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EXCHANGE RISK IN INTERNATIONAL TRADE
UNDER ALTERNATIVE EXCHANGE SYSTEMS:

THE DEVELOPING COUNTRIES' EXPERIENCE

by

Shashikant Gupta

A DISSERTATION
Submitted to
Michigan State University
in partial fulfillment of the requirements
for the degree of
DOCTOR OF PHILOSOPHY
Department of Economics

1980

@ Copyright by
SHASHIKANT GUPTA

1980

ABSTRACT
EXCHANGE RISK IN INTERNATIONAL TRADE
UNDER ALTERNATIVE EXCHANGE SYSTEMS:

THE DEVELOPING COUNTRIES' EXPERIENCE

by

Shashikant Gupta

The question of exchange risk under different inter-
national monetary systems has been the subject of
considerable debate over the last few decades. It is a
central issue in the evaluation of alternative exchange
systems. Till recently, however, the debate was confined
to a theoretical level, because little opportunity existed
for empirical investigation. With the breakdown of the
IMF system of pegged exchange rates in 1973, an empirical
investigation of this issue becomes possible. The
question whether exchange risk is higher under floating
rates or not is examined in this study in the context of
the developing countries' claim that

(l) The increased exchange risk present under

floating rates has hampered their export drive, and

Shashikant Gupta

(2) Their exports are becoming increasingly concen-
trated as a result of the asymmetry of exchange risk
under the present international monetary system.

There are theoretical and empirical dimensions to
these two issues. Theoretically, it needs to be deter-
mined whether an increase in exchange risk would affect
export levels.‘ If so, under what conditions? Then,
two empirical questions arise. Whether exchange risk
increased with the introduction of floating rates. And
if it did, whether the exports of the developing countries
were adversely affected by it.

Examining the theoretical issue in the framework of
the theory of the firm, it was found that when exchange
markets were imperfect, exports could be expected to
decline in the face of higher levels of exchange
risk.

Exchange risk was defined as a function of past
forecasting experience. It was posited that the more
inaccurate the forecasts, the higher the exchange risk
was perceived to be. The Box-Jenkins method of time
series analysis was used to develop a model of exchange
rate forecasting in the five developing countries in the
sample-~India, Israel, Mexico, Korea and Taiwan. It
was found that exchange risk had indeed increased since the
inception of floating rates in 1973, for each of the

five countries.

Shashikant Gupta

The effect of this increase in exchange risk on the
exports of the five countries was examined econometric-
ally. The result of this examination did not reveal any
statistically significant relationship between exchange
risk and exports.

Therefore, the conclusions of this research are:

(a) On a theoretical level, exporting firms in
developing countries can be expected to curtail their
exports when faced with increased exchange risk.

(b) Exchange risk, measured as a function of past
forecasting errors, did increase with the introduction
of floating rates in 1973.

(c) In spite of these two findings, there was no
statistically significant empirical support for the
proposition that the exports of developing countries
have been adversely affected by the higher level of
exchange risk under the present international monetary
system. Neither the volume nor the geographical
diversification of exports were reduced because of

increased exchange risk.

ACKNOWLEDGMENTS

There are several peeple whose guidance and support
I would like to acknowledge. My long-standing thanks
are due to my teachers, Mordechai Kreinin, Norman Obst,
Lawrence Officer and Subbaiah Kannappan whose excellence
in teaching and devotion to research have been a source
of constant inspiration. Thanks are due to Bob Loube
for patiently reading and commenting on the theoretical
part of this research, and also for always giving me
the benefit of his exceptional insights. I am especially
grateful to "Lash" Larrowe, whose deep commitment to
equity and fairness has been a singular influence on
my own thinking. Finally, I would like to acknowledge
my family's Aashirwaad which I know is with me always

and for which I am deeply grateful.

ii

TABLE OF CONTENTS

LIST OF TABLES O O O O O O O O O O O O O O O O 0

LIST OF FIGURES . . . . . . . . . . . . . . . .

CHAPTER

1.
2.

INTRODUCTION AND OBJECTIVES OF STUDY . .

EXCHANGE RATE UNCERTAINTY AND THE
LEVEL OF INTERNATIONAL TRADE . . . . . .

The Model . . . . . . . . . . . . . . . .
Marginal Impact of Uncertainty . . . . .
Conclusions . . . . . . . . . . . . . . .
THE MODELS OF THE EXPORT MARKET . . . . .
The Export Market in a Developing Country

THE MEASUREMENT OF EXCHANGE RISK UNDER
ALTERNATIVE EXCHANGE REGIMES . . . . . .

Exchange Rate Forecasting Methodology . .
Stationarity of Exchange Rate Series . .
Measuring Exchange Risk . . . . . . . . .
Conclusions . . . . . . . . . . . . . . .
ESTIMATION PROCEDURE AND RESULTS . . . .
Aggregate Exports . . . . . . . . . . . .
Bilateral Exports . . . . . . . . . . . .

Single Equation Model . . . . . . .

Simultaneous Equation Model . . . .

iii

14
29
48
51
51

66
74
78
94
107
108
109
123
124
132

Chapter
6. SUMMARY

APPENDIX A . .
APPENDIX B . .
APPENDIX C . .

APPENDIX D . .

BIBLIOGRAPHY

AND

CONCLUSIONS

iv

Page

138

144
149
153
159

161

Table

2.1

LIST OF TABLES

Effect of Increased Exchange Uncertainty
On Output and Forward Market Transactions

Computed x2 Values for Autocorrelation

Function . . .

Monthly
Proxy -

Monthly
Proxy -

Monthly
Proxy -

Monthly
Proxy -

Monthly
Proxy -

Average

Average

Single Equation Estimation
Single Equation Estimation

Single Equation Estimation

Values
INDIA

Values
ISRAEL

Values
MEXICO

Values
KOREA

Values

of Exchange

of Exchange

of Exchange

of Exchange

of Exchange

Uncertainty

Uncertainty

Uncertainty

Uncertainty

Uncertainty

TAIWAN O O O O O I O O O O O O O 0
Value of Exchange Risk - R1 and R
Value of Exchange Risk - R3 and R

Results 1

I
w

R2 .

Results

Results:

Bilateral Exports - KOREA . . . . . . . .

Single Equation Estimation

Results:

Bilateral Exports - MEXICO . . . . . . . .

Single Equation Estimation

Results:

Bilateral Exports - TAIWAN . . . . . . . .

Test of Hypothesis - Values of t-statistic

V

40

93

97

98

99

100

101
102
106
115
116

127

128

129

131

Table

5.7

5.8

5.9

A3.1
A3.2
A4.1
A4.2

Simultaneous System
Bilateral Exports -

Simultaneous System
Bilateral Exports -

Simultaneous System
Bilateral Exports -

Simultaneous System

Estimation
KOREA . .

Estimation
MEXICO . .

Estimation
TAIWAN . .

Estimation

Simultaneous System Estimation

Results:

Results:

Results:

l
55

Results

Results - R2

3

Single Equation Estimation Results - R .

4

Single Equation Estimation Results - R .

vi

134

135

136
156
157
159
160

LIST OF FIGURES

INDIA

ISRAEL

KOREA

MEXICO

TAIWAN

Figure
2.1 Optimal Production and Hedging . .
2.2 Expected Future Spot Rates and
Optimal Production and Hedging . .
2.3 Expected Future Spot Rates and
Optimal Production and Hedging . .
3.1 The Export Market for a Developing Country .
3.2a Bilateral Exports of a DevelOping Country .
3.2b Bilateral Exports of a Developing Country .
4.1 Correlogram of Exchange Rate Series
4.2 CorrelOgram of Exchange Rate Series
4.3 Correlogram of Exchange Rate Series
4.4 Correlogram of Exchange Rate Series
4.5 Correlogram of Exchange Rate Series
4.6 Correlogram of First Differenced
Exchange Rate Series - INDIA . .
4.7 Correlogram of First Differenced
Exchange Rate Series - ISRAEL .
4.8 Correlogram of First Differenced
Exchange Rate Series - KOREA . .
4.9 Correlogram of First Differenced
Exchange Rate Series - MEXICO .
4.10 Correlogram of First Differenced
Exchange Rate Series - TAIWAN .

vii

18

22

42
56
61
62
81
82
83
84
85

87

88

89

90

91

CHAPTER 1

INTRODUCTION AND OBJECTIVES OF STUDY

The issue of exchange risk under alternative inter-
national monetary systems has been the subject of consider-
able debate in the last few decades. It is a central
issue in the evaluation of various exchange mechanisms.
Till recently, however, the debate has been largely
confined to a theoretical level, because little oppor-
tunity existed for empirical investigation, except
in an historical context, or for Canada which floated
its currency during the 1950's. Since the inception
of the IMF system following the meetings at Bretton
Woods, pegged rates have been the norm. In addition,
the interwar period and the Canadian experience with
floating rates are both charaterized by unusual
circumstances, severely limiting the extent to which
findings in these contexts can be generalized. The
emergence of a system predominated by floating rates
in 1973, following the breakdown of the IMF Bretton
Woods system, provides an opportunity to examine this

issue empirically.

The Bretton Woods system functioned relatively
smoothly till the 1960's when it began experiencing
considerable strain as confidence in the U.S. dollar
eroded. The U.S. dollar was the center currency
under the system which, for this reason, was often
referred to as the dollar-exchange standard. The
continuing pressure on the U.S. dollar culminated in
the closing of the 'gold window' and then the devalu-
ation of the dollar under the terms of the Smithsonian
Agreement in 1971. These actions represented deviations
from the central precepts of the IMF system. Conse-
quently, as could have been expected, they provided
only temporary respite. The dollar came under renewed
attack in early 1973. A second devaluation resulted,
but this did not stem the run on the dollar. As a
result, the foreign exchange markets were closed for
three weeks in March 1973, to allow the central bankers
to work out a solution.1

The international monetary system that emerged
once the markets were re-opened was really a hybrid of
pegged and floating rates. Specifically, four sub-

systems could be delineated:

 

1For a lucid account of the circumstances leading to and

surrounding the eventual breakdown of the IMF Bretton
Woods system, see Kreinin, M.E., International Economics:
A Policy Approach, 3rd ed., pp. 180-187 (New York, NY;
Harcourt, Brace & Jovanovich, 1979).

 

 

1) Floating rates adopted by most industrial
nations. These included the United Kingdom, Canada,
Japan and Switzerland, among others. These countries
floated their currencies independently against the U.S.
dollar, thus effectively making the U.S. dollar a
floating currency as well.

2) The joint float adopted by the six original
members of the EEC plus Norway and Sweden. These
countries pegged their exchange rates to one another
and floated jointly against the dollar. On March 13,
1979, the 'snake' was replaced by the European Monetary
System (EMS) in which all nine members of the European
Community except the United Kingdom participate. Under
the EMS, a European Currency Unit (ECU) was created
as a basket of fixed amounts of the nine currencies of
the EC members. Central rates for participating
currencies were established, and fluctuations were to
be kept within a 2.5 percent band around these central
rates.2 An interesting feature of the new system is
the use of a 'divergence indicator' which is triggered
when a currency moves outside a very tight band around
the central rate. When this happens, the country in

question is expected to initiate corrective measures.

 

2 Countries not members of the ‘snake' could set a 6

percent band temporarily. Italy took advantage of
this provision.

Thus, from our present perspective, the main feature
of the EMS is that the joint float is made 'tighter.‘3

Both the independent floats and the joint float were
of the managed ('dirty float') type, with governments
intervening aggressively in the foreign exchange
markets to support their currencies.

3) The pegged rates retained by most
of the develOping countries. The U.S. dollar, the
UK pound and the French franc were the most common
pegs. Pegging their exchange rates to a currency that
'was itself floating meant that the currencies of the
developing countries were also floating against all
other currencies, jointly with the currency they were
pegged to.

4) The exchange rates pegged to a basket of
currencies which was adepted by some of the developing
countries. The SDR was the choice of most of the oil
exporting nations, whereas other countries pegged their
currencies to baskets of their own composition. Pre-
sumably, the baskets were selected so that they most
closely reflected the country's trade structure.

Economists who accepted the superiority of float-

ing rates saw the new system as a step in the right

 

3For details regarding the EMS, the method of deter-
mining the divergence limits, etc., see, "EMS Comes
Into Force After Summit Agreement: New Currency Rates
Set", IMF Survey, March 19, 1979, p. 81, and "The
EuroPean Monetary System", IMF Survey Supplement,
March 19, 1979, pp. 97-100.

 

direction. Others were not so sure. Many of the develop-
ing countries argued for a return to a system of pegged
rates. Their argument essentially rests on the claim
that exchange risk had increased under the new system,

and that as a direct consequence, their export drive is
being hampered. All this has brought the old question of
exchange risk under alternate exchange regimes to the
forefront once again.

As the developing countries see it, the higher level
of exchange risk under the floating rate system trans-
lates into lower exports.4: In addition, they claim
that the considerable progress developing countries have
made in diversifying their exports geographically in
the last two decades is being reversed, if not negated.
The geographical concentration would be a direct conse-
quence of the hybrid nature of the new monetary system.

Clearly, any increase in exchange risk can be expected

 

4Although exchange risk will presumably affect imports
also, only the export side is examined in this study.
Developing countries understandably perceive a reduc-
tion in exports with more alarm than a reduction in
imports. In addition, quotas and exchange restrictions
affect various imported commodities asymmetrically.
Because it is rather difficult to isolate such differ-
ential influences when aggregates are considered:
imports are more difficult to examine than exports. On
the export side, exchange restrictions and other
interventions generally tend to be invariant with
commodity classification.

to be asymmetrical, being lower for the currency to which
the developing country is pegged and higher for all
other currencies. Thus, exports will tend to be biased
towards the former and away from the latter group of
countries.

Hitherto, such claims would have had to be analyzed
in a theoretical framework. But now, with the change

from pegged to floating rates in 1973,5

they can be
analyzed both theoretically and empirically. The
objective of this study is to conduct such an investiga-
tion for five developing countries, India, Israel,
Korea, Mexico and Taiwan. Initially, a broad cross-
section of countries in terms of geographic location
and income level was contemplated for this study.
Because of a severe lack of data, however, only the
above five countries were left from the original sample.
In order to examine the developing countries'
claim, this study seeks to answer the following questions:
1. Whether the claims have theoretical validity,

i.e., from a strictly theoretical perspective,

is there reason to believe that exchange risk

 

5The exact date of transition from one system to the
other is difficult to determine because there has been
considerable turbulence in the international monetary
arena since 1971. This issue is dealt with in detail
in Chapter 4.

could affect export levels? This question is
addressed in Chapter 2.

2. Did exchange risk increase with the introduction
of floating rates? The specification and
measurement of exchange risk under the two
systems (pegged vs. floating rates) is under-
taken in Chapter 4.

3. Even if the conclusions pertaining to these two
questions is in the affirmative, does the empir-
ical evidence indicate that developing countries'
exports have

a) undergone a significant structural
shift as a result of the higher level of ex-
change risk under the floating rate system,
and

b) become biased towards the center
country (the country to which their currency
is pegged) due to the asymmetry in any increase
in exchange risk?

The theoretical specification of the models needed

to examine these two issues is developed in Chapter 3.
The empirical testing procedure and results are presented
in Chapter 5.

A precis of the study and the main conclusions

resulting from it can be found in Chapter 6.

CHAPTER 2

EXCHANGE RATE UNCERTAINTY

AND THE LEVEL OF INTERNATIONAL TRADE

The purpose of this chapter is to examine the manner
in which the decisions of an exporting firm in a
developing country are influenced by exchange rate
uncertainty. This problem is analogous to that of a
domestic firm facing price uncertainty (domestic in the
sense that its output is sold on domestic markets).
The exporting firm usually has the option of hedging
against exchange risk through operations in the forward
exchange market. Accordingly, investigations of the
exporting firm have explicitly incorporated a forward
market for foreign exchange in their models. Domestic
firms, too, have facilities for reducing their exposure
to price uncertainty. In some instances, a futures
market exists for the output of the firm. In addition
to or in lieu of futures markets, domestic firms can
and generally do enter into long-term contracts with
buyers of their products. This serves the purpose of

reducing exposure to price risk much like futures

fi

ti

markets do. Clearly, then, exchange risk for a trading
firm can be analyzed in the same manner as price uncer-
tainty for a domestic firm.

So far, investigations of the domestic firm facing
price uncertainty have abstracted from the futures market
or other means that a domestic firm has of hedging against
price risk.6 Since the two problems are analogous, the
results of the present investigation fill this void and this
is an important extension of the theory of the firm--both
of the domestic and of the trading types.

The problem of the trading firm has been analyzed
in the literature but the results are, by and large,
contradictory and inconclusive. Some authors conclude
that exchange rate uncertainty does not affect the output
decisions of a trading firm, so long as a forward exchange
market exists.7 Others have contended that forward
markets do not fully eliminate the effects of exchange

rate uncertainty, and therefore, output decisions will

 

6Sandmo, Agnar, "On the Theory of the Competitive Firm

Facing Price Uncertainty", ARR, March 1971, pp. 65-73,
and Coes, Donald V., "Firm Output and Changes in
Uncertainty", ARR, March 1977, pp. 249-251.

7Ethier, Wilfred, ”International Trade and the Forward
Exchange Market", ARR, June 1973, pp. 494-503. McKinnon
also examines the question of optimal hedging in McKinnon,
Ronald 1., Money in International Exchange, pp. 89-93 (New
York, NY; Oxford University Press, 1979). His examination
is even more constrained than usual. First, he separates
the production from the hedging decision. Second, he
assumes that the forward rate is equal to both the present
spot rate and the future spot rate. Third, perfect for-
ward markets are assumed. His model bears a striking resem-
blance to Ethier's model and the results are also similar.

10

8'9 The reasons

be influenced by changes in uncertainty.
for the contradictory findings can be traced to some
particularly artificial assumptions adopted in these
investigations, making their results special cases
incapable of being applied generally. All three studies
mentioned above assume, for instance, that the utility

of profits is a quadratic function. Arrow10 has shown
that quadratic utility functions violate the intuitive
and widely accepted concept of decreasing absolute risk
aversion. In addition, it is commonly assumed that
forward exchange markets are perfect in the sense that
costs are insignificant and that cover can be obtained
for all currencies and for any maturity without affecting
the forward rate. Such an assumption is questionable
even for developed countries. For developing countries,
it amounts to a distortion of reality. Consequently,
results founded on such premises are questionable, and

do not lend themselves to generalization.

 

8Clark, Peter B., "Uncertainty, Exchange Risk and the

Level of International Trade, Western Economic Journal,
September 1973, pp. 302-313.

 

9Hooper, Peter and Kohlhagen, Steven W., "The Effect of

Exchange Rate Uncertainty on the Prices and Volume of
International Trade", unpublished manuscript, Federal
Reserve Board, 1978.

