Department of Economics Working Paper

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1 Deparmen of Economics Working Paper Number 3-04 February 03 Forecasing Exchange Raes Ou-of-Sample wih Panel Mehods and Real-ime Daa Onur Ince Appalachian Sae Universiy Deparmen of Economics Appalachian Sae Universiy Boone, NC 8608 Phone: (88) 6-63 Fax: (88)

2 Forecasing Exchange Raes Ou-of-Sample wih Panel Mehods and Real-ime Daa * Onur Ince Absrac his paper evaluaes ou-of-sample exchange rae forecasing wih Purchasing Power Pariy (PPP) and aylor rule fundamenals for 9 OECD counries vis-à-vis he U.S. dollar over he period from 973:Q o 009:Q a shor and long horizons. In conras wih previous work, which repors forecass using revised daa, I consruc a quarerly real-ime daase ha incorporaes only he informaion available o marke paricipans when he forecass are made. Using boosrapped ouof-sample es saisics, he exchange rae model wih aylor rule fundamenals performs beer a he one-quarer horizon and panel esimaion is no able o improve is performance. he PPP model, however, forecass beer a he 6-quarer horizon and is performance increases in panel framework. he resuls are in accord wih previous research on long-run PPP and aylor rule models. Keywords: Exchange Rae Forecasing, aylor Rules, Real-ime Daa, Ou-of-Sample es Saisics JEL Classificaion: C3, C53, E3, E5, F3, F47 * I hank David Papell, Chris Murray, Sebnem Kalemli-Ozcan, Nelson Mark, Luz Kilian, Dean Croushore, anya Molodsova, James Morley, Claude Lopez, Mark Srazicich and Vania Savrakeva for helpful commens and discussions. Deparmen of Economics, Appalachian Sae Universiy, Boone, NC el: + (88) inceo@appsae.edu

3 . Inroducion Following he collapse of he Breon-Woods sysem, he inroducion of flexible exchange rae regimes araced much aenion o he area of inernaional macroeconomics in an aemp o explain exchange rae behavior. heoreical papers such as Dornbusch (976), which exended he Mundell-Fleming model o incorporae raional expecaions and sicky prices and inroduced overshooing as an explanaion for high exchange rae variabiliy, and empirical work such as Frankel (979), which found success in esimaing empirical exchange rae models, inspired research in his field by poining ou he abiliy of macroeconomic models o explain exchange rae variabiliy. he seminal papers by Meese and Rogoff (983a, 983b) pu an end o he amosphere of opimism in exchange rae economics by concluding ha empirical exchange rae models do no perform beer han a random walk model ou-of-sample. heir finding is sill hard o overurn more han wo decades laer. Cheung, Chinn, and Pascual (005), for example, examine ou-of-sample performance of he ineres rae pariy, moneary, produciviy-based and behavioral exchange rae models and conclude ha none of he models consisenly ouperforms he random walk a any horizon. Are empirical exchange rae models really as bad as we hink? Recen sudies have found evidence of exchange rae predicabiliy using eiher panels or innovaive modeling approaches. Engel, Mark, and Wes (007) use panel specificaions of he moneary, Purchasing Power Pariy (PPP) and aylor (993) rule models, Rossi (006) uses he moneary model in he presence of a srucural break, Gourinchas and Rey (007) use an exernal balance model, Molodsova and Papell (009) use a heerogeneous symmeric aylor rule model wih smoohing, and Cerra and Saxena (008) use a broad panel specificaion of he moneary model.

4 A common problem wih he papers discussed above is heir reliance on ex-pos revised daa for he forecasing analysis. Alhough i seems obvious ha ou-of-sample exchange rae forecasing should be evaluaed using real-ime daa, which reflecs informaion available o marke paricipans, i is sill very rare in he exchange rae lieraure. Almos all exising sudies on exchange rae forecasing exploi revised daa which conains fuure informaion, due o revisions and addiions of new daa, ha is no available o eiher policymakers or marke paricipans. Ou-of-sample forecas evaluaions based on ex-pos revised daa yield misleading inference abou he exchange rae models, and informaion problems of marke agens are no accouned in he analysis. Meese and Rogoff (983a) use boh ex-pos revised daa and acual realized values of fuure explanaory variables o es he forecasing abiliy of srucural models. As Rossi (005) emphasizes, o forecas economic variables which are driven by persisen and permanen shocks, he economerician migh measure agen s probabiliy disribuion poorly by using acual realized values of fuure explanaory variables. o forecas exchange raes, which are primarily driven by expecaions, real-ime daa would be more advanageous due o capuring he informaion se of marke paricipans as closely as possible in conras o ex-pos revised daa and acual realized values of fuure explanaory variables. he firs paper o use real-ime daa o evaluae nominal exchange rae predicabiliy is Faus, Rogers and Wrigh (003). Examining he predicive abiliy of Mark s (995) moneary model using real-ime daa for Japan, Germany, Swizerland and Canada vis-à-vis he U.S, hey repor ha he models consisenly perform beer using real-ime daa han fully revised daa. However, none of he models perform beer han he random walk model. More recenly, Molodsova, Nikolsko- Rzhevskyy, and Papell (008, 0) find evidence of predicabiliy wih aylor rule fundamenals using real-ime daa for he Deuschmark/dollar and Euro/dollar exchange raes. Molodsova, Nikolsko-Rzhevskyy, and Papell (008) find evidence of ou-of-sample predicabiliy wih aylor

