Testing the Taylor Model Predictability for Exchange Rates in Latin America

Transcription

1 Tesing he Taylor Model Predicabiliy for Exchange Raes in Lain America Marcelo L. Moura Ibmec São Paulo Rua Quaá 300, São Paulo-SP Brazil CEP: Tel.: ABSTRACT Exchange raes forecasing performance is esed by a model which incorporaes endogenous moneary policy hrough a Taylor rule reacion funcion. Oher usual moneary and equilibrium empirical exchange rae models are also evaluaed for comparison purposes. Predicabiliy is esed by comparing he models o a benchmark random-walk specificaion. We conribue o he recen lieraure in many ways. Firs, we include models of forward looking endogenous moneary policy o he exchange rae forecasing exercise, he Taylor Model. Second, our daa, se across counries, is uniform in erms of economies adoping boh inflaion argeing and flexible exchange rae. Third, our sudy sheds ligh on exchange rae deerminans for emerging economies: Brazil, Chile, Colombia, Peru and Mexico. Despie he increasing economic imporance of his group of counries, sudies abou hem are in relaively shor supply. Our resuls show srong predicabiliy evidence for he Taylor Model and indicae ha assuming models of endogenous moneary policy and presen value of expeced fundamenals is a rewarding sraegy o model exchange rae deerminaion. Key-Words: Exchange Raes, Taylor Rule model, Moneary model, Ineres Rae Pariy; Purchasing Power Pariy; Uni Roo, Coinegraion; Forecasing performance. JEL Codes: F31, F41, F47. 1 Inroducion Brazil, Chile, Colombia, Peru and Mexico are all Lain America Emerging Economies ha have shared free floaing exchange rae arrangemens and inflaion argeing moneary frameworks since lae 90 s. These homogeneous characerisics allow us o evaluae one imporan quesion ha has consiued an acive field of research over he pas few years. When he quesion comes o exchange rae forecasing, is i possible o bea a random walk guess? Wha is new in his sudy? Firs, much of he recen lieraure looks a jus a few models ha are in general old vinage moneary models of he 1970s and 1980s wih an unrealisic assumpion of exogenous moneary policy. Insead, we use an up-o-dae endogenous moneary model based on a Taylor rule reacion funcion. We compare he predicabiliy of his model agains a benchmark random-walk. We also conras he Taylor predicabiliy resuls wih a wider se of models: (i) he radiional moneary model from he 1970s; (ii) models based on produciviy differenials and equilibrium relaionships from he 1980s and 1

2 1990s, and (iii) known relaionships such as he uncovered ineres pariy arbirage resricions and he power purchasing pariy equilibrium condiions. Second, in a plehora of papers abou exchange rae forecasing performance jus a few cover emerging economies, and an even smaller number of sudies are abou Lain America economies. Among he few references are Ferreira (2005), Paiva (2006) and Uz and Keenci (2007). In view of ha, we ry o shed some ligh on he issue of economies where he exchange rae can show a differen paern of response o economic fundamenals from ha of he indusrialized economies. Finally, our sudy covers a period in which a homogeneous se of counries shared similar erms of moneary policy arrangemens and free floaing exchange raes 1. The quesion of exchange rae predicabiliy has a milesone in he work of Meese and Rogoff (1983). Their landmark paper concluded ha macroeconomic models are unable o produce forecass ha are beer han a naive random walk specificaion. Since hen, many oher sudies have followed wih conroversial resuls. For insance, he exchange rae is predicable by using macroeconomic models by Schniasi and Swamy (1989) Kalman-Filer esimaion of ime-varying models and Mark (1995) mean correcion error formulaion of he moneary model. There are also some mixed resuls. Cheung, Chinnn and Pascual (2005) updaes he classic paper of Meese and Rogoff (1983, 1988) using a wider se of models 2. Their resuls do no indicae beer performance in general for he 1990s models and heir answer o is i possible o bea he random walk? is a bold perhaps. A leas, hey hink, i is in erms of he U.S. Dollar, Yen, Canadian Dollar, Swiss Franc and Deusche Mark. Some auhors furher invesigae he resuls wih skepicism. Kilian (1999) and Berkowiz and Giorgianni (2001) raise quesions abou he use of nonparameric boosrapping echnique by Mark (1995) o evaluae ou-of-sample significance. Basically, he auhors show ha predicabiliy resuls crucially depend on he assumed daa generaing process for he boosrapping exercise. Sarno and Taylor (2002) in an exensive survey of he lieraure of he 1980s and 1990s conclude ha he empirical resuls ended o be fragile in he sense ha hey were hard o replicae in differen samples or counries. Despie all he conroversy, a large volume of sudies have recenly shown increasing evidence of exchange rae predicabiliy. In paricular, models assuming endogenous moneary policy presen ineresing resuls. Molodsova and Papell (2007) employ an error correcion formulaion for a model ha incorporaes a Taylor rule reacion funcion. Their empirical esimaion, wih monhly daa from 1973:12 o 1998:12 for a se of 12 indusrialized counries, finds significan predicabiliy when Clark and Wes (2006, 2007) saisics for esing nesed models is uilized. 1 Those definiions of moneary policy arrangemens and exchange rae frameworks follow he classificaion adoped by he IMF, and available a hp:// 2 Our sudy resembles he sudy of Cheung, Chinnn and Pascual (2005), since boh es exchange rae predicabiliy for a wider se of models. However, we see imporan value added in ours. Firs, we include a more realisic model, he Taylor model, which assumes an endogenous moneary policy, and hey do no. Second, we carefully seleced our sample based on counries wih similar characerisics, free floaing exchange raes, and during he same moneary policy regime. Third, saisical significance use Clark and Wes (2006, 2007) saisics which correcs he Diebold Mariano (1995) saisic used by hem. Finally, our sudy is focused on emerging economies while heirs was focused on indusrialized economies. 2