 

loArrow, Kenneth J., Essays in the Theory of Risk-Bearing,
pp. 90-120 (Chicago, 111.; Markham Publishing Company,
1971).

 

11

They are certainly not applicable to developing
countries.

Several imperfections in the financial markets
of developing countries have been identified which
have the combined effect of imposing substantial costs
on transactions in the forward exchange market:12 Among
these, the following are especially pertinent to the
present investigation:

1) In developing countries, the forward exchange
markets are not sufficiently wide or deep to ensure that
forward transactions in all currencies and for all
maturities will be 'perfect.‘ For instance, the market
for irregular maturities (as opposed to multiples of
30 days) are either non-existent or notoriously thin.
Thus, the forward.rates obtained by a firm for such
irregular maturities is bound to be sensitive to the vol-
ume of transactions by the firm. The rates would

incorporate additional premiums, which can be inter-

preted as costs resulting from the nature of the forward

 

llIt should be acknowledged that the studies referred to
above did not intend to explain the behavior of exporting
firms in developing countries specifically. Thus, they
are not subject to criticism in the treatment of the
problem. The point being made is that the results cannot
be applied to developing countries.

2Black, Stanley W., "Exchange Policies for Less Developed
Countries in a World of Floating Rates", Essays in Inter-
gational Finance (#119), (Princeton, NJ: International
Finance Section, Princeton U, December 1976).

 

12

market. The lack of breadth implies, similarly, that
it would be costly or impossible for a firm to obtain
cover in certain currencies.

2) Exchange control, which is in force in most
developing countries, also imposes certain costs on the
trader. In most countries, forward cover is provided
exclusively by the government. For this reason alone,
there is apriori reason to believe that the costs of
forward transactions can be substantial. The government,
unhindered by competitive pressure, has little incentive
to minimize the difference between its buying and selling
rates.

3) Geographically, too, the forward market is
rather stratified, being concentrated in a few selected
urban centers. Exporters in surrounding areas typically
have to incur considerable costs in finding a market. In
addition, information costs even between two metropolitan
areas can be substantial due to inefficient communica-
tions links.

4) As Black points out, the size of even European
markets is small compared to the market in New York.13
The size consideration is even more important in the
case of developing countries. When the size of the

market is small, it is not economic to develop a wide

 

13mid. , p. 20.

13

network of dealers, brokers, interbank arrangements
etc., that are essential for the smooth operation of
the market. Most versions of exchange control restrict
or prohibit citizens from holding and trading in foreign
exchange. Therefore, exporters in these countries cannot
avoid the high costs of the domestic market by shifting
their dealings to the New York or some other well-
developed market.

In order to keep the present investigation general,
a Von Neumann-Morgernstern type utility function is
employed, with only one restriction imposed on it--that
of decreasing absolute risk aversion in the Arrow-
Pratt sense.14 And to incorporate the imperfections
commonly found in the financial markets of the developing
countries, it is assumed that there is a non-trivial
cost associated with forward exchange transactions.
This cost is a function of the volume of transactions

undertaken.

 

JIArrow, op.cit., p. 96.

14

THE MODEL

 

Consider, then, the case of an exporting firm
Operating under the following conditions:

1) The firm produces one homogeneous good, q,
exclusively for export. The export market is assumed to
be perfectly competitive. Thus, the price in foreign
currency, p, is determined exegenously.

2) The firm commits resources to production only
after export orders are secured, so that the foreign
price is known with certainty at the time the production
decision is made.

3) The firm is paid in foreign exchange. It can
convert this to domestic currency through the forward
market today (at the known forward rate, f) or through
the spot market when payment is received.

4) The future spot rate at which uncovered exchange
receipts are converted is a random variable, r, with a
known expected value, 3, based on the firm's subjective
probability distribution for r. This is the source of
all uncertainty in the model.

5) The cost functions for production and for
operations in the forward market are assumed to be
known with certainty, i.e., they are non-stochastic.

The usual assumptions about positive and increasing

15
marginal costs apply, to ensure stability in these
activities. Also, marginal cost is assumed to be zero
at the origin.
We can then write the firm's profit function in

terms of domestic currency, as follows:

PROFITS: a s apfq + (l-o)prq - c1(q)

C2(apfq)

Where:

a prOportion of foreign exchange sold through

the forward market.
p = price in terms of foreign currency

q = quantity of output

omestic currency

— . d
f — the forward exchange rate. [ foreign currency

 

r = the future spot exchange rate, a r.v. with an

expected value of E based on a subjective

omestic currency
foreign currency

 

PIObability distribution: [d

c1(q) = the known (non-stochastic) cost function for
production, with C1'>0.
c2(apfq) = the known (non-stochastic) cost function for

operating in the forward market with CZ'E 0 as

apfq E 0, and C2">0.

The exporter seeks to maximize the expected utility
of profits, where the utility function is of the Von
Neumann-Morgernstern type, so that U'>0 and U"<0, i.e.,

the firm: is risk-averse.

16

Therefore, the objective function is:

Max.: E[U(n)] E E{U[apfq + (l-a)prq - C1(q) - C2(apfq)]}
qu

Necessary and sufficient conditions for a maximum are

BE[U(n)] - - . _ _ u _ u =
-———§§——— = Uq - E{U [apf + (1 a)pr C1 C2 apfl} 0

(2.1)
3E[U(")] — _ I _ - ' -

and the second-order conditions

: _ 2
qu, Uaa < 0, and D _ qu Ucm (Uqa) > 0

are satisfied.

 

2
. . a E[U(n)]
Uij is defined as 31 33

Since U'>0, 2.2 can be written as:

EIU'pr] = EIU'lpf(l-C2') (2.2')

17
Similarly, 2.1 can be written as:
E{U'Il-o)pr - C1"]} = -E[U'][apf(1-C2')]

and, substituting for E(U')pf(l-C2') from 2.2', we

have the result,
E{U'pr} = E{U']C1' (2.1')

Combining 2.1' and 2.2', we can write the first order

condition for a maximum as:
E{U'lpf(1-C2') = E{U'JCl'
Eliminating E(U') this becomes:

pf(1-C2') = Cl' (2.3)

In order to establish the relationship between the output
and the exchange Operations through the forward market,

2.3 can be graphed by noting that:

a _ 2 2 u
3; [pf(1-C2')] — -p f q C2 < 0
f
> 0 when a < 0
-—3— [ f(1-C ')J = - 2fzc " o > 0
3q P 2 up 2 < when a
=0Whena=0

 

pf

18

This is done in Figure 2.1.

pf(1-C2 )Iazml

-f(1-C2')h1<0

 

 

 

A l _
pf(1-C2 )Iao—O
D
E

. _ I
f(l c2 )h3>o
__ l

pf(1 c2 )h4>a3

q
Figure 2.1

Optimal Production and Hedging

19

It is clear that a and q change inversely. As a
declines from a4 to G3, the optimal output which satis-
fies 2.3 increases from E to D.

As a declines further, say to do, the output
increases to A. And, in fact, output increases each
time a declines (to B at a1<0 and to C at d2<al).

We have said nothing, so far, about the firm's
expectations of the future spot rate (E) which is

necessarily an important variable in the decision pro-

cess. In order to see how the firm's expectations come

into play, we first note that from the profit function,15
u = E(w) + (l-a)pq(r-Y)
From which it follows that
U'(1r) 5 U'(E1r) for (1-a)(r-'i:') _>_ o (2.4)
or, multiplying both sides by (l-a)(r-E),
U'(l-d)(r-;) f U'(En)(1-a)(r-E) for all a and r.
(2.5)

If (l-a)(r-§) were negative, the inequality in 2.4 would
be reversed, but upon multiplication by (l-a)(r-F) < 0,

the inequality in 2.5 is preserved.

 

15The procedure adOpted is similar to Sandmo, op.cit.,

p. 67.

20

Taking expectations of both sides and noting that

En is a given number,
E{U'(1-a)(r-E)} f U'lEn](l-a)E(r-f)
The right side goes to zero and thus,
E{U'(1-a)(r-f)} 5 0 (2.6)
Substitution into the first order condition 2.2' yields:
E{U'] (1w)? 3 E{U']f(l-C2')(1-a)
or E(l-a)[? - f(l-C2')] 3 O (2.7)

It can be shown that the equality will hold if and
only if a = 1 (see Appendix 1 for a proof). Hence, we

can say that

E = f(l-C2') <=> d = l (2.8)
Y > f(l-C2') <=° a < l (2.9)
f < f(1-C2') <=> a > 1 (2.10)

21

Furthermore, it is clear from equations 2.8 through

2.10 that
a. f. 0 --> f > f (2.11)
0<a<1 -> EEf (2.12)
a 3 1 -—-> E < f (2.13)

since C2' is negative only when a < 0,

which imply that

a < 1 <=> ‘E 3 f (2.14)

a > 0 <=> E 5 f (2.15)
Similarly, substitution of 2.6 into 2.1' yields:
E{U']p§(l-a) 3 E{U']C1'(l-a)

or, (l-a)(p? - Cl') 3 0, with equality holding if and
only if a = 1 (see Appendix 1 for a proof). Thus, it

is clear that,

a = 1 <=9 pr = Cl' (2.16)
a < 1 <=> p; > Cl' (2.17)
a > 1 <=> pf < C ' (2.18)

22

We can now incorporate equations 2.7 to 2.18 into our

graphical representation of the first order condition

2.3, as shown in Figure 2.2.

 

 

'
c31
a1<0
prl —————————————— "A — '_ '-
o030
pr3 ————— -'—‘—«— )— -— — -_— -
0<a2<1
a4>1 =1

 

 

Figure 2.2

Expected Future Spot Rates and
Optimal Production and Hedging

23

If the expectation of the future Spot rate is higher
than the forward rate, then from equation 2.14, it is
clear that a will be set at less than one. Exactly
where the firm's optimum will be will depend on the
firm's attitude towards risk, the spread between the
two rates, and the confidence it attaches to E (we
shall return to this point later). In view of the
first order condition, all we can say is that the
equilibrium point will lie on the marginal cost curve,
Cl'. Suppose F = fi as shown in the figure. Then AB
is the range within which the firm will operate.

It can choose a quantity of output between A and
B, and can choose an appropriate a (less than unity)
such that the firm is at a point on C1' between AB.
Clearly, several combinations of a and q can be chosen
to reach this optimum. In any event, A represents a
ceiling on the quantity of output, and on the extent
of overt speculation that will be undertaken by the
firm against the domestic currency. Point B on the
other hand represents the minimum output and the
maximum amount of cover that will be sought. Presumably,
the less risk-averse a firm is, the closer it will
choose to be to point A and vice versa.

Now suppose that the eXpected future rate is

below the forward rate, say E3. In this situation, a

24

negative a will not be selected (see equation 2.15).
Point C represents the lower limit on output and the
ceiling on overt speculation against the foreign
currency. Correspondingly, point D is now the ceiling
on output and the lower limit for the extent to which
the exporting firm maintains a long position in the
foreign currency.

One interesting implication of these results is
that it provides a clear set of criteria for distinguish-
ing between overtly speculative behavior (against the
domestic or foreign currency) and hedging activities--
a distinction that has not been made too clearly in
existing literature.

There is a consensus in the literature that a
choice of a outside the range of zero and one represents
overtly speculative behavior either against the
domestic currency (a<0) or against the foreign currency
(a>l). It is within the range 0<a<1 that there is
confusion, and which the present analysis clarifies.
Some authors suggest a value of a=l as the criteria to
distinguish pure traders from speculators. Any value
of a different from one is seen as speculative behavior,
either against the domestic currency (a<l) or against
the foreign currency (a>1). A pure trader would always

set a=1. In this view, so long as a is less than one,

25

a speculative motive is implied regardless of whether
the value of a is negative or not. But, as Einzig
points out, banks consider transactions to be Specula-
tive only when a is negative (or greater than one) and
are reluctant to provide forward cover in these cases.16
For example, New York banks have been found to charge
a ten percent margin deposit for such transactions.17
Such a distinction between transactions where a<0 or a>l
and where 0<a<l is also more intuitive.

Ethier presents another method for distinguishing
between trading and speculative transactions. In his
view, a choice of a different from l-y (where y is a
measure of the sensitivity of domestic prices to
changes in the exchange rate) immediately implies that
pure speculation is being undertaken.18

Both these approaches assume that firm behavior
can realistically be portrayed by 'razor-edge' criteria.
If a firm sets a equal to some critical value (either
1 or, in Ethier's framework, 1-y) it is merely hedging,

whereas if it sets a equal to any other value it

automatically becomes a speculator. It is doubtful if

 

lGEinzig, P., A Dynamic Theory of Forward Exchange, pp.
104-106 (London, Macmillan & Co., 1967).

lzGrubel, H.G., Rorward Exchange, Speculation and the

lgternational Flow of Capital, p. 102 (Stanford, CA;

Stanford University Press, 1966).

 

 

 

lgEthier, op.cit., p. 497.

26

firm behavior can be represented in such an inflexible
manner. More intuitive and reasonable is the result

of the present study. A firm would not set a less than
zero or higher than one except for purely speculative
reasons. There is consensus in the literature too
regarding this, and it warrants no elaboration. On

the other hand, this study concludes that a firm may
set a between zero and one for either hedging purposes
or for pure speculation. An unambiguous answer to
whether a firm is speculating or hedging when it sets

a between zero and one can only be obtained by examining
the circumstances underlying the transaction. This
statement is clarified below.

According to equations 2.14 and 2.15, a firm may
set a in this range (0<a<1) when P :.f and when E i f.
This seemingly non-binding and contradictory condition
is, in fact, the basis for distinguishing between
hedging and speculative transactions.

Suppose that the expected future rate is higher
than the correSponding forward rate (E 1 f). There are
two possible motives for the firm to sell foreign
exchange on the forward market, even though it expects
the future spot rate to be higher. Firstly, the spread
between the rates may not be sufficient to warrant
overt speculation against the domestic currency (a<0),

particularly after considering the costs of forward

27

market transactions. This motive can be ignored, for
the firm would be better off setting a equal to zero

in this case, because the costs of forward market
transactions are a minimum at this point. The second,
and more likely motive is.that although ER; f, the firm
may not be too confident of its prediction of the
future spot rate. Thus, it may consider it possible
that the realized future spot rate falls below the
present forward rate. To 'hedge' against this possi-
bility, the firm chooses to sell part of its foreign
exchange receipts on the forward market, even though it
is below what the firm expects the future spot rate

to be. Therefore, it may be concluded that when a firm
sells foreign exchange in the forward market even
though ER: f, it is engaging in hedging.

Conversely, the firm may set a between zero and
one when the forward rate is higher than the expected
future spot rate (f ;_§). Clearly, the firm would not
select a negative 0 when f 3,? (see equation 2.15). A
positive a will be chosen to speculate against the
foreign currency. With no transactions costs in the
forward market, an a greater than one might have been
chosen, its magnitude depending on the spread between
the two rates and the confidence attached by the firm to

its prediction of the future spot rate, F. In the

28

presence of such costs, however, the firm may find
an a between 0 and l to be Optimal. The precise
value chosen for a will be determined by the spread
and confidence considerations mentioned above, and
the related transactions costs. Given a level of
transactions costs, a will be set closer to l, the
higher the spread and the confidence attached to E
are.

To summarize, we may say that a choice of a outside
the range Of zero and one clearly indicates speculative
behavior. Within this range, however, the firm may be
hedging against exchange risk (if E i_f) or speculating
against the foreign currency (if E 1 f).

Another Observation relates to the setting Of a at
1. In previous literature, it has been assumed that
the trader will choose to set a at 1 unless some specu-
lative profit is sought. Given our new definition Of
speculation, and considering equations 2.8 and 2.16,
the conclusion is that we cannot make such a general
statement. TO set a=1, these two equations must be
satisfied simultaneously. Because they are independent
of each other, satisfying one does not imply that the
other is also fulfilled. Thus, a will be set at one
only if the marginal cost in production (Cl') happens

to equal marginal revenues through the forward rate

29

(pf(1-C2')) and the expected future spot rate (p?) at the
same level Of output. A brief inspection Of Figure 2.2
reveals that such a situation would arise more by

chance than by intention.

The final conclusion from the above analysis is
that exchange rate uncertainty can be expected to
influence a firm's output and forward transaction
decisions. This can be seen by examining the first
order condition, equation 2.3. Although the first
order condition does not explicitly depend on the firm's
utility function, it would be incorrect to conclude from
this that its decisions are independent Of exchange
rate uncertainty. The choice Of output and the choice
Of a are determined jointly by this equation. Both
Of these, in turn, depend on the utility function Of

the firm through equations 2.1' and 2.2'.
Marginal Impact Of Uncertainty

The preceding analysis can be described as the

overall impact Of uncertainty, following Jacques

19

Dreze and Franco Modigliani. An equally interesting

problem is the marginal impact Of uncertainty. Indeed,

 

19Sandmo, Op.cit., p. 67.

30

the effect Of increases in the level Of uncertainty
is more central to this research than is the effect
Of the introduction Of uncertainty into a world
characterized by certainty. The study seeks to examine
the effect on trade levels Of changing from a pegged
exchange rate system to a floating one. Exchange
uncertainty existed under both systems, but the transi-
tion, it is claimed, resulted in an increase in the
level Of exchange uncertainty.

In order to investigate the impact Of an increase
in the level Of risk, the subjective distribution Of r
must be changed to reflect the higher level Of risk.
Several ways to accomplish this exist, but the one
adopted in this study is the 'mean-preserving' spread.
This method has been shown to be superior to the more
commonly used methods such as the mean-variance approach,
where the mean and the variance are both increased.20

The mean-preserving spread is a way to make a
distribution more risky by 'stretching' it while leaving
the mean unchanged. This enables the isolation Of
the effects of increases in risk, and is done by
replacing the random variable in the model with a
linear transformation Of it. Specifically, we replace

r by (yr + 9), imposing the condition that dE(yr + e) = 0.

 

20Rothschild, M. and Stiglitz, J.E., "Increasing Risk
II: Its Economic Consequences", Journal Of Economic
Theory, March 1971, pp. 66-84.

