Efficient Unit Root Tests of real Exchange Rates in the Post-Bretton Woods Era

Transcription

1 Universiy of Connecicu Economics Working Papers Deparmen of Economics January 22 Efficien Uni Roo Tess of real Exchange Raes in he Pos-Breon Woods Era Francis W. Ahking Universiy of Connecicu Follow his and addiional works a: hp://digialcommons.uconn.edu/econ_wpapers Recommended Ciaion Ahking, Francis W., "Efficien Uni Roo Tess of real Exchange Raes in he Pos-Breon Woods Era" (22). Economics Working Papers hp://digialcommons.uconn.edu/econ_wpapers/2217

2 Deparmen of Economics Working Paper Series Efficien Uni Roo Tess of real Exchange Raes in he Pos- Breon Woods Era Francis W. Ahking Universiy of Connecicu Working Paper February Mansfield Road, Uni 163 Sorrs, CT Phone: (86) Fax: (86) hp://

3 Absrac We apply he efficien uni-roos ess of Ellio, Rohenberg, and Sock (1996), and Ellio (1998) o weny-one real exchange raes using monhly daa of he G-7 counries from he pos-breon Woods floaing exchange rae period. Our resuls indicae ha, for eigheen ou of he weny-one real exchange raes, he null hypohesis of a uni roo can be rejeced a he 1e al (1996) DF-GLS es. The uni-roo null hypohesis is also rejeced for one addiional real exchange rae when we allow for one endogenously deermined break in he ime series of he real exchange rae as in Perron (1997). In all, we find favorable evidence o suppor long-run purchasing power pariy in nineeen ou of weny-one real exchange raes. Second, we find no srong evidence o sugges ha he use of non-u.s. dollar-based real exchange raes end o produce more favorable resul for long-run PPP han he use of U.S. dollar-based real exchange raes as Lohian (1998) has concluded. Journal of Economic Lieraure Classificaion: E31, C22

4 Efficien Uni Roo Tess of Real Exchange Raes in he Pos-Breon Woods Era 1. Inroducion The heory of purchasing power pariy (PPP) has a long radiion in inernaional economics. I is a cenral building block in he moneary models of exchange rae deerminaion. In he moneary approach, e.g., Frenkel (1978), PPP is assumed o hold coninuously. This assumpion, however, is a odd wih he frequenly observed deviaions of nominal exchanges raes from heir implied PPP levels. In Dornbusch s (1976) sicky-price moneary model, because prices are sicky in he shor run, PPP is assumed no o hold. For he long run, however, PPP is sill a mainained assumpion. Given he cenral place ha PPP plays in he moneary models of exchange rae deerminaion, i is no surprising ha considerable research has been devoed o is empirical verificaion. Ye anoher reason why i is imporan o know he sochasic propery of real exchange raes has o do wih wha Rogoff (1996) has called he purchasing power pariy puzzle. The puzzle is ha, while moneary shocks combined wih sicky nominal prices or wages can provide an explanaion for he shor-run volailiy of real exchange raes, bu he esimaed half-life of hree o five years for he shocks o damp ou appears o be more consisen wih real raher han nominal shocks. 1 Thus, a knowledge of he sochasic srucure of real exchange raes is useful in deermining wheher shocks o real exchange raes are permanen or ransiory, and if ransiory, wheher hey are predominanly moneary or real shocks. Unil quie recenly, empirical resuls on PPP have no been very encouraging, especially using daa from he pos-breon Woods period [see he survey by Rogoff (1996)]. More recen empirical resuls appear o be more encouraging, bu hey are no very robus, however. We have wo purposes in his sudy. Firs, we es for long-run PPP using daa from he pos-breon Woods period using wo saisical mehods. We sar wih he efficien uniroo ess proposed by Ellio, Rohenberg, and Sock (1996), and Ellio (1998). Nex we allow for a more flexible model srucure by allowing for shifs in he mean or he rend, or boh. Second, we provide a more sysemaic assessmen o Lohian s (1998) asserion ha he failure of he earlier sudies o find favorable evidence of long-run PPP in he pos-breon Woods period is likely due o he use of U.S. dollar as he base currency. In he nex secion, we will briefly review some of he recen empirical sudies on PPP. We discuss he efficien uni-roo ess in secion 3. In secion 4, we discuss our daa se and presen our empirical resuls. In Secion 5, we discuss and presen our resuls using more flexible models ha allow for srucural breaks. Summary and conclusions are in secion 6. 1