3 Mark (2005) builds up an endogenous moneary model based on ineres raes se by independen reacion funcions for each cenral bank and uncovered ineres pariy. His model is successful in capuring he real Dollar-Deusche Mark exchange rae dynamics from 1976 o Engel and Wes (2006) sudy he equilibrium value for he real exchange rae from a similar seup and find suppor for he model using German daa. Besides he Taylor models, pooling informaion wih coinegraion ess seems o add considerable forecasing performance. Groen (2005), Rapach and Wohar (2005) and Mark and Sul (2001) find evidence of predicabiliy for he moneary model, especially over longer horizons. Moivaed by hose new developmens and rying o build up on he recen resuls, we incorporae Lain America economies in he exchange rae predicabiliy analysis. Our focus is o es for coinegraion relaionships and apply a mean correcion error formulaion o he Taylor rule model and a broad se of models in he lieraure of exchange rae deerminaion. We also improve forecasing evaluaion echniques by using Clark and Wes (2006, 2007) saisic raher han ha in Diebold and Mariano (1995), which is subjec o some srong criicism, see Kuns (2003) and Clark and Wes (2006, 2007). This paper is organized in hree addiional secions. Following his inroducion we expose he seleced economic models ogeher wih a deailed descripion of he Taylor model. In secion 3, we apply some diagnosic ess, namely, we es for uni roo in he employed series and evaluae if here is coinegraion in each model. Secion 4 describes he forecasing mehodology and exhibis he predicabiliy resuls. The final secion explores he main conclusions, limiaions and possible exensions of his sudy. 2 Specificaion of he models As poined ou by Engel, Mark and Wes (2007), wo imporan characerisics of moneary policy are ignored in many macroeconomic exchange rae models. Firs, i is endogenous. Second, since he mid-1980s cenral banks have used ineres rae as he policy insrumen raher han money supply. Insead, we assume a Taylor rule reacion funcion, meaning ha ineres raes respond posiively o lagged ineres raes, he curren oupu gap, and he difference beween he expeced inflaion and heir respecive arge. If we also make use of he uncovered ineres pariy relaionship, we can obain he exchange rae as a funcion of he expeced values of fuure ineres raes, oupu gaps and ineres raes. In order o visualize his, assume iniially ha a Taylor's rule funcion for he seleced counry is: i = γ qq γπ Eπ 1 γ yy δi 1 u. Where, i is he log of one plus he insananeous shor-erm ineres rae, q is he log of he real exchange rae, π is he log of one plus he inflaion rae less he inflaion arge and u is a random erm. For he parameers, we assume γ q >0, γπ >0, γ y >0,0 δ <1. Using aserisks o describe similar variables for he foreign counry, we can wrie a similar Taylor reacion funcion for he benchmark counry, 3

