Revew of Economcs & Fnance Submed on 19/09/2013 Arcle ID: 1923-7529-2014-01-01-12 Mohsen Bahman-Oskooee, Tsangyao Chang, and Kue-Chu Lee Purchasng Power Pary n he BRICS and he MIST Counres: Sequenal Panel Selecon Mehod Mohsen Bahman-Oskooee 1 The Cener for Research on Inernaonal Economcs Deparmen of Economcs Unversy of Wsconsn-Mlwaukee, Mlwaukee, U.S.A. E-mal: bahman@uwm.edu Tsangyao Chang Deparmen of Fnance Feng Cha Unversy, Tachung, TAIWAN E-mal: ychang@mal.fcu.edu.w Kue-Chu Lee Deparmen of Cooperave Economcs Feng Cha Unversy, Tachung, TAIWAN E-mal:kclee@fcu.edu.w Absrac: The Sequenal Panel Selecon Mehod (SPSM) procedure s appled o he real effecve exchange raes of BRICS (Brazl, Russa, Inda, Chna, and Souh Afrca) and MIST (Mexco, Indonesa, Souh Korea and Turkey) counres, usng monhly daa over he perod 1994-2012. Whle several panel un roo ess gve us mxed resuls, SPSM classfes he whole panel no a group of saonary seres and a group of non-saonary seres, denfyng saonary seres whn he panel. Emprcal resuls from he SPSM procedure ha uses he Panel KSS un roo es wh a Fourer funcon ndcae ha mean-reverson n real effecve exchange raes holds rue for hese wo groups of counres under sudy. JEL Classfcaons: C22, F31, F37 Keywords: Purchasng Power Pary, BRICS counres, MIST counres, Sequenal Panel Selecon Mehod, Fourer funcon 1 Valuable commens of an anonymous referee are grealy apprecaed. Remanng errors, however, are ours. ~ 1 ~
ISSNs: 1923-7529; 1923-8401 2014 Academc Research Cenre of Canada 1. Inroducon I s no dffcul o fnd sudes whch aemp o es Purchasng Power Pary (PPP) heory eher for a sngle counry or group of counres. Wh advances n me-seres economercs un roo esng procedure, he ask s reduced o one of esablshng wheher real exchange raes are saonary (supporng he PPP) or hey conan a un (rejecng he PPP). The common pracce o es he PPP was o regress he nomnal exchange rae on relave prces and es wheher he consan s zero and he slope s close o uny, mplyng suppor for he PPP. Snce nroducon of conegraon analyss n 1987, he emphass shfed o esablshng he saonary of he resduals of regresson models snce he nomnal exchange rae and relave prces were shown o be non-saonary. These sudes dd no provde much suppor for he PPP. Examples nclude Taylor (1988), Corbae and Oulars (1988), McNown and Wallace (1989), Karfaks and Moschos (1989), Layon and Sark (1990), Km (1990), Bahman-Oskooee and Rhee (1992), and Bahman-Oskooee (1993). Raher han engagng n regresson analyss, anoher srand of he leraure appled un roo ess such as lnear ADF es or Nonlnear KSS o esablsh mean reverng properes of real exchange raes. Agan, hey have provded mxed resuls. Examples nclude Bahman-Oskooee (1995a, 1995b), Taylor (2002), Hasan (2004), Lew, e al. (2004), Lopez, e al. (2005), and Bahman-Oskooee, e al. (2007a, 2007b, 2008). A hrd group of sudes have crczed unvarae un roo ess (lnear or non-lnear) on he ground ha hey do no employ enough observaons over longer perod, hence hey suffer from low power and yeld msleadng resuls. These sudes employ panel un roos and agan provde mxed suppor for he PPP. Some examples are Taylor, e al. (2001), Alba and Park (2003), Kapeanos, e al. (2003), Chorareas and Kapeanos (2004), and Sarno, e al. (2004). Falure o suppor he PPP eher by a unvarae or panel es s also sad o be due o excludng srucural breaks. Indeed, Perron (1989) argued ha f here s a srucural break, he power o rejec a un roo decreases when