Taylor Rules and the Euro

Transcription

1 Taylor Rules and he Euro Tanya Molodsova, * Alex Nikolsko-Rzhevskyy, ** and David H. Papell *** Universiy of Houson May 23, 2008 Absrac This paper uses real-ime daa o analyze wheher he variables ha normally ener cenral banks ineres-raeseing rules, which we call Taylor rule fundamenals, can provide evidence of ou-of-sample predicabiliy for he Unied Saes Dollar/Euro exchange rae from he incepion of he Euro in 1999 o he end of The major resul of he paper is ha he null hypohesis of no predicabiliy can be rejeced agains an alernaive hypohesis of predicabiliy wih Taylor rule fundamenals for a wide variey of specificaions ha include inflaion and a measure of real economic aciviy in he forecasing regression. We also presen less formal evidence ha, wih real-ime daa, he Taylor rule provides a beer descripion of ECB han of Fed policy during his period. While he evidence of predicabiliy is only found for specificaions ha do no include he real exchange rae in he forecasing regression, he resuls are robus o wheher or no he coefficiens on inflaion and he real economic aciviy measure are consrained o be he same for he U.S. and he Euro Area and o wheher or no here is ineres rae smoohing. The evidence of predicabiliy is sronger for realime han for revised daa, abou he same wih inflaion forecass as wih inflaion raes, and weakens if oupu gap growh is included in he forecasing regression. Bad news abou inflaion and good news abou real economic aciviy boh lead o ou-of-sample predicabiliy hrough forecased exchange rae appreciaion. We hank Luisa Corrado and paricipans a he European Area Business Cycle Nework Conference, Using Euro Area Daa: Issues and Consequences for Economic Analysis, and he European Cenral Bank for helpful commens and discussions. * Deparmen of Economics, Universiy of Houson, Houson, TX Tel: +1 (832) vmolod@mail.uh.edu ** Deparmen of Economics, Universiy of Houson, Houson, TX Tel: +1 (832) osnikols@mail.uh.edu *** Deparmen of Economics, Universiy of Houson, Houson, TX Tel/Fax: +1 (713) / dpapell@uh.edu

2 1. Inroducion The behavior of exchange raes beween Europe and he Unied Saes, eiher via muliple currencies unil 1999 or via he euro/dollar exchange rae hereafer, has been one of he mos sudied opics in inernaional economics. The resuls of his research, however, have been less han sellar. The inabiliy o connec exchange raes wih macroeconomic fundamenals, characerized as he exchange rae disconnec puzzle, has produced pessimism regarding he usefulness of empirical exchange rae models and focused aenion on unquanifiable speculaive and psychological facors. A major conribuing facor o his exchange rae pessimism has been he inabiliy of empirical exchange rae models, saring wih he seminal paper of Meese and Rogoff (1983), o forecas nominal exchange raes ou-of-sample beer han a naïve no change, or random walk, forecas. While Mark (1995) provided hope ha he models would forecas beer a long horizons, more recen work such as Cheung, Chinn, and Pascual (2006) concludes ha no model consisenly does beer han a random walk. This lieraure, however, sill employs he empirical exchange rae models of he 1970s used by Meese and Rogoff. A money marke equilibrium equaion, or LM curve, for he foreign counry is subraced from a similar equaion for he domesic counry, producing an equaion wih he ineres differenial on he lefhand-side and money supply, income, and price level differenials on he righ-hand-side. Using Uncovered Ineres Rae Pariy (UIRP) and long-run Purchasing Power Pariy (PPP), and solving expecaions forward, a moneary exchange rae model is derived which can be used for ou-of-sample forecasing. Alernaively, he wo building-blocks of he moneary model, UIRP and PPP, can be used o derive forecasing equaions. The moneary exchange rae model, however, does no reflec how moneary policy is currenly conduced or evaluaed. Saring wih Taylor (1993), he ineres rae reacion funcion known as he Taylor rule, where he nominal ineres rae responds o he inflaion rae, he difference beween inflaion and is arge, he oupu gap, he equilibrium real ineres rae, and (someimes) he lagged ineres rae and he real exchange rae, has become he dominan mehod for evaluaing moneary policy. 1 Following Clarida, Gali, and Gerler (1998), (hereafer CGG), Taylor rules have been esimaed for a number of counries and ime periods. The evoluion of moneary policy evaluaion from LM curves and money supply reacion funcions o Taylor rules has influenced exchange rae modeling. Clarida, Gali, and Gerler (2002) and Clarida (2007) invesigae he derivaion and implicaions of a wo-counry opimizing model wih an open economy IS curve, Phillips curve, and Taylor rule. Engel and Wes (2006), Mark (2007), and Engel, Mark, and Wes (2007) have examined he empirical performance of Taylor-rule based exchange rae models. A major focus of Taylor rule esimaion, pioneered by Orphanides (2001), is he use of real-ime daa ha reflecs he informaion available o Cenral Banks when hey make heir ineres-rae-seing decisions. 1 Asso, Kahn, and Leeson (2007) examine he inellecual hisory of he Taylor rule and is influence on macroeconomic research and moneary policy. 1