4 i = γ π Eπ 1 γ yy δ i 1 u. Noice ha we assumed ha he benchmark counry does no reac o he real exchange rae. Since we are comparing counries wih emerging economies wih he Unied Saes as he benchmark counry, his assumpion seems plausible. The final equaion of he sysem is he uncovered ineres rae arbirage condiion, i i = Es 1 s ρ, where s is he nominal ineres rae, risk premium. E is he condiional expecaion operaor and ρ is a Using hose hree equaions above and assuming ha he home and benchmark counries have similar parameers, we can wrie: ( γ γπ ( π π ) γ ( ) δ ( ) ρ ) s = Es q E y y i i u u 1 q 1 1 y 1 1 This expression can be furher simplified and solved forward yielding: s = p p bσ b X ξ (2.1) * n j j=0 j Where: b 1 1 γ q X = E y y i i ξ = ( γπ 1) ( π 1 π 1 ) γ ( ) δ ( 1 1 ) n j bσ =0b ( u u ρ ) j j j y j j j j j j j Empirical esimaion of equaion (2.1) requires ha we know all he fuure expeced values of inflaion, producion gap and ineres raes, which is no reasonable. Furher, he discoun parameer, b, has o be esimaed beforehand. One alernaive is o make simplifying assumpions abou marke expecaions. We presume ha expecaions for a near fuure can closely approximae he series of fuure expeced values. Formally, we will assume ha we can approximae expecaions for all fuure dae j=1,2,3,, by expecaions a a fixed daa K: E ( π 1 π 1 ) E ( π π ) ( ) ( ), ( 1 1 ) ( ), j j K K E y y E y y j j K K E i i E i i j j K K ξ v λv ρ. 1, (2.2) Plugging (2.2) ino (2.1) and selecing K=12 conducs us o 4

5 b s p p E X v v 1 b * = 12 λ 1 ρ, and o heir respecive empirical specificaion, ( ) ( ) s = α p p β E π π β E y y * β E ( i i ) β embi β q v (2.3) Equaion (2.3) is represened in he las column of able 1. For expecaions, we use Economics Consensus Forecas Survey hisorical daa. Comparing he Taylor specificaion wih every possible model would make he exercise unnecessarily cumbersome. Therefore, we seleced a manageable se of models based on he crieria of having a parsimonious specificaion form and being a well known model in he lieraure of exchange rae modeling. By parsimonious specificaion forms i is mean ha we can nes all models in he same basic block. In paricular, for every model we esed, he exchange rae is a linear funcion of economic fundamenals 3. In mahemaical erms, he log of nominal exchange rae, s, can always be modeled as a linear funcion of k economic fundamenals: s = α β Xˆ (2.4) Noice ha we define he economic fundamenal in logarihmic values and always as he difference of he home counry (Brazil, Chile, Colombia, Mexico and Peru) agains he benchmark counry (he Unied Saes). Table 1 shows all he models used in his sudy wih he economic fundamenals in he rows and he seleced models in he columns. In mahemaical erms, he comparison models, second o sixh columns in able 1, can be considered versions of he nesed specificaion: * ( ) ( ) ( ) ( ) ( ) ( ) s = α I p p β m m β y y β i i β z z β ϖ β ( r r ) β ngd ngd β o β nfa β embi I s v * k (2.5). Where he I s are indicaor variables, aking he value one if he variable is included in he model and zero oherwise, and he β s are he esimaed parameers. The definiion of he variables is given in Table 1. The firs comparison model is he Flexible Price Moneary Model (FPMM) which became very represenaive in he 1970s, afer he emergence of he Breon Woods sysem in 1973, and he adopion of floaing exchange raes by he main indusrialized economies. The FPMM assumes ha, in each counry, he equalizaion of currency supply and demand deermines he price level in each counry. Furhermore, relaive prices in each counry and 3 For simpliciy sake, we have excluded nonlinear models from our analysis. This may sound oo resricive as, in fac, assuming nonlineariies can enhance he exchange rae predicabiliy, see for insance Hnakovska, Lahiri and Vegh (2008). A similar sudy allowing for nonlinear models would be an ineresing nex sep. 5

6 exchange raes are conneced by he purchasing power pariy relaionship. In is reduced form, he exchange rae is a funcion of he relaive money supplies, producion levels, and ineres raes. The nex wo specificaions, in he hird and fourh columns respecively, are he Produciviy Differenial and he Composie Model. They follow a more recen se of exchange rae deerminaion models in he Balassa-Samuelson radiion. The Produciviy Differenial Model includes in he moneary model he produciviy gap beween radable and non-radable secors, which is measured by he respecive inverse raios of price level of each secor. The Composie model includes oher well-known familiar effecs of he exchange rae: he relaive price of non-radables, he real ineres rae differenial, ne governmen deb, erms of rade, and ne foreign asse posiion. As poined ou by Cheung, Chinn and Pascual (2005), his formulaion is quie similar o he behavioral equilibrium exchange rae (BEER) model of Clark and MacDonald (1999). The fifh and sixh columns display specificaions based respecively on he uncovered ineres rae pariy arbirage condiion and he power purchasing pariy equilibrium assumpions. Uncovered ineres pariy assumes ha he change on real exchange raes will only be influenced by he ineres rae differenial. The power purchasing pariy condiion esablishes ha he nominal exchange rae is proporional o he price levels of each counry. 3 Uni roo and coinegraion diagnosic ess The general empirical esimaion of he models in secion 2 implies he following specificaion: s = β ΧΠ ε 0 (3.1). Where X denoes he vecor of explanaory variables, Π is a vecor of parameers and ε is a random erm. However, since we are dealing wih macroeconomic variables, i is very likely ha he exchange rae and many of he explanaory economic fundamenals are non-saionary. Following he seminal work of Engle and Granger (1987), unless [ s, X ] has a long-run relaionship, esimaing (3.1) can lead o spurious regressions. Therefore, before running he models specified in secion 2, we proceed wih some diagnosic ess of non-saionariy (uni roo) and coinegraion relaionship in our series. We run wo uni roo ess: he Augmened Dickey-Fuller (1979) es, herein afer ADF, and he Phillips-Perron (1988) es, in boh, he null assumes ha he series has a uni roo. Boh ess aim o correc he serial correlaion problem on a basic Dickey-Fuller specificaion es. For he ADF, he es regression is given by: y = α y x δ λ y λ y λ y p p H : α = 0 0 H : α < 0 1 The exogenous variables x can be included or no in he regression and allows for he inclusion of a consan or a consan and a rend. The ADF es makes use of Schwarz 6