he saonary alernave s rue and he srucural break s gnored. A common pracce o accoun for srucural break s o nclude dummy varables. However, he avalable un roo ess only allow one or wo dummes. Nunes, e al. (1997), Lee and Srazcch (2003) and Km and Perron (2009), among ohers, demonsrae ha such ess suffer from serous power and sze dsorons due o he asymmerc reamen of breaks under he null and alernave hypoheses. The ssue becomes oo serous when number of breaks s more han wo. To solve he problem, Becker, e al. (2004, 2006) and Enders and Lee (2012) develop ess whch model any srucural break of an unknown form as a smooh process va means of Flexble Fourer ransforms. They argue ha her esng framework requres only he specfcaon of he proper frequency n he esmang equaons. By reducng he number of esmaed parameers, hey ensure ha he ess have good power rrespecve of he me or shape of he break. Thus far we know ha n order o ncrease power of he un roo ess we mus ncrease number of observaons by relyng upon panel ess. We also know ha we mus ncorporae a Fourer funcon o accoun for unknown srucural breaks. However, sandard panel un roo ess have been crczed on he ground ha hey assume homogeney across each un whn he panel. To hs end, Maddala and Wu (1999) and Im, e al. (2003) have developed ess ha perm he auoregressve parameers o dffer across panel members. Even hese ess produce based oucome f some seres whn he panel are saonary and some non-saonary. In conras o hose panel-based un roo ess ha are jon ess of a un roo for all members of a panel and ha are ncapable of deermnng he mx of I(0) and I(1) seres n a panel seng, he Sequenal Panel Selecon Mehod (hereafer, SPSM), proposed by Chorareas and Kapeanos (2009) offers a unque soluon. The mehod classfes he whole panel no a group of saonary seres and a group of ~ 2 ~
Revew of Economcs & Fnance non-saonary seres. In so dong, hey clearly denfy how many and whch seres n he panel are saonary processes. Fnally, here s a growng consensus ha real exchange raes exhb nonlneares and, consequenly, convenonal un roo ess such as he Augmened Dckey Fuller (ADF) es may have low power n deecng mean reverson. 2 As such, saonary ess based on a nonlnear framework mus be appled. Ucar and Omay (2009) propose a nonlnear panel un roo es by combnng he nonlnear framework n Kapeanos, e al. (2003, hereafer, KSS) wh he panel un roo esng procedure of Im, e al. (2003), whch has been proven o be useful n esng he mean reverson of real exchange raes. The man purpose of hs paper s o es he PPP for wo groups of counres,.e., BRICS (Brazl, Russa, Inda, Chna, and Souh Afrca) and MIST (Mexco, Indonesa, Souh Korea and Turkey) usng he Panel KSS un roo es wh a Fourer funcon, based on he Sequenal Panel Selecon Mehod (SPSM) procedure. To hs end we dscuss he daa n Secon 2. The mehod s explaned n Secon 3 wh he resuls n Secon 4. A summary s provded n Secon 5. 2. Daa Our emprcal analyss covers wo groups of counres: BRICS and MIST counres. Monhly real effecve exchange rae (REER) daa over he perod January 1994- June 2012 are used and he daa are aken from he Bank for Inernaonal Selemens (BIS) webse. There has been an exponenal rse n he growh and economc power of he emergng markes ever snce he 1990s, wh he emergng economes n general, and he ranson economes n parcular, havng receved wdespread aenon whn he leraure. Clearly, he BRICS economes sand ou amongs all of he emergng economes, havng demonsraed remarkable economc progress over recen years. Ever snce he recognon of her saus n he sudy Dreamng wh BRICs: The Pah o 2050 (Wlson and Purushoraman, 2003), he emergng markes of he BRICS counres have connued o make sgnfcan conrbuons o global economc growh, and seem lkely se o do so for many decades o come. Indeed, hese economes are posed o become larger, n US dollar erms, han he G6. 