Discussion Paper No. 625

WHY COMMERCIAL BANKS HELDEXCESS RESERVES:THE JAPANESE EXPERIENCE OF
THE LATE ‘90S

Kazuo Ogawa

December 2004

The Institute of Social and Economic Research
Osaka University
6-1 Mihogaoka, Ibaraki, Osaka 567-0047, Japan

December 2004

Why Commercial Banks Held Excess Reserves:
The Japanese Experience of the Late ‘90s*

Kazuo Ogawa
Institute of Social and Economic Research,
Osaka University* This is a substantial revision of the paper I submitted to the Financial ResearchCouncil. I am grateful to Hiroshi Fujiki, Shin-ichi Fukuda, Hideo Hayakawa, Nobuo
Inaba, Kazumasa Iwata, Toshiki Jinushi, Keimei Kaizuka, Hiroshi Koyama, Ryuzo
Miyao, Hiroshi Nakaso, Kunio Okina, Yoshinori Shimizu, Etsuro Shioji, Shigenori
Shiratsuka, Hisashi Tanizaki, Juro Teranishi, Fukujyu Yamazaki, Jyunji Yano, Yukihiro
Yasuda and the participants of the seminars at the Bank of Japan and Kobe University
for extremely valuable comments and suggestions on early version of the paper. This
research was partially supported by Grants-in-Aid for Scientific Research 12124207 of
the Ministry of Education.

Abstract
We investigated, empirically, why Japanese banks held excess reserves in the late
1990s. Specifically, we pin down two factors explaining the demand for excess
reserves: a low short-term interest rate, or call rate, and the fragile financial health ofbanks. The virtually zero call rate increased the demand for excess reserves
substantially, and a high bad loans ratio largely contributed to the increase in excess
reserve holdings. We found that the holdings of excess reserves would fall by half if thecall rate were to be raised to its level prior to the adoption of the zero-interest-rate
policy, and the bad loans ratio were to fall by 50%.

JEL Classification Number: E42, E51, E52, and G21
Keywords: Excess Reserve, Bad loans, Zero-interest-rate-policy

Correspondence to:
Institute of Social and Economic Research, Osaka University,
6-1 Mihogaoka, Ibaraki, Osaka, 567-0047 JAPAN
Tel: +81- 6- 6879-8570 Fax: +81- 6-6878-2766
E-mail: ogawa@iser.osaka-u.ac.jp

1. Introduction
Japanese banks have chronically held excess reserves since the late ‘90s. Figure 1
illustrates the ratio of actual reserves to required reserves for commercial banks as awhole. The increasing trend in the excess reserve ratio has been conspicuous since thesummer of 2001, and this ratio reached a high of 5.88 in October 2003.1 The excess
reserve ratio typically parallels the supply of reserves. In fact, the reserve supply began toincrease when the Bank of Japan announced that it would provide ample funds to pushdown the uncollateralized overnight call rate, or short-term inter-bank money market rate,
as low as possible, in February 1999. This action is known as the “zero-interest-rate
policy.” Furthermore, the reserve supply drastically increased after the Bank of Japan(BOJ) switched its operating target for money market operations from theuncollateralized overnight call rate to the outstanding balances of the current accounts
held at the BOJ in March 2001. The target level of outstanding balances of the BOJ’s
current accounts was valued at around five trillion yen in March 2001, but then rose to
between 30 and 35 trillion yen by January 2004.
However, it should be noted that the reserve supply does not necessarily automaticallycreate a demand for reserves. The aim of this study, therefore, was to shed light on the
demand side of reserves and to conduct an empirical investigation into why commercial
banks hold excess reserves. In actual fact, banks have their own motives for holding
excess reserves. We identified two factors that may have affected banks’ reserve demands
since the late ‘90s. The first of these factors is the nearly zero level of the call rate: theuncollateralized overnight call rate was pushed down to its minimum level after the
adoption of the zero-interest-rate policy. Reserves and call loans are close substitutes; as aresult, banks have more incentive to hold reserves when the call rate is very low.
The second relevant factor is the instability of the financial system. Ever since theoutbreak of financial institution debacles in the late ‘90s, depositors have been very
cautious about choosing which banks to deposit their money in. This implies that, ingeneral, once the balance sheet of a bank deteriorates, depositors will switch deposits
from one bank to another, more healthy one. Therefore, banks with fragile balance sheets
have an incentive to hold reserves, for precautionary reasons.2 Incorporating these factors,
1

