Volume 30, Issue 4 Effcen marke hypohess n emergng markes: Panel daa evdence wh mulple breaks and cross seconal dependence Abd Halm Ahmad Unvers Uara Malaysa S Nurazra Mohd Daud Unvers Sans Islam Malaysa W.N.W. Azman-San Unvers Pura Malaysa Absrac The purpose of hs paper s o re-examne wheher mean reverson propery hold for 15 emergng sock markes for he perod 1985 o 006. Ulzng a panel saonary es ha s able o accoun for mulple srucural breaks and cross seconal dependence, we fnd ha he emergng sock markes follow a random walk process. However, furher analyss on ndvdual seres show ha he majory of sock prces n emergng markes are governed by a mean reverng process. Ths resul, whch s nconssen wh effcen marke hypohess, suggess ha pas nformaon s useful n predcng fuure prces n mos of he markes. The auhors are ndebed o an anonymous referee for helpful commens and suggesons. Any remanng errors are our own. Caon: Abd Halm Ahmad and S Nurazra Mohd Daud and W.N.W. Azman-San, (010) ''Effcen marke hypohess n emergng markes: Panel daa evdence wh mulple breaks and cross seconal dependence'', Economcs Bullen, Vol. 30 no.4 pp. 987-995. Submed: Jun 0 010. Publshed: November 11, 010.
1. Inroducon There has been much neres n pror emprcal sudes n esng wheher sock prce follows a random walk or mean reverng process. The mean reverson of he sock prces would sugges ha curren prces are predcable based on he prevous prces, whch s nconssen wh he weak-form effcen marke hypohess. Conversely, f sock prces follow a random walk process (un roo) any shock wll have a permanen effec on sock prces. As a consequen, sock prces wll reach a new equlbrum pon and, herefore, fuure prces canno be predced based on her hsorcal movemens. Several sudes have esed he valdy of he random walk hypohess (see Chen e al., 00; Raanapakorn and Sharma, 00; Chaudhur and Wu, 003; Phengps, 006; and Narayan, 008, among many ohers). Usng daa from boh developed and developng counres hey fnd no homogenous concluson on he subjec maer. For nsance, Chaudhur and Wu (003) and Phengps (006) have provded conflcng emprcal evdence on he sochasc properes of sock prces n en emergng markes usng unvarae un roo es ha accoun for a sngle srucural break. 1 Whle Chaudhur and Wu (003) fnd ha he sock prces are mean reverng, Phengps (006), who use a dfferen un roo es, fnd ha he majory of he sock prces can be characerzed as a random walk process. One possble explanaon for hs conflcng fndng may be he falure of he aforemenoned sudes o accommodae possble mulple srucural breaks and cross seconal dependence n sock prces. The mporance of mulple srucural breaks should no be underesmaed snce equy markes are affeced by several mporan evens over he pas few decades such as sock marke lberalzaon, economc crses, and changes n economc polcy (Bekaer e al., 00; Henry, 000). Perron (1989) show ha he falure o ake no accoun possble breaks n he seres may lead o underszed es sasc, leadng o ncorrec nferences. In addon, s unrealsc o assume ha ndvdual sock markes are cross seconally ndependen. The mporance of cross seconal dependence seems especally relevan here snce mos of he counres under consderaon are rade-orened. Therefore, any shocks o a counry s sock marke could be easly be ransmed across borders va mpors and expors. Moreover, emergng sock markes are lkely o be affeced by common exernal effecs such as he busness cycles of he Uned Saes. Ths conjecure s confrmed by our resuls usng a formal es proposed by Breusch and Pagan (1980). Maddala and Wu (1999) pon ou ha he falure o accommodae cross seconal dependence n panel un roo and saonary ess may lead o severe sze dsorons. The objecve of hs paper s o re-examne he sochasc properes of sock prces n 15 emergng markes. Our man conrbuon s ha we employ a new panel saonary es due o Carron--Slvesre e al. (005) whch s flexble enough o accommodae an unknown number of mulple breaks and cross-seconal dependence across sock markes. We also nvesgae he sochasc properes of ndvdual sock prces usng he es proposed by Im e al. (005). The resuls of our sudy wll complemen, or possbly aler, he conclusons documened n prevous sudes parcularly by Chaudhur and Wu (003) and Phengps (006). 1 These counres are Argenna, Brazl, Greece, Inda, Malaysa, Mexco, Ngera, Phlppnes, Tawan, and Zmbabwe. 1
