Journal of Applied Input-Output Analysis, Vol. 11 & 12, 2006

Does Monetary Policy Work under Zero-Interest-Rate?1

By

Kazusuke Tsujimura* and Masako Tsujimura"

Abstract
In the spring of 1999, the Japanese call money rate reached to the zero-interest-rate level,

and has remained under quarter percent since then. "Does monetary policy work under zero-interest-rate at all?" is the question to be answered in this study. We are to examine the ef

fectiveness of so-called Quantitative Easing Policy (QEP) introduced by the Bank of Japanin March 2001 using Asset-Liability-Matrix (ALM) derived from the Flow-of-Funds Ac
counts. The conclusions of this article is that the performance of the QEP conducted by the
BOJ is improving gradually in recent days, partially because of the introduction of new
measures including corporate stock and ABS purchasing operations.

1 Introduction
Ten years ago, nobody imagined that the interest rate would ever hit the one percent

level. Nowadays, we are commonly talking about zero-interest-rate. The U.S. Federal
Open Market Committee lowered its intended federal funds rate to one percent on June25, 2003. Actually the federal funds rate was hovering somewhere around one percent
Received July 2005, final version received January 2006.

1 The authors are most grateful to Professor Jiro Nemoto (Nagoya University), the editor of the journal, and the two anonymous referees for their useful advices. The earlier versions of this paper havebeen presented at the following conferences: Japanese Economic Association 2003 Spring Meetings,
Oita, Japan, Jun. 14, 2003; The XII International "Tor Vergata" Conference on Banking and Finance,
Rome, Italy, Dec. 9-11, 2003; Fourth Annual Missouri Economics Conference, Columbia, Missouri,

U.S.A., Apr. 2-3, 2004; Forecasting Financial Markets and Economic Decision-making FindEcon

2004, Lodz, Poland, May 6-8, 2004; Canadian Economic Association 38th Annual Meetings,
Toronto, Canada, Jun. 4~6, 2004; The 21st Symposium on Banking and Monetary Economics, Nice,
France, June 10-11, 2004; 28th General Conference of International Association for Research in In
come and Wealth, Cork, Ireland, August 22-28, 2004. We would like to thank Dr. Shigenori Shirot-

suka (Bank of Japan), Dr. Natacha Valla (European Central Bank), Professor Wladyslaw Milo (University of Lodz), Professor Alena Kimakova (York University), Dr. Richard Werner (Southampton
University), Professor Charles Goodhart (London School of Economics and Political Science) andmany other participants of the conferences for their valuable comments and suggestions.

* Faculty of Economics, Keio University, Tokyo, Japan.

**Keio Economic Observatory, Keio University, Tokyo, Japan. E-mail: mizosita@sanken.keio.ac.jp

50

Journal of Applied Input-Output Analysis, Vol. 11 & 12, 2006

for more than one year till the Fed raised the interest rate by 25 basis points to 1.25
percent on June 30, 2004. As early as in the spring of 1999, the Japanese call money

rate, an equivalent of U.S. federal funds rate, reached to the zero-interest-rate level, andhas remained under quarter percent up to now. (See Figure 1.) In June 2003, even the
key long-term interest rate, the yield of the Japanese Government Bond (JGB), hit 0.43
percent for a brief time. Keynes (1936) suggests that the interest rate oriented monetary
policy become ineffective at near zero interest rate level because of the existence of theliquidity trap. How about some other type of monetary policy, then? "Does monetary
policy work under zero-interest-rate at all?" is the question to be answered in thisstudy.

Figure 1 The Overnight Interest Rates

U.S. Federal Funds Rate
Japanese Call Money Rate

On

On

On

On

On

On

On

On

On

As Bernanke and Reinhart (2004) suggests, there are three alternative monetary

strategies for stimulating the economy that do not involve changing the current valueof the policy rate. Specifically, these alternatives involve (a) providing assurance to fi
nancial investors that short rates will be lower in the future than they currently expect,(b) shifting the composition of the central bank's balance sheet, and (c) increasing thesize of the central bank's balance sheet beyond the level needed to set the short-term

policy rate at zero. By these definitions, so-called Quantitative Easing Policy (QEP)
then newly introduced by the Bank of Japan (BOJ) in March 2001, was a combinationof (b) and (c). (See the following section for the details.) If it is the case, the money
market operations conducted by the monetary authorities should be fully reflected intheir own balance sheets.

In the System of National Accounts (SNA), the financial surplus (i.e. the incre

ment in the difference between the financial assets and the liabilities excluding thechanges in the market value) is corresponding to the balance of savings and invest-

Does Monetary Policy Work under Zero-Interest-Rate?

51

ments in the non-financial economy. Thus, if there are induced changes in the assets
and/or the liabilities of the economic principals (i.e., institutional sectors including cor
porations, households, governments etc.) as results of the shifting in composition and/or the changes in the size of the central bank's balance sheet, the non-financial econ

omy will be affected as well in terms of capital formation and so on. This might be thechannel that the changes in the money market operation would affect the non-financial
economic activities without changing the current value of the policy rate. Since theFlow-of-Funds Accounts (FFA) is a collection of the balance sheets of the economic
principals, by translating those balance sheets into an Asset-Liability-Matrix (ALM)
that is a sector-by-sector matrix, we must be able to calculate the induced effects of the

QEP on the financial as well as non-financial economy by application of the Leontief
inverse commonly used in the input-output analysis. In our experimental study, wewere successful to employ the ALM derived from the FFA to examine the impacts of

the introduction of the QEP on the stagnated Japanese Economy. (See Tsujimura andMizoshita (2003).) It was an attempt to apply the concept of the Leontief inverse to the
ALM originally proposed by Stone (1966) and Klein (1983).

