Looking a in he pas :
Re isi ing he g ow h- e u ns nexus
wi h non-pa ame ic es s
Eka e ini Panopoulou∗Niki as Pi is†Sa an is Kaly i is‡
Ma ch 2006
Abs ac
In his pape we eexamine he linkages be ween ou pu g ow h and eal s ock p ice changes o
he G7 coun ies using a ba e y o non-pa ame ic p ocedu es o accoun o he impac o long-lagged
obse a ions. We ind ha co ela ion be ween g ow h and e u ns is de ec ed a la ge ho izons han
hose ypically employed in pa ame ic s udies. The majo eedbacks eme ge om s ock p ice changes
o g ow h wi hin he i s 6 o 12 mon hs, bu we show ha signi ican eedbacks may las o up o wo
o h ee yea s. Ou e idence also sugges s ha he co ela ion pa e ns diffe subs an ially be ween he
coun ies a hand when he sec o al sha e indices a e conside ed.
JEL classi ica ion: C14, G10, O51.
Keywo ds: eal s ock p ice changes, ou pu g ow h, long- un co a iance ma ix.
Acknowledgmen s: We a e g a e ul o A. An zoula os, D. Mallia opulos, M. Michail, M. Roche and
pa icipan s in he 2005 ASSET Con e ence and he 4 h HFAA Con e ence o help ul commen s and
sugges ions. Financial suppo unde he “PYTHAGORAS II” p ojec co- inanced by he Eu opean So-
cial Fund and he G eek Minis y o Na ional Educa ion and Religious Affai s is g a e ully acknowledged.
The usual disclaime applies.
∗(co esponding au ho ) Depa men o Economics, Na ional Uni e si y o I eland Maynoo h, Co.Kilda e,
Republic o I eland. E-mail: [email protected]. Tel: 00353 1 7083793. Fax: 00353 1 7083934.
†Depa men o Banking and Financial Managemen , Uni e si y o Pi aeus, Ka aoli & Dimi iou 80, Pi eus,
18534, G eece. e-mail: n[email p o ec ed]
‡Depa men o In e na ional and Eu opean Economic S udies, A hens Uni e si y o Economics and Business,
Pa ision S 76, A hens 10434, G eece. e-mail: skaly[email p o ec ed]
1. In oduc ion
Wha is he in e ac ion be ween he goods ma ke and he s ock ma ke ? This ela ionship
has a ac ed conside able empi ical esea ch o e he las hi y yea s.1Ea ly con ibu ions,
beginning wi h he wo k by Goldsmi h (1969), assessed he posi i e ela ionship be ween s ock
e u ns and economic g ow h. Subsequen s udies by, among o he s, Boswo h (1975), Hall
(1978), Fama (1981, 1990), Schwe (1990) and Es ella and Mishkin (1998), ha e ocused on he
US and s ongly indica e ha he s ock ma ke index can se e as a eliable leading indica o in
he US economy. This conclusion e lec s he iew, pu o wa d by Mo ck e al. (1990), ha he
s ock ma ke is la gely a ‘sideshow’, which simply mi o s ‘news’ abou an icipa ed de elopmen s
in i ms’ u u e payou s and ou pu g ow h. Mo eo e , some spo y e idence in he ele an
li e a u e sugges s ha he e is also a nega i e - hough weak- ela ionship be ween cu en
ou pu and u u e s ock p ices in he US (see Pa k, 1997, McQueen and Roley, 1993). This
beha io migh be igge ed by he eac ion o s ock ma ke pa icipan s o o he mac oeconomic
a iables closely linked o ou pu , such as employmen and in la ion, which a e nega i ely ela ed
o u u e ea nings and business condi ions.2
In gene al, he empi ical s udies ha e elied almos exlusi ely on single-equa ion o mul i-
a ia e ec o au o eg essi e (VAR) and panel models o in es iga e he ela ionship be ween
ou pu g ow h and s ock p ice changes. Howe e , single equa ions o ini e-o de mul i a ia e
models may be oo es ic i e o ep esen he ue au oco a iance s uc u e o a gi en mul iple
ime se ies o se e al easons. Fi s , al hough he p ocess assumed may be wide sense s a ion-
a y and pu ely non-de e minis ic, i will ail o ha e an au o eg essi e ep esen a ion i some o
1The heo e ical ela ionship be ween hese sec o s ha e been ounded by B aina d and Tobin (1968) who
poin ed ou ha capi al o ma ion and, consequen ly, ou pu g ow h a e igge ed when he ma ke alues new
capi al highe han i s eplacemen cos (q- heo y o in es men ). Hayashi (1982) has ein o ced his inding by
showing ha unde ce ain assump ions he s ock ma ke alua ion o i ms can be encapsula ed in he neoclassical
in es men model wi h adjus men cos s and se e as he main de e minan o in es men and ou pu g ow h.
Le au and Lud igson (2002) ha e shown ha in he p esence o a ime- a ying isk p emium he q- heo y implies
ha a change in expec ed e u ns al e s u u e s ock p ices and he cos o capi al, hus igge ing a change in
in es men o e longe ho izons. An al e na i e ansmission channel in ol es consump ion, and consequen ly
weal h and ou pu , which may ise a e an inc ease in s ock p ices gene a ed by op imis ic expec a ions o u u e
di idends o , al e na i ely, by a all in in e es a es (Pa ke and Jullia d, 2005). These links may be mo e in ense
in he case o a inancial c isis (Boswo h, 1975). F om a iscal policy poin o iew, Blancha d (1981) has shown
ha a e an expansiona y policy shock, asse p ices change as a esul o an icipa ed changes in eal in e es
a es and p o i abili y, hus affec ing weal h and spending, and spu ing a ise in supply and equilib ium ou pu .
