Out-of-Sample Exchange Rate Forecasting and. Macroeconomic Fundamentals: The Case of Japan

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1 Ou-of-Sample Exchange Rae Forecasing and Macroeconomic Fundamenals: The Case of Japan Takashi Masuki and Ming-Jen Chang * ABSTRACT: The sudy explores he exchange rae forecasing abiliy of a number of macroeconomic fundamenal models and compares hem o a naïve random walk model for he case of Japan during he pos-breon Woods sysem. In order o undersand he ou-of-sample exchange rae forecasing accuracy, we examine he shor-horizons & long-horizons ou-of-sample exchange rae forecasing by differen crieria. We find ha many macroeconomic fundamenal models can bea he naïve random walk model o forecas yen/dollar rae changes in shor- and long-horizons. Moreover, he Taylor rule model canno always significanly perform beer han oher macroeconomic fundamenals, especially in he nonlinear formula seup. In general, he esimaed coefficiens of he inflaion differenials suppor he Taylor rule specificaion. JEL classificaions: C53, F31 Keywords: Exchange rae disconnec puzzle, fundamenals, Japanese yen, ou-of-sample exchange rae forecasing * Masuki: Deparmen of Economics, Osaka Gakuin Universiy. Chang: Corresponding auhor, School of Economics, Universiy of Noingham, Universiy Park, Noingham, NG7 2RD, UK; Phone +44 (0) , mingjen.chang@noingham.ac.uk.

2 1. Inroducion One of he mos famous puzzles in inernaional macroeconomics is why exchange rae and fundamenals are disconneced (see, Meese and Rogoff, 1983; Obsfeld and Rogoff, 2001). 1 The puzzle argues ha exchange rae changes perform considerably weak relaionships wih any macroeconomic aggregaes (see also, Lyons, 2001). A pioneering work, conduced by Meese and Rogoff (1983), argues ha macroeconomic exchange rae models canno perform beer in erms of ou-of-sample forecasing abiliy han a naïve random walk model a shor- o medium-horizons during he pos-breon Woods sysem. Meese and Rogoff use he srucure exchange rae models, which include flexible-price and sicky-price moneary models wih curren accouns, and conclude ha srucural models canno ouperform a random walk model a 1- o 12-monh horizons. Analogously, Baxer and Sockman (1989) and Flood and Rose (1995) illusrae ha exchange raes sharply flucuae afer he esablishmen of he floaing exchange rae sysem, i.e. he pos-breon Woods sysem, while mos macroeconomic aggregaes have no corresponding changes as well. 2 In he real economy, nominal & real exchange raes are more volaile han oher macroeconomic fundamenals, such as oupus, money supplies and commodiy goods prices. Moreover, no model has so far been seemingly powerful enough in inerpreing exchange rae movemens. Obsfeld and Rogoff (2001) argue ha he exchange rae disconnec puzzle migh resul from a combinaion of rade coss, monopoly power and pricing-o-marke in local currency. The exchange rae disconnec puzzle has herefore caused pessimism among inernaional economiss abou he usefulness of heoreical and/or empirical exchange rae models. Saring from Mark (1995), a number of sudies have found evidence of beer forecasing accuracy of exchange rae models a longer horizons raher han a naïve random walk model. However, hese findings have been quesioned by Kilian (1999) and Cheung, Chinn and Pascual (2005). Cheung e al., for example, argue ha no exchange rae model is consisenly beer han a random walk model a any horizons. Engel and Wes (2004, 2005) employ moneary policy rules as he presen value model of exchange raes and find ha exchange raes will approach a random walk process while he discoun facor is near 1. Sarno and Sojli (2009) show empirical evidence o suppor he assumpion ha he discoun facor is near 1 and suppor he 1 I s named as he exchange rae disconnec puzzle (also Meese and Rogoff puzzle or exchange rae deerminaion puzzle). 2 The puzzle is similar o he sock-price disconnec puzzle, which argues he sock price changes have no any sizable effecs on he real economy. 1

3 empirical inabiliy o make he connecion beween exchange raes and fundamenals. More imporanly, Molodsova and Papell (2009) examine exchange rae ou-of-sample predicive accuracy of macro-based fundamenals for he U.S. dollar during he pos-breon Woods regime and show ha he predicive abiliy is sronger wih he Taylor rule model han oher macro fundamenals. Similarly, Kilian and Taylor (2003) and Manzan and Weserhoff (2007) find srong evidence of predicive abiliy for exchange rae models by nonlinear mehods a long-horizons, bu no a shor-horizons. Recenly, Molodsova, Nikolsko-Rzhevskyy and Papell (2008, 2011) re-examine exchange rae ou-of-sample predicive accuracy wih Taylor rule models for some major currencies and obain similar resuls. In recen sudies, some papers use real-ime daa o examine he connecion beween exchange raes and moneary policy (see, for example, Ehrmann and Frazscher, 2005; Molodsova e al., 2011). In paricular, Molodsova e al. (2011) use real-ime daa o es ou-of-sample predicive abiliy for dollar/euro exchange raes by cenral banks ineres rules and find sronger evidence of predicabiliy a shor-horizon (one-quarer-ahead) predicions. The objecive of his paper is o es he forecasing abiliy of he macroeconomic exchange rae models for yen/dollar raes and compare hem o a naïve random walk model. However, differen from some exising lieraure, he sudy specifically focuses on he case of Japan over he pas decades. To explore he case of modern Japan, an imporan even canno be negleced, ha is, he Plaza Accord, which was signed in Sepember 1985 by five developed counries. Afer his Accord, he moneary auhoriy in Japan, i.e. he Bank of Japan (BOJ) focused on a few main moneary policy arges, such as price and exchange rae sabilizaion (see, Clarida, Galí and Gerler, 1998; McKinnon and Ohno, 1997; de Andrade and Divino, 2005). To achieve is curren goal, he BOJ has frequenly adjused he official discoun rae (call rae). The BOJ, in paricular, has conduced some moneary policies, such as he zero ineres rae policy and quaniaive moneary easing, which were no convenional rules, o simulae he economy a ha ime. 3 Following Messe and Rogoff (1983), we apply he macroeconomic model in he sudy o generae forecass a 1- o 24-monh horizons for he yen/dollar rae. In order 3 In order o overcome he deflaionary pressure and simulae he economy in he mid-1990s, he BOJ firs inroduced he zero ineres rae policy in March 1999, which lowered he uncollaeralized overnigh call rae from 0.18% o near zero, 0.04%, because he official discoun rae was already a a low rae (see, Io, 2006). The zero ineres rae policy coninued unil July 2006, excep for Augus 2000 March In March 2001, wih he aim of providing more liquidiy o he financial markes, he BOJ decided o raise he excess reserves in curren accouns o five rillion yen and coninued o mainain hem a he same level a ha ime, which is known as quaniaive easing (subsequenly, he desired level of excess reserves was raised up o he hiry rillion yen). Since hen, he BOJ has considered he quaniaive moneary easing as an alernaive policy insrumen. 2

