Van Eyden, Reneé; Gup a, Rangan; Sheng, Xin; Nielsen, Joshua
A icle
P edic ing mul i-scale posi i e and nega i e s ock ma ke
bubbles in a panel o G7 coun ies: The ole o oil p ice
unce ain y
Economies
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MDPI – Mul idisciplina y Digi al Publishing Ins i u e, Basel
Sugges ed Ci a ion: Van Eyden, Reneé; Gup a, Rangan; Sheng, Xin; Nielsen, Joshua (2025) : P edic ing
mul i-scale posi i e and nega i e s ock ma ke bubbles in a panel o G7 coun ies: The ole o oil
p ice unce ain y, Economies, ISSN 2227-7099, MDPI, Basel, Vol. 13, Iss. 2, pp. 1-25,
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Ci a ion: an Eyden, R., Gup a, R.,
Sheng, X., & Nielsen, J. (2025).
P edic ing Mul i-Scale Posi i e and
Nega i e S ock Ma ke Bubbles in a
Panel o G7 Coun ies: The Role o Oil
P ice Unce ain y. Economies,13(2), 24.
h ps://doi.o g/10.3390/
economies13020024
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A icle
P edic ing Mul i-Scale Posi i e and Nega i e S ock Ma ke
Bubbles in a Panel o G7 Coun ies: The Role o Oil P ice
Unce ain y
Reneé an Eyden 1,* , Rangan Gup a 1, Xin Sheng 2and Joshua Nielsen 3
1Depa men o Economics, Uni e si y o P e o ia, P i a e Bag X20, Ha ield 0028, Sou h A ica;
[email p o ec ed]
2Lo d Ashc o In e na ional Business School, Anglia Ruskin Uni e si y, Chelms o d CM1 1SQ, UK;
[email p o ec ed]
3
Boulde In es men Technologies, Limi ed Liabili y Company, 1942 B oadway Sui e 314C, Boulde , CO 80302,
USA; [email p o ec ed]
*Co espondence: [email p o ec ed]
Abs ac : While he e is a la ge body o li e a u e on oil unce ain y-equi y p ices and/o
e u ns nexus, an associa ed impo an ques ion o how oil ma ke unce ain y a ec s
s ock ma ke bubbles emains unanswe ed. In his pape , we i s use he Mul i-Scale
Log-Pe iodic Powe Law Singula i y Con idence Indica o (MS-LPPLS-CI) app oach o
de ec bo h posi i e and nega i e bubbles in he sho -, medium- and long- e m s ock
ma ke s o he G7 coun ies. While de ec ing majo c ashes and booms in he se en s ock
ma ke s o e he mon hly pe iod o Feb ua y 1973 o May 2020, we also obse e simila
iming o s ong (posi i e and nega i e) LPPLS-CIs ac oss he G7, sugges ing synch onized
boom-bus cycles. Gi en his, we nex apply dynamic he e ogeneous coe icien s panel
da abased eg essions o analyze he p edic i e impac o a model- ee obus me ic o
oil p ice unce ain y on he bubbles indica o s. A e con olling o he impac s o ou pu
g ow h, in la ion, and mone a y policy, we ind ha oil p ice unce ain y p edic s a dec ease
in all he ime scales and coun ies o he posi i e bubbles and inc eases s ongly in he
medium e m o i e coun ies (and weakly he sho - e m) nega i e LPPLS-CIs. The
agg ega e indings con inue o hold wi h he inclusion o in es o sen imen indica o s.
Ou esul s ha e impo an implica ions o bo h in es o s and policymake s, as he highe
(lowe ) oil p ice unce ain y can lead o a c ash ( eco e y) in a bullish (bea ish) ma ke .
Keywo ds: mul i-scale bubbles; oil p ice unce ain y; panel da a eg essions; G7 s ock ma ke s
JEL Classi ica ion: C22; C32; C33; G15; Q02
1. In oduc ion
As poin ed ou by (Be nanke,1983) and (Pindyck,1991), in es men unde unce ain y
and eal op ions implies ha high oil p ice unce ain y c ea es cyclical luc ua ions in
in es men by lowe ing he i ms’ incen i e o cu en in es men . This, in u n, a ec s
cash lows gene a ed by a i m and he discoun a e used o calcula e s ock p ices and,
hence, nega i ely impac s s ock p ices and/o s ock e u ns (Swa ay & Salisu,2018;Chen &
Demi e ,2022). Mo eo e , since s ock p ices a e he sum o discoun ed cash lows, including
di idends, oil p ice unce ain y can ad e sely a ec s ock p ices by dec easing he o e all
p o i ha a i m gene ally uses o pay di idends, wi h his esul ing om he ac ha
i ms need o bea addi ional cos s o a oid isk associa ed wi h oil p ice unce ain y
Economies 2025,13, 24 h ps://doi.o g/10.3390/economies13020024
Economies 2025,13, 24 2 o 25
(Demi e e al.,2015). The heo e ical p edic ion ha oil p ice unce ain y nega i ely d i es
in e na ional s ock p ices and o / e u ns ia he in es men and di idends channels has
been widely empi ically e alua ed (see, o example, Sado sky,1999;Bashe & Sado sky,
2006;Masih e al.,2011;Alsalman,2016;Diaz e al.,2016;Bass,2017;Bena ides e al.,2019;
Rahman,2021).
While exis ing s udies end o ag ee ha oil unce ain y would ad e sely impac
equi y p ices and/o e u ns, an impo an ques ion would be how i a ec s s ock ma ke
bubbles, i.e., i s boom-bus cycles. In ui i ely, i s ock p ices a e accele a ing away om
hei undamen al alue, highe (lowe ) oil unce ain y is likely o lead o a bu s o he
bubble ( u he g ow h) in he ma ke . While he decline in s ock p ices would con inue in
he wake o highe oil unce ain y, a ally could be wi nessed when oil p ice unce ain y
declines. Mo eo e , (Zhang & Wong,2023) poin ed ou ha oil p ice unce ain y nega i ely
impac s s ock liquidi y, which, in u n, is cen al o he e icien unc ioning o ade
and in es o con idence in he inancial ma ke s. Na u ally, de e io a ing (imp o ing)
in es men con idence ollowing highe (lowe ) oil unce ain y could also lead o a collapse
( eco e y) o he s ock ma ke (see Sche bina & Schlusche,2014) o de ailed discussions o
he heo e ical models based on in es o disag eemen , eedback ading, and biased sel -
a ibu ion, used o ela e in es o sen imen o con idence o bubbles). Unde s andably,
wi h emendous luc ua ions in oil p ices wi nessed since he Global Financial C isis,
wha we p opose o in es iga e in his pape is pe inen om he pe spec i e o no only
in es o s bu also policymake s, as bubbles a e known o his o ically no only impac
economic ac i i y (Reinha & Rogo ,2009;Jo dàe al.,2015) bu impac wel a e also
(Na ayan e al.,2016).
