Testing the Monetary Model of Exchange Rate Determination: New Evidence from a Century of Data

Transcription

1 Forhcoming in he Journal of Inernaional Economics Tesing he Moneary Model of Exchange Rae Deerminaion: New Evidence from a Cenury of Daa David E. Rapach Albers School of Business and Economics Seale Universiy 900 Broadway Seale, WA Phone: Fax: rapachd@sealeu.edu Mark E. Wohar Deparmen of Economics Universiy of Nebraska a Omaha CBA 512K Omaha, NE Phone: Fax: wohar@unomaha.edu November 14, 2001 Absrac We es he long-run moneary model of exchange rae deerminaion for a collecion of 14 indusrialized counries using daa spanning he lae nineeenh or early wenieh cenury o he lae wenieh cenury. Ineresingly, we find suppor for a simple form of he long-run moneary model in over half of he counries we consider. For hese counries, we esimae vecor error-correcion models o invesigae he adjusmen process o he long-run moneary equilibrium. In he spiri of Meese and Rogoff (1983), we also compare nominal exchange rae forecass based on moneary fundamenals o hose based on a naïve random walk model. JEL classificaions: C22; C32, C53, F31, F47 Key words: Nominal exchange rae; Moneary model; Coinegraion; Forecasing Corresponding auhor. We are very graeful o Michael Bordo and Alan Taylor for generously providing he daa used in his paper. We also hank Alan Isaac, Michael McCracken, and an anonymous referee for helpful commens on an earlier draf. The usual disclaimer applies. The resuls repored in his paper were generaed using GAUSS 3.5.

2 1 1. Inroducion The moneary model of exchange rae deerminaion posis a srong link beween he nominal exchange rae and a simple se of moneary fundamenals. The moneary model s clear-cu inuiion ha a counry s price level is deermined by is supply and demand for money and ha he price level in differen counries should be he same when expressed in he same currency makes i an aracive heoreical ool for undersanding flucuaions in exchange raes over ime. I also provides a long-run benchmark for he nominal exchange beween wo currencies and hus a clear crierion for deermining wheher a currency is significanly overvalued or undervalued. Despie is heoreical appeal, he moneary model did no escape he Meese and Rogoff (1983) rap ha seemingly ensnared all models of exchange rae deerminaion. In heir seminal paper, Meese and Rogoff (1983) find ha a naïve random walk model ouperforms an array of srucural models, including hose based on moneary fundamenals, in predicing U.S. dollar exchange raes a horizons of up o welve monhs during he lae 1970s and early 1980s. Mark (1995) rekindled hope for he moneary model by showing ha deviaions from a simple se of moneary fundamenals relaive money supplies and relaive real oupu levels are useful in predicing U.S. dollar exchange raes a longer horizons over he period. 1 However, Berben and van Dijk (1998) and Berkowiz and Giorgianni (2001) show ha Mark s (1995) findings hinge criically on he assumpion of a sable coinegraing relaionship among nominal exchange raes, relaive money supplies, and relaive oupu levels. When his assumpion is relaxed, he evidence for exchange-rae predicabiliy in Mark (1995) is grealy diminished, and, in fac, Mark (1995) fails o find evidence of coinegraion among nominal exchange raes and moneary fundamenals in preliminary esing. 2 A number of oher sudies also find lile evidence of coinegraion among nominal exchange raes and moneary fundamenals during he pos-breon Woods floa; see, for example, Meese (1986), Baillie and Selover (1987), McNown and Wallace (1989), Baillie and Pecchenino (1991), and Saranis (1994). 3 The lack of empirical evidence for a sable long-run relaionship among nominal exchange raes and moneary fundamenals renders he moneary model a

3 2 seemingly plausible heoreical model wih lile pracical relevance. A ready explanaion for he failure o find coinegraion beween nominal exchange raes and moneary fundamenals in much of he exan lieraure is he relaively shor spans of daa ypically employed, which cover only he pos-breon Woods floa. Sandard ess ake no coinegraion as he null hypohesis, and he power o rejec his null is exremely low using daa from he pos-breon Woods period alone, which span 25 years or less. I does no help ha he daa are ofen sampled a monhly or quarerly frequencies, as he power of uni roo and coinegraion ess depends on he daa s span, raher han is frequency (Shiller and Perron 1985, Hakkio and Rush 1991). A similar siuaion exiss in he empirical purchasing power pariy (PPP) lieraure. Long-run PPP posis a sable long-run relaionship beween nominal exchange raes and relaive price levels, bu empirical suppor for such a relaionship is scan using daa from he modern floa. 4 Again, his can be aribued o he low power of sandard ess for samples as shor as he modern floa. Given ha PPP is a building block of he moneary model, i is no surprising ha i is difficul o find evidence of coinegraion beween nominal exchange raes and moneary fundamenals during he modern floa. Two responses o he problem of low power appear in he PPP lieraure. Firs, a number of sudies employ panels from he pos-breon Woods floa. As iniially shown by Levin and Lin (1992), panel echniques can grealy improve he power of uni roo and coinegraion ess. Indeed, many panel sudies find suppor for long-run PPP for he pos-breon Woods era, including Frankel and Rose (1996), Oh (1996), Wu (1996), Papell (1997), and Taylor and Sarno (1998). The second response o low power in he PPP lieraure is he use of long spans of daa, ofen covering more han a cenury. For example, Abuaf and Jorion (1990), Glen (1992), Lohian and Taylor (1996, 2000), and A. Taylor (2001a) all use long spans of daa o es long-run PPP. These sudies also find considerable suppor for long-run PPP. Boh he panel and long spanning daa sudies show ha deviaions from long-run PPP are quie persisen and display near-uni-roo behavior, precisely he ype of saionary behavior ha will be difficul for sandard single-counry ess o deec for samples as shor as he modern floa.