 

31

This implies that,

de )—

——= -r

5‘1

We can then differentiate the first order conditions

with respect to y to get:

 

 

d d dd
U = U + U + = 0
3? I <11 cm 3% qu 3? ”cm
(2.19)
d _ d do _
d? [Ua] - an d$'+ Uaa d? + Uav — 0
From which
U U - U U 2
$3 = aq QY qqr'ay . where U..== a ELU(E)] (2.20)
y U _ (U )2 13 31 a]

qu a a go:

The denominator is Obviously positive, since it is
the determinant Of the second order Hessian. Therefore,
the sign Of 3% is the same as the sign Of the numerator,

which depends on:

— fl 0
an — E{U nanq + U waq} (2.21)
= E U" + U' 2.22
UqY { nqu wqy} ( )
— I. 2 '
Uaa - E{U (nu) + U "00} < 0 (2.23)
U = E{U"fl n + U'fl } (2.24)

GY a ‘Y G'Y

32

where,
In 32-1
1 3i
= 32w
1] 31 33

The profit function is:
w = apfq + (l-a)p(yr+e)q - C1(q) - C2(apfq)
and the Objective function becomes:

Max.: E[U(w)] s E{Ulapfq + (l-a)p(Yr+@)q - C1(q)
qr“

- C2(apfq)]}

This yields the following necessary and sufficient

conditions for a maximum:

(2'.
ll

E{U'Iapf(l-C2') + (l-a)p(Yr+e) - Cl']} = 0

C
II

E{U'IPfQ(1-C2') - p(yr+0)q]} = 0

' : _
Uii < O and D - qu Uaa (Uqa) > 0

33

We can evaluate the Uii's defined in equations 2.21-
2.24 at the point where y=l and e=o, and write equation
2.22 as,

UqY = E{U"[(l-a)2(pr-Cl')(pr-p?)q] + U'(1-a)(r-F)p}

after substituting for pf(1-C2') from equation 2.3.
Obviously, qu=0 when a=l. When afil, the second
term is negative from equation 2.6. The first term

may be re-stated as:
E{U"(l-a)2(pr-Cl')q[(pr-C1') + (cl'-pf)1}
_ II 2 I 2 II 2 I - I
- E{U (1-a) (pr-Cl ) q + E U (l-a) q(C1 -pr)(pr-Cl )}

The first term here is negative since the firm is
risk-averse. Also, (l-a)(C1'-p§) is negative from
equations 2.17 and 2.18. Furthermore, it can be shown
that if the firm exhibits decreasing absolute risk
aversion, E{U"(1-a)(pr-C1')q} is positive. Absolute
risk aversion is defined, following Arrow, as
-U"(n)/U'(n) and denoted as Ra(n) > 0. Thus,
decreasing absolute risk aversion implies that

Ra' (17) < 0.

34

Following the line Of reasoning suggested by
Sandmo, let F be the profit level when pf’= Cl'.

Then, with Ra(w) > 0 and Ra'(w) < 0, we have,
Ra(n) 5 Ra(?) for pr 3 Cl' and a < 1,

since 'pr' enters the profit function positively only

when a < 1. In other words,
_ _ ' _
Ra(fl) f Ra(n) for (pr C1 )(1 a) 3 0
Multiplying both sides by -U'[(pr - Cl')(1-a)]. we have,
U"(pr-Cl')(l-a) 3 -U'Ra(?)(pr-Cl')(l-a)

for all 'pr' and a.
Taking expectations Of both sides and noting that

Ra(?) is a given number,
E{U"(pr-Cl')(1-a)} 3 -Ra(?)(l-a)E{U'(pr-Cl')}

The right side is clearly zero from 2.1'.
Therefore, E{U"(pr-C1')(l-a)} 3 0 and we can

conclude that

< O for a f 1

U (2.25)
QY

0 for a = 1

35

Similarly,

UGY E{U"[pfq(l-C2') - prqlll-a)p(r-F)q]

- U'p(r-F)q}

E{u"[(c1'-pr)(1-a)p(r-E)q21 - U'p(r-F)q}

qu . Uga- (2.26)

Ugo: E{U"q(C1'-pr)(l-a)(pr-C1') + U'(Cl-pr)

- U'C2"ap2f2q}

= E{-U"q(Cl-pr)2(1-a) - U'C2"ap2f2q (2.27)

since the expectation of the second term is zero.

Lastly,

C'.
II

II 2
qq E{U [apf + (l-a)pr - Cl' - Cz'apf]

+ U'(-C2"(apf)2 - cl")}

E{U"(1-a)2(pr-C

1')2 - U'[C2"(apf)2 + C1"]}

(2.28)

36

Substituting for Uay from 2.26 into 2.20 and rearranging

terms, we have

do _ l
37 " D' [Uqa + qu TIE-13V qu

U U - (U ) > 0
qq ad go

where D'
Which upon substitution from 2.27 and 2.28 yields,

')2 - U'C2"ap2f2q

qu-

quE{-U"(l-d)q(pr-Cl

+ U"(1-a)q(pr-Cl ~7-1'13T[C1"+C2"(apf)2]}

1 , 2 2 UI C2 II UI qcl II
5. UqY E-U'C2"ap f q + '(T-TZ')‘ (apf)2 q + 737%}

U
1 ' fl 2 2 fl " 2 2 2

+ U'C2"(apf)2q}

.uS—TFAU th2 "up 22f + 01"]}

The term within the brackets {...} can be shown to

I
Ull-l

be positive. The first term, C2"ap2f2 is the negative

Of the slope Of [pf(l-C2')] with respect to q.

37

When a 3 0, the slope of [pf(1-C2')] is non-positive

(see Figure 2.1) and thus,

C2"ap2f2 3 0

From which it follows that

2 2 .

C2"ap f + C1 > 0

On the other hand, when a < 0, we can see from Figure

2.1 that

u 22 ..
-C2 up f < Cl

which implies, once again, that

2 2 .

I
C2 up f + C1 > 0

Furthermore, it has been shown that

f < 0 for a i l
UQY
= 0 for a = 1
< 0 if a > 1
UY
a- > 0 if a < 1

38

We may therefore conclude that,

/ < 0 if a > l

__ < = 0 if a = l (2.29)

 

( >0 ifa<1

In order to solve for %%" we need to evaluate

Uaa at y=1, and e=o.

C.‘
(I

E{U"(fla)2 + U'n }

ca (10.

E{U"(Cl'-pr)2q2 - U'C2"(pfq)2} (2.30)

Then, solving for E? from the equations in 2.19,

d_l _
3% - 5' [Uaqua Uaaqu]

and substituting for UaY from 2.26 we have,

a):
II

1
5' [-UQY TIEET'Uqa - Uaaqu]

U
91 (l-a)
- U' -a [qu + Uaa q 1

39

Finally, substituting for Uqa and Uaa from 2.27 and

2.30, respectively,

d _ 1 u - 2 _ _ I II 2 2
3% - - B. Uga— quml-u (cl' pr) (1 OH} U C2 up f q]

(l-a)
q

 

+ E{U"(Cl'-pr)2(l-a)q - U'C2"(pfq)2 ]}

n 2 2 u 2 2
. «(l-ga- qu{-E[U'C2 up f q + U'C2 p f q

I
I
OH“

2

- U'C2"ap fqu}

1 .. 2 2
= B' TEL—330' quEIU'Cz P f q]

The term in brackets is positive as shown earlier, and

UqY was shown to be negative when a f l, and equal to

zero when a = 1. Hence, we can conclude that,

 

( > 0 if a > 1

Ag .

dY ( < 0 if a < 1 (2.31)
(=Oifa=1

The results contained in equations 2.29 and 2.31 are
summarized in Table 2.1, for the four distinct regions

of o.

40

Table 2.1

Effect of Increased Exchange Uncertainty
On Output and Forward Market Transactions.

 

 

a<0 0§a<1 ' a=1 d>l
Output decreases decreases unchanged increases
ke .
Forward mar t decrease increase unchanged decrease

transactions

 

The four cases are now examined separately to illustrate

the rationality of these decisions.

CASE 1: u<0

 

When a is set at less than zero, the firm is overtly
speculating against the domestic currency, since it
expects the future spot rate to be higher than the
present forward rate. (Because of the way exchange rate
is defined, a higher rate for domestic currency means
it is devalued.) The firm contracts to buy foreign
exchange through the forward market in the expectation
of a speculative profit. This transaction is against
the direction indicated by the export transaction. The

export earnings are left totally uncovered. When the

41

export earnings are received and the forward contract
becomes due (simultaneously, by assumption), the
firm will sell the foreign exchange in the future
spot market. We can, therefore, identify the mar-

ginal profit from the export transaction to be
p? - cl' > o (2.32)

from equation 2.17. The marginal profit from the

speculative transaction can be stated as
pf - pf(l-C2') > o (2.33)

from equation 2.9. In the absence of uncertainty,
production and speculation would both be increased

to the point where these two inequalities became
equalities. Therefore, the lower levels of both
transaction implied by 2.32 and 2.33 can be unam-
biguously ascribed to the presence of uncertainty
surrounding the future spot rate. When the level of
uncertainty increases, production and speculation are
reduced, per Table 2.1, column 1. Such a reduction
increases the spreads in 2.32 and 2.33 by reducing the
marginal costs in both cases. Since p? is unchanged, it
is clear that the firm responds to the increased level
of uncertainty by demanding a larger marginal profit.

This is, of course, characteristic of risk-averse behavior.

42

In terms of Figure 2.3 (shown as Figure 2.2
earlier), the firm moves from a point such as A to

a point below, say B.

“I‘—‘‘‘‘-IIIIIIIIIIIIIIIIIIIIIIIIl"A
pf -

B
pf(l-C2')lao=0
C
D

Figure 2.3

 

 

 

Expected Future Spot Rates and
Optimal Production and Hedging

43

CASE 2: 0$a<1

 

As explained earlier, the firm may set a in this
range for speculative purposes (if f3?) or for hedging
purposes (if :53). These two cases can be analyzed
separately.

First, suppose that £33, so that the firm is
speculating against the foreign currency. In other
words, the firm would cover foreign exchange earnings
from the export transaction, but because it seeks
speculative profit, it leaves a part of its foreign
exchange receipts uncovered for purely speculative
purposes. We may depict this situation by identifying
the marginal profit from the export transaction (with

a=l) to be

C ' - pf(l-C2') = 0 (2.34)

l

by equation 2.3. This equality is understandable since
no uncertainty is involved in this transaction.

The marginal profit from the speculative transac-
tion (i.e. leaving the (l-a)th unit of foreign exchange

uncovered) is

p? - pf(l-C2') (2.35)

which is positive from equation 2.9. According to

Table 2.1, the firm reduces both output and exports

44

in the face of increased uncertainty in this case.

An examination of these two marginal conditions reveals

that such behavior is in keeping with risk-averseness.
Faced with a less certain future spot rate, the firm

seeks to increase the spread in equation 2.35. This it

does by reducing the level of speculation (i.e. by

increasing a). No sooner is this done, however, than

the equality in 2.34 is disturbed. Specifically, the

net marginal revenue from the forward market declines.

The firm, therefore, reduces output to restore the

equality between the marginal cost, and marginal

revenue of its export transaction.21
Conversely, suppose the firm chose an a in this

range in order to hedge against exchange risk. We may

then specify its marginal export condition as
p? - C1' > 0 (2.36)

since the only reason for selling foreign exchange in
the forward market was to reduce the level of exposure
to exchange uncertainty. By equation 2.17, this value
is positive. As before, it can be argued that the
lower level of output implied by 2.36 as compared to

the decision rule under certainty (p? = Cl'), is due

 

21It should be pointed out that since C ' is determined

jointly by q and a, the restoration 0 equilibrium
involves a series of iterations. But because the
final direction of change in these two variables is
known, the process is described in this and following
discussions as a single iteration adjustment, without
affecting the conclusions.

45

to the uncertain future spot rate. Hence, the firm
is reducing exposure to exchange rate partly by
reducing output, and partly by hedging.

The premium (at the margin) paid by the firm to

reduce exposure through hedging is specified by

pf(l-C - pr < 0 (2.37)

2')
which is negative per equation 2.9. An increase in the
uncertainty surrounding the future spot rate would
cause the firm to seek a higher level of cover since
it is risk-averse. Such an action increases the spread
in equation 2.37, increasing the premium. Clearly, the
firm is willing to pay a higher premium to hedge against
the higher level of exchange risk involved.
Simultaneously, the firm is able to reduce exchange
exposure by reducing output, thereby increasing the
spread in 2.36. These changes are consistent with risk-
averse behavior, as specified in Table 2 (column 2), and

depicted in Figure 2.3 as a movement from C to D.

CASE 3: a=l

 

As pointed out earlier, the choice of an a of unity
will be a rare occurrence, since two unrelated conditions

need to be satisfied at this point. Simultaneous

46

satisfaction of these two conditions (equations 2.8

and 2.16) would occur more by chance than by intention.
When such an a is selected, however, the firm totally
covers its foreign exchange earnings, and assumes a
neutral speculative stance. No uncertainty surrounds
the export transaction in this case. Thus, the firm
produces at a point where its marginal cost of produc-
tion exactly equal its net marginal revenue from the

forward market. That is,
_ l = I
pf(l C2 ) Cl (2.38)

defines the firm's production decision. Clearly, a change
in the level of exchange rate uncertainty effects nei-
ther side of 2.38. Thus, no output changes would result,

which is consistent with Table 2 (column 3).

CASE 4: u>l

 

In this situation, the firm is speculating overtly
against the foreign currency. It expects the future spot
rate for domestic currency to be lower (i.e. the foreign
currency to devalue) than the present forward rate-~see
equation 2.13. The firm enters into a forward contract
to sell its entire foreign exchange receipts from the

export transaction. In addition, the firm assumes a

47

long position in forward foreign exchange in anticipa-
tion of a speculative profit.

Here, the output decision is being made by equat-
ing the marginal costs and marginal revenues from the

forward market

The speculative transaction, on the other hand, yields

the following marginal profit

pf(l-C - pr > 0 (2.40)

2')
which is positive from equation 2.10. Following earlier
analysis, we can examine the firm's actions if uncer-
tainty increases. When this happens, the marginal costs

of the speculative transaction is subject to greater

risk. Therefore, a risk-averse firm would seek to

increase the spread in 2.40. This it does by reducing

a, which reduces the value of Cz'. No sooner is this

done, however, than the equality in 2.39 is disturbed since
the marginal revenue from production is now higher. The
firm increases its output in order to restore equilibrium
in its export transaction. Clearly, the directions of
change outlined in this case also conform with risk-

averse behavior, and are consistent with the results

stated in Table 2 (column 4), shown in Figure 2.3 as

a movement from E to F.

48

CONCLUSIONS

 

The following observations summarize the findings
of this chapter.

1) When the choice of a is unrestricted, it is
not possible to unambiguously predict the effect of
increased exchange uncertainty on the level of exports.
The result is dependent on the range in which a was set
prior to the increase in uncertainty. Output and
exports will decline if a had been below one. However,
if the firm is reasonably confident that the foreign
currency will depreciate and the spread between the
forward and future spot rate is large enough, a may be
set at greater than one. In this case, the firm's
exports can be expected to increase. If a large number
of exporters in a country share these expectations, it
may well transpire that such a country's exports would
rise in the face of increased uncertainty.

2) In most developing countries overt speculation
is prohibited. This has the effect of restricting a to
the closed interval between zero and one. In such a

situation, it can be unambiguously predicted that exports

49
will decline in the face of increased exchange rate
uncertainty.22

The results are, it should be noted, contingent
on the presence of significant costs associated with
forward market transactions. If these costs do not exist
or are insignificant, then Ethier's conclusions apply--
i.e. exchange risk will not effect export levels.23 It
has been argued here that in deve10ping countries forward
market costs cannot be ignored, justifying the present
analysis.

The next step in this research is to model the
export sector of a developing country. This is done in
Chapter 3. Then exchange risk is specified in an empir-
ically measurable way in Chapter 4, which also examines
the question whether exchange risk so defined has in
fact increased since the inception of floating rates in
1973.

Before we turn our attention to these issues, one
final observation needs to be made concerning the
question of forward market costs. While it is commonly

assumed that exchange markets in developed nations are so

 

22If asl, output would not change. But, even if a few

firms set a=1, the probability of which it has been
earlier is rather small, it is extremely unlikely that
all firms in a particular country would simultaneously
E5? a at this level. Therefore, when exporters in a
country are considered in the aggregate, this case can
be ignored.

23Ethier, op.cit., p 496.

50

nearly perfect that such costs are insignificant, this
position is not totally unquestionable. For instance,
the European Joint Float serves to minimize exchange
uncertainty between member countries. This would not
have been necessary if financial markets were perfect.
In addition, at a meeting of the Bank for International
Settlements in 1978, officials expressed serious
concern that the volatility of the U.S. dollar has had
a "negative influence on business decisions."24 Such
concerns provide circumstantial, though not conclusive,
evidence that exchange rate uncertainty is a pertinent
factor in trade decisions, even in countries that have
well-developed financial and exchange markets. There-
fore, the results of this investigation may be more

generalizable than is contended here.

 

4Zijlstra, Jelle, Netherlands Central Bank Chief and
BIS Chief, as quoted in the Wall Street Journal, June
13, 1978, p. 13.

 

CHAPTER 3

THE MODELS OF THE EXPORT MARKET

In this chapter, the export market for a developing
country is modeled. The relationship between exchange
rate uncertainty and the level of exports is then
explained in the context of the models of the export
sector. In the first model, the aggregate exports of
a country are considered, whereas the second approach
models the bilateral export markets. Building on the
analysis contained in this chapter, the models are
translated into empirically testable form in Chapter
5, which essentially deals with the empirical portion

of this study.

The Export Market in a Developing Country

 

Before the question of exchange uncertainty is
incorporated in the discussion, it would be instructive
and simpler to develop the models of export supply
and the demand for exports by the importing countries
excluding the uncertainty question. This simplification

is particularly beneficial because the export supply

51

52

and demand for export functions differ somewhat from
traditional ones, in order to account for the special
circumstances pertaining to the export markets in the
developing countries. These have been receiving
increased attention in the literature.

Traditionally, the export supply function is
viewed as an excess supply function, the underlying
assumption being that a domestic market also exists
for the good that is being exported. In this case,
export supply is really a residual between the domes-
tic supply and domestic demand for the good in question.
The export supply function would then include the
variables in the domestic supply as well as domestic
demand functions. Under this approach, the price
elasticity of export supply would be a weighted aver-
age of the domestic demand and supply elasticities.25

It has been argued that this approach is not
suitable for developing countries for two reasons.
First, the export bundle is likely to be vastly
different from the bundle of goods consumed domestic-
ally. Demand patterns and tastes in the export
markets (generally the industrial nations) differ

substantially from those of the domestic markets.

 

2SKreinin, M., International Economics: A Policy Approach,
3rd ed., p. 445 (NYC, NY; Harcourt, Brace Janovich, 1979)

 

53

Secondly, the export sector in developing countries is
typically not well integrated with the rest of the
economy. For these two reasons, it is claimed, the
specification of an export supply function as an excess
supply function would be erroneous. Instead, a pure
supply function is recommended, totally independent
of the domestic demand variables.26

While the observations concerning the developing
countries are by and large accurate, it is not clear
whether the use of an export supply function totally
independent of domestic demand is justified on these
grounds alone. However segregated the export sector
may be, it must still compete with the domestic sector
for productive resources. And domestic demand variables
can and will influence this allocation of resources.
For instance, if domestic prices rise, production
for the domestic market becomes relatively more profit-
able. Resources will shift to domestic production as
a consequence, reducing the output of exportable goods.
Clearly, other domestic demand variables will also
influence export supply, albeit not in as direct a

manner as implied by the use of an excess supply

function.

