~18-

rate. This can be seen by substituting equation (8) into (10) which yields

-w rel

N j nh ON
(11) FO) ty PD EE (ry pes:

To be consistent with the empirical derivations, the numeraire-home
relative price is separated from the numeraire-country j prices by

adding and subtracting p+ from the right hand side of (11). This yields

N N
(12) r(w) = (pt - py +I (pd - p') +2 (t, - w,) el .
1 J 2 4 joj

Note that the real exchange is a function of both Ty's and
wj's, the elasticity shares and the optimal basket weights. The
problem of choosing weights can now be seen as minimizing the objective

function with respect to the weights

(13) Min L = E(r(w) - E(r(w)))2

W.R.T (w)

where r(w) is defined in (12) and the weights satisfying the Problem,

w= (wp eee .w®), are defined as optimal.


-12-

of the EMS weak currencies) yields the same basket value as the ECU.

The failure to reject the null hypothesis in these single country pegged
Pongo baskets comes from the lack of exchange rate variability among
currencies comprising the EMS rather than small variations in weights.

There are two exceptions to these findings: the Italian lira
and the Greek drachma. Both the lira and the drachma dollar exchange
rates had a larger variance than the EMS rates. The drachma was first
included in the ECU basket in September 17, 1984 when the ECU was
redefined. Furthermore, Greece does not participate in the full EMS
arrangements nor has it been coordinating its economic policies with the
other EC countries. It is not. surprising, therefore, that the drachma
Pongo basket does not approximate the ECU. The Italian lira, on the
other hand, is an active participant of the EMS. However it has been
one of the weakest EMS currencies and precipitated the realignment in
July 1985. Pegging to the weakest currency yields an average basket
value be less than the average for the ECU.

Another noteworthy observation from Table 4 is that the U.K.
pound appears to have behaved much like the other EMS currencies. This
observation may be consistent with the rumors that Britain may be
considering to join the EMS. In general, the results over this time
period suggest that if the EMS central rate system is functioning and
all currencies stay within their prescribed bands, then it does not
matter how the ECU is defined, since it will approximately equal any
weighted average basket.

These results may have policy implications. Therefore, three
additional episodes are analyzed. The base date for these other baskets

including the ECU is shifted back to March 13, 1979 -- the day the ECU


-22-

Table 1: Components of the ECU Basket
for September 17, 1984

Count ry@ sy> FX;¢ cd FXECU;& wf
BF 3.71 61.84 059994 45.153 +082165
DK +219 11.112 019708 8.1135 026992
FF 1.31 9.428 -13895 6.8839 .1903
DM +719 3.073 + 23397 2.2438 «32044
cD 1.15 120.2 0095674 87.765 013103
IL 140 1892 -073996 = 1381.5 10134
IP 00871 +99206  .0087797 +72436 012024
LF +14 61.84 0022639 45.153 -0031006
NG +256 3.465 073882 2.53 -10119
EP -0878 +80515 .10905 +58789 = 14935
EcUs + 73016

Notes to Table:

a

Countries are as follows: Belgium (BF), Denmark (DK), France (FF),
Germany (DM), Greece (GD), Italy (IL), Ireland (IP), Luxembourg (LF),
Netherlands (NG), and U.K. (EP).

Sj represent actual currency components in the ECU -- revised on 17
September 1984.

FX; - represent the foreign exchange/dollar rate. Data are from the
Federal Reserve MDL database -- based on noon New York rates.

Cj - dollar equivalent of component in ECU.

FXECU; - represents the central foreign exchange rates in terms of the
ECU.

Wi - represent initial weights. Note that because I use New York
exchange rates rather than the official EC rates these weights are
slightly different from official one. However, the currency components
correspond exactly with the official numbers.

ECU - the dollar value of the basket. It is the sum of the Cj's.


-3-
II. The ECU/EMS

At the heart of the EMS is a system of fixed but adjustable
exchange rates.2 For each currency, central rates are expressed in
terms of the ECU. A grid of bilateral central rates is calculated from
these individual central rates. A band of + 2.25 per cent (or + 6.0 per
cent for the Italian lira) has been established within which each
currency may fluctuate. Theoretically, when the margins are reached the
participating central banks are obliged to intervene. On occasion,
however, central banks have requested changes in their central rates
rather than intervene in the foreign exchange market or change their
economic policies. Provisions were made to thwart frequent realignments
by requiring approval of all participating countries to these
adjustments.

The grid of bilateral central rates and intervention Limits is
supplemented by the divergence indicators which show the movement of the
exchange rate of each EMS currency against the (weighted) average
movement of the other EMS currencies. When a currency crosses its
“threshold of divergence” it activates an early warning system. A
currency is said to have reached its divergence threshold when it
reaches 75 per cent of its band (or spread, that is + 2.25 per cent).
There is the presumption that the authorities concerned will correct
this divergence by adequate measures. In practice, the divergence
indicators have not played as large a role as they were intended since
they do not obligate countries to intervene or otherwise to act.

The ECU plays a central role in the EMS. It serves as the
numeraire for the exchange rate mechanism and also as a means of

settlement and as a reserve asset of EMS central banks.