we constructed a simple theoretical model of bank reserve demand. Using a panel dataset
for banks, we estimated these banks’ optimal demand functions for reserves, as derived
from the theoretical model. The quantitative importance of the aforementioned two
factors was evaluated by means of a simulation analysis, based on the parameter
estimates in the banks’ reserve demand functions.3
Our main findings may be summarized as follows. Using a theoretical model, we wereable to derive each bank’s optimal demand for reserves, which is a decreasing function of
the short-term interest rate and an increasing function of the bank’s financial health,represented by either its bad loan ratio or the rate of change in its share price. It turned outthat both factors significantly impact banks’ reserve demands, as suggested by thetheoretical model. Quantitatively, the effect of the short-term interest rate on reserve
demand was quite large. We found that raising the call rate to 0.05%, its level just before
the adoption of the zero-interest-rate policy, decreased the demand for excess reserves inthe banking sector as a whole by as much as 30-40%. The effect of a bank’s financial
health on its excess reserve demand was also significant. Excess reserves were reducedby 13-29% when the bad loan ratio was halved; this constitutes the goal to be attained by
the end of FY 2004 in the Program for Financial Revival, under the Koizumi
Administration.
The paper is organized as follows. The next section provides descriptive statistics forthe banks’ reserve holdings, which are based on the panel dataset for the Japanesecommercial banks used in our study. Section 3 constructs a simple theoretical model ofreserve demand and derives the optimal demand equation for reserves, which are to be
estimated. Section 4 presents the estimation results, and Section 5 conducts a simulation
analysis, based on the estimation results from the previous section, in order to evaluate
quantitatively the effects of the short-term interest rate and bank financial health onexcess reserve demand. Section 6 concludes the study.

2. To What Extent Did Banks Hold Excess Reserves?
We first calculated the extent to which commercial banks held excess reserves using
panel data for Japanese banks during the period FY 1991 to 2002. We compared the2actual reserve holdings at the end of each fiscal year with the reserves required at thattime. The required reserves were calculated as follows. The reserve requirement ratios fordeposits depend upon the type and amount of deposits, as is shown in Table 1. For
example, when a bank holds three trillion yen as time deposits, the bank should hold18.275 billion yen (= (3000-2500) × 0.012 + (2500-1200) × 0.009 + (1200-500) × 0.0005 +(500-50) × 0.0005) as required reserves.
The required reserves at the end of a fiscal year are computed for each bank in ourpanel dataset, and compared with the actual reserve balance, to gauge the extent to whichbanks hold excess reserves. Our panel data set consists of 145 banks, of which nine arecity banks, three are long-term credit banks, seven are trusts, and 126 are regional banks.
Merged and/or insolvent banks were excluded from the sample. Therefore, our dataset
constitutes an unbalanced panel. The sample period covers the years from FY 1991 to FY
2002. Table 2 presents descriptive statistics of the extent to which banks held excess
reserves. The median of the ratio of actual reserves to required reserves was less than one
until 1996, while it exceeded this value after 1997. It should be noted that the year inwhich the excess reserve ratio began to exceed one was characterized by a number ofbankruptcies of financial institutions. It is likely that banks held excess reserves forprecautionary purposes, to meet the demands of depositors switching from unhealthybanks to healthy ones.
In 2001, the excess reserve ratio again exhibited a sharp increase. The median ofthe excess reserve ratio in 2001 was about twelve times as large as that in 2000. This
sharp increase coincided with the BOJ’s switch of monetary policy target: from theshort-term interest rate to the outstanding balances of the current accounts at the BOJ,
constituting the so-called “quantitative easing” of monetary policy. Under the newmonetary policy regime, the BOJ increased the monetary base substantially.
The standard deviation of the excess reserve ratio also increased after the middle of the‘90s, suggesting that there were diverse reserve holding patterns across banks. This fact
may also be inferred from Figure 2, which illustrates the frequency distribution of theexcess reserve ratios in 1994, 1999 and 2001. The frequency distribution was moredispersed and less skewed to the right in later years.
33. A Model of Bank Demand for Reserves
Consider a bank i, which allocates a given amount of deposits (Di ) to aninterest-bearing asset, and with reserves at a central bank bearing no interest, under thestochastic withdrawal of deposits.4 By allocating all of its deposits to the interest-bearing
asset, and keeping its reserves to the minimum required level, the bank can maximize its
income from interest but runs the risk of being unable to meet large, unanticipatedwithdrawals of deposits. Such a situation may be costly for the bank, as it gives rise toapprehension among depositors regarding the fragility of the bank’s balance sheet, anddepositors may thus be prompted to further withdraw their deposits. Therefore, the bank
optimally allocates its resources between the interest-bearing asset and reserves, tomaximize its expected interest income, while simultaneously taking into account the cost
incurred in the case of reserve shortages.
Formally, the objective function of the bank is stated as follows:[ (~rL (Di − Ri ) − rp ,i E Max 0, X i − Ri