Since the observation period of the previous study was only a little more than halfa year (December 2000 through September 2001), we used the ALM of March 2001 asa benchmark to calculate the effects of the money market operation of the respective
month. After the publication of the paper, we have received many useful comments andsuggestions to which we are more than grateful. Among them, we found some remarks

including the one from Professor Laurence Klein himself to question the stability ofthe parameters implied in the ALM in a longer period. If the economic structure repre
sented by the ALM is easily changeable, it must be difficult to educe the efficacy ofthe monetary policy by means of that. The alterations in the non-financial economy
could be derived either from the shifts in the money market operation or from the mutation in the flow-of-funds structure of the economy reflected in the coefficient matrixof the ALM. In this new treatise, we are to demonstrate a new procedure to distinguish
the former from the latter based on the method of input-output structural decomposi

tion analysis (IO-SDA)2, so that we can tell the significance of the monetary policy inmore precise manner. The expansion of the observation period up to date, which has

been made possible without fearing the confusion of the two causes, put us in position
to determine if the QEP adopted by the BOJ last four years is a success. This will be a

big step forward to examine the usefulness of the monetary policy in a country wherezero interest rate prevails.

Klein (2003) hints that the portfolio parameters of an FFA could be a function of

the relevant interest rates and the inflation rate. If it is the case, we might be able toconstruct a model to trace the serial modulation of the ALM itself, which could be amajor breakthrough to expand the horizon of the traditional flow-of-funds analysis.
2 IO-SDA was originally proposed by Chenery (1960), Chenery, Shishido & Watanabe (1962) and
Carter (1970). The method has been developed by Wolff (1985), Feldman, McClain & Palmer(1987), Blair & Wykoff (1989), Rose & Chen (1991), Martin & Holland (1992), Korres (1996),

Cronin & Gold (1998), Liu & Saal (2001) and Andresso-O'Callaghan & Yue (2000, 2002) among
others. The detailed comparison of the methods is found in Betts (1989) and Dietzenbacher & Los(1998).

52

Journal of Applied Input-Output Analysis, Vol. 11 & 12, 2006

However, when we take only the zero interest rate situations into account, it is a logi

cal contradiction to follow the approach. Actually, in case of today's Japan, the interest
rate remains in the vicinity of nil while the changes in the inflation rate is kept mini

mal somewhere just below zero. Therefore, we had to develop some other line of pro
cedure to single out the very effects of the QEP.
In the first place, we have abandoned the idea to explain why the economic structure symbolized in the ALM has changed at all. Rather, we opted for a simple andeasy scheme. We have just decomposed the observed changes in the non-financial
economy into two parts: (1) the first component attributed to the shifts in the money
market operation, and (2) the second component attributable to the mutation of the
ALM itself. The first component is calculated by multiplying the coefficient matrix of

the ALM of the previous period and the money market operation vector of the period;
and then subtracting the previous period's observed value afterwards. We can calculate
the second component likewise, by multiplying the coefficient matrix of the ALM ofthe period and the money market operation vector of the previous period; and thensubtracting the previous period's observed value. The procedure is an analogy to theway we make the NIPA (National Income and Product Accounts) chain index. Moreover, when we take the rate of change into consideration, the geographic mean of theindices of the first component and the second component is consistent with the observed value as Fisher (1927) demonstrated more than seven decades ago.
The second question we are to answer in this study is how effective is each device
adopted by the BOJ in its money market operations. In this paper, we are to present

the subdivided Nil for each market operation instrument. As we discuss in the follow
ing sections, the QEP has failed to give favourable results in the early stage of its introduction. Therefore BOJ revised its way of money market operation in the course oftrial and error. In the more recent months, the BOJ has introduced drastic measures inface of the prolonged recession and the plunge in the equity prices. One of the mostdramatic decisions is to purchase the corporate stocks from the commercial banks,
which are obliged to keep the corporate stocks in possession under the value of theirequity capital, to cope with the new legislation. Another unprecedented scheme for acentral bank is to purchase the Asset-Backed-Securities (ABS) to smooth the financingof the small and medium-sized enterprises to cover up the shortage of the bills in cir
culation eligible for the BOJ operations. The advantage of the present approach is thecapability to single out the effect of a particular policy device upon a particular sector
so that we can choose the best combination of the operation instruments.

2 The Quantitative Easing Policy
Before going any further, we have to discuss the details of the QEP adopted by the

BOJ. In the spring of 2001, the bank abruptly announced that it would shift the targetof the money market operations from the interbank interest rate (overnight call moneyrate) to the balance of current accounts held by the financial institutions at the central

bank. This means that the BOJ expect the commercial banks and other financial institu
tions to voluntarily build up a balance well over the legally required minimum reserve

Does Monetary Policy Work under Zero-Interest-Rate?

53

Figure 2 The Balance of the Current Accounts with BOJ

0Actual Balance of the Current Accounts:-#-*-x-x—X— Ceiling of the Intended Balance•

Leagally Required Reserves

30

25

120

1
15

in the current account. Simultaneously, the BOJ proclaimed it was to increase the bal

ance of the current accounts (then 4 trillion yen3) by one trillion yen to 5 trillion (while
keeping the official reserve ratio at the previous level!)4 , and was to add the sameamount of JGB on its asset portfolio. The intended amount of the balance of the current accounts was raised to 6 trillion yen in August, then to "above 6 trillion yen" in

September, and even further to 10-15 trillion in December 2001. That was not the endof the story. In February 2002, the BOJ announced that it would "provide more liquid-

3 The balance of the current accounts temporarily increased to 23 trillion yen in December 1999 by
way of precaution against so-called Y2K.

4 At ordinary times, the financial institutions try to keep the balance of current accounts at the level oflegally required minimum reserve. Since the BOJ does not pay interest on the current account bal
ances, the banks do not want to pile up "excess-reserve" while paying interest on the deposit accounts with themselves. Of course zero interbank interest rate does not necessarily mean that all theinterest rates on the bank accounts become zero. Actually in case of Japan, the banks are paying
small amount of interest on the deposits with them while they receive some interest from their bor
rowers. In that sense it is magic, even under zero-interest-rate circumstances, if BOJ could persuade

its customer banks to accumulate as much funds as it wishes. The results are depicted in Fig.2. Afterthe introduction of the QEP in the spring of 2001, the BOJ successfully persuaded the commercial
banks to increase the balance of the current accounts not only well above the legally required mini
mum reserves, but also comfortably above the intended level that they had then proclaimed. One rea

son must be that Japan is experiencing worst credit crunch ever in the aftermath of the financial bub

ble of the 1980's, so that the financial institutions are obliged to have excess reserve as a precaution.

Another reason could be that the call loan rate (typical interbank interest rate) was in the sub-zerodomain from time to time because some foreign banks were able to get profits by borrowing yen
against other currencies of higher interest rate and let it to other banks. However these reasoning
may explain only a part of the story, and the remainder is left to be answered.

