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This is to certify that the

thesis entitled

THE DEMAND FOR AND SUPPLY OF INTERNATIONAL

RESERVES: A SIMULTANEOUS APPROACH
presented by

MOHSEN BAHMANI-OSKOOEE

has been accepted towards fulfillment
of the requirements for

Ph . D. degree in Economics

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DEMAND FOR AND SUPPLY OF INTERNATIONAL RESERVES:

A SIMULTANEOUS APPROACH

By

Mohsen Bahmani-Oskooee

A DISSERTATION

Submitted to
Michigan State University
in partial fulfillment of the requirements
for the degree of

DOCTOR OF PHILOSOPHY

Department of Economics
1981

\.J

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n / .;'
(ff //I\../

To my wife, Negar

ABSTRACT
THE DEMAND FOR AND SUPPLY OF INTERNATIONAL
RESERVES: A SIMULTANEOUS APPROACH

By Mohsen Bahmani-Oskooee

Empirical studies of demand for international
liquidity have generally concentrated on the formulation
and estimation of demand functions. Supply relationships
have typically been handled by assumption, the usual
practice being to assume that the supply of international
reserves is elastic enough to.meet the demand.

The main purpose of this thesis is to develop a
model of demand for and supply of international reserves.
Our model differs from previous studies in several ways.
First, we have tried to eliminate the assumption of elastic
supply by specifying a supply function. Second, incorporated
into the model is the gold price, which allows us to look
at the proposal for which provisions were made in the
International Monetary Fund articles; these suggest that one
possible method of dealing with the shortage of liquidity
is gold revaluation.

Using two-stage least-squares demand functions were
estimated for the period 1972-1977, using quarterly data

for 19 developed countries and 21 less developed countries.

The demand for international reserves is found to be elastic
with respect to the official price of gold. However, it is
found to be inelastic with respect to the market price of

gold (dollar price of gold in London).

Considerable evidence is also found that the
assumption of elastic supply is valid for less-developed
countries.

Third, in order to introduce the possibility of
disequilibrium behavior into the model, an adjustment
mechanism was used which led us to estimate the speed of
adjustment . Estimates of the speed of adjustment are found
to be in the range of almost 3-30 percent, which is in
sharp contrast to what previous studies have found.

The main conclusion from the study is that any model
of demand for international reserves that does not take the
supply side into account is biased. Furthermore, the gold
price exerts a negative effect on the demand for international

reserve 8 .

ACKNOWLEDGEMENTS

It would be impossible to write a dissertation without
receiving assistance from others. This is especially true
for foreign students for whom it is the first time to be
involved in a large research program.

First, I would like to thank my main thesis director,
Lawrence Officer. A thesis student in the area of inter-
national economics could not find a better major professor
than Professor Officer. For the last year of my work, he
was on leave, but I did not feel any pressure. His willing-
ness to devote immediate attention, prompt responses,
perceptive comments and general encouragement all made my
task much easier.

The other members of my thesis committee, Anthony Koo,
Carl E. Liedholm, and Dennis Warner were also extremely
helpful in assistance with a number of issues.

In addition, several faculty members at Michigan
State University offered helpful advice and great comments,
these people include Daniel Hamermesh, Robert Rasche and
Peter Schmidt.

I would also like to thank some of my fellow graduate
students who offered helpful advice and encouragement. These
would include Richard Cervin, John Fizel, Steven Husted and

Edward Weber.

My special thanks go to my wife, Negar Bahmani, who
did not complain too often about all of the time I spent
working on this project. Indeed, she more often complained
because I was not working on it.

Finally, Betsy Johnston edited and Terie Snyder
typed this manuscript. Their expertise is sincerely

appreciated.

i v

LIST OF TABLES

Table Page
2-1 Features of Major Studies on Demand for

Reserves. Regression Techniques. 39
3-l Gold Flows: 1971-1978 65
u-l Estimates of p For Different Countries 86
u-2 Estimates of Demand Function: Equilibrium

Model, Developed Countries. Using

Official Price of Gold 92
n-3 Estimates of Demand Function: Disequilibrium

Model, Developed Countries. Using

Official Price of Gold 93
u-u Estimates of Demand Function: Equilibrium

Model, Developed Countries. Using

Market Price of Gold 9M
u-s Estimates of Demand Function: Disequilibrium

Model, Developed Countries. Using Market

Price of Gold 95
”-6 Estimates of Demand Function: Equilibrium

Model, 21 LDC's. Using Official Price

of Gold 98
4-7 Estimates of Demand Function: Disequilibrium

Model, 21 LDC's. Using Official Price

of Gold 99
”-8 Estimates of Demand Function: Equilibrium

Model, 21 LDC's. Using Market Price

of Gold 100
u-g Estimates of Demand Function: Disequilibrium

Model, 21 LDC's. Using Market Price of

Gold 101
M-lO Comparison of DC's and LDC's Regression

Coefficient Using Official Dollar Price
of Gold 103

LIST OF TABLES

(cont'd.)
Table Page
u-11 Comparison of DC's and LDC's Regression
Coefficients Using Market Price of
Gold 10%
5-1 Estimates of Demand Function: Equilibrium

Model, Developed Countries. Using
Official Price of Gold (after we dropped
income variable from supply side) 109

5-2 Estimates of Demand Function: Disequilibrium
Model, Developed Countries. Using
Official Price of Gold (after we dropped
income variable from supply side) 110

5-3 Estimates of Demand Function: Equilibrium
Model, Developed Countries. Using
Market Price of Gold (after we dropped
income variable from supply side) lll

5-H Estimates of Demand Function: Disequilibrium
Model, DeveIOped Countries. Using Market
Price of.Gold (after we dropped income
variable from supply side) 112

5-5 Estimates of Demand Function: Equilibrium
Model, 21 LDC's. Using Official Price of
Gold (after we dropped income variable
from supply side) 115

5-6 Estimates of Demand Function: Disequilibrium
Model, 21 LDC. Using Official Price of
Gold (after we dropped income variable from
supply side) 116

5-7 Estimates of Demand Function: Equilibrium
Model, 21 LDC's. Using Market Price of
Gold (after we dropped income variable from
supply side) 117

5-8 Estimates of Demand Function: Disequilibrium
Model, 21 LDC's. Using Market Price of
Gold (after we dropped income variable
from supply side) ll8

vi

Table
5—9

5-10

5-11

5-12

5-13

5-17

5-18

5-19

LIST OF TABLES
(cont'd.)

Comparison of DC's and LDC's Regression
Coefficients. Using Official Price of
Gold (after we dropped the income variable
from supply side)

Comparison of DC‘s and LDC's Regression
Coefficients. Using Market Price of
Gold (after we dropped the income
variable from supply side)

Estimates of Demand Function: Equilibrium
Model, 21 LDC's. Using Official Price
of Gold and OLSQ Technique

EStimates of Demand Function: Disequilibrium
Model, 21 LDC's. Using Official Price of
Gold and OLSQ Technique

Estimates of Demand Function: Equilibrium
Model, 21 LDC's. Using Market Price of
Gold and OLSQ Techniques

Estimates of Demand Function: Disequilibrium
Model, 21 LDC's. Using Market Price of
Gold and OLSQ Techniques

Gold Holding of LDC's

Dollar Value of Real GDP Per Capita of
Less Developed Countries in a Decreasing
Order

Estimates of Demand Function: Equilibrium
Model, 13 LDC's. Using Official Price of
Gold

Estimates of Demand Function: Disequilibrium
Model, 13 LDC's. Using Official Price of
Gold

Estimates of Demand Function: Equilibrium
Model, 13 LDC's. Using Market Price of
Gold

vii

Page

120

121

12”

125

126

127

128

130

131

132

133

LIST OF TABLES

(cont'd.)
Table Page
5-20 Estimates of Demand Function: Disequilibrium
Model, 13 LDC's. Using Market Price of
Gold 13a
5-21 Demand Elasticities With Respect to Gold 136

Price From the Most Appropriate Models

viii

LIST OF TABLES

CHAPTER

TABLE OF CONTENTS

ONE - INTRODUCTION

TWO — SURVEY OF THE DEMAND FOR INTERNATIONAL
RESERVE LITERATURE

Introduction

Pre-Floating Rate System Literature
Pre—Floating Rate System Literature
Using Econometrics Techniques
Post-Floating Rate System Literature
Reserve and Speed of Adjustment
Concluding Remarks

Features of Major Studies

THEORY or DEMAND FOR AND SUPPLY or

NTERNATIONAL RESERVES

Introduction

The Demand for International Reserves
The Supply of International Reserves
Disequilibrium Model

FOUR - MODEL SPECIFICATION AND ESTIMATION

RESULTS

”.1 - Introduction

H.2 - Identification

u.3 - Method of Estimation and Data
u.u - Model Specification and Results

FIVE - FURTHER RESULTS AND CONCLUSIONS
5.1 -

5.
5.

0101

2
3

(J14:

Introduction

Implication of the Model

The Model of Demand for and Supply of
International Reserves Without

Income Variables

Conclusions

Concluding Remarks

ix

Page

10
19
32

38

us
me

76

79
79
82
87

106
106

108
135
138

TABLE OF CONTENTS
(cont'd.)

FOOTNOTES

Chapter Two
Chapter Three
Chapter Four
Chapter Five

BIBLIOGRAPHY

Page

139
1H0

1u2
1m:

145

CHAPTER ONE

INTRODUCTION

In the last decade, countries have preferred to
move to a system of.managed floating that is intermediate
between the extremes of fixed rates and a clean float. Since
managing the float requires international reserves, it is
clear that the study of these reserves is as relevant today
as it has been in the past.

If we could measure the need for reserves, we.might
be able to predict their growth rate. Quantitative
methods may answer important questions pertaining to
international liquidity. These methods concentrate on the
purely statistical examination of time series data of
international reserves and attempt to assess the relative
adequacy of reserves by relating present stock to past
performance. Studies using varying degrees of statistical
sophistication have adOpted this approach, and it shall be
adopted here. However, all previous studies have generally
concentrated on the formulation and estimation of demand
functions. Supply functions have typically been handled by
assumption, the usual practice being to assume that the
supply of international reserves is elastic enough to meet

demand.

The main purpose of this thesis is to develop a model
of demand for and supply of international reserves. Our
model differs from previous studies in several ways. First,
we have tried to eliminate the assumption of elastic supply
by specifying a supply function. Second, we incorporate
into our model the gold price, which allows us to look at
the proposal for which provisions were made in the Inter-
national Monetary Fund articles; these suggest that one
possible method of dealing with the shortage of liquidity
is gold revaluation. Third, in order to introduce the
possibility of disequilibrium behavior into our model, an
adjustment mechanism is used which leads us to estimate the
speed of adjustment.

Chapter Two presents an extensive review of the
literature on the demand for international reserves. In
Chapter Three, we develOp the model of demand for and
supply of international reserves. The specific questions
to be analyzed in that chapter are:

Cl) Can the demand for international reserves be

described as a function of a limited number
of variables?

(2) Can the supply of international reserves be

described as a function of a limited number of

variables?

(3) How is the gold price related to the demand for
and supply of reserves?

(H) How would the model change if we introduced the
possibility of disequilibrium behavior into the
model?

Chapter Three attempts to provide answers to these questions.

Chapters Four and Five concentrate on empirical
aspects. Specifically, in Chapter Four, the demand function
is estimated for 19 developed and 21 less developed
countries. In Chapter Five, further attempts are made to
investigate the behavior of less developed countries.
Considerable evidence has been found that the assumption of
elastic supply is valid for the less developed countries.

In the last part of Chapter Five, our conclusions are

presented.

CHAPTER TWO

SURVEY OF THE DEMAND FOR INTERNATIONAL
RESERVE LITERATURE

2.1 - Introduction

 

There are at least five reviews of the literature
relevant to this study: Clower aneripsey [1968], Niehans
[1970], Salant [1970], Grubel [1971], and Williamson [1973].
The justification for writing this review is that since
completion of the last survey, several papers have appeared
which contribute to the stock of knowledge in this field.
This review will consist of two parts: the first will
include a brief summary of the literature previous to the
last survey, and the second part will be devoted to the
expanded description of the literature since the last
survey. At the end, a table will be provided containing

the features of.major demand for reserve studies.

2.2 - Pre-Floating Rate System Literature

 

The oldest approach to the demand for reserves that
is relevant for a gold-standard world is that there is a
direct relationship between desired reserves and the

domestic money supply. The base money is gold held by

central banks, and similar to today's fractional banking
system, the domestic supply of money can be increased if
high-powered money reserves in the form of gold increases.
By 1993, there was general recognition that reserves were
relevant for international purposes rather than for
backing the domestic.money supply. Triffin (19u7) argued
that the demand for reserves could be expected to grow in
line with trade, so that the reserve imports ratio could
be taken as a measure of reserve adequacy. This measure
was used by Harrod (1953), the IIM.F. (1953, 1958, I970),
Stamp (1958), Triffin (1960), Grubel (1965), Machlup (1966),
anleeller (1968).

Besides imports, two other classes of scale
variables are sometimes used. The first consists of
variables such as domestic.money supplies and liquid
liabilities to foreigners. The theoretical justification
for the use of these variables is provided by Johnson
(1958) and Scitovsky (1958). Their empirical relevance
has been tested by Machlup (1966).

The second class consists of variables such as net
external balance, or reserve losses. As Grubel (1971)
interprets them, they reflect the instability of countries'
balance of payments in the past. The theoretical
justification for the use of these variables is provided
by the IMF Reports (1958 and 1970) and Machlup (1966).

Most of these studies have predicted that demand

for reserve will increase by some percentage. For example,

the studies published after a 1970 IMF conference projected
annual increases in reserve demand within a range of three
to four percent. Triffin's projections (1960) led him to
predict severe reserve shortages in the 19605. Among these
studies, one of them deserves special notice; the Machlup
study (1966) appears designed to discredit the use of
ratios in the analysis of the demand for reserves. He shows
the difficulties involved in establishing theoretical
justifications for why any of the ratios he examined (that
is, reserves to imports, reserves to largest annual reserve
losses, reserves to domestic money and quasi-money, and
reserves to liabilities of central banks) should be
constant across countries or through time. His statistical
analysis showed that all ratios are different for the
countries and periods under examination. Machlup was
unwilling to make any forecasts of demand and judgments
about adequacy, and he concluded that the demand for
reserves is not a function of any identifiable variables.
Rather, it is determined by the desire of countries to
have their reserves grow. This has become known as "the
Mrs. Machlup's wardrobe Theory of Monetary Reserves."
Distinction between reserves for transaction
purposes, which are assets of a country's commercial banks,
and reserves for precautionary purposes, which are assets
of central banks, leads us to distinguish between two
studies, one by Heller (1968) and the other by Olivera

(1969).

Heller (1968) used the reserves-imports ratio in
applying Baumol's square-root law to transactions involving
balances of international reserves. His contribution was
to calculate the ratio of commercial banks' foreign exchange
to the square root of imports, which he used as a measure
of the adequacy of international reserves for transaction
purposes.

In a purely theoretical paper, Olivera (1969)
contributed an important insight to the meaning of observed
change in the ratios of reserves to imports. He argued
that precautionary demand for reserves should be a function
of the variance of changes in the level of imports; he
showed mathematically that under some assumptions about
economic behavior, this variance of import changes
increases more slowly than the level of the underlying
economic transactions. More precisely, he showed that the
elasticity of precautionary demand with respect to volume
of transactions is .5. In a simple Baumol-Tobin.model,
therefore, the level of precautionary demand is equal to
the square root of the level of transactions. An
elasticity of .5 implies that the rate of growth of the
demand for cash is equal to that of the square root of
transactions, rather than to that of transactions them-
selves. For this reason, this result is called, "the
square-root law." Both the Heller and Olivera theories
assume that an increase in the volume of transactions

takes the form of an expansion in the number of transactions,

with no increase in the size of individual transactions.
But as Baltensperger (197u) points out, a constant number-
of individual transactions but an increase in their size
(due, say, to inflation) will result in the predicted
elasticity becoming unity rather than 15; this applies to
both theories.