5 2. Review of Recen Empirical Resuls on Tess for Long-Run PPP Recen empirical ess of PPP have mainly focused on he long run given ha here are frequen large and persisence shor-run deviaions from PPP. Two main explanaions have been offered for why researchers failed o find favorable evidence of long run PPP in some of he earlier sudies using daa from he pos-breon Woods period. Firs, i is known ha when German mark is used as he base currency, researchers end o find more favorable resuls for long-run PPP han when he U.S. dollar is he base currency [see Papell (1997), and Papell and Theodoridis (1998) for recen examples]. This leads Lohian (1998) o conclude ha he frequen failures o find evidence in favor of long-run PPP in he pos-breon Woods floaing exchange rae period is no a generic problem o his period. Raher, i is confined o using he U.S. dollar as he base currency and is resriced o he early o mid- 198s when firs here was a subsanial real appreciaion of he U.S. dollar for , and an almos equal offseing real depreciaion for Second, he augmened Dickey-Fuller (ADF, 1981) es is one of he mos generally used ess for PPP, bu his es is known o have low power in small samples agains plausible alernaives, especially agains rend-saionary alernaive [see, for example, Hakkio (1986), and DeJong, Nankervis, Savin, and Whieman (1992)]. Thus, i is no possible o disinguish wheher he failure o find PPP is due o he low power of he ess employed or ha PPP does no hold in he pos-breon Woods floaing period. One way o increase he power of he empirical ess is o use longer span of daa. For example, Diebold, Hused, and Rush (1991), 2 using daa going back o he gold sandard period, Lohian, and Taylor (1996), using daa daing back o he179s and early 18s, found evidence o suppor long-run PPP. On he oher hand, Engel and Kim (1999), using monhly daa daing back o 1885, found evidence of a permanen (i.e., a uni-roo) componen in he U.S./U.K. real exchange rae. In addiion, Rogoff (1996) and ohers have noed ha sudies ha used long spans of daa ypically mix fixed and floaing exchange raes daa, and he economic implicaions of mixing daa from he wo exchange rae regimes are unclear. Moreover, long spans of ime series daa may poenially conain serious srucural breaks. Engel (1996) also argued ha hese sudies can have serious size biases, and may fail o rejec a sizable uni roo. Finally, hese sudies also do no shed much ligh on he quesion of wheher or no PPP is a valid hypohesis in he pos-breon Woods floaing period. Anoher way o increase he power of he uni-roo ess is o use panel daa. Recen examples using daa from he pos-breon Woods floaing exchange rae period include sudies by Jorion and Sweeney (1996), Papell (1997), Papell and Theodoridis (1998), and Koedijk, Schoman, and Van Dijk (1998). These sudies all found evidence o suppor long-run PPP. On he oher hand, O Connell (1998) found lile evidence o suppor long-run 2

6 PPP afer accouning for serial correlaion. Papell (1997) found ha evidence in favor of long-run PPP is dependen on he size of he panel and he counries included. Rogoff (1996) also noed ha wih panel sudies, he evidence of long-run PPP ends o be much more favorable when high inflaion counries are included. Moreover, he inerpreaion of he panel sudies resuls is no always very obvious. For example, Karlsson and Löhgren (2) using Mone Carlo simulaions, found ha for panels wih long spans of daa, he null hypohesis of uni roos can be erroneously rejeced even when only a small proporion of he series is saionary. For panels wih shor spans of daa, however, Karlsson and Löhgren (2) found ha he null hypohesis of uni roos is frequenly no rejeced even when a large fracion of he series is saionary. Thus, hey concluded ha he rejecion or he non-rejecion of he null hypohesis of uni roos in panel uni roo ess do no provide sufficien evidence o conclude ha all he series in he panels are saionary or ha hey all have a uni roo. An excepion, however, is he panel sudy by Sarno and Taylor (1998). Using a special applicaion of he Johansen (1988) Likelihood raio, where he null hypohesis of a uni roo is rejeced only when all he series are saionary, Sarno and Taylor (1998) concluded ha heir four real exchange raes are joinly saionary series. Thus, panel uni roo ess have produced encouraging bu inclusive resuls. Sill oher researchers, using differen empirical mehodologies, found mixed resuls wih daa from he pos-breon Woods period. For example, Cheung and Lai (1998), using more efficien uni roo ess, found more encouraging resuls han when using he ADF ess. Culver and Papell (1999), using he ess proposed by Kwiakowski, Phillips, Schmid and Shin (1992) where saionariy is he null, raher han he alernaive hypohesis, found favorable evidence o suppor long-run PPP. However, a recen sudy by Caner and Kilian (1999) shown ha severe size disorion can resul wih he use of convenional asympoic criical values for ess of he null hypohesis of saionariy if he model under he null hypohesis is highly persisen. On he oher hand, using sizeadjused criical values can overcome he problem of size disorions, bu resul in low power of he ess for economically plausible values of he firs-order auoregressive (i.e., AR (1)) parameer. Finally, Baum, Barkoulas, and Caglayan (1999), allowing for fracional differencing or srucural breaks, found no evidence o suppor longrun PPP, however. Our brief review suggess ha recen empirical sudies have ended o be more supporive of long-run PPP han earlier sudies. However, even-hough here is a growing body of lieraure ha suppors long-run PPP for he pos-breon Woods period, he resuls are no very robus, and consisen individual counry ime series evidence from he pos-breon Woods period coninues o be scarce. 3