)]

(1)

where rL : interest rate on interest-bearing asset

rP ,i : penalty rate for the i-th bank in case of reserve shortage ( rp ,i > rL )Ri : reserve balance of the i-th bank~
X i : stochastic deposit withdrawal at the end of the period

The bank maximizes eq.(1) with respect to Ri subject to the following required reserve
constraint:

Ri ≥ δ i Di
where δ i :required reserve ratio for the i-th bank
The first-order condition is given by 5

4

[

]

~
rp ,i Pr X i ≥ Ri = rL − λ(2)where Pr[ ] indicates probability

λ : non-negative Lagrangean multiplier associated with the required
reserve constraint

The LHS of eq.(2) represents the decrease in the liquidity shortage cost brought about by
increasing reserves, or the marginal benefit of increasing reserves, while the RHS
provides the marginal cost of increasing reserves. When λ > 0 , the bank holds no morethan the required amount of reserves. On the other hand, when the optimal reserve

holdings (Ri* ) exceed the required level, then λ = 0 . Figure 3 illustrates the way in which
the optimal level of excess reserves is determined. When λ = 0 , it is easy to see from thefigure that the demand for reserves depends upon the interest rate ( rL ) and the penalty
rate ( rP ,i ). The demand for reserves increases as the interest rate falls and the penalty rate
rises. This model, while simple, can explain the surge in excess reserve holdings by
Japanese banks that took place in the late ‘90s. The call rate was virtually zero under thezero-interest-rate policy, and the BOJ maintained the call rate to a level as low as possible
under the new monetary policy regime. In the late 90s, banks with massive amounts ofbad loans became insolvent, which may have led to a rise in the penalty rate. For thisreason, depositors became very cautious about the balance sheet conditions of banks in an
unstable financial system. If a bank’s reserves fell short of depositors’ withdrawals, thendepositors may have perceived the balance sheet of the bank to be deteriorating. This
perception would have accelerated the withdrawal of deposits, as well as the potential
bankruptcy of the bank. To avoid such a disaster, banks would have set the penalty ratequite high and increased their demand for excess reserves.

4. Estimation of Bank Demand Equations for Reserves
Derivation of Bank Demand Equations for Reserves
To derive a bank’s optimal demand equation for reserves, we must specify the way in~which banks anticipate deposit withdrawals. We assume that the random variable X i has
5~
a Pareto distribution. Specifically, the density function of X i is written as

θX θ~
f X i = ~ θ0+,1i
Xi

( )

~
X 0,i < X i < ∞(3)where θ , X 0,i : parameters of the distribution

θ > 0, X 0,i > 0

By specifying the density function of deposit withdrawals, we may calculate theprobability that deposit withdrawals exceed reserves, as follows:⎛ R ⎞~Pr X i ≥ Ri = ⎜⎜ i ⎟⎟⎝ X 0,i ⎠

[

]

−θ

(4)