Agains his backd op, we aim o analyze he e ec o a obus me ic o oil unce ain y
on s ock ma ke bubbles o he G7 coun ies (i.e., Canada, F ance, Ge many, I aly, Japan, he
Uni ed Kingdom (UK), and he Uni ed S a es (US)) o e he mon hly pe iod o Feb ua y
1973 o May 2020 in a panel da a se ing. The choice o he G7 is no only d i en by he
a ailabili y o da a ha allows us o co e nea ly i e decades o ex eme mo emen s in
he s ock ma ke s o hese de eloped economies bu also due o he ac ha he G7 bloc
accoun s o nea ly wo- hi ds o global ne weal h and nea ly hal o wo ld ou pu , and
hence, dynamics o bubbles in hese s ock ma ke s a e likely o ha e wo ldwide spillo e
e ec s and impac he sus ainabili y o he global inancial sys em (Das e al.,2019). A
he same ime, he decision o ely on panel da a eg essions is mo i a ed by he high
deg ee o synch oniza ion o he indica o s o he bubbles o hese coun ies, which we
discuss in de ail below. Bu e en hough we conduc he es ima ion in a panel se ing, we
allow o he e ogeneous esponses o bubbles o oil unce ain y (and o he con ols) by
u ilizing he Random Coe icien s (RC) app oach o (Swamy,1970) o de i e bo h o e all
and coun y-speci ic esul s.
As a as de ec ing bubbles, we no only use he Log-Pe iodic Powe Law Singula i y
(LPPLS) model, o iginally de eloped by (Johansen e al.,1999,2000;So ne e,2003) o
bo h posi i e (upwa d accele a ing p ice ollowed by a c ash) and nega i e (downwa d
accele a ing p ice ollowed by a ally) bubbles, bu we also apply he Mul i-Scale LPPLS
Con idence Indica o s (MS-LPPLS-CI) o (Demi e e al.,2019) o cha ac e ize posi i e and
nega i e bubbles a di e en ime scales, i.e., sho -, medium- and long- e m, co esponding
o es ima ion windows associa ed wi h ading ac i i ies o e one o h ee mon hs, h ee
mon hs o a yea , and one yea o wo yea s, espec i ely. No e ha he iden i ica ion o
bo h posi i e and nega i e mul i-scale bubbles is no possible based on o he exis ing wide
a ay o s a is ical es s (see Balcila e al.,2016;So ne e e al.,2018) o de ailed e iews),
which poin s o he sui abili y and added alue o ou applied me hodology. In ac , we
conside his as impo an because i would allow us o gauge he possible asymme ic
Economies 2025,13, 24 3 o 25
e ec o oil unce ain y on he equi y ma ke bubbles o he G7, gi en ha c ash and
eco e y a di e en ho izons can ca y di e en in o ma ion o ma ke pa icipan s as
sugges ed by he He e ogeneous Ma ke Hypo hesis (HMH; Mülle e al.,1997).
To he bes o ou knowledge, his is he i s pape o analyze he e ec o oil unce -
ain y on six indica o s o mul i-scale posi i e and nega i e bubbles in he G7 coun ies
based on a he e ogeneous coe icien s panel da a model. In he p ocess, we add o he
li e a u e on oil p ice unce ain y and s ock e u ns by now conside ing he e ec o he
o me on he boom-bus cycles o he la e . In addi ion, ou pape also aims o p o ide
a new p edic o o an al eady la ge se o ac o s iden i ied as d i e s o bubbles (see
So ne e e al.,2018) o a de ailed e iew), wi h us also con olling o some o he p omi-
nen a iables in ou analyses. The emainde o he pape is o ganized as ollows: Sec ion 2
discusses he da a and he basics o he econome ic model. Sec ion 3p esen s he empi ical
indings in ol ing he de ec ion o bubbles, as well as he e ec s o in es o sen imen
on he six LPPLS-CIs o bubbles in he panel o G7 coun ies. Finally, Sec ion 4concludes
he pape .
2. Da a and Econome ic Model
2.1. Da a
We i s ob ain weekly bubble indica o s, de i ed based on he na u al loga i hmic
alues o he daily di idend-p ice a io o he se en coun ies, using he di idend and
he s ock p ice index se ies in hei local cu encies, ob ained om Re ini i Da as eam.
Appendix Ao he pape ou lines he ma hema ical de ails o how he MS-LPPLS-CIs
a e ob ained and closely ollows he p esen a ion o Demi e e al. (2019). The gene a ed
bubbles indica o s co e he weekly pe iod o he i s week o Janua y 1973 o he ou h
week o May 2020. Since ou con ols, ollowing Ca aiani e al. (2023), namely, he mac oe-
conomic a iables, besides he indica o o oil unce ain y, a e a a mon hly equency,
o ob ain a mon hly alue o each o he mul i-scale con idence indica o s, we ake he
a e age o each o he scales weekly alues ha all wi hin a gi en mon h.
The e olu ion o he MS-LPPLS-CIs can be used o de ec c ashes and allies in eal-
ime. To his end, we plo he sho -, medium-, and long- e m indica o s (g een, pu ple,
and ed lines) while we show he log p ice- o-di idend a io as a black line in Figu e 1a. A
la ge LPPLS-CI alue o a pa icula scale shows ha he LPPLS signa u e is p esen o
many o he i ing windows o which we calib a ed he model, making i a mo e eliable
bubble indica o . The key message con eyed by Figu e 1a is ha he e a e many peaks in
he LPPLS-CIs p eceding subs an ial shi s in he log p ice- o-di idend a io.
We no e ha he bubble indica o s ac oss he G7 coun ies, in gene al, display peaks in
he pe iods co esponding o c ashes and eco e ies be o e and a ound he collapse o he
B e on Woods sys em in 1973, he “Black Monday” episode in 1987, he Asian Financial
C isis o 1997, he Do -com bubble bu s om 2000 o 2002, he Global Financial C isis o
2007 o 2008, he Eu opean so e eign deb c isis om 2009 o 2012, he “B exi ” in 2016,
and o some ex en du ing he COVID-19 episode. In o he wo ds, he MS-LPPLS-CIs a e
capable o p o iding leading in o ma ion on all he majo episodes o booms and bus s
wi nessed globally om 1973 o 2020.
