Purchasing Power Parity and Real Exchange Rate in Japan

Transcription

1 MPRA Munich Personal RePEc Archive Purchasing Power Pariy and Real Exchange Rae in Japan Long, Dara Ocober 008 Online a hp://mpra.ub.uni-muenchen.de/11173/ MPRA Paper No , posed 17. Ocober 008 / 3:05

2 Purchasing Power Pariy and Real Exchange Rae in Japan * Dara LONG Ocober 008 Absrac This paper examines he validiy of boh he shor-run and long-run purchasing power pariy (PPP) hypoheses in Japan using wo esimaion mehods, namely, a uni roo es and an Auoregressive Disribued Lag (ARDL) coinegraion es. Some imporan findings are obained from our analysis. The firs es reveals he mean reversion of real exchange rae (RER) in he long-run. On he oher hand, from he second es, we found ha here is a srongly robus long-run PPP relaionship bu no significan shor-run PPP relaionship. Furhermore, unlike he previous lieraure, his paper confirms he sabiliy of he esimaed resuls by CUSUM and CUSUMQ ess. Overall, he resuls sugges ha PPP hypohesis in Japan srongly holds for he long-run while no for he shor-run. JEL classificaion: C, F31, F41 Keywords: PPP, Real Exchange Rae, Uni Roo, ARDL o coinegraion * I would like o hank Professor Akira Kohsaka of Osaka School of Inernaional Public Policy, Osaka Universiy for his valuable commens, encouragemens, and guidance. Sovannroeun Samreh, Research Fellow of Insiue of Social and Economics Research, Osaka Universiy is also graeful for various consrucive discussions. The auhor also acknowledges he full financial suppor from he Minisry of Educaion, Culure, Spors, Science and Technology (MEXT), Japan hrough Japanese Governmen Scholarship program. Needless o say, any remaining errors are mine. Graduae School of Economics, Osaka Universiy. Address: 1-7, Machikaneyama, Toyonaka, Osaka , Japan. longdara@gmail.com 1

3 1. Inroducion Purchasing Power Pariy (PPP) hypohesis is a fundamenal assumpion for many open macroeconomic models. PPP hypohesis posulaes a proporional relaionship beween a nominal exchange rae and relaive price levels; his also implies he consancy of real exchange rae (RER) over ime. The inuiion is sraighforward. If he long-run PPP relaionship exiss, any shor-run deviaions, such as depreciaion of a currency, will ransmi o he change of inflaion or capial movemen. This adjuss and equilibraes he rade flows; as a resul, i ends o reurn he exchange rae level. Beyond being he fundamenal elemen for many exchange rae models, PPP heory also provides some implicaions such as serve as a predicion model for exchange raes as well as a benchmark for judging he movemens of exchange raes since i relaes o undervaluaion or overvaluaion of a counry s currency and enables inernaional comparison of various naional income levels. As shown above, wih a lo of implicaions of PPP hypohesis, is validiy has been a subjec of ineres for many researchers. 1 Besides simple regression, wo major mehodologies have been used o examine he validiy of PPP hypohesis, namely, he augmened Dickey Fuller (ADF) uni roo es and he Johansen-Juselius coinegraion echnique. The ADF uni roo es enables us o examine he saionariy of RER, or alernaively, a mean revering process of RER. On he oher hand, he Johansen-Juselius coinegraion allows us o es he long-run relaionships among variables in absolue PPP model. Among he previous sudies of he mean revering process, Adler and Lehmann (1983) esed he null hypohesis ha RER follows a random walk, or he archeypal non-mean revering ime series process; hey could no

4 rejec he random walk model. Fraser e al. (1991) esed he uni roos in several secoral RERs using disaggregaed daa. Besides hese, Papell (1997), O`Connell (1998), Papell and Theodoridis (1998), and Coakley e al. (005) are empirical sudies using panel uni roo es. However, from hese researches, i is shown ha only a few sudies could be able o rejec he null hypohesis of uni roo in RER. As for he coinegraion echnique as a more generalized approach for esing he long-run validiy of PPP hypohesis, earlier sudies include Taylor (1988), Enders (1988), Mark (1990), Layon and Sark (1990), Baharumshah and Ariff (1997), and Taylor and Sarno (1998). These sudies migh suffer from a number of deficiencies. Based on he convenional Johansen-Juselius coinegraion echnique, he power of he es migh no be srong enough o mee he assumpion ha all variables be I(1). To solve his problem, his paper employs he Auoregressive Disribued Lag (ARDL) approach o coinegraion, a relaively recen economeric echnique developed by Pesaran e al. (1996, 001) o esimae he shor-run and long-run sable relaionship among variables. This approach ess he coinegraion relaionship wihou requiring he same order of inegraion of all variables. Hence, i can be viewed as more discerning in is abiliy o rejec a false null hypohesis. Regarding coinegraion and sabiliy issues, we refer o Bahmani-Oskooee and Chomsisengphe (00) which examined he money demand funcion in indusrial counries. Though hey found ha here is evidence of coinegraion relaionships in hose seleced counries, when incorporaing he CUSUM (Cumulaive Sum of Recursive Residuals) and CUSUMQ (Cumulaive Sum of Square of Recursive Residuals) sabiliy ess ino coinegraion procedure, some signs of insabiliy are 3