3 Ineres rae reacion funcions using real-ime daa have been esimaed by Orphanides (2003, 2004) and Rudebusch (2006) for he Unied Saes, Nelson (2003) for he Unied Kingdom, Clausen and Meier (2003) and Gerberding, Worms, and Seiz (2005) for Germany, and Sauer and Surm (2007), Gerdesmeier and Roffia (2004), Gorer, Jacobs, and de Haan (2007), and Surm and Wollmershauser (2008) for he Euro Area. Alhough he argumen for using real-ime daa seems a leas as compelling for exchange rae forecasing as for Taylor rule modeling, virually all exisen lieraure on exchange rae predicabiliy uses fully revised daa o assess he ou-of-sample performance of empirical exchange rae models. The firs, and unil recenly only, paper o use real-ime daa o evaluae nominal exchange rae predicabiliy is Faus, Rogers and Wrigh (2003). They examine he predicive abiliy of Mark s (1995) moneary model using real-ime daa for Japan, Germany, Swizerland and Canada vis-à-vis he U.S. dollar and conclude ha, while he models consisenly perform beer using real-ime daa han fully revised daa, hey do no perform beer han he random walk model. There are (a leas) wo poenial reasons for he failure of empirical exchange rae models o forecas beer han a random walk ou-of-sample. The firs, as described above, is he oumoded naure of he models. The second, however, is ha he DMW ess commonly used o compare predicive abiliy, hose of Diebold and Mariano (1995) and Wes (1996) are, as demonsraed by Clark and McCracken (2001), severely undersized when used wih nesed models. Molodsova and Papell (2008), exploiing recen economeric work by Clark and Wes (2006), es he ou-of-sample predicabiliy of nominal exchange rae changes using Taylor rule fundamenals for 12 counries from 1973 o While real-ime daa is no available during he pos-breon Woods period for mos of he counries, hey consruc oupu gaps as deviaions from quasirevised rends in poenial oupu, where he rends, while incorporaing daa revisions, are updaed each period so as no o incorporae ex pos daa. Alhough hey find srong evidence of shor-run predicabiliy wih quasi-revised daa for mos of he considered currencies using Taylor rule fundamenals, hey do no produce forecass wih real-ime daa. 2 In Molodsova, Nikolsko-Rzhevskyy, and Papell (2007), we inegrae research on moneary policy evaluaion and ou-of-sample exchange rae predicabiliy wih real-ime daa. We esimae Taylor rules for he Unied Saes and Germany and use he esimaion resuls o srucure an invesigaion of predicabiliy for he dollar/mark exchange rae. We esimae Taylor rule ineres rae reacion funcions wih real-ime daa for he Unied Saes and Germany from 1979, he beginning of he European Moneary Sysem (EMS), hrough 1998, he adven of he Euro, and o use hese specificaions as fundamenals for evaluaing ou-of-sample forecasing of he Unied Saes Dollar/Deusche Mark nominal exchange rae wih real-ime daa. We find ha evidence of predicabiliy increases wih he use of real-ime, raher han revised, daa and wih models 2 Engel, Mark and Wes (2007) use a more consrained version of he Molodsova and Papell (2008) specificaion wih fully revised daa. They find less evidence of shor-horizon predicabiliy, bu more evidence of long-horizon predicabiliy, han Molodsova and Papell. 2

4 ha allow differenial inflaion and oupu coefficiens in he Federal Reserve and Bundesbank reacion funcions and include he exchange rae in he Bundesbank reacion funcion. This paper uses real-ime daa o evaluae ou-of-sample predicabiliy of he Unied Saes Dollar/Euro exchange rae from he incepion of he Euro in 1999 o he end of We firs ask wheher Taylor rules appear o be a reasonable approximaion of ineres rae seing for he Unied Saes and he Euro area during his period. Since esimaion of Taylor rules wih (a mos) eigh years of daa did no seem compelling, we sar wih visual evidence from a sandard Taylor rule specificaion, similar o ha presened by Taylor (1993). We find ha simple Taylor rules generally rack he direcion of ineres rae movemens for boh he Federal Reserve Sysem (Fed) and he European Cenral Bank (ECB), alhough he fi is no nearly as close as in Taylor (1993). In paricular, he shorfall of he Federal Funds Rae below he Taylor rule rae for he Unied Saes for 2002 o 2006, emphasized by Taylor (2007a) as a cause of he housing price bubble, is also eviden wih real-ime daa. Having esablished ha Taylor rules provide, a he leas, some informaion ha is useful for undersanding Fed and ECB moneary policy, we proceed o see if hey are useful for ou-of-sample exchange rae predicabiliy. A he onse, we need o make clear he disincion beween forecasing and predicabiliy. If we were evaluaing forecass from wo non-nesed models, we could compare he mean squared predicion errors (MSPE) from he wo models, scaled o produce he DMW saisic, and deermine wheher one model forecass beer han he oher. In our case, however, he null hypohesis of a random walk and all alernaive models are nesed and we use he Clark and Wes (2006) adjusmen of he DMW saisic o achieve correc size. Predicabiliy, wheher he vecor of coefficiens on he Taylor rule fundamenals is joinly significanly differen from zero in a regression wih he change in he exchange rae on he lef-hand-side, is herefore no equivalen o forecasing conen, wheher he MSPE from he alernaive model is significanly smaller han he MSPE from he null model. Pu differenly, we are using ou-of-sample mehods o evaluae he Taylor rule exchange rae model, no invesigaing wheher he model would poenially be useful o currency raders. We examine ou-of-sample exchange rae predicabiliy wih Taylor rule fundamenals. The saring poin for our analysis is he same as for he Taylor rule model of exchange rae deerminaion, he Taylor rule for he Euro Area is subraced from he Taylor rule for he Unied Saes. There are a number of differen specificaions ha we consider. While each specificaion has he ineres rae differenial on he lef-hand-side, here are a number of possibiliies for he righ-hand-side variables. 1. Taylor posied ha he Fed ses he nominal ineres rae based on he curren inflaion rae, he inflaion gap - he difference beween inflaion and he arge inflaion rae, he oupu gap - he difference beween GDP and poenial GDP, and he equilibrium real ineres rae. Assuming ha he ECB follows a similar rule, we consruc a symmeric model wih inflaion and he oupu gap on he righ-hand-side. Following he resuls in CGG for Germany, we can also posi ha he ECB includes he difference beween 3