5 rule fundamenals only using real-ime daa as opposed o ex-pos revised daa and confirm he conclusion of Faus, Rogers and Wrigh (003) ha exchange rae dynamics migh reac more o he marke s conemporaneous beliefs abou he fundamenals han rue underlying fundamenals. here are no sudies on exchange rae forecasing wih real-ime daa for a reasonably large number of counries over he pos Breon Woods period because of he limied availabiliy of realime daa for counries oher han he U.S. In his paper, I consruc a quarerly real-ime daase ha conains 9 OECD counries (Ausralia, Canada, France, Germany, Ialy, Japan, Neherlands, Sweden, he Unied Kingdom) vis-à-vis he U.S. dollar over he period from 973:Q o 009:Q o evaluae boh shor and long-horizon ou-of-sample forecasing performance of he linear exchange models using PPP and aylor rule fundamenals. I consruc real-ime price and inflaion daa from he Inernaional Financial Saisics (IFS) counry pages using he consumer price index (CPI), and esimae real-ime oupu gaps using he indusrial producion index. A problem associaed wih recen papers presening evidence of exchange rae predicabiliy is ha hese sudies employ only a es developed by Clark and Wes (006) (henceforh, CW es). he CW saisic adjuss he Diebold and Mariano (995) and Wes (996) (henceforh, DMW es) saisic o correc for size disorions. If wo models are non-nesed, he DMW es is appropriae o compare he mean square predicion errors (MSPE s). Applying DMW ess o compare he MSPE s of wo nesed models, however, leads o non-normal es saisics, and using sandard normal criical values usually resuls in very poorly sized ess wih far oo few rejecions of he null. his is a problem for ou-of-sample exchange rae forecasing because, since he null is a random walk, all ess wih srucural models are nesed. While he CW adjusmen produces a es wih correc size, Rogoff and Savrakeva (008) argue ha i canno evaluae forecasing performance because i does no es he null hypohesis of equal MSPE s of he random walk and he srucural model. In order 3

6 o saisfy he condiions for a good exchange rae forecasing model, empirical sudies need o presen evidence ha he exchange rae model has MSPE ha is significanly smaller han ha of he random walk model, which canno be done solely wih CW es in he case of forecasing bias. hey advocae he use of DMW ess wih boosrapped criical values o produce correcly sized ess. Engel, Mark and Wes (007) find ha panel error-correcion exchange rae models wih PPP fundamenals are able o produce large improvemens in ou-of-sample forecasing a longer horizons. Because hey use ex-pos revised daa, he exchange rae models in heir sudy conain fuure informaion ha was no available o marke paricipans. Forecass ha are produced using fuure news in he informaion se of he linear model canno be evaluaed wihin an ou-of-sample forecasing exercise. Forecass wih real-ime daa, however, do no conain any unrealized fuure informaion in he informaion se of he linear model, and hus are a rue ou-of-sample forecas. Molodsova and Papell (009) find evidence of ou-of-sample predicabiliy wih he aylor model a shor horizon using single-equaion esimaion. Alhough hey use ex-pos revised daa o calculae inflaion, hey esimae oupu gaps wih quasi-real-ime daa in order o capure he informaion available o cenral banks as closely as possible. Quasi-real-ime daa is consruced wih ex-pos revised daa, bu he rends do no conain fuure observaions and he daa poins are used wih a lag for esimaion. While quasi-real-ime daa does no conain fuure observaions, i capures revisions which are no available o marke paricipans. herefore, forecasing exercises wih quasireal ime daa are also no rue ou-of-sample forecass. his paper evaluaes ou-of-sample forecasing wih PPP and aylor rule fundamenals using my newly consruced real-ime daase for 9 OECD counries vis-à-vis he U.S. dollar wih single- Rogoff and Savrakeva (008) consider he scale bias where he observed value is over- or under prediced by a cerain percen. Engel, Mark and Wes (007) use moneary and aylor Rule models as well. However, he ou-of-sample predicabiliy of he PPP model dominaes he oher wo models a longer horizons. 4

7 equaion and panel error-correcion frameworks based on boosrapped DMW and CW es saisics. 3 he ou-of-sample forecas resuls wih PPP fundamenals confirm he findings in Engel, Mark and Wes (007) ha he predicabiliy of he PPP model increases wih he panel specificaion and he PPP model has higher predicive power a long horizons. Evidence of long-erm predicabiliy wih he PPP model is found for 6 ou of 9 counries wih he CW es and 5 ou of 9 counries wih he DMW es agains he drifless random walk. he exchange rae model wih PPP fundamenals using panel daa ouperforms he drifless random walk for all he counries in he sample a he 6-quarer horizon regardless of which es saisic is used. he predicabiliy wih aylor rule fundamenals, in conras, is greaes wih he singleequaion specificaion, and he aylor rule model has higher forecasing power a he shor horizon as indicaed in Molodsova and Papell (009). Evidence of shor-erm predicabiliy wih aylor rule model is found for ou of 9 counries wih boh es saisics agains he drifless random walk wih single-equaion esimaion. he exchange rae model wih aylor rule fundamenals using a single-equaion framework ouperforms he drifless random walk for 4 ou of 9 counries wih he CW es and 5 ou of 9 counries wih he DMW es a he one-quarer horizon. he resuls are in accord wih previous research on PPP and aylor rule models. he PPP model works bes wih he panel specificaion a he 6-quarer horizon. Research on PPP shows no evidence of shor-run PPP, and Papell (997) finds considerably more suppor for long-run PPP wih panel mehods han wih univariae ess. Since he persisence of deviaions from PPP is relaively homogeneous across counries, panels help o reduce he noise and increase he forecasing power of he PPP model. 3 I would like o evaluae he ou-of-sample forecasing abiliy of he moneary model. However, i is no possible o obain a coheren series of real-ime money supply for all he counries. 5

8 Imposing idenical moneary rules across all counries in a panel srucure does no produce successful ou-of-sample exchange rae forecass, and he aylor rule model performs he bes wih single-equaion esimaion a he one-quarer horizon. Moneary policy rules implemened by cenral banks since he early-o-mid 980s se ineres raes for relaively shor periods and differ across counries. Clarida, Gali and Gerler (998) provide empirical evidence of how ineres rae reacion funcions differ among OECD counries. Gerdesmeier, Mongelli and Roffia (007) compare he moneary policies implemened by he Eurosysem, he Fed and he Bank of Japan, and also find differences in esimaed aylor rule coefficiens. Since cenral banks arge shor-erm nominal ineres raes and, in general, follow differen ineres rae seing rules, higher forecasing power of he aylor rule model in a single-equaion framework a he shor horizon is plausible.. Daa he real-ime quarerly daa used in his sudy covers he pos-breon Woods period from 973:Q o 009:Q for 0 OECD counries: Ausralia, Canada, France, Germany, Ialy, Japan, Neherlands, Sweden, he Unied Kingdom, and he Unied Saes. he daase is consruced from he counry ables of IMF's Inernaional Financial Saisics (IFS) books, regularly published on a monhly basis since 948. he real-ime daa has he usual riangular forma wih vinage daes on he horizonal axis and calendar daes for each observaion on he verical axis. he erm vinage corresponds o he dae when a ime series of daa becomes available o marke paricipans. here is ypically a one-quarer lag beween he vinage dae and he laes daa poin a ha vinage. he realime daa a ime acually represens daa hrough period -. For each subsequen quarer, he new vinage includes boh newly released daa and revisions o he hisorical daa. he firs vinage in he real-ime daase is for 973:Q and he daa series in each vinage sar from 958:Q. 6

