SHIFTS IN PERSISTENCE IN TURKISH REAL EXCHANGE RATES HALUK ERLAT

Transcription

1 Vol., Sepember 2009 SHIFTS IN PERSISTENCE IN TURKISH REAL EXCHANGE RATES HALUK ERLAT Deparmen of Economics Middle Eas Technical Universiy 0653 Ankara, Turkey Fax: Prepared for presenaion a he 29 h Annual Meeing of he Middle Eas Economic Associaion, January 2-5, 2009, San Francisco, USA.

2 Vol., Sepember Inroducion We have invesigaed he long-run behaviour of Turkish Real Exchange raes (RER) in hree previous papers. In Erla (2003) we made use of uni roo ess ha accouned for boh muliple srucural shifs in he deerminisic erms and ouliers, and found ha more han one shif may exis. The series invesigaed were he RERs based on he German DM and $US Exchange raes wih he Consumer Price Index (CPI) and he Wholesale Price Index (WPI) used for he price variables. In Erla (2004), using he same daa, we esed for uni roos agains nonlinear saionariy generaed by an Exponenial Smooh Transiion Auoregressive (ESTAR) model and found ha, for he CPI-based DM series, uni roo ess ha ook ino accoun muliple srucural shifs beer explained he persisence in he RERs. Finally, in Erla and Ozdemir (2005), we considered reaing he problem in erms of a panel of real exchange raes ha showed very srong dependence and found ha, due o his dependence, using panel approaches o esing for uni roos did no provide us wih any new evidence ha an RER based on he German DM may provide. Hence, he findings in Erla and Ozdemir (2005) lead us o reurn o he domain of Erla (2003, 2004) and ask if he shifs observed in hese sudies may also indicae shifs in he naure of persisence; namely, wheher hey indicae shifs from I(0) o I() or vice versa. Since muliple shifs had been found in Erla (2003), we used he regression-based mehod recenly developed by Leybourne, Kin and Taylor (2007) as a generalizaion of Leybourne, Kim, Smih and Newbold (2003). Leybourne e al (2007) apply heir approach o he logarihm of he yields on 0 year Governmen bonds for he UK, he USA, Canada and Ausralia, while Yoon (2008), in fac, applies i o he US/UK real exchange rae ha covers he period 79 o 990. In Erla (2008), we have applied he Leybourne e al (2003), singleshif es o monhly Turkish inflaion raes. Shifs in persisence in inflaion have also been considered by Chiquiar, Noriega and Ramos-Francia (2008) for Mexico and by Halunga, Osborn and Sensier (2008) for he UK and USA. They, however, use raio-ess where he null hypohesis is ha he series is I(0) for he full period. In he presen paper, we shall sar by esing if he RER series have a uni roo for he period as a whole. We shall use he DFGLS saisic proposed by Ellio, Rohenberg and Sock (996) since i is he saisic used by Leybourne e al (2003) and Leybourne e al (2007). We shall also use he es due o Kwiaowski, Phillips, Schmid and Shin (KPSS) (992), where he null hypohesis is saionariy, for corroboraion. We shall nex apply he

3 Vol., Sepember 2009 single-shif es of Leybourne e al (2003) and see if he muliple-shif es of Leybourne e al (2007) provides us wih addiional evidence. The plan of he paper is as follows. In he nex secion we describe he ess menioned above. We hen, briefly, describe he daa, which happens o be he same used in Erla (2003 and 2004). In secion four we give he empirical resuls and, in secion five, our conclusions. 2. The Tes Saisics We shall no describe he KPSS es since i is, now, quie well known. The same may also be said for he DGFLS es bu since he subsequen ess are all based on i, a descripion would be useful. The DFGLS es is based on firs esimaing () y = β ' d + u where d =, β = β 0 or d = (, )', β = ( β 0, β)', and u = δu + ε, δ <, by Generalized Leas Squares (GLS), which involves regressing (2) y = [ y, y δ y,, y δ y ]' * 2 T T on (3) d = [ d, d δ d,, d δ d ]' * 2 T T We obain δ by assuming ha δ akes on values in he neighborhood + ( c / T ) where c < 0. The choice of c, c, yields δ. The residuals from his esimaion, uˆ = y ˆ β ' d are used GLS o form he equaion, aking auocorrelaion in he disurbances ino accoun, as p (4) uˆ = ρuˆ ˆ + γ u + ε i i i= where ρ = δ and ρ = 0 is esed. The choice of c differs depending upon he model he DFGLS es is applied o. In he presen case, c = 7.0 if here is only an inercep and c = 3.5 if here are boh an inercep and a rend erm. The es for a single shif in a ime series, Leybourne e al (2003) apply he DFGLS saisic recursively. We may express heir model as 2