54

Journal of Applied Input-Output Analysis, Vol. 11 & 12, 2006
Figure 3 The Assets of the BOJ@ Foreign investment insecurities

120■ Deposits with agencies£3 Corporate stocks

DJGB

60

40

0 Repurchase agreement
and securities lendingtransactions

20

EH Bills purchased□ BOJ lending facility

Figure 4 The Liabilities of the BOJ□ Financial Surplus■ Others

II Resale agreement andsecurities borrowing
tions

H Current accounts held by
the government

E3 Current accounts held byfinancial institutions

0 Banknotes in circulation

ity to meet a surge in demand irrespective of the target of current account balances,(then) around 10 to 15 trillion yen". The target level was lifted to 15-20 trillion yen in
October 2002, 17-22 trillion in March 2003, 22-27 trillion5 in April, 27-30 trillion in
May 2003 and finally to 30-35 trillion yen in January 2004. (See Figure 2.)
Under the zero interest rate situations, the means of the money market operation
could have decisive significance. As we have mentioned earlier, in the first phase of the
QEP, it was the BOJ's intention to increase JGB in their asset portfolio. This line ofpolicy was officially maintained at least till October 2002, when it announced that itTable 1: Balance sheets of the BOJ (100 million yen)Dec-97
AssetsBanknotes in circulation

Mar-98

Liabilities

AssetsJun-98

Liabilities

AssetsSep-98

Liabilities

AssetsDec-98

Liabilities

AssetsMar-99Liabilities

AssetsJun-99Liabilities

AssetsSep-99Liabilities

AssetsMar-00Dec-99Liabilities

Liabilities

Assets587154529946537599Current accounts held by financial institutions

526885599865553298563469554547695920

34992

58105

40456

Current accounts held by the government
Foreign currency deposits

57233

43743

61676

46632

60577

233860

4995

49527

5682

6553

5169

20243

24709

35252

59547

0

0

0

0

0

0

0

0

0

Assets6121651834131303110

Loans to private financial institutions
Bills purchased and sold

49275
49132

51545

53223

20299716976

13061746783

12816260787

195856

11904

99991

8376

58026

17601

0

35993

0

19909

Repurchase agreement and securities lending transactions
Financing Bills
Central government securities and FILP bonds

12808511230012960411377042789

11200010039911061012671611032079901

14149351470

18310084895

185572407189101320405952

Structured-financing instruments
Corporate stocks

51180

39672

37454

15587

38008
81865

2202

I

2202

1

2202

1

2002

1

2002

1

2002

1

1202

1

1202

2

277

33929

267

9476

276

3552

269

2

274

33543

265

9496

263

11593

254

1

260

36034

247

4837

139

2356

215

4419

78

1974

6220

4118

2507

1985

2601

4724

102

2109

143

4866

4362

2579

4373

50

35727

176

40608

616

43044

73

43401

3403

41875

390

37695

7

56303

7

54993

534

54980

7

50594

7

53163

465

52629

35568
50729

306212346926

839862

839862

47

36115

7

52815

1006702

Liabilities

Assets

884621

Dec-O0Liabilities

Assets

47

38584

7

54070

905095Mar-01

Liabilities

Assets1000502

Sep-01

Jun-01

Liabilities

Assets937285

Liabilities

Assets

3950

39113

7

50921

940969Dec-01

Liabilities

Assets0889860889860Assets11492101149210

AssetsLiabilities

594060598541676197628296652395639081

732980720965724467

51804

52255

68270

58143

57058

124794156154276107150532

63769

88542

93827

220725123691

15479759651

12928467229

1083847

Assets

83418

3244

101

370

729

355

553

306

437

7983

7501

8274

14087

5300

6323

8161

9900

3892

3464

5249

50974

18259

22407

40093

28069

98200

43863

148621

65017

1730784800

2071433000

295184091511

347250129960463831

172342461643191142248342224114

154391

187162

1457601802601182272063277492

437291

Structured-financing instruments

7131

42719906335462800095415

476241093289

5955230652078014874380300
674949

0

65804

68799

1921271172777004950237496279974

46188

60325

17654648096

7365420Liabilities
185326

1525

10918

7

1083847

714122

194327924322

33135

Sep-02

Jun-02

Liabilities

1

53085

50104

Mar-02

Liabilities

435451060710

94096976809

435114057637

937285130135441312041617
1000502

202860451103069108
905095268623401700057729
884621228556379981051820
10067022347853870920

Sep-00

Jun-00Assets225526362416048402

Banknotes in circulation

Central government securities and FILP bonds

79670

1

276246

Financial surplus or deficit

Financing Bills

99257

2202

OthersCurrent accounts held by financial institutions
Current accounts held by the government
Foreign currency deposits
Loans to private financial institutions
Bills purchased and sold
Repurchase agreement and securities lending transactions