4 3 In regard o he moneary model, wo recen sudies by Groen (2000) and Mark and Sul (2001) follow he firs response in he PPP lieraure and es for a sable long-run relaionship beween nominal exchange raes and moneary fundamenals using panel coinegraion ess for he pos-breon Woods floa. Ineresingly, hese sudies boh find srong evidence of coinegraion among nominal exchange raes, relaive money supplies, and relaive real oupu levels using panel coinegraion ess. Mark and Sul (2001) acually find suppor for a very simple long-run moneary model ha imposes basic homogeneiy resricions. They also find ha nominal exchange rae forecass based on he moneary model are generally superior o forecass of a naïve random walk model. Given ha he main criicisms of Mark (1995) are based on he lack of coinegraion among nominal exchange raes and moneary fundamenals, he recen findings of Groen (2000) and Mark and Sul (2001) again rekindle hope in he abiliy of moneary fundamenals o rack nominal exchange raes. While Groen (2000) and Mark and Sul (2001) follow he firs response in he PPP lieraure and use panel daa from he modern floa, no sudy pursues he second response in he PPP lieraure and ess he moneary model using long spans of daa. In his paper, we pursue his second response. Jus as Greon (2000) and Mark and Sul (2001) es he moneary model in a panel framework, moivaed by he findings of PPP in panel sudies, we es he moneary model using long spans of daa, moivaed by he findings of PPP in sudies uilizing long spans of daa. In paricular, we apply a baery of uni roo and coinegraion ess o annual daa daing back o he lae nineeenh or early wenieh cenury for 14 indusrialized counries in order o es he long-run moneary model of exchange rae deerminaion. By using long spans of daa, we are able o side-sep some of he problems ha poenially plague panelesing procedures. Of paricular concern is he possibiliy of concluding ha all counries in a panel saisfy he long-run moneary model when, in fac, some individual counries are no well characerized by he moneary model. 5 Our esimaion resuls exhibi considerable suppor for a simple long-run moneary model of U.S. dollar exchange rae deerminaion for France, Ialy, he Neherlands, and Spain; moderae suppor for

5 4 Belgium, Finland, and Porugal; and weaker suppor for Swizerland. For hese eigh counries, we hus find a leas some evidence of a heoreically consisen long-run link beween nominal exchange raes and a simple se of moneary fundamenals. Along wih Groen (2000) and Mark and Sul (2001), our findings are noeworhy given he he lack of empirical suppor in much of he exan lieraure for he long-run relaionship among exchange raes and moneary fundamenals implied by he moneary model. In conras, we fail o find suppor for he long-run moneary model for Ausralia, Canada, Denmark, Norway, Sweden, and he Unied Kingdom using long spans of daa. For he counries for which we find suppor for he simple long-run moneary model, we consider wo addiional opics. Firs, we esimae vecor-error correcion models for nominal exchange raes and moneary fundamenals in order o es for weak exogeneiy. This gives us insigh ino he adjusmen process hrough which he long-run equilibrium relaionship beween exchange raes and moneary fundamenals is mainained. Second, in he spiri of Meese and Rogoff (1983) and Mark (1995), we compare ou-of-sample exchange rae forecass from a naïve random walk model wih forecass based on moneary fundamenals. In line wih he recen work of Berben and van Dijk (1998) and Berkowiz and Giorgianni (2001), we find ha here is a close connecion beween he ou-of-sample forecas performance of he moneary model and he weak exogeneiy es resuls. The res of he paper is organized as follows. Secion 2 presens a simple heoreical moneary model and oulines our esing sraegy. Secion 3 repors our es resuls for he long-run moneary model, including uni roo and coinegraion ess. Secion 4 analyzes error-correcion models suggesed by our coinegraion es resuls. Secion 5 compares ou-of-sample forecass of nominal exchange raes based on moneary fundamenals wih hose of a naïve random walk model. Secion 6 summarizes our main findings.

6 5 2. Theoreical Framework and Tesing Sraegy A number of relaionships underlie he basic varian of he moneary model. We emphasize ha we have in mind a long-run equilibrium relaionship. Firs, sable money demand funcions are assumed for he domesic and foreign counries: 6 m p = α 1i + α 2 y, (1) m 1i 2 p = α + α y, (2) where m is he money supply, p is he price level, i is he nominal ineres rae, and y is real oupu (all a ime ). Wih he excepion of he nominal ineres rae, lower-case leers denoe log-levels. Aserisks denoe a foreign variable. Noe ha he money demand parameers, α 1 and α 2 ( α 1 < 0 and α 2 > 0 ), are assumed o be idenical in he domesic and foreign counries. In our empirical work below, he U.S. serves as he domesic counry. Second, purchasing power pariy is assumed: e = p p, (3) where e is he nominal exchange rae measured in he number of unis of foreign currency per uni of domesic currency. Solving (1) and (2) for yields: p and p and subsiuing he resuling expressions ino (3) e = ( m m ) α ( i i ) α ( y y ). 1 2 Finally, he moneary model ypically assumes uncovered ineres pariy: i ( + 1 i = E e I ), where E( I ) is he expecaions operaor condiional on informaion available a ime. If e is I(0) or I(1), 7 hen e + 1 will be equal o zero in he seady sae (absracing away from any deerminisic rend growh in e ), so ha i = i. This leaves: e = ( m m ) α ( y y ). (4) 2 Equaion (4) is a basic form of he moneary model ha esablishes a long-run relaionship beween he

7 6 nominal exchange rae and a simple se of moneary fundamenals. Mark and Sul (2001, p. 32) emphasize ha (4) can be viewed as a generic represenaion of he long-run equilibrium exchange rae implied by modern heories of exchange rae deerminaion, as a relaionship like (4) can be also derived from he Lucas (1982) and Obsfeld and Rogoff (1995) equilibrium models. Mark (1995) and Mark and Sul (2001) impose he addiional resricion ha α 2 = 1 in (4), yielding he simple form of he moneary model: e = ( m m ) ( y y ). Tesing he long-run moneary model enails esing for he exisence of a sable long-run relaionship among e, m m, and y y, or, equivalenly, esing wheher deviaions of e from a linear combinaion of m m and y y are saionary. Our firs sep in esing he basic long-run moneary model is hus o examine he inegraion properies of e, m m, and y y using he uni roo ess from Ng and Perron (2000), which have goods size and power properies. If e ~ I (0), hen m m and y y mus also boh be I(0) in order for he nominal exchange rae deviaions o be I(0). 8 In fac, if e, m m, y y ~ I(0), his is sufficien o esablish he saionariy of nominal exchange rae deviaions from any linear combinaion of he relaive money supply and relaive oupu level. If e ~ I (1), a necessary condiion for he long-run moneary model is ha one of, or boh of, m m and y y also be I(1) (and neiher can be inegraed of an order greaer han one). When e, m m, y y ~ I (1), he long-run moneary model requires hese hree variables o be coinegraed, and so we esimae he following coinegraing relaionship: e = β + β ( m m ) + β ( y y ), (5) We esimae (5) using OLS, fully modified OLS (Phillips and Hansen 1990, FM-OLS), dynamic OLS (Saikkonen 1991, Sock and Wason 1993, DOLS), and he mulivariae maximum likelihood procedure of Johansen (1988, 1991, JOH-ML). As is now well known, OLS esimaes of β 1 and β 2 in (5) are super-consisen. However, hey are no asympoically efficien, and he OLS covariance marix for he