7 informaion crieria o selec he lag lengh p auomaically. The Phillips and Perron (1988) es uses a es regression similar o he ADF wihou he p lagged difference erms; hey modify he -raio of he α coefficien in order o correc for serial correlaion of he es saisic. For fundamenals ha are expeced o grow over ime, we specify he uni roo ess wih a consan and a ime rend. Those series are he price level, he money supply and he indusrial producion level. For all he oher series, we expec a long - run equilibrium value which does no grow over ime and we specified he es wih a consan bu no ime rend. Table 2.1 displays augmened Dickey-Fuller ess, for he macroeconomic variables used in our models. In mos of he cases, 60 ou of 80, we fail o rejec he null of uni roo a using 90% confidence inervals. Table 2.2 shows he Phillips-Perron ess where we rejec he null of uni roo more ofen, 25 ou of 80 cases. Looking a boh ess, we see srong evidence of saionariy for he indusrial producion levels, real ineres raes and expeced indusrial producion gap. Since our daa span, 1999:01 o 2007:12, comprehends a period of low indusrial producion growh in Lain-America economies ( ), we do no ake he las resuls oo lierally. In general, we have srong empirical evidence o believe ha he esimaing equaion (3.1) involves non-saionary [ s, X ] series. Therefore, we now es if [ s, X ] co-inegrae by using he Engle-Granger wo-sep procedure, as described in Davidson and MacKinnon (1993) 4. The es is based on firsly regressing (3.1) by ordinary leas squares. For each counry, empirical esimaion uses monhly daa from January 1999 o December 2007, a full sample of 108 observaions. From hese esimaed regressions, he second sep of he procedure consiss in generaing esimaed residuals series, ˆ ε, for each model, running he auxiliary regressions ˆ ε = γεˆ u 1 (3.2). and esing for he null of no-coinegraion of γ = 0. The inuiion behind he es is ha if [ s, X ] displays a long-run relaionship, alhough hose variables are non-saionary, hey will produce saionary residuals and he parameer γ will be zero. As poined ou by Engle and Granger (1987), -saisics for γ under he null will have no sandard disribuion, depending on he sample size and he number of parameers. For his reason, we use Davidson and MacKinnon (1993) repored asympoic criical values for his es. Table 3 shows resuls for he coinegraion ess. They show srong co-inegraion evidence for boh he uncovered ineres pariy model, for all counries, and for he Taylor model, for Brazil, Chile and Mexico. For Colombia, here is also some evidence of coinegraion in he produciviy differenial and in he power purchasing pariy model. Recall ha unless he model has a coinegraion relaionship, is esimaion in levels will lead 4 Noe ha we could es for more han one coinegraion relaionship as suggesed by he Johansen (1995) approach suggess. However, he exchange rae economic models described in secion 2 predic jus one relaionship among he variables and ha is wha we wan o es in his sudy. This jusifies our opion for a simpler procedure of esing only he coinegraion relaionship using he Engle and Granger (1987) mehod. 7

