23
4, XXIII, 2020
Economics
DOI: 10.15240/ ul/001/2020-4-002
COINTEGRATION ANALYSIS
OF THE WORLD’S SUGAR MARKET:
THE EXISTENCE OF THE LONG-TERM
EQUILIBRIUM
Elena Kuzmenko1, Luboš Smu ka2, Wadim S ielkowski3,
Jus as Š eimikis4, Dalia Š eimikienė5
1 Czech Uni e si y o Li e Sciences, Facul y o Economics and Managemen , Depa men o Economics,
Czech Republic, ORCID: 0000-0002-2091-4630, [email p o ec ed];
2 Czech Uni e si y o Li e Sciences, Facul y o Economics and Managemen , Depa men o Economics,
Czech Republic, ORCID: 0000-0001-5385-1333, [email p o ec ed];
3 Czech Uni e si y o Li e Sciences, Facul y o Economics and Managemen , Depa men o Economics,
Czech Republic, ORCID: 0000-0001-6113-3841, [email p o ec ed];
4 Uni e si y o Economics and Human Science in Wa saw, Facul y o Managemen and Finances, Finance and
Accoun ing Depa men , Poland, ORCID: 0000-0003-2619-3229, [email p o ec ed];
5 Vilnius Uni e si y, Kaunas Facul y, Ins i u e o Social Sciences and Applied In o ma ics, Li huania, ORCID:
0000-0002-3247-9912, [email p o ec ed] (co esponding au ho ).
Abs ac : This pape add esses he issue o in e connec ion among majo suga ma ke s and
commodi y/exchange s ocks in di e en pa s o he wo ld using he Johansen coin eg a ion
app oach and ec o e o co ec ion model. Due o a high deg ee o suga ma ke agmen a ion
and co esponding di e si y in p ice le els and i s ola ili y in di e en egions, he esul s o ou
analysis sheds some ligh on he e y ac o a ‘single’ global suga ma ke exis ence and can be
impo an no jus wi h ega d o p oduce s and buye s o suga bu o he in e na ional in es o s
as well, bo h in he ligh o isk go e nance and maximizing p o i abili y. Using he e alua ion o he
ex en o connec ion among egional suga ma ke s, one can assess po en ial bene i s a ailable
o in es o s h ough in e na ional di e si ica ion be ween he analyzed ma ke s. Ou analysis has
e ealed he p esence o mu ual in e ac ion among he selec ed suga ma ke s/commodi y s ock
exchanges in indi idual egions and con i med he long- e m equilib ium among hem. The e o e,
despi e an ob ious di e si y in p ice le el and hei luc ua ions in di e en wo ld egions, he
selec ed o he analysis egional suga ma ke s a e ac ing oge he as a single o ganism. The
de e mining o he ex en o which he analyzed suga ma ke s a e in e connec ed ha e signi ican ly
s eng hen he unde s anding o he la es suga p ice de elopmen al ends. In addi ion, he esul s
o his s udy opened space and mapped ou clea objec i es and measu able a ge s o po en ial
esea ch – o e eal wha ma ke s can be e e ed o as leading ones in a sense ha namely hey
p ima ily se e as a sou ce o p ice u bulence. In summa y, ou esul s e ealed and con i med he
long- e m equilib ium among hem and he ou comes o his s udy opened he new esea ch ealms
and iden i ied he clea and measu able a ge s o he u u e empi ical esea ch in his ield.
Keywo ds: Suga , exchange/commodi y s ocks, coin eg a ion, VECM, equilib ium.
JEL Classi ica ion: O13, Q13, Q18.
