A Resolu ion o he Fishe Effec Puzzle: A Compa ison
o Es ima o s
Eka e ini Panopoulou∗
Na ional Uni e si y o I eland, Maynoo h and Uni e si y o Pi aeus, G eece
Feb ua y 2005
Abs ac
This pape a emp s a esolu ion o he Fishe effec puzzle in e ms o es ima o choice.
Using bo h sho - e m and long- e m in e es a es o 14 OECD coun ies, we ind ample
e idence suppo ing he exis ence o a long- un Fishe effec in which in e es a es mo e one-
o-one wi h in la ion. Ou esul s sugges ha he eason why he Fishe effec has no ound
suppo in e na ionally lies on he es ima ion me hod. When he hypo hesis o a uni coefficien
ela ing in e es a es o expec ed in la ionis es edwi hin heAu o eg essi eDis ibu edLag
(ADL) amewo k, which is in a ian o he in eg a ion p ope ies o he da a, he Fishe
effec easily su i es he empi ical e idence. Simila , bu less obus , esul s a e eached on
he g ounds o he P e-Whi ened Fully Modi ied Leas Squa es (PW-FMLS) o he Johansen’s
(JOH) es ima o s.
JEL Classi ica ion: E40; E50; C12; C13;
Keywo ds: Coin eg a ion Es ima o s; Fishe Effec ; ADL; DOLS; Small-sample p ope -
ies
Acknowledgmen s: Financial suppo om he G eek Minis y o Educa ion and he Eu-
opean Union unde “H aklei os” g an is g ea ly app ecia ed. I am g a e ul o A. An zoula os,
S. Kaly i is, G.Ha dou elis, D. Mallia opulos, M. Roche, M. Hu ley, N.Pi is, D. Thomakos, E.
Tza alis and semina pa icipan s a he IIIS Minicon e ence on In e na ional Financial In e-
g a ion, Na ional Uni e si y o I eland and he Uni e si y o Peloponesse o help ul sugges ions
and commen s. The usual disclaime applies.
∗Co espondence o: Eka e ini Panopoulou, Depa men o Economics, Na ional Uni e si y o I e-
land Maynoo h, Co.Kilda e, Republic o I eland. E-mail: [email protected]. Tel: 00353 1 7083793. Fax:
00353 1 7083934.
1
1 In oduc ion
A as li e a u e is de o ed o he size o he esponse o nominal in e es a es o
changes in expec ed in la ion, b oadly known as he Fishe effec .1The mone a y
neu ali y implica ions o diffe en Fishe effec alues unde lie his long-s anding
in e es in he opic. Mo e speci ically, long- un supe neu ali y o money is associa ed
wi h a coefficien ela ing in e es a es o expec ed in la ion equal o one, while a
alue below uni y implies subs an ial long- un non-neu ali ies.
In his ein, he s a iona i y o he ex-an e eal in e es a e has some impo an
implica ions. As sugges ed by he s anda d consump ion asse p icing model, eal
in e es a es should ollow he pa e n o consump ion g ow h, which is clea ly a
s a iona y a iable. Mo eo e , he neoclassical g ow h heo y based on dynamic op-
imiza ion o a ep esen a i e economic agen implies ha he eal a e should be
cons an in he s eady s a e, being p opo ional o he ep esen a i e consume ’s a e
o ime p e e ence. Un o una ely he e is no consensus among economis s abou he
ue size o he Fishe effec . The e a e se e al p oblems ha plague empi ical es i-
ma es o he Fishe effec . Da by (1975) in oduced he effec o axes on he size o
he Fishe effec . He a gued ha nominal in e es a es should inc ease by mo e han
he inc ease in expec ed in la ion o compensa e deb holde s o a lowe a e - ax e-
u n since in e es income is usually axed as o dina y income. In his case, we should
ob ain a Fishe effec es ima e g ea e han one. A second p oblem is he gene ally
unobse ed na u e o he expec ed in la ion a e. When ac ual ealized in la ion is used
o p oxy expec ed in la ion an e o s-in- a iables bias is in oduced on he es ima e o
he Fishe effec . Ano he issue in ol es he ime se ies p ope ies o he da a unde
conside a ion when es ima ing a ela ionship like he Fishe effec . The only case ha
s anda d leas squa es echniques a e alid is when he se ies a e second-o de s a ion-
a y. In he e en o in eg a ed a iables, he only way o es ablish a heo e ical Fishe
ela ionship is ia coin eg a ion echniques.
Finally, e en when applying he app op ia e coin eg a ion me hods, se e e p ob-
lems may a ise associa ed wi h he implemen a ion o coin eg a ion, such as he low
powe o coin eg a ion es s o he pe o mance o he a ious es ima o s in small
samples. C owde and Hoffman (1996) sugges ed ha he es ima o choice migh
accoun o he con adic o y e idence in he li e a u e. Speci ically, he au ho s a -
ibu e he diffe en conclusions eached in he li e a u e ega ding he ela ionship
be ween in la ion and in e es a es o he diffe ences in he small sample p ope ies
o he O dina y Leas Squa es (OLS), he Dynamic Leas Squa es (DOLS) and he
Johansen’s (JOH) maximum likelihood es ima o s. Mo e ecen ly, Capo ale and Pi is
(2004) show ha he es ima o s equen lyemployedinempi icals udies,namelyOLS
and Fully Modi ied Leas Squa es (FMLS), a e he ones wi h he leas desi able small
1See e.g. Coo ay, 2003 and he e e ences he ein.
2
sample p ope ies. The inabili y o hese es ima o s o p o ide efficien es ima es in
small samples is likely o be esponsible o he o e ejec ion o he Fishe hypo hesis.
Speci ically, he au ho s show ha when he es ima o s wi h he bes p ope ies a e
chosen, he e idence is s ongly suppo i e o he Fishe effec in he US.
In his s udy, we use bo h sho - e m and long- e m in e es a es and p o ide
in e na ional e idence on a long- un Fishe effec , i.e. ha in e es a es and in la ion
mo e one- o-one in he long- un o 14 OECD coun ies. Using a a ie y o asymp o -
ically efficien coin eg a ion es ima o s we a emp o explain he Fishe effec puzzle
in e ms o es ima o choice. We a ibu e he sca ce e idence o an in e na ional
Fishe effec in he li e a u e o he poo small sample pe o mance o he es ima o s
employed so a . We pa icula ly ocus on wo ypes o coin eg a ion es ima o s ha
a ise in he con ex o he Hend y-s yle Au o eg essi e Dis ibu ed Lag (ADL) models.
The i s ype is usually e e ed o as he DOLS es ima o (see S ock and Wa son,
1993) and a ises om a s a ic coin eg a ion equa ion augmen ed by cu en and pas
alues o he i s diffe ence o he eg esso . The second ype, he ADL es ima o
(see Pesa an and Shin, 1999), is based on he p ojec ion o he coin eg a ion e o on
he ull in o ma ion se , i.e. he cu en and pas alues o he i s diffe ence o he
eg esso plus he pas alues o he coin eg a ion e o . In an ex ensi e Mon e Ca lo
s udy, Panopoulou and Pi is (2004) highligh ed he po en ial pi alls o employing he
DOLS es ima o as opposed o he ADL one in small samples o a wide a ie y o Da a
Gene a ion P ocesses (DGPs). The au ho s showed ha he ADL es ima o , which
u ilizes he exac p ojec ion o he coin eg a ion e o on he ull in o ma ion se , offe s
a be e amewo k o es ima ing he coin eg a ion ec o han he DOLS es ima o
ha u ilizes an app oxima e p ojec ion o he coin eg a ion e o on in o ma ion p o-
ided only by he e o ha d i es he eg esso . To his end, he beha io o he
ADL es ima o seems o be he limi ing one o he DOLS es ima o . Fo compa ison
pu poses, we also include some o he commonly used coin eg a ion es ima o s, such as
he OLS and he semipa ame ic FMLS es ima o o Phillips and Hansen (1990) and
he Johansen’s maximum likelihood es ima o (1988, 1991).