8 o spurious regressions. Therefore, we expec o obain robus and meaningful esimaes leading o exchange rae predicabiliy only for he models ha passed he coinegraion ess. This verificaion will be explained in he following secion. 4 - Forecasing Exercise The ou-of-sample forecasing analysis followed he mean correcion error mehodology used by Cheung, Chinn and Pascual (2005). Firsly, we esimae specificaion (3.1) for each model obaining he fundamenal value for he exchange rae: F = ˆ β Χ Π ˆ (3.3). 0 The second sep is o esimae he following mean correcion equaion: s s = φ( F s ) v (3.4). k The esimaed parameers of equaion (3.4) are used o forecas fuure values of he exchange rae a he horizons of k = 1, 3, 6 and 12 monhs ahead. Noe ha, by using (3.4) o predic fuure exchange rae, we have rue ex-ane forecass. Only informaion available a ime is used o esimae he fuure exchange rae a k. Forecasing is done according o rolling regressions on (3.3) and (3.4). Firs we divide he oal sample of size T ino wo subses: one for esimaion, and he oher for forecasing. The esimaion sub-sample has a fixed size of D wih T<D. Using daa up o observaion D, we firs esimae he exchange rae mean correcion model, equaions(3.1), (3.3), and (3.4). From (3.4) we obain one-, hree-, six- and welve-monh exchange rae predicions for each model. Nex, we displace he esimaion sample one period ahead, o =2 o = D 1 keeping he size of he iniial sample fixed on D observaions. Again, we predic he exchange rae for one-, hree-, six- and welve-monh ahead. We repea his procedure unil he exhausion of he sample. In he end, for each model, we will have a series of exchange rae predicions of one-, hree-, six- and welve-monh ahead of respecive sizes T-D-1, T-D-3, T-D-6 and T-D- 12. The prediced exchange raes are hen compared wih hose forecas by a drif less random walk specificaion where: s = s (3.5). k Table 4 displays Theil s raio of he Roo Mean Squared Prediced Error 5 (RMSPE) for each model in able 1, divided by he RMSPE of he random walk. 5o check for robusness, he able repors resuls for wo differen forecasing samples, Nov/04 o Dec/07 5 T 2 RMSPE = Σi== D k( s sˆ ) where sˆ is he esimaed and s is he acual value of he exchange rae, T is he sample size and k is he forecasing horizon. 8

9 (D = 70) and Jan/04 o Dec/07 (D = 60). To es he saisic significance of his raio, we used he saisic proposed by Clark and Wes (2006, 2007), in which, under he null hypohesis, here is no difference beween he wo esimaions forecasing performance, ha is, he forecasing generaed by he economic models is as good as he forecasing generaed by a drifless random walk. Values of he Theil s raio below one indicae ha he economic models under evaluaion had a lower RMSPE han hose generaed by he random walk model. As expeced by he heory, models ha presened beer ou-of-sample predicabiliy exhibi empirical evidence of coinegraion beween he exchange rae and he macroeconomic fundamenals. Paricularly, he bes forecasing performance is obained when he Taylor model is used, which shows evidence of predicabiliy for all he seleced counries. The evidence is paricularly srong for Brazil, Colombia, Chile and Mexico; he Taylor Model ouperforms he random walk in 21 ou of 28 cases. For hese counries, we emphasize forecasabiliy a longer horizons. The Taylor model ouperforms he random walk in 7 ou of 8 cases a 12-monhs-ahead predicions. Ineresingly enough, he oher economic models also presen some predicabiliy. Neverheless, hey ouperform he random walk in a much less expressive way han he Taylor model; besides i is more difficul o find a paern across counries or horizons for hose models. These resuls go in he direcion of many ohers in he lieraure where comparison models can have some predicabiliy, bu i is no very robus, see Sarno and Taylor (2002). Anoher fac o poin ou is he excellen performance of he PPP model for Colombia. I may indicae ha he Colombian cenral bank arges is moneary policy o keep he purchasing power level of is exchange rae consan. 4 Conclusions Engel and Wes (2005) nes all exchange rae models in a raional expecaions presen-value framework and show ha beaing a random-walk can be oo srong a benchmark, even if he model is rue. Sandard models imply near random walk behavior in he exchange raes and he power o bea he random walk in ou-of-sample forecass is low. Tha is clearly he case in our exercise. Even hough we found srong predicabiliy evidence in favor of he Taylor model, i is a igh win; he lowes Theil s raio is 0,843. We find he predicabiliy resuls for an endogenous moneary policy model very promising for new research. No surprisingly, we found ha using more plausible assumpions, uch as he cenral bank following an endogenous moneary policy and exchange raes responding o expecaion fundamenals, is probably a rewarding research sraegy. For insance, recen sudies like Engel and Wes (2005) and Chen, Rogoff and Rossi (2008) show ha exchange raes are influenced by he presen value of economic fundamenals. The linear and simple formulaion of he Taylor rule model confers some limiaions o his sudy. Recen resuls for moneary policy, see Qin and Enders (2007) and Cukierman and Muscaelli (2008), demonsrae ha non-linear Taylor rules are beer suied o model he cenral bank reacion funcion. We also ignored he fac ha pooling informaion across counries generally improves predicabiliy, see Engel, Mark and Wes (2007). Fuure research should look o non-linear Taylor rule models and pooling esimaion. 9

