344 Ekonomický časopis, 57, 2009, č. 4, s. 344 358 Purchasing Power Pariy and Coinegraion: Evidence from Lavia and Slovakia Michaela CHOCHOLATÁ Absrac This paper deals wih he analysis of he purchasing power pariy beween Lavia and he euro area and beween Slovakia and he euro area using he Engle-Granger and Johansen coinegraion echniques. Lavia and Slovakia became members of he European Union in May 2004 and have been already he members of he Exchange Rae Mechanism II (ERM II) preparing for he euro adopion. The whole analysis was done on monhly daa covering he period January 999 May 2008. Boh he Engle-Granger and he Johansen mehod did no confirmed he purchasing power pariy (PPP) validiy in boh analysed cases. Keywords: exchange raes, harmonized index of consumer prices (HICP), purchasing power pariy, coinegraion, Engle-Granger mehod, Johansen mehod JEL Classificaion: F3 Inroducion The European Union (EU) is one of he larges economies in he world. I consiss of 27 Member Saes and has a populaion of 493 million. The greaes expansion of he EU ook place on s May 2004 when 0 new counries (Cyprus, he Czech Republic, Esonia, Hungary, Lavia, Lihuania, Mala, Poland, he Slovak Republic and Slovenia) acceded o he EU. Bulgaria and Romania are he laes members, having joined on s January 2007. The adopion of he euro (i.e. he enrance ino he Economic and Moneary Union EMU) has become an Michaela CHOCHOLATÁ, Ekonomická univerzia v Braislave, Fakula hospodárskej informaiky, Kaedra operačného výskumu a ekonomerie, Dolnozemská cesa /b, 852 35 Braislava 5, Slovenská republika; e-mail: chocholaam@yahoo.com Acknowledgemens: This research was suppored by he gran projec VEGA No. /4652/07 Analysis of he curren problems of he Slovak economy developmen before he enrance ino he European Moneary Union economerical approach.
345 imporan issue for all new EU Member Saes which are commied o ulimaely adoping he euro afer fulfilmen of he convergence crieria among hem he exchange rae sabiliy and price sabiliy. The exchange rae sabiliy is conneced wih he membership in he Exchange Rae Mechanism II (ERM II) for a leas wo years. The exchange rae of he naional currency agains he euro mus no flucuae around he cenral pariy more han ±5% during he ERM II membership. Esonia, Lihuania and Slovenia became ERM II members already on 28h June 2004, Lavia, Cyprus and Mala on 29h April 2005 and Slovakia on 28h November 2005 and fixed he cenral pariies of he naional currencies o he euro. Some of hese counries have already complied wih all he convergence crieria and joined he EMU Slovenia on s January 2007, Cyprus and Mala on s January 2008, and Slovakia is going o join he EMU and adop he euro on s January 2009. Anoher convergence crierion is he price sabiliy measured by he inflaion rae. The relaionship beween he developmen of he exchange rae and he naional price levels represens an essence of he purchasing power pariy (PPP) heory. Purchasing power pariy is one of he key docrines in inernaional economics. Many open economy macroeconomic models use PPP as a long-run equilibrium condiion. PPP represens a simple relaionship beween exchange rae, domesic prices and foreign prices. PPP saes ha he equilibrium or long-run exchange rae beween wo counries is equal o he raio of heir relaive price levels. The concep of PPP is generally aribuable o he Swedish economis Gusav Cassel, who formulaed he approach in 920s. Cassel s heory represens a synhesis of he work of he nineeenh-cenury Briish economiss, among hem David Ricardo (he originaor of he heory of comparaive advanage). The esing of he PPP has become popular in 970s since he adven of he flexible exchange raes. Before he mid-980s ess of PPP concenraed on parameer resricions using he ordinary and generalized leas squares mehods. Around he mid-980s, ess of PPP sared o ake new direcions, which was conneced wih he sharp progress in economerics for nonsaionary ime series. The sudies have sared o use he concep of saionariy (esing for uni roos) and coinegraion. Some of he laes sudies use also he panel echniques o solve he problem of he shor sample size analyzing he ime series daa from a large number of counries (see e.g. Sideris, 2005). The analysis of he PPP esing he long-run relaionship beween he exchange rae and naional price levels has become a very imporan and ineresing issue also for he counries which plan o adop he euro.