In gene al, smalle c ashes o allies can bes be eco e ed using sho e ime scales,
while longe ime scales help o de ec la ge c ashes o allies, wi h he sho - e m LPPLS-
CIs p eceding he medium- e m ones and he la e leading he long- un indica o s, i.e.,
ma u a ion o he bubble heading owa ds ins abili y is p esen ac oss se e al dis inc
ime-scales. Mo e impo an ly, we obse e a simila iming o he s ong (posi i e as well
as nega i e) MS-LPPLS-CI alues in he c oss-sec ion o G7 coun ies, in line wi h he
in ui ion ha boom and bus cycles o he se en de eloped equi y ma ke s o en occu in
Economies 2025,13, 24 4 o 25
andem, mo i a ing he need o use a panel-based app oach o analyze he impac o oil
p ice unce ain y on s ock ma ke bubbles.
Economies 2025, 13, x FOR PEER REVIEW 4 o 25
ime-scales. Mo e impo an ly, we obse e a simila iming o he s ong (posi i e as well
as nega i e) MS-LPPLS-CI alues in he c oss-sec ion o G7 coun ies, in line wi h he in-
ui ion ha boom and bus cycles o he se en de eloped equi y ma ke s o en occu in
andem, mo i a ing he need o use a panel-based app oach o analyze he impac o oil
p ice unce ain y on s ock ma ke bubbles.
Economies 2025, 13, x FOR PEER REVIEW 4 o 25
ime-scales. Mo e impo an ly, we obse e a simila iming o he s ong (posi i e as well
as nega i e) MS-LPPLS-CI alues in he c oss-sec ion o G7 coun ies, in line wi h he in-
ui ion ha boom and bus cycles o he se en de eloped equi y ma ke s o en occu in
andem, mo i a ing he need o use a panel-based app oach o analyze he impac o oil
p ice unce ain y on s ock ma ke bubbles.
Figu e 1. Con .
Economies 2025,13, 24 5 o 25
Economies 2025, 13, x FOR PEER REVIEW 5 o 25
Figu e 1. Con .
Economies 2025,13, 24 6 o 25
Economies 2025, 13, x FOR PEER REVIEW 6 o 25
Figu e 1. Con .
Economies 2025,13, 24 7 o 25
Economies 2025, 13, x FOR PEER REVIEW 7 o 25
(a)
(b)
Figu e 1. (a) Mon hly Mul i-Scale LPPLS-CIs o he G7 Coun ies; (b) Model-F ee Es ima e o Oil
P ice Unce ain y.
Nex , we u n ou a en ion o he main p edic o , i.e., oil p ice unce ain y, depic ed
in Figu e 1b. One mus ealize ha unce ain y is a la en a iable and needs o be meas-
u ed. Gi en his, he majo i y o he s udies men ioned in he in oduc ion ely on uni-
a ia e o bi a ia e Gene alized Au o eg essi e Condi ional He e oskedas ici y
(GARCH) models applied o he oil p ice e u ns o de i e me ics o oil p ice unce ain y
o ela e o s ock p ice and/o e u ns. In o he wo ds, GARCH-based oil p ice unce ain y
is ully de e mined by changes in he le el o oil p ice, and as a esul , i is impossible o
disen angle unce ain y abou he oil p ice and changes in he oil p ice le el (Jo, 2014).
Gi en his, (Rahman, 2021) p oposes a new measu e o oil p ice unce ain y by u ilizing
S ochas ic Vola ili y (SV) in a S uc u al Vec o Au o eg essi e (SVAR) model (in ol ing
oil and s ock p ices and a mone a y policy ins umen ). In his model, oil p ice unce ain y
0.2
0.4
0.6
0.8
1.0
1.2
1.4
1.6
1.8
2.0
1975 1980 1985 1990 1995 2000 2005 2010 2015 2020
Oil p ice unce ain y (opu)
Figu e 1. (a) Mon hly Mul i-Scale LPPLS-CIs o he G7 Coun ies; (b) Model-F ee Es ima e o Oil
P ice Unce ain y.
Nex , we u n ou a en ion o he main p edic o , i.e., oil p ice unce ain y, depic ed in
Figu e 1b. One mus ealize ha unce ain y is a la en a iable and needs o be measu ed.
Gi en his, he majo i y o he s udies men ioned in he in oduc ion ely on uni a ia e o
bi a ia e Gene alized Au o eg essi e Condi ional He e oskedas ici y (GARCH) models ap-
plied o he oil p ice e u ns o de i e me ics o oil p ice unce ain y o ela e o s ock p ice
and/o e u ns. In o he wo ds, GARCH-based oil p ice unce ain y is ully de e mined by
Economies 2025,13, 24 8 o 25
changes in he le el o oil p ice, and as a esul , i is impossible o disen angle unce ain y
abou he oil p ice and changes in he oil p ice le el (Jo,2014). Gi en his, (Rahman,2021)
p oposes a new measu e o oil p ice unce ain y by u ilizing S ochas ic Vola ili y (SV) in
a S uc u al Vec o Au o eg essi e (SVAR) model (in ol ing oil and s ock p ices and a
mone a y policy ins umen ). In his model, oil p ice unce ain y is he condi ional a iance
o he oil p ice change o ecas e o , and hus, i e ol es independen ly o any change in
he oil p ice le el.
1
Despi e he inno a i eness o his app oach o e GARCH-based models
in measu ing oil p ice unce ain y, he me ic is no ee om he s uc u e o any speci ic
heo e ical model. Gi en hese empi ical issues in cons uc ing an app op ia e me ic o oil
p ice unce ain y, (Nguyen e al.,2021) ha e p oposed a no el cons uc ion o he oil p ice
unce ain y index ha is uncondi ional on a model.
2
These au ho s de elop a measu e
o oil p ice unce ain y as he one-pe iod-ahead o ecas e o a iance o a o ecas ing
eg ession wi h SV in he esidual e ms. The no el y o his cons uc ion app oach lies
in i s lexibili y in including a la ge numbe o addi ional in o ma ion ha is impo an in
explaining luc ua ions in oil p ices, namely, exchange a e, oil p oduc ion, global economic
condi ion, and co-mo emen in he uel ma ke . In his sense, he index is able o cap u e
unce ain y in oil p ices a he han ola ili y as measu ed by bo h GARCH and SV models.
Acco ding o Figu e 1b, heigh ened oil p ice unce ain y coincides wi h he i s and
second oil c ises o 1973 and 1979. These e en s a e also associa ed wi h subs an ial posi i e
and nega i e s ock ma ke bubbles ac oss all G7 coun ies, as e iden om Figu e 1a.
Following he oil c ises o he 1970s, oil unce ain y peaked again du ing he i s hal o
1986, coinciding wi h a p olonged pe iod o posi i e s ock ma ke bubbles ac oss all G7
coun ies and a sho - medium- and long- e m ime scales. A s ong bull ma ke o e due
o a co ec ion since 1982, exace ba ed by heigh ened oil unce ain y, culmina ed in he
Black Monday s ock ma ke c ash o Oc obe 1987.