Officer (1976) argues that, in the real world, it
is reasonable to expect changes in the volume of inter-
national transactions to take the form of changes both in
number and size. Then the theoretically predicted
elasticities of demand with respect to the volume of
international transactions would be between 25 and unity
for both the Heller and Olivera theories.

Officer has tested both of these theories, using
a comprehensive measure of the volume of international
transactions instead of the conventional merchadise-import
flow. His measure, for a given country in a given year,
is the sum of all gross flows (total credits or total
debits) in the country's balance of payments. Using
annual data for the period 1959-1970, Officer has used the
following model for developed countries:

(1) log R = a + b log T + u where u = + w

t put-1

(2) log E = c + d log T + v where Vt:' qvt_l +6:

Equation (1) tests the Olivera theory, and equation (2)
tests the Heller theory. If these theories are to be

accepted, then b and d, which are elasticity coefficients,

must be positive, significant, and lie between .5 and l.

The Olivera hypothesis, which predicts a transaction
elasticity of demand for reserves within the interval .5 to
l and requires the use of official reserves (held by
central banks) for R in equation (1), is satisfied for
most countries in his sample. However, the Heller
hypothesis, which predicts the same elasticity range and
requires the use of reserves held by commercial banks for
E in equation (2), is rejected by his evidence. Nearly
all countries in his sample exhibit elasticities substan—
tially above unity.

Makin (197u) has looked at the effect of exchange
rate flexibility on the demand for international reserves,
specially, the elasticity of demand with respect to a
change in trade volume. He showed that the elasticity
of demand for precautionary reserves with respect to an
increase in exchange rate flexibility (defined as a widening
of bands about parity) is estimated to lie between minus
one-third and minus two—thirds. This result, of course,
gives some idea as to the extent to which increases in
exchange rate flexibility can be expected to counteract
the impact of an increased volume of world trade upon the
demand for reserves by central banks.

Even for the United States as a major supplier of
the dollar component of the reserves, the degree of
exchange rate flexibility should carry a special signifi-

cance. Increased exchange rate flexibility, if available

10

to the United States, can reduce that country's dependence
upon its reserve currency role in view of its relatively
vulnerable reserve position.
2.3 - Pre-Floating Rate System Literature UsingEconometric

Techniques

During the 19605, as computer technology was

developing, many economists thought of using econometric
methods, mainly regression techniques. The reason, as Grubel
(1971) points out, may be due to the ready availability
of computers, programs, and sufficiently long time series
of observations needed in the calculations. The first
study to use regression techniques was by Kenen and Yudin
(1965), who mainly attempted to introduce a new version
of the demand for reserve function. They claimed that
the imports-reserves ratio does not tell us very much.
It shows how long a country could finance its imports if
it were suddenly depriVed of all its foreign exchange
earnings, and they theorized that reserves should be
compared to the variations in payments and receipts that
countries actually expect to experience. After inspection
of major countryies' statistics, they suggested that while
reserve changes are basically stochastic and approximately
normally distributed, they are also serially dependent.

Therefore, the Markov process of

(3) AR = DAR + at

11

in which 0 < O < l and e N N(E, 6:), could be used to

t
describe a country's stochastic balance of payment.
Kenen and Yudin (1965) computed the least-squares
estimates of ARt = e + PARt-l
(average size of country's reserve losses), P is an estimate

, where E approximates E

of p (the carry-forward or duration of a series of losses),
and 5e is an estimate of6E (the standard error of reserve
losses) in equation (3). They estimated these proxies for
in industrialized countries using monthly data during the
period 1958-1962 and then used them in cross-country
regressions. The selected years were 1957 and 1962, they
found the level of reserve holdings to be an increasing
function of all three proxies of reserve instability. In
the 1957 regression, only the coefficient of 6e was
significant; however, in the‘l962 regression, all coefficiets
were significant. They also took account of two other
variables which may affect the reserve holding behavior

of countries: the opportunity cost of holding reserves and
the level of "liquid" liabilities that governments regard
as claims on their reserves. As a proxy for Opportunity
cost of holding reserves, they supposed that reserve
accumulation is usually accomplished at the expense of
capital formation and that the "social marginal product"

of capital varies inversely with per capita income.
Therefore, per capita income was used as a proxy for

opportunity cost. The following equation was employed:

 

I)!

12

(5) R. = 80 + Blpi + 826

X.
it si + B3‘p’it+ BuLit + 6it

where (%). represents per capita income in the ith country,
and Lit represents that country's liabilities. Since 83
and 8” turned out to be insignificant, the inclusion of per
capita income and liabilities did not improve the overall
fit.

Thorn (1967) critizes Kenen and Yudin's chaim. As
he puts it:

"It shall be shown that their "disturbance

hypothesis" tells us no more, and perhaps less,

than the hypothesis they discarded and that their

statistical results are inconclusive."
Thorn develops the theoretical argument that countries have
a desired ratio of reserves to imports that they attempt
to maintain as imports grow. He formulates that a country's
demand for international reserves (Rt) is determined by a

policy parameter, the target ratio of reserves to imports

(r0), and the actual level of imports (It):

(6) Rit = IitrO

Then he considers the 1960 reserve-to-import ratio for each
country as its reserve target and estimates the following
equation for the same 14 industrialized countries studied

by Kenen and Yudin (1965) for the years 195R, 1957, 1962,

and 196u:
(7) log Rit = a0 + a1 108 lit + a2 log r1 1960
where i Z l, .... l”.

13

In none of the equations were al and a2 significantly
different from unity, nor was the constant term significantly
different from zero. Thorn also gets higher Rz's compared
to R-2 of Kenen and Yudin. Based on this result, he
concluded that there is insufficient evidence to reject
the "import-target ratio hypothesis." The import-target
reserve ratio hypothesis yields results as good as the
"disturbance hypothesis" in terms of the Kenen-Yudin
criterion, even with the crude method of determining the
target ratios employed above.

' In their reply, Kenen and Yudin (1967) brought out
the weakness of Thorn's paper, stating that he had used an
economic model that totters on the brink of tautology.

b .t b2i

li _
t 0e and lit - RiOe

(b1i and b2i are the rates of growth of ith country

t

They showed that since Ri = R1

reserves and imports between the base date for ri0 and the

current period to which equation (6) applies), then the

definition of ri0 yields the tautology: Ritz Iitrio

or, logarithmically:

(8) log Rit = (b - b2i) t + log Iit + log ri0

1i

This is identical to Thorn's equation (7), with a = (b .-b )t

0 li 2i

and a = a = 1. No wonder, then, that a and a2 in equation

1 2 l
(7) are never significantly different from unity.
Courchene and YoussefCl967), rather than estimating

cross—section equations,estimated two time-series equations

:for9 countriesusing<quarterly data over the period 1958—1968.

19

In the first equation, a country's reserve holdings have
been related to imports (M) and to the long-term interest
rate (r), which is taken to be a proxy for the opportunity
cost of holding reserves. In the second equation, again,
a country's reserve holdings have been related to the
money supply and long-term interest rates (r). To justify
the use of imports, reference has been.made to the quantity
theory of money and its international implications. The
use of domestic money supply is defended with the help of
Johnson's monetary model of the balance of payments (1958)
and Scitovsky's (1958) theoretical considerations on the
relationship between the domestic money supply and foreign
payments imbalances. Assuming the existence of a stable
demand function over time, their empirical results support
the idea that demand by individual countries for reserves
can be represented as a function of the money supply and
the long-term interest rate.

Kelly (1970) has introduced a new variable into the
demand functions; he has replaced the measure of variability
of balance of payment introduced by Kenen and Yudin (1965)
with the standard deviation of exports. This has the
advantage of reducing the simultaneity problem posed by
the fact that some parts of the payments balance, for example,
imports, are influenced by adjustment policies rather than
being exogenous, as supposed in the theory. This advantage
is bought at the cost of ignoring other causes of instability.

Kelly (1970) pooled annual data for the period 1953-1965 for

15

H6 countries (#6 countries X 13 years = 598 observations).
Using dummy variables for each country, he estimated the

following equations:

- M y_.
(9) log R - al log S(X) + a2 log y + a3 log P + e
M
(10) log R = bl log S(X) + b2 log y + b3 log A + bu log L
+ u
where S(X) = standard deviation of exports;
M _ . .
y — average propenSity to import;
% = per capita income as a proxy for
opportunity cost;
A:

again proxy for

opportunity cost

foreign assets-
L = liabilities

His results are very good. All of the independent
variables were significant, and all but the import prOpen-
sity and foreign liabilities variables had the expected
sign.

Kelly was expecting to get a negative sign for E,
but he got a positive one. This is the case for most of
the other studies examined here, a point discussed in
later pages. However, the positive sign of % simply
indicates that % reflects the degree of openness of the
economy rather than the average propensity to import.

Kelly also used equation (9) in estimating cross-
section equations for each year (1953—1965). He concluded

that:

16

"The constancy of the coefficients for the
annual cross-sections over a 13-year period
provides a strong base on which to predict the
growth in demand for reserves. If export
variance and foreign assets and liabilities
continue to grow at the same rates (5.8, 10.u,
and 9.8 percent respectively) and the same
import responsiveness is maintained, then the
demand for reserves will increase at an
average annual rate of 5.9 percent."

Clark (1970) assumed that policy makers have some
desire to maintain a given target level of reserves, and as
long as reserves depart from the desired level, the country
will attempt to induce a balance-of—payment surplus (or

deficit), S*t° This is given by

(11) 8* = y(R* - R

t-l

where R* is the average stock of reserves (desired
reserves). Clark argues that the actual balance of
payment surplus or deficit (St) is equal to the desired
change in reserves (8*t), plus a random term which measures

the net capital account:

(12) S 8* + s

t t t

Combining (11) and (12), he obtained:

: 3'! ..
(13) Rt yR + (1 y) Rt_l + at

With the assumption that the target level of reserves can
be respresented by a linear time trend, that is,

R*t = R*0 + kt, Clark got the following equation:

(19) R = yR*

+ _ +
t ykt + (1 Y) Rt- E

0 1 t

17

or

(15) Rt = a + bt + th-l + et

Clark employed equation (15) using monthly data for 38
countries over the period 1958-1967. His results were
satisfactory, the speed of adjustment, 7, was in the
expected range (between zero and one in all cases but one).
His estimate of 5e was then used in a cross-country
regression analysis to explain average reserves and proved
highly significant, even after the data were deflated by
the value of trade to prevent correlation due to size.
The independent variables used in cross-country regressions
did not differ from those used in previous studies.

Archibald and Richmond (1971) also used equation
(15) originally employed by Clark (1970). Their empirical
finding is that the variance of the disturbances around
their time trend increased during the period 1961-1967,
which supports the assumption made by Clark (1970) in
formulating equation (15). The refined measure of instability
is used not in the estimation of an equation of the demand
for reserves, as was done by others, but primarily in
estimating the likelihood that countries will run out of
reserves.

Flanders (1971) was the first and only person to use
the ratio of reserves to imports as the dependent variable.
She used as measures of payments instability some indices

which had been developed by others for purposes of analyzing

18

the effects of commodity stabilization schemes. She also
explored a large number of other independent variables,
mainly foreign exchange holdings by private banks, official
holdings of foreign exchange, rate of growth in GNP, the
ratio of exchange rate to the cost of living index, per
capita income, and indices of export instability. All these
have been discussed as being theoretically relevant as
influences on individual countries' reserve holdings.

Flanders reports that the "empirical results of the
study were a dismal failure" (p. #3). What factors might
account for this failure? Is it because the reserve—import
ratio rather than the reserve itself is used as a dependent
variable, or is cross-section analysis inappropriate
because of the small number of countries (18, 26 and 57)
in the sample, or is it the selection of so many independent
variables? The important point is that Flanders has
introduced new independent variables that should be
explored in future studies.

As mentioned, the use of the reserve-import ratio as
a dependent variable may not be appropriate. Except for
Flanders, all other studies have used reserves rather than
the reserve-import ratio. Reserves are demanded in order
to finance the deficit, and the higher the imports of a
country, the more reserves will be demanded by that country
in order to finance the imports. It is generally accepted
in the literature that there is a positive relation between

reserves and imports, so if R = A + bM + ck + s (where

19

k is vector of other dependent variables), then R/M==a/M
+ b + c k/M + u. But Flanders fails to do so. She just
weights reserves by l/M and not the right-hand side
variables, and perhaps this is why her results are not
satisfactory.

Tobin (1973) has used several definitions of payments
imbalances as independent variables in the demand for free
world reserves, such as payments imbalances on current
account (I1), in the liquidity concept (I3), and in the
basic balance sense (In) for different developed country
groupings. His empirical results are not so satisfactory.
In his first equation, in which reserves are regressed on
I1, Tobin concludes, "such a result is, of course,
theoretically absurd" (p. 536). In another case, when
reserves were regressed on I3, it is understood that this
measure of reserve demand has only limited usefulness.
Finally, Tobin's least-squares regressions between reserves
and In yielded a statistically insignificant result, that

is, a low t-statistic.

2.9 - Post-Floating Rate System Literature

 

Frenkel (197u-A) has reexamined the relation between
reserve holdings and the openness of the economy within a
price-adjustment model. In contrast with the Keynesian
prediction that reserve holdings are inversely related
to the average propensity to import (discussed in more

detail in Chapter 3), he argues that there exists a positive

§ .

.5.

'.

V-

'5

.
a

a‘

-

 

20

association between reserve holdings and openness. This
positive association is not explained by the standard
priceless Keynesian model, but can be explained by the
price-adjustment model. Frenkel's empirical results
support the idea.

In another paper, Frenkel (197u-B) employed the

following model:

log m + a2 log 6 + a3 log M + 6

log R = a0 + a1

He used it to compare the demand for reserves of developed
countries with that of less developed countries. In that
equation, M stands for imports, m represents the import-GNP
ratio, and 6 is the measure of the variability of inter-
national receipts and payments, which represents the
trend-adjusted yearly disturbance in a country's stock of
international reserves. The value of 6 for each year was
estimated by computing the standard deviation over the
previous fifteen years of the trend-corrected annual
observations of the level of reserves.

Frenkel's empirical results cover 22 developed
countries and 33 less developed countries over the period
1963-1967. Cross-section equations were estimated for each
year for both groups and then for all 55 countries together.
These estimates were found to be stable over time, and it
was found that the holdings of reserves are positively
and significantly related to all three independent variables

and had high R2. The results also suggest that the

21

behavior of the developed countries with respect to their
holdings of reserves differs from that of the less develOped;
therefore, it is desirable to analyze these groups separately.
Some explanations were offered for these differences, and

it was suggested that emphasis should be given to the
monetary aspects of the problem.

Iyoha (1973) has developed a model that assumes an
optimal balance of payments strategy for less developed
countries. His model is a welfare maximizing model with
respect to the production possibility frontier of the
economy, which produces two goods, importables and exportables.
The question was how to determine the optimal balance of
payments strategy for a developing country. With Iyoha's
model, the problem was reduced to one of finding the
optimal level of imports in any year - given the amount of
reserves the country owns at the beginning of that year.

One way to determine the optimal level of imports in each
state was then developed. It was found that the optimal
import level rises as a function of reserve holdings and
depends on the social discount rate, the degree of self-
sufficiency of the economy, the expected stream of export
earnings, and the degree of instability of export
receipts.