The layou o his pape is as ollows: Sec ion 2 p o ides a b ie li e a u e e iew on
he Fishe effec and a discussion o he Fishe equa ion. Sec ion 3 ou lines he econo-
me ic me hodology used in he empi ical analysis. Sec ion 4 p esen s es ima es o
he Fishe equa ion ob ained by he ADL and DOLS es ima o s o bo h ou da ase s,
along wi h es ima es ob ained om he OLS, FMLS and JOH es ima o s. Sec ion 5
summa izes he main indings o he pape .
2 B ie li e a u e e iew
Ex an e eal in e es a es appea o be a key a iable when in es men - sa ings
decisions and asse p ices de e mina ion a e conside ed. Thei long- un beha io is
3
o en analyzed in he con ex o he Fishe (1930) ela ionship, linking nominal a es
o expec ed in la ion and equi ing ull adjus men o he o me o he la e . The
impo ance o his adjus men p ocess s ems om he ac ha pe manen shocks o
ei he in la ion o nominal a es should no be ansla ed in o pe manen dis u bances
o eal a es hemsel es, which would be p oblema ic in he con ex o s anda d models
o in e empo al asse p icing.
Howe e , hus a he empi ical e idence has no been suppo i e o he Fishe
ela ionship. Nume ous s udies ha e ound ha he slope coefficien in a eg ession o
in la ion agains nominal a es is signi ican ly diffe en om one, a leas o e ce ain
pe iods, (see e.g. Mishkin 1992 and E ans and Lewis, 1995).
Fo mally, he ‘Fishe effec ’ can be exp essed as:
i (m)=πe
(m)+ e
(m)(1)
whe e i (m)is he m-pe iod nominal in e es a e a ime , πe
(m)deno es he expec ed
a e o in la ion om ime o +m,and e
(m)is he ex-an e eal in e es a e.
Assuming a ional expec a ions (see, e.g. Mishkin, 1992), ealized in la ion is linked
o expec ed in la ion as ollows:
π (m)=πe
(m)+e (2)
whe e e is a whi e noise p ocess, o hogonal o πe
(m).I we u he assume ha he
p ocess ollowed by he eal in e es a e is a whi e noise p ocess wi h a mean equal o
, wea eable o es o heFishe effec in he con ex o he ollowing eg ession:
i (m)= +θπ (m)+ν (3)
The null hypo hesis o be es ed can ake he o m:
Fishe hypo hesis holds ⇔(i) ν is I(0) and (ii) θ=1.
The i s o hese condi ions, i.e. he condi ion ha i (m)and π (m)a e coin e-
g a ed p ocesses is suppo ed by he bulk o empi ical e idence in he li e a u e. On
he o he hand, when dealing wi h he second condi ion, es ima es o θappea o be
signi ican ly diffe en om uni y, leading o he Fishe effec puzzle.
Mishkin (1992) was one o he i s o sugges ha due o he appa en non-
s a iona i y o nominal in e es a es and in la ion a possible sou ce o he low Fishe
effec es ima es is he spu ious eg ession p oblem discussed by G ange and Newbold
(1974). He co ec ly poin ed ou ha he Fishe ela ion should be ea ed wi hin
he con ex o a coin eg a ed sys em, as in Engle and G ange (1987). Mishkin used
he Engle-G ange OLS p ocedu e o es ima e he Fishe effec bu did no de i e any
s ong conclusions due o he la ge s anda d e o s o he es ima ed pa ame e s.
Subsequen s udies used mo e efficien es ima ion p ocedu es and gene ally ound
4
suppo o a long- un Fishe ela ion in he U.S. E ans and Lewis (1995) used he
DOLS es ima o and C owde and Hoffman (1996) used he Johansen gaussian maxi-
mum likelihood es ima o . C owde and Hoffmann (1996) sugges ed ha he es ima o
choice migh accoun o he con adic o y e idence ga he ed so a . In pa icula , he
au ho s a gue ha diffe ences in he small sample p ope ies o he OLS, DOLS and
JOH es ima o s a e esponsible o he as ly diffe en conclusions eached in he li -
e a u e abou he ela ionship be ween in la ion and in e es a es. Thei analysis,
howe e , was much mo e limi ed han ou s as hey compa ed only h ee es ima o s in
e ms o small sample bias.
Mo e ecen ly, A kins and Coe (2002) ound e idence suppo ing he long- un
Fishe effec o bo h Canada and he US using a a ie y o in e es a es and he
ARDL bounds es de eloped by Pesa an e .al (2001) which is capable o es ing o
he exis ence o a long- un ela ionship ega dless o he in eg a ion p ope ies o he
unde lying se ies. Fahmy and Kandil (2003) con i med ha in la ion and in e es a es
exhibi common ends in he long- un and mo e in a one- o-one ela ion a long ho i-
zons, speci ically when he asse s’ ma u i y exceeds wo yea s. Thei da ase includes,
excep o US, UK, Ge many and Swi ze land.
Capo ale and Pi is (2004) employed i ually all a ailable single-equa ion es i-
ma o s and allowed o al e na i e da a equencies along wi h s uc u al b eaks.2
The au ho s examined whe he (i) diffe ences in he es ima e o θ om one can be a -
ibu ed o small sample bias and (ii) ejec ions o he null e lec he use o asymp o ic
c i ical alues a he han he empi ical ones. They ound e idence in a o o bo h
claims, which implies ha he Fishe hypo hesis su i es e en when less sa is ac o y
es ima o s a e employed p o ided ha he empi ical c i ical alues a e used. Choosing
he es ima o wi h he minimum bias and shi in he dis ibu ion o he associa ed
-s a is ics, alid in e ence can be conduc ed in suppo o he Fishe iden i y.
Howe e , hei s udy was con ined o he US, which is he coun y usually employed
in empi ical s udies on he Fishe hypo hesis. The e is some e idence, hough, on he
nominal in e es a es and in la ion ela ionship in o he indus ialized coun ies. Tes -
ing whe he he Fishe ela ionship holds in e na ionally is o in e es since a necessa y,
bu no sufficien , condi ion o eal in e es a es o be equalized in e na ionally is ha
he Fishe ela ion holds in each coun y indi idually. Rose (1988) examined he in-
eg a ion p ope ies o nominal in e es a es and in la ion o 18 OECD coun ies.
He concluded ha in la ion does no appea o ha e a uni oo , while nominal in-
e es a es do. By con as , Kous as and Se le is (1999) examined 10 indus ialized
coun ies and es ablished ha he condi ions o meaning ul Fishe effec s, i.e. ha
in la ion and in e es a es a e I(1) and coin eg a ed p ocesses, hold. The au ho s,
2These coin eg a ion es ima o s (mos o which a e asymp o ically efficien ) deal wi h he second
o de effec s (long- un co ela ion and endogenei y effec ) p esen in he OLS asymp o ic dis ibu ion,
ei he pa ame ically o non-pa ame ically.
5

howe e , we e no able o p o ide s ong e idence in suppo o he Fishe hypo hesis,
i.e. o es ablish a uni coefficien .
3 Econome ic Me hodology
In his sec ion, we conside wo asymp o ically efficien coin eg a ion es ima o s on
which ou analysis is based, namely he ADL and DOLS es ima o s. The la e is a
widely-used coin eg a ion es ima o sugges ed by Saikonnen (1991), Phillips and Lo e-
an (1991) and S ock and Wa son (1993), while he i s de eloped by Pesa an and
Shin (1999) is a ely employed in empi ical applica ions despi e i s supe io i y in many
aspec s. Nex , we show how hese es ima o s a e de i ed and compa e hei p ope -
ies. We also b ie ly discuss he OLS, FMLS and JOH es ima o s. To acili a e he
discussion, we employ he Phillips iangula ep esen a ion o a coin eg a ed sys em.
Le z and u be wo bi a ia e p ocesses, wi h z =[y ,x
]>and u =[u1 ,u
2 ]>.
