BUSINESS
24th

REPORT
ANNUAL<tstro;>."pt

RESEARCH INSTITUTE FOR ECONOMICSAND BUSINESS ADMINISTRATIONKOBE UNrvERSITY
1978

KOBE
ECONOMICBUSINESS&REVIEW
24th

ANNUAL REPORT<B:t"C3RESEARCH INSTITUTE FOR ECONOMICSAND BUSINESS ADMINISTRATIONKOBE UNIVERSITY

1978

CONTENTS
Page
The Demand for International

Currencies and Reserves......................,...................Masahiro FuJiTA

NobuoMiyATA 1
Studies for the Prediction of Shipping Markets-ASurveyandtheirApplications- ...........................TetsujiSHiMoJo 39

A Note on the International Transmission of
Policy Effects under Flexible Exchange Rates ..........,....Kazuhiro IGAwA 61

A Control Estimation Approach toTime-yaryingParameterModels .................................YukioUcHiDA 69

FOR INTERNATIONAL
CURRENCIESTHEDEMANDAND RESERVES
Masahiro FuJiTA

AND
Nobuo MIyATA
We can not find the economy without rnoney in an actual world. In an international economy, therefore, we should start with the analysis ofholding international
currencies. According to the IMF's definition of liquid foreign reserves, we will define
the holdings ofinternational currencies as the sum of the official gold and gold tranche

positions, the SDR position, and the holdings of convertible foreign currencies. The
rates of foreign exchanges are supposed to be fixed throughout our analysis.
The motives for holding ofinternational currencies, which owe to Keynesian classification, can be classified into three heads: the transactions motive, the precau-

tionary motive, and the speculative motive, In the international economy, however,these motives have to be modified, where we have less developed institutions as com-pared to our national economy. (a) The transactions motive-one reason for hoiding
offoreign currencies is to bridge the interval between external receipts and payments.

The strength of this demand depends on the international balance of payments, andon the discrepancy (the time interval) between the hour we will have external payments

and the hour we will receive from foreign countries. (b) The precautionary motiveforeign currencies are held to provide for contingencies requiring urgent imports tomeet a bad harvest or other disasters. (c) The speculative motive-we should like todeal with only autonomous international long-term capital movements in this head,because they are related to long-term interest rates as Keynesian speculative demandfor domestic money is. Exchange arbitrage or speculation and short-term capital
movements are excluded. Especially, hot money is excluded because of its politicalinstability.

1. The Transactions Motive
International currencies are held by a country to bridge the interval between its
external receipts and payments. The determinants of this demand, as shown in the following paragraphs, are the time interval between its external payments and receipts,
and the mean value and the variance of its daily, statistically independent balance of
payments. The international currencies held by the monetary authority are only a reflex of international transactions in the private sectors. Therefore, the monetary au-

MASAHIRO FUJITA, NOBUO MIYATA

2

thority does not assume to play an important role on the holdings of foreign reserves
except in the case of the precautionary motive.

Time is divided into discrete, uniform intervals called "week". The markets,
where all contracts are made, are open only on Monday of each week. And the fulfi1-•
ments of the contracts are carried out on any other days during the week. The net pay-ments due,i) Z(m,-l,), consists of the excess payments due for a given hour of theweek and the sum of excess payments due for the preceeding hours. Let us assume
that k is a maximum random variable representing the net payments due at any given
time (T) in the week. Ifk is bigger than the initial amount of foreign reserves, M, thecountry cannot fulfi1 the payment obligations during the week. Therefore, a cumulative possibility function for k, T==Pb(k sgM), is an indicator of security level against
possible illiquidity. The level of security depends on the initial holdings of foreign

reserves, M, the daily balance of payments, m,-l,, and the time interval. The smaller
the initial holdings are, the higher the possibility of insolvency wi11 be. The bigger

the daily balance of payments or the time interval is, the greater the value ofk, andthen the risk against insolvency) will be.

All contracts on Monday involve our expectations for daily receipts and our daily
payment plans in the following six days during the week. Therefore, the daily balancesof payments can be divjded into two parts: the statistically jndependent part and thepart affected by the preceeding days' balances of payments on which our expectations
and plans are reflected. Figure 1 shows an example of a country's balances ofpayments
deficjt

the part affected by theprevious day's balance
the part of daily,
statistically
oo
,s

ij

E
o
E
ts

eN
g

M
8

independent balance

T

T'

o

o
ts.

1

"o

l
1
t

B

,

the part of daily,
statisticallyindependentbalance

1
1

'
1
'
1
I

the sum of daily deficit, k'1'

surplusFig 1l

An Example of Daily Balance of Payments in a Week

1) Meinich, P., A Monetary General Equilibribrium Theoryfor an International Economy, 1971.

E
g
e

3
THE DEMAND FOR INTERNATIONAL CURRENCIES AND RESERVES

which are indicated by a thick continuous line. The daily balances of payments startwith a deficit on Tuesday and are reversed into a surplus at time T. They are the sum of
the statistically independent part and the part (shaded part) affected by the preceeding

days' balances ofpayments. The maximum net payment due, k, which shouldbe paid byinitial holdings, M, is equal to the integration of the dialy balances of payments fromO to T. Suppose the shaded part is proportionate to the previous day's balance of
payments at the rate ofr. Ifthis ratio r is equal to zero, the shaded part will disappear

and the reverse point T will be moved to T'. The increase in r, on the contrary, will
make the reverse point delay forward, and the period of deficit balances will be longer.
Therefore, the ratio r can be taken as an effective indicator to show the time interval

between the external payments and receipts.
Let us divide the statistically independent part of the daily balances of payments
into its expectation and variance, and focus only on the expectation under the usualassumption ofthe constant variance. The public holdings of foreign reserves are supposed to be a reflex ofindividuals' holdings in the private sectors. And the distributionsof wealth and income in the country are also supposed to be given. On Monday when
all contracts are made, an individual or the country can change only the total transac-

tions, m, which will be carried out on the following days during the week. The total
amount of receipts, l, is constant because it means the total export value of the coun-try. The reduction ofthe total amount ofpayments, m, wM decrease its expectation,
E(m). And the decrease in E(m) will reduce the expectation of daily transactions,E(m,) or E(m,-1.). If r is constant, the reduction of E(m,-l,) wiil decrease thestatistically independent part of daily balances of payments. (If the statistically inde-

pendent part is constant, the ratio r will decrease.) Consequently, the reduction of

total transactions, m, will make the maximum value, k=Z (m.-l,), be smaller andwill improve the level of security, T. Then, the security level may be defined by n==

T (MIP, a., r, mlP), where P is the price level and a. is the standard deviation ofdaily, statistically independent balances of payments.
The higher the level of security is, the greater the social utility will be increased.

Accordingly, z may be inserted into the social utility function, U= U(z, LIP), where

LIP is the real holdings of foreign reserves at the end of the week. Maximizing thesocial utility function, subject to the budget restraint, eq. (3),1 OU

-R-O, (1)P OLIP

1 OU Onp o. •-o.lp -1-O, (2)M=m-l+L. (3)From eqs. (1)-(3), we can get the demand function ofinternational currencies,

MASAHIRO FUJITA, NOBUO MIYATA

4

L- L(a., r, MIP). (4)Eq. (1) is related to the Meinich's stock of value which represents the speculative demand for international currencies. Eq. (2), on the other hand, is related to the transac--

tions demand. Therefore, eq. (4) involves two types of demands, speculative and trans-

actions. However, we may conclude that eq. (4) represents explicitly the transactions
demand for international currencies because it has the parameters, a., and r.

An example is found in the Kenen and Yudin's article,2) which estimated thetransactions demand. Kenen and Yudin tested the normality of foreign reserve changedRt, by using a Markov process,

ARt=e+pARt-i+ut. (5)The variance of ut, a., is closely related to the variance of aRt. If the value of a2,R ishigh, the riskness against insolvency, and then the demand for reserves, will be increased. Therefore, we can say that they estimated our security level, n, in the reverseÅíorm, 1- 7-z. In addition, e and g., in eq. (5) are completely identical to our mean andvariance of daily, statistically independent balances of payments, because they are themean and the variance of independent residuals, ut. On the parameter, p, in eq. (5),however, Kenen and Yudin imposed the constraint, Osgp S1, and defined it as the"carry-forvvard" of all past disturbances embodied in pARt-i. It is identical to
Clark's3) speed of adjustment for external disequilibrium which must not have any
negative value. On the contrary, however, our parameter, r, in eq. (4) is not the carry-

forward, but only a coefllcient of responseMto the previous day's balance of payments
which may have negative value. All liabilities occured on Tuesday, for example, mustbe paid on Tuesday in our model. They must not be transfered to the next day,Wednesday, for we have not any credit organization. Therefore, our r is only the ratio

oftoday's balance ofpayments affected to the previous day's balance. When we estimate p in eq. (5), the value ofp can take a negative sign. Therefore, we had better not

impose the restriction on the sign ofp and recognize that it is the estimated value ofr in eq. (4).

Kenen and Yudin estimated the regression coefficients for eq. (6) which depended
on the estimated parameters, e, p, and a., per capita income, y, and liquid liabilities,

Lt, or domestic money supply, Mt, of 14 countries.

Rit = Po + Piei + P?pi + P3o.i + P4yi + PsLit + eit, (6)where i denotes each country and t denotes 1957 or 1962. In this cross-section analysis,
p was arbitrarily fixed at zero when the estimated p was negative or not singnificantly
2) Kenen, P. B. and F. B. Yudin, The Demand for International Reserves, R. E. Stat., Vol. 47,
Aug. 1965.
3) Clark, P. B., Optimum International Reserves and the Speed of Adjustment, J. P. E., Mar.1
Apr. 1970.

5
THE DEMAND FOR INTERNATIONAL CURRENCIES AND RESERVES

different from zero in eq. (5). Consequently, they concluded that y and L, should be
eliminated from eq. (6), because the estimated values of P4 and Ps were not significantly different from zero. Then, they estimated again for eq. (6').

Rit = Po + Biei + B2pi + P3a.i + eit'• (6')
The variables, y and Lt, which Kenen and Yudin eliminated from eq. (6), are closely
related to the store of value described in eq. (1) above. And the estimated regression
coeMcients, e, p, and a., for the second equation (6') are related to transactions motive

only. Therefore, we can say definitely that they estimated the transactions demand forforeign reserves only.
In their article, the parameters, e andp, were ultimately eliminated from eq. (6').

And the demand for reserves was defined as a function of only a.. This eliminationofe can be greatly appreciated, for the demand function is similar to our equation (4).

But we cannot agree with the elimination ofthe parameterp. In eq. (4), the parameterr can take a positive or negative sign. But it had better not be set at zero, because it

represents the time interval between the external payments and receipts in the country concerned. We consider, therefore, that the elimination ofp is misleading.

We estimated the holdings of foreign reserves at the end of 1972 in Table 1. Alldata were taken from IMF: International Financial Statistics. The normal equation (5),and all other cross-sectional models used in Kenen and Yudin's article were tested
again. In estmating e, p, and a., we deleted outliers from the series data by applying
Anscombe's procedure`) of rejection ofoutliers to the liquid reserve changes, AR,, for

we could not get any available in.`ormation about political or institutional changes.

Consequently, we obtained the similar results about the estimated parameters, e, p,
and a., to their table. Table 2-Table 6 show these ieast-squares estimates e, p, and a.,for the various kinds ofperiods. In Table 2 and Table 3, we used the 181 monthly and

61 quarterly reserve data for the period, December 1957-December 1972. The t-test
was satisfied at the O.05 or O.1 level of significance in the majority of countries. The

similar result was also obtained in Table 4 and Table 6, in which we used the 6imonthly reserve data for two periods, December l957-December 1962 and December

1967-December 1972. But Table 5, which related to the period, December 1962December 1967, gave us a different result. The estimated p was significantly different

from zero only in five countries such as France, Italy, New Zealand, Sweden and
Switzerland. All other countries did not satisfy the t-test.

4) Anscombe, F. J., The Rejection ofOutliers, Teehnometrics, Vol. 2, 1960. Let n be the number ofobservations and k be the number of independent variables in a normal equation. If the least-squares
error is 1uftf 1 >eau' the Mth observation, Ru, will be deleted as a outlier, where e=3.06(1-l.851n-k).
And the least-squares method will be applied again to the remaining observations, dRi, riR2,...,
dRM-i, dRM+i,..., dRN. If the inequality is still maintained, a new observation numbered Mwil1 bedeleted. This procedure wil1 be used iteratively until 1uM 1 <eau results.

aTable 1 Foreign Reserve Holdings in 1972, Computed from Kenen and Yudin's Best Equation: Rt==Po+P3 aui(millions of dollars)

Austria

Belgium

CanadaDenmark
FinlandFranceGermany
ltaly

Japan
Netherlands

NewZealand
NorwaySwedenSwitzerland

UnitedKingdom

FuilPeriod Analysis:Monthly
DateqDec. 1957-Dec.1972.
ActualReserves

FullPeriod Analysis:Quatterly
Data,DeÅë. 1957-Dec.1972.

ShortPeriod Analysis:Monthly
DateqDec. 1967-Dec.1972.

R2 =O.72
ExcessorComputedReserves

R2 =O.78
Computed
Excessor

Shortfal1

Reserves

R2 =.79
ExcessorComputed

Shortfal1

Reserves

Shortfall

2,719.00
3,s7e.oo
6,049.80
854.80757.8010,O15.00
23,785.00
6,079.00
18,365.00
4,785.00
578.001,325.00
1,575.00
7,488.00
5,647.00

4,271.67
4,136.64
5,060.72
3,941.62
3,403.69
5,618.01
22r413•15
6,074.97
4,431.20
5,535.97
3,331.52
3,787.91
3,478.91
12,486.11
5,921.32-1,552.67-266.64989.08-3,086.81-2,645.89
4,396.99

3,O02.94
4,355.71
4,302.86
3,515.21
2,526.31
7,055.82
23,365.42
7,896.90
4,987.36
5,126.90
2,755.16
2,733.58
3,311.68
le,848.81
8,108.74-283.S4-485.71

3,973.69
3,991.8e
4,535.98
3.586.09
3,047.48
5,428.35
23,699.18
6,066.38
6,731.02
5,336.69
2,928.47
3,467.71
3,286.74
12,959.19
4,854.62-1,254.69

1,371.85
4.03

13,933.80-750.97-2,753.52-2,462.91-1,903.91-4,998.11-274.32

1,746.94-2,660.41-1,768.51
2,959.18

419.58-1,817.90
13,377.64-341.9e-2,177.16-1,408.58-1,736.68-3,360.81-2,460.74-121.80
1,513.82-2,731.29-2,289.68
4,589.65
85.82
12.62
11,633.98-551.69-2,350.47-2,142.71-1,71L74-5,471.19
792.38

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Table 2 Autoregressive Equations: Full Period Analysis (Monthly Changes ine(t-value)

Austria

Belgium

Canada8.97224*(3.46142)
7.91894*(2.39524)
7.50254

FinlandFranceGermany

2.40251(1.01474)(O.11514)

2.00725

O.08939(1.65056)(1.30003)

19.63516*(2.79550)

O.40249*(10.07723)
O.05047

50.69834*(3.42943)'

Italy

Japan
Netherlands

NewZealand
Norway

X2

R2

Dw

by

O.07030

2.11502

O.35655X2

32.96990(v=19)
a9.70175(v=9)
a5.08187

1.86783

41.95734

a14.39884

a11.21965

O.474482.16185

70.74265

50.23699

44.28324

O.O0875

2.00308

31.24738

a2s.soooo

a12.14286

O.06285

2.07274

16.07173c35.85714

c22.54286

O.61190

2.18296

88.10248

c34.43195

c21.00000

O.092811.80896183.07280

a18.98701

25.00780(1.52622)

19.75753*(2.49088)
15.16611*(3.66131)
11.26659*(2.91229)

O.38299*(6.31378)
O.20713*(18.43698)-O.O0759(-O.15778)

O.429311.84021102.33703

a25.26590

a15.72832

O.82836

1.69286

51.13308

a22.97436

a15.15385

O.O1214

1,93973

49.39032

43.15205c20.28655

1.69591(1.32908)

O.35571

O.37955

2.02419

16.87762

a11.36158

a5.31638

O.07256

1.6381220.82276

c32.71429

c17.47619

O.46596

2.29876

21.46902

c31.95349

c18.00000

O.115312.54804

162.76618

116.23353

91.02395

O.243631.76400

97.55070

c30.80952

c20.80952

Sweden5.95320*(3.66617)
2.74945

Switzerland

15.46668(1.64528)(1.22595)

UnitedKingdom-O.05370(-O.91611)
O.28966*(5.10398)
O.44817*(7.13945)
O.O0787(1.34674)

Denmarkp(t--value)

Reserves, Dec. 1957 - Dec. 1972)

6.10998(O.80863)*(5.53362)-O.05086(-O.93737)
O.38361*(6.95873)-O.08450*(-1.79913)
O.11684*(3.39673)" Significantly different from zero at O.05 level.
aDistributionsmarked "a" are those that satisfied the xi test for normality at the O.05 level

8
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tu

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ot' significance.

c Wound satisfy the Å~' test for normality at the O.Ol level of significance.

"ooTable 3 Autoregressive Equations: Full Period Analysis (Quarterly Changes in Reserves, Dec. 1957 - Dec.
e(t-value)

Austria23.07445*(3.04553)

Belgium

CanadaDenmark
FinlandFranceGermany
Italy

34.31622*(2.30927)
20.88914(1.39762)
8.58355(1.14733)
6.53081(1.43953)

71.gn228*(2.42794)
322.89605*(2.86534)
33.24857(1.00951)

Japan

37.89330*(2.08121)

Nethearlands

NewZealandi

41.90470*(2.88564)
5.94387(1.07765)

Norway17.44'196*(.3.24392)

SwedenSwitzerland

UnitedKingdom

17.82988*(2.10102)
105.08042*(3.24704)
21.42356(O.15029)

p(t-value)

1972)
X2

X2

R2

Dw

dw

(v=19)

O.18271*(1.75310)

O.19060

1.93588

51.22457

a12.57143

a3.64286

021623

O.16275

1.96002102.26305

a16.59322

a5.91525

O.34935

2.13997100.80634

a18.76923

a6.07692

O.12132

1.9865956.13697

a12.82456

a4.92982

O.21137

2.06969

33.04479

all.42105

a1.77193

O.666312.58895

205.81047

a21.14286

a9.71429

O.33491

1.46841827.89520

48.20690

44.75862

O.34179

2.00121237.89095

a13.03448

a6.82759

O.90878

1.31036126.91478

a25.47059

a14.29412

O.02661

1.5911198.60653

a25.456!4

a16.85965

O.22901

1.76637

41.77332

a17.27119

a11.33898

O.05482

1.9781937.17291

a16.48276

c10.27586

O.282621.6893163.00026

a24.75862

a17.17241

O.61959

1.97057

239.18382

a28.96491

21.77193

O.335142.26674245.97099

a20.42857

an.soooo(v=9)(1.60561)

O.20049*(2.84425)
O.14689(1.35521)

O.12614*(1.90234)
O.45114*(6.70181)
O.28474*(2.86374)
O.34773*(2.92225)
O.35258*(15.43281)
O.O1966

Note: See note for Table 2.

-,)•

c

(O.19741)

O.26007*(2.05182)-O.05032(-O.41082)
O.29763*(2.43889)-O.62988*(-5.99109)
O.23913*(2.82122)

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Tab]e 4 Autoregressive Equations: Short Period Analysis (Monthly Changes ine(t-value)

Austria

Belgium

CanadaDenmark
Finland5.27950*(1.90988)
12.83129*(3.16515)-7.12391(-1.11666)
O.72577(O.35963)

O.67766(O.58338)

FranceGermany
Italy

Japan
Netherlands

NewZealand
NorwaySwedenSwitzerland

UnitedKingdom

45.96968*(3.98969)
63.39336*(3.08950)
22.87583*(2.38857)
16.95919*(2.69801)
12.56985*(2.15585)
O.04729p(t-value)

O.47055*(3.90143)
O.32442*(3.80171)
O.52848*(6.23377)-O.18654(-1.51120)
O.28064*(2.25131)
O.17465

Reserves, Dec. 1957-Dec. 1962)
X2

R2

Dw

ou

O.44375

1.79698

O.44011(v=9)

19.67149

1.9103030.01676

a17.73684

a11.59649

O.63852

2.12258

47.16180

39.71429

c18.64286

O.14841

2.1159315.33403

a13.72414

a5.10345

O.258111.73966

8.49908

a20.62069

a10.96552

O.15780

1.6865469.62757

a9.31579

a3.52632

O.18266

1.96820154.26269

a26.15789

a13.70175

O.477392.06848

63.39325

a22.01695

a7.27119

O.350031.92095

45.10822

a24.75862

c18.20690

O.09906

1.9437843.15037

a22.69492

a13.03390(1.55888)

O.14035*(1.71259)
O.50427*(4.25680)
O.33643*(2.99313)
O.09829

X2(v=19)
a13.20339

a7.94915(O.75159)

O.40120*(3.70048)

O.42677

1.66572

14.86866(O.02419)

a21.31034

a7.86207

2.73141*(2.14211)
6.05203*(3.37117)
10.09240-O.11338

O.124392.214139.62094a17.17241(-O.93813)
O.29013*(3.06544)
O.O0969

a8.55172

O.361101.71061

12.90287

a17.03509

a2.12281

O.OI097

1.96224

51.79931(1.42940)(O.08139)

a23.35088

a8.08772

O.26771026937

O.26457

1.96750105.30127

a20.62069

a13.03448(O.O1895)*(2.30001)

Note: See note for Table 2.

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6
Table 5 Autoregressive Equations: Short Period Analysis (Monthly Changes in Reserves, Dee.
e(t-value).Austna

Belgium

CanadaDenmark
FinlandFranceGermanyItalyp(t-value)

X2

(v=9)
a7.27119

O.07885

1.97255

31.03847

O.12672

1.9759625.86742

a15.23729

a3.88136

O.1!880

1.23876

44.67247(O.36594)(1.33690)

a24.71429

a11.14286-O.05256

O.05251

1.9966230.48537

a17.94915

a8.96610-2.30424-O.07709

O.07732'

1.9950915.12309(-1.16034)
22.22081*(2.59339)
26.85933(1.54917)
22.68864*(1.87172)(-O.58553)
O.48923*(4.26508)

a18.62712

a14.72881

O.484642.09660

50.00635

a21.24561

a9.84211-O.18143

o.13oes

2.04499131.54228

a14.55932

a5.23729

O.647631.65853

90.67355

a19.14035

a5.63158

O.Ol9482.06348

25.87203a26.15789

c17.56140

O.02233

1.9971743.59033

a19.98305

a8.28814

O.395882.04087

14.30308

a15.10345

a6.13793

O.11276

1.9285425.37963

a15.91525

a7.61017

O.242192.08570

18.89689

c31.65517

a15.10345

O.36685

2.14630

141.35469

53.88136

29.64407

O.04238

1.71487

88.03785

a15.18182

a10.27273

5.55023(1.38663)(-O.39701)(-IA1346)
O.67497*(6.43863)
O.O1621(O.1447)-L18019-15.06550

O.38712*(3.40487)-O.18540(-1.32173)
O.20745*(2.13348)-O.40382*(-3.16537)
O.02251(-1.26742)(O.30884)(-O.62798)
7.48439*(2.21633)
2.57401(1.03524)

19.31829(1.04880)

UnitedKingdom

X2-O.08040(-1.10303)
11.26806*(1.91744)

Switzerlandou(-O.59716)
O.18630(1.39518)
O.05466

NewZealandSwedenDw

7.55214*(1.83484)
10.95090*(2.80799)
2.20894-3.78398

NorwayR2(v=19)
a17.94915

Japan

Newzealand

1962 - Dec. 1967)

O.02233

rl

-'

Z

o
co
c

(O.16863)

Note: See note for Table 2.

