Testing the Real Interest Parity Hypothesis in Six Developed Countries

Transcription

1 Tsing h Ral Inrs Pariy Hypohsis in Six Dvlopd Counris Auhor Shi, Jami, Li, Bin, Alxiadis, Sam Publishd Journal Til Inrnaional Rsarch Journal of Financ and Economics Copyrigh Samn EuroJournals Publishing, Inc. Th aachd fil is rproducd hr in accordanc wih h copyrigh policy of h publishr. Plas rfr o h journal's wbsi for accss o h dfiniiv, publishd vrsion. Downloadd from hp://hdl.handl.n/7/79 Link o publishd vrsion hp:// Griffih Rsarch Onlin hps://rsarch-rposiory.griffih.du.au

2 Inrnaional Rsarch Journal of Financ and Economics ISSN 5-7 Issu () EuroJournals Publishing, Inc. hp:// Tsing h Ral Inrs Pariy Hypohsis in Six Dvlopd Counris Qi Shi Griffih Businss School, Griffih Univrsiy Brisban, QLD, Ausralia mousjimmy@3.com Bin Li Griffih Businss School, Griffih Univrsiy Brisban, QLD, Ausralia b.li@griffih.du.au Sam Alxiadis School of Economics, Financ and Marking RMIT Univrsiy, Ausralia Absrac In his papr, w conduc uni-roo ss (including ADF, PP, KPSS and DF-GLS ss) on h x pos ral inrs ras in six dvlopd counris (Canada, Franc, Japan, Ialy, Singapor, h UK agains h US). W also us ral inrs ra diffrnial (RID) o xamin whhr ral inrs ra pariy holds in hs counris. Our rsul suppors ha ral inrs ras ar man rvring and h ral inrs pariy (RIP) hypohsis holds in h majoriy of h chosn counris. Kywords: Inrs Ra Diffrnial, Inrs Ra Pariy, Uni Roo Ts.. Inroducion Sinc 9s, h mos significan chang of h financial mark has bn h gradual ingraion of financial mark wih h dvlopmn of globalizaion. Financial policis of vry counry ar owards inrnaionalizaion and libralizaion. Rcnly, h flow of inrnaional capial has bcom mor frqun in rms of qualiy and quaniy. In h long rm, h inflow and ouflow of inrnaional capial will hav a significan impac on dirc financial invsmn and h growh of h conomics of h domsic counry; howvr, in h shor rm, i will caus h insabiliy of xchang ra, h pric of scuriy, inrs ras and h dmand for domsic currncy. To pursu a mor fficin capial mark, financial policis of ach counry gradually rlax h rsricion of capial flows bwn naions. Th floaing of h currncy of a naion will dircly affc is xpors and impors, hrby affcing is balanc of paymn and h pric of commodiy. Howvr, no only h xchang ra will affc conomic aciviis, bu h inrs ra is also anohr imporan facor. Inrs ra will affc a counry s invsmns, savings, h dmand for domsic currncy, and so on. I will also affc h pric of commodiy and h balanc of paymn. Each counry can ak advanag of is monary policy o chang h inrs ras, hrby having

