M PRA
Munich Personal RePEc Archive
Comment on ’A Forecasting Equation for
the Canada-US Dollar Real Exchange
Rate’
Robert Kollmann
ECARES, Université Libre de Bruxelles and CEPR
1993
Online at https://mpra.ub.uni-muenchen.de/69893/
MPRA Paper No. 69893, posted 10 March 2016 06:00 UTC
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JL|N 11 '93
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Discussion
RobertKollmann*
rcrdingRobenAmanourd Simonvur l'Iqdea'l rtudyon
I geadyenjoyed
rarc(RPF)Oand
rcaJexchurge
rhccana&-u.s.bilareral
berwecn
rhereiarionship
focul
rerrnsof sa& drringthe1971'91period.Thegutbonspec{ficelly
Canada's
on energyErms of uade (TOTENRGY)urd oa cornmoditiesrcrms of tradc
(TOTCOMOD).
Theylrg,uethatRPFX,TOTENRGYurd TQTCOMOD(in logs)
vrriablesarecohtegnted- i.0.,tbatthcrc
andthatthese
processes
followunit-root
of thesevrriables.The
is Elineu resrictionrhattiestogetheltherend behaviour
ontbcbssis
forecutsof RPFX,whicbarcSpoeta6d
papErshowsrhatout.of.samplc
of past valuesof RPFX,TOTENRGY'TOTCOMODand RDIFF,ourperfcnt
modtl of therealexcbrngetltc' Thisis an
genetatcd
usingarandom-walk
forrcas:,s
rcsult,giventhefiadingby Meeseurd Rogoff(1933)thgta random'
intercsring
rate oulpcrfonnsscveralrtnrcturslrnodclsof the
w{k modelof rhe exchange
rate.
exchange
concernintunitrootr utd $e
I wiJlfocusontheevidonce
In my commcnts,
The
issueof cointegrrtionbctwccn,ht *l cxchurgcrete8ndthecrms of radc'
uscdin theirstudy'
kindlymgdervailable19mc thcd.ctE
aurhors
Dickey'Fullcr(ADF)(19?9)unlt-roottts!' I fnd
ApplyingtheAugrncnted
utd
no evidenceagainstthe unir-roothlpotheslsfor the loguithml of RPFX
the
ToTENRGXwhichconfirmsthcurdydr of Amanornd vur Nordcn.llowevcr'
.
for weful illscutsbns'
I thankR, Anunoard S,wn Norden
266
t
lt ,,
f ' (ct's N'tii'n '
JUN 11 '93
P
g?I36PN BRNK OF CRNADRI'1FR
1
267
D lsc ttsslon : Robt rt K ollnuwt
is incoucludw.Tlble I reputr
aunitrootin ID(TOTCOMOD)
cvidenceconcerning
resultsfrom rhc ADF rcsuWc scothrt thc ouromc of tlrc ADF talt &pcadr
crirically on thc lag lengh uscdin rhe tesu fsr low lrg lcngrhr,dro unit'nrot
hyporhesis
is notrcjcced,whilofor lag lcnghslrcsttr thur 6, thenull hpotbcsir
of r unit rootin thelog of TOTCDMODis rejecrcdu 10pcr cent.
Tlble I
ADF Testsfor Unlt Rootsin Log of Non.EnergyCommodity
Tbrrnsof Trade
Leg length
Teststatlstic
8
6
7
1
2
3
4
5
-2,26 -2.08 .2.t2 |2,42 -2.68 .2.80 -3.34 -3,U
(')
Lsg length
Teststatistic
(+)
14
15
13
9 1 0 1 1 L2
-3.91
-4.28
-3.26 -3.73 -3.91 .3.66 -4.05
(r)
(r+)
(.+)
(rf)
(rrr)
(rr*)
(**)
of rtrcnullhypohcsirthatthcrricl hara unittootg
Note: (.). (r.) rrd C") denotcrcjectioru
Thcublc dlowr fa r linsar
drcl0 percgnt,5 pcrcentutd I pcrccntlcvclt,resgcctiveJy.
dcrcrministicrend h dre prcccetfor In(IOTCOMOD).Unda thc oull hypothceir
,r+b'r+2, holds,whcrt (2,) hrs mesttzoro,lf (2,) followr u
ln(fOTCOlvlOD)
1N (k+ l) procsr! with s unit root hcn 0 ' 0 holdr in thc following mod!l':
l
vrluerof tbc
&r - c + p.r + 0.rr- I * Ef-I,' &,-i+ 3,. Tle abterepoructudcntizcd
choiccrof rhclaglength'1c'Ctitictlvtluct arctrbuhtcd
of g for <li.ffercnt
OLSesdmarcr
in Fullcr(1976).
asB &$cribedby
cointegration
I appliedrhe 2o urd 2, single+quation
Tbtt
phillipsandouliads(1990)todataonRPFX,TOIENRGYrndTOTCOMOD.
rcsuls areshowrrin Tlblc 2. Accordingto thoscrtsultg,onectnnoSrcjecttbc null
lcvelir u.redt
cvcnwhena 50perceotsignifcancc
of nocointegrEtion,
hyporhesis
coinrgrrtiontcltt prcrcntedby Arnrnoutd
In consast,thesingle+quadon
(rcc
wlth colnteEation
va1 Nordcnyield resultsthgtEremucbmolt conslstent
TEbles
3 and4 of DeirPaPer).