We u he assume ha u is a VAR(1) p ocess, d i en by e =[e1 ,e
2 ]>and he
gene a ing mechanism o y is gi en by he sys em
y =θx +u1 (4)
∆x =u2 (5)
Ãu1
u2 !=Ãa11 a12
a21 a22 !Ãu1 −1
u2 −1!+Ãe1
e2 !(6)
and
Ãe1
e2 !˜NIID"Ã0
0!Ãσ11 σ12
σ12 σ22 !# (7)
o =1,2,...T.
Bo h eigen alues o he ma ix A=[aij],i,j =1,2a e assumed o be less han
one in modulus, in o de o y and x o be I(1) a iables, and he coin eg a ion e o
o be an I(0) p ocess. The long- un co a iance ma ix Ωand he one-sided co a iance
ma ix ∆,needed o de ine he asymp o ic nuisance pa ame e s, a e gi en by equa ions
(8) and (9), espec i ely
Ω=(I−A)−1Σ(I−A>)−1(8)
∆=G(I−A>)−1(9)
whe e Σdeno es he inno a ions co a iance ma ix o he VAR and Gis he uncondi-
ional co a iance ma ix o u gi en by,
ecG =(I−A⊗A)−1 ecΣ(10)
6
An ea ly esul by S ock (1987) shows ha he OLS es ima o o θob ained om
(4) is supe -consis en , ega dless o he p esence o empo al and/o con empo aneous
co ela ion be ween he eg ession e o , u1 ,and he e o ha d i es he eg esso ,
u2 .On he o he hand, in gene al, he asymp o ic dis ibu ion o he OLS es ima o o
θ alls ou side he Local Asymp o ic Mix u e o No mals (LAMN) amily and con ains
nuisance pa ame e s. The eason o he p esence o non-s anda d asymp o ics is ha
in he p esence o con empo aneous and empo al co ela ion be ween he elemen s o
u , wo ypes o second-o de asymp o ic effec s a e p esen in he limi ing dis ibu ion
o he OLS es ima o (see Phillips and Lo e an 1991): The i s is he nuisance pa a-
me e , ω12/ω22 ha desc ibes he “long- un co ela ion” effec , due o non-diagonali y
o he long un co a iance ma ix Ω=[ωij],i,j =1,2.The second is he nuisance
pa ame e δ21 =P∞
k=0 E(u20u1k) ha desc ibes he “endogenei y” effec .
In o de o emo e he second o de effec s pa ame ically, we mus employ a new
eg ession model whose e o e m is o hogonal o u2 and u2 −i,i=1,2,.... This can
be done by employing he condi ional expec a ion o u1 ei he on he cu en and pas
alues o u2 o on he cu en and pas alues o u2 plus he pas alues o u1 .The
i s and second condi ioning in o ma ion se s esul in he DOLS and ADL es ima o s,
espec i ely. Nex , we show how hese es ima o s a e ac ually de i ed, s a ing om
he la e .
3.1 The ADL es ima o
The ull sys em (4) and (5) wi h e o s speci ied by (6) - (7), implies he ollowing
condi ional densi y o y :
D(y |x ,z0
−1,λ
1)=N(θ1x +c1y −1+c2x −1+c3x −2,σ2
)(11)
whe e λ1≡(θ1,c
1,c
2,c
3,σ2
)and
θ1=θ+σ12
σ22
(12)
c1=a11 −a21
σ12
σ22
(13)
c2=a12 −σ12
σ22
(a22 +1−a21θ)−a11θ(14)
c3=(a22
σ12
σ22
−a12)(15)
σ2
ν=σ11 −σ2
12
σ22
(16)
This condi ional model can be w i en as he ADL(q, ) eg ession, wi h o de s (q, )=
(1,2):
y =θ1x +c1y −1+c2x −1+c3x −2+ν (17)
7
The new e o e m, , is now o hogonal o u2 ,u −1,u −2,...and i s a iance is gi en
by (16).
In he con ex o he ADL(1,2) model he coin eg a ion pa ame e θis equal o he
long- un mul iplie o y wi h espec o x , ha is
θ=θ1+c2+c3
1−c1
(18)
We can es ima e (17) by OLS and hen use (18) o ob ain an efficien es ima e o
θ. Howe e , addi ional compu a ions a e equi ed o ob ain he a iance o his es i-
ma e (see Bane jee e . al. 1993). A mo e con enien app oach, p oposed by Bewley
(1979), ans o ms he model (17) in such a way ha a poin es ima e o θand i s
a iance can be ob ained di ec ly. A e some algeb aic manipula ion, model (17) can
be equi alen ly w i en as:
y =δ0∆y +θx +λ0∆x +λ1∆x −1+η (19)
whe e
δ0=−c1
(1−c1)λ0=−c2+c3
(1−c1)λ1=−c3
(1−c1)η =1
(1−c1)ν
Es ima es o he coefficien s and hei s anda d e o s can be ob ained by using he
Ins umen al Va iables (IV) es ima o , wi h he o iginal ma ix o eg esso s, i.e. he
a iables in (17), being he ins umen al a iables (see Wickens and B eusch 1988).
This means ha he ADL es ima o o θis e y easy o apply since i in ol es only IV
es ima ion echniques.
3.2 The DOLS es ima o
The ADL model, de i ed abo e, may be hough o as a ising om p ojec ing u1 on
he ull in o ma ion se B=(u2 ,u −1,u −2,...), ha is
E(u1 |B)=σ12
σ22
e2 +a11u1 −1+a12u2 −1(20)
As al eady men ioned, he second-o de effec s can be deal wi h by p ojec ing u1 on a
subse o his se , namely A=(u2 ,u
2 −1,u
2 −2,...),A⊂B:The esul ing condi ional
expec a ion in ol es an in ini e sum,
E(u1 |A)=
∞
X
i=0
βiu2 −i(21)
whe e βia e unc ions o he pa ame e s in (6)-(7). This condi ional expec a ion does
no admi a pa simonious ep esen a ion analogous o (20). On he o he hand, i
allows o di ec subs i u ion o his exp ession in o (4), hus yielding he ollowing
8
model
y =θx +
∞
X
i=0
βi∆x −i+υ (22)
whe e υ is, in gene al, a se ially co ela ed e o e m. In pa icula , υ ollows he
AR(1) model
υ =γ2υ −1+ε (23)
whe e γ2is he MA coefficien in he ARMA (2,1) ep esen a ion o u2 .SimpleOLS
applied o (22) yields he DOLS(p) es ima o o S ock and Wa son (1993), whe e p
deno es he lag leng h o he i s diffe ences o he eg esso added o (22). The se ial
co ela ion o υ does no aise any se ious p oblems in he es ima ion o θ,p o ided
ha a consis en es ima o o he long- un a iance o υ is employed, such as he one
p oposed by Newey and Wes (1987). Al e na i ely, he applica ion o Gene alized
Leas Squa es (GLS) on (22), ensu es alid asymp o ic in e ences on θ.3In his case,
he es ima o in use is he DGLS(p) one.
In p ac ice, howe e , he second e m on he igh -hand side o (22) has o be
eplaced by an app oxima ion in which he in ini e sum is unca ed a i=p.The
esul ing model accommoda es a unca ion emainde ha is likely o inc ease he
bias o he DOLS(p) es ima o o θ. This bias g ows wi h he pe sis ence o he coin e-
g a ion e o . Inc easing he unca ion poin educes he DOLS bias, bu inc eases i s
a iance. Mo eo e , es ima ing (22) by OLS is no easible i p is oo la ge compa ed o
he sample size. Saikkonen (1991) speci ies an uppe bound o he a e a which p is
allowed o inc ease wi h he sample size T, which is gi en by he condi ion p3/T →0.
Ne e heless, his condi ion canno be used o de ine he op imal alue o p o any
gi en sample size.