4 Vol., Sepember 2009 (5a) y = β ' d + u (5b) u = ρu + γ u + ε p i i i= The null hypohesis is ha he series is I() hroughou he sample and he alernaive hypoheses may be a shif from I(0) o I() or from I() o I(0). Leing τ = T B / T, T B being an unknown shif poin wih [.] indicaing he ineger par of he argumen, in he firs case we es (6) H : ρ = 0, =,, T 0 H : ρ < 0, =,,[ τt] 0 ρ = 0, = [ τt ] +,, T and, in he second, (7) H : ρ = 0, =,, T 0 H : ρ < 0, = T,, T [ τt ] 0 ρ = 0, = T [ τt],, To es H 0, equaion () is esimaed recursively by GLS, which implies ha he las ransformed observaions in (2) and (3) will now be y[ T ] δ y[ T ] and d[ T ] δ d[ T ], respecively and c will be aken as The residuals from hese regressions are used o esimae (4) and recursive -raios of ρ, (τ ) are obained. The es saisic is aken o be ρ he minimum of hese -raios. If he minimum value exceeds he appropriae criical value, hen he swich poin will be he τ-value ha corresponds o his minimum. To es H 0 he series is reversed as z + and he procedure described above is applied o he z. We = y T shall call he saisic o es H 0, min DFGLS F and he saisic o es H 0, min DFGLS R. When here is more han one shif in persisence, he coefficien being esed, ρ, will be ime-varying and will be denoed by τ τ ρ i. Supposing here are m shifs, hen under he alernaive hypohesis changes from I(0) o I() imply ha ρ i = 0 if ρi < 0 if and changes from I() o I(0) imply ha ρ i < 0 if ρi = 0. Suppose m = 2 and ha we wan o es if he firs shif is from I() o I(0) while he second shif is from I(0) o I(). Leybourne e al (2007) sugges wha hey call a doublerecursive procedure. Insead of a single rimming scalar, τ, in he single-shif case described τ τ 3

5 Vol., Sepember 2009 above, we now have wo, λ and τ. λ is assumed o lie in (0,) while τ is resriced o lie in ( λ,]. Thus, he GLS regressions described by (2) and (3) will no only have he las ransformed observaions for he single shif case bu he firs observaions will change from y and d o y[ λ T ] and d[ λ T ] so ha he subsequen ransformed observaions become y + δ y, ec. and d[ τt ] + δ d[ τt ], ec, respecively. Thus, he single-shif procedure for [ τt ] [ τt ] esing H 0 is applied recursively o he samples saring from [ λ T ] for a given λ, he -raios of ρ from (7), now denoed as ρ ( λ, τ ), are minimized over τ, o yield (8) min DFGLS( λ) = min ρ ( λ, τ ), λ (0,) τ ( λ,] and hen, hese min DFGLS( λ ) saisics are minimized over λ o yield (9) min DFGLS( λ, τ ) = min min DFGLS( λ) = λ (0,) min min F ρ λ (0,) τ ( λ,] ( λ, τ ) Thus, in he m = 2 case we are considering, λ will be he poin where he series shifs from I() o I(0) and τ will be he poin where i shifs from I(0) o I(). c will now be aken as When m = 2 we end up obaining hree subperiods. In he firs and las periods he ime series is I() while, in he middle period, i is I(0). We may coninue implemening his procedure o he wo I() subperiods o see if hey conain furher subperiods ha are I(0). 3. The Daa In order o compare our resuls wih hose in Erla (2003, 2004), we use he same daa se as in hese wo references. I consiss of Turkish real exchange raes wih he $US and he German DM. The CPIs and WPIs upon which he RERs are based, were obained from he Inernaional Financial Saisics daabase in he case of he US and Germany and, in he Turkish case, hey were downloaded from he Turkish Cenral Bank daabase. The wo exchange rae series were also obained from his daabase. We denoe he naural logs of he resulan four RERs series as LRERUSCPI, LRERUSWPI, LRERDMCPI and LRERDMWPI. These four series are monhly and cover he period The Turkish prices indexes are 987 based and he US and German indexes have been convered o his 4