3 Inrnaional Rsarch Journal of Financ and Economics - Issu () 9 impacs on h conomy of his counry. Wih h ingraion of financial conomics and h frqun flow of capial, ach counry howvr could no mploy an indpndn monary policy. Purchasing powr pariy (PPP) and uncovrd inrs pariy (UIP) can b usd o invsiga h cross-bordr conomic aciviis. Thos wo hypohss ar h basics of monary horis. Combining h PPP, UIP and h Fishr quaion, on can obain h ral inrs ra pariy (RIP) ha is an imporan indicaor of masuring inrnaional capial flow. Th RIP argus ha if vry invsor xpcs raionally o mak his financial dcision, and hr ar no barrirs among global marks, h ral inrs ra of ach counry mus b h sam. If h RIP hypohsis fails o hold, i implis ha policy makrs can mak monary policis indpndnly. In his papr, w s man rvrsion in h x pos ral inrs ras in six dvlopd counris (Canada, Franc, Japan, Ialy, Singapor, h UK vis-a-vis h US). W mploy ral inrs ra diffrnial (RID) o xamin whhr ral inrs ra pariy holds in hs counris. W apply uni roo ss including ADF, PP, KPSS and DF-GLS ss. Our rsul suppors ha ral inrs ras ar man rvring and h ral inrs pariy (RIP) hypohsis holds in h majoriy of h chosn counris. Th rmaindr of h papr is organisd as follows. Scion rviws rlvan liraur. Scion 3 dvlops sabl hypohss, and Scion inroducs h mhodology. Scion 5 prsns h daa, and Scion provids h mpirical rsuls. Scion 7 concluds.. Rlad Liraur Ovr h las 3 yars, h majoriy of h world s govrnmns hav undrakn drgulaion and libralisaion of hir financial marks in ordr o simula a grar dgr of ingraion bwn hir marks and hos of h rs of h world. Mark ingraion allows a counry o rais is sandard of living and lads o grar capial flows by faciliaing commodiy and financial arbirag, which in urn liminas h diffrnc bwn hs counris ral ras of rurn. An implicaion of financial mark ingraion, howvr, is ha h grar a counry is ingrad, h lss conrol domsic monary auhoriis hav in influncing and pursuing sabilisaion policis sinc if ral ras ar qualisd across counris, h abiliy o which h auhoriis can influnc hir counris ral inrs ra is limid o h xn o which hy can influnc h world ra. A vas amoun of rsarch has bn conducd on h opic of whhr or no ral inrs ras ar man rvring and h gnral conclusion dpnds on h ss h rsarchrs us. Sudis of his hypohsis usually bgin wih h Fishr rlaion, which sas ha h nominal inrs ra adjuss o changs in h xpcd inflaion ra and h ohr ky focus is on ral inrs pariy (RIP) condiion which provids dirc vidnc on whhr or no h procss of financial drgulaion has ld o grar mark ingraion and capial mobiliy and hrfor limiing monary auhoriis impac on h sabilisaion of policis. For insanc, Mishkin (9), Goodwin and Grnns (99), Chung and Crowdr () s RIP by xamining h hypohsis ha x-an ral inrs ras ar qual across counris whras Cumby and Obsfld (9) s RIP by amping o drmin whr hr is any corrspondnc bwn nominal inrs ras and inflaion diffrnials. Cumby and Mishkin (9) find a significanly posiiv inrnaional linkag of ral inrs ras, bu i is lss han compl, i.., lss han on-o-on rlaionship and i hus implis ha monary policy is abl o influnc h conomy. Moosa and Bhai (997) s h dgr of ingraion bwn Asian counris by xamining Uncovrd Inrs Pariy (UIP) and x an Purchasing Powr Pariy (PPP) and hy find srong suppor of validiy of UIP and x an PPP in almos all cass. Moosa and Bhai (99) prsn vidnc of man rvrsion in x an ral inrs ras and hir diffrnials using h Philips-Ouliaris (99) saisic, h Sims (9) Baysian s and h varianc raio s. Th convnional ss such as h Dicky-Fullr (979) saisic, F-saisic, h Box-Pirc (97) and h Ljung-Box (97), ar unabl o disinguish bwn wha is a nar random walk and wha is a ru random walk and hus h rsuls may b biasd. Anohr rason as o why

