Bilateral and multilateral exchange rate and purchasing power parity indexes: the aggregation problem

Bilateral and multilateral exchange rate

and purchasing power parity indexes: the

aggregation problem

Galy, Michel

Banque de France, 39 rue Croix des Petits Champs, 75001 Paris, France

16 June 1982

Online at https://mpra.ub.uni-muenchen.de/62436/

B

BANQUE DE FRANCEANQUE DE FRANCE D.G.S.E.

D.G.S.E.

Direction des Changes

Direction des Changes

C 87 No. 6

C 87 No. 6

B

Biillateralateral aandnd MultMultiilaterallateral ExchangeExchange RateRate

and

and PurchPurchaassiingng--PowerPower--ParityParity IIndexes:ndexes:

TheThe AAggregationggregation ProblemProblem

Michel Galy (*)

Michel Galy (*)

I.

I. _{IIntrodntroduu ctct iionon andand SummarySummary} With

With thethe ggeennereraalliizzatatiionon ofof hhiighgh variabivariabillityity iinn exchangeexchange rratesates

after

after thethe cocolllapselapse ofof thethe BrettoBrettonn--WoodWood S System,ystem, policympolicymaakekerrss havehave i

incrncreeasasiingngllyy relirelieedd onon weweiighghtteded avaveeragerage ofof exchangeexchange raterate iindexesndexes

(

(nnoommiinalnal eeffectffectiive exchve exchaangenge raterate iindexndex) ) oror iindexesndexes ofof competitivcompetitiveenessness (

(rreealal eeffectffectiiveve exchangeexchange raterate oror purchaspurchasiing-pong-powweerr-p-paarityrity iindendexx))iinn order

order toto assessassess thethe nneeeded forfor andand thethe magnimagnitudetude ofof exchangeexchange raterate

adjustments

adjustments.. However,However, thesethese indexesindexes areare plaguplagueedd byby mamannyy methodo

methodollogogiicalcal problemsproblems thatthat lliimitmit thethe sscopecope forfor ttheheiirr i

implementatmplementatiionon aass rerelliiababllee iinnddiicatorscators andand coconnseqsequuententllyy asas targetstargets

for

for popolliicymcymaakkers.ers.

I

Inn ththiiss paper,paper, wwee wwiillll addressaddress ononllyy oneone ofof thethe mainmain

limitations

limitations of of these indexes. namely, the these indexes. namely, the ad-hocad-hoc charactercharacter ofof thethe determination

determination ofof thethe weightweightiingng ssystemystem ususeedd iinn tthheeirir conconsstructtructiion. on. TToo

s

solveolve ththiiss problem,problem, aa new new kindkind ofof indexindex isis proposed,proposed, whichwhich isis based

based onon aa completecomplete systemsystem ofof exportexport demanddemand ffuunnctctiiononss. 1/. 1/ TThehe paperpaper i

iss oorrggaanniizzeded aass fofolllloowwss:: SectSectiionon IIII briefbriefllyy revirevieewsws thethe methodologymethodology

of

of availableavailable effectieffectiveve exchangeexchange raterate indexeindexess and and eemmpphhaassiizzeess thetheiirr d

diiscordscordiingng vviieewsws andand thethe rerellatedated ddiifficultiesfficulties iinn intinteerrpretingpreting thei

theirr evolutionevolutions.s. IInn SectionSection IIIII,I, aa newnew conceptconcept ofof effectiveeffective exchange

exchange raterate iiss defineddefined,, whichwhich ttaakkeses advantageadvantage ofof thethe aggregativeaggregative

(*) M. Michel Galy is deputy director at Banque de France. The views

(*) M. Michel Galy is deputy director at Banque de France. The views

expressed in this paper do not reflect necessarily the position of

expressed in this paper do not reflect necessarily the position of

the french monetary authorities.

the french monetary authorities.

1

1// AA reviewreview ofof complcompleettee ssystemsystems ofof consumerconsumer ddeemmandand

funct

simple meaning: the 'real effectlve exchange

late of

a glven coufltty

ls

equal

to lts

n6roalizeA export Earket share

ln

volume

'

and the

ratio

of the effective exchaEge rales

of

two countrles

is

equal Eo Lhelr bl1aleral

exchange

late lndex.

The resE!1c!1ve assutrptlons underlylng

lhis iesult

are poiflted

ouE. In

Sectlon V, an emplrical aoalysls

's

developed to

test

the

rellability of

these i.nilexes as eeonodic

indlcalors' Iir

connec-tion w-lth Ehis' a conParlson

Is

llaale

rith

the fur:dts Merlo lndex' lrhlch

gives clealence

to

the ael.r lndexes.

finallyt

Section

vI

PresenEs the con-clusion aad

offers

some suggestiofls coflcernlng the Praclical i'npleoentallon

of

these ifldexes.

II-

A Revlew

of

Avallable Effective Exchange Rates

Indexes a$d the Need

for

Co[sistenc

with the supplessio[

in

1971

of

a stable

llnk

belween gold and the g.S. _d.o11ar, central bankers !'ere deprive'l

of

a common siandard able to

oeasure the

telative

PosiEior

of

Eheir

'lodestic currency

!o\{ard

all

olhel

culrencies.