2Ano he possible explana ion o his pa e n may be ha i e lec s coun e cyclical mac oeconomic policy
h ough he eac ion unc ion o mone a y au ho i ies. Fo ins ance, in a pe iod o unan icipa ed ecession he
Fedmay eac by educingin e es a es, husinducing a ise in s ock p ices, as in es o s ind he s ock ma ke
mo e p o i able. On he o he hand, a ise in ou pu g ow h is usually conside ed as a sign o u u e in la ion,
which affec s nega i ely u u e g ow h and e u ns, and policymake s may espond by aising in e es a es which,
in u n educes he u u e cash lows o i ms.
1
he oo s o he Lau en expansion o i s mo ing a e age ep esen a ion lie on he uni ci cle.
Second, he p ocess may admi a ep esen a ion o in ini e o de , which implies ha i s ini e
app oxima ion may gi e misleading esul s in common size samples.3Thi d, when pa ame -
ic models a e employed in which ou pu g ow h is explained by lagged and con empo aneous
s ock p ice changes, as in Fama (1981, 1990) and Ba o (1990), i is implici ly assumed ha he
la e a e weakly exogenous o he pa ame e s o in e es , hus esul ing in inconsis en and/o
inefficien es ima o s i his assump ion ails o hold. Finally, he p oblem o app oxima ing
he ue da a gene a ion p ocess by, say, a ini e-o de VAR may be pa icula ly acu e when
da a on s ock e u ns a e employed. The wo k by Fama and F ench (1988) and Po e ba and
Summe s (1988) sugges s he p esence o ansi o y componen s in s ock p ices wi h e u ns
showing posi i e au oco ela ion o e sho pe iods ( e lec ing e.g. he well-known momen um
effec , as in Jegadeesh, 1990), bu nega i e au oco ela ion o e longe pe iods (due e.g. o
mean e e sion o undamen als). In iew o such an au oco a iance s uc u e he use o a
ini e-o de VAR, o any o he app oxima ing pa ame ic model, becomes ques ionable.4
The pu pose o his s udy is o ein es iga e sys ema ically his bi a ia e ela ionship by
using non-pa ame ic es s o long- un co ela ion be ween g ow h and s ock e u ns o he
G-7 coun ies. To emedy po en ial ca ea s associa ed wi h he use o s anda d pa ame ic
echniques in he empi ical in es iga ion o he g ow h- e u ns nexus, we es ima e he long-
un co a iance ma ix o he wo se ies ia ke nel-based es ima ion echniques, which in ol e
only he choice o a ke nel and a bandwid h pa ame e o es ima e he co a iance ma ix o
he p ocess ha equals he spec al densi y o he p ocess a equency ze o.5Based hen
3Lue kepohl and Poski (1996) discuss he p oblems ha a ise in causali y es ing by i ing ini e VAR
models o in ini e-o de p ocesses. The au ho s p o e ha he use o s anda d Wald es s o G ange -causali y
can indeed be jus i ied unde mo e gene al egula i y condi ions, bu in small samples hese es s end o ejec
he null hypo hesis o no causali y mo e o en han indica ed by asymp o ic signi icance le els. Addi ional easons
ha may p oduce misleading in e ences in es ing o causali y wi hin VARs a e ela ed o he ime he e ogenei y
p ope ies o he ec o p ocess unde conside a ion. Fo ins ance, i he p ocess does admi a ini e-o de VAR
ep esen a ion, bu con ains uni oo s and exhibi s coin eg a ion, hen some es ima ed coefficien s o he VAR(p)
model con e ge o nons anda d limi ing dis ibu ions wi h a as e a e han T1/2. In such a case, es ing o
G ange causali y equi es p io knowledge o he numbe and loca ion o uni oo s in he sys em. See, o
example, Sims e al. (1990), and Toda and Phillips (1993).
4To ou knowledge, he only s udy ha has a emp ed o ackle wi h his issue by use o a non-pa ame ic
echnique is Hassapis (2003), who has applied he And ews (1991) p ocedu e o es ima e he long- un co a iance
ma ix o ou pu g ow h and inancial a iables. The au ho in es iga es he ela ionship be ween Canadian and
U.S. inancial ma ke a iables and Canadian g ow h and inds ha as he numbe o au oco a iances ha a e
assigned a non-ze o weigh inc eases, he eedback om selec ed Canadian o U.S. inancial a iables (including
s ock p ices) o u u e Canadian ou pu g ow h inc eases.
5These me hods we e i s p oposed by Pa zen (1957) and P ies ley (1962). Con ibu ions o he co a i-
ance es ima ion li e a u e include among o he s Whi e (1984), Newey and Wes (1987, 1994), And ews (1991),
Robinson (1991) and B.E. Hansen (1992).
2
on he de i a ion o a no mal asymp o ic app oxima ion o he spec al densi y ma ix o he
p ocess, we a e able o de i e he asymp o ic dis ibu ion o he long- un co ela ion coefficien
be ween he se ies a hand and es o i s signi icance. The agg ega e co ela ion coefficien
can be u he decomposed in o he con empo aneous and empo al c oss co ela ion, in o de
o acili a e he analysis o he co a iance pa e n be ween g ow h and e u ns. We use he
non-pa ame ic me hodology p oposed by Hong (2001) o pe o m hypo hesis es ing. The es
is based on he esidual c oss-co ela ion unc ion o he se ies and is obus o dis ibu ional
assump ions, which a e likely o be impo an he e since he a iables a hand ypically exhibi
bo h au oco ela ion and/o condi ional ola ili y effec s.