7 3. Tesing For Uni Roo In his paper, we use wo of saisical mehods o sudy long-run PPP using daa from he pos-breon Woods era for weny-one real exchange raes. We sar wih a more efficien univariae uni roo es proposed by Ellio, Rohenberg, and Sock (1996), and Ellio (1998). Nex, we allow for a more flexible model srucure, such as shifs in he mean or he ime rend, for hose real exchange rae series ha we canno rejec he null hypohesis of a uni roo using he more efficien uni-roo ess. Since we are using only univariae ime series of he real exchange raes, we avoid he poenial problems associaed wih using panel daa. Furhermore, since our daa are from he pos-breon Woods period, we also avoid he criicisms of using long spans of daa ha mixed boh fixed and floaing exchange raes daa. Previous sudies on long-run PPP using efficien uni-roo es include Cheung and Lai (1998), Caner and Kilian (1999), and Kuo and Mikkola (1999). Cheung and Lai (1998), using daa from he pos-breon Woods period, examined en real exchange raes using he efficien uni-roo es of Ellio e al (1996). Kuo and Mikkola (1999) sudied only he U.S./U.K. real exchange rae using daa spanning 134 years, hus mixing boh fixed and flexible exchange rae periods. The main purpose of he sudy by Caner and Kilian (1999) was o sudy he size and power of ess ha have saionariy as he null hypohesis. They use he efficien uni-roo es of Ellio e al (1996) o sudy long-run PPP as a comparison o hose ess. Our paper is a much more horough sudy of long-run PPP using a larger daa se, and using he efficien uni-roo ess of boh Ellio e al (1996) and Ellio (1998), in addiion o using ess ha allow for a more flexible model srucure. To be specific, we define he real exchange rae in naural logarihm form as: q = e + P * P, (1) where q is he naural logarihm of he real exchange rae, e is he naural logarihm of he nominal exchange rae, defined as he domesic currency price of one uni of foreign currency, P is he naural logarihm of an index of he domesic price level, and * P of long-run PPP involve esimaing an equaion similar o is he naural logarihm of an index of he foreign price level. Convenional ADF ess k q = α + ρq 1 + αi q i + ε, (2) i= 1 4

8 where α is a consan, is he firs difference operaor, i.e., q = q q, and ε is a serially uncorrelaed 1 error process. Long-run PPP requires ha ρˆ < 1. If ρˆ = 1, here is a uni-roo in he real exchange rae series, shocks o he real exchange rae are permanen and long-run PPP does no hold. The efficien uni-roo ess of Ellio e al (1996) and Ellio (1998) are similar, differing only in he iniial condiion assumpion. We will review briefly he ess and poin ou he differences. The efficien uni-roo es of Ellio e al (1996) is based on he poin opimal ess. In general, while no uniformly mos powerful uni-roo es of H : ρ = 1 agains he general alernaive : ρ < 1 exiss, here is an opimal es, however, agains a specific O H A local alernaive H : ρ =ρ< 1, where ρ = 1+ c / T, c < is a specific consan, and T is he sample size. A Using a sequence of Neyman-Person ess of he null hypohesis of a uni roo agains a se of saionary local alernaives, Ellio e al (1996) derived he asympoic maximal power envelope. From he power calculaions, Ellio e al (1996) shown ha subsanial power gain over he sandard ADF es could be obained from a modified ADF es, which hey called he DF-GLS es. The DF-GLS es involves esimaing he following equaion wih ordinary leas squares: q d = δ k d d d q 1 + δ i q i + ς, (3) i= 1 d d where is a serially uncorrelaed error process, q is he locally derended series of q, where ς q d = q z β, (4) and z = ( 1, ), for he locally derended series wih a consan and a linear rend, and = 1, for series wihou a z linear rend. Finally, β is he vecor of leas squares regression coefficiens of q~ / = [q ρ L) q,... 1, ( 1 2, (1 ρl) q T ] on ~ z / = [ z1, (1 ρl) z2,..., (1 ρl) z T ], and L is he lag operaor, i.e., Lz. A -es is used o es he null hypohesis H δ agains H : δ < 1 z. = 1 : = Ellio s (1998) efficien uni-roo es, denoed as DF-GLS u, differs from Ellio e al (1996) in is assumpion abou he iniial value of he alernaive model. Specifically, boh Ellio e al (1996) and Ellio (1998) A assume ha heir daa ( y1, y2,..., yt ) are generaed according o y = d + u, and (5) u ρu + v, (6) = 1 5