4 o compare our resuls o exchange rae forecasing sudies, we apply numerous convenional crieria o measure he forecasing errors and modern mehods o es exchange rae ou-of-sample forecasing accuracy wih a naïve random walk model. The convenional ways of forecasing accuracy are as follows: mean absolue error (MAE); roo of mean squared error (RMSE); and Theil U. The modern ways of forecasing abiliy are: mean squared forecas error (MSFE) developed by Diebold and Mariano (1995), i.e. DM es; an exension work by Diebold and Mariano (1995) and Wes (1996), i.e. W-DM es; and Clark and Wes (2006), i.e. CW es, are used in he sudy. We examine he forecasing abiliy for yen/dollar exchange rae daa by boh sandard linear and nonlinear models (see also, Qin and Enders, 2008). A simple logisic nonlinear model is used as he nonlineariy formula o fi any possible policy argeing changes in Japan. We uniquely compare he paper for he case of Japan which experienced wo differen economic long run changes from boom o recession while he economic policy for he Japanese governmen urned from conservaive o aggressive. We find ha he ou-of-sample exchange rae forecasing errors for he Taylor rules and oher macroeconomic models measured by using convenional crieria are similar. The forecasing abiliy for many macroeconomic models significanly ouperforms he naïve random walk model in boh shor- and long-horizons, while he ou-of-sample exchange rae forecasing accuracy wih Taylor rule model, paricularly in he logisic nonlinear model seup, canno be always beer han hose wih oher macroeconomic fundamenal models. These findings are differen from Molodsova and Papell (2009) s conclusions. One possible reason could be ha he BOJ implemened an almos zero ineres policy afer he 1990s, so ha ineres rules are no longer good indicaors for exchange rae changes. Finally, he plos of he esimaed coefficiens of inflaion difference are sill suppored for he Taylor principle specificaion. The res of his sudy can be organized as follows. Macroeconomic fundamenals are presened in Secion 2. Secion 3 discusses he daa sources and ou-of-sample forecasing. The empirical resuls are repored in Secion 4. Finally, we conclude. 2. Exchange Rae Models In order o undersand exchange rae ou-of-sample forecasing abiliy, some imporan macroeconomic models are employed o examine he exchange rae disconnec puzzle. They are presened as follows. 3

5 Taylor Rules The linkage beween he exchange raes and macro fundamenals arose when moneary auhoriies se he arge ineres rae by he Taylor rule in Following Clarida e al. (1998) and Molodsova and Papell (2009), a simple arge ineres rae rule can be seup by he domesic (Japan) counry s cenral bank. 4 We assume ha he domesic (Japan) counry s cenral bank cares abou he yen/dollar rae, bu he foreign (he U.S.) counry doesn. The domesic cenral bank ses he arge level of he real exchange rae in he ineres rule o make purchasing power pariy (PPP) hold. I reduces he ineres rae if he exchange rae appreciaion is aken from is PPP, or vice versa. I can be obained as: i Jap Jap q E y, (1) * Jap Jap q 1 y where E is he mahemaical expecaions condiional on he informaion se in period. The superscrip Jap denoes Japan and he US is he Unied Saes. s is he log nominal yen/dollar exchange rae and p denoes he difference beween Japan and he U.S. log price levels, so ha he log real exchange rae can be q s p. * i is he arge ineres rae (a he shor-erm ineres rae), is he inflaion rae (wih annual rae, difference of log consumer price index (CPI) level). y is he deviaion of he log oupu from rend and denoes shocks o moneary policy rule. The arge ineres rae reacion funcion for a foreign (he U.S.) couner-par economy can be obained as: i * US US 1 y US US E y. (2) The large foreign counry counerpar doesn really care abou he exchange rae wih oher small foreign economies, so ha here is no real exchange rae in he reacion funcion of he arge ineres rae rules. Rearranging Eq. (1) from Eq. (2), we have: i * q E y, (3) q 1 y where Jap US. We define he difference beween Japan and he U.S. arge ineres raes as i * i * Jap i * US, he difference beween Japan and he U.S. inflaion 4 Over he pas decades, he BOJ remarkably has argeed he inflaion rae before 1990, bu urned o arge oupu gap more afer 1990 (see also, de Andrade and Divino, 2005). 4