5 he exchange rae and he arge exchange rae, defined by PPP, in is Taylor rule and consruc an asymmeric model where he real exchange rae is also included I has become common pracice, following CGG, o posi ha he ineres rae only parially adjuss o is arge wihin he period. In his case, we consruc a model wih smoohing so ha lagged ineres raes appear on he righ-hand-side. Alernaively, we can derive a model wih no smoohing ha does no include lagged ineres raes. Models wih and wihou smoohing can be symmeric or asymmeric. 3. If he Fed and ECB respond idenically o changes in inflaion and he oupu gap, so ha he coefficiens in heir Taylor rules are equal, we derive a homogeneous model where relaive (domesic minus foreign) inflaion and he relaive oupu gap are on he righ-hand-side. If he response coefficiens are no equal, a heerogeneous model is consruced where he domesic and foreign variables appear separaely. The homogeneous and heerogeneous models can be eiher symmeric or asymmeric, wih or wihou smoohing. 4 The mos sraighforward way o consruc an exchange rae forecasing equaion is, using UIRP, o replace he ineres rae differenial wih he expeced rae of depreciaion and use he variables from he wo counries Taylor rules o forecas exchange rae changes, so ha an increase in eiher inflaion or he oupu gap would produce a forecas of exchange rae depreciaion. This approach, however, is unsaisfacory for hree reasons. Firs, an exensive lieraure has shown ha regressing exchange rae changes on ineres rae differenials no only does no produce coefficiens equal o one, as prediced by UIRP, i ofen produces negaive coefficiens. Second, he recen carry rade lieraure indicaes ha counries wih high ineres raes appear o have appreciaing currencies. Third, as argued by Clarida and Waldman (2007), if an unexpeced increase of he inflaion rae above is arge creaes he expecaion ha he cenral bank will respond by raising he ineres rae, he exchange rae will appreciae, raher han depreciae, in response o he news. We herefore use Taylor rule fundamenals, he variables ha ener various specificaions of he Taylor rule, o forecas exchange rae changes. These impose resricions on he direcion of he forecass, bu do no allow us o back ou implied coefficiens of he Fed and ECB Taylor rules from he esimaed coefficiens in he exchange rae forecasing equaion. Using real-ime daa wih Taylor rule fundamenals, we find very srong evidence of ou-of-sample predicabiliy for he Dollar/Euro exchange rae. The srong evidence comes almos enirely from symmeric specificaions which do no include he real exchange rae in he forecasing regression. The resuls are robus o wheher he specificaion is homogeneous or heerogeneous and o wheher he oupu gap is consruced 3 While mos sudies of ECB ineres-rae-seing policy do no incorporae exchange raes, De Lucia and Lucas (2007) find ha inclusion of he nominal rade-weighed exchange rae improves heir Taylor rule esimae for he ECB. 4 If, in addiion o having he same inflaion response and ineres rae smoohing coefficiens, he wo cenral banks have idenical arge inflaion raes and equilibrium real ineres raes, here is no consan on he righ-hand-side. Oherwise, here is a consan. Since he resricions necessary o eliminae he consan seem very unlikely o be fulfilled, we only esimae models wih a consan. 4

6 by Hodrick-Presco (HP) filering, aken from OECD esimaes, or proxied by he unemploymen rae. Specificaions wihou smoohing provide marginally more evidence of predicabiliy han specificaions wih smoohing. Does our evidence of predicabiliy for he Dollar/Euro exchange rae come from Taylor rule fundamenals, or is i driven by eiher inflaion or he oupu gap, bu no boh? In order o answer his quesion, we esimae forecasing regressions where inflaion, he HP filered oupu gap, he OECD measured oupu gap, and he unemploymen rae ener separaely. The resuls are similar o hose where inflaion and a measure of economic aciviy ener joinly, indicaing ha boh componens of Taylor rule fundamenals are imporan for ou-of-sample predicabiliy. We also invesigae predicabiliy wih revised daa, recognizing ha we are no longer replicaing he environmen experienced by marke paricipans. In conras o many applicaions of real-ime daa, we expec ha, because he exchange rae is an asse price, predicabiliy can decrease wih revised daa because informaion is being used ha was unavailable boh when he forecass were made and when he forecased exchange rae was realized. We find ha predicabiliy decreases when he revised OECD measured oupu gap, which is consisenly larger han he real-ime OECD measured oupu gap, is in he forecasing regression. In conras, predicabiliy does no change wih he revised HP filered oupu gap or he unemploymen rae, neiher of which are sysemaically differen from heir real-ime counerpars. I is ofen asked wheher he experience of he Bundesbank during he EMS period provides a good predicor for he acions of he ECB. The answer from his paper is clearly no. In our earlier work on he Mark/Dollar exchange rae wih real-ime daa, we found evidence of predicabiliy only wih heerogeneous coefficiens and asymmeric specificaions, wih or wihou smoohing. For he Euro/Dollar rae, we find ha he evidence of predicabiliy is much sronger wih symmeric specificaions, somewha sronger wih smoohing, and doesn depend on wheher he coefficiens are homogeneous or heerogeneous. Clarida and Waldman (2007), using an even sudy mehodology, find evidence ha a surprise increase in inflaion causes he exchange rae o appreciae in he very shor run. We find srong suppor for heir proposiion ha bad news abou inflaion is good news for he exchange rae. Using he mos successful homogeneous and symmeric specificaion, an increase in U.S. inflaion relaive o Euro Area inflaion causes forecased dollar appreciaion whaever measure of real economic aciviy is included in he forecasing regression. We also find ha good news abou oupu or unemploymen is good news for he exchange rae. An increase in he U.S. oupu gap relaive o he Euro Area oupu gap causes forecased dollar appreciaion while an increase in U.S. unemploymen relaive o Euro Area unemploymen causes forecased dollar depreciaion. 5

7 2. Taylor Rule Fundamenals We examine he linkage beween he exchange rae and a se of fundamenals ha arise when cenral banks se he ineres rae according o he Taylor rule. Following Taylor (1993), he moneary policy rule posulaed o be followed by cenral banks can be specified as (1) i = π φ π π γ * * * + ( ) + y + r where inflaion, and * i is he arge for he shor-erm nominal ineres rae, π is he inflaion rae, * π is he arge level of y is he oupu gap, or percen deviaion of acual real GDP from an esimae of is poenial level, * r 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 here is no disincion beween he acual and arge nominal ineres rae. Alernaively, he difference beween he naural rae of unemploymen and he unemploymen rae can replace he oupu gap. 5 According o he Taylor rule, he cenral bank raises he arge for he shor-erm nominal ineres rae if inflaion rises above is desired level and/or oupu is above poenial oupu. The arge level of he oupu deviaion from is naural rae y is 0 because, according o he naural rae hypohesis, oupu canno permanenly exceed poenial oupu. The arge level of inflaion is posiive because i is generally believed ha deflaion is much worse for an economy han low inflaion. Taylor assumed ha he oupu and inflaion gaps ener he cenral bank s reacion funcion wih equal weighs of 0.5 and ha he equilibrium level of he real ineres rae and he inflaion arge were boh equal o 2 percen. * The parameers π and which leads o he following equaion, * r in equaion (1) can be combined ino one consan erm µ r φπ * * =, (2) i * = µ + λπ + γy where λ =1 + φ. While i seems reasonable o posulae a Taylor rule for he Unied Saes ha includes only inflaion and he oupu gap, i is common pracice o include he real exchange rae in specificaions for oher counries, (3) i * = µ + λπ + γy + δq where q is he real exchange rae for he Euro Area. The raionale for including he real exchange rae in he Taylor rule is ha he cenral bank ses he arge level of he exchange rae o make PPP hold and increases 5 Blinder and Reis (2005) use his measure. 6

