitative
understanding of the transmission of monetary policy it is necessary to
decompose the sluggish loan growth during the lost decades in Japan into
demand and supply factors in a more rigorous manner. Second, while we findthat changes in long-term interest rates affect banks’ loan supply, such changes

41

in loan supply may not materially affect client firms’ real activities such as
investment and employment if firms are not credit constrained due to theavailability of other sources of funds. In order to assess the true significance ofthe two transmission channels, one has to know the elasticity with which
borrower firms can switch between borrowing from banks and other sources offunds, which may be heterogeneous depending on firms’ and banks’characteristics as well as the closeness of firm-bank relationships. Third, while
we find evidence that a reduction in long-term interest rates led banks toparticularly increase loan supply to credit-constrained and riskier firms, whether
banks’ portfolio composition shifted toward riskier assets remains an open
question. It may well be the case that the magnitude of the changes in banks’
portfolio composition differs across banks, so that one has to find a way tocontrol for the aggregate loan demand that each bank faces in examining theshift in bank portfolios. How firms respond to loan supply shocks to their lenderbanks, how important bank loan supply shocks are for the economy, and how
banks’ asset portfolios shift in response to changes in long-term interest rates
are issues we leave for future research.

42

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45

Table 1: Definition of variables
This table presents the definition of variables used in the main estimations (Table 3). All independent
variables are as of 1 year prior (t-1) to the dependent variable.
Variable

Definition

Dependent variable
ΔLOANS

Log change in firm i 's total loans outstanding from bank j .
Loans outstanding include short-term loans, long-term loans, andbills discounted.

Key independent variables
ΔBONDRATE

Difference between the forward rate observed in year t-1 for 10-yearbonds starting in year t and the forward rate observed in year t-2 forthe same 10-year bonds starting in year t

BK_CAPGAIN

Bank j 's capital gains/losses due to changes in prices of bonds held

Macroeconomic controls
ΔLOANRATE

Change in average interest rate of newly contracted loans
including bills discounted

ΔGDP

Change in Japan's nominal gross domestic product

ΔTOPIX

Log change in Tokyo Stock Price Index (TOPIX)

Bank characteristics
BK_CAP

The ratio of bank j 's net worth over total assets

BK_CAP_SQ

Squared value of bank j 's net worth ratio

BK_LIQThe ratio of bank j 's liquid assets over total assets. Liquid assets
include cash and due from banks, call loans, government bonds,
and local government bonds.

BK_ROABank j 's total net income over total assets

BK_lnTAThe logarithm of bank j 's total assets

BK_MAIN

1 if firm i regards bank j as its main bank, 0 otherwise

Firm characteristics
F_CAP

The ratio of firm i 's net worth over total assets

F_LIQ

The ratio of firm i 's liquid assets over total assets

F_ROA

The ratio of firm i 's total net income over total assets

F_ΔSALES

Log change in firm i 's gross sales

F_lnTAThe logarithm of firm i 's total assets

F_lnAGEThe logarithm of (1 plus firm i 's age)

F_lnNBANKS

The logarithm of (1 plus the number of banks with which firm itransacts)

46

Table 2: Summary statistics
This table presents summary statistics of the variables used in the main estimations (Table 3). Definitionsof variables are provided in Table 1.

