Exch a nge r at e a nd fu n da m en ta l s:

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1 Exch a nge r a e a nd fu n da m en a l s: he case of Brazil* Marcelo L. Moura Adauo R. S. Lima Rodrigo M. Mendonça Resumo O desempenho de previsão para fora da amosra é esado para um amplo conjuno de modelos empíricos de axa de câmbio em uma economia emergene com axa de câmbio fluuane e regime de meas de inflação. Comparado à lieraura recene de modelos de previsão da axa de câmbio, nós incluímos um conjuno mais exenso de modelos. São esados modelos radicionais da década de 1980, modelos de equilíbrio comporamenal da axa de câmbio dos anos de 1990 e um modelo baseado na regra de Taylor. Nese úlimo, o modelo incorpora um função de reação do Banco Cenral, na qual a axa de juros é definida de acordo com uma regra de Taylor. Nossos resulados demonsram que modelos de regra de Taylor e de equilíbrio comporamenal da axa de câmbio, ese úlimo combinando diferenciais de produividade com ajuses de careira, êm desempenho fora da amosra superior a um passeio aleaório. Evidências de poder de previsão ambém são obidas para modelos parcimoniosos baseados em argumenos de paridade descobera da axa de juros. Palavras-chave: modelos de regra de Taylor, modelos moneários, previsibilidade fora da amosra, coinegração, modelos de correção de erros. Absr ac Forecasing performance is esed for a broad se of empirical exchange rae models for an emerging economy wih independenly floaing regime and inflaion arge moneary arrangemen. Compared o he recen lieraure on ou-of-sample exchange rae predicabiliy, we include a more exensive se of models. We es vinage moneary models of he 1980 s, exchange rae equilibrium models of he 1990 s and a Taylor Rule based model. This las model assumes an endogenous moneary policy, where he Cenral Bank follows a Taylor rule reacion funcion o se ineres raes. Our resuls show ha Taylor Rule models and Behavioral Equilibrium Exchange Rae models, he las one combining produciviy differenials wih porfolio balance effec, have superior predicive accuracy when compared o he random walk benchmark. Some ou-of-sample predicabiliy is also obained wih parsimonious models based on uncovered ineres pariy argumens. Keywords: Taylor rule models, moneary models, ou-of-sample exchange rae predicabiliy, coinegraion, mean correcion error models. JEL classificaion: F31, F41, F47. * We would like o hank an anonymous referee, paricipans a he 7h Brazilian Finance Meeing and a he 15h World Congress of he Inernaional Economic Associaion for heir very helpful commens on previous versions of he paper. All possible remaining errors are ours Ibmec São Paulo Business School. Adress conac: Rua Quaá 300, São Paulo SP Brazil CEP: marcelom@isp.edu.br. Ibmec São Paulo Business School. Adress conac: Rua Quaá 300, São Paulo-SP Brazil CEP: adauorsl@isp.edu.br. Ibmec São Paulo Business School. Adress conac: Rua Quaá 300, São Paulo SP Brazil CEP: rodrigomm1@ibmecsp.edu.br. Recebido em março de Aceio para publicação em seembro de Econ. aplic., São Paulo, v. 12, n. 3, p , JULHO-SETEMBRO 2008