8 7 esimaed coefficiens is inappropriae for inference, as i is asympoically biased. In conras, he FM- OLS, DOLS, and JOH-ML esimaes are asympoically efficien and yield covariance marices appropriae for inference. We es for coinegraion among e, m m, and y y using he Phillips and Ouliaris (1990), Hansen (1992), and Shin (1994) single-equaion procedures, as well as he Johansen (1988, 1991) sysem-based procedure, which are based on he OLS, FM-OLS, DOLS, and JOH-ML esimaes, respecively. In addiion, we es he simple form of he moneary model ha implies β 1 = 1 and β = 1 by esing he saionariy of e [( m m ) ( y y )] using he same uni roo ess ha 2 we use for he individual series, as well as he Horvah and Wason (1995) es for coinegraion wih a pre-specified coinegraing vecor. Noe ha for a few counries, our uni roo es resuls indicae ha e, m m ~ I (1), while y y ~ I (0). For hese counries, we proceed wih he coinegraion analysis as described above bu wih β 2 = Moneary Model Tes Resuls 3.1 Daa The daa used in his sudy consis of annual observaions for he nominal exchange rae (foreign currency per U.S. dollar), he money supply relaive o he U.S., and real GDP relaive o he U.S. for 14 counries: Ausralia, Belgium, Canada, Denmark, Finland, France, Ialy, he Neherlands, Norway, Porugal, Spain, Sweden, Swizerland, and he Unied Kingdom. The nominal exchange rae series are from A. Taylor (2001a), and he money supply and real GDP series are from Bordo and Jonung (1998) and Bordo, Bergman, and Jonung (1998). The counries considered are deermined by daa availabiliy. The daa run from he lae nineeenh or early wenieh cenury o he lae wenieh cenury and hus cover a variey of inernaional moneary arrangemens, including he classical gold sandard, he Breon Woods era, and he modern floa. The exac sample period for each counry is repored in he ables below. All variables are measured in log-levels. 9

9 8 3.2 Uni Roo Tes Resuls For he 14 counries considered, we firs invesigae he inegraion properies of e, m m, and y y using he Ng and Perron (2000) DF-GLS and MZ α uni roo ess, which are varians of he well-known Dickey and Fuller (1979) and Phillips and Perron (1988) ess, respecively. Boh of hese ess use GLS-derending (as in Ellio, Rohenberg, and Sock 1996) in order o maximize power, and a modified informaion crierion o selec he lag runcaion parameer in an effor o minimize size disorions. Ng and Perron (2000) find ha he DF-GLS and MZ α saisics have good size and power properies in exensive Mone Carlo simulaions. 10 Table 1 repors he resuls for he DF-GLS and ess for our daa. Columns (1) and (5) of Table 1 show he counry, ime period, variable esed, and wheher a linear rend was included in he uni roo ess. The inclusion of a linear rend is indicaed by visual inspecion of he series, as well as formal saisical ess. 11 MZ α Because differen ess yield conradicory resuls on a few occasions, we designae he variables in Table 1 as I(1), I(0), or I(1) or I(0) in Table 1 according o he following simple decision rule. We designae a varable as I(0) if boh of he ess rejec he null hypohesis of nonsaionariy a convenional significance levels or if a leas one es rejecs a he 5 percen significance level. If neiher es rejecs he null hypohesis of nonsaionariy a convenional significance levels, we designae he variable as I(1). Finally, if only one es rejecs a he 10 percen level, we designae he series as I(1) or I(0). m m Based on he uni roo es resuls in Table 1, we conclude ha all hree of he variables, e,, and y y, are I(1) for Ausralia, Belgium, France, Ialy, Spain, and he Unied Kingdom. All hree variables are found o be I(0) for he Neherlands. For Finland and Porugal, we find ha e and m m are each I(1), while y y ~ I (0). For Denmark and Norway, we find ha e ~ I (0), while m m ~ I(1) ( y y is inconclusive for Denmark and y y ~ I (0) for Norway). For Sweden, our

10 9 es resuls indicae ha e ~ I (0) and m m, y y ~ I (1). Finally, for Canada and Swizerland, our uni roo es resuls are inconclusive for e, while hey indicae ha m m, y y ~ I (1). 12 Nex, we discuss he implicaions of our uni roo es resuls for esing he long-run moneary model using coinegraion procedures. For he Neherlands, all hree variables are saionary, so we conclude on he basis of he uni roo es resuls alone ha deviaions of e from any linear combinaion of m m and y y are saionary for he Neherlands. For Ausralia, Belgium, France, Ialy, Spain, and he Unied Kingdom, e, m m, and y y are all I(1). In he nex subsecion, we hus proceed o es for a coinegraing relaionship among hese hree variables, as required by he long-run moneary model. Finland and Porugal appear o be an inermediae case, wih he nominal exchange rae and he relaive money supply being I(1), bu wih he relaive oupu level being saionary. For hese counries, he long-run moneary model requires a coinegraing relaionship beween only e and m m, as here are no long-run changes in y y. In he nex subsecion, we hus es for coinegraion beween he nominal exchange rae and he relaive money supply for Finland and Porugal. For Denmark, Norway, and Sweden, e is saionary, bu m m ~ I(1). We can hus conclude on he basis of he uni roo es resuls alone ha he long-run moneary model does no hold in hese counries over our sample. 13 For Canada and Swizerland, i is difficul o ell wheher e is I(1) or I(0). If e ~ I (0), we have direc evidence agains he long-run moneary model, as i requires e ~ I (1) if m m, y y ~ I (1) hese wo counries, we give he moneary model a chance and es for coinegraion among e,. For m m, and y y under he assumpion ha e ~ I (1). 3.3 Coinegraion Tes Resuls We repor coinegraing coefficien esimaes for en counries in Table 2 (excluding he Neherlands, Denmark, Norway, and Sweden on he basis of he uni roo es resuls in Table 1). Column (1) of Table