APA S yle Ci a ion: Kuzmenko, E., Smu ka, L., S ielkowski, W., Š eimikis, J., & Š eimikienė,
D. (2020). Coin eg a ion Analysis o he Wo ld’s Suga Ma ke : The Exis ence o he Long-
e m Equilib ium. E&M Economics and Managemen , 23(4), 23–38. h ps:///doi.o g/10.15240/
ul/001/2020-4-002
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24 2020, XXIII, 4
Economics
In oduc ion
In gene al, suga ma ke s a e among he
as es de eloping ma ke s in he wo ld (Huang
& Xiong, 2020). The signi ican global ma ke
libe aliza ion esul ed in he as g ow h o supply
and s ocks (Zucke indus ie, 2018). A he
same ime, con inuous changes in consump ion
pa e ns a e a ec ing he global demand o
suga and suga p oduc s (Muhammad e al.,
2019). On he o he hand, global suga ma ke
is s ill in luenced by he exis ing p o ec ionis s
measu es (see Solomon, 2014). I is o no e
ha p o ec ionis policies a e applied in suga
ma ke s by bo h de eloped and de eloping
coun ies (Haley, 2016). E en ually, global
suga ma ke appea s o be su e ing because
o high-applied a i s, limi ed a i quo as and
p oduc ion subsidies (da Cos a e al., 2015). As
a esul , his is e lec ed in p ice ansmission
and signi ican suga p ice di e ences exis ing
among indi idual egions in he wo ld. Ano he
speci ic ea u e o global suga ma ke is i s
no able p ice luc ua ion which is a esul o
specula i e ade ac i i ies. This ob iously
happens since inancial ins umen s p oli e a ed
and became in u n objec s o specula ion
(S a oš e al., 2013). Especially wi hin he las
decade he global suga ma ke a ac ed sho -
e m-o ien ed in es o s. Those a e in e es ed
in dynamic and apid changes in p ice
de elopmen as hei ac i i ies a e bo h p ice
educ ion and p ice g ow h o ien ed (Sm čka e
al., 2012). This e en ually esul s in a pa icula
agmen a ion in de elopmen o global suga
ma ke which bea s co esponding p oblems
e lec ed in mu ual p ice de e mina ion and
i s adequa e ansmission. Wi h his ega d, i
becomes ha d o alk abou he exis ence o
such a single global ma ke o suga . I is, in
ac , ep esen ed by se e al egional ma ke s
ha a e mo e o less in e connec ed (Lich ,
2008). Ne e heless, he e y deg ee o
in e connec ions among hese egional ma ke s
ha may exis h ough pa icula bila e al o
mul ila e al ag eemen s (Reinbe g , 2018), is
no e iden and, hus, is wo h o be s udied.
A he same ime he suga p ice is also
a speci ic ca ego y, since i s alue is a esul
o mu ually de e mined supply and demand
in e ac ions ela ed only o a ma ginal
po ion o eal p oduc ion. I is es ima ed ha
app oxima ely only o y pe cen o global suga
p oduc ion is ealized h ough ee ma ke
(Reinbe g , 2018). The majo i y o global suga
p oduc ion is ealized and sold being based on
mu ual con ac s be ween suga p oduce s and
oods u p oduce s (Reinbe g , 2018). As i was
speci ied he global suga p ice o ma ion and
mu ual p ice in e ac ion a he le el o wo ld
ma ke is ex emely di icul p ocess and he e
a e nume ous ac o s and a ious s akeholde s
ha may and do in luence his p ocess
(Zucke indus ie, 2017). In o de o unde s and
he p ocess o suga p ice o ma ion a leas a
he le el o suga p oduc ion, which is di ec ly
con ac ed, i is necessa y, i s , o unde s and
he ela ions exis ing among indi idual ma ke s
all a ound he wo ld.
The p oblem o suga p ice de elopmen
a he le el o selec ed commodi y s ock
exchanges was add essed in he ollowing
se e al s udies published in he pas . Tahi e
al. (2016) examined con empo aneous as well
as causal ela ionship among ading olume,
e u ns and suga p ice ola ili y. Resende
and Candido (2015) assessed he exis ing
ela ionship among he suga cane sec o
( ep esen ed by E hanol and Suga ), Oil,
BRL/USD Exchange Ra e and B azilian s ock
ma ke ( ep esen ed by he BOVESPA – Bolsa
de Valo es de São Paulo – Index). Láza o
(2013) analyzed a suga p ice index o Ha ana
S ock Exchange. Če mák (2009) analyzed he
s a e o global suga ma ke in gene al and he
ole o NYSE (New Yo k) and LIFFE (London).
Tanne e al. (2018) analyzed suga p ice
de elopmen in he p ocess o wo ld economy
inancializa ion and in luence o specula ions.