41966

1

Other external claims and debts

Total

51201

19241332761902202

Deposits with agencies
Accounts receivable/payable

70186

Liabilities

785490

0

0

Corporate stocks

1202

1

1202

1

1202

1

1202

1

1202

1

1202

1

1202

1

1202

1

1202

1

1202

1

Deposits with agencies

9146

251

11167

241

1446

245

34360

235

9383

238

4430

232

3488

237

35487

229

9471

235

5327

227

Accounts receivable/payable

4254

94

1934

131

4843

807

1638

792

3425

138

3642

127

1835

215

2884

234

3634

134

2961

142

172

38516

10424

42876

9295

42796

12843

41132

11863

43196

7

58381

12

55674

15

55444

7

54424

7

55722

Other external claims and debts

31416

Others48139

Financial surplus or deficit
Total

240

32101

7

54320

38024

890735890735

Dec-02
AssetsBanknotes in circulation

916859

35776

7

56484

916859Mar-03Liabilities

Assets798383Current accounts held by financial institutions

200
24574

1092512

39144

7

59236

1092512

Jun-03Liabilities

Assets753579195626
63311

218
52529

56375
1199751

Sep-03Liabilities

Assets7553471212375

38607

12

54329

1212375

Dec-03Liabilities

Assets7438752893153092971199751

9835
79876

68879

1190309

Mar-04

Liabilities

Assets8133233456001190309

88473
1230281Jun-04

Liabilities

Assets75766530030712302811420308

Assets759094363601

1420308

Sep-04

Liabilities

70694

74311
1283093

Dec-04

Liabilities

Assets337339350726331784

323

1150

1952

250

258

272

357

348

267

Loans to private financial institutions

1932

2903

1681

1712

1412

1412

1461
254815
60953
76243

1412

1111

45556

Bills purchased and sold28042217014

29126102351856003

Repurchase agreement and securities lending transactions

80537

13395312188017610863960

132704

Financing Bills

22177

Central government securities and FILP bonds

813115Structured-financing instruments

85938

78208

8105980254203

24179

84148

162844109426811782040533

238429060602

11911499615

795955042431

27219225708

111338

198853134922854699829251310

130805515

71304

2900530360734077702

22272654119

221566

62129

12807

1

16069

1

19637

1

20196

1

20689

1

21005

1

Deposits with agencies

3137

229

38710

0

8813

3

3122

3

139

1

30826

0

5214

Accounts receivable/payable

3089

146

2895

135

3410

257

2858

102

3181

235

2780

279

2679

13756

43672

11241

44554

10275

42904

13797

42773

20070

42918

7130

44716

7

54265

7

54430

7

55128

8

53382

8

53068

8

53096

53284

Total
Source: Bank of Japan

91755
1314181131418178936

1475439147543990313
1329781132978148778

1379720137972064720

1360210136021052614
1536664

1536664

1156
21064

2

21491
1526

0

161

0

177

2198

59

2365

84

7056

46576

4158

45341

8

53401

8

52097

42970
1378581895684

1128

1

43724

50761

869071

1315

2708

Financial surplus or deficit

45462

24014

Corporate stocks

Other external claims and debts
Others44817

136616

8466241204

Liabilities
824484758817

Current accounts held by the government
Foreign currency deposits

1461351283093137858111437862

5727
167

66260

56550
143786211495535

1495535

12389
7

77086

12954521295452i

56

Journal of Applied Input-Output Analysis, Vol. 11 & 12, 2006

would increase the monthly outright purchase of the JGB from 1 trillion yen to 1.2 trillion yen. Some other measures included the easing of the restrictions on the use of theLombard-type lending facility (August 2001 and February 2002), more active purchaseof Commercial Papers (December 2001) and the extension of maturities for the bills
purchased eligible for the operations (October 2002). More dramatic measures were on
their way. In October 2002, the BOJ asked permission to purchase corporate stocks inthe form of "money in trust" and the Ministry of Finance (MOF) authorized it immedi
ately. In June 2003, the BOJ announced the scheme for the outright purchases of theABS, and it was put in practice by the end of the following month.

Figure 3 and Figure 4 as well as Table 1 show the changes in the asset and liabil
ity portfolios of the BOJ under the QEP. As indicated in the height of the pillars, thetotal of the assets and the liabilities have increased gradually since the introduction of
the policy in the spring of 2001. It is obvious that the balance of the current accounts
has risen dramatically. However, that is not the only cause to make the monetary basegrow. The balance of the banknotes has swelled as well, most probably because of thepolicy shift in April 2002 to allow the liquidation of insolvent financial institutions. On
the asset side, there is no doubt that the JGB enlarged its magnitude significantly not
only in size, but also in the proportion to the total assets. Another instrument that has
expanded its position is bills-purchased in open market operations, especially in more
recent days. In contrast to that, the balance of repurchase-agreement and securitiesborrowing-transactions has been slashed after the introduction of the QEP.

3 DataThe BOJ publishes Flow of Funds Accounts of Japan quarterly. It contains three ta
bles: (1) financial transactions, (2) financial assets and liabilities, and (3) reconciliation
between flows and stocks. The ALM used in this paper has been compiled from the fi
nancial assets and liabilities tables of the FFA from December 1997 through December

2004 every three months6. Only the summary of the compilation procedure from the
FFA to the ALM is shown here, so refer to Tsujimura and Mizoshita (2003) for details.

We start from two tables E and R, which are constructed by picking out the assets andliabilities vectors separately from the balance sheets of the FFA. Figure 5 presents thecomponents of the E and R tables.

E is a matrix that shows the portfolio of the fund-employment of each institu

tional sector, e and sE are vectors that represent the excess liabilities and the sum ofeach row, respectively, s is the vector that consists of either the sum of the assets or theliabilities, whichever is larger.

5 The intended amount of the balance of the current accounts was increased to 27~32 trillion yen in
October 2003.

6 In our scheme, assets are evaluated in current value while the liabilities are evaluated in book value.
For further details, see Tsujimura and Mizoshita (2004).

Does Monetary Policy Work under Zero-Interest-Rate?

57

Figure 5 Components of E- and R- tables
institutional

institutional

sectors

sectors

- 3

1-1

E

If

o
r"1

sE

R

sR

p'
s'

s'

en

E =

"sE"

Si

#22

e2m
e =

sE =

sf

s =

si

em

Cnm

en\

6:

Si

s2

SM

where, n denotes the number of financial instruments and m denotes the number of institutional sectors. R is a matrix showing the portfolio of the fund-raising of each insti

tutional sector, and P and sR are vectors that represent the excess assets and the sum ofeach row, respectively.

Tim'
R =

T2\

r22

P =
Tn\

rn2

rnm

V

Pi

r2m

Pi

sR =

s2R

s =

s2

Pm

It is possible to make out two different sheets of square matrices, the ALM, using
E and R tables in alternative procedures. One is Y table based on the fund-raising port

folio, the other is Y* table based on the fund-employment portfolio. Superscript * denotes the case of fund-employment. To compile Y-table in accordance with the fundraising portfolio, first, matrix R is substituted for matrix U (use table or use matrix)
and the transposed matrix E* is substituted for V (supply table or make matrix).
U=R

(1)
(2)

In the case of Y*-table that represents the fund-employment portfolio, we take matrix

E as U* and R1 as V*.

it=e

(3)
(4)

58

Journal of Applied Input-Output Analysis, Vol. 11 & 12, 2006

Each element of the coefficient matrices B and B* are defined as follows:b,j = -

(5)b'i = J.