11 10 2 gives he counry, sample period, and wheher a rend is included in he coinegraing vecor. 14 Based on he uni roo es resuls in Table 1, we esimae he coinegraing relaionship, e y = β + β ( m m ) + β ( y ), for Ausralia, Belgium, Canada, France, Ialy, Spain, Swizerland, 0 1 and he Unied Kingdom, while we esimae he coinegraing relaionship, e = β + β ( m m ), for Finland and Porugal. Table 2 includes OLS, FM-OLS, DOLS, and JOH-ML esimaes. Following he applicaions in Hansen (1992), we use he quadraic kernel and he Andrews (1991) auomaic bandwidh selecor wih Andrews and Monohan (1992) prewhiening when compuing he FM-OLS esimaes. 15 Following Sock and Wason (1993), we se he number of leads and lags in he DOLS esimaor equal o wo, and we use an auoregressive procedure o compue robus sandard errors. We also repor a Sock and Wason (1993) Wald es (SW-Wald) of he join hypohesis ha β 1 = 1 and β 2 = 1, as implied by he simple moneary model ha ses he common income elasiciy of money demand o uniy (see column (8) of Table 2). We selec he lag order for he JOH-ML esimaor by sequenially esing a VAR in levels using he Sims (1980) modified likelihood-raio saisic, a maximum lag order of five, and he 10 percen significance level. 16 We also presen a 2 χ es due o Johansen (1991), labeled JOH- χ, ha 2 we use o es he join null hypohesis ha β 1 = 1 and β 2 = 1 in he coinegraing vecor (see column (11) of Table 2). For Belgium, Ialy, and Spain, all four esimaion procedures generally yield parameer esimaes close o he heoreical values implied by he simple moneary model ( β 1 = 1 and β 2 = 1). 17 The coinegraing coefficien esimaes for Belgium are very close o hose implied by he simple moneary 2 model, and he SW-Wald and JOH- χ ess canno rejec he join resricion ha β 1 and β = 1 for Belgium. For Ialy, he SW-Wald es also canno rejec he join resricion ha β 1 = 1 and β 2 = 1. For Spain, he join resricion is rejeced by boh he SW-Wald and JOH- χ ess, apparenly due o β 1 esimaes ha are significanly less han one. While less han one in saisical erms, he β 1 esimaes are 2 1 = 2

12 11 sill relaively close o heir heoreical value of uniy in magniude. On he whole, he esimaed coinegraing relaionships for Belgium, Ialy, and Spain are consisen wih he simple long-run moneary model. The OLS, FM-OLS, and DOLS coefficien esimaes for France are also very close o hose implied by he simple moneary model, and he SW-Wald es canno rejec he null hypohesis ha β 1 =1 and β 2 = 1. The JOH-ML esimaor for France yields a β 1 esimae very close o uniy, and while he esimae for β 2 has he correc sign, i is quie small in magniude and saisically insignifican. 18 Phillips (1994) provides a possible explanaion for he discrepancy beween he JOH-ML β 2 esimae and he FM-OLS and DOLS β 2 esimaes. Phillips (1994) shows ha coinegraion coefficien esimaes based on reduced rank regressions (such as JOH-ML) can have Cauchy-like ails and no finie ineger momens in finie samples, so ha ouliers can be expeced o occur more frequenly han oher asympoically efficien esimaors such as he FM-OLS and DOLS esimaors. 19 The JOH-ML β 2 esimae appears o be an oulier for France. Turning o he resuls for Swizerland in Table 2, we see some suppor for he moneary model. The FM-OLS esimaes are reasonably close, and he DOLS esimaes are very close, o he values implied by he simple moneary model. Using he SW-Wald es, we canno rejec he null hypohesis ha β 1 =1 and β 2 = 1. However, he same null is rejeced using he JOH- χ es, apparenly due o he JOH-ML esimae of β 2. As wih France, he resuls in Phillips (1994) sugges ha he DOLS esimae of β 2 and he SW-Wald es are more reliable han he JOH-ML esimae and he JOH- χ es. There is lile suppor in he coinegraing coefficien esimaes for he moneary model for Ausralia, Canada, and he Unied Kingdom. For Canada, all four esimaion procedures yield esimaed β 2 coefficiens ha are of he wrong sign and saisically insignifican. 20 While he coefficien esimaes for Ausralia have he correc sign, hey are ypically insignifican, and while he coefficien esimaes are he correc sign for he Unied Kingdom, he β 1 esimaes are all more han wo sandard errors below 2 2

13 12 heir prediced heoreical value of uniy. 0 1 Recall ha we consider he coinegraing relaionship, e = β + β ( m m ), for Finland and Porugal, as i appears ha y y ~ I (0) in hese counries. For Finland, hree of he four β 1 esimaes are close o heir prediced value of uniy, while all four β 1 esimaes are close o heir prediced value of uniy for Porugal. 21 Overall, we are able o obain coinegraing coefficiens esimaes consisen wih he long-run moneary model in Table 2 for Belgium, Finland, France, Ialy, Porugal, Spain, and Swizerland. The nex sep is o deermine if a coinegraing relaionship exiss beween he nominal exchange rae and he moneary fundamenals in hese seven counries. 22 Table 3 repors he resuls from four differen coinegraion ess. The firs is he well-known Phillips and Ouliaris (1990) es (PO- Z ) ha ess he saionariy of he OLS residuals using a Phillips α and Perron (1988)-ype procedure. We use he quadraic specral kernel and he Andrews (1991) auomaic bandwidh selecor wih prewhiening when compuing he semi-parameric adjusmen for he PO- Z saisic. We also repor resuls for he popular Johansen (1988, 1991) race es. 23 The PO- Z α and race ess boh ake no coinegraion as he null hypohesis and coinegraion as he alernaive hypohesis. We consider wo addiional ess, due o Hansen (1992) and Shin (1994), ha es he null hypohesis of coinegraion agains he alernaive of no coinegraion. If we ake he moneary model as our mainained hypohesis, he null of coinegraion may be more appropriae han he null of no coinegraion. The Hansen (1992) L c saisic is based on he on he FM-OLS residuals, while he Shin (1994) C µ saisic is consruced from he DOLS residuals. 24 For France, Ialy, and Spain, all four ess α indicae he exisence of a coinegraing relaionship a convenional significance levels, and coinegraion is indicaed by hree of he four ess for Finland and Porugal. The coinegraion for Belgium and Swizerland. L c saisic poins o As he esimaed coinegraing coefficiens are close o β 1 = 1 and β 2 = 1 in Table 2 for Belgium, Finland, Frace, Ialy, Porugal, Spain, Swierland, a complemenary es of he simple long-run