Acco ding o hei indings conside able
suga p ice ola ili y o a la ge ex en was
due o ope a ions in specula i e unds (hedge
unds). Ge o kyan (2018) s udied sho - e m
sensi i i y among exchange ma ke p essu e
and a ious domes ic and ex e nal ac o s
in p ima y commodi y-expo ing eme ging
ma ke s. Agbenyegah (2014) analyzed suga
ma ke speci ic and he ole o commodi y
s ock exchange ope a o s a he le el o B azil,
Thailand and China in ela ion o NYSE. Sa an
(2011) iden i ied he basic undamen als o he
global suga ma ke . He analyzed suga ma ke
speci ics in ela ion o commodi y ma ke , suga
and suga c ops p oduc ion, in e con inen al
exchange and wo ld ma ke .
In he ligh o he discussed abo e, he
in e connec ion among majo suga ma ke s in
he wo ld may ha e c i ical ele ance no jus o
p oduce s and buye s, bu o in e na ional equi y
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4, XXIII, 2020
Economics
in es o s bo h in he ligh o isk go e nance
and maximizing p o i abili y. By e alua ing he
ex en o connec ion among suga ma ke s in
di e en pa s o he wo ld, we can es ima e
he exis ence o po en ial gains o in es o s
h ough in e na ional di e si ica ion be ween
he examined ma ke s (Gio , 2003). Because
i he le el o coin eg a ion among hem
inc eases, he bene i o di e si ica ion alls
(Na ayan, 2005). Ne e heless, he e y ac o
he exis ence o such a long- e m equilib ium
(which can be e e ed o as a hypo hesis o
a ‘single global suga ma ke ’) bea s impo an
implica ions as o po en ial in es o s, so as o
selle s, sugges ing ha s udying o coin eg a ion
would be aluable o all in e es ed pa ies.
De e mining he ex en o which he analyzed
suga ma ke s a e in e connec ed would
signi ican ly b oaden he awa eness o he
la es suga p ice de elopmen ends.
The main aim o his pape , hus, is o
analyze he in e connec ion (i any) ha exis
among wo ld majo suga ma ke s. Speci ically,
o es o he p esence and deg ee o he co-
mo emen o e he 5-yea pe iod om 2012
ill 2017 we conduc a coin eg a ion analysis
ega ding he ollowing eigh global suga
ma ke playe s – suga exchange s ocks and
In e na ional Suga alliance:
1. NYSE/New Yo k S ock: New Yo k No. 11;
2. LSE/London S ock Exchange: London
No. 5;
3. NCDEX/Na ional Commodi y and
De i a i es Exchange – Kolhapu -M G ade
(India);
4. ISA/In e na ional Suga Ag eemen ;
5. 3B/B azil Bolsa Balcao/B azil – São Paulo
ESALQ;
6. BMV/Bolsa Mexicana de Valo es/Mexico;
7. Zhengzhou Commodi y Exchange/ZCE
China;
8. MOEX/Moscow Exchange Russia.
The esul s o he analysis will help o gain
insigh in o how coin eg a ion among suga
ma ke s con ibu es o de elopmen o suga
p ice in di e en pa s o he wo ld.
The es o he s udy is o ganized as ollows:
sec ion 2 desc ibes da a and me hodology used
in he esea ch, sec ion 3 p o ides a de ailed
p ocedu e o applica ion he p esen ed abo e
me hods along wi h he achie ed esul s
and discusses hem, sec ion 4 akes s ocks
o ele an ou comes and summa izes he
conclusions.
1. Me hodology
1.1 Da a Desc ip ion
The aw da a, consis ed o daily closing p ices
a he selec ed s ock exchanges, we e e ie ed
om Lich -In e ac i e. The co esponding
s ock exchanges we e selec ed acco ding
o a p inciple o ep esen a i eness. The
h ee impo an ep esen a i es o Ame ican
con inen ’s suga a e B azil, Mexico and USA.
B asil Bolsa Balcao is ypical ep esen a i e
o La ino Ame ican suga ma ke , NYSE
is ep esen a i e o No h Ame ican suga
ma ke and Bolsa Mexicana de Valo es can be
e e ed o as a b idge be ween bo h p e iously
men ioned ma ke s. The mos impo an suga
ma ke s o India (Na ional Commodi y and
De i a es Exchange) and China (Zhengzhou
Commodi y Exchange) we e selec ed o be
ep esen a i es o Asian suga ma ke . Bo h
ins i u ions ha e been ope a ing unde he
speci ic na ional ood ma ke egula ion and
hei s suga p ice de elopmen is qui e speci ic
one in compa ison o o he ma ke s ep esen ed
by e.g. NYSE o LIFFE. London S ock Exchange
(being a ypical ep esen a i e o wes e n
Eu opean suga ma ke p ice o ma ion) and
Moscow Exchange (which ope a es unde he
signi ican na ional egula ion) we e chosen as
ep esen a i es o Eu opean egion.