K
>
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=
"pu
o
a
kH

o
K
:e

L
>

Table 6 Autoregressive Equations: Short period Analysis (Monthly Changes in Reserves,e(t-value)

Austria

Belgium

19.93472*(2.16417)
7.97304

Denmark
FinlandFrance33.70466*(2.39203)
5.31208(O.78333)(1.13005)

6.29522*(1.71773)
7.26962

O.29867*(2.30330)
O.40718*(6.02858)
O.12423(O.37871)

GermanyItaly

235.79829*(1.72412)
9.43737(O.42636)

Japan

O.1543998.03417*(3.33579)

O.23108*(1.79801)
O.26415*(6.27394)

19.72521-O.12745

NewZealand*(1.67475)
4.09779(-1.54188)
O.29306*(2.54939)-O.13901(-1.09646)
O.44882*(3.73796)-O.29461

NorwaySweden13.84478*(2.30162)
6.66831

Switzerland

49.43356(1.31350)(O.92842)

UnitedKingdom

25.90548*(.1.69421)

Dw

au

O.09267

1.98392

O.21378X2(v=9)*(-2.65378)
O.13130*(2.78649)

:
m
U
tn
K
>
Z
v
o
pa
-z
8
tu

67.59316(v=19)
a23.37288

a11.67797

2.09535

71.08975

a19.14035

a9.14035

O.35058

1.87432

96.95633

a17.86207

a9.58621

O.06894

1.98198

51.90013

a17.94915

a9.30508

O.26287

2.00292

26.20361

a24.72881

a8.96610

O.636122.41780

139.37353

a28.13208

a15.49057

O.124311.98448

1O15.24339

a24.72881

a19.47458

O.192542.07426

169.70114

a23.37288

a9.98305

O.64101

1.46182201.29348

a23.28571

a14.71429

O.156311.67434

85.21820

a26.85714

a13.64286

patu

O.29663

2.14237

20.54660

a8.20690

a1.65517aO.05894

2.0560744.95277

a15.91525

a7.27119

O.42753

2.1110737.57625

a20.66102

a8.12712

O.309592.50607402.51282

a16.48276

a9.58621

O.33365

1.41825112.10249

a43.54545

a23.72727(O.94586)

Netherlands(1.45316)

X2

R2(1.22571)

O.21304*(1.91884)
O.33573*(2.99790)
O.14894(O.81026)

Canadap(t-value)

Dec. 1967 - Dec. 1972)

pa

z
>
H
p
o
Z
>
v
a
C
pa
Z
-.d

tu

ua

>
7
U
T
tn
tn
tu

"
<
tu
ua

Note: See note for Table 2.

:

-N

Dec. 1957 -Table 7 Tests for Stability of the Standard Error (oii): Full Period Analysis (Monthly Changes in Reserves,

P2

R2

Dw

O.02904

O.09749'

1.99785(t-value)
Austria

Bartletttest-O.02484

Canada(-O.23597)
O.04260

40.94922-O.O1795

Finland(-O.23211)
O.10706

France-O.02910

O.10752

1.9951344.94836

O.100392.00565

60.91871

Italy

Japan

-O.O0615

O.06494

1.97969

O.25123

1.97867

60.40965

O.319121.9951024.95130

O.10035

2.00009

O.200171.50118

O.40784

2.17129

O.38934

1.90241

O.17986

1.67450

36.97845

55.84945

25.00780

353.40758

O.29076

1.92355*(3.89)105.65941*(4.26)

O.30104

1.58146

O.32038

1.9873636.23989

O.40341

2.1048138.67709

24.37720

O.243141.83025*(3.28)14.37353*(2.31)

O.15783

1.94251

O.84660

O.065511.99479

O.389992.34971

O.18826

1.50072

O.44520

1.93578O.04568

1.92850

1.95633

aILI1838

NewZealandO.36460

2.011122.78472(1.46783)(1.32)-O.09722

O.15786

1.99070

52.15086(-1.29333)
O.09212O.40077

2.01280

27.78106-O.35005*(-4.76367)

O.477881.87928

88.87491

O.03965

O.19137(1.19296)(O.52315)

1.59491*(2.57)

O.07340

UnitedKingdom

O.34198

11.36010-O.11304

Switzerland

20.47824*(5.98)3.20577*(5.66)(-1.50832)
O.10847

Switzerland

1.6848538.25488

Netherlands

NorwayO.32625*(2.86)(-O.38503)(-O.O1819)
O.10703(1.40964)
O.25158*(3.41199)

IL63957*,(4.88)(1.40752)

Germany

Dw*(4.61)(O.56043)

DenmarkR2(x21v=4)(O.37328)

Belgiumx(t-value)

Dec. 1972)

5.99989*(5.56)3.20726*(2.70)470.11557*(6.48)1.99269

a7.33976

28.88486(L16)' Significantiy different from zero at the O.05 level. ,a Distributions marked "a" are those that satisfied the Bartlett x2 test at the O.05 or O.Ol level of significance.
of1inear trend, ut2 =uo2 + )Cr, whqn ut2 is treated as apoint-estimate of au2.
Xis coeffidient
thep, is the coefficient estimated from the equation, ARt = e + p, ARt-i + p, ARt- 2 + u't.

K
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ca

Table 8 Tests for StabMty of the Standard Error (Oii): Full Period Analysis (Quarterly Changes in Reserves, Dec. 1957 - Dec. 1972)p2(t-value)•

R2

Dw

Austria-O.21223

O.14598

1.75341

Belgium(-1.08845)
O.18372
O.031616.65669

O.19175

1.92690

O.18082

1.97350

aLM71329.17799

Finland-O.49776*(-4.01933)-O.06817

France(-O.46507)
O.03105

O.449481.955549.89321-O.09238

O.13791

1.810219.79218

Japan
Netherlands

NewZealandl

NorwaySwedenSwitzerland-O.29197*(-2.21466)-O.02402(-O.17243)
O.37534*(2.56355)

O.46509

1.99183

36.60453

2,,25369

144.18707

O.091211.85066

O.315972.31561

O.533172.13362

O.32674

2.28664

O.343411.48889

O.35208

1.64892

O.21216

2.33690

O.29674

1.23926

O.32344

1.41359

O.080111.73308

O.488992.18586

O.390972.28668(1.22)

358.47155
144.56102
34.05889
1448.13642

O.16961

1.95566

33.66134

28245.39480*(3.01)

O.36018

1.81678

a2.49897

883.29965*(1.92)

O.52308

1.94697

4.51828592.33357*(2.41)

O.27979

1.92413a3.41080

302.79068*(2.75)

aO.11903

20.61918-O.39019*(-3.18073)

O.43426

O.38331*(3.00657)-O.OIOOI(-O.07084)
O.O1574

O.335171.97660

27.24932

O.21387

1.90300

16.27569

169.65402

O.25507

1.99249

10.931682120.23960

O.337652.28666

O.256431.98364a5.31583*(2.86)27.10611

O.O04482.00638

1.64673(1.17)

O.04169

59.03942*(4.35)*(3.36)(O.26584)(O.03)

:tuH
v
tu
K
>
Z
v
-o
pa
---,

*(2.89)(O.11609)

UnitedKingdom

O.10195*(2.77)(-O.67283)
Italy

Dw

*(4.82)(O.22531).

Germany

33.12399

R2*(2.58)(O.23187)

Denmarkx(t-value)(x2,v=1)(1.26)(1.29102)

CanadaBartletttest

Z
tu
pa

7
>
H
B
o
Z
>
v
o
cpa
"
tu
Z
fi
'tu
op

>
Z
v

pu
tu

tn
tu
pa

<
tu

m

Note: See note for Table 7.
asx
Dec. 1957 - Dec. 1962)

Table 9 Tests for Stabmaty of the Standard Error (Oii): Short Period Analysis (Monthy Changes in Reserves,p2(t-value)
Austrai

Belgium

CanadaDenmark
Finland-O.08731(-O.58414)-O.O1964(-O.14559)-O.14664(-1.08948)-O.30771*(-2.31480)
O.O1667

Bartlettte$t

R2

Dw

O.43182

1.87312

a4.10948

O.19287

2.00860

aO.38614-O.08748

Italy

NewZealand'NewzealandSwedenSwitzerland

2.03804

O.098091.79852

O.14980

L54811

O.045071.73059

O.13791

1.88611

O.065431.90209

a1.oo16o-1.16417(1.25)(-1.52)

O.09374

O.47174

1.91405
2.06643a030s32

57.76032

a2.69559

440.67710(1.06)(1.44)

1.95426

a5.43531

111.81832

O.29449

1.88189

O.06880

1.45167

O.09273

1.69176*(2.55)

O.340642.08573

ao.oolg2-12.75816

O.09483

1.86686

aO.05936-18.02780(-O.52)(-O.70)O.347932.01596

aO.99250-O.93175

O.05716

2.30256

a1.28170(-O.43)
O.36869

O.114641.90520

O.063542.01058

O.O0418

1.22781

O.124661.77023

O.O14612.08777(O.48)

O.32260

1.99161

aO.12194(1.01107)

O.10655

O.46906

aO.22015

O.06103(O.03)

O.09389

1.79669

aO.74087

36.37331(O.93)(O.53084)

UnitedKingdom

2.27570

1.63488

O.11270

O.08134

O.04988

O.32592

O.12833-O.15417(-1.12520)
O.13387-3.53462

33.89680(O.21918)

Norway1.48050

2.01831

O.12393(O.92601)

O.26052*(1.99091)-O.07407(-O.59725)
e.02776O.30528

O.51972(O.81905)

Japan

Dw

12.01134*(2.64)(-O.37)112.83583*(4.06)
3.06694

GO.63136)
GermanyR2(x2,v=1)(O.12030)

Francex(t-•value)

O.11472(O.80122)
Note: See note for Table 7.

1.99916

a2.69507-15.57176(-O.11)

K
>
m
>
=
-pu
o
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C
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-'

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K
?
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>

Table 10 Tests for Stability of the Standard Error (ou)P2(t-value)
Austria-O.12844

Belgium(-O.94164)
O.15739

CanadaDenmark
FinlandFranceGermanyItaly(1.092M)-O.223e9*(-1.70209)-O.13454(-1.00726)
O.03641{O.27041)
O.17512(1.08384)-O.09800: Short Period Analysis (Monthly Changes in Reserves, Dec. 1962 - Dec.

R2

Dw

O.14783

1.93212

Bartletttest

aO.61282-O.04719

O.13287

1.95278

a1.03559-O.06129

NewZealand(-O.45553)
O.06769

NorwayO.42361

2.05330

a3.31385

Switzerland

O.147391.79091

aO.06779

UnitedKingdom

O.18391

1.65670

O.15377

1.76686

O.12106

2.31485

O.02920

2.07931

O.082421.99411

O.031111.72880

O.067092.04089

10.56544*(2.16)

O.24774

1.91468

12.62952-37.19301
6.12788(O.92)

O.08575

2.00349

a1.46505-O.62581

O.172811.94686

aO.43960-17.95687(-O.22)(-O.61)

O.09896

1.95953

a1.43059

O.41275

1.98373

a1.03912-45.37687
47.18809(O.50)

O.13280

1.92215

aO.47299

O.06456

2.01976

aO.02335-2.85779

O.O17222.24967(-O.13)
O.90484

O.05101

1.97349

O.22871

1.80302

O.O0585

1.888311.99643

aO.66934-O.21776

O.18588

1.89808

a5.99068(-1.54700)
O.13686

O.27726

2.01053

a2.42830(O.38)

18.10717*(2.05)
O.19795(O.04)(O.74115)

O.47208

1.91525

a4.35448

515.19091

O.21150

1.60098

O.085191.96463

a5.09515*(1.93)168.50225*(1.88)

O.21159

1.40225(-O.59713)

:H
m
U
m
K
>
Z
v
-o
pa

-Z
m
pa
Z
-o
Z
>
v
a
cpa
)-

(-O..23)

O.33548-O.34401*(-2.58135)-O.08204

1.84595(-1.53)(O.49705)

SwedenO.06433

5.43104(1.74)(-O.34969)
Netherlands

Dw(O.49)(-O.53581)
Japan

1967)

R2

(x2,v=1)(-O.73766)-O.07143x(t-value)

pa
tn

Z
fi
t-u
ua
>
Z
v
pa
tu

m
tn
pa

<
ta

m

Note: See note for Table 7.

aaTable 11 Tests for Stability of the Standard Error (ou): Short Period Analysis (Monthly Changes in Reserves. Dec. 1967 - Dec. 1972)
P2(t-value)
Austria-O.OOI17

R2

Dw

O.15905

1.99599(x2,v=,1)
11.88297-O.05522

127.62578

O.10649

1.98524

81.63847

a3.24584

Canada-O.15163

O.36467

Denmark(-1.12378)
O.02304

O.153811.95625-O.03519

Italy

Japan

-O.04539(-O.33631)
O.16248(1.20580)
O.20441

1.98147

1.16932

ao.o43os

O.04319

1.77390(O.33)

O.23249

1.96210

a4.59079

19.79732*(2.71)

O.31357

1.94008

O.31000

1.99480a3.03121-391.50309

O.14396

1.84693O.02519

1.34717(-1.45)

O.13289

2.00757

aO.05885

2586.60975(O.19)

O.20944
O.27074

1.97105

2.07129

9.09663583.50065

O.17752

2.17008

82.91669*(1.70)1950.12411

O.493172.09061

O.129212.04005*(4.32)

Netherlands-O.16443

O.07972

1.94167

NewZealand(-1.24595)
O.14345(1.08149)

O.27961

1.91490-O.09564

O.18373

SwedenSwitzerland

UnitedKingdom(-O.73820)
O.15122(1.09810)

1.53088

O.24782(1.54253)

NorwayO.15152-217.24940(-O.26129)

Germany

1.94289*(-2.17)10.02843(O.51240)

FranceO.30189

aO.30542(O.16666)

O.07025

Dw(1.52)(-O.40628)

FinlandR2*(2.61)(-O.O0864)
Belgiumx(t-value)

Bartletttest

96.00222

20.47546(O.96)

1.98222

aO.05269-6.06610

O.10077

2.14588

aO.87333(-1.26)12.64055

O.06587

1.99840

e.O1459

1.96630

O.18172

1.28644O.438281.80187(O.50)

O.433422.02482

aO.61253

1.90851(O.11)-O.36918*(-2.85862)

O.47988

O.02745(O.20206)

O.212111.89099a6.15918

2845.68422*(1.72)

Note: See note for Table 7.

1.98437!6.60390612.81294•*(3.72)

K

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C
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-

17
THE DEMAND FOR INTERNATIONAL CURRENCIES AND RESERVES

The value ofp was negative, but significantly different from zero in Switzerland in

all tables (except for Table 4). Therefore, it was theoretically wrong in Kenen and
Yudin's article. However, we should not neglect it, even ifit was only one country.

The x2 test for normality was tabulated on the last two columns in Table 2-Table
6. We split a normal distribution into 1O or 20 cells whose frequencies were equally 10

or 5 O/.. And we recorded the observed frequencies of outcomes in the corresponding
cells. The last two columns, therefore, involved two kinds of x2 values; one was with
v==9 and other was v= 19. The most countries passed the x2 test for normality. In orderto test the statistical independence ofresiduals, ut,on the other hand,we calculated the

Durbin-Watson's ratio, Dw, and an additional term, p2, for the autoregressive equation. They were arrayed in Table 2-Table 6 and Table 7-Table 1 1 respectively. Theysuggested that the residuals, ut, were statistically independent. The Bartlett x2 and 2 inTable 7-Table l1 provided the homogeneity test for variance, e.. They, however,
did not give us any satisfactory results.

The calcutated parameters, e, p, and a., were used as the input data into the crossTable 12 Cross-Sectional Models (millions ofdollars)Rit-""Bo+Bie+ 6,pi+6,oui
Bo

6,

6,

+Eit
6,

Dw

R2

1.92

O.92

2.27

O.79

2.18

O.92

2.10

O.82

2.66

O.87

2.68

O.97

1.90

O.79

1.82

O.85

2.14

O.74

2.26

O.89

FullPeriod
Analysis(Month!yChangesin
Reserves)

Rs7

131.484-3.543

1,215.306(O.51)(-O.51)(1.40)

Rn

1,195.520

333.422*(1.98)

6,719.201-17.553(1.07)(-O.64)7.457*(3.35)(1)(O.64)

8.619*(2.27)

FullPeriod
Analysis(Quanterly

Changesin
Reserves)

Rs7

187.081-3.697-470.199(O.80)(-O.65)(-O.51)

Rn

79.18352.430(121)(2)(O.04)

13,457.393*(1.92)

4.905(O.29)

ShotPeriod
AnalysesRs7-338.881-8.494637.017(-O.97)(-O.65)(O.69)

R62-272.103

27.998*(3.07)

1,589.752*(2.47)

R62

67.510

(3)

(4)

R67
R67

(5)Rn

31.591*(5.17)

34.608*(8.11)(-1.11)104.862*(2.88)(O.13)

17.664177.390*(4.38)

998.58118.497*(3.27)(O.57)

435.971-24.706(O.53)(-1.32)(O.53)

18.744*(3.68)(O.22)(O.03)

827.417342.432

98.593*(2.78)

4,458.568(1.54)'

9,168.065(1.68)" Significantly different from zero at the O.05 level.

13.901*(2.81)-O.495(-O.05)

MASAHIRO FUJITA, NOBUO MIYATA

18

sectionai models. According to Kenen and Yudin's procedure,p was fixed at zero andthe corresponding estimates ofe and a. were respectively replaced by the mean change
in reserves and the simple deviation of aRt, when p was negative or not significantly
different from zero. Table 12-Table 14 present the regression coeflicients for the vari-

ous cross-sectional models generated from possible combinations of e, p, and a.. The
least-sequares estimates in these tables were generally characterized by the high valuesofR2 and Dw. The values on row (4) in Table 13 and Table 14, however, were com-paratively low, which related to the period, December l962-December 1967. As
shown in Table 5, the value ofp was fixed at zero in more than ten countries for thisperiod. Accordingly, there was not any time interval between external payments andreceipts in almost countries.
In Table 12, the coeflicient, Pi, attached to e was negative when e was not signifi-

cant, while it was positive when e was significant. This fact is contradictory to thetheoretjcal presumptjon : the country that antjcjpates a positive change jn reseryes in
the near future will take small reserves as being suMcient to finance its deficit balance.
Table 13 Cross-Sectional Models (rnillions of dollars)

Rit=Bo' 62pi+B3oui+eit
B,

6o

B,

Dw

R2

1.87

O.91

1.95

O.73

2.04

O.93

2.21

O.81

2.75

O.88

1.68

O.95

1.43

O.63

1.52

O.55

2.68

O.72

1.87

O.81

FullPeriod
Analysis(Monthly
Changesin
Reserves)

131.679

1,205.947(O.53)(1.46)

1,177.172

7,599.862(O.57)(1.09)

Rs7

213.020-357.753(O.95)

R72-288.718(-O.41)
11,862.534(-O.16)(1.69)-367.475

841.875(-1.08)(1.00)-177.852

914.519(-O.56)(1.16)

494.4542,414.905(O.78)(1.34)

739.9074,504.493(O.84)(1.80)

586.211

4,154.705(O.69)(1.40)

227.870

10,380.657(O.12)(1.52)

Rs7
(1)

Rn

8.062*(8.22)

34.896*(4.21)

FullPeriod
Analysis(Quarterly

Changesin
Reserves)(2)

ShortPeriod
Analyses

Rs7
(3)

R62
R62
(4)

R67
R67
(5)

Rn

Note: See note for Table 12.

6.075*(9.17)

24.512*(4.62)

28.673*(7.07)

44.229*(11.67)

20.457*(3.19)

21.396*(2.40)

7.870*(4.13)

23.572*(5.40)

19
THE DEMAND FOR INTERNATIONAL CURRENCIES AND RESERVES

Table 14 Cross-Sectional Models (millions ofdollars)
Rit--il}

Rit"Be+Biei-eit+B2pi+eit

6,

Dw R2

6,

Rit=6o

Dw R2

+&aui

Dw R2

6,

FullPeriodAnalyis(Monthly
Changesins'Reserves)

45.363Rs7*(•6.54)Rn*(4.96)(1)

214.841

1.30

O.87

-901,067

1.65

O.13

(-O.46)
2.24

O.79-1520.485

7.619

1.91

O.90

1.89

O.72

1.89

O.93

2.09

'O.78

2.62

O.88

1.45

O.95

O.86

O.60

1.00

O.62

2.33

O.70

L98

O.79

*(7,84)
1.58

O.04(-O,15)32.102*(4.04)

FullPeriodAnalysis(Quarterly

Changesin
Reserves)

14.451

Rs7

1.42

O.86

*(6.43)(2)

67.684

R72
ShortPeriodAnaly-*(4.75)1170.770

1.96

O.14

1.99

O.78

18030.063

6.024*(9.57)(O.50)

2.31

O.33

26.218*(4.71)(1.63)

ses

36.412

Rs7

74.237(3)

R62*(4.82)R.2*(2.55)114.166
193.321(4)R67*(4.15)R67*(2.69)R72*(6.87)22.048
(5)

2.18

O.52

*(2.49)89.276-64.234

1.77

O.Ol

(-O.04)
1.53

O.78-483.208*(7.00)

O.98

O.05

(-O.18)1.39

O.53

1686.696

2.18

O.73
O.56

1.22

O.20

O.88

3742.886
(L29)

1.38

-520.562

1.04-3623.098(-O.32)19.364*(2.96)

O.21

19.357*(2.02)

O.04(-O.13)
2.11

43.564*(11.48)(O.72)
1.33

28.061

6.855*(3.76)

1.57

O.09

21.038*(4.97)

Note: See note for Table 12.

Pi must be negative ife is significant. Accordingly, the variable, e, should be deleted
from the normal equation. After deleting, we estimated the coefficients for the normal

equation which contained per capita income, y, and domestic money supply, Mt, inTable 15. The estimated coeflicient, P3, attached to a., was significantly different fromzero for all periods. But the coefficients, P2 and P4, which were attached to p and y,were not. Although p was not significant in all periods, we ought not to forget that theestimate, p, was fixed at zero in more than ten countries for the period, December

1962-December l967 and in about five countries on the average for other periods.
The supply of domestic money, Mt, on the other hand, was significant only in 1972
for each period.

Finally, we calculated the holdings of foreign reserves in l957 and 1962 to com-pare our estimations with Kenen and Yudin's. They were tabulated in Table 16. 0n
the last two columns, we made two pairs of rankings derived from columns (1) and(2) in Table 16 and the corresponding columns in Kenen and Yudin's article. The
rank correlation coefficients for two columns were r=O.742 in 1957 and r==O.728 inMASAHIRO FUJITA, NOBUO MIYATA

20

Table 15 Cross-Sectional Mode]s (rnillions of dollars)
Rit=6o+62pi+33aui+ 4Yi +,Mit+eit

Bo

6,

B,

B,

6s

Dw

R2

2.32

O.91

2.56

O.93

2.26

O.93

2.68

O.91

2.67

O.87

1.68

O.94

1.70

O.62

1.71

O.45

2,99

O.72

2.52

O.94

FunPeriod
Analysis(Monthly
Changesin
Reserves)

Rs7(1)R72-90.00717.972(-O.20)(O.77)-3,319.447-3,551.828(-O.96)(-O.76)

7.853*(7.83)

24.307*(4.41)

O.167

O.020

(O.41)(1.33)

1.061(1.20)

e.138*(5.06)

FullPeriod
Analysis(Quanterly

Changesin
Reserves)

Rs7(2)R72-459.767-O.075(-O.96)(-o.oo)-3,750.436-630.206(-O.96)(-O.10).-893.083(-1.47)159.512896.645(O.20)(1.01)

1,539.864

2,437.732(O.82)(1.32}

2,073.787

4,321.465(O.92)(1.61)

1,644.720

3,035.941(e.94)(O.91)-17776.203

1,269.975(-O.55)(O.26)

6.015*(9.32)

19.981*(4.80)

O.494

O.O12

(1.42)(O.97)

O.971

O.115*(3.62)(1.00)

ShortPeriod
Analyses

Rs7
(3)

R62
R62
(4)

Re7
R67

(5)Rn

29.511*(6.75)(1.02)

878,115

O.492-O.O07(1.09)'-O.215(-O.39)-O.OOI(-O.46)(-O.21)44.360*(10.70)

23.327*(3.35)

21.984*(1.98)-O.923O.05(-O.78)(O.45)-O.705

O.05(-O.66)7.657*(3.95)

17.410*(5.16)(O.M)-O.626

O.021(-O.77)
O.486(1.26)
O.109*(4.19)(Q.54)

Note: see note forTable 12.

