On Optimal Currency Areas: Common Shocks Versus Common Persistence of Shocks

G imm, Louisa; S einkamp, S en; Wes e mann, F ank
A icle — Published Ve sion
On Op imal Cu ency A eas: Common Shocks Ve sus
Common Pe sis ence o Shocks
In e na ional Jou nal o Finance & Economics
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John Wiley & Sons
Sugges ed Ci a ion: G imm, Louisa; S einkamp, S en; Wes e mann, F ank (2024) : On Op imal
Cu ency A eas: Common Shocks Ve sus Common Pe sis ence o Shocks, In e na ional Jou nal o
Finance & Economics, ISSN 1099-1158, John Wiley & Sons, L d., Chiches e , UK, Vol. 30, Iss. 4, pp.
3825-3837,
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In e na ional Jou nal o Finance & Economics, 2025; 30:3825–3837
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In e na ional Jou nal o Finance & Economics
RESEARCH ARTICLE OPEN ACCESS
On Op imal Cu ency A eas: Common Shocks Ve sus
Common Pe sis ence o Shocks
LouisaG imm | S enS einkamp | F ankWes e mann
Osnab ück Uni e si y, Ins i u e o Empi ical Economic Resea ch, Osnab ück, Ge many
Co espondence: S en S einkamp (s en.s einkamp@uni-osnab ueck.de)
Recei ed: 13 Ma ch 2023 | Re ised: 1 No embe 2024 | Accep ed: 11 No embe 2024
Funding: This wo k was suppo ed by Bundesbank's Regional o ice in B emen, Lowe Saxony and Saxony- Anhal , as well as he Sie e - Founda ion.
Keywo ds: codependen business cycles| exchange a e egime choice| op imum cu ency a ea| se ial co ela ion common ea u e
ABSTRACT
The Op imal Cu ency A ea (OCA) li e a u e has been ocusing on he co- mo emen o business cycle shocks as a key policy
c i e ion. We documen in a simple Ba o–Go don amewo k ha , in addi ion o a high co ela ion o shocks, a common pe -
sis ence o shocks is a ele an OCA c i e ion. The model p o ides a concep ual unde pinning o empi ical s udies ha ha e
used he Se ial Co ela ion Common Fea u es (SCCF) es o e alua e common cu ency a eas. We apply he SCCF es o a se
o coun ies ha could po en ially in oduce he Eu o and ind o he pe iod om 1999 (Q1) o 2019 (Q3) only li le e idence ha
he acceding coun ies sha e a common cyclical esponse pa e n wi h he Eu opean Mone a y Union (EMU) agg ega e.
JEL Classi ica ion: E52, F36, F41
1 | In oduc ion
In he empi ical li e a u e on op imum cu ency a eas, he mos
common app oach has i s been used in he classical a icle by
Bayoumi and Eicheng een(1993). The au ho s conduc a end-
cycle decomposi ion and analyse he con empo aneous co ela ion
o sho - e m shocks, in e p e ed as demand shocks.1 The app oach
d aws i s in ui ion om Mundell's(1961) wo k on op imum cu -
ency a eas and i has mo e ecen ly been o mally illus a ed by
Be ge , Jensen, and Schjelde up(2001). Howe e , i neglec s a key
ea u e o mac oeconomic da a, he pe sis en and o en complex
se ial co ela ion pa e n o shocks. I he eby misses ou on he
po en ial spillo e e ec s o he shock in o subsequen pe iods.
In a pa allel s and o he li e a u e, s a ed by Beine, Candelon,
and Hecq (2000) and summa ised in De Haan, Inklaa , and
Jong- A- Pin(2008), he pe sis ence o he shocks is indeed he
ocus o he analysis. The au ho s employ he Se ial Co ela ion
Common Fea u es (SCCF) es , ini ially de eloped by Engle and
Kozicki (1993), o analyse whe he he impulse esponse pa -
e ns o ex e nal shocks a e simila ac oss coun ies.
Ou con ibu ion o his li e a u e is o o mally demons a e
ha a common pe sis ence o shocks—and no only hei con-
empo aneous co ela ion—is indeed a necessa y condi ion o
minimising he cos s associa ed wi h adop ing a common cu -
ency. Building on he heo e ical se ups o Be ge , Jensen, and
Schjelde up(2001) and Bleaney(2000), we pos ula e a new c i-
e ion ha p o ides an ex ension o he analy ical amewo k
by Mundell (1961). In ou adap ion o he model, shocks a e
iden ical ac oss coun ies bu au oco ela ed wi h di e en pe -
sis ence pa ame e s. In his se ing, we documen ha he s ud-
ies elying on he SCCF es a e indeed applying an app op ia e
complemen a y es ing p ocedu e.2
The opic o Op imal Cu ency A eas is a classic in he li e a-
u e on in e na ional inance and he e is a enewed in e es in
he opic as he Eu opean mone a y union keeps expanding.