I'urtherrore,

for

Ehe monelaiy authorlties rho were

strivlng

to malIltain a seeml'ngly orilerly exchange

lates

sysieo, the need

for

adjus!.

uents was blurred by the increasing

volatilily {fl

exehange rates

of

the

nralor cultencies, and by the uncertahtles surroundiog the effects of

lhese

nultiple

exchange tate vatlations on the eco:rony competltive[ess aril

presuuably on

lts

extelnal account

Positiofl'

Moreover' the empirical value

of

the xnost poPular theoEy

of

exche[ge rate deEermination among

lre11 as prlvale _{ba[ks, follnd}

_lt

_{oore convenlent}

_to

_{!e1y on aggregate} lndexes fron a relevaDt basket

of

nomiflal exchange rates (noEi[al

effec-tlve

exchange raEe) and

of real

exchange rares (reaf effective exchange

rate).

fhe

latter

index

ls

obtalneal by deflattng the forme! by a

cor-lespolldlng index

of

relatLve

pllces; ln

other words,

thls

iadlcator

ls

rBerely a rreighEed avetage

of

PPP

bllateral

lndexes.

Ilowever, the econonic interpretation

of

the flucluaEions

of

these weighteal indlcators

is

hanpered by tbe

fact that

lndexes produced by varlous fustitutLons

2/ for

the same cullercy, prouide

iather

discordlng views on

lts

aclual

posltlon.

The reasons

for

Ehese dlvergences can be

Eraced back

!o

differeaces

in

the inp11clt or

expliclt

theorles

undet-lylrlg

the coflstluctloo

of

these ifldexes. Wlth the exceptloo

of

the Fundrs

MERM lodexr they

all rely

on vaxious aspects

of

the _PPP

theory.

That

ls,

the appralsal

of

a currency posiEion

is

deterdred by comparlsoo

of

a

norEinal effective exchaoge

rate

index

lrlttl

a consislent indicator of

Beighted

_{relative prices, 3/}

The luncl's MERM 1[dex

is

based on a flore

1/

See OlEicer (1976) and Isard (L978).

2/ ffF,

0ECD, BIS,

U.s.,

Treasury, I'ederal Reserve

of

Nelr York, Banque

de France, llorgan Guaranty Trust Company

etc....

.

3/ It is

uorth noting here

that in

such a framelrork, the

real

aad noml-rtal effective exchange rate lndexes play only a !o1e

of hdicators

on the adequacy

of

the presenE

bilateral

exchange rate

set.

The anplitude

of

a

oeeded change

in

the 1eve1

of bilateral

exchange rates

is

deEernlrea

in

an unique way by bl1atera1

lnllatlon differentials. All

other solutions

oould be inconslslert

at

a

multilateral

1eve1

if

PPP

ls to

be mainEai.ned.

In

other lerors,

for practical

implelnentatioo

of

a currency realignment

co&plex _{lheoretical franren otk}

_1/

_{lrhich provides}

an

posltlon _{by refereoce}

_to

_the

traale balance effecEs

rate

varlatlons-

,

Ihese various _{approaches have resulted}

_in

_lBportant

nethodological dlEferences which aEe reElected

_in:

(i)

The tr'elghting

_syste'

_thaE

_ls

_{deteroined by three}

_factors:

the countrles whose _{currencies axe includeal}

_lllto

_{the basket, the}

methoalology

and econonic _{basls used to measure the}

_relative

share

of

each collntxy 2l

(these ('eighEs _{orlglnate nost often frod lhe}

_bilateral

or

multilateral

lnternaElorlal trade aad exceptlonally

_fro

_{a highly conplex nloalel as in} the Fu$dts MERM), _{and the base perloal}

_for

_{the lrelghtsr celcufatioa.}

(ii)

The prices

_that

_{are chosen accorillng}

_to

_{the oblecEives} that the authorities _{are alming}

_at

_{(conpetitlveness}

_of

Ehe export sector, _and

of

the _{inport-subsitute sector, curren! account}

_or

_basic

balance Positior)

,

3/

(iil)

The matheoatical _formulations

_that

_are

_either

_arlthmeEie,

geometllc

_ot

_{harmonic averages}

_{of bilateral}

_{exchaage rate}

or

p?p _{indexes. 4/} Hokever, explaining lhe reasons

_for

_{these illsEottions cloes trot help}

veEy euch policymakers qrho _have

_to

_{figure ouE what are the relevanE}

obJec-tives for

the

bllaleral

exchange rates

_{of their}

_ilotrpstic

_currency.

_In

,

t!.

?=

't't

rouodarlons

_ot

_the MERI,I

index-estioation

_of

_{a curreBcy}

of lts effectlve

exchange

2l In

Rhomberg (1976)

_for

_lnslance,

_{1t is}

_{shoL'rl rhar the Netherladats}

i:r}.d":

_oy

_z6.t

_per

1,i.

_{cenE depending} revaluaced -on rhe _on period _{the lreighting}

tstrlts

Litni.- iy-ro.

i

p..'."".

_".

systero applied

t;

the effective

€xchenge

_late

_calculation.

3/

-0n the relevant

price

lndexes,

for

inplementatlon oE the ppp Eheory

see,

for

instance, Balassa (1964), Kravts

..d

l_tp""y

(1971);Ofiicer (I9i6).

4/

See Pincon (1.979) who demonslrales

_that

_{lhe geometric aveiage}

_is

_lhe

most suitable mathemaEical concept

for

_constructio;

_of

_an

_effectlie

_exchange

doroestic _{curlency, 1rl the aggregate aDal}

_at

_lhe

bLlatelal level

as r.rell.

III.

A Theorecical Franer,roik

fo!