6 raes as Jap US, and also he difference beween Japan and he U.S. deviaion of he log oupu from rends as y y Jap y US. Following Clarida e al. (1998), we * assume he acual ineres rae i parially adjuss o he arge, i ( 1 ) i i 1, and [0,1 ] capures he degree of ineres rae smoohing. 5 Based on uncovered ineres pariy holds wih ineres rae smoohing, i s a sraighforward process o obain an exchange rae forecasing equaion by using Eq. (3). Uncovered Equiy Reurns Pariy (URP) By following Lucas (1982) and Cappiello and Sanis (2005), he sudy assumes an arbirage mechanism when he expeced equiy reurns in he domesic counry are less han anoher foreign counry, as he yen/dollar exchange rae associaed wih he markes offering he lower rae of equiy reurns is expeced o appreciae. 6 The exchange rae change in period +1 herefore can be obained as: s 1 0 1Er 1, (4) where is risk premium and r r Jap r US denoes he difference beween Japan and he U.S. equiy reurns. The equiy reurns for Japan and he U.S. are calculaed from he sock price indices of he Tokyo Sock Price Index and he Dow Jones Indusrial Average Index. Uncovered Ineres Raes Pariy (UIRP) By using UIRP, he expeced exchange rae changes should be equal o he expeced nominal ineres rae differenial beween he domesic and foreign counry. Based on he UIRP assumpions, we may apply i o he forecasing equaion of he exchange rae changes. Following Engel and Wes (2005), and Clark and Wes (2006), we obain: s 1 0 1Ei 1, (5) where ε is a forecasing error. By Eq. (5), a posiive expeced ineres rae differenial 5 In fac, we incorporae hree differen parially adjusmens in he sudy, i.e., no smoohing, he 1 s order parial adjusmen (n=1), and he 2 nd order parial adjusmen (n=2), see Clarida e al. (1998) for more deails. 6 Regarding he analyical soluions of he URP, one may refer o Appendix A in Cappiello and Sanis (2005). 5

7 implies a forecasing of he domesic currency appreciaion. 7 Moneary Approach (MA) Following MacDonald and Taylor (1994) and Mark (1995), he sandard moneary approach o he exchange rae changes can be explained as a deviaion of moneary fundamenals and can be obained as: s m y, (6) where κ 0 is a drif erm in his forecasing equaion and he real money supply is defined as he broader classificaion of nominal money supply (M 2 ) divided by aggregae price level. And, m m Jap m US is he difference beween Japan and he U.S. log of real money supplies. Purchasing power pariy (PPP) Finally, we can es he forecasing accuracy of exchange rae changes by using he convenional PPP fundamenals. Many exising sudies poin ou he long-run PPP holds over pas decades. We herefore are going o use he relaive prices beween Japan and he U.S. as fundamenals for he exchange rae forecasing model (see also, Engel and Wes, 2005). We assume he moneary auhoriies arge he PPP level of he exchange rae and he rule implies ha he domesic counry increases ineres raes when he currency faces an appreciaion o he arge level. The relaionship can be obained as: s p, where ζ is a forecasing error of exchange rae changes forecased by relaive price changes beween he domesic and foreign counry. 3. Daa and Empirical Mehodologies 3.1 Daa sources The ime series daa is enirely composed of seasonally unadjused monhly observaions from January 1973 Augus The seasonally unadjused daa is made o esimae srucural and seasonal parameers on a consisen basis and o preven he use of cerain informaion which is no available a he ime of a given forecas (see also, Meese and Rogoff, 1983). The bilaeral daa ses for Japan and he 7 To simplify our esimaions, he saic expecaions are applied in pracice; ha is, E x x 6 1.

8 U.S., he spo and forward exchange raes, shor-erm ineres raes, a broader classificaion of money supply (M 2 ), and he sock price index are colleced from he same daes. All of he daa is obained from publicly available sources. The primary daa source used o consruc economic fundamenals is obained from he IMF s Inernaional Financial Saisics (IFS) daabase. We apply he seasonally unadjused indusrial producion index as a proxy for counries naional oupu because he gross domesic produc (GDP) is available only a quarerly frequency. 8 The price level is employed by CPI and he inflaion rae is defined o be an annual rae. Tha is measured as he 12-monh difference of he CPIs. The money marke rae is used as a measuremen of he shor-erm ineres rae ha he moneary auhoriy ses each period. 9 The oupu gap is measured as he difference beween acual and poenial oupus. Because he poenial oupu is unobservable, we herefore consider he percenage deviaions of acual oupu from a linear rend, a quadraic ime rend and a Hodrick and Presco (1997) rend as alernaive measuremens, respecively Ou-of-Sample Forecasing and Nonlineariy Tess Ou-of-Sample Forecasing. To evaluae he performance of differen exchange rae ou-of-sample forecasing models o a naïve random walk process, we employ some of convenional crieria, which are MAE, RMSE and Theil s U saisic and compare our basic findings wih he exising sudies. MAE is an orhodox forecasing appraisal crierion and is usually adoped for a convenional forecas evaluaion crierion because i does no permi he offseing of each oher for over- and under-forecasing. Addiionally, RMSE is anoher simple/popular crierion for measuring he forecas errors wih he penaly of huge errors by square (see also, Meese and Rogoff, 1983). Finally, Theil s U saisic is defined as he raio of RMSE o he random walk forecass. Therefore, if he value of Theil s U saisic is less han 1, ha means he model has beer performance raher han random walk specificaions. In fac, Theil's U saisic is he raio of he RMSE forecas for he unresriced and resriced regression model. 11 The above saisics of forecasing errors are helpful for comparison of he ou-of-sample forecasing accuracy of macroeconomic fundamenal models wih a 8 For he oupu gap daa, some sudies also use he difference beween he naural rae of unemploymen and acual unemploymen rae o replace i (see, for example, Molodsova e al., 2011). 9 Treasury bill raes and inerbank offer raes are used for shor-erm ineres raes. 10 Following Molodsova and Papell (2009), we adop a smooh parameer of he HP filer equal o 14,400 o de-rend he monhly oupu series. 11 When he Theil s U saisic is less han 1, i implies ha he RMSE for unresriced model forecass is less han he RMSE for resriced model forecass. 7