9 Seasonally adjused indusrial producion index (IFS line 66c) is used as a measure of counries income, since quarerly GDP daa are no consisenly published and no available for some counries for much of he ime span. he price level in he economy is measured by he consumer price index (CPI) (IFS line 64) and seasonally adjused by applying a one-sided moving average of he curren observaion and 3-lagged values. he inflaion rae is he annual inflaion rae calculaed using he CPI over he previous 4 quarers. he oupu gap is calculaed as he percenage deviaion of acual oupu from a Hodrick- Presco (997) (HP) rend. 4 For he firs vinage, he rend is calculaed using he daa for 958:Q- 97:Q4, for he second vinage, i is calculaed using he daa for 958:Q-973:Q, and so on. As wih any mehod ha uses a one-sided filer, he esimaions migh be subjec o end-of-sample uncerainy which is exacerbaed wih real-ime daa, consising of he las observaions in each daa vinage. o ake ino accoun he end-of-sample uncerainy in oupu gap esimaion using real-ime daa, I follow Wason s (007) mehod using an AR (8) model o forecas he oupu growh - quarers ahead before calculaing he rend. 5 6 he release daes for real-ime variables vary across counries and he iming of daa release is very crucial for forecas evaluaion. For example, he indusrial producion index for Germany is released approximaely 38 days afer he end of he reference monh, while he U.S. indusrial producion index is released from o 8 days afer he reference monh. o minimize he ime beween he release of he daa and he sar of he forecas, he quarerly real-ime daase is 4 he smoohness parameer for HP filer is 600 wih quarerly daa. 5 While Wason (007) also suggess o backcas he series, he series in each daa vinage exends hrough 958:Q, which is long enough o remove he disorions in he beginning of he sample creaed by a onesided filer. 6 HP Filer is seleced as he mos commonly used filer in he lieraure. Ince and Papell (0) also provide he evidence ha correlaions beween real-ime and ex-pos oupu gap esimaes wih differen filers for he same counries are similar. 7

10 consruced using he daa available in second monh of each quarer. Nominal exchange raes are aken from he IFS CD-ROM (IFS line ae) defined as he end-of-period U.S. dollar price of a uni of foreign currency. 7 Exchange raes for he Euro area afer 998 are normalized by fixing foreign currency per dollar o he Euro/Dollar rae as in Engel, Mark and Wes (007). he series of real-ime inflaion and oupu gaps are consruced from he diagonal elemens of he real-ime daa marix and conain only he laes available observaions a each period. For each counry, his daa represens a vecor of quarerly observaions from 973:Q o 009:Q, hus resuling in 45 observaions. able presens summary saisics for real-ime and revised inflaion and oupu gap for each counry in he sample. wo observaions are apparen: Firs, he differences beween average real-ime and revised inflaion raes are very close as opposed o he differences beween average real-ime and revised oupu gaps. he differences beween he average real-ime and revised inflaion varies from 0.00 percenage poins (for Japan) o percenage poins (for U.K.), while he difference beween he average real-ime and revised oupu gap varies from 0.75 percenage poins (for Sweden) o.34 percenage poins (for Ialy). Second, average real-ime oupu gaps are negaive for all he counries, which implies ha he oupu gaps are being revised upwards on average. According o he summary saics in able, policy recommendaions based on real-ime and revised daa may differ subsanially wih mos of he differences coming from he revisions in oupu gaps. 7 Since quarerly averaged exchange raes migh cause serial correlaion for exchange rae changes, I use he end-of-period exchange raes. 8

11 3. Mehodology he economeric analysis in his sudy is based on panel esimaion of he predicive regression, () where and. 8 In he predicive regression, denoes he naural log of he nominal exchange rae, measured as he domesic price of U.S. dollar (which serves as base currency) for counry i a ime. he deviaion of he exchange rae from is equilibrium value is denoed by, and sands for he fundamenal in he exchange rae model ha is deermined eiher by PPP or aylor rule. he forecas horizon, akes on he value of for shor-horizon and 6 for long-horizon regressions. he regression error,, conains unobserved componens, where is he individual specific effec, is he ime-specific effec, and is he residual idiosyncraic error. 3. PPP Fundamenals Numerous sudies ha es for uni roos in real exchange raes using panels of indusrialized counries have found srong rejecions in he pos-973 period. he srong rejecions of uni roos encourage esing he forecasing power of exchange rae models wih PPP fundamenals. Recenly, Engel, Mark and Wes (007) have shown ha PPP fundamenals forecas well a long horizons. Rogoff and Savrakeva (008) also conclude ha PPP specificaion performs he bes ou of all he specificaions hey ry. 9 Under PPP fundamenals, () 8 For single-equaion framework, ime-specific effec is zero. 9 Rogoff and Savrakeva (008) compare he forecasing power of he moneary model, he aylor rule model and a srucural model based on he Backus-Smih opimal risk sharing condiion. 9