8 (decreases) he nominal ineres rae if he exchange rae depreciaes (appreciaes) from is PPP value. Based on he evidence in CGG and Molodsova, Nikolsko-Rzhevskyy, and Papell (2007) ha he real exchange rae enered he Taylor rule for he Bundesbank during he European Moneary Sysem period, we allow for he possibiliy ha i should be included in he ECB s Taylor rule. I has also become common pracice o specify a varian of he Taylor rule which allows for he possibiliy ha he ineres rae adjuss gradually o achieve is arge level. Following CGG, we assume ha he acual observable ineres rae i parially adjuss o he arge as follows: (4) i ( ρ ρ + v * = 1 ) i + i 1 Subsiuing (3) ino (4) gives he following equaion, (5) i ( ρ µ λπ γ δ ρ + v = 1 )( + + y + q ) + i 1 where δ = 0 for he Unied Saes. To derive he Taylor-rule-based forecasing equaion, we consruc he ineres rae differenial by subracing he ineres rae reacion funcion for he Euro Area from ha for he U.S.: (6) i ~ i = α + α ~ ~ uπ π αeππ + αuyy αeyy αqq + ρui 1 ρei 1 + ~ ~ η where ~ denoes Euro Area variables, subscrips u and e denoe coefficiens for he Unied Saes and he Euro Area, α is a consan, = λ( 1 ρ) and αy = γ ( 1 ρ) for boh cenral banks, and αq = δ ( 1 ρ) α π for he ECB. 6 While he mos direc way o derive a forecasing equaion would be o posulae ha UIRP holds, so ha he expeced rae of depreciaion is proporional o he ineres rae differenial, empirical work on UIRP and (more recenly) carry rade clearly shows ha he assumpion of UIRP a he one-quarer-ahead horizon is unwarraned. Insead, we ake a more descripive approach. Suppose ha he U.S. inflaion rae rises above is arge level. According o he Taylor rule, he Fed will increase ineres raes, which ends o make he dollar more aracive and cause i o appreciae. A similar argumen would imply ha an increase in Euro Area inflaion above is arge would make he euro appreciae. Clarida and Waldman (2007) characerize his predicion as bad news abou inflaion is good news for he exchange rae. 7 The link beween higher inflaion and exchange rae appreciaion poenially characerizes any counry where he cenral bank uses he ineres rae as he insrumen in an inflaion argeing policy rule. In 6 As shown by Engel and Wes (2005), his specificaion would sill be applicable if he U.S. had an exchange rae arge in is ineres rae reacion funcion. 7 Clarida and Waldman (2007) consruc a model ha combines a Taylor rule wih a Phillips curve o derive condiions under which a surprise increase in U.S. inflaion will appreciae he exchange rae, and use even sudy mehodology o es he model. Clarida (2007) discusses furher implicaions of ha model. Engel (2007) argues ha his resul appeared earlier in Engel and Wes (2006). Taylor (2007b) follows a similar descripive approach. 7

9 he conex of he Taylor rule, wo addiional predicions can be made. Firs, if he U.S. oupu gap increases, he Fed will raise ineres raes and cause he dollar o appreciae. Similarly, an increase in he Euro Area oupu gap will cause he euro o appreciae. Thus good news abou oupu is good news for he exchange rae. Second, if he real exchange rae for he Euro Area depreciaes and i is included in he ECB s Taylor rule, he ECB will raise is ineres rae, causing he Euro o appreciae and he dollar o depreciae. If here is no smoohing, all ineres rae adjusmens are immediae. Suppose ha U.S. inflaion rises above arge. The Fed will raise he ineres rae by λ π, where π is he change in he inflaion rae. If here is smoohing, he adjusmen is gradual. The Fed will raise he ineres rae by (1-ρ) λ π in he firs period. In he second period, he ineres rae will be (1-ρ 2 ) λ π above is original level, followed by (1-ρ 3 ) λ π, and so on. If inflaion is only brough down slowly, he maximum impac on he ineres rae will be approximaely λ π, he same as wih no smoohing. Oherwise, i will be smaller. Once inflaion sars o come down, so will he ineres rae. Since he ineres firs rises and hen falls following an increase in inflaion, he Taylor rule provides no predicion regarding he affec of he lagged ineres rae on he exchange rae. These predicions can be combined wih (6) o produce an exchange rae forecasing equaion. (7) s ω ω π ω ~ π ω ω ~ ω ~ ~ ω + 1 = uπ + eπ uyy + eyy + qq uii 1 + eii 1 + ω η The variables is he log of he U.S. dollar nominal exchange rae deermined as he domesic price of foreign currency, so ha an increase ins is a depreciaion of he dollar. The reversal of he signs of he coefficiens beween (6) and (7) reflecs he presumpion ha anyhing ha causes he Fed and/or ECB o raise he U.S. ineres rae relaive o he Euro Area ineres rae will cause he dollar o appreciae (a decrease ins ). Since we do no know by how much a change in he ineres rae differenial (acual or forecased) will cause he exchange rae o adjus, we do no have a link beween he magniudes of he coefficiens in (6 ) and (7). A number of differen models can be nesed in Equaion (7). If he ECB doesn arge he exchange rae δ = ω q = 0 and we call he specificaion symmeric. Oherwise, i is asymmeric. If he ineres rae adjuss o is arge level wihin he period ω ui = ω ei = 0 and he model is specified wih no smoohing. Alernaively, here is smoohing. If he coefficiens on inflaion, he oupu gap, and ineres rae smoohing are he same in he U.S. and he Euro Area, so ha ω uπ = ω eπ, ω uy = ω ey, and ω ui = ω ei, inflaion, oupu gap, and lagged ineres rae differenials are on he righ-hand-side of Equaion (7) and we call he model homogeneous. Oherwise, i is heerogeneous. 3. Taylor Rules, he Fed, and he ECB If we were wriing his paper in 2018 insead of 2008, we would sar by esimaing Taylor rules using real-ime daa for he Fed and ECB o provide a guide o he facors ha migh affec ou-of-sample 8