Two po en ial new membe coun ies, Bulga ia and Romania,
ha e exp essed hei in e es in EMU membe ship, and C oa ia
ecen ly joined he EMU in 2023. In an empi ical assessmen ,
Deska - Šk bić, Ko a ac, and Kuno ac(2021) a gue ha he can-
dida e coun ies a e indeed in a good posi ion o join he common
This is an open access a icle unde he e ms o he C ea i e Commons A ibu ion License, which pe mi s 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.
© 2024 The Au ho (s). In e na ional Jou nal o Finance & Economics published by John Wiley & Sons L d.
3826 In e na ional Jou nal o Finance & Economics, 2025
cu ency, using an ad anced e sion o he classical empi ical
me hod p oposed by Bayoumi and Eicheng een(1993).3 In ou
empi ical applica ion o he SCCF es , we ake a esh look a
he e idence.
Taking he pe sis ence o shocks in o accoun , we ind much
mo e limi ed e idence suppo ing an Op imal Cu ency A ea
o he majo i y o EMU- candida e coun ies. Among he coun-
ies analysed, Sweden comes closes o o ming an Op imal
Cu ency A ea wi h he cu en EMU coun ies. Fo Sweden,
using he Cubadda(2001) app oach, we indeed canno ejec he
null hypo hesis o a common cycle in ou benchma k eg ession.
Fo C oa ia, Hunga y and he Czech Republic, we ejec he null
o a common cycle, bu we do ind some common cyclical ele-
men s when conside ing a less s ic e sion o he common ea-
u es es — he es o codependence ha allows o an ini ially
asymme ic esponse in he i s qua e . Finally, all coun ies
exhibi some highe - o de codependence o o de wo o h ee,
which, howe e , is ha dly ele an in p ac ice, gi en he o e all
sho - li ed cyclical na u e o GDP shocks in qua e ly da a.
In Sec ion 2, we p esen ou concep ual model amewo k.
Sec ion 3 gene alises ou main indings o highe - o de AR-
p ocesses and discusses why he SCCF es is indeed a model-
consis en es o OCAs. Sec ion 4 co e s p elimina y es s,
including isual inspec ions o he co elog ams and assess-
men s o he seasonal uni oo and coin eg a ion p ope ies.
Sec ion5 de ails ou main indings on common cyclical ea u es
and he sensi i i y analysis, while Sec ion6 concludes.
2 | Rela ionship o he Exis ing Li e a u e
The como emen o business cycles in he con ex o he li e a-
u e on Op imal Cu ency A eas is one o he mos ex ensi ely
explo ed ields o empi ical mac oeconomics. Be o e p esen ing
ou model and main esul s, we would like o highligh how ou
app oach is di e en om some key e e ences in he li e a u e.
Fo he heo e ical pa , he mos closely ela ed pape is by
Be ge , Jensen, and Schjelde up(2001) on exchange a e egime
choice. Thei model is s a ic and he e o e, i only inds ha he
con empo aneous co ela ions ma e o he decision o join a
common cu ency (o , mo e b oadly, ix he exchange a e o an-
o he coun y). Ou pape uses hei se up o a Ba o–Go don
model o mone a y policy and ollows hei app oach o doing
he wel a e compa isons. The new aspec in ou pape is ha he
e o e m, ha is, he shocks, can be au oco ela ed. Fo sim-
plici y, we assume ha he con empo aneous shocks a e iden-
ical, which allows us o ocus on he dynamic eac ions only.
This way, we a e able o highligh ha a high con empo aneous
co ela ion is no su icien , and addi ional es s o he ype p e-
sen ed in his pape a e needed.
We a e no he i s au ho s, howe e , o add an au oco ela ed
e o e m o a Ba o–Go don se up. The pape by Bleaney(2000)
has done so and has al eady epo ed he impac o au oco ela-
ion on he in la ion bias, which is he main ocus o mone a y
models on he ime- inconsis ency o mone a y policy. Ou
Lemma1 will eplica e he esul o hei model. The di e ence
be ween ou heo e ical model and he one o Bleaney(2000) is
ha we ake he analysis one s ep u he and conduc wel a e
compa isons. Tha is, we compa e—unde he assump ion o
pe ec ly co ela ed shocks— he wel a e losses om he wo
choices o joining o no joining he mone a y union, and docu-
men ha he di e ence be ween he wo wel a e le els depends
on he pe sis ence pa ame e s. I he pe sis ence is no iden i-
cal, we ind ha he e is an addi ional wel a e loss ha has no
been epo ed in ei he Be ge , Jensen, and Schjelde up(2001)
o Bleaney(2000).