(6)

In the same manner, each element of the coefficient matrices D and D* are defined asfollows:(7)d« = j(8)

The m x m coefficient matrices C and C* are estimated using the institutional sector
portfolio assumption.
C = DB(9)C* = D*B*(10)

Then each element of the transaction quantity matrices Y and Y*are obtained as fol
lows,

(11)

yl = cusj(12)

The above procedure leads us to Y and Y* tables depicted in Fig.6.

Figure 6 Components of Y- and Y*- tablesjiinstitutional

institutional

sectors

sectors

Y

S

Y*

P

s

Does Monetary Policy Work under Zero-Interest-Rate?

59

4 Methodologies
4.1. Evaluation of the Quantitative Easing Policy
It is necessary to treat BOJ, the central bank, as an exogenous institutional sector in or
der to analyse the effect of the monetary policy by estimating the induced amount ofdemand and supply of funds through the intersectoral financial transactions represented

in the Leontief inverse. The fundamental equations respect to Y and Y* tables are expressed as follows:
CbojS + £j=S

(13)

CbojS + Pj=S

(14)

where Cboj and Cboj are the matrices obtained from the matrices C and C* respectably,by removing the row and the column containing the elements concerning the BOJ. £jisa (m- 1) x 1 vector of which each element is the sum of excess liabilities and the li
abilities of the BOJ. Pjis a (m - 1) x 1 vector which contains the sum of excess assets
and the BOJ's financial assets. Solving each equation for s yields

s=(I-Cboj)-1£j(15)

s=(I-Cboj)-iPj(16)

where I denotes (m-l)x(m-l) unit matrix, (I - Cboj)"1 is the (m - 1) x (m - 1) Le
ontief inverse matrix, which gives the demand for funds as induced by each institu

tional sector, and(I-Cboj)"1 is the (m-1) x (m-1) Leontief inverse matrix, bywhich we can calculate the amount of ultimately induced supply of funds. For simplifi

cation, let us denote (I - Cboj)"1 as T and (I - Cboj)"1 as T*. From the viewpoint of thenon-financial economy, the induced demand for funds means gross induced savings(GIS), the amount of new savings required, while the induced supply of funds refers togross induced investment (Gil) that enables us to make still more investments.
It is possible to calculate the effect of the QEP carried by the BOJ using Leontief
inverse in the same framework described above. £Bojis a n x 1 vector of which element£Bon is the liability held by the BOJ in the form of financial instrument i. The n x 1
vector Pboj is the assets vector where element pBou denotes the financial instrument iheld by the BOJ. Vectors eBoj and Pboj then should be transformed into (m-1) x 1
vectors fe and £>, each of which is classified by institutional sector in order to make itpossible to use Leontief inverse. The method of transformation adopted here is as follows:

fe =Dboj£boj(17)

fp =DbojPboj(18)

where Dboj and Dboj are (m-1) x n matrices obtained by omitting the row of BOJ

from D and D* respectively. Given eBojand pBojexogenously, the induced savings andthe induced investments are calculated as follows:60

Journal of Applied Input-Output Analysis, Vol. 11 & 12, 2006

Vs = (I -Cboj)"1 fe(19)

Vi = (I -Cboj)"1 f?

(20)

where ?sis the (m- 1) x 1 vector of induced savings and element rjsi denotes the induced savings generated in institutional sector i, ?iis the (m - 1) x 1 vector of induced

investments, where element Vn indicates induced investment generated in institutional

sector i. Note that GIS [Hs = S* tf«] is the sum of the elements ?s, and Gil [H, =Si Vu] is the sum of the elements of Vi. Subtracting GIS from Gil, we obtain Nil asfollows:

H^Ht-Hs(21)

Nil calculated by (21) have significant economic meanings, that is whether current policy stimulate the capital formation in the non-financial economy or not.

4.2. Decomposition of the changes in Nil
We have calculated the GIS, Gil and Nil for December 1997 through December 2004
quarterly. It is possible to decompose the cause of increasing or decreasing of these indices into two elements. These are 1) the portion attributed to BOJ's monetary policy,
that is fe and £>, and 2) the segment attributable to the structural change of the financial market, i.e., T and T*. Let fe, (fP,,) be the (m - 1) x 1 vector of liabilities (Assets)held by BOJ at period t, and T, (I?) be the (m - 1) x (m - 1) Leontief inverse matrix
at period t. The decomposition of the output change over a period can be calculated as

the first difference of HNh which is:

AHNl = HNt - HNt.x(22)

AHNI = {HIt - HSt) - (#„_, - //»_,)(23)

In the matrix notation, by using equations (19) and (20), (23) could be transformed to:

AHNI = (iTX, - iT,fc,,) - (i-RA^i - iT,_,fe,,-i)(24)

The IO-SDA method we have adopted is the arithmetic average of the Laspeyres andPaasche decomposition that is proved to be exact and non-arbitrary7.

iTX,-iT£,Q-(i^2iTrfp,,-iTf£,Q-(iT^^^2(25)

where i is the (m - 1) x 1 vector, which contains a column of Is. As proved in the Ap7 For further details, see Betts (1989). The deference between the traditional IO-SDA and ours is that
all the components in (25) are scalars instead of vectors because they are multiplied by i\Does Monetary Policy Work under Zero-Interest-Rate?

61

pendix 1, equation (24) could be transformed to (25), so that we can trace the change
in the Nil to two sources. While the first term of the right hand of equation (25) repre
sents the effects of the changes in the BOJ's fund-raising or fund-employment portfo
lio, the second term represents the effects of the mutation in the Leontief inverse. De

noting Aft as the first term, and AT, as the second term, (25) can be simplified as:

AHM = Aft +AT,

(26)

Furthermore, we have another method of decomposition to compare the ratio of the
Nil at t to the Nil at t - 1, which is based on the well-known Fisher's ideal formula ofindex numbers8. The decomposition of the Nil's change over a period can then be cal
culated as the ratio of HNtto HNl.u

sir

Hm

.__.