The res of he arcle s organzed as follows. Secon II descrbes he emprcal mehodology. Secon III presens he daa and emprcal analyss, and he fnal secon concludes.. Mehodology In hs paper, we rely on wo newly developed panel es o esablsh he sochasc properes of sock prces n 15 emergng marke. They are panel saonary es by Carron-- Slvesre e al. (005) and panel un roo es by Im e al. (005). Boh ess allows for mulple srucural breaks n he seres. The panel saonary by Carron--Slvesre e al. (005) s a generalzed verson of he Hadr s (000) panel saonary es for he case of mulple srucural breaks. Le y be he sochasc process of sock prces whch under he null hypohess s characerzed by he followng daa generaon process: where y,,, (1) where m m,, k D( Tb, k ), k DU, k,, 1, () k1 k1 ~..d. (0, ) and, 0, consan wh = 1,.., N ndvduals and = 1,,T, v,, me perods. The dummy varables ( T b, k and DU k, D ), are defned as D ( T b, k ) = 1 for = T b, k and 0 elsewhere and DU, k, =1 for > T b, k and 0 elsewhere. The Carron--Slvesre e al. (005) mehod ncludes ndvdual srucural break effec (shfs n he mean) f β 0 and emporal srucural break effec (shfs n he ndvdual me rend) f, k 0. The specfcaon above has hree characerscs. Frsly, srucural breaks can have dfferen effecs on each ndvdual me seres specfed by, k and, k. Secondly, srucural breaks can occur a dfferen locaons snce here s no resrcon on he daes of he breaks, T b, k Tb, k, 1,.., Nand hrdly, ndvduals can have dfferen numbers of srucural breaks whch s capured by m m j, j,, j 1,..., T. Based on he saonary es proposed by Hadr (000), he general expresson for he es sascs s N 1 T 1 LM ( ) N ( ˆ T Sˆ, ) (3) 1 Apar from hese wo esng procedures, we also employ a baery of he frs generaon es. Snce hey are wdely used n he leraure, we skp he explanaon of he frs generaon ess.
where S, ˆ, j j 1 ˆ denoes he paral sum process ha s obaned usng he esmaed OLS resduals of (1). The 1,,, lm T T E( S, T ˆ s a conssen esmae of he long-run varance of ), = 1,.,N, whch allows he dsurbances o be heeroscedasc across he cross-seconal dmenson. n (3) ndcaes he dependence of he es on he daes of he break. For each ndvdual, s defned as he vecor (, 1,...,, m ) ( Tb,1 / T,..., T / T ) b, m ndcaes he relave posons of he daes of he breaks n he whole me perod. In addon, o deec he numbers of break n each ndvdual me seres, Carron--Slvesre e al. (005) employ he procedure of Ba and Perron (1998) whch allows each ndvdual un o have a dfferen number of breaks wh heerogenous break locaon across un. Afer deermnng he vecor, he es sascs for he null hypohess of a saonary panel wh mulple shfs s defned as: N ( LM ( ) ) Z( ) N(0,1) (4) where and are compued as averages of ndvdual and means and varances of LM () and has sandard normal dsrbuon. I should be noed ha he above es sasc assumes ha ndvduals are cross seconally ndependen. However, hs assumpon s clearly unrealsc n a globalsed economy where he shocks overpass he borders of he economes. In order o accommodae for crosssecon dependence of he es sasc, Carron--Slvesre e al. (005) suggesed compung he boosrap dsrbuon followng a procedure proposed by Maddala and Wu (1999). Im e al. (005) propose a panel LM un roo es ha s robus o srucural shfs. The es begns wh he compuaon of unvarae LM un roo es sascs for each seres. Then, he panel LM es sascs s obaned by averagng he opmal unvarae LM un roo -es sascs ( LM ). Specfcally, he panel LM es s defned as: LM N 1 barnt LM N 1 (5) In addon, Im e al. (005) consruc a sandardzed panel LM un roo es sascs by leng E( L T ) and V ( L T ) o defne as he expeced value and varance of LM respecvely under he null hypohess. Then, he sandardzed es sasc s gven by: N ( LM barnt E( LT )) LM (6) V ( LT ) 3