Rega ding he empi ical li e a u e, he mos closely ela ed
a icle is he one by Beine, Candelon, and Hecq(2000).4 This
pape is he i s ha has used an ea ly e sion o he common
ea u es es and in e p e ed i in he con ex o he li e a u e
on op imal cu ency a eas. Ou con ibu ion o his pape is o
p o ide a heo e ical unde pinning o he a gumen hese au-
ho s ha e made. A u he empi ical con ibu ion is o use a
mo e elabo a e e sion o he common ea u es es , de eloped
by Cubadda(2001), who in his esea ch has highligh ed he im-
po ance o using non- seasonally- adjus ed da a when analysing
common cycles. Addi ionally, we also ake a much mo e ecen
da a se and apply he es ing app oach o a se o coun ies ha
cu en ly indeed ace he policy decision on whe he o no o
join a mone a y union.5
A hi d key e e ence is he a icle o Deska - Šk bić, Ko a ac,
and Kuno ac(2021): The au ho s s udy h ee Eu o- candida e
coun ies (Bulga ia, C oa ia and Romania), bu only ocus on
con empo aneous co ela ions. The con ibu ion o Deska -
Šk bić, Ko a ac, and Kuno ac (2021), howe e , is no only
o apply he basic se up o he classic a icle o Bayoumi and
Eicheng een(1993). Ins ead, hey use s a e- o - he- a Bayesian
echniques o illus a e ha shocks in he candida e coun ies
and he Eu o A ea a e qui e simila . Based on hei analysis, hey
conclude ha he coun ies a e ‘ eady o join’ he EMU, a policy
s a emen which in ligh o ou indings and he addi ional OCA
c i e ion pos ula ed in his pape may be oo s ong, o a leas
incomple e om he impo an pe spec i e o dynamic esponse
pa e ns.
3 | A Concep ual F amewo k
To mo i a e he use o a Se ial Co ela ion Common Fea u es
es , we se up a e y simple model in he classical Ba o and
Go don(1983) amewo k. This model builds on Be ge , Jensen,
and Schjelde up(2001) who ha e analysed he op imal exchange
a e egime choice in he p esence o con empo aneous coun y-
speci ic shocks. The decision on he exchange a e egime in
his model is based on he di e ence in expec ed losses in bo h
egimes. We also build on he esea ch o Bleaney(2000), who
has expanded he Ba o–Go don amewo k o include au oco -
ela ed shocks. The basic indings in his li e a u e can be epli-
ca ed in ou se up.
Ou con ibu ion is o highligh he implica ions o au oco -
ela ed shocks o he exchange a e egime choice and o ace
hei e ec s on he in la ion bias, ou pu and wel a e.
Fi s , we analyse he case o lexible exchange a es. We s a
wi h a s ochas ic e sion o he Lucas- supply schedule:
3827
whe e
y
is ou pu ,
𝜋
he in la ion a e and
𝜋e
is expec ed in la-
ion.
𝜀
is an e o e m, which we assume o ollow an AR(1)
p ocess,
𝜀 =𝛾𝜀 −1+
.
is a whi e noise shock, and
𝛾
measu es
he deg ee o pe sis ence o he shock. We assume
0<𝛾<1
, ha
is,
𝜀
is posi i ely au oco ela ed bu he s ochas ic p ocess is
s a iona y. The cen al bank minimises he ollowing quad a ic
loss unc ion:
subjec o he in la ion a e.6 Fo simplici y, we assume ha
he cen al bank can con ol he in la ion a e di ec ly. The
ime- s uc u e o he model is as ollows:
𝛼,𝜆
, as well as o -
eign in la ion and he ou pu a ge ,
𝜋∗,y∗
, a e p ede e mined.
A he beginning o he pe iod, wo ke s o m in la ion expec-
a ions. The cen al bank hen chooses he op imal in la ion
a e a e obse ing he shock
, which has ze o mean and
a a iance o
𝜎2
. The ea e
y
and
L
ollow om he Philips
cu e based on
𝜋
and
𝜋e
. Equilib ium alues o
𝜋
and
y
a e
hen gi en by:
and y=𝛾𝜀 −1+
1
1+𝛼
2
𝜆
.
These exp essions simpli y o he amilia exp essions in he li -
e a u e when se ing he pe sis ence pa ame e
𝛾
equal o ze o.
Lemma 1. The pe sis ence o shocks a ec s he in la ion bias.
P oo .
E
[𝜋]
𝛾≠0
=𝛼𝜆
(
y∗−𝜀
−1
𝛾
)
.E[𝜋]
𝛾≠0
−E[𝜋]
𝛾=0
=−𝜀
−1
𝛼𝜆𝛾.■
.