L
JLh{ 11 '93
P.4
Ba:36Pf1 B$0< 0F C$IADA lfA
Discttttion : R obcri Eollmann
26E
Trble 2
Phillips and Oullarls (1988)libstsof
No-ColntegratlonHypothesis
Left -hand-gidevariable
ln(RPFX)
ln(TOTCOMOD)
rnFOrrxRGY)
2o
2,
-8.00
-13.25
-8.41
-1.95
-2.68
-2.10
Notc: Tlrt rsruls rrc rporud for all possiblccholccrfc thc b!'hrnd'd&
vsrirblc rsod in thc coinogntingngrcsrion.llro 6rrt columnhdisrtcr whrt
'ln'Ffcrt
vrriableis usedon theleft-handridcof thocoinagruingn5reslon
o thcnaucl logarithm,
To computettrc teet $$istics, lt ir nccssrry b concct fu tcrisl
of he residurlsof he cdntcsndnSrc3rurionr.
in the6nt rti.Ecrcnces
conelatjon
Thc Neweyurd Wcrt (l9n) mcdrodwrs uscdfor thu p{ttPostrdlowing for
($c gulS 11! not rcnsi[veO drc relcctednumbcrof
l0 autoconeladons
A tincertinc Ecndw8sincludodin Orecoinngratiryagrcsion
autoconeladons).
The gridcrl vrluel for thc 2s srd,2, w rlslisdcr rrc .15.89tld '2.E5,
at rlrc50 pcr centlcvel (0renull hlpo0resbis rcjectcdif ttc tcst
respecdvely.
suusic is smajlerhan rhccriticrt vdue).Thac cridcrl vduel wcreobaincd
usinga MonloCulo erpcrimcntwith 2,000rtplicrtionr of rivrrirta rgtdom'
.
innovrdone
Gauesirn
500)widrindcpendeot
walkdmexries (of lenStn
(1988)multi-e4uation
rcstfor
alsoapplylohurscn's
Amuo ud vanNorden
follow a
thgtthe vadablesundsrconsidcration
This tcstsssumes
coinregrarion.
I
with &e
(VAR)wirh Gaussluergrs.Whilc experimenting
vectorauroreglsslon
of the VAR ic criticelfor the
tesqI foundthst thc choiccof the osd€E
Johansen
of thetcst.Thc Schwancriterion(seeludgeet 81.,1985),rclectea VAR
outcome
of crrdcr1 whenappliedto the systemof variablcsconsisdngof ln@PFlQ,
Amuro lnd YEnNordcnwork
ln contrast,
andIn(TOTEI'IRGY).
InCIOTCOMOD)
by Doan(1990)
with a VARof order20 (theyusea likelihood'ndotestsutgested
o dercrmiocthc lag lcng$). Teblc3 showsrssultsftom lohanscntrsts tbat st1?
level,we concludlfrom
bgsed
on EVARof ordsr2.Usinga 5 percentrignif,cance
.)
)
'93
JLIN 11
9 q
@.?37Pt1 BRI'K 0F C${ADC l'lFR
269
: RobcrtKoUmann
Discnssion
cointcslatiagvlctcr ln tbc tytlcll
Tbble3 tharrhctearctwo linerrly indcpendcnt
of In(RPniO,hCfOTEI'fROl)rnd hCfOTCOlrlOD)'md
of variablesconsisdng
notjus3onecointegnthSvects, ar rirggesedby Amurorad vur Nordcn
Appl>"ngths lohursentrJt o tboblvariatctytrn condsdntof b(RPF&
and InGOTENRGY),ar woll ar to tho fyttrm corlsdng of InRPt 0 tnd
yieldsno cvidcnccof cointrgrldon.It rppcan,howswr, thu
InCIOTCOMOD),
In(TOTENRGY)and In(TOTC\IMOD) ara colnagrarc4 r.r can bc reclr ftlst
Table4. In fact, Table4 ruggesu(at thc I per cent lcvel) hat then lre two
coinrcgnting vectors in ttrc lystem conrisdng of h$OTEI'IRGY) and
hCrOTCOMOD).which cur only bc suc if both variablerrre aend'nadonlry
witb the
in TbblcI rls notlnconristeat
(rccallthEttheADF unit-roottestrprescnted
thatthc npo
Thir suggestr
is Eend.cutionary).
thsrInCIOTCOMOD)
hypothesis
relationsin the aivariatesystcm,ln(RPF)Q,I1(TOTENRGY)and
cointegradng
merclyrcffcctrhofact that the last Fpo variables!rc rcnd'
11(TOTCOMOD),
stadonary.