Fo he pu pose o ha ing a so o
p ice de elopmen benchma k, one mo e
ep esen a i e o independen suga p ice
o ma ion was chosen – ISA suga p ices. Being
an In e na ional Ag eemen i s objec i e is o
secu e expanded in e na ional collabo a ion
ela ed o wo ld suga issues, p o ide a o um
o in e go e nmen al consul a ions on suga
so as o imp o e he wo ld suga economy,
acili a e ade by collec ing and p o iding
in o ma ion on he wo ld suga ma ke and
o encou age inc eased demand o suga ,
pa icula ly o non- adi ional uses (EC, 2018).
As a esul , ISA p ice is based on suga p ice
eco ds p o ided by indi idual ISA con ac o s:
Eu opean Economic Communi y, A gen ina,
Aus alia, Aus ia, Ba bados, Bela us, Belize,
B azil, Came oon, Colombia, Cos a Rica,
Cuba, Cô e d’I oi e, he Dominican Republic,
Ecuado , Egyp , El Sal ado , E hiopia, Fiji,
Finland, Gua emala, Guyana, Hondu as,
Hunga y, India, I an, Jamaica, Japan, Kenya,
La ia, Malawi, Mau i ius, Mexico, Moldo a,
Mozambique, Nige ia, Pakis an, Panama,
Pa aguay, he Philippines, Russia, Se bia and
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26 2020, XXIII, 4
Economics
Mon eneg o, Sou h A ica, Sudan, Swaziland,
Swi ze land, Tanzania, Thailand, T inidad and
Tobago, Tu key, Vie nam, Zambia, Zimbabwe.
Thus, hese coun ies-con ac o s es ablished
he simila ly named alliance ISA.
Some di e ences in measu emen uni s
we e adjus ed, o example, lb. was ecalcula ed
o ons, US cen s – o US dolla s. Bu a he
same ime local cu ency uni s emained
unchanged in ha mony wi h Alexande
(2001), who s ongly ecommends pe o ming
coin eg a ion analysis among ma ke s using
p ices exp essed in local cu encies o be e
e lec ion he co-mo emen s in di e en
coun ies. Such a non-con e ing o a common
cu ency ensu es elimina ing any po en ial
exchange a e ola ili y. Since he analyzed
coun ies ha e di e en non- ading days, we
ho oughly examined he whole da ase o
ensu e consis en da a ep esen ing main eigh
suga ma ke s playe s. Since, in addi ion, he e
was ound a numbe o missing obse a ions,
i was decided o ans o m he ini ial daily-
based da a in o a weekly-based da a se using
a geome ic mean. As a esul , we used weekly
closing p ices o suga in hei na u al loga i hm
aded on he eigh main suga ma ke s since
23. 08. 2012 un il 16. 05. 2017. As a esul , ou
da ase co e s 5-yea weekly ime ame ha
comp ises 247 obse a ions.
1.2 Tes ing o a Uni Roo and
Coin eg a ion
Coin eg a ion may be e e ed o as a s a is ical
exp ession o equilib ium ela ionship among
mu ually connec ed a iables sha ing gene ic
s ochas ic ends. A e publishing by Engle and
G ange (1987) hei seminal pape , which was
b oaden in he ollowing yea s, a coin eg a ion
analysis has become a obus echnique o
analyzing gene al endencies in ime se ies,
ensu ing a obus me hodology o simula ion
bo h long- un and sho - un ends in an
analyzed phenomenon.