14 13 moneary model for hese counries is o es wheher e [( m m ) ( y y )], he deviaion of he exchange rae from he level prediced by he simple moneary model, is saionary. This is anamoun o esing for coinegraion beween he exchange rae and he moneary fundamenals wih pre-specified coinegraing coefficiens of β 1 = 1 and β 2 = 1. We es he saionariy of he deviaions using he wo uni roo ess used for he individual series in Table 1, and he resuls are repored in Table 4. Table 4 also repors resuls for he mulivariae Horvah and Wason (1995) es of he null hypohesis of no coinegraion agains he alernaive hypohesis of coinegraion wih pre-specified coinegraing coefficiens β 1 = 1 and β 2 = As discussed in Horvah and Wason (1995), his es is poenially more powerful han univariae uni roo ess when esing for coinegraion wih a known coinegraing vecor. Noe ha we consider he deviaion, e ( m m ), for Finland and Porugal, in line wih he previous resuls. Also noe ha we include he deviaion e [( m m ) ( y y )] for he Neherlands in Table 4. The uni roo ess in Table 1 clearly indicae ha each componen of he deviaion is saionary for he Neherlands, and so we expec he deviaion o be saionary. We include he Neherlands as a robusness check of he Table 1 resuls. For Belgium, Ialy, he Neherlands, and Spain, he DF-GLS and MZ α ess boh indicae ha he deviaion is saionary a convenional significance levels. The Horvah and Wason (1995) es suppors he simple long-run moneary model for six of he seven counries for which i is relevan. (I is no relevan for he Neherlands.) Figure 1 presens graphs of he nominal exchange rae deviaions from he level prediced by he simple moneary model for he eigh counries examined in Table 4. Verical lines are drawn for he years 1913, 1946, and 1970 o roughly depic differen inernaional exchange rae regimes: classical gold sandard, inerwar period, Breon Woods era, and he modern floa. 26 A endency for mean-reversion in each deviaion is eviden in Figure 1. (For France and Swizerland, he deviaions appear saionary around a rend.) I is also eviden from Figure 1 ha deviaions from he moneary fundamenals can be quie subsanial and persisen. Because of his, i will be difficul o deec he long-run relaionship

15 14 beween he nominal exchange rae and moneary fundamenals using daa from he modern floa alone. 27 Also noe ha he early 1980s sand ou in Figure 1 as a period where U.S. dollar exchange raes diverge considerably from he underlying moneary fundamenals. The U.S. dollar appears subsanially overvalued during his period, as is widely believed. To summarize he resuls of his secion, we find considerable suppor for a very simple form of he long-run moneary model of U.S. dollar exchange rae deerminaion for France, Ialy, he Neherlands, and Spain using long daa spans. We find moderae suppor for Belgium, Finland, and Porugal and weaker suppor for Swizerland. From Figure 1, we see ha long spans of daa will generally be required o deec he long-run equilibrium relaionship implied by he moneary model. 4. Error-Correcion Models In order o gain insigh ino how he long-run equilibrium is resored beween nominal exchange raes and moneary fundamenals, we esimae he following bivariae vecor error-correcion model (VECM) in e and f, where f = ( m m ) ( y y ) : p p e = γ 0 + γ 1i e i + γ 2i f i + λ e, z z 1 + ε1 i= 1 i= 1, (6) p p f = δ 0 + δ1i e i + δ 2i f i + λ f, z z 1 + ε 2 i= 1 i= 1, (7) where z = e f. We esimae he VECM for all of he counries in Table 4, wih he excepion of he Neherlands, due o he saionariy of he nominal exchange rae and moneary fundamenals in he Neherlands. Following he lead of Tables 2-4, we use f = m m for Finland and Porugal. Table 5 repors OLS esimaes of he error-correcion coefficiens, λ e, z and λ f, z, ha govern he adjusmen o he long-run equilibrium. For Belgium, Finland, and Ialy, he error-correcion coefficien in he exchange rae equaion ( λ e, z ) is significan, while he error-correcion coefficien in

16 15 he fundamenals equaion ( λ f, z ) is insignifican. This implies ha he moneary fundamenals are weakly exogenous for hese counries (see Engle, Hendry, and Richard 1983). In oher words, when deviaions from he long-run equilibrium occur in Belgium, Finland, and Ialy, i is primarily he exchange rae ha adjuss o resore long-run equilibrium over our sample, raher han he moneary fundamenals. For Porugal and Spain, he resuls are reversed: λ e, z is insignifican, while λ f, z is significan, so ha he exchange rae is weakly exogenous for hese counries over our sample. When deviaions from he long-run equilibrium occur in Porugal and Spain, i is he moneary fundamenals ha bear he brun of adjusmen over our sample. 28 λ e,z and λ f, z For France and Swizerland, an inermediae resul obains, as boh error-correcion coefficiens,, are significan (and have he correc sign), so ha neiher he exchange rae nor he moneary fundamenals are weakly exogenous. Boh he nominal exchange rae and he moneary fundamenals adjus o resore long-run equilibrium for hese wo counries over our sample. The differen adjusmen mechanisms a work in he differen counries over he las cenury likely reflec varying degrees of commimen o nominal exchange rae sabiliy Nominal Exchange Rae Forecasing An imporan srand of he exan lieraure invesigaes he forecasing performance of he moneary model of exchange rae deerminaion. In heir seminal paper, Meese and Rogoff (1983) repor ha ouof-sample forecass of moneary models canno ouperform a naïve random walk model for U.S. dollar exchange raes for Germany, Japan, and he Unied Kingdom during he period. 30 However, in a well-known paper, Mark (1995) shows ha pas nominal exchange rae deviaions from he level prediced by he simple moneary model, z = e [( m m ) ( y y )], are useful in predicing U.S. dollar exchange raes a longer horizons for he period The Mark (1995) finding is noeworhy, given he pessimism generaed by Meese and Rogoff (1983). In he spiri of Meese and