2 396 Exchange rae and fundamenals 1 Inroducion In he presen sudy, we es he adequacy of he empirical exchange rae models for an emerging commodiy-based economy wih independenly floaing regime. 1 Our purpose is o assess he ou-of sample fi of hose models. Our analysis replicaes for an emerging economy he sudy carried ou in he classic aricle by Meese and Rogoff (1983) bu wih a broader se of economic models and using rue ou-of-sample exercises. 2 The original Meese and Rogoff work showed ha a simple drifless random walk model would be more effecive for he exchange rae forecasing han he models ha involve macroeconomic fundamenals. Meese and Rogoff s research has generaed an exensive lieraure. Mark (1995) argues ha he moneary fundamenals migh obain some success o explain he behavior of he exchange rae if he saisical ess were given more power. However, a hos of auhors, for example, Kilian (1999) and Berkowiz and Giorgianni (2001) remained skepics and suggesed ha he resuls obained by Meese and Rogoff may sill seem robus, even afer all he daa and inense academic invesigaion gahered for over weny years. Some excepions o his skepicism are presen in recen works. Chen (2004) analyzes commodiies producers (Ausralia, Canada and New Zealand) for OCDE counries. The auhor concludes ha for Ausralia and New Zealand he global price of heir respecive expored commodiies is likely o have a meaningful and sable impac on heir respecive currencies. However, in he case of Canada, he evidence was less conclusive. Guo and Savikcas (2006) make use of variables ha reflec he agens expecaion owards he fuure behavior of he economic fundamenals, like he erm srucure of ineres raes, credi risk, and he idiosyncraic risk of he Unied Saes sock marke, among ohers. Their analysis sugges ha he idiosyncraic risk of hose asses forecas he American dollar s behavior facing he G7 s main currencies, and conclude ha he exchange rae does no follow a drifless random walk.. Cheung, Chinn and Pascual (2005) added oher models and elemens of he 1970s radiional specificaions in he deerminaion of he exchange rae, such as, he ne foreign asses and he differenial of relaive produciviy in he radable goods secor beween counries, he Balassa (1964) and Samuelson (1964) effec. The auhors concluded ha, in line wih a grea par of he exising lieraure, i is very difficul o find empirical esimaions of srucural models ha may consisenly ouperform a random walk, having he mean-squared errors as basis of comparison. On he oher hand, he srucural models provide a beer forecasing for exchange rae movemens han ha provided by he random walk. 1 This definiion follows he exchange rae arrangemens adoped by he IMF, and available a hp:// exernal/np/mfd/er/index.asp 2 In his seminal work, Meese and Rogoff (1983) used realized fuure values of explanaory variables o forecas fuure exchange raes.

3 Marcelo L. Moura, Adauo R. S. Lima, Rodrigo M. Mendonça 397 Specific sudies for Brazil, like Muinhos, Alves and Riella (2003), sae ha he random walk is no he bes hypohesis o explain he behavior of he exchange rae in Brazil. Using daa from May 1999 o December 2001, he auhors conclude ha a model derived from he heory of uncovered ineres rae pariy capures he Brazilian exchange rae s behavior beer. This model akes ino consideraion he sovereign risk premium (in he sudy measured by he C-Bond spread, in relaion o Treasury Bills, as a variable in he specificaion of he uncovered pariy. Unil mid 2000 s, as highlighed by Sarno and Taylor (2002), hough he heory of exchange rae deerminaion had produced a series of models, esimaions boh in and ou- of-sample did no show srong empirical suppor. The resuls ended o be fragile in he sense ha hey were hard o replicae in differen samples or counries. However, new developmens in he mid 2000 s changed he perspecive and shed some new ligh in he field. Engel and Wes (2005) analysis of raional expecaions presen-value model showed ha beaing a random-walk can be a oo srong benchmark, even if he model is rue. A he same ime, he use of endogenous moneary models, see Molodsova and Papell (2007), and new panel daa echniques, see Rapach and Wohar (2004) found improved resuls in ou-of-sample predicabiliy. As a recen paper from Engel, Mark and Wes (2007) suggess in his ile: Exchange Rae Models Are No as Bad as You Think. In conclusion, he exising lieraure up o now allows us o draw some imporan conclusions. Firs of all, i is difficul o find empirical economic models ha consisenly ouperform a drifless random walk for he ou-of-sample esimaions. Second, more recen exchange rae models improve he predicive accuracy of he models. Finally, economic variables ha have forward-looking componens may improve he resuls of he models for he ou-of-sample forecasing. The purpose and conribuion of his work is o carry ou a deailed sudy abou he ouof-sample forecasing performance of exchange rae models o an emerging economy like he Brazilian economy. The following secion presens he economic models used in his work. In Secion 3, we analyze he forecasing performance of he esimaed models agains ha of he drifless random walk. We follow he mean correcion error mehodology suggesed by Cheung, Chinn and Pascual (2005), in which he assessmen crierion is he Mean Squared Prediced Error (MSPE), however, we improve on his work in wo ways. Firs, we es significance using Clark and Wes (2006, 2007) saisic insead of he one in Diebold and Mariano (1995), which is subjec o some srong criicism, see Kuns (2003) and Clark and Wes (2006, 2007). Second, we include he Taylor Rule Model based on a more realisic hypohesis of endogenous moneary policy. The las secion presens he conclusions of he sudy.