I aq’s in asion o Kuwai in 1990 had signi ican ami ica ions o global s ock ma ke s,
leading o inc eased unce ain y and bea ish sen imen . The in asion led o a sha p spike
in oil p ices and consequen ly inc eased in la ion and educed economic g ow h, ypically
nega i e o s ock ma ke pe o mance. As wi h many geopoli ical c ises, in es o s pull
ou iskie asse s like equi ies and mo e owa ds sa e asse s such as gold and go e nmen
bonds. This e ec shows up as posi i e asse bubbles, mos no ably in Ge many and he US.
The nex episode o heigh ened oil ma ke unce ain y s a ed owa ds he end o 1998,
wi h subs an ial posi i e s ock ma ke bubbles ac oss all coun ies, bu mos p onounced
o he US. The posi i e bubble indica o s o he US emained high up o 2002, e lec ing
bo h he impac o he Eas -Asian c isis and he Do -Com Bubble on global s ock ma ke s.
Ou model- ee es ima e o oil p ice unce ain y indica es ano he spike owa ds he
end o 2008, u he nega i ely con ibu ing o he Global Financial C isis.
As is u he e iden om Figu e 1b, he COVID-19 pandemic, which eme ged a he
end o 2019 and became a global heal h c isis in 2020, had p o ound e ec s on he global
economy and a ious indus ies, wi h he oil and gas indus ies mos se e ely impac ed
h ough a collapse in demand, s o age issues and a p ice wa be ween majo oil p oduce s
in he OPEC+ g oup. The pandemic also accele a ed discussions abou he u u e o oil
and he po en ial o a mo e apid ansi ion o enewable ene gy sou ces—leading o a
signi ican inc ease o unce ain y in he oil ma ke , d i en by no only immedia e demand-
side shocks bu also longe - e m conside a ions abou he u u e o ene gy consump ion.
Al hough mos coun ies in he sample egis e some posi i e bubble e ec s, posi i e
bubbles a e mos no iceable in he case o he US.
Rega ding he mac oeconomic con ol a iables included in he analysis, we use
mon h-on-mon h g ow h o indus ial p oduc ion, mon h-on-mon h Consume P ice Index
(CPI)-based in la ion a e, and change in he in e es a e, wi h all ans o ma ions o he
Economies 2025,13, 24 15 o 25
Wi h oil p ice unce ain y showing up as ha ing s ong nega i e e ec s on posi-
i e bubbles compa ed o o he adi ional mac oeconomic and inancial indica o s, i is
ecommended ha in es o s and policymake s should be ca e ul when he le el o oil
unce ain y ends o ise a he ime he s ock ma ke s a e booming because his could imply
an imminen c ash. A he same ime, when s ock p ices a e acing ela i ely less se e e
bea ish egimes, highe oil p ice unce ain y can lead o deep equi y ma ke down u ns.
Acco dingly, policymake s should moni o ising oil p ice unce ain y closely and imple-
men expansiona y mone a y and iscal policies o ensu e he e i al o he equi y ma ke
(And é e al.,2023), as di ec ly con olling oil p ice unce ain y is likely o be di icul due
o i being d i en by oil ma ke -speci ic shocks and geopoli ical e en s (Qian e al.,2022).
As pa o u u e esea ch, in ligh o he la ge li e a u e on he ela ionship be ween
oil p ice o e u ns and s ock p ice o e u ns (see Degiannakis e al.,2018), and (Smy h &
Na ayan,2018) o comp ehensi e e iews), i would be in e es ing o conside he e ec
o oil p ices on s ock ma ke bubbles. Bu ealizing ha oil p ices a e d i en by a ious
shocks namely, oil-supply, global economic ac i i y, oil-speci ic consump ion demand
and in en o y demand (Kilian,2009;Baumeis e & Hamil on,2019), ha ing di e en
di ec ional impac s on s ock p ices (Kilian & Pa k,2009), we will need o decompose oil
p ice mo emen s due o hese inno a ions o de ec he impac on bubbles in possibly a
ime se ies-based s uc u al SVAR model, which will also allow us o dis inguish be ween
opposing e ec s o highe oil p ices on s ock ma ke s o oil-expo ing and impo ing
coun ies (Wang e al.,2013).
10
A he same ime, ou cu en analysis can also be ex ended
o eme ging economies.11
Au ho Con ibu ions: Panel da a analysis and w i e-up o panel esul s, R. .E.; Concep ualiza ion o
he esea ch idea, w i e-up o backg ound, heo e ical backg ound, and li e a u e e iew, R.G.; Panel
da a analysis, X.S.; Es ima ion o bubbles indica o s and w i e-up o ele an segmen s associa ed wi h
bubbles es ima ions, J.N. All au ho s ha e ead and ag eed o he published e sion o he manusc ip .
Funding: This esea ch ecei ed no ex e nal unding.
In o med Consen S a emen : No applicable.
Da a A ailabili y S a emen : Da a will be made a ailable upon eques om he au ho s, as unde -
lying da a has been ob ained om a subsc ip ion-based sou ce. Compu e codes a e a ailable a
h ps://pypi.o g/p ojec /lppls/ (accessed on 17 Sep embe 2023).
Con lic s o In e es : The au ho s decla e ha hey ha e no compe ing in e es s.
Appendix A. Es ima ing he Mul i-Scale Log-Pe iodic Powe Law
Singula i y (LPPLS) Model
(Filimono & So ne e,2013) de eloped a s able and obus calib a ion scheme o he
ollowing LPPLS model gi en by:
ln E[p( )] =A+B( c− )m+C( c− )mcosωln( c− )m−ϕ(A1)
whe e pa ame e
c
ep esen s he c i ical ime ( he da e o he e mina ion o he bubble);
A
is he expec ed log alue o he obse ed ime se ies, i.e., he s ock p ice-di idend a io, a
ime
c
;
B
is he ampli ude o he powe law accele a ion; and
C
is he ela i e magni ude o
he log-pe iodic oscilla ions. The exponen o he powe law g ow h is gi en by
m
, while
ω
and ϕ ep esen he equency o he log-pe iodic oscilla ions and a phase shi pa ame e ,
espec i ely
We make use o his s able and obus calib a ion scheme, and ollowing Filimono
and So ne e (2013), e o mula e Equa ion (A1) o educe he complexi y o he calib a ion
Economies 2025,13, 24 16 o 25
p ocess by elimina ing he nonlinea pa ame e
ϕ
and expanding he linea pa ame e
C
o
C1=Ccos ϕand C2=Ccos ϕ.