In another paper, Iyoha (1976) used the findings
from his 1973 article and concluded that the optimal level
of reserves (RP) depends mainly on expected export receipts

(Xe), the variability of export earnings (62), the interest

22

rate on foreign exchange holdings (r), and the degree of
openness of the economy (0). Hence, the specification of
the determinants of optimum reserve is:

P

R = f(Xe,62,r,p); f f f f > 0

19 23 3) n
This Specification has been used in a lagged adjustment
model in order to specify the demand for reserves function.

The model is:

- e 2
(16) R - a0 + alx + a26 + a3r + ago + a5R_l + a6R_2 + 8

Following Adelman and Chenery (1966), expected export
earnings were estimated for each LDC for 1950-1969, and
the disturbance variance of the estimated equation was
used as a measure of the variability of export receipts.
Also, the discount rate was used as a proxy for the
opportunity cost of holding reserves (r).

Equation (16) was tested using cross-country data
from 29 less developed countries in 1970 and performed
extremely well. Iyoha's most interesting result concerns
the opportunity cost of holding reserves. Before his
study, no cross-section study had obtained a significant
result for the opportunity cost of the reserve holding
variable. Finally, Iyoha's regression equation (16)
explains more than 93 percent of the systematic variations
in the reserve holding behavior of less developed countries
in 1970.

Iyoha's significant coefficient of r in his model

23

(a3) has been attacked by both Hipple (1979) and Shinkai
(1979). They argue that Iyoha has misinterpreted his
results. He makes no allowance in his regression for
compositional differences in the reserve stocks of different
countries. Not all components of reserves of a country

can earn interest. There is an investable component
(foreign exchange) and a sterile component (gold, SDRs,

and the IMF position). Iyoha has entered only the yield
rate in his equation for reserve demand and has made no
adjustment for these compositional factors.

Another weakness of Iyoha's analysis is his
selection of a statistical series for the yield rate in each
country, which is an internal yield rate. This is
incorrect, since the only meaningful yield rate for
invested foreign exchange reserves must be an external
yield rate. The bulk of internatiOnal reserves is held
in U.S. dollars. Since the dollar must have carried the
same interest rate, it would appear that the effect of the
interest rate could not have been captured by a cross-
country analysis. Iyoha obtained a positive effect because
he used country-specific interest data (discount rate of
each country).

Shinkai suggests that if one is to capture an effect
of the opportunity cost of holding reserves, one should
have a variable such as (rS- r Country-Specific) that
measures the net gain (inverse cost) of holding reserves

instead of investing the equivalent sum within the country.

29

In a cross-regression r$ is a constant, and one should obtain
a negative coefficient on the country-specific interest
rate.

Worrell (1976) has looked at both the costs and
benefits of holding reserves in the long term. He argues
that the consequences of holding a reserve stock last into
the long term and may have implications for the country's
rate of economic growth. His model gives a framework for
evaluating these long-term consequences. There is no need
to explain Worrell's model in great detail here. The only
part which might be relevant for our purposes is the way
in which he relates the reserve holding behavior of the
authorities to the structure of the whole economy. He
chose four variables to represent the structure of the
economy: export earnings (X), capital inflows from abroad
(K), changes in the money supply (dMs), and government
expenditures (G). The model was tested for the Jamaican
economy using monthly data between January 1968 and

December 1971. The results were:

(17) Rt = 12.51 + 0.72 Rt_l + 0.01 dMSt + .079 xt
(2.52)* (12.93) (0.0a) (3.17)
+ 0.36 Kt + 0.20 Gt + at
(1.50) (1.01)
R2 = 0.948

The coefficients of individual variables are not always

25

significant and do not always have the signs and values we
would expect, but because of good R2 the standard error of
the error term (St) was used in constructing his model.

As mentioned, Worrell tried to relate the reserve
holding behavior of the authorities to the structure of
the whole economy. But do those four variables represent
the structure of the whole economy? We believe they do
not. There are other important variables that Worrell
failed to include. For example, there is no doubt about
the positive relation between the reserve holdings of a
country and the level of imports. If one is talking about
the structure of an entire economy, the macro model of
that economy, which includes many variables, should be
considered.

Frenkel (1978) has analyzed the role of international
reserves under a regime of pegged exchange rates and under
a regime of managed float. The model he used looks exactly
like what we have seen so far. The level of reserves is
related to three main variables: imports (IM), import-
GNP ratio (m), and a measure of variability of balance of
.mayment (6). The functional form of the demand function

is assumed to be:

ln R = a0 + a1 1nd + a2 ln IM + a3 1n m + u

The cross-sectional ordinary least-squares estimates of
the demand for reserves by develOped and less developed

countries was obtained for each year from 1963 to 1975, and

26

the results were satisfactory.

In the second step, estimates of demand for inter-
national reserves were obtained by pooling time series and
cross-section data. In order to examine the effect of the
move to a regime of flexible exchange rates, the sample
was divided into two periods: the pegged exchange rate
period (1963-1972) and the flexible exchange rate period
(1973-1975). This division was justified using the method
proposed by Quandt (1958, 1960) to analyze switching
regressions.

The coefficients of the cross-sectional equations
remained stable within each of the periods. Comparing
developed and less developed countries, it was seen that
in both periods the coefficients of the constant term,
the variability measure.and the average propensity to
import were higher for the developed countries, while the
coefficients cf imports were lower. All of these
differences were significant at the 95 percent confidence
level for the period of pegged exchange rates; for the l
latter period, however, the two groups differed signifi-
cantly only in their constant term. It was also concluded
that the demand for reserves by less developed countries
is less sensitive to variability measures than the demand
by the developed countries.

In addition, a Chow test was applied; it led to
the conclusion that the developed and less developed
countries manifest different behavior concerning the holdings

of international reserves.

27

Both the Quandt method and the Chow test led to
rejection of the hypothesis that regression coefficients
remained stable before and after 1972. The overall
inference is that the system had changed by the end of
1972.

Heller and Khan (1978) have examined the demand for
international reserves during the period when the inter-
national monetary system shifted from par value arrangements
to greater exchange rate flexibility. Their analysis focused
on the question of whether there was a shift in demand
functions in 1973, and if so, in which direction. Their
work is similar to that of Frenkel (1978), but with
different country groupings. Following the literature on
the subject, they used the standard model in which demand
for international reserves (RD) is related to three
variables: (a) the ratio of imports to domestic income
(é); (b) the level of imports (I); and (c) a measure of
variability of balance of payment (62). Their estimating

equation for reserves is specified in log-linear terms as:

2

log (l) + a log I + a log 6 ti-u

(18) log Rt = a + a1 y t 2 t 3

0 t

Their definition of 62 differs from what we have seen so
far. They define it as the variability of reserves and
employ a two-step procedure to calculate it. In the first
stage, they use the time-series methodology of Box and
Jenkins (1970) and estimate autoregressive integrated moving

average (ARIMA) models for reserves. More specifically,

28

after transforming the level of reserves, R , into a

t

stationary series, R*t, where R*t = log Rt - log R

they fit the ARIMA model described as:

t-l’

(19) ¢(L)R*t = 6(L)v.t

where ¢(L) and 0(L) are polynomial functions of the lag

operator, L, and v is serially uncorrelated with noise

t
errors. The results, Gt’ are obtained after estimating
equation (19), and their squares values, 312, are
interpreted as a measure of the variability of reserves.
In the second stage, they estimate equation (18)

with a polynomial lag function imposed on Vt2'

I
(20) log Rt = a + a1 log (§) + a log It

0 t 2
1 *2
+ a d. log v . + u
3 1:0 1 t-i t

the Oi are the weights attached to the current a lagged
values of $2t, and k represents the number of lagged
periods to be considered.1

The model was tested for six different country
groups: the world; the world, excluding oil exporting
countries; the world, excluding oil exporting countries and
the United States; industrial countries; industrial
countries, excluding the United States; and the less
developed areas, using quarterly data over the period

1969—1976.

29

In considering their results, an important point must
be made. As was observed before, all studies so far have
obtained a positive al (elasticity with respect to import-
GNP ratio). Even Kelly (1970), who argued that we would
expect al to be negative, got a positive coefficient. Heller
and Khan came up with a negative al for all six groups.

This supports Kelly's position and also implies a more
"Keynesian" role for the import-GNP variable.

Heller (1966) has described the argument for the
negative relation between reserves and marginal propensity
to import. He concluded that, for a given change in foreign
demand,

Assume that foreign demand for the countries
exports falls off, creating a balance of payments
deficit....The amount of dampening necessary to
bring about balance of payments equilibrium will
depend mainly on the prOpensity to import....It
is evident that the dampening required in the
closed economy is larger than the dampening
required in the open economy and inversely
proportional to the prOpensity to import....It is
possible to avoid the adjustment to an external
disequilibrium if the monetary authorities of the
country have resources at its disposal which can
be used to finance the external disequilibrium,
thus rendering adjustment unnecessary. The
resources which are at the disposal of the
monetary authority and which can be used for such
contingencies are the liquid international
reserves....An increase of m would decrease the
level optimal reserves. This is to be expected,
as an increase in the propensity to import will
lower the benefits per unit of reserves used to
finance the imbalance as measured in incomes
which would have to be foregone otherwise.2

The positive coefficient for import-GNP ratio.may have
5

many explanations. First, it is not representative 01

the marginal propensity to import, and it represents the

30

openness of the economy, that is, the larger the import-GNP
ratio, the more open is the economy. Consequently, the more
reserves are needed to finance any external disequilibrium.
Second, the marginal propensity to import has a positive
influence on reserves because there are income fluctuations
due to internal exogenous shifts in demand as well as external
shifts.

The result of Heller and Khan's stability test
indicates that there was clearly a shift in the demand for
international reserves by industrial countries when the
move to a floating rate system occurred. However, the
change was not sudden and appears to have taken place
toward the end of 1973, rather than in the earlier part
of the year, when the actual change occurred. Insofar as
non-oil developing countries are concerned, the move toward
more flexibility in exchange rates did not appear to
affect their behavior significantly. This group seems to
have had a shift in demand function in the period 1971-1972
rather than at the inception of managed floating. That
they did not change their basic behavior pattern can
perhaps be attributed to the fact that, for most of them,
the exchange rate regime did not change, as they continued
generally to follow a policy of pegging their currency to
another major currency.

Heller and Khan found that, after the structural
change in 1973, the function explaining reserve behavior

continued to be stable in the period of managed floating.

31

This was the case for both industrial and developing
countries.

Finally, it was observed that there was some
empirical evidence supporting the hypothesis that, for
industrial countries, the demand for reserves should be
reduced as exchange rates become more flexible. Surprisingly,
the reverse seems to hold true for non-oil develoPing
countries. Their holdings of reserves during the floating
rate period have tended to be higher than the levels that
would have been implied by their behavior during the fixed
rate period.

Heller and Khan believe that the greater degree of
uncertainty and variability in these countries' payments
balances resulting from being pegged to a floating currency
may well be the explanation.

Two articles, one by Frenkel (1978) and the other by
Heller and Khan (1978), have supported the idea that the
demand for international reserves will be affected if there
is a move from a pegged exchange rate system to a managed
floating system.

Using new and revised data, (1963-1977) Frenkel
(1980) has extended his 1978 analysis to cover the period
up to 1977. The analysis of this new and revised data base
has altered the numerical values of the parameter estimates
(particularly for the less developed countties) but has not
altered the conclusion reached originally, namely, the

system underwent a structural change by the end of 1972.

32

He found that during the pegged exchange rate period (1963-
1972) the two groups of countries differed significantly in
terms of their response to the exogenous variables. These
differences have diminished significantly during the more
recent period of the managed float.

In an unpublished paper, Bilson and Frenkel (1979)
have developed a dynamic adjustment model of the demand for
international reserves. They have shown that countries'
behavior with respect to their holdings of international
reserves can be described in terms of a small number of
variables. They have found evidence that deviations of
actual from desired reserve holdings triggers a process of

adjustment that is fairly rapid.
2.5 - Reserves and Speed Of Adjustment

A typical.model used to estimate the speed of
adjustment has been the partial adjustment model, that is,
countries adjust their current stock of reserves in
proportion to the discrepancy between actual and desired

reserves. The partial adjustment model can be written as:

(21) R - R = 7(R*t - R ) + w

t t-l t-l

where Rt and R* denote, respectively, actual and desired

t
stocks of reserves at period t, y denotes the speed of

adjustment, and wt denotes an error term.

Since the desired level of reserves is unobservable,

33

the partial adjustment model must be supplemented by an
hypothesis concerning the determinants of the desired
stock. In the Bilson and Frenkel model, the desired
reserves function pertaining to country n for period t

takes the following form:

x. =
(22) ln R n 80 4' 81 In (Sn

t +821nynt+831nm +u

t nt nt

where 6, y, and m are defined to be the variability
measure, the value of GNP, and average propensity to import,
respectively. Bilson and Frenkel have taken account of
country-specific factors (which affect the demand for
reserves) by employing the error component model pioneered
by Balestra and Nerlove (1966). In that model, the error
term unt in equation (22) is decomposed into two independent
components: un, specific to the country, fixed through
time, and independent of other countries' specific

components; and e serially uncorrelated. Formally, u

nt’

can be expressed as:

nt

(23) unt = un + ent

Equation (22) can be rewritten as:

* :
(2”) 1n R n BO+'811J15n

t +821nynt+831nm +u +e

t nt n nt

Substituting equation (29) in the dynamic adjustment equation

(21) and after some manipulation, they got:

3H

(25) ln R = B + 8 1n 5n + 82 In ynt + 83 ln m

nt 0 l t nt
l-y l
- __. + _
Y A 1n Rnt + un Y Vnt
where A 1n Rnt = 1n Rnt - ln Rnt-l and vnt = Yent + wnt'

Equation (25) has been rewritten in terms of country
averages. Using "n" to denote the average over time of a

series pertaining to countryri ,they obtain

0

(26) 1n Rn0 = 80 + 81 ln 6n0 + 82 1n yn0
+ 83 ln m - i3111 1n R + u + l»v
n y n n y n

Equation (26) was estimated for a sample of 22 developed
countties and for a sample of 32 less developed countries
over the period 1969—1972. During these years the inter-
national monetary system was characterized as a pegged
exchange rate regime. Since the estimates showed that the
coefficient of the average growth rate was insignificant,

it was removed from the estimating equation. Even so,

the residual from the cross-sectional equation (26) was used
as an estimate of the country-specific factor in the desired
reserves function, which is:

A

2" = A A A A
(27) In R nt BO+-811J1Ont+-B21J1ynt4- BBJJlmnt + un

The estimated coefficients from (26) were used to generate

the desired reserves, R* from equation (27), then

nt’

incorporated into the partial adjustment model by writing

35
the adjustment equation as

(28) 1n R = a + a

* + +
nt 0 ln R nt a In R v

1 2 nt-l nt

where the country specific factor, un, has been incorporated
into the definition of desired reserves. In equation (28),

a provides an estimate of the speed of adjustment. The

l
estimated value of the speed of adjustment is .591 for
developed countries, .935 for less developed countries.
Bilson and Frenkel also estimated the speed of
adjustment without including the country-specific factor.

In this case, we need to substitute equation (22) in (21)

and estimate the following equation:

(29) ln R = y8

nt +Yelln 6n

0 t ”8.2 1" ynt +783 1“ mnt

+ (1-Y) 1n Rnt-l + vn

Equation (29) was estimated for the same countries and
same time period (1969-1972), and the estimated value of
Y happens to be low. Bilson and Frenkel concluded that
including the country-specific factor provides higher
estimates of the speed of adjustment.

They also discussed the determinants of the speed
of adjustment, and it was shown that the parameter is not
a fixed one, but rather a stable function of a limited
number of variables. They extended their analysis to the
post-Bretton-Woods period of managed float, and the result

was that the move to a new exchange rate regime was

36

associated with changes in the speed of adjustment by which
countries eliminate divergencies between desired and actual

levels of reserves.