When he coin eg a ion analysis e ealed
he exis ence o a coin eg a ing ec o , we
can d aw a conclusion ha he in es iga ed
ime se ies will no di e ge in he long- un,
and will e u n o an equilib ium le el ollowing
any sho - un shi ha may occu . The 5-yea
pe iod ensu es collec ing necessa y and
su icien in o ma ion o s udy he po en ial
p esence o a long- e m equilib ium among he
selec ed suga ma ke s. To examine inancial
ime se ies wi h he use o coin eg a ion
echnique, he ime se ies in i le els ha e o
be non-s a iona y and in eg a ed o he same
o de (I(n)), meaning ha hese se ies become
s a iona y a e a n-di e en ia ing p ocedu e.
Va iables a e conside ed o be coin eg a ed
i hey a e in eg a ed o he same o de and
ha e a s a iona y linea combina ion o all he
a iables included in o he analysis.
A he p esen ime wo main app oaches
o in es iga e coin eg a ion exis : Engle-
G ange s wo s ep es ima ion me hod (1987)
and Johansen’s maximum likelihood me hod
(1997) based ei he on he ace s a is ic o
he maximum eigen alue s a is ic. The Engle-
G ange s app oach bea s one e y impo an
sho coming – despi e he ac , ha i is qui e
simple o conduc , i can only be pe o med
on a maximum o wo a iables and equi es
much mo e obse a ions o p e en po en ial
es ima ion mis akes (B ooks, 2014). Wi h ega d
o he abo e, since ou goal is o examine eigh
exchange s ocks, we will apply he Johansen’s
me hodology (1997) enabling he analysis in
a mul i a ia e amewo k.
P io o applying he la e we, i s , es he
se ies o op imal lag leng h (as o indi idual
a iables and so o an unde lying VAR
model) and, second, conduc wo di e en
bu consis en wi h each o he he Augmen ed
Dickey-Fulle (ADF) and he Phillip-Pe on (PP)
uni oo es s o ensu e ha he analyzed ime
se ies ha e he same o de o in eg a ion. Since
he ADF es loses i s powe o high numbe
o lags (p) and PP es does no (Ghosh e al.,
1999), we pe o med bo h o hem, whe e i was
needed, o e i y and con i m he co ec ness
o he esul . The model (ADF) o check he
p esence o a uni oo is:
(1)
whe e Δ is he di e ence ope a o ;
y is he na u al loga i hm o he se ies;
T is a end a iable;
λ and ψ a e pa ame e s o be es ima ed and
ε is he e o e m.
The op imal lag leng h was ound by
selec ing he model wi h he lowes Schwa z
Bayesian In o ma ion C i e ion (SBIC) and
Akaike In o ma ion C i e ion (AIC), which
ensu es he needed accu acy. As pe li e a u e
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4, XXIII, 2020
Economics
ela ed o coin eg a ion analysis, he SBIC is
usually mo e consis en bu ine icien , while
AIC is no as consis en , bu is usually mo e
e icien (B ooks, 2014).
Ha ing pe o med he uni oo es s on
he analyzed ime se ies and con i med all
he ime se ies a e in eg a ed o he same
o de , we conduc ed a mul i a ia e Johansen
es in ol ing all 8 a iables. This enables
o in es iga e he p esence o a long- e m
equilib ium (i any).
The Johansen app oach implies
a maximum likelihood me hod ha iden i ies
a numbe o coin eg a ing ec o s in a non-
s a iona y VAR ( ec o au o eg ession) wi h
es ic ions imposed, known as a VECM ( ec o
e o co ec ion model). Johansen’s es ima ion
model can be w i en he ollowing way:
,
(2)
whe e X = (X1 , X2 , …, Xn ) is a n*1 ec o
o he n-coin eg a ed a iables, which a e
supposed o be in eg a ed o o de I(n);
μ = (μ1, μ2, …, μn) is a n*1 ec o o in e cep s;
β´ = (β(1), β(2), …, β( )) is he n* coin eg a ing
ma ix consis ing o he -coin eg a ing ec o s.
β´ ep esen s he long- un coin eg a ing
ela ionship be ween he a iables; α is a n*
ma ix o he -adjus men coe icien s o each
o he n a iables, whe e is he numbe o
coin eg a ing ela ionships in he a iables, so
ha 0 < < n. α es ima e he speed a which
he a iables adjus o hei equilib ium; Γi a e
n*n ma ixes o au o eg essi e coe icien s;
() is a VAR o sho - un componen ;
ε = (ε1 , ε2 , ..., εn ) is a n*1 ec o o mu ually
unco ela ed whi e noise dis u bances om
(0, ∑) (Kocenda & Ce ny, 2007).