The substitution of eq.(4) into eq.(2) and the rearrangement of terms yields the following
reserve equation:log Ri = log X 0,i −⎛r −λ ⎞⎟
log⎜ L⎜ r ⎟θ
⎝ p ,i ⎠1(5)~
It is quite likely that the bank’s subjective distribution of X i depends on the bank’s

attributes. When the balance sheet of a bank deteriorates, the bank may anticipate a large
amount of deposit withdrawals. In other words, the condition of a bank’s balance sheet
affects the distribution of its deposit withdrawals. We specify a bank’s balance sheet
condition using the bad loans ratio ( BADLOAN ). That is, we express X 0,i as a functionof deposits and the bad loans ratio.
X 0,i = αDηI BADLOAN iε(6)where α > 0,η > 0, ε > 0

Deposits are included in eq.(6) as a scale factor. Substituting eq.(6) into eq.(5) andarranging terms, we obtain the following optimal demand equation for reserves:
6log Ri = log α + η log Di + ε log( BADLOAN i ) −⎛r −λ⎞⎟
log⎜ L⎜ r ⎟θ
⎝ p ,i ⎠1(7)

For estimation purposes, we transform the demand equation for reserves into thedeviation from required reserves. First, when λ > 0 , banks do not hold any excess
reserves, so the deviation of optimal reserves from the required level is zero. In otherwords, the following equation is specified in logarithmic form:log Ri − log δ i Di = 0(8)Second, when the optimal demand for reserves exceeds the required level, the demand forexcess reserves is expressed aslog Ri − log δ i Di = log α − log δ i + (η − 1) log Di + ε log( BADLOAN i ) −⎛r ⎞log⎜ L ⎟ (9)⎜r ⎟θ
⎝ p ,i ⎠1

Since we can identify from the data which banks held excess reserves, we may estimate
the system of reserve demand equations, (8) and (9), using a Tobit.

Description of the Data
We briefly explain the variables used in estimation. The variable ( Ri ) represents thereserve balance of an individual bank at the BOJ. Deposits ( Di ) consist of all types ofdeposits, including certificates of deposit and debentures outstanding. The amount of
required reserves is calculated based on the deposit balances and the requirement ratios
provided in Table 1, as was discussed in Section 2. The required reserve ratio ( δ i ) is
obtained by dividing the required reserves by deposits.
The bad loans ratio is calculated in two different ways: (1) the ratio of risk
management loans to total loans ( BADLOAN 1i )6and (2) the ratio of non-performing
loans (NPL) under the Financial Reconstruction Law ( BADLOAN 2 i ). 7 The variable
7

BADLOAN 1i is available for the period including and following 1997, while the variable
BADLOAN 2 i is available for the period including and following 1998. Accordingly, theestimation period in each case begins with the year in which the bad loans ratio first
becomes available. We also use the rate of change in the share price ( SHAREi ) as a proxy
for the market’s perception of the banks’ financial health. 8 Table 3 presents thedescriptive statistics for the bad loans ratio. The variable BADLOAN 1i exhibited anincreasing trend until 2001, in terms of both the mean and the median, while the same
trend was observed for BADLOAN 2 i in terms of the median. Figure 4 presents thefrequency distribution for bad loans ratios in 1998 and 2002, both of which are calculated
from the risk management loans. There are considerable differences between the shapesof the frequency distributions in both years. In 2002, the peak of the frequency
distribution rose, and the distribution was more skewed to the left. The correlation
coefficient for these two measures is quite high (0.8982). However, the market’s
perception of banks’ financial health does not necessarily closely reflect the bad loans
ratio. In fact, the correlation coefficient between BADLOAN 1i and SHAREi is -0.1719,
and that between BADLOAN 2 i and SHAREi is -0.1803.
The penalty rate is likewise treated in two different ways. First, the penalty rate istreated as constant across banks and years. In this case, the penalty rate is subsumed into
the constant term. Second, the ratio of operating profits to total equity is employed. The
idea behind this is that the banks, the reserves of which are short of deposit withdrawals,
will eventually go insolvent and lose their entire operating profits. The interest rate is theuncollateralized overnight call rate.