= ~H—

^ ^

which is:8Hm =<\ T T

H I, — HSt)

In matrix notation, using equations (19) and (20), (28) can be transformed to:

8Hm =

'

"

'

(29)

1 1 /-ilp,f-l - 11 r-lle,/-l

Expanding (29) yields (see Appendix 2):

8Hm = /—V iT,*-ifp,-i - iT.ife,-,

V iT^fp,,-! - iTV.fe,.,x—

iT^fp,,-, - iT,fe,-,(30)

iTf!,fp, - iT^.fc,

where i is the unit vector. The first square root on the right hand side of (30) means
the effect of the changes in the BOJ's fund-employment or fund-raising portfolio, andthe second square root does that of the changes in the Leontief inverse. Denoting 8ft as
the first square root, and 8T, as the second square root, (30) can be further simplified
as:

8HNt = Sft x8Tt

(31)

This relation is originated in the property of the Fisher index (Fisher (1927))9 . Al
though SHNtis the changing rate from t - 1 to t, it can be used as chain index as well.
When we calculate the changing rate from term 0 to term r, that is given by:

f[8HNt= II 8ft x n<Jr,

/=i

t=i

t=i

(32)

8 Fisher (1927), pp.243-248.
9 It should be noted that all the components become scalar by multiplying i', so that (30) reduces tothe original Fisher's formula.

62

Journal of Applied Input-Output Analysis, Vol. 11 & 12, 2006

5 The Results
There is an asymmetry in the propagation of the supply and the demand of the funds

in the financial system. The demand for funds should be eventually financed by thegross induced savings (GIS), while the supply of funds brings gross induced invest
ments (Gil) in due course. The QEP requires the central bank to choose two items si

multaneously, one in assets and another in liabilities. This action changes Gil on the

one hand and the GIS on the other. The asymmetry in the propagation process gives
net induced investments (Nil) as a difference between the Gil and the GIS. The signand the amount of the Nil is nothing but the indicator of the effectiveness of the monetary policy made on the non-financial economy. A policy that induces a positive num

ber of Nil gives an expansion in the economy, so that it will be welcomed, especiallyin the course of a recession. In contrast, a money market operation that yields a negative Nil, i.e., net induced savings (MS), weakens the economy so that it should be
avoided while the depression prevails10.

The fluctuations in the three indices, GII(H,), GIS(Hs) and NII(HN), between
March 1998 and December 2004 are depicted in Figure 7 quarterly. Just for informa
tion, same three indicators between March 1980 and March 200411 are presented in
Figure 8 annually. The first impression might be that the GIS is a mirror image of theGil. Since the asset and the liabilities are matched up on the balance sheet of the BOJ,
these two indices fluctuate hand in hand. However, the Nil that is the difference be
tween the Gil and the GIS is not stable at all. In Figure 8, the Nil remains negative
between 1980 and 1986 and then stays in the positive domain from 1987 through1993. The indicator turned into negative in 1994 and remained so since then. As it isobvious in Figure 7, despite the introduction of the QEP in March 2001, the Nil stayedin the negative region throughout the period. In that sense, the policy did not help tobail out Japan from its worst recession in more than five decades. But the magnitudeof the Nil is not stable by any means. After the inauguration of the policy, the Nil experienced a set back for more than one year, and the indicator started to show gradualimprovement suggesting that the performance of the money market operation was getting better. Especially in 2004, the improvement seems rather obvious.
The quarterly changes in the Nil alongside its decomposition are shown in Figure
9. Although the Nil stayed in the negative region throughout the period, the indicator
moved favourably in and after December 2001. The pillars are divided into two parts:
the dotted portion indicates the alteration attributed to the changes in the portfolio of
the central bank, and the segment with oblique lines attributable to the mutation of thecoefficients of the ALM. As far as the absolute value is concerned, in 23 out of 28
cases (82 per cent), the contributions of the shift in money market operation reflectedin the asset and liability portfolio of the central bank are greater than those of the mutation of the ALM. Same thing is demonstrated in Figure 10 in a different manner. The
solid line presents the changes in the Nil as a proportion to the previous period. Like
wise, the broken and dotted lines display those attributable to the BOJ portfolio and
10 For further discussion in this respect, see Appendix 3.
11 End of Japanese fiscal year 1979-2003.

Does Monetary Policy Work under Zero-Interest-Rate?

63

Figure 7 Quarterly Fluctuations in Gil, GIS and Nil

555S5g8SgSSsSo8SqSSSSSS

Figure 8 The Fluctuations in Gil, GIS and Nil (March of the year)
400

.0.

J2SL

13"

'B -100

-200

-300

1980 1981 1982 1983 1984 1985 1986 1987 1988 1989 1990 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004

the mutation in ALM respectively. Do mind that the larger the proportion, the absolutemagnitude of the Nil increases in the negative domain. This picture more or lessclearly tells us that the shifts in the portfolio of the central bank have absolute signifi
cance to the performance of the non-financial economy in most periods. Actually, in 24
out of 27 cases (90 per cent), the direction of the effects of the money market opera
tion coincides with that of the Nil in total. Comparing to this, in only 11 out of 27
cases (41 per cent), the direction of the effects of the mutation of ALM coincides with

64

Journal of Applied Input-Output Analysis, Vol. 11 & 12, 2006

Figure 9 The Decomposition of the Changes in Nil (differences)

-20

-40

Figure 10 The Decomposition of the Changes in Nil (proportion)•

Changes in Nil—■— Effect of changes in money market operation- - -A- - - Effect of mutation in ALM

that of combined NIL Therefore, it can be said that the money market operation plays
a dominant role in the determination of the Nil, which in its turn influence the rise andthe fall of the non-financial economy.

The next question to be answered is what kind of money market operation brings
favourable effects on the NIL Table 2 presents per-unit Gil (in the descending order)

Does Monetary Policy Work under Zero-Interest-Rate?

65

and GIS (in the ascending order) generated by each available device of money market

operations. Since Nil is the difference between Gil and GIS, the greater is preferred tothe smaller in Gil while the smaller is preferred to the greater in GIS. It is obvious at
the first glance that the newly introduced device, the purchase of the ABS, is more effi
cient than any other instruments to push up the NIL Among the traditional money mar
ket operation tools, the bill purchasing operation and the loans to the commercial

banks are the most powerful of all, followed by repurchase agreement and securities
lending transactions by narrow margin. The purchasing of corporate stocks, also a newcomer, follows close behind the bill purchasing operation. Unfortunately, JGB, theleading item in the BOJ asset portfolio, gives only small GIL On the liabilities side,bill-selling operation is the best device to raise funds because it gives least burden interms of GIS12. The issuance of the bank notes as well as the repurchase agreement andthe securities lending transactions give relatively smaller GIS. In contrast to that, thecurrent accounts at BOJ held by the financial institutions and the government are a lit
tle more burdensome to the economy.