Johansen (1991) sugges s wo di e en
es s a is ics o es ing coin eg a ion: he
T ace es and he Maximum eigen alue es .
The la e is used less o en compa ed o he
ace s a is ic me hod because no solu ion o
he mul iple- es ing p oblem has ye been ound
(S a aCo p, 2013). The T ace es es s he
null hypo hesis ha he e a e no mo e han
coin eg a ing ela ions. Res ic ing he numbe
o coin eg a ing equa ions o be o less implies
ha he emaining (K – ) eigen alues a e ze o.
Johansen (1995) de i es he dis ibu ion o he
ace s a is ic:
(3)
whe e T is he numbe o obse a ions and
a e he es ima ed eigen alues.
Fo any gi en alue o , la ge alues o
he ace s a is ic a e e idence agains he null
hypo hesis ha he e is o ewe coin eg a ing
ela ions in he VECM.
Then we no malize he esul ing
coin eg a ing ela ionship on one o he a iables
so ha he coe icien on his a iable equal o
one. We could selec any o he a iable, bu in
ha mony wi h Juselius (2006) he a ios among
coe icien s in coin eg a ing ela ionships a e
he same, i espec i e o which a iable is used
o no malize he da a.
We enume a e he indi idual s eps o ou
me hodology o he coin eg a ion analysis
below:
1. Uni Roo Tes s (ADF plus PP i needed);
2. Johansen’s coin eg a ion es ing (Mul i a ia e
amewo k using all 5 speci ica ions o he
es );
3. T ace es ;
4. Mul i a ia e long- un/sho - un analysis –
VECM cons uc ion (no maliza ion agains
lnBRA, since i is he bigges suga ma ke
among o he s);
5. Pos -es ima ion analysis.
All es s we e ca ied ou in S a a 13.01
s a is ical so wa e.
2. Resul s and Discussion
This sec ion p o ides he ou comes o all he
es s ha we e ca ied ou . The calcula ions
we e pe o med in S a a 13.01 using na u al
loga i hms o all a iables (p ices). G aphs o
all he analyzed ime se ies a e ep esen ed in
Fig. 1.
2.1 Tes ing o a Uni Roo
P io o es o coin eg a ion o i he
coin eg a ing VECM we e i y s a is ical
p ope ies o he se ies: whe he o no hey a e
s a iona y. As i can be seen om he Fig. 1, all
he se ies seem o be non-s a iona y p ocesses
ha combine a andom walk wi h a s ochas ic
end.
The g aphs show ha al hough he se ies
appea o mo e simila ly, he ela ionship
among hem is no clea .
Be o e applying he ADF and PP es s o
ou da a, i s we need o iden i y he op imal
lag o de o each o he s udied se ies. The
op imal numbe o lags was selec ed acco ding
o he esul s o he es s applied o all he
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28 2020, XXIII, 4
Economics
Fig. 1: G aphical ep esen a ion o he analyzed ime se ies
Sou ce: own
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29
4, XXIII, 2020
Economics
se ies bo h in le els and i s di e ences, wi h
he use o he ollowing c i e ia, such as inal
p edic ion e o (FPE), Akaike’s in o ma ion
c i e ion (AIC), Hannan–Quinn in o ma ion
c i e ion (HQIC), Schwa z Bayesian in o ma ion
c i e ion (SBIC) and sequen ial likelihood- a io
(LR). The summa y o he ob ained esul s is
gi en in Tab. 1.
As i can be seen om he Tab. 1, ela i ely
high numbe o lags was ecommended o
dlnIND, lnMEX se ies, as well as o lnBRA
se ies bo h in le els and i s di e ences. Fo
ha eason, when es ing men ioned se ies o
he p esence o a uni oo , bo h Augmen ed
Dickey-Fulle and Phillips-Pe on es s will be
used as i was explained in he me hodology.