IFDP
NUMBER

270

269

268

267

266

265

264

263

262

261

260

259

258

257

256

-33-

International Finance Discussion Papers

TITLES

Assertion Without Empirical Basis: An
Econometric Appraisal of Monetary Trends

in ... the United Kingdom by Milton Friedman
and Anna J. Schwartz

Canadian Financial Markets:
Proposal for Reform

Was It Real? The Exchange Rate Interest
Differential Relation, 1973-1984

The U.K. Sector of the Federal Reserve's
Multicountry Model: The Effects of
Monetary and Fiscal Policies

Optimal Currency Basket in a World of
Generalized Floating: An Application to
the Nordic Countries

Money Demand in Open Economies:
Substitution Model for Venezuela

A Currency

Comparing Costs of Note Issuance Facilities
and Eurocredits

Some Implications of the President's Tax
Proposals for U.S. Banks with Claims on
Developing Countries

Monetary Stabilization Policy in an Open
Economy

Anticipatory Capital Flows and the Behaviour
of the Dollar

Simulating Exchange Rate Shocks in the MPS
and MCM Models: An Evaluation

Trade Policy for the Multiple Product
Declining Industry

Long Memory Models of Interest Rates, the
Term Structure, and Variance Bounds Tests

Currency Substitution and the New Divisia
Monetary Aggregates: The U.S. Case

The International Transmission of Oil Price
Effects and OPEC's Pricing Policy

The Government's

AUTHOR(s)

David F. Hendry
Neil R. Ericsson

Garry J. Schinasi
Richard Meese
Kenneth Rogoff

Hali J. Edison

Hali J. Edison
Erling Vardal

Jaime Marquez

Rodney H. Mills

Allen B. Frankel

Marcus H. Miller

Arnold Kling

Arnold Kling

Catherine Mann

Gary S. Shea

Jaime Marquez

Jaime Marquez


-19-

The first-order conditions after minimizing (13) are as follows:

N N
1 1 1 1
(14) an (a, - t) Cov (ej> ey - % Cov (pi -p, ey
J
we = Cov (pt - pr, -) = 0 for q=2,...N .-

The N-1 equations in (14) are rewritten in matrix and vector

notation.
(15) a@w-1t)-a(t1)-T#0 ,
where
Nn = Cov (ey es an (N - 1) by (N - 1) variance-covariance

matrix of exchange rates.

a = Cov (ph - pr, es an (N - 1) by (N - 1) Covariance matrix

between the numeraire-country g exchange rates and the

relative price of the (N - 1) foreign countries and
the numeraire country.

T = Cov (pt - pe, et) an (N - 1) column vector of the

covariance between the numeraire-country q exchange rate
and the relative price between the numeraire and home

country.
From (15), the solution with respect to the optimal weights, w°, can be

derived as:
(16) wettola tt+oir.

Both Lipschitz and Sundararajan (1980, 1982) and Edison and
Vardal (1985) discuss in detail the implications of equation (16) and
the various special cases. In this paper the focus is on applying
equation (16) to the German situation by comparing the German optimal

basket path with the path of the ECU.


BF

DK

FF

DM

GD

IL

IP

LF

NG

EP

BF

-982
2995
+996
557
898

2992

+995

+884

DK

98

-979

+535

-857

2977

+982

-979

875

-25-

Table 4: Correlogram of Exchange Rates
September 17, 1984 to December 12, 1985

FF

997
507
+848
-997
2995
+996

+917

DM

+562
879
+992
+996
2999

-895

GD

+859

477

+553

+561

+207

IL

1

-883

878

-878

-607

IP

1

+992

991

+926

LF

1

2995

+884

NG

1

-899

EP


-21-
V. Conclusion

During the past year or so there has been a great deal of
discussion at the policy-making level and in financial markets about the
stability of the ECU. This paper has sought to examine the sensitivity
of the ECU to changes in its currency composition and to compare the
path of the ECU to that of an optimal basket in the case of Germany.
The results derived in this paper suggest that the ECU is stable. The
first experiment indicated that when there is little exchange rate
variability within the currencies that comprise the ECU the value of the
ECU remains invariant to weight changes. The second experiment
demonstrated that the optimal basket for German is not unlike the ECU.
Both of these results are based on preliminary work and should be

interpretated as tentative.



-16-
the exchange rate index, the reference currency (the home country), time
and weights, respectively. The home country's bilateral exchange rate
with respect to currency j at time t is written as Eb (t). The

effective exchange rate index for the home country is defined as a

geometric average.

h N h w
(6) I(t, w= (EB (t)/E(o)) I.
jol i j

+N and the

In this basket, there are N currencies with weights Wj, j=l.
sum of the weights equals one, £ Wj 1. When Thet ,w) is greater than
Th(o,w) this implies a depreciation of the home currency. Equation (6)
is rewritten in log form where lower case letters denote logs of

variables (with the exception of weights and parameters):

N
(7) ie, w= 5 wi (eh (t) - ef (o)) .
ja jd j

Furthermore, if the home numeraire exchange rate, ef,

is
pegged to a log-linear basket of n currencies with weights, Wj> then one

can write

(8)

For the purpose of this paper, it is assumed that the German
policymaker is concerned with minimizing fluctuations in the real
exchange rate index at some target r*, and that the weights (wy"s) in
the currency basket are policy instruments. The policy problem is to

determine the weights at each point in time which minimize the cost of


-8-
private sector. This addition requires considering the ECU in terms of
portfolio decisions.