3 Secondly, s esmaed ha abou hree-fourhs of he ancpaed ncrease n GDP by he BRICS and MIST economes s lkely o come from hgher-end real growh. Boh he BRICS and MIST counres are already playng mporan roles n global fnancal developmen, exerng sgnfcan nfluences on economc growh hroughou he global economy and markes. Vsual nspecon of he REER seres for hese wo groups of counres: BRICS and MIST counres reveal sgnfcan upward and/or downward rends for mos of he counres durng hs sample perod. From hese fgures, for mos of he seres, here seems o be some nonlnear adjusmen paerns. 2 Reasons for he nonlnear adjusmen are he presence of ransacons coss ha nhb nernaonal goods arbrage and offcal nervenon n he foregn exchange marke. For some oher facors see Bahman-Oskooee, e al. (2008). 3 In he early repor, only Brazl, Russa, Inda, and Chna consued he BRIC group; Souh Afrca was added he follow-up, gvng he curren verson of BRICS. The G6 refers o he Uned Saes, he Uned Kngdom, Japan, Germany, France, and Ialy. ~ 3 ~
ISSNs: 1923-7529; 1923-8401 2014 Academc Research Cenre of Canada 3. Mehodology 4 As menoned above, our mehod s based on a non-lnear panel un roo es. Such es has already been nroduced by Ucar and Omay (2009) who combned he nonlnear framework n Kapeanos, e al. (2003, KSS) wh he panel un roo esng procedure of Im, e al. (2003) as n equaon (1): k 3, ξ δ, 1 θ, j, j ν, j= 1 X = + X + X + (1) where he null of lnear nonsaonary H : 0 0 δ =, for all s esed agans alernave of nonlnear saonary H : <0 0 δ, for some. Bahman-Oskooee, e al. (2013) hen ncorporae a Fourer funcon no (1) and arrve a equaon (2): X 2πk 2πk ξ + ε (2) k1 3, = + δ X, 1 + θ, j X, j + a,1 sn( ) + b,1 cos( ) j= 1 T T where = 1,2,..., T. The raonale for selecng [sn( 2π k / T ),cos(2πk / T )] s based on he fac ha a Fourer expresson s capable of approxmang absoluely negrable funcons o any desred degree of accuracy. In (2) k represens he frequency seleced for he approxmaon, and [ a, ] measures he amplude and dsplacemen of he frequency componen. I also follows b j ha a leas one frequency componen mus be presen f here s a srucural break. 5 Agan, followng Bahman-Oskooee, e al. (2013) we apply he Chorareas and Kapeanos s (2009) SPSM procedure o equaon (2) by akng he followng seps: Frs, we esmae equaon (2) for he enre panel. If he un-roo null s rejeced, we accep ha he seres n he panel are saonary and move o he second sep. In he second sep, we remove he seres wh he mnmum KSS sasc snce s denfed as beng saonary. Fnally, we go back o he frs sep for he remanng seres, or sop he procedure f all he seres are removed from he panel. The fnal oucome s separaon of he whole panel no ses of saonary and nonsaonary seres., 4. Emprcal Resuls Before applyng he above mehod we frs apply several unvarae me seres un roo ess so ha we can examne he null hypohess of a un roo n each counry s real effecve exchange rae (naural log REER). Based on he resuls n Table 1, here s no queson ha hree unvarae un roo ess he Augmened Dckey and Fuller (1981, ADF), he Phllps and Perron (1988, PP), and he Kwakowsk, e al. (1992, KPSS) ess all lead us o conclude ha he REERs of he mos of he counres conan un roos and rejec he PPP. 6 Ths oucome s conssen wh ha of he 4 Ths secon closely follows Bahman-Oskooee, e al. (2013). 