Capo ale, Guglielmo Ma ia; Gil-Alaña, Luis A.; Ime i, Ami
A icle
Exogenous shocks and ime- a ying p ice pe sis ence in
he EU27
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Sugges ed Ci a ion: Capo ale, Guglielmo Ma ia; Gil-Alaña, Luis A.; Ime i, Ami (2024) : Exogenous
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Exogenous shocks and ime- a ying p ice pe sistence in
he EU27
Guglielmo Ma ia Capo ale, Luis A. Gil-Alana & Ami Ime i
To ci e his a icle: Guglielmo Ma ia Capo ale, Luis A. Gil-Alana & Ami Ime i (2024) Exogenous
shocks and ime- a ying p ice pe sis ence in he EU27, Jou nal o Applied Economics, 27:1,
2329857, DOI: 10.1080/15140326.2024.2329857
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© 2024 The Au ho (s). Published by In o ma
UK Limi ed, ading as Taylo & F ancis
G oup.
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REVIEW ARTICLE
Exogenous shocks and ime- a ying p ice pe sis ence in
he EU27
Guglielmo Ma ia Capo ale
a
, Luis A. Gil-Alana
b,c
and Ami Ime i
d
a
Economics, B unel Uni e si y London, London, UK;
b
Facul y o Economics, Edi icio Amigos, Uni e si y o
Na a a, Pamplona, Spain;
c
Economics, Uni e sidad F ancisco de Vi o ia, Mad id, Spain;
d
Economics,
Uni e si y o Business and Technology, P is ina, Koso o
ABSTRACT
This pape analyses mon hly p ice pe sis ence in he EU27 coun ies
o e he pe iod 2010–2022 using a ac ional in eg a ion ame-
wo k, whe e he measu e o pe sis ence is he ac ional di e en-
cing pa ame e d. In addi ion o ull sample es ima es, subsample
and ecu si e ones a e ob ained o examine ime a ia ion. On he
whole, he esul s p o ide clea e idence ha bo h he exogenous
shocks conside ed (namely, he COVID-19 pandemic and he
Russia-Uk aine wa ) ha e gene ally inc eased p ice pe sis ence in
he EU27 (despi e hei he e ogenei y), al hough he ecu si e es i-
ma es sugges ha hei impac migh ha e peaked and migh now
be dec easing. The e o e, any policies adop ed o coun e ac hose
shocks should be g adually phased ou . The excep ions a e he
Sou he n Eu opean coun ies, whe e p ice pe sis ence appea s o
ha e dec eased, hough in I aly he ecu si e analysis indica es ha
i is now ising sha ply.
ARTICLE HISTORY
Recei ed 28 Ma ch 2023
Accep ed 5 Ma ch 2024
KEYWORDS
P ice pe sis ence; ac ional
in eg a ion; COVID-19
pandemic; Russia-Uk aine
wa
1. In oduc ion
The wo ld economy has ecen ly been hi by wo exogenous shocks wi h global
consequences, namely he COVID-19 pandemic and he ene gy c isis esul ing om
he Russian in asion o Uk aine. Bo h o hem ha e had epe cussions no only on he
eal economy, bu also on p ices, which ha e isen sha ply in coun ies h oughou he
globe. An in e es ing issue is whe he o no he e ec s o hose shocks on p ices will be
long-li ed in o de o be able o adop app op ia e policy esponses. This is he ocus o
he p esen s udy, which p o ides e idence on he deg ee o p ice pe sis ence in each o
he 27 Eu opean Union membe s a es (EU27) o e a sample pe iod including bo h he
COVID-19 pandemic and he Russia-Uk aine wa . Mo e speci ically, he aim o he
analysis is o es ablish whe he he e has been any ime a ia ion in he deg ee o
pe sis ence as a esul o hose wo shocks. Fo his pu pose, a ac ional in eg a ion
model o mon hly log-p ices is es ima ed i s o e a sample ending in Decembe 2019
CONTACT Luis A. Gil-Alana [email p o ec ed] Facul y o Economics, Edi icio Amigos, Uni e si y o Na a a,
Pamplona E-31009, Spain
JOURNAL OF APPLIED ECONOMICS
2024, VOL. 27, NO. 1, 2329857
h ps://doi.o g/10.1080/15140326.2024.2329857
© 2024 The Au ho (s). Published by In o ma UK Limi ed, ading as Taylo & F ancis G oup.