Conslstent Btlateral

eqd Mu1rllareral Irdices

In thls

sectlon, we

lay

doim lrhat the effeclive

ia

intended

to

Eeasure and lre assess _{the theoretical}

assoclaled

_{wlth lhis}

_measurenenE.

exchaage Eate index

fraEework

_{that is}

our oblecti.ve

_{is twofold. flrst,}

we lrant

to build

a set

of

aggregate indlcators devoted

_to

_{the evaluarloo}

_of

_{the itrlpact}

_of

_{slnultaneous variatloos}

in

prlees and e:<change rates on the traileal goods sector'of a glveo econooy

rfith

respect

to

lhe traded goods sectors

of all

other

countries.

Second,

lre want

to lnfer

from

thls

set

of

.ggr"gJa. tlalicators a consiste[t set of

bilateral

indexes.

The theoretical fraoer"rork employed

_for

coflstructloo

of

these inalexes

relies

on the following strlngent assumptlons:

(1)

Conditloos

for

arbitrage prevai.l

ln

rnarkets

for

gooals _{afld assets}

denoniaated 1Il various

_{currencies. If not,}

_{only the analysis}

_{of bllateral}

exchange

rate

effects rrou!.d have been

televant-(ii)

The aoalysis

ls

aestrlcted

to

traded goods

_,hich

_{can be defineil}

as speclfic

subslitures"

in

the sense

of fhetl (1980),

Thl.s assulption

co[es

lo

focus nainly on

industrial

goods, _{siflce aala Eaterlals ard}

indus-t!1e1 goods are

llkely to

be r.speciflc complenreats.,,

for i[slance,

one

than substltutes; Ehat

is,

alt increase

in

lhe re].atlve price

_of

_either

goods !1111 reduce the demand

for

_{the other.}

(lii)

_{There ale n countries and each counEry produces}

only one coroposlte

_industrial

good, _the prlce

of

which

ts

aenominatea to the domestlc currency

of

the ieporting country.

(tv)

_{Ttre corlsumer}

_{allocates his}

_{expenalitures between tradeil}

and

nontxaded good sectors accordlng

to

a group

_{of utility}

_{fuoctions endowed}

with the property

of

block independence as atefineat by Theit (1980). _This

assu&ption a11or,rs us Eo deal only

nlth

_the

_utillry

_functlon

_of

_{the traaled}

goods secEor.

(v)

A11 consuraers are

ratlonal

and paraEeters

_{of their}

_deoanil

func-!1orl

ale stable.

They are endowed rritb,the €ame systed

of

preferences. Further_

rnore, goods have lncolle

_{elasticlties ldentically}

_equal

_{to 1.}

_{So we can} aggregate

all

coasuaers

In

oniy one egenE who aLlocates

its

expendltuies

betweeo the coErposlte

industrlal

goods accordlng

to

the budget coastralntl

P.

(5)n.-!i!ar,

j=r,...n

Jrl

The notations have the followhg 6eantng:

M-

is

the world

total

export

of industrlal

goods expressed

in

curredcy 1,

qj is

the volude

of

conposlle goods expoEted by country

j at

Ehe domestic

price P.

_]1l

and 1,=

is

the bllaEera1 exchange rate between

l

and

_J

currencies. 1/

In this

context, Ehe \ror1d coosuner

is

assumed

to dlstrlbute

his expendltures beEween the Ir conposile goods, _{so that he oaxlElzes a certaln} preferedce _funcrion which can be expressed

either in

teros

of

quanElties

(direct utIl1ty functio[) or

Lil terms _o!

fuflctloB).

_1/

_Ihe

_lattea

_{approach lurkes}

dlrect

consumer denand _{functions. 2/}

Tte

lndirect utillty

fuoctlon

Vl

consr.stedt _wlth

_{thls set.of}

restric-tive

_{assuEpttons has the fo11ow1ng forE:}

illoirhtuil=pr

Relations (7) and (8) defioe respeorlvely

aggregate world prlce expressed

in

culrency 1. a tlegelerate fortfl

of

the Ewo most coooooly useal

the additive

indlrect

utility

functlon anil lhe

functton.3/

prices and lncone

(lndlrect

_utilify

it

straightfonrard

_to

_{derive Ehe}

0 < cr, <

I el,

39j =

I

the prlce

_of

good

_J

_{and the}

Note thar funcrion

(6) is

speclflcatlons,

_{that is,}

Itanslog

lndirect utillty

r

p!r1l

(6)

vr(Ml,

rwrl

₌

_\l

_,,itrr

(7)

Pw. _1l

-(8)

_kr

₌

- -l_

_1-

-u

n pull

l1l

EroB

relatlon (6)

_{a consisten! set}

_of

_{ordinary aleroanal equallons}

1/

The

duallty

U.tr.,een

tr

Lau (1969).

2/

For

at

allalysis

of

advantages _{offered by the ioalirect}

_utllity

_approach see corllan (1976),

.9/-

The addltlve and lranslog lrdirecE

utillry

fuflctio[s proposeal

respec-lively

by stone (1954) _{and Chrtsrensen and A11t} (1975) _{trave- the following} fofins:

-

additive lndj.Eect

uEiltry:

_{V = Exp[tci Ln}

pi -

_Ln(M

_{- I pl}

_Bi)

_{+ k]}

v = ExP[rdr

r"

+-+

_i

i

ur:

"^

#*

?,

uhete ors and grs are parameters, l,lhen Brs are

identically

nul1, these lwo

for

the n conposite goods, can be obtained by aPPlylng the Royrs

theoreo:

I/

av_

av.