1962. Therefore, the hypothesis ofindependence was rejected.

2. The Precautionary Motiye
Foreign reserves are held to provide for contingencies requring urgent imports tomeet a bad harvest or other disasters. The strength of this demand depends not only on

the population or the productivity of the country,but also on her abilityofborrowing
from foreign governments or international financial instjtutions. If the liquid reserves

fell below a certain minimum level, the country would feel impelled to adopt severe

readjustment measures, and short or medium private loans abroad would be reduced
to zero or negative values. And also oMcial financial institutions would hesitate tofavour the deficit country with oMcial loans because of her unhealthy economic policy.

The minimum reserve level, therefore, can be regarded as an effective indicator to theprecautionary demand for international currencies. The 20 or 30 0/. ratio or reserves

Table 16 Foreign Reserve Holdings in 1957 and 1962, Computed from Kenen and Yudin's Best Equation; Dec. 1957 - Dec.

1962

(miMons of dollars)

ActualReserves

Austria522.00

Rankof
Kenen

1962

1957

Computed

Excessor

Reserves

Shortfal1(1)

109.03

ActualReserves

1,077.00

Computed Excessor
Reserves

927.28(1)

Shortfal1(2)

andYudin's

Kenen

(2)

Table3andYudin's

Table3(1957)(1962)

149.726

5

6

7

Belgium

1,148.00

412.97703.26444.74

1,753.00

1,377.97

375.033

3

3

4

Canada1,936.00

1,184.36

751.742,560.50

2,124.88

2

1

2

5

Denmark

172.00333.57
99.46-16L37255.60304.004,049.00
6,957.00

804.02

12

13

13

13

7

9

10

10

3,81L98435.62-548.42-136.56
273.02

6,790.67

166.33

-

m

'

-

80.64

440.56

France'2,271.e6-1,626.06

Germany

180.10645.005,197.00

4,189.69

1,O07.31

ItalY

1,479.00

1,639.83-160.83-298.74

4,068.00

2,832.oo

1,236.00

11

6

1

1

2,022.00

2,035.42-13.42

13

11

9

2

FinlandJapan

828.001126.74'

1

7

5

9

Netherlands

1,os6.oe

1,040.06

15.94

1,943.00

1,900.86

42.14

9

8

7

6

NewZealand
NorwaySweden152.00270.20156.84-126.20172.00718.05

10

12

12

14

40.06

303.00529.65-546.05-225.75

8

10

11

11

196.90481.00223.03257.97802.00632.41

169.594

4

4

8

Switzerland

1,898.00

1,690.43

207.582,919.00

2,910.55

8.45

5

2

8

3

UnitedKingdom

2,274.00

2,815.80-541.80

3,308.00

4,657.70-1,349.70

14

14

14

12

g
:
m
U
tu
K
>
Z
v
o
x
-Z
b-

:l

tn
pu

z
>
.
o
z
>
v
o
c
7
"tu
zg2
p.-

Eg

>
z
v
pu
m
ca
tu

T
<
m
ua

I)l

MASAHIRO FUJITA, NOBUO MIYATA

22

to imports which was proposed by Triflin has been widely accepted as the minimum
reserve level.5) Table 17 shows the mean values ofthe reserve ratios calculated fromyearly data (1957-1971) for 40 countries. The most major countries maintained areserve ratio of not less than 30 O/.. The low ratio which was less than 20 O/. was foundonly in a few countries. Complementarily, we tested whether these means were kept
constant during ten years. The test introduced to solve this type of problem was therank-sum test.6) The results were arrayed in Table 18. The yearly data were split into

two groups. The number ofdata in two gorups were N and N-K. We calculated the
median for each group, for it was natural to test the difference of two medians rather

than the difference of two means in nonparametric situations. The hypothesis Ho:ei == e2 vvas rejected only in six countries. All other countries passed the test.

Before introducing the rank-sum test, we checked the randomness of the reserveimport ratio data. The test based on runs was used in Table l9. Each reserve-importratio was replaced by the letter a if it was larger than the median and by the letter b if

it was smaller than the median. Ni and N2 denoted the number ofb's and ds in theset. U denoted the total number of runs. We obtained Ni = 7, IV2 = 8 and U == 2 or
3 in the most of countries. Therefore, the hypothesis of randomeness was rejected inalmost countries. The fact that the size of U was small and IVi was nearly equal to N2
Table 17 Means and Variances of Reserve Ratios to Imports

1957-1971
Indust.Count.
u.s.

UnitedKingdom
Indust.Europe
Austria
Belgiurn

Denmark
FranceGermany
Italy

Netherlands

NorwaySwedenSwitzerland

CanadaJapan

OtherDep.Areas
Finland
Spain

TurkeyMean

Variance

O.484
O.853
O.214
O.453
O.594
O.349
O.168
O.405
O.549
O.576
O.321
O.215
O.197
O.963
O.325
O.315
O.388
O.220
O.451
O.380

O.208
2.774

Australia

OD71

LatinAmerica

O.069
O.086
O.072
O.02S
O.387
O.220
O.336
O.056
O.O14
O.029
O.138
O.044
O.311
O.039
O.065

Argentina

O.731
O.647

NewSealandBrazilMexicoPeru

Venezuela
OtherAsia

Burma
CeylonChina,Rep.
India

Indonesia

Korea
Malaysia
Pakistan
Philippines

Singapore'Ihailand

All data are taken from IMF: IFS; 1972 Supplement.

5) TriMn, R., Gotd and the Dollar Crisis, 1962.
6) Hoel, P. G., EiementarJ, Statisties, 2nd ed., 1967, 252-255.

Mean

Variance

O.467
O.169
O.343
O.292
O.277
O.369
O.229
O.559
O.287
O.677
O.227
O.489
O.323
O.192
O.359
O.436
O.354
O.160
O.125
O.869

O.232
O.075
O.020
O,437
O.174
O.025
O.170
O.111
O.O12
O.746
O.228
O.186
O.183
O.556
e.175
O.098
O.540
O.042
O.021
O.186

23
LHE DEMAND FOR INTERNALIONAL CURRENCIES AND RESERVES

Table 18 Rank-Sun Test for Reserve Ratios to Imports.

Indust.Count.

1957-1971 1957-1971 Kyears
median median1
mean

IV-Kyears

O.470
O.820
O.200
O.470
O.60G
O.360
O.160
O.390
O.540
O.560
O.320
O.210
O.210
O.960
O.330
O.260
O.390
O.220
O.390
O.310
O.500
o.16e
O.350
O.260
O.280
O.360
O.220
O.530
O.280
O.710
O.24O
O.520
O.290
O.100
O.340
O.420
O.310
O.150
O.120
O.890

O.390
O.450
O.150
O.455
O.570
O.345
O.160
O.390
O.470
O.520
O.260
O.240
O.160
O.900
O.295
O.24O
O.340
O.180
O.350
O.240
O.350
O.105
O.350
O.340
O.290
O.345
O.240
O.530
O.270
O.780
O.140
O.420
O.260
O.1OO
O.310
O.450
O.210
O.200
O.130
O.890

u.s.

O.484
O.853

UnitedKingdomO•.214

Indust.Europe

O.453
O.594
O.349
O.168
O.405
O.549
O.576
O.321
O.215
O.197
O.963
O.325
O.315
O.388
O.220
O.451
O.380
O.467
O.169
O.343
O.292
O.277
O.369
O.229
O.559
O.287
O.677

Austria

Belgium

Denmark
FranceGermany
Italy

Netherlands

NorwaySwedenSwizerland

CanadaJapan

OtherDev.Areas
Finland
Spain

TurkeyAustralia

NewZealandLatinAmerica
Argentina
BrazilMexicoPeru
Venezuela

OtherAsia

Burma
CeylonChina,Rep.
India
Indonesia

Korea
Malaysia
Pakistan
Phmappines
Singapore[[1iadand,O.227

O.489
O.323
O.192
O.359
O.436
O.354
O.160
O.125
O.869

O.590
1.180
O.255
O.510
O.620
O.380
O.165
O.430
O.580
O.680
0.365
O.195
O.220
O.970
O.360
O.325
O.430
O.240
O.630
O.345
O.540
O.180
O.340
O.240
O.255•
O.370
O.210
e.555
O.295
O.565
O.245
O.565•

O.290
o.17e
O.395
O.380
O.450
O.145
O.110
O.880

median2 (K,N-K)

rank-sum
testR

(8,7)
(8,7)
(8,7)
(5,10)('8,7)(5,10)(8,7)(8,7)(10,5)

(8,7)
(8,7)
(8,7)
(8,7)
(10,5)

(7,8)
(8,7)
(7,8)
(7,8)
(8,7)
(8,7)
(8,7)
(9,6)
(8,7)
(8,7)
(8,7)
(7,8)
(8,7)
(8,7)
(8,7)
(8,7)

(10,5)

(8,7)
(8,7)
(9,6)
(8,7)
(8,7)
(8,7)
(8,7)

29*
29*

40
54

48
54
51

6!
25
41

32*
87*

41
26
70
43
71
71
51

46
41
33

63

67
64
73
67
58
53
7!
27
43

58
32
43

85*
29*

(10,5)

71
53

(8,7)

58

* rngans that the mean value does not pass the two sided test with a= O.05.

All data are taken from IMF, IFS; 1972 Supplement.

meant that a sequence of identical letters which was proceeded was not easily followed
by a different letter. In other words, the initial ratio of reserves to imports was maintained for several years. The sign test for trend offers strong support for this fact. The
results of the sign test were tabulated in Table 20,

Another reason for holding reserves is to keep the confidence of domestic money.
This kind of holdings can be classified into the precautionary demand. Reserve ratio
to domestic money supply or foreign liabilities is utilized as a significant indicator, be-cause the reduction ofthis ratio looses in the confidence ofdomestic money.An exam-

MASAHIRO FUJITA, NOBUO MIYATA

24

Table 19 Test for Randornness

IndustCount.
u.s.

UnitedKingdom
IndusgEurope
Austriai

Belgium

Denmark
FranceGermany
Italy

Netherlands

NorwaySwedenSwitzerland

CanadaJapan

OtherDec.Areas
Fin!and
Spain

TurkeyAustralia

NewZealandLatinAmerica
Argentina
BrazilMexicoPeru

Venezuela
OtherAsia
BurrnaCeylonChina,Rep.
India

Indonesia

Korea
Malaysia
Pakistan
Philippines

Singapore
Thailandmedian

N,

N,

U

O.470
O.820
O.200
O.470
O.600
O.360
O.160
O.390
O.540
O.560
O.320
O.210
O.210
O.960
O.330
O.260
O.390
O.220
O.390
O.310
O.500
O.160
O.350
O.260
O.280
O.360
O.220
O.530
O.280
O.710
O.240
O.520
O.290
O.100
O.340
O.420
O.310
O.150
O.120
O.890

7
7
7

8
8
8
8
8
8
8

2
2

7
7
7

7
7
7

7
7
7

7
7

4
3

test
.reJected

rejected
rejected
rejeeted7

accepted3

rejected5

accepted83

rejected882rejeÅëted

5

accepted3

2

rejected
rejected5

accepted3rejeÅëted

8
8
8

7
7
7

8
8
8
8
8
8

6

9

7
7

8
8

5
7
7

5

10

3

rejected

7
7
7
7
7

8
8
8
8

7
7
7

8

7

5
6

10

4

9

5

accepted
accepted
accepted
accepted
accepted
accepted
accepted

5
7

10

2

8
9
8

4

9
8

5

7

7

6
7
6
7
7
7
7
7

8
8
8
8

6

accepted4rejeÅëted

7

6

accepted
accepted4

rejected

accepted
accepted
accepted

6

3

2
6
2
8
6
3

rejected
rejeeted
rejected
rejected

accepted
accepted
rejected

accepted
accepted
rejected

ple is found in Courchene and Youssef's article,7) in which the reserve ratio todomestic money supply was called the country's ability of domestic money to spend
externally. Table 21-Table 24 represent the regression coeMcients estimated by using

the same method as Courchene and Youssef. The demand for reserves was a functionof domestic money supply modjfied by the Iong-term jnterest rate, rt, jn their article.
Our data used were consisted of 56 quarterlytime series observations during the period,

1959(I)-1972(IV). We divided all data into 26 quarterly observations such as 1959(I)-1965(II), 1962(II)-1969(I), and 1966(III)-1972(IV). And we tried to estimate the7) Courchene, T. J. and G. M. Youssef, The Demand for International Reserves, J. P. E, Vol. 75,

Aug. 1967.

25
THE DEMAND FOR INTERNALIONAL CURRENCIES AND RESERVES

Table 20 Sign Test for TrendssindusLCount.
u.s.

UnitedKingdom
lndust.Europe
Austria

BebjumDenmark
FranceGermany
Italy

Netherlands

NorwaySwedenSwitzerland

CanadaJapan

OtherDev.Areas
Finland
Spain

Turkey

3.031
5.629
2.165
O.433
O.433
1.299
1.299
2.165
O.433
O.433
2.165
O.433
1.299
2.165
1.299
1.299
O.433
1.299
O.433
1.299

*

Australia*

NewZealand*Latiniinierica

Argentina
BrazilMexicoPeru*

Venezuela
OtherAsia
Burrna*CeylonChina,Rep.
lndia

*

lndonesia

Korea
Malaysia
Pakistan
Philippines

Singapore
Thailand

1.299
O.433
O.433
O.433
O.433
2.165
O.433
1.299
O.433
1.299
2.165
2.165
O.433
2.165
O.433
O.433
1.299
O.433
O.433
O.433

The countries marked ""' do not have any trend.

regression coeflficients in eachperiod. Ifthe Durbin-Watson's ratio was ill-conditioned,

we used the iterative procedure8) to remove auto-correlation in regression residuals.

(Table 22 corresponds to Table l in the Courchene and Youssef's article.) In all
tables, the coeMcients, b, listed on columns (1) and (2) were significantly different fromzero. The coeMcients, b2, on columns (4) and (7), however, were significantly different
from zero only in a few countries. Especially, the estimate, b2, on column (10) was not
significantly different from zero in almost countries. Therefore, it can be said that thevariable, rt, should be deleted from the regression equation. In addition, thecoefficient, bi, on column (9) was negative or not significantly different from zero inabout four countries in each table. It must not be negative, because an increase indomestic money supplyin circulation will produce theoretically an increase in the hold-ings of foreign reserves. Therefore, we had better use the estimated coeMcient oncolumn (2) as an indicator to explain the confidence of domestic money, which represents the average reserve ratio to domestic money supply. In Table 25, we arrayed thereserve ratios estimated on column (2) in Table 21-Table 24 again.

We often find a wrong idea that the demand for reserves should be consisted entirely ofthe precautionary demand, for our reserve data available are only oMcial data
and the monetary authority does not engaged in foreign trade or speculative activities.

For example, Thorn9) defined the demand for reserves as a function of imports, Rt=

8) Johnston, J., Econometrie Method, 1963, 192-195

9) Thorn, R. S., The Demand for International Demand: A Note in Behalf of the Rejected
Hypothesis, R. E. Stat., Vol. 49, Noy. 1967,

*

*
*
*

8

Table 211972 (IV) (nominal terms)

Regression Estimates for Reserves: Quarterly Data, 1959 (I) -Rt=a+biXt+b2rt+e't

Rt=a+bXt+et,

whereXtequals

whereXt equals
Money
Imports
Supply

b(1)

b(2)

b,(3)

b,
(4)

Switzerland

Netherlands

SwedenDweden

2.873
3.974
O.446
*(24.12) *(35.99) *(18.13)
O.731
O.563
O.333
*(19.43) *(26.69) *(12.20)
O.408
O.786
O.100
*' (7.39)*(3.37)*(7.02)
O.247
O.305
O.312
(1.33)*(6.79)*(4.68)Germany

1.816*(11.94)

Belgium

O.705*(17.61)

O.557*(1392)

O.327,*(2427)Italy

O.963*(12.45)

O.058*(12.88)

Japan

2.465*(8.47)

O.155*(13.51)

Australia

2.196*(4.76)

O.761*(9.16)

R2

Dw
(5)

-2374.239 O.972*(-5.58)1.340-880.890 O.955*(-4.95) O.702-2.060 O.696(-1.67) O.486
140.272 O.513(O.37) O.163
2.208*(9.25)-3649.642*(-2.09)
O.858
O.465
317.458 O.920(O.14) O.587
1.067*(8.36)-70736.434 O.859(-1.03) O.420
5.401*(9.93)
1059.053*(-5.93)
O.856•O.43024.235 O.518
2.130(O.11) O.114*(2.72)
O.699*(11.60)* Significantly different from zero at the O.05 level.

Iterative

b,(6)

O.551
*(25.88)
O.297*(14.68)
O.196*(4.05)
O.296*(4.38)

b,(7)

R2

Dw
(8)

-1226.170 O.985*(-4.69)1.583-394.849 O.966*(-2.24)

O.702-443.133 O.696*(-2.06) O.482
23.341 O.664(O.18) O.583
3194.945*(2.18)
O.890
O.580
-54.560 O.955(-o.e3) O.482
O.059*(8.56)-18166.679 O.863(-O.29) O.302•-763.926*(-10.65)
O.962
O.812
1.071
-489.132 O.814*(8.83)*(-3.29) O.371

b,(9)

O.551
*(25.88)
O.299*(8.99)O.087(1.52)-O.OG9(-O.39)O.654*(11.09)

O.572*(5.97)

O.327*(16.67)

O.260*(8.60)

O.259*(21.99)

Procedurefor

Xt= MoneySupply

MoneySupply

Imports

R2

b2(10)

Dw(11)-1226.170 O.985*(-4.69)1.583-210.950 O.863(-O.91)1.980-17.344 O.337(-O.06) L732
19.365 O.055(O.08) 1.639-185.168 O.656(-1.04) 1.877
264.626 O.768(O.23)

L916

O.021 -77781.571 O.175(-1.14) 1.776(L71).-536.040*(-4.93)
O.897
1.642
160.172 O.219
O.O02*(2.05) 1.874(O.03)
O.220*(13.23)

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Table 22 RqgTession Estimates for Reserves: Quarterly Dateq

1959 (I) - 1965 (II) (nominal terms)

Rt=a+bXt+et,

Rt=a+biXt+b2rt+e't

where Xtequals

where Xtequals

Importsb(1)MoneySupply
b(2)

b,(3)

b,
(4)

Switzerland

Netherlands

Denmark
SwedenGermany
Belgium
Italy

Japan
Australia

R2

b,(6)

Dw
(5)

2.617
2.801
O.432
-416.306 O.935*(13.26) *(14.46)*(9.65)(-O.87) 1.390
O.943
e.452
O.914
-75.087 O.883*(9.68) *(10.95)*(7.28)(-O.37) O.876
1.070
O.399
1.545
-788.943 O.881*(7.73)*(7.81)*(7.95)*(-3.02)
1352
O.990
O.317
148.189 O.794
O.909*(6.78)*(3.90)*(4.79)(O.45) O.957
1.532
1.677. -1728.780 O.718
O.397*(5.36)*(5.79)*(4.74)(-O.71) O.360
1.243
1.286
O.465
-1376.628 O.928*(12.49) *(18.56) *(11.98)(-1.06) 1.251
O.861
o.esg
1.106 -91443.986 O.633*(4.05)*(3.98)*(4.72)(-1.34) O.697
O.665
O.042
O.902 •-106.572 O.768*(5.38)*(5.25)*(5,67)*(-2.16) O.567
1.652
1.551
O.916
-519.166 O.783*(4.07)*(4.81)*(5.32)*(-3.90) O.579
Note: See note for Table 21.

Iterativeb,(7)

O.511 -1033.193*(11.82)*(-2.36)O.507
261.855*(8.74)(1.32)

O.575 -1187.758*(10.72)*(-5.26)
O.221
693.209*(3.18)*(2.64)

R2

Dw
(8)
O.954
1.016

O.912
O.779
O.930
O.515
O.757
O.935

45.047 ,O.739*(5.06)
O.260(O.02)
O.462
390.089 O.964*(17.47)(O.44) O.972
O.195 •-328.494 O.879*(8.89)1.032*(-5.82)O.070 .--174.358
O.816*(6.69)O.516*(-3.45)O.784 -360.580 O.783
O.872*(4.81)*(-2.58)
O.396

Procedure for

Xt= MoneySupply

MoneySupply

Imports

b,(9)

O.546
*(8.24)O.414*(4.43)

O.519

b,
(1O)

R2

Dw

(11)

-1088.486 O.893(-1.81) 2.022
186.856 O.701(O.88) 1.549-812.141 O.769*(5.79)*(-2.99)-O.028-192.051 O.409*(-2.25)
O.102

593.964 O.106(-Lll)

1.847
1.950

(1.06)(O.54) 1.838

e.444*(10.36)
O.!47-M4.938 e.gos(-O.30)1.928.-131.583 O.591(-1.83) 1.657
O.O09 -55997.983 O.204(O.95)(-1.71) 1.536-262.248 O.200-O.031(-O.24)(-1.69) 2.042•*(3.63)

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8

Table 23 Regression Estimates for Reserves: Quarter!y Dateq 1962 (il) - 1969 (I) (nominal terms)

Rt=a+biXt+b2rt+e't

Rt--a+bXt+et,
whereXt equals
Money
Imports

whereXtequals

Suly

b(1)

b(2)

2.694
*(9.04)

Netherlands

O.546*(7.53)

Denmark
SwedenO.395*(2.48)O.196(1.44)

Germany
Belgium

O.671*(4.45)

O.532

Italy

*(4.21)
1.763*(5.39)J.apanO.319

Australia-O.2ou*(2.27)(-O.74)

O.397

R2

b,(3)

b,

2.948

-312.166 O.870(4)

Switzerland

Dw(5)(-O.53) 2.787
O.475
O.228
-494.963 O.872*(8.38)*(6.93)*(-2.84) O.827
O.485
O.061
-101.869 O.374(1.63)(1.75)(-O.36) O.320-O.476-O.0831125.696 O.731(-1.07) *(-2.94)•*(5.14) O.904
O.830 -1606.534 O.767
O.237*(6.04)*(5.57)*(-3.19) 1.222
O.252
O.377
3647.950 O.668*(2.50)*(6.19)(1.73) O.603
1.700
O.121
•-232.991 O.748*(5.33)*(8.92)(-1.63) O.625
O.391 -18557.167 O.504
O.023*(2.09)*(3.65)(-O.46) O.400
O.516-O.060-340.328 O.360(1.26)(-e.74)*(-2.26) O.457*(10.35)*(5.19)Note: See note for Table

21.

Iterative

b,(6)

b,
(7)

R2

Dw
(8)

16.686 O.895(O.04) 3.016*(6.18)0201 -390.479 O.879*(-2.22) O.855*(7.18)177.869 O.212
O.025(O.45) O.307(O.29)
665.776 O.696-O.134*(4.82) O.813*(-2.36)
O.274 -1445.127 O.826*(-3.56) 1.494*(7.35)0214 2327.775 O.782*(4•.32)(1.32) O.486
O.121 •-341.887 O.927*(-4.28) O.689*(11.78)O.044 -78383.006 O.614(-1.68) O.456*(3.13)
O.044-224.026 O.279(-1.87) O.326(O.46)
O.395

Procedure for

Xt= MoneySupply

MoneySupply

Imports.b,(9)b,(1O)

R2

Dw
(11)

16.686 O.895(O.04) 3.016
O.137-263.164 O.552*(3.02)(-1.29) 1.571-O.091-253.387 O.270(-O.81) 1.580(-120)-O.070-216.816 O.387*(-2.42)(-O.49) 1.753
O.247 -1366.175 O.755*(5.63)*(-2.72) 1.684
O.038
218.104 O.215(O.81)(O.42) 1.836
O.097 •- 307.295 O.723*(4.22)*(-2.59) 1.506
O.O15 -36107.534 O.372(-1.24) 1.629*(2.21)-O.051-8.976 O.144(-O.08) 1.690(-O.67)
O.395'*(6.18)

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Rt=a+biXt+b2rt+e't

Rt=a+bXt+et,

whereXtequals

whereXtequals
Importsb(1)Switzerland

Netherlands

Denmark
SwedenGermany
Belgium
Italy

Japan
Australia

Money
Supply
b(2)

b,

b,

(3)

(4)

R2

Dw
(5)

O.539
4.247
3263
-3833.639 O.951*(10.66) *(19.69) *(14.00)*(-4.76) 1.771
O.799
O.385
O.600 -1705.530 O.957*(8.34) *(14.21)*(9.92)*(-7.27) 1.652
O.244
O.086
O.6M -480.409 O.286(1.71)*(2.43)(1.73)(-1.13) O.627
O,157
O,385
O.715 -1710.805 O.353(O.93)*(3.68)*(2.34)*(-2.14) O.378
2.614
O.842
2.768
-1891.328 O.890*(9.93)*(7.01)*(6.30)(-O.68) O.602
O.578
O.330
O.673 -11136.029 O.795*(6.33)*(8.75)*(6.28)(-1.58) O.791
O.400
O.026
O.558
-117.666 O.532*(3.09)*(4.20)*(3.27)(-1.38) O.582
4.483
O.251
6.447 •- 1482.312 O.843*(5.70) *(14.31)*(7.78)*(-3.70) O.613
4.247
1.297•
6.412-393.386 O.355*(2.29)(1.77)*(7.48)(-O.69) O.237
Note: See note for Table 21.