Econometric Issues
We estimated eqs.(8) and (9) by pooled Tobit. The following procedure was used toclassify banks, according to whether they have excess reserves. When a bank’s actual
reserves exceed the required reserves by at least 10%, then it is identified as holding
excess reserves. This conservative classification with respect to banks holding excess
reserves reflects the unavailability of the daily deposit data upon which the reserve
requirement should be based.9 During estimation, we added dummy variables to account8

for the different types of banks, i.e., dummy variables for city banks (DCITY), long-term
credit banks (DCREDIT), and trusts (DTRUST). We also added the dummy variable(DPOLICY) to control for the monetary policy regime change that occurred in March
2001. Thereafter, the monetary base increased substantially in order to satisfy the target
set for the current accounts balance at the BOJ.

Estimation Results
Table 4 presents the estimation results for banks’ demands for reserves. The
estimation is conducted for six specifications, where three variables are used to represent
the banks’ financial health, and where two account for the penalty rate. The estimation
results are quite satisfactory, in the sense that the coefficient estimates of the three key
variables determining the demand for reserves are statistically significant, irrespective of
the model specification. Deposits exert a significantly positive effect on reserve holdings.
The call rate has a negative effect on the demand for reserves, as is predicted from thetheoretical model in Section 3.10 The two bad loans ratios also affect the demand forreserves positively, which implies that banks with higher bad loans ratios increased theirreserves. Furthermore, increases in the rate of change in share prices decreased thedemand for reserves, though this effect is insignificant.
Table 5 tabulates the elasticities of reserve demands with respect to deposits, the callrate, and the bad loans ratio, for the four types of banks holding excess reserves. Theseelasticities are calculated on the basis of the results of the estimation with BADLOAN 1i
as the bad loans ratio, and the ratio of operating profits to total equity as the penalty rate.11
12

The deposit elasticity is generally close to one, except for city banks, in which case it ismuch less than one (0.4491). The interest-rate elasticity ranges from -0.1816 to -0.4146,
while the elasticity with respect to the bad loans ratio ranges from 0.2149 to 0.5010. The
magnitude of this elasticity is smaller for city banks because, of these, a lower proportionof banks held excess reserves.

95. The Effects of the Short-term Interest Rate and Bank Financial Health on the Demandfor Excess Reserves: A Quantitative Evaluation
In the previous section, we found that both the short-term interest rate and banks’financial health are significant explanatory variables of the demand for reserves. Basedon the parameter estimates of the demand equation for reserves, and using simulation
analysis, we evaluated quantitatively the extent to which changes in the short-term
interest rate and/or banks’ bad loans ratios affected the demand for excess reserves.
Specifically, we took the following steps. First, we calculated the theoretical values ofexcess reserves by substituting the actual exogenous variables for 2002 into the estimateddemand equation for reserves, or eq.(9), and subtracted the required reserves. Next, we
calculated the predicted value of excess reserves under different scenarios of the call rate
and the bad loans ratio. We assumed that the call rate was raised to its level prior to theadoption of the zero-interest-rate policy. In other words, the call rate was set to its level inMarch 1998, or to 0.05%.13 With regard to the banks’ financial health, we considered acase in which the bad loans ratio was halved. This scenario is consistent with the Koizumi
Structural Reform Plan, introduced in October 2002, which specified that
non-performing loans should be reduced by 50% within one year.
The predicted excess reserves thus calculated were summed up across banks, and theaggregated excess reserves were compared with their baseline value. Table 6 indicates theextent to which banks’ excess reserves are reduced under the different scenarios for thecall rate and the bad loans ratio, and under four different specifications of the reserve
demand equation. When the call rate is raised, excess reserves are reduced by as much as
40% in the constant penalty case, and by about 30% in the variable penalty case.
Although the magnitude of the reduction in excess reserves is slightly less for the case inwhich the banks’ financial health is improved, it is not negligible in this case. Excess
reserves are reduced by 13% to 29%. When increases in both the call rate and banks’financial health are implemented simultaneously, the holdings of excess reserves are
reduced almost by half.