The new o mula ion can be w i en as
ln E[p( )] =A+B( )+C1(g)+C2(h)(A2)
whe e
=( c− )m
g=( c− )mcos[ωln ( C− )]
h=( c− )msin[ωln( c− )]
To es ima e he h ee nonlinea pa ame e s:
{ c,m,ω}
, and 4 linea pa ame e s:
{A,B,C1,C2}
, we i Equa ion (A2) o he log o he p ice-di idend a io. This is done by
using L2no m o ob ain he ollowing sum o squa ed esiduals:
F( c,m,ω,A,B,C1,C2)=
N
∑
i=1hln p(τi)−A−B( i)−C1(gi)−C2(hi)i2(A3)
Since he es ima ion o he h ee nonlinea pa ame e s depends on he ou linea
pa ame e s, we ob ain he ollowing cos unc ion:
F( c,m,ω)=min
A,B,C1,C2
F( c,m,ω,A,B,C1,C2)=F c,m,ω,ˆ
A,ˆ
B,ˆ
C1,ˆ
C2(A4)
Sol ing he op imiza ion p oblem allows o he es ima ion o he ou linea pa ame e s:
{ˆ
A,ˆ
B,ˆ
C1,ˆ
C2}=a g min
A,B,C1,C2
F( c,m,ω,A,B,C1,C2)(A5)
which can be done analy ically by sol ing he ollowing ma ix equa ion:
N∑ i∑gi∑hi
∑ i∑ 2
i∑ igi∑ ihi
∑gi∑ igi∑g2
i∑gihi
∑hi∑ ihi∑gihi∑h2
i
ˆ
A
ˆ
B
ˆ
C1
ˆ
C2
=
∑ln pi
∑ ilnpi
∑gilnpi
∑hilnpi
(A6)
Nex , he h ee nonlinea pa ame e s can be de e mined by sol ing he ollowing
nonlinea op imiza ion p oblem:
{ˆ
c,ˆ
m,ˆ
ω}=a g min
c,m,ωF( c,m,ω)(A7)
We use he Sequen ial Leas Squa es P og amming (SLSQP) sea ch algo i hm (K a ,
1988) o ind he bes es ima ion o he h ee nonlinea pa ame e s { c,m,ω}.
The LPPLS con idence indica o , in oduced by So ne e e al. (2015), is used o
measu e he sensi i i y o bubble pa e ns in each coun y’s log p ice-di idend a io ime
se ies. The la ge he LPPLS con idence indica o (CI), he mo e eliable he LPPLS bubble
pa e n and ice e sa. I is calcula ed by calib a ing he LPPLS model o sh inking ime
windows by shi ing he ini ial obse a ion
1
o wa d in ime owa d he inal obse a ion
2
wi h a s ep
d
. Fo each LPPLS model i , he es ima ed pa ame e s a e il e ed agains
es ablished h esholds, and he quali ied i s a e aken as a ac ion o he o al numbe o
posi i e o nega i e i s. A posi i e i has es ima ed
B<
0, and a nega i e i has es ima ed
B>0.
Economies 2025,13, 24 17 o 25
Following he wo k o (Demi e e al.,2019), we inco po a e bubbles o a ying
mul iple ime scales in o his analysis. We sample he ime se ies in s eps o 5 ading
days. We c ea e he nes ed windows [
1
,
2
] and i e a e h ough each window in s eps o
2 ading days. In his manne , we ob ain a weekly esolu ion om which we cons uc he
ollowing indica o s:
•
Sho - e m bubble: A numbe
∈[0, 1]
which deno es he ac ion o quali ied i s
o es ima ion windows o leng h
d
:
= 2− 1∈[30 : 90]
ading days pe
2
. This
indica o comp ises o (90 −30)/2 =30 i s.
•
Medium- e m bubble: A numbe
∈[0, 1]
which deno es he ac ion o quali ied i s
o es ima ion windows o leng h
d
:
= 2− 1∈[30 : 90]
ading days pe
2
. This
indica o comp ises o (300 −90)/2 =105 i s.
•
Long- e m bubble: A numbe
∈
[0, 1] which deno es he ac ion o quali ied i s
o es ima ion windows o leng h
d
:
= 2− 1∈[30 : 90]
ading days pe
2
. This
indica o comp ises o (745 −300)/2 =223 i s.
•
Fil e condi ions: A e calib a ing he model, he ollowing il e condi ions a e
applied o de e mine which i s a e quali ied:
m∈[0.01, 0.99]
ω∈[2, 15]
c∈[max( 2−60, 2−0.5( 2− 1)),min(252, 2+0.5( 2− 1))]
O>2.5
D>0.5
whe e,
O=ω
2πln c− 1
c− 2
is he numbe o oscilla ions, and
D=m|B|
ω|C|
cap u es he
damping pa ame e equi ed o ensu e ha he c ash haza d a e, h( ), is non-nega i e.
Appendix B. Random Coe icien s (RC) Es ima ion
T adi ional ixed- and andom-e ec s models inco po a e panel-speci ic he e ogenei y
by including a se o nuisance pa ame e s ha p o ide each panel wi h i s own cons an
e m. Howe e , in hese models, all panels sha e common slope pa ame e s – a es ic ion
ha is o en less desi able as changes in independen a iables may exe a he e ogeneous
impac on he dependen a iable in ques ion. Random—coe icien s (RC) models (Swamy,
1970) a e mo e gene al, allowing each panel o ha e a ec o o andomly d awn slopes
om a dis ibu ion common o all panels. Acco ding o Poi (2003), he implemen a ion o
he RC es ima o ensu es he bes linea unbiased p edic o s o he panel-speci ic d aws
om his dis ibu ion.
Conside a gene al andom-coe icien s model, wi h y being he dependen a iable
and X being he p edic o , o he o m:
yi=Xiβi+εi(A8)
In he case o RC, each panel-speci ic
βi
is ela ed o an unde lying common pa ame e
ec o β:
βi=β+ i(A9)
whe e
E{ i}=
0,
E i ′
i=Σ
,
En i ′
jo=
0 o
j=i
, and
En iϵ′
jo=
0 o all
i
and
j
.
Equa ions (A8) and (A9) may be combined o ge :
yi=Xi(β+ i)+εi=Xiβ+ui
Economies 2025,13, 24 18 o 25
wi h ui≡Xi i+εi. Fu he mo e:
Euiu′
i=En(Xi i+εi)(Xi i+εi)′o=XiΣX′
i+σii I≡Πi
The Ppanels can be ep esen ed in s ack o ma :
y=Xβ+u(A10)
whe e:
Π≡Euiu′
i=
Π10
0Π2
· · · 0
· · · 0
.
.
..
.
.
0 0
....
.
.