 

26See Grossman, G.M., "A Quarterly Econometric Model of
the Exporting Behaviour of Some Nonindustrial Countries",
unpublished manuscript, M.I.T., 1978.

 

54

It may be concluded from the above discussion
that although it is correct to view the export supply
function of a developing country as a pure supply
function, certain domestic demand variables must also
be included in the formulation. Accordingly, the
export supply function employed in this study is

specified as:

S 8

xi = Xi (Px.' Pd.' Yi) ' (3.1)
1 1
where,
x: is the exports supplied by country i.
Px is the price index for export.
i
Pd is the domestic price index, entering (1)
i
as a scale variable.
Yi is an index of domestic productive capacity.

It is also a scale variable, included on the
assumption that as a country's capacity to
produce rises, so will exports, ceteris

paribus.27

 

27Grossman, G.M., op.cit., criticizes the use of Y in

the export supply function in this manner. The reason
being that supply is determined by prime costs.
Grossman, therefore, uses wage rates instead. Again,
the reasoning is correct, but his solution does not
seem apprOpriate. Wages are just one component of
prime costs. Data on these costs are not available,
however, and hence the use of wages alone. There is
little reason to believe that changes in wages

55

The world demand for a country's exports is assumed

to be perfectly elastic.28

This assumption is justified
so long as the exports of the country are being studied
do not represent a significant portion of total world
exports of commodities involved. A perfectly elastic
demand for export is the equivalent of a perfectly
elastic supply function which is commonly assumed for
a small importing country.29
Under the small country assumption, the export
price is exogenously determined in the markets of the
importing countries. The exporting country cannot
influence this price and simply adjusts supply in
keeping with the exogenously determined price.

The effect of exchange rate uncertainty on the

level of exports can now be illustrated. Figure 3.1

 

27( contd . )

accurately reflect changes in overall prime costs.
Therefore, in the present study, the use of Y is
preferred, especially because it has yielded tolerably
good statistical fits in the past. See Goldstein, M.
and Khan, M.S., "The Supply and Demand for Exports:

A Simultaneous Approach", REStat» March 1977, pp.
275-286. Admittedly, this is not a satisfactory
solution, but is one necessitated by data considera-
tions.

2Tor'analternative formulation, dropping the small
country assumption, see Appendix 3.

29The proof of the present proposition is also similar,
and one can be found in Kreinin, M., op.cit., p. 445.

56

Export Price

 

 

 

SI
xi x?
1
Demand for
P Exports
X I I d

| I (xi)
I I
I I
I I
I I
I I

Q2 Ql Quantity

Figure 3.1

The Export Market for
a Developing Country

shows the export market of a small country, as described
above. If exchange rate uncertainty reduces exports,

as the developing countries have claimed, it can be
incorporated into the model by specifying the export

supply function as follows:

_ 5
xi - xi (Pxi, Pdi, Yi, Ri) (3.2)

where all the variables are as defined earlier, and R1

is a proxy for exchange rate uncertainty for country i.

57

In terms of Figure 3.1, the effect of an increase
in exchange uncertainty is depicted by a leftward
shift in the export supply function (from x: to Xi').
As a result of the increase in the level of exchange
uncertainty, exports decline from 001 to OQZ, at an
unchanged export price of Px'

It should be noted that for some commodities such
as oil, exporting countries are able to exert consi-
derable power in the export market. In such cases,
the small country assumption would not be appropriate,
especially since the exports of such countries are
highly concentrated in these commodities. By and large,
the countries being studied here (Mexico, Israel,
Taiwan, India and Korea) do not possess monopoly
power in any single commodity market, and therefore,
the small country assumption is justified. In addi-
tion, aggregate exports are being considered, so that
whatever little market power may exist in a particular
commodity, it is sufficiently diluted to pose no
serious problem.

A second approach used in this study to test
for the effect of exchange risk on deve10ping countries'
ability to export examines structural shifts in their
bilateral export supply functions. This test applies

only to those countries that did not change their

58

exchange rate practices when the managed float became
operative in 1973. Thus, Mexico, Taiwan and Korea
are the three countries for which this test is used.
India and Israel both changed their pegging practices
during the past six years.

Without loss of generality, consider a develOping
country, A, whose currency is pegged to the U.S.
dollar. Bearing in mind that after March 1973, the
U.S. dollar was floating against all other major
currencies, it is easy to see that the changes in the
level of uncertainty influencing A's exports to the
U.S.A. and to all other countries would be asymmetrical.
By way of illustration, we write A's exchange rate

vis-a-vis country i (other than the U.S.A.) as:

__ C
r. - r i: ri (3.3)

r. is A's exchange rate in units of currency 1.
rc is A's exchange rate in units of U.S. 3.

r. is the exchange rate of the U.S. $ in units
of currency i.

Under the adjustable peg system, both rc and r:

were officially pegged rates, allowed to fluctuate

within a small band (4 1/2% since 1971) around this

59

central rate. With the change in the monetary system,
r: became a floating rate, and its increased volatility
would be transmitted directly to ri through the still
pegged rc. Consequently, the uncertainty associated
with A's exports to the U.S.A. would be less than
that associated with its exports to other countries.
In other words, if the developing country claim is
correct, we should observe a structural shift in exports
away from other countries towards the U.S.A. The
important point to note is that this structural shift
takes place independent of the level of uncertainty
surrounding exports to the U.S.A. With the introduc-
tion of managed floats, uncertainty in exports to
the U.S.A. may have also increased. The structural
shift would still occur because the relative level
of uncertainty has become lower for exports to the
U.S.A.

This observation forges the link between the
two tests used in this study, and also explains why
the second test is non-trivial. Suppose it is found
that the aggregate exports of country A have not
declined significantly in the face of increased uncer-
tainty. The aggregate analysis may conceal a
structural shift which the second test would reveal.

With the existing pressure on businessmen in

60

developing countries to export, they may have responded
to the increased uncertainty by diverting their exports
to the less uncertain market (i.e. the U.S.A.) in lieu
of reducing the overall level of exports. On the

other hand, if aggregate exports were found to be
dampened due to increased uncertainty, the issues
raised in the second test would still be interesting.
Developing countries, have, over the last two decades
or so, made considerable progress towards diversifying
their exports, thereby reducing their historic depend-
ence on a single market. A structural shift in exports
to the center country implies that this geographical
diversification effort would be thwarted--something
that is perceived to be a serious impediment to
continued progress in the develOping countries.

Figures 3.2(a) and (b) depict the situation in
terms of bilateral export supply functions. In the
first, the bilateral export supply function from the
developing country to its center country shifts to

U
the right (x: to X8 ), whereas it shifts to the left

c
for other countries (x: to x: ). Figure 3.2(b) shows
the other possibility, where both functions shift to
the left, but the shift is significantly smaller for

the center country.

61

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m~.m musmflm

mmfluucsoo Hmnuo Had ou manomxm

suflucmso suflucmso

 

muucsoo kucoo on manomxm

 

 

 

 

mownm uuomxm

 

mowum unomxw

62

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n~.m musmflm

mmfluusoou Hwnuo Had on muuomxm mapssou Hmucmo ou manomxm

Suspense huflusmoo

 

 

 

 

 

«Dana uhomxm Unaum unomxm

63

To examine this hypothesis empirically, the bi-
lateral exports of country i to country j are

specified as,

s _ s
Xij - Xij (Px.'Pd.p Yi’ D) (3.4)
1 1
where,
xij = exports of country i to country j.
j = l for exports to the center country, and
= 2,..,n for exports to other countries.
D = dummy variable to account for the change

in the exchange rate system in March 1973.
D is set at zero for periods prior to
1973 (Qtr 2) and to one for subsequent

periods.

Other variables are as defined earlier. Invoking
the small country assumption, we can ignore demand

considerations.30

If it is true that uncertainty has
affected exports, then the coefficient of the dummy
variable should be larger for the center country (j=l)

than for exports to the other countries (jfl).

 

:uThe assumption is justified where i's exports to j
are a small fraction of j's global imports for each
commodity. The proof is straightforward, and one can
be found in Appendix 2. Obviously, the small country
assumption is less tenable for bilateral exports than
it is for aggregate exports. Therefore, the supply
functions are also estimated in a simultaneous model
(see below).

64

Whether or not the small country assumption is
appropriate when considering bilateral exports is very
much an open question. The choice is bound to be
arbitrary, since there is seldom any unambiguous cri-
teria on which the decision can be based. Therefore,
in this study, the small country assumption is later
drOpped and the export supply function is re-estimated
as part of a simultaneous equation system. A close
correspondence between the two sets of results would
suggest that the small country assumption is valid.

A definitive answer is not expected, but it is felt
that this procedure would provide useful information
for judging when a small country assumption is appro-
priate.

In the simultaneous approach, the equations
in 3.4 are combined with corresponding bilateral
demand for export functions of several (four or
five of the largest trading partners) countries for
country i's exports. The entire system is presented

below:

5 _ s
d _ d

where,

65

xgj = the demand by country j for country i's
exports.
Pd = the domestic price index in country j.
3
Y3. = an index of real income in country j.
Px = the world export price index. A bias is
w

introduced in this index due to the inclu-

sion of country i's export prices, but this
bias is deemed negligible. Of the countries
being studied, none exports a significantly

large fraction of total world exports.

All other variables have been defined earlier. The
estimation is conducted under the assumption that the

export markets are in equilibrium,

i.e. X.. = X.. (3.6)

The next chapter develops a proxy for exchange risk,
and presents the empirical results of its measurement
under pegged and floating exchange rates. The computed
values of the exchange risk variable are then used in
the empirical tests of the hypothesis that exchange
rate uncertainty has dampened the eXports of the five
countries being examined. This is the subject of

Chapter 5.

CHAPTER 4

THE MEASUREMENT OF EXCHANGE RISK
UNDER ALTERNATIVE EXCHANGE REGIMES

The question of exchange rate uncertainty has
received considerable attention in the past, since
it is one of the central issues in the broader debate
concerning the merits of alternative exchange regimes.
While the particular arguments in the debate are not
central to the present research, one consequence of
this ongoing debate which is of interest here is that
considerable light has been shed on the otherwise
complex concept of exchange rate uncertainty. As can
be expected, research interest in this concept has
been rekindled since floating rates became the domi—

nant exchange policy internationally in 1973. It

 

31Opponents of flexible exchange rates have contended
that the question of exchange rate instability is
one of the most serious criticisms of the freely
floating exchange rate system. For a review of the
issues and the arguments on both sides, see Friedman,
M., "The Case for Flexible Exchange Rates", in Caves,
R.E. & Johnson, H., eds., Readings in International
Economics, Chapter 25 (Homewood, Ill; RiChard D.
Irwin, Inc., 1969); Morgan, E.V., "Theory of Flexible
Exchange Rates", AER, June 1955; Sohmen, E., "Flexible
Exchange Rates, (CETcago, Ill: U of Chicago Press,

; Kreinin, M.E., cp.cit., Chapter 10; Caves,

 

 

66

67

would be instructive to separate and categorize the
various views on this subject (i.e. what the appro-
priate proxy for exchange uncertainty is), in order
to clearly understand current thinking.

Historically, attention has been focused on the
exchange volatility of spot exchange rates. In fact,
earlier discussion almost exclusively centered around
exchange rate volatility. The question was whether
Speculation under freely floating rates would stabi-

lize or destabilize exchange rates.32

Consequently,
the variance or standard deviation of the spot rate
were given prominence as the preferred proxies for
exchange uncertainty. This traditional interest in
exchange volatility lingers on today, and has recently
been employed in empirical tests of exchange risk

under the present monetary system.33

 

31(contd.)

R.E., "Flexible Exchange Rates", AER, May 1963; Liu,
Ta-Chung, "The Elasticity of U.S. Import Demand: A
Theoretical & Empirical Reappraisal", IMF Staff Papers,
February 1954; Lanyi, A., "The Case for Floating Ex-
change Rates Reconsidered", Essays in International
Finance # 72, (Princeton, N.J.; Princeton U., 1969);
Slack, S.,77Exchange Policies for Developing Countries
in a World of Floating Rates", Essays in International
Finance # 119, (Princeton, N.J.; Princeton U., 1976).

 

 

 

 

 

32Friedman, M., 0p.cit., p. 426.

33Cline, W., International Monetary Reform and the
Develpping Countries, pp. 17-19 (Washington, D.C.;
Brookings Institution, 1975) and Hooper, P. & Kohl-
hagen, S.W., o .cit., are examples of recent re-
search employing exchange volatility measures.

 

 

68

Following essentially the same line of reasoning,
Suss34 develops a series of proxies for exchange rate
uncertainty--deviations of spot rates from moving
averages, percentage changes in these deviations,
and so on. These measures are then used to examine
exchange rate volatility (or variability) under the IMF
and the managed float system for eight industrial
nations. Her conclusion was that volatility had
increased in terms of all the measures since 1973.

The main criticism of these approaches is that
they imply an equivalence between exchange rate vola-
tility and exchange rate uncertainty. Such a premise
totally ignores the role of expectations. Expectations
of future spot rates are crucial when exchange risk is
discussed, and cannot therefore be ignored. It is
the deviations of expectations from realized future
spot rates that are the essence of exchange uncertainty.
If expectations are always realized, no uncertainty
can be said to exist. For instance, under a system of
immutably fixed rates, expectations of future spot
rates would always equal existing rates, and will there-
fore always be realized. No exchange uncertainty

exists in this situation. Only when the future spot

 

34S‘uss, B., "The Variability of ExChange Rates Under
Alternative Regimes", unpublished manuscript, IMF,
December 1976.

 

69

rate cannot be predicted with unerring accuracy does
the question of exchange uncertainty arise.35
One situation where variance can be equated with
uncertainty is where the underlying attitude towards
risk is assumed to be represented by a quadratic
utility function, as Clark has assumed.36 Earlier
it was pointed out that such a utility function
violates the widely accepted concept of decreasing
absolute risk aversion. In view of this, equating
variance with uncertainty on this ground is not
considered an acceptable rationale.
Farber, et. al.37used a different approach to

investigate the issue of exchange risk under the

two exchange regimes. Their research indicated that

 

35Interestingly enough, Hooper, P. and Kohlhagen, S.W.,
op.cit., conduct various tests of exchange rate
uncertainty under the assumption that traders' expec-
tations of future exchange rates are always realized.
Clearly, such an approach leaves no scope for
exchange uncertainty, though the authors contend
that it does (see pp. A2 and F5).

3ESClark, P., "Uncertainty, Exchange Risk & the Level

of International Trade", Western Economic Journal,
September 1973, pp. 302-313.

37Farber, A., Roll, R., & Solnik, B., "An Empirical

Study of Risk Under Fixed and Floating Exchange",
Journal of Monetapy Economics, pp. 235—265, supple-
mentary series, I977.

70

the standard deviations of exchange rates had in-
creased in the floating period. However, they found
that the distributions had changed in other ways as
well. For instance, kurtosis was measured at a
significantly higher level under the fixed rates
than under floating rates. In both cases, kurtosis
was significantly different from 3.0, indicating a
non-normal distribution. Intuitively, the higher
kurtosis in the fixed period implies that in this
period the probabilities of extreme changes were
larger. This is in keeping with the nature of the
adjustable par system, in which currencies' values
,are changed by relatively larger amounts and less
frequently than under floating rates.

This finding raises the question of what is
perceived to be more risky--a sequence of rather
small changes as in the floating system, or a sequence
of even smaller changes interspersed with larger
changes as in the pegged rate period--by all investors
considered together. To resolve this issue, the authors
attempted to establish first order stochastic dominance
of one sample distribution over the other .38 Such a

result would have satisfactorily dealt with the

 

381bid., pp. 248-249.

71

criticism presented earlier of equating volatility
with uncertainty--simply because of the way stochastic
dominance is defined. However, their results were
largely inconclusive, the dominance statistic not
being significantly different from 50 percent in
the majority of the cases.39
In an attempt to incorporate expectations into
his measure of uncertainty, Ginman40 uses a variation
of the Hicksian concept of elasticity of expectations.
Specifically, he defines a coefficient of expectations,

y, as his proxy for uncertainty based on the follow-

ing relationship,

* _ * = _ *
rt rt-l Y<rt rt-l) 0 5 7 < 1 (4'1)
where rt is the exchange rate in time t and the aster-

isks indicate expected values.
As it stands, 7 can be easily recognized as the

adjustment coefficient in an adaptive expectations

41

mOdel. This approach has been criticized on the

 

39Ibid., pp. 250-251.

40 Ginman, P., The Relative Effects of Uncertainty on
Import Volume Underffiiexible and Pegged Exchange
Rates: *The Canadian Experience 1951—1964, unpuB-
lished doctoralgdissertation, Michigan State
University, E. Lansing, MI., 1969.

41Madala, G.S., Econometrics, p. 144 (New York: NY:

McGraw Hill, 1977).

 

72

grounds that y is really not a reasonable measure
of uncertainty.42

The essential element of exchange risk, as argued
earlier, is the inability forecast exchange rates
accurately. The more inaccurate the forecasts are,
the higher the perception of uncertainty will be.
Thus, exchange risk can best be described in terms
of past forecasting experience, i.e. the accuracy
with whiCh forecasts were made in the past. Where
the inaccuracy of forecasts in the immediate past
has increased, exporters would be hesitant to make
commitments on the basis of present forecasts, simply
because they will have less confidence in the relia-
bility of these forecasts.

Similar approaches have been used in other
investigations of exchange risk under floating rates.
Aliber,43 in studying the question of transactions
costs and risks associated with floating exchange
rates in eight industrial countries, uses the mean
absolute difference between predicted and spot
rates. He uses the forward exchange rates as his

proxy for predicted rates, under the assumption

 

42Clark, p., op.cit., p. 303.

43Aliber, R.Z., "The Firm Under Pegged and Floating
Exchange Rates", Scandinavian Journal of Economics,
#2, 1976, pp. 309-322.

 

73

that these rates are unbiased predictors of the
markets expectation of the spot rate on the date
of the maturity of the forward contract.44

While the use of forecasting error as a proxy
for exchange rate uncertainty is precisely what is
considered appropriate, the approach taken in this
study is that forward rates are not unbiased pre-
dictors for expected future rates. It was shown
earlier that when the expected value of the future
rate exactly equalled the forward rate for the
corresponding maturity, net of marginal costs, complete
hedging would be undertaken by exporters. In such a
situation, exchange risk will not affect export deci-
sions (see Chapter 2 and Appendix 1). Abstracting
from costs, as Aliber does, the corresponding conclusion
is that total hedging will occur when the forward
rate exactly equals the predicted rate for the date

45

of maturity of the forward contract. Consequently,

the use of forward rates as a proxy for expected rates

 

44H00per, P. & Kohlhagen, S.W., o .cit., found that this
proxy yielded strong statistica? results in their
examination of the effects of exchange risk on the
trade of several industrial countries.