12 where is he log of he U.S. price level, and is he log of he price level of counry i. I use he real-ime CPI o measure of he naional price level. Subsiuing PPP fundamenals () ino equaion (), I use he resulan equaion for forecasing. 3. aylor Rule Fundamenals When cenral banks se he ineres rae according o he aylor rule, he linkage beween he exchange rae and a se of fundamenals can be examined. According o aylor (993), cenral banks se he moneary policy as: (3) where is he arge for he shor-erm nominal ineres rae, is he inflaion rae, is he arge level of inflaion, poenial level, and is he oupu gap, or percen deviaion of acual oupu from an esimae of is is he equilibrium level of he real ineres rae. I is assumed ha he arge for he shor-erm nominal ineres rae is achieved wihin he period, so ha here is no disincion beween he acual and arge nominal ineres rae. he parameers and in equaion (3) can be combined ino one consan erm and we have: (4) where. If he cenral bank ses he arge he level of exchange rae o make PPP hold, equaion (4) becomes: (5) where is he real exchange rae. he cenral bank increases (decreases) he nominal ineres raes if he exchange rae depreciaes (appreciaes) from is equilibrium value under PPP assumpion in he aylor rule. Allowing he ineres rae o achieve is arge level wihin he period: 0 (6)

13 and is he nominal ineres rae. Subracing he aylor rule equaion for he foreign counry from ha for he base counry, he U.S. (denoed by 0 ), equaion (6) becomes: (7) Imposing he uncovered ineres rae pariy condiion, he expeced change in nominal exchange raes is equal o he ineres differenial: (8) Molodsova and Papell (009) refer o he specificaion (8) as homogenous asymmeric aylor rule wih no smoohing. hey esimae he parameers and in equaion (8) counry-bycounry in a rolling regression framework. Raher han esimaing he coefficiens, I follow he approach developed by Engel, Mark and Wes (007), who posi a aylor rule such ha =.5, =0. and =0.. Imposing fixed coefficiens for all he counries is preferable for wo reasons. Firs, increasing he number of parameers o be esimaed in a panel may reduce he efficiency of forecass and bring noise o he sysem. Second, his approach provides a beer comparison of forecass obained wih real-ime daa and hose obained wih ex-pos revised daa in Engel, Mark, and Wes (007). he aylor rule fundamenals o be used in forecasing equaion () become: (9) I is well known in he lieraure ha he uncovered ineres rae pariy condiion does no hold in he shor run. Wih an error correcion specificaion, he exchange rae forecasing model,, is used o generae ou-of-sample forecass boh a he shorhorizon (where k=) and he long-horizon (where k=6).

14 4. Ou-of-Sample Forecasing 4. Esimaion o produce ou-of-sample forecass, he sample has o be spli ino wo componens, insample and ou-of-sample. he in-sample componen is updaed recursively o esimae he parameers in equaion () wihin boh single-equaion and panel frameworks. For single equaion esimaion, he parameers (consan and β) are esimaed counry-by-counry wih OLS. For panel esimaion, he parameers (counry-specific effecs, ime specific effecs, and β) are esimaed by leas squares dummy variable (LSDV) mehod. Following Mark and Sul (00) and Engel, Mark and Wes (007), he predicive regression is esimaed hrough 98:Q4. For k= (k=6), he predicive regression is used o forecas -sepahead (6-sep-ahead) exchange rae reurns in 983:Q (986:Q4). hen, he in-sample componen is updaed recursively by exending he sample up o 983:Q and equaion () is re-esimaed a each sep. For k= (k=6), he predicive regression is used o forecas -sep-ahead (6-sep-ahead) exchange rae reurns in 983:Q (987:Q), and he loop coninues unil he las observaion. A he end, 05 forecass for k= and 90 overlapping forecass for k=6 are derived wih boh PPP and aylor rule fundamenals. One crucial poin for muli-period ahead forecass in he panel framework is ha he ime effec needs o be forecased. For k-period ahead forecass, he ime effec in period +k is calculaed by aking he recursive mean of he ime effec unil period, such as. 4. Comparisons of Forecass Based on MSPE o compare he ou-of-sample forecasing abiliy of he wo nesed models, his sudy focuses on he minimum mean-squared predicion error (MSPE) approach, which became dominan

15 in he lieraure afer Meese and Rogoff (983a, 983b). Forecass of linear and random walk models are calculaed as: Linear Model: Drifless Random Walk: (0) Random Walk wih Drif: where is he esimaed drif erm. 0 aking he difference beween acual and prediced values of exchange raes gives he predicion error. he MSPE approach selecs a model which has significanly smaller MSPE han he random walk wih or wihou he drif. 4.3 Ou-of-Sample es Saisics o measure he relaive forecas accuracy of he linear model agains he drifless random walk and he random walk wih drif, I use wo alernaive es saisics: he Diebold-Mariano and Wes (DMW) and he Clark-Wes (CW) saisics he Diebold-Mariano and Wes (DMW) es Suppose ha a maringale difference process and a linear model are given as: Model : y e Model : y X ' e where E ( e ) 0 where he dependen variable is he change in he exchange rae. Under he null hypohesis, populaion parameer 0 and exchange rae follows a random walk. For simpliciy le us concenrae on one-sep-ahead forecasing. Assume ha sample size is +; he firs R observaions are used for esimaion and P is equal o he number of forecass. So we have, +=R+P, where 0 he recursive mean of he ime effec in parenhesis for he linear model is removed in he single-equaion case. 3

16 +=45, R=40 and P=05 for one-sep-ahead forecasing. Informaion prior o is used o forecas for period =R, R+, R+,,. he firs forecas is for he period R+ and he final forecas is for he period +. he esimaed forecass for he random walk and he srucural model are 0 and X ' and is he regression esimae of. Afer esimaing he forecass, he respecive predicion errors for he models are e, y and e, y X. hus, he sample MSPE s of he wo models become: y P P and P ( y X ) () P Diebold and Mariano (995) and Wes (996) consruc a -ype saisics which is assumed o be asympoically normal and he populaion MSPE s are equal under he null. Defining he following equaions, f e, e, f P f P () he DMW es saisic is V P P ( f f ) f DMW (3) P V he asympoic DMW es works fine wih non-nesed models. However, he size properies of he asympoic DMW es have been widely criicized for nesed models. Clark and McCracken (00, 005) and McCracken (007) show ha he limiing disribuion of he DMW es for nesed models under he rue null is no sandard normal. Undersized DMW ess cause oo few rejecions 4