10 exchange rae predicabiliy. Since ha opion is precluded and we are skepical ha much can be learned from esimaing Taylor rules wih eigh years of daa, we sar wih a more descripive mehod. We firs describe he real-ime daa available for he U.S. and Euro Area since 1999, and hen provide visual evidence ha Taylor rules wih real-ime daa provide a useful characerizaion of ineres rae seing by he Fed and ECB Real-Time and Revised Daa We use real-ime quarerly daa from 1999:Q4 o 2007:Q4 for he Unied Saes and he Euro Area. The real-ime daa for he U.S. comes from Philadelphia Fed Real-Time Daase for Macroeconomiss, described in Croushore and Sark (2001), and he real-ime daa for he Euro Area is from he OECD Original Release and Revisions Daabase. 9 Boh daa ses have a riangular forma wih he vinage dae on he horizonal axis and calendar daes on he verical. The erm vinage denoes he dae in which a ime series of daa becomes known o he public. 10 For each subsequen quarer, he new vinage incorporaes revisions o he hisorical daa, hus providing all informaion known a he ime. The revised daa is consruced from he 2007:Q4 vinage in boh real-ime daases. For each forecasing regression, we sar in 1991:Q1 and use 34 quarers o esimae he hisorical relaionship beween he Taylor rule fundamenals and he change in he exchange rae, and hen use he esimaed coefficiens o forecas he exchange rae one-quarer-ahead. We use rolling regressions o predic 32 exchange rae changes from 2000:Q1 o 2007:Q4. Since we use vinage daa, he esimaed coefficiens are based on revised daa, bu he forecass are conduced using real-ime daa. 11 We use he GDP Deflaor o measure inflaion for he U.S. and he Harmonized Index of Consumer Prices (HICP) o measure inflaion for Euro Area. Following Taylor (1993), he inflaion rae is he rae of inflaion over he previous four quarers. The exchange rae, defined as he quarerly-averaged US dollar price of a Euro, and he shor-erm nominal ineres raes, defined as he ineres rae in he hird monh of each quarer, are aken from OECD Main Economic Indicaors (MEI) daabase. The shor-erm ineres rae is he money marke rae (EONIA) for Euro Area and he Federal Funds Rae for he U.S. Since ineres daa for he Euro Area does no exis prior o 1994:Q4, we use he German money marke rae from he IMF Inernaional Financial Saisics Daabase (line 60B) for he earlier period. The real Euro/USD exchange rae is calculaed as he deviaion of he nominal exchange rae from he arge defined by Purchasing Power 8 Recen papers ha compare Taylor rules for he Fed and ECB, including De Lucia and Lucas (2007) and Gerdesmeier, Mongelli, and Roffia (2007), use eiher Bundesbank or synheic Euro Area daa o exend he sample back o 1993, and herefore canno use real-ime daa. 9 An alernaive would be o use Euro Area Business Cycle Nework daa, bu i does no sar unil There is ypically a one-quarer lag before daa is released, so real-ime variables daed ime acually represen daa for period An alernaive mehod of consrucing real-ime daa is o use diagonal daa ha does no incorporae hisorical revisions. Wih ha mehod, he esimaed coefficiens would also use real-ime daa. Since he vinages are no available before 1999 and we only have 32 forecas periods, we do no have ha opion for his paper. 9

11 Pariy, where he wo counries price levels are measured by he CPI for he U.S. and he HICP for he Euro Area. We use wo differen measures of he oupu gap. Firs, we consruc quarerly measures of he oupu gap from inernal OECD esimaes. This daa comes from he semi-annual issues of OECD Economic Oulook. Each issue conains pas esimaes as well as fuure forecas of annual values of he oupu gap for OECD counries including he European Union. Since boh esimaes and forecass are annual, we used quadraic inerpolaion o obain quarerly esimaes. 12 The second measure of he oupu gap uses HP derended real indusrial producion. 13 Indusrial producion daa sars in 1990:Q1. While applying he HP filer, we ake ino accoun of he end-of-sample problem by forecasing and backcasing he indusrial producion series by 12 quarers in boh direcions assuming ha growh raes follow an AR(4) process. A similar mehodology is used in Wason (2007) and Clausen and Mayer (2005). Forecased OECD oupu gap growh is calculaed as he difference beween he forecased OECD oupu gap in ime (+4) and he curren OECD oupu gap. The forward-looking specificaions use he Philadelphia Fed Survey of Professional Forecasers (SPF) forecas daa, which originally consiss of annualized quarer-over-quarer GDP deflaor inflaion forecass a differen horizons. We conver i ino year-over-year raes by aking he average of 4 consecuive inflaion forecass. For he U.S., SPF daa is available for he enire sample. For he Euro Area, he only comparable SPF daa which is available is he 1-year-ahead HICP inflaion forecas. The firs round of he survey was conduced in 1999:Q1. This means ha we do no have he same forecas for 1991:Q1, which is he saring poin for our "vinage" regressions. To deal wih his issue, we noe ha he firs "vinage" regression which he public could have run using OECD real-ime daa was in 1999:Q4 when he firs OECD vinage was published. A ha ime, inflaion daa for 1990:Q1-1999:Q3 was available. To consruc he +4 inflaion forecas for any vinage, we use he realized +4 values of inflaion (which is someimes inerpreed as he "raional" +4 forecas of inflaion) before 1998:Q4 and real-ime Euro Area SPF forecass from 1999:Q1 o 2007:Q4. The real-ime and revised daa are depiced in Figure 1. In line wih all research in his area since Orphanides (2001), he differences are much larger for oupu gaps han for inflaion, reflecing he changes in poenial oupu, as well as he daa revisions hemselves, for he former bu no he laer. Revisions in unemploymen are much smaller han revisions in he oupu gaps for boh he U.S. and he Euro Area. For he U.S., he revisions in he HP filered oupu gap are larger han he revisions in he OECD esimaed oupu gap, while he opposie is rue for he Euro Area. The larges revisions are for he OECD real-ime 12 Since he daa is updaed semi-annually, we assume ha in he quarer following he period in which he esimaes are released, he public uses he esimaes and forecass from he previous quarer. They ge updaed only afer he nex release of he Economic Oulook. See Nikolsko-Rzhevskyy (2008) for deails. 13 We use indusrial producion insead of GDP because he laer does no sar unil 1995 for he Euro Area in he OECD daabase. 10