45Farber, A.L., et.al., "A Note on the Optimal Level
of Forward Exchange Transactions", unpublished manu-
script, University of Brussels and CORE, September
1975.

 

74

is not considered appropriate, because such an assump-
tion severely constrains the scope of the analysis.
It may even be argued that the restriction is so
severe that the results become trivial. No amount
of exchange risk will affect export decisions, since
all future earnings in foreign exchange are always
sold through the forward market, at a known price.
The next section presents the approach taken in this

study to develop a proxy for exchange rate uncertainty.

Exchange Rate Forecasting Methodology

 

The Box-Jenkins stochastic time series model is
the statistical tool employed in this study to fore-
cast exchange-rates.46 The choice of this method is
predicated on the recognition of the weaknesses of
the methods used hitherto, and on certain institutional

considerations pertaining to the countries being examined

in this study. Time series analysis examines the past

 

46Box, G.E.P. and Jenkins, G.M., Time Series Analysis,

(San Francisco, CA; Holden Day, 1970) is the baSic

text on this subject, and a useful presentation

is also contained in Pindyck, R.S. and Rubinfeld,

D.L., Econometric Models and Economic Forecasts,
Chapters 13-17, (New York City, NY; McGraw Hill, 1976).

75

behavior of a time series in order to infer something
about its future behavior. The model does not seek

to establish any causal relationship between the variable
being examined and its determinants.

While this approach may be criticized because it
ignores widely accepted determinants of exchange rates,
such as changes in reserve positions and in differen-
tial inflation and interest rates, it is considered an
apprOpriate method for simulating the exporters' behavior
in deve10ping countries for several reasons.

First, data on such determining variables is seldom,
if ever, available in a timely and reliable manner.

The notorious lag in the availability of data would
severely impair its usefulness in forecasting purposes,
especially where essentially short-term forecasts are
needed. Second, as stressed throughout, the financial
markets in develOping countries are rudimentary at best,
and access to forward markets is highly regulated. Such
regulation essentially breaks down the accepted linkages
between these variables and exchange rates. For
instance, differential interest rates cannot elicit the
kinds of response from capital flows in developing
countries as they can in industrial nations, simply
because the citizens of such countries are prohibited by

law from holding financial assets in foreign currency.

76

Consequently, they have little bearing on exchange rate
movements. Also, due to the severity of government
regulation, exporters in general do not consider for-
ward rates as an element in their decision making.47
Lastly, even if exporters did have access to the infor-
mation in a timely manner, and financial institutions
were fully developed, it is questionable whether they
possess the sophisticated skills necessary for the
design and use of complex models of exchange rate
determination--or even whether the costs of such an
effort would be considered justified, given their scale
of Operation.

Consequently, it is considered quite reasonable
to assume that exporters in developing countries operate
almost exclusively in a world of spot rates, and
it follows directly from this argument that the time
series model may be a more accurate representation of
reality than one would allow initially.

To summarize the discussion so far, the proxy for
exchange risk adopted in this study may be defined

as some function of past forecasting errors:

 

47Conversations with a leading exporter from Northern
India revealed that in addition to the primitiveness
of the forward market, government regulations inhibit
Indian exporters from taking positions in the forward
market. The regulations are so complex and cumbersome
that it is typically not worthwhile to hedge exchange
positions through the Government-run forward markets.

77

R = f(r* - r) (4.2)

where,

R is the proxy for exchange risk.

r* is the forecasted future spot rate in the past.

r is the observed spot rate in the period for

which the rate was forecast as r*.

Time series analysis is used to establish fore-
casted values, r*.

The basic assumption underlying time series analysis
is that the series being forecasted is generated by a
random process which has a structure that can be identi-
fied and described. The description is in terms of the
way that randomness is embodied in the process and does
not attempt to establish any causal relationship
between the forecasted series and other variables. In
other words, given an exchange rate series r

t-n'rt-n+1' o o o

..,r in period t, the assumption is that the series is

t
a set of jointly distributed variables, and the aim
of time series analysis is to specify the probability
distribution function which assigns probabilities to
all poSSible combinations of values of rt-n' rt-n+l’
. . . , rt. The probabilities of alternative future

states could then be determined on the basis of this

probability distribution function.

r.‘

.‘ vl ‘

78

It is important to note that the attempt is to
capture the characteristics of the series' randomness,
and not necessarily to identify the actual distribution
of the series which may be far more complicated and

48 Thus, a simple model which

impossible to specify.
is a reasonable approximation of the actual distribu-
tion is used for forecasting purposes. Clearly, the
usefulness of the model depends on how accurately it

represents the true probability distribution of the

series.

Stationarity of Exchange Rate Series

 

The first step in time series analysis is the
identification of a model which captures the randomness
of the series. The stationary of the series is, in
turn, an important first consideration in this identi-
fication process. A stationary series is one whose
stochastic properties are invariant with respect to
time, i.e., the probability of a given fluctuation
from a mean level (which is itself constant over time)
is the same at any point in time. If these stochastic

properties change over time, the series is termed

 

4BPindyck, R.S. and Rubinfeld, D.L., op.cit., p. 431.

79

non-stationary. The task of describing a stochastic
process is greatly simplified if the series is sta-
tionary.

Thus, it is expedient to determine if the series
being examined (exchange rates in our case) is sta-
tionary, and if not, whether it can be readily trans-
formed into one. A convenient indicator which can be
used to determine if a series is stationary is the
autocorrelation function which provides a measure of
the degree of correlation between neighboring points
in a series. The autocorrelation with lag k (pk) for
the exchange rate series r

r . ., rt, is

t-n' t-n+l"

defined as

E[(r -u ) (r -u )1
t r t+k r (4.3)

 

 

p =
k /%[(rt-pr)?lzt(rt+k-ur)21

where,
pk is the autocorrelation with lag k.
pr is the mean of the series, and
E is the expectations operator.

For a stationary series, the variance at time t is
the same as that at time t+k, and therefore, the deno-
minator in 4.3 becomes the variance of the stochastic

process. Thus,

80

Cov (rt, rt+k)

= 42 (4.4)
a
r

 

9k

In practice, pk is estimated by the sample auto-

correlation function, defined as,

 

T-k _ __
2 (rt-r)(rt+k-r)
pk 'r '
— 2
2 (rt-r)
t=l

A characteristic of stationary series is that the
autocorrelation functions drops off sharply as k, the
number of lags, is increased. This can be used to
decide if a particular series is stationary or not.
The monthly exchange rate series49 of India, Israel,
Mexico, Korea and Taiwan for the period of pegged ex-
change rates and for the floating rate period were
used to compute sample autocorrelation functions. The

results are shown in Tables 4.1 to 4.5.50 It is clear

 

49SDR per unit of National Currency.

50There is an unresolved issue concerning the choice of
a date of transition from pegged to floating rates.
This question is addressed in detail later, but for
the time being, it should be pointed out that for the
purpose of identifying the structure of the exchange
rate series, 1971 (Qtr. 1) was used as the cut-off
date. This choice was made for two reasons. First,
by March 1971, several countries had announced their
intention of floating their currencies, and several
others were clearly about to follow (see Farber, et.

81

r
5.0

.1
30.0

1_
25.0

I
20.0

xs'.o
LHG (K)

I
10.0

 

- q q d
e; me as me. 0.?

ounmmmd Lac mummmm wnmo

 

o
o

 

0.0

 

94 was one 9+? 9....
mklfikma LDC mummmm mama

Correlogram of Exchange Rate Series - INDIA

Figure 4.1

82

1* 1
15.0 20.0

LHG (K)

1
‘000

 

o
0

 

e: W...
omlnmmu

1 .
0.0 m.ou O.~I

not mmHmmm ammo

(in 20.0 257.0 33.0
LHG (K)

r
10.0

I
5.0

 

o
O
o

 

4

q 4 q
as me 3. me. e..-

wuufiumfi mac mummmm ammo

Correlogram of Exchange Rate Series - ISRAEL

Figure 4.2

83

 

0
o

 

ems wee
oulmmma

HI. q
9.0 m.? 0.7.

doc mummmm ono

 

0.0

 

9% .4... ewe mm? as-
mmlfiumu LDC mmHmmm ammo

Correlogram of Exchange Rate Series - KOREA

Figure 4.3

84

Mexico's exchange rate remained
unchanged at 0.08 SDR per Peso
throughout the period 1957-1970,
and therefore a correlogram for
this series could not be

constructed.

1.0
.4

(L5
J

DJ)
11

‘OJS
1

 

DRIG SERIES HCF 1971-78

“1.0

 

s'.o 10.0 16.0 20.0 235.0 30.0
LBS (K)

5’
c:

Correlogram of Exchange Rate Series - MEXICO

Figure 4.4

85

 

 

 

OMW mbu
ek-kmmi

owe mfl. o4;
toe museum page

0
0

 

 

e: mwe ewe mm? o...
mmufimmfi mom muEmm ammo

0.0

Correlogram of Exchange Rate Series - TAIWAN

Figure 4.5

86

from these tables that, without exception, the series
are non-stationary. The sample autocorrelation declines
rather gradually as the lag increases from 1 to 30. To some
extent, this is to be expected, since most time series
in economics are non-stationary. However, many of the non-
stationary series can be easily transformed into
stationary series by the process of differencing. A
non-stationary series which when differenced n times
yields a stationary series is referred to as a homo-
geneous non-stationary series of order n.

The ten exchange rate series being examined (two
for each of the five countries) were differenced once,

that is, the series

9: = r -r = Ar (4.6)

was constructed and the sample autocorrelation function
for lags between 1 and 30 were computed. The resulting
correlograms are presented in Figures 4.6 to 4.10. It
was found that, without exception, each differenced
exchange rate series, Art, was stationary. The conclu-
sion is that these exchange rate series are homOgenous

non-stationary of order 1.

 

50(contd.)

al., 0 .cit., p. 240). Second, if any lag were to be
discovered in the structure, observations from the
post-1971 period would have to be used to obtain
forecasts for the post-1973(I) period.

l

1.0

0.5
1

.5

l

DIFF' 1 HCF 19257-70
(L0

 

87

 

 

 

c!
7 T I T T T fl
0.0 5.0 10.0 15.0 20.0 25.0 30.0
LHG (K)
O
.41
93
ID
.L .54
t\
2
‘l. O
c3 6‘
c:
fl
ID
t?“
o
c!
T. f T T 7 T 1
0.0 5.0 10.0 15.0 20.0 25.0 30.0
LHG (K)

Correlogram of First Differenced
Exchange Rate Series - INDIA

Figure 4.6

1.0

0.5

DIFF 1 HOP 1957-70
.5 0.0

“1.0

0.0 0.5 1.0

DIFF l HCF 1971-78
“0.5

“1.0

l

J

W

88

 

 

 

 

 

1
T T T 1T T *1
0.0 5.0 10.0 15.0 20.0 25.0 30.0
LHG (K)
1 W“—
T T T T T 1
0.0 5.0 10.0 15.0 20.0 25.0 30.0
LHG (K)

Correlogram of First Differenced
Exchange Rate Series - ISRAEL

Figure 4.7

1.0

0.5

DIFF l HCF 1957-70
'0.5 0.0

0.5

0.0

DIFF 1 HCF 1971-78
'0.5

l

89

1

LA

I

l

 

 

T

I I T T 1
0.0 5.0 10.0 15.0 20.0 25.0 30.0
LHG (K)

1

 

 

l I T f
(0.0 5.0 10.0 15.0 20.0 25.0 30.0
LHG (K)

Correlogram of First Differenced
Exchange Rate Series - KOREA

Figure 4.8

0.5 1.0

$05

DIFF‘ l HCF 1971-78

'1.0

90

Mexico's exchange rate remained
unchanged at 0.08 SDR per Peso

throughout the period 1957-1970,
and therefore a correlogram for

this series could not be

 

 

constructed.
q
1
T’ T’ 1 ‘1* 1’ 1
0.0 5.0 10.0 15.0 20.0 25.0 30.0

LHG (K)

Correlogram of First Differenced
Exchange Rate Series - MEXICO

Figure 4.9

DIFF 1 BC? 1957-70

DIFF l HCF 1971-78

 

91

 

 

 

O.

u:

O...

c:

o’-

u:

o'-

I

9

T I I 1* I I 1

0.0 5.0 10.0 15.0 20.0 25.0 30.0
LHG (K)

ca

u:

61

c:

D.-

u:

0"

l

9

T I T T7 T’* I I

0.0 5.0 10.0 15.0 20.0 25.0 30.0
LHG (K)

Correlogram of First Differenced
Exchange Rate Series - TAIWAN

Figure 4.10

92

In addition, it was found that the differenced
series, Art were reduced to white noise. An examina-
tion of Table 4.1 will make this clear. The chi-square
statistic computed from the sample autocorrelations
and their corresponding standard errors was insigni-
ficant at the 95 percent level of confidence in all
ten cases, and at the 90 percent level for all but one
case. This was somewhat of a surprise, but the con-
sistency of the finding among all nine series strengthened
the conclusion that exchange rates for these countries
during the two alternative exchange regimes were best

characterized by a random walk process,

+ e (4.7)

with E(et) = 0 and E(et,es) = 0 for all t # s. In other

is drawn indepen-

t.
dently from a probability distribution with 0 mean.51

words, each successive change in r

Forecasting such a series is straightforward.

Given the exchange rate series, r

rt-n' t-n+l""' rt'

the forecast for one period ahead, rz+1, is given by,

*

rt+l = E{rt+1 rt, rt_1,..., rt-n] (4.8)

But, + e and e 1 is independent of

rt+1 rt t+i ' t+

 

51Pindyck, R.S. and Rubinfeld, D.L., 0p.cit., pp. 432-440.

93

Table 4.1

Computed x2 Values for
Autocorrelation Function

 

 

 

x2 Statistic
Country 1957-1970 1971-1978
India 38.159** 33.125**
Israel l9.9l6** 6.043**
Mexico (1) 10.036**
Korea 29.007** ll.807**
Taiwan 40.277* 13.587**

 

* Not significantly different from 0 at 95% level of
confidence.

** Not significantly different from 0 at 90% level of
confidence.

(1) Mexico's exchange rate remained unchanged throughout
this period, and hence, no value could be computed
for it.

94

rt, rt-1""’ rt-n (from 4.7). Thus, the forecast

for one period ahead is simply,

*

rt+l + E(e

= r (4.9)

t t+l) = rt
The forecast two periods ahead is,

*
rt+2

E[rt+2 rt' rt-1'°°" rt-n]

E[rt+l + et+2]

Elrt + et+i + et+2]

Similarly, the forecast I periods ahead will also

be rt.

Measuring Exchange Risk

 

The forecasting scheme resulting from the analysis
of the previous section is used to develop measures
of exchange risk under the pegged and floating rate
systems. Two functional forms are used in this study,
the root mean square error and the mean absolute error
of the forecasts. The purpose of using both forms is
to ensure the stability of the results. It is the
inherent characteristic of most measures that they are
either particularly sensitive to the frequency of the

changes in the variable being examined or to the

95

magnitude of the changes. Since exchange rates fluc-
tuated more frequently but by relatively smaller amounts
under the floating rates, the use of one measure with a
particular sensitivity to either frequency or magnitude
could easily introduce bias into the results. Therefore,
two measures are used, one which is sensitive to
frequency (mean absolute error) and another which is
more sensitive to the magnitude of the changes (root
mean square error). The stability of the resulting
values of exchange risk under both measures would indi-
cate their robustness.

Specifically, the two measures of exchange risk

used are,

Mean Absolute Error:

 

 

 

1 T *
R = — Z r _. - r _. (4.11)
t T i=1 t i t i
and,
Root Mean Square Error:
T
_ 1 * _ 2
Rt _ ///T 1:1 (rt-i rt-i) (4.12)

where,

96

Rt is the measure of exchange risk in period t.

r; is the exchange rate forecasted for period
t in period t-l.

rt is the observed exchange rate in period t.

Based on the discussion in the previous section, we
know that the best forecast of future rates is rt, and

therefore, 4.11 and 4.12 may be written as,

 

 

1 1. 12 ,
Rt = 17 i rt-i-l ' rt-i (4'13)
and,
12
2 _ 1 _ 2
Rt - /1-§ 1:1(rt_i_l rt-i) (4.14)

respectively, for T = 12.

l 2
t and Rt

floating rate systems are given in Tables 4.2 to 4.6

The values of R under the pegged and

for the five countries under consideration. Table 4.7
shows the mean values of these measures under the two

exchange regimes.52

 

521t should be noted that because these values are 193
invariant with respect to the unit of measurement,
only intra country comparisons between the two
periods are meaningful. The values for different
countries under the same regime would be comparable
only if they were normalized.