346 The main aim of his paper was o analyse he validiy of he PPP in counries which paricipae(d) in ERM II in 2008 (January July) and are preparing for he enrance ino he EMU, i.e. in Balic Saes (Esonia, Lavia and Lihuania) and in he Slovak Republic. 2 In Esonia and in Lihuania, he Moneary Auhoriies commied hemselves o reain he exchange rae of Esonian kroon agains he euro and Lihuanian lias agains he euro, respecively, unchanged a he cenral pariy rae during he ERM II membership in order o mainain he sabiliy and oher benefis of a fixed exchange rae regime. In case of Lavia, he Bank of Lavia unilaerally limis he la s exchange rae agains he euro o ±% of he cenral rae. The cenral pariy of he Slovak koruna agains he euro in ERM II changed wo imes (he possible flucuaion was ±5% around he cenral pariy). On 8h July 2008 he conversion rae beween he Slovak koruna and he euro was se a 30.260 SKK/EUR, which corresponded o he cenral pariy of he Slovak koruna agains he euro wihin he ERM II a ha ime. Since he exchange raes of he Esonian kroon and Lihuanian lias agains he euro do no change wihin he ERM II, he paper concenraes on he analysis of he PPP beween he Lavian la and he euro and beween he Slovak koruna and he euro using he coinegraion echniques (he Engle-Granger wo-sep mehod and he Johansen procedure). The analysis was done on monhly daa for he period January 999 May 2008 in order o capure he period afer inroducing he euro as a virual currency for cash-less paymens and accouning purposes in Member Saes.. Theoreical and Mehodological Issues.. The PPP Formulaion In is simples form he absolue PPP saes ha he exchange rae beween wo currencies mus equal o he raio of price levels in hese counries. Le P denoe he price level in a foreign counry, P he corresponding price level in a domesic counry and E he nominal exchange rae defined as he domesic price of a foreign currency in ime. Then he following equaion can be used o describe he PPP relaionship: P E = () P 2 Denmark is a Member Sae paricipaing in he ERM II wih a special saus which grans he righ o choose wheher or no o adop he euro. Denmark and he Unied Kingdom use he socalled op-ou clause, which means ha hey do no ye wish o become par of he euro area.
347 or alernaively as P = E. P (2) which means ha he price levels in all counries mus be he same when measured in he same currency (he law of one price). If we denoe F he domesic value of he foreign price level, i.e. F = E. P, he PPP of he form (2) can be wrien (afer rearranging) in he following form: F = P (3) The PPP can be also formulaed in erms of he real exchange rae Q which should equal o when he absolue PPP holds: Q E. P P = (4) The whole analysis is usually done for logarihmic ransformaions (denoed by small leers of variables) of he above menioned equaions. Equaions (), (3) and (4) rewrien in he empirically esable forms are as follows: e ( p p ) = θ 0 + θ + ξ (5) and f = ϕ 0 + ϕ p + ε (6) q = e + p p (7) where e denoes he logarihm of he exchange rae E, and loga- rihms of he price levels in domesic ( ) and foreign counry ( P ), f he logarihm of he domesic value of he foreign price level (i.e. f = e + p ) and q logarihm of he real exchange rae Q. θ 0, θ, ϕ 0 and ϕ are unknown parameers, ξ and ε are error erms reflecing any shor-run deviaions from he long-run equilibrium caused by sochasic shocks. The long-run PPP is said o hold if he real exchange rae q defined in (7) is saionary. To es he saionariy of q various mehods can be used. However he analysis is usually done using he Augmened Dickey-Fuller (ADF) es or Phillips-Perron (PP) es (see e.g. Bahmani-Oskooee and Barry, 997; Chocholaá, 2005, 2007; Enders, 995; Harris, 995; Rublíková, 2003). The analysis of he PPP validiy based on coinegraion heory uses usually eiher he Engle-Granger wo-sep mehod or he Johansen procedure (see e.g. Bahmani-Oskooee and Barry, 997; Chocholaá, 2007; Enders, 995; Harris, 995; Islam and Ahmed, 999; McNown and Wallace, 990; Rublíková, 2003; P p p