6 Vol., Sepember 2009 base. No significan seasonaliy was found in any of he series. The US-based series are ploed in Figure and he DM based series in Figure 2. Figure Plos of CPI and WPI Based Real Exch ange Raes w ih The US LRERUS CPI LRERUS WPI Figure 2 Plos of CPI and WPI Based Real Exch ange Raes Wih G erman y LR ER DMCP I LRERDMW PI 4. Empirical Resuls Table conains he resuls of he DFGLS ess applied o he period as a whole. We find ha he DFGLS es indicaes a uni roo in he DM-based series in models wih and 5

7 Vol., Sepember 2009 wihou a rend erm. For he US-based series, however, we find some weak evidence of saionariy for LRERUSCPI and LRERUSWPI in boh models. The KPSS resuls corroborae hese findings for LRERDMCPI for he inercep + rend model and for LRERDMWPI for boh models. For he US-based RERs we find ha here is corroboraion only for LRERUSCPI in he inercep only case. The sronges evidence of he series being I() hroughou appears o come from he KPSS resuls. Coupled wih he DFGLS resuls, i would be safe o say ha he wo DM- Table Uni Roo Tess p DFGLS m KPSS LRERDMCPI Inercep Inercep +Trend ** LRERDMWPI Inercep ** Inercep +Trend ** LRERUSCPI Inercep -.89 * ** Inercep +Trend * ** LRERUSWPI Inercep * Inercep +Trend *** Noes:. The criical values for he DFGLS es are from Ellio, Rohenberg and Sock (996), Table. Inercep Inercep + Trend 0% 5% % 0% 5% % The criical values for he KPSS es are from Kwiaowski e al (992), Table. * Significan a 0 percen Inercep Inercep + Trend 0% 5% % 0% 5% % ** Significan a 5 percen *** Significan a percen based series are I(). The evidence of I(0) for he US-based series is weak and here is almos no corroboraion from he KPSS resuls. Table 2 conains he single-shif-in-persisence resuls. We find ha here are no shifs in persisence for LRERDMCPI, eiher from I(0) o I() or from I() o I(0). On he oher hand, we find shifs from I(0) o I(), in boh models, for LRERDMWPI in

8 Vol., Sepember 2009 Table 2 min DFGLS Tess for a Single Shif in Persisence min DFGLS F Dae min DFGLS R Dae LRERDMCPI Inercep Inercep +Trend LRERDMWPI Inercep ** Inercep +Trend * * LRERUSCPI Inercep * Inercep +Trend * * LRERUSWPI Inercep Inercep +Trend *** Noes: The criical values (T = 200) for he min DFGLS F and min DFGLS R ess are from Leybourne e al (2003), Table. * Significan a 0 percen Inercep Inercep + Trend 0% 5% 0% 5% ** Significan a 5 percen *** Significan a percen (inercep) and (inercep + rend). This series also shows some evidence of a shif from I() o I(0) in , for he inercep + rend case. For LRERUSCPI he shifs are apparenly from I() o I(0) for boh models and on he same dae, and also from I(0) o I() in he inercep + rend case, in , which happens o be he end of he period, implying ha he series is I(0) for he full sample. In he case of LRERUSWPI, here appears o be no shif from I() o I(0) bu a definie shif from I(0) o I() in he inercep + rend case, in Finally, urning o Table 3, we find ha here appears o be saisically significan muliple shifs in all bu wo cases; namely, in LRERDMCPI in he inercep + rend model and in LRERUSCPI in he inercep model. The longes I(0) subperiod is found for LRERDMCPI for he inercep model; o For LRERDMWPI, he I(0) period is a single observaion in (for inercep only) and his corresponds o a single shif from I(0) o I() as was found in Table 2. The I(0) period is a lile longer fro he inercep + rend model bu is sill less han a year. Similar I(0) subperiods are also shor for LRERUSCPI and LRERUSWPI. 7