This is an Open Access a icle dis ibu ed unde he e ms o he C ea i e Commons A ibu ion License (h p://c ea i ecommons.o g/
licenses/by/4.0/), which pe mi s un es ic ed use, dis ibu ion, and ep oduc ion in any medium, p o ided he o iginal wo k is p ope ly
ci ed. The e ms on which his a icle has been published allow he pos ing o he Accep ed Manusc ip in a eposi o y by he au ho (s) o
wi h hei consen .
( he pe iod be o e he COVID-19 pandemic), hen o one ending in Janua y 2022 ( he
pe iod be o e Russia-Uk aine wa ) and las ly o he ull sample ending in
Decembe 2022; in addi ion, ecu si e analysis is ca ied ou o shed u he ligh on
he possible p esence o ime a ia ion.
The adop ed amewo k is mo e gene al han he s anda d one based on he dicho omy
be ween I(0) s a iona i y and he I(1) non-s a iona i y. Speci ically, i allows o ac ional
as well as in ege deg ees o di e en ia ion. Mo eo e , i p oduces a di ec measu e o
pe sis ence in he o m o he es ima ed ac ional di e encing pa ame e d. Finally, i is
in o ma i e on whe he he e ec s o shocks a e ansi o y o pe manen and he na u e o
he dynamic adjus men p ocess. This is essen ial in o ma ion o policy make s o decide
on app op ia e ac ions. No e ha ou analysis is uni a ia e and he e o e canno shed ligh
on he speci ic channels h ough which shocks can a ec p ices. Howe e , i is s ill use ul o
policy make s since knowledge o whe he o no he e ec s o shocks will pe sis can help
hem decide on he app op ia eness o policy in e en ion.
In he exis ing li e a u e a ious pape s ha e analysed in la ion pe sis ence using
di e en me hods. Fo ins ance, F an a e al. (2010) es ima ed ARFIMA models and
ound ha among he new membe s o he Eu opean Union some (Bulga ia, Cyp us, he
Czech Republic, Mal a, Romania, and Slo akia) exhibi pe sis ence le els simila o hose
o he eu o a ea coun ies, whils o he s (Es onia, Hunga y, La ia, Li huania, Poland,
and Slo enia) a e cha ac e ised by much highe pe sis ence. Capo ale and Gil-Alana
(2011) conside ed Gegenbaue p ocesses o some Eu opean coun ies and ound mean
e e sion in all cases, which implies ha he e ec s o exogenous shocks on in la ion a e
ansi o y and he e o e he e is no need o ac i e policies o espond o hem. Gil-Alana
e al. (2016) analysed he in la ion a e in he G7 coun ies allowing o nonlinea i ies; in
pa icula , hey applied ac ional in eg a ion me hods based on Chebyshe polynomials
in ime. They ound e idence o uni oo s in he UK, Canada, F ance, Japan and he
USA, o mean e e sion in Ge many, and o explosi e pa e ns in I aly. J. Cues as e al.
(2016) examined he in la ion di e en ials be ween se en Cen al and Eas e n Eu opean
Coun ies (CEECs) and he Eu ozone. They ound e idence o nonlinea i ies in mos
cases, bu o pe sis ence only in a ew ones. No e ha a lo o he a ailable empi ical
e idence can be a ionalized in e ms o he con ac ing model de eloped by Fuh e and
Moo e (1995), in which agen s a e conce ned wi h ela i e eal wages.