17 16 Rogoff (1983) and Mark (1995), we examine he ou-of-sample forecasing performance of he simple moneary model using our long spans of daa for he counries in Table 5. Mark (1995) compues recursive ou-of-sample forecass a he k-horizon based on moneary fundamenals. He esimaes he following equaion hrough period 0 < T, where T is he size of he available sample, in order o generae he firs k-horizon forecas for he moneary model: 0 ˆ + k e = α ˆ( k; 0 ) + β k ( k; ) z. (8) eˆ Equaion (8) is hen re-esimaed using daa hrough period in order o generaed a second k- horizon forecas for he moneary model, and his process is coninued hrough period T k. These k- horizon forecass are hen compared o he k-horizon forecass from a naïve random walk model. The forecass are compared using Theil s U, he raio of he roo mean squared predicion error (RMSE) for he moneary model o he RMSE for he random walk model, and he Diebold and Mariano (1995) es for equal predicive abiliy based on he MSE crierion. Mark (1995) finds ha forecass from he moneary model are ofen superior o hose of he naïve random walk model, especially a longer horizons. Berkowiz and Giorgianni (2001) challenge he robusness of Mark s (1995) findings by showing ha hey hinge criically on he assumpion ha z is saionary (ha is, ha nominal exchange raes and moneary fundamenals are coinegraed). This is problemaic for Mark (1995), as he fails o find evidence of coinegraion beween nominal exchange raes and moneary fundamenals for his pos- Breon Woods daa. However, we do find evidence of coinegraion for he counries in Table 4, so he saionariy of z is much less of an issue for our daa. 31 We follow Mark (1995) and compare forecass from he moneary model, (8), wih hose obained from a simple random walk wih drif model. 32 Recen heoreical work by McCracken (1999) and Clark and McCracken (2001) is relevan for our forecasing exercise. McCracken (1999) shows ha while he popular Diebold and Mariano (1995) saisic has a sandard asympoic disribuion when i is used o compare one-sep-ahead forecass beween nonnesed models, i has a nonsandard disribuion

18 17 when used o compare forecass beween wo nesed models. When comparing (8) agains he random walk wih drif model, we are, of course, comparing nesed models. Clark and McCracken (2001) show ha similar resuls hold for he Ericsson (1992) and Harvey, Leybourne, and Newbold (1998) forecas encompassing ess. While here are no heoreical resuls for ess beyond he one-sep-ahead horizon for nesed models (a he ime of he wriing of his paper), Berben and van Dijk (1998) and Berkowiz and Giorgianni (2001) show ha he one-sep-ahead horizon is he mos imporan horizon for he predicive regression (8). We use five ess from Clark and McCracken (2001) o compare recursive ou-of-sample onesep-ahead forecass from (8) o hose of a random walk wih drif for he counries considered in Table 5. The firs wo ess, MSE-F and MSE-T, are versions of he popular Diebold and Mariano (1995) and Wes (1996) ess. They are used o es he null hypohesis ha he MSE of he moneary model (MSE MF ) is equal o he MSE of he random walk wih drif model (MSE RW ) agains he alernaive hypohesis ha MSE MF < MSE RW. The oher hree ess are he ENC-T es of Harvey, Leybourne, and Newbold (1998), he ENC-REG es of Ericsson (1992), and he ENC-NEW es developed by Clark and McCracken (2001). The null hypohesis for each of hese ess is ha forecass from he random walk wih drif model encompass he forecass from (8). Forecas encompassing is based on opimally consruced composie forecass. If he forecass from he random walk wih drif model encompass forecass based on (8), his essenially means ha forecass from (8) provide no addiional informaion ha is valuable in forecasing exchange raes apar from he informaion already conained in he random walk wih drif model. If we can rejec he null of forecas encompassing, hen forecass from (8) provide informaion above and beyond he informaion already in forecass from he random walk wih drif model. For all five ess, he firs recursive forecas is generaed using he firs half of he available sample. Inferences are based on he asympoic criical values in McCracken (1999) and Clark and McCracken (2001). Clark and McCracken (2001) find ha hese asympoic criical values work well in finie samples in exensive Mone Carlo simulaions. They also esablish he following ranking of he

19 18 power of he various ess based on exensive Mone Carlo simulaions: ENC-NEW > MSE-F, ENC-T, ENC-REG > MSE-T. The forecasing resuls are repored in Table 6. Column (2) gives he forecas period for each counry, and column (3) repors Theil s U (RMSE MF /RMSE RW ). There is considerable evidence of exchange rae predicabiliy based on moneary fundamenals for Belgium, Ialy, and Swizerland. These resuls are consisen wih hose in Table 5, where he error-correcion coefficien in he exchange rae equaion is significan for Belgium, Ialy, and Swizerland. For hese hree counries, we expec he exchange rae o adjus o resore he long-run moneary equilibrium, and hus moneary fundamenals should be helpful in predicing fuure exchange raes. In conras, here is no evidence ha moneary fundamenals improve exchange rae forecass for France, Porugal, and Spain. Again, his is consisen wih he resuls in Table 5, where he error-correcion coefficien in he exchange rae equaion is insignifican for Porugal and Spain and only significan a he 10 percen level for France. For hese hree counries, he error-correcion coefficien in he fundamenals equaion is significan, indicaing ha i is primarily he moneary fundamenals insead of he nominal exchange rae ha adjus o resore he long-run moneary equilibrium. Given ha he moneary fundamenals do he adjusing, i is no surprising o find ha nominal exchange rae deviaions from he long-run equilibrium are no helpful for predicing fuure exchange raes for France, Porugal, and Spain. There is relaively lile evidence ha moneary fundamenals improve forecass for Finland, alhough he ENC-NEW es, which Clark and McCracken (2001) find o be he mos powerful of he five ess, is significan a he 10 percen level. 33 The resuls in Tables 5 and 6 have imporan implicaions for ess of he moneary model based on exchange rae predicabiliy. Berkowiz and Giorgianni (2001) recommend esing for coinegraion and esimaing a VECM before proceeding o exchange rae forecasing, as he forecas resuls will depend criically on he exisence of coinegraion and weak exogeneiy. Our resuls srongly suppor heir recommendaion. If we only look a he forecasing resuls in Table 6, we would conclude ha he moneary model does no hold for hree or four of he counries in Table 6, as he moneary fundamenals