106. Concluding Remarks
We empirically investigated why Japanese banks held excess reserves in the late ‘90s.
We were able to pin down two factors that explain the demand for excess reserves: a low
short-term interest rate, or call rate, and banks’ fragile financial health. The nearly zero
call rate substantially increased the demand for reserves, and the high bad loans ratio also
contributed to the observed increase in reserve holdings. A quantitative evaluation ofthese factors was also conducted. It was found that excess reserve holdings may be halved
by raising the call rate to its level prior to the zero-interest-rate policy, and by decreasing
the bad loans ratio by 50%. The Japanese financial system is gaining stability as banks
rapidly eliminate bad loans, and this elimination should lead to a reduction in excess
reserve holdings.

11

Footnotes
1

There are two spikes in the figures, each of which corresponds to Year 2000 and Fiscal
Year 2002 problems. On those occasions, the policy authority provided ample liquidity tomeet a surge in demand and secure stability in the financial markets.
2
See Shirakawa (2002) for a detailed discussion of the factors that have contributed to anincrease in banks’ reserve demands since the late ‘90s.
3
Hosono et al. (2001), Hayashi (2001), and Uesugi (2002) investigated the liquidity
effect using daily reserve data. The relationship between the equilibrium short-term
interest rate and the reserve supply may be obtained by aggregating banks’ reserve
demands. Our focus in this study was to examine what motivates individual banks to holdexcess reserves.
4
The following model of reserve demands comes from Chapter 8 in Freixas and Rochet(1997).
5
It can be shown that the objective function of the bank is a concave function of reserves,
so the solution to the first-order condition is guaranteed to be a maximum of the objectivefunction.
6
Risk management loans include loans to borrowers in legal bankruptcy, past-due loans
in arrears by six months or more, loans in arrears by three months or more but less thansix months, and restructured loans.
7
The NPLs under the Financial Reconstruction Law are defined as the sum of the assets
classified as “bankrupt/de facto bankrupt,” “doubtful,” and “special attention.”
8
Some banks are not listed on the stock exchange, so these are excluded from the sample
in the estimation of the demand equation for reserves incorporating the share price.
9
To check for robustness, we also used a more conservative definition of excess reserves.
In this case, banks with actual reserves exceeding the required reserve by 50% wereidentified as banks holding excess reserves. Under this definition, the estimation results
remained qualitatively unchanged.
10
Loan and Wood (2002) also reported that the interest rate has a significantly negative
effect on the reserve demands of commercial banks in the U.S.A.
11
The elasticities are calculated by multiplying the adjustment factor by the original
parameter estimates. See Chapter 16 of Wooldridge (2002) for a discussion of adjustment
factors.
12
The elasticities based on the other specifications are calculated in a similar way. They
are not reported here, since they follow the same pattern as that reported in the text. Theseelasticity estimates are available upon request from the author.
13
It is assumed that the penalty rate does not change.

12References[1] Freixas, X. and J.-C. Rochet(1997). Microeconomics of Banking, The MIT Press.
[2] Hayashi,F.(2001).” Identifying a Liquidity Effect in the Japanese Interbank Market,”International Economic Review 42, pp.287-315.
[3] Hosono,K., Sugihara,S. and T.Mihira(2001) Kinyu Seisaku no Yukosei to Genkai(Effectiveness and Limits of Monetary Policy), Toyo Keizai Shinposha, (in Japanese).
[4] Lown,C.S. and J.H.Wood(2003).” The Determination of Commercial Bank Reserve
Requirements,” Review of Financial Economics 12, pp.83-98.
[5] Shirakawa,M.(2002).” Ryoteki Kanwa Saiyogo 1 nenkan no Keiken (Experienceduring One Year after Adoption of Quantitative Easing Policy),” in Komiya,R. andNippon Keizai Center(eds.) Kinyu Seisaku Rongi no Soten: Nichigin Hihan to sono
Hanron (Issues of Monetary Policy Debates: Criticism of the Bank of Japan and
Rebuttal) , Nippon Keizai Shinbunsha, pp.157-234. (in Japanese)[6] Uesugi,I.(2002).” Measuring the Liquidity Effect: The Case of Japan,” Journal of
the Japanese and International Economies 16, pp.289-316.
[7] Wooldridge,J.M.(2002). Econometric Analysis of Cross Section and Panel Data, The
MIT Press.