9 where d is a deerminisic componen which may or may no conain a deerminisic linear rend, and v is a saionary error process which may or may no be serially correlaed. Ellio e al. assumed ha he iniial value of u, i.e., u is zero boh when ρ = 1 and when ρ < 1, so ha u =. Ellio (1998) assumed ha u is zero 1 v 1 when ρ = 1, so ha u = also, bu when ρ 1, u has mean zero and variance 1 v 1 < 1 Var( (1 ρ v 2 ). Since he alernae ) assumpion involves he unknown parameer ρ, Ellio (1998) has shown ha since his unknown parameer does no disappear asympoically, he likelihood es saisics and he power of he ess will differ from he opimal es in Ellio e al (1996), and a differen se of he criical values of he es saisics are derived in Ellio (1998). To u d implemen he DF-DLS es, equaion (3) is esimaed by leas squares, wih q z, and β are as defined before, excep ha now ~ z q~ 2 1/ 2 = [( 1 ρ ) z, ( 1 ρl )z = ) / [( 1 ρ ) 1/ q1, (1 ρl q2,..., ( 1 ρl) q T ], and,... 2, (1 / ρ L) z T ]. In pracice, however, i is difficul o know wheher he sample daa conform o he daa generaing models of Ellio e al (1996) or Ellio (1998). We repor es resuls for boh in our paper. Following Ellio e al. (1996), we use c = 7 for es wih a consan, and c = for es wih a consan and a linear rend. Asympoic criical values of he es saisics are derived in Ellio e al (1996). For he DF-GLS u es, we also follow Ellio (1998) and use c = 1 in boh es wih a consan, and es wih a consan and a linear rend. We discuss our daa se and presen our empirical resuls in he nex secion. 4. Empirical Resuls The source of our daa is he OECD G-7 counries, supplied on a diskee. Our daa consis of monhly observaions from April 1973 o February 1999 for he G-7 counries, and are no seasonally adjused. The G-7 counries are he U.S., he U.K., Canada, Germany, Ialy, France, and Japan. In all cases, we use he consumer price index as our measure of he average price level. The only bilaeral nominal exchange rae available on he diskee uses he U.S. dollar as he base currency, i.e., foreign currency per U.S. dollar. Since, we are also ineresed in wheher he use of non-u.s. dollar based real exchange raes may produce differen resuls, as oher sudies have found, we herefore also compued real exchange raes based on he pound serling, he Canadian dollar, he German mark, he Ialian lira, he France franc, and he Japanese yen. These non-u.s. dollar based exchange raes are compued as cross-raes. 3, 6

10 We sar our empirical ess by firs presening in Table 1 our es for uni-roo using he ADF es. This is moivaed by wo facors. Firs, our resuls provide an updae on previous research hrough he beginning of 1999, and i is ineresing o find ou wheher an addiion of several more years of daa would have made a difference in he ADF ess for uni roo. Second, he ADF uni-roo es resuls will provide a comparison o he efficien uniroo ess of Ellio e al (1996), and Ellio (1998). Noe also ha we provide uni-roo es resuls for fory-wo real exchange raes (six real exchange raes for each of he seven currencies). Of course, here are only weny one differen real exchange raes since he real exchange rae of counry A s currency per uni of counry B s currency is simply he inverse of he real exchange rae of counry B s currency per uni of counry A s currency. This is done so ha we can examine how real exchange raes based on non-u.s. dollar would behave compared o he U.S. dollar based real exchange raes. The ADF regression acually esimaed is l q = β + λq 1 + βi q i + βl η, (7) i= 1 where = a linear deerminisic ime rend, and η is a serially uncorrelaed error process wih zero mean and consan variance. The lag lengh for he lagged firs-differences is deermined by using a general-o-specific mehod recommended by Ng and Perron (1995) and Perron (1997). We sar by esimaing Equaion (7) wih a predeermined maximum lag lengh, call his lmax. We es he saisical significance of his pre-deermined maximum lag using he convenional -saisic a he 1% significance level. If i is no saisically significanly differen from zero, his lag is dropped and we re-esimae Equaion (7) wih l = lmax-1. This process is repeaed unil he las included lag is saisically significan a he 1% significance level. We sar wih an upper bound for lmax = 12, and a lower bound of lmax = 1. If, however, he lag lengh deermined is he same as he upper bound lmax value, we sar over wih lmax = 14. Noe ha we have included a linear ime rend o allow for he possibiliy ha he real exchange rae may be rend-saionary. 4 We repor our empirical resuls for boh wih and wihou a linear ime rend, however. Column 2 of Table 1 shows he lag lengh chosen for he models. In columns 3 and 4, we show he - saisic for he hypohesis H : λ = wihou and wih a linear ime rend, respecively. We use he criical values a he 5% and he 1% significance levels from Fuller (1976) and he lag-adjused criical values for exac sample size from Cheung and Lai (1995). For he ADF es resuls wihou a linear ime rend, he null hypohesis is no rejeced a he 5% significance level for all cases. A he 1% significance level, he null hypohesis is no rejeced 7