Iterative

MoneySupply

Imports
b,(6)

b,
(7)

O.560
*(18.40)
O.321*(9.96)
O.161

8
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Table 24 Regression Estimates for Reserves: Quarterly Data, 1966 (llD - 1972 (IV) (nominal terms)

R2

Dw
(8)

-773.436 O.971(-1.48)1.730-832.856 O.957*(-2.93) 1.104-42.248 O.454*(2.66)(-1.51) O.864
O.451
652.416 O.623*(4.21)(-1.76) O.989
O.872 -1424.745 O.890(-O.69) 1.110*(9.07)
O.334 -1637.058 O.861*(8.12)(-O.31) O.560
O.032 -98875.508 O.653*(4.37).
(-1.44) O.601
O.271 •- 578.187 O.961*(17.21)*(-3.40) 1.064
1.584-485.988 O.862*(8.09)*(-2.47) O.811

Procedure for

Xt" MoneySupply
b,
(9)

O.560
*(18.40)
O.318*(5.97)
O.094

b,
(1O)

-773.436(-1.48)-743.345(-1.79)-78.045(1.15)(-O.20)O.O16-130.389(O.31)(-O.14)O.850 -2620.601*(5.53)(-O.85)
O.211 2226.176*(3.29)(O.28)

O.O06 •-134.715(O.38)(-L17)

O.258 .-476.837*(11.96)*(-2.13)-O.049193.621(-O.51)*(3.20)

R2

Dw
(11)
O.971
1.730
O.903
1.964
O.285
1.591
O.083
1.739
O.778
1.870

O.522
1.522
O.252
1.819
O.925
1.760
O.584
1.785

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30

Table 25

MASAHIRO FUJITA, NOBUO MIYATA

Regression Coefficients Estimated frorn Courchene and Youssers Equation
1959(I)'1972(IV)1959(I)-"
1965(II)

1962(II)1969(I)1972(IV)

O.466
O.ss3
O.100
O.305
O.557
O.327
O.058
O.155
O.761

O.432
O.452
O.339
O.317
O.397
O.465
O.089
O.042

O.397
O.228
O.061

O.539
O.385
O.086
O.385
O.842
O.330
O.026
O.251
1.298

Switzerland
Netherlands

Denmark
SwedenGerrnany
Belgium
Italy

Japan
Austria1966(III)'--O.083
O.237
O.252
O.121
O.023

OS16

-O.060

Table 26 Growth Rates of Rt and It

logRt=a+bt+eit
Austria

Belgium

CanadaDenmark
FmiandFranceGermany
Italy

Japan
Netherlands

NewZealand
NorwaySwedenSwitzerland

UnitedKingdom

logIt=a+Bt+et

a

s

Dw

R2

6.9253

O.0428(2.97)

L19

O.60(52.97)7.1005(127.81)7.4334(98.10)5.3723(38.22)

O.0633

1.77(10.36)

O.0610O.80(7.32)

O.0773

O.91(5.00)

5.2709O.0513(32.15)(2.84)

7.1240O.1323(29.21)(4.93)

8.4574

O.0639(80.45)(5.53)

7.6574

O.0783(82.80)(7.64)

6.8609

O.0985(63.24)(7.73)

7.1388
O.0669(9.89)(116.10)5.1443 -O.0206(26.37)(-O.96)
5.1977
O.111O(91.47)(17.76)6.2475
O.0451(60.50)(3.97)
7.4334
O.0793(169.96)(16.44)8.0233 -O.O084(95.90)(-O.85)

O.93

O.38
1.60

O.80
O.81
1.40
1.24

1.08

O.94

B

Dw

R2

7.4809O.07372.22

O.98(233.07)(20.87)
1.11

O.99

O.43

O.95

2.17

O.99

1.55

O.96

O.99

O.98

1.06

O.99

1.51

O.98

1.77

O.99

O.99

O.98

1.53

O.81

1.03

O.99

1.39

O.99

1.09

O.98

O.52

O.97

(SL

7.8790(216.57)
O.98
8.4223(134.49)
O.79
7.1025(281.56)
O.58
6.5696(112.28)
O.79
8.3806(157.36)
O.82
8.7600(226.98)
O.90
7.9656(151.16)
O.90
7.9550(219.85)
O.93
8.0376(186.58)
O.26
6.5552(106.63)
O.97
6.9681(21T91)
O.79
1.02
1.55

7.6011(249.38)
O.97
7.3626(166.18)
O.24
9.3481(165.91)

O.72

The yearly data (1957-1971) were taken from IMF, IFS,

O.1OO1(25.02)

O.0802(11.64)

O.0888(32.01)

O.0853(13.25)

O.1012(17.28)O.1050(24.73)

O.1133(19.55)O.1401(32.98)

O.0989(20.89)O.0356(5.27)

O.0834(23.73)

O.0829(24.71)

O.0961(19.72)

O.0886(14.36)1972 supplement.

31
THE DEMAND FOR INTERNATIONAL CURRENCIES AND RESERVES

rolt. He wrote it in the logarithmic form,log Rit= cro + cri log lit+ a2 1og rig6o+ eit, (7)and estimated the regression coeMcients. Though he obtained higher coefficients ofdetermination and significant t-values for the regression coeMcients, his model was atautology. If Rit and Iit can be written as Rit = Rio exp (biit) and Iit = Iio exp (b2it),the definition of the reserve ratio to imports becomes rio = (Ritflit) exp [b2i-bii)t],where bii and b2i are the rates of growth of ith country reserves and imports between
the base data for rio and the current period in which eq. (7) applies. Rewriting logarithmically,log Rit= (bii-b2i) t+ log lit+ log rio. (8)This equation is identical to Thorn's eq. (7) when cre = (bii-b2i) t and ai = cr2 == 1•

The conditions which ai and a2 were nearly equal to unity and ao was incresasing withthe passage of time t, were confirmed by Kenen and Yudin.iO) In order to makesure of the validity of the equations, Rit==Rio exp (bii t) and Iit ==Iio exp (b2i t), we
estimated the regression coefficients for them in Table 26.

The precautionary demand for foreign reserves is mainly controlled by the government or the monetary authority of the country concerned. Our eq. (4), howeyer,
was only a reflex ofthe private sectors' behaviors. Accordingly, it has to be modified

by the precautionary demand. Namely, the demand for reserves will be shifted by thereserve ratio to imports and the reserve ratio to domestic money supply.

3. TheSpeculativeMotive
As described in section 1, the speculative motive is related to our eq. (1). In themodels of portfolio selection applied to the explanation of long-term foreign asset

holdings, investors have the opportunity to choose from a whole range of combinations of expected rates of returns and variances by picking up the appropriate size ofdomestic and foreign assets. Suppose that a world consisting oftwo countries has only

three types of wealth: real assets, money, and bonds. Populations, income, andwealth are constant. Grubel,ii) for example, established the model ofinternationallydiversified portfolios. The expected rate of returns, E(ii,2), and risk, V(ii,2), on the
average investor's portfolio in Country 1 are,E(ii,2)=Pi ii+P2 i•a, (9)V(ii,2) =: Pi ai+2Pr P2 ai,2+PL, a22, (10)10) Kenen, P. B. and E. B. Yudin, The Demand for lnternational Reserves: Reply, R. E. Stat.,Vol. 49, Nov. 1967.
11) Grubel, H. G., Internationally Diversified Portfolio: Welfare Gains and Capital Flows, A.
E. R., Dec. 1968.

MASAHIRO FUJITA, NOBUO MIYATA

32

P,+P, =1, (1 1)

where subscripts 1 and 2 refer to the two countries, ii and i2 are the rates ofinterest on

bonds, oi2, ai and ai,2 variances and covariance of returns, and Pi and P2 the proportions of bonds of Country 1 and County 2 respectively held in the average portfolioof Country 1. Eqs. (9)-(1 1) altogether will depict an efficient frontier curve on the E-

V space. The optimal value ofthe rate ofreturns and variances will be obtained at the
point of the eflicient frontier tangent to one of indifference curves, which draw thesocial expected utility on the same E-V space. Therefore, the optimal holdings offoreign assets (including foreign reserves) depend on the size of total wealth assets
held by the public, the size of interest differential, the size of risk differential,the de-gree of correlation of returns on domestic and foreign assets (p=ai,21ai a2), andtastes of the public.

In the models of portfolio balance, money is an asset bearing expected yield in
the form of opportunity cost and the least risk. Accordingly, the demand for foreign
reserves can be defined as the function ofthe opportunity cost ifthe risk is constant or

zero. The opportunity cost is usually measured by the rate of returns on long-term
government bonds, i, or per capita income, y. Heller's applicationi2) of the Baumol-

Tobin model to foreign reserves is assiciated with this kind of opportunity cost. n
stands for the cumulative probability of financing external imbalances by using reserves, R.. The opportunity cost of holding reserves is equal to iR., and the loss ofnational income is (1lm)R. ifthe external imbalances, R., is adjusted by expediturechanging policies, where m is the marginal propensity to import. Then the net gain ofholding reserves is defined by the equation of n(11m)R.-iR.. Maximizing this equation, we get n.=iR., where n. is the probability with which the country will have to
use the nth dollar. Suppose that the country has a consecutive series of deficit balancefollowed by a consecutive series ofsurplus balance, the sizes ofwhich are equal to theaverage absolute change in reserve, h. If the probability of each deficit is assumeed tobe fifty per cent, the probability n. is given by the probability of the occcurrence ofxconsecutive deficits of size h. Then, z.=(O.5)"ih, where x:==nlh. Optimal holdingsof reserves are''log(im)Ropt :==h l.g o.s' (12)Heller estimated the optimal holdings of reserves in 1963 for eq. (12).

Table 27 shows the optimal reserves at the end of 1972 estimated for the same
equation as Heller. These optimal reserves are the mixture of the precautionary demandwith the speculative demand, though Heller claimed that they were the precautionary
demand only. He instisted that the government action of adjusting imbalances due to12) Heller, H. R.,

Optimal International Reserves, E. J., June 1966.

33
THE DEMAND FOR INTERNATIONAL CURRENCIES AND RESERVES

Table 27 Optional Reserve Holdings in 1972, Computed from Heller's Equation (millions of doilars)

Belgium

CanadaFranceGermany
Italy

Japan
Netherlands

SwedenSwitzerland

UnitedKingdom
UnitedStates

r

m

h

Ropt

Rlg721

Rig721Ropt

O.0704
O.0723
O.0735
O.0790O.0747
O.0700O.0688
O.0729O,0497
O.0891
O,0563

O.418
O.186
O.127
O.145
O.146
O.068
O.359
O.180
O.270
O.161
O.048

194.201
303.370788.7071644.0pa
427.6632362.769
205.441124.019267.708690.078812.245987.911
1886.023
5318.78e
10601.060
2788.000
10380.102
1097.005
775.403
1665.144
4225.841
6931.175

3870.000
6050.000
10015.000
23785.000
6079.000
18365.000
4785.000
1575.000
7488.000
5647.000
13150.000

3.917
3.208
1.883
2.244
2.180
1.769
4.362
2.031
4.497
1.336
1.897

the precautionary motive would have an dominating influence on holding a certain
stock of reserves. In his eq. (12), however, the government action depends on our ob-

servation period. Suppose that a country experienced 20 million dollars negative
reserve change in 1960. If the observation period is over 1951-1970, the deficit balance to be adjusted by the country is one million dollars per year. If it is over 1955l964, however, the deficit balance to be adjusted is doubled per year. Accordingly, thegovernment action of adjusting imbalance is determined arbitrarily by our observers.

There is not any guide line to the government action. If the observation period isshorter, the government action of adjusting imbalance will more drastic. Therfore, hismodel does not have any sufficient indicator to the precautionary demand. His opportunity cost of holding reserves, on the other hand, was given directly by the yieldforgone if these assets would have been invested. And it was compared to the loss ofnational income. Who would compare these costs, z(11m)R.-iR., ? He neglectedthat the reserves were the reflex of the transactions and speculative demands in theprivate sectors. Is it not necessary to make any assumption about investors' maximizing behaviors in his model? If his model has implicitly these investors' behaviors,
his R,pt will jnvolve the speculative demand for foreign reserves. In short, it can be

sai dthat his optimal reserves calculated from eq. (12) were the specialized precau-

tionary demand, in which the speculative demand was unconsciously included.
In Heller's model, the total deficit balance was supposed to be canceled out by the

total surplus balance in the observation period. And the yearly reserve changes werecorrected for the trend estimated by a least-squares regression, which might have prevailed during the period. The size of yearly deficit or surplus with the probability offifty per cent, therefore, was h calculated as the mean of the absolute least-squares
residuals. Suppose that the yearly reserve changes in a country are observed as shownin Fig. 2. The simple sum of these changes is not equal to zero. The regression residuals, hovvever, are canceled by each other during the period. The typical year-to-yearchanges in reserves can be graphed hypothetically in Fig. 3, for the absolute least-MASAHIRO FUJITA, NOBUO MIYATA

34

ARt

ARt
*

*

*

*

t trend

N
s

tt
N

'

N

i

N

------------ -----------trend

N

N

N

Å~.`Å~ t-/

/

1

1

.-. -- --

o
time

o

time

*

Fig 2

*

Observed Yearly Reserye Changes (millions of dollars)

Rt

Ro+2h

.
IN
IN

Ro+ h

Ro

Ro-h

1/X

'

/

t

IN
-N
/N
xtN
/7Å~

N -//N
Nx
Å~

'

1/XÅ~

'

IN
tN
IN

Ro-2h
time
Fig 3

Average Absolute Changes in Reserves (h = 3)

squares residuals, h, is two million dollars per year. What kind of the regression
equation was used to calculate h in Fig. 2? Heller's purpose was to estimate a "static
optimal reserves" which the country held. Therefore, it might be a horizontal line or
an ordinaly U-type sine curve, for these two equations had a stable level of reservechanges, a displacement from which would result in a backward movement. To makesure ofit, we calculated the values ot' h from various kinds of regression equations andcompared them with the values of Heller's h in Table 28. The last two columns gaveTable 28 Tlte Values ofh Computed from the Various Kinds of Rqgression Equations (Yearly data: 1949 - 1963)
Heller's

LinearQuatratichEquation
139.686
137.811296.652524.283
213.443226.240
168.101
63.05678.286547.167
847.189

Equation

Belgium

15LO

Canada

122.7
425.1
527.0
275.2
235.8

FranceGermany
Italy

Japan
Netherlands

SwedenSwitzerland

UnitedKingdom
UnitedStates

166.4
58.4
1OO.1

553.8
862.0

138.362125.125
310.763464.e43235.948229.064
165.02558.72679.232550.349845.083

Cubic
EquationU-typeSinecurve

Horizontal
Line

138.821107.881309.247151.353
123.645152.837134.755
419.408527.071239.980226.878
169.51062.051101.898568.867
869.327431.547463.289240.632
230.276421.780
158.589
195.085167.28e56.40579.234528.162733.346165.811
57.11198.916572.428
849.387

Table 29 Discrepancies and Stable Levets
StableLevels

Discrepancies

U-typeSineCurve

U-typeSineCurve

Horizontal
Line

1.837
12.055

O.353
O.905
6.447

-5.692

Japan-63.711-24.528-5.524-35.220-8.922

Netherlands-O.6'89

Sweden-1.289-1.184

Belgium

CanadaFranceGermany
Italy

Switzerland

UnitedKingdom
UnitedStates

18.628-12.613

O.071

3.110
4.651
1.798
15.067
7.327

HorizontalLine
InitialLevel=
FinalLevel

Initial

Final

Level

Level

92.174298.875
589.257
197.85370.857101.143309.143254.971168.99680.111
123.405203.60292.170298.844589.213
197.906-- 86.115
254.952
168.988
80.103123.402203.585-1068.501-1068.436-655.786-86.162532.500
206.857
130.857
122.57134.929102.143
99.786

8
x
m
vtn
K
>
z
v
o
pu
-z
H
x
Z
>
:
o
z
Q
v
a
C
t:rl

pa
pa

m
Z
o
p-

tu
ua
)•

z
v
T
tu
m
tn
pu
<
tu
m
x

MASAHIRO FUJITA, NOBUO MIYATA

36

Table 30 Optional Reserves Holdings in 1960

Table 31 Indices of Adequancy of Reserves,

Calculated from Heller's Equation(miMons of dollars)-Rig631Ropt

Ropt

Ropt

869
866

872.6
868.8
3284,5

Belgium

Canada3783.51656.51719.9Germany

927.5
372.3
610.5

Netherlands

Belgium
France3192

Germany

3.773

Italy

1893
1770
933
379
616

Japan
Netherlands

SwedenSwitzerland

UnitedKingdom
UnitedStates

3810
8085

3935.88176.9CanadaFrance
Italy

Japan

SwedenSwitzerland

UnitedKingdom
UnitedStates

Rig72!Ropt

2.23
3.01
1.54
2.03

3.571
2.955
1.738

1.73
1.16

2.001
O.948
4.016
1.868
4.504
1.176

2.25
2.01
5.00
O.83
2.08

Z035

1.861

us closer values to Heller's h than other columns, except in the case of Italy and theUnited Kingdom. Which is suitable for the trend, a horizontal line or an ordinary U-

type curve? Heller did not make any suggestion about this problem. We made thediscrepancies between Heller's h and our values calculated from these two equationsin Table 29. The corresponding stable levels of reserye changes were also listed in thesame table. Suppose that it is desirable for the countries to maintain a higher levelof reserve inflows. It will be easily shown that the best equation to calculate h is thehorizontal line for Germany, Italy and the United States, and the U-type sine curvefor other countries. Complementarily, we calculated the optimal reserve levels in Table 30, so as to compare them with Heller's R,pt in 1963.

0ur close inspection just described suggests that the main defect of Heller's model
is to be found in the absence of a structual disequilibrium in international accounts.

The consecutive imbalance in the country concerned made the least-squares trend shift
up or down in his model. But it was not reflected in the optimal reserve Ievel, Ropt,because it was eliminated from the calculation of h. This elimination reveals that thecountry suffering from the consecutive deficit balance may take unexpectedly a highindex of adequancy of reserves, R.,t..ilR,pti..t. For exampie, see the case of theUnited States in Table 31. In addition, the structual trend in his model was a horizontal line or an ordinary U-type sine curve. These two types of curves were guessedfrom Heller's aim of study; the measurement of a static reserve level. Why should thestructual trend be expressed only in these two curves? It is difficult for us to find a morepersuasive answer about this question.

Now, we have to complete our model. As described in section 1, our eq. (4)included the store of values which related implicitly to the speculative motive. Let us

modify it to be able to deal with bond market clearly. Suppose that individuals will
maximize their utilities obtained from expected interest on bonds, subject to thebudget

restraint including interest on bonds held on Monday and the purchases of new bonds

37
THE DEMAND FOR INTERNATIONAL CURRENCIES AND RESERVES

during the week.i3) D stands for the number of bonds outstanding, each paying $1
of interest per year perpetually. They are homogeneous and gilt-edged securities. The

holdings of bonds on Monday are Dli. Individuals buy (D*-D)!i of new bonds, receive interest on bonds, D, and carry forward D"li in nominal value to the next week.
If other things are equal and the effect ofbond holdings, D"/i, on utility is neglected,

we get6$ ,(.a.Y.) -2, (i3)where e is the rate at which the holdings of bonds are converted into in dollar terms.
If D*li i's measured in dollars, e is equal to one. The variances and covariance of re-turns are assumed to be constant. Therefore, we will get a new function of reserves
which involves explicitly new parameters such as the rates of interest on bonds, andvariances and covariance of returns;

L:== L(au, r, 6, iJ,aj2, ai,2, i)l[,e pDiJj ), (14)where 6is the indicator to the precautionary demand and subscript 1' is each country.
We have studied the demand for international currencies. The motives for holding
them were classified into three heads : the transactions motive, the precautionary motive, and the speculative motive. Our conclusion is eq. (14). When we wish to estimate

the demand for international currencies, the Kenen and Yudin's procedures are better
than Heller's . But setting p at zero will be wrong, because it means the neglection oftime interval between externai payments and receipts. Therefore, we will have to devise

any other parameter when p is not significantly different from zero. The reason why
we reject the Heller's equation can be ascribable to the fact that it eliminates the trendof reserve changes. The reserve level calculated from eq. (12) may be different far fromthe demand for reserves we wish to estimate.
The foreign exchange rate has been fixed throughout our analysis. In the case of
the flexible exchange rate system, however, all parameters in eq. (14) will be changed
freely. pt stands for one of parameters, a. and r, to explain the transactions motive.
All interactive effects between the transactions motive and the speculative or precau-

tionary motive on marginal utilities, O(aUIOnOzlO(LIP))10(LIP),O(OUIO(LIP)10T
On!O(L!P) and O(O UfO(LIP))fOz, are supposed to be zero. Using eqs. (1)-(3), we obtaina(OoU. o(OLTIp)) dz

d(LIP)- On dpt <o,dy o(OoU.,s8p)) ,(z.,+Ogo(ÅíOLik') (,s)13) Cf. Gurley, J. G. and E. S. Shaw, Money in a Theory of Finanee,mathematical appendix.

1960, chaps. 2 and 3, and38

MASAHIRO FUJITA, NOBUO MIYATA

where dnldpt < O, OnlO(LIP) > O from On!O(m!P) < O, and O(6UIOn Orr/O(LIP))16T

Ozfa(LIP)<O and O(OU/O(LIP))10(LIP)<O from diminishing marginal utility.
Therefore, an increase in a.2 (the variance of statisticaliy independent part of dailybalance ofpayments) or r (time interval), which is induced by the variable foreignexchange rate, will reduce the holdings of international currencies.

Eq. (15) will have to be modified by the bond market. A decrease in the rate ofinterest on foreign bonds, i2, will increase the foreign reserve holdings. If the risk at-tached to foreign assets, o22, or the degree of correlation of returns on domestic andforeign assets, p, is greater, on the other hand, the holdings ofinternationa] currencies

will be decreased. The convertor, e, will be also changed. Therefore, the sign of eq.
(15) will not be easily determined. The parameter 6 to explain the precautionary motive, however, will be expected to be a stabilizing factor in the demand for international currencies.

STUDIES FOR THE PREDICTION
OF SHIPPING MARKETS-A SURVEY AND THEIR APPLICATIONSTetsuji SHIMoJo

CONTENTSI Preface
II Collection and Calculation ofData
III Analyses of Relations between Indicators

IV Models for Prediction of Shipping Markets
V Tentative Conclusion for the Prediction

System of the Shipping Markets

BIBLIOGRAPHY

APPENDIX THREETYPESOFSIMULATIONMODELSIN SHIPPING MARKETSI Econometric Models
II Technological Sequential Models
III Behaviourar Distribution Models

I Preface

The desire to predict the future of shipping markets has led to many types ofeffort by those, not only who are concerned in the industry, but also who are interested

in the movements of the markets. It has beeh a common objective since the birth of
mankind to know the future situations as early and exactly as may be possible. In theirlong history, innumerable methods have been proposed and attempted.
Limiting them within prediction in shipping markets, there remain various inher-

itances from propositions handed down by word of mouth, for example `A peak a
decade' or `High in winter low in summer' about business cycles in the shipping markets, to propositions of experts, for example `Charter hire rate index increases before
and decreases after the freight rate index.' Though not so explicit and apparent, there

are many sorts ofexperimental rules to predict the future ofthe shipping markets cor-

responding to the complexity of the cases. And some of them became more reliable
and some were forgotten through the tests of experiences.