Fu he e idence on in la ion pe sis ence was p o ided by Robalo Ma ques (2004) o
bo h he US and he Eu o A ea; he poin ed ou ha he esul s a e sensi i e o he
unc ion used o p oxy he in la ion mean, and ound highe pe sis ence in he 60s and
70s. Cogley e al. (2010) ocused on he US in la ion gap, measu ed as he di e ence
be ween in la ion and end in la ion, and epo ed ha pe sis ence inc eased du ing he
1980s and dec eased a e he Volcke disin la ion, whils Pi e i and Reis (2007) ound
ha i was ela i ely s able. Mayo al (2007) modelled he in la ion a es o 21 OECD
coun ies using ac ional in eg a ion me hods and ound gene ally high and ela i ely
s able pe sis ence. Capo ale e al. (2020) applied long-memo y echniques o long uns o
da a o he UK and he US by applying long-memo y me hods and also concluded ha
in la ion pe sis ence in hese wo coun ies was gene ally s able o e he ime pe iod
1660–2016. Howe e , Capo ale and Gil-Alana (2020) ound an inc ease in he deg ee o
pe sis ence in he 16 h cen u y and mo e ecen ly a e WWI and in he las qua e o he
20 h cen u y in he case o he UK when conside ing a longe sample om 1216 o 2010.
2G. M. CAPORALE ET AL.
Capo ale e al. (2022) again used long- ange dependence me hods and ound high
pe sis ence in he G7 o e he pe iod Janua y 1973 - Ma ch 2020. Finally, Capo ale
e al. (2023) e alua ed he impac o he COVID-19 pandemic and o he Russia-Uk aine
wa on he deg ee o pe sis ence o in la ion in bo h he EU27 and he eu o zone using
a ac ional in eg a ion amewo k. They ound a signi ican inc ease in in la ion pe sis-
ence, bu also ha he ull-sample esul s imply only empo a y e ec s o he wo shocks
being conside ed.
In con as o he s udies discussed abo e, he p esen one ocuses on log-p ices a he
han he in la ion a e, and hus p o ides e idence on he deg ee o pe sis ence o a possibly
nons a iona y se ies such as p ices a he han aking i s di e ences o make i s a iona y.
I also makes an impo an con ibu ion o he exis ing li e a u e by examining in g ea e
dep h he case o Eu ope. Mo e p ecisely, as in Capo ale e al. (2023), i uses long-memo y
and ac ional in eg a ion me hods o analyse he impac o bo h he COVID-19 pandemic
and he Russia-Uk aine. Howe e , in con as o ha s udy, i ocuses on he e olu ion o
p ice hemsel es a he han he co esponding in la ion a e. Mo eo e , i examines hei
s ochas ic beha iou in each o he 27 EU membe s a es. In pa icula , i in es iga es ime
a ia ion in p ice pe sis ence in each o hem, hus p oducing a no el se o empi ical esul s
no p e iously a ailable in he li e a u e.
The emainde o he pape is s uc u ed as ollows: Sec ion 2 ou lines he me hodol-
ogy; Sec ion 2 desc ibes he da a and discusses he empi ical indings; Sec ion 3 o e s
some concluding ema ks.
2. Me hodology
Di e en measu es o pe sis ence ha e been used in he li e a u e. A simple one is gi en
by he au o eg essi e coe icien in an AR(1) model (o he sum o he coe icien s in an
AR(p) one), wi h highe alues co esponding o highe deg ees o pe sis ence. Howe e ,
a se ious limi a ion o his app oach is ha i imposes an exponen ial a e o decay on he
au oco ela ion alues; mo eo e , i assumes s a iona i y I(0) o he se ies o in e es . By
con as , in he p esen s udy we adop a mo e gene al amewo k allowing o ac ional
o de s o in eg a ion and a (much lowe ) hype bolic a e o decay in he es ima ed
di e encing pa ame e d, which measu es he deg ee o pe sis ence. This ype o model
encompasses he s anda d AR(p) ones, which a e a special case o he I(d) speci ica ion
wi h d-di e enced se ies.