20 19 do no improve exchange rae forecass for hese counries. However, he resuls in Tables 2-4 indicae ha here is suppor for he long-run moneary model for all of he counries in Table 6. As discussed above, he discrepancy can be explained by he resuls in Table 5: he inabiliy of moneary fundamenals o improve exchange rae forecass in some counries can largely be aribued o he weak exogeneiy of he exchange rae in hose counries. 6. Conclusion Groen (2000) and Mark and Sul (2001) es he moneary model using panel daa from he modern floa, moivaed by sudies ha find suppor for long-run PPP using panel daa from he modern floa. Similarly, we es he moneary model using daa spanning he lae nineeenh or early wenieh cenury o he lae wenieh cenury, moivaed by sudies ha find suppor for long-run PPP using long spans of daa. Using uni roo and coinegraion ess, we find considerable suppor for a simple form of he longrun moneary model of U.S. dollar exchange rae deerminaion for France, Ialy, Spain, and he Neherlands. We find moderae suppor for Belgium, Finland, and Porugal and weaker suppor for Swizerland. Togeher wih Groen (2000) and Mark and Sul (2001), we show ha suppor for he longrun moneary model of exchange rae deerminaion is no as elusive as i once appeared. However, our resuls also sugges ha he suppor for he moneary model in Groen (2000) and Mark and Sul (2001) may be oversaed. We idenify a number of counries Ausralia, Canada, Denmark, Norway, Sweden, and he Unied Kingdom for which he long-run moneary model does no hold, while he panel coinegraion ess in Groen (2000) and Mark and Sul (2001) require one o accep he moneary model for each member of he enire panel. I would be useful o examine he robusness of he Groen (2000) and Mark and Sul (2001) resuls o various subpanels and o formally es for heerogeneiy across panel members. For he counries for which we find suppor for he simple long-run moneary model, we consider wo addiional opics. Firs, we esimae vecor error-correcion models for nominal exchange raes and

21 20 moneary fundamenals in order o es for weak exogeneiy. This analysis provides insigh ino o adjusmen process hrough which he long-run equilibrium relaionship beween exchange raes and fundamenals is resored afer a shock. We find ha he adjusmen process can vary across counries. Second, we compare ou-of-sample exchange rae forecass from a naïve random walk model wih hose based on moneary fundamenals. Consisen wih he recen work of Berben and van Dijk (1998) and Berkowiz and Giorgianni (2001), we find ha here is a close connecion beween he ou-of-sample forecas performance of he moneary model and he weak exogeneiy es resuls. Our resuls sugges direcions for fuure research. Given ha long-run PPP appears o hold for mos counries over long ime spans, he failure of he long-run moneary model for some counries using long spans of daa mus be due o insabiliy in he long-run relaionship beween relaive price levels and moneary fundamenals for hose counries. I would hus be informaive o search for insabiliies in he long-run relaive price level-moneary fundamenals relaionship in he counries for which he long-run moneary model fails. In counries for which here is suppor for he long-run model, i would be ineresing o examine he adjusmen process o he long-run equilibrium relaionship implied by he long-run moneary model in more deail by calculaing impulse responses for nominal exchange raes and moneary fundamenals in a VECM framework. Finally, recen research by M. Taylor and Peel (2000) suggess ha nominal exchange rae deviaions from underlying moneary fundamenals display nonlinear mean-reversion. I would be ineresing o explore his possibiliy for he counries for which we find suppor for he long-run moneary model using long spans of daa.

22 21 References Abuaf, N., Jorion, P., Purchasing power pariy in he long run. Journal of Finance 45, Andrews, D.W., Heeroskedasiciy and auocorrelaion consisen covariance marix esimaion. Economerica 59, Andrews, D.W., Monohan, J.C., An improved heeroskedasiciy and auocorrelaion consisen covariance marix esimaor. Economerica 60, Baillie, R.T., Pecchenino, R.A., The search for equilibrium relaionships in inernaional finance: he case of he moneary model. Journal of Inernaional Money and Finance 10, Baillie, R.T., Selover, D.D., Coinegraion and models of exchange rae deerminaion. Inernaional Journal of Forecasing 3, Berben, R.-P., van Dijk, D., Does he absence of coinegraion explain he ypical findings in longhorizon regressions? Economerics Insiue, Erasmus Universiy, Repor Berkowiz, J., Giorgianni, L., Long-horizon exchange rae predicabiliy? Review of Economics and Saisics 83, Bordo, M.D., Jonung, L., A reurn o he converibiliy principle? Moneary and fiscal regimes in hisorical perspecive, in: Leijonhuvhud, A. (Ed.), Moneary Theory as a Basis For Moneary Policy, MacMillan, London. Bordo, M.D., Bergman, M., Jonung, L., Hisorical evidence on business cycles: he inernaional perspecive, in: Fuhrer, J.C., Schuh, S. (Eds.), Beyond Shocks: Wha Causes Business Cycles, Conference Series No. 42, Federal Reserve Bank of Boson, pp Cheung, Y.-W., Lai, K.S., Finie-sample sizes of Johansen s likelihood raio ess for coinegraion. Oxford Bullein of Economics and Saisics 55, Chinn, M.D., Meese, R.A., Banking on currency forecass: how predicable is change in money? Journal of Inernaional Economics 38, Clark, T.E., McCracken, M.W., 2001, Tess of equal forecas accuracy and encompassing for nesed models. Journal of Economerics 105, Cushman, D.O., The failure of he moneary exchange rae model for he Canadian-U.S. dollar. Canadian Journal of Economics 33, Dickey, D.A., Fuller, W.A., Disribuion of he esimaors for auoregressive ime series wih a uni roo. Journal of he American Saisical Associaion 74, Diebold, F.X., Mariano, R.S., Comparing predicive accuracy. Journal of Economics and Business Saisics 13, Ellio, G., Rohenberg, T.J., Sock, J.H., Efficien ess for an auoregressive uni roo. Economerica 64,