· · · ΠP
Es ima ing he pa ame e s in Equa ion (A9) is a s anda d p oblem, which can be
sol ed wi h gene alized leas squa es (GLS):
ˆ
β=X′Π−1X−1X′Π−1y=∑iX′
iΠ−1
iXi−1∑iX′
iΠ−1
iyi=∑iWibi(A11)
whe e
Wi
is he Gene alized Leas Squa es (GLS) weigh and
bi=X′
iXi−1X′
iy
. The
esul ing
ˆ
β
o he o e all (na ional) esul is, he e o e, a weigh ed a e age o he s a e-
speci ic OLS es ima es. Fo mo e de ails on
ˆ
β
a iance speci ica ion and GLS weigh , e e
o Poi (2003).
To ob ain he s a e-speci ic
ˆ
βi
ec o s, Judge e al. (1985) sugges ha i a en ion is
es ic ed o he class o es ima o s
β*
i
o which
Eβ*
i
βi=βi
, hen he s a e-speci ic
OLS es ima o
bi
is app op ia e. Following G eene’s (1997) sugges ed me hod o ob aining
he a iance o
ˆ
βi
, i ollows ha
ˆ
β
is bo h consis en and e icien , and al hough ine icien ,
biis also a consis en es ima o o β.
Poi (2003) also sugges s a es o de e mine whe he he coun y-speci ic
βi
s a e
signi ican ly di e en om one ano he . The null hypo hesis is s a ed as:
H0:β1=β2=· · · =βP(A12)
and he es s a is ic is de ined as:
T≡∑P
=1bi−β†′nˆ
σ−1
ii (XiXi)obi−β†(A13)
whe e β†=n∑P
=1ˆ
σ−1
ii (XiXi)o−1∑P
=1ˆ
σ−1
ii (XiXi)bi.
The es s a is ic Tis dis ibu ed as χ2wi h k(P−1)deg ees o eedom.
Economies 2025,13, 24 19 o 25
Appendix C. Addi ional Resul s
Economies 2025, 13, x FOR PEER REVIEW 19 o 25
Appendix C. Addi ional Resul s
Figu e A1. Impulse esponse unc ions om a panel ec o au o eg essi e model o nega i e and
posi i e equi y bubbles due o a one-uni shock o he model- ee es ima e o oil p ice unce ain y
iden i ied using Cholesky decomposi ion: Feb ua y 1975 o May 2020. No e: The PVAR models o
he G7 comp ise o he a iables in he ollowing o de : Oil p ice unce ain y (opu); indus ial p o-
duc ion g ow h (ip_g ow h); consume p ice index in la ion (in l); in e es a e diffe ence (i _diff);
long- e m nega i e bubble (l _neg) o medium- e m nega i e bubble (m _neg) o sho - e m nega i e
bubble (s _neg) o long- e m posi i e bubble (l _pos) o medium- e m posi i e bubble (m _pos) o
sho - e m posi i e bubble (s _pos), wi h he blue line showing he mean esponses o a one uni
shock o opu, along wi h he 95% con idence bands ( ed do ed lines).
Table A1. Random coefficien es ima ion o con empo aneous effec s o nega i e and posi i e eq-
ui y bubbles due o a model- ee es ima e o oil p ice unce ain y: Feb ua y 1975 o May 2020.
(1) (2) (3) (4) (5) (6)
l _neg m _neg s _neg l _pos m _pos s _pos
l.l _neg 0.678 ***
(20.54)
l.m _neg 0.413 ***
(14.79)
Figu e A1. Impulse esponse unc ions om a panel ec o au o eg essi e model o nega i e and
posi i e equi y bubbles due o a one-uni shock o he model- ee es ima e o oil p ice unce ain y
iden i ied using Cholesky decomposi ion: Feb ua y 1975 o May 2020. No e: The PVAR models o he
G7 comp ise o he a iables in he ollowing o de : Oil p ice unce ain y (opu); indus ial p oduc ion
g ow h (ip_g ow h); consume p ice index in la ion (in l); in e es a e di e ence (i _di ); long- e m
nega i e bubble (l _neg) o medium- e m nega i e bubble (m _neg) o sho - e m nega i e bubble
(s _neg) o long- e m posi i e bubble (l _pos) o medium- e m posi i e bubble (m _pos) o sho - e m
posi i e bubble (s _pos), wi h he blue line showing he mean esponses o a one uni shock o opu,
along wi h he 95% con idence bands ( ed do ed lines).
Economies 2025,13, 24 20 o 25
Table A1. Random coe icien es ima ion o con empo aneous e ec s o nega i e and posi i e equi y
bubbles due o a model- ee es ima e o oil p ice unce ain y: Feb ua y 1975 o May 2020.
(1) (2) (3) (4) (5) (6)
l _neg m _neg s _neg l _pos m _pos s _pos
l.l _neg 0.678 ***
(20.54)
l.m _neg 0.413 ***
(14.79)
l.s _neg 0.248 ***
(8.42)
l.l _pos 0.775 ***
(46.19)
l.m _pos 0.582 ***
(17.55)
l.s _pos 0.323 ***
(16.82)
oilunc 0.00549 0.00847 *** 0.00246 * −0.0140 *** −0.0106 *** −0.00514 ***
(1.46) (4.08) (1.84) (−7.05) (−7.25) (−3.69)
ip_g ow h −0.244 ** −0.164 *** 0.0436 −0.0445 0.122 *** 0.141 *
(−2.42) (−8.29) (1.61) (−0.42) (3.26) (1.89)
in l 0.418 ** −0.285 *** 0.0369 −0.861 * −0.696 *** −0.0167
(2.16) (−4.19) (0.36) (−1.86) (−3.35) (−0.09)
i _di 0.000924 −0.000903 0.000470 0.000316 −0.000104 −0.00355 ***
(0.91) (−0.73) (0.64) (0.32) (−0.06) (−3.09)
cons an −0.00155 −0.00161 0.00290 *** 0.0164 *** 0.0162 *** 0.0123 ***
(−0.61) (−1.21) (3.08) (6.39) (11.16) (11.29)
# obse a ions 3808 3808 3808 3808 3808 3808
# g oups 7 7 7 7 7 7
Tes o pa cons ancy,χ2112.70 60.96 54.60 44.60 66.14 35.38
d.o. 36 36 36 36 36 36
P ob. 0.0000 0.0058 0.0241 0.1538 0.0016 0.4978
No e: l(one-mon h lag); Oil p ice unce ain y (opu); indus ial p oduc ion g ow h (ip_g ow h); consume p ice
index in la ion (in l); in e es a e di e ence (i _di ); long- e m nega i e bubble (l _neg); medium- e m nega i e
bubble (m _neg); sho - e m nega i e bubble (s _neg); long- e m posi i e bubble (l _pos); medium- e m posi i e
bubble (m _pos); sho - e m posi i e bubble (s _pos); -s a is ics (based on boo s apped obus s anda d e o s) in
pa en heses; * p< 0.10, ** p< 0.05, *** p< 0.01.