Table 2: Per unit Gil and GIS produced by each money market operation device (Dec 2004)(2004Q4). Assets of BOJ

Gil

Liabilities of BOJ

GIS

0.0266

Asset-Backed-Securities

4.4386

Bills sold

Loans to private financial institutions

4.1272Banknotes in circulation

3.0409Bills purchased

3.9787

Resale agreement and securities bor

3.1190rowing transactions
Corporate stocks

3.9291

Current accounts held by financial in

Repurchase agreement and securities

3.1636

Current accounts held by the govern

3.6301stitutions

lending transactions

3.7380ment

JGB

1.9217

Financing Bills

1.4608

Note: The amount of Gil and GIS produced by increases of 1 unit in asset or liability items.

One advantage of the ALM analysis is that it gives more detailed figures on the
sector-by-sector Gil and GIS generated by the money market operations. The summa

rized results are listed in Table 3. The non-financial private enterprises are the largest

beneficiary of all in terms of the relative proportion of Gil to GIS in general. Both of
the newly introduced BOJ's devices of money market operation, i.e., corporate stockand ABS purchasing operations, give large per unit Gil to this sector. In sharp contrast

to this, money market operations do not benefit households well; rather they give moreburdens in the form of GIS. Unless the central bank sells bills to finance it, any type ofmoney market operation fails to produce positive Nil on the households. The financial
institutions are affected a lot by the money market operations in either way. The ABS

and bill purchasing operations as well as the central bank loan directed to them give
12 The problem is that bill-selling operation causes least GIS because most of the available bills are
eventually purchased by the BOJ itself.

66

Journal of Applied Input-Output Analysis, Vol. 11 & 12, 2006

Table 3: Monetary operation options and Gil GtS for each institutional sector (2004Q4)
Nonfinancial private enterprises

AssetsCorporate stocks

GH
1.6966

Liabilities

GIS

Bills sold

0.0017

Asset-Backed-Securities

0.9277

Current accounts held by the government

0.1991Loans to private financial institutions

0.8342

Repurchase agreement and securities borrow-

0.2297

Bills purchased

0.7234Current accounts held by private financial in-ing transactions

0.3673stitutions

Repurchase agreement and securities lending

0.5542Banknotes in circulation

0.6825transactions

JGB

0.1683Financing Bills

0.0992

Households and Private nonprofit institutions seving households
AssetsGil

Asset-Backed-Securities

0.4219Loans to private financial institutions

0.4182

Liabilities

GIS

Bills soldResale0.0043agreement

andsecurities

borrowing

0.5561transactions

Bills purchased

0.3359Current accounts held by the government

0.7401

Corporate stocks

0.3148Current accounts held by private financial in-

0.8657stitutions

Repurchase agreement and securities lending

0.2359Banknotes in circulation

1.0529transactions

JGB

0.0775

Financing Bills

0.0365

Financial institutions
AssetsGH

Liabilities

GIS

Asset-Backed-Securities

2.5494

Bills soldBills purchased

2.3988Banknotes in circulation

1.1917Loans to private financial institutions

2.3276

Current accounts held by the government

1.D8411.5841

Repurchase agreement and securities lending

1.9701

Resale agreement

borrowing

2.0725Current accounts held by private financial in-

2.2129transactions

0.0193andsecurities

transactions

Corporate stocks

1.5219stitutions

JGB

0.6103Financing Bills

0.2285

Nonfinancial public institutions
AssetsFinancing Bills

Gn

Liabilities

GIS

1.0967

Bills sold

0.0013JGB

1.0657Banknotes in circulation

0.1138Loans to private financial institutions

0.5472Current accounts held by private financial in-

0.1841stitutions

Asset-Backed-Securities

0.5396

Resaleagreement

andsecurities

borrowing

0.2608transactions

Bills purchased

0.5206

Repurchase agreement and securities lending

0.4034transactions

Corporate stocks

0.3960Current accounts held by the government

1.2148Does Monetary Policy Work under Zero-Interest-Rate?

67

relatively large Gil to the financial institutions. However, the commercial banks' own
current accounts with BOJ give GIS of 2.2; which will offset most of the Gil createdby any devices of the central bank operation. Although both per unit Gil and GIS are
generally small in the non-financial public institutions including central and local gov
ernments, they tend to be benefited by FB and JGB operations. JGB purchasing opera

tion, BOJ's prominent operation device, gives significant Gil to non-financial public institutions while giving minimal Gil to the private sectors.

6 Conclusions
The above-mentioned observation put us in position to determine if the QEP adopted

by the BOJ last four years is a success without fearing the confusion of the two causes,
i.e., the effects attributed to the BOJ's monetary policy itself and those attributable tothe structural changes in the financial market. The analysis suggests that the effect of
the former is obviously greater than that of the latter. This reconfirms the usefulness of
the ALM derived from the FFA in the assessment of the effects of the money market

operations13. It is proved that the selection of the operation instrument is vital because
there are vast differences between their effects on the non-financial economy. Moreover
we can tell that each operation method give conflicting net results on different institu
tional sectors.

To overcome the persistent recession, it is preferable to adopt money market op

eration devices that create more Nil in the non-financial sectors rather than in public
sectors. In this regards, the open market operation of JGB, the device the BOJ has selected at the first stage of the QEP, is the least likely candidate. JGB creates relatively
large amount of Nil in the public sector, but gives only small amount in the private
sectors. Comparing to this, those traditional money market operation devices like billpurchasing or lending facilities induces more favourable effects on the private sectors

in terms of NIL Although it is criticized as unusual measures for a central bank, the introduction of new instruments including corporate stocks and ABS to BOJ's asset port
folio widens the opportunity to create more Nil in the private sectors.
Four years has passed since the introduction of the QEP by the BOJ that is fighting against the worst recession in the post-war Japan where zero-interest-rate is a mat
ter of fact. The overall performance of the QEP is improving gradually in recent days,
partially because of the introduction of the new measures including corporate stock and
ABS purchasing operations. As a conclusion it can be said that some type of monetary

policy could work even under zero-interest-rate. BOJ, the pioneer in this field, is getting some experiences through trial and error, but still it is a long way to be truly successful.