We u ilize mon hly da a om he G-7 coun ies o in es iga e he bi a ia e ela ionship
be ween s ock p ice changes and indus ial ou pu g ow h in he con ex o hese non-pa ame ic
me hodologies. Un il now, exis ing s udies (including, among o he s, Ba o, 1990, Fama, 1990,
and Schwe , 1990), ha e ocused in he impac o cu en and lagged s ock p ices on u u e
ou pu in he US, whe eas ewe s udies ha e in es iga ed his pa e n in o he de eloped
economies, like Canada (Ba o, 1990), Japan, Ge many and he UK (Mullins and Wadhwani,
1989), and he G-7 coun ies (Choi e al., 1999). In line wi h he empi ical li e a u e on he
issue, ou objec i e is no o es al e na i e heo ies on he de e mina ion o he g ow h- e u ns
nexus, bu a he o employ a ecen ly de eloped gene al econome ic amewo k o ein es iga e
he di ec ion o causali y and he s eng h o he co ela ion pa e ns be ween eal s ock p ice
changes and ou pu g ow h o he G-7 coun ies.6
In con as o he bulk o he li e a u e ha has es ablished ha he majo eedbacks eme ge
om s ock e u ns o g ow h wi hin he i s six o wel e mon hs, ou indings indica e ha
he effec may las o up o wo o h ee yea s. In pa icula , ou esul s indica e a posi i e
co ela ion be ween s ock e u ns and g ow h in he G-7 coun ies (wi h he excep ion o I aly).
Decomposing his long- un co ela ion o allow o con empo aneous and empo al eedbacks, we
6The e a e se e al easons why his ela ionship migh be diffe en be ween de eloped coun ies (Mau o,
2003, Binswange , 2004). Fi s , he size o some G-7 economies is ela i ely small compa ed o he US and he
p oduc ion o se e al la ge i ms ha a e lis ed in domes ic s ock ma ke s akes place ab oad, which ende s
hem less sensi i e o an icipa ed de elopmen s in domes ic eal ac i i y. Also, he deg ee o openess in Eu opean
economies and in Canada is a lo highe han in Japan and he U.S. and, consequen ly, o eign dis u bances may
ha e weakened he associa ion be ween domes ic s ock e u ns and he eal sec o o he economy. Mo eo e ,
in coun ies whe e he s ock ma ke egula ions a e o English o igin he g ow h- e u ns link should be highe
because manage s a e less p o ec ed om sha eholde s and, hence, less able o pu sue e.g. in es men s a egies
in he case o a nega i e ma ke sen imen . In addi ion, hese economies sha e some common cha ac e is ics,
such as g ea e possibili y o akeo e s, lowe gea ing a ios, and smalle ole o employees in decision making.
3
ind ha he long- un co ela ion is mainly igge ed by he eedbacks om s ock p ice changes
o u u e ou pu g ow h wi h he s onges eedbacks occu ing o US, Japan, Ge many, and he
UK. The mos in e es ing inding is ha when he numbe o au oco a iances ha a e assigned
a non-ze o weigh inc eases, he eedback om s ock p ice changes o ou pu g ow h inc eases,
eaching a peak a a ange be ween eigh een o wen y- ou mon hs, whe eas weake effec s may
las up o hi y-six mon hs. On he o he hand, wi h he excep ion o he UK we do no ind
any e idence o subs an ial co ela ion unning om ou pu g ow h o s ock e u ns. As ega ds
he co ela ion pa e ns om sec o al indices we es ablish ha he e a e la ge a ia ions ac oss
sec o s and coun ies wi h subs an ial in o ma ion encoun e ed in dis an lags as well.
Ou main con en ion is hus ha he e a e alid g ounds o expec ing he g ow h- e u ns
nexus o be one wi h long- e m impac s. Hence, hese indings complemen and ex end hose
epo ed by Fama (1990), Schwe (1990), Ba o (1990), Choi e al. (1999) and o he au ho s
who ha e epo ed ha he e is a s ong posi i e link be ween s ock e u ns and u u e indus ial
p oduc ion ha eaches i s maximum a a o ecas in e al o app oxima ely 6 o 12 mon hs,
depending on he ho izon o e u ns. Ou app oach sugges s ha s ock p ices a e co ela ed wi h
upwa d mo emen s in indus ial p oduc ion a longe in e als as well, while use ul in o ma ion
is also con ained in he sec o al s ock p ice indices. Hence, he non-pa ame ic me hodologies
u ilized he e seem o p o ide addi ional in o ma ion abou he effec o he inancial on he
eal sec o o he economy ha can be ob ained by examining he pas beha io o he s ock
p ice changes a ho izons ha a e unlikely o be cap u ed by pa ame ic single-equa ion o
mul i a ia e eg essions. Finally, ou app oach sugges s ha he inding o a nega i e co ela ion
be ween ou pu g ow h and u u e s ock p ice changes, epo ed by Pa k (1997) and McQueen
and Roley (1993) o he US economy, is mainly d i en by he nega i e associa ion o US
ou pu g ow h wi h u u e changes in he Basic Indus ies and he Consume Goods sha e
indices. Howe e , wi h ew excep ions his associa ion is no b oadly suppo ed by agg ega e
o sec o al da a om o he de eloped economies.
The es o he pape is s uc u ed as ollows. Sec ion 2 ou lines he non-pa ame ic p o-
cedu es used o he empi ical es ima ion o he g ow h- e u ns ela ionship and sec ion 3 de-
sc ibes he da a a hand. Sec ions 4 and 5 p esen and commen he empi ical esul s o he
G-7 coun ies. Sec ion 6 concludes he pape .
4