Depending on he sign o he shock in he p e ious pe iod,
his e ec can ei he s eng hen o educe he in la ion bias,
ha is, highe - han- op imal in la ion a es due o he ime-
inconsis ency p oblem. This p elimina y esul is known om
Bleaney(2000), who de i es he implica ions o in la ion pe -
sis ence, which is shown o depend on he deg ee o shocks' au-
oco ela ion and he exchange a e egime.
Mo e impo an ly in he con ex o ou o e all ques ion on
he impac o pe sis ence on he op imal exchange a e egime
choice is he ollowing inding ha can be de i ed by plugging
he alues o
𝜋
and
y
in o he loss unc ion.
Lemma 2. The shock pe sis ence does no a ec expec ed
losses in a lexible exchange a e case.
P oo .
L
𝛾>0
lex −L𝛾=0
lex =−𝜆𝛾𝜀 −1
(
𝜆𝛼2+1
)(
2y−𝛾𝜀 −1
)
and E
[
L𝛾≠0
lex
]
−E
[
L𝛾=0
lex
]
=0.
■
I is impo an o keep in mind ha while he cen al bank
chooses he op imal in la ion a e a e obse ing he shock, he
shock is s ill a s ochas ic a iable when he exchange a e egime
is decided upon. The e o e, i s mean- ze o cha ac e is ic needs
o be aken in o accoun when compu ing he expec ed agg e-
ga e wel a e loss. Unde lexible exchange a es, when a cen al
bank can ully espond o posi i e and nega i e shocks, he au o-
co ela ion does no cons i u e an addi ional wel a e loss o he
economy.7
Nex , we conside he case o ixed exchange a es, o equi alen ly
a small coun y ha joined a mone a y union (pe manen ly ixed
exchange a es). We ha e he same au oco ela ed ou pu unc ion,
y
=𝛼
(
𝜋
−𝜋
e
)
+𝜀
wi h
𝜀 =𝛾𝜀 −1+
, bu , in his case, in la ion
is de e mined by he pu chasing powe pa i y, which is gi en by
whe e
𝜃
is he shock om he o eign coun y, which we also
assume o be au oco ela ed:
whe e
u
is a whi e noise shock and
𝛿
cap u es he deg ee o pe -
sis ence o shocks in he o eign coun y. The ou pu o he home
coun y is, he e o e:
y =𝛼u +𝛾𝜀 −1+
. We can plug bo h ex-
p essions in o he loss unc ion:
As he cen al bank has ixed i s exchange a e and is impo ing
he in la ion a e om ab oad, he in la ion a e is no longe a
choice pa ame e .
To ocus on asymme ic pe sis ence and i s implica ions o wel-
a e and exchange a e egime choice, we now se
u=
. Tha is,
he s ochas ic elemen s o he ime- se ies p ocess a e iden ical
and any di e ences a e only d i en by he pe sis ence pa ame-
e s
δ
and
γ
. In he e minology o he OCA heo y, his cap u es
he case o symme ic shocks wi h asymme ic e ec s.8
P oposi ion 3. When joining a mone a y union, he e is an
addi ional wel a e gain/loss om asymme ic pe sis ence.
P oo .
E[
L𝛿≠𝛾
ix
]
−E
[
L𝛿=𝛾
ix
]
= a
(
𝜃
)(
𝛿2−𝛾2
)
, wi h a
(
𝜃
)
=
𝜎2
(
1−𝛿2
)
.
The exp ession is ze o i , and only i ,
𝛿=𝛾.■
No e ha he exp ession o he addi ional wel a e e ec can
ge nega i e i shocks a e mo e pe sis en in he joining coun y
han in he mone a y union
(𝛾>𝛿
)
. Tha is, he e is always an
a gumen o ancho unila e ally agains a s able coun y. I ol-
lows ha common pe sis ence in wo coun ies o ming a mone-
a y union is a new c i e ion o Op imal Cu ency A eas ha so
a has no been pos ula ed o mally in he li e a u e.
Co olla y 4. The only symme ic equilib ium whe e wo
coun ies ind i op imal o o m a mone a y union is when
𝛿=𝛾
.