Mo e p ecisely, we es ima e he ollowing model:
y ¼β0þβ1 þx ;ð1LÞdx ¼u ; ¼1;2;...;(1)
whe e y
is he obse ed ime se ies, in ou case he (logged) Ha monized Index o
Consume P ices (HICP); β
0
and β
1
a e espec i ely he in e cep and he coe icien on
a linea ime end; L is he lag ope a o , i.e., L
k
x
= x
-k
, and x
is assumed o be I(d), whe e
d is he deg ee o di e en ia ion. As o he e o e m u
, we assume (weak)
au oco ela ion
1
; howe e , ins ead o imposing a speci ic ARMA model, we use a non-
1
Au oco ela ion can be de ined as weak o s ong. Weak au oco ela ion is usually associa ed o models wi h alues o
he au oco ela ion unc ion decaying a an exponen ial a e such as he Au oReg essi e Mo ing A e age (ARMA)
models; s ong au oco ela ion is ins ead cha ac e ised by a much lowe a e o decay, o ins ance a hype bolic one as
in he case o ac ionally in eg a ed models (wi h d > 0).
JOURNAL OF APPLIED ECONOMICS 3
pa ame ic me hod due o Bloom ield (1973) ha app oxima es ARMA s uc u es wi h
e y ew pa ame e s and is e y sui able in he con ex o ac ional in eg a ion, as shown
by Gil-Alana (2004).
No e ha he ac ional di e encing polynomial in L abo e can be expanded o any
eal d as
1Lð Þd¼X
1
j¼0
d
j
� �1ð ÞjLj¼1dL þd d 1ð Þ
2L2. . .
and hus, x
can be exp essed as
x ¼d x 1dðd1Þ
2x 2þ. . . þu :
In his con ex , i he di e encing pa ame e d is a non-in ege alue, x
will be a unc ion
o all i s pas his o y, and he highe he alue o d is, he highe is he deg ee o
dependence be ween he obse a ions. Tha is he eason why his pa ame e is used as
a measu e o pe sis ence in he da a. Mo eo e , i d > 0, he se ies exhibi s long memo y
due o he ac ha he spec al densi y unc ion ends o in ini y as he equency
app oaches ze o, and mean e e sion akes place as long as d is smalle han 1 since
he impulse esponse coe icien s decay hype bolically o ze o. Co a iance s a iona i y
holds i d < 0.5, and he se ies becomes mo e nons a iona y as d inc eases abo e 0.5, he
eason being ha he a iance o he pa ial sums inc ease in magni ude wi h d (F an a
e al., 2010). This ype o p ocesses was o iginally in oduced by G ange (1980, 1981),
G ange and Joyeux (1980) and Hosking (1981) and i s jus i ica ion was based on he
concep o agg ega ion by au ho s such as Robinson (1978) and o he s. They a e now
commonly used in he analysis o ime se ies da a. Mo eo e , he ac ha d can be any
eal numbe allows o conside a wide ange o speci ica ions, including: 1) sho memo y
p ocesses (i d = 0); 2) long-memo y co a iance s a iona y p ocesses (0 < d < 0.5); 3)
nons a iona y p ocesses wi h a mean e e ing pa e n (0.5 ≤ d < 1); 4) uni oo s o I(1)
p ocesses (d = 1), o e en explosi e pa e ns (d ≥ 1).
I is also impo an o know ha he es ima ion o he de e minis ic e ms (β
0
and β
1
)
in Equa ion (1) a e clea ly a ec ed by he assump ions made wi h espec o x
. In
pa icula , i x
is assumed o be sho memo y o I(0), he esul s will be biased and
inconsis en i i is in ac I(d) wi h non-ze o d. No e ha in ou app oach we join ly
es ima e all he pa ame e s in he model, since he wo equa ions in (1) can be join ly
w i en as:
~
y ¼β0~
1 þβ1~
þu ; ¼1:2;. . . (2)
whe e
~
y ¼ ð1LÞdy ;~
1 ¼ ð1LÞd1;~
¼ ð1LÞd ;
whe e 1 is a ec o , whose elemen s a e equal o 1 and a ime end, and since u
is I (0)
by cons uc ion, we can use s anda d - es s o de e mine he signi icance o he
coe icien s.