2. Non-pa ame ic es s o he g ow h- e u ns co ela ion
Conside he ‘long- un’ co ela ion coefficien be ween ou pu g ow h, y ,and eal s ock
e u ns, x . The long- un co a iance ma ix Ωo he p ocess Z =[y ,x
]>is de ined as:
Ω≡


ωyy ωxy
ωxy ωxx


=lim
T→∞ T−1
T
X
i=1
T
X
j=1
E(ZiZ>
j)(1)
In p ac ice, only a ac ion o he sample au oco a iances is used o es ima e he asymp o ic
a iance Ω,by employing a class o ke nel es ima o s and he selec ion o a bandwid h pa ame e ,
M, wi h he es ima o o Ωgi en by:
ˆ
ΩT=
T
X
j=−T
k(j/M)ˆ
Γ(j)(2)
whe e ˆ
Γ(j)=









1
T
T
P
=j+1
(Z ZT
−j) o j≥0,
1
T
T
P
=−j+1
(Z +jZT
) o j<0









,and k(·)is a eal- alued ke nel.7The es i-
ma o b
Ωis a consis en es ima o o Ω o uncondi ionally ou h- o eigh h-o de s a iona y
andom a iables, and o any gi en bandwid h {M}, such ha M→∞and M/T1/2→0.
Mo e impo an ly, his long- un co a iance ma ix gi en by (2) is equal o 2π imes he spec al
densi y ma ix e alua ed a ze o, an analogy which enables us o u ilise he ele an asymp o ic
heo y o spec al densi y es ima ion. Speci ically, unde ce ain egula i y condi ions, hese
nonpa ame ic spec al densi y es ima o s ha e been shown o app oxima e he no mal dis ib-
u ion.8The elemen s o b
Ωa e join ly no mally dis ibu ed and his join dis ibu ion enables us
o de i e he asymp o ic dis ibu ion o he long- un co ela ion coefficien es ima e be ween
he wo se ies o in e es , y and x ,de ined as ˆρxy ≡ˆωxy
√ˆωxx ˆωyy ,wi h ˆρxy no mally dis ibu ed as
7He e, we employ he Quad a ic Spec al (QS) ke nel ha gi es a non-ze o weigh o all he sample c oss
co ela ions and is bes wi h espec o an Asymp o ic T unca ed Mean Squa e E o (ATMSE) c i e ion in he
class Kas p o ed by And ews (1991). The au ho , in an ex ensi e Mon e Ca lo s udy, epo s cases whe e he
ke nel es ima o s o Ωyield con idence in e als whose co e age p obabili ies a e oo low. This p oblem is no
associa ed wi h a poo choice o a speci ic ke nel o bandwid h pa ame e and is pa icula ly se e e when he e
is conside able empo al dependence in he da a. In such a case, da a il e ing be o e es ima ing Ωmay yield
mo e accu a ely sized es s a is ics han s anda d ke nel es ima o s; see And ews and Monahan (1992). In he
con ex o he p esen s udy, howe e , such a da a p ewhi ening is unecessa y since bo h s ock p ice changes and
ou pu g ow h exhibi s ong mean e e ing p ope ies.
8See G enande and Rosenbla (1953), Ande son (1971), and P ies ley (1981). Sufficien egula i y condi ions
o ob aining such a esul is ha Z =
∞
S
j=0
ψjε −j,whe e ε is an i.i.d. p ocess wi h (E(ε )=0,E(ε2
)<
∞,E(ε4
)<∞,and
∞
S
j=0