4 7 Inrnaional Rsarch Journal of Financ and Economics - Issu () convnional ss fail o suppor ral inrs qualisaion across counris is ha hy ignor ransacion coss (Goodwin and Grnns, 99). Goodwin and Grnns (99, p.) no ha h non-synchronous variaions of individual inrs ras in rspons o local financial condiions may hav ld o h incorrc rjcion of man rvrsion vn hough h mark in qusion is in fac ingrad and fficin. In rspons o his finding, hy propos an alrnaiv modl o allow for non-synchronous vns and conclud ha h vidnc is much srongr han commonly found. Kinal and Lahiri (9) propos a modl o drmin h xpcd ral inrs ra in which h ffc of pric xpcaions is considrd and hy find vidnc ha bwn h priod h pric forcass drivd ar unbiasd. Givn h raional xpcaions hory h acual ral inrs ra is qual o h x-an ral inrs ra plus an rror rm, hir modl posulas ha h random forcasing rrors ar no confound o h variaion of h x-an inrs ra. 3. Hypohsis Dvlopmn Th ral inrs pariy (RIP) hypohsis posulas ha h x-an ral inrs ra is consan and h nominal inrs ra diffrnial is xacly qual o h amoun of h inflaion ra diffrnial. If his is h cas, hn financial marks will b ingrad and capial will b fr o flow in and ou of counris. Our null hypohsis is hus ha h ral inrs ra pariy holds for ach counry. Moosa and Bhai (99) argu ha h RIP rquirs h following assumpions: h validiy of covrd inrs ra pariy (fficincy of domsic and forign capial marks), purchasing powr pariy (fficincy of commodiy and financial marks) and h unbiasdnss of h forward ra as a forcasr of h fuur spo ra, h mahmaical quaions of which ar as follows: f s = i i, () s s = p p, () f (3) s whr s is h logarihm of h spo xchang ra, f is h logarihm of h forward xchang ra, i ( i ) is h domsic (forign) nominal inrs ra, s + is h logarihm xpcd inrs ra a im +, s is h logarihm of h spo xchang ra, and p + ( p + ) is h inflaion ra ha can b calculad as h firs ordr diffrnc of h x-an logarihm of domsic (forign) consumr pric indx. From () and (), w can obain s s = i + i, () which is h uncovrd inrs pariy (UIP) condiion. Subsiu () ino () yilding p + p + = i i, (5) Th RIP hypohsis is no only basd on UIP condiion and x an PPP, and mor imporanly, i is basd on h Fishr ffc. Th Fishr ffc implis ha h nominal inrs ra is qual o h sum of h ral inrs ra and h inflaion ra. This hypohsis is hus givn as i = r + p, and () + + i = r + p, (7) + + whr r + is h x-an ral inrs ra. Equaions () and (7) suggs ha h Fishr condiion is valid boh in h domsic counry and forign counris. Rarranging (5) yilds h ral inrs pariy condiion: r = r. () + +

5 Inrnaional Rsarch Journal of Financ and Economics - Issu () 7 If x an ral inrs ra is consan bwn diffrn counris, h x-an inrs ra diffrnial is man rvring and ha ral inrs ra pariy holds. Thrfor, assuming raional xpcaions: r = r + ε, (9) r = r + ε, () whr ε + I (), ε + I(), and ε + = p + p +, and ε + = p + p +, w can obain r r = rid = ξ, () whr ξ+ = ε + ε +, ξ + I() and rid sands for ral inrs diffrnial bwn domsic counry and h forign counry. Ex pos RIP also implis x an RIP undr h assumpion of raional xpcaions. Th long-run RIP holds in h cas ha h x pos ral inrs ra diffrnial is zro man saionary.. Mhodology Our s modl is spcifid as: rid = γ + γrid + ε. () In our modl, if rid is man rvring in h long run, h RIP hypohsis holds in h long-run quilibrium. Our objciv is hus concnrad on prforming uni roo ss on rid. W us Augmnd Dicky-Fullr (ADF) s, Phillips-Prron s, and h KPSS s, which ar inroducd on by on blow... ADF Ts Th augmnd Dicky Fullr s (ADF) is a s for a uni roo in a im sris daa. I is an augmnd vrsion of h Dicky Fullr s. ADF is h convnional mhod for sing uni-roo. Th ADF modl is sad as follows: k rid = α + β + ( ρ ) rid + θ rid + ε, (3) i i= whr α is h drif, is h drminisic rnd indpndn variabl, k is h lag lngh, andε is h whi nois. Th null hypohsis of h s is ha: ρ - =, which implis ha h sris is a random walk. Th firs alrnaiv hypohsis is ha: ρ - < and α =, which implis ha h sris is zro man saionary and h RIP holds. Th scond alrnaiv hypohsis is ha: ρ - < and α, which implis ha h sris convrgs o h man valu ha is no qual o zro. Th RIP hypohsis dos no hold probably du o counry spcific risk prmium. If rid convrgd o h whi nois procss, i will b consisn wih h RIP hypohsis, sinc h shocks will gradually hav no ffc. An imporan pracical issu of h ADF s is h spcificaion of h lag lngh p. If p is oo small, srial corrlaion in h rrors will bias h s. If p is oo larg, h powr of h s will suffr. Ng and Prron (995) suggs a procss o slc a lag o provid rlaiv sabiliy in h daa by sing an uppr bound and hn simaing h uppr bound o s for significanc. Th ADF s is a convnional and popular mhodology o s h uni roo. Howvr, i is flawd whn applid in hs hr siuaions: small sampls, srucural braks, and nar random walk. ADF is wll-known of is low powr o dc h diffrnc bwn h uni roo and nar random walk, spcially whn h sampl siz is small. On h ohr hand, h sandard s will b biasd if hr is a srucural chang. Prron (99) shows ha h powr of his s o rjc h null hypohsis of a uni roo, whn h undrlying sris is saionary wih a brak in ihr is man or rnd, falls as