On he con a y, he ADL es ima o does no accommoda e any unca ion emain-
de and mo e impo an ly, yields consis en es ima es o he long- un coefficien s ha
a e asymp o ically no mal i espec i e o whe he he unde lying eg esso s a e I(1) o
I(0). Finally, i is easy o show ha he only case ha he ADL and DOLS es ima o s
a e equi alen is his o a non-au oco ela ed e o in (4), which is a highly unlikely
case in he case o mac oeconomic applica ions. Speci ically, he coin eg a ion e o is
usually ound o exhibi a high deg ee o pe sis ence.
3.3 O he Coin eg a ion Es ima o s
The OLS es ima o : This is he o dina y leas squa e es ima o applied o he s a ic
equa ion (4).
The Fully Modi ied Leas Squa es (FMLS) es ima o : Phillips and Hansen
3No e ha in he case o a linea eg ession which in ol es an I(1) s ic ly exogeneous eg esso ,
he OLS is asymp o ically equi alen o he GLS es ima o (see K ame 1986, Pa k and Phillips 1988).
9
imi a e he one o he DOLS class o es ima o s, while signi ican gains eme ge om
he employmen o he p e-whi ened e sion o he FMLS es ima o . This es ima o
pe o ms almos as well as he ADL one. On he o he hand, he pe o mance o
JOH is a he ambiguous and leads o mixed esul s. The es ima es p oduced by his
es ima o a e p obably biased upwa ds leading o es ima es ha in many cases exceed
uni y signi ican ly.
Re e ences
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17
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in highe -o de in eg a ed sys ems, Econome ica, 61, 783-820.
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and he Es ima ion o T ans o med Reg ession Models, Economic Jou nal, 98,
(Con e ence 1988), 189-205.
18
19
Appendix: Tables
Table 1A: Es ima ion Resul s – Qua e ly sho - e m in e es a es
Coun y Aus alia Belgium Canada
Es ima o θ
ˆ s.e ( θ
ˆ)
- es
Ho: θ
ˆ=1 θ
ˆ s.e ( θ
ˆ)
- es
Ho: θ
ˆ=1 θ
ˆ s.e ( θ
ˆ)