17 5 of he null and may miss he saisical significance of he linear exchange rae model agains he random walk he Clark- Wes (CW) es Clark and Wes (006, 007) show ha he sample difference beween he MSPE s of wo nesed models in DMW es is biased downward from zero in favor of he random walk. P P P P P X P X y P X y P y P f P ) ( ) ( (4) Under he null hypohesis, he exchange rae follows a random walk, such ha,, y e e. Since he independen variables are no correlaed wih he disurbance erm, he firs erm in equaion (4) is equal o zero. Clark and Wes (006, 007) show ha P X P 0 ) ( because esimaing he parameers of he alernaive model under he rue null (which are zero) brings noise ino he forecasing process. Clark and Wes (006) recommend an adjused DMW saisic ha adjuss for he negaive bias in he difference beween he wo MSPE. Defining he adjusmens as follows, ) (,, X e e ADJ f P P ADJ ADJ X P f P f ) ( (5) P ADJ ADJ f f P V ) ( P X y is zero, because he equaliy of,, e e under null hypohesis suggess ha ), ( ), ( ) ( X e E X e E X y E. Since 0 ), ( X e E by assumpion, we have 0 ), ( ) ( ), ( X e E E X e E.

18 he CW es saisic is ADJ f CW (6) ADJ P V he CW es has become one he mos popular ou-of-sample es saisic in he exchange rae lieraure. However, Rogoff and Savrakeva (008) show ha he CW es canno always be inerpreed as a minimum MSPE es as he DMW es. heir sudy presens a proof ha in he presence of forecas bias, he null hypohesis of he CW and he DMW ess are no necessarily he same. If one can rejec he null of CW es, he rue naure of exchange rae does no follow a random walk. Neverheless, even if he rue model follows some oher model raher han a random walk, one can sill apply he DMW saisics o es wheher he random walk and he srucural model have equal MSPEs. 4.4 Boosrapping Ou-of-Sample es Saisics Size disorions of he DMW es in small samples can be reduced by boosrapping he finie sample disribuion of he es saisics. Kilian (999) sae ha unlike asympoic criical values, correcly specified (mainaining he coinegraion beween he exchange rae and fundamenals under he null hypohesis) boosrap criical values adap for he increase in he dispersion of he finie-sample disribuion by iself. Kilian (999) also sugges ha he boosrap is appropriae for muli-period ahead forecass. Based on simulaion evidence, Li and Maddala (997) and Li (000) also indicae boosrapped ess have smaller size disorions and higher es power han asympoic ess in coinegraing sysems. Howbei, Berkowiz and Kilian (000) emphasize he imporance of boosrapping ype implemened o preserve coinegraing relaionships in he daa. In he presence of he scale bias, he null hypohesis of he CW and he DMW ess are differen. 6

19 hey argue ha coinegraion appears o be a parameric noion and parameric boosraps are more accurae han non-parameric ones. Mark and Sul (00) and Rogoff and Savrakeva (008) apply boosrapped ou-of-sample ess o deec forecasing abiliy of linear exchange rae models agains random walk in a panel framework. he boosrap mehods are similar in boh sudies. Mark and Sul (00) implemen parameric boosrap and esimae error correcion equaions wih seemingly unrelaed regressions (SURs); however, Rogoff and Savrakeva (008) use semi-parameric boosrap and esimae error correcion equaions wih counry specific OLS regressions. Having insignifican boosrapped DMW es saisics in cerain cases, as opposed o highly significan asympoic CW es, Rogoff and Savrakeva (008) criicize he asympoic CW es o be oversized and has less power han he boosrapped DMW es in he presence of forecas bias. 3 Oversized asympoic CW es would cause oo many rejecions of he null hypohesis ha exchange rae does no follow a random walk. I may deec spurious saisical significance and favor he alernaive, srucural exchange rae model. In his paper, I evaluae he ou-of-sample predicive abiliy of exchange rae fundamenals based on boosrapped criical values for CW and DMW ess. Rogoff and Savrakeva s (008) mehod of boosrap (which imposes coinegraion resricion beween he exchange rae and he fundamenals) for each counry is used in his sudy as follows: s (8) z d l z js j jz j j j u 3 In he echnical appendix of Clark and Wes (007), he unadjused power of he boosrapped DMW es is higher han ha of he asympoic CW es for recursive regressions wih one-sep-ahead forecass. 7

20 where s is he nominal exchange rae and z is he deviaion of exchange rae from fundamenal as defined in equaion (). s s s k and z z z k where k is he forecas horizon, is a consan and is a rend. o conrol for auocorrelaion in he error correcion equaion (ECE) lags of s and z are included. Akaike s informaion crierion is used for each counry o deermine he opimum number of d and l and o figure ou wheher o include a consan or a rend or boh in he ECE. he sum of coefficiens on lags of z is resriced o. s and z simulaed recursively afer re-sampling he esimaed residuals ( and u ). o reduce he bias caused by he iniial values of he recursion, he firs 00 observaions are hrown away and a new sample is creaed. Applying he esimaion procedure again, es saisics are calculaed wih he pseudo-daa. his process is repeaed 000 imes and semi-parameric boosrap disribuion is derived. Since he ess considered are one-sided ess, he p-values of DMW and CW ess are he percenage of he boosrapped disribuion above he esimaed es saisic using he realized daa. are 5. Empirical Resuls his secion compares one- and 6-quarer-ahead ou-of-sample performance of he linear exchange rae model wih PPP and aylor rule fundamenals o ha of he random walk model wih and wihou drif using a newly consruced real-ime daase. he ables repor he MSPE raio, he raio of he MSPE of he srucural model o ha of he random walk, and he DMW and CW es saisics wih heir respecive boosrapped p-values. A significan DMW or CW es saisic implies ha he linear exchange rae model ouperforms he random walk wih or wihou he drif ou-ofsample. 8