6 7 Inrnaional Rsarch Journal of Financ and Economics - Issu () h siz of h brak incrass. By conras, Franss and Haldrup (99) show ha h siz of h ADF s was snsiiv o h prsnc of oulirs. In paricular, hy show ha a a nominal 5% significanc lvl, h mpirical siz of h ADF s incrass wih an incras in ihr h frquncy of oulirs, or h siz of h oulir, concluding ha h implicaions of his yp of daa irrgulariis will nd o produc spurious saionariy... Phillips-Prron Uni Roo Ts Th Phillips-Prron (PP) uni roo ss diffr from h ADF s mainly in how i dals wih srial corrlaion and hroskdasiciy in h rrors. In paricular, whr h ADF s us a paramric auorgrssion o approxima h ARMA srucur of h rrors in h s rgrssion, h PP s ignors any srial corrlaion in h s rgrssion. D Jong al. (99) shows ha h Dicky Fullr s saisics hav bn criicisd for hir low powr, spcially in disinguishing bwn uni roos and nar uni roos and in small sampl daa. On h ohr hand, h Phillips Prron (PP, 9) s is mor robus o srial corrlaion, im dpndn hroscdasiciy and rgim changs (Moosa and Bhai, 997). Th calculaion of Phillips-Prron s is basd on h rgrssion uˆ = au ˆ ˆ + kˆ. () z Thn h ˆ a saisic, a ransformaion of h sandardisd simaor T ( a ˆ -), is givn by: T zˆ = T ( aˆ ) ( / )( s ) ˆ a Tl sk T u, (5) whr T is h sampl siz, and h consisn simas s k and s T ar givn by T ˆ k = s T k, and () T ˆ l T ˆ ˆ T = + sl s s = = s +, (7) s T k T w k k for som choic of window such as w = - s / ( l + ). Th z ˆ sl saisic, a ransformaion of h rgrssion saisic, is givn by: T / T / zˆ = uˆ ˆ ˆ ( a ) / st ( / )( st s k ) s T l T u. () Ths wo saisics ar drivd using an sima s T, which is basd on h rsiduals k ˆ from h auorgrssion of u ˆ on u ˆ -. s k and s T hlp o dvlop his ss for uni roos which could b mployd undr vry gnral condiions. Undr h null hypohsis ha π =, h PP Z and Z a saisics hav h sam asympoic disribuions as h ADF -saisic and normalisd bias saisics. On advanag of h PP ss ovr h ADF s is ha h PP s is robus o gnral forms of hroskdasiciy in h rror rm. Anohr advanag is ha h usr dos no hav o spcify a lag lngh for h s rgrssion. Th ADF and PP ss hav vry low powr agains I() alrnaivs ha ar closr o bing I(). Tha is, uni roo ss canno disinguish highly prsisn saionary procsss from nonsaionary procsss vry wll. Also, h powr of uni roo ss diminish as drminisic rms ar addd o h s rgrssions. Tha is, ss ha includ a consan and rnd in h s rgrssion hav lss powr han ss ha only includ a consan in h s rgrssion. For achiving maximum powr agains nar random walk, rcn ss proposd by Ellio, Rohnbrg and Sock (99) and Ng and Prron () can b usd.