ψj
<∞.
5
ollows (see he Appendix o he de ailed de i a ion):
T
M(ˆρxy −ρxy)∼N³0,¡1−ρ2
xy¢2´(3)
An ad an age o his me hodology is ha he long- un co a iance ma ix can be decom-
posed in o he con empo aneous co a iance ma ix Gand he empo al co a iance ma ix Λ
(o Λ>), i.e. Ω=G+Λ+Λ>whe e G≡


gyy gxy
gxy gxx


=E(Z0Z>
0)and Λ≡


λyy λyx
λxy λxx


=
∞
P
k=1
E(Z0Z>
k). This, in u n, implies ha he long- un co ela ion coefficien ρxy can be decom-
posed as:
ρxy =µgxy
√ωxxωyy¶+µλyx
√ωxxωyy¶+µλxy
√ωxxωyy¶≡cxy + yx + xy (4)
Rela ionship (4) exp esses he long- un coefficien , ρxy,as he sum o he con empo aneous co -
ela ion coefficien , cxy, he empo al co ela ion coefficien , yx, desc ibing eedbacks om pas
ou pu g ow h o cu en eal s ock e u ns (y →x ), and he empo al co ela ion coefficien
xy ha desc ibes eedbacks o he opposi e di ec ion (x →y ).
While we a e able o exploi he asymp o ic no mali y o he es ima o o he wo-sided
long- un co a iance ma ix and de i e he ele an dis ibu ion o he long- un co ela ion
coefficien , o mal hypo hesis es ing on he basis o he con empo aneous co ela ion coefficien ,
cxy, and he empo al co ela ion coefficien s, xy and yx is no easible. The main eason is
ha asymp o ic no mal app oxima ions o he espec i e componen s o he spec al densi y
ma ix a e no a ailable, since he off-diagonal elemen s o he one-sided long- un co a iance
ma ix can no be exp essed in e ms o pe iodog ams.
To ci cum en he lack o o mal hypo hesis es ing on he decomposed co ela ion coeffi-
cien s, we indi ec ly in es iga e hei signi icance by es ing o he exis ence o causal ela ions
in he mean o wo se ies in he con ex o he non-pa ame ic me hod pu o wa d by Hong
(2001). In pa icula , conside again he bi a ia e s a iona y and e godic s ochas ic p ocess
Z =[y ,x
]>. The es is based on he sample c oss-co ela ions unc ion o he s anda d-
ized esiduals and in ol es wo s ages. In he i s s age, we es ima e uni a ia e ime-se ies
models o bo h he se ies unde sc u iny and in he second s age, we calcula e he sample
c oss-co ela ions o he s anda dized esiduals o ou pu g ow h and eal s ock e u ns, buy and
6
bux espec i ely.9The sample c oss-co ela ion unc ion o uy and ux (bτx,y(k))isgi enby:
bτx,y(k)≡b
Cx,y(k)
qb
Cx,x(0) b
Cy,y(0)
(5)
whe e b
Cx,y(k)= T−1PT
=k+1[buy bux −k],k=0
T−1PT
=−k+1[buy +kbux ],k<0
is he sample c oss-co a iance, b
Cx,x(0),
b
Cy,y(0) a e he sample a iances o he s ock e u ns and ou pu g ow h, espec i ely and
Tis hesamplesize. The es s a is ic,Q, p oposed by Hong (2001) is gi en by he ollowing
o mula:
Q=TPT−1
j=1 k2(j/M)∗bτ2
x,y(j)−C1T(k)
p2∗D1T(k)(6)
whe e C1T(k)=PT−1
j=1 (1 −j
T)∗k2(j/M),D1T(k)=PT−1
j=1 (1 −j
T)∗(1 −j+1
T)∗k4(j/M)
and k(j/M)is a weigh ing unc ion.10 Unde he null hypo hesis o no causali y and some
app op ia e egula i y condi ions, he Q- es ollows asymp o ically a N(0,1) dis ibu ion.11
This me hodology allows o bi a ia e condi ional mean speci ica ion and includes he case o
in ini e uncondi ional a iance, which is o en encoun e ed in empi ical s udies on s ock e u ns.
Tes ing o he signi icance o he con empo aneous co ela ion coefficien be ween wo se ies is
pe o med by employing he ypical sample co ela ion coefficien , which is also asymp o ically
no mal (Ande son, 1971); assuming ha he ue alue o he co ela ion coefficien is q, he
co ela ion coefficien es ima o is hen dis ibu ed as bqx,y →N³q, (1−q2)2
T´.
3. Da a
To gauge his empi ical ela ionship be ween ou pu g ow h and s ock e u ns, we use ex-
is ing measu es o ou pu and eal composi e and sec o al s ock p ice changes o he G-7
coun ies. Ou da a se is mon hly and co e s he pe iod om Janua y 1973 o Augus 2003.
As a measu e o he g ow h a e o ou pu we use he indus ial p oduc ion index (seasonally
adjus ed) om Thomson Financial (ob ained by Da as eam). Following Fama (1990) and o he
au ho s, eal s ock p ice changes a e ob ained by use o Da as eam-calcula ed composi e and
sec o al indices, app op ia ely adjus ed o he in la ion a e o he coun ies unde conside a-
ion. So, apa om he o al ma ke agg ega e index and he o al non- inancial ma ke index,
9In ou s udy, we employ he ypical ARMA(p,q)-GARCH(1,1) models, he co ec o de o which is de e -
mined by means o he Akaike in o ma ion c i e ion.
10In he p esen s udy, we use he QS ke nel.
11No ice ha he Q− es is an one-sided es and uppe - ailed c i ical alues should be used.
7
he ollowing sec o al indices a e employed: Financial, Basic Indus ies, Gene al Indus ies,