5 Enders and Lee (2012) sugges ha he frequences n Equaon (2) should be obaned va he mnmzaon of he sum of squared resduals. Ther Mone Carlo expermens sugges ha no more han one or wo frequences should be used because of he loss of power assocaed wh a larger number of frequences. 6 Wh some excepons, we found ha he un roo null hypohess was rejeced for Inda, Indonesa, and Souh Afrca when he ADF es was used. The PP es also rejeced he un roo hypohess for boh Inda and Indonesa. The KSPP es also fals o rejec he saonary null hypohess for boh Inda and Souh Korea (see Table 1). ~ 4 ~
Revew of Economcs & Fnance exsng leraure and may be due o he low power of hese hree unvarae un roo ess. Falure o suppor he PPP could also be due o he fac ha movemen of he real effecve exchange raes could be non-lnear n naure. Level Table 1. Unvarae un roo ess 1 s dfference ADF PP KPSS ADF PP KPSS Brazl -1.548(2) -1.556(4) 0.413[11] -9.629(1) -9.737(4) 0.117[4] Chna -2.476(1) -2.510(1) 0.574[11] -10.746(0) -10.507(5) 0.235[1] Inda -2.931(1) -2.607(3) 0.267[11] -11.004(1) -11.911(11) 0.079[5] Indonesa -2.824(1) -2.608(1) 0.911[11] -12.862(0) -12.749(5) 0.046[3] Souh Korea -2.384(2) -2.418(5) 0.209[11] -10.797(1) -8.171(22) 0.049[6] Mexco -1.757(6) -2.403(4) 0.354[11] -9.220 (1) -12.234(10) 0.084[6] Russa -2.033(3) -1.823(6) 1.183[11] -6.837(2) -9.795(0) 0.054[5] Souh Afrca -2.644(1) -2.551(4) 0.740[11) -11.419(0) -11.459(1) 0.076[3] Turkey -2.217(2) -1.952(3) 1.653[11] -10.009(1) -10.407(6) 0.052[4] Noes:, and ndcae sgnfcance a he 10%, 5% and 1% level, respecvely. The number n parenhess ndcaes he lag order seleced based on he recursve -sasc, as suggesed by Perron (1989). The number n he brackes ndcaes he runcaon for he Barle kernel, as suggesed by he Newey-Wes es (1994). As menoned before, o ncrease power we shf o panel-based un roo ess and allow cross-seconal and emporal dmensons o be combned. Tables 2 and 3 on he followng pages repor he resuls for he frs generaon and second generaon panel-based un roo ess. Three frs generaon panel-based un roo ess LLC (Levn, e al., 2002), MW (Madalla and Wu, 1999), and he Im-Pesaran-Shn (Im, e al., 2003) es, all yeld he same resuls, ndcang ha REERs are saonary n he BRICS and MIST counres. A serous drawback of he frs generaon panel-based un roo ess s ha hey do no ake (possble) cross-seconal dependences no accoun n he panel-based un roo es procedure. O Connell (1988) pons ou ha falure o consder conemporaneous correlaons among daa wll bas he panel-based un roo es oward rejecng he jon un roo hypohess. Cross-seconal dependences are aken no accoun by he second generaon panel un roo ess. Hence, hese mehods offer a superor way o sudy he long run behavor of he REERs. Four second generaon panel-based un roo ess of Ba and Ng (2004), Cho (2002), Moon and Perron (2004), and Pesaran (2007) are used n our sudy. Table 3 repors he resuls of hese four second generaon panel-based un roo ess. Resuls from hese four ess ndcae ha REERS are all saonary n he BRICS and MIST counres. Our resuls sgnfy ha REERs are saonary and PPP holds n hese counres. As we saed earler, panel-based un roo ess are jon ess of a un roo for all members of a panel and ha are ncapable of deermnng he mx of I(0) and I(1) seres n a panel seng. Furhermore, f we fal o ncorporae he srucural breaks n he model, he oucome would be based. Hence, we proceed o es he saonary of REERs by usng he SPSM procedure mxed wh he Panel KSS un roo es wh a Fourer funcon. ~ 5 ~