(9)

_Ql

-

-

_UElrr|

r*i

(RoY's rdentity)

so that we get:

av.

(c--1)

0r

(ro)

_;rl;-c.

rr.r1

|

*ri

,i'

j+i

3V.

',

ol

tut

(1i)

q=

4

I*,.r

=-F

Iioal1y,

coEblntng

relation (9),

(10) ard (11) ylelds the demand equallor

for

good

l:

(a'-1)

di Mt *t.t !

*,

=

1-

c,

(12)

_{ai = ai IVii}

I

_{', p!I.}

.r,. '

itl

i

Jra

itr whlch, accorilllrg

to

assunptLon

(v)'

income

elasticlty ls

equal to

ooe.

Note a1so,

that thls telatlofl ls

a sl1trPllfled forn

of

the classical

alenanil fuDctiod

fo!

exporr, lrhlch Lncludes

at

Least three explanatoly

M{

variables,

1.e.,

the worlal ilem4nd

ln

volune

_{$;i> ' tttt}

export prlce

of

the

reportlng country Prril wlth a negetlve

elastlcity

-t"a

_

_t'0)'

arld the

aggregate prices

of

fo?elgr coopellng Soods (n

PLil) ith

a Posltive

J

elasllclty ( f cr=I-cr).

Jll

J*L "

The budget shares

lrl of

the

!'oltd

consulner can be obtained by applying (12)

to

(5) $rhlch

ylelds

the followlng relatlon:

(13)

u,

-

*f ""

or

(12)

by:-5

_yiera",

I1

,r",

or

r[

-

*ri-'

i

*,]

JF1

the6e results desn that

ln

the speclftcatlon

of

the

indlrect ut1llty

fuuction

(6),

two strorg hyporheses are eab€dded:

(t)

rhe prtcb

_{elasllctry of}

_subsrlturton

_of

_{each good}

_ts

_srltcr1y

equal

to {ts

budget share

ln

the qrorlal

_total

_erport;

(tt)

Equatlo& (12) deflnes an expenilltute sysreB rrlth coflstant bualget shares,

_{if stabtllty In}

_{coflsumelst behavtor Ls assuned. These concluslons} are not surprlsfug,

for lt

caa be Ehorrn that lhe dual dtrecL

ulility

fullc-t1o$

of

relatlon (6) has a si$ple cobb-Douglas

forn:

II

qll. rtu..fo.", ai.

effecllve exchange rale ludex ster@lag froE thts

ull1lty

funcEloa

ls

oalned

hereafter Cobb-DougLas lndex.

IV.

Derlvarton

_of

_{the NoElral} add Real

Effecflve Exchange Rpte Indexes

flavtng speUed out our objectlves

js vell

as the Eheoretical- assrEptloos

thlch have pelEilted us

to

consttuct a conslEtonr r,rcr1d systrii

of

exporr demand

equallons, we are nor, able !o derlve froE equarioa (12) a corresponillng set of

effecttve exchaflge rate

hdexes. Iri

order to do

thar, lt ls

recessary to

slngle out the variables

In relalIon

(12) nhlch accouot

fot

the effecEs

of

compeiltiveness on the export volune

of

country

1.

Dtvldtng 6oth stdes

wlth t a - l-d

JJi

J*i

Relatton (14) stales that the ro.nallzeal oarke! share 1Ir voluae

of

good L

depe[ds otrly oo the grlce substltutlotr

effecls.

Second, one notlces that

telatlon

(14) 18 not elEered

_lf

_{al1 vsrlables ere specifled}

_ln

_{tero6 of}

lndexes havlng a unllary base. 1/

FolLoving

thls

coflve[ti.on, the

real

effectlve exchange _rate

todex PPPI

of

currency

I

can be deflned

frou

(14) as fotlows:

s,

-r

c:

₊

*l]

p!,

(r5)

_PPP.

₁

_{= Pw-.' I p*r-]}

₁₁

_j-

_{1l= -l}

.

1l

P"r,

pl

Jll

Relalion (15) poillts _out

_that

_the

_real

_{effective exchange}

rate

of

a glvetr courrtly can be expressed by the

latlo

of

a wotld price

ladex

_-

coepreheodlng

all

countrles

_-

to

the alooestic

prlce

index

of

the

reportlng

_{country. Ttls}

index

ls

equal

to

the nofi!.a1lzed export narket

share

of

the country.

To obtal.n the norlnal effectlve exchange

rate

lndex

of

currency 1,

lre can use

relatlons

(7) and

(8)

ro

rat'rlre

equatton (15) as foltorr€:

[

_,ol

(16)

PPP.

_{= =';'}

-

F

'--' ---1

_{[ raj p}

_lf.pf

,

J

-tl "1

J*1

so

that

the no.Binal effecEive exchange

rale

(-\)

ard Ehe undeflated world

priee

(i)

lndexes are deflneil respectlvely es:

_ai

(17) 1, - [ 1,; !,lth t

d,

=

1-a,

,

'J'J-q.Jr

J+I

Jll

_

o.i

(18) P = [Pt'w{thlol-t.