97

Table

4.2

Monthly Values of Exchange Uncertainty Proxy - INDIA

1960-1971(March) & l973(Apri1)-1978

 

 

J-n- rob. II-r- Apr- II-y. Jun. .702. Aug. 00;). Oct. Nov. Dec.
22
‘t " 1'2 J1 r0-2—2 ’t-i
2900 .0000 .0055 .0050 .0055 .0050 .0059 .0002 .0002 .0059 .0050 .0000 .0007
2902 .0050 .0005 .0057 .0057 .0059 .0050 .0050 .0050 .0073 .0005 .0002 .0070
2902 .0079 .0003 .0070 .0070 .0000 .0000 .0005 .0003 .0052 .0000 .0002 .0002
2903 .0033 .0029 .0025 .0030 .0030 .0020 .0023 .0029 .0020 .0027 .0020 .0023
2900 .0023 .0023 .0023 .0007 .0000 .0022 .0022 .0025 .0022 .0030 .0032 .0039
2905 .0002 .0003 .0005 .0000 .0052 .0050 .0050 .0005 .0000 .0055 .0057 .0009
2900 .0000 .0005 .0000 .0052 .0005 .0000 .2330 .2335 .2332 .2327 .2313 .2323
2907 .2323 .2320 .2329 .2325 .2323 .2325 .0039 .0030 .0030 .0030 .0030 .0090
2900 .0220 .0230 .0200 .0235 .0209 .0270 .0200 .0297 .0222 .0227 .0232 .0275
2909 .0202 .0207 .0290 .0292 .0292 .0292 .0229 .0290 .0207 .0297 .0220 .0220
2970 .0297 .0292 .0270 .0273 .0259 .0235 .0222 .0230 .0223 .0220 .0200 .0200
2972 .0200 .0252 .0207 - - - - - - - - -
2973 - - - .2209 .2200 .2002 .2002 .2277 .2350 .2505 .2390 .2300
2970 .2020 .2927 .2020 .2930 .2003 .2020 .2972 .2000 .2702 .2009 .2590 .2075
2975 .2320 .2030 .0000 .0002 .0573 .0097 .0703 .0000 .0002 .0009 .0003 .0000
2970 .0020 .0702 .0707 .0700 .0703 .0500 .0503 .0520 .0030 .0500 .0023 .0023
2977 .0077 .0092 .0030 .0057 .00251- 0029 .0550 .0520 .0029 .0500 .0090 .0500
2970 .0520 .0700 .0753 .0952 .2222 .2209 .2300 .2027 .2392 .2350 .2557 .2523
22
5: “fl; tilkt-i-l ’0—2’2

2900 .0073 .0002 .0002 .0000 .0002 .0000 .0005 .0005 .0000 .0057 .0050 .0053
2902 .0050 .0050 .0072 .0072 .0073 .0070 .0070 .0072 .0092 .0202 .0200 .0090
2902 .0200 .0202 .0090 .0000 .0007 .0000 .0005 .0000 .0000 .0000 .0000 .0000
2903 .0039 .0030 .0033 .0039 .0000 .0037 .0030 .0033 .0020 .0029 .0020 .0027
2900 .0027 .0027 .0027 .0023 .0020 .0023 .0037 .0039 .0030 .0007 .0000 .0050
2905 .0050 .0057 .0057 .0050 .0003 .0000 .0002 .0000 .0002 .0070 .0075 .0070
2900 .0009 .0009 .0070 .0075 .0070 .0000 .7950 .7950 .7950 .7950 .7950 .7950
2907 .7950 .7950 .7950 .7950 .7950 .7950 .0000 .0000 .0000 .0000 .0000 .0205
2900 .0233 .0235 .0239 .0237 .0202 .0207 .0205 .0200 .0200 .0293 .0293 .0229
2909 .0230 .0230 .0202 .0202 .0200 .0200 .0259 .0239 .0253 .0200 .0273 .0273
2970 .0202 .0230 .0227 .0220 .0222 .0292 .0272 .0200 .0200 .0207 .0222 .0222
2972 .0222 .0202 .0202 - - - - - - - - '
2973 - - - .2029 .2027 .2900 .2923 .2090 .2003 .2752 .2090 .2000
2970 .2000 .2200 .2200 .2222 .2200 .2250 .2220 .2290 .2093 .2007 .2005 .2950
2975 .2709 .2332 .2250 .0007 .0075 .0900 .2003 .2037 .2223 .2203 .2205 .2209
2970 .2073 .2053 .2052 .2002 .2002 .0700 .0050 .0007 .0539 .0007 .0752 .0752
2977 .0795 .0000 .0000 .0700 .0700 .0705 .0732 .0002 .0020 .0720 .0059 .0702
2970 .0735 .2232 .2232 .2030 .2730 .2737 .2023 .2059 .2033 .2020 .2993 .2972

98

Table 4.3

Monthly Values of Exchange Uncertainty Proxy - ISRAEL

1960-1971(March) & 1973(April)-1978

 

 

Jan. rob. lax. Apt. lay. Jun. 301. Aug. 00p. Oct. lav. Doc
13
“t - fiizl tt’i‘l - tt’i
1060 0.0 0.0 0.0 0.0 0.0 0.0003 0.0166 0.0167 0.0167 0.0167 0.0167 0.0350
1061 0.0333 0.0333 0.0333 0.0333 0.0333 0.0333 0.0350 0.0333 0.0333 0.0333 0.0333 0.0333
1063 0.0350 0.0333 0.1333 0.1333 0.1333 0.1350 0.1350 0.1167 0.1167 0.1167 0.1167 0.1003
1063 0.1003 0.1000 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0
1060 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0
1065 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0
1066 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0
1067 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0017
1060 0.0017 0.0017 0.0017 0.0017 0.0017 0.0017 0.0017 0.0017 0.0017 0.0017 0.0017 0.0
1060 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0
1070 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0
1071 0.0 0.0 0.0 - - - - - - - - -
1073 - - - 0.0033 0.0033 0.0033 0.0033 0.0033 0.0033 0.0033 0.0033 0.0033
1070 0.0033 0.0033 0.0153 0.0 0.0 0.0 0.0 0.0003 0.0050 0.0001 0.1053 0.1039
1075 0.3001 0.3006' 0.3157 0.3301 0.3363 0.3305 0.3013 0.3577 0.3537 0.3106 0.3177 0.1000
1076 0.1030 0.1070 0.1537 0.1550 0.1500 0.1606 0.1606 0.1600 0.1670 0.1130 0.1313 0.1301
1077 0.1000 0.1000 0.1001 0.1505 0.1506 0.1506 0.1530 0.1615 0.1006 0.1001 0.1063 0.6751
1070 0.6063 0.7000 0.7635 0.7003 0.0030 0.0160 0.0030 0.0337 0.0636 0.0603 1.0306 0.5338
13
a: . fitilkt'bj - std”

1060 0.0 0.0 0.0 0.0 0.0 0.0300 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
1061 0.0577 0.0577 0.0577 0.0577 0.0577 0.0577 0.0500 0.0577 0.0577 0.0577 0.0577 0.0577
1063 0.0000 0.0577 0.3513 0.3513 0.3513 0.3500 0.3500 0.3000 0.3000 0.3000 0.3000 0.3076
1063 0.3076 0.3076 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0
1060 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0
1065 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0
1066 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0
1067 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.1003
1060 0.1003 0.1003 0.1003 0.1003 0.1003 0.1003 0.1003 0.1003 0.1003 0.1003 0.1003 0.0
1060 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0
1070 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0
1071 0.0 .0.0 0.0 - - - - - - - - -
1073 -- - - 0.1073 0.1073 0.1073 0.1073 0.1073 0.1073 0.1073 0.1073 0.1073
1070 0.1073 0.1073 0.0530 0.0 0.0 0.0 0.0 0.0011 0.0163 0.0103 0.0311 0.6356
1075 0.6361 0.6360 0.6373 0.6370 0.6377 0.6370 0.6303 0.6030 0.6010 0.6006 0.6006 0.3573
1076 0.3560 0.3500 0.3630 0.3635 0.3601 0.3670 0.3660 0.3603 0.3605 0.1300 0.1001 0.1070
1077 0.1515 0.1565 0.1533 0.1603 0.1603 0.1603 0.1650 0.1773 0.3100 0.3135 0.3150 1.7303
1070 1.7333 1.7056 1.7007 1.7500 1.7500 1.7500 1.7003 1.7060 1.0055 1.0057 1.0300 0.6103

99

Table 4.4

Monthly Values of Exchange Uncertainty Proxy - MEXICO

1960-1971(March) & 1973(April)-l978

 

 

Jan. Feb. Mar. Apr. lay. Jun. Ju1. Aug. lop. Oct. lov. Doc.
13
't ’ I; ‘51 ‘0-2-2 ‘0—1
1060 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0
1061 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0
1063 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0
1063 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0
1060 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0
1065 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0
1066 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0
1067 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0
1060 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0
1060 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0
1070 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0
1071 0.0 0.0 0.0 - - - - - - - - -
1073 - - - 0.136 0.136 0.136 0.136 0.136 0.136 0.136 0.136 0.136
1070 0.136 0.136 0.005 0.0 0.0 0.0 0.0 0.001 0.015 0.030 0.031 0.001
1075 0.050 0.073 0.005 0.000 0.106 0.111 0.111 0.105 0.157 0.150 0.153 0.100
1076 0.130 0.131 0.111 0.110 0.100 0.107 0.111 0.070 0.056 0.775 0.010 1.101
1077 1.501 1.605 1.003 1.006 1.000 1.011 1.033 1.003 1.050 1.103 1.110 0.753
1070 0.301 0.357 0.305 0.313 0.310 0.330 0.350 0.360 0.300 0.377 0.365 0.030
13
‘: "V/Ié 1£1“0-1-2 ' '0-2’2

1060 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0
1061 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0
1063 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0
1063 0.0 0.0 0.0 0.0 0.0 0.0 7 0.0 0.0 0.0 0.0 0.0 0.0
1060 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0
1065 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0
1066 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0
1067 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0
1060 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0
1060 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0
1070 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0
1071 0.0 0.0 0.0 - - y - - - - - .- -
1073 - - - 0.310 0.310 0.310 0.310 0.310 0.310 0.310 0.310 0.310
1070 0.310 0.310 0.150 0.0 0.0 0.0 0.0 0.000 0.000 0.050 0.063 0.071
1075 0.000 0.106 0.115 0.110 0.136 0.137 0.137 0.175 0.100 0.101 0.100 0.107
1076 0.100 0.171 0.166 0.160 0.165 0.165 0.166 0.115 0.070 3.533 3.537 3.000
1077 3.165 3.173 3.330 3.331 3.331 3.331 3.331 3.333 3.333 1.005 1.000 1.511
1070 0.633 0.601 0.333 0.300 0.300 0.350 0.375 0.300 0.330 0.330 0.060 0.533

100

Table 4.5

Monthly Values of Exchange Uncertainty Proxy - KOREA

l960-1971(March) & 1973(April)-1978

 

 

Jan. Feb. lax. Apr. lay. Jun. .7321. Aug. 0012. Oct. lov. Doc.

. 12

4 'Iéglfidd ”‘91
1060 0.0 0.0 1.252 1.252 1.252 1.252 1.252 1.252 1.252 1.252 1.252 1.252
1061 1.252 0.167 5.010 5.010 5.100 5.100 5.100 5.100 5.100 5.100 5.100 5.100
1062 5.100 2.503 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0
1063 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0
1060 0.0 0.0 0.0 0.0 0.0 10.076 10.076 10.076 10.076 10.076 10.076 10.076
1065 10.076 10.076 10.076 11.003 11.710 2.505 2.505 2.505 2.566 2.566 2.566 2.566
1066 2.566 2.566 2.566 1.000 1.303 0.123 0.123 0.123 0.061 0.061 0.061 0.061
1067 0.061 0.203 0.203 0.300 0.202 0.202 0.303 0.363 .0.363 0.363 0.363 0.666
1060 0.015 0.733 0.733 0.673 0.673 0.673 0.612 0.552 0.670 0.036 1.067 0.020
1060 0.500 0.500 0.607 0.713 0.700 0.000 0.000 0.000 0.026 0.007 0.007 1.032
1070 1.032 2.010 1.000 1.055 2.006 2.050 2.130 2.160 2.005 2.030 1.100 0.002
1071 0.065 1.055 1.225 - - - - - - - - -
1073 - - - 5.270 0.050 0.035 0.100 0.100 0.000 0.000 0.163 0.163
1070 0.163 0.322 1.767 0.310 0.310 0.310 0.310 0.351 0.705 1.000 1.150 1.061
1075 10.032 11.000 11.530 11.000 12.370 12.566 12.575 13.075 10.023 10.570 10.306 10.100
1076 5.056 0.700 0.300 0.030 0.100 0.130 0.306 3.030 2.170 1.035 1.001 1.051
1077 1.703 1.720 1.716 1.323 1.101 1.110 0.050 1.326 1.051 1.056 1.050 2.232
1070 2.003 3.360 3.075 3.050 3.050 0.031 0.036 5.207 5.000 5.700 7.030 0.666

12

‘02: ' V193 £filmy-2d ’0—1’2
1060 0.0 0.0 0.336 0.336 0.336 0.336 0.336 0.336 0.336 0.336 0.336 0.336
1061 0.336 10.000 13.310 13.310 13.310 13.310 13.310 13.310 13.310 13.310 13.310 13.310
1062 13.310 0.672 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0
1063 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0
1060 0.0 0.0 0.0 0.0 0.0 36.201 36.201 36.201 36.201 36.201 36.201 36.201
1065 36.201 36.201 36.201 36.350 36.017 5.300 5.300 5.300 5.300 5.030 5.300 5.300
1066 5.300 5.300 5.300 0.000 0.012 0.301 0.301 0.301 0.213 0.213 0.213 0.213
1067 0.213 0.660 0.666 0.600 0.665 0.665 0.607 0.727 0.727 0.727 0.727 1.270
1060 1.502 1.007 1.007 1.301 1.301 1.301 1.376 1.360 1.020 1.600 1.700 1.000
1060 1.115 1.115 1.130 1.162 1.105 1.207 1.207 1.206 1.203 0.000 1.100 0.000
1070 0.000 0.010 0.011 0.010 0.000 0.006 0.056 0.067 0.061 0.002 3.006 1.075
1071 1.112 1.226 1.361 - - - - - - - - -
1073 - - - 10.037 10.330 10.230 10.106 10.106 10.170 10.170 10.100 10.100
1070 10.100 10.200 5.070 0.770 0.770 0.770 0.770 0.700 1.720 1.006 2.003 2.332
1075 31.160 31.273 31.310 31.303 31.300 31.306 31.306 31.733 31.002 31.003 31.000 31.076
1076 7.103 6.660 6.056 6.557 6.300 6.375 6.000 0.003 2.050 2.506 2.507 2.500
1077 2.261 2.266 2.261 1.507 1.351 1.200‘ 1.126 1.063 2.015 2.021 2.507 2.005
1070 3.070 0.267 0.300 0.506 0.506 5.005 5.305 5.050 6.006 6.060 0.570 11.036

101

Table 4.6

Monthly Values of Exchange Uncertainty Proxy - TAIWAN

l960-l97l(March) & 1973(April)-1978

 

 

Jan . r015 . lat . Apr . lay Jun . Jul . Aug . Sap . Oct . lov . Dec
12
R: ' ‘I3ifl r0-1-1 ’0—1
1900 .2901 .0775 .0775 .1707 .2700 .1702 .2702 .2009 .2329 .1095 .1095 .1095
2901 .1095 .1095 .2095 .0202 .0129 .0129 .0129 0.0 0.0 0.0 0.0 0.0
1902 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0
2903 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 .0007 .0107 .0207
1900 .0107 .0107 .0207 .0207 .0107 .0107 .0107 .0107 .0107 .0202 0.0 0.0
2905 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0
1900 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0
2907 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0
2900 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0
1909 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0
1970 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0
1971 0.0 0.0 0.0 - - - - - - - - -
1973 - - - .1905 .1905 .1905 .2905 .2905 .2905 .1905 .1905 .2905
1970 .2905 .2905 .0319 0.0 0.0 0.0 0.0 .0031 .0055 .0732 .0953 .1202
1975 .1031 .2235 .2021 .2902 .3200 .3030 .3000 .0001 .0020 .0092 .0702 .0027
1970 .0292 .3700 .3390 .3009 .3297 .3250 .3305 .2300 .2705 .1519 .1523 .1530
1977 .2307 .1300 .1357 .2000 .0905 .0001 .0755 .1051 .1200 .1252 .2000 .1750
1970 .2201 .2007 .2730 .3025 .3025 .3002 .3079 .5000 .5002 .5370 0575 .7070
12
R: " WA; 1:1 r0-1-2 " ’0-2’2

2900 0.7701 0.2050 0.2050 0.3030 0.3033 0.3033 0.3033 0.3033 0.3355 0.3200 0.3200 0.3200
1961 0.3200 0.3200 0.3200 0.0001 0.0000 0.0000 0.0000 0.0 0.0 0.0 0.0 0.0
1962 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0
1963 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0023 0.0027 0.0027
1960 0.0207 0.0027 0.0027 0.0027 0.0027 0.0027 0.0 0.0 0.0 0.0 0.0 0.0
1965 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0
1966 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0
1967 0.0 0.0 0.0 0.0 0.0 0.0 0.0“ 0.0 0.0 0.0 0.0 0.0
2900 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0
1969 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0
1970 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0
2971 0.0 0.0 0.0 - - - - - - - - -
1973 - - - 0.5000 0.5000 0.5000 0.5000 0.5000 0.5000 0.5000 0.5000 0.5000
1970 0.5000 0.5000 0.2200 0.0 0.0 0.0 0.0 0.0107 0.1075 0.1755 0.2917 0.2100
1975 0.2500 0.3299 0.3550 0.3000 0.3925 0.3920 0.3950 0.5372 0.5032 0.5079 0.5029 0.5702
2970 0.5051 0.5209 0.5001 0.5209 0.5027 0.5010 0.5030 0.3093 0.2230 0.1907 0.1900 0.2909
2977 0.2770 0.1702 0.2777 0.1222 0.1000 0.1020 0.0092 0.1000 0.2500 0.2509 0.2000 0.2203
2970 0.3000 0.3355 0.3300 0.3005 0.3005 0.3997 0.0200 0.0522 0.0000 0.0023 0.0012 0.9527

102

Table 4.7

Average Value of Exchange Risk - R1 and R2

 

Mean Under
Floating Rates

Mean Under
Pegged Rates

 

 

Country 1960-1971(March) 1973(April)-1978
12

R: = 1'13 1:1 rt-i-l " rt-i
India 0.02 0.11
Israel 0.02 0.26
Korea 2.12 9.27
Mexico 0.00 0.42
Taiwan 0.02 0.24

R12: =/112 .IE (rt-i-l t-1

1=1

India 0.08 0.13
Israel 0.05 0.52
Korea 5.99 9.62
Mexico 0.00 0.78
Taiwan 0.05 0.37

 

103

It was pointed out earlier that the choice of an
appropriate transition date from pegged to floating
systems is a difficult one to make. This is so because
the period between March 1971 and March 1973 is almost
impossible to classify under either pegged or floating
rate systems. By March 1971, many countries had
announced their intention to float their currencies,
and others were clearly going to follow suit. After
several months of turmoil, exchange rates were pegged
once again, following the Smithsonian Agreement of
August 1971. When these arrangements collapsed in
March 1973, the floating rate system became installed
on a wide and permanent basis.53

Earlier research has indicated that choosing either
March 1971 or March 1973 as the transition date can
significantly affect the results of an analysis of
exchange rate volatility under the alternative systems.
Cline,54 for instance, chose March 1973 as the transi-
tion date, and his finding was that exchange volatility
had not significantly increased with the introduction

of floating rates. But this choice implies that the

 

53Yeager, L.B., International Monetary Relations: Theory,

History & Policy, 2nd, ed}, pp. 576-588 and 505-610
TNew York, NY; Harper & Row, 1976).

 

 

54Cline, W.R., op.cit., p. 17.

104

period between March 1971 and August 1971 should be
classified under pegged rates, which is not justifiable
simply because several currencies were floating during
this time. Other researchers used March 1971 as the
date of transition55 and came to an Opposite conclu-
sion.

Clearly, the choice of the transition date could
have resulted in these contradictory findings. There-
fore, the approach taken in this study is that neither
date should be used as a transition point, but rather,
the entire period March 1971 to March 1973 should be
deleted from the analysis of exchange risk. This
period should properly be viewed as a transition period
which can be classified neither as pegged nor as floating.
Accordingly, the average forecast errors presented in
Table 4.7 consider the period 1960 (I) to 1971 (I) as
representing the pegged system, and the period 1973 (II)
to 1978 (IV) as representing the floating system.