5 found in he cases of Swizerland and he UK. 3 This means ha coinegraion relaionship does no imply he sabiliy of he esimaed model; appropriae sabiliy ess need o be conduced addiionally afer coinegraion is esablished. Considering his, unlike he previous sudies, in his paper he sabiliy ess, namely CUSUM and CUSUMQ are also implemened in order o invesigae he sabiliy of he esimaed regression. This paper aims o conribue o he lieraure by presening an empirical invesigaion of wheher or no he shor-run and long-run PPP hypohesis holds for he case of Japan. Two esimaion mehods, namely, he ADF uni roo es and he ARDL coinegraion es are employed. Exising empirical researches of coinegraion of PPP are mainly based on radiional economeric echniques (Johansen coinegraion) wihou examining he sabiliy siuaion of he esimaed regression. In his paper, we adop a sae-of-he-ar economeric mehod namely ARDL o coinegraion and o confirm he sabiliy of he esimaion resuls, he sabiliy ess namely CUSUM and CUSUMQ are conduced. Moreover, aking srucural breaks ino consideraion, we use he quarerly daa saring from 1970, he saring poin a which mos of he leading economies moved from fixed exchange rae o he floaing exchange rae sysem, so-called he saring poin of falling of he Breon woods sysem. To deal wih he srucural breaks menioned in some lieraure, in addiion o he full sample (1970Q1-006Q4) esimaion, by using he same echniques we analyze he subperiod spanning for 15 years from 1970Q1-1984Q4 o 199Q1-006Q4 by rolling hem yearly, all sum up o be 3 subperiods. These subperiod esimaions help examine he robusness of PPP hypohesis. 4

6 The ouline of he remainder of his paper is as follows. In secion, he heoreical frameworks and he mehodology processes of he models are menioned, while he explanaions of daa and empirical resuls are provided in secion 3. Secion 4 provides he robusness of esimaion resuls as well as he resuls of subsample analysis. Finally, some conclusions are drawn in secion 5.. Theoreical Framework.1. Absolue PPP Theory Absolue PPP saes ha given he same currency, a baske of goods will cos he same in any counry. 4 This can be hough as a generalizaion of he law of one price (LOP), which suggess ha once convered o a common currency, he same good should cos he same price in differen counries. The LOP and absolue PPP can be expressed respecively as below: P P i = P S, (1) * i * i = P S, () where P i and P i * are he domesic and foreign prices for good i respecively and S i is he nominal exchange rae, or he domesic price of a uni of foreign currency. Similarly, P and P * are he prices of he idenical baske of goods in he domesic and foreign counries respecively and S again is he nominal exchange rae a ime. Absolue PPP implies ha he nominal exchange rae equals o he raio of he wo relevan prices, as shown below. 5

7 P S = (3) P * Expressing equaion (3) in erm of he logarihm as lower-case leers, i akes he following form. s = p p (4) * Thus, by conducing he regression on equaion (4), we are able o examine he shor-run and long-run relaionships of PPP hypohesis... Mean Revering Process Theory According o is definiion, real exchange rae (RER) can be wrien as: Z S P *, (5) P where Z is he real exchange rae; S is he nominal exchange rae (S yen per US dollar), P and P* are consumer price index (CPI) of Japan and he Unied Saes respecively. Expressing equaion (5) in erm of he logarihm, we obain: z s p + p, (6) * where he lower-case leers denoe he logarihm of each variable in equaion (5) respecively. Based on PPP hypohesis, he logarihm of RER should be idenically equal o zero. I is worh noing ha he movemens in RER are anamoun o he deviaions in PPP condiion. Hence, a necessary condiion for he long-run PPP o hold is ha RER be 6

8 mean revering. Generally, such invesigaion has esed he null hypohesis of non-mean reversion agains he alernaive of mean reversion. The exisence of he uni roo of RER implies ha RER is non-saionary; as a resul, here is no evidence ha RER will reurn back o is mean value suggesing ha PPP hypohesis does no hold. 3. Empirical Analysis 3.1. Daa The daa used for he analysis in his paper are obained from Inernaional Financial Saisics (IFS) CD-ROM (007) released by Inernaional Moneary Fund (IMF). We use quarerly daa ha span from 1970Q1 o 006Q3 as 1970 is he saring poin of shifing o he flexible exchange rae regime for mos counries in he world. Exchange raes are period-average and period-end value of Japanese currency (Yen) per uni of he US dollar as shown respecively in line RF.ZF and AE.ZF of he IFS daabase. For domesic and foreign (he Unied Saes) price variables, Consumer Price Index (CPI) as shown in line 64ZF are used for esimaion. Regarding RER variable, i is calculaed according o he definiion in equaion (6). I is confirmed from he augmened Dickey Fuller (ADF) uni roo ess ha he domesic (Japan) CPI daa is I(0) while he foreign (he US) CPI daa is I(1). 5 These resuls, he inconsisen inegraion order of he variables in he sysem, sugges he inappropriaeness of using Johansen-Jesulius coinegraion mehod o conduc he analysis. 7