2.6 - ConcludingRemarks

 

In most of these studies, there is general agreement
that imports, average propensity to import, and the measure
of balance of payment variability are the three major
determinants in the reserve demand functions. These
variables always had significant coefficients and the
expected signs. In a cross-section study, the use of a
measure of balance of payment variability has been a
tradition, even if there are some limitations. The.main
drawback is that actual changes in reserves need not
provide the exact measure of the disturbance since “
countries may use some other policies, Kenin and Yudin
(1968, p. 398), who used this measure are aware of this
possibility and assume thattthe estimate is not affected
by national policies. To what extent this assumption
holds is questionable. It might be true that in a cross-
section study we can ignore the limitation and follow
Heller, who claims "any bias that might actually be
introduced is probably very small and neglibible."3
However, in a time-series study, the effect of national
policies on this variable cannot be ignored.

The second variable most authors agree should be

37

dropped from the reserve demand function is the opportunity
cost of holding reserves. The major reason is that any
proxy that has been used for this variable has shown
insignificant coefficients. Iyoha (1976) was the first to
claim that he had found a significant relation, but we have
discussed the criticism of his work by Hipple (1979) and
Shinkai (1979).

We agree that the Opportunity cost of holding
reserves is not a major independent variable in reserve
demand functions. First, it is impossible to measure the
true opportunity cost of holding reserves. Second, it is
difficult to come up with a proxy for this variable, and
in all the studies reviewed, the opportunity cost had
insignificant coefficients. For these reasons, we will
not include this variable in our demand function.

The third and major issue that the studies agree
on is the implicit assumption that the supply of international
reserves is elastic enough to meet the demand of the countries
for reserves. Emphasis in the literature has been on the
demand for reserves, but it is important to point out that
the supply is also likely to be related, in part, to the
variables that enter the demand function. However, these
variables enter the supply function with opposite signs.

To the extent that the assumption of elastic supply is not
fulfilled, the estimate of the demand functions may embody
a simultaneous-equation bias. However, in a model that

involves both demand and supply, the problem of estimating

38

parameters has special features that are not present when
a model involves only a single relation. We will specify
a supply function and try to solve this simultaniety
problem.

The last topic that must be mentioned is the gold
market. The soaring price of gold in the 19703 has been
one of the most important features of the international
money market. None of the studies reviewed has tried to
look at the effect of gold prices on the demand for inter-
national reserves. We will try to capture this effect.

In the next chapter, an attempt will be made to
build a framework in which the demand for and supply of
international reserves will be taken care of simultaneously.
In that model, we will also take into account the last

problem mentioned above, gold prices.

2.7 - Features of Major Studies

 

Table 2-1 summarizes all the studies reviewed here,
by author and year of publication, in terms of the indepen-
dent variables used and other features as indicated in the

table.

39

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93

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CHAPTER THREE

THE THEORY OF DEMAND FOR AND SUPPLY OF
INTERNATIONAL RESERVES

3.1 Introduction

 

If economists could measure the need for reserves,
they might be able to agree on the right way to predict their
growth rate. Most of the economists who suggest drastic
reform do so because they predict a shortage of international
reserves. Consequently, if we can measure the need for
reserves ar,more precisely, the amount of international money
that countries would like to hold, then we might be able to
answer or give some suggestions about the proper growth rate.
Quantitative methods may answer important factual questions
pertaining to international liquidity. We may ask, for
example, if national holdings of reserves exhibit any
rational pattern; if they do, we may be able to describe the
national demand for reserves of a "typical" country, then
appraise the distribution of global reserves.

Quantitative approaches to the optimal reserve problem
have been adopted in the literature. This approach concen-
trates on the purely statistical examination of time series

data of international reserves and attempts to assess the

95

96

relative adequacy of reserves by relating present stock to
past performance. Papers of varying degrees of statistical
sophistication by all those who were listed in Table l of
the previous chapter have adopted this approach and shall be
adopted by us. But as mentioned in the previous chapter,
all previous works have assumed the supply of international
reserves is elastic enough to meet the demand, but what if
this is not the case? Even in 1919, the year in which the
gold standard broke down, Triffin suggested that the demand
for reserves was growing faster than the supply could do
unless the United States ran a deficit. This indicates that
the assumption of elastic supply of reserves is not valid.
Especially in econometric studies,vflunione attempts to
estimate the demand side without taking into account the
supply equation, the results embody a simultaneous-equation
bias. Thus, it is our task in this chapter not only to
specify a demand function, but also to write down a supply
function and discuss its determinants.

Most discussions of the adequacy of international
reserves have pointed out the trade-off which exists between
financing a payments deficit by drawing on reserves and
making adjustments within the economy to reduce the deficit.1
The primary function of reserves is to serve as a buffer
stock which finances temporary discrepancies between a
country's international payments and receipts, thereby making
it unnecessary for a country to adjust completely to every

l>alance of payments disturbance. Nevertheless, most countries

97

can be expected to reconstitute reserves which have been
lost in the course of financing a payments deficit. This
implies that any given reserve movement has two components;
one which represents adjustments to present and past
balance of payments disturbances, and one which represents
the true disturbance. In the last section of this chapter,
a modified partial adjustment model will be specified, and
we will try to estimate the speed of adjustment.

Since our study covers the period of managed
floating system, one might ask whether in the period of
free float there is any need to hold international reserves,
since exchange rate variations will eliminate any
imbalances. Several attempted explanations for the
absence of a decline in reserve use were contained in the

Fund's Annual Report, 1979. These, briefly, are as follows:

1. Exchange rates are managed in the present
system rather than being allowed to float
freely without intervention.

II. There are motives for holding reserves other
than to finance payments imbalances, and
these motives, such as the need to use reserves
as a basis for foreign borrowing, may not have
changed.

111. Countries that were floating at that time may
well have been anxious to return to fixed rates

and accordingly maintained an appropriate level

98

of reserves.
IV. The present system is one in which the currencies
of the majority of countries are pegged to a
single currency or a composite of currencies. In
such a framework, it is possible that countries
pegged to a single floating currency would increase
reserve use because of the added variability in
payments balances caused by the movement of
exchange rates between third currencies and the
intervention currency. While the Annual Report of
1979 was concerned with the behavior of reserves
in the period 1973-1979, some of these arguments
continue to be relevant. In particular, the
last argument can be viewed as applicable to most
non-oil developing countries even now.
Also, Williamson (1979) has argued that the standard
view rests on the key assumption that demand and supply
curves for foreign exchange are invariant with respect to the
exchange rate system, and this assumption may not be
warranted. In addition, destabilizing capital flows may
result in an increased use of reserves in the move from a par
value system, and if there is a secular rise in these
destabilizing flows, the use of reserves may increase over
time.2
Recent SDR allocation in late 1979, early 1980, and

1981 (forthcoming) is also an indication of need for reserves

and supports the general idea that in the period of managed

99

float countries still want to hold reserves.

Heller and Khan (1978) and Frankel (1979) statis—
tically tested and concluded that there has been structural
change in the system with resPect to demand for reserves
which occurred in 1973. But in his recent work, using
revised and correct data,Frenkel (1980) accepts the fact that
the change was not that drastic:

"Finally it should be noted that even though,

as a statistical matter, the system underwent a

structural change, the extent of the change has

not been as drastic as one might have expected.

In fact, forecasting reserve holdings during the

period 1973-1977, yield extremely good predictions."

Frankel (1980), p. 301.

We conclude that there is a general agreement that demand
for reserves will depend on what kind of exchange rate
system is in existence. If all countries in the world were
in the system of free float, maybe there would not be any
need for reserves. However, for reasons mentioned above,

that is not the case for our period of study (1972-1977),

in which the gold price has been soaring.

3.2 The Demand for International Reserves

 

In this section an attempt is made to ascertain the
determinants of the demand for international reserves by the
monetary authorities of the countries.studied. An important
aim of this section is to improve on the specifications of
the demand for reserve functions that exist in the

literature.

50

Reserves and imports - The relationship between
reserves and imports has been highly popularized in
discussions of reserve adequacy. The most common variant of
this approach to the demand for reserves is nothing but an
application of the strict quantity theory to the inter-
national payments sphere, with the level of imports taking
the place of transaction, T. The question that remains is
whether the growth of trade (measured by the growth of
imports) will raise the demand for reserves. There really
cannot be serious doubt that it will. Most of the models
that we reviewed in Chapter Two agree that reserve demand
should grow in line with imports. Implicit in much of the
discussion (and a property of the strict quantity theory) is
the assertion that reserves should grow proportionally with
the level of imports (that is, the demand for reserves with
respect to the level of imports is unit elastic). This, of
course, need not be the case. Olivera (1969) derived a
square root laWS,analogous to the Baumol-Tobin theorem on
the demand for money, which stated that the demand for
reserves would grow in proportion to the square root of
trade, implyingaUIelasticity of 0.5. 19fitswas tested by Officer
(1976) and an affirmative answer'obtained, that is, the
elasticity of demand for reserves with respect to imports is
between 1/2 and 1.

It has been generally accepted that countries hold
international reserves in order to finance their imbalances

(deficits). Allowing for the fact that a proportional

51

increase in trade (approximated by the size of imports, M)
may also increase the deficit of a country, we would expect
a positive relation between reserves held by that country
(in order to finance the increased deficit) and its level of
imports. So we conclude that the first determinant of
demand for reserves in our model is the level of imports, M,
and we would expect the relation to be a positive one:

that is, more reserves will be demanded, the higher is the

level of imports.

Reserves and propensity to import - The second

 

determinant of the demand for international reserves is
propensity to import. The rationale for the use of this
variable stems from an application of the Keynesian "price-
less" model of the foreign trade multiplier.

Let us consider the simplest Keynesian version of a
small economy with fixed prices of commodities; further-
more,let us set the prices to equal unity. In equilibrium

aggregate demand must be equal to aggregate supply,that is:

Y = C + I + G + x - M (l)

where Y = level of total output;

C = consumption expenditure,which depends on the
level of output in the economy. Let us assume
the following consumption function:

C = C + cY where %% = c is marginal
propensity to consume;

I = investment expenditure, independent of output

level (I);

a .o
:v

_.. I.

C»
.. e

52

G = government expenditure (G);

X = level of_exports which is determined by foreign
demand (X);

M = level of imports which depends on output level.
Let us assume that the import-function takes
the following form:

M = M'+ mY where %% = m is marginal
propensity to import.
Let us now substitute all the above mentioned functions in

equation (1); we get:

Y=E+cY+T+§+R~<fi+mY> (2)
Solving equation (2) for Y yields the following:

- 1 — — — — —
Y-l_c+m(C+I+G+X-M) <3)

 

The balance of trade could be expressed as:
T=x-M='>'<-H-my (u)

and substituting (3) into (9) we get:

-—_—_ m - — — —_—
T-X M l_¢+m<c+1+0+x M) (5)

 

Assume there is a decline in export earnings. The resulting
deficit in the balance of trade due to a given reduction in

export earning is:

 

 

 

92:1.- m - l-C
(13(- l+c+m-l-c+m
or
9g: : s i n: ‘where l - c = s (6)
dX

From equation (6), it is obvious that the larger is marginal

propensity to import, the smaller becomes deficit and

53

consequently the smaller will be the demand for reserves in
order to finance the deficit.3 This implies an inverse
relation between the optimal holdings of reserves and the
marginal propensity to import.”

In the absence of dataon the marginal propensity to
import, earlier empirical studies employed instead the
ratio of imports to income, that is, the average propensity
(typically referred to as the degree of "openness" of the
economy). The coefficient of the average propensitytx>import
frequently appeared with the "wrong" (positive) sign when
used to estimate the demand for reserves, except in Heller
and Khan (1978).' This positive coefficient led many authors
to argue that average propensity to import should not be
interpreted as a proxy for marginal propensity to import but
rather as a proxy for "openness," thus measuring the extent
to which the economy is vulnerable to external disruptions.
Accordingly, the positive coefficient on the average
propensity reflects the fact that the demand for reserves is
a positive function of external vulnerability.

Frenkel (1979-A) has investigated the relation
between reserve holdings and the average propensitytxnimport,
using an alternative theory of the adjustment mechanism.

The basic characteristic of his theory is its emphasis on
the role of relative prices and the price level. His
analysis is confined to the long-run equilibriumcfi’astation-
ary, fully employed economy. An affirmative answer was

concluded from this theory: demand for reserves is

59

positively related to the average propensity to import.
Frenkel (1979-A) assumed a fully employed economy

in long-run equilibrium (that is, the long-run stock

demand for assets is satisfied and thus savings are zero,

and income equals expenditures). Furthermore,1u3assumed a

two-commodity economy which is specialized in the production

of first commodity. Let the output of the fully employed

economy be:
Ql = Q1 (7)
The demand functions for the two goods are homogeneous of

degree zero in money prices (P1,P2) and money income (P101)

and thus can be written as:

C1 = Cl(q, qu) (8)
C2 = C2(q,qu) (9)
Pl
where q E F. represents the terms of trade. It is also
2

assumed that the price of importables (P2) is exogenously
given by the rest of the world. The terms of trade, however,
are not assumed to be given since the price of exportables
(P1) is determined endogenously.

Long-run equilibrium requires that:

PC +PC = P6

1 1 2 2 1 (10)

Dividing both sides of (10) by P yields:

2

qu + C2 = qu (ll)

55

Similar relationships hold in the foreign country. In

particular, foreign demand for domestic output is given by:

ac f
f _ f f 1
Cl - Cl (q, (I ), E?— > 0 (12)

where (f) denotes the foreign country and of is a shift
parameter of foreign demand.

The stock demand for cash balanges depends on the
price level (P) and on real income (3%31). Let us assume

this demand function is linearly homogeneous in all prices:

P6
Md = PL (-%rl) (13)
The consumer price level (P) is a linear homogeneous function
of the prices of the two goods with elasticities that are
equal to the relative shares of expenditures on these gOOdS

in total expenditures, such that

P P
LP o —J--- = — ° ——-—3P . —.2_ - —
l
_} PiCi

where mi = -:— (i = 1,2) is the average propensity to

P Q

l l _ _
consume the ith good, and ml + m2 = 1.

Furthermore, assume the exchange rate is pegged.
.Accordingly, the stock supply of cash balances (MS) is propor-
‘tional to the holdings of international reserves (R). For

simplicity assume:
M = R (15)

The long-run equilibrium conditions are: (a) the demand for

56

domestic output equals its supply; and (b) the existing
stock of cash balances equals the desired stock. Using

equations (7) - (15) these conditions can be written as:

 

 

_ f f _
Cl(q, qu) + Cl (q, a ) - Ql = 0 (16)
P '6
PL (JP-l) - R = 0 (17)
From equatign (11) it is seen that a given change in foreign
8C
demand ( 1f)daf affects the price of exportables (the terms
8a
of trade) according to:
f
-—E- = _} _ f (18)
' - _
do (BCl/aq) + (1 ml) ml/q Q1 + 3Cl /aq

f
8C1 3C

where (153), and é—g-ae) are, respectively, the slopes of the
domestic and foreign excess demand for exportables. The
term in the denominator of equation (18) is the standard
Marshall-Lerner condition which has to be negative for
stability. Thus, assuming stability, —9%r > 0

A given improvement in terms ofcfiiade raises real

income and creates excess demand for money that [from (17)]

is equal to:

R[ml + nL(l-ml)1/q _
P Q
>0 andY=—lP—l.