9 naïve random walk model, bu hey sill do no provide any saisical ess for he differences beween models. Oher han comparing he forecasing errors for differen models, Diebold and Mariano (1995) develop a saisical es procedure for comparing he forecas accuracy of wo differen forecasing models. The DM saisic is o es he null hypohesis of equal forecas accuracy for he wo differen models. However, he DM es is based on an asympoic sandard normal disribuion assumpion under he equal forecas accuracy null hypohesis. In he sudy, he DM saisic is measured by a loss differenial based on he mean squared error and MAE of alernaive forecasing models. We hen compare he ou-of-sample forecasing performance wih he above exchange rae fundamenals by MSFE. We examine wheher he exchange rae models forecas are significanly superior o a naïve random model by using he popular Diebold and Mariano (1995) es. In order o accoun for he problem of moneary policy argeing before/afer 1990, we adop he non-lineariy models o evaluae he forecasing abiliy. The approach is used o examine he nonlinear exchange rae forecasing models. The relevan sudies on comparing he exchange rae ou-of-sample forecasing abiliy of wo models (macroeconomic fundamenal srucural model and naïve random walk model) are based on differen measuremens. One of he mos popular measuremens of predicive accuracy is he mean squared predicion error (MSPE). To evaluae he ou-of-sample predicive accuracy of he models using he MSPE comparisons, we employ Diebold and Mariano (1995) and Wes (1996) o es he wo non-nesed models. I is well known ha he W-DM saisic is appropriae for comparisons of non-nesed models; however he applicaion of W-DM saisic usually resuls in bias sized ess when comparing MSPE for wo nesed models. This is a well-known problem for comparing he ou-of-sample exchange rae forecasing accuracy because he null hypohesis is a naïve random walk process. Even hough he W-DM saisic is effecive for non-nesed models, i is remarkably undersized when adoped for he comparison of he forecasing accuracy of nesed models. This shorcoming migh be imporan for nominal exchange rae forecasing since mos exchange rae models are nesed and null hypohesis is a maringale difference process. To use he undersized es migh resul in he bias of non-rejecion of he random walk null hypohesis. However, mos ess of macroeconomic fundamenal models are nesed wih he resul ha he null hypohesis of he naïve random walk model canno be rejeced by he sandard W-DM es. 12 Moreover, he W-DM es 12 One possible reason for he srucure models of exchange rae forecasing failing o bea a naïve random walk model in he exising lieraure is ha hey usually compare he forecasing abiliy using Diebold and Mariano (1995) and Wes (1996). 8

10 demonsraes low power which makes he es poor in idenifying deparures from he null hypohesis (see Rossi, 2005). In order o illusrae he forecasing abiliy of he srucural models for exchange raes (yen/dollar), we employ he Clark and Wes (2006) es as one of he mehods. In fac, he CW es is he exension of Diebold and Mariano (1995) and Wes (1996) es which is effecive for nesed models when comparing he wo models MSPEs. The Clark and Wes (2006) es correcs he possible bias of he undersized problem in nesed models using he W-DM es. The CW saisic is preferable o he W-DM procedure especially when applied o wo nesed models. I has been incorporaed for he upward shif in he sample MSPE of he alernaive models. Following Molodsova and Papell (2009), we employ he Diebold and Mariano (1995), Wes (1996) and Clark and Wes (2006) o es he forecasing accuracy of nominal exchange rae changes by using alernaive macroeconomic models for Japan during he pos-breon Woods sysem. Nonlineariy Tess. To confirm he nonlineariy for exchange rae forecasing by macroeconomic fundamenals, his sudy includes wo popular lineariy ess by using Tsay (1989) and Hansen (1997). If he model is idenified o be nonlinear, we hen re-examine he forecasing using a simple nonlinear form. We assume he nonlinear specificaion of macroeconomic fundamenals follows a simple logisic smooh ransiion model (see also, Qin and Enders, 2008). 13 Tsay (1989) is one of he mos convenional ways o deec nonlineariy for a series. However, a common problem for simple nonlineariy ess is caused by he nuisance parameers, such as hreshold parameers. Accordingly, Hansen (1997) develops a saisic procedure which considers he problems of undeeced nuisance parameers based on he null hypohesis of lineariy. Following Hansen (1997), he nonlineariy saisic is based on a sandard es wih an asympoic disribuion. Using he resuls of Tsay (1989) and Hansen (1997), we es such a change by he sup Wald crierion and idenify ha a break in behavior occurs. 4. Empirical Resuls In he subsecion, we compare he ou-of-sample exchange rae forecasing performance wih he above exchange rae macro fundamenals by differen crieria. We examine wheher he exchange rae model forecass are significanly superior o a 13 Tachibana (2006) formulaes he BOJ reacion funcion, which has a coefficien dummy aking a value of one if an inflaion rae is wihin he arge zone and a value of zero oherwise, o invesigae he BOJ s inflaion zone argeing policy reacions. 9

11 naïve random model by using some convenional measuremens and saisical ess, he Diebold and Mariano (1995) es, an exension of he Diebold and Mariano (1995) and Wes (1996) es, and he Clark and Wes (2006) es. In order o accoun for he problem of moneary policy argeing before/afer 1990, he lineariy/nonlineariy models are applied o evaluae he forecasing abiliy. 4.1 Exchange Rae Forecasing by Linear Model In order o evaluae he basic scenario for he forecasing abiliy of he yen/dollar rae in he models, we firsly repor he simple forecasing errors and basic saisical ess by using a linear regression model wih each of he fundamenals described above. To evaluae he ou-of-sample exchange forecasing of he models, we examine hem by he leas square mehod in rolling regressions. We make one-monh-ahead forecass for he linear regression model wih every macroeconomic fundamenal, use daa over he ime period January 1973 December 1982 for our esimaions, and reserve daa for ou-of-sample forecasing. Each model is esimaed by using he firs 120 observaions and so he one-monh-ahead forecas is herefore generaed. The firs observaion is hen dropped, an addiional observaion a he end of he sample is added, and re-esimaed, and so on and so forh. The simple esimaions for he linear ou-of-sample exchange rae forecasing model are lised in Tables 1-2. In Table 1, we illusrae he esimaions for he one-monh-ahead exchange rae forecasing error of he Taylor rules (no ineres rae smoohing, smoohing wih n=1 and n=2), URP, UIRP, MA and PPP by using convenional crieria, MAE, RMSE and Theil U saisic. In a similar way o Meese and Rogoff (1983), he MAE saisics are generally abou 1/3 lower han RMSE. By comparing he forecasing errors of MAE and RMSE, we find all of he srucural exchange rae forecasing models, Taylor rules or oher macroeconomic models, o forecas he exchange rae changes ha perform wih similar resuls. However, if we examine he ou-of-sample forecasing accuracy using Theil U saisic, Taylor rule models (no smoohing and smoohing) perform beer han oher macroeconomic fundamenal models. In all of he differen ypes of he Taylor rule models, he smoohing model has beer forecasing accuracy han non-smoohing model and he forecasing errors can provide a basic scenario for exchange rae forecasing for he yen/dollar rae. However, he resuls presened in Table 1 do no answer he quesion of wheher our models ouperform he random walk model or no. Moreover, he simple forecasing error crieria, MAE, RMSE and Theil U, canno provide any saisical ess for forecasing performance, so ha we hen apply some recen developed mehodologies, DM, W-DM and CW, o reexamine he linear 10