4 | F om Model o Da a
The empi ical implica ion om he concep ual amewo k dis-
cussed abo e is ha he pe sis ence o shocks in wo coun ies
o ming a mone a y union should be iden ical. A ypical way
o measu e he pe sis ence is looking a es ima es o he hal -
li es o he eal GDP g ow h a es, which o he se o acceding
coun ies o he EMU a e epo ed in Figu e1. This p elimi-
na y inspec ion o he da a sugges s ha he coun ies may in-
deed o m an Op imal Cu ency A ea, as he pe sis ence in he
y
=𝛼
(
𝜋
−𝜋
e
)
+𝜀
(1)
L
lex =E
[
𝜆
(
𝛼
(
𝜋 −𝜋e
)
+𝛾𝜀 −1+ −y∗
)
2+𝜋2
]
𝜋
=𝛼𝜆
(
y∗−𝜀 −1𝛾
)
−
𝛼𝜆
(
1+𝛼2𝜆
)
𝜋 =𝜋∗+𝜃 ,
𝜃 =𝛿𝜃 −1+u ,
(2)
L
ix =E
[
𝜆
(
𝛼u +𝛾𝜀 −1+ −y∗
)2
+
(
𝜋∗+𝛿𝜃 −1+u
)2]
3828 In e na ional Jou nal o Finance & Economics, 2025
candida e coun ies is no s a is ically di e en om ha o he
mone a y union.
This simpli ied app oach, howe e , has wo sho comings. Fi s ,
he s anda d e o s o hal - li e es ima es a e known o be la ge.
Thus, i is ha dly a eliable sou ce o in o ma ion. Second, i ab-
s ac s om he possibili y o highe - o de au o eg essi e p o-
cesses, which a e common in qua e ly mac oeconomic da a.
Mos ime se ies on GDP ypically display bo h a pa ial au oco -
ela ion unc ion ha is signi ican o abou ou o six qua e s,
as well as a s ong seasonal pa e n.
When ex ending P oposi ion3 o highe - o de AR(p) p ocesses
o he same o de o
𝜃
and
𝜀
, we ge he ollowing exp ession o
he addi ional wel a e loss unde asymme ic pe sis ence:
Thus, no only he pe sis ence pa ame e s o he AR(1)- e m
bu all coe icien s in he AR(p) p ocess need o be iden ical o
his exp ession o be ze o, ha is,
∣𝛿i
∣=
||𝛾i||,
∀
i.
In ui i ely,
Equa ion(3) can be in e p e ed as he expec ed squa ed de ia-
ion o he wo p ocesses.9
The empi ical app oach o a se ial- co ela ion- common-
ea u e es (SCCF), which was i s de eloped by Engle and
Kozicki(1993), hus indeed cons i u es a model- consis en em-
pi ical app oach o assess he exis ence o an Op imal Cu ency
A ea. I es s o a common highe - o de AR(p) p ocess in di -
e en ime se ies by iden i ying he exis ence o a linea com-
bina ion o wo a iables ha is ee o au oco ela ion. An
al e na i e in e p e a ion o he SCCF is ha he impulse e-
sponse pa e ns o wo a iables, when aced wi h a common
exogenous shock, need o be iden ical.
Conc e ely, he es o codependence assumes ha wo ime se-
ies ollow an AR(p) p ocess o he same o de :
X ,Y ∼AR(p)
and he s a egy is o sea ch o a linea combina ion o he wo
ime se ies such ha :
Z=X −𝛽Y ∼AR(0)
.
In o de o ind his linea combina ion, we i s es ima e he
ollowing eg ession equa ion:
whe e
X ,Y
symbolise g ow h a es o equal AR p ocesses. In a
second s ep, we examine he es ima ed esidual
𝜔
ia an F- es
ha is e alua ed using a:
𝜒2
- dis ibu ion:
I he wo coun ies ollow a common esponse pa e n, he
coe icien s in he second eg ession should join ly be insigni -
ican . Ou null hypo hesis is
H0
: The e is a SCCF. Tha is, i he
lagged g ow h a es exe no in luence on he esidual o he
eg ession abo e, he e is a SCCF. The al e na i e is
H1
: The e
is no SCCF.
In p ac ice o sa egua d agains possible endogenei y issues in
he wo ime se ies, he eg ession is ypically es ima ed ol-
lowing a wo- s age leas squa es app oach using
X −k,Y −k
, wi h
k=1, …,p
, as he ins umen s. A somewha weake es han
he s ic SCCF is he es o codependence o highe o de .
Codependence exis s i a linea combina ion o
X
and
Y
, each
ollowing an AR(p) p ocess, can sho en ha p ocess o AR(p- j).
In his app oach, he ime se ies do no ha e o immedia ely e-
u n o hei equilib ium in he same way a e a shock. In he
empi ical analysis below, we epo bo h app oaches bu no e
ha only he s ic SCCF is consis en as a es o he OCA c i e-
ion de eloped in he p e ious sec ion. Fu he mo e, bo h es s
can be conduc ed wi h a wo- s age leas squa es eg ession o
wi h a GMM app oach. In he ables below, we epo he esul s
o bo h es ima ion echniques.