Variable

Units

Mean

SD

Min

Median

Max

%

-5.21

66.18

-310.27-3.50

321.89

BONDRATE% points

-0.35

0.32

-0.89

-0.45

0.21

BK_CAPGAIN

%

0.04

0.18

-1.53

0.08

1.59

% points

-0.05

0.12

-0.23

-0.05

0.15

GDP

%

-0.60

1.87

-4.60

0.20

1.80

TOPIX

%

-4.41

16.85

-38.38

-2.34

38.53

BK _ CAP

%

4.55

1.43

0.38

4.50

15.54

BK _ CAP _ SQ

%

22.72

14.34

0.15

20.25

241.45

BK _ LIQ

%

22.49

7.20

4.62

21.08

72.95

BK _ ROA

%

0.60

0.24

-1.83

0.60

4.82

BK _ lnTA

Mil. yen

16.05

1.85

10.69

15.58

19.02

0.37

0.48

0.00

0.00

1.00

Dependent variable

LOANS
Key independent variables

Macroeconomic controls

LOANRATEBank characteristics

BK _ MAIN
Firm characteristics

F _ CAP

%

23.02

19.32

-99.41

20.00

88.93

F _ LIQ

%

41.71

20.15

1.83

40.76

94.76

F _ ROA

%

0.70

4.65

-40.15

0.77

21.63

F _ SALES

%

1.21

21.91

-122.420.48

138.09F _ lnTA

1,000 yen

14.75

1.60

8.25

14.66

23.18

F _ lnAGE

Years old

3.57

0.61

0.69

3.71

4.88

F _ lnNBANKS

Banks

1.91

0.43

1.10

1.95

2.77

47

Figure 1: Developments in key variables
These figures present developments in key variables used in the main estimations (Table 3). Definitionsof variables are provided in Table 1 and in the text.

(a) Bank loan growth rate ()

annual change, %40

75 percentile

30

Median20

25 percentile

10
0
-10
-20
-30
-40
FY 02

03

04

05

06

07

08

(b) 10-year forward rates (
3

09

10

11

12

13

14

)
% points%(1)-(2) (RHS)

2(1) Observed at t-1(2) Observed at t-2

2

1

1

0
FY

0

-1
02

03

04

05

(c) Banks’ capital gains (
0.6

06

07

_

08

09

10

11

12

13

14

)

over total assets, %

0.4
0.2
0.0
-0.2

75 percentile-0.4

Median25 percentile

-0.6
FY 02

03

04

05

06

07

08

48

09

10

11

12

13

14

Table 3: Estimation results for the portfolio balance channel and the bankbalance sheet channel
This table presents the estimation results on bank loan growth,, controlling for various
covariates and fixed effects outlined in the text. ***, **, * indicate significance at the 1, 5, and 10% level,
respectively. Standard errors in parentheses are heteroskedasticity-robust standard errors clustered at thebank level.
(i)

(ii)

(iii)

(iv)

Key independent variables-1.59*(0.84)
4.60 *** 3.57
(1.36)(2.05)

BONDRATEBK_CAPGAIN
∆

*

4.65
(2.78)

_∆

*

4.62
*
(2.74)-4.40 ***
(1.05)

Macroeconomic controls

LOANRATEGDPTOPIX

7.18**(3.17)-0.11(0.21)
0.16 ***(0.03)

Bank characteristics

BK _ CAPBK _ CAP _ SQ
BK _ LIQ
BK _ ROA

BK _ lnTA
BK _ MAIN

1.38** 1.99 *** 2.86 *** 3.17 ***(0.68)(0.70)(1.00)(1.17)-0.20 ** -0.22 *** -0.31 *** -0.33 ***(0.08)(0.08)(0.11)(0.12)
-0.01
0.06
0.17
0.15
(0.12)(0.12)(0.11)(0.10)
-0.45
-0.65
-1.83
-2.19
*
(1.12)(1.12)(1.32)(1.20)-10.50 ** -7.47* -6.41-0.56(4.37)(4.28)(4.13)(4.38)
2.82 *** 2.78 *** 3.36 *** 3.36 ***(0.64)(0.64)(0.69)(0.69)

Firm characteristics

F _ CAPF _ LIQ
F _ ROA
F _ SALES
F _ lnTAF _ lnAGEF _ lnNBANKS
Fixed effects
Firm
Year
Firm-year
Bank
Observations
Adjusted R 2

0.46(0.04)
0.07(0.02)
0.17(0.04)
0.05(0.01)-17.01(1.56)-14.09(2.37)-4.57(0.80)***