11 for hree of weny-one real exchange raes. When he ADF regression includes a linear ime rend, he null hypohesis is rejeced for hree of weny-one real exchange raes a he 5% significance level, and an addiional wo real exchange raes a he 1% significance level. In sum, a oal of seven of weny-one, or 33% of he real exchange raes, are found o be eiher saionary or rend-saionary a he 1% significance level or beer using he convenional ADF approach. Thus, he addiion of a few more years of monhly daa appears o have no significan impac on he power of he ADF uni-roo es. There is some evidence o sugges ha non-u.s. dollar-based real exchange raes, e.g., Japanese yen-based and German mark-based real exchange raes, do appear o provide more favorable long-run PPP resuls. The improvemen in resuls over U.S. dollar-based real exchange raes is marginal a bes, however. Moreover, using Pound serling-based or Ialian lira-based real exchange raes produce equally dismal resuls as using U.S. dollarbased real exchange raes. Thus, our ADF resuls provide no suppor o Lohian s (1998) asserion ha he frequen failures o find favorable evidence of long-run PPP in earlier sudies for he pos-breon Woods period is confined o using U.S. dollar as he base currency. Table 2 repors he resuls for boh he DF-GLS and he DF-GLS u ess. The lag lenghs used in hese wo ess are he same as hose deermined for he ADF es repored in Table 1. Wha we repor in Table 2 are he - saisics for he null hypohesis H δ agains he alernaive hypohesis : δ <. Saring wih he : = DF-GLS es wihou rend, a he 5% significance level, he null hypohesis of a uni roo is rejeced in five cases. A he 1% significance level, he null hypohesis is rejeced for hree addiional real exchange raes. When a linear rend is included, he null hypohesis is rejeced a he 5% significance level for six real exchange raes, and he null hypohesis is rejeced a he 1% significance level for nine addiional real exchange raes. In all, he DF-GLS es suggess ha eigheen of weny-one real exchange raes, or abou 86% of he cases, are eiher saionary or rendsaionary a he 1% significance level or beer. This represens a significan improvemen over he resuls of he convenional ADF es. The mos favorable resuls come from he franc-based and he yen-based real exchange raes where in each case all six real exchange raes are eiher saionary or rend-saionary a he 1% significance level or beer. This is followed by he U.S. dollar-based, he Canadian dollar-based, and he mark-based real exchange rae wih five ou of six real exchange raes each. For he lira-based real exchange raes, we have only four ou of six cases where he real exchange raes are eiher saionary or rend-saionary a he 1% significance level or beer. Overall, we conclude ha here are no major differences in resuls beween U.S. dollar-based or non- U.S. dollar-based real exchange raes, wih perhaps he Ialian lira-based real exchange raes as he excepions. 8 H A