10 References CHEN Y-C.; ROGOFF, K.; ROOSI, B. Can Exchange Raes Forecas Commodiy Prices?, NBER Working paper Series, WP 13901, March, CHEUNG, Y; CHINN, M.D.; PASCUAL, A.G. Empirical exchange rae models of he nineies: are any fi o survive?. Journal o Inernaional Money and Finance, v. 24, p , CLARK, T. E.; WEST, KENETH, D. Using ou-of-sample mean squared predicion errors o es he maringale difference hypohesis, Comparing Predicive Accuracy. Journal of Economerics, v. 135, p , CLARK, T. E.; WEST, KENETH, D. Approximaely Normal Tess for Equal Predicive Accuracy in Nesed Models. Journal of Economerics, v. 138, p , CUKIERMAN, A.; MUSACTELLI, A. Nonlinear Taylor Rules and Asymmeric Preferences in Cenral Banking: Evidence form he Unied Kingdom and he Unied Saes. The B.E. Journal of Macroeconomics, v.8 issue 1, p. 1-29, DAVIDSON, R.; MACKINNON, J.G. Esimaion and Inference in Economerics, Oxford Universiy Press, DIEBOLD, F. X.; MARIANO, M. Comparing Predicive Accuracy. Journal of Business and Economic Saisics, v. 13, p , DICKEY, D.A.; FULLER, W.A. Disribuion of he Esimaors for Auoregressive Time Series wih a Uni Roo, Journal of he American Saisical Associaion, 74, , ENGEL, C; WEST, K.D. Exchange raes and Fundamenals Journal of Poliical Economy, v. 113, p , ENGEL, C.; MARK, N. C.; WEST, K.D. Exchange rae models are no as bad as you hink. NBER Working Paper Series, w13318, ENGLE, R.F..; GRANGER, C.W.J. Co-inegraion and error correcion: represenaion esimaion and esing. Economerica, v.55, p , FERREIRA, J.E.A. Effecs of Fundamenals of he Exchange Rae: A Panel Analysis for a Sample of Indusrialized and Emerging Economies, manuscrip, GROEN, J.J.J. Exchange Rae Predicabiliy and Moneary Fundamenals in a Small Muli-Counry Panel, Journal of Money, Credi and Banking 37, , KILIAN, L. Exchange raes and moneary fundamenals: evidence on long-horizon predicabiliy. Journal of Applied Economerics, v. 14, p , KUNST, R. M. Tesing for relaive predicive accuracy: A criical viewpoin. Reihe Oknomie Economics Series, v. 130,

11 MACKNINNON, J. D. Criical values for coinegraion ess. In: ENGLE, R.F..; GRANGER, C.W.J. (Eds.), Long-run Economic Relaionships: Readings in Coinegraion. Oxford Universiy Press., 1992, P MACKNINNON, J. G. Numerical Disribuion Funcion for Uni Roo Tess. Journal of Applied Economerics, v. 11, p , MARK, N. C. Exchange raes and fundamenals: evidence on long-horizon predicabiliy. American Economic Review, v. 85, p , MARK N. A.; SUL, D. Nominal Exchange Raes and Moneary Fundamenals: Evidence from a Small Pos-Breon Woods Sample, Journal of Inernaional Economics 53, 29-52, MEESE, R.; ROGOFF, K. Empirical exchange rae models of he sevenies: do hey fi ou of he sample?. Journal of Finance, v. 43, p , MOLODTSOVA, T.; PAPELL, D. Ou-of-sample exchange rae predicabiliy wih Taylor Rule Models. Universiy of Houson Working Paper, PHILLIPS, P.C.B.; PERRON P. Tesing for a Uni Roo in Time Series Regression, Biomerika, 75, , 1988 PAIVA, C. Exernal Adjusmen and Equilibrium Exchange Rae in Brazil, IMF Working Paper, WP/06/221, QIN, T.; ENDERS, W. In-sample and ou-of-sample properies of linear and nonlinear Taylor rules, Journal of Macroeconomics, v. 30, p , RAPACH, D. E.; WOHAR M. E.. Tesing he Moneary Model of Exchange Rae Deerminaion: A Closer Look a Panels. Journal of Inernaional Money and Finance, 23, pp , SARNO, L.; TAYLOR, M.P. The economics of exchange raes. Cambridge: Cambridge Universiy Press, 2002, cap. 4, p , SCHINASI, G. J.; SWAMY, P.A.V.B. The Ou-of-Sample Forecasing Performance of Exchange Rae Models When Coefficiens Are Allowed o Change. Journal of Inernaional Money and Finance, 8(3), pp , Sepember, UZ, I.; NATALYA, K. Panel Analysis of he Moneary Approach o Exchange Raes: Evidence from he new EU members and Turkey. Emerging Markes Review, vol. 9, p ,