0.47(0.04)*** 0.06(0.02)*** 0.16(0.04)*** 0.05(0.01)*** -17.47(1.54)*** -6.05(2.95)*** -5.73(0.83)YESNO
YES
379,989
0.04

49

***
***
***
***
***
**
***

YES
YES
YES
379,989
0.04

YES
YES
379,989
0.21

YES
YES
379,989
0.21

Table 4: Estimation results for the risk-taking channel: Interaction termswith banks’ capital gains
This table presents the estimation results on bank loan growth,, when interaction terms between
banks’ capital gains,_, and firm characteristics are included. Columns (i)-(iii) show theresults when_is interacted with a firm’s asset size, capital-asset ratio, and TDB score,respectively. Other independent variables included in the estimations are bank characteristics variables,
firm-year fixed effects, and bank fixed effects (as in the specification in column (iii) of Table 3). ***, **,* indicate significance at the 1, 5, and 10% level, respectively. Standard errors in parentheses areheteroskedasticity-robust standard errors clustered at the bank level.

Interaction term with
BK_CAPGAIN
Small (low)Large (high)Bank characteristics
Fixed effects
Firm-year
Bank
Observations
Adjusted R 2

(i)

(ii)

(iii)

dum _ F _lnTA _ small

dum _ F _dum _ F _CAP _ small

SCORE _ low

15.52(5.04)
0.92(2.91)

9.13(2.84)-2.38(4.64)

6.79(3.60)
3.98(3.46)

***

***

YES

YES

YES

YES
YES
379,989
0.21

YES
YES
379,989
0.21

YES
YES
379,109
0.21

50

*

Appendices for Online Publication

51

Appendix A. Background figures for the developments in monetary policy
and bank portfolios in Japan
Figure A–1: Monetary policy measures and long-term interest rates inJapanThis figure presents development in monetary policy measures and long-term interest rates. Monetary
policy measures are the uncollateralized overnight call rate and the amount of Japanese government bonds(JGBs) held by the Bank of Japan. Long-term interest rates are represented by the 10-year yield on newly
issued JGBs.
Sources: Bank of Japan, Japan Bond Trading Co., Ltd.

3%

trillion yen
Amount of JGBs held by the BOJ (RHS)

300

Call rate (overnight, uncollateralized)
10-year JGB yield on newly issued bonds

2

250

1

200

0

150

-1

100

-2

50

0

-3
FY 00

01

02

03

04

05

06

52

07

08

09

10

11

12

13

14

Figure A–2: Japanese banks’ asset portfolios and asset returns
These figures present developments in Japanese banks’ asset portfolios (bonds and loans) and asset returns
using aggregate data. Panel (a) shows the ratio of Japanese government bond (JGB) holdings to total loans
outstanding, (b) shows the annual rate of change in loans outstanding to corporations, and (c) shows theaverage interest rate on newly contracted loans including bills discounted. The return on JGBs is presented
in Figure 1.
Source: Bank of Japan(a) Banks’ asset portfolios: Bonds/loans ratio
45

%

40
35
30
25
20
15
10
FY 00

01

02

03

04

05

06

07

08

09

10

11

12

13

14

(b) Annual growth rate of loans to corporations
annual change, %
5
4
3
2
1
0
-1
-2
-3
-4
-5
FY 00
01
02

03

04

05

06

07

08

09

10

11

12

13

14

05

06

07

08

09

10

11

12

13

14

(c) Average loan interest rate
2.5

%

2.0

1.5

1.0

0.5
FY 00

01

02

03

04

53

Appendix B. Bank portfolio selection model
To derive theoretical predictions on the effect of long-term interest rates on banklending, we construct, as mentioned in the text, a simple bank portfolio selection
model. In this Appendix, we provide a detailed analysis of banks’ portfolio
selection with the VaR constraint, from which we abstracted in the text.
As in Section 3, the VaR constraint is given by the following inequality:
A.1
and

where

, which represent the unexpected

losses on loans and bonds at the time of stress. We assume that

and

are

negative.
From the Kuhn-Tucker conditions, we obtain

where

∗

and

∗

∗∗

∗

(A.2)

∗∗

∗

(A.3)

are the optimal amount of loans and bonds without the VaR

constraint, which are given by equations (A.4) and (A.5) below.
∗

1

∗

1

(A.4)
(A.5)

54

represents the shadow price of a bank’s capital
multiplier associated with equation (A.1)), and(i.e., the Lagrange

andare given by

0

(A.6)

0

(A.7)