7 Inrnaional Rsarch Journal of Financ and Economics - Issu () KPSS Ts Kwiakowski, Phillips, Schmid and Shin (KPSS, 99) s us h LM saisic o s h uni roo. Th ims sris rid is h sum of h drminisic rnd, a random walk and h rror rm. Th KPSS modl is as follows: T s v = T σ, (9) k i () i = s =, =,..., T whr i is h rgrssion cofficin of rid on inrcp and im, σ k is h varianc of rid in long priod, k is h numbr of laggd priods, T is h numbr of h sampl, and v is h asympoic disribuion. Th null hypohsis is ha rid is lvl saionary and saionary around a linar rnd and h alrnaiv hypohsis is ha rid has a uni roo. If v is largr han h significan lvl, w will rjc h null hypohsis and conclud ha rid has a uni roo. Th advanag of h KPSS is ha o som xn KPSS allvias h problm ha is prsn wih h ADF s. Kwiakowski, Phillips, Schmid and Shin (99) argu ha KPSS s can disinguish a sris ha appars o b saionary, sris ha appar o hav a uni roo, and sris for which h daa ar no sufficinly informaiv o b sur whhr hy ar saionary or ingrad. Prron (99) and Chn () invsiga h bhaviour of h KPSS s in h prsnc of prmann changs in h inrcp and/or rnd of a saionary sris. Thy find ha h KPSS s has h powr o rjc h null hypohsis of lvl and rnd saionariy of a sris in h prsnc of hs braks... DF-GLS Ts Ellio, Rohnbrg and Sock (99) propos a modifid Dicky-Fully s (h DF-GLS s). This uni roo s is mor powrful han h ADF s. Is rgrssion funcion is: d d d d X = a X + a X + + a X + ε, () P p d whr X is h drndd sris. Whn DF-GLS only conain h inrcp, h valu is h sam as h ADF s, and is criical valu is as pr h ADF s. Whn DF-GLS s conains boh rnd and inrcp, is disribuion is diffrn from h ADF s, and is criical valu is as pr h ERS s. KPSS and DF-GLS ar boh rcnly nw ss innding o dal wih h flaws ha ADF and PP ss hav. Howvr, as hs nw ss probably hav rmdid h problms h ADF and PP ss hav whil som nw problms appar. Brifly spaking, up o now, hr is no such an advancd uni roo s which is asy and convninc o solv all h problms. 5. Daa W us h daa for h following dvlopd counris: Canada, Franc, Japan, Ialy, Singapor, h UK, and h US which is a bnchmark counry. Th sampl daa consiss of quarrly obsrvaions on Consumr Prics Indx (CPI), and inrs ra. Th daa ar sourcd from h IMF s Inrnaional Financial Saisics (IFS). W choos h sampl priod 9Q-9Q bcaus afr 9s h world financial marks bcam rlaivly mor ingrad. Thr ar wo kinds of inrs ras for us o choos from: 3-monh Trasury bill and 3-monh dposi ra. W choos 3-monh Trasury bill ra (prcn pr annum) for Canada, Ialy, Franc, UK, Singapor, and h US; and w choos 3-monh dposi ra for Japan. In rgards o h choic of mauriy, as sad by h liquidiy prmium hory in which invsors nd o prfr bonds wih shor-rm mauriis rahr han bonds wih longr-rm mauriis sinc hy nd o bar lss inrs-ra risk.