12 TABLES Table 1- Exchange Rae Models Models - Nominal Exchange Rae is he Dependen Variable Independen Variables Noaion Taylor Moneary Prod. Dif. Composie U.I.P. P.P.P. Consan α Expeced Inflaion - Targe E(π - π*) Expeced Ind. Prod. Gap E(y - y*) Expeced Ineres Raes E(i - i*) Real Exchange Rae q EMBI embi Price Level p - p* Money Supply - M1 m - m* Indusrial Producion y - y* Ineres Raes i - i* Produciviy Differenial z - z* Relaive Price of Tradables w - w* Real Ineres Rae r - r* Governmen Deb ngd - ngd* Terms of Trade o - o* Ne Foreign Asses nfa - nfa* Lagged Ineres Rae s Noe: The nominal exchange rae is he logarihm of end of he monh marke raes in counry's currency by U.S. Dollars. Each independen varibale series is defined as he logarihm of he raion of heir respecive nominal values for he reference counry and he Unied Saes, excep for EMBI, which is already defined as a spread agains he Unied Saes Treasury bonds. 12

13 Table Uni Roo Augmened ADF Tess - Individual Series Series Brazil Chile Colombia Mexico Peru Exchange Rae -0,927-1,349-2,576-1,003 0,421 Expeced Inflaion - Targe -3,270** -2,754* -1,993-3,595*** -2,639* Expeced Ind. Prod. Gap -3,028** -3,068** -1,602-2,770* -1,970 Expeced Ineres Raes -1,605-2,197-1,763-1,646-1,563 Real Exchange Rae -0,427-1,153-1,515-3,119** -0,787 EMBI -0,947-1,474-1,134-2,066-1,145 Price Level (a) -0,584-1,639-0,835-2,021-3,44* Money Supply - M1 (a) -1,252-1,810-2,459-2,927 0,056 Indusrial Prodcion (a) -3,567** -3,275* -1,848-10,835*** -2,432 Ineres Raes -1,265-1,906-1,582-1,455-1,017 Produciviy Differenial -1,418-2,370-1,126-1,854-3,293** Relaive Price of Tradables -2,130-3,919*** -2,476-2,005-1,734 Real Ineres Rae -3,036** -1,728-5,345*** -4,240*** -1,28 Governmen Deb -2,231-2,768* -1,838-3,697*** -0,898 Terms of Trade -0,411-1,932-1,032-1,218-0,053 Ne Foreign Asses -0,041-1,171 0,123-4,472*** -2,120 Noe: The able repors he -saisics of he augmened Dickey-Fuller ess assuming a consan and no-ime rend excep on cases (a), which assumes a consan and a ime rend. The es regression uses he Schwarz informaion crieria for auomaic lag lengh selecion. The aserisks a he righ of he numbers, ***, ** and * denoe saisical significance a 1%, 5% and 10% respecively using MacKinnon (1992, 1996) asympoical values. Table Uni Roo Phillips PerronTess - Individual Series Series Brazil Chile Colombia Mexico Peru Exchange Rae -1,910-1,534-2,477-0,998 0,538 Expeced Inflaion - Targe -2,480-2,640* -1,978-4,934*** -2,457 Expeced Ind. Prod. Gap -2,909** -5,441*** -4,684*** -7,540*** -5,623*** Expeced Ineres Raes -1,105-2,045-1,805-1,797-1,321 Real Exchange Rae -0,874-1,335-1,151-3,229** -1,078 EMBI -0,971-1,510-0,892-2,097-1,046 Price Level (a) -0,294-1,713-1,465-2,981-2,887 Money Supply - M1 (a) -1,367-2,542-2,353-2,924 0,026 Indusrial Prodcion (a) -3,468** -5,692*** -7,661*** -10,827*** -7,673*** Ineres Raes -0,755-1,931-1,625-1,600-1,040 Produciviy Differenial -2,775* -2,051-1,056-1,990-3,328** Relaive Price of Tradables -2,900** -4,911*** -2,760* -9,561*** -2,017 Real Ineres Rae -3,857*** -2,244-4,883*** -4,390*** -1,113 Governmen Deb -2,195-3,101** -2,281-4,696*** -0,750 Terms of Trade -0,642-1,558-0,506-1,258 0,001 Ne Foreign Asses 0,578 2,830 1,557-3,613*** -2,092 Noe: The able repors he p-values of he Phillips-Perron (1988) nonparameric es assuming a consan and no-ime rend excep on cases (a), which assumes a consan and a ime rend. The es esimaes a non-augmened Dickey-Fuller equaion and modifies he -raio of he es saisic in order o correc for serial correlaion. The aserisks a he righ of he numbers, ***, ** and * denoe saisical significance a 1%, 5% and 10% respecively using MacKinnon (1992, 1996) asympoical values. Table 3 - Engle and Granger Two-Sep procedure - Augmened ADF coinegraion es of residuals. Counries # of dep. Asymp. Criical Values Model Brazil Chile Colombia Mexico Peru variables 1% 5% 10% Taylor -6,93*** -5,231** -3,249-4,897** -2, ,25-4,71-4,42 Moneary -3,83-2,852-2,811-2,676-4, ,96-4,42-4,13 Prod. Dif. -2,952-3,879-4,373* -3,007-3, ,96-4,42-4,13 Composie -3,248-3,877-3,91-3,404-2, ,25-4,71-4,42 U.I.P. -9,624*** -7,241*** -6,54*** -8,849*** -9,184*** 1-3,43-2,86-2,57 P.P.P. -0,699-1,667-3,19** -1,266 0, ,43-2,86-2,57 Noe: This able presens ADF ess of he residuals generaed by OLS esimaes of each model for each counry. Aserisks denoe rejecion of he null of no-coinegraion a a 5% significance level, asympoical criical values were obained from Davidson and Mackinnon (1993). 13