- es
Ho: θ
ˆ=1
OLS 0.411 0.107 -5.537 0.433 0.116 -4.873 0.598 0.118 -3.415
ADL(1,2) 0.721 0.272 -1.028 0.722 0.414 -0.671 0.959 0.199 -0.202
JOH 1.294 0.241 1.218 1.351 0.312 1.124 1.195 0.151 1.291
FMLS 0.499 0.190 -2.628 0.573 0.194 -2.204 0.677 0.138 -2.334
PW-FMLS 0.891 0.204 -0.532 0.971 0.373 -0.079 1.101 0.188 0.535
DOLS 1 0.510 0.121 -4.069 0.509 0.152 -3.235 0.695 0.126 -2.417
DOLS 2 0.563 0.130 -3.360 0.540 0.170 -2.704 0.756 0.132 -1.853
DOLS 3 0.584 0.136 -3.053 0.551 0.183 -2.456 0.786 0.134 -1.592
DOLS 4 0.592 0.141 -2.903 0.548 0.189 -2.389 0.799 0.136 -1.481
DOLS 5 0.597 0.146 -2.770 0.549 0.193 -2.337 0.810 0.135 -1.408
DOLS 6 0.603 0.151 -2.639 0.555 0.190 -2.340 0.813 0.134 -1.391
DOLS 7 0.616 0.155 -2.485 0.570 0.183 -2.350 0.819 0.133 -1.360
DOLS 8 0.629 0.157 -2.365 0.590 0.173 -2.379 0.823 0.133 -1.329
DOLS 9 0.647 0.160 -2.212 0.608 0.166 -2.360 0.835 0.133 -1.235
DOLS 10 0.669 0.162 -2.047 0.620 0.169 -2.244 0.843 0.135 -1.164
DOLS 11 0.692 0.162 -1.897 0.622 0.177 -2.138 0.854 0.137 -1.071
DOLS 12 0.713 0.161 -1.784 0.615 0.185 -2.078 0.862 0.140 -0.991
DOLS 13 0.732 0.160 -1.670 0.617 0.196 -1.959 0.875 0.141 -0.887
DOLS 14 0.754 0.159 -1.546 0.636 0.203 -1.796 0.886 0.142 -0.804
DOLS 15 0.772 0.157 -1.446 0.659 0.211 -1.614 0.895 0.143 -0.734
DOLS 16 0.792 0.156 -1.337 0.687 0.219 -1.426 0.905 0.143 -0.668
DOLS 17 0.811 0.153 -1.233 0.732 0.224 -1.197 0.916 0.142 -0.594
DOLS 18 0.832 0.152 -1.106 0.776 0.225 -0.994 0.923 0.140 -0.554
DOLS 19 0.847 0.152 -1.008 0.813 0.224 -0.835 0.927 0.136 -0.542
DOLS 20 0.853 0.152 -0.968 0.853 0.218 -0.675 0.927 0.133 -0.549
DGLS 1 -0.021 0.055 -18.589 0.095 0.057 -15.950 0.116 0.050 -17.871
DGLS 2 0.153 0.084 -10.139 0.228 0.083 -9.290 0.253 0.074 -10.034
DGLS 3 0.289 0.114 -6.244 0.411 0.108 -5.470 0.406 0.104 -5.735
DGLS 4 0.368 0.132 -4.798 0.368 0.125 -5.075 0.505 0.124 -3.999
DGLS 5 0.364 0.149 -4.259 0.160 0.149 -5.658 0.643 0.137 -2.609
DGLS 6 0.299 0.164 -4.268 0.101 0.165 -5.464 0.581 0.155 -2.702
DGLS 7 0.267 0.182 -4.035 0.056 0.179 -5.277 0.634 0.168 -2.185
DGLS 8 0.184 0.200 -4.076 0.113 0.190 -4.661 0.609 0.179 -2.181
DGLS 9 0.050 0.223 -4.259 0.205 0.201 -3.965 0.706 0.183 -1.613
DGLS 10 0.072 0.240 -3.868 0.325 0.211 -3.198 0.657 0.194 -1.769
DGLS 11 0.195 0.247 -3.263 0.401 0.223 -2.683 0.671 0.203 -1.623
DGLS 12 0.270 0.254 -2.876 0.320 0.233 -2.921 0.609 0.217 -1.807
DGLS 13 0.186 0.275 -2.962 0.179 0.240 -3.417 0.641 0.220 -1.628
DGLS 14 0.376 0.264 -2.361 0.126 0.251 -3.488 0.686 0.227 -1.383
DGLS 15 0.395 0.270 -2.238 0.006 0.267 -3.717 0.629 0.244 -1.520
DGLS 16 0.361 0.285 -2.242 -0.161 0.281 -4.128 0.640 0.254 -1.421
DGLS 17 0.366 0.294 -2.157 -0.255 0.301 -4.170 0.769 0.241 -0.961
DGLS 18 0.498 0.284 -1.772 -0.145 0.319 -3.584 0.837 0.239 -0.683
DGLS 19 0.612 0.278 -1.396 -0.271 0.347 -3.664 0.857 0.244 -0.586
DGLS 20 0.468 0.311 -1.710 -0.169 0.373 -3.135 0.783 0.262 -0.828
No es
1. The Newey and Wes (1987) me hod is employed in he DOLS(p) es ima o .
2. An AR(1) model is assumed o he e o s in he DGLS(p) es ima o .
20
Table 1B: Es ima ion Resul s – Qua e ly sho - e m in e es a es
Coun y F ance Ge many I eland
Es ima o θ
ˆ s.e ( θ
ˆ)
- es
Ho: θ
ˆ=1 θ
ˆ s.e ( θ
ˆ)
- es
Ho: θ
ˆ=1 θ
ˆ s.e ( θ
ˆ)
- es
Ho: θ
ˆ=1
OLS 0.441 0.09 -6.185 0.444 0.095 -5.832 0.488 0.201 -2.544
ADL(1,2) 0.707 0.234 -1.249 0.787 0.366 -0.579 1.278 0.668 0.416
JOH 0.918 0.187 -0.440 1.575 0.157 3.671 1.535 0.854 0.626
FMLS 0.438 0.130 -4.336 0.526 0.157 -3.021 0.749 0.403 -0.621
PW-FMLS 0.627 0.228 -1.637 1.339 0.178 1.910 1.248 0.525 0.471
DOLS 1 0.475 0.094 -5.591 0.631 0.123 -2.995 0.687 0.260 -1.203
DOLS 2 0.492 0.098 -5.168 0.881 0.148 -0.805 0.820 0.269 -0.668
DOLS 3 0.500 0.104 -4.833 0.982 0.163 -0.109 0.840 0.312 -0.511
DOLS 4 0.499 0.110 -4.547 0.968 0.169 -0.192 0.773 0.330 -0.688
DOLS 5 0.505 0.116 -4.284 0.938 0.174 -0.355 0.795 0.310 -0.662
DOLS 6 0.507 0.120 -4.106 0.907 0.176 -0.528 0.814 0.307 -0.604
DOLS 7 0.512 0.122 -3.991 0.876 0.179 -0.693 0.816 0.314 -0.584
DOLS 8 0.521 0.123 -3.900 0.831 0.179 -0.948 0.904 0.307 -0.312
DOLS 9 0.530 0.122 -3.840 0.786 0.183 -1.169 1.047 0.320 0.148
DOLS 10 0.538 0.122 -3.780 0.749 0.191 -1.313 1.188 0.305 0.616
DOLS 11 0.547 0.123 -3.679 0.719 0.196 -1.430 1.237 0.305 0.777
DOLS 12 0.552 0.125 -3.590 0.669 0.193 -1.714 1.248 0.312 0.795
DOLS 13 0.551 0.125 -3.587 0.634 0.192 -1.910 1.318 0.302 1.054
DOLS 14 0.551 0.126 -3.581 0.617 0.195 -1.969 1.315 0.310 1.016
DOLS 15 0.556 0.128 -3.471 0.609 0.197 -1.987 1.294 0.315 0.932
DOLS 16 0.561 0.133 -3.307 0.579 0.198 -2.127 1.347 0.331 1.049
DOLS 17 0.563 0.139 -3.156 0.554 0.205 -2.181 1.358 0.313 1.142
DOLS 18 0.567 0.143 -3.035 0.529 0.213 -2.210 1.400 0.299 1.337
DOLS 19 0.577 0.145 -2.912 0.522 0.224 -2.135 1.498 0.283 1.760
DOLS 20 0.588 0.146 -2.824 0.504 0.231 -2.151 1.589 0.297 1.984