8 7 Inrnaional Rsarch Journal of Financ and Economics - Issu () Thr ar hr sps rquird o g h ral inrs ra and h ral inrs ra diffrnial agains h US. Firs, w calcula h inflaion ra. W ransfr h daa by h following quaion: π + = ( CPI + CPI ) / CPI. () Scond, as h inrs ras in h daabas ar nominal inrs ras, w us h Fishr quaion (h nominal inrs ra minus h xpcd inrs ra) o g h ral inrs ra: r = i π + k, (3) Whr r is h ral inrs ra in spo, priod k; and i is nominal inrs ra in h spo, priod k; π + k is h xpcd inflaion ra from spo o spo + k. Th x pos ral inrs ra is hus h nominal inrs ra minus h xpcd inflaion ra. Third, w us h following quaion o obain h ral inrs ra diffrnial (RID): RID = r r, () whr RID is h ral inrs ra diffrnial agains h US a spo, r is h ral inrs ra of domsic counry in spo, and r is h ral inrs ra of h US. Th condiion of ral inrs pariy follows: r( ) = α + βr ( ) + ε, (5) whr r is h ral inrs ra of domsic counry, hand, if α =, β = and ~ I() r is h ral inrs ra of h US. On h on ε I, hr xiss ε, h RIP condiion holds. On h ohr hand, if ~ () a coingraing rlaionship bwn h domsic counry and h US, in ohr words, hr is a sabl rlaionship bwn hm in h long run, and h RIP condiion will b convrgd in h fuur. Th im-sris plo for h ral inrs ras and ral inrs diffrnial sris can b found in Figur and Figur, rspcivly. Figur : Ral Inrs ra for G and h US CANADA FRANCE ITALY JAPAN

9 Inrnaional Rsarch Journal of Financ and Economics - Issu () 75 Figur : Ral Inrs ra for G and h US - coninud 7 SINGAPORE UK US - Figur : Ral Inrs Ra Diffrnial of G agains h US CANADA/US FRANCE/US ITALY/US JAPAN/US SINGAPORE/US UK/US

10 7 Inrnaional Rsarch Journal of Financ and Economics - Issu (). Empirical Findings Th scion provids h mpirical sing rsuls basd on h sing mhods w inroducd in h prvious scion. W mploy convnional uni roo ss: ADF, PP, KPSS o s ral inrs ra and ral inrs ra diffrnial in ordr o xamin whhr hr is man rvrsion in ral inrs ras and whhr h RIP hypohsis holds. Furhrmor, w us a mor powrful uni roo s, DF-GLS s. As h rsul of ADF and DF-GLS ar all vry snsiiv o h numbr of lags chosn. Th opimal lag is givn by h minimum valu of h Schwarz Informaion Cririon for ADF and DF-GLS. On h ohr hand, h KPSS and PP ss ar snsiiv o h numbr of bandwidh, and hrfor w choos h Nwy-Ws bandwidh as h opimal bandwidh. Th null hypohsis of h ADF, PP, DF-GLS s is ha h im sris has a uni roo (I()), h alrnaiv hypohsis of h ADF, PP, DF-GLS s is ha h im sris is saionary (I()). Th null hypohsis of h KPSS s is ha h im sris is saionary (I()), h alrnaiv hypohsis of KPSS s is ha h im sris has a uni roo (I()). Tabl o Tabl show h sing rsuls wih consan only and boh h rnd and consan. Tabl dmonsras ha h ADF s dos no suppor I() for Franc, Ialy and Japan whil suppors I() for Canada, Singapor, h UK and h US. Th PP s hav lss powr han h ADF s, and i dos no suppor I() for Franc and Ialy, whil suppors I() for Japan, Canada, Singapor, h UK and h US. By conras, h KPSS s has mor powr han h ADF and PP ss and i shows ha h sris of all h counris ar saionary. Tabl : ADF, PP, KPSS Tss for h Ral Inrs Ra of G and h US in Lvl Tabl shows ha h sris bcom saionary for all h counris afr h firs diffrnc. Th ADF s shows ha h ral inrs ras of Canada, Singapor, h UK, and h US ar I(), and of Franc, Ialy, and Japan ar I(). Th PP s shows ha h ral inrs ras of Canada, Singapor, Japan, h UK, and h US ar I() and of Franc and Ialy ar I(). Th KPSS s shows ha h ral inrs ra of all h counris ar I().