Cyclical Se ices, Non-Cyclical Se ices, In o ma ion Technologies, Cyclical Consume Goods,
Non-cyclical Consume Goods, U ili ies.12
4. Empi ical e idence
In his sec ion we apply he non-pa ame ic echniques ou lined abo e o examine he em-
pi ical ela ionship be ween g ow h and s ock e u ns. We emphasize ha , ollowing Fama
(1990), Schwe (1990) and o he s, we do no y o disc imina e among a ious heo e ical
hypo heses. Ins ead, we implemen he es ima ion and es ing s a egy ou lined in sec ion 2 o
in es iga e non-pa ame ically he s eng h and he di ec ion o co ela ion be ween eal s ock
p ice changes and ou pu g ow h o he G-7 coun ies.
4.1. Long- un co ela ion be ween g ow h and e u ns
We begin he empi ical analysis wi h he es ima es o he long- un co ela ion be ween
g ow h and s ock e u ns. The i s column in he uppe pa o Table 1 epo s he ele an
igu es o he agg ega e ma ke e u ns a he highes bandwid h examined (36 mon hs). This
choice o bandwid h, i.e. he numbe o au oco a iances ha a e assigned a non-ze o weigh ,
ep esen s one en h o ou sample and ensu es ha he majo i y o he effec s ha e been aken
in o accoun . Wi h he excep ion o I aly, es ima es o he long- un co ela ion ange om
0.488 (Japan) o 0.656 (UK). The second column epo s he s anda d de ia ion o he poin
es ima es o he long- un co ela ion based on (3). As was shown in he p e ious sec ion, he
a iances o he poin es ima es a e in e sely ela ed o he ue alue o he long- un co ela ion
coefficien s. Acco dingly, I aly has he lowe long- un co ela ion and hus exhibi s he highe
s anda d de ia ion o he espec i e es ima e. The nex column epo s he espec i e igu es
o all he coun ies. In his espec , he long- un co ela ion o he es o he coun ies is
ound o be signi ican ly diffe en om ze o.13 No su p isingly, he only coun y o which we
canno ejec he null hypo hesis o ze o long- un co ela ion is I aly.14 In hesamemode,we
12The Da as eam codes o he co esponding s ock ma ke indices a e he ollowing: TOTMKXX, TOTLFXX,
BASICXX, GENINXX, CYSERXX, NCYSRXX, ITECHXX, UTILSXX, CYCGDXX, NCYCGXX, whe e XX
s ands o he coun y code, i.e. CN (Canada), FR (F ance), BD(Ge many), IT (I aly), JP (Japan), UK and
US. In he same mode, he Consume P ice Index code is he XXI66...CE and he Indus ial P oduc ion code is
XXI64...F. All he epo ed esul s we e ob ained by p og ams w i en in E- iews 4.1 and a e a ailable om he
au ho s upon eques .
13These es s a e pe o med based on he asymp o ic app oxima ion o he dis ibu ion o he ze o long- un
co ela ion, which is shown o be s anda d no mal.
14In p inciple, we could also calcula e he ange o bandwid hs o e which we ejec he null hypo hesis o a ze o
8
by S ock and Wa son, 2003). I is likely ha a subsan ial po ion o in o ma ion is los by
he need o es ima e pa simonious single-equa ion and mul i a ia e pa ame ic models, which
in u n educes hei o ecas ing abili y. Hence, al hough he e idence p esen ed he e can only
be in e p e ed en a i ely in e ms o o ecas ing abili y, he e is some indica ion ha some
p edic i e con en could be ound i la ge lags o s ock p ice changes a e u ilized in pa ame ic
speci ica ions aiming a p edic ing ou pu in he G-7 coun ies.
Theme hodemployedhe ecanalsobeapplied o o he cases in which pa ame ic me hods
lea e empi ical ques ions open. Fo ins ance, Thoma and G ay (1998) claim ha , con a y o he
iew popula ly held in he li e a u e, inancial a iables (money supply and in e es a es) do no
p o ide any p edic i e powe o u u e indus ial g ow h. The au ho s no e ha , gi en ha he
p edic i e powe o pa ame ic models should be e alua ed in ou -o -sample o ecas ing, much o
hei powe is he ou come o speci ic ou lie s. The non-pa ame ic empi ical s a egy used he e
can be ex ended o he es ima ion and hypo hesis es ing o he long- un co a iance s uc u e
be ween mone a y a iables and eal ac i i y. Ano he p omising ou e o u he esea ch
in ol es he links be ween domes ic and in e na ional s ock po olios and u u e ou pu . Dumas
e al. (2003) poin ou ha an open ques ion in he s udy o in e na ional inancial ma ke s is
whe he s ock ma ke s co ela ions ac oss coun ies can be explained by economic undamen als.
Empi ical indings on his issue ha e no been uni e sally conclusi e (see Smi h, 1999) and he
p esen me hodology could shed some ligh on he links be ween a ia ions in in e na ional
agg ega e o sec o al s ock ma ke links and unde lying economic a iables.
15