Rather than derive optimal weights for the ECU, in this paper
various weighting schemes with economic justification are devised and
are evaluated. If the results show that the value of the ECU is not
highly sensitive to changes in its composition then deriving optinal
weights is not important. One would expect that the value of the ECU
would be sensitive to these changes. This sensitivity is evaluated by
comparing mean values of different baskets. Other ways of assessing
these differences may be considered at a later date.8

At each re-composition of the ECU, the EMS countries must
decide and agree on the appropriate weighting scheme. Let us assume
that they choose wj(0) to represent each country's share. This w, is
then used to define the quantity of each member currency, s;, usec to
create and calculate the ECU basket. Note that these sj's are fixed and
are not changed again until the basket is redefined. To calculate. the
sj it is further assumed that the value of the ECU at time 0, ECU(0),
and the ith foreign currency exchange rate in terms of a U.S. dollar,
FX;(0), are known. Thus, repeating equation (1),

(2) Sq = wy(0) * ECU(O) * FX;(0).
The value of the ECU in subsequent periods is determined by using the

market quoted exchange rates and the sj's derived in equation (2).

. n 1
(3) Ecu(t)= © sy* oe ,
tel F(t)

For the purposes of comparison, alternative baskets, referied to as

"Pongos" are defined. They are similar to the ECU except that the initial


-31-

References:

Edison, H. J. and E. Vardal (1985) "Optimal Currency Basket in a World
of Generalized Floating: An Application to the Nordic Countries,"
Board of Governors of the Federal Reserve, International Finace
Discussion Paper, No. 266, October.

European Documentation, The ECU, 1984.
European Economy, "The European Monetary System," July 1979, No. 3.
Krasker, W. (1980), "The Peso Problem in Testing for Efficiency of

Forward Exchange Markets," Journal of Monetary Economics, Vol 6, pp
269-76.

Lipschitz, L. and V. Sundararajan (1980), "The Optimal Basket in a World
of Generalized Floating," IMF Staff Paper, pp 80 - 100.

(1982), "The Optimal Currency Basket in a World of
Genaralized Floating with Price Uncertainty," in Michael B. Connolly
ed. The International Monetary System: Choices for the Future, New
York, Praeger, 1982.

Polak, J. J. (1979), "The SDR as a Basket of Currencies," IMF Staff
Papers, Vol 26, December pp 627 - 53.


-28-

0g

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-5-
immutable, its composition can be changed by unanimous consent and by
the addition of currencies to the basket as the EC expands.

The calculation of the amount of each currency component
within the ECU involves two steps. First, the weights reflecting the
currency's importance in the basket are chosen. Second, these weights
are converted into actual quantities using the current exchange rate.
The actual units of each currency remain constant and are used in the
calculation of the daily ECU. In order to prevent a break in the
valuation of the ECU, the day the currency components are calculated the
previous day's value of the ECU is used. This maintains continuity.

More precisely the components of the basket are based on the
following calculation which assumes the value of the ECU at time 0 is

known.

(1) Sq = ECU(O) * (Wy(0) * FX; (0))

Sj TM quantity of currency i in the ECU
Wy = weights of currency i, expressed as a proportion,
determined by political and economic factors.
FXj(0) = exchange rate for currency i in terms of U.S.
dollars.3

ECU(0) = dollar/ECU exchange rate at time of change.4
Thus, the dollar value of the ECU at time t is given by summing the
actual units of each currency which have been converted into dollars
(that is, ECU(t) = I Sy * 1/FXy).

Table 1 presents the components used to calculate the ECU on
September 17, 1984, which was the date the EC officially revised the
definition of the ECU. Column one gives the country names and column

two reports the actual number of units of each currency used in the


~4-

The ECU is a basket of currencies. It is valued following a
standard basket technique. The quantity of each currency in the basket
is fixed. Over time the value weight of each component changes as that
component's currency market value with respect to the numeraire changes
relative to that value of the other currencies. As Polak (1979) has
pointed out, this type of basket has not only a spot value in texms of
any reference currency, but at least in principle, also a forward rate.
These properties permit the ECU to become a market asset.

This important property is not available in baskets
constructed differently such as by the asymmetrical or adjustable peg
method. Both of these methods also value the basket in terms of a group
of currencies. However, in neither method is the quantity of the
currencies fixed as in the ECU basket; rather the relative initial
values of the currencies are maintained. For example, in a basket
constructed by the adjustable peg method, the common way of defining an
optimal currency basket for a single country, a change in one country's
exchange rate in either direction causes an offsetting adjustment in the
quantity of that currency in the basket in order to maintain the
currency's initial value weight. The only difference between the
asymmetric and the adjustable method is that the former one makes these
adjustments only for the devaluing currencies.