J

Besides,

1t

is

worEh notlng Ehat bllaEeral lndexes (PPP.r, 1rr)

Let PPPi ard

countrles 1 end _J

(19)

PPPr.j

<2L)

\

(o1+oj)

(1-di-ol ₎

= tr.J ' trl

=

ttj

_'

PPP,

_l

be the

real

effectlve exchaflge rare {natexes for and PPP,,

_rl'

their btlarerat

l$dex. so lhar:

_

'J

1.. P-

_1l

'

1

ApplicaElon

of

(16)

_to

rhe

rarlo

ppp./ppp. _vtelds:

1

l'

PPP. p-

I-/rn\

1-l.l

'-'-

PPP

-

P. i

and slrlce

definlEior

(17) impllesr

t

_tJ (c1+c1)

1J

l

k=1 k+l r?e get ihe

(22',)

result:

?PPI =

t,

- ooo

'rl

t,

'"'ij

fhat is,

the

bllateral

noninal

or teal

exchange

rale

index bet\,reen

countrles

l

and

j

oust be equal

to

the raEio

of

theia

effective

indexes,

lurolng now

to

the

slatistical

propertles

of

the

effecllve

exchange

rate

indexes and those

of

Eheir conrponenEs, we notice thaE Prrl and F are

lD

fact divisla

lndexes

1/

whlch therefote are endoweil

of all

the relevaflt

properties

of

lndex ouobers,

U

Eowever, Ehis

ls

not

totally

the case for

PPP. _ii and

i.

whlch

saiisfy

Ehe propoltiooallty

rule

only under partlcular

coodittoos.

This asserllon can be deoonstrated by way

of

comparlson betveen the lndex PPP. ard the usual form

of

the

leal

effectlve exchange rate

1-Jndex PPP. which

is

deflned as:

!/

ror

a

deiinitton

of this

type

of

lndex see

Divista

(1925).

Z/

The maln propertles

ot

Liidex nurBhers are

circularlty,

tlxoe_reverslbllily,

faator-reversibillty, tdentlty,

transl!lvlty,

homogeneity and _{ProportlonallEy.}

1k

(23)

PPP1

_r

- Jli

_p-

_{with tcrr-I,}

1J'J

Ji!1

"

ohere rhe

vecar

_{leil is}

_{dtfferert for}

_{each couEtly:}

Plr -

-

o

(24)

_arl

₌

_TTili

J*r

PPP1 and PPPI specl.flcatioE caIr be corpareil _{eastly only}

_in

_{tr;o cases:}

(t)

The purchasltlg _po\rer

_{patity Is strlctly vertfied;}

_under

_this

assunptlon, _{the tl.ro} lndexes provlde _obvlously

_sihllar

_results.

(tl)

_{Bl1ateral devlatlons fron} ppp

_for

_{countiy 1 ate}

_{slEilar all}

over the

_{countries. IIr that}

_{case, the trro deflnj.Elons are llnkeal together} by the follor'Itrg relaEion:

(2s)

_PPPi

_{= rrel(l-"ll}

_,

that

is,

the hlgher the export market share

of

country

i

(nr),

_{the lower}

uil1

be the weight atlached

to

a glven _{deviatlon froltr} ppp.

To prove

it,

suppose thar

ln

equarlon (15)

all

rhe pi,r.l

bilareral

indexes iacrease _{by the sane aEount so that t/e can nrrite:}

(26)

_Pw,.

₌

_{P. v.}

_wirh

_{i I j}

ull

Equatloo (15) becones:

a-

o

1-c.

(27)

PPP.

₁

-

Pw.

-^ r

T

'

11 J f = {

since

t

al

= 1-41

_'

J*t

j*l

Applying no!, the usual ?Pp, spectftcatlon (23) under lhe saae hypothesls,

(28)

PPPI _s1flce

_{f, a-_}

= 1

J1J

Jll

I! ls

thetr readlly

verlfied

thar

identlry

(25).

relations

(27) and (28) yietd

It is

north ootlng

_{that thls}

partlcular properly

_of

p?pl

_Is

_equally

shared by lEs component

f,

_{the nonlnal effec!1ve exchange}

_rate

_1ndex.

It

meane

that

_{the magnitude}

_{of its}

_{fluctuations clepenils}

_or

the export Darket

share

of

_{the reporting economy,}

_{or to}

_rrord

_{it differently,}

on the prtce

elasti.cities of

substitution

ln

_{the export sector}

_of

_{the world econouy,}

lf

assumptlons 1{legrated

_{ln telatlon}

(6) _{are satlsfled.}

v.

In

chi.6

sectio[,

_the

_{enpilical valldlty of}

_{the theoretical fraoewotk}

ptesented

_la

_Sectlons

_III

_and

_Ms

_put

_{to test.}

_{Siflce we}

are corcerned only by the probleo

_of

_{cooslstercy between}

_multilateral

_and

_bllateral

indexes, the analysis could be focuseil either on the

real

(ppp)

_or

_the

noEinal

(I)

concepts

of

effecti.ve exchange

_rate.

_The

_1atler

_alternatlre

i6

chosen hele

for

practl.cal reasons

of

data

avatlabillry.

Two lssues are _to be consldered. FlrsE,

ic ls

necessary

to

test

lhe strong assumptions nrhlch _{underlie the}

_{i[dlrect utiliEy fu[ction,}

_1.e., the

stabiliEy of

exporE narke! shares

ill

value and lhe

fact

thaE by

deflnilion

Ehe price

elasticities of

_{substitution ate}

_{hferior to}

_udlty.

Second,

_{lt is cruclal to}

_see lrherher the

f.speciflcatioa

s111 or

will

not stand the

test of

emplrlcal

analysis,

For

this

purpose, a conparisoo

will

be nade rriEh the IIER]Y index

or

rhe per:od 1970/1980.