Appendix: Asymp o ic dis ibu ion o he long- un co ela ion coefficien
He e we de i e he asymp o ic dis ibu ion o he long- un co ela ion coefficien ˆρxy.Gi en
ha he co a iance be ween any wo elemen s o he spec al densi y ma ix, o example (a, b)
and (c, d),isequal o ac bd + ad bc, we ob ain he ollowing asymp o ic dis ibu ion o he
elemen s o b
Ω:
T
M






ˆωxx −ωxx
ˆωyy −ωyy
ˆωxy −ωxy






∼N






0,






2ω2
xx 2ω2
xy 2ωxxωxy
2ω2
xy 2ω2
yy 2ωyyωxy
2ωxxωxy 2ωyyωxy ωxxωxy +ω2
xy












(A1)
In o de o de i e he asymp o ic dis ibu ion o he long- un co ela ion coefficien ˆρxy ≡
ˆωxy
pˆωxx ˆωyy
we apply he del a me hod wi h he ans o ma ion ec o Jequal o he pa ial
de i a i es o ρxy wi h espec o ωxx,ωyy and ωxy:
J=·∂ρ
ϑωxx
∂ρ
ϑωyy
∂ρ
ϑωxy ¸
Speci ically, we ge ha :
∂ρ
ϑωxx
=
∂µωxy
√ωxxωyy¶
ϑωxx
=−ωxy
2ω2
xx√ωxxωyy
∂ρ
ϑωyy
=
∂µωxy
√ωxxωyy¶
ϑωyy
=−ωxy
2ω2
yy√ωxxωyy
∂ρ
ϑωxy
=
∂µωxy
√ωxxωyy¶
ϑωxy
=1
√ωxxωyy
Se ing Q heasymp o ic a ianceo heΩma ix in (A1), he asymp o ic a iance o he
long- un co ela ion coefficien is calcula ed as ollows:
P=JQJ0
16
A e some simple algeb a, we ha e:
P=(ω2
xy −ωxxωyy)2
ω2
xxω2
yy
=(ρ4
xy +1−2ρ2
xy)=(ρ2
xy −1)2(A2)
I ollows om (A1) and (A2) ha :
T
M£ˆρxy −ρxy¤∼N³0,¡1−ρ2
xy¢2´
which is equa ion (3) in he ex .
17
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20