DGLS 1 0.272 0.073 -10.039 -0.045 0.042 -24.719 -0.167 0.263 -4.440
DGLS 2 0.410 0.096 -6.166 -0.057 0.078 -13.505 -0.307 0.429 -3.046
DGLS 3 0.584 0.114 -3.637 0.586 0.139 -2.980 0.865 0.577 -0.233
DGLS 4 0.501 0.128 -3.903 0.758 0.170 -1.422 1.112 0.577 0.195
DGLS 5 0.548 0.143 -3.165 0.772 0.195 -1.172 1.205 0.576 0.357
DGLS 6 0.503 0.155 -3.205 0.766 0.212 -1.103 1.208 0.579 0.360
DGLS 7 0.458 0.168 -3.232 0.867 0.230 -0.578 1.717 0.740 0.969
DGLS 8 0.477 0.175 -2.987 0.796 0.241 -0.849 1.673 0.714 0.942
DGLS 9 0.500 0.180 -2.784 0.716 0.244 -1.168 1.662 0.709 0.933
DGLS 10 0.476 0.189 -2.780 0.667 0.251 -1.328 1.664 0.689 0.964
DGLS 11 0.550 0.190 -2.369 0.753 0.261 -0.948 1.728 0.702 1.037
DGLS 12 0.637 0.195 -1.862 0.622 0.255 -1.482 1.676 0.746 0.905
DGLS 13 0.624 0.201 -1.871 0.541 0.252 -1.820 1.804 0.803 1.001
DGLS 14 0.565 0.210 -2.073 0.491 0.260 -1.957 1.913 0.849 1.075
DGLS 15 0.588 0.215 -1.916 0.520 0.267 -1.800 1.687 0.960 0.716
DGLS 16 0.609 0.218 -1.794 0.500 0.283 -1.766 1.985 1.014 0.971
DGLS 17 0.580 0.226 -1.857 0.475 0.294 -1.787 2.115 1.096 1.017
DGLS 18 0.550 0.237 -1.900 0.419 0.308 -1.885 2.431 1.227 1.166
DGLS 19 0.525 0.247 -1.922 0.440 0.322 -1.742 2.506 1.298 1.161
DGLS 20 0.480 0.263 -1.980 0.417 0.334 -1.746 2.441 1.200 1.201
No es
1. The Newey and Wes (1987) me hod is employed in he DOLS(p) es ima o .
2. An AR(1) model is assumed o he e o s in he DGLS(p) es ima o .
21
Table 1C: Es ima ion Resul s – Qua e ly sho - e m in e es a es
Coun y I aly Ne he lands No way
Es ima o θ
ˆ s.e ( θ
ˆ)
- es
Ho: θ
ˆ=1 θ
ˆ s.e ( θ
ˆ)
- es
Ho: θ
ˆ=1 θ
ˆ s.e ( θ
ˆ)
- es
Ho: θ
ˆ=1
OLS 0.480 0.122 -4.252 0.415 0.084 -6.964 0.547 0.106 -4.255
ADL(1,2) 0.999 0.239 -0.003 0.902 0.209 -0.469 1.135 0.573 0.235
JOH 1.014 0.164 0.088 0.998 0.190 -0.009 1.425 0.196 2.164
FMLS 0.594 0.108 -3.758 0.524 0.140 -3.405 0.795 0.177 -1.155
PW-FMLS 0.772 0.182 -1.250 0.806 0.192 -1.006 1.245 0.220 1.105
DOLS 1 0.532 0.119 -3.937 0.505 0.099 -5.027 0.712 0.143 -2.012
DOLS 2 0.568 0.113 -3.820 0.546 0.109 -4.174 0.799 0.164 -1.226
DOLS 3 0.595 0.101 -4.011 0.566 0.114 -3.827 0.855 0.173 -0.844
DOLS 4 0.615 0.091 -4.231 0.579 0.114 -3.676 0.876 0.171 -0.724
DOLS 5 0.634 0.081 -4.497 0.587 0.112 -3.689 0.911 0.162 -0.550
DOLS 6 0.645 0.075 -4.706 0.598 0.108 -3.713 0.963 0.148 -0.249
DOLS 7 0.657 0.070 -4.885 0.610 0.105 -3.722 0.999 0.134 -0.010
DOLS 8 0.659 0.070 -4.842 0.620 0.101 -3.747 1.014 0.125 0.115
DOLS 9 0.662 0.073 -4.644 0.629 0.098 -3.776 1.035 0.123 0.282
DOLS 10 0.659 0.075 -4.557 0.642 0.096 -3.737 1.056 0.124 0.451
DOLS 11 0.657 0.076 -4.499 0.659 0.094 -3.625 1.068 0.125 0.544
DOLS 12 0.659 0.076 -4.512 0.673 0.092 -3.542 1.071 0.126 0.562
DOLS 13 0.664 0.075 -4.490 0.689 0.092 -3.404 1.077 0.124 0.619
DOLS 14 0.673 0.074 -4.414 0.708 0.092 -3.186 1.094 0.118 0.790
DOLS 15 0.677 0.074 -4.343 0.729 0.093 -2.924 1.111 0.112 0.990
DOLS 16 0.676 0.076 -4.276 0.740 0.093 -2.779 1.115 0.109 1.055
DOLS 17 0.673 0.076 -4.313 0.748 0.095 -2.653 1.121 0.106 1.141
DOLS 18 0.671 0.077 -4.271 0.755 0.097 -2.533 1.129 0.102 1.270
DOLS 19 0.669 0.079 -4.187 0.764 0.098 -2.407 1.142 0.098 1.450
DOLS 20 0.673 0.079 -4.149 0.774 0.098 -2.301 1.148 0.097 1.522
DGLS 1 0.161 0.059 -14.144 0.174 0.045 -18.455 -0.014 0.045 -22.728
DGLS 2 0.235 0.101 -7.577 0.360 0.055 -11.606 -0.014 0.069 -14.757
DGLS 3 0.445 0.135 -4.105 0.423 0.070 -8.289 0.017 0.108 -9.076
DGLS 4 0.577 0.151 -2.812 0.511 0.082 -5.938 -0.074 0.130 -8.248
DGLS 5 0.666 0.154 -2.170 0.471 0.099 -5.357 -0.172 0.150 -7.816
DGLS 6 0.663 0.165 -2.043 0.458 0.113 -4.785 -0.164 0.175 -6.646
DGLS 7 0.791 0.180 -1.164 0.508 0.126 -3.903 0.076 0.201 -4.601
DGLS 8 0.853 0.179 -0.821 0.536 0.139 -3.327 0.165 0.218 -3.836
DGLS 9 0.949 0.199 -0.259 0.450 0.153 -3.603 0.214 0.239 -3.292
DGLS 10 1.094 0.225 0.418 0.365 0.170 -3.729 0.265 0.263 -2.793
DGLS 11 1.054 0.238 0.227 0.463 0.176 -3.048 0.517 0.294 -1.644
DGLS 12 0.958 0.223 -0.189 0.433 0.187 -3.041 0.310 0.315 -2.189
DGLS 13 0.931 0.224 -0.310 0.382 0.200 -3.086 -0.039 0.320 -3.252
DGLS 14 0.942 0.239 -0.243 0.429 0.206 -2.773 -0.145 0.343 -3.335
DGLS 15 0.951 0.243 -0.204 0.636 0.198 -1.833 -0.094 0.389 -2.811
DGLS 16 0.966 0.228 -0.148 0.794 0.206 -0.999 -0.160 0.416 -2.791
DGLS 17 0.965 0.232 -0.150 0.808 0.218 -0.884 -0.221 0.447 -2.732
DGLS 18 0.955 0.250 -0.179 0.764 0.226 -1.044 -0.394 0.480 -2.906
DGLS 19 0.956 0.264 -0.168 0.791 0.235 -0.891 1.176 0.232 0.760
DGLS 20 0.995 0.297 -0.016 0.776 0.244 -0.921 1.222 0.227 0.976
No es
1. The Newey and Wes (1987) me hod is employed in he DOLS(p) es ima o .
2. An AR(1) model is assumed o he e o s in he DGLS(p) es ima o .

22
Table 1D: Es ima ion Resul s – Qua e ly sho - e m in e es a es
Coun y Po ugal Sweden Swi ze land
Es ima o θ
ˆ s.e ( θ
ˆ)
- es
Ho: θ
ˆ=1 θ
ˆ s.e ( θ
ˆ)
- es
Ho: θ
ˆ=1 θ
ˆ s.e ( θ
ˆ)