Fo he es ima ion we use a simple e sion o a es ing p ocedu e de eloped in
Robinson (1994) ha is based on he Lag ange Mul iplie (LM) p inciple. I es s he
4G. M. CAPORALE ET AL.
null hypo hesis H
o
: d = d
0
o any eal alue d
0
in (1), and he chosen es ima e o d is he
alue o d
0
p oducing he lowes s a is ic. This alue is he same as he one ob ained
h ough he Whi le unc ion in he equency domain which is he objec i e unc ion in
Robinson’s (1994) p ocedu e. This me hod is e y sui able o ou pu poses, since: (i) i
allows us o es ima e d, he deg ee o pe sis ence, o any eal alue d
0
, including possibly
nons a iona y p ocesses (d
0
≥0.5) wi hou needing o ake i s di e ences as ins ead
equi ed by s anda d p ocedu es based on uni (o ac ional) oo s; (ii) i has an
asymp o ic no mal dis ibu ion; (iii) i is he mos e icien es in he Pi man sense
(Pi man, 1948) agains local depa u es, which is impo an since d
0
is a ac ional alue.
A ull desc ip ion o his me hod can be ound in Gil-Alana and Robinson (1997).
3. Empi ical esul s
Fo he analysis we use he log ans o ma ion o seasonally unadjus ed mon hly da a o
he Ha monized Index o Consume P ices (HICP) in each o he 27 Eu opean Union
(EU) membe s a es; hese se ies ha e been ob ained om Eu os a ( he s a is ical o ice
o he Eu opean Union) and a e a ailable on he Bloombe g pla o m, wi h he sample
pe iod going om Janua y 2010 o Decembe 2022. Figu e 1 displays he HICP se ies o
each o he EU27.
2
An upwa d end in he mos ecen yea s is immedia ely no iceable.
I is no ewo hy ha a ew se ies display some deg ee o seasonali y, especially in he
case o he Sou he n Eu opean coun ies. Howe e , his does no seem o be an impo an
issue, since when assuming a seasonal AR p ocess o he e o e m, he co esponding
coe icien is ound o be e y close o 0 in all cases, including G eece, I aly and Spain
( hese esul s a e no epo ed o sa e space).
Table 1 displays he es ima es o he di e encing pa ame e d in Equa ion (1) and hei
associa ed 95% con idence in e als o each se ies and unde h ee di e en speci ica-
ions, namely: (i) se ing β
0
= β
1
= 0, i.e., assuming ha he e a e no de e minis ic e ms
in he model (column 2); (ii) se ing β
1
= 0, i.e., including only an in e cep in he model
(column 3); (iii) allowing o bo h an in e cep and a linea ime end (column 4). The
coe icien s in bold a e hose om he selec ed speci ica ion on he basis o he s a is ical
signi icance o he es ima ed coe icien s as indica ed by he co esponding - alues. The
sample pe iod o hese esul s ends in Decembe 2019, i.e., be o e he onse o he
COVID-19 pandemic.
Table 2 epo s he es ima ed model coe icien s o each se ies. I can be seen ha he
ime end is signi ican in all cases excep ha o Slo akia, indica ing lack o s a is ical
signi icance; mo e speci ically, i is posi i e and anges om 0.028 in G eece o 0.210 in
Es onia.
3
Fu he , he es ima ed alues o d a e posi i e in all cases, which implies he
p esence o long memo y (d > 0) in all coun ies excep Mal a, whe e he I(0) hypo hesis
canno be ejec ed gi en he wide con idence in e al. E idence o mean e e sion (d
2
No e ha we do no conside he agg ega e se ies because, as al eady men ioned, Robinson (1978) and G ange (1980)
bo h showed ha ac ional in eg a ion can esul om he agg ega ion o he e ogenous AR p ocesses wi h ime-
a ying coe icien s. Simila a gumen s we e la e made by o he au ho s such as Cioczek-Geo ge and Mandelb o
(1995), Taqqu e al. (1997), Chambe s (1998), Pa ke (1999), Oppenheim and Viano (2004), Za a oni (2004), Be an e al.