13Figure 1 Excess Reserve Ratio
6

5

4

3

2

1

0
1995.01 1995.07 1996.01 1996.07 1997.01 1997.07 1998.01 1998.07 1999.01 1999.07 2000.01 2000.07 2001.01 2001.07 2002.01 2002.07 2003.01 2003.07

The Excess reserve ratio is defined as the ratio of actual reserve to required reserve.
Data Source: The Bank of Japan Homepage

Figure 2 Frequency Distribution of Excess Reserve Ratio in 1994

70

60

50

40

30

20

10

0
-0.5

0.5-1

Data Source: Nikkei Financial Data

1-1.5

1.5-2

2-3

3-5

5-7

7-10

10-15

Median=0.91 Standard Deviation=1.56

15-20

20-30

30-40

40-50

50-

Figure 2 Frequency Distribution of Excess Reserve Ratio in 1999
20
18
16
14
12
10
8
6
4
2
0
-0.5

0.5-1

Data Source: Nikkei Financial Data

1-1.5

1.5-2

2-3

3-5

5-7

7-10

10-15

Median =4.00 Standard Deviation=39.38

15-20

20-30

30-40

40-50

50-

Figure 2 Frequency Distribution of Excess Reserve Ratio in 2001
30

25

20

15

10

5

0
-0.5

0.5-1

Data Source: Nikkei Financial Data

1-1.5

1.5-2

2-3

3-5

5-7

7-10

10-15

Median=15.18 Standard Deviation=39.25

15-20

20-30

30-40

40-50

50-

Figure 3
Determination of Optimal Demand for Reserve[~
Pr X i ≥ Ri

]

rL
rp ,i

０

δ i DiRi*

Ri

Figure 4
Frequency Distribution of Bad Loans Ratio in 1998
Based upon Risk Management Loans
30

25

20

15

10

5

0
0-1

1-2

Data Source: Nikkei Financial Data

2-3

3-4

4-5

5-6

6-7

7-8

8-9

9-10

10-

Figure 4
Frequency Distribution of Bad Loans Ratio in 2002
Based upon Risk Management Loans
30

25

20

15

10

5

0
0-1

1-2

Data Source: Nikkei Finacial Data

2-3

3-4

4-5

5-6
％

6-7

7-8

8-9

9-10

10-

Table 1
Reserve Requirement Ratios(1) Reserve Ratios on Deposits
Type of deposits

Amount of deposits

Reserve ratio (%)

Time Deposits
including Certificatesof Deposit

2.5 trillion yen -1.2

1.2 - 2.5
trillion yen

0.9

500 billion- 1.2 trillion yen

0.05

50 - 500 billion yen

0.05

2.5 trillion yen –1.3

1.2 - 2.5
trillion yen

1.3

500 billion- 1.2 trillion yen

0.8

50 - 500 billion yen

0.1

Other deposits(2) Reserve Ratios on Debentures Outstanding
Type of banks

Reserve ratio (%)

Banks,
long-term credit banks
and foreign exchange bank

0.1

Notes: The reserve ratios in the table are effective on October 16, 1991.
Data Source: The Bank of Japan Homepage

Table 2
Descriptive Statistics of Banks’ Excess Reserve
Fiscal year
1991
1992
1993
1994
1995
1996
1997
1998
1999
2000
2001
2002

Ratio of actual reserve to required reserve
MedianStandard deviation
0.9564
0.97300.93370.90850.98280.99601.01911.1884
3.9963
1.193615.1764
12.6861

Data Source: Nikkei Financial Data

2.82
2.79
2.76
1.56
5.36
7.23
8.65
25.78
39.38
24.59
39.25
52.65

Table 3
Descriptive Statistics of Bad Loans Ratio(%)
Fiscal
year

1998
1999
2000
2001
2002

ratio of risk managementloans to total loans( BADLOAN1i )ratio of non-performing loans
under Financial Reconstruction
Law to total loans( BADLOAN 2 i )MeanMedianMeanMedian