348 Sideris, 2005). If he PPP holds, he variables in equaion (5) and (6), respecively mus be coinegraed and he esimaed parameers θ and ϕ, respecively mus equal o..2. Nonsaionariy and Coinegraion As i was already menioned above, he early sudies dealing wih he esing of PPP used he ordinary or generalized leas squares o esimae he PPP model. Laer developmens of economerics in he area of nonsaionariy have shown ha he majoriy of he economic variables is nonsaionary. The problem, which arise in his conex is ha in case of nonsaionary variables he sandard -saisic can no be used o infer he significance of esimaed coefficiens. To avoid his issue, he coinegraion approach was developed. The essence of he coinegraion approach is based on analyzing wheher a linear combinaion of nonsaionary variables is saionary. The Engle-Granger Mehod The Engle-Granger mehod (Engle and Granger, 987) is he simples and nowadays widely used coinegraion approach for a bivariae sysem defined e.g. by he equaion (6). In he firs sep of his mehod he variables f and p are esed for heir order of inegraion using e.g. he ADF or PP es. We can disinguish he hree cases which will eiher lead us o he nex sep or will sugges sopping he procedure (see e.g. Aseriou and Hall, 2007; Lukáčik, Lukáčiková and Szomolányi, 2007): if boh variables are inegraed of he same order (wih excepion of saionariy) which requires he coinegraion concep, we can proceed wih he nex sep, if boh variables are saionary, i.e. I(0), he classical regression analysis can be applied (we do no need o follow he coinegraion concep), if he variables are inegraed of differen order, i is possible o conclude ha hey are no coinegraed (for more informaion on his area see e.g. Enders (995). Afer idenificaion ha he variables f and p are inegraed of he same order d (in economics usually d = ), we can esimae he long-run PPP equaion (6) by he sandard regression mehod. In case of coinegraion he residuals obained from his equaion mus be inegraed a an order less han d. 3 The residual sequence from his equaion can be denoed by εˆ. We can hen perform e.g. he ADF es aking ino accoun ha he residual sequence εˆ comes from a regression equaion, so we do no need o include an inercep erm nor a ime rend, i.e. 3 Many auhors use he erm coinegraion o refer o he case in which boh variables are I(), so ha here exis a linear combinaion ha is I(0), i.e. saionary.
349 n Δ ˆ ε = δεˆ + δ Δ ˆ ε + ϑ (8) i i+ i= 2 Since he residual sequence εˆ is generaed from a regression equaion i is no appropriae o use he classic ADF ables. The adequae criical values are in comparison o he classic ADF values more negaive and can be found in Mc Kinnon (99). The accepance of he null hypohesis ha he residual sequence εˆ conains a uni roo means, ha he variables f and p are no coinegraed and he PPP relaionship does no hold. This is because, in his case, any shor-run deviaion from he PPP relaionship will be cumulaive and permanen and ha he variables will no have a common rending relaionship (Islam and Ahmed, 999). The rejecion of he null hypohesis also implies ha he variables are coinegraed (i.e. confirmaion of he long-run equilibrium relaionship beween hese variables). If he variables f and p are coinegraed, he residuals from he equilibrium regression (6) can be used o esimae he error-correcion model (ECM) expressing he dynamics of he equilibrium relaionship beween he wo variables. The ECM connecing he shor-run and long-run effecs of he variables can be in general wrien as: Δ = + + Δ + + Δ + Δ + Δ + + Δ + (9) f μ γε ψ f... ψ p f p ω0 p ω p... ωq p q ν where f and p are nonsaionary I() variables which are coinegraed, ε is he saionary lagged residual represening he deviaions from he long-run equilibrium (6), ν is a whie noise disurbance erm, μ, ψ,...,ψ p, ω 0,...,ωq are unknown parameers of he ECM model and γ represens he speed of adjusmen parameer. In he las sep of his procedure i is necessary o evaluae he model adequacy. Enders (995) presens several diagnosic ess which can be used in order o deermine wheher he esimaed ECM is appropriae. The Johansen Mehod The applicaion of he Engle-Granger mehod is adequae in a bivariae sysem (one coinegraing vecor). In case of more han wo variables here may occur more han one coinegraing relaionships which he Engle-Granger mehod can no rea. 4 Johansen (988) developed a more general echnique applicable also in case of more han wo variables (for N number of variables we 4 For broad discussion abou he drawbacks of he Engle-Granger approach see e.g. Aseriou and Hall (2007).