- es
Ho: θ
ˆ=1
OLS 0.517 0.114 -4.255 0.579 0.077 -5.466 0.596 0.089 -4.501
ADL(1,2) 1.107 0.258 0.416 0.975 0.399 -0.063 0.860 0.209 -0.669
JOH 1.254 0.129 1.976 1.352 0.147 2.394 1.344 0.125 2.758
FMLS 0.716 0.157 -1.802 0.864 0.156 -0.867 0.776 0.149 -1.503
PW-FMLS 1.051 0.187 0.273 1.259 0.188 1.378 1.256 0.169 1.516
DOLS 1 0.651 0.124 -2.808 0.772 0.094 -2.437 0.742 0.100 -2.573
DOLS 2 0.866 0.119 -1.125 0.891 0.099 -1.095 0.858 0.105 -1.349
DOLS 3 0.906 0.099 -0.946 0.970 0.100 -0.303 0.913 0.118 -0.737
DOLS 4 0.921 0.090 -0.880 0.992 0.100 -0.077 0.915 0.121 -0.702
DOLS 5 0.914 0.091 -0.941 1.009 0.098 0.094 0.906 0.124 -0.762
DOLS 6 0.913 0.093 -0.943 1.042 0.092 0.457 0.892 0.128 -0.840
DOLS 7 0.913 0.094 -0.927 1.070 0.091 0.777 0.880 0.136 -0.887
DOLS 8 0.927 0.094 -0.785 1.071 0.092 0.771 0.874 0.139 -0.910
DOLS 9 0.935 0.094 -0.694 1.072 0.093 0.775 0.874 0.141 -0.897
DOLS 10 0.934 0.095 -0.701 1.075 0.096 0.783 0.884 0.137 -0.850
DOLS 11 0.933 0.096 -0.697 1.077 0.097 0.794 0.876 0.133 -0.934
DOLS 12 0.934 0.098 -0.671 1.078 0.099 0.784 0.848 0.130 -1.170
DOLS 13 0.944 0.098 -0.569 1.078 0.101 0.778 0.820 0.130 -1.388
DOLS 14 0.950 0.098 -0.508 1.083 0.102 0.809 0.807 0.132 -1.471
DOLS 15 0.947 0.101 -0.531 1.093 0.102 0.909 0.791 0.134 -1.554
DOLS 16 0.942 0.106 -0.553 1.103 0.100 1.026 0.788 0.141 -1.503
DOLS 17 0.947 0.109 -0.493 1.114 0.096 1.191 0.774 0.154 -1.467
DOLS 18 0.962 0.110 -0.344 1.124 0.091 1.371 0.759 0.170 -1.414
DOLS 19 0.981 0.110 -0.168 1.131 0.088 1.491 0.742 0.185 -1.396
DOLS 20 0.992 0.110 -0.074 1.143 0.083 1.719 0.737 0.197 -1.336
DGLS 1 -0.032 0.043 -23.845 -0.026 0.048 -21.275 0.075 0.048 -19.282
DGLS 2 -0.065 0.088 -12.078 -0.116 0.077 -14.520 0.020 0.078 -12.616
DGLS 3 0.093 0.159 -5.707 0.013 0.121 -8.185 0.383 0.120 -5.142
DGLS 4 0.352 0.188 -3.442 0.045 0.149 -6.431 0.624 0.145 -2.594
DGLS 5 0.460 0.199 -2.718 -0.127 0.164 -6.886 0.659 0.169 -2.020
DGLS 6 1.054 0.125 0.431 -0.018 0.185 -5.509 0.647 0.185 -1.908
DGLS 7 1.101 0.134 0.749 0.275 0.218 -3.329 0.553 0.200 -2.236
DGLS 8 1.128 0.141 0.912 0.363 0.247 -2.582 0.499 0.214 -2.345
DGLS 9 1.159 0.149 1.065 0.223 0.271 -2.868 0.471 0.224 -2.365
DGLS 10 1.170 0.157 1.083 0.960 0.221 -0.182 0.568 0.240 -1.800
DGLS 11 1.198 0.173 1.143 1.059 0.212 0.279 0.684 0.261 -1.209
DGLS 12 1.177 0.166 1.064 1.077 0.220 0.349 0.652 0.277 -1.258
DGLS 13 1.158 0.161 0.984 1.077 0.223 0.345 0.491 0.284 -1.792
DGLS 14 1.181 0.179 1.013 1.054 0.218 0.248 0.461 0.299 -1.802
DGLS 15 1.249 0.215 1.161 0.988 0.237 -0.051 0.364 0.306 -2.078
DGLS 16 1.194 0.208 0.934 0.037 0.396 -2.434 0.386 0.325 -1.890
DGLS 17 1.184 0.217 0.848 -0.043 0.419 -2.487 0.335 0.344 -1.934
DGLS 18 1.219 0.230 0.950 1.036 0.224 0.161 0.317 0.366 -1.866
DGLS 19 1.158 0.224 0.706 1.125 0.184 0.678 0.220 0.378 -2.065
DGLS 20 1.190 0.255 0.746 1.183 0.155 1.183 0.029 0.396 -2.455
No es
1. The Newey and Wes (1987) me hod is employed in he DOLS(p) es ima o .
2. An AR(1) model is assumed o he e o s in he DGLS(p) es ima o .
23
Table 1E: Es ima ion Resul s – Qua e ly sho - e m in e es a es
Coun y UK US
Es ima o θ
ˆ s.e ( θ
ˆ)
- es
Ho: θ
ˆ=1 θ
ˆ s.e ( θ
ˆ)
- es
Ho: θ
ˆ=1
OLS 0.416 0.052 -11.337 0.696 0.092 -3.301
ADL(1,2) 0.912 0.137 -0.645 1.053 0.197 0.267
JOH 1.092 0.105 0.874 1.451 0.174 2.599
FMLS 0.583 0.119 -3.503 0.802 0.149 -1.326
PW-FMLS 0.926 0.149 -0.493 1.218 0.165 1.322
DOLS 1 0.602 0.081 -4.933 0.783 0.100 -2.163
DOLS 2 0.691 0.090 -3.455 0.846 0.109 -1.414
DOLS 3 0.746 0.102 -2.493 0.872 0.114 -1.121
DOLS 4 0.748 0.101 -2.488 0.887 0.122 -0.931
DOLS 5 0.751 0.101 -2.472 0.900 0.129 -0.779
DOLS 6 0.764 0.097 -2.440 0.917 0.134 -0.618
DOLS 7 0.777 0.091 -2.461 0.930 0.140 -0.502
DOLS 8 0.781 0.088 -2.491 0.947 0.146 -0.363
DOLS 9 0.783 0.088 -2.478 0.962 0.148 -0.256
DOLS 10 0.779 0.089 -2.481 0.977 0.150 -0.156
DOLS 11 0.780 0.089 -2.478 0.990 0.154 -0.066
DOLS 12 0.780 0.089 -2.456 1.004 0.157 0.024
DOLS 13 0.781 0.090 -2.442 1.012 0.158 0.077
DOLS 14 0.781 0.090 -2.427 1.025 0.158 0.161
DOLS 15 0.781 0.090 -2.431 1.037 0.160 0.231
DOLS 16 0.783 0.090 -2.408 1.056 0.161 0.346
DOLS 17 0.786 0.090 -2.390 1.077 0.163 0.471
DOLS 18 0.783 0.092 -2.372 1.089 0.165 0.540
DOLS 19 0.779 0.094 -2.348 1.096 0.166 0.581
DOLS 20 0.775 0.096 -2.333 1.110 0.168 0.654
DGLS 1 0.041 0.036 -26.561 0.158 0.059 -14.185
DGLS 2 0.120 0.052 -16.974 0.357 0.094 -6.871
DGLS 3 0.460 0.075 -7.241 0.549 0.116 -3.900
DGLS 4 0.440 0.087 -6.462 0.616 0.133 -2.888
DGLS 5 0.396 0.096 -6.296 0.634 0.143 -2.560
DGLS 6 0.371 0.110 -5.738 0.718 0.152 -1.863
DGLS 7 0.578 0.121 -3.478 0.687 0.162 -1.936
DGLS 8 0.710 0.120 -2.413 0.737 0.170 -1.547
DGLS 9 0.835 0.118 -1.402 0.761 0.179 -1.339
DGLS 10 0.736 0.132 -1.996 0.746 0.192 -1.324
DGLS 11 0.712 0.146 -1.972 0.704 0.208 -1.423
DGLS 12 0.789 0.142 -1.491 0.827 0.214 -0.809
DGLS 13 0.800 0.146 -1.373 0.826 0.225 -0.772
DGLS 14 0.852 0.145 -1.020 0.877 0.233 -0.528
DGLS 15 0.892 0.151 -0.716 0.772 0.257 -0.887
DGLS 16 0.907 0.160 -0.584 0.718 0.277 -1.021
DGLS 17 0.890 0.161 -0.686 0.981 0.253 -0.074
DGLS 18 0.885 0.162 -0.709 1.075 0.257 0.291
DGLS 19 0.910 0.172 -0.524 1.025 0.270 0.092
DGLS 20 0.962 0.200 -0.191 1.026 0.279 0.092
No es
1. The Newey and Wes (1987) me hod is employed in he DOLS(p) es ima o .
2. An AR(1) model is assumed o he e o s in he DGLS(p) es ima o .
24
Table 2A: Es ima ion Resul s – Annual long- e m in e es a es
Coun y Aus alia Belgium Canada
Es ima o θ
ˆ s.e ( θ
ˆ)
- es
Ho: θ
ˆ=1 θ
ˆ s.e ( θ
ˆ)
- es
Ho: θ
ˆ=1 θ
ˆ s.e ( θ
ˆ)
