Cointegration Analysis of the World’s Sugar Market: The Existence of the Long-term Equilibrium

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 EM_4_2020.indd 23 18.11.2020 12:27:45 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 EM_4_2020.indd 24 18.11.2020 12:27:45 25 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 EM_4_2020.indd 25 18.11.2020 12:27:46 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 EM_4_2020.indd 26 18.11.2020 12:27:46 27 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 EM_4_2020.indd 27 18.11.2020 12:27:46 28 2020, XXIII, 4 Economics Fig. 1: G aphical ep esen a ion o he analyzed ime se ies Sou ce: own EM_4_2020.indd 28 18.11.2020 12:27:47 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 EM_4_2020.indd 29 18.11.2020 12:27:48 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 EM_4_2020.indd 30 18.11.2020 12:27:48 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 EM_4_2020.indd 31 18.11.2020 12:27:48 38 2020, XXIII, 4 Economics Sm čka, L., Hönig, V., & H omádko, J. (2012). Kde je budoucnos cuk o a nic í České Republice [Whe e is he u u e o suga indus y in he Czech Republic]. Lis y Cuk o a nické a Řepařské, 128(5–6), 193– 198. 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