(2013), Ve a-Valdés (2021) and o he s.
3
No e ha he signi icance o he ime end coe icien does no suppo he end-s a iona i y ep esen a ion since, as
explained abo e, he wo equa ions in (1) can be join ly es ima ed as in equa ion (2). A end-s a iona y model would
be suppo ed by he da a i d = 0, a hypo hesis ha is decisi ely ejec ed by he esul s epo ed in he ables.
JOURNAL OF APPLIED ECONOMICS 5
Figu e 1. Mon hly ime se ies plo s o he HICP se ies in he EU27 coun ies (2015 = 100).
6G. M. CAPORALE ET AL.
Table 1. Es ima es o he di e encing pa ame e . Sample ending in Decembe 2019.
Coun y No e ms An in e cep An in e cep and a linea ime end
AUSTRIA 0.93 (0.73, 1.21) 0.59 (0.53, 0.65) 0.38 (0.23, 0.57)
BELGIUM 0.92 (0.73, 1.19) 0.68 (0.61, 0.88) 0.75 (0.59, 0.96)
BULGARIA 0.94 (0.77, 1.22) 1.05 (0.91, 1.22) 1.05 (0.92, 1.21)
CROATIA 0.92 (0.74, 1.19) 0.82 (0.61, 1.23) 0.87 (0.68, 1.20)
CYPRUS 0.93 (0.76, 1.20) 0.75 (0.42, 1.26) 0.80 (0.57, 1.27)
CZECH REP. 0.92 (0.74, 1.21) 0.93 (0.74, 1.24) 0.94 (0.77, 1.20)
DENMARK 0.94 (0.74, 1.18) 0.62 (0.52, 0.95) 0.79 (0.65, 0.97)
ESTONIIA 0.94 (0.76, 1.19) 1.04 (0.73, 1.41) 1.03 (0.84, 1.40)
FINLAND 0.93 (0.75, 1.19) 1.01 (0.81, 1.25) 1.00 (0.89, 1.16)
FRANCE 0.91 (0.74, 1.20) 0.81 (0.61, 1.14) 0.88 (0.72, 1.12)
GERMANY 0.93 (0.72, 1.18) 0.79 (0.64, 1.42) 0.80 (0.57, 1.36)
GREECE 0.95 (0.78, 1.23) 0.28 (0.11, 0.55) 0.43 (0.19, 0.70)
HUNGARY 0.95 (0.76, 1.21) 1.02 (0.77, 1.31) 1.02 (0.85, 1.28)
IRELAND 0.92 (0.72, 1.19) 0.58 (0.46, 0.86) 0.62 (0.45, 0.88)
ITALY 0.93 (0.75, 1.21) 0.37 (0.28, 0.46) 0.21 (0.07, 0.38)
LITHUANIA 0.93 (0.75, 1.20) 0.70 (0.59, 0.86) 0.72 (0.58, 0.88)
LUXEMBOURG 0.92 (0.74, 1.20) 0.63 (0.53, 0.91) 0.79 (0.65, 0.95)
LATVIA 0.94 (0.74, 1.19) 0.81 (0.63, 1.07) 0.83 (0.66, 1.09)
MALTA 0.91 (0.72, 1.15) 0.68 (0.40, 1.47) 0.68 (−0.08, 1.52)
NETHERLANDS 0.92 (0.74, 1.19) 0.61 (0.51, 0.82) 0.65 (0.49, 0.85)
POLAND 0.93 (0.75, 1.20) 1.16 (0.99, 1.43) 1.13 (0.99, 1.36)
PORTUGAL 0.91 (0.74, 1.18) 0.46 (0.37, 0.55) 0.35 (0.17, 0.58)
ROMANIA 0.95 (0.77, 1.20) 1.11 (0.91, 1.36) 1.10 (0.95, 1.32)
SLOVAKIA 0.94 (0.74, 1.18) 1.28 (1.10, 1.54) 1.27 (1.09, 1.55)
SLOVENIA 0.94 (0.76, 1.24) 0.51 (0.43, 0.62) 0.50 (0.37, 0.69)
SPAIN 0.94 (0.76, 1.22) 0.36 (0.27, 0.46) 0.24 (0.08, 0.44)
SWEDEN 0.92 (0.73, 1.20) 0.89 (0.79, 1.04) 0.88 (0.76, 1.04)
The alues in pa en hesis a e he 95% con idence bands o he es ima es o d. In bold, he selec ed speci ica ion o each
se ies on he basis o he s a is ical signi icance o he de e minis ic e ms.