3|?"
rflm

where ”L

nL is the elasticity of the demand for real cash balances
with respect to real income. Therefore, the given change in

foreign demand will affect the holdings of international

57

reserves according to:

 

 

f
1 3C1
' ’ f
.%.93? = q 3“ ____ f > 0 (19)
do 8Cl , lel 8Cl

 

If openness is defined in terms of the share of imports in
GNP (5?), the effect of mg on reserve holdings can be
ascertained by differentiating equation (19) with respect to
El = (l - 5,). It can be verified that the condition for
a positive association between reserve holdings and openness
is that:
> ‘3C1/,Q)' + aclf/aq + ($}) 51
(acl/aq)' + aclf/aq

”L (20)
Since the denominators or denominator of the right-hand side
of (20) are negative (from the Marshall-Lerner condition),
and since ”L > 0, it is clear that if the numerator of (20)
is positive, the conditions must be satisfied. If, however,
the numerator of the right-hand side of (20) is negative,
a sufficient condition for a positive association between
Openness and reserves is that ”L 3 l (for ml > 0). Empirical
studies on the demand for money suggest that, in general,
"L does not fall short of unity and accordingly imply that
condition (20) is satisfied; thus, reserve holdings depend
positively on the average propensity to import.

In any case, the expected sign between reserve holding

behavior of a country and average prOpensity to import

58

could be either negative, supporting the "priceless"
Keynesian model, or positive, supporting the price-adjustment
model of Frenkel. As we saw in the previous chapter,
empirical results have supported both.

Reserves and the Price of Golds- The third determinant

 

of the demand for international reserves in our model is the
gold price. Between 1999, when the U.S. Treasury's gold
holdings peaked at $29 billion, and 1960, U.S. gold holdings
dedlined by $8 billion. This redistribution of gold among
the world's central banks was deemed necessary to provide the
financial basis for the postwar growth in world trade. But
by 1960 there was growing recognition that the total supply
of gold available for central banks as a group was too small
to meet their demand. By 1965 the private demand for gold
had increased above the level of production; central banks
sold $50 million of gold from their reserves to hold the
price at $35. Uncertainties about the future sterling parity
led to a surge in the private demand for gold. In 1967
central banks sold $1.6 billion of gold to private parties to
prevent the price from rising above $35. And in the first
ten weeks of 1968, sales to private parties reached $700
billion. These flows of gold from central banks to the
private parties led the Nixon administration to close the
so-called "gold window."

The suspension of gold transactions by the U.S.
Treasury in 1971 reflected a shortage of gold which has

persisted for most of the following;years. The supply of gold

59

available to central banks has been less than the desired
level because, while production has grown slowly, the private
demand for gold as a commodity - for use in industry and
especially for hoarding and speculation -' has grown rapidly.
Thus, if private demand for gold increases, less gold is
available to central banks. Similarly, if the central bank
demand for gold increases - that is, if the banks agree to
pay a higher price for gold - they will bid gold away from
private users.

Two kinds of measures might have resolvedtflmzshortage;
either the private demand for gold might have been reduced
by lowering the commodity price level, or the supply might
have been increased by raising the monetary price of gold.
Since the scope for reducing the private demand was small,
this led some economists to suggest the latter course:
increasing the gold price in order to reduce not only the
shortage of gold, but also the shortage of international
reserves as a whole.

Some other economists have argued that an increase in
the gold price would be inflationary; private parties would
spend more as a result of their revaluation gains. This
concern might be valid if gold were still used as a domestic
money, but with gold's monetary role limited to transactions
among central banks and with private gold holdings such a
small fraction of private wealth, it has much less force now.
Some central banks might follow a somewhat more expansive

policy as a result of their revaluation gains. Any increase

60

in commodity price levels from an increase in the monetary
price of gold would be small relative to the increases
resulting from other sources.

Higher gold price not only will stimulate gold
production, but also will reduce the demand for it. Since
the gold component of total reserves of a country will be
revalued, this will make the demand of that country for
international reserves as a whole drop. Consequently, a
negative relation between the reserve holding behavior of

a country and gold price would be expected.

Reserves and Measure cf Balance of Payment Variability -

The need for reserves is obviously related to the
degree of variability in a country's international trans-
actions. All authors adopting a quantity-theory approach to
the demand for reserves have used the level of a country's
imports as an index of the value of transactions to be
financed with reserves. Realizing that reserves are actually
used to finance the difference between payments and receipts,
others have used measures of the variability in this differ-
ence as an indicator of the need for international reserve
assets. For example, Kenen and Yudin (1965) have taken the
variance of the error term of an estimated first-order auto-
regressive scheme as a.measure of the variability in a
country's external account: ARt = pARt-l + Et'

In cross-section studies the use of measure of balance

of payment variability has been a tradition even if there

61

are some limitations. The main limitation of this measure
is that actual changes in reserves need not provide the
exact measure of the disturbance since countries may use
some other policies. Monetary, fiscal, and trade policies,
such as tariffs and quotas, are often used by countries for
the purpose of reducing the impact of these disturbances on
their reserves. If these policies are successful, then the
observed fluctuations in reserves will be reduced. Kenen
and Yudin (1965, p. 296), who used this measure, are aware
of this possibility and assume that the estimate is not
affected by national policies. To what extent this
assumption holds is questionable. It might be true that

in a cross-section study we can ignore that limitation and
follow Heller, who claims "any bias that might actually be
introduced is probably very small and negligible" (1966, p.
310). However, in a time-series study (or pooled cross-
section and time-series) the effect of national policies

on this variable cannot be ignored, and since our study is
one of pooled cross-section, time-series we will not include

this variable in our model.

Reserves and Opportunity Cost of Holding Reserves -

Liquid international reserves held by the monetary
authorities arepei¢:of the total capital resourcescd a country.
'Phese reserve assets could have been invested productively.

The differential betweentflmasocial yieldcxlcapital invested

and the yield on liquid international reserves is the

62

appropriate concept of the opportunity cost of holding liquid
international reserves. The measurement of the proper
opportunity cost is complicated, and as our table at the end
of the previous chapter indicates, different studies have
used different proxies for this variable. For example,

Kenen and Yudin (1965) have used per capita income; Courchene
and Youssef (1967), long run interest rates; Kelly (1970),
per capita income; Clark (1970), per capita income; Flanders
(1971), per capita income; Iyoha (1976), interest rate on
foreign exchange holdings. All of these studies found an
insignificant relationship between reserves and the opportunity
cost variable. Iyoha (1976) was the first one who claimed

a significant relation between reserve and opportunity cost,
but he misinterpreted his results. He makes no allowance

in his regression for compositional differences in the
reserve stock of different countries. Not all components of
reserves of a country can earn interest. Another weakness

of Iyoha's analysis is his selection of a statistical series
for the yield rate in each country, which is an internal
yield rate. This is incorrect since the only meaningful
yield rate for invested foreign exchange reserves must be an
external yield rate.

Therefore, we assume that the opportunity cost of
liolding reserves is not a major independent variable in
reserve demand functions. First, it is impossible to measure
the true opportunity cost of holding reserves. Second,

it it difficult to come up with a good proxy for it,

63

and in all studies reviewed the opportunity cost had an
insignificant coefficient. For those reasons we will not
include this variable in our demand functions.

There are other determinants that have been used in
specific studies. Since no significant relation has been
found, we will not include them in our study. They are, for
example, money supply or change in money supply, used by
Kenen and Yudin (1965), Courchene and Youssef (1967), and
Worrell (1976). Expected export earnings were used by
Iyoha (1976) and export earnings by Worrell (1976).

Let us now put all determinants of the reserve demand

function together:

d 2

R = f(M, 5 , r, MS, X)

“(J
00

where M = imports, = average propensity to import,

'<HZ ‘<HZ

Pg = gold price ($), 62 = measure of variability of balance

of payment, r = opportunity cost of holding reserves,

.7.
u

money supply, and X = export earning, with fl > 0,

AV

0, f3 < 0, f9 < 0, f5 > 0, f6 < 0.
But for reasons which were explained above, we will
exclude several determinants in our demand function. The

demand function which we will utilize is:

d M
R = P M, _, P )
( y g

69

3.3 The Supply of International Reserves

In this section we will try to assert the determinant
of the supply of international reserves and specify a supply
function.

Supply of reserves consists of three components:

I. Gold

II. Convertible foreign exchange (mainly dollars)

III. Special Drawing Rights (SDR's)

Reserves and Gold - The fact that a high price of

 

gold will stimulate gold production is no surprise. A glance
through Table 3.1 and the following estimated relation
between gold flows and dollar price of gold supports the

idea that there exists a positive relation between these two
variables.

The positive and almost significant coefficient of
1.59 supports our claim. An important question which is
related to our analysis is: will there be a contribution
to official gold stocks (and consequently to official
reserves) due to the higher price of gold?

Table 3.1 again shows that the higher market price of
gold (relative to official price of gold) prompts the central
authority to sell gold. Assuming that they have sold gold
in exchange for convertible foreign currencies (mainly
dollars), than it is safe to conclude an affirmative answer
to our question: the higher market price of gold will

make the official supply of reserves increase. We conclude

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memmnoosm ovm>woe we: 0 e22 moors

mNHN.o m

m

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0m mm.H + mH.>mHH mzz

"cowwmamo Umpmfiwpmo mafizoaaom may smoflmcoo .m>w#ooamnoe cw memo omens one 0%

common cw

 

 

65

 

 

mmm mm.:mH mb.:mH mm.o:H m.mma mm.NHH om.:w mm.m: paow mo wowoa Loaaoa
Hana mmmfi smza HHHH mama moza msmfi mama mmwmzoosm mom>eom umz
mum mum mm m cm w HmH: mm moamm HmHOflwmo

oon wmwcoaaou
OH: Ho: NH: m:H 0mm mum mam :m Lew: moms? poz

cowposoooe OCH:
mmm mmm 5mm mmw mooa HNHH mmHH wmma paooz pwfic3EEouncoz
whoa puma coma mbma :wma mhma mwma Hmma

mbmfilabmfi msofim Ufiow

H.m mqm<H

mach cameo:
zaaaom mo mwcocoeaou

66

that a positive relation between gold price and supply of

international reserves would be expected.

Reserve and Convertible Foreign Exchange (DOllars) -

 

The other reserve component is foreign exchange, which
consists principally of dollars. We can distinguish two
theories about the mechanism governing the supply of dollar
reserves. The traditional theory, expounded by Triffin
(1960) and repeated by him and many others on innumerable
subsequent occasions, treats the supply of dollars as
determined by the U.S. deficit. The deficit is the result
of complex factors, such as demand-management policies
(monetary or fiscal) in the United States and the rest of
the world and historical relative cost levels. .This is a
supply-oriented theory of the supply of dollar reserves.

The second theory is, in contrast, demand oriented.
As Williamson (1973) argues, "the theory claims that the
United States deficit is primarily a residual which is
determined by the reserve-accumulation desires of the rest
of the world; any American effort to reduce the deficit
would be countered by adjustment policies on the part of
other countries designed to reestablish their desired rate
of reserve growth." The supply-oriented theory emphasizes
the dependence of the U.S. deficit on U.S. actions, and
the demand-oriented theory emphasizes the dependence of
the U.S. deficit on the policy of the rest of the world.

There is no empirical result showing which theory is

67

better. Williamson (1971) argued, on the basis of a
casual inspection of the time series on the U.S. deficit,
that there is every sign of its being supply determined
in the short run, but conceded that it was probably
influenced by the desire for reserves in the long run. For
our purpose, there is no need to distinguish which.theory
is better. The fact is that the dollar component of
international reserves is affected by the size of the U.S.
deficit. Even if the above discussion applies for the
period of the par-value system, for reasons cited in the
introductory part of this.chapter, we still believe that the
deficit of the reserve-currency countries, and mainly the
United States, will contribute to the bulk of international
reserves. This is the case whether it is caused by the
excess demand Of other nations for international reserves,
or by an excess supply of dollars due to U.S. unwillingness
to eliminate its deficit.

The U.S. balance of payment includes two major
accounts: the capital account and the current account.
The capital account will be in deficit if American
investment overseas exceed that of foreigners in the United
States. An econometric study by Bell led to the general
conclusion that "shifts in the flow of private capital,
in particular in U.S. private capital flowing overseas,
have been a major cause of United States deteriorating
balance of payments position since 1956."

What makes American investors invest overseas

68

(especially in industrialized countries) or foreigners invest
in the United States? We assume it is the real rate of
return on investment. Whenever.this rate is higher in the
rest of the world compared to the United States, then capital
outflow will take place, and that will lead to a growing
U.S. deficit and, consequently, to the supply of dollars (and
the supply of international reserves as a whole will grow).
In contrast, if the rate of return on investment is higher
in the United States compared to that of the rest of the
world, then capital inflow will take place, which will result
in a surplus in U.S. balance of payment. That will reduce
the supply of dollars and, consequently, the total supply of
international reserves will go down. We can conclude that it
is the differential rate of return on investment between the
United States and the rest of the world which will cause the
capital account and,consequently, the U.S.deficit'mofluctuate.
Another part of the U.S. deficit, as mentioned above,
is due to current accounts, which include the exports and
imports of goods and services plus private remittances and
government grants. The last items, that is, private
remittances and government grants, are assumed to be
insensitive to any economic variable. They are controlled
by private parties and government, and since they are the
minor items in current accounts, we will concentrate on
exports and imports of goods and services. The question is,
what will cause the U.S. current accounts to fluctuate?

We will assume it is the differential price level between

69

the United States and the rest of the world that gives
rise to the fluctuating U.S. deficit. If the prices are
higher in the United States than they are in the rest of
the world, then the United States will export less and
import more, and this will result in deficit. If the U.S.
price level happens to be less than that of the rest of
the world, then the opposite will be the case. It is also
evident that the imports of any country are positively
related to its real output level. So, if the U.S. economy
is growing faster than the rest of the world, then the
United States will import more, its deficit will increase,
and the supply of reserves will go up.

It is worth allocating some space at this point
to the monetarist veiw of this issue. The balance of
payments is viewed by the monetarists as essentially a
monetary phenomenon. Payments imbalances are rooted in
the relationship between the demand for and the supply of
money. The demand for nominal money balances (Md) is a
stable function of the price level (P., level of real income
(Y), and of the interest rate (i). Md==f(P,Y,i), with
fl' > 0, f2' > 0, and f3‘ < 0. Money supply (M8), for which
demand is a stable function, is a constant multiple (k) of
the monetary base. In turn that base has two components:
domestic credit created by the monetary authorities (D) and
an international component (R). In notational form,

M8 = k[D + R], where k is the money multiplier.

'5‘.-

me...»

A--\
sum.
.

A‘vg
Fl 2
vs...»

:I

A
In..-

70

A surplus or deficit in the balance of payments
reflects stock disequilibrium between demand for and supply
of money. A surplus on the basis of "official reserve
transactions" occurs when demand for money balances exceeds
the money stock. If the excess demand for money is not
satisfied from domestic sources, such as by an increase in
domestic money supply, funds will be attracted from abroad to
satisfy it. And such an inflow can be generated through a
surplus on commodity trade or on the service account; direct
investment for foreign companies; or an attraction of private
long-term or short-term portfolio funds. The precise
composition is immaterial; the important point is that the
excess demand for money stock will generate a balance of
payments surplus. But assuming no intervention by the
monetary authorities to "offset" or "neutralize" the
resulting inflow of funds, such a surplus is necessarily
temporary and self-correcting. It will continue only until
the money stock rises to the level necessary to satisfy the
demand for money balances, that is, until the excess demand
for money is eliminated.7

Alternatively, a balance of payments deficit reflects
an excess supply of money as a stock. When the stock of
money exceeds the demand for money balances, people try to
get rid of the excess supply. They do that by increasing
purchases of foreign goods and services, by investing abroad,
or by transferring short- or long-term portfolio funds

abroad to acquire foreign assets. Thus the deficit on

F 1

c

z.

2»

r.

5

LI

h

a

71

official reserve transactions is viewed as a spillover of the
excess supply of money; its composition is immaterial. Again
the deficit is temporaryand self-correcting.