ISSNs: 1923-7529; 1923-8401 2014 Academc Research Cenre of Canada As a benchmark, we frs repor he resuls of he Panel KSS un roo es whou a Fourer funcon. Table 4 repors he resuls of Panel KSS un roo es whou a Fourer funcon on he REERs where we gve a sequence of he Panel KSS sascs wh her boosrap p-values on a reducng panel, he ndvdual mnmum KSS sasc, and he saonary seres denfed by hs procedure each me. As we can see from Table 4, he null hypohess of a un roo n naural log of REER s rejeced when he Panel KSS un roo es was frs appled o he whole panel, producng a value of -2.409 wh a p-value of 0.000. Levn, Ln and Chu (2002) Im, Pesaran and Shn (2003) Maddala and Wu (1999) Noes: Levn, Ln and Chu (2002): Table 2. Frs Generaon Panel Un Roo Tess ρ -2.934 (0.002) ˆρ _ bar, -0.031-2.259-2.543 ~ 6 ~ B ρ -3.419 W bar, bar (0.005) P MW Z MW 32.481 (0.019) 2.414 (0.008) C ρ -3.373 Z _ bar Z, -2.642 (0.004) DF DF bar -1.998-1.631 (0.051) p denoes he adjused -sasc compued wh a Barle kernel funcon and a common lag runcaon parameer gven by K 13 = 3.21T (Levn and Ln, 2002). Correspondng p-value s n parenheses. ˆρ s he pooled leas squares esmaor. Correspondng sandard error s n parenheses. B p denoes he adjused -sasc compued wh a Barle C kernel funcon and ndvdual bandwdh parameers (Newey and Wes, 1994). p denoes he adjused -sasc compued wh a Quadrac Specral kernel funcon and ndvdual bandwdh parameers. Fnally, C p denoes he adjused -sasc compued wh a Barle kernel funcon and a common lag runcaon parameer. Correspondng p-value s n parenheses., and ndcae sgnfcance a he 10%, 5% and 1% level, respecvely. Im, Pesaran and Shn (2003): _ bar (respecvely _ bar ) denoes he mean of Dckey Fuller DF DF (respecvely Augmened Dckey Fuller) ndvdual sascs. Z, bar s he sandardzed Z s he sandardzed DF _ bar sasc and assocaed p-values are n parenheses., bar _ bar sasc based on he momens of he Dckey Fuller dsrbuon., W denoes he sandardzed _ bar sasc based on smulaed approxmaed momens (Im, e al., 2003, able 3). The correspondng p-values are n parenheses. ndcaes sgnfcance a he 5% level. Maddala and Wu (1999): where P denoes he Fsher s es sasc defned as P 2 log ( p ) MW MW bar = ; p are he p-values from ADF un roo ess for each cross-secon. Under H 0 ; 2 has χ dsrbuon wh 2N of freedom when T ends o nfny and N s fxed. ZMW s he sandardzed sasc used for large N samples: under H0; Z MW has a N (0, 1) dsrbuon when T and N end o nfny. P MW
Ba and Ng (2004) Moon and Perron (2004) Cho (2002) Pesaran (2007) Revew of Economcs & Fnance Table 3. Second Generaon Panel Un Roo Tess ˆr Z c eˆ 5 3.001 (0.001) a -14.15 P b -4.574 m Z 8.809-5.866 P CIPS 8-2.930 (0.010) P c eˆ 36.004 (0.007) ˆ pool ρ MQ c MQ 3 3 B a 0.954-14.17 L -6.422 CIPS -2.930 (0.010) B b f -4.54 Noes: Ba and Ng (2004): ˆr s he esmaed number of common facors, based on IC crera funcons. c c P s a Fsher s ype sasc based on p-values of he ndvdual ADF ess. Z s a eˆ sandardzed Cho s ype sasc for large N samples. P-values are n parenheses. The frrs esmaed value 1ˆr s derved from he flered es MQ f and he second one s derved from he correced es MQ., and ndcae sgnfcance a he 10%, 5% and 1% level, respecvely. Moon