In fact, the methods actually being used to predict the markets and to forecast
future movements ofcargo can hardly be other than such experimental rules. Futhermore, most of them are merely assumptions deduced from the past experiences of theforecasters, rather than propositions examined by the real data. And many of them are

TETSUJI SHIMOJO

40

so vague that they can not be expressed in any forms ofpropositions. Nevertheless, it
can not be denied that they are used most frequently in the real world and that they
have been giving actual results of their own. This type of prediction, generally known
as intuitive prediction, is apt to be thought as a very simple method, but, in fact, theprocedures employed use very rnany experimental rules and very complex calculations. That is the reason why the method had never been described in terms of literaldeduction, nor attested theoretically.i)

Another type of prediction, far simpler compared with the intuitive prediction, is
actually used. Though it can not be compared with the intuitive prediction in accuracy
and delicacy, it is peculiar in view of its objectivity and repetitiveness. Because of thefact, this method is used most commonly in the practical world to complement theintuitive prediction, and is calculated repeatedly tiil the user is satisfied. This is theeasiest method ofprediction as neither the experimental rules nor the strict theory arenecessary, and everybody can use this method with a little ability to collect data andto calculate them. We can call it the clerieal prediction.

The intuitive prediction, assisted by the clerical prediction, is now the dominant
practical method of prediction in the real world. In contrast with it, the journalistic

prediction, bureaucratic prediction, or academic prediction can hardly satisfy thepractical requirements, because the objects of these methods are too general to matchpractical needs, though it is natural in view of their inherent characteristics.

In this paper, we will survey the various methods ofprediction and the fundamental studies advocating them, limiting them within the forecast of shipping markerts,
and consider what efforts are needed in order to build more practical methods of prediction. This objective would seem to be an intention to improve the practicability ofbureaucratic and academic prediction, but, in our consciousness, it is rather an intention to raise the level of the cierical prediction which can be combined with the intuitive prediction.

II Collection and Calculation of Data
The most important task for the clerical prediction is collecting data. Some kinds
ofprediction can be finalized with only appropriate data. Bross says that the simplest
method ofprediction, persistency prediction, can often give us the most correct predic-tion.2) Port charges and turn-round times in the port at which they are making their

1) Shimojo [50]. By the way, Shimojo [47] classified preditions into (1) intuitive, (2) journalistic,(3) bureaucratic, and (4) academic predictions.

2) Bross, Irwin D. J., `Design for Decision', New York, 1953, Chap. 3. He listed as simple methods ofprediction, (1) persistency, (2) trejectory, (3) cyclic, (4) associative, (5) analogue, and (6)hindsight predictions.

STUDIES FOR THE PREDICTION OF SHIPPING MARKETS41-A SURVEY AND THEIR APPLICATIONSship call can be predicted by the data of other ships which called most recently at theport.

Prediction of the future situations should begin with an investigation on the same
objects at the times closest to the present. Predictions utilizing this information as it is,or some modification of the data involving the rates of change or smoothing depend
upon a premise that the circumstances at the times closest to the present will remainunchanged in the near future. As far as the premise would be accepted, these methodsof prediction are the simplest ones.

Table 1 shows some results of these very simple methods of prediction, namely,
the correlation coefficients and the percentages oferrors to the mean values of their
original data when (A) the persistency prediction and (B) the trajectory prediction areused for the indexes and monthly average freight rates in the several routes. The correlation coeMcients are calculated between the predicted value pt and the actual value

At, and percentages of the standard diviations ofn(Pt-At) to the mean value ZAtln

t=t1 prediction means
are added to the table. Needless to say, the persistency
Pt = At-1,
and the trajectory prediction isPt = v4t-i+(At-i-At-2)•
Table 1 Correlation and errors of very simple methods

NameofDataMonthly Data

PeriodA
NorwegianVoyage 50-75.9833

NorwegianTanker 50-74
FreightIndex

.9436

56-72

GrainRates
H.R./Japan
CoalRates
Gulf/U.K.

GrainRates
P.G.IJapan
TankerRates
P.G.IU.K.&C.TankerRates

A

B

.9828

6.6%

.9167

14•1%o.9368

14.oe/.

24.8

.9437

26.3

.7731

48.1

.7690

56.1

.9577

10.9

.8763

20.3

.8858

17.6

.8390

27.3

53-74

.9642

13.2

.9326

18.9

.9128

20.6

.8837

26.6

5474.

.9327

19.6

.8654

29.5

.8778

26.0

.7914

38.0

52-73

.8910

33.1

.8120

48.1

.7445

47.3

.6720

65.5

.52-73

.9189

33.7

.8517

49.5

.7329

56.7

.6613

76.6

CharterIndex

GulflJapan

QuartprlyData

B
6.3O/.

Observing the table, we can pick up some problems important for our present
investigation. In Table 1, we took up only the freight rates that may be the most interesting object for the shipping markets, but it is worth trying to take up the amount ofinternational trade, the sea-borne cargo movements, the tonnage of fleet, etc. as theobjects of prediction.

TETSUJI SHIMOJO

42(1) Prediction period : The first problem is about the period between the time of prediction and the object time of the prediction. We will call this period the prediction

period. The accuracy of prediction is likely to be higher, the shorter the prediction

period. This matter has a close connection with the problem of how strong a confidence the predicter can have in his own prediction.3) In Table 1, compare the precision in the prediction of monthly data with that of quarterly data. There can be foundapparent differences.

(2) Nature ofdata: Another kind ofdifference in the prescision is found in the Table
1 . This difference depends on the natures ofindicators. In general,predictionsoftramp
rates are more precise than that of tanker. Are they caused by the differences between

the nature oftramp market and that of tanker market, or between the methods used
to make up these jndicators?

(3) Coverage of data: The most important nature of data is the coverage, whichmeans how many components the data are representing. Even if every individual event
is random, the more events the data may include, the Iess the randomness ofdata willbe. We can see in Table 1 that freight indexes are more precise than the freight rates as

the former have bigger coverage than the latter.

Through the observation of Table l, we can list up the three problems so as toselect the method of prediction. In addition to them, we must consider the following
problems ;(4) Divisible and indivisible indicators : Freight rates and their indexes are indivisible

indicators in the sense that no part of the value corresponds to any real things. Tonnages of fleet and cargo are, on the contrary, in this sense, the divisible indicators, al-though they are distinguished into the stock and flow quantities respectively inanother classification of statistics. If two ways of classification of statistical data wereapplied to the shipping market data, there are defined four types of statistics; stock
divisible (fleet), stock indivisible. (rate level), fiow divisible (cargo movement), andflow indivisible (rate index). Such peculiarities of the data will be important problems

at our processing the data and selecting the method of prediction.

(5) Change of natures by calculation : The problems mentioned above will make newproblems during the calculation of data. Monthly data will become improper for thepersistency prediction when they have been processed into quarterly data, and they
will lose their seasonal characteristics when they have been processed into annual data.

Annual rates of change of the tonnages may be indivisible data, and an average ofseveral indicators may have larger coverage and less variableness.

Most of the published indicators have been processed by some definite intensions,so that we must be aware ofthe methods by which they were processed, in order to use3) Shimojo [56] Appendix I.

STUDIES FOR THE PREDICTION OF SHIPPING MARKETS-A SURVEY AND THEIR APPLICATIONSthem properly for our purposes. Many of the published data, however, can not fit our
purposes as they are. And modification of data to fit our purposes will require us toprepare much more information. Otherwise, we must overcome the difference between the data and our intention by means of the alteration of our model.
In a sense of fitness to our purposes, the raw data are the most favorable as they
have less definite intention. There remain, however, some diMculties in dealing withthe raw data, the difficulty ofcollecting them and the dilliculty of processing them be-cause of their massive volume.
In case where raw data of less volume are suMcient, for example in statistical inference from sampling, we can more easily deal with raw data by means of classificationand summation for the purpose of prediction. Considering the change of natures by

calculation, however, we must always ask ourselves which should be done before
others, prediction, classification or summation.

"Decomposition" is one of the most popular method of the clerical prediction.
Dividing the object of prediction properly, some simple prediction will be proceededin each of the division, and finally the results of each division will be consolidated into

a conclusion. In this method, peculiar consideration of each division can be made, sothat this may be a thoroughgoing prediction.
We have discussed some problems in the stage ofclerical prediction, where a single
indicator is the object of simple prediction. For this popular method, there is no out-

standing work we can quote, so that we can not help making an abstract discussion.
For the sake ofour objective, however, the following chapters shall compensate for thelack of concreteness of this chapter.

III Analyses of Relations Between Indicators

No indicator can exist independently of the others. Especially, economic indicators, always have some sort of relationship with other economic indicators or pastvalues of their ovvn. Knowledge about these relations between various indicators,
therefore, will be an important piece of information for prediction purposes. For thisreason, analyses of relationship between indicators are very important tasks.

As far as prediction is concerned, the following four types analyses of relation-

ship between the indicators have been made;1. Relation to its own past value
Putting a time series back for some periods and calculating correlation coeMcients with its original time series for every periods put back, we can obtain a peculiar

curve named a correlogram. Similarly, we can also estimate parameters for a multivariate equation in which a time series is explained by itselfwith tjme lags of l, 2, 3,

etc. Correlation coeMcients and parameters obtained in such methods will offer useful43TETSUJI SHIMOJO

44

information about cycles of the indicators.`) We can predict their future value withsome significant information we obtained.
There is a study to attempt prediction by a transient probability matrix of freightrates during a period.5) This matrix will be almost a unitary matrix as far as we canobserve in Table 1. While, there were observed the relationships between the rate level

and the changes of freight rates. The higher the rate level may be, the bigger thechanges of freight rates, so that it will be more diilicult to predict the future in the pros-perous times of the market.

The most apparent cyclical movement in the shipping market indicators may be
the seasonal fiuctuations, of which a Iot of studies haye been made.6) Some otherstudies have employed the Census Method or the spectral analysis method to analyze
the other fluctuations of the shipping market indicators.7)

The common intention of these studies is to attempt to find some cyclic patterns
out of the shipping market indicators and to discover the peculiarity in their move-ments through pursuing the causes of the cyclic patterns. It may not be intended toutilize the cyclic pattern directly in the prediction ofthe shipping markets. We have tobear in mind that these studies offered very much informatjon usefu1 for the Iater
analyses.8)

2. Sequential relations between indicators

When we can observe an indicator always preceding another, we can predict the
future movernent of the latter through observation of the preceding indicator. Thoughsuch an apparent relation can hardly seen, it is often said that charter hire increases
before and decreases after freight rate, and we can find not a few studies to prove thesaying.9) There are also some important indications that the freight rates and charter
hire rates may have close relationships with the length of charter periods or frequency

of future contracts, or with the balance between rates for outward and homeward
VoYages.10)

3. Economic causal relations
Since the econometric methods came to be used in the shipping market forecast-ing, many attempts have been made to build models consisting of some equations
which express the economic causal relations between variables in the shipping markets. Starting from the basic assumption that freight levels are determined by the4) Shimojo [49] shows correlogram, and distributed lag model is used in Miyashita [241.

5) Hiramoto [6].
6) Sawa [35], Matsumoto [21] and Lewis [17] are especialiy important works,
7) Yamada [41] utilized Census Method, and Moridaira [28] utilized the spectrat analysis on
freight rates.

8) Isserlis [11], Wogemam [44], Tinbergen [39], Einarsen [5], Meuldijk [22] and Shimojo [48].
9) Lewis [17], Maeda [18], VVeston [45] etc.
10) Lewis [17], Shimojo [54], Zannetos [46].

STUDIES FOR THE PREDICTION OF SHIPPING MARKETS-A SURVEY AND THEIR APPLICATIONSdemand and supply ofthe shipping services, the freight level function has traditionallybeen explained by the quantity of cargo movements and the tonnage of fleet,")though each of these variables are occasionally replaced by the rate of change of eachvariable.i2)

Freight level has been considered to be related the prices of cargo carried, thedistance carried, the quantity of fleet operated or the laid-up tonnage, etc., and manystudies have adopted these variables as their explanatory variables.i3) Some studies

use the compound variables processed from demand and supply variables to explain
the freight levels.i4)

Most of the models quoted above center around the freight level function, in
which many kinds of explanatory variables are used. Meanwhile, these explanatory
variables have to be explained by other factors, so that the models of several equations came to be seen gradually often along with the possibility of utilizing the com-puters. We have, however, to postpone these models to the next chapter.
4. Statistical causal relations

It is the fundamental relation that the demand and supply reflect the prices, andthat the prices give influences to the quantities of demand and supply. However, even

ifthe changes ofyarious quantities are observed in the shipping markets, we cannot
state how much changes they will finaliy give to the freight markets, before the relation

has been measured between the change in freight rates and the changes in the quanti-

ties of demand and supply.
Poor harvest of grain or strikes in coal mine or ports are reflected in the shipping

markets in different way according to times and places they may take place. Many
events are reported daily, but most of them are neither quantitative nor measurable,
so that we can not use them for our prediction. Even if they are quantitative, theirrelation to the shipping markets must have been known.
There is a study that classifies the various events occurred around the shipping

markets, and that deduces the statistical relations between the frequencies of eachclass of events and the changes of shjpping markets.i5) This study aims the statisticalcausal relations rather than the economic causal relations. These types of studies seem
more to be contributing in searching the factors which have close relation to the shipping markets than to be useful for the prediction.

By the similar methods, it is possible in the future to evaluate the non-numerical
data in relation to the shipping markets, and to deduce the behavioural patterns of the11) Matsumoto [20], Tinbergen [40] and Koopmans [15] are predecessors of the series.
12) Kogane [14], Mori [26], Osawa [33], Suguki [38], etc.
I3) Matsumoto [19], Bates [1], Deakin [31, Miyashita [25], etc.

14) Quantity carried per carrying capacity in Koopmans [16], Shipping market estimating index
in Yoshimura [43], degree of busyness in Shimojo [49], etc.

I5) Shimojo & Yoshida [52].

45TETSUJI SHIMOJO

46

ship-owners and charterers from the contracts they have concluded in the past. We
expect the more convenient methods and the more appropriate applications of themwill be developed in the near future.

,x- ee es

The analyses of relations between shipping indicators can not always be useddirectly in prediction of the markets. Their contribution to the prediction was to sup-ply us with information on such things as parameters in behavioural equation, adoptability of the form of equation in, say, the freight function, effects of processing andcombining of variables, cycles of freight rates and their index, changes of seasonal
fluctuation patterns, and so on. And it must be the function of clerical prediction to

use this informations.
To improve the levels of clerical prediction with this information, another important consideration must be given. It is usually so long time since the information

has been found out or estimated that it can not be employed in our present purpose.
We must estimate new parameters with the latest data. Not only that,but we may haye
to modify the rnodels and processing method of variables. That is, we need to update
this information including the methods ofestimation.

IV Models for Prediction of Shipping Markets•

Based on information obtained through the analyses of relations among various
indicators in the shipping markets, we can build models for prediction of the shipping

markets in a wider sense. Models having only one equation are also included, but wewiil hereafter discuss the common problems relating to models consisting of multiple

equations. One of the purposes for which we use the multi-equation systems js tomake the models dynamic and appropriate for prediction.

There are not so many studies in model building and prediction ofshipping markets, and we can find only a few examples which consist of several equations including

a freight determining function. That may be not only because of diMculty in making
a function determining the freight level, but also because most of such models areintended to predict the demand on shipbuilding, ifi which the variable of freight levelstand merely as an exogeneous variable.i6)

Meanwhile, the models taking the shipping markets as their centre and explaining
the processes of determining the freight levels and chartering hire rate levels can beclassified into several types-the econometric models, the system dynamic models, themodels in dynamic programming, the behavioural distribution models, and so on.
16) Chapter IV of Shimojo [51]. There appeared thereafter some models, e.g. Japanese Shipbuilders Association Models (one ofwhich was Suganuma [37]), Ishiwata-Moridaira [91, and Norman[31].

STUDIES FOR THE PREDICTION OF SHIPPING MARKETS-A SURVEY AND THEIR APPLICATIONSOf these, we can now discuss the following three types of simulating models.i7)

1. Econometric models
There are a few econometric models which include the freight level indicators as
endogenous variables, such as Ishiguro model and Yamada model both of which relate

to the world shipping markets, Kagoike's tramp market model, Niida model, Suzuki

model and Ishiwata-Moridaira model, the last three of which are Tanker market
models.i8) We must not fail to refer to the Charemza's tanker market model of disequilibrium.i9) In recent years, we heard about models that were actually used forprediction of the shipping market, but we do not know these models in detail.

All of these models are built around three most important variables, the freightlevel, the quantity of demand and quantity ofsupply, and place other variables to explain them, in almost similar way which the freight level reflect the tonnage of ships

supplied through the orders for new buildjng Dfships and the layjng-up of ships. And
it is a common idea in these models that the freight leyel doesn't feed back to the quan-tity ofdemand because its reflection can be negligible in the macro-scopic models.

2. System dynamic models
The only model is presented by Raff who utilizes the techniques of Industrial
Dynamics developed by Forrester.2e) This model traces a logical series from the world

demand for petroleum oil to the tanker markets, though the behavioural decisionsof oil companies to operate their own and chartered fleet of tankers, and of independ-ent owners to coordinate their fleet. This model contains about 350 equations andenable us to observe the movement under definite conditions. These types of models

are expressed in the language named DYNAMO and simulated under the program ofthe same name.
The Ruff's model, in general with this type of model, is a system of the popularor assumptional logics described in eacb of the equations. Parameters describing therelations between variables are given by experience or as selectable assumption. Thisis a peculiarity of this type of model, in comparison with the econometric models inwhich the estimation of parameters is one of the most important tasks.
This peculiarity makes the type of model able not only to determine the values ofvariates for any period but also to create any sort of variables regardless of data avail-able. Raff did not intend to predict but proposed a set of assumptions concerning thestructure of tanker markets. This model, however, shows us the possibility that we canuse these types of models jn predjctjon of the market jf we would model the frejght17) Dynamic Programming Model of Devanny [41 Part II is neglected here, as it is an optimizing
model of operating plans in the shipping firms.
18) Ishiguro [7], Yamada [42], Kagoike [13], Niida [30], and Ishiwata-Moridaira [10].

19) Charemza [2].
20) Raff [34] uses the technique devetoped by Jay W. Forrester of M. I. T.

47

TETSUJI SHIMOJO

48

determining processes in detail and supply them with accurate data.

3. Behavioural distribution model
Johansen's production function can be applied in the shipping markets.2i) We
can use the supply schedule which is made by summation from the individual production function of each ship. By giving the cost informations for the world merchant
fleet by flag, age, kind, size, etc., we may have a list of assumed or nearly actual world

merchant fleet. Under some various conditions classification and summation will'produce respective cost distribution of the fieet, or supply schedule.22)

We can generate a lot ofcargo offers in similar way by route and by item. Simulating the processes these cargo offers would select appropriate ships, we could build amodel determining the freight and charter hire rate level in any submarkets. Needlessto say, these types of models can not reproduce the reality even if the same distribu-

tions as reality were given to them. These can simulate not more than stochasticallysame situation of the market. But they can be usefu1 in such a prediction as, say, whatchanges will take place on the share of Japanese fleet in case of an increase in theseamen's wages.23)

ee ce "eThese three types of models have their own peculiarities and problems. In ourview, their respective peculiarities are complementary to others, not substitutional
for each other. To this point we will discuss below.24)

The econometric models are the most popular for us, and the most advanced
theoretically and experimentally. They are, especially treating with macroscopic struc-tures, the most powerful technique, as far as the necessary data can be furnished. As

we have stated, however, data around the shipping markets are very poor, not only
that, but it is almost impossible to obtain immediate data necessary for the prediction, as many of them are covering world-wide matters. This point can not be recoveredby only the methods in econometrics.

In contrast, the system dynamic models and the behavioural distribution models
do not depend so much on data. These models are built more freely by means of theparameters and distributions which can be measured mainly from the cross sectional
data at the latest point of time. They can be modified and improved by the frequent
simulations. Ifneeded, they can contain the equation that changes its form according
to changes ofsituations, and be designed to select one ofmore submodels accordingly.

The shipping markets are excellently dependent, and one of the most sensible21) Johansen [12].

22) Devanny [4] PartIseems to us to be amodel of similar idea, but we can not obtain any detailed information.
23) Shimojo [55] is an attempt of the kind.
24) See Appendix for the detailed discussion of these three types of models.

STUDIES FOR THE PREDICTION OF SHIPPING MARKETS-A SURVEY AND THEIR APPLICATIONSobjects, to environmental changes, so that the prediction ofthem must utilize the mostelastic models. Placing the econometric models in the center, and preserving the economic and statistical strictness, it will be necessary as a minimum to use the system
dynamic models and the behavioural distribution models in the role that they can playmost effectively for their respective characters.

V Tentative Conclusion for the Prediction System of the Shipping Markets
It might not be true that the prediction of shipping markets was the most important problem for the shipping firms and the bureaus concerning to the shipping indus-

try. Moreover, even ifit can be an important problem, the one they think so may not

be the predictions which we have been discussing above. Prediction needed by thepractical interests would be more concrete, e.g. a freight rate appropriate for a certain

item of cargo to be carried through a certain route, or a charter hire rate for acertain newly built ship, etc.

There are manymore uncontrollable factors, for the shipping interests than thosedealt with by most of the models discussed above. For the uncontrollable factors, wemust as firms decide our countermeasures through the prediction of them.
Limiting our objective the prediction of a freight rate for a certain route, we will

face many more diMculties than we have discussed above. One ofthe biggest problem
is the data. The data around the shipping markets are limited. For this reason, theshipping market models will be very small ones which contain, at most, only ten or
several more equations, including the shipbuilding markets.
The shipping market is a truely complex market. It is said to be divided into in-numerable submarkets, by routes, items of cargo, forms of transport, forms of contracts, etc. Nevertheless, the data is scarce for these individual submarkets. Although

we can find a study for relations among these submarkets placing an overburden on
the data,25) the scarcity of data seems to be preyenting the development of the study.

We must start immediately to furnish the data, but such efforts cannot makefruits in short time. It may be impossible for the shipping market models of econo-

metric type to respond immediately the practical needs. Whatever the structualchanges mean to be, in order to include it into our model, we can not help inducing
somewhat different types of techniques. For a prediction method which is able to use
any pieces of data very immediately, is there nothing but the intuitive prediction tradi-tionally having been employed?
The intuitive prediction method has inany strong points that the other methods
do not have, and at the same time, it has many vital weak points. In order to recover25) Miyashita [24].

49TETSUJI SHIMOJO

50

the weak points, the clerical prediction method has been used in the practical world.
We have surveyed the techniques to be induced in the clerical prediction. We believethat the mechanization ofprediction must be necessary in order to make the clericalprediction exert its ability with all ofthese effective weapons.

The ideal prediction system of shipping markets must contain at least the following abilities in addition to the functions the present clerical prediction system alreadyhas;(1) Abilities to compile, estimate, test, update and simulate the econometric, system

dynamic and behavioural distribution models.
(2) Abilitieg easily to register, update and retrieve the data of any types; time series,

cross section, surveyed and individual.

(3) Abilities to numericize the non-numeric data through dialogues with the decision
maker, in order to give an explicit basis to his intuitive prediction.

Our tentative problem is (1) of the above, to build a new consolidated model.
Firstly we have to pick up many probleTns in the course of examining various types ofmodels proposed in the past, to investigate the causes of the problems, and to search
for new techniques to delete or overcome the causes. Such series of efforts and ideas
will, we believe, be the foundation of more effective prediction systems. We can only
refer to a fact that a voluntary group has started its activity for the purpose.

Nevertheless, the probelm of (2) is still the most diMcult problem for us, for which

we have nothing to offer. There must be much of data, concrete and precise, being
used in the practical activities ofshipping firms. Even the data not used any longer byfirms may contain much informations usefu1 for us. That is the reason why we would
like to expect the conprehension and cooperation of the shipping firms to our efforts.