350 can have only up o N coinegraing vecors). The Johansen coinegraion mehod is based on maximum-likelihood esimaion procedure which enables o capure he feedback effecs beween variables and is independen of he choice of endogenous variable. The Johansen procedure is based on a vecor auoregression (VAR) represenaion of a vecor of N saionary variables, X ( =, 2,..., T ) as follows: X = Π X + Π 2X 2 +... + Π k X k + φ D + u (0) where u, u 2,..., u T are N-dimensional i.i.d. normal variables, D conains a se of condiioning variables (e.g. consan, seasonal dummies) and he X is a vecor of all he endogenous variables in he sysem. In his paper he vecor X is of dimension N = 2 because i conains wo endogenous variables f and p defined in equaion (6). In case ha all variables in X are nonsaionary and achieve saionariy afer being differenced once, he model (0) can be rewrien in he form of vec- error correcion model (VECM) as or follows: where i ΔX + = Γ ΔX + Γ 2ΔX 2 +... + Γ k ΔX k + + ΠX + φ D u () Γ I + Π + Π +... + Π = ( i =, 2,..., k ) and Π ( I Π Π... ) 2 k =. 2 Πk The Π marix ( N N ) conains informaion regarding he long-run relaionship. The rank r of his Π marix, where 0 < r < N will deermine he number of coinegraing vecors in he VAR sysem. We can define wo marices α and β (boh N r ) such ha Π = αβ where α includes he speed of adjusmen coefficiens and β is he long-run marix of coefficiens (each column of his marix corresponds o one coinegraing vecor). Johansen developed a mehodology ha aims o es he rank of he Π marix in (). We can disinguish hree differen cases (see e.g. Aseriou and Hall, 2007; Lukáčik, 2007; Paerson, 2000):. When Π has a full rank (i.e. r = N ), hen he variables in X are I(0). The VAR model should be used in levels o model his case. 2. When he rank of Π is zero hen here are no coinegraing relaionships and i is appropriae o use he VAR model in firs differences. 3. When Π has a reduced rank (i.e. r < N ) and herefore here are r < N coinegraing relaionships. The VAR model should be formulaed as he VECM. In he firs sep of he Johansen approach i is necessary o es for he order of inegraion of he variables using e.g. he ADF es. In he nex sep we have o find he appropriae lag lengh of he VAR model (all variables in levels) using
35 e.g. Akaike informaion crierion (AIC), Schwarz crierion (SC) or likelihood raio (LR) es. The seleced VAR model should also pass all he residual diagnosic ess. Anoher imporan issue is wheher o include an inercep and/or a rend in eiher he shor-run model (he VAR model) or he long-run model (he coinegraing equaion CE), or in boh models. The appropriae model can be chosen applying he so-called Panula principle which is based on esing of he join hypohesis of boh he rank order and he deerminisic componens (see Aseriou and Hall, 2007; Gio and Peijean, 2004; Johansen, 992). I is common o decide among he hree ou of he five cases of he possible model specificaions (see Aseriou and Hall, 2007; Harris, 995; Lukáčik, 2007; Paerson, 2000): 5 Model 2: Inercep (no rend) in CE no inercep in VAR, Model 3: Inercep (no rend) in CE and VAR, Model 4: Inercep and rend in CE no rend in VAR. The model selecion is based on values of he es saisics esing he hypohesis ha Π is less han full rank marix, i.e. r < N. The esing procedures deermining he number of coinegraing relaionships are based on wo likelihood es saisics known as he race es saisic ( λ race ) and maximal eigenvalue es saisic ( λ max ) which are defined as follows 6 : and λ race N () r = T ln( ˆ λi ) (2) i= r+ (, + ) = ln( λ ˆ ) (3) λ max rr T r+ where T is he number of usable observaions. The null hypohesis in he firs case ( λ race ) is ha he number of coinegraing vecors is less han or equal o r, while in he second case ( λ max ) we es he null hypohesis, ha he rank of Π equals r agains he hypohesis ha he rank is r +. Boh saisics are disribued 2 as χ wih appropriae degrees of freedom ( N r) where N is he number of endogenous variables and r denoes he value of he rank under he null hypohesis. The Panula principle is also based on esimaion of all hree above presened models and presenaion of he resuls from he mos resricive alernaive (i.e. r = 0 and Model 2) hrough he leas resricive alernaive (i.e. r = N and Model 4). The model selecion procedure comprises of moving from he 5 The models are marked as in EViews. The use of models and 5 is from he economic heory poin of view unusual (Model : No inercep or rend in CE or VAR and Model 5: Inercep and rend in CE linear rend in VAR). 6 More informaion abou he srucure of hypohesis ess for coinegraing rank can be found e.g. in Paerson (2000).