and Perron (2004): c a and b are he un roo es sascs based on de-facored panel daa (Moon and Perron, 2004). Correspondng p-values are n parenheses. pooled esmaes of he auo- regressve parameer. and kernel funcon n spe of a Quadrac Specral kernel funcon. Cho (2002): he m B a e ˆ ˆ ρ pool s he correced B b are compued wh a Barle P es s a modfed Fsher s nverse ch-square es. The Z es s an nverse normal es. The L es s a modfed Log es. p-values are n parenheses. Pesaran (2007): CIPS s he mean of ndvdual Cross seconally augmened ADF sascs (CADF). CIPS denoes he mean of runcaed ndvdual CADF sascs. Correspondng p-values are n parenheses. P denoes he neares neger of he mean of he ndvdual lag lenghs n ADF ess. Afer mplemenng he SPSM procedure, we also found Souh Korea s saonary wh he mnmum KSS value of -2.905 among he panel. Then, Souh Korea was removed from he panel and he Panel KSS un roo es was mplemened agan o he remanng se of seres. Afer ha, we found ha he Panel KSS un roo es sll rejeced he un roo null wh a value of -2.348 (p-value of 0.000), and Inda was found o be saonary wh he mnmum KSS value of -2.641 among he panel hs me. Then, Inda was removed from he panel and he Panel KSS un roo es was mplemened agan o he remanng se of seres. Afer ha, we found ha he Panel KSS un roo es sll rejeced he un roo null wh a value of -2.306 (p-value of 0.010), and Indonesa was found o be saonary wh he mnmum KSS value of -2.594 among he panel hs me. Then, Indonesa was removed from he panel and he Panel KSS un roo es was mplemened agan o he remanng se of seres. The procedure was connued unl he Panel KSS un roo es faled o rejec he un roo null hypohess a he 10% sgnfcance level, and fnally we found ha hs procedure sopped a he sequence 7, when he REERs for 7 counres (.e., Souh Korea, Inda, ~ 7 ~
ISSNs: 1923-7529; 1923-8401 2014 Academc Research Cenre of Canada Indonesa, Turkey, Chna, Russa, and Souh Afrca) were removed from he panel. To check he robusness of our es, we connued he procedure unl he las sequence. We found ha he Panel KSS sasc all faled o rejec he un roo null hypohess for he res of sequences. Apparenly, he SPSM procedure usng he Panel KSS un roo es whou a Fourer funcon provded evdence supporng he long-run valdy of PPP for 4 ou of 5 BRICS counres and 3 ou of 4 MIST counres beng suded. Ths leads us o he conclusons ha PPP holds for mos of he counres, wh he excepon of 2 counres (.e., Mexco and Brazl) under sudy. Table 4. Resuls of KSS es on PPP Sequence OU sasc Mn. KSS sasc Seres 1-2.409-2.905 Souh Korea 2-2.348-2.641 Inda 3-2.306(0.010) -2.594 Indonesa 4-2.258(0.010) -2.582 Turkey 5-2.193(0.030) -2.512 Chna 6-2.114(0.080) -2.414 Russa 7-2.013(0.080) -2.281 Souh Afrca 8-1.879(0.330) -1.963 Mexco 9-1.797(0.180) -1.797 Brazl Noes: OU sasc s he nvaran average KSS, NL sasc (Ucar and Omay, 2009). Enry n parenhess sands for he boosrap p-value. The sgnfcance level s 10%. The maxmum lag s se o be 8. The boosrap replcaons are 5000. Fnally, o accoun for srucural breaks, we rely upon he Panel KSS un roo es wh a Fourer funcon as n equaon (2). Frs, a grd-search s performed o fnd he bes frequency, as here s no a pror knowledge concernng he shape of he breaks n he daa. We esmae equaon (2) for each neger k = 1,...,5, followng he recommendaons of Enders and Lee (2012) ha a sngle frequency can capure a wde varey of breaks. The resdual sum of squares (RSSs) ndcaes ha a sngle frequency (k=1) works