Table 2. Es ima ed coe icien s in selec ed models. Sample ending in Decembe 2019.
Coun y D In e cep ( - alue) Time end ( - alue)
AUSTRIA 0.38 (0.23, 0.57)* 89.85 (136.43) 0.151 (15.81)
BELGIUM 0.75 (0.59, 0.96)* 89.77 (123.12) 0.152 (6.33)
BULGARIA 1.05 (0.92, 1.21) 94.81 (220.44) 0.101 (2.07)
CROATIA 0.87 (0.68, 1.20) 91.59 (262.58) 0.097 (5.30)
CYPRUS 0.80 (0.57, 1.27) 93.23 (116.31) 0.058 (1.81)
CZECH REP. 0.94 (0.77, 1.20) 91.86 (277.10) 0.139 (5.99)
DENMARK 0.79 (0.65, 0.97)* 92.79 (272.63) 0.080 (6.16)
ESTONIA 1.03 (0.84, 1.40) 85.42 (197.49) 0.210 (4.66)
FINLAND 1.00 (0.89, 1.16) 89.59 (299.99) 0.121 (4.43)
FRANCE 0.88 (0.72, 1.12) 92.78 (245.10) 0.105 (5.08)
GERMANY 0.80 (0.57, 1.36) 91.69 (194.51) 0.118 (6.30)
GREECE 0.43 (0.19, 0.70)* 98.98 (141.25) 0.028 (2.61)
HUNGARY 1.02 (0.85, 1.28) 87.57 (231.25) 0.196 (5.19)
IRELAND 0.62 (0.45, 0.88)* 96.02 (285.13) 0.048 (6.56)
ITALY 0.21 (0.07, 0.38)* 93.67 (186.50) 0.088 (12.81)
LITHUANIA 0.72 (0.58, 0.88)* 91.54 (209.81) 0.152 (11.74)
LUXEMBOURG 0.79 (0.65, 0.95)* 89.58 (139.49) 0.139 (5.65)
LATVIA 0.83 (0.66, 1.09) 91.73 (209.53) 0.137 (7.04)
MALTA 0.68 (−0.08, 1.52) 88.99 (83.56) 0.135 (4.87)
NETHERLANDS 0.65 (0.49, 0.85)* 90.90 (161.44) 0.125 (9.35)
POLAND 1.13 (0.99, 1.36) 91.32 (342.21) 0.134 (3.17)
PORTUGAL 0.35 (0.17, 0.58)* 93.74 (179.17) 0.092 (12.30)
ROMANIA 1.10 (0.95, 1.32) 85.21 (185.44) 0.210 (3.20)
SLOVAKIA 1.28 (1.10, 1.54) 91.16 (306.88) —–
SLOVENIA 0.50 (0.37, 0.69)* 93.15 (189.36) 0.101 (12.34)
SPAIN 0.24 (0.08, 0.44)* 94.87 (202.44) 0.082 (12.79)
SWEDEN 0.88 (0.76, 1.04) 95.47 (245.74) 0.102 (4.80)
In pa en hesis in he hi d and ou h columns he associa ed - alues. * deno es e idence o mean e e sion
a he 95% le el.