21 5. PPP Fundamenals One-quarer-ahead single-equaion forecasing resuls wih he PPP model are presened in able. No evidence of ou-of-sample predicabiliy is found wih he PPP model agains he drifless random walk for any exchange rae. he ou-of-sample performance of he PPP model improves agains he random walk wih drif. Shor-erm predicabiliy is found for Canada and Sweden wih he CW es and for 4 counries (Canada, Germany, Japan, and Neherlands) wih he DMW es a he one-quarer horizon. Panel one-quarer-ahead forecass using PPP fundamenals in able 3 are only slighly beer han single-equaion forecass in able. he exchange rae model wih PPP fundamenals using panel daa significanly ouperforms he drifless random walk only for Japan. he evidence of predicabiliy of he PPP model wih panel esimaion, jus like in he single-equaion case, increases agains he random walk wih drif a one-quarer horizon. Shor-erm predicabiliy is found for 5 ou of 9 counries (Ausralia, Canada, Germany, Japan, and Sweden) wih he CW es and for Ausralia and Sweden wih he DMW es. he low predicive power of he PPP model a he one-quarer horizon using panel and single-equaion esimaions is no surprising. Exising sudies concerning he half-life of PPP, he expeced number of years for a PPP deviaion o decay by 50%, find half-lives of around.5 years. 4 Accouning for he slow adjusmen of real exchange raes in advanced economies, one would expec he predicive abiliy of PPP model o be low a shor horizons. Sixeen-quarer-ahead ou-of-sample forecass wih he PPP model and single-equaion esimaion are presened in able 4. he evidence of long-erm predicabiliy is sronger compared o one-quarer-ahead forecass using he single-equaion framework wih rejecions of he random 4 See Wu (996), Papell (997, 00), Murray and Papell (00), Choi, Mark and Sul (006) for deails concerning he half-lives of PPP deviaions. 9

22 walk null found for 4 counries (France, Germany, Neherlands, and Sweden) wih he CW es. More evidence of long-erm predicabiliy is found agains he random walk wih drif. Ou-ofsample exchange rae predicabiliy is found for 7 ou of 9 counries (Ausralia, Canada, France, Germany, Japan, Neherlands, and Sweden) wih he CW es and for 3 ou of 9 counries (Ausralia, Canada and Neherlands) wih he DMW es. he ou-of-sample predicabiliy of he PPP model wih a single-equaion framework is clearly improved a he l6-quarer horizon compared o onequarer horizon. he PPP model performs bes wih he panel specificaion a he 6-quarer horizon. As repored in able 5, he evidence of predicabiliy is found for 6 ou of 9 counries (Canada, France, Germany, Japan, Neherlands, and Sweden) wih he CW es, and for 5 ou of 9 counries (Canada, Germany, Japan, Neherlands and Sweden) wih he DMW es. Panel forecass a long horizon are even more sriking agains he random walk wih drif. Ou-of-sample predicabiliy is found for all he counries in he sample regardless of which es saisic is used. Because he persisence of deviaion from PPP across counries is relaively homogenous, panel esimaion becomes more efficien and he predicabiliy of he panel exchange rae model wih PPP fundamenals is much higher han he single-equaion framework. 5. aylor Rule Fundamenals Following Engel, Mark, and Wes (007), predicive regressions using aylor rule model are esimaed where he coefficiens on inflaion, oupu gap, and real exchange rae are fixed a cerain values. One-quarer-ahead single-equaion forecass wih aylor rule are repored in able 6. Evidence of shor-erm predicabiliy is found only for Japan. he exchange rae model wih aylor fundamenals works much beer agains he random walk wih drif. Evidence of ou-of-sample predicabiliy found for 4 ou of 9 counries (Ausralia, Canada, Japan, and Sweden) wih he CW 0

23 es and for 5 ou of 9 counries (Ausralia, Canada, Japan, Neherlands, and Sweden) wih he DMW es. Comparing ables 6 and 7, he performance of aylor rules does no improve in a panel framework, as incorporaing differen moneary policies operaed by cenral banks in a panel framework does no help o forecas exchange raes ou-of-sample. 5 One-quarer ahead forecasing resuls for he aylor rule model wih a panel framework are repored in able 7. No evidence of ou-of-sample predicabiliy is found agains he drifless random walk regardless of which es saisic is used. he resuls are sronger agains he random walk wih drif. Evidence of predicabiliy is found for 4 ou of 9 counries (Ausralia, Canada, Japan, and Sweden) wih he CW es and for 5 ou of 9 counries (Ausralia, Canada, Germany, Japan, and Sweden) wih he DMW es. able 8 presens 6-quarer-ahead single-equaion forecass using he aylor rule model. Evidence of long-erm predicabiliy is found only for Germany wih CW es agains he drifless random walk. he single equaion forecass wih he aylor rule model perform beer agains he random walk wih drif. Evidence of long-erm predicabiliy is found for Neherlands and Sweden, wih he CW es and for 5 ou 9 counries (Ausralia, Canada, Japan, Neherlands, and Sweden) wih he DMW es. Panel forecass wih he aylor rule model a he 6-quarer horizon perform poorly. As repored in able 9, no evidence of eiher long-erm predicabiliy is found agains he random walk, wih or wihou drif, for any of he counries in he sample regardless of which es saisic is used. Low forecasing power of he aylor rule model a he shor horizon is reasonable because cenral 5 See Clarida, Gali and Gerler (998) and Gerdesmeier, Mongelli and Roffia (007) for comparisons of ineres rae reacion funcions among counries.

24 banks arge shor-erm nominal ineres raes. hese resuls are in accord wih previous work using revised or quasi-real-ime daa. Molodsova and Papell (009) repor ha he evidence of shor erm predicabiliy disappears a longer horizons wih a single equaion aylor rule model, and Engel, Mark and Wes (007) do no find more evidence of predicabiliy wih panel models. 6. Conclusions he purpose of his paper is o invesigae how real-ime daa affecs ou-of-sample predicabiliy of PPP and aylor rule exchange rae models a shor and long horizons using singleequaion and panel frameworks. he vas majoriy of empirical sudies on exchange rae forecasing over he pos-breon Woods period use ex-pos revised daa, which conain fuure informaion ha was no available o policymakers and marke paricipans a he ime he forecass were made. herefore, i canno be used o evaluae predicabiliy of exchange rae models ou-of-sample. Forecass wih real-ime daa, however, do no conain any unrealized fuure informaion in he informaion se of he linear model, mimic he informaion se of marke agens as closely as possible, and hus can be used o consruc a rue ou-of-sample forecas. Engel, Mark and Wes (007) find ha panel error-correcion exchange rae models wih PPP fundamenals are able o produce large improvemens in ou-of-sample forecasing a longer horizons. Because hey use ex-pos revised daa, he exchange rae models in heir sudy conain fuure informaion ha was no available o marke paricipans. he resuls in his paper show ha panel esimaion increases he predicabiliy of he PPP model relaive o single-equaion esimaion. Having relaively homogenous deviaions from PPP across counries cause panel esimaion o be more efficien and esimaing he predicive regression wih panel daa increases he forecasing power of he PPP model. A he 6-quarer horizon, evidence of predicabiliy is found wih panel