bes for mos of he seres, wh he excepon of sequence 9 we found he bes frequency o be (k=3), and for he sequences of 3 and 5, we found he bes frequency o be (k=5) (see he fourh column a he Table 5). Table 5 repors he resuls of Panel KSS un roo es wh a Fourer funcon on he naural log of REERs where we also gve a sequence of he Panel KSS sascs wh her boosrap p-values on a reducng panel, he ndvdual mnmum KSS sasc, and he saonary seres denfed by hs procedure each me. As we can see from Table 5, he null hypohess of un roo n REER was rejeced when he Panel KSS un roo es was frs appled o he whole panel, producng a value of -3.092 wh a very small p-value of 0.000. Afer mplemenng he SPSM procedure, we also found Brazl s saonary wh he mnmum KSS value of -3.894 among he panel. Then, Brazl was removed from he panel and he Panel KSS un roo es was mplemened agan o he remanng se of seres. Afer ha, we found ha he Panel KSS un roo es sll rejeced he un roo null wh a value of -2.992 (p-value of 0.000), and Turkey was found o be saonary wh he mnmum KSS value of -3.501 among he panel hs me. Then, Turkey was removed from he panel and he Panel KSS un roo es was mplemened agan o he remanng se of seres. Afer ha, we found ha he Panel KSS un roo es sll rejeced he un roo null wh a value of -2.919 (p-value of ~ 8 ~
Revew of Economcs & Fnance 0.000), and Russa was found o be saonary wh he mnmum KSS value of -3.493 among he panel hs me. Then, Russa was removed from he panel and he Panel KSS un roo es was mplemened agan o he remanng se of seres. The procedure was connued unl he Panel KSS un roo es faled o rejec he un roo null hypohess a he 10% sgnfcance level, and fnally we found ha hs procedure sopped a he las sequence of 9, when he REERs for all of he 9 counres (.e., Brazl, Turkey, Russa, Souh Korea, Mexco, Chna, Inda, Indonesa, and Souh Afrca) were removed from he panel. Apparenly, he SPSM procedure usng he Panel KSS un roo es wh a Fourer funcon provded srong evdence favorng he long-run valdy of PPP for boh BRICS and MIST counres beng suded. 7 Table 5. Resuls of KSS wh Fourer es on PPP Sequence OU sasc Mn. KSS Fourer( K ) Seres 1-3.092-3.894 1 Brazl 2-2.992-3.501 1 Turkey 3-2.919-3.493 5 Russa 4-2.823-3.308 1 Souh Korea 5-2.726-3.154 5 Mexco 6-2.619-2.763 1 Chna 7-2.572(0.010) -2.759 1 Inda 8-2.478(0.020) -2.541 1 Indonesa 9-2.414(0.050) -2.414 3 Souh Afrca Noes: OU sasc s he nvaran average KSS, NL sasc (Ucar and Omay, 2009). Enry n parenhess sands for he asympoc p-value. The sgnfcance level s 5% or less. The maxmum lag s se o be 8. The asympoc p-values are compued by means of Boosrap smulaons usng 5000 replcaons. 5. Conclusons Purchasng Power Pary (PPP) Theory s one of he oldes heores ha res o esablsh he lnk beween nomnal exchange rae and relave prces. Old sudes red o es hs heory by regressng he nomnal exchange rae on relave prces. They were crczed on he ground ha he resuls suffered from a spurous regresson problem. Combnng he nomnal exchange rae and relave prces ogeher yelds only one varable,.e., he real exchange rae. More recen sudes, herefore, have nvesgaed he mean reverng properes of he real exchange raes as a es of PPP. If he real exchange rae crosses s mean very frequenly, s sad o be saonary, supporng he PPP. Oherwse, may conan a un roo and rejec he PPP. Unvarae un roo ess were crczed for her low powers. Panel un roo ess are proposed as an alernave. However, sandard panel un roo ess yeld only one answer ha mplcaes every member of he panel equally. In hs paper we apply a mehod ha classfes he 7 For some oher exchange-relaed and PPP ssues see Moosa (1994), Beach, e al. (1993), Bleaney (1992), Horne (2004), Baffoe-Bonne (2004), Arze (2003), Holmes (2002), Apergs (1998), Jung (1995), Hojman (1989), and Sjolander (2007). ~ 9 ~