II

Pw

J1l

^1

t

'1

The

stability

tesE

_{inlends to}

_{iletermlne whether}

L970/1980 Ehe evolutioo

of

_{lhe exporE Earket share of}

during the period

a given country

followed

or

not a statlonary randoE _lralk process. _{?o lmple.aent}

_thts

_tesE,

recourse

_is

nade

_to

_{the quarterry}

_total

_expolts

_of

_{the rnai[}

1g.lndusrrlal

counErles. Durlng the pertod under _{strrdy, a great deal}

_of

_sEructurat

deforoations _{r018ht have affecred the relacrve welghts}

of

these countrles

in lntelnatlonal

_trade,

_nadely:

_extenslon

_of

_the

comdon narket, anal

the raptd gro\rth

_in

_{ol1 anal gas exports by lhe Netherlanals,}

Ilorn ay and United KingdoB

folloring

_{the huge price lncreases 1n f973}

ard. 197e.

Allowance

_ls

_nade

_for

_{these syslenatic}

_alteritlons,

by assuEtng _that narket share defoftEtions _{can be represelted by an expodeotlal trenat}

havlrlg _{the follorring usual speclfication:}

(29) 1a(w.) = ai

TRE\'D

* ci *

"i

,

rrhere

!r. is

_{the export narkeE share}

_of

_country

_{i in}

_{the group}

_of

1g coun_

trles,

TREND has

its

_{obvlous neaning aoa[}

_{el ls}

_{the vecto!}

_of

_{the regressioa}

reslduals. If a. is

not

_{slgntflcantly differeat fror}

_zero,

_lt

_{neaus Ehat}

the average value

of

the !0arker share

of

the .eporting country 1s equal to

the constanE

of

the regressio[ (expressed

_io

_{exponential). As the results}

in

Table 1

poiit out,

the degree

of

slgdlficance

of

lhe coefflcie.rEs

ls

considerably higher

fo!

the consEanEs (column

₅₎

_thalr

_for

_{the Ereads}

(colunn

_3),

_{Moreover, the standaril erEor (column 6) LndicaEes thaE the} spreading

_of

_{the market share values, once the}

_{tre*l ls}

_reEoveal,

_ls

.-11

_':'::o

st"t

Itafy,

Netherlands, S!,rltzer1and, Austria, Nohray, Sweden, F1n1and, Spatr, Uniied Klngdom,

Australia, Ireland.

_{These couniries}

_I,ili

_{be nored here_} at-ler,by the folloiring s)rrbots: US, CA, JA, BE, DK, FR, _cE,

_IT,

NE, SZ,

Table

1.

Structural Deforrnations

ir

ExporE tr{arke! Shares

of

the Maln

Industrial

countrles (Quarre!1y _{dara 1-1970/4-L980)}

Countrles

Average L97 5

uarke! share (1) Standard of estidate (6) Ecponentlal

' coeffl-

Studenrr

cleflE

*

test

(2). (3)

Constant _^

'coeff{-

SEudenE\

clent *

test

(4)

Box-Plerce uhite-noise test

"

on

residuals-R'

(Las=12) CHIZ

(7)

(8)

_'t*

(s) US CA JA BE DK FR GE IT NE AU NO sw FI SP IJK IR

t9.6

7"

6.0 t0.2 5.0 1.5 15.5 6.4 6.2 1,3 1.2 3.0 0.9 1.3 0.4 -.00196 -.00905 .00391 -.00059 -.00031 .00283 .00027 .00226 .00201 .oo24|

.0027 3

.00641 -.0056r .0022 .00974 -.00000 -.00707 .00743 -3.1 -16,3 4.a -L.2 7.3 0.6 3.1 3.6 3.8 4.2 -9.1 13.4 0 9.0

-L.674 tl

-2,54

*

-4.15

't

-2.461 r,

-1,824 _'t -2.842 t -2-865 r.

-3.785 't

-4.36t

t

-4.549 * -3.429 ,,

-4.63tL* -4.499 "..

-2.488 * -3.736 r.

-103.3 -t77.6 -112.5 -240.2 -392.4 -246.8 -168.2 -150.9 -198.3 -233.8 -416.8 -225,4 -273.9 -249,5 -240.L -9t.2 -133.8 -250

-t

4.6 6.9 3.9 3.4 3.5 6.1 4.7 3.4 6.5

6.r

b.r 8.9 6-9

.19

120.6

.86

34.7

.35

66.3

.04

59.3

.59

19.0

.s6

46.a

,01

53.8

,19

33.3

.23

49,3

.26

LO4.7

.62

L6.1

,67

34.3

.L9

24.L

.811

19.9

.0

81.7

.51

45.2

-66

69.6

One asterisk lndicates

Tvo asterlsks lndlcale

nolse

patiern.

Level

that

coefftcient

lhat

residuals of

of

slgnlflcance 1s

are

signlflcant

at the regression are

1 per ceot.

1 per cen! 1eve1.

[image:16.612.53.581.89.624.2]

lrhite-These

results are not

s'ufflclent,

howevet,

_to

_{accept the}

_{valldity of}

_the

assump_

tioD

of

constaot narket

_{shares. It iE}

_{also lecessary}

_to

doo;osrrate tha! residuals are whiEe

oolse.

_{The outcoEe}

_of

_{rhe Box_pierce Test (Table}

1,

ColuEn

8),

_Lndicales

_{that this}

_{1s true}

_for

4 counllles ou!

of

18.