25 esimaion for 6 ou of 9 counries wih he CW es and 5 ou of 9 counries wih he DMW es agains he drifless random walk and for all of he counries agains he random walk wih drif regardless of which es saisic is used. One-quarer-ahead forecass of he exchange rae model wih PPP fundamenals are weaker han long-horizon forecass. Srong predicabiliy of he PPP model a longer-horizons wih panel esimaion is in accord wih esimaed half-lives of PPP deviaions of around.5 years, and confirms he findings in Engel, Mark and Wes (007). Molodsova and Papell (009), using ex-pos revised daa o calculae inflaion and quasireal-ime daa o esimae oupu gaps, find evidence of ou-of-sample exchange rae predicabiliy wih he aylor rule model a shor horizon using single-equaion esimaion. While quasi-real-ime daa does no conain fuure observaions, i capures revisions which are no available o marke paricipans in real-ime. herefore, quasi-real ime daa also canno be used o produce rue ou-ofsample forecass. Ou-of-sample forecasing exercises in our sudy show ha he predicabiliy of he aylor rule model is higher a he shor horizon han a he long horizon as in Molodsova and Papell (009). Evidence of shor-erm predicabiliy wih he single-equaion aylor rule model is found for ou of 9 counries wih boh es saisics agains he drifless random walk, and for 4 ou of 9 counries wih he CW es and 5 ou of 9 counries wih he DMW es agains he random walk wih drif. Since, cenral banks arge shor-erm nominal ineres raes, low predicive abiliy of aylor rules a he long-horizon is no surprising. In conras o PPP model, panel aylor rule exchange rae models are unable o improve he forecass compared wih single-equaion esimaion, which is consisen wih he resuls in Engel, Mark and Wes (007). As shown in Clarida, Gali and Gerler (998), ineres rae funcions are differen among he OECD counries, and so he assumpion of idenical moneary policy rules for all he cenral banks in panels is no very realisic and no suppored by he daa. 3

26 Acknowledgemens I hank David Papell, Chris Murray, Sebnem Kalemli-Ozcan, Nelson Mark, Luz Kilian, Dean Croushore, anya Molodsova, James Morley, Claude Lopez, Mark Srazicich and Vania Savrakeva for helpful commens and discussions. 4

27 References Berkowiz, J., Kilian, L., 000. Recen Developmens in Boosrapping ime Series. Economeric Reviews 9, -48. Cerra, V., Saxena, S. C., 008. he Moneary Model Srikes Back: Evidence from he World. IMF Working Papers 08/73. Cheung, Y.-W., Chinn, M. D., Pascual, A.G., 005. Empirical Exchange Rae Models of he Nineies: Are Any Fi o Survive? Journal of Inernaional Money and Finance 4, Choi, C.-Y., Mark, N., Sul, D., 006. Unbiased Esimaion of he Half-Life o PPP Convergence in Panel Daa. Journal of Money, Credi, and Banking 38, Clarida, R., Gali, J., Gerler, M., 998. Moneary Rules in Pracice: Some Inernaional Evidence. European Economic Review 4, Clark,. E., McCracken, M. W., 00. ess of Equal Forecas Accuracy and Encompassing for Nesed Models. Journal of Economerics 05, Clark,. E., McCracken, M. W., 005. Evaluaing Direc Muli-Sep Forecass. Economeric Reviews 4,

28 Clark,. E.,Wes, K. D., 006. Using Ou-of-Sample Mean Squared Predicion Errors o es he Maringale Difference Hypohesis. Journal of Economerics 35, Clark,. E.,Wes, K. D., 007. Approximaely Normal ess for Equal Predicive Accuracy in Nesed Models. Journal of Economerics 38, 9-3. Diebold, F., Mariano, R., 995. Comparing Predicive Accuracy. Journal of Business and Economic Saisics 3, Dornbusch, R., 976. Expecaions and Exchange Rae Dynamics. Journal of Poliical Economy 84, Engel, C., Mark, N. C.,Wes, K. D., 007. Exchange Rae Models Are No as Bad as You hink. In: Acemoglu, D., Rogoff, K., Woodford, M. (Eds.), NBER Macroeconomics Annual 007. Universiy of Chicago Press, pp Faus, J., Rogers, J. H., Wrigh, J. H., 003. Exchange Rae Forecasing: he Errors We ve Really Made. Journal of Inernaional Economics 60, Frankel, J. A., 979. On he Mark: A heory of Floaing Exchange Raes Based on Real Ineres Differenials. American Economic Review 69,

29 Gerdesmeier, D., Mongelli, F. P., Roffia, B., 007. he Eurosysem, he US Federal Reserve and he Bank of Japan: Similariies and Differences. Journal of Money, Credi, and Banking 39, Gourinchas, P.-O., Rey, H., 007. Inernaional Financial Adjusmen. Journal of Poliical Economy 5, Hodrick, R. J., Presco, E.C., 997. Poswar U.S. Business Cycles: An Empirical Invesigaion. Journal of Money, Credi, and Banking 9, -6. Ince, O., Papell, D. H., 0. he (Un)Reliabiliy of Real-ime Oupu Gap Esimaes wih Revised Daa. Unpublished Manuscrip. Appalachian Sae Universiy. Kilian, L., 999. Exchange Raes and Moneary Fundamenals: Wha Do We Learn from Long- Horizon Regressions? Journal of Applied Economerics 4, Li, H., 000. he Power of Boosrap Based ess for Parameers in Coinegraing Regressions. Saisical Papers 4, Li, H., Maddala, G., 997. Boosrapping Coinegraing Regressions. Journal of Economerics 80, Mark, N. C., 995. Exchange Rae and Fundamenals: Evidence on Long-Horizon Predicabiliy. American Economic Review 85,