JOURNAL OF APPLIED ECONOMICS 7
a mul i a ia e amewo k o in es iga e hese issues in he con ex o ac ional
coin eg a ion, using amewo ks such as he ac ional CVAR (i.e., FCVAR) model
p oposed by Johansen and Nielsen (2010, 2012). Fu he possible ex ensions could
conside non-linea s uc u es in he de e minis ic pa o he model, such Chebyshe
polynomials in ime (as in J. C. Cues as & Gil-Alana, 2016), Fou ie unc ions (Gil-Alana
& Yaya, 2021) o neu al ne wo ks (Yaya e al., 2021) wi hin a ac ional in eg a ion
amewo k.
Acknowledgmen s
Commen s om he Edi o and wo anonymous e iewe s a e g a e ully acknowledged. Luis
A. Gil-Alana also g a e ully acknowledges inancial suppo om he G an PID2020-113691RB-
I00 unded by MCIN/AEI/10.13039/501100011033, and om an in e nal P ojec om he
Uni e sidad F ancisco de Vi o ia.
Disclosu e s a emen
No po en ial con lic o in e es was epo ed by he au ho (s).
Funding
The wo k was suppo ed by he Minis e io de Ciencia e Inno ación [PID2020-113691RB-I00].
No es on con ibu o s
Guglielmo Ma ia Capo ale is P o esso o Economics and Finance, Di isional Lead o Economics
and Econome ics, and Di ec o o he Cen e o Empi ical Finance a B unel Uni e si y London.
He is also a CESi o Resea ch Ne wo k Fellow and an RCEA (Rimini Cen e o Economic
Analysis) Senio Fellow. P io o aking up his cu en posi ion, he was a Resea ch O ice a he
Na ional Ins i u e o Economic and Social Resea ch in London; a Resea ch Fellow and hen a
Senio Resea ch Fellow a he Cen e o Economic Fo ecas ing a London Business School;
P o esso o Economics a he Uni e si y o Eas London; P o esso o Economics and Finance
and Di ec o o he Cen e o Mone a y and Financial Economics a London Sou h Bank
Uni e si y (LSBU).
P o . Luis A. Gil-Alana comple ed his Ph.D. a he London School o Economics in 1997. He has
published mo e han 500 pape s in heo e ical and applied econome ics and wo ks as a P o esso
a he Uni e si y o Na a a, Pamplona, Spain and as a Senio Resea che a he Na a a Cen e o
In e na ional De elopmen and a he Uni e si y F ancisco de Vi o ia in Mad id, Spain.
Ami Ime i is Assis an P o esso in Facul y o Managemen , Business and Economics in
Uni e si y o Business and Technology in P ish ina, Koso o. He comple ed his PhD a Cy il
and Me hodius Uni e si y in Skopje, No h Macedonia, in 2004, in he a ea o In e na ional
Economics. He ob ained his Mas e deg ee a IIUM, Kuala Lumpu , Malaysia, in 2008, in he ield
o Finance. He has been esea ch ellow a Depa men o Economics, Uni e si y o G az and
mobili y s a in Slo ak Uni e si y o Ag icul u e in Ni a in 2014 and Uni e si y o Deb ecen in
2019, including ull ime acul y in he Bah ain om 2015 o 2018. Addi ionally, has pa icipa ed in
many in e na ional con e ences and has published a icles mainly in mac oeconomics, ime se ies,
shocks, ou ism and EU in eg a ion.
14 G. M. CAPORALE ET AL.
ORCID
Guglielmo Ma ia Capo ale h p://o cid.o g/0000-0002-0144-4135
Luis A. Gil-Alana h p://o cid.o g/0000-0002-5760-3123
Ami Ime i h p://o cid.o g/0000-0003-3546-9362
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16 G. M. CAPORALE ET AL.