Table A2. Random coe icien es ima ion p edic i e esul s o nega i e and posi i e equi y bubbles
due o nominal oil p ice e u ns: Feb ua y 1973 o May 2020.
(1) (2) (3) (4) (5) (6)
l _neg m _neg s _neg l _pos m _pos s _pos
l.l _neg 0.658 ***
(21.21)
l.m _neg 0.463 ***
(13.80)
l.s _neg 0.244 ***
(8.41)
l.l _pos 0.779 ***
(47.09)
l.m _pos 0.582 ***
(17.40)
l.s _pos 0.321 ***
(16.47)
Economies 2025,13, 24 21 o 25
Table A2. Con .
(1) (2) (3) (4) (5) (6)
l.oil_ e u ns −0.000106 −0.0000317 −0.00000734 −0.0000668 −0.00000533 −0.0000428
(−1.62) (−1.09) (−0.28) (−1.49) (−0.12) (−0.76)
l.ip_g ow h −0.179 ** −0.0234 −0.0655 0.172 *** 0.167 ** 0.0565
(−2.08) (−0.37) (−1.04) (3.16) (2.40) (1.58)
l.cpi_g ow h 0.371 0.226 0.387 *** −0.178 −0.951 *** −0.522 ***
(1.19) (1.05) (4.53) (−0.42) (−2.94) (−3.85)
l.i _di 0.00151 0.000351 0.00224 *** −0.00156 −0.00213 −0.00265 **
(1.13) (0.93) (5.63) (−1.31) (−1.44) (−2.24)
cons an 0.00257 *** 0.00398 *** 0.00454 *** 0.00555 *** 0.00893 *** 0.00934 ***
(4.40) (7.44) (13.25) (4.71) (9.84) (26.01)
# obse a ions 3997 3997 3997 3997 3997 3997
# g oups 777777
Tes o pa cons ancy,χ2102.76 70.23 533.72 40.66 76.26 35.94
d.o. 36 36 36 36 36 36
P ob. 0.0000 0.0006 0.0290 0.2727 0.0001 0.4716
No e: l(one-mon h lag); Oil p ice e u ns (oil_ e u ns); indus ial p oduc ion g ow h (ip_g ow h); consume p ice
index in la ion (in l); in e es a e di e ence (i _di ); long- e m nega i e bubble (l _neg); medium- e m nega i e
bubble (m _neg); sho - e m nega i e bubble (s _neg); long- e m posi i e bubble (l _pos); medium- e m posi i e
bubble (m _pos); sho - e m posi i e bubble (s _pos) -s a is ics (based on boo s apped obus s anda d e o s) in
pa en heses; ** p< 0.05, *** p< 0.01.
Table A3. BRICS sample: Random coe icien es ima ion p edic i e esul s o nega i e and posi i e
equi y bubbles due o a model- ee es ima e o oil p ice unce ain y: Feb ua y 1999 o May 2020.
(1) (2) (3) (4) (5) (6)
l _neg m _neg s _neg l _pos m _pos s _pos
l.l _neg 0.521 ***
(7.75)
l.m _neg 0.450 ***
(9.18)
l.s _neg 0.230 ***
(5.56)
l.l _pos 0.702 ***
(23.08)
l.m _pos 0.502 ***
(15.96)
l.s _pos 0.245 ***
(4.95)
l.oilunc 0.0000485 0.00224 0.00158 −0.00280 −0.00145 −0.00165
(0.01) (0.82) (0.67) (−1.04) (−0.46) (−0.40)
l.ip_g ow h −0.00940 0.0155 −0.0799 ** 0.0531 0.0433 0.0973 **
(−0.78) (0.73) (−2.06) (1.35) (1.05) (2.25)
l.in l 0.0426 −0.108 −0.0883 0.0438 −0.231 −0.0682
(0.37) (−0.75) (−0.64) (0.27) (−0.71) (−0.42)
l.i _di −0.00398 0.00134 * 0.00180 * 0.00570 0.00241 0.00177
(−1.27) (1.67) (1.69) (0.94) (0.97) (1.01)
cons an 0.00155 0.00206 0.00472 * 0.00616 ** 0.0105 *** 0.0108 ***
(0.42) (0.74) (1.81) (2.37) (3.17) (2.73)
# obse a ions 1264 1264 1264 1264 1264 1264
# g oups 555555
Tes o pa cons ancy 55.74 38.12 31.15 32.97 25.21 27.61
d.o. 24 24 24 24 24 24
P ob. 0.0002 0.0337 0.1494 0.1047 0.3943 0.2767
No e: l(one-mon h lag); Oil p ice unce ain y (opu); indus ial p oduc ion g ow h (ip_g ow h); consume p ice
index in la ion (in l); in e es a e di e ence (i _di ); long- e m nega i e bubble (l _neg); medium- e m nega i e
bubble (m _neg); sho - e m nega i e bubble (s _neg); long- e m posi i e bubble (l _pos); medium- e m posi i e
bubble (m _pos); sho - e m posi i e bubble (s _pos) -s a is ics (based on boo s apped obus s anda d e o s) in
pa en heses; * p< 0.10, ** p< 0.05, *** p< 0.01.
Economies 2025,13, 24 22 o 25
Table A4. BRICS sample: Random coe icien es ima ion p edic i e esul s o he coun y-speci ic
impac o a model- ee es ima e o oil p ice unce ain y on nega i e and posi i e equi y ma ke
bubbles: Feb ua y 1999 o May 2020.
(1) (2) (3) (4) (5) (6)
l _neg m _neg s _neg l _pos m _pos s _pos
B azil l.opu 0.0023 0.0042 −0.0005 −0.0085 0.0037 −0.0023
(0.59) (0.66) (−0.09) (−0.80) (0.18) (−0.30)
Russia l.opu −0.0028 0.0031 0.0016 0.0033 0.0020 −0.0088
(−0.60) (0.47) (0.31) (0.60) (0.18) (−1.19)
India l.opu −0.0014 0.0008 0.0036 −0.00006 −0.0047 −0.0023
(−0.26) (0.09) (0.68) (−0.01) (−0.31) (−0.30)
China l.opu −0.0093 * −0.0099 −0.0003 −0.0015 0.0035 0.0082
(−1.90) (−0.99) (−0.06) (−0.12) (0.25) (1.12)
Sou h A ica l.opu 0.0108 ** 0.0078 * 0.0040 −0.0154 −0.0129 −0.0032
(2.49) (1.63) (0.77) (−0.82) (−0.90) (−0.44)
No e: l(one-mon h lag); Oil p ice unce ain y (opu); long- e m nega i e bubble (l _neg); medium- e m nega i e
bubble (m _neg); sho - e m nega i e bubble (s _neg); long- e m posi i e bubble (l _pos); medium- e m posi i e
bubble (m _pos); sho - e m posi i e bubble (s _pos) -s a is ics in pa en heses; * p< 0.10, ** p< 0.05.