BIBLIOGRAPHY (* in Japanese)[1] Bates, Thomas H., `A Linear Regression Analysis of Ocean Freight Rates',
Transportation Research, 1969-9.

[2] Charemza, Wojciech, `Simulation and Forecasting based on a Fair-Jaffee
Model'. Fuculty of Production Economics, University of Gdansk, 1975?
[3] Deakin, B. M., Shipping Conferences, A Study of their Origins and Develop-

ment and Economic Practices, Cambridge, 1973.

[4] Devanny III, J. W., A Model of the Tanker Charter Market and a Related

Dynamic Program, Shi ping Management, Bergen, 1973.
[5] Einarsen, J., Reinvestment Cycles and their Manifestation in the Norwegian
Shipping Industry, Oslo, 1938.
"[6] Hiramoto, Fumio, `A view in Quantity of Newly Shipbuilding Orders', Fune no

Kagaku, 1961-1.

STUDIES FOR THE PREDICTION OF SHIPPING MARKETS 51-A SURVEY AND THEIR APPLICATIONS-*[7]

Ishiguro, Takashi, `Econometric Prediction of Ocean Freight Rates', Monthly

Review ofJapan Development Bank, 1963.
*[8]

Isiwata, Shigeru, `Analysis of Shipbuilding Demand by Econometric model',Review of Japan Maritime Research, 1968-1 1.

*[9]Ishiwata, Shigeru & Soichiro Moridaira, `Econometric Analysis of World
Tanker Market; Review ofJapan Maritime Research, 1973-9.

*[1O]& , `Short-term Prediction Model of Oil Tanker Market,
Review ofJapan Maritime Research, 1974-5-6.

[11]Isserlis, L., `Tramp Shipping Cargoes and Freights', J. of the Royal StatisticalSociety, 1938.

[12]

Johansen, Leif, `Empirical Illustrations based on data for Norwegian Tankers',

Production Fttnction, London, 1972.
*[13]

Kagoike, Sohei, `Econometric Analysis on Tramp Freight Market,' Review of*[14]

Kogane, Yoshihiro, `Econometric Analysis on Shipping Markets', Kaiun[1 5]

Koopmans, T. C., Linear Regression Analysis ofEconomic Time Series, 1937.

Shi ping Research, 1963-7.
Kenkyu Shiryo, 1957-5.

[i 6], Tanker Freight Rates and Tank-ship Building, Haarlem, 1939.

[17]

Lewis, Arthur, `The Interelation of Shipping Freights', Overhead Costs, 1951.

*[18]

Maeda, Yoshinobu, `The Interrelation between Charter Hire and Freight',

Konan Ronshu, 1954-12.
*[19]

Matsumoto, Ichiro, `On the Trend Line of American Timber Freights', Kaiun
Geppo, 1929-10.

*[20], `On the Prediction of Tramp Freights', Kaiun Geppo, 1932-1.

*[21], `Bulk Cargo Movements and Fleet Operation in Near Seas,' .Kaiun,
1936-7.

{22]

Meuldijk, Jr., J., `Der Englische Schifbau wahrend der Periode 1870-1912 unddes problem des Ersatsboues, Weltwirtschaft Arehiv, 1952.

*[23]

Miyashita, Kunio, `Econometric Analysis of Linked D-S Substituting Behaviour in Shipping Market', Review of Japan Shipping Economics Assoc., 1973.

rk• [24], `Econometric Analysis of Individual D-S Behaviour in ShippingMarket', Kokumin Keizai Zasshi, 1975-4.

*[25], `Econometric Analysis for Ocean Freight Levels', Kokumin Keizai
Zasshi, 1975-5.

*[26]

Mori, Hiroshi, `Demand Supply Movements on World Fleet and Freight inPost War', Review ofJapan Industrial Bank, 1957-1.

*[27], `On Recent Prediction Studies of Shipping Market Movements',
Review of Japan Industrial Bank, 1959-8.

*[28]

Moridaira, Soichiro, `Cycles and Lags of Shipping Markets', Review of Japan

TETSUJI SHIMOJO

52

Maritime Research, l974-l1.
*[29]

Nakagawa, Hironobu, `Forecasting on Up and Down of Freight', Kaiun Chosa
Geppo, 1956-ll.

*[30]

Niida, Masumi, `An Econometric Analysis of Tanker Spot Rate Market',
Review of Shi ping Research, 1963.

[31]

Norman, Victor, `Norwegian Shipping in the National Economy', Bergen, 1971.

*[32]

Osawa, Toshio, `On the Tramps', Review of Japan Industrial Bank, 1960-10.

*[33]Osada, Kozo, `Forecasting of Tanker Demand by Structural Model', Kaiun,[34]

Raff, Alfred I., Dynamics ofthe Tank-ship Industry, M. I. T., 1960.

1967-2.

*[35]

Sawa, Sempei, `Seasonal Fluctuation in Operation of Japanese Tramp Cargo
Vessels', Appendix to Japanese Translation of Slapelfeld Schi:ffahrt Frachten

Markt, Oct. 1933.
*• [36][37], `Expectation on Ocean Freight', Kai'i Kenkyu, 1957.

Suganuma, Kiyoshi, `A Method for Short to Medium-range Demand Forecastsin Shipbuilding, Shipping Management, 1973.

*• [38]

Suzuki, Toru, `Econometric Analysis of Tanker Indicators and Market Forecasting', Review of Japan Long-term Credit Bank, l965-2.

[39]

Tinbergen, J., `A Shipbuilding Cycle? (193I)', Selected Papers, Amsterdam,[40]

Tinbergen, J., `Tonnage and Freight (1934)', Selected Papers, Amsterdam, 1959.

*[41]

Yamada, Hiroyuki, `Post War Fluctuation Processes of Ocean Freights', Review

1959.

of Shipping Research, 1964-2.
: [42], `Analyses of Ocean Freight Fluctuations', Review of Shipping Research, 1964-4-5.

*[43]

Y6shimura, Yoshiharu, Kaiun Shikyo Hendo Ji'o Kanken (Observation ofFluctuation in Shipping Markets), 1942.

[44]

Wagemann, E., Structur und Rythmus der Weltwirtschaft Berlin, 1931.

[45]

Weston, W. G., `Shortterm Freight Market Forecasting', Westinform Shipping[46]

Zannetos, Zenon S., The Theory ofOil Tankship Rates, M. I. T., 1966.

Report No. 50, 1955.
*[47]

Shimojo, Tetsuji, `Data and Method in Forecasting Tramp Market, Kai'i Kenkyu, 1957-10.

*[48], `Cyclical Fluctuation Analysis for Ocean Freights', Kai'i Keizai,
1958-11.

*[49], `Econometric Analysis of Freight Level', Kaigai Kai'i Joho, 1961-5.

*[50], `Decision Making in Shipping Management.' Kaiun, 1962-1-3.

[51], `The Quantitative Analysis of Shipping Markets-A Survery weighting on Japanese Works-', Review of Kobe University of Mercantile Marine,

STUDIES FOR THE PREDICTION OF SHIPPING MARKETS-A SURVEY AND THEIR APPLICATIONS-

53

1973-1.

& Shigeru Yoshida, `Factor Analysis on Shipping Markets', Review*[52]

ofKobe Univ. ofMercantile Marine, 1975.
*[53], `Determining Factors and their Effects on Freight Rates', Annual
Review of Japan Shi ping Economics Assoc., 1975.

[54], `Expectations in the Shipping Exchanges', Kobe Economic and Business Review, No. 22, 1976.

*[55], `A Simulation ofTanker Market', Kokumin Keizai Zasshi, 1976-6.

[56], `Some Bargaining Process Models in the Shipping Exchanges', Kobe
Eeonomic andBusiness Review, No. 23, l977.

*• [57], `Observation and Measurement of Tanker Spot Contracts', Keizai
Keiei Kenkyu, 1977.

APPENDIX THREE TYPES OF SIMULATION MODELS IN SHIPPING

MARKETS
Foreword
The shipping market is an excellently competitive market. Demanders as well as
suppliers of shipping services should decide their own behaviours, by observing the
movements of shipping markets. For the suppliers of the shipping services, aboye all,the prices are far beyond their control, and only to be expected and predicted, in ac-

cordance wjth N. Wiener's words; "There are two sorts ofvariates. We can control
the one. But we cannot control the other variate so that we must predict its movementin the future."

The shipping markets that determine the ocean freight rates, are not only of very
complex structures, but also reflect very delicately various events in the world andchange their structures bit by bit. Attempts to simulate the market movement by somemodels, therefore, in spite of their frequent and long time efforts, will be successfu1

for only a very short time.i)
In this paper, we have described these efforts in short, dividing them into three
types of simulation models. Here, we will discuss three models out of respective types,
in order to pursue for their peculiarities in more detail, and investigate to the causes inthe shipping market that have made it diilicult for us to build such simulating models.

l) See Shimojo [51].

TETSUJI SHIMOJO

54

I EconometricModels
Grasping the shipping markets in macro-scopic way, it is a peculiarity of thistype of models to explajn the processes of determining some general freight market
indicator in the world. The tramp freight rate index or tanker freight index are usedas the freight market indicator according to their objective.

We will take up Ishiwata-Moridaira Model as an example of the type of model.2)

This was developed as a short-term prediction model of the tanker markets, andconsisted of four sectors, cargo movement, tonnage of fleet, shipbuilding and freightmarkets. This included 17 variables, apart from 6 dummy variables, constituting
8 behavioural functions and 5 definitional equations in quarterly basis. This is rather

small in comparison with the general econometric models, but the largest one for the

shipping markets. That may be caused by one of characteristics of the shipping market models.
In this model, the freight market indicator is explained by the rate of change incargo movement, freight market indicator ofthe last period, and rate ofchange in thefreight market indicator during the last period. The tonnage of fleet is not used todetermine the freight market indicator, but, instead, it is explained by the past freightmarket indicator through the quantity of shipbuilding.

Generally speaking, the model closely follows the theoretical structure. The
theoretical structure itself, however, is a system ofassumptions and the one describedvery abstractly. It must, therefore, be a job of `high degree of freedom' to specify amodel suitable for the theoretical structure corresponding the yariables to those data

which are available actually. Even though it can be done rather freely, the econometric model could not be free from their inherent restrictions.

One of the restrictions is that a suMcient length of time series must be obtainedfor every variable in the model. Every variate in the theoretical structure can hot always be observed in reality as it is. We must find something else as similar as possible,

or make ourselves some substitutes by means of processing other data.

For the quantity demanded for shipping services, the seaborne cargo movements
have been used traditionally. They are, however, the quantity transported or supplied

ex-post rather than demanded. Meanwhile, the tonnage of fleet used as the quantity
supplied is not more than the capacity supplied, which is very inelastic in short term.

Therefore, for a macro-model of shipping market, a form of explaining the rate ofchanges of freight rates by rneans ofthe rates ofchanges of quantity transported might

be the most reasonable. The Ishiwata-Moridaira model includes an effect of expectation in addition to the above.
2) Ishiwata-Moridaira [1O] is the newest, in which many experiences in the past are employed.

STUDIES FOR THE PREDICTION OF SHIPPING MARKETS-A SURVEY AND THEIR APPLICATIONSShipping market is not so simple as can be expressed by only ten equations or such.

Nevertheless, the reason why no larger models had been made may be due to the factthat only a limited number ofvariates can be furnished in forms of time series data. In

comparison with tramp market, there have been more examples of analysis and modeling for tanker market, because of availability of data and less complexity in cargo
items.

Tramp market can not been expressed satisfactorily in such a simple model. The
number of variables will be multiplied according to variety of cargo items, and, con-sequently, will need much more equations. We can never find any data for sufficient
length of times to support such a complex theoretical structure. This is the one of the

obstructions in the way of the econometric analysis of shipping markets.

Another restriction to them is a problem of time lags. The relations between
variates appeared in the theoretical structure are sometimes expressed with some timelags. These time lags are jncluded in model by means of djfference equations or djstrjbuted lag models. Apart from time intervals of actually available data, the restrictionof a fixed `difference' oftime is unavoidable for this type ofmode13).

In order to build up more precise models according to the theoretical structure,

we must resolve these two problems. We must, therefore, develop a model of a
new type which can be effective to both whole and part; i.e. on the one hand, themodel may divide the market into various routes, items of cargo, types of contracts,
etc. or the fieet into several types, sizes, flags, etc., and on the other hand the model

may sum them up to the total demand classified by each behavioural pattern and to
the total supply sorted by each rank oftheir operating costs.

Moreover, in order to trace the processes of determining and varying the freightrates or charter hire rates, which had been united into a concept of freight level, we
must employ a more elastic way of expression. Elasticity of expectation and periodical

substitution in future transactions must be included in the model in order to express

the bargaining processes of contracts by means of various lead times and durations.
We should overcome the restrictions on the data and techniques with all effort forthese purposes.

II Technological Sequential Models

Even the most complex technological structure in a macroscopic view can bedivided into the simplest physical rules. The shipping market, ifit be grasped as an ac-

cumulation ofindividual behaviours, could be expressed as a series of comparatively
simple decision making as well. Raff proposed a tanker market model of this type by

3) For the variety in the shipping businesg. cycles, see Moridaira [28] and Shimojo [48].

55TETSUJI SHIMOJO

56

means of System Dynamics.4)
In this model, when the demand ofoil is given as an exogeneous variable, oil companies will decide their orders to build new tankers and to charter tankers according totheir operating fleet of tankers. Tanker brokers consequently decide the charter hire
rates through negotiations with the tanker owners, who decide to increase or decrease
their own fleet of tankers. Shipbuilders receiving orders to build new tankers, will de-Iiver new tankers to oil companies and tanker owners with some time lags according
to availability of their building docks. The tanker market will develop in accordancewith the movement of demand and supply of tanker services, conserving these connectlons.

Raff's model consists of seven sectors, i.e., four sectors in oil company, oil sup-plying, chartering, operating and coordinating sectors, in addition to three environmental sectors, tanker broker, tanker owner, and shipbuilder. Each sector, utilizing

informations input from other sectors, decides his behaviour and behaves it. Thesebehaviours are described in about 350 equations.

These 350 equations can be sorted into four types of equations. Level equations
define changes of variates with a certain time lag. Rate equations define the rates ofchanges. Auxiliary equations are to define relations between variables And initial
equations define initial values of the variables. In addition to that, there are various
types offunctions which express some definite distribution ofvalues or some time lags.

In any way, these equations do not always need steps that estimate their parametersby means of data in the past.

Each equation represents a very simple relation between the system variables.
Informations apriori or parameters in these equations seem to be deduced by a bitof empirical observations, so that we will not need much detailed informations in thepast. This may be a peculiarity of the models of this type.

As an aspect that determines freight rates or charter hire rates we can trace themodel as follows: Given the total tonnages oftanker fleet existing and being operated,
the tanker broker sector calculates the ratio of operating fleet, and deduces a charter

hire rate level immediately from a static supply scheme which is prepared to indicate
correspondences between the charter hire rates and the ratio of operating fleet. At thesame time, the tanker broker sector supplies an expectation of the charter hire rates,
which will be employed by the rest of sectors for their future planning.

The supply scheme in this model is a definite relation between the two variables,

and is based on an assumption that the scheme will not be affected by the variationof operating costs of tankers or other factors in the shipping markets. The scheme
shapes a curve with a minimum level up to 90 O/. of the ratio of operating fleet, steep4) Raff[34].

STUDIES FOR THE PREDICTION OF SHIPPING MARKETS-A SURVEY AND THEIR APPLICATIONSupward up to 97 O/., and with constant level onward.

The supply curve of shipping services, in general, having the ratio of operating
fleet as abscissa, seems to converge to a point, x == 1, y = lay-up point freight rateofthe most economical ship, and looks like a hyperbola in the senond quadrant. Raff
gives a similar curve as his supply scheme, but gives no idea how he has deduced it.
We can consider it to be arbitrary assumption, as well as the other parameters of themodel.
In contrast to the macroscopic inclination of the econometric models, the tech-

nological sequential model seems to have a rather microscopic inclination. These
peculiarities might be caused by the factthat the former dependedupon the time series
data while the latter intended to approach to individual logical processes. We can at-

tempt, therefore, to combine these two types of models. Operations to summarize
the results obtained from the simple logical models, to deliver the summation to themacro-model, and to divide the results obtained by the macro-model, will not cause
serious errors if the time intervals will be small enough.

In the clerical systems forprediction of shipping markets which are very frequently

utilized in shipping firms, there can be frequently seen the decomposition method inwhich the value of variable is predicted for each subdivision of the system and then the

conclusion will be deduced from them by means ofsummation or other simple consolidation. A simulation model of the shipping markets can be built up of such forms ofoperatlons.

The behaviour of each subdivision can be described as comparatively simple
logical process in this type of model, but, if we assume that their behaviour is decided

by taking the whole behaviour of the market into their consideration, the simulation
will need a large number of repetition to summarize and to divide. Such a process will

be disposed as a simultaneous equation system in most of econometric modeis, but
this is not always possible.

No simultaneous equation system is accepted by the System Dynamics, butinstead, the system is recommended to be expressed as a sequential system with muchsmaller time intervals. Such iterative solution is employed by the econometric models
containing non-linear equations as well. If we do not place any severe restrictions on
the time intervals in the model, we will be able to express all kind of models as sequen-

tial systems, and simulation will be much easier.

III Behavioural Distribution Models
The supply scheme in Raff model was given as a static and definite one. But, ingeneral, the scheme should be varied from time to time according to various environmental changes. A supply scheme placing the supply capacity on the abscissa seems to57

TETSUJI SHTMOJO

58

be given its shape by the distribution of operation costs of the fleet. Above all, to know

position of a certain ship group in the scheme will require us to draw a total supply
scheme by means of the cost distribution of the fieet.

Johansen using the data of 377 Norwegian tankers supplied by Eide,5) deduced amacroscopic and short-term production function from their capacity distribution.
Carrying capacity per ton-mile of each tanker was firstly classified by both amountsof fuel consumption and labour necessity, and the function was deduced from the
distribution.

Starting at this idea, we drew supply schemes for each type of Japanese fleet,6)
assuming some levels ofunit prices of fuel and labour. We can draw such a scheme of
fu11 cost including capital costs of the ships if needed. However, the supply schemeof only Japanese fleet will be useless for any shipping market models. We could drawa world total supply scheme for any type of ships, if we have detailed specifications
for the world fleet.
As an initial attempt, we collected world tanker data classified by flag, age andsize, and gave each rank of ships the same specifications as the corresponding rank ofJapanese ships, but we had to give some estimated values to the number of crew andwage rates according to the fiag. From these data we could calculate the operating
costs in a certain route for each ships, and could get a supply scheme for the route, andpositions ofJapanese ships in the scheme.7)

Such an idea seems to be employed widely in the simulating models of shipping
markets. From these data we could obtain informations in regard of behaviour nolonger of individual tankers but of tanker group classified by flag, age, and size. Thismay be based on an assumption that every tanker within a group will be have in thesame way as the other tanker within the group. This assumption can be accepted themore easily, ifthe more detailed classification has been done.

New building of ships, scrapping, casualties, or changes of flags may modify
gradually the constitutions of each group, and consequently delicate changes of sup-ply scheme of the world tanker may take place. We can simulate these changes bymeans of handling the individual data from a group to another, and get the supply
schemes of any time points.

The demand for shipping services can be explajned by the accumulation of demander's behaviour as well. If we can classify world total cargo movement into groups

by cargo items, routes, sizes of cargo lots, etc., we might obtain a demand scheme
which could be corresponding to the supply schemes.
To investigate these possibilities, we have dealt with the following attempts in5) Johansen [12].
6) Shimojo [55].
7) ibid.

STUDIES FOR THE PREDICIION OF SHIPPING MARKETS-A SURVEY AND THEIR APPLICATIONSour tanker market simulation: Firstly a number of oil transportation offers weregenerated randomly according to the real distributjon of them. Each offer, then, wasconfronted with each tanker, and the most convenient and cheapest tanker was foundout. This was a fixture. But the freight rate for the fixture was given at the end of theweek by the highest rate in the fixtures fixed during the week. For the rnarket price of
the week could be thought as the supply price of marginal supplier.

Assuming a certain level ofdemand, we have repeated such simulations for someseventy weeks. We can observe the results on profit of each tankers, and find out
which types of tankers were the most favourable at that conditions of markets. Furthermore we can see the facts that the most favourable types of tankers will depend

considerably upon the market conditions.
This type of simulationwas a sort of Monte Carlo experirnents.We can find someinclination of the results only after numerous trials have been done under a certam
condition. The result of each trial is merely the one seen by chance, so that many trials

have to be done. But for some purposes this type of simulation can supply useful in-formation.
If we could prepare much more detailed data for the ships and cargo, we could
employ them in this type of simulation under various conditions using the distributions in which ships and cargo offers had been realized. And we would like to say thatthe demand and supply schemes in the shipping model should be produced in thismethod.

59

A NOTE ON THE INTERNATIONAL TRANSMISSION OF
POLICY EFFECTS UNDER FLEXIBLE EXCHANGE RATES
Kazuhiro IGAwA
1. Introduction*

In a famous paper [3], R. A. Mundell demonstrated the following conclusions
about the international transmission of the effects of fiscal and monetary policies
under a flexible exchange rate system. Under flexible exchange rates;(Conclusion 1): Expansive fiscal policy increases income both at home and abroad(Conclusion 2): Monetary expansion increases income at home and decreases it
abroad.
These rather surprising conclusions are derived from a model with capital mobility. If interest rates are affected by economic policies, the capital account, which issensitive to changes in the level of interest rates, changes. Under a flexible exchange

rate system, the trade balance should adjust to keep the balance ofpayments equal tozero. This change in the trade balance plays the role of transmitter.

His conclusions are intended to replace the traditional theory that, under theflexible rates, there is no change in trade balance and therefore no effects from businesscycle disturbances originating abroad.

As a device for a simple demonstration ofthe role of capital mobility, Mundell's
model is an interesting one. However, the assumption in his capital flow function thatnet capital flow is a function only of the levels of domestic and foreign interest rates,

is unrealistic. In the short-run, it is well known that capital fiows also depend on theforeign exchange rate, and this fact is emphasized by Niehans [4]. Dornbusch [1] attempted to rehabilitate Mundell's model by arguing that the level of the foreign exchange rate looses the power to affect capital fiows in the long-run. However, it is rea-

sonable that, in long-run full stock-fiow equilibrium, interest rates also loose thispower (or have effects in the opposite direction) as Tsiang explained in his paper [5].

Therefore, it seems that Mundell's model is insuMcient to explain the real world

phenomena.
In this paper, we reinvestigate the above Conclusions 1 and 2 by using more realistic models which will be expressed in the following sections. Our conclusions, which" I wish to acknowledge helpful discussion with Mr. Hara ofOsaka University and his interesting
paper F2], which treats the same problem from a different point of view. In his paper, he stresses thefacts that demand for money and the level of saving (expenditure) depend on the exchange rate.
These are factors that MundelI neglected for simplification.

62

KAZUHIRO IGAWA

will be explained in Sections 3 and 4, are summarized as Statements 1 and 2, corresponding to Conclusions 1 and 2 respectively. Under fiexible exchange rates;(Statement 1): In the short-run, expansive fiscal policy increases income both athome and abroad and this transmission effect is larger or smaller than that obtainedin Mundell's model, depending on the degree to which capital fiows are sensitive or
insensitive to interest rates. In the long-run, however, expansive fiscal policy will in-crease income at home and normally decrease it abroad.
(Statement 2) : In the short-run, monetary expansion increases income both at home
and abroad. In the long-run, it increases income abroad but the direction of incomechange at home is ambiguous.
These statements should not be surprising if one is not committed to the applica-

bility of Mundell's model to real world phenomena but believes on the basis of pastexperience in a positively interrelated international transmission mechanism.

2. An Alternative Short-run Model
It is convenient to show first the Mundell-type model, expressed by the foliowing
set of equations.