23 22 Engle, R.F., Hendry, D., Richard, J.-F., Exogeneiy. Economerica 51, Ericsson, N.R., Coinegraion, exogeneiy, and policy analysis: an overview. Journal of Policy Modeling 14, Frankel, J.A., Rose, A.K., Empirical research on nominal exchange raes, in: Rogoff, K., Grossman, G. (Eds.), Handbook of Inernaional Economics, Vol. 3, Norh Holland, Amserdam, pp Frankel, J.A., Rose, A.K., A panel projec on purchasing power pariy: mean reversion wihin and beween counries. Journal of Inernaional Economics 40, Froo, K.A., Rogoff, K., Perspecives on PPP and long-run real exchange raes, in: Rogoff, K., Grossman, G. (Eds.), Handbook of Inernaional Economics, Vol. 3, Norh Holland, Amserdam, pp Glen, J.D., Real exchange raes in he shor, medium, and long run. Journal of Inernaional Economics 33, Groen, J.J.J., The moneary exchange rae model as a long-run phenomenon. Journal of Inernaional Economics 52, Hakkio, C.S., Rush, M., Coinegraion: how shor is he long run? Journal of Inernaional Money and Finance 10, Hansen, B.E., Tess for parameer insabiliy in regressions wih I(1) processes. Journal of Business and Economic Saisics 10, Harvey, D.I., Leybourne, S.J., Newbold, P., Tess for forecas encompassing. Journal of Economics and Business Saisics 16, Horvah, M.T., Wason, M.W., Tesing for coinegraion when some of he coinegraing vecors are prespecified. Economeric Theory 11, Johansen, S., Saisical analysis of coinegraing vecors. Journal of Economic Dynamics and Conrol 12, Johansen, S., Esimaion and hypohesis esing of coinegraion vecors in Gaussian vecor auoregressive models. Economerica 59, Kilian, L., Exchange raes and moneary fundamenals: wha do we learn from long-horizon regressions? Journal of Applied Economerics 14, Levin, A., Lin, C.-F., Uni roo ess in panel daa: asympoic and finie-sample properies. Discussion Paper 92-23, Deparmen of Economics, Universiy of California-San Diego. Lohian, J.R., Taylor, M.P., Real exchange rae behavior: he recen floa from he perspecive of he las wo cenuries. Journal of Poliical Economy 104,

24 23 Lohian, J.R., Taylor, M.P., Purchasing power pariy over wo cenuries: srenghening he case for real exchange rae sabiliy: a reply o Coddingon and Liang. Journal of Inernaional Money and Finance 19, Lucas, Jr., R.E., Ineres raes and currency prices in a wo counry world. Journal of Moneary Economics 10, MacDonald, R., Taylor, M.P., The moneary model of he exchange rae: long-run relaionships, shor-run dynamics, and how o bea a random walk. Journal of Inernaional Money and Finance 13, Mark, N.C., Exchange raes and fundamenals: evidence on long-horizon predicabiliy. American Economic Review 85, Mark, N.C., Sul, D., Nominal exchange raes and moneary fundamenals: evidence from a small pos- Breon Woods panel. Journal of Inernaional Economics 53, McCracken, M.W., Asympoics for ou of sample ess of causaliy. Working Paper, Louisiana Sae Universiy. McNown, R.A., Wallace, M., Coinegraion ess for long-run equilibrium in he moneary exchange rae model. Economics Leers 31, Meese, R.A., Tesing for bubbles in exchange markes: a case of sparkling raes. Journal of Poliical Economy 94, Meese, R.A., Rogoff, K., Empirical exchange rae models of he sevenies: do hey fi ou of sample? Journal of Inernaional Economics 14, Ng, S., Perron, P., Lag lengh selecion and he consrucion of uni roo ess wih good size and power. Economerica, forhcoming. Obsfeld, M., and Rogoff, K., Exchange raes dynamic redux. Journal of Poliical Economy 103, Oh, K.-Y., Purchasing power pariy and uni roo ess using panel daa. Journal of Inernaional Money and Finance 15, Oserwald-Lenum, M., A noe wih fraciles of he asympoic disribuion of he maximum likelihood coinegraion rank es saisics: four cases. Oxford Bullein of Economics and Saisics 54, Papell, D.H., Searching for saionariy: purchasing power pariy under he curren floa. Journal of Inernaional Economics 43, Phillips, P.C.B., Some exac disribuion heory for maximum likelihood esimaors for coinegraing coefficiens in error correcion models. Economerica 62, Phillips, P.C.B., Hansen, B.E., Saisical inference in insrumenal variables regression wih I(l) processes. Review of Economic Sudies 57,

25 24 Phillips, P.C.B, Ouliaris, S., Asympoic properies of residual based ess for coinegraion. Economerica 58, Phillips, P.C.B., Perron, P., Tesing for a uni roo in ime series regression. Biomerika 75, Rogoff, K., The purchasing power pariy puzzle. Journal of Economic Lieraure 34, Saikkonen, P., Asympoically efficien esimaion of coinegraing regressions. Economeric Theory 7, Saranis, N., The moneary exchange rae model in he long run: an empirical invesigaion. Welwirschafliches Archiv 130, Sarno, L., Taylor, M.P., Purchasing power pariy and he real exchange rae. Journal of Economic Lieraure, forhcoming. Shiller, R.J., Perron, P., Tesing he random walk hypohesis: power versus frequency of observaion. Economic Leers 18, Shin, Y., A residual-based es of he null of coinegraion agains he alernaive of no coinegraion. Economeric Theory 10, Sims, C.A., Macroeconomics and realiy. Economerica 48: Sock, J.H., Wason, M.W., A simple esimaor of coinegraing vecors in higher order inegraed sysems. Economerica 61, Taylor, A.M., 2001a. A cenury of purchasing power pariy. Review of Economics and Saisics, forhcoming. Taylor, A.M., 2001b. Poenial pifalls for he purchasing-power pariy puzzle: sampling and specificaion biases in mean-reversion ess of he law of one price. Economerica 69, Taylor, M.P., The economics of exchange raes. Journal of Economic Lieraure 33, Taylor, M.P., Peel, D.A., Nonlinear adjusmen, long-run equilibrium and exchange rae fundamenals. Journal of Inernaional Money and Finance 19, Taylor, M.P., Sarno, L., The behavior of real exchange raes during he pos-breon Woods period. Journal of Inernaional Economics 46, Wes, K.D., Asympoic inference abou predicive abiliy. Economerica 64, Whie, H., A heeroskedasiciy-consisen covariance marix and a direc es of heeroskedasiciy. Economerica 48: Wu, Y., Are real exchange raes nonsaionary? Evidence from a panel daa es. Journal of Money, Credi, and Banking 28,