4 398 Exchange rae and fundamenals 2 Speci fica ion of he model s The Flexible Price Moneary Model (FPMM) was very represenaive in he 1970s when he floaing exchange raes were adoped by he main indusrialized economies, afer he collapse of Breon Woods sysem in According o Sarno and Taylor (2002), his model became he dominan exchange rae model during he 1970s, for earlier sudies on his see Frenkell (1976) and Mussa (1976, 1979). The basic inuiion of he FPMM is o assume 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 exchange raes are relaed by he purchasing power pariy relaionship. The soluion of he FPMM leads o an exchange rae equaion where he exchange rae is deermined by relaive money supplies, oupu levels and ineres raes. More specifically, in economeric erms, he equilibrium equaion o be esimaed can be presened by: ( ) ( ) ( ) s =β +β m m +β y y +β i i + v (2.1) where s is he exchange rae logarihm (R$/US$), m and m * he M1 logarihms in Brazil and in he Unied Saes, respecively; y and y * he indusrial producion logarihm in boh counries and i and i * he logarihm for he shor-erm ineres raes for Brazil and he Unied Saes, respecively. 3 The variable v is a random erm. Despie he fac ha he FPMM was he dominan approach o deermine he exchange rae in he early 1970s, is weak empirical resuls led o he concepion of models ha ook over fricions in he economy, inducing anoher form of convergence for long-run marke equilibrium. Dornbusch (1976) inroduces he idea of sicky prices in he shor run o he exchange models, which enables jumps in he nominal and/or real exchange rae o beyond is long-run equilibrium value. The exisence in he sysem of variables ha jump, in his specific case, he exchange rae and he ineres rae, would make up for he sickiness in oher variables, ha is, he prices of goods. Thus, he adjusmen velociy in various markes would be differen. Consider π and π as logarihms of he inflaion raes in Brazil and in he Unied Saes respecively. The Dornbusch (1976) SPMM, capures price sickiness in boh economies by he following equilibrium equaion: ( ) ( ) ( ) ( ) s =β +β m m +β y y +β i i +β π π +ν (2.2) where ν is a random erm. The moneary models formerly shown, flexible prices and sicky prices, assume he perfec subsiuion beween home and exernal asses and heir effecs on he exchange rae. However, 3 (1+ pre swap ineres rae logarihm) was used for he domesic raes and he USA raes.

5 Marcelo L. Moura, Adauo R. S. Lima, Rodrigo M. Mendonça 399 he exisence of home-bias (home agens preference for home asses), liquidiy difference, solvency risk, ribuary differences and even he currency-exchange risk can affec he presumed equilibrium in he moneary models, which makes he home asses and he exernal asses imperfec subsiues. Following Sarno and Taylor (2002), he main idea in he Porfolio Balance Model - hereafer PBM - is o consider ha ne financial wealh can be allocaed ino money, domesic issued bonds and foreign bonds. A he equilibrium, exchange rae and nominal ineres raes equae supply and demand of hose hree financial asses. In he reduced-form, he equilibrium exchange rae will be a funcion of relaive money supplies and he sock of domesic and foreign bonds. Mos of he empirical esimaes of he PBM showed poor resuls, see Bisignano and Hoover (1982) and Dooley and Isard (1982). However, longer daa span and esimaion for an emerging economy, like he Brazilian, moivaes us o es his model as well. In paricular, we use he following empirical specificaion for he porfolio model: ( ) ( ) s =β +β ( m m ) +β i i +β ngd ngd +β embi +β nfa + v (2.3) * where he addiional variables ngd is he logarihm of he ne governmen deb o GDP, inernal plus exernal less inernaional reserves, embi is he counry risk sovereign spread measured by he EMBI+ Brazil 4, nfa is he logarihm of he public secor dollar denominaed ne foreign asses. Aseriks denoe he same variables for he reference counry, he Unied Saes. The nex specificaions follow a more recen se of exchange rae deerminaion models model in he Balassa-Samuelson radiion. Following Cheung, Chinn and Pascual (2005) we use firs a Produciviy Differenial model where he produciviy gap beween radable and nonradables secors play a crucial role in deermining he equilibrium exchange rae. The Produciviy Differenial is given by he following equaion: ( ) ( ) ( ) ( ) s =β +β m m +β y y +β i i +β z z +ν (2.4) where z gives he logarihm of produciviy raio of he radable o he nonradable secor, which is measured by he respecive inverse price level raios of each secor. Besides he Balassa-Samuelson effec, we can also include oher well-known familiar effecs o he exchange rae in order o esablish a link beween he exchange rae and he relevan economic variables. Tha is exacly he idea of Clark and MacDonald (1999) Behavior Equilibrium Exchange Rae Model hereafer BEER. More specifically, he BEER model 4 This index is compued by J.P. Morgan invesmen bank.