}r - E(i, Y)+T(Y, Y*, T)+G
Y* = E* (i\', Y*)-T(M)

M =- L(i, Y)

M* == L*(i*, Y*)
T+ C(i, i*) == O

Yis output,
E is expenditure
We call this the M-model.
Here,,iis the level ofinterest
rates, 6 is government expenditure on home goods, M is the money supply and L isthe demand for money, all for the home country. The variables with asterisk refer tothe foreign country. T is the trade balance and C is net capital infiow (outflow if it isnegative) of the home country. n is the foreign exchange rate (defined as the domestic currency price of foreign exchange).
The price level of home goods (or foreign goods) is constant in terms of home (orforeign) currency and is expressed as unity by choosing the appropriate unit. In his
paper Mundell assumed perfect capital mobility for simplicity and for the merit ofpos-

ing a stereotype. However, we use a more general model where we can treat the caseof imperfect capital mobility. Besides the above features, the above model is funda-

mentally the same as the one by Mundell.
The partial derivatives in this model and the following two models have the following usual properties:

aEIOi = Ei<O, (OE*16i*- E*,<O)

63
A NOTE ON THE INTERNATIONAL TRANSMISSION OF
POLICY EFFECTS UNDER FLEXIBLE EXCHANGE RATES

oElay = E,>o, (oE*/ay* -- E*,>o)
OT/OY=: T,<O, (OTIOY* = T*,>O)

Ey+Tv>O, (E'y'T"y>O)
oLloy = L,>o, (oL*loy* == L*,>o)oLloi = Li<o (oL*/ai* = L*i<o)
The following properties are assumed for the M-model.

(A-1) oc!ai = c,>o, oc/oi* == c*,<o(A-2) OTIaT - T.>O
In our alternative short-run model, we assume a different role of the foreign exchange rate. It is empirically well known that the effects of a change in foreign exchange rate on trade balance can be expressed as "J curye" effects. That is, exchange
rate depreciation causes the trade balance to deteriorate in the very short-run and thengradually improves it from that Ievel. In the lofig-run, the trade balance will improvefrom the initial level under Assumption (A-2),

This implies that depreciation must produce capital infiow in the short-run, undera flexible exchange rate system. As we are no interested in the short-run dynamics but

the properties of short-run comparative statics, the above role of the exchange rate
may be specified as follows. We assume (A-2)' instead of (A-2) and introduce a further

assumption (A-3) in addition to (A-1)(A-2)' T. =-O(A-3) aCIOrr = C. >O
These mean that the trade balance does not move, but the capital account improves
with a depreciation in foreign exchange rate. Obviously, jf T. is negative our majnconclusion in this paper is strengthened.

Whether the trade balance deteriorates (as in "J curve" theory) or improves (asMundell assumed) will depend on the situation of the economy and the time period
concerned. In this paper, however, we are interested only in the fact recently observedin the real world; namely that the foreign exchange rate is not effective for short-run

adjustments in the trade balance. Thus we believe (A-2)' as a realistic assumption.

With this assumption and the assumption of foreign exchange stability, C. must be
positive as shown in (A-3).

Our short-run model can now be expressed as

Y == E(i, Y)+T(Y, Y*)+G
Y* = E*(i*, Y*)-T(Y, Y*)(S) M=L(i, Y)
M* = L*(i*, Y*)
T+ C(i, i", n) = O"KAZUHIRO IGAWA

We call this the S-model.

3. Short-run Policy Effects
Let us investigate and compare the policy effects of those two types of model.
From the M-model, we can derive the following results by total differentiation.

1-Ey-Ty, 'T"y, -Ei, O, -TT

dY

Ty, 1-E"y-+-T"y, O, -E"i, Tx

dY*

L, o Li oodio L*y o L*i odi*

Ty T*y Ci C'*i Tz .

drt=: 1dG+ OdM

oo
Ol
oo
oo
We then get the following policy effects:(1) (dY!dG)M= T.Li{L*y(C"i+E*i)+L"i(1avE"y)}IA
where, A is the determinant of the above (5Å~ 5)square matrix and is positive fromstability conditions. The sign of (dYldG)M is positive by the assumed
properties ofpartial derivatives.

(2) (dY"!d6)M = T.L*tL,Ct!A>O(3) (dY!dM)M = T.{L"y(E"iEi+EtC"i-E"tCD-(1 -E*,) (Ci-Ei) L"i} ld>O(4) (dY"ldM)M = L"iT. (1-Ey)CilA<O
By the same procedure we get the following from the S-model,....O dY =-Cl dG+ OdM....O dY* O O....O di O 1....O di* O O.... c. dz o,j owhere points in this square matrix express the same elements as in the previous square

matrlx.

(5) (dYfdG)s = C.Li{(1-Ets'y+T"y)L"i+E"iL"y}lds
where ds is the determinant of the above square matrix and is positive from stability
conditions. (dYldG)s will be positive.

65
A NOTE ON THE INTERNATIONAL TRANSMISSION OF
POLICY EFFECTS UNDER FLEXIBLE EXCHANGE RATES(6) (dY*ldG)s == -C.L"iLiTylds>O(7) (dy/dM)s == C.Ei{(1'E*y+T",)L"i+E"iL"y}IAs>O(8) (dY"ldM)s = -C.EiTyL"ilds>O
For the M-model, intuitive explanations of Equations (1) and (2) are as follows.

An increase in government expenditure on home goods produces an increase in effective demand for home goods and this increases output. As the output level increases,

the interest rate in the home country must increase to keep the demand for homemoney constant. This increase in the interest rate induces capital inflow. To maintainthe balance of payments in equilibrium, the trade balance should be deteriorated. The
trade balance deterioration in the home country implies an increase in the effective

demand for foreign goods and this in turn increases output in the foreign country.

So far about Mundell's model.
The above explanations are also applicable to the corresponding equations (5)and (6) in our S-model. The differences in the results are not qualitative but quantita-

tive. If, in the absence of exchange rate adjustment, the trade balance deterioration
effect is larger than the capital account improvement effect, then exchange rate adjustment produces a greater increase in Y and a smaller increase in Y* in the M-model
than in the S-model. Conversely if the trade balance deterioration is initially smaller

than the capital account improvement, then, following exchange-rate adjustment, theincrease in Yis smaller and the increase in Y" is larger in the M-model than in the S-

model. This is because a depreciation of the exchange rate improves the trade balancein the M-model but improves only the capital account in the S-model.
0n the other hand, the intuitive explanations for monetary policy in the M-model-Equations (3) and (4)-, are as follows. The increase in home money supply decreases the home interest rate and induces capital outflows. This must be matched bytrade balance improvement through changes in the exchange rate. This in turn increases output in the home country and decreases it in the foreign country. The inter-est rate deceases in the foreign country. So far about Mundell's model.

In the case of our S-model, -Equations (7) and (8) -to maintain the balance of
payments the trade balance is not affected by exchange rate adjustment. Therefore,
the capital outflow induced by the fall in the home interest rate must be balanced bycapital infiow through a depreciation in foreign exchange rate. Therefore, the only
channel to affect effective demand in the home country is a change in home expenditure induced by the interest rate change. As the interest rate decreases in the homecountry, the home expenditure level increases. This increases home output and induces a trade balance deterioration. This deterioration in turn induces an increase in

output level in the foreign country. This type of transmission mechanism has been
well known sjnce the Keynesian revolution.

KAZUHIRO IGAWA

66

It must be noted that the interest rate in the foreign country increases notwithstanding the decrease in the home country. This is explained as follows. The relative

decrease in the home interest rate shifts demand from home securities to foreign
securities. However, this demand shift is counter balanced by a demand shift in the

opposite direction caused by the depreciation of the foreign exchange rate. This
point expresses one of the main features of our S-model.

4. Long-runPolicyEffects
As Dornbusch [1] mentioned,it might be more appropriate to interpret Mundell's
model as a specification of longer-run phenomena. We agree with this so far as the
specification of the long-run role of the exchange rate is concerned. In the long-run,however, we must interpret the capital flow function as relating adjustments in capital

flows to an increase in wealth. That is, division ofan increment ofwealth depends on
the level ofinterest rates in both countries. This point is strongly expressed by Tsiang.

However, to treat fiow capital movements properly, it is necessary to consider them ina growth model in which intertemporal relations are important.
In this paper, we are not interested in a growing economy but rather in treating astationary economy. Therefore, stock adjustment capital movements have an importtant role, and the appropriate long-run stationary model is different from both theM- and S-models. This is because, after portfolio adjustments are completed, thecapital account should be zero in the case of stock adjustment. Furthermore, it now
becomes necessary to treat explicitly international net interest payments (services
account), which is not explicitly included in the short-run M- or S-models. The reason
for this is that, if the capital account is zero, the balance of trade plus service accounts

should be zero in the stationary state.

We can set up the following model for the long-run economy. We shall call it the

L-model.

y== E(i, y)+T(y, y*, n)+G
Y* == E*(i*, Y*)-T(L)

M =- L(i, Y)

M* == L*(i*, Y*)
T+S(i, i*, n) == O

This L-model has three properties:(i) The trade balance depends on z assuming Marshall-Lerner conditions are
satisfied in the long-run. Therefore (A-2) is assumed.
(ii) As flows adjustments ofcapital are neglected, the capital account is zero in thelong-run.

67
A NOTE ON THE INTERNATIONAL TRANSMISSION OF
POLICY EFFECTS UNDER FLEXIBLE EXCHANGE RATES(iii) Net interest payments in terms of foreign currency, S, is

S = i* PV-iW*1rr
where, W is holdings of foreign securities by home residents and W" is holdings ofhome securities by foreign residents. As W(W*) is positively related to i" (i) andnegatively related to i (i"), through portfolio adjustmets, we can assume the followlng propertles.

(A-4) OSIOi = Si<O, OSfOi* - Si*>O(A-5) OS16z == S.>O
From the above L-model we obtain the following relations and policy effects.

r. ... . dY ==1)dG+

O dM.... . dY* O'.... . di O.... . di* Olo1oo) dn,Ty Ty" Si Si" T.+S.

owhere points in the square matrix show the same elements as in

the case of the

M-model(g) (dYldG). =- (d.)iilAL
where AL is the determinant ofthe above square matrix and (]L)ii is the cofactor of

the element in first row and first column. The Hicksianstability condition gives

us the sign of (d YldG)L>O(10) (dY"/dG)L == -L*i(T.LiS,+LySiTn)/aL(11) (dYfdM)L = T.[Si {(1-E"y+T"y)L"i+L*yE"i+T"y-Ei(T'yL"i-L"yS"D]/aL

L*• i}{-T.(1-E )Si+S.T Ei}IAL>O(12) (dY"ldM)L=-L*iyy
The intuitive explanation
as follows. (9) and (10), an increase in
ForisEquations

government expenditure on home goods
will increaseof homegoods. output
This
increase in Y produces ofbothdeterioration
the
trade balance and, through an increase in the homeinterest rateof the services account. Therefore, thedeterioration'

foreign exchange rate must depreciate. If the services account is relatively insensitive
to depreciation of T, the trade balance must improve after the adjustment in n to maintain the total balance of payments. In this case Y* will decrease. On the other hand, if

S. is large enough, the services account will improve after the adjustment in T. Thisimplies that the trade balance deteriorates from its initial level and thus increases Y".

This, however, will be a rare case.

For Equations (1 l) and (1 2), the jncrease in home money supply reduces the homeinterest rate and this reduction improves the services account and increases home ex-

KAZUHIRO IGAWA

68

penditure. Therefore, the trade balance should deteriorate, which will bring about achange in n. Whether Y increases or not depends on the relative magnitude of thechanges in Eand T. Ifthe change in Eis larger than that in T, Ywill increase and vice-versa. Y*, on the other hand, increases unambiguously because ofthe decrease in T.

5. ConcludingRemarks
The pioneering work of Mundell has stimulated many to his works. This paper is

one such attempt and our main modifications come from recent experience in theforeign exchange market.
Our demonstration used extremely simple models, following Mundell's example.
It is possible, however, to extend the analysis to more complex cases. In this paper wehave not analyzed the dynamic process of transmission which seems very important.

Analyses of short-run dynamics related to the foreign exchange market, long-run
dynamics of market adjustments and economic growth will be necessary extensions.
If we introduces flow capital adjustments in a long-run growth model, we will get dif-ferent conclusions from those in our long-run stationary model.

REFERENCES[1] Dornbusch, K., "Exchange Rate Expectations and Monetary Policy," Journal ofInternational Economics, Vol. 6, No. 3, Aug. 1976.

[2j Hara, M., "The Terms of Trade, Capital Flows, and Employment Insulation
Effects," Discussion Paper No. 8, Osaka Univ. Aug. I977.

[3] Mundell, R. A., "Capital Mobility and Stabilization Policy under Fixed andFlexible Exchange Rates," Chap. 18 in International Economics, Macmillan, N, Y.,

1968.
[4] Niehans, J., "Some Doubts about the EMcacy of Monetary Policy under Flexible
Exchange Rates," Journal oflnternational Economics, Vol. 5, Aug. 1975.

[5] Tsiang, S. C., "The Dynamics of International Capital Flows and Internal andExternal Balance," Cuarterly lournal ofEconomics, Vol. 89, No. 2, May 1975.

A CONTROL ESTIMATION APPROACH TO
TIME-VARYING PARAMETER MODELS*
Yukio UcHmA
This paper presents an effective control estimation approach to the adaptive
nonlinear econometric models in time-varying structures by using small sample timeseries data. We can observe that the estimated errors of endogenous variables are verysmall based on the final test, and that the proposed method finds a satisfactory solu-

tion to both the under-size problem and the structural change problem in the econometric literature.

1. Introduction
Econometricians have for some time been aware ofthe fact that the well-behaved
assumptions imposed on tbe estimation oftime-invariant parameter models frequently
appear invalid under realistic situations. More recently, a great deal of attention has

been paid to the problem oftime-varying parameters.i) When considering the structural changes, for example, statistical data for long time periods are often not availa-

ble. As a result, we encounter the so-called under-size problem in the estimation ofsimultaneous econometric relationships. Such problems may be reduced by an effective method for estimation oftime-varying parameters.

Current research on the time-varying parameter problem has been developed in
the three areas of (i) the time-varying parameter problem for adjusting the constantterm in regression equations, (ii) random-parameter models or systematic (nonrandom) variation models and (iii) the applications of Kalman filtering and smoothing techniques to econometric models.2)
In this paper we present a control estimation method for nonlinear econometricmodels represented by adaptive form in time-varying structures. This method is developed based on the small sample time-series data. The state variable representation ofan adaptive econometric model is given in Section 2. Section 3 through Section 5
discuss a method of estimating time-varying parameters by using the state variable
form. In Section 6, the proposed method is numerically experimented, and the results* I wish to thank Professors H. Sadamichi and H, Myoken for their valuable suggestions and comments on an earlier draft ofthis paper. Ofcourse, I take sole responsibility for any remaining errors.
1) For recent detailed discussion oftime-varying parameters, see the special issue of the Annals of

Economic and Social Measurement [6] and Sant [5].
2) For the Kalman filtering and smoothing techniques, refer to Kalman [4], Arimoto [1] andBryson and Ho [3].

70 YUKIO UCHIDA
are compared with those ofthe least squares method. Some concluding remarks are
given in Section 7.

2. State Variable Representation of an Adaptive Econometric Model
Consider the general adaptive econometric model described by

yt=a(Lyt, pt, 0t)+ut (1)where y, p, 0 and u are the vectors of the endogenous variables, predetermined vari-ables, time-varying parameters, and random disturbances, respectively; all thevectors have compatible dimensions. Additionaly, it is assumed that

E(ut)=O, E(utu'.)-6t, 9t (2)where 6t, is the Kronecker delta. Let the vector of the exogenous variables be denotedby x. Then the predetermined variables are classified as

vt-lf{xt, xt-1, xt-2, ......} (3)Zt-!E{jVtml, Yt.2, ),t.3, •.......,} (4)Pt =(II:m, )• (5)From (4) the vector ofpredetermined endogenous variables can be represented by thefollowing first-order difference equationz, == ztz,-,+Ay, (6)where the elements in the matrices A and A consist ofzero and unity only.3)
It follows from (1) and (5) that

Vt=cr (yt, z,-,, 0,, v,)+u,. (7)Definest=(;,`) (8)C- (L O). (9)Then (6) and (7) can be expressed ass,=tB (s,, s,-,, 0,, v,)+C'u, (10)jyt= Cst (1 1)

which stand for the state variable form ofthe adaptive econometric model.

3) For the description of Equation (6),see also the example given in Section 6.

A CONTROL ESTIMATION APPROACH TO
TIME-VARYING PRRAMETER MODELS

71

3. The Control Estimation Method
The estimation problem of time-varying parameters consists of minimizing thesum of the residual square

IXZI., u',u,. (12)However, it is not possible in general to implement this method. In this paper, there-

fore, we present an alternative method that is well suited to the estimation of time-varying parameter models.
Before proceeding to the discussion, some notations are defined as follows :{stO, ytO, ztO, etO} ,'m,, {st*, yt", zt*, 0t*} ,T", and {so, st, yt, vt} ,Tm, denote the sequences ofprior estjmates, posterior estimetes, and data, respectively. For the sake of convenience, it is supposed that so==soO:=so*, and that zo=zoO==zo*. Thus, in the sequence {so,stO, ytO, ztO, 0tO, vt} ,T.,, it follows that

JVtO = cr(YtO, 7t-10, 0tO, Vt)(l3)

ztO = A zt-10 + A ytO(14)

sto = p(sto, st-lo, eto, vt)(15)

JvtO = CstO.

(16)

Similarly, it is also observed in {so, st", ytS,zt", 0t*, vt} thatyt* == a(yi zt-i 0i vt)(1 7)

zt* := dzt-i,* + Ayt*(l8)

st* = P(st*, st-i*, et*, vt)(19)

yt* = Csi

(20)

Assume that performance measure is given by
ip - ZtT.,i Åët(2l)

ipt = (yt - yt*)' et(y,-y,*) + (e,e-o,*)' R,(o,o-e,*)(22)

where the i-jth elements in the weight matrices et and Rt are defined ase,(i,.i) =: y?(il),Rt(i,j) -= k• o,2i/),• k>o,

(23)

(24)

The problem to be considered
to find Ot*,'
the isposterior
estimates
ofparameters so as
to minimize the performance measure (21) subject (9)to theconstraints
and(13) (8),through (20).

This method is replaced by the optimal control problem when we regard

0t and yt as the vectors of the control variable and thetarget variable,
respectively.

72 YUKIO UCHIDA
Thus we call this method control estimation.

4. The Linearized Approximation and Control Estimation
First, let us approximate the nonlinear model (IO) in the neighborhood of {s,,stO, 0te, vt} tT-i ass, ;!f ie (sto, st.,o, eto, v,) + OoPstO (st - s,o) + -oOsP,-O, (stH, -s,u,o)+OoPel (o,-o,o)+c'. (2s)where terms higher than the second term are ignored, and where

OoPs,O -- oas, p(s,o, s,-,o. e,o, v,). . (26)similarly, both --51tflP-l-- and geP,O are defined as in (26).

By substituting (15) in (25), we have the solution to st ass,=A, s,.,O+B,0,+b,+C,u, (27)where(At• Bt• Ct) == (J- OoP,,O )7' (oO,P,-O,• Oofie:•C') (28)b, =s,O-(A,s,-,+B,0,O). (29)Second, we explain the control estimation of the linearized model. Estimators oftime-varying parameters 0t in (27) are given by4)o,*=e,o-o,m (3o)0tM=gt+Gt st-i* (31)whereg, = [R,+B,'(,Hr,-l-Cte,C) B,t]-i B,r [h,-C'e,y,+(H,+C'e,C)(be+BtetO)] (32)G, == [R,+B,'(H,+C'e,C) B,]-i B,' (H,+C'e,C) A, (33)h,-, = (A,-B,G,)' [h,-C'e,y,+(H,+C'e,C) (b,+B,0,O)] (34)H,-,- (A,-B,G,)' (H,+Cre,C) A, (35)and (t-:1, 2, ......, T)

hT=O, HT=O. (36){gt, Gt, ht, Ht, ho, Ho},'", as shown above are obtained by solving backward4) The derivation of (30) through (39) is giyen in the Appendix.

A CONTROL ESTIMATION APPROACH TO
TIME-VARYING PARAMETER MODELS

73

period by period. Thus the minimal value ipL of ip is calculatedasÅëL == so' Ho so + 2ho' so + qo

(37)

where

9T =O

(38)

9t-i == gt + yt'Qtyt + gt' Rtgt + (bt+BtOOtO-Btgt)'[2 (h,-C'e, y,) + (H,+C'e,C) (b,+B,0,O-B, g,)].
(t - 1, 2, ......, T)(39)

5. The Control Estimation ofa Nonlinear ModelIn this section we use the results obtained in the previous section to give the con-trol estimation algorithm of a nonlinear model, The dimensions ofyt and 0t are NY
and NO, respectively.

START:STEP 1 : Determine the prior estimates {0tO} ,'=, oftime-varying parameters and theweight k. Find the prior estimates {stO} ,'m, of state variables as the solution to(13) and (14). Go to STEP 6, where l==O, {st"==stO} ,iL,.

STEP 2: Perform the linearized approximation of the model in the neighborhoodof {so, s,O, vt, 0tO} ,'--, and obtain {At, Bt, bt} ,'=,.

STEP 3: Obtain {gt, Gt} ,T.., from (32) through (39), and set t=1.

STEP 4: Find the revised values 0tM and the posterior estimates et" of parametersfrom (30) and (31) and also obtain the posterior estimates st* of state variables as

the solution to (17) and (18). Go to STEP 5 when t=T. Otherwise, repeat thisstep, where t== t+ 1 .

STEP 5: The average revised value T,i (O/.) at each period for each parameter iscalculated byrre` = iOO x l/ NiT Z,T-.i Zpt• =e,( 0o`,T((i'i) )2. (4o)STEP 6: The average error of estimate zyi(%.) at each period for each endogenous
variable is calculated by

nyt == loo x }/ Åí1-i(jVt-YN,";I T2t(Yt-Yi)• (41)
Go to STEP 2 when l=O. Otherwise, go to STEP 7.
STEP 7: Go to STEP 8, when for any i-th component ofparameter

eot,M,il')) <EPS. (42)Otherwise, go to STEP 2, where l==l+1, {stO==si 0tO=0t"} ,'ni•YUKIO UCHIDA

74

STEP 8: Obtain the performance value Åë from (20) and (21) and calculatezAr == 100Å~ 957ÅëL• (43)
STOP:
Several remarks are called for on the above algorithm.
Remark 1.1: TN stands for the error value(O/.) due to the linearized approximation

ofthe nonlinear model. The above algorithm using the linearized model is notdesirable when zN is large.

Remark 1.2: The prior estimates of time-varying parameters may be replaced byestimates of time-invariant parameters {0t=0} ,T=, based on the existing estimation

methods.
Remark i.3: It can be told by experience that k is less than O.1. In some cases, it isdesirable that it be about O.Ol.
Remark 1.4: nyO stands for the average error of estimate in the final test of the priorestimate. The prior estimate of parameter js not desirable when rryO is large, since

the above algorithm gives no guarantee that the posterior estimate of a parameter converges to the true value of the parameter.

Remark 1.5: We can observe the convergent properties ofthis algorithm by finding
the locus ofnyO, Tvi and n,t, l=1,2, ......
Remark 1.6: nyi denotes the average error of estimate in the final test of the posterior

estlmate.

6. AnlllllstratiyeExample
As an illustrative example we estimate the time-varying parameters in a simple
model ofwage-price relationships.

The Model:

vart = cro,t+ ai,t Wt-,+ a,,t Yt + cr,,, ETAt-, (44)

Pt=Po,t+Pi,, P,.,+P,,, W,-, (45)Where
W: real wage index in industry as awhole; calendar year 1970=loo.

P: price index (GNP deflator), calendar year 1970=1oo.
Y: GNP at market prices; in constant 1970 prices (billion yen).
ETA : productivity of labor; in constant 1970 prices (billion yen per ten

thousand workers).
Data: half-yearly data from the first halfof 1956 to the second halfof 1973.

Estimation Period: from the first halfof 1957 to the second halfof 1973.
Prior Estimates ofParameters: ordinary least squares estimates.