12 one-monh-ahead exchange rae forecasing models, and repor he saisical es resuls in Table In general, in mos of he srucural models examined by DM and W-DM, he resuls seemingly suppor he findings of Messe and Rogoff (1983) in which he srucural models canno bea a naïve random model. When his argumen is verified again by he CW es, we find his conclusion is ambiguous. The forecasing abiliy of some exchange rae forecasing models are saisically significanly beer han ha of a naïve random model a he 10% significan level, alhough some models are no. More specifically, all Taylor rules models wihou consan do perform beer one-monh-ahead forecasing accuracy han ha of a naïve random walk model. However, he exchange rae forecasing errors migh resul in bias if he yen/dollar is nonlinear bu examined by a simple linear model (see, Qin and Enders, 2008). We herefore have o examine he nonlineariy for srucural models in he nex subsecion. [inser Tables 1-2: abou here] 4.2 Exchange Rae Forecasing by Nonlinear Model Because he observaion periods in he sudy cover he Japanese yen exchange rae in he pos-breon Woods sysem (January 1973 Augus 2011), in his ime period, he Japanese economy experienced high economic growh in he early years and hen fell ino deep recessions. Thus, he moneary policy of he BOJ has had differen argeing behaviors over he pas decades (see, Mckinnon and Ohno, 1997; de Andrade and Divino, 2005). These changes may resul in he nonlineariy of yen/dollar behavior over he pos-breon Woods era. 15 We herefore examine he nonlineariy of our exchange rae forecasing macroeconomic fundamenal models by wo popular mehodologies, Tsay (1989) and Hansen (1997). We find ha mos models rejec he null hypohesis of lineariy a he 1% significan level as he yen/dollar rae changes when serving as he hreshold variable using boh Tsay (1989) and Hansen (1997) ess; see Table The resuls imply ha here are nonlineariies for he yen/dollar rae forecasing models in he pos-breon Woods sysem. This migh resul in incorrec conclusions if he models are only examined by simple linear models, 14 Alhough Taylor rules (wih no smoohing and wih smoohing, n=2) are no lised in he laer ables, hey illusrae similar resuls. However, hey are requesed upon auhors. 15 Some sudies, such as Orphanides and Wieland (2000) and Dolado, Maria-Dolores and Naveira (2005) argue ha he asymmeric policy responses of he moneary auhoriies o inflaion deviaions from arge and oupu gaps lead o he nonlineariy in he reacion funcions. 16 Even when we recheck i using differen hreshold variables, i.e. ineres raes or inflaion raes, we sill obain similar conclusions. 11

13 alhough rue processes are nonlinear. Thus, he models are reexamined using nonlinear assumpion. 17 [inser Tables 3-5: abou here] In Table 4, he Taylor rule and oher macroeconomic models wih a nonlinear (logisic) adjusmen erm are re-examined using he DM es, W-DM es and CW es. 18 Mos Taylor rule models rejec he null hypohesis of no differen forecasing abiliy a leas a he 10% significan levels by he DM es and W-DM es for wo models. Of paricular ineres, when he srucural models one-monh-ahead forecasing performance is examined by he CW es, only he Taylor rule model (oupu gap measured by linear rend) and he URP wih consan are saisically significan a he 10% level, beer han a naïve random walk model. However, based on he imporan even of he Plaza Accord in Sepember 1985, here migh be a srucural change in Ocober 1985, so we place a dummy variable (Dummy = 1 for Ocober 1985-Augus 2011; Dummy = 0, oherwise) and he dummy variable is applied o a consan erm, a linear ime rend and a quadraic ime rend. Similarly, we repor he saisical ess for forecasing accuracy and find all of he exchange rae forecasing models are a leas a he 5% significan levels rejecing he null hypohesis of wo models indifference by he DM es and W-DM es. Bu, he one-monh-ahead yen/dollar rae forecasing abiliy for whole srucural models, esed by he CW es, canno rejec null hypohesis even a he 10% significan levels. This implies ha incorporaing he imporan even, he Plaza Accord, in our model does no improve he forecasing accuracy of he yen/dollar rae changes in he shor-horizon. However, regarding ou-of-sample exchange rae forecasing accuracy, economiss are concerned abou no only shor-horizons, such as one-monh-ahead, bu also long-horizons (see, for example, Meese and Rogoff, 1983; Mark, 1995). Accordingly, we hen repor oher shor- and long-horizons yen/dollar rae forecasing wih each of he fundamenals described above in Tables 6a-6b and 7a-7b. [inser Tables 6a-6b and 7a-7b: abou here] 17 In order o confirm he nonlinear propery of he models, we also reexamine he residuals of our nonlinear models, and find here is no nonlineariy any more afer he models are seup by logisic formula. Needless o say, he resuls are also requesed upon auhors. 18 Our nonlinear specificaion basically follows he Model 4 in Qin and Enders (2008); however, we here adop simple backward-looking rules raher han forward-looking rules in esimaing our models. 12