9 Vol., Sepember 2009 Table 3 min DFGLS Tess for Muliple Shifs in Persisence p min DFGLS(λ,τ) I(0) regime sar I(0) regime end LRERDMCPI Inercep ** Inercep +Trend LRERDMWPI Inercep ** Inercep +Trend ** LRERUSCPI Inercep Inercep +Trend *** LRERUSWPI Inercep ** Inercep +Trend ** Noes: The criical values (T = 200) for he min DFGLS es are from Leybourne e al (2007), Table. Inercep Inercep + Trend 0% 5% % 0% 5% % ** Significan a 5 percen *** Significan a percen In order o compare hese resuls wih hose in Erla (2003, 2004) we have consruced Table 4 from some of he resuls in Tables 3 and 4 in Erla (2003) and Table 2 in Erla (2004). The model and procedures from which hese resuls are obained are briefly described in he Appendix. When srucural shifs in he deerminisic erms are aken ino accoun based on he Augmened Dickey Fuller (ADF) saisic, as in Erla (2003), we find evidence of saionariy in LRERUSCPI when here is a single shif in he deerminisic erms and his is bolsered furher when muliple srucural shifs are aken ino accoun. Evidence of saionariy is also found for LRERDMCPI and LRERDMWPI when here are muliple shifs. We also noe ha he shif dae for LRERUSCPI is 994.0, which is simply a monh away from he single I(0)- o-i() shif in There does no appear o be any oher proximiy in he daes for he srucural shifs and he shifs in persisence. When he alernaive hypohesis is he ESTAR model, as in Erla (2004), hen he nonlinear uni roo es based on GLS derending (GLS-DT) of he series indicaes ha, once again, LRERUSCPI and LRERDMWPI are saionary. 8

10 Vol., Sepember 2009 Table 4 Uni Roo Tes Resuls wih Srucural Shifs and Agains a Saionary ESTAR Model Single Shif Muliple Shif ESTAR p minadf τ p minadf τ τ 2 p GLSDT LRERDMCPI *** LRERDMWPI ** ** LRERUSCPI * *** ** LRERUSWPI Noes:. This able was compiled from Tables 3 and 4 in Erla (2003) and Table 2 in Erla (2004). 2. The criical values for he single srucural shif min ADF es is from Zivo and Andrews (992, Tables 2-4) The criical values for he muliple srucural shif min ADF es is from Ohara (999, Table ) There is only one criical value for he GLS-DT es from Kapeanios and Shin (2002) * Significan a 0 percen ** Significan a 5 percen *** Significan a percen 5. Conclusions. The uni roo ess applied o he full period indicae ha he DM-Based series are nonsaionary bu ha he US-based series show some evidence of saionariy. When shifs in he deerminisic erms are aken ino accoun, we find ha he evidence for saionariy in LRERUSCPI becomes sronger and coninues o be so when esed agains he ESTAR model. In he case of muliple shifs, one now finds he DM-based series o also show saionariy and ha one of hem, LRERDMWPI, also exhibis nonlinear saionariy. 2. We obain furher evidence of saionariy for LRERUSCPI from he es of a single shif in persisence from I(0) o I() as he shif dae is simply he end of he period. Mos single shifs in persisence are observed for movemens from I(0) o I(). This is he case for LRERDMWPI and LRERUSWPI, wih he laer showing raher srong evidence of such a shif. The shif daes, for he inercep + rend case, are quie close for hese wo series. 9

11 Vol., Sepember In he case of muliple persisence shifs, we observe shifs for all series bu he majoriy of hem indicae raher shor I(0) subperiods excep LRERDMCPI. The shif in LRERDMWPI indicaes a single dae as he shif period, which pracically implies an I(0) o I() shif and, as was found using he single shif es, on he same dae. 4. Where does his analysis leave us? Taking shifs ino accoun, eiher in he deerminisic erms or in he naure of persisence, does lead o modificaions of he resuls obained from uni roo ess applied o he full period. However, he shif daes in hese wo ypes of shifs rarely come close, le alone coincide and, in muliple shifs in persisence, he I(0) subperiods are raher shor. Searching for furher I(0) periods in he wo I() periods did no give meaningful resuls. References Busei, F. and A.M.R. Taylor (2004): Tess of Saionariy Agains a Change in Persisence, Journal of Economerics, 23, Chiquiar, D., A.E. Noriega and M. Ramos-Francia (2008): A Time-Series Approach o Tes for a Change in Inflaion Persisence: The Mexican Experience, Applied Economics, 99999:, -9. URL: hp//dx.doi.org/0.080/ Ellio, G., T.J. Rohenberg and J.H. Sock (996): Efficien Tess for a Uni Roo, Economerica, 64, Erla, H. (2003): The Naure of Persisence in Turkish Real Exchange Raes, Emerging Markes Finance and Trade, 39(2), Erla, H. (2004): Uni Roos or Nonlinear Saionariy in Turkish Real Exchange Raes, Applied Economics Leers,, Erla, H. (2008): Are There Shifs in Persisence in he Turkish Inflaion Raes?, Topics in Middle Easern and Norh African Economies, elecronic journal, Volume 0, Middle Eas Economic Associaion and Loyola Universiy Chicago, hp:// Erla, H. and N. Ozdemir (2005): Panel Approaches o Invesigaing he Persisence in Turkish Real Exchange Raes, Working Paper, Deparmen of Economics, Middle Eas Technical Universiy. Franses, P.H. and N. Haldrup (994): The Effecs of Addiive Ouliers on Tess for Uni Roos and Coinegraion, Journal of Business and Economic Saisics, 2(4),