These results inteEal

_to

prove

_that

_{the very strlngent hypothesls of} coflstant narket shares

_is

_{not deprlved}

_of

_{enplrical relevance.}

Eurlhennore, one rrould expec!

thls

hlrpothesis

_to

pelform _{better wher lhe analysis 1s}

restrlcted !o

indusErlal goods, _as

_{lt is}

_edvocaEeal

_in

_Sectio[

_fI.

Turni.g oow

to

Ehe proble'

_0f

_{the maSnirude}

_of

_{the price}

_efasticities

of

sutsti.tution, _{a'e notice}

_{that for}

_{a glveD country}

_i,

the aggregate _{elas_}

tlcily ls

equal

_{to (ai-l). 1/}

_since

_{dl is}

_{never greater thad}

20 per cent,

it

Eeans

lhat

price

_{elasticitles will}

_{?aoge between _1 anil}

-.g

1It the aggregaEe and betnreen _{a -0.0 and} _0.2

_at

_{a b1Iatera1}

_1evel.

_These

values seen rather _{senslble accorillng}

_to

_{prevj.ous emplrlcal studles. 2/}

Moreover, as Rholoberg (1976) _scated

_ln

_{the case}

_of

_{the tlERll index, what}

i.s lnportanE

ilr

the deteadflation

of

Ehe welght given

_to

_{a country In}

a curre[cy basket, 1s not the absolute oagnitude

_of

price elasticitj_es

but

lheir relative

1eve1-Having shor^'n

that

Ehe _{assuoptlons unalerlyldg the Cobb_Dougtas}

_utillry

function are not so

unteellstlc

when

lnternatioral

_lrade

_is

_constdereal

See equation (12).

2/ h palr

(1981) _{a sustained 1 per ceflt ilepreclalion}

_ln

_{lhe German}

excha$ge

tate

_{durlng 6 quarteis e[ta11s lhe lollowlng volune export varia_}

tlons

1n perceotage

_for:

_{US = -.008, CA}

₌

_{.034, JA = .015, BE = _.096,}

Df = --00S, FR _{= -.071,} cD ₌

_-.052,

rr

_{= -.064, NE = -.104, sz = -.061,}

at

a highl.y aggregated 1eve1,

_{lt is}

_tenptlng

_to

_{conpare the lndex 1-}

_lrith

other publlshed effective _{exchatrge raEes.}

The tdea of 'a r,relghted exchange

_rate

_index

_{takhg lnlo}

_{account the} lnpact

of

prLce

_elasticlties

_{oo lnEernatiolal trade took forts.for}

the

first

tlme

tn

the Fundts MER.Y

l[dex. ! elso,

_{as alreaily nenttoneal, the}

MERU

lE

the onry publtshed _{in.ex which re1les on an}

_exprlcit

_theoretrcal

fraoenork.

For these two reason6, a comparisoo

wtll

be oade

with

the

MXRI{ ladex

in

ordet

to

_{evaluate to iirhat extefit the}

_ieslrictlve

assunptlons

iEplied by the conslsledcy property

_affect

_{the representatlon}

_{of I}

_{as a}

reliable

econo.iic indicator

of

the effects

of

exchange aate vartations on

coEpe E i tiveoess.

This exercise has been conpteted

for

the period l97O/I980 oll the average quarEe!1y exchange rate

of

the

ig lndustrlal

coufltlles previously

elted.

The base perlod

for

the MERM tndex publlshed 1Il

I.F.S.

_{has been}

Dodlfled and 16 1

for

the

flrst

quarEer

of

1970. The

i

index

is

calcu-lated on the sade basls uslng average exchange rates published

in

I.F.S.

ana export market shares

for

1975 (see Table

1,

column

1),

Charts of

MERM _and

I

are depicted

in

appenalix. Irr _{a more}

sFthetlc

_{graph given}

hereinafEer, the average quarterLy growEh _rates

of

MERM and

f

are plotted

agaiast each olher

for

every

couotry. If

the tr,o sets

of

indexes r{ere

aflke, aLl

lntersecting polnts rrould have been put oIl lhe

diagonal.

As

It

could have been expected,

thls

1s not the case.

EFTECTIVE EXCHFNGE fl61E INOEXE5 SVERRGE OUflTERLY GROHTH RRTES

r0t 1970,/01 l98ll

o

o

o

o

a

o

a

I

o

ct

6

ct

><.^ r.,r B

oo

Zo

a

5o

o

o

E?

oq

CJ,

c;

o

o

C)

ci

o

20

-o.o21-o-ots

-0.010

-0.005 0.000

0.005

NERM INOEX

0.0

olle [otLces

that

12 intersecting points out

of

18 are located on the

right-ha[d slde

of

the

diagonal. Ihis fact

points

to

the existeoce

of

a

systenatlc bias betrieen ihe tlro sets

of

lndexes; wlth the ME8U

l

lex, the appleclatloo arld depreclatlo[ intenil

to

be respectively larger afld saaller

than

r.tth

the Cobb-DougLas

index,

However,

in

splte

of

thi.s dlsEorting

aspeet,

lt ls

worEh noting

that

the lllte?secting polnts are close

to

the

gtraight _I1ne

_{particularly in}

_{the case}

_of

_{8 eountries}

_that

_{are_:} St

ltzer-laud, Austrla, Bel8tun, UniEed States, Fialand, United Kingdoo, flance and

Svede[.

It

Eeans

lhat

the t!.o lndexes are glving rather sirnllar resulls

ln

terms

of evolutlon.