The numercal values for E( L T ) and V ( L T ) are n Im e al. (005) and he asympoc dsrbuon s unaffeced by he presence of srucural breaks and s sandard normal. 3. Emprcal resuls The daa used n hs paper are obaned from he Inernaonal Fnance Corporaon s Emergng Marke Daabase (IFC-EMDB). The U.S. dollar-denomnaed sock prce ndces are from 1985 o 006 coverng 15 emergng markes. The sampled counres are Argenna, Brazl, Chle, Colomba, Inda, Jordan, Souh Korea, Malaysa, Mexco, Ngera, Paksan, Phlppnes, Tawan, Thaland, and Zmbabwe. All sock prces are ransformed no naural logarhmc form pror o he analyss. We argue ha he assumpon of cross-seconal dependence s lkely o hold n hs analyss. One way of esng he appropraeness of hs assumpon s o apply he LM es developed by Breusch and Pagan (1980). 3 The es for he hypohess ha all correlaon coeffcens are jonly 0 s defned as N 1 LM T r j 1 j1 where T s number of me seres observaon, N s number of counres, and r j s he j h resdual correlaon coeffcen, dsrbued as wh N ( N 1) / degree of freedom under he null of no cross secon dependence. The hypohess of cross seconal ndependence s esed on he resduals of ndvdual seres obaned by runnng OLS regresson of each seres on s own lag and deermnsc componens (nercep and me rend). The es sascs show srong evdence of cross-secon dependence as he null of no cross-secon dependence can be rejeced a he 5% level of sgnfcance (LM sasc: 697.48; p-value: 0.000). Nex, we proceed o esng he saonary of sock prces. We frs apply a baery of he frs generaon panel un roo ess whou breaks whch nclude un roo ess by Levn e al. (00) and Im e al. (003) and he panel saonary es due o Hadr (000). Resuls are presened n Table 1. Based on he Levn e al. (00) and Im e al. (003) es resuls, we could no fnd any evdence ha suppor mean reverson hypohess as he null of un roo canno be rejeced n boh cases a he usual level. Conssen wh he prevous fndng, he resul of Hadr (000) panel saonary es reveals ha he null of mean reverson can be rejeced a he 5 percen level. 3 Breusch and Pagan (1980) es s more approprae for our sample snce he cross secon dmenson (N) s small relave o he me dmenson (T). In he case of small T and large N, one may consder Pesaran e al. (008) esng procedure. We hank he referee for he suggeson. 4
Table 1: The frs generaon panel un roo ess Tes sascs p-value Levn, Ln and Chu (00) 0.46 0.665 Im, Pesaran and Shn (003) -.153 0.357 Hadr (000) 13.886 0.000* Noes: * denoes rejecon of null a he 5 percen level. I should be emphaszed however ha he frs generaon panel un roo ess above end o under rejec he null for no akng no accoun he exsence of srucural changes n he underlyng seres. Falure o consder any possble break pons n he seres may lead o a msleadng nerpreaon of saonary wh srucural break(s) as a un roo. A number of sudes have lnked sock markes o major economc crses, such as he Asan Fnancal Crss n 1997 and he Ocober 1987 marke crash, and also o sock marke lberalzaon. Moreover, he frs generaon ess gnore he cross seconal dependence whch was shown o be relevan for hs sudy. However, gnorng cross seconal dependence n un roo or saonary es may lead o ncorrec nferences. In order o ge a beer nsgh on he presen ssue, he nex logcal sep s o examne he properes of sock prces usng a panel es ha allows for he presence of srucural changes and smulaneously conrol for cross secon dependence. We apply he panel saonary es developed by Carron--Slvesre e al. (005) o our daase and accoun for cross-secon dependence of he sock prces by compung crcal values usng a boosrap procedure followng Maddala and Wu (1999). 4 Apar from conducng he panel es of saonary for all counres, we also examne a panel of Asan counres. 5 Our resuls are based on he assumpon ha he long-run varance s homogenous and heerogeneous. Under each of hese assumpons, we conduc panel ess by allowng for a maxmum of fve srucural breaks seleced usng he modfed Schwarz nformaon creron (LWZ) of Lu e al. (1997). The resuls of hese exercses are repored n Table. As shown n he able, he analyss for he overall sample srongly ndcaes rejecon of he null of saonary rrespecve of wheher he long-run varance s homogenous or heerogeneous. Also, he resuls for he Asan subsample ndcae ha he null can be rejeced a he usual level of sgnfcance. These fndngs srongly sugges ha sock prces n emergng markes can be characerzed as a random walk (un roo) process. Ths fndng whch s conssen wh he effcen marke hypohess suggess ha sock prces nsananeously respond o all relevan nformaon n he marke. 4 Ineresed readers may refer o Maddala and Wu (1999) and Carron--Slvesre e al. (005) for he deals of he boosrap procedure. 5 We would lke o analyze a panel of Lan Amercan counres bu daa lmaon mpedes he mplemenaon of he analyss. 5