Table3
Varlables
in System(19tt) Testsfor Cointegratlon:
Johansen
1n(TOTCOMOD)
1n(RPFX),1n(TOTENRGY)'
Numberof
cointegrating
vcctorS
<3
<2
<1
Maxlmum.
Tbsce
stattstic
llkellhood
rtatlstic
(rr*)
47,89
1t.601*r;
3.14
29.2t('rf)
15.46
1**1
3,14
orrrVARof ordcrI A$rilb er)
Notc: Thcrcsrrutisticlreporadin tlb trblcrn bascd
pcr
cartlcvotr,rupccdwln(Gidcal
atJ pcrccntandI
and(mr1dcnoasignificrncc
urdluscllrs,1990')
fromTbbteA2of Johansen
valuqs
,1
J|JN 11
'93
q$nDR
@:38P11 BRI'K OF
F.b
|'FR
DIscussb n: Robert Kolhrlp,nn
270
tn thesccomneaudi$srfu tbose
thete3tFsuln dcscribcd
Vn conclusion,
prcsenrcd
by Amanourd vur Nordcn.Thc frct thatdiCorentnrdrded methods
urdtrcotrurd colncgndnl eleuonr most
yleldwi&ly varyingrtsuls conccrning
lilely rcf,ecu tre shonncssof the ramplc pcrtod corrldcred ln tbe P$ct
bo rn taarerdngtrrk gorfunuc
(approximately
20 p,rrs of data).filencc,lt woul,cl
t8tr urd tho
therelcdonship
betwpcnCrnada'rrcalcxcbange
o invcstigatc
1gscrrch
termsof mds usinga longerrarnplcPcriod.
Thble4
ln SystemVarlgbles
(19E9)
Testsfor Colntegration:
Johensen
tn(RPffi ), ln (TOTEhIRGD'1n(TOTCOMOD)
Numberol
cointegrating
vcct0rs
<2
<l
Tlace
statistic
Madrmrm.
likcllhood
rtatlstlc
33,34(+**)
(rrr)
13.40
19.94('**)
13.40(.r.)
!,iote: Secnoteo Trbtc3.
Refercnces
"DisEribudons
Tlme
of theEstimatonfsr AuorcSressive
Dickey,D. andW.Fuller,
Sericswirtr a Unit Root""fotrnal of the AntericanStat'stlcalAssoctation
74 (June1979):427'43L
19E8.
VAREconomcuicc,
Evanstoni
Dou1,T.Llst's lv{antul&{fSVtstott3.O0.
'
scrles.NcwYolk:Johnwiley,1976.
Futier,w, Inrodrctlonto srcttsttcalTlme
of MovtngAverageP8lEmetets."
for a unit Rootin thePrcsence
Hali, A. .,Tusting
49'56.
Z6(1989):
Btometrika
Vcctqr."Jotaml of Ecorcmic
S."statisticalfuralysisof CoinrcSration
Johansen,
l98E):Z3l'254'
andControt12(Junc'september
Dynamics
5
'93
Jl$l 11
q{'trDn llFn
@:38PN Bgt'{< OF
27I
Dltclrrslon'RoDtrl Kohminn
Esdnuionrndlnftroncson
s. andK lussllus"'MSxinum'Liksubood fu lvloacy: oiord
Johanscn,
ro the Dcmrnd
Appticadonr
coinagnti;;;,h
52Otry 1990):169'210.
atisrcrlsrtcs
BullertnoTicorumtcs
Iudge,o.lW.Grifith;RCaners!,H.LutkgPohl;uldT.l,,l,,TtuTl|.ofyd
Nlw YorlcJohnWllcy'1985'
practics
oiirL**rrlcs, 2ndedidon.
'dii-ot
Meesc,R.andKRogof!''EmplrlcfExchur3cRrtcModslloftbsscvcnticr:Do
14
srmpto?,'7;*A of Intcrnalorcl Economics
Thoy n,
1983):3'24'
(FcbruarY
and
ilsamskcdaltisity
Semi-Dcfulto
Posldvc
Sirnplo
wsst."A
K
and
w.
Nowey,
AutocontladonConsisEnr-couuianccM&trix.''Ecotwnutr|ca55
1987):703-?08'
(lv{aY
Phillips,P.c.B.urdS.ouliadt...AsymptotichoPeni;^lofRcsidualBcsedTbsts
foCointegradon.,,economet,i'ose(January1990):165.193.
(;
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