It is fairly obvious from these figures that
exchange risk increased substantially with the intro-
duction of floating rates, on the average. On both

1

measures, Rt and RE, exchange risk increased by a

factor of more than five, with the exception of

 

ssFarber, A., Roll, 0., and Solnik, B., op.cit., p. 236.

105

Korea in terms of R: and India and Korea in terms
2
of Rt'

With the intention of further establishing the
robustness of the chosen measures of exchange risk,

two other measures were computed which have been used

 

commonly
12 12
3 1 l 1
R = z 7: r _._. - r _. (4.15)
t 13' i=1 1'2 j=1 t 1 3 t 1
and,
12 w12
4 l 1 2
R = z ( 2 r _0-0 - r _0) (4.16)
t 12 i=1 12 j=1 t 1 j t 1

Measured in this way, also, exchange risk was
found to have increased (by a factor of 8 or more,
except in the case of Korea and India), as shown in
Table 4.8. In no case does risk appear to have declined.
The underlying assumption in 4.15 and 4.16 is that ex-
porters forecast exchange rates on the basis of their

average value over the past twelve months, i.e.,

1 12

* —
rt - 12 j: rt-j (4.17)

106

Table 4.8

Average Value of Exchange Risk - R3 and R4

 

 

 

Mean Under Mean Under
Pegged Rates Floating Rate
Country 1960-1971(March) 1973(Apri1) 1978
R3 = 1 122 1 122 r -
t 12 i=1 If j=12 t-1-j t-1
India 0.14 0.27
Israel 0.09 1.31
Korea 12.72 21.66
Mexico 0.00 1.54
Taiwan 0.10 0.89
R: = /Il; 1’32 (1];2' 1’32 rt-i-' ' rt-1)2
i=1 j=l 3
India 0.20 0.32
Israel 0.12 1.04
Korea 16.30 27.42
Mexico 0.00 1.91

Taiwan 0.12 1.50

 

107

CONCLUSIONS

 

It seems fairly reasonable to conclude from the
results presented in Tables 4.7 and 4.8 that exchange
risk had indeed increased under the floating rate
system. Whether or not the increase significantly
affected these countries' ability to exports, as the
theory in Chapter 2 suggests, is quite another matter.
The increased uncertainty may not have been of a large
enough magnitude to measurably affect exports, given
exporters ability to deal with it. Chapter 5 addresses
this issue statistically, along the framework outlined

in Chapter 3.

CHAPTER 5

ESTIMATION PROCEDURE AND RESULTS

Export supply is examined empirically in this
chapter, to evaluate the influence of exchange risk
on export level. For aggregate exports, the model of
export supply specified in equation 3.1 is used for
all five of the develOping countries being examined--
India, Israel, Korea, Mexico and Taiwan. Of these,
only the latter three maintained pegged rates (to the
U.S. dollar) throughout the observation period 1962-
1978. India and Israel changed their pegging practices
during this period, and thus the models of bilateral
export supply discussed in Chapter 3 cannot be applied
to them. For the others, the models of bilateral
exports specified in equation 3.4 (single equation) and
equations 3.4-3.6 (simultaneous system) are used to
examine whether their exports showed a structural shift
towards the U.S.A. after 1973. As discussed in Chapter

3, such a bias could be expected if exchange risk were

108

109

important to the export decision, because it is asymmetri-

cal for those currencies which are pegged to another.
Aggregate Exports

The functional form of the export supply equation
represented by equation 3.1 is assumed to be log-linear,

so that in estimable form it can be written as:

S -
log Xt. - 80. + 80 log XPIt. + 82 log DPIt.

+£§ log CAPt
1 1 1 1 1 1 i

1

. 4
+ 34 R3 + z B D + e
. = 1

1 ti n l 4+n. n ti
(5.1)
where,
xi. is the supply of exports in period t by
1 country i.
XPIt. is the price index of country i's exports in
1 period t.
DPIt. is i's domestic price index in period t.
1
R3. are the measures of exchange risk in period t.
l R1 and R2 are used, both having been defined

in the last chapter based on the time-series
analysis of the exchange rates. For complete-

ness, the results of estimating equation 5.1

110

2 and R: (defined in equations 4.15

with R
and 4.16) are presented in Appendix 4,

Tables A4.1 and A4.2.

CAPt is a measure of the productive capacity of

country i in period t.
D are quarterly dummies, with n = 1,2,3.

D4 is the dummy employed to account for the
period 1971(II) to 1973(1) which it was
determined could not be classified as either
representative of the pegged or the managed

floating rate systems.

at is a stochastic disturbance term with the
following usual56 properties assumed:

(i) at is normally distributed (Normality)
i
(ii) E(et ) = 0 (Zero Mean)
i

0 0 0 2
(111) E(e )
ti

II
o

(Homoskedasticity)

Non-antoregression is not assumed. It is tested for,
using the Durbin-Watson test. Where the hypothesis of
non-antoregression cannot be rejected, an assumption of

first order serial correlation is made and the equations

 

56Kmenta, J., Elements of Econometrics, p. 202 (New York,
N.Y.; Macmillan, 1971).

111

are re-estimated using the Cochrane-Orcutt iterative
technique.57
The specification of 5.1 is similar to that
generally employed in estimations of export supply
functions, except in two respects. Most previous
efforts have assumed zero homogeneity of export supply
with respect to export and domestic prices, and have
estimated the elasticity of a single price variable in
relative (ratio) form. In this study, it has been
considered preferable to test for zero homogeneity in-
stead of imposing the condition by assumption.58
The absence of money illusion is often thought of
as equivalent to zero homogeneity. This is not correct.
In fact, the absence of money illusion is neither a
sufficient nor a necessary condition for zero homogeneity.
The point is that the bundles of goods represented in
the domestic price index and the export price index are
likely to be different, particularly for developing
countries. Even if they were the same, the weights of

different commodities in the two indices may be

different. In this case, if the domestic and export

 

57See Madala, G.S., Econometrics, Chapters 8 and 12

(New York, N.Y.; McGraw Hill, 1977) for a discussion
of this subject. ‘

 

58This procedure was suggested in relation to the estima-

tion of aggregate import demand functions in Tracy, M.
and Ginman, P.J., "An Empirical Examination of the Tra-
ditional Aggregate Import Demand Model", RE Stat,
February 1976, pp. 75-80.

112

prices of the same good increased by equivalent amounts,
the ratio of the two indices would change. In reality,
the relative competitive position of the good has not
changed between the domestically sold and exported
units.59
The second area of departure from traditional
formulation is in the manner in which the capacity vari—
able is defined. Most previous formulations have used
income or industrial production as a proxy for capacity.
The changes in industrial production from quarter to
quarter can hardly be assumed to reflect changes in pro-
ductive capacity. It is more likely that the quarterly
fluctuations in part measure changes in utilization rates.
Productive capacity will change more gradually. There-

60

fore, following Goldstein & Khan, the measure used

for productive capacity, log CAP is the logarithm

t'
of the trend of industrial production.

Equation 5.1 for each of the five countries was
first estimated by ordinary least squares (OLSQ).
Where the hypothesis of non-antoregression could not

be rejected (because the computed Durbin—Watson Statistic

fell in either the inconclusive or the rejection

 

591bid., p. 70.

60Goldstein, M. and Khan, M.S., "The Supply & Demand for

Exports: A Simultaneous Approach", RE Stat, March
1977, p. 285.

113

regions),61 these equations were re-estimated using

the Cochrane-Orcutt iterative method, as discussed
earlier. An asymptotic 't-test' was then performed

on the estimate of the autoregression parapeter, p.
Where the null hypothesis of non-antoregression could
not be rejected--this generally happened in those cases
where the computed Durbin-Watson statistic had fallen
in the inconclusive region--the OLSQ estimation results
were presented.

In addition to the usual estimation results, the
value of h (the sum of the estimated elasticities with
respect to export and domestic prices) was also computed
for each equation to test the zero homOgeneity hypothesis.
Both estimated coefficients B1 and 02 , of which h is the
sum, are asymptotically normally distributed, and thus
h is too. Under zero homogeneity 81 and 82 would be
equal but of opposite sign and therefore their sum,

h, would be zero. The null hypothesis to be tested is

= O (5.2)

 

6JMadala, G.S., Op.cit., p. 284.

114

The t-statistic to test the hypothesis that h=0 is

formulated as

t = (5.3)

 

 

The estimation results using the two measures of uncer-

1 and R2, are presented in Tables 5.1 and

tainty, R
5.2.62 The numbers in parentheses below the estimated
coefficients are the corresponding t-statistics. Some

of the coefficients have known expected signs and the
interpretation of the price elasticity of export supply
(82 )is more complex than usual. Therefore, it is
impgrtant to specify precisely the hypothesis to be
tested for each of the estimated coefficients.

The elasticity of exports with respect to productive
capacity is expected to be positive (83 >0); the cross
elasticity of exports with respect to dimestic prices
and the coefficient of the uncertainty variable are
expected to be negative (821' 841 < 0). For these three
coefficients, a one-tailed t-test is appropriate. For

the other five coefficients (excluding 811), the two-

tailed test is employed.

 

62Owing to data constraints, the observation periods for
the five countries were not identical. They were: India
1962-77, Israel 1962-78, Korea 1963-78, Mexico 1962-77,

Taiwan 1962-78. All data is from, ”International
Financial Statistics", IMF.

115

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117

The test for the own price elasticity of export
supply is more complex. Jones and Berglas have proven
that this elasticity (811) can take on the negative

-1.63 In other words, whereas

values of greater than
supply elasticity is usually confined to positive
values, the aggregate export supply price elasticity
can also take on a value between 0 and -1. This holds
true for aggregate exports even when the supply elasti-
city of each individual exported commodity is positive.
This can be seen by noting that if balanced trade pre-
vails, the relationship between the price elasticities
of aggregate export supply and aggregate import demand
is

l (5.4)

Elasticity of = _ Elasticity of
Export Supply Import Demand

It is clear from this relationship that if the elasti-
city of import demand is very low, the elasticity of
export supply may become negative, reaching -1 as the
former goes to O.

The explanation for this, stated in simple terms,
is that the income effect of an improvement in the

terms of trade could swamp the usual production effect.

 

3Jones, R.W. and Berglas, E., "Import Demand & Export
Supply: An Aggregation Theorem", AER, March 1977,
pp. 183-1987.

118

The relative price effect on imports is small where the
elasticity of import demand is very low. Consequently,
an increase in the price of exports could result in lower
exports because although more exportables are produced,
even more are now consumed domestically.

The testing procedure for the esimated price
elasticity of export supply (Bli) is complicated by the
fact that 811 can be both positive and negative (greater
than -1). A single one- or two-tailed test is no
longer adequate, because the acceptance region is
disjoint. Instead, a two-step procedure as defined by

the hypotheses 5.5-5.8 must be employed.

Step 1
Null hypothe51s: Ho: Bli = 0 (5.5)
Alternate hypothesis: HA: Bli # 0 (5.6)

If the null hypothesis 5.5 is rejected and gli < 0,

Step 2
Null hypothesis: Bli = -l (5.7)
Alternate hypothesis: Bli > -1 (5.8)

which is a one-tailed test. Clearly Step 2 is redundant

if Bli > 0.

119

The t-statistic for Step 2 is constructed as
follows:
811"‘1’

t8 = . (5.9)
11 Standard error of Bli

 

We can now state the entire set of tests for
all the estimated elasticities and coefficients as

follows:

Null hypotheses: H01: 8.. = 0 (5.10)

H02: 81. = -1 (5.11)

II
3.3
‘
N
‘
O
0
O
‘
U1

where j = 0,1,...,8 and 1

Alternate hypotheses: HA1: 83i > O (5.12)
HA2: 811 > -1 (5.13)

HA - 3.. 7! 0, j = o,1,5,...,0
(5.10)

HA4: Bo- <00j=204
(5.15)

where i = 1,2,...,5 in all cases. Clearly H02 and HA2
are employed if and only if hypothesis 5.10 is rejected

for 811 and éli < 0.

120

At the 5 percent level of significance, the rejec-
tion region for the one-tailed test is defined by a
t-statistic of 1.645 of appropriate sign. For the two-
tailed tests, it is defined by a t-statistic of 1.96.

It is clear from the estimation results that the
assumption of zero homOgeneity in prices can be
rejected for three of the five countries (Israel, Korea,
Mexico) at the 5 percent level of significance, indicating
that price elasticities should be estimated separately,
without the usual constraint which implicitly assumes
zero homogeneity.

Another interesting feature is the relatively small
price elasticities coupled with large and highly signi-
ficant coefficients on the productive capacity variable
for every country. This is consistent with the export-
oriented development strategy of these countries. The
pressure to export is particularly significant, and
consequently, export price does not play as important a
role in the export decision as does capacity. Interest-
ingly, productive capacity is significant even for
countries such as Mexico and India which are generally
viewed as import substituting countries. The evidence
indicates that even these countries are export-oriented.

Another important reason for the significance of

productive capacity in export decisions relates to a

121

particular feature of some export incentive schemes.

In India, for instance, exporters are granted import
licenses in direct proportion to their export volume.
Because of generally stringent import limitations, these
import licenses command extremely high premiums.

Indeed, profits of several hundred percent over the
licensed import value are not uncommon, just from the
sale of the licenses themselves. It is understandable,
then, that export prices have less impact on the export
decisions.

The uncertainty variable is significantly negative
only in the case of India when R1 is used. With R2,
it becomes significant for Israel also. The conclusion
is that exchange rate uncertainty does not adversely
affect aggregate exports in each country. While this
may seem surprising at first, examination of the effect
of export incentive schemes (such as the one cited for
India) explains this unexpected result.

Typically, in trade analyses, a separation between
exporters and importers is assumed. However, many
export incentive schemes cause exporters to become de
facto importers. Thus, any exchange risk perceived
in the export market is offset by exchange risk in
the opposite direction as the exporter participates

in the import (or import license) market. In this

122

situation, obviously, exchange rate uncertainty will
not deter exports to the extent that it would for
pure exporters.

Another explanation for the small influence of
exchange uncertainty on export decisions relates to
the currency denomination of export contracts. Clearly,
if all export contracts are denominated in domestic
currency, the entire burden of exchange risk is borne
by the importer. The converse is true if all exports
are denominated in the importer's domestic currency.
When they are denominated in a third currency, the
risk is shared. It is extremely difficult, if not
impossible, to determine the currency denomination
of exports of a country. Data on this simply does not
exist in published form. Some efforts have been made
to estimate the proportion of exports denominated in
domestic currency for exports of the U.S.A. and Sweden.64
Such an estimation was not undertaken for the countries

being examined in this study because the question raised

here is different. The important distinction is not

 

64Grassman, Sven, "Currency Distribution and Forward
Cover in Foreign Trade: Sweden Revisited, 1973",
Journal of International Economics, May 1973, pp. 215-
222, and Magee, S.I., WU.S. Import Prices in the
Currency-Contract Period", Brookings Papers on Economic

ACtivitx, I/74, pp. 117-164.

 

 

123

between the proportion of export contracts denominated
in domestic versus foreign currency, because hardly

any exports are denominated in domestic currency in

the countries being examined. The question, instead,

is whether exports are denominated in a center currency
(such as the U.S. dollar for Mexico) or in the currency
of the importing country. This would be very difficult,
if not impossible, to determine.

We now turn to the influence of exchange risk on
the bilateral trade of the three countries which main-
tained pegged rates with a major currency. These
countries are Mexico, Korea and Taiwan, all three
having been pegged to the U.S. dollar throughout the

observation period.65

Bilateral Exports

 

The objective of examining the bilateral export
supply function, as discussed earlier, is to test if
the exports of those developing countries that consis-
tently pegged their currencies to one major currency
underwent a structural shift towards the center currency,

when floating rates were introduced in 1973. Korea, Mexico

 

65Observation periods are the same as for aggregate

exports. Bilateral trade flow data are from "Direction
of Trade", IMF. All other data are from "International
Financial Statistics", IMF.

124

and Taiwan fall into this category (of the five coun-
tries considered in this study)--and the U.S. dollar
was the center currency in all three cases. The four
(or five, depending on data availability) largest
importers of their exports were identified for the pur-
pose of this investigation, based on exports in the
first quarter of 1973. As could have been expected,
the U.S.A., being the center country, was among the

t0p four importing countries (although no necessarily
the largest), in each case.

Each developing country's bilateral export supply
function to its largest importing nations is estimated
first as a single equation and then as a simultaneous
equation system. This was deemed important, because
a comparison of the results would indicate whether the
small country assumption is justified for bilateral

trade (see the discussion in Chapter 3 on this point).

Single Equation Model

 

The single equation model of bilateral export
supply specified in equation 3.4 can be written in

estimable form as

125

s _ 0
log Xij - aij + aijlog Pxi + 01.109 Pdi + ai.log CAPi
4 4 4+n 1
+ 0.. U + Z 0.. D + 0.. . (5.16)
1] n=1 1) n 13

The subscript i represents the exporting country,
and the subscript j represents the importing country.
The time subscript, t, is omitted for notational con-
venience. U is a dummy variable used to capture struc-
tural shifts in the supply function, and is the focus of
attention in this investigation. It takes on a value
of O for the period prior to 1973 (II) and a value of
unity thereafter. All other variables are the same as
defined in the context of equation 5.1 except that
Xij now represents bilateral exports from country i
to country j.

The hypotheses tested are also the same as for
the aggregate export supply equation, with the exception
of “gj (the coefficient of the uncertainty dummy, U)
which replaces 84.

As explained earlier, “ij can be either positive
or negative for the center country, but in either case,
we would expect that the coefficient is larger for the

center country than it is for the other countries.

Assigning j=l for the U.S.A., we can say that

126

“11 - aij > 0, j = 2,3,... and (5.17)

l for Korea
1 = 2 for Mexico
3 for Taiwan

if it is true that exports are biased towards the center
country.

The t-test used to test the hypothesis 5.17 is

 

 

_ “11 ' ij
t — (5.18)
/ A A _ A A
/ Var “11 + Var aij 2 Cov(ail,aij)
j = 2,3,...
1 = 1,2,3.

Of course, if aij and &il are both insignificantly
different from zero, the t-statistic defined in 5.18
will also be insignificant.

The results of estimating 5.17 are presented in
Tables 5.3-5.5 for Korea, Mexico and Taiwan respectively.
Again, the numbers in parentheses below the estimated
values of the coefficients are the corresponding t-
statistics. As before, the equations were estimated
using the Cochrane-Orcutt iterative method for adjust-
ing for serial correlation. If the p was found to be

insignificant based on an asymptotic t-test, the equations

were re-estimated using ordinary least squares.