6 400 Exchange rae and fundamenals assumes a reduced form economeric specificaion where he real equilibrium exchange rae is affeced by ransiory facors, random disurbances, and he exen o which he economic fundamenals are away from heir susainable values. In our specificaion of he BEER model, we followed closely he specificaion used in Cheung, Chinn and Pascual (2005). The se of explanaory variables includes he relaive price * of nonradables, ϖ, he real ineres rae differenial, r r, ne governmen deb o GDP raios, ngd ngd, erms of rade, o and ne foreign asse posiion, nfa : ( ) s =β + p p +β ϖ +β ( r r ) +β ngd ngd +β o +β nfa + v (2.5) * * We also es a parsimonious model based on uncovered ineres rae pariy (UIP) condiions. This model has been exensively esed in he lieraure wih poor resuls, see Hodrick (1987) for survey resuls. However, recen sudies poined o more hope for he UIP models, for insance, Flood and Rose (2002) show ha UIP models end o work beer using more recen daa from he 1990s, Chinn and Meredih (2004) using a larger span of daa and incorporaing long-erm ineres rae differenials also achieve beer in-sample esimaes for he UIP. Given ha an emerging economy is subjec o many risks no capured by he ineres rae differenial, we assume wo flexible funcional forms. The firs assumes ha he exchange rae will be a funcion of shor erm ineres rae differenials, ( ) s =β +β i i +ν (2.6) 0 1 while a second specificaion includes he counry-risk, measure by he EMBI+ index menioned earlier: ( ) s =β +β i i +β embi +ν (2.7) As poined ou by Engel, Mark and Wes (2007), wo imporan characerisics of moneary policy were ignored up o now. Firs, i is endogenous. Second, since he mid-1980s cenral banks have used ineres rae as he insrumen policy, no money supply. Therefore, our las model incorporaes endogenous moneary policy se by he definiion of he shor-erm ineres rae according in he spiri of Taylor (1993) cenral bank reacion funcion. Following he line of New-Keynesian moneary models, we apply a Taylor Rule model. The Taylor model for exchange rae deerminaion was employed recenly by Engel and Wes (2006), Mark (2007), Clarida and Waldman (2007) and Molodsova and Papell (2007). In general, moneary policy rules are summarized by a Taylor s rule funcion: i =γ q +γ Eπ +γ y +δ i + u q π + 1 y 1 m

7 Marcelo L. Moura, Adauo R. S. Lima, Rodrigo M. Mendonça 401 We assume γ > 0, γ > 1, γ > 0, 0 δ< 1. For he foreign counry: q i =γ Eπ +γ y +δ i + u π + 1 y 1 m π y Using he wo Taylor Rules above wih he uncovered ineres pariy condiion: i i = Es s +ρ * + 1 where ρ denoes a risk-premium and informaion, we can wrie: q s p + p = b b E f * + j j= 0 + j 1 b 1 +γ q ( ) ( ) E he condiional expecaions condiioned on ime f = ( γπ 1) Eπ + 1 Eπ + 1 +γy y y +δ( i 1 i 1) + ( um um ρ ) In paricular, using he las expression we can specify his model by he following economeric equaion: 5 * * s =β 0 +β1( PDV ( y) PDV ( y ) ) +β2( PDV ( π) PDV ( π ) ) * +β3( PDV ( i) PDV ( i ) ) +β 4embi +β 5q 1+ v (2.8) + j where PDV ( x) b j= 0 b Ex+ j denoes he presen value of expeced fuure variables. For he Taylor Rule Model we used hisorical expecaions from he Consensus Forecas Economics Survey using a value of b=0, Ou-of-sample forecasing 3.1 Coinegraion diagnosic ess A general expression for he relaion wih he exchange rae is: s =β 0 +ΧΠ+e (3.1) 5 The lagged erm for he real exchange rae accouns for he serial correlaion of he exchange rae and he relaive * price level difference, p p 6 This value was obained by direc esimaion of i =γ qq +γπ Eπ + 1+γ y y +δ i 1+ um for Brazilian daa and using 1 b ( 1 +γ q ). We used an H-P filer o esimae he produc gap and inflaion expecaion from Consensus Forecas for expeced inflaion.