Se ies Lag Se ies Lag
In le el In i s di e ences
lnNY 2dlnNY 1
lnLON 2dlnLON 1
lnIND 2dlnIND 4
lnISA 2dlnISA 1
lnBRA 4 dlnBRA 4
lnMEX 3dlnMEX 2
lnCHN 2dlnCHN 1
lnRUS 2dlnRUS 1
Sou ce: own
Se ies Da a
(lags)
Model
modi . Tes s a is ic C i ical
alue (5%) P- alue Rejec H0Conclusion
lnNY
In le els
(2)
N
C
CT
−0.450 ADF
−2.001 ADF
−1.964 ADF
−1.950
−2.880
−3.431
x
0.2862 ADF
0.6206 ADF
No
No
No I(1)
Fi s
di e ences
(1)
N
C
CT
−10.106 ADF
−10.093 ADF
−10.087 ADF
−1.950
−2.880
−3.431
x
0.0000 ADF
0.0000 ADF
Yes
Yes
Yes
lnLON
In le els
(2)
N
C
CT
−0.538 ADF
−1.911 ADF
−1.836 ADF
−1.950
−2.880
−3.431
x
0.3270 ADF
0.6869 ADF
No
No
No I(1)
Fi s
di e ences
(1)
N
C
T
−10.710 ADF
−10.704 ADF
−10.728 ADF
−1.950
−2.880
−3.431
x
0.0000 ADF
0.0000 ADF
Yes
Yes
Yes
lnIND
In le els
(2)
N
C
CT
0.285 ADF
−0.983 ADF
−1.476 ADF
−1.950
−2.880
−3.431
x
0.7593 ADF
0.8371 ADF
No
No
No
I(1)
Fi s
di e ences
(4)
N
C
CT
−7.114 ADF
−7.106 ADF
−12.517 PP
−7.384 ADF
−12.660 PP
−1.950
−2.881
−3.431
x
0.0000 ADF
0.0000 PP
0.0000 ADF
0.0000 PP
Yes
Yes
Yes
Tab. 1: Recommended lag o de s o all he s udied se ies
Tab. 2: Tes ing o he p esence o a uni oo o all inpu da a using ADF and PP es s
– Pa 1
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30 2020, XXIII, 4
Economics
Then applying he ecommended lag, we
checked he p esence o a uni oo in each
se ies bo h in le els and i s di e ences.
I we canno ejec he null hypo hesis ha
he analyzed se ies does ha e a uni oo , hen
his se ies is conside ed o be a non-s a iona y
p ocess. Ha ing es ed all he se ies o he
p esence o a uni oo wi h he use o bo h es s
(when needed only, i.e. in case o high numbe
o lags) in all modi ica ions, i was con i med
Se ies Da a
(lags)
Model
modi . Tes s a is ic C i ical
alue (5%) P- alue Rejec H0Conclusion
lnISA
In le els
(2)
N
C
T
−0.498 ADF
−1.955 ADF
−1.890 ADF
−1.950
−2.880
−3.431
x
0.3067 ADF
0.6599 ADF
No
No
No I(1)
Fi s
di e ences
(1)
N
C
CT
−10.022 ADF
−10.012 ADF
−10.015 ADF
−1.950
−2.880
−3.431
x
0.0000 ADF
0.0000 ADF
Yes
Yes
Yes
lnBRA
In le els
(4)
N
C
CT
0.889 ADF
0.708 PP
−1.158 ADF
−0.683 PP
−1.995 ADF
−2.164 PP
−1.950
−2.881
−3.431
x
0.6915 ADF
0.8511 PP
0.6039 ADF
0.5103 PP
No
No
No
I(1)
Fi s
di e ences
(4)
N
C
CT
−4.562 ADF
−6.486 PP
−4.600 ADF
−6.503 PP
−4.590 ADF
−6.495 PP
−1.950
−2.881
−3.431
x
0.0001 ADF
0.0000 PP
0.0000 ADF
0.0000 PP
Yes
Yes
Yes
lnMEX
In le els
(3)
N
C
CT
1.023 ADF
1.114 PP
−0.096 ADF
0.141 PP
−2.915 ADF
−2.751 PP
−1.950
−2.880
−3.431
x
0.9499 ADF
0.9687 PP
0.1575 ADF
0.2154 PP
No
No
No I(1)
Fi s
di e ences
(2)
N
C
CT
−6.813 ADF
−6.888 ADF
−7.069 ADF
−1.950
−2.880
−3.431
x
0.0000 ADF
0.0000 ADF
Yes
Yes
Yes
lnCHN
In le els
(2)
N
C
CT
0.148 ADF
−1.138 ADF
−1.799 ADF
−1.950
−2.880
−3.431
x
0.6996 ADF
0.7051 ADF
No
No
No I(1)
Fi s
di e ences
(1)
N
C
CT
−9.908 ADF
−9.889 ADF
−10.016 ADF
−1.950
−2.880
−3.431
x
0.0000 ADF
0.0000 ADF
Yes
Yes
Yes
lnRUS
In le els
(2)
N
C
CT
−0.520 ADF
−2.215 ADF
−3.734 ADF
−1.950
−2.880
−3.431
x
0.2009 ADF
0.0202 ADF
No
No
Yes I(1)
Fi s
di e ences
(1)
N
C
CT
−9.446 ADF
−9.442 ADF
−9.444 ADF
−1.950
−2.880
−3.431
x
0.0000 ADF
0.0000 ADF
Yes
Yes
Yes
Sou ce: own
No e: N = model wi h no cons an and no end; C = model wi h a cons an , CT = model wi h a cons an and end.