9 3.. Esimaion Model and Mehodology Mean Revering Process Esimaion A popular esimaion mehod used o es he mean revering process of RER is he augmened Dickey Fuller (ADF) uni roo es. Since his approach is widely known for economiss we presen is basic idea in he Appendix Absolue PPP Coinegraion Esimaion The esimaion form of he equaion (4) may be wrien as below: s = c + β ( p p ) + ε * (7) where c is consan erm and ε is a disurbance erm. Theoreically, i is expeced ha β = 1. Absolue PPP model can be represened in he form of he unresriced error correcion model as below: Δs n n * * γ iδs i + δ iδ( p i p i ) + λ1s 1 + λ ( p 1 p ) 1 i= 1 i= 1 = α + + ε (8) Before esing he model, we presen a brief explanaion of he ARDL approach o coinegraion. As menioned in Pesaran and Pesaran (1997), here are wo seps for implemening he ARDL approach o coinegraion procedure. Firs, we es he exisence of he long-run relaionship beween he variables in he sysem. In paricular, he null hypohesis H λ = λ 0 of having no coinegraion or no long-run 0 : 1 = relaionship among variables in he sysem is esed agains he alernaive hypohesis 8

10 H λ λ 0 by judging from he F-saisics. Since he disribuion of his 1 : 1 F-saisics is non-sandard irrespecive of wheher he variables in he sysem are I(0) or I(1), we use he criical values of he F-saisics provided in Pesaran and Pesaran (1997) and Pesaran e al. (001). In here, here are wo ses of criical values, when all variables are I(0) or I(1). For each applicaion, he wo ses provide he bands covering all he possible classificaions of he variables ino I(0) or I(1), or even fracionally inegraed ones. If he compued F-saisics is higher han he appropriae upper bound of he criical value, he null hypohesis of no coinegraion relaionship is rejeced; if i is below he appropriae lower bound, he null hypohesis canno be rejeced, and if i lies wihin he lower and upper bounds, he resul is inconclusive. Secondly, afer he exisence of he coinegraion relaionship beween variables is confirmed, he lag lenghs of variables are chosen; in his paper, we choose by using Akaike Informaion Crierion (AIC). Afer he lag lengh is seleced, he shor-run, he error correcion, and he long-run model are esimaed. Then, he sabiliy ess, namely, CUSUM and CUSUMQ ess are conduced Esimaion Resuls Resuls of Uni Roo Tes for RER In implemening he ADF uni roo es, hree seps are required. Firs sep is o judge wheher he sample has a rend or no, while he second sep is o selec an opimal lag lengh. The final sep is o conduc a uni roo es of RER. Following he esimaion procedure of he mean revering of RER, es resuls of he null hypohesis H : ρ 0 (having uni roo in he process of RER) are shown in Table. 0 = 9

11 Table provides he resuls of he ADF uni roo ess of boh period-average and period-end values of RER when including an inercep bu no a rend. For judging wheher RER have a rend or no, Figure 1 ells us ha, in he whole sample, here are wo rends for RER, down from 1970 o 1995 and up from 1995 o 006. From his, we judge ha here is no single rend over he whole sample. Wihin he maximum lag lengh of 4, four lag selecion crieria, namely, Maximized Log-Likelihood (LL), Akaike Informaion Crierion (AIC), Schwarz Bayesian Crierion (SBC), and Hannan-Quinn Crierion (HQC), are used. From Table 1 a lag lengh of 4 is seleced o be opimal for boh period-end and period-average values wih he es saisics value of and , respecively. These resuls are summarized in Table. I is clear ha boh cases of he period-average and period-end exchange raes are significan a 5% implying ha he long-run PPP hypohesis holds for he case of Japan Resuls of ARDL coinegraion es for PPP Following he process explained in secion 3.., in he firs sep, we es wheher here is a long-run relaionship among variables in he sysem. 6 Table 3 provides he resuls of F-saisics when he maximum lag lenghs are se from (6 monhs) o 4 (4 years). I is clear from he resuls ha even hough all of he cases could no be rejeced, lag lengh up o 4 has he bes power among all of rejecing he null hypohesis of no coinegraion relaionship among variables. As also menioned in Bahmani-Oskooee and Nasir (004), he resuls of F-saisics are jus he preliminary ones while hose of he second sep are more efficien and considerable in ARDL approach o coinegraion, he insignificance of F-saisics a his sep should no be a major concern. 10