8 402 Exchange rae and fundamenals where X denoes he vecor of explanaory variables, Π is a vecor of parameers and e is a random erm. Since many of he macroeconomic variables are no saionary, we need o es if [ s, X ] has a long-run relaionship in order o avoid spurious regressions. Following he seminal work of Engle and Granger (1987) we es if [ s, X ] co-inegrae by using MacKinnon (1991) criical values for he Engle-Granger wo-sep procedure. Empirical esimaion uses monhly daa from January 1999 o December 2007, a full sample of 108 observaions. 7 Using he full sample, we firs esimae (2.1) o (2.8) and generae he esimaed residuals series, e ˆ, for each model. Then, we run he regression: e ˆ =α+γe ˆ + u (3.2) 1 and es for he null of no-coinegraion of γ = 0. 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 MacKinnon (1991) criical values. Resuls for he Engle-Granger coinegraion ess are presened on Table 1. They show ha he Produciviy Differenial, he Porfolio and he Sick Price Moneary models does no coinegrae. This means ha specificaions (2.2) o (2.4) do no produce meaningful esimaes leading o spurious regressions. However, we will keep hose models in our forecasing exercise jus for scienific curiosiy o evaluae if we can obain any predicive accuracy of hem, he heory should say ha we will no. 7 Excep for he Taylor Model where limied daa availabiliy reduced he sample o March 2001 o December 2007, a oal of 81 observaions. The appendix gives a deailed descripion of he daa.

9 Marcelo L. Moura, Adauo R. S. Lima, Rodrigo M. Mendonça 403 Table 1 - Coinegraion ess for he Exchange Rae Models Model T-Saisic Number of explanaory variables Diagnosic resuls BEER -4,941 5 Coinegraion a 5% significance level Produciviy Differenial -2,993 6 No coinegraion Flexible Price Moneary -4,237 4 Coinegraion a 5% significance level Sicky Price Moneary -3,630 5 No coinegraion Porfolio -4,098 6 No coinegraion Unc. Ineres Pariy -4,201 2 Coinegraion a 1% significance level Unc. Ineres Pariy wih Embi -4,256 3 Coinegraion a 5% significance level Taylor -4,261 5 Coinegraion a 10% significance level Noe: Asympoical criical values obained from MacKinnon (1991) assuming a no-rend saisics corresponding o equaion (3.2). The coinegraion ess on Table 1 assume ha here is only one coinegraion relaionship. A more general alernaive, given he presence of many macroeconomic series in our models, would be o es for he presence of muliple coinegraion relaionships. 8 Table 2 presens resuls of he Johansen (1991) VAR-based coinegraion ess. For he Taylor and he Uncovered Ineres Pariy wih EMBI models, Johansen s ess confirm he resul of he Engle-Granger es and presens jus one coinegraion relaionship. However, for some oher models here is evidence of more han one coinegraion vecor. In paricular, we fail o rejec he null of a mos one coinegraion equaion for he following models: BEER, wih evidence of four coinegraion relaionship a 1% significance level and six a 5%; produciviy differenial, wo a 1% and four a 10%; sicky price moneary, wo a 5% and porfolio, hree a 1%, four a 5% and five a 10%. This las resul suggess he use of Vecor Error Correcion models for hose models. However, he drawback of using VEC in forecasing a long horizons is he need of including shorerm dynamics of he explanaory variables. For insance, Groen (2000) uses he VEC approach in order o esimae a moneary model and forecass up o 4 years ahead. However, informaion abou he values of he shor-run dynamics for years 1, 2 and 3 ahead are no available a ime. If we wan rue ex-ane forecass, some sor of VEC modeling wihou he shor-run dynamics is necessary for rue forecass and we leave his opic for fuure research. 8 We hank an anonymous referee for his commen.