Each member of the EC is supposed to have a share in the ECU
reflecting its economic strength. The respective shares, or weights,
are determined not only by reference to each country's gross national
product, but also with reference to its participation in the
Community's external trade and its quotas under the short-term monetary

support system. Note, however, that the ECU is not completely


-17-
deviations from the policy target. To this end, the policymaker is

assumed to possess the following quadratic objective function
(9) L=E(r- r%)2 .

To simplify matters it is further assumed that the target is expected to
be achieved, that is r* = E(r).
Note that the real exchange rate index is defined as
N

eh _ oh li
(10) r fey POF Ey Gey PD

where

r = real exchange rate

ph = home country price index

e; = numeraire - jth country exchange rate

pJ = jth country price index

WO elasticity weights.

It is assumed that the authorities know exactly what these elasticity
weights are. They are used to define the real exchange rate index and under
certain. circumstances the optimal currency basket weights, Wy, will equal
these elasticity weights.12

According to equation (8), basket weights are shown to affect the

home numeraire exchange rate. This will in turn affect the real exchange


-7-

to be mutually accepted; they will by themselves not modify the external
value cf the ECU."7 This means that on the day a change in definition
of the ECU becomes effective the value of the ECU according to both the

old anc the new definition will be exactly the same.

III. The Weighting Scheme of the ECU

This section focuses on the impact of alternative weighting
schemes on the currency composition of the ECU and on the dollar value
of the ECU. It is important to examine how sensitive the value of the
basket is to these changes because of the ECU's increasing importance in
financial markets. Moreover, the EC has the opportunity to alter the
currency composition of the ECU at least every five years. By 1989 it
will be necessary for the EC Commision to redefine the ECU. It is
possible that an earlier change may occur if either Spain or Portugal
joins the EMS exchange rate system. However, the increase of private
use of the ECU in the last two years indicates that the official weights
are adequate. On the other hand, private use could increase by even
more if the ECU were redefined.

A typical approach in defining weights for a country's basket
index has been to derive optimal weights by specifying the policymaker's
(or country's) objective function and by minimizing the variance of this
function in which the target variable is either the real or nominal
exchange rate. However, in the case of the EMS with ten member
countries, following this: procedure is more difficult, though not
impossible. It is not obvious what type of objective function should be
used and how the individual members should be considered. A further

complication to this problem is to give weight to the ECU's role in the


-23-

Table 2: Mean of the Pongo and ECU Baskets
Tests for Differences in these Mean®

Type of Sept. 17, 1984 March 13, 1979 Dec. 2, 1979 March 1983
Pongo Dec. 11, 1985 Dec. 31, 1982 March 1981 Sept. 14, 1984
EXP> 74993 1.209 1.37 +845
(09088) (328) (.631) (.01)
IMPC 7485 1.21 1.37 +84
(.41311) (.327) (.813) (.14)
cnpvd 74819 1.21 1.366 84
(.4917) (.448) (1.04) (1.33)
GNPe 74901 1.208 1.37 +836
(.2951) (.182) (.735) (2.36)
EQf +741 1.18 1.35 8
(1.91) (2.6) ##* (3.32) ##* (13.6) #3
BFS 75363 1.1587 1.338 +739
(.7287) (5.2737) #** (4.66) #** (43.5) se
DKS + 75786 1.094 1.235 +73
(1.6724) (12.894) #%* (23.41) *#* (35.7) #8
FFS +7586 1.1612 1.345 +712
(1.7723) (4.99) #8 (3.625)#** — (42.1) ##*
DMs 75533 1.2217 1.361 +943
(1.0815) (1.853) (.957) (29.0) #**
cbs +6533 -- -- _-
(24.703) ***
IL8 72349 1.13 1.31 +706
(7.136) #** (7.978) #** (8.74) sie (42.8) sie
IPs +7587 1.174 1.33 771
(1.84) (3.8266) *** (5.04) ##* (22.1) #9
NG& +7552 1.199 1.342 +905
(1.04) (.9617) (4.2154) #% (18.0) Hie
EPS 7486 1.362 1.533 959
(3434) (19.538) #** (32.81) #9 (3.2.1) Heese
Actual ECU +75034 1.2069 1.368 +845

Notes to Table:

“ex indicates that the mean of the ECU is significantly different from
the mean of the Pongo .

a Test Statistic based on Behrens-Fisher Test:
't' = (mean(Pongo)-mean(ECU) )/(SQRT((var(Pongo)+var (ECU) )/T))

b Exp Pongo Basket -- weights based on export shares:source OECD.

c Imp Pongo Basket -- weights based on import shares:source OECD.

d GNPV Pongo Basket -- weights based on nominal GNP shares:source
OECD.

e GNP Pongo Basket -- weights based on real GNP shares:source OECD.

£ EQ Pongo Basket -- weights based on equal shares.

g single country peg -- for country mnemonic see note to Table 1.