12 In he second sep, we esimae he equaion (7) and selec he lag lenghs of he variables in he sysem based on Akaike Informaion Crierion (AIC). Based on he F-saisics resuls, he maximum lag lengh is se up o 4. Table 4 provides he resuls of he lag lengh selecion of he variables, which is ARDL(4,0) and of he diagnosic ess of he shor-run model. 7 They show ha, only he lagged exchange rae variables are saisically significan a 1% and he relaive price coefficien is no saisically significan, suggesing ha, in he shor-run, PPP hypohesis does no hold. From he resul of he adjused coefficien of deerminaion ( R = ), i is clear ha he overall goodness of fis of he esimaed equaions is very high. Moreover, he diagnosic es resuls indicae ha he shor-run model passes all of he ess for serial correlaion, funcional form, and heeroscedasiciy. Therefore, we argue ha he esimaed shor-run model performs well. Table 5 provides he ARDL es resuls of an error correcion model. The resuls indicae ha a coefficien of he error correcion erm, EC -1 has an appropriae sign (negaive) and is saisically significan a 10% level. In paricular, he esimaed coefficien of EC -1 is , implying ha he speed of adjusmen o he long-run equilibrium is 3.56%. Specifically, he esimaion resul of he error correcion erm akes he following form. * EC = e ( p p ) c To es he sabiliy of he model, we employ he ess of CUSUM and CUSUMQ. Figure 4 and 5 provide he oucomes of CUSUM and CUSUMQ ess respecively. Since he plos of boh CUSUM and CUSUMQ are wihin 5% of criical bands, his 11

13 suggess he sabiliy of he esimaed model. Table 6 demonsraes he resul of he long-run relaionship of he variables in he model. I shows ha given maximum lag lenghs of higher han 4, he coefficiens ( p *) are srongly saisically significan a 1% and have an expeced sign p (posiive value close o 1). These indicae ha PPP hypohesis holds in he long-run in Japan. Specifically, he esimaed resul of he long-run model is shown as below: e = ( p p * ) ( value) (9.4) (5) In order o check he robusness of he resuls, we also esimae he long-run relaionship of PPP hypohesis by seing he maximum lag lengh from o 4 (Table 6). I is eviden ha for all he maximum lag lenghs, he coefficiens of he relaive price and error correcion erm are saisically significan wih he expeced signs. In paricular, he relaive prices are significanly posiive wih he esimaion value close o 1 and he error correcion erms are significanly negaive wih he speed of adjusmen wihin 3.5% and 4.5%. Furhermore, i is worh noing ha when allowing he maximum lag lengh o be long enough (a leas 1 year) he degree of significance could be improved for boh he relaive prices and he error correcion erms. 4. Robusness and Subsample As menioned in mos of he lieraure, a srucural break is a concern for esimaing and esing he validiy of PPP hypohesis. Hence, o confirm he robusness of he esimaion and ake a srucural break ino consideraion we divide he full sample 1

14 ino subsamples by using rolling esimaes over he 15-year subsample periods; all sum up o be 3 subsamples Subsamples of Uni Roo Tes for RER As menioned in esimaion resuls of he ADF uni roo for he full sample, he firs sep of his es is o judge wheher he esimaion samples have a rend or no. Figure shows he plo of RER of each of he subsamples wih he judgmen of having a rend or no rend in he parenhesis nex o heir sample periods. Subsequenly, he opimal lag lengh could be chosen by exacly he same way as in he whole sample period described in subsecion Afer hese wo processes are done, we are ready for implemening he ADF uni roo es. Following he same procedure for all he 3 subperiods, we summarized he ADF uni roo es resuls by ploing is p-value of rejecing he null hypohesis (RER is non-mean reversion) ino he Figure 3. The resuls of he p-value of rejecing he null hypohesis sugges ha hough some subperiods are srongly significan in rejecing null hypohesis, specifically subperiod 11, 15, 16,, and 3, when allowing only 15 years as he esimaion sample, he power of rejecing he null hypohesis seems o be weak in mos of he subperiods. From he changing endency, we should noe ha he likelihood of rejecion seems o be sronger for he recen subsamples. 4.. Subsamples of ARDL coinegraion es for PPP For subsample periods, since he mos imporan resuls for judging he long-run PPP relaionship are hose of he second sep, in paricular, he long-run parameers and 13

15 he error correcion erm coefficien, we provide only hese resuls of each subperiod and lised hem in Table 7. I is obvious ha only very few subsamples have boh saisically significan coefficiens of error correcion erms and relaive prices. For insance, in subperiod 9, 10, 1, and 16, he coefficiens of relaive prices are posiively significan and of he error correcion erms are negaively significan; hese imply he long-run relaionship of PPP hypohesis in Japan. However, his evidence seem o be weak since i is shown ha hough he relaive prices are saisically significan, hey are much bigger han he expeced value (posiive close o 1), for insance, in subperiod 10, he relaive price become Furhermore, for oher cases, boh he coefficiens of relaive prices and error correcion erms are no saisically significan simulaneously. I is found ha he coefficiens of error correcion erms end o be more significan in he recen sample, while of he relaive prices are no significan, on he oher hand. These resuls are congruen wih he resuls of mean revering process, implying ha shor span (15 years) of sample has weak es power o rejec he null hypohesis. This evidence is consisen wih he resuls of Mone Carlo experimens of Lahian and Taylor (1997) and Sarno and Taylor (00) which showed ha shor span daa has a very low power o rejec he null hypohesis. 5. Conclusions This paper invesigaes he validiy of boh he shor-run and long-run purchasing power pariy (PPP) hypoheses in Japan using wo esimaion mehods, namely, he augmened Dickey-Fuller (ADF) uni roo es for real exchange rae (RER) and he Auoregressive Disribued Lag (ARDL) coinegraion es for PPP. This laer 14