Since he i s p oposal o he SCCF by Engle and Kozicki(1993)
and Vahid and Engle(1993, 1997), he e ha e been se e al ad-
ancemen s in he es ing p ocedu e ha a e ele an o ou
da ase . Fi s , as shown by Cubadda(1999) he co- exis ence o
seasonali y and au oco ela ion equi es an in eg a ed app oach
o modelling he da a. The usage o de- seasonalized da a may
lead o an inco ec inding o common cycles. As all coun ies
in ou da ase indeed ha e a seasonal componen , his poin is
pa icula ly ele an o ou analysis.
In he ollowing empi ical sec ion, we i s conside he long-
e m end dynamics be o e inally conduc ing he Se ial
Co ela ion Common Fea u es es . We pe o m bo h he
s ong o m o he SCCF- es , as well as he less es ic i e
es o codependence, which was i s discussed in Vahid and
Engle(1997).10
5 | P elimina y Analysis
The qua e ly eal GDP se ies' (1999Q1–2019Q3) we e ex ac ed
om Eu os a and a e displayed in Figu e2 in seasonal di e -
ences. Eyeballing he da a, we see immedia ely some commonal-
i ies ac oss coun ies, such as he boom pe iod in he mid- 2000s,
he cyclical down u n a e he global inancial c isis in 2007/8,
as well as a ebound and a enewed ecession a e he onse o
(3)
a
(𝜃 )
P
∑
p=1
(𝛿2
p−𝛾2
p)+2 a (𝜃 )
P−1
∑
p=1
P
∑
q=p+1
𝜑q−p(𝛿p𝛿q−𝛾p𝛾q
)
X =c+𝛿Y +𝜔 ,
𝜔
=c+
∑p
k=1
𝛼kX −k+
∑p
k=1
𝛽kY −k+e
FIGURE 1 | Hal - li e es ima es [qua e s]. This igu e depic s hal -
li e es ima es (± 2 s anda d e o s) based on he impulse esponse o an
uni a ia e ec o au o eg essi e model wi h 4 lags.

3829
he so e eign deb c isis in 2010 and again a ebound he ea e .
Since oughly 2012, mos coun ies ha e displayed a ela i ely
s eady g ow h pa h.
A s anda d esponse o an exogenous shock is hen displayed
in Figu e3. Fo each coun y, we show he co elog ams ha
display he au oco ela ion o each ime se ies. Con empo aneous
co ela ions a e epo ed in Table1. I can be in e p e ed as he
cyclical esponse pa e n o each coun y o an exogenous shock.
In his ep esen a ion o he da a, we al eady see ha he e-
sponse pa e ns can be qui e di e en ac oss coun ies—despi e
he simila i ies o he hal - li es epo ed in he p e ious sec ion.
FIGURE 2 | G aphical analysis o (seasonal) eal GDP g ow h a es. This igu e depic s seasonal g ow h a es o eal GDP o Bulga ia (BGR),
Czech Republic (CZE), C oa ia (HRV), Hunga y (HUN), Poland (POL), Romania (ROU), Sweden (SWE), he 12 ounding eu o a ea membe s (EA12),
consis ing o Aus ia, Belgium, Finland, F ance, Ge many, G eece, I eland, I aly, Luxembou g, he Ne he lands, Po ugal and Spain.
3830 In e na ional Jou nal o Finance & Economics, 2025
Each o he acceding coun ies in his igu e is displayed o-
ge he wi h he co elog am o he EA12 coun ies— he se o
coun ies o which we ha e a consis en da ase o 83 obse a-
ions as ull Eu ozone membe s.11 The EA12 agg ega e is cha -
ac e ised by a ypical posi i e au oco ela ion o abou 4–5
qua e s and a nega i e, bu somewha smalle , au oco ela-
ion, o he 4–8 qua e s he ea e . Thus, when accumula ing
hese impulse esponse pa e ns in he GDP g ow h a es, one
ge s he ypical up- and- down swing pa e ns in he associa ed
le els o GDP a ound i s end. The ea e , he e a e u he
ups and downs, which, howe e , a e s a is ically insigni ican
(we omi he s anda d e o s in his g aph o a be e isual
illus a ion o commonali ies and di e ences in he poin
es ima es).
FIGURE 3 | Au oco elog am. This igu e shows es ima ed sample au oco ela ion unc ions o eal GDP g ow h a es (seasonal di e ences o
logged alues) o e 36 qua e s.
3831
The co elog ams o he acceding coun ies, by con as , a e
qui e di e en . Excep o Poland and Sweden, mos coun ies
display a much longe posi i e au oco ela ion and a delayed cy-
clical ebound. Cumula i ely, his would imply a much longe
cycle. While his i s pass gi es a isual imp ession o he da a,
a o mal es on he colinea i y o impulse esponse pa e ns
needs o be conduc ed o p ecisely pin down which coun y may
ul il he OCA c i e ion pos ula ed in he p e ious sec ion and
which coun ies do no .