10 404 Exchange rae and fundamenals Table 2 - Johansen Coinegraion Tess - race saisics Model None A mos 1 A mos 2 A mos 3 A mos 4 A mos 5 A mos 6 BEER 247,1 *** 169,2 *** 102,7 *** 68,8 *** 40,6 ** 22,4 ** 5,5 Produciviy Differenial 105,3 *** 61,4 *** 33,2 * 18,7 * 9,0 * Flexible Price Moneary 57,5 ** 31,0 19,5 * 8,9 * Sicky Price Moneary 93,8 *** 57,5 ** 30,5 17,3 7,1 Porfolio 146,6 *** 96,1 *** 62,3 *** 38,4 ** 18,5 * 5,2 Unc. Ineres Pariy 13,5 2,5 Unc. Ineres Pariy wih EMBI 35,1 * 15,5 4,4 Taylor 79,6 ** 49,1 26,5 10,5 2,9 Noe: Johansen coinegraion ess were based on he assumpion of a consan and no rend in he esimaion equaion. Aserisks ***, **, * denoe rejecion of he null a 1%, 5% and 10% significance levels. 3.2 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 (2.1) o (2.8) as represened by equaion (3.1), obaining he fundamenal value for he exchange rae: F =β ˆ +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. Noice ha, using (3.4) we avoid he problem of using fuure unknown explanaory fundamenals o predic he exchange rae. In our exercise, only informaion available a ime is used o esimae he fuure exchange rae. We used he echnique of rolling regressions on (3.4). Iniially, we esimaed (3.1) using daa from January 1999 hrough Ocober 2005, a oal of 70 observaions. Then, for each esimaed model, we made one-, hree-, six- and welve-monh projecions ahead for he exchange rae level. A a second momen, we displaced, using he rolling regression mehod, he esimaion of he models one period ahead, keeping he size of he iniial sample. We repeaed he procedure o he exhausion of he sample. This procedure is hen compared wih he forecasing of a model ha assumes he exchange rae following a drif less random walk, ha is: s s + k = (3.5)

11 Marcelo L. Moura, Adauo R. S. Lima, Rodrigo M. Mendonça 405 Table 3 displays Theil s raio beween he Roo Mean Squared Error 9 (RMSE) of each specificaion and he RMSE of he random walk. To es he saisic significance of his raio, we used he saisic proposed by Clark and Wes (2006, 2007), in which, under null hypohesis, here is no difference beween he wo esimaions forecasing performance. Tha is, he forecasing generaed by he economic models is as good as he forecasing generaed by a drifless random walk. Thus, numbers inferior o one indicae ha he economic models ouperformed a drifless random walk for he ou-of-sample forecasing of he exchange rae n-periods ahead; numbers superior o one indicae ha he economic models underperformed a drifless random walk. Table 3 - RMSE raios Model 1-monh 3-monh 6-monh 12-monh BEER 89** 37* 21* 0,982 Produciviy Differenials 1,039 1,349 1,995 1,669 Flexible Price Moneary 1,061 1,359 2,007 1,654 Sicky Price Moneary 80* 1,309 1,874 1,705 Porfolio 1,177 1,471 1,476 1,298 Unc. Ineres Pariy 84** 0,993 0,989 01*** Unc. Ineres Pariy wih Embi 1,005 1,003 92** 80*** Taylor 30** 58** 60*** 81*** Noe: RMSE raios are defined as model RMSE divided by random-walk RMSE, values lower han one indicae ha he economic model had a beer ou-of-sample performance han he random walk. Aserisks ***, **, * denoe rejecion of he null a 1%, 5% and 10% significance levels. As expeced by he heory, models ha presened beer ou-of-sample predicabiliy are he ones ha co-inegrae he exchange rae and macroeconomic fundamenals. In paricular, he bes forecasing performance is obained using he BEER and Taylor models. Ineresingly, a parsimonious model based on uncovered ineres pariy also shows a saisfacory forecasing accuracy, especially for 6 and 12 monh-ahead horizons. Figures 1 and 2 plos he random walk and compeing models forecass compared o acual exchange raes for 6-monh and 12-monh-ahead forecass. From he graphs we can see many ineresing aspecs. Firs, all models capure he exchange rae appreciaion of he end of 2004 o December Second, he random-walk guess, which is he same exchange rae series displaced six or welve monhs-ahead is a good forecas and hard o bea. Third, alhough all models are able o predic an appreciaion rend from 2004 o 2007 heir esimaed exchange is almos always above is acual value. Fourh, he major deviaions of he prediced and 9 ( ˆ ) 2 N 1 s s RMSE = =, where sˆ is he esimaed and N sample size. s is he acual value of he exchange rae and N is he