International Finance Discussion Papers
Number 282

May 1986

IS THE ECU AN OPTIMAL CURRENCY BASKET?

by

Hali J. Edison

NOTE: International Finance Discussion Papers are preliminary materials
circulated to stimulate discussion and critical comment. References in
publications to International Finance Discussion Papers (other than an
acknowledgment by a writer that he has had access to unpublished
material) should be cleared with the author or authors.


-10-

approximately the same magnitude as the ECU. The "t" statistic
represents the test between means. The null hypothesis is rejected at
the 5 percent level if this test is greater than 1.96 or at the one
percent significance level at or greater than 2.576. The first four
Pongo baskets represent four alternative weighting schemes reflecting
each country's share of total EC exports, imports, nominal GNP, real GNP
respectively. The test statistics show that the means of these
alternative Pongos are not significantly different from the ECU. The
failure to reject the null hypothesis may be due to small differences in
the Pongo and the ECU or may be due to little exchange rate variability
for the currencies that comprise the ECU. These results reported above
may be due to small changes in weights between the baskets. Table 3
presents the ECU's and the Pongo's weights (wj's and #,'s) and currency
amounts (sj's and 5;'s). These Pongo shares and amounts are not
identical to the actual ECU; however, they are not radically different.

To evaluate these results more fully 11 additional Pongo
baskets over the same time period are considered. The first of these
additional baskets gives equal weight to the countries. This basket
incorporates larger changes in 5; than the first four Pongo baskets and
yet still includes the currency of all member countries. The other
baskets are designed to represent a single country peg -- a weight of 1
is given to a different country in each successive basket. The design
of these baskets goes against the EC's principle that the ECU should
represent each member country rather than be a technical unit. These
single country baskets are not considered realistic alternatives; they
are merely designed to assess the sensitivity of the ECU to weight

changes. Recall from (2) that the initial value of the ECU or the


-9-
‘economic’ weights are fij(0). Given these weights a new set of currency

amounts, 5;, are determined
(4) By =w-y(0) * ECU(O) * FXj(0) .

These 5; are then used to calculate the value of the Pongo.

as 1
(5) Pongo(t) = = so* say:
i=l Fx, (t)

The construction of the Pongo as shown in (5) is the same as the ECU
except that the sj's are different.

To determine whether the ECU is sensitive to changes in its
composition the mean of the ECU is compared with the mean of each Pongo.
The dollar value of the ECU and the Pongo are calculated using daily
exchange rate data. The null hypothesis of this experiment is that the
mean of the Pongo is not significantly different from the ECU. If the
null ‘aypothesis is not rejected this suggests that the ECU is invariant
to the currency composition.?

Table 2 contains the results of this experiment. Column one
presents results using data from September 17, 1984 to December 12,1985.
September 17th is a natural starting point because it is the day the EC
redefined the ECU's composition. Thus in this experiment September 17th
is the base date, the date when the Pongo equals the ECU.

The first two rows of Table 2 give the mean (of the Pongo)
and the "t" statistic obtained when testing for the difference in mean
between the Pongo and the ECU. The mean value of the ECU is reported in

the last row of column 1. The mean of the Pongo ought to be


10

ll.

12

13

-30-

A computer program was used which calculated the position of each day's
bilateral exchange rate against the bilateral grid. The central rates
were updated whenever there was a realignment.

The analysis in this section is based on my joint work with Erling
Vardal.

Edison and Vardal (1985) explain these conditions in complete detail.

For details see Lipschitz and Sundararajan (1982).


-29-

Footnotes:

%

The author is a staff economist in the International Finance
Division, Board of Governors of the Federal Reserve System. This
Paper was originally presented at the ECU conference at New York
University on January 31, 1986. The author has benefited from
discussions with many of her colleagues, in particular James Berry,
Owen Evans, Catherine Mann, and John Morton. The usual caveat that
the remaining errors are my own responsibility applies. The views
expressed herein are solely those of the author and do not
necessarily represent the views of the Federal Reserve System or any
members of its staff.

As explained in an official EEC’ publication on the ECU.

Most of this section draws on the paper "The European Monetary System"
published in European Economy (1979).

The exchange rates used for calculating the ECU are well defined. The
central bank in each member state communicates a representative market
exchange rate for its currency against the U.S. dollar. The dollar has
been chosen as giving the most representative rate in all financial
centers. The rates are taken from the exchange market at 2:30 p.m.
They are communicated by the National Bank of Belgium to the EC
Commission which uses them to calculate the ECU equivalent first in
dollars and then in the currencies of the member state. If an exchange
rate market is closed, the central bank agrees on a representative
exchange rate for the currency against the dollar which is communicated
to the EC Commission.

The ECU rate is assumed to be known at the calculation. In 1979 it was
equivalent to the old value of the European Unit of Account (EUA). The
EUA was constructed in such a way that on June 28, 1974 one EUA = 1 SDR
= one ounce of fine gold.

The market reacted very calmly to this change. The timing was as
expected. It occurred approximately five years after the previous
revision.

See "The European Monetary System."
ibid.

Another crucial characteristic which should be examined is the
volatility of each basket.

The interpretation of the test statisitics we use assumes normality. It
is possible that with the EMS tendency to have large jumps in parity
that this assumption is violated (that is, we have the Peso problem as
described in Krasker (1980)). This problem needs to be addressed;
however, it is beyond the scope of the paper.