16 sae-of-he-ar mehod has he advanage over he convenional Johansen-Jesulius coinegraion mehod because i does no require ha all he variables in he sysem have he same order of inegraion, specifically I(1). Some imporan findings are obained from our analysis. By using he ADF uni roo es, we are able o find he evidence supporing he mean reversion of RER for he long-run. Moreover, from he resul of he ARDL coinegraion es, we found ha here is a srongly robus long-run PPP relaionship while he shor-run relaionship is no found o be saisically significan. The significance of he esimaed coefficiens for he long-run PPP hypohesis and he error correcion erm (ECT) wih he righ expeced sign, posiive close o 1 and negaive less han 1 respecively sugges ha here is a coinegraion relaionship among variables in he sysem. These resuls are also suppored by robusness check via seing various maximum lags ( o 4) for esimaion. Furhermore, from he resuls of he sabiliy es confirmed by CUSUM and CUSUMQ ha have no been conduced in mos of he previous sudies, i is found ha hey are sable wihin 5% significan level. Therefore, overall, he resuls seem o sugges ha here exiss a significan boh saisically as well as economically, sable long-run relaionship of PPP hypohesis for he case in Japan while he evidence for he shor-run could no be found. Besides, when dividing he full sample ino subsamples only very weak evidence is found in boh mehodologies. From he ADF uni roo es, only few resuls sugges he rejecion of he null hypohesis of he mean reversion of RER and similarly from ARDL o coinegraion resuls we could no find srong evidences of he long-run relaionship among variables of PPP hypohesis. Therefore hese resuls indicae ha he 15

17 es power of shor span (15 years) of sample is no srong enough o rejec he null hypohesis or, alernaively saying, i has weak evidence ha PPP hypohesis holds. This evidence suppors he resuls of Mone Carlo experimens of Lahian and Taylor (1997) and Sarno and Taylor (00) which showed ha shor span daa has a very low es power o rejec he null hypohesis. These resuls seem o sugges ha for esing PPP hypohesis ample long span daa should be used. 16

18 Foonoe 1 Taylor (003), Taylor (006), and Taylor and Taylor (004) are he bes lieraure surveys of he PPP hypohesis and he exchange rae. In paricular, his allows us wheher or no RER is consan around is mean value in he long-run. 3 CUSUM and CUSUMQ sabiliy ess are originally developed by Brown e al. (1975). 4 Anoher version of he PPP heory is he relaive PPP saying ha he rae of growh in he exchange rae offses he differenial beween he rae of growh in home and foreign price indices. 5 The resuls of he uni roo es could be provided upon reques. 6 The esimaion resuls are compued by using he Microfi 4.1 (Oxford Universiy Press). 7 Wih he seleced maximum lag lengh he esimaion sample is adjused o be 1971Q o 006Q4. 17

19 Appendix: Mean Revering Process Suppose ha he RER does rever o a consan long run mean. Then under weak addiional assumpions and according o Wold s heorem, he RER should have he following p-h order auoregressive form: where p 0 + βi i + ε i= 1 z = β z (1) ε is a whie-noise disurbance. Suppose ha RER can be isolaed from all shocks, specifically ε = 0 for all. If he RER is mean revering, hen i mus in he absence of shocks and given enough ime sele down o is long run equilibrium level, z*. Seing he ε = 0 and puing all he values of he RER equal o he long run equilibrium level z* in equaion (1), we can solve he for z* as: z β 0. () 1 β * = p i= 1 p If = βi = 1, hen z* is undefined; he process of z is hough o have uni roo i 1 implying ha any shocks impared o he RER will be permanen. In oher word, i will no p behave in a mean revering fashion and is long run equilibrium does no exis. = βi < 1, herefore, is a necessary condiion for he exisence of long run equilibrium. I is worhy i i 1 noed ha he RER. p = βi > 1 i 1 is no an alernaive because his would imply explosive behavior of Equaion (1) can be expressed as: Δz p θiδz i + i= 1 = β + ρz ε (3) 0 where ε is again a whie-noise disurbance and Δz = z z 1. Tesing he null hypohesis H : ρ 0 of equaion (3) is equivalen o esing he null hypohesis of he exisence of uni 0 = roo in he process of z (no mean revering). Therefore, rejecion of he null hypohesis H : ρ 0 implies ha he RER is mean revering. 0 = 18