12 406 Exchange rae and fundamenals esimaed values are in general a he beginning of he forecasing window, during 2005 and Excepions are he models ha had RMSE raios significanly lower han one in Table 3, namely, he Taylor model and he UIP wih EMBI a six and welve-monhs-ahead forecas, and he BEER model a six-monhs ahead forecas. 3.3 Daa discussion Given he srong predicabiliy resuls of he BEER and Taylor models, we find useful o discuss he mos relevan series. 10 Figure 3 presens he exchange rae and he explanaory variables for he BEER model while Figure 5 does he same for he Taylor model. Figure 6 presens he remaining explanaory variables used on oher models. Looking firs o he exchange rae series, we see clearly wo disinc periods. From 1999 o 2003 he real/dollar exchange rae has clear endency owards depreciaion and from 2003 o 2007 he endency is reversed o an appreciaion movemen. This movemen coincides wih he confidence crisis in he Brazilian economy during 2002, jusified by invesor s uncerainy abou he presidenial elecions during ha year, he favoriism and poserior vicory of he lef-wing governmen. For he BEER model, however, i is no only abou invesor s and poliical uncerainy. From 1999 o 2002, he macroeconomic fundamenals already poined o a depreciaion endency. In Figure 3, we can see his by looking a he upward movemen on he relaive price index, ne foreign asses and ne governmen deb. Afer 2002, he new eleced governmen srongly signals for a conservaive moneary and fiscal policy, and ne governmen deb and relaive CPI prices sabilizes. In response o exernal favorable condiions, we also verify a decrease in ne foreign asses, explained by foreign domesic invesmen and curren accoun surpluses, and he improvemen of erms of rade. In conclusion, worsening in inflaion levels, ne governmen deb and increase in ne foreign asses in explains he depreciaion movemen; aferwards, sabilizaion of inflaion and deb, decrease of ne foreign asses and exernal favorable condiions in erms of rade and price of radables appreciaed he currency. Compared o he BEER model, he Taylor model uses a differen approach o explain he movemen of exchange raes during he 2001 o 2007 period. 11 Figure 4 shows clearly he srong depreciaion in 2002 moivaed by an equally sharp deerioraion of expecaions in erms of lower growh raes, higher inflaion raes and a counry risk increase. In response, we see a poserior increase in expeced ineres raes a he end of From 2003 o 2007, improvemen of fundamenals explained he real/dollar appreciaion: lower expeced inflaion, higher expeced growh raes, lower counry risk and lower expeced ineres raes. 10 Again, we hank an anonymous referee for his suggesion. 11 Noe ha, due o daa unavailabiliy for earlier periods, he Taylor model was esimaed for he March 2001 o December 2007 period.

13 Marcelo L. Moura, Adauo R. S. Lima, Rodrigo M. Mendonça 407 Finally, when we look a he oher explanaory variables no included in he BEER and Taylor models (see Figure 5), i is clear why hey fail o predic he exchange rae. Apar from he produciviy differenial, which presens a negaive relaionship wih he nominal exchange rae, inflaion raes, money supply and indusrial producion levels had lile relaion wih he exchange rae. This illusraes our empirical resuls ha old vinage moneary models, like he FPMM and he SPMM, had lile explanaion power o he nominal exchange rae, a leas for he Brazilian economy. 4 Conclusions The resuls of his sudy show ha he economic variables may explain he behavior of an independenly floaing exchange rae in an emerging economy like he Brazilian. The specificaions herein esimaed generaed resuls consisen wih hose forecased by he heoreical economic models. The bes performance was obained using more realisic models, like he Taylor rule model, or models ha combine produciviy differenials wih porfolio balance effec models, like he BEER model. Parsimonious models, based on uncovered ineres pariy models also perform paricularly well given is simpliciy. These resuls indicae ha he exchange rae in Brazil is linked wih curren and fuure economic fundamenals and does no follow a random walk. These resuls corroboraes recen lieraure on ou-of-sample exchange rae predicabiliy, see Engel, Mark and Wes (2007) and, for he Brazilian case specifically, he analysis carried ou by Muinhos, Alves and Riella (2003). In line wih he analysis of Obsfeld and Rogoff (1996), he exchange rae as well as he price of any asse reflecs he agens expecaions owards he behavior of oher variables. Fuure sudies should ry o es hese resuls in oher emerging economies. Appendix Daa descripion The daa cover he period from January 1999 o December 2007, he main sources used were Bloomberg and a DaaSream Advance Thomson. Those daases collec macroeconomic informaion direcly from Naional Sources, IMF Inernaional Financial Saisics, World Bank and oher major daases. Bellow, we deail he mehodology used for collecing daa.