-6-
calculation of ECU's. Column 3 shows the actual exchange rates
vis-a-vis the dollar. Column 4 gives the dollar equivalents of currency
units appearing in column 2. The sum of the entries in column 4 yields
the dollar value of the ECU. Column 5 presents the central bilateral
rates in terms of the ECU, while column 6 gives the initial share
values, Wj.

The composition of the ECU must be distinguished from the
weight of each component in the ECU. Although the composition, sj, of
the ECU is fixed, the value weight of each component changes as that
component's currency market value changes relative to the other
currencies in the basket. Thus an appreciation of the DM vis-a-vis the
other EMS currencies will increase the DM's value weight.

Furthermore, the distinction between realignments and
revisions to the definition of the ECU is important. Realignments occur
from time to time and are adjustments to the bilateral central rates.
This change in turn affects the bilateral grid and the position of the
fluctuation bands. During a realignment the actual definition of the
ECU remains unchanged. A revision to the definition, a recomposition of
the ECU, alters the actual number of units of each currency.

Revisions to the definition of the ECU have been provided for
in the EMS apparatus. A change in the definition of the ECU can be
decided by the Council of Ministers of the EC and a decision can be
obtained through a unanimous vote of all the member countries. The
Council's resolution of December 5, 1978 stipulates "the weights of the
currencies in the ECU will be re-examined and if necessary, revised
within a period of 6 months of entry into force of the system and
thereafter every five years or, on request if the weight of a currency

has changed by 25%."6 A second safeguard was provided: "Revisions have


-20-

The evaluation of the optimal weights is done using monthly
data over the period March 1979 to May 1985. German trade shares are
used to represent the elasticities, Ty'Ss Some of the smaller EMS
countries, Luxembourg and Greece, in particular have been omitted from
the calculation. However, Japan, Switzerland and the United States were
included. Realistically, if Germany were to create an independent
basket, then it seems reasonable that these latter countries would be
included. There is at least one caveat to this exercise that needs to
be mentioned It is assumed that the German policymakers observe accurate
data on prices. In practice, prices are not accurately observed, and
this introduces uncertainty into the problem. This uncertainty implies
that the weights are not truly optimal .13

Chart 4 illustrates the path of the optimal currency basket
derived from the formulae in equation (16) and the path of the ECU
converted into DM (DM-ECU). The German basket is consistently above t:he
DM-ECU basket. This chart suggests that the DM would have been
generally weaker vis-a-vis most currencies if Germany it were to
stabilize its real exchange rate index. However, the differences are
quite small. Chart 5 depicts the optimal currency basket path and the
DM/$ exchange rate indexed also to 100 in March 1979. The paths of
these two baskets are dramatically different. The conclusion one draws
from this chart is that the optimal exchange rate basket is not very

different from the ECU peg but is very different from a DM/$ peg.


CHART & DOLLAR/ECU EXCHANGE RATE

DAILY SERIES

CHART 2: SELECTED DOLLAR EXCHANGE RATE
DAILY SERIES

= 10
—j 100

— 90

CHART % SELECTED DOLLAR EXCHANGE RATES
DAILY SERIES

70
60

so

40
1979 1981 1983 1985

-26-


-2-
peg than a fixed exchange rate system, the ECU may be highly sensitive
to changes in weighting schemes. If the results indicate the ECU is
sensitive to changes in weights, then this suggests that studying the
question of optimal weights for the ECU is important. This extension
is, however, beyond the scope of this paper.

The second purpose of this paper is to investigate the
issue of whether Germany would be better off with a differently weighted
ECU-type basket. It is assumed that the goal of Germany is to stabilize
its exchange rate in terms of a basket of currencies which will
minimize the fluctuation in the real exchange rate. This part of the
paper follows the standard literature on optimal currency baskets as
discussed in Edison and Vardal(1985) and Lipschitz and Sundararajan
(1980). The single country optimal basket is compared to the ECU
basket.

The paper is organized as follows: Section II presents the
main institutional features of the EMS and the definition of the ECU.
Section III evaluates the composition of the ECU under various weighting
schemes. The results show that under certain circumstances, in
particular when there are only small fluctuations from the central.
rates, the definition of the ECU is of little importance given the
entire EMS apparatus. Section IV evaluates the optimal currency basket
for Germany, a major country in the EMS, and compares these results with

the ECU weights. Section V presents concluding remarks.


-13-
was first defined. Column 2 of Table 2 reports the results covering the
period March 13, 1979 to December 21, 1982. Because six EMS
realignments occurred over this period, a sub-sample of this period
which exhibited stability is also examined -- December 2, 1979 to March
20, 1981. Lastly, the period after the 7th EMS realignment -- March
1983 -- until the change in ECU composition, September 17, 1984, is also
examined. In each of these episodes the same experiments as described
earlier are considered.

As in the first period, the means of the economic weighted
Pongos are not significantly different from that of the ECU. This
result. suggests (at least empirically) that the ECU is not sensitive to
small fluctuations in weighting schemes. In contrast to the first
period, however, the null hypothesis is rejected in nearly every single
country peg and equal weighted basket case. In some instances the
Deutsche mark and the Netherlands guilder are exceptions.