20 Reference [1] Adler, M. and B. Lehmann, 1983, Deviaions from Purchasing Power Pariy in he long run. Journal of Finance, 38, [] Bahmani-Oskooee, M. and A. B. M. Nasir, 004, ARDL Approach o Tes he Produciviy Bias Hypohesis. Review of Developmen Economics, 8(3), [3] Bahmani-Oskooee, M. and S. Chomsisengphe, 00, Sabiliy of M Money Demand Funcion in Indusrial Counries. Applied Economics, 34, [4] Baharumshah, A. Z. and M. Ariff, 1997, Purchasing Power Pariy in Souh Eas Asia Economies: A Coinegraion Approach, Asian Economic Journal, 11(), [5] Brown, R. L., Durbin, J., and J. M. Evans, 1975, Techniques for Tesing he Consancy of Regression Relaionships over Time. Journal of he Royal Saisical Sociey, Series B (Mehodological), 37, [6] Coakley, J., Flood, R., Fueres, A., M., and M. P. Taylor, 005, Long-run Purchasing Power Pariy and he heory of general relaiviy: he firs ess. Journal of Inernaional Money and Finance, 4, [7] Choudhry, T., 005, Asian Currency crisis and he generalized PPP: evidence from he far eas, Asian Economic Journal, 1, [8] Enders, W., 1988, ARIMA and coinegraion ess of PPP under fixed and flexible exchange rae regimes. Reviews of Economics and Saisics, 70, [9] Fraser, P., Webser, A. and M. P. Taylor, 1991, An empirical Examinaion of long-run Purchasing Power Pariy as a heory of inernaional commodiy arbirage. Applied Economics, 3, [10] Inernaional Financial Saisics CD-ROM, 007, Inernaional Moneary Fund. [11] Lahian, J. R. and M. P. Taylor, 1997, Real Exchange Rae Behavior: he Recen Floa from he Perspecive of he Pas Two Cenuries. Journal of Poliical Economy, 104,

21 [1] Layon, A. P. and J. P. Sark, 1990, Coinegraion as an empirical es of Purchasing Power Pariy. Journal of Macroeconomics, 1, [13] Lopes, C., Murray, C. J., and Papell, D.H., 005, Sae of he ar uni roo ess and purchasing power pariy. Journal of Money, Credi and Banking, 37, [14] Mark, N., 1990, Real and nominal exchange raes in he long run: an empirical invesigaion. Journal of Inernaional Economics, 8, [15] O`Connell, P. G. J., 1998, The overvaluaion of Purchasing Power Pariy. Journal of Inernaional Economics, 44, [16] Papell, D. H., 1997, Searching for saionary: Purchasing Power Pariy under he curren floa. Journal of Inernaional Economics, 43, [17] Papell, D. H. and H. Theodoridis, 1998, Increasing evidence of Purchasing Power Pariy over he curren floa. Journal of Inernaional Money and Finance, 17, [18] Pesaran, M. H. and B. Pesaran, 1997, Microfi 4.1 (Window Version). Oxford Universiy Press. [19] Pesaran, M. H., Shin, Y., and R. J. Smih, 1996, Bounds Tesing Approaches o he Analysis of Level Relaionships. DEA working paper 96, Deparmen of Applied Economics, Universiy of Cambridge. [0] Pesaran, M. H., Shin, Y. and R. J. Smih, 001, Bounds Tesing Approaches o he Analysis of Level Relaionships. Journal of Applied Economerics, 16, [1] Sarno, L. and M. P. Taylor, 00, Purchasing Power Pariy and he Real Exchange Rae. Inernaional Moneary Fund Saff Paper, 49, [] Taylor, A. M. and M. P. Taylor, 004, The Purchasing Power Pariy Debae. Journal of Economic Perspecives, 18(4), [3] Taylor, M. P., 1988, An empirical examinaion of long run Purchasing Power Pariy using coinegraion echniques. Applied Economics, 0, [4] Taylor, M. P., 003, Purchasing Power Pariy. Review of Inernaional Economics, 11(3), 0

22 [5] Taylor, M. P., 006, Real Exchange Rae and Purchasing Power Pariy: mean-reversion in economic hough. Applied Financial Economics, 16, pp [6] Taylor, M. P. and Sarno, L., 1998, The behavior of real exchange raes during he pos-breon Woods period. Journal of Inernaional Economics, 46,

23 Tables and Figures Table 1: The Augmened Dickey Fuller Uni Roo Tes of RER (no rend) End Value Tes Saisics LL AIC SBC HQC DF a a ADF(1) ADF() ADF(3) ADF(4) b a a Average Value Tes Saisics LL AIC SBC HQC DF ADF(1) a ADF() ADF(3) a a ADF(4) b 3597 a Noe: 1. a and b denoe respecively he maximum value among various lags of a crierion (herefore he number of lag order suggesed for selecion by ha crierion) and he final es saisics seleced afer all.. LL, AIC, SBC, and HQC denoe respecively maximized Log-Likelihood, Akaike Informaion Crierion, Schwarz Bayesian Crierion, and Hannan-Quinn Crierion. Table : ADF Uni Roo Resul of RER include an inercep bu no a rend 143 observaions from 1971Q o 006Q4 RER Average Period Value End Period Value T-saisics *** -.958*** Noe: 1. *, **, ***, and **** are respecively significan of 15%, 10%, 5%, and 1%.. Criical Value for he ADF saisic are , , and for 10%, 5%, and 1% respecively.