11 Inrnaional Rsarch Journal of Financ and Economics - Issu () 77 Tabl : ADF, PP, KPSS Tss for h Ral Inrs Ra (Firs Diffrnc) of G and h US in Lvl Nx, w xamin h uni roo of ral inrs ra diffrnial and h rsuls ar prsnd in Tabl 3 and Tabl. Firs of all, h ADF s shows ha h RID of Canada, Japan and Singapor all rjc h null hypohsis which implis ha hy ar saionary (I()). Th s on h RID of Franc, Ialy and h UK canno rjc h null hypohsis ha hy hav a uni roo (I()). Tabl 3: ADF, PP, KPSS Tss for h Ral Inrs Ra Diffrnial of G agains h US in Lvl

12 7 Inrnaional Rsarch Journal of Financ and Economics - Issu () Tabl : DF-GLS Ts for h Ral Inrs Ra Diffrial of G agains h US in Lvl Scond, h PP s shows ha h null hypohsis is rjcd for Canada, Japan, Singapor and h UK, bu canno b rjcd for Franc and Ialy. Third, h KPSS s shows ha all h RID of h counris ar saionariy (I()). Finally w apply a mor powrful s, DF-GLS s (prsnd in abl ) and find ha for Canada, Franc, Japan, Singapor and h UK, h s rjc h null hypohsis ha ar saionary (I()) xcp for Ialy. Alhough h ADF, PP, KPSS and DF-GLS ss ar all convnional uni roo ss, hy ar all basd on an indpndn quaion. Whn a nar uni roo is prsn wihin h daa, h convnional uni roo ss hav low powr and canno disinguish bwn a uni roo and a nar uni roo. Ths convnional uni roo ss ar basd on h condiion ha h sampl is infini. Our sampl is fini and as a rsul h convnional uni roo ss nd no o work vry wll. In shor, among hs four uni roo ss, h ADF is h wors, and h PP s prforms slighly br. Howvr h KPSS and DF-GLS s hav h abiliy o disinguish a nar uni roo from a uni roo and hrfor produc mor accura rsuls. 7. Summary and Concluding Rmarks In his papr w conduc four kinds of uni roo ss: ADF, PP, KPSS and DF-GLS on h ral inrs ras in six dvlopd counris: namly, Canada, Franc, Japan, Ialy, Singapor and h UK vis-a-vis h US. Boh h ADF and PP ss ar wak whn daling wih small sampl wih nar random walk. Similar o h finding of Moosa and Bhai (99), whn w us low powr ADF and PP ss, our rsul show ha h ral inrs ra and RID of only som of h G counris ar saionary. In conras, whn w us mor powrful KPSS and DF-GLS ss, w find ha h ral inrs ra and RID of mos of h G counris ar saionary. Our rsul suppors ha ral inrs ras ar man rvring and h ral inrs pariy (RIP) hypohsis holds in h majoriy of h chosn counris. For fuur rsarch, a possibl vnu is o us h varianc raio s on h ral inrs ra and RID. In addiion, a smingly unrlad rgrssion (SUR) can b usd o sima h sysm of h quaions, as Wu and Zhang (99) argu ha h SUR is mor fficin han h singl quaion