14 Table 4 - RMSPE Raios Model Horizon Brazil Chile Colombia Mexico Peru Forecasing Sample: Nov/04 o Dec/07 Taylor 1 1,058 1,018 0,971* 0,987 0,993** 3 0,915*** 1,011 0,886*** 0,958** 1, ,880*** 1,019 0,833*** 0,937*** 1, ,843*** 0,985** 1,016 0,964** 1,001 Moneary 1 1,106 0,969*** 1,053 0,991 1, ,45 0,995 1,18 0,955** 1, ,789 1,168 1,356 0,759*** 1, ,428 1,354 1,208 0,685*** 0,938*** Prod. Dif. 1 1,076 0,973** 1,018 0,991 1, ,345 0,914*** 1,073 0,949*** 1, ,674 1,079 1,268 0,791*** 1, ,390 1,442 1,355 0,73*** 1,196 U.I.P. 1 1,000 1,009 0,973** 1,006 1, ,900*** 1,002 1,056 0,973* 0, ,178 1,021 1,019 1,040 1, ,903*** 0,982** 1,086 0,989** 1,026 P.P.P. 1 1,027 1,053 0,971** 1,004 1, ,234 1,204 0,930*** 1,037 1, ,596 1,452 0,895*** 1,157 1, ,630 1,688 0,865*** 1,181 1,489 Forecasing Sample: Jan/04 o Dec/07 Taylor 1 1,049 0,987* 1,055 0,992 1, ,961** 0,992* 0,985** 0,952*** 1, ,927*** 1,015 0,804*** 1,018 1, ,877*** 0,988* 0,829*** 0,950*** 1,068 Moneary 1 1,106 1,013 1,053 1,034 1, ,394 1,033 1,167 1,111 1, ,813 1,118 1,402 1,206 1, ,442 1,399 1,407 1,161 1,040 Prod. Dif. 1 1,084 0,995 1,015 1,035 1, ,329 1,045 1,062 1,127 1, ,713 1,239 1,187 1,221 1, ,413 1,520 1,201 1,187 1,199 U.I.P. 1 1,006 0,990** 0,955*** 1,019 0, ,920*** 1,040 1,045 0,988* 1, ,133 1,010 0,981* 1,048 1, ,946*** 1,141 1,058 0,953*** 1,036 P.P.P. 1 1,064 1,049 0,987 1,017 1, ,247 1,179 0,931*** 0,973** 1, ,588 1,367 0,857*** 1,023 1, ,536 1,669 0,711*** 1,074 1,364 Noe: The number in each cell is he raio of roo mean square predic errors (RMSPE) of he seleced model divided by he RMSPE of a benchmark drifless random-walk for horizons of 1, 3, 6 and 12 monhs ahead. Numbers bellow uni indicae ha he seleced model had a lower forecasing error han he random walk. The aserisks a he righ of he numbers, ***, ** and * denoe saisical significance a 1%, 5% and 10% respecively using Clark and Wes (2006, 2007) saisics. Forecasing errors are based on rolling regressions wih a fixed sample size. The oal sample size has a oal of 108 observaions and goes from Jan/99 hrough Dez/07. 14