12 esimaes of he oupu gap for he Euro Area, which are subsanially below he revised esimaes from 1999:Q4 o 2004:Q2. These poins are illusraed in Table 1 ha provides summary saisics of revised and real-ime daa. The average U.S. real-ime inflaion and unemploymen rae are virually he same as he revised inflaion and unemploymen rae and he average Euro Area real-ime inflaion and unemploymen rae differ from heir revised counerpars insignificanly. The larges differences are found beween he average U.S. real-ime and revised HP filered oupu gap and Euro Area OECD oupu gap. These differences are very close in size and equal o 1.14 percenage poins for he U.S. and 1.13 percenage poins for Euro Area. The average U.S. real-ime and revised OECD oupu gap and Euro Area real-ime and revised HP filered oupu gap differ by 0.05 and 0.11 percenage poins, respecively. These differences sugges ha policy recommendaions based on HP filered oupu gap for he U.S. and OECD esimaes of he oupu gap for he Euro Area may be subsanially differen wih revised and real-ime daa. Table 2 shows he descripive saisics on daa revisions in our sample. A posiive and significan value for he mean of he revision indicaes ha he variable was on average revised upwards, so ha he exisence of measuremen errors or he availabiliy of new informaion (or boh) made he saisical agency realize ha he inflaion rae and/or he oupu gap was higher han perceived in real-ime. We can see ha he mean revision for inflaion and unemploymen is essenially zero for boh he U.S., and insignifican for Germany. Boh HP filered oupu gap for he U.S. and OECD esimaes of he oupu gap for he Euro Area are on average revised upwards. To explore he naure of daa revisions in our sample, we examine he correlaions beween he daa revisions, defined as X revised-x real-ime, and he real-ime and revised series. According o Mankiw and Shapiro (1986), if daa revisions represen pure noise, hey should be uncorrelaed wih he revised daa bu correlaed wih he real-ime series. The opposie should be rue if daa revisions represen pure news. The correlaions in Table 2 indicae ha revisions in he Euro Area HP filered oupu gap represen pure news and revisions in Euro Area OECD oupu gap are dominaed by news. The revisions in Euro Area inflaion and unemploymen represen mosly noise. The properies of news are more pronounced in he U.S. revisions of inflaion and he HP filered oupu gap, while revisions of he U.S. OECD oupu gap and unemploymen are dominaed by noise. 3.2 Taylor Rules for he Fed and ECB We provide visual evidence of how closely ineres rae seing by he Fed and he ECB can be characerized by a Taylor rule wih real-ime daa. In panel A of Figure 2, we depic he acual U.S. and Euro Area ineres rae and he counerfacual ineres rae implied by a Taylor rule wih a coefficien of 1.5 on inflaion, 0.5 on he oupu gap, an inflaion arge of 2 percen, an equilibrium real ineres rae of 2 percen, and no smoohing. Excep for using real-ime raher han revised daa and a differen ime period, his is 11

13 exacly he exercise conduced in Taylor (1993). We use GDP real-ime inflaion for he US, HICP real-ime inflaion for he Euro Area, and OECD esimaes of he oupu gap. 14 The resuls for he U.S. show ha, while he Federal Funds rae and ineres rae implied by he Taylor rule are clearly posiively correlaed, he Federal Funds rae is consisenly below he rae implied by he Taylor rule from 2002:Q4 o 2007:Q1, nearly exacly replicaing he resuls repored by Taylor (2007a) wih revised daa. 15 Taylor (2007a) argues ha he gap beween he acual Federal Funds rae and he rae implied by he Taylor rule was an imporan conribuing facor o he housing price bubble in he U.S. Our resuls show ha, in he conex of his argumen, he discrepancy is no an arifac of using revised daa ha were no available o he Fed a he ime ha ineres-rae-seing decisions were made, bu also appears in real-ime daa. For he Euro Area, while he overall fi is closer, he acual Money Marke Rae is below he rae implied by he Taylor rule from 2003:Q1 o 2007:Q1. While his is similar o he paern found for he U.S., he magniude of he gap is much smaller for he Euro Area han for he U.S. I is ofen argued ha moneary policy evaluaion should be conduced wih forward-looking daa. In panel B of Figure 2, we depic forward-looking specificaions, for which we use he +4 SPF inflaion forecass for boh he Euro Area and he U.S. Everyhing else, including he coefficiens on inflaion and he oupu gap, he inflaion arge of 2 percen, and he equilibrium real ineres rae of 2 percen, is he same as wih conemporaneous inflaion. For he U.S., he paern is similar o ha found wih conemporaneous inflaion excep ha i sars in 2002:Q3 and ends in 2005:Q4. In addiion, he gap beween he acual Federal Funds rae and he rae implied by he Taylor rule is smaller wih forecased inflaion. For he Euro Area., he acual Money Marke rae wih forecased inflaion is very close o he rae implied by he Taylor rule for almos he enire period, wih he acual rae higher in and he implied rae higher in Wih forecased inflaion, we can consruc ex ane real ineres raes as he nominal ineres rae minus he expeced rae of inflaion, and calculae he equilibrium real ineres rae, 1.45 percen for he U.S. and 1.33 percen for he Euro Area, as he average real ineres rae over he period. The resuls wih a forward-looking specificaion and calculaed equilibrium real ineres rae are shown in panel C. According o Equaion (1), he equilibrium real ineres rae has a poin-for-poin affec on he nominal ineres rae, so his lowers he ineres rae implied by he Taylor rule by 0.55 percen for he U.S. and 0.67 percen for he Euro Area. For he U.S., he gap beween he acual Federal Funds rae and he rae implied by he Taylor rule sars in 2002:Q3 and ends in 2005:Q4 and is smaller is smaller o ha found wih an equilibrium real ineres rae of 2 percen. For he Euro Area, he acual Money Marke rae wih forecased inflaion is above he rae implied by he Taylor rule for mos of he period, and hey are very close from 2003:Q2 o 2006:Q3. Using real-ime daa visual mehods ha make no aemp o produce a good fi beween he acual and implied ineres raes, we have shown ha he Taylor rule provides a good approximaion of ineres rae 14 Figures for HP filered daa (no repored) are similar. 15 In Taylor (2007a), he acual and implied pahs diverge in 2002:Q2 and merge again in 2006:Q3. 12