12 We nex urn o he DF-GLS u resuls in Table 2. Firs hing o noe is ha, compared o he DF-GLS resuls, here are fewer cases where he null hypohesis of a uni roo is rejeced. In all, only nine ou of weny one real exchange raes, or abou 43%, can be characerized as eiher saionary or rend-saionary a he 1% significance level or beer. More imporanly, no addiional real exchange rae is found o be saionary or rendsaionary ha was no found by he DF-GLS es. These resuls are slighly beer han he resuls from he ADF ess, bu are clearly much wors han he resuls using he DF-GLS ess. Since we are looking for evidence of longrun PPP in he pos-breon Woods era, we herefore accep he more favorable resuls provided by he DF-GLS es. This leaves hree real exchange raes ha long-run PPP does no appear o hold he Canadian dollar/u.s. dollar, he serling/lira, and he mark/lira raes. We invesigae hese hree real exchange raes furher in he nex secion. 5. Srucural Breaks and Long-Run PPP In his secion, we use a more flexible ADF regression by allowing for he possibiliy of srucural breaks in he real exchange rae ime series. We sar wih he simples srucural-break model where here is only one break poin, and furher limi our aenion o he class of models where he breakpoin is endogenously deermined. The firs srucural-break model ha we consider is he innovaional oulier model of Perron (1989, 1997): q = µ + µ DU + γ + γ 1 1 ) l 1 + λi q 1 + i= 1 D( TB + φq ξ, (8) where TB is he single break-poin in he ime series, DU = 1 for > TB, and elsewhere; D ( TB) = 1 for = TB + 1, and elsewhere; and ξ is a serially uncorrelaed error process. The null hypohesis of a uni-roo is H : φ = 1. The lag lengh for Equaion (8) is chosen by he same general-o-specific mehod described earlier. The break-poin is deermined by using he maximum of he absolue value of he -saisic on. 5 A rim value of 15% is also used a he beginning and he end of he daa series o rule ou he possibiliy of he break-poin occurring a hose wo end poins. Our resuls for he remaining hree real exchange raes are presened in Table 3. Saring wih he serling/lira real exchange rae, he break-poin dae idenified is 1985:6. We have no ready explanaion for his break-poin dae. The null hypohesis of a uni-roo is barely no rejeced a he 1% significance level ( vs a he 1% criical significance level). For he mark/lira exchange rae, he break-poin dae idenified is 1992:7. This seems reasonable since i is sufficienly close o he exchange rae crisis of Sepember 1992 when he lira was devaluaed by abou 15% agains he mark because of speculaive aacks on he lira and oher European currencies belonging o he Exchange Rae Mechanism. The mean-break erm (DU) is 9 µ 1

13 highly significan and is sign is consisen wih a devaluaion of he lira agains he mark. Moreover, he null hypohesis of a uni roo is rejeced a he 5% significance level ( vs. 4.8 a he 5% criical significance level). Finally, he break-poin dae of 1986:5 for he Canadian dollar/u.s. dollar is also reasonable since i is wihin he period of he sharp real depreciaion of he U.S. dollar beween 1985 and The sign of he meanbreak erm is also consisen wih his explanaion, alhough we canno assess is saisical significance since we canno rejec he null hypohesis of a uni roo a he 1% and he 5% significance levels. We have ried more complicaed srucural-break models for he serling/lira and he Canadian dollar/u.s. dollar real exchange raes. For example, we have allowed for a simulaneous break in he inercep and he ime rend (Perron, 1997), wo breaks in he inercep (Clemene, Monañés, and Reyes, 1998), wo breaks in he inercep and he ime rend or combinaion of he wo (Lumsdaine and Papell, 1997), bu found no significan improvemen over he simpler srucural break model given by Equaion (8). These resuls are hus no repored. We are somewha surprised by hese resuls especially wih he models wih wo srucural breaks, since, a prior, we believe ha hey are good candidaes for he Canadian dollar/u.s. dollar real exchange rae given he behavior of he U.S. dollar real exchange rae in he 198s discussed earlier. In sum, using a more flexible ADF specificaion by allowing for srucural breaks urned up one addiional case of long run PPP for he mark/lira real exchange rae. A case could also be made for he serling/lira real exchange rae where he null hypohesis of a uni roo is barely no rejeced a he 1% significance level. We are, however, unable o uncover any evidence in favor of long-run PPP for he Canadian dollar/u.s. dollar real exchange rae. 6. Summary and Conclusions Recen empirical sudies, using differen empirical mehodologies o overcome he weaknesses of he convenional ADF ess, have found increasingly supporive evidence of long-run PPP. Consisen individual ime series evidence from he pos-breon Woods era, however, coninues o be scarce. We applied he efficien ess for a uni roo proposed by Ellio e al (1996) and Ellio (1998) o weny-one ime series of real exchange raes using monhly daa from he pos-breon Woods period of he G-7 counries. We find evidence o suppor long-run PPP a he 1% or beer significance level for eigheen ou of he weny-one real exchange raes using he Ellio e al (1996) DS-GLS es. Using a flexible ADF regression by allowing for he possibiliy of srucural breaks, we are able o find evidence of long-run PPP for one addiional real exchange rae. In all, we find supporive evidence for long run PPP for nineeen ou of weny-one real exchange raes. 1

14 Second, our resuls sugges ha here are only marginal differences beween U.S. dollar-based and non- U.S. dollar-based real exchange raes, boh when he empirical resuls are supporive and no supporive of long-run PPP. Thus, we have no evidence o suppor Lohian s (1998) asserion ha he failure o find favorable evidence of long-run PPP in earlier sudies for he pos-breon Woods period can be aribued o using U.S. dollar as he base currency. Raher, our resuls srongly sugges ha, more han likely, i is due o he low power of he saisical ess employed. Our sudy, even-hough we find evidence favorable o long-run PPP, should be viewed as an exploraory sudy. One area ha fuure research should address is he following. We have seen ha he use of he DF-GLS es or he DF-GLS u es can produce raher differen resuls. A he momen, we know of no operaional way o disinguish beween when he DF-GLS or he DF-GLS u es should be used. A resoluion of his quesion should be helpful no only o researchers in inernaional finance, bu researchers in oher areas as well. 11