Table : Panel saonary es due o Carron--Slvesre e al. (005) Tes sascs Crcal values 10% 5% 1% Overall sample: Homogeneous 8.0 * 3.13 4.50 7.89 Heerogeneous 56.43 * 56.7 66.7 80.30 Asan regon: Homogeneous 51.49 * 4. 8.17 35.53 Heerogeneous 39.4 * 61.71 73.1 105.57 Noes: * denoes rejecon of null a he 5 percen level. The maxmum numbers of srucural breaks s 5 and were seleced usng he modfed Schwarz nformaon creron (LWZ) of Lu e al. (1997). The crcal values were compued usng boosrap dsrbuon echnque wh 000 replcaons. A lmaon of he above esng procedure s ha he rejecon of null does no mples ha all sock prces conan un roo. Insead, only ndcaes ha sock prces n some counres may have un roo. However, he es s no able o pon ou whch sock prces are really nonsaonary. To address hs problem, we complemen he above fndngs wh he resuls of un roo esng of Im e al. (005) whch allow us o check he sochasc properes of ndvdual seres. Two models were esmaed namely, Model A ha allows breaks n nercep, and Model C ha allows breaks n boh nercep and rend. Resuls are presened n Table 3. As shown n he able, resuls for Model A reveal ha he null of un roo can be rejeced a he 5 percen level n he case of Argenna, Chle, Mexco, Ngera, Paksan, Phlppnes, Tawan, Thaland, and Zmbabwe. Ths resul suggess ha effcen marke hypohess only hold n four counres namely Brazl, Colomba, Inda and Jordan. Meanwhle, for Model C he null can be rejeced a he usual level excep for Brazl, Colomba, and Souh Korea. By and large, he resuls reveal ha he majory of he sock prces can be characerzed as a mean reverng process, mplyng ha fuure prces can be predced usng hsorcal prces. Ths fndng s conssen wh Chaudhur and Wu (003) who fnd mean reverng behavor of sock prces n en emergng markes. 6
Table 3: Panel un roo es due o Im e al. (005) Counry Model A lag Model C lag Argenna -4.14* 0-7.998* 0 Brazl -3.1906 4-5.4969** 5 Chle -4.3461* 0-6.1787* 6 Colomba -.98 0-4.7981 6 Inda -.831 6-10.0366* 5 Jordan -3.7679** 6-11.074* 6 Souh Korea -3.116 0-4.5030 5 Malaysa -.8768 6-10.7457* 6 Mexco -4.3558* 0-10.0035* 6 Ngera -5.9111* 0-6.044* 0 Paksan -4.8817* 0-7.56* 6 Phlppnes -5.1787* 0-5.804* 6 Tawan -6.0107* 0-5.174* 0 Thaland -5.5888* 5-5.883* 0 Zmbabwe -4.0017* 6-6.737* 4 Panel LM es sascs -9.044* Noes: * and ** denoes he rejecon of null a he 5 and 10 percen level, respecvely. The crcal values for he unvarae LM sascs for model A are -3.84 (5% level) and -3.504 (10% level). The crcal values for model C are -5.73 (5% level) and -5.3 (10% level). The correspondng crcal values for he panel LM sascs are -1.645 and -1.8. 4. Conclusons In hs paper, we re-examned he valdy of effcen marke hypohess n 15 emergng sock markes by applyng a new panel saonary developed es by Carron--Slvesre e al. (005) whch s flexble enough o accommodae mulple breaks. A prelmnary analyss on sock prces shows ha hey are cross-seconally dependen. Snce he es by Carron--Slvesre e al. (005) s no able o accoun for cross seconal dependence, we compue he crcal values of he es sascs va a boosrap-based mehod as suggesed by Maddala and Wu (1999). In so dong, we managed o accoun for he sock prce dependence. The resul shows ha he sock prces follow a random walk process, lendng suppor o he effcen marke hypohess. However, furher evdence based on he Im e al. (005) esng procedure show ha he majory of sock prces n emergng markes are mean reverng. References Ba, J. and Perron, P. (1998) Esmang and esng lnear models wh mulple srucural changes Economerca 66, 47 78. Bekaer, G., Harvey, C. and Lumsdane, R. (00) Dang he negraon of world equy markes Journal of Fnancal Economcs 65, 03-47. Breusch, T. S. and Pagan, A. R. (1980) The Lagrange Mulpler Tes and Is Applcaons o Model Specfcaon n Economercs Revew of Economc Sudes 47, 39-53. Carron--Slvesre, J. L., Del Barro, T. and Lopez-Bazo, E. (005) Breakng he panels: an applcaon o he GDP per capa Economercs Journal 8, 159-175. 7
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