An in eg al pa o he analysis o common cycles is he con-
side a ion o ends and seasonal elemen s in he da a. We,
he e o e, s a he o mal eg ession analysis by conduc ing he
espec i e es s needed o he subsequen analysis o common
cycles. Table2 epo s he seasonal uni oo es s (HEGY),12
which shows ha he ime se ies o all coun ies a e in eg a ed
a he ze o equency, a plausible inding as all da a a e in logged
le els. A he equency π/2, all coun ies including he EA12
excep Bulga ia and C oa ia a e s a iona y. The Czech Republic
and Sweden a e u he s a iona y a equency π.
We ake hese s a iona i y p ope ies in o accoun when es ing
o coin eg a ion in he nex s ep. Table3 shows ha all coun-
ies excep o Romania, Hunga y and he Czech Republic
indeed a e coin eg a ed, and hus sha e a common long- e m
end wi h he EA12. Rega ding he coin eg a ion a equency
π, we ind ha Bulga ia and Poland also sha e a common s o-
chas ic seasonal end wi h he EA12.
While no di ec ly ele an o he OCA li e a u e, i is e y im-
po an o ake accoun o hese cha ac e is ics o he da a when
pe o ming he es o common se ial co ela ion in he nex
sec ion. We will—whe e e necessa y—include he e o co -
ec ion e m in he lis o ins umen s when conduc ing he
common ea u es es s.
6 | Codependence and Common Cycles
We now ge o he main pa o he analysis— he es o he
exis ence o common cyclical pa e ns ac oss coun ies, ha is,
a common impulse pa e n o an exogenous shock. The esul s
a e summa ised in Table4. The e a e in p inciple wo di e -
en app oaches o conduc a es o a common se ial co ela ion
ea u e, one is eg ession- based and one is based on canonical
co ela ion analysis, simila o he Engle- G ange wo- s ep and
he Johansen mul i a ia e app oach o he coin eg a ion es . In
ou exe cise, we ake he la e app oach and es ima e he pa-
ame e s wi h OLS as well as wi h GMM.13
When s a ing wi h he s ic o m o iden ical impulse esponse
pa e ns, we need o conside he i s column o es s a is ics
and associa ed p- alues, labelled ‘codependence o o de ze o’.
This able illus a es ha indeed mos o he coun ies do no
sha e a common impulse esponse pa e n, no e en Poland,
which appea ed o be qui e simila o he EA12 when ini ially
eyeballing he da a. The only coun y which indeed sha es a
common impulse esponse pa e n appea s o be Sweden.
A somewha weake de ini ion o a common cycle could be used
whe e he ini ial esponse (a lag 1) is allowed o be di e en ,
bu all subsequen lags would be equi ed o be iden ical. This is
conside ed o be a codependen cycle o o de one and may also
be o ele ance o he OCA case, al hough i does no ollow
TABLE 1 | Co ela ion coe icien s.
BGR ROU HRV HUN POL CZE SWE
EA12 0.307*** 0.442*** 0.730*** 0.760*** 0.515*** 0.810*** 0.880***
[2.90] [4.43] [9.13] [10.54] [5.41] [12.44] [16.65]
No e: Table1 epo s (Pea son) co ela ion coe icien s be ween coun ies' eal GDP g ow h a es (seasonal di e ences). - S a is ics o he null o he coe icien being
unequal o ze o a e gi en in pa en hesis. *** indica es s a is ical signi icance a he 1% le el. The sample pe iod is 1999Q1–2019Q3.
TABLE 2 | HEGY- seasonal uni oo es s o log- le els (seasonally unadjus ed).
Coun y
F equency
0π π/2 All seasonal equencies
EA12 −2.455 −2.179 14.803*** 12.010***
BGR −1.919 −2.537* 3.240 4.910
ROU −1.996 −1.747 7.308** 6.173**
HRV −2.305 −1.878 1.250 2.004
HUN −1.699 −2.653* 13.402*** 12.517***
POL −2.403 −2.658* 11.690*** 10.321***
CZE −2.202 −3.890*** 10.252*** 11.714***
SWE −3.286* −2.939** 14.022*** 11.974***
No e: *, **, *** indica e s a is ical signi icance a he 10%, 5%, and 1% le el, espec i ely. Reg esso s include, in e cep , end and seasonal dummies. Op imal lag o de
be ween 1 and 7 is de i ed om he Akaike In o ma ion C i e ion.
3832 In e na ional Jou nal o Finance & Economics, 2025
di ec ly om ou model. When applying his less s ic c i e ion,
Table4 shows ha he Czech Republic and C oa ia also display
some simila i y in he sense o a common, bu no pe ec ly syn-
ch onised common cycle. Finally, when conside ing highe o -
de s up o h ee, we ind a common ea u e o all coun ies o
a leas one o he wo es ing p ocedu es.