30 Mark, N. C., Sul, D., 00. Nominal Exchange Raes and Moneary Fundamenals: Evidence from a Small Pos-Breon Woods Panel. Journal of Inernaional Economics 53, 9-5. McCracken, M. W., 007. Asympoics for Ou-of-Sample ess of Granger Causaliy. Journal of Economerics 40, Meese, R. A., Rogoff, K., 983a. Empirical Exchange Rae Models of he Sevenies: Do hey Fi Ou of Sample? Journal of Inernaional Economics 4, 3-4. Meese, R. A., Rogoff, K., 983b. he Ou of Sample Failure of Empirical Exchange Rae Models. In: Frenkel, J.A. (Ed.), Exchange Raes and Inernaional Macroeconomics. Universiy of Chicago Press, pp Murray, C. J., Papell, D. H., 00. he Purchasing Power Pariy Persisence Paradigm. Journal of Inernaional Economics 56, -9. Molodsova,., Papell, D. H., 009. Ou-of-Sample Exchange Rae Predicabiliy wih aylor Rule Fundamenals. Journal of Inernaional Economics 77, Molodsova,., Nikolsko-Rzhevskyy, A., Papell, D. H., 008. aylor Rules wih Real-ime Daa: A ale of wo Counries and One Exchange Rae. Journal of Moneary Economics 55, S63-S79. 8

31 Molodsova,., Nikolsko-Rzhevskyy, A., Papell, D. H., 0. aylor Rules and he Euro. Journal of Money, Credi, and Banking 43, Papell, D. H., 997. Searching for Saionariy: Purchasing Power Pariy Under he Curren Floa. Journal of Inernaional Economics 43, Papell, D. H., 00. he Grea Appreciaion, he Grea Depreciaion, and he Purchasing Power Pariy Hypohesis. Journal of Inernaional Economics 57, 5-8. Rogoff, K., Savrakeva, V., 008. he Coninuing Puzzle of Shor Horizon Exchange Rae Forecasing. Naional Bureau of Economic Research Working Paper 407. Rossi, B., 005. esing Long-Horizon Predicive Abiliy wih High Persisence, and he Meese- Rogoff Puzzle. Inernaional Economic Review 46, 6-9. Rossi, B., 006. Are Exchange Raes Really Random Walks? Some Evidence Robus o Parameer Insabiliy. Macroeconomic Dynamics 0, aylor, J. B., 993. Discreion versus Policy Rules in Pracice. Carnegie-Rocheser Conference Series on Public Policy 39, Wason, M., 007. How Accurae Are Real-ime Esimaes of Oupu rends and Gaps? Federal Reserve Bank of Richmond Economic Quarerly 93,

32 Wes, K. D., 996. Asympoic Inference abou Predicive Abiliy. Economerica 64, Wu, Y., 996. Are Real Exchange Raes Nonsaionary? Evidence from a Panel-Daa es. Journal of Money, Credi, and Banking 8,

33 able. Descripive Saisics A. INFLAION Real-ime Daa Revised Daa Mean SD Min Max Mean SD Min Max Ausralia Canada France Germany Ialy Japan Neherlands Sweden U.K U.S B. OUPU GAP Real-ime Daa Revised Daa Mean SD Min Max Mean SD Min Max Ausralia Canada France Germany Ialy Japan Neherlands Sweden U.K U.S Noes: he saisics repored for each variable are: Mean, he mean, SD, he sandard deviaion, Min, and Max, he minimum and maximum values. he daa is for 973:Q-009:Q. 3

34 able. Single Equaion -Quarer-Ahead Forecass Using PPP Fundamenals No Drif MSFE raio CW P-value DMW P-value Ausralia Canada France Germany Ialy Japan Neherlands Sweden U.K Drif MSFE raio CW P-value DMW P-value Ausralia Canada France Germany Ialy Japan Neherlands Sweden U.K Noes: he able repors he MSFE raio, defined as he raio of MSFEs of he linear exchange rae model o ha of he benchmark model (random walk wih and wihou he drif), he CW saisics and he DMW saisics for he ess of equal MSFEs. All repored ess are one-sided. Bold fon denoes he p-value of respecive es saisic significan a 0 % level based on semi-parameric boosrap. Saring in 973:Q, I esimae recursive regressions wih a 40-quarer iniial window o predic exchange rae changes from 983:Q o 009:Q. 3

35 able 3. Panel -Quarer-Ahead Forecass Using PPP Fundamenals No Drif MSFE raio CW P-value DMW P-value Ausralia Canada France Germany Ialy Japan Neherlands Sweden U.K Drif MSFE raio CW P-value DMW P-value Ausralia Canada France Germany Ialy Japan Neherlands Sweden U.K Noes: he able repors he MSFE raio, defined as he raio of MSFEs of he linear exchange rae model o ha of he benchmark model (random walk wih and wihou he drif), he CW saisics and he DMW saisics for he ess of equal MSFEs. All repored ess are one-sided. Bold fon denoes he p-value of respecive es saisic significan a 0 % level based on semi-parameric boosrap. Saring in 973:Q, I esimae recursive regressions wih a 40-quarer iniial window o predic exchange rae changes from 983:Q o 009:Q. 33

36 able 4. Single Equaion 6-Quarer-Ahead Forecass Using PPP Fundamenals No Drif MSFE raio CW P-value DMW P-value Ausralia Canada France Germany Ialy Japan Neherlands Sweden U.K Drif MSFE raio CW P-value DMW P-value Ausralia Canada France Germany Ialy Japan Neherlands Sweden U.K Noes: he able repors he MSFE raio, defined as he raio of MSFEs of he linear exchange rae model o ha of he benchmark model (random walk wih and wihou he drif), he CW saisics and he DMW saisics for he ess of equal MSFEs. All repored ess are one-sided. Bold fon denoes he p-value of respecive es saisic significan a 0 % level based on semi-parameric boosrap. Saring in 973:Q, I esimae recursive regressions wih a 40-quarer iniial window o predic exchange rae changes from 983:Q o 009:Q. 34