352 mos resricive alernaive owards he leas resricive one, o compare a each sage he rank es saisic o is criical value and only sop when he firs ime he null hypohesis is no rejeced. An imporan characerisic of he Johansen mehod is ha i enables esing for he possible linear resricions regarding coefficiens of he marices α and β. 7 2. Empirical Issues In his secion we ry o analyse he validiy of he PPP using he coinegraion echniques (Engle-Granger mehod and Johansen mehod). We analysed he price and exchange rae monhly daa for Lavia and Slovakia for he period January 999 May 2008 (3 observaions). The price levels P and P are defined as he harmonized indices of consumer prices in domesic counry (Lavia, Slovakia) and foreign counry (euro area), respecively in ime relaive o a base monh (January 999 =.00). E refers o an index of he domesic currency price of foreign exchange (LVL/EUR and SKK/EUR, respecively) relaive o he same base monh. The domesic value of he foreign price level F was calculaed as described above. The whole analysis was done on he logarihmic ransformaion of he variables P and F using he equaion (6). The daa for analysis were obained from he Eurosa web-page (epp.eurosa.ec.europa.eu) and he European Cenral Bank web-page (www.ecb.in), he whole analysis was done in economeric sofware EViews 5.. 2.. Engle-Granger Mehod: Coinegraion Resuls In he firs sep of his mehod we esed he variables f and p for heir order of inegraion using he ADF es (see Table ). T a b l e ADF Tes Resuls for Variables f and p Level s Difference rend and inercep inercep neiher rend nor inercep rend and inercep Lavia f 2.88728 0.30466 0.69784 7.4558 p 2.45206 6.836923.82367 9.397838 Slovakia f 2.26290 0.998073.68929 7.562946 p 2.325429 2.7306 2.720396 9.67882 Noe: The symbol denoes he rejecion of he null hypohesis on he 0.0 significance level. Source: Own calculaion using EViews 5.. 7 For more deails abou esing linear resricions in Johansen approach see e.g. Enders (995).
353 The values of he ADF saisics indicae ha boh variables in boh counries have one uni roo, i.e. have a characer of I(). Since he variables from equaion (6) are inegraed of he same order, we can proceed in esing wheher hey are coinegraed. We can esimae he long-run PPP equaion (6) by he sandard regression mehod (simple OLS Ordinary Leas Squares) and hen apply he ADF es on he residual sequence εˆ using he equaion (8). The esimaed equaions (6) are as follows: Lavia: f = 0.085387 + 0. 8949 p Slovakia: f = 0.078942 0. 3256 p The analysed residuals εˆ were boh for Lavia and Slovakia nonsaionary wih corresponding ADF saisics.35463 and.87575, respecively. 8 From he nonsaionary characer of he residuals in boh counries i is clear ha he variables are no coinegraed a herefore he PPP could no hold. 2.2. Johansen Mehod: Coinegraion Resuls In his sep we esed he PPP validiy in he above menioned counries using he Johansen maximum-likelihood esimaion procedure. Since he variables f and p were in par 2. idenified in boh counries o be inegraed of he order, i.e. I(), we can proceed wih he Johansen procedure in order o find ou if he variables are