6.1
7.7
8.1
8.7
8.2

4.5
6.0
6.9
8.1
8.1

7.5
10.0
9.4
10.0
9.0

5.6
6.6
7.6
9.0
8.8

Notes: Risk management loans include loans to borrowers in legal bankruptcy,
past due loans in arrears by 6 months or more, loans in arrears by 3 months or more
and less than 6 months, and restructured loans.
The non-performing loans under the Financial Reconstruction Law are defined as
the sum of the assets classified as “bankrupt/de facto bankrupt”, “doubtful”, and“special attention.”
Data Source: Nikkei Financial Data

Table 4 Estimation Results of Optimal Demand Equation for Reserve
Choice of banks’balance sheet variableand penalty rate

Constant

DepositCall rate

Bad loans ratioor share pricechangeCity banks

Dummy variables
Long-term
Trustcredit banks
banks-19.3073*** 1.5453*** -0.9554***(-14.32)(19.09)(-10.24)

0.5771***(3.89)-0.9914**(-2.07)-0.6204(-0.93)0.5564(1.44)

0.5931***(3.89)

1.6518*** 618(28.38)-1009.00-15.0960*** 1.5531*** -0.6279***(-11.67)(18.61)(-8.28)0.7588***(4.58)-1.0974**(-2.27)-0.3234(-0.44)0.2812(0.70)

0.7259***(4.65)

1.6708*** 597(27.90)-980.38-18.1284*** 1.4303*** -0.9426***(-13.49)(16.92)(-10.34)0.3014**(2.09)-0.8260*(-1.75)-0.3444(-0.53)0.6311*(1.66)

0.4194***(2.66)

1.6133*** 548(27.24)-903.41-14.0622*** 1.4422*** -0.6290***(-10.90)(16.47)(-8.28)0.4938***(3.04)-0.9334*(-1.95)-0.0391(-0.05)0.3507(0.88)

0.5341***(3.30)

1.6416*** 530(26.80)-882.02

Monetaryσpolicy change

NOBS
LOGL

BADLOAN1
Case 1
Constant penalty rate
Case 2
Variable penalty rateBADLOAN2
Case 3
Constant penalty rate
Case 4
Variable penalty rate

Share price change
Case 5Constant penalty rate
Case 6
Variable penalty rate

-17.5540*** 1.3032*** -0.9735*** -0.6614(-11.01)(13.24)(-9.79)(-1.54)-0.3524(-0.71)0.9609**(2.56)

0.6495***(4.16)

1.5456*** 476(24.87)-754.08-14.7277*** 1.3443*** -0.7190*** -0.5445(-9.43)(13.02)(-8.59)(-1.21)-0.5970(-1.17)0.7637*(1.91)

0.7924***(4.99)

1.5805*** 465(24.57)-745.34

Notes: σ : standard deviation of disturbance LOGL: logarithm of likelihood function NOBS: number of observations
Values in parentheses are t-values. *, **, ***: significant at 10%, 5%, and 1% level, respectively

Table 5
Estimates of Reserve Demand Elasticity
Types of banks

DepositCall
rate

Bad loanratio

City banks

0.4491-0.18160.2194Long-term creditBanks

1.0255-0.41460.5010Trust banks

0.8902-0.35990.4349

Regional banks

0.9462-0.3825

0.4623

Notes: The elasticity is calculated for banks holding excess reserveon the basis of estimation results with BADLOAN1i as
the bad loan ratio and the ratio of operating profits to total
equity as penalty rate.

Table 6
Effects of Call Rate Increase and Reduction of Bad Loans Ratio on Demand for Excess
Reserve: Quantitative Evaluation by Simulation Analysis(%)
Choice of banks’balance sheet variableand penalty rate

Change of excess reserve by
increase of call rate reduction of
to 0.05%
bad loans ratio
total
by 50%BADLOAN1
Case 1
Constant penalty rate

-40.1

-22.8

-51.7

-29.6

-28.8

-47.9

-39.4

-12.8

-45.9

-29.3

-19.9

-41.9

Case 2
Variable penalty rateBADLOAN2
Case 3
Constant penalty rate
Case 4
Variable penalty rate