To u he explo e he obus ness o he limi ed inding on a
common seasonal pa e n, we i s conside he choice o lag
leng h in he common ea u es es . In ou baseline speci ica-
ion, he lag leng h was de e mined by he Akaike In o ma ion
C i e ion (AIC). Howe e , unde speci ica ion o he lag leng h
migh lead o an o e - ejec ion o he null hypo hesis o ‘no
common se ial co ela ion ea u e’ as any emaining au oco -
ela ion in he esiduals would be picked up in he second s age
o he es . We, he e o e, also explo ed o he lag s uc u es o
illus a e his poin . Table5 shows he esul s when adding o
d opping one lag, compa ed o he one indica ed by he AIC. We
indeed ind ha wi h a sho e lag leng h, he e is an e en s on-
ge ejec ion o he null hypo hesis, while a a la ge lag leng h,
we canno ejec a common se ial co ela ion ea u e o he
case o he Czech Republic a he con en ional 5% signi icance
le el anymo e, when using he 2SLS p ocedu e ha leads o a p-
alue o 0.068. We ne e heless keep he AIC as ou benchma k.
This is because he al e na i e Schwa z In o ma ion C i e ion
indica es he same o ewe lags o be included in he exe cise.
Also, when using he 10% le el, he esul o he Czech Republic
would be nega i e, and he GMM es e en ejec s he common
ea u e a 5%.
As ano he obus ness check, Table6 epo s he esul s o he
ea lie canonical co ela ion- based e sion o he common ea-
u es es o Tiao and Tsay(1989), o which he p e iously e-
po ed es can be seen as a gene alisa ion. Schleiche (2007)
showed ha he op imal GMM es ima o ends o sligh ly unde -
ejec and he Tiao and Tsay es ends o sligh ly o e - ejec a
sample sizes compa able o hose in ou analysis. When using
his es , howe e , we con i m mos o he indings abo e, excep
o Sweden, which acco ding o he s ic common ea u es es
does no cons i u e an Op imal Cu ency A ea wi h he EMU
coun ies.
O e all, he e idence o common pe sis ence and he simila -
i y o au o eg essi e coe icien s be ween he EU12 and he
TABLE 3 | Seasonal coin eg a ion es s o log- le els (unadjus ed)
wi h end/bi a ia e agains EA- 12.
0
𝝅
Lags = 0 ≤ 1 = 0 ≤ 1
BGR 723.073*** 0.217 16.342*** 6.761
ROU 58.485 0.532 7.793* 3.103
HRV 618.462*** 2.112 8.017* 2.320
HUN 611.625* 0.251 6.119 0.568
POL 521.180*** 0.022 15.258*** 0.754
CZE 57.885 0.000 — —
SWE 714.640** 3.334 — —
No e: T ace s a is ics. *, **, *** indica es he ejec ion o he null based on
linea ly in e pola ed c i ical alues o Lee and Siklos (1995). Op imal lag o de
be ween 1 and 7 is de i ed by Akaike In o ma ion C i e ion o he bi a ia e VAR
incl. de e minis ic ends and seasonal dummies.
TABLE 4 | Op imal GMM es .
Coin eg a ion
a equency
Codependence o o de
0 1 2 3
Lags Null S a . P ob. S a . P ob. S a . P ob. S a . P ob.
BGR 0,
𝜋
7GMM 46.26 0.000 39.02 0.001 32.24 0.006 24.79 0.053
2SLS 28.59 0.018 26.41 0.034 13.07 0.597
ROU — 5 GMM 72.60 0.000 56.05 0.000 44.22 0.000 32.63 0.000
2SLS 34.80 0.000 33.56 0.000 12.63 0.180
HRV 0 6 GMM 31.70 0.002 27.26 0.007 24.67 0.016 19.12 0.086
2SLS 18.75 0.095 16.59 0.166 9.94 0.621
HUN — 6 GMM 43.42 0.000 34.26 0.000 28.20 0.003 16.08 0.138
2SLS 21.14 0.032 19.93 0.046 7.73 0.737
POL 0,
𝜋
5GMM 77.16 0.000 62.86 0.000 45.12 0.000 28.88 0.002
2SLS 42.15 0.000 39.28 0.000 11.66 0.390
CZE — 5 GMM 19.35 0.022 10.41 0.319 5.92 0.747 4.75 0.855
2SLS 7.61 0.574 7.60 0.575 2.70 0.975
SWE 0 7 GMM 17.24 0.244 12.85 0.538 9.82 0.775 10.11 0.754
2SLS 9.75 0.780 7.60 0.909 7.77 0.901
No e: Op imal GMM/2SLS χ2 es s a is ics and ela i e p- alues. Lag o de selec ion, see Table3.