Closer examination of the period of December 1979 to March
1981 helps to understand the general results obtained in these
additional periods. Note that there are differences in the ECU and
Pongo baskets between the first period (September 1984 to December 1985)
and the other periods. First, in the additional periods the currency
amounts used in the ECU calculation represent those defined in 1979.
The initial weighting scheme used to derive these amounts differ
slightly between the two periods. This is partly due to the inclusion
of the Greek drachma in the latter period and partly due to changes in
relative economic importance attributed to the various countries.

Note that this December-March period approximately spans the

same interval, 326 days, as that of the first period. Moreover, it is a


-15-
to its weighting scheme. This conclusion implies that the EC should be

able to sustain the ECU under the weighting scheme they have currently

devised.

IV. Comparison of Single Country Currency Basket Peg and the ECU -- The

Case of Germany

This section focuses on analyzing German exchange rate policy
assuming its real exchange rate is pegged to a basket other than the
Ecu.11 The object of the exercise is to compare the derived optimal
basket path with that of the ECU basket path. It is a simple
counterfactual experiment, attempting to answer the question: Is the
EMS or the ECU basket peg an optimal policy for Germany?

There has been concern about the stability of the EMS.
However, if the ECU basket path closely approximates the optimal basket,
then this suggests that the Germans may be willing to continue their
participation in the EMS rather than opt for some other policy. This
result further suggests general stability for the ECU. The experiment
could also be considered for any or all of the other EMS countries.
However, it is certainly easier to investigate the optimality of a
currency basket for an individual country, than it is for ten countries
jointly.

The type of exchange rate index considered in this section is
similar to the adjustable peg described in section II. The weights are
fixed and the amount of each currency adjusts. This is in contrast to
the ECU basket, where the currency amounts are fixed and the weights
adjust reflecting changes in relative values of the exchange rate. The

nominal exchange rate index is denoted as qh (t,w) where I, h, t, w are


Is the ECU an Optimal Currency Basket?
by
Hali J. Edison*

I. Introduction

When the European Monetary System (EMS) was launched in March
1979 it was stipulated that in this system the European Currency Unit
(the ECU) was to play an important role. Since that time the ECU and
the EMS have become closely interwoven. Furthermore, in recent years
the ECU has become an important entity on its own. In the wake of the
official ECU, a private ECU was developed. Today the private ECU leads
a life of its own and is legally independent of the official ECU's
function as the European Community's (EC's) unit of account. By 1984,
ECU-denominated bonds were the third most important in the Eurobond
market. ECU-denominated bank deposits, loans, and bond issues are
governed by private contracts which are not guaranteed by the Community
or national monetary authorities. However, the official definition of
the ECU as laid down by the EC serves as the basis for its private use.
Typically financial institutions stipulate in their contracts that the
ECU used is that defined by the EC and ensure that any changes in the
composition of the ECU basket are allowed for in terms of the contract .1

The composition of the ECU might be different for private use
than it is for official use. The first purpose of this paper is to
examine the composition of the ECU. In order to investigate this issue
I shall first review how the current ECU is defined, its role in the
EMS, and the method used to update its definition. Alternative methods
of defining the ECU are then examined to investigate the impact of the
weighting scheme on the value of the ECU. If the currencies involved in
the EMS truly remain close to their central rates, then it is not clear
that the value of the ECU should be sensitive to changes in its

definition. On the other hand, because the EMS is more like a crawling


~24-

Table 3: Initial Weights (Wj) and Currency
Amounts (Sj's) for the ECU and Pongo Baskets
September 17, 1984

ECU EXPORT IMPORT GNPV GNP
Wi Si Wy Si Wi Si Wi Si Wi Si

BF .082 3.71 +088 3.97 -093 4.19 +035 1.58 2041 1.85
DK .027 +219 +027 222 +028 «22° .025 +202) .025 +202
FF .19 1.31 167 1.14 +168 1.15 .225 1.54 -235 1.62
DM .32 2719 +294 66 +257 -57) «281 63 +287 +64
GD .013 1.15 008 70 -016 1.40 .015 1.31 014 1.22
IL .102 140 +126 174. +142 196. 16 291 +137 189

IP .012 -008 +017 012 016 -O11 .008 -005 .007 -005
LF .003 14 -- -- -- -- 001 -045 .002 +009
NG .101 +251 112 +283 +104 +263 .057 +144 .058 -146
EP 15 -0878 +161 +094 +176 +103 .194 114.194 114

Note to Table:
Formula use to derive sj's is:
sj = wy(0) * ECU(O) * FX;(0).


ABSTRACT

Recently the role of the ECU has increased and there has been
concern whether it is sustainable. The first part of this paper
examines the composition of the ECU and investigates the impact of
changes in this composition on the value of the ECU. The results show
that when there is little exchange rate variability among the currencies
that comprise the ECU or when the changes in composition are small the
value of the ECU remains stable. The second part of this paper
constructs an alternative, optimal basket of currencies for Germany and
compares this basket to the ECU. The path of the optimal basket

resembles the ECU path but is dramatically different from the DM/$.