To recapitulate, the monetary approach to the balance
of payments is concerned strictly with long-run equilibrium
and rests on two central assumptions: (a) the demand for
money is a stable function of a limited set of variables;
and (b) countries do not pursue stabilization or offsetting
policies, either because they cannot stabilize over a long
period or because they do not wish to do so. Although not
central to the approach itself, many of its adherents also
believe that (c) wage-price flexibility fixes output at the
full employment level, at least in the long run, so that
the Keynesian income adjustment mechanism is irrelevant,
and (d) perfect substitution ih consumption (that is, infinite
cross-elasticity of substitution) across countries in both
the product and the capital markets ensures a single price
for each commodity and a single rate of interest. In other
words, the world consists of a single integrated market for
all traded goods and for capital. The "law of one price"
obtains throughout the globe. Consequently, changes in
relative prices are not possible, and the elasticities
approach is rejected. Adherents to assumption (c) and (d)
in addition to (a) and (b) are often called "global

V

monetarists-' In previous pages we concluded that if real

rate of return on investment is higher in the United States

72
compared to that of the rest of the world, there will be an
inflow of funds that will create a balance of payments
surplus in the United States.

Since interest rates could be used as a proxy for
rate of return on investment, if the rate of interest is
higher in the United States compared to that of the rest of
the world, that means the opportunity cost of holding money
is higher in the United States, which in turn brings a
decrease in the demand for money. The resulting excess
supply of money would be dissipated abroad in the form of
an external deficit, which is in disagreement with our
conclusion. With respect to the current account, we
concluded that a differential price level will play a role
in the U.S. deficit, that is, if the U.S. price level is
higher than that of the rest of the world, then the U.S.
balance of payments will deteriorate. Again, monetarists
would disagree with our conclusion. An exogenous rise in the
U.S. price level relative to the price level of the rest of
the world, with real income held constant, increases the
demand for money in accordance with the demand-for-money
function. The portion of this increase not supplied from
domestic sources is reflected in a balance of payments
surplus. As in the case of interest rates, this result
conflicts with what we concluded in our model.

Because of the "law of one price," global monetarists
\Mbuld be in complete disagreement with us also. In their

\d;ew there will be neither differential interest rates nor

73

differnential price levels among the countries.

Reserves and SDRs - Under the system of fixed exchange

 

rates, which existed prior to the early 1970s, the value of
many currencies were fixed in terms of the U.S. dollar.

The value of the dollar, in turn, was fixed in terms of gold.
Since the United States guaranteed other central banks that
dollars could be converted into gold, central banks in
general regarded their dollar as being "as good as gold."
Thus, the dollar was used to supplement gold as international
reserves.

While other central banks were willing to accept
dollars as reserve assets, foreign holdings of dollars could
not expand sufficiently to satisfy foreign central banks'
demand for reserves without a continuous U.S. balance of
payments deficit. The United States could not continue
running such deficits, however, without casting doubt upon
the ability of the U.S. government to maintain the fixed
relative value of dollars.

The elimination of the U.S. deficit and a
corresponding reduction in the growth of international
reserves during the last half of the 19605 led to increasing
uncertainty as to how future increases in the demand for
reserves could be satisfied. It was against this background
that the International Monetary Fund (IMF) member countries
decided to create an international reserve asset. The

supply of, and confidence in, this new asset would be

cpl‘

-151

.nn

"F
V»

‘5‘

 

79

independent of any one country's domestic economic policies.
The new type of reserve asset which was created to
help improve the functioning of the international payments
system was the Special Drawing Right, which came into
existence in 1969. SDRs were created as bookkeeping entries
and were essentially given to all IMF member countries
electing to receive them. These bookkeeping entries were
designed to be transferred directly between central banks
in settlement of balance of payments deficits, with the IMF
guaranteeing their value in terms of a fixed amount of gold.
Actual holders of SDRs have included only the central banks
and treasuries of IMF member countries which have agreed to
accept them, and the IMF itself. Private institutions
(such as cOmmercial banks) and individuals (such as importers

and exporters) cannot hold SDRs.

By allocating SDRs, the world supply of reserves
Could be increased while the U.S. balance of payments
deficit could be corrected. Elimination of the U.S. deficit
would ensure confidence that the prevailing foreign currency
vaer of the dollar could be maintained. The fixed exchange
rate system could thus be preserved, with the SDR becoming
the main reserve asset. ‘

Although the SDR has become generally accepted as an
international reserve asset, the quantitative impact of
SDRS upon total international reserves has been relatively
minOr. Following their initial allocation in 1970, SDRs

c“(35301.1nted for about 3 percent of total international

I 4. In C II I l.‘
n . V. Y. H... J.
A... mu 3. —. .nn
. . A. a! z. "a

”A”.
bye“.

\vr
Ye

 

I...
‘9‘

75

reserves. Following the second and third allocations in
1971 and 1972, SDRs accounted for about 5 percent and 5
percent, respectively, of total world reserves.

Because our estimation results are based on the period
197 32-1977, no further allocations of SDRs have been made
duzrzing that period, and the total amount of SDRs in that
period remained at 9.31 billion, we cannot include
an3r identifiable independent variables in our supply function
vfluiczh accounts for variation in SDR component of supply of
reserves, because there has been no variation in that
component.8

Taking into account all factors that might affect
the: supply of international reserves, we will assume our

supply function takes the following form:

8 - - -
R ' FEPg’ (rU.S. rR.O.W.)’ (Pu.s. PR.O.W.) ’
yU.S. ' yR.O.W.)J
where P = gold price;
:rU S = real rate of return on investment in the United
' ' States;
Tia O W = real rate of return on investment in the rest
° ° ' of the world;
:PU'S = average price level in the United States;
PR_ 0 W = average price level in the rest of the world
° ' ' corrected by exchange rates;
st'S = real GNPNin the United States; and

3U{. O.W. real GNPin.the rest of the world.

76

We can now put together the demand for and supply of

reserve functions:

D M
Demand R = f(M, Y’ Pg)
5 .. - ..
SUPPly R ’ F[Pg’ (50.6. rR.O.w.)’(Pu.s. PR.O.W.)’
(YU.S.-YR.O.W.)J

The identification of the system and its specification and

estimation :results are presented in the next chapter.

3.9 Disequilibrium Model

 

In order to introduce the possibility of disequilibrium
behavior into our model, we use an adjustment equation.
It seems reasonable to assume that the behavior of economic
policy makers is governed, at least implicitly, by the desire
to maintain a given target level of reserves. This stock of
reserves is used to finance discrepancies between payments
and receipts, but eventually steps will be taken to bring the
level of reserves back to the target level. More specifi-
cally, it is assumed that a country wishes to hold an average
stock of reserves, R*, and in each period wishes to eliminate
any gap between R* and the stock of reserves at the beginning

of the period, R by a certain proportion 7. As long as

t-l’

reserves depart from the desired level, the country will
attempt to induce a balance of payment surplus (or deficit),

ARt’ which is given by the following stock-adjustment equation:

AR = y(R* — R+ ) (3.5.1)

t -1

77

Substituting our demand function from'the previous section

for R*, we get:9

AR

M
t Mt4-a2(Y) + a P - R ) (3.5.2)

y(a 4-a
0 t 3 gt t l

l

01"

- M
R - a0 +a Mt4-a2Y(Y) + a

t t t'1

(3.5.3)

Since ARt is specified as adjusting to excess demand, the
gold price adjusts to condition of excess supply.
s

AP = MR - R* ), A > 0 (3.5.9)
gt t t

In this framework an increase in excess supply will lower
the gold price, and conversely for a decrease.

Substituting our supply function from the previous

section in (3.5.9), we get:10
AP =),[R-b-bP -b(r -r )
gt t 0 1 gt 2 U.S. R.O.W. t
’ b3 (Pms. ‘PR.O.w.)t + bu(yu.s. -yR.O.W.)t]
(3.5.5)

Relation (3.5.5) could be summarized and written in the

following form:

- 1
R1: - 130 + (bl+'>'\') Pg ~X Pg 4‘ b2 (1‘ . - l"

_ D -
3 U.S. ‘R.O.W.)t+b9(yU.S. yR.O.W.)

78

Equations (3.5.3) and (3.5.6) together form a simultaneous

equation model which we will estimate in the next chapter.

CHAPTER FOUR
MODEL SPECIFICATION AND ESTIMATION RESULTS

9.1 - Introduction

 

In this chapter, we will try to specify the model
of demand for and supply of reserves in several different
ways. The difficulty and problems of each model will be
pointed out. Then the estimated results for each model
will be presented.

Our concern is to estimate the demand function by
taking into account the endogeneity of the supply side,
too, but no estimates of the supply function will be
presented.

When one attempts to estimate any single equation of
a system of equations, one faces the problem of identifi-
cation. Our model is no exception, and in the next section
we will look at the identification problem and then at the

method of estimation.

9.2 - Identification

 

The basic requirement an economic model must
satisfy is that the number of the variables whose values
are to be explained must be equal to the number of indepen-

dent relationships in the model, i.e., to the number of

V-fr-

:4

80

different pieces of relevant information; otherwise, the
values of these variables would not be determinate. In
addition to the variables whose values are to be explained,
a model may, and usually does, contain variables whose
values are not affected by the mechanism described by the
model. This leads to a distinction between those variables
whose values are to be explained by the model and those
that contribute to providing such an explanation; the

former are called endogenous and the latter exogenous

 

variables.

In order to identify the endogenous and exogenous
variables in our model, we shall write down the demand
and supply equations again. More specifically, we shall
specify them in a linear form, so that we can look at the

identification problem easily:

(Demand) R = a0 + alM + a2 g + a3 Pg + a
(Supply) R = b0 + bl Pg + b2 (rU.S:'rR.O.W.)
+ b3 (PU.S. 'PR.O.w.) + bu (yusf yR.O.W.) + ‘1
Endogenous variables: R and Pg
Exogenous variables: M, %, rU.S.’ rR.O.W.’ PU.S.’ PR.O.W.’

yU.S. ’ yR.O.W.

Since our concern is to estimate the demand function, we

shall only identify that function.

81

The model in matrix form reads thus:

 

 

 

r N
5'0 b0
-1 -1
al 0
r a2 0
- M
l’R’M’y’Pg’(rU.S.- I‘R.O.w.)’ a3 b1 5
+
() b = 0
L(Pu.s.' PR.O.w.)’(-"’U.s.’ yR.O.W.) 2 u
0 b
3
L0 bu
J

In order for the demand function to be identified, two
conditions must hold , order and rank conditions.
(I) The order condition says that the number<xfrestrictions
(i.e., the exogenous variables that are not in the demand
function) in the demand function must be greater than or
equal to the number of equations in the system minus one.
In our case, (3 g 2-1 = 1), so the order condition holds.
(II) The rank cOndition says:

Rank of 68 = G-l,
where B is the matrix of coeffecients in the system, G is
the number of equations, and 6 is the matrix to be formed

based on the number of restrictions on the demand function.

 

 

 

 

 

 

(‘30 b0”
-1 -1
al 0
f l
00000100faz 0 [0 62‘
58 = 0 0 0 0 0 0 1 0 as b1 = 0 b3
00000001 0 b2 0b”
\ L0 b9
(0 52 ‘
Rank of 0 h3 = l, which is the same as G-l = 2-1 = l,
b
L ”J

 

 

the rank condition holds also, and our demand function is

identified.
9.3 - Method of Estimation and Data

The model will be tested for two groups of
countries, developed and less developed, according to the
IMF classification 1 . The major concern is with the
developed countries because they usually hold 60 percent
of the total world reserves. Oil exporting countries,
which are excluded from our study, hold 25 percent. Only
15 percent is held by other countries (the less developed).

Quarterly data have been examined for the period
1972-1977. The initial year was chosen because it was in
1972 that the official dollar price of gold began its
increase; 1977 was the last year for which data were

available

83

The long-run government bond yield has been used as
a proxy for rate of return on investment in each country.
Our study uses pooled time series and cross-section data.
One approach to specifying the behavior of the distur-
bances when dealing with cross-section and time series
data is to combine the assumptions that we frequently
make about cross-sectional observations with those that
are usually made when dealing with time series. The
frequent assumption about cross-sectional observations
(for example, observations on individual countries) is
that the regression disturbances are mutually independent
but heteroskedastic. One usually suspects that the
disturbances in time series data are autoregressive,
although not necessarily heteroskedastic. When dealing
with pooled cross-section and time series observations,
we may combine these assumptions and adopt a cross-
sectionally heteroskedastic and time-wise autoregressive
model. This model is characterized as follows:

2

(9.3.1) E (cit) = Oi (heteroskedasticity)

(9.3.2) E (Si ) = 0 (i ¢ j) (cross-sectional

e.
t 3t independence)

9. . E. = . . + . ' = °

( 3 3) 1t plel,t-l ult and i # countries
(autoregression)

We need an estimate of pi and Oi2 for each country, and

we then transform the data in order to get an unbiased

and consistent estimate of coefficients.

89

Following Kmenta (1971, pp. 510-11), we first apply
the ordinary least-squares method to all (NxT) observations

to obtain the regression residuals e. From these we

 

it'
can obtain estimates of pi, let us say, pi, by
A 2e. e. A
pi = 1t :Jt'l . Next, we use the pi's to transform the
Be

i,t-l
observations in accordance with the following relation:

A

yit-piyit-l ‘9 (1’91” B‘xit’PiXit-i’ + uit
(0.3.4)

Now we can apply the ordinary least-squares method to the

above equation, for which we have N(T-l) observations.

A

The resulting regression residuals, let us say, uit’ can be
used to estimate the variances of uit (i.e., oii)
2 1 T A2 .
by Sui = T:K:I t§2 uit where k is # of regressors
. 2 _ 2 2
Since Gui - Oi (1 - Oi)
It follows that a: can be estimated by:
2
2 _ “2 _ Sui
Si ' Oi ' EETE—T
i

O O O O 2 0
Since pi is a conSistant estimator of pi and s . is a

ui
O O 2 A 2 O 0 O
conSistant estimator of Gui, Oi is a conSistent estimator
2
of 0..
1

With one more transformation our task is completed.

This is the transformation of (9.3.9) in accordance with

85

the following relation:

 

 

 

(u 3 5) yit-piyit-l = “(l-pi) + S(Xit-pixit-l) + uit
Oi Oi Oi Oi
uit
In (9.3.5) the disturbance E—- has the ideal conditions
i
“it Emit 9? “it
because E(7r—) = -:—7 = -%'= 1 and =r— is homoskedastic.
Oi Edi Oi Oi
Oi was calculated for developed countries using
A Xe. 3.
pi = 1t 1;-1 , and the results are shown in Table 9-1.
2e.
it-l

A glance through Table 9-1 gives the impression
that the pi's are almost the same for all countries. For
that reason we will assume that all countries have the
same p in other words,

(9.3.6) pi = p. for l 5 3
3 and i,j = 1,2,3,...19
Furthermore, due to computational problems, we will also
assume that
for i # j

(9.3.7) o: = o.
and i,j = 1,2,...19

This second assumption simply means, since we are putting
all countries in one group, we are assuming that the
observations of all countries come from the same population.
All our estimated results are based on those two
assumptions.

The Two-stage least-squares method was employed in

ESTIMATES OF 0 FOR DIFFERENT COUNTRIES

86

TABLE 9-1

 

 

 

COUNTRY pi
Germany 0.98759
Switzerland 0.98660
U.K. 0.97752
New Zealand 0.97310
Canada 0.98221
France 0.99395
Ireland 0.99111
Italy 0.98781
Netherland 0.98129
Norway 0.99888
Denmark 0.97762
Belgium 0.98880
Austria 0.98791
Japan 0.98792
Australia 0.99729
Sweden 0.98659
Spain 0.97521
Iceland 0.96982
Finland 0.98827

 

 

87

estimating the demand function for developed countries,

with the assumption that

‘t

H
..—-l
u
N
u
N
I:

= pa. + u

(9.3.8) 6. it-l it

It

i 19

H
|-’
0
N
0

Of course, we have assumed that the relation (9.3.8) holds

within each country, but not between countries.