- es
Ho: θ
ˆ=1
OLS 0.251 0.185 -4.062 0.450 0.165 -3.345 0.574 0.151 -2.821
ADL(1,2) 1.166 0.353 0.469 0.761 0.356 -0.672 1.032 0.254 0.126
JOH 1.561 0.313 1.792 1.779 0.372 2.093 1.068 0.178 0.384
FMLS 0.368 0.170 -3.717 0.714 0.128 -2.241 0.900 0.215 -0.464
PW-FMLS 1.337 0.296 1.140 1.007 0.203 0.032 1.234 0.205 1.142
DOLS 1 0.314 0.197 -3.488 0.535 0.193 -2.415 0.661 0.141 -2.398
DOLS 2 0.507 0.160 -3.083 0.598 0.214 -1.879 0.734 0.144 -1.841
DOLS 3 0.623 0.172 -2.190 0.641 0.210 -1.713 0.826 0.148 -1.175
DOLS 4 0.687 0.178 -1.761 0.710 0.202 -1.434 0.856 0.132 -1.092
DOLS 5 0.745 0.173 -1.472 0.760 0.178 -1.344 0.882 0.107 -1.097
DOLS 6 0.814 0.149 -1.249 0.827 0.140 -1.238 0.909 0.082 -1.099
DOLS 7 0.898 0.125 -0.817 0.887 0.108 -1.043 0.932 0.080 -0.856
DOLS 8 0.955 0.106 -0.429 0.914 0.097 -0.890 0.961 0.089 -0.436
DOLS 9 1.019 0.090 0.209 0.949 0.089 -0.574 0.963 0.085 -0.438
DOLS 10 1.067 0.090 0.744 0.968 0.097 -0.334 0.964 0.089 -0.407
DOLS 11 1.106 0.083 1.284 0.962 0.119 -0.325 0.981 0.101 -0.193
DOLS 12 1.117 0.082 1.435 0.955 0.141 -0.321 0.989 0.104 -0.109
DOLS 13 1.125 0.097 1.286 0.924 0.171 -0.445 1.039 0.119 0.326
DOLS 14 1.144 0.117 1.230 0.911 0.197 -0.451 1.083 0.147 0.561
DOLS 15 1.146 0.153 0.954 0.856 0.215 -0.669 1.082 0.178 0.462
DOLS 16 1.151 0.154 0.981 0.781 0.211 -1.039 1.088 0.209 0.419
DOLS 17 1.176 0.160 1.098 0.820 0.235 -0.767 1.096 0.234 0.409
DOLS 18 1.192 0.165 1.162 0.883 0.254 -0.463 1.071 0.259 0.273
DOLS 19 1.271 0.182 1.491 1.030 0.312 0.097 1.110 0.333 0.330
DOLS 20 1.220 0.233 0.941 1.268 0.373 0.719 1.193 0.411 0.470
DGLS 1 0.174 0.058 -14.216 0.212 0.075 -10.572 0.234 0.083 -9.285
DGLS 2 0.298 0.089 -7.887 0.355 0.110 -5.882 0.441 0.110 -5.065
DGLS 3 0.315 0.115 -5.982 0.276 0.128 -5.635 0.579 0.130 -3.231
DGLS 4 0.388 0.137 -4.469 0.243 0.186 -4.079 0.633 0.161 -2.278
DGLS 5 0.385 0.161 -3.825 0.223 0.224 -3.479 0.700 0.163 -1.843
DGLS 6 0.448 0.174 -3.169 0.436 0.243 -2.327 0.791 0.173 -1.207
DGLS 7 0.659 0.174 -1.961 0.785 0.201 -1.071 0.859 0.160 -0.885
DGLS 8 0.808 0.143 -1.343 0.812 0.213 -0.886 0.916 0.104 -0.810
DGLS 9 0.955 0.104 -0.437 0.924 0.158 -0.480 0.925 0.101 -0.736
DGLS 10 1.050 0.079 0.634 1.046 0.163 0.284 0.971 0.125 -0.232
DGLS 11 1.110 0.075 1.472 1.088 0.175 0.501 0.988 0.131 -0.091
DGLS 12 1.113 0.082 1.378 0.971 0.189 -0.156 0.983 0.148 -0.116
DGLS 13 1.115 0.088 1.306 0.974 0.218 -0.122 1.058 0.163 0.358
DGLS 14 1.138 0.099 1.387 1.090 0.244 0.367 1.085 0.177 0.481
DGLS 15 1.141 0.105 1.337 1.036 0.268 0.133 1.088 0.197 0.448
DGLS 16 1.135 0.127 1.062 0.969 0.318 -0.099 1.126 0.241 0.523
DGLS 17 1.163 0.157 1.041 1.000 0.365 0.000 1.151 0.267 0.565
DGLS 18 1.170 0.192 0.885 1.015 0.456 0.033 1.196 0.334 0.586
DGLS 19 1.279 0.236 1.182 1.452 0.414 1.091 1.408 0.407 1.002
DGLS 20 1.334 0.267 1.252 1.912 0.414 2.205 1.579 0.530 1.092
No es
1. The Newey and Wes (1987) me hod is employed in he DOLS(p) es ima o .
2. An AR(1) model is assumed o he e o s in he DGLS(p) es ima o .
25
Table 2B: Es ima ion Resul s – Annual long- e m in e es a es
Coun y F ance Ge many I eland
Es ima o θ
ˆ s.e ( θ
ˆ)
- es
Ho: θ
ˆ=1 θ
ˆ s.e ( θ
ˆ)
- es
Ho: θ
ˆ=1 θ
ˆ s.e ( θ
ˆ)
- es
Ho: θ
ˆ=1
OLS 0.334 0.151 -4.425 0.615 0.092 -4.196 0.551 0.054 -8.295
ADL(1,2) 0.767 0.283 -0.824 0.675 0.205 -1.587 0.686 0.127 -2.470
JOH 1.185 0.186 0.996 0.818 0.1383 -1.317 0.892 0.109 -0.993
FMLS 0.515 0.143 -3.397 1.136 0.277 0.490 0.833 0.156 -1.071
PW-FMLS 0.870 0.168 -0.772 1.622 0.303 2.052 1.047 0.158 0.299
DOLS 1 0.421 0.170 -3.398 0.645 0.098 -3.614 0.577 0.060 -7.064
DOLS 2 0.529 0.157 -3.002 0.662 0.119 -2.844 0.646 0.069 -5.138
DOLS 3 0.640 0.142 -2.541 0.613 0.130 -2.973 0.687 0.068 -4.588
DOLS 4 0.674 0.136 -2.392 0.574 0.147 -2.902 0.706 0.065 -4.554
DOLS 5 0.729 0.134 -2.032 0.604 0.151 -2.629 0.726 0.062 -4.440
DOLS 6 0.778 0.132 -1.687 0.618 0.144 -2.643 0.730 0.060 -4.520
DOLS 7 0.810 0.133 -1.424 0.653 0.145 -2.399 0.754 0.057 -4.337
DOLS 8 0.836 0.135 -1.218 0.705 0.131 -2.252 0.774 0.054 -4.195
DOLS 9 0.947 0.136 -0.389 0.766 0.119 -1.971 0.780 0.052 -4.208
DOLS 10 0.994 0.124 -0.049 0.813 0.135 -1.393 0.813 0.054 -3.446
DOLS 11 1.043 0.125 0.341 0.842 0.164 -0.963 0.842 0.056 -2.843
DOLS 12 1.082 0.134 0.614 0.811 0.200 -0.949 0.866 0.061 -2.188
DOLS 13 1.114 0.145 0.782 0.793 0.269 -0.768 0.864 0.075 -1.805
DOLS 14 1.105 0.147 0.715 0.847 0.322 -0.477 0.927 0.099 -0.732
DOLS 15 1.131 0.163 0.800 0.889 0.397 -0.281 0.884 0.119 -0.976
DOLS 16 1.131 0.161 0.814 0.852 0.480 -0.309 0.857 0.089 -1.611
DOLS 17 0.997 0.177 -0.020 0.769 0.474 -0.487 0.804 0.093 -2.116
DOLS 18 1.068 0.217 0.313 0.776 0.394 -0.569 0.806 0.094 -2.067
DOLS 19 1.178 0.227 0.784 1.149 0.248 0.599 0.727 0.124 -2.203
DOLS 20 1.478 0.255 1.872 1.141 0.216 0.652 0.755 0.164 -1.500
DGLS 1 0.147 0.063 -13.457 0.567 0.126 -3.436 0.319 0.087 -7.809
DGLS 2 0.255 0.089 -8.395 0.698 0.149 -2.036 0.367 0.108 -5.886
DGLS 3 0.392 0.117 -5.218 0.646 0.167 -2.128 0.534 0.110 -4.222
DGLS 4 0.372 0.140 -4.485 0.523 0.180 -2.651 0.612 0.104 -3.746
DGLS 5 0.441 0.171 -3.270 0.519 0.195 -2.464 0.683 0.095 -3.335
DGLS 6 0.639 0.184 -1.970 0.569 0.220 -1.965 0.675 0.095 -3.411
DGLS 7 0.695 0.191 -1.595 0.510 0.258 -1.896 0.699 0.081 -3.694
DGLS 8 0.777 0.134 -1.672 0.640 0.265 -1.361 0.738 0.071 -3.689
DGLS 9 0.857 0.143 -1.000 0.709 0.275 -1.058 0.751 0.070 -3.552
DGLS 10 0.891 0.173 -0.629 0.823 0.284 -0.625 0.795 0.069 -2.988
DGLS 11 0.968 0.146 -0.222 0.794 0.292 -0.706 0.820 0.074 -2.445
DGLS 12 1.028 0.132 0.212 0.769 0.318 -0.725 0.845 0.080 -1.952
DGLS 13 1.092 0.144 0.639 0.744 0.385 -0.665 0.844 0.092 -1.693
DGLS 14 1.060 0.175 0.343 0.730 0.420 -0.643 0.887 0.116 -0.976
DGLS 15 1.046 0.168 0.273 0.903 0.535 -0.181 0.863 0.099 -1.382
DGLS 16 1.104 0.196 0.530 1.017 0.578 0.030 0.834 0.110 -1.503
DGLS 17 1.049 0.247 0.200 0.976 0.500 -0.049 0.831 0.131 -1.296
DGLS 18 1.013 0.343 0.039 1.365 0.420 0.869 0.777 0.146 -1.532
DGLS 19 0.844 0.501 -0.310 1.590 0.571 1.035 0.759 0.188 -1.285
DGLS 20 1.108 0.533 0.202 1.273 0.526 0.520 0.928 0.191 -0.376
No es
1. The Newey and Wes (1987) me hod is employed in he DOLS(p) es ima o .
2. An AR(1) model is assumed o he e o s in he DGLS(p) es ima o .