15 References Baum, Chrisopher F., Barkoulas, John T., Caglayan, Musafa, Long memory or srucural breaks: can eiher explain nonsaionary real exchange raes under he curren floa? Journal of Inernaional Financial Marke, Insiuions & Money 9, Caner, Mehme, Kilian, Luz, Size disorions of ess of he null hypohesis of saionariy: evidence and implicaions for he PPP debae. Universiy of Michigan Working Paper. Cheung, Yin-Wong, Lai, Kon S., Lag order and criical values of he augmened Dickey-Fuller es. Journal of Business and Economic Saisics 13, Cheung, Yin-Wong, Lai, Kon S., Pariy reversion in real exchange raes during he pos-breon Woods period. Journal of Inernaional Money and Finance 17, Clemene, Jesús, Monañés, Anonio, Reyes, Marcelo, Tesing for a uni roo in variables wih a double change in he mean. Economics Leers 59, Culver, Sarah, Papell, David H., Long run purchasing power pariy wih shor-run daa: evidence wih a null hypohesis of saionariy. Journal of Inernaional Money and Finance 18, DeJong, David N., Nankervis, John C., Savin, N. E., Whieman, Charles, Inegraion versus rend saionariy in ime series. Economerica 6, Dickey, David A., Fuller, Wayne A., Likelihood raio saisics for auoregressive ime series wih a uni roo. Economerica 49, Diebold, Francis X., Hused, Seven, Rush, Mark, Real exchange raes under he gold sandard. Journal of Poliical Economy 99, Dornbusch, Rudiger, Expecaions and exchange rae dynamics. Journal of Poliical Economy 84, Ellio, Graham, Efficien ess for a uni roo when he iniial observaion is drawn from is uncondiional disribuion. Forhcoming in Inernaional Economic Review. Ellio, Graham, Rohenberg, Thomas J., and Sock, James H., Efficien ess for an auoregressive uni roo. Economerica 64, Engel, Charles, Long-run PPP may no hold afer all. Discussion Series #96-5, Insiue for Economic Research, Universiy of Washingon. Engel, Charles, Kim, Chang-Jin, The long-run U.S./U.K. real exchange rae. Journal of Money, Credi and Banking 31, Par 1, Fuller, Wayne A., Inroducion o saisical ime series. New York: John Wiley & Sons. Frenkel, Jacob A., A moneary approach o he exchange rae: Docrinal aspecs and empirical evidence, in J. A. Frenkel and H. G. Johnson, eds., The economics of exchange rae (Addison-Wesley, Reading) Hakkio, Craig S., Does he exchange rae follow a random walk? A Mone Carlo sudy of four ess for a random walk. Journal of Inernaional Money and Finance 5, Johansen, S., Saisical analysis of coinegraion vecors. Journal of Economic Dynamic and Conrol 12,

16 Jorion, Philippe, Sweeney, Richard, Mean reversion in real exchange raes: Evidence and implicaions for forecasing. Journal of Inernaional Money and Finance 15, Karlsson, Sune, Löhgren, Mickael, 2. On he power and inerpreaion of panel uni roo ess. Economics Leers 66, Koedijk, Kees G., Schoman, Peer C., Van Dijk, Mahijs A., The re-emergence of PPP in he 199s. Journal of Inernaional Money and Finance 17, Kuo, Biing Shen, Mikkola, Anne, Re-examining long-run purchasing power pariy. Journal of Inernaional Money and Finance 18, Kwiakowski, Denis, Phillips, Peer C. B., Schmid, Peer, Shin, Yongcheol, Tesing he null hypohesis of saionariy agains he alernaive of a uni roo. Journal of Economerics 54, Lohian, James R., Some new sylized facs of floaing exchange raes. Journal of Inernaional Money and Finance 17, Lohian, James R., Taylor, Mark P., The recen floa from he perspecive of he pas wo cenuries. Journal of Poliical Economy 14, Lumsdaine, Robin, Papell, David H., Muliple rend breaks and he uni-roo hypohesis. Review of Economics and Saisics 79, Murray, Chrisian J., Papell, David H., 22. The purchasing power pariy persisence paradigm. Journal of Inernaional Economics 56, Ng, Serena, Perron, Pierre, Uni roo ess in ARMA models wih daa-dependen mehods for he selecion of he runcaion lag. Journal of he American Saisical Associaion 9, O Connell, Paul G. J., The overvaluaion of purchasing power pariy. Journal of Inernaional Economics, 44, Papell, David H., Searching for saionariy: Purchasing power pariy under he curren floa. Journal of Inernaional Economics 43, Papell, David H., Theodoridis, Hrisos, Increasing evidence of purchasing power pariy over he curren floa. Journal of Inernaional Money and Finance 17, Perron, Pierre, The grea crash, he oil price shock, and he uni roo hypohesis. Economerica 57, Perron, Pierre, Furher evidence on breaking rend funcions in macroeconomic variables. Journal of Economerics 8, Rogoff, Kenneh, The purchasing power pariy puzzle. Journal of Economic Lieraure 34, Sarno, Lucio, Taylor, Mark P., Real exchange raes under he recen floa: unequivocal evidence of mean reversion. Economics Leers 6,