9.9 - Model Specification and Results

 

All of our models have been specified in linear form.
This is the form that all previous studies have assumed,
including that of Box and Jenkins (1970), which concentrates
on the linear model with an autoregressive process. We

first tried to specify the system in log-linear form:

(9.9.1)

(Demand) log Rit = a0+ a1 log Mit+ a2 log (%)it+ a3 log Pgt
+ sit

(Supply) log Rit = b0+bl log Pgt+b2 log (.rtU'S°-ritR'O'w°)
+ 153 log (PtU.S._PitR.O.W.)
+ b9 log (ytu.s._yitR.O.w.) + uit

The terms (rtU'S'-ritR'O'w°) and (PtU'S°-PitR°O'w') happen

to be sometimes zero or a negative number, the logs for
which do not exist; for that reason, we had to choose other

specifications.

88

In order to solve this difficulty, we propose two
different models. The first choice is to specify the

system in linear form only.

(9.9.2)
MODEL I
M
(Demand) R. = o 4-c M. +-o (—) +-o P + s.
it 0 1 it 2 y 1t 3 git it
(9.9.3)
U.S. 'R.O.W.
(Supply) R. = B +'B P + B (r -r )
it 0 l git 2 it
+ 83(PU'S°-PR'O'W') + Bu(yU°S'-yR°O°w°).
it 1t
+ uit
i = 1,2,3, ... 19 (19 DC's)
t = 1,2, ... 29 (19721 - 1977IV)
where r = real rate of return
But rU'S’ = rnU'S' - PER'O°W' - depreciation (Expected)
rR.O.W. = rnR°O'w' _ PER'O'W'
then rU'S' - rR'O'W' = rnU'S' - rnR°O'w' - depreciationc¢’$
(9.9.9)

and rn = nominal rate

PE = Expected rate of inflation

Long-run government bond yield has been used as a proxy
for rn and unit value of imports, which is adjusted by
exchange rates for P.

There is no generally accepted way in which to

model expectations. Traditionally, inflationary

89

expectations have been thought of as some average of past

inflation rates.

One example would be a weighted average

of inflation rates in the last four years, with relatively

heavy weight on the more recent past. There is no

particular advantage that attaches to a four-year average,

nor any evidence that makes us select that number. We will

make the simplifying assumption that the expected rate of

inflation is equal to the last period's rate of inflation.

The same applies for the expected depreciation of the

dollar.

The second choice is, rather than taking differen-

tial interest rates, differential price levels, and

differential real GNP, we can take their ratios. In this

case, we can specify the system in log-linear form and

look at the elasticities. Thus we have:

MODEL II
(Demand)

(Supply)

where cl

ln

ln

 

git

M
. =c+o lnM.+OLln(-) +alnP +6.
it 0 1 it 2 y it 3 git it
rU'S'
it: 80+Bllnpg. *len‘m’
it r
PU.S. yU.S.
* 331“ (W)- " BEN-7:76:07) +uit
it y .
it
3 1n Rit
3_IH_M_—i - Elasticity of demand for reserves
it with respect to imports
3 1n Rit
M Elasticity of demand with respect to
8 (Y)°t average prOpensity to import.
i
3 ln R. _ . . ,
it ElastiCity of demand With respect
3 ln P to gold price.

90

As mentioned in the previous chapter, we also are
interested in the speed of adjustment. This led us to
conclude that we must estimate our model when the market is
in disequilibrium.

We borrow the model from the previous chapter and

again specify it in linear and log-linear form.3

MODEL III

R. = c + c M. +

M
It 0 lit c2037) +cP +c R. +6:

it git 9 it-l it

) + d2(PU.S._PR.O.W.)

it it

U.S. R.O.W.
it 0 1 (r 'r

+ d3(yU.S._yR.O.W.) + d” Pg + d5 Pg. + u
it it it-l

it
Again, we specify Model III in log-linear form by
including the ratios instead of differentials. This leads

us to our last model.

91

MODEL IV
1n Rit = c0 + cl ln Mit + c2 1n (g) + c3 1n P
y it git
+ Cu 1" Rit-l + git
rU°S° PU.S.
1" Rit ' D0 + D1 1“ ('_"_R.O.w.), 4‘ D2 1" (—O—_R. .w.)
r it P it
U.S. '
+ D3 1n (ZRTOTWTJ + D9 1n Pg. + D5 1n Pg. + uit

Tables 9-2 through 9-5 show the estimated results
for all four models (only for the demand function) using
the official dollar price of gold as well as the market
price of gold (dollar price of gold in London), as
indicated. Two kinds of results are represented in these
tables, estimates without autoregressive assumptions and
estimates with autoregressive assumptions about disturbance
terms. The former are indicated by INST (two-state least-
squares) and the latter by TSCORC (two-stage least-squares
combined with Cochrane-Orcutt transformation).

Let us elaborate on our results. First, in all
16 cases, all variables have the theoretically expected
sign. In particular, the gold price has a negative
coefficient in all the cases, supporting our model.
Secondly, the coefficients are significantly different

from zero in most of the cases. For example, gold price

92

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93

 

 

 

 

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99

 

 

 

 

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95

 

 

 

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96

has a significant coefficient in 19 of 16 cases.

The import-GNP ratio has a negative coefficient
in 19 cases, supporting the "priceless" Keynesian theory
discussed in the previous chapter.

Imports has a positive coefficient in all cases,
significantly different from zero in most. In some cases,
the elasticity of reserve demand with respect to imports
happens to be between 0.5 and unity, supporting the
"square-root" law.

In any estimated relations, economists are concerned
with the policy implications of the results. For policy
purposes, our main concern is to look at the suggested
proposal for which provisions were made in the IMF articles.
These suggest that one possible method of dealing with the
shortage of liquidity is gold revaluation.

Our Model III-INST (table 9-3) suggests that if the
official price of gold is increased by one dollar, the
demand for total international reserves will drop by $33.33
million. This is based on the assumption that these 19
developed countries represent the major demanders in the
world. 5 Model II-TSCORC, Table 9-2, suggests that,
again, if the official price of gold goes up by one percent,
then demand for total reserves will drop by 1.91 percent,
which is an indication of elastic demand with respect to
the price of gold. However, Model II-TSCORC, table 9-9,
which uses the market price of gold, shows an inelastic

demand with respect to gold price. (In that equation,

97

elasticity is 0.805.)

We may conclude that demand for international
reserves is elastic with respect to the official price of
gold. However, it is inelastic with respect to the market
price of gold. As for the speed of adjustment, we must
refer to the disequilibrium model. Model IV-INST, tables
9-3 and 9-5, suggests that the estimated speed of
adjustment is almost 35 percent,6 which means, in the
developed countries sample, that more than 35 percent of
the adjustment is completed within one year.

For the purpose of comparison, we estimated four
models for a group of 21 less developed countries; the
results are presented in Tables 9-6 through 9-9. Five
countries had to be excluded because data were not
available on their government bond yield or their discount
rate and real GNP. These were the Dominican Republic,
Panama, El Salvador, Paraguay, and the People's Republic
of China.

Some insights may be given concerning our estimated
results. In table 9-6, Model I-INST happens to have a
low R2 and a low Durbin-Watson statistic. Again, the
TSCORC might be the relevant method of estimation. However,
as Model I-TSCORC or Model 11 in table 9-6 indicate, the
coefficient of gold price takes the wrong (positive) sign.

But if we consider a disequilibrium market, the results

98

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HIHm_Hme.o.+mm CH Hmo.o I m CH wHo.o I 2 CH wmboo.o I mmwm.o n m CH UmOOmB
>H HOUOZ
mom n 2 mm.hmm n h
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HHH HOUOZ
man u 2 mp.Hm:N n m
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HIHm mo.H + mm wum.o I m 5H.mH I Z Hoooo.o + hm.mm n m BmZH

 

 

 

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"ZOHBozom oz<2mn mo mme<zHHmm

ammo: onmmHaHoommHo

mI: mqm<H

102

in table 9-7 with Model III-INST show a satisfactory result,
suggesting that if the official price of gold goes up by
one dollar, the demand for reserves by less developed
countries will drop by $9.28 million. Model IV-INST
suggests that if the official gold price went up by one
percent, then demand for reserves would drop by 13.87
percent, indicating an elastic demand with respect to the
offical gold price. The same argument applies for tables
9-8 and 9-9, which show the result when the market price
of gold is used. Again, the result of the disequilibrium
model is much more satisfactory than the result of the
equilibrium model.

With respect to speed of adjustment, we need to
refer to model III-INST and model IV-INST. Our result
shows that the speed of adjustment happens to be about 0.11,
indicating that in the less developed countries sample,

11 percent of adjustment is completed within one year.

To compare the result for developed with less
developed countries, we put all results together in tables
9-10 and 9-11.7

The models that should be used to compare the
results are Model I-TSCORC, Model II-TSCORC, Model III-
INST, and Model IV-INST. Because in the equilibrium model

the other two models have a very low R2 and in the

103

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109

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HHI: m4m<b

105

disequilibrium model the inclusion of Rt-l in demand
function makes the Durbin-Watson statistic biased toward
2, model III-TSCORC and Model IV-TSCORC are irrelevant.
However, if the criterion for forecasting and
prediction purposes is the model with a high R2 and
significant coefficients, then model IV-TSCORC is relevant

also. In that model, the R2

for both developed and less
developed countries is about 9:98, and all variables have
the theoretically expected signs and significant
coefficients. The exception is the gold price for less
developed countries, and this might lead us to choose
Model IV-INST; in it all variables have the expected signs,
and all coefficients are significantly different from zero.
As Model IV-INST indicates, a one percent increase in the
official price of gold will make developed countries'
demand for reserves drop by 22.29 percent, whereas it will
make demand for reserves in less developed countries drop
by 13.87 percent.

With respect to the speed of adjustment, the figures
are l-0.65 = 0.35 for developed countries and 1-0.89 = 0.11
for the less developed. This indicates that in the
developed countries sample, 35 percent of the adjustment is
completed within one year, whereas in the less developed
countries the comparable figure is only 11 percent.

As Model I-TSCORC indicates, the gold price for both
groups of countries takes the wrong (positive) sign. This

fact will be investigated in the next chapter.

CHAPTER FIVE

FURTHER RESULTS AND CONCLUSIONS

5.1 - Introduction

In the previous chapter, we found that the official
gold price took the wrong (positive) sign in Model I-TSCORC
using data from both developed and less developed countries.
However, this was not the case in any of the disequilibrium
models. One might conclude that the disequilibrium model
is more appropriate than the equilibrium model.

In this chapter, we shall discuss our model in more
detail and trythfind out why the gold price did not take
the theoretically expected sign. Before doing so, we
should point out one implication of our model of demand

for and supply of reserves.

5.2 - Implication of the Model

 

In the last chapter, we used the two-stage least-
squares method to estimate our demand function. We know
that, in the first stage, the right hand side endogenous
variable, gold price, was regressed on all other exogenous

variables. We obtained:

106

107

P "=a0'I-a:L Mit+a2 (M) + a3 (rU'S'-rR'O'w°)
U.S._ R.0.W.)

+ a (P P + a5 (y

” it it
The official price of gold was obtained by multiplying the
SDR value of gold by the dollar value of SDR. Since the
SDR value of gold is fixed at 35 SDR per ounce, if we
divide both sides of the above equation by 35, then the
left-hand side variable will be only the exchange rate
between the dollar and SDR, or the dollar value of SDR.

We wanted to know how much variation in the dollar value

of SDR is explained by the above equation; for that reason,

we estimated the equation and the results are as follows;

U.S. R.0.W.
-r

pg = 90.95 + 0.000099 + 1.69 9 - 0.007 (r >

(139.6)***(2.79)***(2.6)** (2.92)**

_ 0.007 (PU.S._PR.O.W.) _ 0.000” (yU.S._yR.O.W.)
(l.82)** (0.892)
2

with R = 0.0967.

As the R2 indicates, about 5 percent of the variation of
the dollar against SDR is explained by our model. It seems
that the income differential between the United States and
the rest of the world exerts no effect (insignificant
coefficient). For that reason, we dropped real income from

our model and tried to see how this affected our results.

108

5.3 - The Model of Demand for and Supply of Reserves
Without Income

 

 

After dropping income differential, our model looks

like:

D

R = f(M, £3, Pg)

R8 = FEPg, (rU.S._rR.O.W.), (PU.S._PR.O.W.)J

Again, we specified the model in linear and log-linear
form in both the equilibrium and disequilibrium cases, as
in the previous chapter. However, this time we used CPI
for p instead of the unit value of imports. Also, we
assumed that the expectations are exact, so the expected
rate of inflation at this period is the current year
inflation rate. With those assumptions, we first estimated
the same four models discussed previously for developed
countries. The results are shown in tables 5-1 through
5—9.

Let us elaborate on our results. First, in all 16
cases, all variables have the theoretically expected signs.
In particular, the gold price has a negative coefficient
in all the cases; this supports our model, which was not
the case in Model I-TSCORC of Chapter 9. Second, the
coefficients are significantly different from zero in most
of the cases. For example, gold price has a significant
coefficient in 19 of 16 cases.

The import-GNP ratio has a negative coefficient in

10 cases, thus supporting the "priceless" Keynesian theory,

109

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to.

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110

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111

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112

 

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113

discussedlhlthe previous chapter.

Imports have a positive coefficient in all cases and
are significantly different from zero in most cases. In
some, the elasticity of reserve demand with respect to
imports happens to be between 0.5 and unity, supporting
the "square-root" law.

As noted earlier, in any estimated relations we are
concerned with the policy implications of the results. For
policy purposes, our main concern is with the proposal for
which provisions were made in the I.M.F. Articles, that is,
one possible method of dealing with the shortage of
liquidity is gold revaluation.

Our Model I-TSCORC, (Table 9-2) suggests that if the
official price of gold is increased by one dollar, then
demand for total international reserves will drop by $265.57
million, based on the assumption that the 19 developed
countries in our sample represent the major demanders in
the world.

Model II-TSCORC, (Table 9-2), suggests that, again,
if the official price of gold rises by one percent, then
the demand for total reserves will drop by 3.19 percent,
which is an indication of elastic demand with respect to
gold price. However, Model II-TSCORC, (Table 9-9) which
uses the market price of gold, shows an inelastic demand
with respect to gold price. In that equation, elasticity

is 0.897, which is an indication of inelastic demand.

119

We may conclude that the demand for international
reserves is elastic with respect to the official price of
gold. However, it is inelastic with respect to the market
price of gold. With respect to the speed of adjustment,
we need to refer to the disequilibrium model. Model IV-
INST (Tables 9-3 and 9-5), suggests that the estimated
speed of adjustment is almost 9 percentl, which means that
in the developed countries sample, more than 9 percent of
the adjustment is completed within one year. Our estimated
speed of adjustment happens to be low, as was the case in
Clark's (1970) and Iyoha's (1976) studies.

For the purpose of comparison, we estimated four
models for a group of 21 less developed countries. The
results are presented in Tables 5-5 through 5-8.

Let us elaborate on our estimated results. In

table 5-5, Model I-INST happens to have a very low R2

(i.e., R2 = 0.073) and low Durbin-Watson statistic. Again,
the TSCORC might be the relevant method of estimation.
However, as Model l-TSCORC in table 5-5 indicates, the
coefficient of gold price again takes the wrong (positive)
sign, and it is not significantly different from zero.

But if we consider the disequilibrium market, the results
in table 5-6 with Model III-INST show a satisfactory result.
This suggests that if the official price of gold rises by

one dollar, the demand for reserves by less developed

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117

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118

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mlm mHm<H

119

countries will drop by $16.95 million. Model IV-INST
suggests that if the official gold price rises by one
percent, then demand for reserve will drop by 9.6 percent,
indicating an elastic demand with respect to the official
gold price.