Appendix 1

13 For further investigation in the stability of the parameters involved in the ALM in a longer perspec
tive, see Tsujimura and Mizoshita (2004).

68

Journal of Applied Input-Output Analysis, Vol. 11 & 12, 2006

Equation (25) in the main text is obtained through the following manipulation of (24):

AHN, =(iT,X, - ITA,) - (i'TC.f,,-, - iT,-,fc.,-,)(24)

2 (iTX,- iT,fc,,) - 2 (iTU,., - iT,-,fc,,-,)

+

2
(»)

(«)

{(rn,fp,,-r:r,-,fe,)-(iT,t,fp,-,- iT,-,fe.,-,)}+{(i' 11 ip,t — 1 Jr,f£.,)-(iTX.,-,-iT,fe,-,)}
2
(iv)

+

(i)

[[lit ip,t-i ~~ lT,fe.,-,)-(iT,!,f,,-, -iT,f,,-,)R{(i T,X,-i']r,fc,,)-(iT!,fp.,-iT,-,fc.,)}

2

(25)

The differences in Nil caused by the transition of f from t - 1 to t while T and r*
are kept at t-1.

(ii) The differences in Nil caused by the transition of f from t-1 to t while T and V
are kept at t.

(iii) The differences in Nil caused by the transitions of T and V from t-1 to t while f
is kept at t-1.

(iv) The differences in Nil caused by the transitions of T and V from t-1 to t while f
is kept at t.

Therefore the first term of (25) represents the differences in Nil caused by thetransition of f from t-1 to t, equally arithmetically weighted by F and F* at t - 1 and t.
Likewise, the second term of the equation indicates the differences in Nil caused by

the transitions of T and V from t-1 to t, equally arithmetically weighted by f at t - 1
and t.

Appendix 2
Equation (30) in the main text is obtained through the following manipulation of (29):cv TT
SHNt =

iTr fp,tiTffe,/(29)

1 1 t-\lp,t-l — 1 1 t-lle,t-l)I(iTX., - iTfc,)2.fp, - iT,-,fe,)(i'n.fp.,-, - iT,-ife,-,)xx/ (iT,*fp.,-, - iT,fc.,-,)(iff)(iTX.,-, - iT,fc,,-,)(iTX.,-, - iTfc,-,(iTX., - iTfc.,)(iTX,-, - iTfc.,-,)

X(iT,*fp., (iv)J

(iT,!,fp., - iT,-,fc,)

Does Monetary Policy Work under Zero-Interest-Rate?

(i)

69

The rate of change in Nil caused by the transition of f from t - 1 to t while T andr are kept at t- 1.
(ii) The rate of change in Nil caused by the transition of f from t - 1 to t while T andI* are kept at t.
(iii) The rate of change in Nil caused by the transitions of T and F* from t - 1 to t
while f is kept at t- 1.

(iv) The rate of change in Nil caused by the transitions of T and r* from t - 1 to t
while f is kept at t.

Therefore the first term of (30) represents the rate of change in Nil caused by thetransition of f from t - 1 to t, equally geometrically weighted by T and F at t - 1 and t.
Likewise, the second term of the equation indicates the rate of change in Nil caused by

the transitions of T and V from t - 1 to t, equally geometrically weighted by f at t - 1
and t.

Appendix 3
We apply the techniques of cointegration tests developed by Engle and Granger (1987)
to examine the casual relationship between the rate of change in the GDP and the NIL

For simplification, the former is noted as RGDP. Table A~l reports the summary ofaugmented Dickey-Fuller (ADF) test using the annual data from March 1980 to March
200414. (a) is the null hypothesis that a single unit root exists in RGDP and ARGDR
Based on the ADF -1 statistics, the null hypothesis of a unit root in RGDP is not rejected at 1 percent significance level, while that in ARGDP is rejected, (b) is the null
Table A-l: ADF test statistics for RGDP and Nil(a) ADF test statistics for RGDP
without time trendwith time trend
RGDP-2.891439(0.1822)-1.679476 (0.4284)

0

0

Lags

ARGDP

-4.975085**(0.0030)-5.069016**(0.0005)
0

0

Lags

(b) ADF test statistics for Nil
without time trendwith time trend
Nil-2.250718

Lags-0.834724 (0.7908)
0

1

Lags
ANn

(0.4419)-4.850579**(0.0043)-4.477876**1(0.0021)
1

Values in parentheses are MacKinnon (1996) one-sided p-values.

** indicate that the null hypothesis that a single unit root exists can be rejected at 5% significancelevel. Optimal lag length was chosen based on the Schwarz Information criterion (SIC).

14 End of Japanese fiscal year 1979-2003.

70

Journal of Applied Input-Output Analysis, Vol. 11 & 12, 2006

Table A-2: Unrestricted Cointegration Rank Test (Trace)
Hypothesized

No. of CE(s)EigenvalueTrace0.05 Critical

Statistic

Value

Prob.**

None*

0.468696

15.76984

15.49471

0.0455

At most 1

0.051833

1.224157

3.841466

0.2685

Trace test indicates 1 cointegrating eqn(s) at the 0.05 level* denotes rejection of the hypothesis at the 0.05 level** MacKinnon-Haug-Michelis (1999) p-values

Table A-3: Unrestricted Cointegration Rank Test (Maximum Eigenvalue)
Hypothesized
No. of CE(s)Eigenvalue

Max-Eigen0.05 Critical

Statistic

Value

Prob.**

None *

0.468696

14.54569

14.2646

0.0451

At most 1

0.051833

1.224157

3.841466

0.2685Max-eigenvalue test indicates 1 cointegrating eqn(s) at the 0.05 level* denotes rejection of the hypothesis at the 0.05 level** MacKinnon-Haug-Michelis (1999) p-values

hypothesis that a single unit root exists in Nil as well as in ANIL The result is that thenull hypothesis of a unit root in Nil is not rejected, while that in AMI is rejected.
Then, it suggests that both RGDP and Nil are characterized by 1(1) process. Table A~2
and A-3 present the results of VAR-based cointegration tests developed by Johansen(1991, 1995). The results indicate that the null hypothesis of no cointegration is rejected at 5 percent significance level. The results indicate that RGDP and Nil are cointegrated and have a long run equilibrium relationship.

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