17 Table 1 Univariae ADF Tes Resuls (λ) l (λ) wih rend wihou rend Base Currency: U.S. Dollar Canada U.K ** Germany Ialy Japan France Base Currency: Canadian Dollar U.S.A U.K Germany ** Ialy ** Japan ** France Base Currency: Pound Serling U.S.A ** Canada Germany Ialy Japan France Base Currency: German Mark U.S.A Canada ** U.K Ialy Japan * France ** * Base Currency: Ialian Lira U.S.A Canada ** U.K Germany Japan France Base Currency: Japanese Yen U.S.A Canada ** U.K Germany * Ialy France * Base Currency: French Franc U.S.A Canada U.K Germany ** * Ialy Japan * Noe: *,** Denoe he rejecion of he null hypohesis a he 5% and he 1% significance levels, respecively. + The lag lengh is 1 for he Canadian dollar/lira real exchange rae when esimaed wihou a linear ime rend. 14

18 Table 2 Efficien Uni-Roo Tess DF-GLS DF-GLS u l Wihou rend Wih rend Wihou rend Wih rend Base Currency: U.S. Dollar Canada U.K ** -2.78** ** Germany * Ialy * ** -2.55** Japan ** France * Base Currency: Canadian Dollar U.S.A U.K ** Germany * ** ** Ialy * * Japan * * France ** ** Base Currency: Pound Serling U.S.A ** -2.78** ** Canada ** Germany ** Ialy Japan ** France ** Base Currency: German Mark U.S.A * Canada * ** ** U.K ** Ialy Japan * * France * * -3.77* * Base Currency: Ialian Lira U.S.A * ** -2.55** Canada * * U.K Germany Japan * * France ** Base Currency: Japanese Yen U.S.A ** Canada * * U.K ** Germany * * Ialy * * France * * Base Currency: French Franc U.S.A * Canada ** ** U.K ** Germany * * -3.77* * Ialy ** Japan * * Noe: See noes o Table 1. 15

19 Table 3 Srucural Break Models Exchange Rae Coefficien of: Serling/Lira Mark/Lira Canadian Dollar/U.S. Dollar Consan (4.521) (4.91) (1.146) DU (3.897) (4.813) (2.967) E E E-5 (3.668) (4.795) (3.279) D(TB) (2.856) (1.162) 2.78) q (47.78) (6.14) (91.95) Lag lengh: saisic for H : φ * = Break dae: 1985:6 1992:7 1986:5 Noes: * Denoes he rejecion of he null hypohesis a he 5% significance level. The absolue value of he -saisic is given in parenhesis below he esimaes. 16

20 Foonoes 1 A recen paper by Murray and Papell (22) has shown ha he half-life esimaes are exremely unreliable, however. 2 I should be noed ha in addiion o using long span of daa, Diebold, Hused and Rush (1991) also used fracional differencing in heir model. Thus, i is no possible o disinguish wheher heir finding of favorable evidence of long-run PPP is due o he long span of daa or o he use of auoregressive fracionally inegraed moving-average process (ARFIMA). 3 This assumes cross-rae equaliy excep for ransacion coss. This is probably a valid assumpion for he G-7 counries. Alernaively, as long as he measuremen error is a saionary process, our ess for uni-roo will no be affeced. 4 Some researchers, e.g., Cheung and Lai (1998), and Koedijk, Schoman, and Van Dijk (1998), have found ha he sochasic processes of some of he real exchange raes canno be adequaely modeled wihou he inclusion of a linear deerminisic ime rend. The linear deerminisic ime rend is generally inerpreed as represening sysemaic differences in produciviy growh beween radable and non-radable goods in he wo counries. On he oher hand, some researchers, e.g., Papell and Theodoridis (1998), consider a linear ime rend in he real exchange rae as inconsisen wih long-run PPP. 5 Alernaive mehods for deermining he break-poin as suggesed in Perron (1997) produce similar resuls. 17