The same argument applies for tables u-8 and 4-9,
which show the results when the market price of gold is
used. Again, the result of the disequilibrium model is
much more satisfactory than the result of the equilibrium
model.

With respect to the speed of adjustment, we need to
refer to Model III-INST and Model IV—INST. Our results
show that the figure is between 9 percent and Zn percent;
that is, in the less developed countries sample, between
9 percent and 2H percent of the adjustment is completed
within one year.

To compare developed and less developed countries,
we again put all results together in tables 5-9 and 5-102.

The models that should be used to compare the
results are Model I-TSCORC, Model II-TSCORC, Model III-
INST, and Model IV—INST. Because in the equilibrium model
the other two models have a very low R2 and in the

disequilibrium model the inclusion of R in the demand

t—l

function makestflmaDurbin—Watson statistic biased toward22,so

120

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122

Model III-TSCORC and Model IV—TSCORC are irrelevant.

In Model I-TSCORC or Model II-TSCORC for less
developed countries, mostcfi’the coefficients are insignifi-
cant, and the gold price again takes the wrong (positive)
sign. This led us to investigate the demand function in
less developed countries in much more detail. We again
looked at the first stage of the two-stage least-squares
method, in which the gold price was regressed on all
exogenous variables. The estimated relation between gold
price and all other exogenous variables using the ordinary

least-squares method is:

R.O. .
Pg = 90.11 1 0.00058 M + 1.38 g + 0.075 (rU'S'-r w )
(232.8) (5.19) (2.52) (3.5)
_ 0.002 (PU.S._PR.O.W.)
(l.u)
22 = 0.097 Dw = 0.9125

The same relation was estimated using the Cochrane-Orcutt

procedure; the result is as follows:

M

P = Hl.78 + 0.000021 M + 0.0397 y + 0.0135 (rU°S°-rR'O'W')
(136.6) (0.132) (0.097) (0.369)
+ 0.00095 (PU'S'-PR'O'W°)
(0.978)
R2 = 0.71
Dw = 1.31

As the results indicate, the fit is very poor in the first.

123

equation, and all coefficients are insignificant in the
second. This led us to assume that the supply of reserves
is given for less developed countries, and they have no
control over it. Consequently, we estimated the demand
function for less developed countries by using the
ordinary least-squares method; the results are presented
in tables S-ll through S-lu.

As the results indicate, the estimated coefficient
of gold price is not satisfactory in the equilibrium
model. In Model I-OLSQ or Model II-OLSQ it is negative
but insignificant, and in Model I-CORC and Model II-CORC
it has a positive but significant signs. Thus, we need
further investigation of the behavior of less developed
countries with respect to gold price.

We looked at the gold holding of less developed
countries during our period of estimation, 1972-1977.

The data in table 5—15 show that the gold holdings of

some countries did not vary as gold prices increased. One

reason might be the fact that the gold component of their
total reserve is very small. For example, for countries
such as Honduras and Paraguay, it was so small that they

only began reporting data in 1977. It was thus necessary

12”

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125

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126

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127

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TABLE 5-15

128

GOLD HOLDING OF LDC's
(Million Ounces)

 

 

 

 

Country 1972 1973 ’197u 1975 1976 1977
Brazil 1.33 1.33 1.33 1.33 1.33 1.52
Columbia 0.93 0.u3 0.u3 .1.13 1.Hl 1.73
China 2.30 2.30 2.30 2.30 2.23 2.31
Dominican Rep. 0.09 0.09 0.09 0.09 0.09 0.10
El Salvador 0.u9 0.H9 0.u9 0.89 0.49 0.50
Egypt 2.u3 2.u3 2.43 2.u3 2.u3 2.u3
Greece 3.50 3.50 3.61 3.63 3.65 3.73
Honduras ----- ---- ---- ---- ---- 0.01
Israel 1.19 1.10 1.10 1.10 1.10 1.16
India 6.95 6.95 6.95 6.95 6.95 7.36
Jordan 0.80 0.80 0.80 -0.80 .80 .81
Korea 0.11 0.11 0.11 0.11 0.11 0.15
Mexico ”.94 n.63 3.66 3.66 1.60 1.76
Peru 1 09 1.00 1.00 1.00 1.00 1.00
Paraguay ---- ---- ---- ---- ---- 0.01
Portugal 26.88 27.53 27.80 27.72 27.67 2H.1l
Panama ---- -—-- ---- ---— ---- ----
Pakistan 1.57 1.60 1.59 1.59 1.62 1.62
Srilanka -—-- ---- ---- ---- ---- ----
South Africa 17.93 18.99 18.25 17.75 12.67 9.72
Turkey 3.57 3.57 3.57 3.57 3.57 3.63

 

Source:

International Financial Statistic.

129

to classify the less developed countries into two groups.

The classification is based on real GDP per capita.
In their paper, Kravis, Heston and Summer (1980) calculated
real GDP per capita for almost all countries in terms of
dollars, using the purchasing power parity theory. We
borrowed the numbers from their study and used these in
table 5-16, which shows the dollar value of real GDP per
capita for our period of estimation.

A glance at table 5-16 shows that real GDP differs
from country to country.' In the first less developed
group are those countries that had a real per capita income
of more than $1,000 in 1977. In the second group are those
with real per capita income of less than $1,000. Why was
$1,000 chosen as a benchmark? We simply looked at the last
year (1977) and noted where the gap was the widest. As
table 5-16 indicates, the widest gap was between $1,0u0
and $821. Fortunately, our classification coincides with
what we found in table 5-15. In other words, countries
in the second group are also those whose holding did not
change as the gold price increased.

The estimation results for the 13 less developed
countries5 in the first group are presented in tables 5-17
through 5-20.6

As our results indicate, Model II-OLSQ and

130

TABLE 5-16

DOLLAR VALUE OF REAL GDP PER CAPITA

OF LESS DEVELOPED COUNTRIES

IN A DECREASING ORDER

 

 

 

 

 

 

 

 

 

 

Countries T1972 1973 1978 1975 1976 1977

O Israel 3108 3168 3258 3366 3187 3088

23 Greece 2137 2325 2238 2362 2518 2889
3... Brazil 1300 1838 1516 1565 1669 1717
C“? Portugal 1861 1618 1616 1898 1526 1633
Do South Africa 1399 1880 1898 1899 1513 1506

as Panama 1837 1896 1508 1508 1885 1837

8': Mexico 1300 1358 1391 1808 1375 1365

(9 0 Turkey 959 971 1069 1110 1175 1196
mg Peru 1105 1126 1179 1192 1201 1175
3v Colombia 918 966 998 1018 1091 1076

-H Dominican Rep 877 978 969 1009 1058 1070
H Korea 767 778 818 867 961 1080
Q,. Paraguay 680 673 707 720 753 821

330 £1 Salvador 680 688 716 788 782 755

so Jordan 576 552 596 580 590 692

”3 Honduras 621 625 599 588 611 627

'2 a Srilanka 861 893 583 538 550 553

o 0 Egypt 508 500 878 506 517 588

88 Pakistan 837 882 885 850 885 859

mv India 317 321 313 332 329 383

Source: International Comparison of Real Product and its

1950-1977,
Review of

R. Summers, I.B. Kravis,
Income and Wealth,

Composition:
and A. Heston,
March 1980.

 

131

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132

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133

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134

 

 

 

 

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135

Model IV-CORC are satisfactory in terms of our theory7
Based on these two models, the elasticity of demand with
respect to the official price of gold is 2.02 percent,
which means as gold prices rise by one percent, demand
for total reserves by this sample of less develOped
countries will drop by 2.02 percent. As we saw before,
the elasticity for developed countries was 3.19 percent.
Model IV—CORC indicates that the speed of adjustment
for this group of less developed countries is u percent
(1 — .96 = .ou), which means that in the lB-country sample,
n percent of the adjustment is completed within one year.
It should be pointed out that the speed of adjustment for
developed countries also was H percent.
The results for the second group of less developed
countries were not satisfactory (that is, a very low R2 and
insignificant coefficients). Therefore, we do not present

the results.

5.” - Conclusions

An interesting finding is that the price of gold
(official or market) exerts a negative effect on the demand
for liquidity. Furthermore, the demand for reserves with
respect to the official price of gold is elastic, but with
respect to the market price it is inelastic. It appears
that this elasticity is smaller for less develOped than for
developed countries. This might be due to the fact that the
latter hold larger amounts of gold than do the former.

Table 5—21 summarizes our findings.

 

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136

 

 

 

 

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137

Our results indicate that market price of gold would
be a more appropriate measure to use in valuing the gold
component of official reserves of all countries. More
precisely, if IMF allows the official price of gold to be
the same as its market price, an increase of almost lloopercent
then if the demand for reserves will drOp by almost 13 billion
dollars. In other words, by revaluing the gold, we will be
able to solve the shortage of reserves by almost 13 billion
dollars.8

With respect to the speed of adjustment, it was
almost four percent for both groups of countries, indicating
that almost four percent of adjustment is completed within
one year.

We also found that the coefficient of the import-

GNP ratio takes a negative sign in all models, regardless
of whether the official or market price of gold is used.
This negative coefficient implies a.more "Keynesian" role
for this variable.

The effect of imports is small for developed as
compared to less developed countries. The elasticity is
less than unity for developed countries, indicating economies
of scale. It is greater than unity (1.1u) for less develOped
countries, indicating diseconomies of scale. This difference
might be due to the fact that in the period of estimation
Cl972-1977), most develOped countries moved to a managed
float, whereas most less developed countries did not.

Moving from a fixed exchange rate system to a managed

138

floating system will reduce the demand for reserves because
fluctuations in exchange rates will reduce the deficit due

to higher import levels.

5.5 - Concluding Remarks

In this thesis, we developed a simultaneous equation
model of demand for and supply of international reserves,
and we applied it in analyzing the behavior of developed
and less developed countries. We have shown that the
reserve demand function as well as the supply function can
be specified in terms of a small number of variables. We
provided evidence that the demand for international
reserves is negatively related to gold price, which is a
unique finding in the literature. We also provided
evidence that deviations of actual from desired reserve
holdings trigger a process of adjustment, this led us to
estimate our model when the market is in disequilibrium.
We found that log-linear models give a better result than
linear models, which supports Box-and Jenkins (1970),
who claim that log-linear models have the best fit for

international data.

FOOTNOTES

CHAPTER TWO

FOOTNOTES

lSee see how these lagged periods are determined, see
the original paper, pp. 631.

2For more details see Heller (1966), pp. 209-30u.

3Heller (1966), p. 310.

139

CHAPTER THREE

FOOTNOTES

1See, for example, Archibald and Richmond (1971).

2See Williamson C197u) and Haberler (1977).

3For more discussion, see Frenkel L197MHA1 and Heller
(1966).

”In this model we have assumed a linear consumption
function with constant marginal propensity to consume,
which implies a constant marginal propensity to save. If,
however, an increase in m.is associated with a decline in
s, then the effects of "openness" on the balance of
trade is ambiguous and depends on the difference of (m-s).

5For source of data on this page, see Robert Z.
Aliber, The InternatiOnal Money Game, 3rd ed., (1979),
pp. 75-9”.

6Numbers in brackets are t-ratios, and the gold price
coefficient is almost significant at a = 0.10.

7Formore details and for reasons for the self«
correcting mechanism, see M.E. Kreinin and L.H. Officer,
The Monetary ApprOach to the Balance of Payments: ”A
Survey, Princeton Studies in International Finance, No. MB,
l978.

8SDRs were allocated to those IMF member countries
that elected to receive them in proportion to the size of
each country's quota. Upon becoming a.member of the IMF,
a country must agree upon the size of its quota. Twentye
five percent of the quota is deposited in the form of an
international reserve asset (usually gold or U.S. dollars).
The remaining 75 percent is deposited in the form of the
country's domestic currency. These quotas then form a pool
of IMF members' currencies from which one member can borrow
another member's currency. The specific SDR allocations
are: SDR 3.ul billion on January 1, 1970 (each participant
received 16.8 percent of its quota), SDR 2.95 billion in
1971 (10.7 percent of quota), SDR 4.03 billion in l979
LlO.H percent of quota), and SDR H.033 billion in 1980.

1H0

1H1

9The specification of demand for reserves is assumed
to take the following form:

(1 __ -M

Rt - a0 + a1 Mt + a2 CY) + a3 Pg

1: 't

10The supply function is specified in the following
form: .

S - -

Rt ‘ bo + b1 Pgt + b2 (ru.s. rR.0.W.)t

+ b3 (PU.S. " PR.O.W.) + bu Cyu.s.’yR.o.w.)

CHAPTER FOUR

 

 

FOOTNOTES

1List of countries on which analysis is based:
Australia » Brazil
Austria China
Belgium Colombia
Canada Dominican Rep.
Denmark _ Egypt
France El Salvador
Finland Greece
Germany Honduras
Iceland Israel
Ireland India
Italy Jordan
Japan Korea
Netherlands Mexico
New Zealand Peru
Norway Paraguay
Spain Portugal
Sweden Panama
Switzerland Pakistan
United Kingdom Srilanka

South Africa
Turkey

 

 

All data for all countries were available from International
Financial Statistics and IMF tapes.

142

193

2Since quarterly GNP was not available for some
countries, a quarterly figure was generated using annual
GNP. The method used was based on a linear import function:
M = a + bY, where M = imports and Y = GNP. However, for
our purposes, the quarterly series to be estimated (Y) was
regressed on imports (See Chow and Lin (1976). So, using
annual observations, we estimated the following function for
those countries;

Yt = c + d Mt + 6t
By then using quarterly data for M, we obtained a quarterly
series for v. However, the generated quarterly data for y,
let us say y, were adjusted, such that yI + yII + yIII

+ yIV = y, where y is the the annual observed data. Countries
to which this procedure was applied are: Belgium, Denmark,
Iceland, Ireland, the Netherlands, New Zealand, Norway,
Sweden, Switzerland, Spain, and all 21 less developed
countries. The R2 ranged from 0.65 to .92.

3These are equations (3.5.3) and (3.5.6) from Chapter
3 with the following changes:

c0 = any, 01 = aly, c2 = azy, c3 = a3y

0
II

M 1-7 therefore Y = l-c = speed of adjustment

u
do ‘ bo’ d1 = bl’ d2 = b2’ d3 = b3
- 1 _ 1
bu-fi+buandd5--7\-

”Only in model I-TSCORC does the gold price take the
wrong sign.

5"Gold revaluation needs to be distinguished from
dollar devaluation, such as was embodied in the Smithsonian
Agreement in December 1971. Both involve a change in the
gold/dollar parity, but gold revaluation is directed to
changing the relationship between gold and currencies in
general while dollar devaluation changes the relation
between the dollar and other currencies essentially
unchanged." Williamson (1973, p. 71u).

6(l- coefficient next to Rt
of adjustment.
7Table 4-10 reflects the results when the official
gold price has been used, and table H-ll shows the result
when the market price of gold is used.

—1) = y, where y = speed

CHAPTER FIVE

FOOTNOTES

l(l-coefficient next to Rt-l) = 7. Where y = speed
of adjustment.

2Table 5-9 reflects the results when the official
gold price is used, and Table 5-10 shows the results when
the market price of gold is used.

3Numbers in parentheses are t-values.

IJ'Other coefficients have the right sign, and they are
significant, especially in Model II-OLSQ; in that model, the
elasticity of demand with respect to imports is 0.831,
supporting the square root-law.

5The People's Republic of China was put back into the
first group. ,

6In both cases, that is, using the official gold price
and the market price of gold.

7In both cases, that is, using the official gold price
and the market price of gold.

8These estimates are based on an elasticity of 3.19

and total reserve at the end of l977 which stood at 261699
.million SDR.

1m:

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