14 408 Exchange rae and fundamenals The following series for he Brazilian price indexes were used: he IPCA, calculaed by IBGE was used as consumer inflaion rae measure, he IPA-DI, esimaed by FGV, as radable inflaion rae indicaor. Tradable and non-radable price indexes for Brazil were obained direcly from DaaSream Advance Thomson. For he Unied Saes, he Consumer Price Index was used as he consumer price index, he Service CPI Less Energy Services (CPIn), as nonradable inflaion rae measure, and he Producer Price Index (PPI), as radable goods inflaion rae measure. The Bureau of Labor Saisics calculaed he US series. In all he cases, we used he original series wihou seasonal balance. As produc proxy, given he absence of GDP monhly series in boh counries, he indusrial producion original series for Brazil and he Unied Saes, calculaed by IBGE and by he Bureau of Labor Saisics were respecively, used, boh series were seasonally adjused by he X(11) mehodology. The exchange rae (R$/US$) used refers o he average marke price a each monh obained a DaaSream Advance - Thomson. The SELIC Rae and he FED Fund Rae were used as shor-run ineres raes for Brazil and he Unied Saes, respecively. For Brazil, governmen exernal and inernal deb daa and inernaional reserves were provided by he Cenral Bank of Brazil (BCB). The risk premium used was EMBI + Brazil (Emerging Marke Bond Index Brazil) calculaed by J. P. Morgan, which measures he risk spread of he Brazilian sovereign exernal deb over a general risk-free bond, in he case, he Unied Saes Treasury. The ne foreign asses is no published monhly by he Cenral Bank of Brazil; hus, a June-2005 ne exernal liabiliies based series was buil and updaed wih June-2005 monhly curren accoun liquidiy, which is also provided by he BCB.

15 Marcelo L. Moura, Adauo R. S. Lima, Rodrigo M. Mendonça 409 Figure 1 6 Monh ahead forecass (acual exchange rae vs. compeing models) Random Walk AcualExchangeRae Prod.Differenial Acual Exchange Rae BEER Acual Exchange Rae FPMM Acual Exchange Rae SPMM AcualExchangeRae UIP AcualExchangeRae 1.2 UIPw/EMBI Acual Exchange Rae Taylor AcualExchangeRae Porfolio Acual Exchange Rae Noe: Acual and forecased exchange raes are in naural logarihms.

16 410 Exchange rae and fundamenals Figure 2 12 Monh ahead forecass (acual exchange rae vs. compeing models) 1.2 Random Walk AcualExchangeRae Prod.Differenial Acual Exchange Rae BEER Acual Exchange Rae FPMM Acual Exchange Rae SP MM AcualExchangeRae UIP AcualExchangeRae 1.2 UIPw/EMBI Acual Exchange Rae Tayor Acual ExchangeRae Porfolio Acual Exchange Rae Noe: Acual and forecased exchange raes are in naural logarihms.

17 Marcelo L. Moura, Adauo R. S. Lima, Rodrigo M. Mendonça 411 Figure 3 Exchange rae and explanaory variables of he BEER model Exchange Rae - R$/$ Relaive Price Index - CPI Ne Foreign Asses.0 Ne Governmen Deb Terms of Trade Real Ineres Rae Differenial Price of Tradables Noe: All he variables are in naural logarihms and, excep for he exchange rae, are he raios of Brazilian over he American values.

18 412 Exchange rae and fundamenals Figure 4 Exchange rae and explanaory variables of he Taylor model 1.4 Exchange Rae - R$/U$ Presen Value - Expeced Oupu Growh Rae Presen Value - Expeced Inflaion Raes.18 Presen Value - Expeced Ineres Raes Counry Risk - EMBI Brazil Noe: All he variables are in naural logarihms and, excep for he exchange rae and he EMBI, are he raios of Brazilian over he American values.

19 Marcelo L. Moura, Adauo R. S. Lima, Rodrigo M. Mendonça 413 Figure 5 Exchange rae and oher explanaory variables Excahnge Rae -R$/$ Inflaion rae: (1 + rae) Money supply: M1 - seas. adj. Indusrial Porducion -seas. adj Produciviy Differenial: radables / non-radables Ineres Raes Noe: All he variables are in naural logarihms and, excep for he exchange rae, are he raios of Brazilian over he American values.

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