ISSNs: 1923-7529; 1923-8401 2014 Academc Research Cenre of Canada real effecve exchange raes of all members whn a panel o saonary and non-saonary seres. The mehod s known as he Sequenal Panel Selecon Mehod (SPSM) proposed by Chorareas and Kapeanos (2009). We apply hs procedure o es he PPP for a group of BRICS (Brazl, Russa, Inda, Chna, and Souh Afrca) and MIST (Mexco, Indonesa, Souh Korea and Turkey) counres, usng monhly real effecve exchange rae (REER) daa from January 1994 o June 2012. Whle several sandard panel un roo ess gve us mxed resuls, SPSM classfes he whole panel no a group of saonary seres and a group of non-saonary seres and clearly denfes how many and whch seres n he panel are saonary processes. Emprcal resuls form he SPSM usng he Panel KSS un roo es wh a Fourer funcon ndcae ha mean-reverson n REER holds rue for hese wo groups of counres under sudy. References [1] Alba, J.D. and D. Park (2003), Purchasng power pary n developng counres: Mul-perod evdence under he curren floa, World Developmen, 31(12): 2049-2060. [2] Apergs, Ncholas (1998), Budge Defcs and Exchange Raes: Furher Evdence from Conegraon and Causaly Tess, Journal of Economc Sudes, 25(3): 161-178. [3] Arze, A.C., J. Malndreos, and S. Chrsoffersen (2003), Moneary Dynamcs, Exchange Raes and Parameer Insably: An Emprcal Invesgaon, Journal of Economc Sudes, 30(5): 493-513. [4] Baffoe-Bonne, J. (2004), Dynamc Modellng of Fascal and Exchange Raes Polcy Effecs n a Developng Counry: A non-srucural Approach, Journal of Economc Sudes, 31(4): 57-75. [5] Bahman-Oskooee, M. (1993), "PPP Based on Effecve Exchange Rae and Conegraon: 25 LDCs Experence wh s Absolue Formulaon", World Developmen, 21(6): 1023-1031. [6] Bahman-Oskooee, M. (1995a), "Real and Nomnal Effecve Exchange Raes for 22 LDCs: 1971I-1990IV", Appled Economcs, 27(7): 591-604. [7] Bahman-Oskooee, M. (1995b), "Real Effecve Exchange Raes and he Purchasng Power Pary: Experences of 19 Indusral Counres", Economc Noes, 24(2): 239-250. [8] Bahman-Oskooee, M. and H-J Rhee (1992), "Tesng for Long-Run Purchasng Power Pary: An Examnaon of Korean Won", Inernaonal Economc Journal, 6(1): 93-103. [9] Bahman-Oskooee, Mohsen, Kuan, Al M. and Zhou, Su (2007a), A Cenury of Purchasng Power Pary: Furher Evdence", Economcs Bullen, 6(31): 1-9. [10] Bahman-Oskooee, Mohsen, Kuan, Al M. and Zhou, Su (2007b), Tesng PPP n he Non-lnear STAR Framework, Economcs Leers, 94(1): 104-110. [11] Bahman-Oskooee, M., Kuan, A. M., and Zhou, Z. (2008), "Do real exchange raes follow a nonlnear mean reverng process n developng counres", Souhern Economc Journal, 74(5): 1049-1062. [12] Bahman-Oskooee, M., T. Chang, and K. Hung (2013), Revsng Purchasng Power Pary n Lan Amerca: Sequenal Panel Selecon Mehod, Appled Economcs, 45(32): 4584-4590. [13] Ba, J. and Ng, S. (2004), A Panc aack on un roos and conegraon, Economerca, 72(4): 1127-1177. [14] Beach, E.D., Nancy Corell Kruse, Noel D. Ur. (1993), "The Docrne of Relave Purchasng Power Pary Re-examned", Journal of Economc Sudes, 20(1): 3-23. ~ 10 ~
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