12 Vol., Sepember 2009 Halunga, A., D.R. Osborn and M. Sensier (2008): Changes in he Order of Inegraion of US and UK Inflaion, Economics Leers, doi:0.06/j.econle Kim, J.Y. (2000): Deecion of Change in Persisence of a Linear Time Series, Journal of Economerics, 95, Kwiaowski, D., P.C.B. Phillips, P. Schmid and Y. Shin (992): Tesing he Null Hypohesis of Saionariy Agains he Alernaive of a Uni roo. How Sure are we ha Economic Time Series Have a Uni Roo?, Journal of Economerics, 54, Leybourne, S., T.H. Kim, V. Smih and P. Newbold (2003): Tes of a Change in Persisence Agains he Null of Difference-Saionariy, Economerics Journal, 6, Leybourne, S., T.H. Kim and A.M.R. Taylor (2007): Deecing Muliple Changes in Persisence, Sudies in Nonlinear Dynamics and Economerics, (3), -3. Newey, W. and K. Wes (987): A Simple, Posiive Semi-Definie, Heeroscedasiciy and Auocorrelaion Consisen Covariance Marix, Economerica, 55, Newey, W. and K. Wes (994): Auomaic Lag Selecion in Covariance Marix Esimaion, Review of Economic Sudies, 6, Ohara, H.I. (999): A Uni Roo Tes wih Muliple Trend Breaks: A Theory wih an Applicaion o U.S. and Japanese Macroeconomic Time Series, Japanese Economic Review, 50(3), Yoon, G. (2008): Furher Evidence on Purchasing Power Pariy Over Two Cenuries wih Muliple Changes in Persisence, Applied Economics Leers, 5, Zivo, E. and D.W.K. Andrews (992): Furher Evidence on he Grea Crash, he Oil Price Shock, and he Uni Roo Hypohesis, Journal of Business and Economic Saisics, 0(3), Appendix The resuls for he uni roo ess involving a single shif in he deerminisic erms were obained from (A) y = β + β + ρ y + α DU ( τ ) + δ DT ( τ ) + γ y + ψ D( T ) + ε 0 i i ri aor i i= r= i= 0 p m p+ where

13 Vol., Sepember 2009 DU ( τ ) = 0 for =,, τ = for = τ +,, T DT ( τ ) = 0 for =,, τ = τ for = τ +,, T D( T ) = for = T ao ao = 0 oherwise The firs wo dummies accoun for he shifs in he inercep and rend, respecively. τ indicaes he shif poin and is deermined endogenously using a sequenial procedure due o Zivo and Andrews (992). The es saisic is he minimum value of he sequenially obained -raio of ρ, which we call min ADF, and ˆ τ corresponds o he shif poin for which min ADF is obained. The hird dummy variable is included o accoun for ouliers in he daa. The way i is inroduced in (A) is due o Franses and Haldrup (994) who show ha he disribuion of he uni roo es is no effeced when his is done. The resuls for he uni roo es involving, say, n, muliple shifs in he deerminisic erms were obained from n (A) y = β0 + β + ρ y + αidu ( τ i ) + δidt ( τ i ) + γ i y i + ε i= i= i= n p The procedure is again sequenial wih he ˆi τ indicaing he shif poins for which min ADF is obained. The deails of his procedure may be found, e.g., in Ohara (999). The resuls for he uni roo ess agains an ESTAR model are based on esimaing (A3) p 3 ϕ γ i i ε i= uˆ = uˆ + uˆ + where u ˆ is he GLS-derended value of y, as described in he main ex above, and he es saisic he sequenially obained -raio of ϕ. The rend equaion conains boh an inercep and a rend erm and c is now aken o be For he deails of his procedure see, e.g., Erla (2004). 2

14 Vol., Sepember