14 seing by boh he Fed and he ECB since For he U.S., he major deviaion occurred beween 2003 and 2006 and, as described by Taylor (2007a), was produced because he acual Federal Funds rae was consisenly below he rae implied by he Taylor rule. For he ECB, he differences beween he acual and implied ineres raes are smaller, and he acual Money Marke rae was neiher consisenly above nor below he rae implied by he Taylor rule. 4. Forecas Comparison Based on MSPE Each model s ou-of-sample predicabiliy is compared o ha of he maringale difference process using an adjused es saisic, which is consruced as described in Clark and Wes (2006). We are ineresed in comparing he mean square predicion errors from he wo nesed models. The benchmark model is a zero mean maringale difference process, while he alernaive is a linear model. Model 1: y = ε Model 2: y = ' X β + ε, where E ( ε ) = Suppose we have a sample of T+1 observaions. The las P observaions are used for predicions. The firs predicion is made for he observaion R+1, he nex for R+2,, he final for T+1. We have T+1=R+P, where R=34, and P=32 quarers. To generae predicion for period =R, R+1,, T, we use he informaion available prior o. Le βˆ is a regression esimae of β ha is obained using he daa prior o. The one-sep ahead predicion for model 1 is 0, andx+ 1βˆ for model 2. The sample forecas errors from he models 1 and 2 are e ˆ = 1, + 1 y+ 1 and eˆ 2, + 1 = y+ 1 X+ 1βˆ, respecively. The corresponding MSPE s T for he wo models are ˆ1 σ = P y + 1 and σ ˆ = y 2 P ( + 1 X ˆ + 1β ). = T P+ 1 T = T P + 1 We are ineresed in esing he null hypohesis of no predicabiliy agains he alernaive ha exchange raes are linearly predicable. 16 Thus, H : σ σ 1 2 = 0 H : σ 1 σ 2 > 0 Under he null, he populaion MSPE s are equal. We need o use he sample esimaes of he populaion MSPE s o draw he inference. The procedure inroduced by Diebold and Mariano (1995) and Wes (1996) uses sample MSPE s o consruc a -ype saisics which is assumed o be asympoically normal. To consruc he DMW saisic, le 16 We use he erm predicabiliy as a shorhand for ou-of-sample predicabiliy in he sense used by Clark and Wes (2006, 2007), rejecing he null of a zero slope in he predicive regression in favor of he alernaive of a nonzero slope. 13

15 ˆ1 2 ˆ T 2 1 = e, e2, and f = P f ˆ + 1 = T P+ 1 fˆ Then, he DMW es saisic is compued as follows, 2 = ˆ σ 1 2 ˆ σ 2 (8) DMW T f =, where Vˆ 1 = P ( fˆ + 1 f ) 1 P Vˆ = T P+ 1 Clark and Wes (2006) demonsrae analyically ha he asympoic disribuions of sample and populaion difference beween he wo MSPE s are no idenical, namely he sample difference beween he wo MSPE s is biased downward from zero. This means ha using he es saisic (8) wih sandard normal criical values is no advisable. I is sraighforward o show ha he sample difference beween he wo MSPE s is uncenered under he null. 2 (9) ˆ σ T T T T T ˆ 1 σ = P fˆ = P y 1 P ( y X ˆ 1 1β ) = 2P y X ˆ 1 1β P ( X ˆ + 1β ) = T P+ 1 = T P+ 1 = T P+ 1 = T P+ 1 = T P+ 1 Under he null, he firs erm in (9) is zero, while he second one is greaer han zero by consrucion. Therefore, under he null we expec he MSPE of he naïve no-change model o be smaller han ha of a linear model. The inuiion behind his resul is he following. If he null is rue, esimaing he alernaive model inroduces noise ino he forecasing process because i is rying o esimae parameers which are zero in populaion. In finie samples, use of he noisy esimae of he parameers will lead o higher esimaed MSPE. As a resul, he sample MSPE of he alernaive model will be higher by he amoun of esimaion noise. To properly adjus for his shif, we consruc he correced es saisic as described in Clark and Wes (2006) by adjusing he sample MSPE from he alernaive model by he amoun of he bias in he second erm of equaion (9). This adjused CW es saisic is asympoically sandard normal. When he null is a maringale difference series Clark and Wes (2006, 2007) recommend adjusing he difference beween MSPE s as described above and using sandard normal criical values for inference. 17 I is imporan o undersand he disincion beween predicabiliy and forecasing conen. The CW mehodology ess wheher he regression coefficien β is zero raher han wheher he model-based forecas is more accurae han he random walk forecas. Since he CW saisic is consruced by adjusing he sample MSPE from he alernaive model by he amoun of bias under he null, i is enirely possible for he null 17 Because he null hypohesis for he CW saisic is a zero mean maringale difference process, we can only es he null ha he exchange rae is a random walk, no a random walk wih drif. Clark and Wes (2006, 2007) argue ha sandard normal criical values are approximaely correc and advocae using hem insead of boosrapped criical values. Clark and McCracken (2007) consider he impac of daa revisions on ess of equal predicive abiliy. Because he nominal exchange rae is unrevised and a random walk under he null, even predicable real-ime daa revisions do no have an impac on he asympoic disribuions and he Clark and Wes resuls can be used. 14

16 hypohesis ha β = 0 o be rejeced even when he sample MSPE from he random walk forecas is smaller han he sample MSPE from he model-based forecas. 5. Empirical Resuls 5.1 Taylor Rule Fundamenals Tables 3-7 presen resuls for one-quarer-ahead forecas comparisons using CW saisics. Table 3 presens he cenral resuls of he paper. Wih a symmeric specificaion ha does no include he real exchange rae in he forecasing regression, no smoohing, and heerogeneous coefficiens, he random walk (no predicabiliy) null hypohesis is rejeced a he 1 percen level in favor of he alernaive hypohesis of ou-of-sample predicabiliy for he Euro/Dollar exchange rae wih Taylor rule fundamenals when boh inflaion and eiher he HP filered oupu gap, he OECD esimaed oupu gap, or he unemploymen rae is included in he forecasing regression. Wih a symmeric specificaion, no smoohing, and homogeneous coefficiens, he rejecions are nearly as srong, 1 percen for inflaion and eiher he HP filered oupu gap or he unemploymen rae and 10 percen for inflaion and he OECD oupu gap esimae. The resuls for symmeric specificaions wih smoohing are also srong. Wih heerogeneous coefficiens, he null is rejeced a he 1 percen level for inflaion and he HP filered oupu gap and a he 5 percen level for inflaion and eiher he OECD esimaed oupu gap or he unemploymen rae while, wih homogeneous coefficiens, he null is rejeced a he 1 percen level for inflaion and eiher he HP filered oupu gap or he unemploymen rae and a he 10 percen level for inflaion and he OECD oupu gap esimae. The resuls for he asymmeric specificaions, which include he real exchange rae in he forecasing regression, are much weaker. While, wih no smoohing and homogeneous coefficiens, he null is rejeced a he 5 percen level for inflaion and eiher he HP filered oupu gap or he unemploymen rae and a he 10 percen for inflaion and he OECD oupu gap esimae, i can only be rejeced, a he 10 percen level, for he OECD oupu gap esimae wih heerogeneous coefficiens. Wih smoohing, he null canno be rejeced a he 10 percen level for any of he specificaions. We have presened evidence ha, using symmeric specificaions ha do no include he real exchange rae in he forecasing regression, he random walk (no predicabiliy) null hypohesis can be consisenly rejeced in favor of he alernaive hypohesis of ou-of-sample predicabiliy for he Euro/Dollar exchange rae wih Taylor rule fundamenals. Since he specificaions include inflaion and eiher he HP filered oupu gap, he OECD esimaed oupu gap, or he unemploymen rae in he forecasing regression, i is no clear, however, wheher he source of he rejecions comes from inflaion, a measure of real economic aciviy, or boh. This quesion is addressed in Table 4 by reporing CW saisics when eiher inflaion or a measure of real economic aciviy, insead of boh, is included in he forecasing regressions. For he symmeric 15