A CONTROL ESTIMATION APPROACH TO
TIME-VARYING PARAMETER MODELS
Weight: k=O.O1.
Each variable is defined asjp, == (W,, P,)'

ve == (Yt, ETAt-i)'
Zt == (Wt, PVt-i, Pt, Pt-i)'
St = (JVt', Zt')'
et = (ao,t. al,t, a2,t, a3,t, Po,t, Pi,t, P2,t)'

OOOO 10OIOO OO
a:A-=Ol.
0001
oooo oo
All the results obtained are summarized in the Tables 1 and 2 and Figures 1
through 11.
Remarks on the results given in the tables and figures are as follows.

Remark 2.1: The estimated errors of W and P using the control estimation method
are extremely small. (See Table 2, and Figures 1, 2 and 11.)

Remark 2.2: Speed of the convergence of the control estimation algorithm is very
fast. (See Table 2, Figure 10 and Figure 11.)
Remark 2.3: The transient patterns of cro,t* through cr3,t* appear similar. (See Figures

3 through 6.) Also, the transient patterns of Po,t" through P2,t* appear similar.

(See Figures 7 through 9.)

7. ConcludingRemarks
Despite the simple model used in the experiments, the estimated errors of theendogenous variables are substantially improved. The characteristic features of thecontrol estjmatjon method are as follows.

Remark 3.1: The control estimation method is simultaneous for the whole model,
unlike the single estimation method.
Remark 3.2: The usual sirnultaneous estimation method is applied to the case where

the number of observations is larger than the number of parameters. On theother hand, the proposed method can also be applied to the under-size case.
Remark 3.3: Structural cha'nges, which are unobservable in time-invariant structures,are identified by estimates of time-varying parameters. Thus by the use of a time-yarying model, long period data can be analysed eyen where structural changes
are present.
Remark 3.4: It may be possible to predict correctly the parameters in the future byusing the up-to-date value ofparameters.

75

YUKIO UCHIDA

76

Remark 3.5: The effects of seasonal change about parameters are observable.

Remark 3.6: The final test of the model can be implemented in connection with theestlmatlon.
Remark 3.7: The stability of parameters are observed by finding the locus the esti-mates of time-varying parameters.
Remark 3.8: The Kalman filter in the engineering control literature has been devised

as a method ofestimating unobservable variables. The control estimation method

proposed here is applicable to estimation of both time-varying parameters andunobservable variables.5)

APPENDIX
As far as we are concerned with the derivation of the control estimates of a linearized model, we now assume that {si yt*} ,T., denotes the solution to the linearized

model. Then we have

st*=Atst-i*+Btet*+bt (A,1)

yt"=Cst". (A,2)

Next we define the following function as

2t-i= min ErqiÅë, (A,3)

er. t<r<T(subject to (22), (A,1) and (A,2))
By the principle of optimality in dynamic programming ([2]), 2t-i can be expressed by
the following successive equation.

2t-i=min (ipt+Rt). (A,4)

et*Accordingly, 0t* is calculated, step by step Iike T, T-1, ..., l. Forthe sake ofconveni-

ence, we assume:

hT=O, HT == O, gT=O (A,5)
2T=sT*'HTsT" +2hT'sT"+qT == O. (A,6)
It follows from (A,4), (A,6) and (22) that the optimization at period T is

2T-i = min (ÅëT+2T)== Min [(YT-YT")'eT(YT-YT") + (0TO-0T")'RT(0TO-eT")+sT"'HT sT*+2hT' sT*+gT]. (A,7)
From (A,1), (A,2) and (A,7) we obtain5) For the estimation of unobservable variables using the control estimation method,(7].

see UchidaA CONTROL ESTIMATION APPROACH TO 77

TIME-VARYING PARAMETER MODELS

2THi == min [(ATsT"i" + BTOT" + bT)' (HT+C'eTC) (ATsT-i*

eT'+ B.0.* + b.) + 2(h.-C'e. y.)' (A.s.-.,* + B.e.* + bT)+ (e.e - 0T*)'RT(0TO - e.*) + qT + y.e.y.. (A,8)

aRT-,==O, and using the following identity equation
Now calculate

OOT'[RT + B.(H.+C'eTC)B.]-i R. ==I-[R.+B.(H.+C'e.C)BT]-iBi(H.+C'e.C)B., (A,9)
then eT* is given as

0.* = eTO - [R.+B.'(H.+C'e.C)B.]-i B.'[h.-C'e.y.

+ (HT+C'eTC) (bT+BTOTO+A.s.-,*)]. (A,10)
By defining 0TM, gT and GT as (31), (32) and (33), we obtain (30) at period t= T. Subsitution of eT" in (A,10) for (A,8) yields

2T-i = sT-i*' HT-i sT-i* + 2hpi' sT"i* + g,,-i (A,11)
where hT-i, HT-i and qT-i are defined as (34), (35) and (39). Notice that we use

G.'R.G. - (A.-B.G.)' (H.+C'e.C) BTG. (A,I2)
to calculate HT-i. In similar procedure, the optimization at periods T-1, T-2, ..., 1 isdone with replacing the above T by Tny-1 T-2, ..., 1. Therefore the minimal value diLof Åë iseL = min Åë (Subject to (21), (22), (A,1) and (A,2))e,1<t<T= 2o== so'Hoso+ho'so+qo• (A,13)
REFERENCES[1] Arimoto, S., Kalman Filter, Sangyo Tosho, 1977. (in Japanese)[2] Bellman, R. E., Dynamic Programming, Princeton University Press, 1957.
[3] Bryson, A. E. and Y. C. Ho, Applied Optimal Control, John Wiley & Sons, 1975.

[4] Kalman, R. E., "A New Approach to Linear Filtering and Prediction Problems,"
Trans. ASME, J. Basic Eng., Vol. 82 (1960), pp. 35-45.

[5] Sant, D. T., "Generalized Least Squares Applied to Time-Varying Parameter
Models," Annals qf Economic and Social Measuremet, Vol. 6, No. 3 (July 1977),

pp. 301-314.
[6] Special Issue on Time-varying Parameters, Annals of Economic and Social Measurement, Vol. 2, No. 4 (October 1973).

[7] Uchida, Y., "A Note on the Estimation of Unobservable Data," Annual Reporton Economic andBusiness Administration, Vol. 28, No. 1 (1978), Research Institutefor Economics & Business Administration, Kobe University, (in Japanese).

al

Table 1 The Prior Estimates (the Least Squares Estimates) and the Posterior Estimates (the Control Estimates) of Parameters

1958.1

ao,t
4.8e9
4.816
4.828

.2

4.821

1959.1

4.828
4.824
4.813
4.813
4.825
4.812
4.804
4,793
4.786
4.805
4.808
4.796
4.783
4.790
4.798
4.803
4.809
4.800
4.801
4.805
4.807
4.806
4.809
4.810
4.806
4.807
4.816
4.815
4.808
4.798

t

1957.1.2.2

1960.1.2

1961.1.2

1962.1.2

1963.1

8
-•
es

.2

1964.1.E.2u1965.1

9

1966.1

H
E

8

.2
.2

1967.1.2

1968.1.2

1969.1.2

1970.1•.2

1971.1.2

1972.1.2

1973.1.2

L.S.E.
(t-value)

4.807

al,t
O.7737
O.7834
O.7979O.7895
O.7988O.7940O.7786
O.7804
O.7952
O.7784
O.7678O.7495O.7404
O.7681
O.7737
O.7534
O.7307O.7407O.7563
O.7633
O.77470.7578O.7587
O.7680O.7725
O.7698O.7760O.7800O.7696
O.7727
O.7961
O.7969O.7758O.74485.1630E-04
5.1723E-04
5.1841E-04
5.1790E-04
5.1869E-04
5.1858E-04
5.1685E-04
5.1721E-04
5.1883E-04
5.1702E-04
5.1569E-04
5.1329E-04
5.1232E-04
5.1566E-04
5.1644E-04
5.1356E-04
5.1070E-04
5.1175E-04
5.1404E-04
5.1492E-04
5.1663E-04
5.1394E-04
5.1415E-04
5.1557E-04
5.1632E-04
5.1586E-04
5.1691E-04
5.1763E-04
5.1585E-04
5.1637E-04
5.2026E-04
5.2068E-04
5.1690E-04
5.1168E-04

a3,t
O.8950O.8955
O.8967
O.8959O.8969O.8962
O.8954
O.8954
O.8969O.8953
O.8945
O.8933
O.8921
O.8946
O.8951
O.8934
O.8910O.8925
O.8935
O.8942
O.8952
O.8937
O.8936
O.8946
O.8950O.8947
O.8953
O.8957
O.8947
O.8950O.8974
O.8972
O.8953
O.8924

O.771010.4985

5.1607E-04
3.6783

O.89481.6454

Ct2,t

Bo,t

-7.9847E-02-7.9860E-02-7.9866E02-7.9862E-02-7.9858E-02-7.9857E-02-7.9853E-02-7.9855E-02-7.9849E-02-7.9850E-02-7.9855E02-7.9859E-02-7.9854E-02-7.9853E-02-7.9852E-02-7.9853E-02-7.9853E-02-7.9854E-02-7.9851E-02-7.9852E-02-7.9853E-02-7.9854E-02-7.9854E-02-7.9855E-02-7.9855E-02-7.9855E-02-7.9854E-02-7.9856E-02-7.9858E-02-7.9859E-02-7.9858E-02-7,9857E-02-7.9855E-02-7.9849E-02-7.9855E-02

6,,t

B,,t

O.7530O.6962
O.6694
O.6870O.7060O.7094
O.7269O.7186
O.7468O.7461
O.7169O.7002
O.7261
O.7293
O.7349O.7285
O.7286
O.7275
O.7428O.7370O.7308O.7265
O.7248
O.7172
O.7167O.7203
O.7244
O.7112
O.6981
O.6838
O.6894
O.6964
O.7225
O.7781

O.3639O.3511
O.3456
O.3493
O.3535
O.3543
O.3580O.3563
O.3623
O.3622
O.3559O.3522
O.3579O.3586
O.3599O.358S
O.3585
O.3583
O.3618O.3604
O.3590O.3581
O.3577
O.3559O.3557
O.3566
O.3576
O.3544
O.3512
O.3477
O.3490e.3507
O.3572
O.3708O.71986.2934

O.35653.7119

K
c
6
o
C
a
:
b.-

v

>

A CONTROL ESTIMATION APPROACH TO
TIME-VARYING PARAMETER MODELS

Table 2The Average Revised Value Te and the Average Error of Estimate rry.

2

Rny(%)

2ne(%)o3.310'

1

O.1485

X7.8462E-02

26.3607E-03

2.1786E-03

3

2.1119E-04

7.8481E-05

48.3189E-06

3.3382E06

53.7484E-07

1.5800E-07

9e

A: the estimated error of the control estimate (%)
B: the estimated er:or Qf the least squares estimate (9e)

4.47

o.oo

-5.59

Figure 11960.1 1965.1 1970.1

The Error of Estimate of the Real Wage Index (VV) in the Final Test

79

YUKIO UCHIDA

80

9e
7.37

A: the estimated error of the control estimate (%)
B: the estimated error of the least equares estimate (%)

B

o.oo

A

-5.11

1960,1 1965.1 1970.1

Figure 2

The Error of Estimate of GNP De('Iator (P) in the Final Test

A: the control estimate
B: the least squares estirnate

4.828

A

4.807

B

4.783
1960.1Figure 3

1965.1 1970.1
The Estimate of Parameter cro,tA CONTROL ESTIMATION APPROACH TO
TIME-VARYING PARAMETER MODELS

A: the control estimate
B: the least spuares estirnate

O.7988A

O.7710B

O.7307

1960.1Figure 4

O.OO052068

1965.1 1970.1
The Estimate of Parameter ai,t

A: the control estimate
B: the least equares estimate

A
O.OO051607

B

O.OO051070

1960.1Figure 5

1965.1 1970.1
The Estimate of Parameter cr2,t81

YUKIO UCHIDA

82

A: the control estimate
B: the least squares estirnate

O.8974

O.8948

O.89101960.1

1965.1 1970.1

Figure 6

The Estimate of Parameter a3,t

A: the contrel estimate
B: the least equres estimate-O.079847-A-e.079855
B-O.0798661960.1Figure 7

196S.1 1970.1
The Estimate of Parameter Po,t

A CONTROL ESTIMATION APPROACH TO
TIME-YARYING PARAMETER MODELS

O.7781

A: the control estimate
B: the least squares estimate

A

O.7198B

O.6694

1960,1Figure 8

1965.1 1966.1
The Estimate of Parameter Pi,t

O.3708
A: the control estimate
B: the least squares estimate

A

O.3565
B

O,3456

1960.1Figure 9

1965,1 1970.1
The Estimate of Parameter P2,t83

YUKIO UCHIDA

84(%)
Te2 (%)

vrg

O.15

3.0

O.10

2.0

O.05

1.0

o.oo

o.o

Figure 10

1 2' 34 52

The Average Reyised Value rre

Figure 11

Ol23452

The Average Error of Estimate nv

BUSINESS
KOBE ECONOMIC&REVIEW

CONTENTS
NO. 19 (1972)
Patterns of Export Trade of Argentina and Brazil:

A Comparative Study ....................................Fukuo Kawata
Entrepreneurship in America ................. ......................Tadakatsu Inoue
Generalization ofTwo-Gap Theory ................. ..................Hikoji Katano
Aocounting Measurement and Homomorphism ............................lsao Nakano
An Interpretation of Two Stage Least Squares
Estimators as Indirect Least Squares
Estimators in the Overidentified Case ....................Hiroshi Sadamichi

A Note on the One-dimensional Random Search ........................Komayuki Itow
Exchange Rate Systems and Distribution of

Seigniorage ............................................KazuhiroJgawa

NO. 20 (1973)
An Analysis of the Brazilian

Balance ofPayments: 1960-1972 ....

••••••................Fukuo Kawata

International Money Flow and
the Multinational Corporations . . . . . .
Esiimation of Investment Allocation...,...,............Masahiro

Ratios of Japanese Economy: 1960-1969
Available Jobs and Employment inJapanese Foreign-going Shipping ......

....................Hikoji Katano

Assets Choice and Optimal Internationa) Reserves .

.....................Kaiuhiro Igawa

Fuiita................Hiromasa Yamamoto
Homomorphism and Business Income Measurement . .......................Isao Nakano

NO. 21 (1975)
Regional Development Policies of Japan in Recent Quarter

ofthe Twentieth Century ..................................Minoru Beika
National Income and Expenditure
at Factor Cost in Japan 1955-1970:

A Macro-Accounting for Growing Economy ................Nobuko Nosse
EMciency and Acceptability in Optimal Growth Path ......................Hikoji Katano
An Equitable Distribution of the Costs and Benefits of Economic

Integration ........................................YoshiakiIVishimukai
Japanese Business Abroad: Past, Present and Future ....................Hideki Yoshihara

NO. 22 (1976)
Pioneering in Australian Direct Trade

LifeofF.Kanematsu,1845-1913 ...........,...,........Tadakatsu Inoue

Productivity Bargaining and the Change of Labour
Management Relations in the Japanese Foreign-going

Shipping;1965-1973 ...,........................
On an Interpretable Depreciation Method ....................

....Hiromasa Yamamoto............Isao Nakano

A New Type of Data Banking System-BEICA System- .............................
Expectation in the Shipping Exchange .........................
International Capital Movements andReal Capital Accumulation .......................

.......Hiroshi Sadamichi.........Tetsoji Shimoio.........Kazuhiro Igawa

Legal System of the Free Movement of Workers and Migration

Trends in the European Economic Comrnunity....................

NO. 23 (1977)
Alternative Approaches to the

Accounting for Education ..................................Nobuko IVosse
Personnel Management ofJapanese Companies
in Thailand: A Field Paper ..............................Hideki Yoshihara
Evaluation of Performance Using

MultipleCriteria ........,...............................KomayukiItow
Some Bargaining Process Models in
the Shippjng Exchange ....................................Tetswfi Shimoio
Asset Diversification under the Flexible

Exchange Rate System .........................,,.........Kazuhiro Igawa

Kunio Soh

KOBE UNIVERSITY ECONOMIC REVIEW 23, 1977
Edited by Faculty of Economics,
Kobe University, Kobe, JapanCONTENTS
A Theory Ofthe Labor Supply andthe Supply Curve ofLabor ................................Osamu Tanaka
Infiation as an Expression ofClass Antagonisms ........................................Nobue Okishio
The End of Free Trade? ..............................................Kiyoshi Ikemoto
Economic Reform and Enterprise Behavior-The Validity of the Material Incentive

System in the USSR- ....................................PVataru Fukuda
An Econometric Analysis ofJapanese Population Growth............................Mitoshi Yamaguchi
rtlllll:ti"'',-i'dHllTlidti"i:t'iSIUntiii'"idptPllMIiJP-iiviTlil[11iithmd-11Hllrirth,,ivilllllt,"h,db:"i[HUbiiri,itrtlllU"piitulvillH]Hidthrltiivll[111ei'lhilrilllllNbdh,,"dTHE ANNALS OF THE SCHOOL OF
BUSINESS ADMINISTRATIONKOBE UNIVERSITY 1977
Edited by the School of Business Administration,

Kobe University, Kobe, JapanCONTENTS
Development and Present State of Organization Theory

in the German-Speaking Countries ..........................Erwin Grochla
Neuere Entwicklungen in der

Deutschen Betriebswirtschaftslehre ........................Wolfgang Lticke
Grundfragen und Neue Probleme bei der Gestaltung

des Arbeitseinkommens der Werktatigen
imSozialismus ........................................EkkehardSachse
Theorems of Investment Truncation ................Kazuhisa Matsuda and IVobuo Okishio
The Critical Systematization of

Accounting Postulates ......................................Ryuii Takeda
A Conceptual Note on Corporate Strategy andOrganizationalStracture ..................................TadaoKagonot,llb"iTvlllelllli"hi,r,dlMrll"hi,Iv,11]Il""Ihi,villlrllltidlihu,ilrllillt,tli,Fll,11rliMtbith,itvtlHFIIi,dh,,,1"111Mll,rh-,viPIHIsliilh-d),ililllll,11iit,41itlHlrlvbi,,,,1i/tlMtl

KOBE UNIVERSITY LAW REVIEWInternational Edition No. 11, 1977
Edited by Faculty of Law
Kobe University, Kobe, JapanCONTENTS
Social Responsibility of Corporation ..................................Ichiro Kawamoto
Legal Analysis of Nihon Netsugaku Case ...,..........................Katsuro Kanzaki

RESEARCH INSTITUTE FORECONOMICS AND
BUSINESS ADMINISTRATION,
KOBE UNIVERSITYHISTORICALSKETCHIn 1919, a research organization named the Institute for Commerce was foundedin Kobe Higher Commercial School, one ofthe chiefpredecessors ofKobe University,with a gift made by F. Kanematsu & Company, a leading mercantile firm in Kobe. The
organizatjon was designed to carry on and facilitate integrated research on businessand commerce and to formulate and publish the results ofthese studies and investigations in such form as to make them available to the business community.

With the founding of Kobe University of Commerce, successor of Kobe Higher
Commercial School, in 1929, the Institute extended
its research activities by adding'

several divisions. One was the famous Latin-American Library, which soon became
the center of research in this field in Japan. A room for statistics equipped with various

computing machines was established and began publication of Jtiyo"' To-kei Keizai
monthly and Sekai Bo-eki To-kei annually. A filing room was prepared to deposit press
clipping files systematically arranged by topics and dates. Another room was designed
to become the center of all possible original records and data having to do with the

beginning and progress of Japanese business.

On the campus of Kobe University of Cornmerce, another organization named
the Institute for Business Mechanization was founded in 1941 utilizing businessmachines donated by the IBM Corporation and others. With Professor Yasutaro

Hirai as its head a broad and forward-looking plan for business mechanization in

Japan was developed.
In 1944, Kobe University of Commerce changed its name to Kobe University of
Economics. After the War, however, the University was consolidated with three othercolleges in Hy6go Prefecture to become Kobe University. With this development, thetwo Institutes were also amalgamated into the Research Institute for Economics andBusiness Administration, Kobe University. At present, the Institute, with its twenty

five fu11-time professional staff members, carries on studies and investigations ininternational economy, business administration, and information systems in Japan.

LOCATION AND BUILDINGSThe Research Institute for Economics and Business Administration is located on
the campus of Kobe University, Rokko, Kobe. It consists of two three-storied build-ings. One is named the Kanematsu Kinenkan and has a fioor space of about 2,900
square meters, which includes a president's room, forty-one offices, six rooms used asa library, a room for statistics, etc. Another is built in 1964. It has a fioor space ofabout 1,900 square meters, which is chiefiy used as the Documentation Center for
Business Analysis, a library and a conference room.

ORGANIZATION
Under the directorship of the president, the Institute operates with two researchgroups. Each research group and its sections are as follows:

A Group of International Economy(1) International Trade(2) International Finance(3) Maritime Economics(4) Latin-American Economy(5) Oceanian Economy(6) International Labour Relations
B Group of Business Administration(1) International Management(2) Business Administration and Information Systems(3) Accounting(4) Business Statistics
Besides the regular work of the Institute, research committees may be created tocarry on any special work requiring thejoint study of academic and business circles.
At present, there are five standing research committees, as follows: Experts Group on

the World Trade Structure, Committee of International Finance, Committee of Infor-

mation Systems, Committee of Oceanian Economy and Committee of Maritime
Labour.
For convenience and greater eMciency in carrying out its research activities, theInstitute has a general oMce which is responsible for 1) the collection and preservationof a comprehensive collection of books, periodjcals, pamphlets, and original records
and data offinance, trade, commerce, industry and business generally; 2) the classifi-

cation, cataloguing, indexing arranging, annotation and compilation of these researchmaterials; and 3) the formulation and publication of the results ofthe investigations
and studies accomplished by the professional staff members of the Institute.

As an affiliated institute, the Documentation Center for Business Analysis has
been established in 1964. It is the first systematic information facilities in the field of

business administration in Japan that has been recognized and authorized by the
Ministry of Education. The purpose is to collect and to make intensive control of all
kinds of materials on business administration and to make them availabe to scholars,

universities, governments, and business world with the aid of modern documentation
techniques.

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RESEARCH INSTITUTE FORECONOM!CS & BUSINESS ADMIN[STRAT!ON
KOBE UNIVERSITY

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ECONOMICRESEARCH I ADMINISTRATIONRESEARCH

Seiji SAsAKI.li of Maritime Minor ] Minoru BEIKA
Professor

Ecopomy V,
Dr. of Economics l'iliToru KANo

profcssor of lnternational l

FinancelDr. of Economics l TadakatsulNouEiProfessor of lntcrnational :Law I' Akio
MoRI
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i Masahiro FuJITAilProfcssor of lnternational iIiProfesscrr of lnternational l

FinanceDr. of Economics ll
l Nobuko NossE

Hikoji KATANO

Trade l:Dr. of EconomicslIiPh. D. in Statisttcs l'

i Isao NAKANOProfessor of lnternational i
Hiromasa YAMAMoTOl

Labour Relations i
Yoshiaki NlsHtMUKAI

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GROUPOFINTERNATIONAL l GROUPOFBUStNESS

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Jiro yAe

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Director : Tadakatsu INovE
Secretary: J]sabuvo TARuMOTO

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1 Hideki YosH[HARA

Professor of Regional i

Study on Latin i
America I Hiroshi SAoAMIcHI}

Tetsuji SH[MoJe

Associate Professor of ll

Maritime Economy ll Kornayuki lTow

Kazuhiro IGAwA

Associate Professor of iinternational Trade liKunio SoH

ResearchAssociateol'lnter- :, Yukio UcHIDA
national Labour Relatiens i:
Office : Thc Kancmatsu Memorial Hall

KeBE UNIVERSITYROKKO, KOBE JAPAN

Professor of Business

Administration andInformation Systems
Dr. of Business Administratton

Professor of Internatienal

Management
Professor of Business

FinaneeDr. of Business Adrn{n{ytratlonProfessor of Business
Statistics

Dr. of Busincss Adminls.
tratlon.

Associate Professor of

Accounting
Associate Profssor of

Intcrnational Matiagement
Associate Professor of
Busincss Statistics

Ph. D. in Econometrics
Associatc Prefcssor ef

Business Administration
and Inforrnation Systems
Research Associate ot
Business Statistics

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