14 In order o undersand he shor- and long-horizons exchange rae forecasing accuracy for he above models we described in he sudy, we repor he alernaive ou-of-sample forecas horizons for he whole srucural models a 1, 2, 3, 6, 12, 18 and 24 monhs, see Tables 6a-6b and 7a-7b (The linear model forecas horizons are repored in Tables 6a-6b; and he nonlinear model are repored in Tables 7a-7b). In general, he exchange rae ou-of-sample forecasing in boh shor- and long-horizons using linear Taylor rule models wihou consan are beer ha of naïve random walk models esed using he CW es, bu linear Taylor rule models wih consan ouperform in forecasing performance he naïve random walk model a leas a he 10% significan level only in a few cases. However, only he UIRP model by linear formula wih consan, ou of oher macroeconomic fundamenal models, displays significanly beer exchange rae forecasing accuracy han he naïve random walk model in boh shor- and long-horizons a leas a he 5% significan level using he CW es; see Table 6b. Moreover, yen/dollar rae forecasing accuracy by PPP model wihou consan a 1, 2 and 6 monhs is also beer han a random walk model a he 5% or 10% significan level using he CW es. However, when he yen/dollar rae forecasing abiliy of he linear macroeconomic models we described above is examined by he DM or W-DM saisics, we find only models, such as he Taylor rule (oupu gap measured by linear rend) wih consan, he UIRP wihou consan, he MA wih/wihou consan and he PPP wih consan, have generally beer forecasing accuracy in shor- and long-horizons han a naïve random walk model; see Tables 6a-6b. Because here is srong evidence o suppor nonlineariies in he exchange rae forecasing models, we hus re-examine and repor he ou-of-sample exchange rae forecasing a 1, 2, 3, 6, 12, 18, 24 monhs wih he forecas horizons in Tables 7a-7b. According o he nonlinear models resuls, we find ha ou-of-sample exchange rae forecasing abiliy using Taylor rules is significanly beer han he naïve model in he long-horizons of 24 monhs, a leas a he 10% significan level for whole cases wihou/wih consan using he CW es. In addiion, he exchange rae forecasing accuracy wih Taylor rule (oupu gap measured by linear rend) wih consan ouperforms a random walk model using he CW es also a 1 and 6 monhs. I should be noed ha yen/dollar rae forecasing by URP model wih consan significanly performs beer han a random walk model a he 10% significan level for whole horizons excep for 3 monhs. Furhermore, in exchange rae forecasing by UIRP model wih/wihou consan, he MA model wih/wihou consan and he PPP model wih consan are ofen beer han a naïve random walk model a median- and long-horizons; see Table 7b. In general, he exchange rae forecasing accuracy by 13

15 Taylor rules canno always perform beer han oher macroeconomic fundamenal models in shor- or long-horizons. 4.3 Coefficiens Forecasing In he above subsecion, we presen he ou-of-sample exchange rae forecasing accuracy for macroeconomic models, and conclude ha he linear Taylor rule models wihou consan, linear UIRP model wih consan, nonlinear URP wih consan and UIRP wih consan can usually bea a naïve walk model. In conras wih Molodsova and Papell (2009), he Taylor rule models canno usually ouperform oher macroeconomic models, especially in a logisic nonlinear formula. The possible reasons migh be ha he BOJ implemened an almos zero ineres rae policy afer he 1990s, so ha he ineres rae could no fully reac o inflaion, oupu gaps, or even real exchange rae changes in Japan. Accordingly, he Taylor rule models could no always ouperform oher macroeconomic models in yen/dollar rae forecasing. In he subsecion, we plo he coefficiens forecasing o idenify wheher our empirical coefficien is consisen wih he expecaions of a heoreical model seup. The coefficiens of Taylor rule models wih he 10% confidence inervals for 3 differen GDP gap measuremen assumpions are illusraed. The esimaed inflaion differenial coefficiens wihou consan by linear regression model are repored in Figures 1a-1c. The Japanese inflaion differenial coefficiens (difference beween Japan and he U.S. inflaion) reacing o he nominal exchange rae changes are negaive excep for , and he confidence inervals covers zero; see Figures 1a-1c. The paerns of inflaion differenial coefficiens for all 3 differen GDP gap assumpions are similar. The negaive inflaion differenial coefficiens imply ha a relaive increase in Japan s inflaion rae causes he BOJ o raise he nominal ineres rae more han poin-for-poin so as o raise he real ineres rae. In oher words, an increase in inflaion differenials causes yen/dollar rae appreciaion by he Taylor rule specificaion. In general, he illusraions of inflaion coefficiens suppor he Taylor rule principle in heoreical expecaions. However, similar o he findings in he exchange rae forecasing by he Taylor rules, he 10% confidence inervals for inflaion differenial coefficiens mosly cover zero, since he BOJ canno fully adjus he nominal ineres rae reacing o inflaion rae changes under an almos zero ineres rae environmen. We illusrae he esimaed coefficien on real exchange rae and GDP gap differenials (only he linear rend GDP gap assumpion is repored) which are illusraed on Figures 2-3. Moreover, he esimaed coefficiens of real exchange rae changes are almos all negaive excep for (i s around he ime of he 14

16 Asian Financial crisis). The coefficiens are significanly negaive in and during he subprime crisis (i.e. afer 2007). Generally speaking, he findings suppor our heoreical expecaions, bu are he same as he findings in he coefficiens of inflaion differenials, while he 10% confidence inervals mosly include zero. Similarly, he BOJ canno freely adjus ineres raes by he Taylor rule specificaion o reac o real yen/dollar rae changes or oupu gap changes under a zero ineres rae environmen. [inser Figures 1a-1c and 2-3: abou here] The esimaed coefficiens of he GDP gap are mosly posiive excep in he subprime crisis (ha is, afer 2007), which is agains our expecaions, alhough he confidence inervals conain zero in mos esimaions. Furhermore, he paerns of forecas coefficiens on real exchange rae and GDP gap differenials are quie disinc. Figures 4a-4c illusrae he same evoluion of coefficiens on inflaion differenials wih consan. The flucuaions of he coefficiens are considerably similar o hose in Figures 1a-1c. Finally, he esimaed forecas coefficiens in Taylor rules wih consan are all consisenly repored in Figures 4a-4c and 5-6. [inser Figures 4a-4c and 5-6: abou here] 5. Concluding Remarks Following he seminal papers of Messe and Rogoff (1983) and Mark (1995) on exchange rae forecasing, we complee he sudy o generae forecass a 1- o 24-monhs horizons for yen/dollar rae changes. A variey of univariae ime series echniques are used for examining he forecasing abiliy for our daa. A number of mehods for measuring exchange rae ou-of-sample forecasing of srucural models compared o a naïve random walk model are employed. The convenional ways of forecasing accuracy: MAE, RMSE and Theil s U saisic are used. A number of modern saisics of forecasing abiliy: MSFE developed by Diebold and Mariano (1995), an exension of Diebold and Mariano (1995) and Wes (1996) and a version of MSFE es developed by Clark and Wes (2006) are used in he sudy also o measure he forecasing accuracy of linear/nonlinear models. 15