IFDP
NUMBER

282

281

280

279

278

277

276

275

274

273

272

271

-32-

International Finance Discussion Papers

TITLES

1986
Is the ECU an Optimal Currency Basket?

Are Foreign Exchange Forecasts Rational?
New Evidence from Survey Data

Taxation of Capital Gains on Foreign
Exchange Transactions and the Non-neutrality
of Changes in Anticipated Inflation

The Prospect of a Depreciating Dollar
and Possible Tension Inside the EMS

The Stock Market and Exchange Rate Dynamics

Can Debtor Countries Service Their Debts?
Income and Price Elasticities for Exports
of Developing Countries

Post-simulation Analysis of Monte Carlo
Experiments: Interpreting Pesaran's (1974)
Study of Non-nested Hypothesis Test Statistics

A Method for Solving Systems of First Order
Linear Homogeneous Differential Equations
When the Elements of the Forcing Vector
are Modelled as Step Functions

International Comparisons of Fiscal Policy:
The OECD and the IMF Measures of Fiscal
Impulse

An Analysis of the Welfare Implications of
Alternative Exchange Rate Regimes: An
Intertemporal Model with an Application

1985
(partial listing)

Expected Fiscal Policy and the Recession
of 1982

Elections and Macroeconomic Policy Cycles

AUTHOR(s)

Hali J. Edison

Kathryn M. Dominguez

Garry J. Schinasi

Jacques Melitz

Michael K. Gavin
Jaime Marquez
Caryl McNeilly

Neil R. Ericsson

Robert A. Johason

Garry Schinasi

Andrew Feltenstein
David Lebow
Anne Sibert

William H. Branson
Arminio Fraga
Robert A. Johnson

Kenneth Rogoff
Anne Sibert

Please address requests for copies to International Finance Discussion

Papers, Division of International Finance, Stop 24, Board of Governors of

the Federal Reserve System, Washington, D.C.

20551.


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-1l1l-
Pongo is the same no matter what the weighting scheme is. This feature
forces the currency amounts to alter dramatically when the weights move.
For example, in the 'DM peg', 2.51 Deutsche mark defines the Pongo. In
the actual ECU basket there are .719 Deutsche marks.
The results in column one of Table 2 show that the mean of the

Pongo is not significantly different from the ECU for 9 of the 11
baskets. This result is somewhat surprising. Ex-ante, one would have
thought that the value of the Pongo under these single country pegs
would not be similar to the ECU because of the diverging strengths and
weaknesses of the various currencies. However, when examining the
position of various currencies in relation to the EMS bilateral grid
over this 308 day period (actual market days), only 9 days are observed
to be at either the floor or the ceiling assuming the spread of +: 2.25
per cent (: 6.0 per cent for Italy). Eight of these days occurred
immediately prior to the realignment of central rates on July 19, 1985.
Note that in total 6,468 bilateral exchange rates are observed.
Furthermore, only during 76 days was one or more bilateral exchange

_ rates observed to be greater (less) than 75 per cent over (under) the
EMS central rate.t9 In general, there was little tension in the EMS
over this period. Charts 1 to 3 show that the ECU and its member
currericies all moved more or less uniformly against the U.S. dollar.
During this period there was not a great deal of fluctuation among the
individual EMS currencies cross rates. Table 4 reports the correlation
matrix of EMS currency dollar exchange rates. The correlation amongst
the currencies is extremely high -- most correlations are greater than
.98. Therefore, defining the Pongo in terms of either the Deutsche mark

(one of the EMS strong currencies) or in terms of the French franc (one


-14-
period between two sets of realignments. Unlike the first period
examined, this period is characterized by a weak dollar. However, if
the only difference between the periods was the EMS currencies’
relationship to the dollar, then one would expect the results obtained
in the earlier periods to hold during this period. In addition to the
weak dollar, there was considerably more strain on the EMS system. Even
though very few days were observed at the actual floor or ceiling, 34 to
be precise, more than 52 percent of all bilateral rates were at least 75
Percent (+ 1.68 per cent -- the divergence indicator band) of the ‘legal
spread' from the central rate. This condition is dramatically different
from the other period where very few bilateral rates fluctuated beyond
the divergence band. It appears that the null hypothesis is rejeczed in
this instance because of the divergence in exchange rates between EMS
countries. This result is consistent with the earlier observation that
if the EMS central rate system is functioning and currencies remain
close to the central rates then it does not matter how the ECU is
defined.

The observations made from the December-March period extend to
the two other periods. During the March 1983 - September 1984 peri.od
the strain on the EMS was much greater. Nearly every bilateral exchange
rate was at or exceeded the ‘divergence band’. In general, the results
of the additional periods indicate that the initial weights are
important, especially when currencies deviate from the central rate.

A more Positive conclusion that can be drawn from this
exercise, though tentative, is that if EMS countries continue to follow
similar economic paths which eliminate variability in their cross

exchange rates as they recently have, then the ECU will not be sensitive