17 specificaions wihou smoohing, he random walk (no predicabiliy) null can be rejeced in favor of he alernaive a he 1 percen level wih he HP filered oupu gap, he OECD oupu gap esimae, and he unemploymen rae and a he 5 percen for inflaion wih boh homogeneous and heerogeneous coefficiens. Because he null can be rejeced when eiher inflaion or any of he real economic aciviy measures are included in he forecasing regression, his consiues evidence of ou-of-sample exchange rae predicabiliy from a specificaion wih Taylor rule fundamenals raher han a specificaion ha is solely focused on eiher inflaion or real aciviy. 18 As wih he specificaions ha include boh variables, he evidence of predicabiliy weakens wih a symmeric specificaion wih smoohing, weakens furher wih an asymmeric specificaion wihou smoohing, and disappears wih an asymmeric specificaion wih smoohing. The nex opic ha we consider is predicabiliy wih revised daa. While we subscribe o he view ha, because revised daa was no available o marke paricipans a he ime forecass were made, only realime daa should be used o evaluae predicabiliy, he use of revised daa is so ubiquious in he ou-ofsample lieraure ha we choose o use i. The resuls wih revised daa are repored in Table 5. For he symmeric specificaions wih eiher homogeneous or heerogeneous coefficiens, he evidence of ou-ofsample exchange rae predicabiliy is equal o ha wih real-ime daa when inflaion and eiher he HP filered oupu gap or he unemploymen rae are in he forecasing regression. The evidence of predicabiliy, however, weakens when inflaion and he OECD esimaed oupu gap are included. This is consisen wih he visual evidence in Figure 1 ha he differences beween he revised and real-ime daa are larger for he OECD esimaed oupu gap han for he eiher he HP filered oupu gap or he unemploymen rae. I is ofen argued ha forward-looking moneary policy rules provide a superior descripion of cenral banks behavior han rules based on he mos recen esimaes of inflaion. Following Orphanides (2001, 2003), mos of his lieraure uses Greenbook forecass for he U.S. Since Greenbook forecass are no publicly available pas 2002 and here is no equivalen for he ECB, we use SPF forecass for boh. Then resuls are depiced in Table 6 wih he curren inflaion rae replaced by forecased inflaion four quarers ahead. 19 We find no evidence ha ou-of-sample exchange rae predicabiliy is improved by using forecased raher han acual inflaion. For he wo mos successful specificaions, he symmeric model wih and wihou smoohing, here is very lile difference beween using curren and forecased inflaion. This is in accord wih Taylor s (1999) view ha, because hey incorporae he same informaion, inflaion forecas rules are no more forward-looking han rules based on lagged daa. For he wo less successful asymmeric 18 If he random walk null was no rejeced wih eiher inflaion or he real economic aciviy measures, ha would also have consiued evidence of predicabiliy wih Taylor rule fundamenals. If, however, he null was rejeced for eiher inflaion or he real aciviy measures, bu no boh, ha would no have been evidence of predicabiliy wih Taylor rule fundamenals. 19 Given he one-quarer lag in daa releases, we use forecass of inflaion made in period wih daa hrough period 1 for period

18 specificaions, he evidence of predicabiliy decreases wihou smoohing and remains nonexisen wih smoohing. A second example of forward-looking Taylor rules, also considered by Orphanides (2003), adds he forecased rae of growh of he OECD esimaed oupu gap (which is equivalen o he forecased rae of oupu growh minus he forecased rae of poenial oupu growh) o he specificaions ha include inflaion forecass and a measure of real economic aciviy. 20 The resuls of adding forecass of oupu gap growh o our forecasing regression are depiced in Table 7. Alhough his specificaion has inuiive appeal and has worked well in esimaion of Taylor rules for he U.S., i worsens ou-of-sample predicabiliy for he Dollar/Euro exchange rae. The evidence of predicabiliy decreases for he symmeric specificaions and remains low-o-nonexisen for he asymmeric specificaions. 5.2 Tesing for Superior Predicive Abiliy Since we are esing simulaneously hypoheses ha involve 24 differen alernaive models, convenional p-values can be misleading. As a resul of exensive specificaion search, we may misake significan resuls generaed by chance for genuine evidence of predicive abiliy. To address he issue of muliple hypohesis esing, we perform he es of superior predicive abiliy (SPA) proposed by Hansen (2005). The SPA es is designed o compare he ou-of-sample performance of a benchmark model o ha of a se of alernaives. This approach is a modificaion of he realiy check for daa snooping developed by Whie (2000). The advanages of he SPA es are ha i is more powerful and less sensiive o he inroducion of poor and irrelevan alernaives. 21 We are ineresed in comparing he ou-of-sample performance of linear exchange rae models o a naïve random walk benchmark. The SPA es can be used for comparing he ou-of-sample performance of wo or more models. I ess he composie null hypohesis ha he benchmark model is no inferior o any of he alernaives agains he alernaive ha a leas one of he linear economic models has superior predicive abiliy. In he conex of using he CW saisic o evaluae ou-of-sample predicabiliy, he null hypohesis is ha he random walk has an MSE which is smaller han or equal o he adjused MSE s of he linear models. Therefore, rejecing he null indicaes ha a leas one linear model is sricly superior o he random walk. SPA p-values ake ino accoun he search over models ha preceded he selecion of he model being compared o he benchmark. A low p-value suggess ha he benchmark model is inferior o a leas one of he compeing models. A high p-value indicaes ha he daa analyzed do no provide srong evidence ha he benchmark is ouperformed. 20 Orphanides (2003) shows how his rule relaes o moneary growh argeing. 21 Hansen (2005) provides deails on he consrucion of he es saisic and confirms he advanages of he es by Moner Carlo simulaions. We use he publicly available sofware package MULCOM o consruc he SPA-consisen p- values for each counry. The code, deailed documenaion and examples can be found a hp:// 17