H
0: a iable con ains a uni oo , H1: a iable was gene a ed by a s a iona y p ocess.
Tab. 2: Tes ing o he p esence o a uni oo o all inpu da a using ADF and PP es s
– Pa 2
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31
4, XXIII, 2020
Economics
ha all he ime se ies a e in eg a ed o he
same o de I(1). Phillips-Pe on es s lead o
simila conclusions. The summa y o he esul s
is gi en in Tab. 2.
Since all he analyzed se ies a e I(1)
p ocesses i gi es us all necessa y p econdi ions
o de ec a coin eg a ion among he analyzed
ma ke s. The esul s o he coin eg a ion es
will be used u he o es ima ing VECMs.
2.2 Tes ing o Mul i a ia e
Coin eg a ion
To check he p esence o absence o
a coin eg a ion ec o (s) we employed he
Johansen maximum likelihood app oach
wi h di e en speci ica ions o coin eg a ing
ela ions (Johansen, 1995) as desc ibed
p e iously in he me hodology. We decided
o ocus on mul i a ia e coin eg a ion es ing
among all he analyzed se ies oge he wi h
he use o T ace es . The esul s a e displayed
in Tab. 3.
Acco ding o he esul s displayed abo e we
can conclude ha he analyzed se ies do ha e
one coin eg a ing ec o . Since a coin eg a ion
among all he se ies exis s, i makes sense
o access long- un and sho - un coe icien s
o he unde lying model. We no malized he
Se ies es ed Tes speci ica ion Null hypo hesis
T ace es 1
lnISA/lnNY/lnLON/lnBRA/
lnMEX/lnIND/lnCHN/lnRUS
Cons an 2Rejec ed** ( = 1)
Rcons an 3Fails o ejec
T end4Rejec ed** ( = 1)
R end5Fails o ejec
None6Fails o ejec
Sou ce: own
No e: 1H0: se ies a e no coin eg a ed ( = 0); 2Include an un es ic ed cons an in model; 3Include a es ic ed cons an
in model; 4Include a linea end in he coin eg a ing equa ions and a quad a ic end in he undi e enced da a; 5Include
a es ic ed end in model; 6Do no include a end o a cons an ; **H0 ejec ed a he 5% signi icance le el.
Se ies
Long- un ela ionship Sho - un ela ionship
No malized
coin eg a ing
coe icien s
P- alue E o co ec ion e m
(speed o adjus men ) P- alue
lnBRA 1.000 − −0.020** 0.013
lnISA 4.412*** 0.000 0.015 0.390
lnNY −4.641*** 0.000 0.016 0.415
lnIND 0.532** 0.046 0.011 0.390
lnLON −0.125 0.800 0.018 0.250
lnMEX −1.224*** 0.000 0.043*** 0.000
lnCHN 0.444* 0.064 −0.009 0.336
lnRUS −0.432** 0.049 −0.011 0.560
Sou ce: own
No e: *The coe icien is signi ican a he 10% signi icance le el; **The coe icien is signi ican a he 5% signi icance
le el; ***The coe icien is signi ican a he 1% signi icance le el.
Tab. 3: Mul i a ia e Johansen’s coin eg a ion es s esul s
Tab. 4: Mul i a ia e VECM summa y ou come
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38 2020, XXIII, 4
Economics
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