coinegraed. Afer idenificaion of he same order of inegraion of he analysed variables in boh counries i follows he deerminaion of he opimal lag lengh of he unresriced VAR model. The opimal lag lenghs idenified by AIC, SC and LR are in Table 2 (as we use he monhly daa, he maximal lag lengh considered was 2). T a b l e 2 Opimal Lag Lengh of he Unresriced VAR AIC SC LR Lavia 6 lags lag 8 lags Slovakia 2 lags lag 2 lags Source: Own calculaion using EViews 5.. Table 2 indicaes ha he used informaion crieria suggesed differen appropriae lag lenghs. In such cases he lieraure (see e.g. Paerson, 2000) recommends for VAR and VEC models o use he Schwarz crierion (SC). We also 8 The regression wih he reversed order of variables of he form p = ϕ 0 + ϕ f + ε was also esimaed. The residuals from his alernaive equaion were also idenified as o be nonsaionary in boh counries. εˆ
354 re-esimaed he VAR wih a lag lengh of boh in case of Lavia and Slovakia. The VAR residual serial correlaion Lagrange Muliplier (LM) es values for lag were 3.66906 and.94394, respecively which indicaes he exisence of he serial correlaion on he significance level 0.0 and 0.05, respecively. We herefore proceeded o include 2 lags ino he VAR model in boh cases. 9 The appropriae model regarding he deerminisic componens was chosen applying he so-called Panula principle. The procedure of he appropriae model selecion is based on he fac ha we move from he mos resricive model (named Model 2), 0 a each sage comparing he race or he maximal eigenvalue es saisic o is criical value, sopping (and herefore choosing he model) only when he null hypohesis is no rejeced for he firs ime (see Aseriou and Hall, 2007; Gio and Peijean, 2004; Harris, 995; Johansen, 992). The resuls from he esimaed models for boh counries are in Table 3. T a b l e 3 The Panula Principle Tes Resuls r N r Model 2 Model 3 Model 4 Lavia Trace saisic 0 2 35.3879 (20.2684) 22.528 (5.4947) 38.98027 (25.872) 0.90508 (9.64546) # 0.576 (3.84466) 6.76892 (2.5798) Maximal eigenvalue saisic 0 2 34.4728 (5.8920) 2.949 (4.26460) 22.235 (9.38704) 0.90508 (9.64546) # 0.576 (3.84466) 6.76892 (2.5798) Slovakia Trace saisic 0 2 29.24995 (20.2684) 2.73574 (5.4947) # 28.3728 (25.872) 3.08965 (9.64546) 0.898622 (3.84466).02650 (2.5798) Maximal eigenvalue saisic 0 2 26.6034 (5.8920).8372 (4.26460) # 7.078 (9.38704) 3.08965 (9.64546) 0.898622 (3.84466).02650 (2.5798) Noe: The MacKinnon-Haug-Michelis 0.05 criical values are in parenheses. The symbol # indicaes he firs ime ha he null hypohesis can no be rejeced on he 0.05 significance level. Source: Own calculaion using EViews 5.. From he resuls in Table 3 i is clear ha he appropriae model is in case of Lavia he Model 2 wih one coinegraing vecor (which could mean he confirmaion of he PPP validiy), while in case of Slovakia he Model 3 wih no coinegraion apparenly excludes he validiy of he PPP. 9 These models already fulfilled he condiion of no serial correlaion. 0 The above defined Model and Model 5 were no considered here since hey are no likely o happen (see e.g. Aseriou and Hall, 2007; Gio and Peijean, 2004; Paerson, 2000).