Table 1. Long- un co ela ion es ima es be ween ou pu g ow h (y) and s ock p ice changes (x)
Coun y Long-Run
Co ela ion
S anda d
De ia ion
-s a
Ho: ρxy =0
-s a
Ho: ρxy =ρ
Con empo aneous
co ela ion
Tempo al
co ela ion
x
→
y
Tempo al
co ela ion
y
→
x
Sample pe iod: 1973-2003
Canada 0.556 0.221 2.536 -0.203 (ρ=0.6) 0.041 0.353 0.162
F ance 0.564 0.219 2.536 -0.201 (ρ=0.6) 0.116 0.362 0.086
Ge many 0.491 0.243 2.219 -0.040 (ρ=0.5) -0.021 0.451 0.061
I aly 0.194 0.309 0.862 -0.034 (ρ=0.2) -0.033 0.190 0.037
Japan 0.488 0.244 2.216 -0.041 (ρ=0.5) -0.022 0.476 0.034
UK 0.656 0.183 2.988 -0.158 (ρ=0.7) 0.116 0.422 0.118
US 0.583 0.211 2.641 -0.083 (ρ=0.6) -0.018 0.498 0.103
Sample pe iod: 1989-2003
Canada 0.575 0.210 2.005 -0.130 (ρ=0.6) 0.001 0.278 0.296
F ance 0.549 0.219 1.918 -0.254 (ρ=0.6) 0.090 0.321 0.138
Ge many 0.412 0.260 1.439 -0.374 (ρ=0.5) -0.131 0.424 0.119
I aly 0.371 0.271 1.296 0.562 (ρ=0.2) 0.084 0.285 0.002
Japan 0.275 0.289 0.961 -0.957 (ρ=0.5) -0.030 0.348 -0.043
UK 0.565 0.214 1.974 -0.844 (ρ=0.7) 0.033 0.368 0.164
US 0.648 0.182 2.264 0.239 (ρ=0.6) -0.020 0.395 0.273
No es: The bandwid h o he 1973-2003 pe iod is 36 mon hs and o he 1989-2003 pe iod is 18 mon hs; see sec ion 2 in ex o de ails.
Table 2A. Hypo hesis es ing o empo al co ela ion: om s ock p ice changes o ou pu g ow h
Q- es
Coun y/Bandwid h 3 6 9 12 18 24 30 36 48
Canada No No No No Yes** Yes** Yes** Yes** Yes**
F ance No No No No No No No No No
Ge many No No Yes** Yes** Yes** Yes** Yes** Yes** Yes**
I aly Yes* Yes** Yes* No No No No No No
Japan Yes** Yes** Yes* No No No No No Yes*
UK No No Yes* Yes** Yes** Yes* No No No
US Yes** Yes** Yes** Yes** Yes** Yes** Yes** Yes** Yes**
Table 2B. Hypo hesis es ing o empo al co ela ion: om ou pu g ow h o s ock p ice changes
Q- es
Coun y/Bandwid h 3 6 9 12 18 24 30 36 48
Canada No No No No No No No No No
F ance No No No No No No No No No
Ge many No No No No No No No No No
I aly No No No No No No No No No
Japan No No No No No No No No No
UK No No No Yes** Yes** Yes** Yes** Yes** Yes**
US No No No No No No No No No
No es: Q- es deno es he Hong (2001) es ; see sec ion 2 o de ails.* deno es s a is ical signi icance
a he 5% le el and ** a he 1% le el.
Table 3. Hypo hesis es ing o con empo aneous co ela ion
Coun y
Con empo aneous
co ela ion
qxy
-s a
Ho: qxy =0
Canada 0.103 1.947
F ance 0.099 1.877
Ge many 0.005 0.095
I aly 0.039 0.734
Japan 0.041 0.774
UK 0.059 1.128
US -0.017 -0.317
No es: qxy deno es he Ande son (1971) es ; see sec ion 2 o de ails.
.0
.1
.2
.3
.4
5 10 15 20 25 30 35
cxy yx xy
To al ma ke index
.0
.1
.2
.3
.4
5 10 15 20 25 30 35
cxy yx xy
To al non- inancial ma ke index
-.1
.0
.1
.2
.3
.4
5 10 15 20 25 30 35
cxy yx xy
Financial index
-.1
.0
.1
.2
.3
5 10 15 20 25 30 35
cxy yx xy
Basic indus ies index
.0
.1
.2
.3
5 10 15 20 25 30 35
cxy yx xy
Gene al indus ies index
-.1
.0
.1
.2
.3
.4
5 10 15 20 25 30 35
cxy yx xy
Cyclical se ices index
-.1
.0
.1
.2
.3
.4
.5
5 10 15 20 25 30 35
cxy yx xy
Non-cyclical se ices index
.0
.1
.2
.3
5 10 15 20 25 30 35
cxy yx xy
In o ma ion echnology index
-.1
.0
.1
.2
.3
5 10 15 20 25 30 35
cxy yx xy
U ili ies index
-.4
-.2
.0
.2
.4
.6
5 10 15 20 25 30 35
cxy yx xy
Cyclical consume goods index
Figu e 1
CANADA: Decomposed long- un co ela ion coe icien be ween ou pu g ow h and s ock p ice changes
-.1
.0
.1
.2
.3
.4
5 10 15 20 25 30 35
cxy yx xy
To al ma ke index
-.1
.0
.1
.2
.3
.4
5 10 15 20 25 30 35
cxy yx xy
To al non- inancial ma ke index
-.1
.0
.1
.2
.3
.4
5 10 15 20 25 30 35
cxy yx xy
Financial index
-.1
.0
.1
.2
.3
.4
5 10 15 20 25 30 35
cxy yx xy
Basic indus ies index
-.1
.0
.1
.2
.3
.4
5 10 15 20 25 30 35
cxy yx xy
Gene al indus ies index
-.2
-.1
.0
.1
.2
.3
.4
5 10 15 20 25 30 35
cxy yx xy
Cyclical se ices index
-.1
.0
.1
.2
.3
.4
.5
5 10 15 20 25 30 35
cxy yx xy
Non-cyclical se ices index
-.1
.0
.1
.2
.3
.4
5 10 15 20 25 30 35
cxy yx xy
In o ma ion echnology index
-.4
-.2
.0
.2
.4
.6
5 10 15 20 25 30 35
cxy yx xy
Cyclical consume goods index
-.1
.0
.1
.2
.3
.4
5 10 15 20 25 30 35
cxy yx xy
Non-cyclical consume goods index
Figu e 2
FRANCE: Decomposed long- un co ela ion coe icien be ween ou pu g ow h and s ock p ice changes