17 We find ha he ou-of-sample exchange rae forecasing abiliy for he linear Taylor rule models wihou consan, linear UIRP model wih consan, nonlinear URP wih consan and UIRP wih consan can bea a naïve walk model. In oher words, hese models significanly perform beer in exchange rae forecasing accuracy for boh shor- and long-horizons. By conras o Molodsova and Papell (2009) s finding, he Taylor rule models canno always ouperform oher macroeconomic models, especially in a logisic nonlinear formula. The possible reasons could be ha he BOJ kep an almos zero ineres rae over he pas decade in Japan, so ineres rae rules can no longer be a good indicaor o forecas exchange rae changes in yen/dollar raes. Fuure sudies can involve differen nonlinear macroeconomic fundamenals model seups and examine more currencies o clarify he exchange rae disconnec puzzle. Acknowledgemens The auhors would like o hank Kimiko Sugimoo and Jyh-Lin Wu for valuable discussions on he original idea of his projec. The usual disclaimer applies. References Baxer, M. and A. Sockman, (1989) Business Cycles and he Exchange Rae Regime: Some Inernaional Evidence, Journal of Moneary Economics 23, Cappiello, L. and R.A.D. Sanis, (2005) Explaining Exchange Rae Dynamics: The Uncovered Equiy Reurn Pariy Condiion, European Cenral Bank Working Paper Series 529. Cheung, Y.-W., M.D. Chinn and A.G. Pascual, (2005) Empirical Exchange Rae Models of he Nineies: Are Any Fi o Survive? Journal of Inernaional Money and Finance 24, Clarida, R., J. Galí and M. Gerler, (1998) Moneary Rules in Pracice: Some Inernaional Evidence, European Economic Review 42, Clark, T.E. and K.D. Wes, (2006) Using Ou-of-Sample Mean Squared Predicion Errors o Tes he Maringale Difference Hypohesis, Journal of Economerics 135, de Andrade, J.P. and J.A. Divino, (2005) Moneary Policy of he Bank of 16

18 Japan-Inflaion Targe versus Exchange Rae Targe, Japan and he World Economy 17, Diebold, F. and R. Mariano, (1995) Comparing Predicive Accuracy, Journal of Business and Economic Saisics 13, Dolado, J.J., R. Maria-Dolores and M. Naveira, (2005) Are Moneary-Policy Reacion Funcions Asymmeric? The Role of Nonlineariy in he Phillips Curve, European Economic Review 49, Ehrmann, M. and M. Frazscher, (2005) Exchange Raes and Fundamenals: New Evidence from Real-Time Daa, Journal of Inernaional Money and Finance 24, Engel, C. and K.D. Wes, (2004) Accouning for Exchange Rae Variabiliy in Presen Value Models when he Discoun Facor is Near One, AEA Papers & Proceedings 94, Engel, C. and K.D. Wes, (2005) Exchange Raes and Fundamenals, Journal of Poliical Economy 113, Flood, R. and A. Rose, (1995) Fixing he Exchange Rae Regime: A Virual Ques for Fundamenals, Journal of Moneary Economics 36, Hansen, B.E., (1997) Approximae Asympoic P-Values for Srucural Change Tess, Journal of Business and Economic Saisics 15, Hodrick, R.J. and E.C. Presco, (1997) Poswar U.S. Business Cycles: An Empirical Invesigaion, Journal of Money, Credi and Banking 29, Io, T., (2006) Japanese Moneary Policy: and Beyond, Bank for Inernaional Selemens paper 31, Kilian, L., (1999) Exchange Raes and Moneary Fundamenals: Wha do We Learn from Long-Horizon Regressions? Journal of Applied Economerics 14, Kilian, L. and M.P. Taylor, (2003) Why is I So Difficul o Bea he Random Walk Forecas of Exchange Raes? Journal of Inernaional Economics 60, Lucas, R., (1982) Ineres Raes and Currency Prices in a Two-Counry World, Journal of Moneary Economics 10, Lyons, R., (2001) The Microsrucure Approach o Exchange Raes, Cambridge, MA: MIT Press. 17