127

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130

All the estimated elasticities had expected signs,
although many were not significant. The productive
capacity variable once again performed strongly being
significant in all cases for Korea and Taiwan and for
Mexico's exports to the U.S.A.

The uncertainty dummy performed in a consistent
but unexpected manner--exports were, if anything
shifting away from the U.S.A. Each of the t-statistics
(defined in equation 5.18) was found to be negative,
indicating a shift of exports away from the U.S.A. In
the case of exports to Germany by Korea and Mexico,
this structural shift was statistically significant
(see Table 5.6). The unambiguous conclusion from these
results is that the exports of these deve10ping
countries did not shift in favor of the center country
as a result of asymmetric exchange risk.

It should be noted at this point that these results
are based on single equation estimation. Thus, it could
very well be that differential growth and inflation
rates among the importing countries since 1973 swamped
the effect of exchange risk and accounted for the
apparent shift in exports away from the center country.
This would be clarified if estimation was conducted
using a simultaneous approach--because the export

demand function would include domestic inflation and

131

 

 

 

 

 

 

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132

buying power of the importing countries as explanatory
variables. In the next section, the estimation pro-
cedure and results of the simultaneous model are

discussed.

Simultaneous Equation Model

 

The simultaneous model defined by equations 3.4-
3.6 is assumed to have a log-linear form as before.
The bilateral export supply function is the same as
equation 5.16 and is reproduced below for convenience

with the rest of the testable simultaneous model,

3 _ 0 l 2 3
Xij - “ij + aij log Pxi + aij log Pdi + aij log CAPi
+ a4 u + g a4+“ D + £2 (5 18)
1 n=1 1) n 13
and
d _ 0 2 3
Xij — aij + all log Pxi + aij log Pd' + aij log Yj
+ a lo P + g 4+n D + e3 (5 l9)
ij 9 xw n-l ij n 1 '
x? = x?. (5.20)

133

where
ng is the demand for country i's exports by
country j;
de is the domestic price index in j

Y. is the gross national product of j

P is the price index of world exports

and all other variables have been defined earlier. The
time subscript has been omitted for notational con-
venience.

The bilateral export supply equation (5.18) was
estimated by the two-stage least squares method,
correcting for serial correlation where necessary.

As in earlier estimations, equations were re-estimated
without the adjustment for serial correlation, if p was
found to be insignificantly different from zero based
on an asymptotic t-test. The results are presented in
Tables 5.7-5.9 for Korea, Mexico and Taiwan respec-
tively.

As can be seen from the estimated elasticities

l 2 3
ijl Bijl Bij

(B ), no significant improvement in the
results was obtained by employing a simultaneous model.
The conclusion is, first, that the small country
assumption seems to be valid for bilateral exports as

well, at least in the case of the three countries

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z<3H<s u manomxm .mumum..m
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m.m manwfi

137

examined in this study. Second, there is no evidence

to

suggest that exports have been biased towards the

U.S.A. The coefficients of the uncertainty dummy

are insignificant in all cases except for the exports

by

Korea and Mexico to Germany--and in these cases,

the signs of the coefficient indicate a movement

towards Germany which is not a center country.

66

 

66

The computation of a t-statistic as defined in equation
5.18 is extremely complex for the simultaneous equation
model especially when estimation requires an adjustment
for autoregression. Fortunately, because the coeffi-
cients of the uncertainty variable were insignificant,
this computation was not undertaken. The results were
bound to be insignificant. For Germany's imports from
Korea and Mexico, the t-statistic would have had the
wrong sign in any case, even if it were significant.

CHAPTER 6

SUMMARY AND CONCLUSIONS

The study was conducted to examine the developing
countries' claim since the inception of the floating
exchange rate system in 1973 that

(1) The increased exchange risk present under
floating exchange rates has hampered their ability to
export;

(2) The influence of exchange risk is asymmetrically
felt in exports to the center country (i.e. to the
country to whose currency the developing countries'
currencies are pegged) and in exports to all other
countries. It was argued that faced with lower risk
in their traditional markets, exporters in developing
countries would prefer to concentrate their exports to
the center country.

Before these claims could be evaluated, two under-
lying questions needed to be addressed. The first
related to the influence of exchange risk on the export

decisions of an exporting firm. This micro question has

been addressed in the literature either in the context

138

139

of a domestic firm with no access to futures contracts
(which corresponds to the case of an exporter with no
access to forward exchange markets) or in the context
of a trading firm with access to a perfect forward
exchange market. In addition, previous discussions
employed specific utility functions, and therefore,
their generalization was questionable.

In Chapter 2 of this study, the influence of exchange
risk was analyzed using a general utility function with
the only restrictions imposed being that marginal utility
is positive and declining (u'>0, U"<O) and that the firm
exhibits decreasing absolute risk aversion. Another
important generalization was achieved by allowing the
forward exchange market to be imperfect. In this
general framework, it was found that a firm's export
decision would be influenced by exchange risk. In most
developing countries, where overt exchange speculation
is generally prohibited and forward markets are imper-
fect, exchange risk could be expected to have an inverse
relationship with exports. The two extreme cases of a
non-existent forward exchange market and a perfect
forward exchange market become special cases of the
general model. Thus, a reconciliation between contra-

dictory conclusions in existing literature was achieved.

140

Exchange risk has historically been equated with
exchange variability (volatility). This approach
totally neglects the important role of expectations.
It was argued here that inability to forecast future
exchange rates (i.e. forecasting error) is a more
appropriate indicator of exchange risk. The rationale
for rejecting variability as an appropriate measure
of risk is, simply stated, that if exchange rates could
be forecasted with accuracy a mere increase in vola-
,ti1ity would not imply a greater risk. It could be
argued that the distinction is trivial because only
if exchange rates have a known unchanging and deter-
ministic relationship with other variables (whose
future values are known with certainty) is perfect
forecasting possible. And because such a situation
is unlikely, the distinction is not important. But
the issue is one of degree. At times, exchange rates
may be easier to forecast than at others, and this
relates not to their volatility per se, but to the
knowledge of their underlying structure.

Based on this concept of exchange risk (and a
few authors have employed it recently), time series
analysis was used to obtain forecasts of exchange
rates. Forward rates have been used elsewhere as

proxies for exchange rate expectations with some

141

success. Several justifications were provided in
Chapter 4 for the choice of the alternative method
employed in this study. Four proxies for exchange
risk were developed, and it was found that exchange
risk was considerably larger in the period of floating
rates than it had been under pegged rates, by each
measure.

This analysis provided the basis for addressing
the two central empirical questions raised by the
developing countries. The aggregate export markets
of India, Israel, Korea, Mexico and Taiwan, and the
bilateral export functions for Korea, Mexico and Taiwan
were modeled both as single equations and as simultaneous
systems to test these two hypotheses.

In the context of aggregate exports, the notion that
exchange risk had dampened exports did not have empiri-
cal support. The conclusion, in short, is that although
exchange risk had increased significantly since the
introduction of floating rates and on a theoretical
micro level exporters could be expected to reduce
exports as a result, there is no empirical evidence to
suggest that this did occur. Several interesting
possibilities arise from this finding. First, the
influence of exchange risk on export levels may be so
weak that its effect cannot be identified empirically.

Second, it may be that for institutional reasons

142

traders in these countries may be active in both import
and export markets, thereby largely neutralizing the
effect of exchange risk on exports. Lastly, the
currency denomination of export contracts has an impor-
tant bearing on this issue and may explain why theore-
tical expectations were not realized in the empirical
tests.

Following the line of argument presented in Chapter
3, if exchange risk had a bearing on export levels,
then for developing countries that kept their currency's
pegged to a major currency, exports could be expected
to shift structurally towards this center country. The
increase in exchange risk would be asymmetric vis-a-vis
the center currency and all other currencies. Because
of pegging practices, the increase will be lower for the
center currency. In testing for such a shift in the
exports of Korea, Mexico and Taiwan, in both a single
equation and a simultaneous model, it was found that
there was no empirical evidence to support this argument.
Once again, the conclusion is not as unambiguous as it
may sound. The comments made in the context of aggre-
gate exports apply here also, and the currency denomina-
tion of exports contracts could possibly be even more

important in the case of bilateral exports.

143

The unresolved issues, although considered beyond
the scope of the present investigation, represent
potential areas for future research. When the effects
of these institutional and other factors can be identi-
fied and their influence on the relationship between
exchange risk and export levels measured, an unambiguous
answer to the question can be obtained. In the interim,
the conclusion must be that there is insufficient
empirical evidence to support the hypothesis that the
increased exchange risk under floating rates has
adversely affected the export performance of the
developing countries.

In view of this, it is particularly interesting
that exchange rate stability continues to receive
increasing attention in international fora, such as
the IMF. At the annual IMF meetings held in Belgrade
in October 1979, exchange stability was considered
to be a pressing issue even by the industrial nations
of Europe whose financial and exchange markets are

generally posited to be perfect.

APPENDIX A

APPENDIX A

Proposition: Complete hedging will occur if and only if

 

the expected marginal revenue of converting foreign
exchange through the future spot market exactly equals
the net marginal revenue of conversion through the

forward market and the marginal production costs, i.e.

a = 1 _ii pE= f[1 - cz'm] = C1'(q)

144

145

Proof:

:1
III

apfq + (l—a)prq - C1(q) - C2(apfq)
Adding and subtracting pfq, we have:
n = (1-a)pq(r-f) + pfq - C1(q) - 02(apfq)

From which,

Egigilll = E{U'(fl)[(1-a)p(r—f) + pf - C '
a 1
- C2"apf]} = 0 (Al.l)
3§igélll = E{U'(n)[pq(f-r) - c2" pfq]} = o (A1.2)
When a = l, we have, from 1.1,
pf[l-C2'] = Cl' (Al.3)

and from Al.2, noting that n = pfq — Cl (q) — C2(apfq)

when a = l (i.e. it is non-stochastic), we get

”I

p/q = p/q . f[l-cz'] (A1.4)

f[l-C

HI
n

I
or 2 ]

Al.3 and A1.4 together imply that p? = Cl'.

146

For sufficiency, we need to show that if Al.3 and Al.4

hold, the hessian:

 

 

 

 

 

" 2 2 ‘
a E[U(n)] a E[U(n)]
3 2 3g 3a
q
32E[U(n)] 82E[U(n)]
L aq 3a 302

 

is negative definite. Specifically, we need to show

that the determinate of H [H2] > 0. When Al.3 and

2!
Al.4 hold:

 

 

 

2
a El”;"” = E{U"[(l-a)p(r-f) + pf - cl' - Cz'apf]2
Bq
- U'ICl" + C2"(apf)2]} (Al.5)
32E[U(n)] 2
2 = E{U"[Pq(f‘r) - Cz'pfq]
aq
- U' c2"(pfq)2} (Al.6)
32E[U(n)]
aq 3a = E{U"[(l-a)p(r-f) +_pf - Cl'

- Cz'apfltpq(f-r) - Cz'pfq]

+ U'[p(f-r) - Cz'pf - C2"ap2f2q]} (Al.7)

147

 

When a = 1, we know from Al.3 and Al.4 that pf (l - C2')
= Cl' , and f'= f(l - Cl'). Upon substitution,
equations A1.5 - Al.7 reduce to:
32 2
——— E[U(n) = - E{U'IC " + C "(pf) } (Al.5')
a 2 1 2
q
32 2 — 2 2
2 E[U(w)] = E{U"[(pq) (r-r) - U'C2"(pfq) }
3a
(Al.6')
——3—2— mum] = E{U'I (E-r) - c " 2:2 1} (Al 7')
3q 3a p 2 p q °

Furthermore, at a = l, n is non-stochastic. Therefore,

 

we can write, for equations Al.5' - Al.7',
32 2
-—— E[U(fl)] = - U'IC " + C (Pf) ]
2 l 2
3q
32 2 2 n 2
2 E[U(n)] = U"[(pq) or] - U'[C2 (pfq) ]
8a
where a: E Variance of r and
2
3 _ _ . u 2 2
WE[U(W)]- U Czpfq

respectively.

148

Finally, the determinant of H2 is:

- u'Icl" + c2"<pf)21[U"(pq2)o: - U'c2"(pfq)21

_ [U'Cznpzfquz

= — U! U" Cl"(pq)203 + (U')2Cl" C2fl(pfq)2
_ I u n 2 2 2 2
U U C2 (p f q) or

2 2

up f 2

2

+ [U' c2"p £qu2 - [U' c2 q]

The last two terms cancel out. Since, U"(n) < 0 and

C1" (q), C2"(F), U(n) > 0, we can conclude that |H2| > 0,

completing the proof.

APPENDIX B

APPENDIX B

Proposition: The demand for a country's exports to

 

another country approaches perfect elasticity when
these exports represent a small fraction of the latter

country's aggregate imports.

149

150

Proof:67

The global demand by country j for a commodity (x)

can be stated as,
W = X(PX , Pw) + [W - X] (PX , Pw) (A2.l)
where,
X is j's demand for country i's exports of commodity
W is j's global demand for x.

P is i's export price for x.

P is export price for x from all other exporting

countries.

 

67'1.'h.e proof is similar to the one provided in Kreinin,
M.E., International Economics: A Policy Approach,
3rd ed. (New York, NY; Harcourt, Brace & Jovanovich,
1979) for aggregate exports.

 

151

Differentiating A2.l with respect to Px'

dP 3P 3P dP 3P 3P dP
x x w x x w x
(A2.2)
P
Multiplying both sides by 3% and re-writing terms in

the form of elasticities, we get,

 

w
= —n + n o + — o — _ +
x [w x] X X dPx an an

l
J
x|£

[w-x] Px 5" [ax alw-XJ]

(A2.3)
where,

”w is the price elasticity of demand, of j's global
swig
w

imports of x, with respect to Px' i.e. - 35—
x

”x is the price elasticity of demand for i's exports

3x32:

Of X, 1060, - _—
an )(

is the cross price elasticity of demand for
P

a[w-x] , x
an lw-xl

n [w-x}

other countries' exports of x, i.e.,

Rearranging terms, A2.3 may be written as,

x w x [w-x] x de X an BPw

(A2.4)

152

When i's exports of x to j (X) are a very small fraction
of j's total imports of X (W), then

de
——roo >m,and 317:0

X

 

xlz

It follows directly from these observations that,

T] ———*°° as

x W 0
Summing over all commodities exported by i to j, we may

conclude that this relationship holds in the aggregate,

thus completing the proof.

APPENDIX C

APPENDIX C

For completeness and also to verify the validity
of the small country assumption the aggregate export
supply function (equation 5.1 and reproduced below as
equation A3.l) is estimated in a simultaneous model,
with export prices being determined endogenously. The
trend in the literature has been towards simultaneous

68 but it is not clear whether the incre-

estimation,
mental effort and complexity is justified in terms of
the results, i.e. whether the simultaneous approach
yielded significantly superior results.

By estimating the export supply equation as both

a single equation and a simultaneous system in this

study is defined by equations A3.1-A3.3.

Country i's Export Supply

 

S .—
log Xt. — 80. + 81 log XPIt. + 82 log DPIt. + 83.1ogiCAPt.
1 1 i i 1 l i i
i 4
+ 8 R + z B D + e (A3.1)
4i t1 n=1 4+ni n ti

 

68See for example, HOOper, P. and Kohlhagen, S.W., "The

Effect of Exchange Rate Uncertainty on the Prices and
Volume of International Trade", Un ublished, 1978;
Goldstein M. and Khan, M.S., ”The SuppIy and Demand for
Exports: A Simultaneous Approach", REStat, March 1977,
p. 285; and Grossman, G.M., "A QuarterIy Econometric
Model of the Exporting Behavior of Some Non-Industrial
Countries", gnpublished, MIT, 1978. The last is of
particular interest since it is concerned with deve10p-
ing countries.

 

153

154

World Demand for Countryyi's Exports

 

d
log Xt. = a0. + a1 log XPIt. + 32
l 1 1

log XPW + a

t 3 log wxot

+

Ilran

1

a D + n
n 3+ni n ti (A3.2)

Equilibrium in Export Market of Country i

 

X . = X (A3.3)

where,

X3 is the world demand for country i's exports in
i

period t;

XPWt is the price index of world exports in period t;

WXQt is real world purchasing power;

“t is the stochastic error term;
i

and all other variables have been defined earlier.
This specification of the demand function for a
country's export is similar to that used generally in
the literature. Total world exports have been used to
measure real world purchasing power for reasons of

data availability, although some researchers have argued

155

that it is a preferred measure because it reflects
some of the restrictions in trade which world income

would not.69

Quarterly data on income is just not
available for most countries.

The export supply functions of the five countries
under consideration (India, Israel, Korea, Mexico and
Taiwan) were estimated using 2 SLS. An adjustment for
serial correlation was made in the initial estimation
and an asymptotic t-test conducted on Rho (9). Where
the null hypothesis, p=0, could not be rejected, the
equations were re-estimated by ordinary least squares
(OLS) .

The results of the estimation are presented for R1

and R2, the two alternative formulations of the uncer-
tainty variable, in Tables A3.l and A3.2. In the case
of India and Korea, serial correlation existed, but for
Israel, Mexico and Taiwan, the OLS results are shown
because p was insignificant at the 95 percent level of
confidence.

A comparison of the export supply elasticities
derived from simultaneous estimation with those estimated

by single equation estimation (Tables 5.1 and 5.2)

clearly reveals that no appreciable improvement in the

 

69Polak, J.J., An International Economic System, pp.

47—51 (Chicago, 111.; University of Chicago, 1953).

 

156

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158

results resulted from simultaneous estimation. The
conclusion is that, at least for the five countries
examined here the small country assumption on the export
supply side was appropriate. Unfortunately, there is

no justification for a generalization of this conclusion.

APPENDIX D

159

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BIBLIOGRAPHY

BIBLIOGRAPHY

Aliber, R.Z., "The Firm Under Pegged and Floating Exchange
Rates", Scandinavian Journal of Economics, #2, 1976.

 

Arrow, Kenneth J., Essays in The Theory of Risk Bearin ,
Markham Publishing Company, Chicago, IllinOis, l9 1.

Black, Stanley W., "Exchange Policies for Less DevelOped
Countries in a World of Floating Rates", Essa s in
International Finance #119, International Finance
Section, Princeton University, Princeton, N.J.,
December 1976.

 

Box, G.E.P. and Jenkins, G.M., Time Series Analysis,
Holden Day, San Francisco, CA, 1970.

Caves, R.E., "Flexible Exchange Rates", American Economic
Review, May 1963.

Caves, R.E. and Johnson, H. (eds.), Readings in Inter—
national Egonomics, Richard D. IrWin, Inc.,
Homewood, Ill., 1969.

 

Clark, Peter B., Uncertainty, Exchange Risk and the
Level of International Trade", Western Economic
Journal, September 1973.

Cline, W., International Monetarpreform and the DeveloE-
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