13 Inrnaional Rsarch Journal of Financ and Economics - Issu () 79 simaion bcaus h SUR fully xplois h informaion in cross-counry corrlaions and h SUR aks advanag of cross-quaion paramr rsricion. Acknowldgmns Qi Shi would lik o hank Gorg Tawadros for many hlpful commns on h arly vrsion of his papr. Bin Li is graful for financial suppor from Griffih Univrsiy undr h Griffih Univrsiy Nw Rsarchr Gran, Projc Numbr: 73. Rfrncs [] Box, G.E.P. and D.A. Pirc, 97, Disribuion of rsidual auocorrlaion in auorgrssiv ingrad moving avrag im sris modls, Journal of h Amrican Saisical Associaion, 5, pp [] Chn, M.Y.,, Tsing saionariy agains uni roos and srucural changs, Applid Economics Lrs 9, pp [3] Chung, S.Y. and W.J. Crowdr,, Why ar ral inrs ras no qualizd inrnaionally, Souhrn Economic Journal, 7, pp. -5. [] Cumby R.E. and M. Obsfld, 9, Inrnaional inrs-ra and pric-lvl linkags undr flxibl xchang ras: A rviw of rcn vidnc, in FO Bilson, R Marson (Eds.), Exchang Ra: Thory and Pracic, NBER books, Naional Burau of Economic Rsarch, Inc. [5] Cumby, R.E. and F.S. Mishkin, 9, Th inrnaional linkag of ral inrs ras: Th Europan-US conncion, Journal of Inrnaional Mony and Financ, 5, pp [] Dicky, D.A., and W.A. Fullr, 979, Disribuion of h simaors for auorgrssiv im sris wih a uni roo, Journal of h Amrican Saisical Associaion, 7, pp [7] DJong, D.N, J.C Nankrvis and N.E Savin, 99, Th powr problms of uni roo ss in im sris wih auorgrssiv rrors, Working Papr, Univrsiy of Iowa. [] Ellio G., T.J. Rohnbrg and J.H. Sock, 99, Efficin ss for an auorgrssiv uni roo, Economrica,, pp [9] Franss, P.H., and N. Haldrup, 99, Th ffcs of addiiv oulirs on ss for uni roos and coingraion, Journal of Businss and Economic Saisic,, pp [] Goodwin, B.K. and T.J. Grnns, 99, Ral inrs ra qualizaion and h ingraion of inrnaional financial marks, Journal of Inrnaional Mony and Financ, 3, pp. 7-. [] Kinal, T., and K. Lahiri, 9, A modl for x an ral inrs ras and drivd inflaion forcass, Journal of h Amrican Saisical Associaion, 3, pp [] Kwiakowski, D., P.C.B. Phillips and P. Schmid, 99, Tsing h null hypohsis of saionariy agains h alrnaiv of a uni roo, Journal of Economrics, 5, pp [3] Ljung, G.M. and G.E.P Box, 97, On a masur of lack of fi in im sris modls, Biomrika, 5, pp [] Mishkin, F.S., 9, Th ral inrs ra: A muli-counry mpirical sudy, Canadian Journal of Economics, 7, pp [5] Moosa, I.A. and R.H. Bhai, 99, Som vidnc on man rvrsion in x an ral inrs ra, Scoish Journal of Poliical Economy, 3, pp [] Moosa, I.A. and R.H. Bhai, 997, Ar Asian marks ingrad? Evidnc for six counris vis-à-vis Japan, Inrnaional Economic Journal,, pp [7] Ng, S. and P. Prron, 995, Uni roo ss in ARMA modls wih daa-dpndn mhods for h slcion of h runcaion lag, Journal of h Amrican Saisical Associaion, 9, pp. -.

14 Inrnaional Rsarch Journal of Financ and Economics - Issu () [] Ng, S. and P. Prron,, Lag lngh slcion and h consrucion of uni roo ss wih good siz and powr, Economrica 9, pp [9] Prron, P., 99, Th Gra Crash, h oil pric shock and h uni roo hypohsis, Economrica 57, pp. 3-. [] Phillips, P.C.B. and S. Ouliaris, 99, Asympoic propris of rsidual basd ss for coingraion, Economrica, 5, pp [] Phillips, P.C.B. and P. Prron, 9, Tsing for a uni roo in im sris rgrssion, Biomrika, 75, pp [] Sims, C.A., 9, Baysian skpicism on uni roo conomrics, Journal of Dynamics and Conrol,, pp [3] Wu, Y. and H. Zhang, 99, Man rvrsion in inrs ras: Nw vidnc from a panl of OECD counris, Journal of Mony, Crdi and Banking,, pp. -.