A perlrsal

of

charts pxesented

la

appendix coofiros

this

asser!10a.

tr'ron

lhls

comparlson we can draw the

follol'tng

conclusiors: dertvaElon

of

an

eflective

exchaflge

rate

fron a systen

of

deEand funcllons eflalor,red with

exact aggregatlve ptoPertles does oot preveot

lhts

lrdex fron belng e reliable

econoulc l$dicator

of

exchange taEe variatlons olr coopetltiveness ,

v L - concLusaon

In this

paper a new concept

of

lrelghled

teal

ana! nooinal exchadge

indexes has been proposed

_lhai

provide

direelly

conslstenE

bilateral

rate

nultlleteial

values.

Under the assumptioil

goods 1s stenlning flom

derRorstrateil

that

thls lhe nornallzed market the results

of

a

brief

that

the export detrand

for lnduslrial

Cobb-Douglas

utlll.ty furicllon' lt ls

real effecllve

exchaflge rate lndex 1s equal to

restrlctive

agsuoptlonE lnposed _{by the} aggregatlve plopetties

_of

_the

deuand functr.oos

ca

rot be easLly disittssed on ao enplrlcal

grounil.

fhere_

fote, 1t turig

out'that

thls

sort

of

lrelghted eachaBge

rate

ladex nlght

be tleeDeil on a vEluable tool vhether pollcyoaker6 are

[egotlsting

a cur-ietlcy lealignEent

in

a tegLonal flxeal exchaoge rate 6yateE, or vhethet

they

ele

tryttrg

to

target a glveE er<ternal value

fo!

ther.r aloEestl.c

Artus,

J.R"

and Rhonberg,

R.R.,

nA

Multilateral

Exchange Rate _{Model, "}

IME

Staff

Papers, Nover&er 19?3.

Bafassa,

B. ,

"The Purchasing Power

Parity

&ctrine:

A Reappraisal,"

,Journaf

of Politieaf

trconomy,

Vol.

?2.

Decenber 1964.

BarLen,

A

.P.,

"The Svslem

oI

Consumer Demand Func!ions Approach :

A Review'i

in

Eronriers

of

OuanEitaEive Lconom'cs by M.D.

Inr r iaI

iqator,

Nor!h-HolIaid,

1911.

chrisLensen,

l.R .,

Jorqenson, O.W.and Lau, l.J.,"Transcenden!af Loqarithmic

Utilirv

Funclions,"

The American Econo'nic Peview,

VoI.

65, No.3,

1915.

Divisia, 8., \'indice

Mon6taire

et

.la Th6orie de

la

Monnaie

_,"

Revue

cl'iconomre

Polrrique,.

j9,

I925.

Fair,

R.C.,

"Estimated Output,

Prlce. Interest

Rate. and Exchange

Rate l,inkages Among

Countries,"

_NBER, working Paper No. 6?7. Gorman, W.M.. _"Tr:ieks

with

Utility

Functioas.'r

in

Essays

in

Econonrc

Analysis

is

by

M.J.

Artis

and

A

_"8.

Nobay, CaFbridge

university

Press, Iondon. 19f6.

Isard.

P.,

"Exchange Rate Deteaminaaioni A Survey

of

PopuLar views and Recent Model"s.

"

Pri[eeton

Studies

irr

lnteinational

Finance,

No.42,

May 1978.

Kravis,

I.B.

and

lipsey. R.f",

_'Price

Competitivenes

s in

Woxld

Trade.r' NBER. New Yo.k 1971"

lau. L.,J.,

"Direcl

and

lndirect Utifity

Functions: Theory and

Application.

t'

InsLilute

of

Business Economic Research, Workiag Paper No. 10. Berkeley. March 1969.

officer, L.tt..

"The PuichasinE Powei

fa.iay

Theory

of

trxchanqe

Rates: A Review

Article,"

IMf

Slaff

Papers. March 1916.

pinon, R.?

_"Reflexions M6thodologiques Concernant

]es

Calculs de

Taux de Change Ponderes

et

d

_'Indices de Competitivit6,

_"

Cahiers

liconomiques

et

Monetaires de

la

Banque de France,

No.

10, 19?9.

Rhomberg. R-R

.,

_"Indices

of

nffective

Exchange

Rates."

IME

Staff

Papers, March 1976.

Roy.

R..

_"De

t'Uti1it6,'i

Herman

et Cie, Paris.

19d2.

Stone.

R.,

_"Linear

Expenditure Systems and Demand

Analysis:

An

Application

to

the

Pattern

of British

Demand,

"

Economic

Journal,

Vo].64,

1954.

TheiI,

H.,

rr?he System-Wide Approach

to

Microeconoidcs.

_"

The

IITEEIES 965! Cl I-q70_1.)

_ _{- -} , _ _ _ _{- - - .} PHEXTU

2.t

i.?

1.5 1.3

Li

0.9 a.7 0.5

6. .J

2. I

Lg

t.7

1.5

i.5

l,i

4.7 0- 5 0- 3

131

i970

i3i

1172

131

t97 4

13

1976

13i

t97A

i 31

n8fl|6

-__-___-__. flrExt!

2.1

i.g

t.?

i.5

t.J

1, r

0.9

2. i

1.9

1.7

i-5

t.3

l-i

0-

I

o.7 0.5 0.J 0.7 0.5 0".1

1313131

197A

t972

NIE:IES 36sl Ci i970-i.'

---.fi{EtJa

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