24 Table 3: F-saisics of Bound Tess, 10%CV[3.18, 4.16], 5%CV[3.793, 4.855] Lag Order F-saisics Noe: 1. *, **, ***, and **** are respecively significan of 15%, 10%, 5%, and 1%.. The numbers in brackes are criical values. Table 4: Auoregressive Disribued Lag Esimaion Resul (Dependen Variable: Exchange Rae, ) e Variables ARDL(4,0) seleced based on AIC e (0.0831)**** e (0.1346)**** e (0.1348)**** e (0.0835) *** ( p p *) (0.0357) c (0.096)** R DW-saisics.0004 SE of Regression Serial Correlaion F(4, 16)= [0.978] Diagnosic ess Funcional Form F(1, 19)=.1183[0.148] Heeroscedasiciy F(1, 134)= [0.508] Noe: 1. *, **, ***, and **** are respecively significan of 15%, 10%, 5%, and 1%.. The numbers in parenheses are sandard errors. 3. The numbers in bracke are p-value of he ess. 4. AIC denoes Akaike Informaion Crieria. 3

25 Table 5: The Error Correcion Represenaion for he seleced ARDL model (Dependen Variable: Difference of Exchange Rae, Δ e ) Regressor ARDL(4,0) seleced based on AIC Δe (0.0830)**** Δe (0.0859)*** Δe (0.0835)*** Δ( p p *) (0.0357) Δ c (0.96)** EC (0.0194)** R * EC = e ( p p ) c Noe: 1. *, **, ***, and **** are respecively significan of 15%, 10%, 5%, and 1%.. The numbers in parenheses are sandard errors. 3. AIC denoes Akaike Informaion Crieria. Table 6: Long Run Esimaion Resul of Full Sample (1970Q1-006Q4) (Dependen Variable: Exchange Rae, ) e Maximum Lag Order Expeced Value of coefficien Relaive Price ( p p *) ARDL based on AIC Error Correcion Term (0.7854) ARDL(,0) (0.018)* (0.716) ARDL(,0) (0.0188)* (0.5673)** ARDL(4,0) (0.0194)** (0.548)*** ARDL(4,0) (0.0199)** (0.4845)*** ARDL(4,0) (0.006)*** (0.4795)*** ARDL(4,0) (0.006)*** (0.5097)*** ARDL(4,0) (0.00)** (0.4457)**** ARDL(4,0) (0.046)** (0.4550)*** ARDL(4,0) (0.060)** (0.493)*** ARDL(4,1) (0.057)** (0.497)*** ARDL(4,1) (0.06)** Noe: 1. *, **, ***, and **** are respecively significan of 15%, 10%, 5%, and 1%.. The numbers in parenheses are sandard errors. 3. AIC denoes Akaike Informaion Crieria. 4

26 Table 7: Long Run Esimaion Resul of Rolling Sample of 15 years (Dependen Variable: Exchange Rae, ; Lag order: 4) e Sub-Period Expeced Value of coefficien Relaive Price ( p p *) ARDL based on AIC Error Correcion Term (1) 1970Q1-1984Q (0.4809) ARDL(,3) (0.0479)**** () 1971Q1-1985Q (0.83) ARDL(,0) (0.0375)*** (3) 197Q1-1986Q (0.7738) ARDL(,0) (0.048)** (4) 1973Q1-1987Q (1.561) ARDL(,0) (0.045) (5) 1974Q1-1988Q4 1.6 (.6) ARDL(,0) (0.046) (6) 1975Q1-1989Q (0.9931) ARDL(,0) (0.0389) (7) 1976Q1-1990Q (0.8879)* ARDL(,0) (0.0407) (8) 1977Q1-1991Q (1.6797) ARDL(,1) (0.047) (9) 1978Q1-199Q (0.977)* ARDL(,0) (0.0406)* (10) 1979Q1-1993Q (0.7749)**** ARDL(,0) (0.0403)*** (11) 1980Q1-1994Q (0.9491)**** ARDL(,0) (0.0495) (1) 1981Q1-1995Q (0.437)**** ARDL(4,0) (0.0663)** (13) 198Q1-1996Q (0.6578)**** ARDL(4,5) (0.0969) (14) 1983Q1-1997Q (618) ARDL(4,0) (0.0704) (15) 1984Q1-1998Q (1.776) ARDL(,0) (0.050) (16) 1985Q1-1999Q (0.7994)** ARDL(4,0) (0.0506)*** (17) 1986Q1-000Q (0.6687) ARDL(4,1) (0.0555) (18) 1987Q1-001Q (0.765) ARDL(4,1) (0.0613)** (19) 1988Q1-00Q (0.6955) ARDL(4,1) (0.0597)** (0) 1989Q1-003Q (0.5883) ARDL(4,1) (0.5811)*** (1) 1990Q1-004Q (0.4669) ARDL(4,0) (0.0565)*** () 1991Q1-005Q (0.4403) ARDL(4,0) (0.0601)*** (3) 199Q1-006Q (0.881) ARDL(4,0) (0.0644)**** Noe: 1. *, **, ***, and **** are respecively significan of 15%, 10%, 5%, and 1%.. The numbers in parenheses are sandard errors. 3. AIC denoes Akaike Informaion Crieria. 5

27 Figure 1: The Real Exchange Rae Movemen for Whole Period (No Trend) End Period Logarihm Value Average Period Logarihm Value Q1 1973Q3 1977Q1 1980Q3 1984Q1 1987Q3 1991Q1 1994Q3 1998Q1 001Q3 005Q1 6