19 MacDonald, R. and M.P. Taylor, (1994) The Moneary Approach o he Exchange Rae: Raional Expecaions, Long-Run Equilibrium and Forecasing, IMF Saff Papers 40, Manzan, S. and F.H. Weserhoff, (2007) Heerogeneous Expecaions, Exchange Rae Dynamics and Predicabiliy, Journal of Economic Behavior & Organizaion 64, Mark, N., (1995) Exchange Rae and Fundamenals: Evidence on Long-Horizon Predicabiliy, American Economic Review 85, Mckinnon, R.I. and K. Ohno, (1997) Dollar and Yen: Resolving Economic Conflic beween he Unied Saes and Japan, Cambridge, MA: MIT Press. Meese, R.A. and K. Rogoff, (1983) Empirical Exchange Rae Models of he Sevenies: Do They Fi ou of Sample? Journal of Inernaional Economics 14, Molodsova, T., A. Nikolsko-Rzhevskyy and D.H. Papell, (2008) Taylor Rules wih Real-Time Daa: A Tale of Two Counries and One Exchange Rae, Journal of Moneary Economics 55, S63 S79. Molodsova, T., A. Nikolsko-Rzhevskyy and D.H. Papell, (2011) Taylor Rules and he Euro, Journal of Money, Credi and Banking 43, Molodsova, T. and D.H. Papell, (2009) Exchange Rae Predicabiliy wih Taylor Rule Fundamenals, Journal of Inernaional Economics 77, Obsfeld, M. and K. Rogoff, (2001) The Six Major Puzzles in Inernaional Macroeconomics: Is There a Common Cause? NBER Macroeconomics Annual 15, Orphanides, A. and V.W. Wieland, (2000) Inflaion Zone Targeing, European Economic Review 91, Qin, T. and W. Enders, (2008) In-Sample and Ou-of-Sample Properies of Linear and Nonlinear Taylor Rules, Journal of Macroeconomics 30, Rossi, B., (2005) Tesing Long-Horizon Predicive Abiliy wih High Persisence, and he Meese Rogoff Puzzle, Inernaional Economic Review 46, Sarno, L. and E. Sojli, (2009) The Feeble Link beween Exchange Raes and Fundamenals: Can We Blame he Discoun Facor? Journal of Money, Credi and Banking 41, Tachibana, M., (2006) Did he Bank of Japan Have a Targe Zone for he Inflaion 18

20 Rae? Economics Leers 92, Tsay, R.S., (1989) Tesing and Modeling Threshold Auoregressive Processes, Journal of he American Saisical Associaion 84, Wes, K.D., (1996) Asympoic Inference abou Predicive Abiliy, Economerica 64,

21 Table 1. Forecasing Errors: Linear Model Tess Taylor Rule (No smoohing) Taylor Rule (Smoohing, n=1) Taylor Rule (Smoohing, n=2) URP UIRP MA PPP Quadraic Quadraic Quadraic Linear Trend Trend HP Filer Linear Trend Trend HP Filer Linear Trend Trend HP Filer w/o Consan MAE RMSE Theil U w/ Consan MAE RMSE Theil U Noe: Linear model (All he models have homogeneous coefficiens).

22 Table 2. Tess for Superior Forecasing Abiliy: Linear Model Tess Taylor Rule URP UIRP MA PPP Linear Trend Quadraic Trend HP Filer w/o Consan DM W-DM * CW * * * * w/ Consan DM * * ** W-DM * CW * * *** Noe: The Taylor rule model is assumed o be smoohing (n=1). The p-value of he CW es is calculaed via -disribuion. ***, **, and * denoe saisical significance a he 1%, 5%, and 10% levels, respecively.

23 Tess Taylor Rule Table 3. Nonlineariy Tess URP UIRP MA PPP Linear Trend Quadraic Trend HP Filer w/o Consan Tsay Tes 1) *** *** *** *** *** *** Hansen Tes 2) *** *** *** *** *** *** w/ Consan Tsay Tes 1) *** *** *** *** *** *** *** Hansen Tes 2) *** *** *** *** *** *** *** Noes: The Taylor rule model is assumed o be smoohing (n=1). The hreshold variable is he lag of he nominal exchange rae change. ***, **, and * denoe saisical significance a he 1%, 5%, and 10% levels, respecively.

24 Table 4. Tess for Superior Forecasing Abiliy: Nonlinear Model Tess Taylor Rule Linear Trend Quadraic Trend HP Filer URP UIRP MA PPP w/o Consan DM *** ** ** W-DM ** * * CW w/ Consan DM *** *** ** * ** W-DM ** ** ** * ** CW * * Noes: The Taylor rule model is assumed o be smoohing (n=1). Nonlinear model is in he logisic formula (All he models have homogeneous coefficiens). The p-value of he CW es is calculaed via -disribuion. ***, **, and * denoe saisical significance a he 1%, 5%, and 10% levels respecively.

25 Table 5. Tess for Superior Forecasing Abiliy: Model wih Dummy Variable Tess Taylor Rule Linear Trend Quadraic Trend HP Filer URP UIRP MA PPP w/o Consan DM *** *** *** *** *** *** *** W-DM *** ** ** ** *** *** ** CW w/ Consan DM *** *** *** *** *** *** *** W-DM ** ** ** ** ** *** ** CW Noe: The Taylor rule model is assumed o be smoohing (n=1). The p-value of he CW es is calculaed via -disribuion. ***, **, and * denoe saisical significance a he 1%, 5%, and 10% levels, respecively.

26 Table 6a. Taylor Rule Exchange Rae Forecasing: Linear Model w /o Consan Linear Trend Quadraic Trend HP Filer h RMSE DM W-DM CW RMSE DM W-DM CW RMSE DM W-DM CW * * * * * * * * *** *** ** ** ** ** ** ** * * * ** * * w / Consan Linear Trend Quadraic Trend HP Filer h RMSE DM W-DM CW RMSE DM W-DM CW RMSE DM W-DM CW * ** * ** ** ** ** ** ** ** *** *** * * *** *** *** *** Noes: The Taylor rule model is assumed o be smoohing (n=1). ***, **, and * denoe saisical significance a he 1%, 5%, and 10% levels, respecively.

27 Table 6b. Oher Macroeconomic Fundamenals Exchange Rae Forecasing: Linear Model w /o Consan URP UIRP MA PPP h RMSE DM W-DM CW RMSE DM W-DM CW RMSE DM W-DM CW RMSE DM W-DM CW * * * ** * * * ** ** * * * ** * * ** *** *** ** ** *** *** * * ** *** * * w / Consan URP UIRP MA PPP h RMSE DM W-DM CW RMSE DM W-DM CW RMSE DM W-DM CW RMSE DM W-DM CW *** * ** * ** ** ** *** *** ** ** ** *** *** *** ** ** *** *** ** *** *** *** *** ** *** *** *** ** *** *** *** *** *** Noe: ***, **, and * denoe saisical significance a he 1%, 5%, and 10% levels, respecively.

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