Substituting (A.2) and (A.3) into (A.1) yields
∗

∗

0

(A.8)

Thus, from equations (A.2) and (A.3), it can be easily seen that the optimal
amount of loans and bonds under the VaR constraint,

∗∗

and

∗∗

, is smaller

than the optimal amount of loans and bonds without the VaR constraint,
∗

∗

and

.
Let us now consider the comparative statics of the effects of a change

in

on

∗∗

. From equation (A.2), we have
∗∗

∂ ∗
∂

∂
∂

(A.9)

∗∗

0
1

⁄

(A.10)

055(A.11)

0 andBecause∗0 , the first term

negative, while the second term∗in equation (A.9) isis positive. The first term shows that anincrease in

reduces the unexpected loss on bonds and reduces the Lagrange

multiplier, therefore relaxes the VaR constraint. It therefore has a positive

impact on∗∗. The second term shows that an increase inraises the amountof bond holdings, which in turn tightens the VaR constraint (increases the
Lagrange multiplier). Thus, it has a negative impact on
of

∗∗

on

∗∗

. The overall effectdepends on the relative magnitude of these two opposing effects.

Next, we consider the comparative statics of the effects of a change in
on

∗∗

.
∗∗

0

Because an increase inimpact on∗∗(A.12)

always relaxes the VaR constraint, it has a positive.

Next, we extend our analysis above (the benchmark case) to a three-asset model.
Assume that there are two kinds of loans: safe loans ( ) and risky loans ( ). We
define the riskiness of loans in terms of the mean, standard deviation, and56

Sharpe ratio of the return on loans. Specifically, we assume that the return on
risky loans has a higher mean and higher standard deviation than safe loans,while the Sharpe ratio of risky loans is lower than that of safe loans:(A.13)(A.14)(A.15)
Equation (A.15) implies that loans are risky if they do not offer a sufficiently
large risk premium to compensate for their return volatility.
As in the benchmark case, we assume that the returns of all three assets
are independent from each other. Banks’ profits and balance sheets therefore
take the following form:(A.16)s. t.

(A.17)The VaR constraint takes the following form:(A.18)

0
Similar to the benchmark case, banks’ choose,andto maximize (4)subject to the VaR constraint (A.18). The optimal portfolios are given by57

where

∗

and

∗∗

∗

(A.19)∗∗∗(A.20)∗∗∗(A.21)

are respectively defined as:
1∗(A.22)
0(A.23)(A.24)The Lagrange multiplieris [now] given by
∗

∗

∗

0

(A.25)We are interested in how the ratio of riskier loans to safer loans changes
as banks’ net worth and long-term interest rates change. Note that equations(A.19) and (A.20) imply that∗∗

(A.26)∗∗

Inspection of equation (A.26) reveals that, under assumption (A.15),
∗∗

/ ∗∗

0

(A.27)

Recall that the Lagrange multiplier represents the shadow value of banks’ net
worth under the VaR constraint. Equation (A.27) implies that when the VaR58

constraint loosens banks invest in riskier loans with a lower Sharpe ratio.
Similar to equation (A.8) in the benchmark case, equation (A.25) implies that
(A.28)

0

In other words, when banks’ net worth increases, the VaR constraint loosens.
Combining equations (A.27) and (A.28), we obtain
∗∗

/ ∗∗

∗∗

/ ∗∗

0

(A.29)

This implies that when banks’ net worth increases due to a capital gain fromlong-term bonds, they increase loans to riskier firms more than loans to safer
firms.
∗∗

Next, we analyze how/ ∗∗ changes when the long-term interest

rate declines. Note that
∗∗

where

∗∗ / ∗∗

/ ∗∗

∗∗

/ ∗∗

(A.30)

0 (equation (A.27)). Similar to the benchmark case inequation (A.9), the sign ofdepends on the size of the two offsetting effects(the relative values of the first term and the second term):
∂ ∗
∂

∂
∂
where

0 and

(A.31)

0 are defined analogously to equations (A.10) and59

(A.11). Therefore, the effect of the decline in the long-term interest rate on∗∗/ ∗∗ is ambiguous.

60