355 Since he model specificaion wihou a consan erm in VAR (Model 2 in case of Lavia) is very unlikely, we used he Model 3 indicaing also he exisence of one coinegraing vecor. The esimaed VECM (based on Model 3) for Lavia considering one coinegraing vecor and 2 lags is as follows: Δ f = 0.000498( f + 0.97p.884) + 0.374Δf 0.77Δf 2 0.26Δ p + 0.244 Δ p + 0.002 2 Δ p = 0.002009( f + 0.97p.884) + 0.037Δf 0.090Δ f 2 + + 0.035Δp 0.00Δ p + 0.005 2 The consrucion of he VECM enables o synhesise he saisical shor-run dynamic relaionships and long-run equilibrium relaionships. The long-run informaion in above presened equaions is included in parenhesis (normalized coinegraing vecor) and he remaining erms (variables in firs differences) represen he shor-run dynamics. The coefficiens 0.000498 and 0.002009 of he lagged residual are he speed of adjusmen coefficiens represening also he sabiliy of he sysem. The absolue values of hese coefficiens are less han one, which indicaes ha he sysem is sable (see Islam and Ahmed, 999). The values of he speed of adjusmen coefficiens are very small and indicae ha only 0.0498% and 0.2009%, respecively, of any deviaion from he long-run equilibrium is correced wihin a monh. Finally we esed he residuals of his VECM model using he LM (Lagrange Muliplier) es and Urzua normaliy es. Since he LM (2) = 5.553, are he residuals ill he lag 2 uncorrelaed (he order of 2 for he LM es was deermined by he opimal lag srucure which was earlier idenified o be of order 2). The Urzua normaliy es is a mulivariae exension of he Jarque-Bera residual normaliy es, which compares he hird and fourh momens of he residuals o hose from he normal disribuion. The Jarque-Bera saisics and corresponding p-values (in parenheses) for individual componens are 2.079 (0.002) and 0.65 (0.92) respecively. The join es saisic (p-value in parenhesis) based on residual covariance Urzua orhogonalizaion is 3.646 (0.36). This means ha alhough he hypohesis ha he residuals from he firs VECM equaion are normally disribued can be rejeced on significance level 0.2%, he hypohesis ha he residuals are mulivariae normal could no be rejeced. The deeced deviaion from normaliy does no render he coinegraion ess invalid (see Islam and Ahmed, 999). For more precise informaion abou hese ess see e.g. EViews 5 User s Guide.
356 Conclusion The main aim of his paper was o es he PPP validiy beween Lavia and he euro area and beween Slovakia and he euro area using he wo approaches of he coinegraion heory he Engle-Granger mehod and he Johansen mehod. The whole analysis was based on equaion (6). The applicaion of he Engle-Granger mehod based on OLS esimaion showed ha he residuals from equaion (6) were for boh counries nonsaionary, and herefore he PPP could no hold. The use of he Johansen mehod based on maximum-likelihood esimaion gives more ineresing resuls. The coinegraing relaionship beween variables f and p was in case of Slovakia no confirmed which means he rejecion of he PPP validiy. In case of Lavia here was idenified one coinegraing relaionship and herefore he appropriae VECM was esimaed and he residuals of his model were esed using he ess for uncorrelaedness and normaliy. Alhough he exisence of one coinegraing relaionship in Lavian case could speak for he PPP validiy, he fac ha he long-run coefficien ˆϕ = 0.97 was clearly differen from, speaks for rejecion of he PPP in case of Lavia as well. The fac ha he presened resuls do no suppor he PPP validiy is no surprising and one of he main reasons could be faser growh of non-radable o radable prices in boh analysed counries in comparison o relaive prices of he euro area (he Balassa-Samuelson effec). In case of Lavia also he fixed exchange rae regime may accoun for deviaions from he long-run PPP. In case of Slovakia Maeso-Fernandez e al. (2006) poined ou he fac ha he iniial cenral pariy of he SKK/EUR exchange rae ( EUR = 38.4550 SKK), which changed wice during he in ERM II membership, was raher far away from is equilibrium value. The dynamics of his exchange rae can be herefore characerised by he reducion of he iniial disequilibrium, which may make he impression ha here is no long-run relaionship beween analysed variables. The problemaic validiy of he PPP heory was idenified by several auhors dealing wih he PPP analysis for ransiion counries, iner alia, Benčík e al. (2005), Chrisev and Noorbakhsh (2000), Boršič and Bekö (2006) and Sideris (2005). Benčík e al. (2005) analysed he Balassa-Samuelson effec in he Slovak Economy in 995 2004. They poined ou several problems why he PPP doesn hold and he presence of he Balassa-Samuelson effec can provide one of he possible explanaions. Chrisev and Noorbakhsh (2000) who use he coinegraion approach o analyse he PPP validiy in six cenral and eas European counries (Bulgaria, Czech Republic, Hungary, Poland, Romania and Slovakia) in 990 998 idenified he produciviy shocks, inflexible exchange rae regimes, non-radable goods and services, slower domesic price adjusmens o
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