No es
1
Using his amewo k, Rahman (2021) p o ides e idence ha inc eased oil p ice unce ain y has a nega i e e ec on ( eal) s ock
e u ns o he US.
2
The da a o he oil unce ain y index can be ob ained om he websi e o D . Bao H. Nguyen a : h ps://si es.google.com/si e/
nguyenhoaibao/da ase s/oil-ma ke -unce ain y?au huse =0 (accessed on 23 Augus 2023).
3h ps://www.oecd.o g/sdd/oecdmaineconomicindica o smei.h m (accessed on 23 Augus 2023).
4
The SSRs a e de i ed om he websi e o D . Leo K ippne : h ps://www.ljkm a.com/ (accessed on 23 Augus 2023) No e ha
he SSR es ima es used in his pape a e de i ed om he wo ks o K ippne (2013,2015) due o hei co e age in ol ing he G7,
besides being conside ed an imp o emen o e hose ob ained by Wu and Xia (2016) ( o he Eu o a ea, he UK and he US), as
discussed in de ail by K ippne (2020). The SSR is based on models o he e m s uc u e, which essen ially emo es he e ec
ha he op ion o in es in physical cu ency (a an in e es a e o ze o) has on yield cu es, esul ing in a hypo he ical “shadow
yield cu e" ha would exis i he physical cu ency we e no a ailable. The “shadow policy a e” gene a ed in his manne ,
he e o e, p o ides a measu e o he mone a y policy s ance a e he ac ual policy a e eaches ze o. The main ad an age o he
SSR is ha i is no cons ained by he Ze o Lowe Bound (ZLB), and hus allows us o combine he da a om he ZLB pe iod
wi h ha o he non-ZLB e a and, in u n o use i as he common me ic o mone a y policy s ance ac oss he con en ional and
uncon en ional mone a y policy episodes.
5h ps://global inancialda a.com/ (accessed on 17 Sep embe 2023).
6
No e ha he applica ion o he Hausman (1978) es sugges ed ha oil p ice unce ain y and he con ol a iables a e exogenous
o he speci ica ion, wi h comple e de ails o hese esul s a ailable upon eques om nega i e and posi i e equi y ma ke bubbles
ac oss he h ee ime scales p esen ed in Table 1. The au ho s. Hence, in Table A1 in Appendix C, we depic he con empo aneous
e ec s o all he p edic o s.
7
These esul s in e ms o he sign a e also con i med, along wi h delayed signi ican e ec s, in Figu e A1 in Appendix C, ia
impulse esponse unc ions, ollowing an oil p ice unce ain y shock, iden i ied using Cholesky decomposi ion, on six Panel VAR
(PVAR) models wi h a iables o de ed as ollows: opu, ip_g ow h, in l, i _di , and a speci ic MS-LPPLS-CI o he G7.
8These indings a e consis en o con empo aneous opu, as epo ed in Table A1.
9All non-boo s apped esul s a e a ailable om he au ho s upon eques .
10
This line o easoning is pe haps con i med by ou inding o insigni ican p edic i e impac s o eplacing oil p ice unce ain y in
ou model in Equa ion (1) wi h nominal WTI oil p ice e u ns on he MS-LPPLS-CIs, as epo ed in Table A2 in Appendix C.
As ini ial analysis, we ela ed he daily measu e o c ash isk, as gi en by he Chicago Boa d Op ions Exchange (CBOE)’s S&P
500 skewness index, wi h lagged oil-supply and demand as well as inancial shocks based on a SVAR decomposi ion by Ready
(2018), and ound ha skewness is only nega i ely impac ed (wi h a coe icien o
−
75.915) in a s a is ically signi ican manne
(a he 5% le el), i.e., he c ash isk inc eases due o inancial unce ain y o e 2 Janua y 1990 o 9 Feb ua y 2024. This esul
was again con i med when we used he lagged co po a e ea nings shock o Miescu and Mum az (2024), which is a p oxy o
posi i e inancial shock, o ob ain a s a is ically signi ican (a he 1% le el) posi i e (wi h a coe icien o 0.311) ela ionship wi h
skewness, i.e., inc eases in co po a e ea nings which signals educ ion in inancial unce ain y, educes c ash isk by inc easing
he skewness, o e he pe iod o 18 Janua y 1990 o 16 Oc obe 2019.
Economies 2025,13, 24 23 o 25
11
As a p elimina y analysis, esul s a e p esen ed in Tables A3 and A4 in Appendix Co he pape o he BRICS (B azil, Russia,
India, China and Sou h A ica) coun ies. Table A3 con ains he combined esul s, while Table A4 con ains he coun y-speci ic
esul s, ocusing on he impac o lagged oil p ice unce ain y on posi i e and nega i e s ock ma ke bubbles a he sho - medium-
and long- e m scales. As can be seen, unlike he case o he G7 coun ies, which p esen s wi h o e all s ong esul s o posi i e
MS-LPPLS-CIs, we ind no causal impac o oil p ice unce ain y on s ock ma ke bubbles in he sho , medium o long e m.
Coun y-speci ic e ec s o he nega i e MS-LPPLS-CIs a e also weak in he case o he BRICS coun ies, wi h only Sou h A ica
p esen ing a signi ican nega i e impac o lagged oil p ice unce ain y on nega i e s ock ma ke bubbles in he long and medium
e ms. The di e ences may be a ibu ed o se e al economic, s uc u al and ins i u ional di e ences be ween he G7 and BRICS
coun ies. BRICS coun ies, such as Russia and B azil, a e esou ce-dependen economies wi h a signi ican eliance on oil and
commodi y expo s. This may make hei s ock ma ke s mo e di ec ly ied o oil p ice le els a he han unce ain y. In es o s in
hese ma ke s may ha e adjus ed expec a ions o equen oil p ice luc ua ions, educing he sensi i i y o bubbles o unce ain y.
G7 coun ies, on he o he hand, a e gene ally mo e di e si ied and less elian on oil expo s. Ins ead, oil p ice unce ain y
ac s as a b oade economic isk ac o , in luencing in es o beha iou and con ibu ing o specula i e bubbles in s ock ma ke s.
Addi ionally, BRICS s ock ma ke s a e less ma u e, while G7 ma ke s a e mo e ins i u ionalized and mo e esponsi e o economic
unce ain ies. Oil p ice unce ain y can ampli y isk a e sion and specula ion, uelling bubbles.
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