28 Figure : Rolling of he Real Exchange Rae Movemen Moving by 15 years (In parenhesis, T and NT denoe Trend and No Trend respecively.) RER1: 1970Q1-1984Q4 (NT) RER: 1971Q1-1985Q4 (NT) RER3: 197Q1-1986Q4 (NT) RER4: 1973Q1-1987Q4 (NT) RER5: 1974Q1-1988Q4 (NT) RER6: 1975Q1-1989Q4 (NT) Q1 1971Q3 1973Q1 1974Q3 1976Q1 1977Q3 1979Q1 1980Q3 198Q1 1983Q3 1971Q1 197Q3 1974Q1 1975Q3 1977Q1 1978Q3 1980Q1 1981Q3 1983Q1 1984Q3 197Q1 1973Q3 1975Q1 1976Q3 1978Q1 1979Q3 1981Q1 198Q3 1984Q1 1985Q3 1973Q1 1974Q3 1976Q1 1977Q3 1979Q1 1980Q3 198Q1 1983Q3 1985Q1 1986Q3 1974Q1 1975Q3 1977Q1 1978Q3 1980Q1 1981Q3 1983Q1 1984Q3 1986Q1 1987Q3 1975Q1 1976Q3 1978Q1 1979Q3 1981Q1 198Q3 1984Q1 1985Q3 1987Q1 1988Q3 RER7: 1976Q1-1990Q4 (NT) RER8: 1977Q1-1991Q4 (NT) RER9: 1978Q1-199Q4 (T) RER10: 1979Q1-1993Q4 (T) RER11: 1980Q1-1994Q4 (T) RER1: 1981Q1-1995Q4 (T) Q1 1977Q3 1979Q1 1980Q3 198Q1 1983Q3 1985Q1 1986Q3 1988Q1 1989Q3 1977Q1 1978Q3 1980Q1 1981Q3 1983Q1 1984Q3 1986Q1 1987Q3 1989Q1 1990Q3 1978Q1 1979Q3 1981Q1 198Q3 1984Q1 1985Q3 1987Q1 1988Q3 1990Q1 1991Q3 1979Q1 1980Q3 198Q1 1983Q3 1985Q1 1986Q3 1988Q1 1989Q3 1991Q1 199Q3 1980Q1 1981Q3 1983Q1 1984Q3 1986Q1 1987Q3 1989Q1 1990Q3 199Q1 1993Q3 1981Q1 198Q3 1984Q1 1985Q3 1987Q1 1988Q3 1990Q1 1991Q3 1993Q1 1994Q3 RER13: 198Q1-1996Q4 (T) RER14: 1983Q1-1997Q4 (NT) RER15: 1984Q1-1998Q4 (NT) RER16: 1985Q1-1999Q4 (NT) RER17: 1986Q1-000Q4 (NT) RER18: 1987Q1-001Q4 (NT) Q1 1983Q3 1985Q1 1986Q3 1988Q1 1989Q3 1991Q1 199Q3 1994Q1 1995Q3 1983Q1 1984Q3 1986Q1 1987Q3 1989Q1 1990Q3 199Q1 1993Q3 1995Q1 1996Q3 1984Q1 1985Q3 1987Q1 1988Q3 1990Q1 1991Q3 1993Q1 1994Q3 1996Q1 1997Q3 1985Q1 1986Q3 1988Q1 1989Q3 1991Q1 199Q3 1994Q1 1995Q3 1997Q1 1998Q3 1986Q1 1987Q3 1989Q1 1990Q3 199Q1 1993Q3 1995Q1 1996Q3 1998Q1 1999Q3 1987Q1 1988Q3 1990Q1 1991Q3 1993Q1 1994Q3 1996Q1 1997Q3 1999Q1 000Q3 RER19: 1988Q1-00Q4 (NT) RER0: 1989Q1-003Q4 (NT) RER1: 1990Q1-004Q4 (T) RER: 1991Q1-005Q4 (T) RER3: 199Q1-006Q4 (T) Q1 1989Q3 1991Q1 199Q3 1994Q1 1995Q3 1997Q1 1998Q3 000Q1 001Q3 1989Q1 1990Q3 199Q1 1993Q3 1995Q1 1996Q3 1998Q1 1999Q3 001Q1 00Q3 1990Q1 1991Q3 1993Q1 1994Q3 1996Q1 1997Q3 1999Q1 000Q3 00Q1 003Q3 1991Q1 199Q3 1994Q1 1995Q3 1997Q1 1998Q3 000Q1 001Q3 003Q1 004Q3 199Q1 1993Q3 1995Q1 1996Q3 1998Q1 1999Q3 001Q1 00Q3 004Q1 005Q3 7

29 Figure 3: The P-Value of Rejecing he Uni Roo of Real Exchange Rae of Each Period End Period Value Average Period Value 0% 5% 10% 15% 0% 5% 30% 35% 40% 45% 50% 55% 60% 65% 70% 75% 80% Figure 4: Plo of Cumulaive Sum of Recursive Residuals (CUSUM) Figure 5: Plo of Cumulaive Sum of Square of Recursive Residuals (CUSUMQ) 8