Real Exchange Rate Behavior: Evidence From Malaysia, Singapore, and Thailand. Kit Soon Tan, Lan Thi Phuong Nguyen

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1 Economics World, Ocober 2015, Vol. 3, No. 9-10, doi: / / D DAVID PUBLISHING Real Exchange Rae Behavior: Evidence From Malaysia, Singapore, and Thailand Ki Soon Tan, Lan Thi Phuong Nguyen Mulimedia Universiy, Cyberjaya, Malaysia Malick Ousmane Sy RMIT, Melbourne, Ausralia Cheng Ming Yu UTAR, Kuala Lumpur, Malaysia In his paper, he mean reversion behavior of CPI-based real exchange raes in US dollar is invesigaed for hree Souheas Asian economies: Malaysia, Singapore, and Thailand. Using linear and non-linear uni roo ess o deec possible endogenous break(s), real exchange raes for currencies of he hree counries are examined for he long-run purchasing power pariy (PPP) during he period of January 1980 o December Resuls show ha srucural breaks mosly occur in wo periods: 1985 and 1997/1998, and ha, he evidences for he PPP hypohesis are relaively mixed for hese hree counries. Resuls obained from all es fail o provide sufficien evidences for he non-linear adjusmen of real exchange raes owards PPP. The misalignmen in exchange raes canno be found during he sudy period due o a relaively high persisency of real exchange raes (half-life > hree years) found for all he hree counries. Moreover, Engle-Granger procedure and Johansen mulivariae coinegraion mehods are also carried ou. The resuls indicae ha a sronger evidence of PPP exiss for he hree counries relaive o he USA afer allowing for he presence of srucural break(s), implying ha he hree Asian counries were affeced by global financial crises during he sudy period. In brief, he findings reveal ha misalignmen in he hree Souheas Asia economies is relaively slow; boh exchange raes and price levels of hese counries converge in he long run. Keywords: purchasing power pariy (PPP), real exchange rae, uni roo ess, endogenous break, exchange rae behavior, Engle-Granger coinegraion es, Johansen coinegraion es Inroducion Since he breakdown of he Breon Woods sysem, sudies on real exchange raes have been received much aenion from he academic world. Real exchange raes have grea impacs owards he compeiiveness of a counry in he inernaional rade marke, reflecing in reurn is naional produciviy. The flucuaion of purchasing power pariy (PPP) exchange raes over a long period of ime has been a he cenre of macroeconomics sudy. As a PPP exchange rae is used o measure a long-run exchange rae for individual Ki Soon Tan, BFE suden, Mulimedia Universiy, Cyberjaya, Malaysia. Lan Thi Phuong Nguyen, Ph.D., senior lecurer, Faculy of Managemen, Mulimedia Universiy, Cyberjaya, Malaysia. Malick Ousmane Sy, Ph.D., professor of finance, School of Economics, Finance and Markeing, RMIT, Melbourne, Ausralia. Cheng Ming Yu, Ph.D., professorial chair, Faculy of Accounancy and Managemen, UTAR, Kuala Lumpur, Malaysia. Correspondence concerning his aricle should be addressed o Lan Thi Phuong Nguyen, Faculy of Managemen, Mulimedia Universiy, Jalan Mulimedia, Cyberjaya, Malaysia. nguyen@mmu.edu.my.

2 196 REAL EXCHANGE RATE BEHAVIOR currencies, i requires a consan real exchange rae ha demonsraes mean reversion over ime and is no driven by sochasic rends. Examining he behavior of real exchange rae hrough is adjusmen owards he equilibrium level may provide a comprehensive view of self equilibraing of he inernaional macroeconomic sysem. If an economy experiences real srucural changes which hen require adjusmens of relaive prices, PPP may no be he guide for day-o-day flucuaion of exchange raes, bu valid for he long run (Harvey, 2001). According o Ellio and Pesaveno (2004), a lenghy long-run mean reversion in real exchange raes may sugges ha weak compeiion among naions do no lead o heir long-run price convergence. Moreover, he economic and poliical forces regularly buffe he currency of a naion, keeping is value away from equilibrium. Moreover, he misalignmen of exchange raes during he 1990s causing financial urbulences and currency crises across borders has drawn researchers aenion on he use of ime series of real exchange rae. In his paper, he volailiy of real exchange raes in hree seleced Souh Eas Asia counries: Malaysia, Singapore, and Thailand, is invesigaed for a period of January 1980 o December Specifically, mean reversion of real exchange raes will be esed in he presence of endogenously deermined srucural breaks for all he hree counries in he sample. The sudy is expeced o provide furher empirical evidences on he long-run PPP phenomenon in he hree seleced counries. To overcome he weakness of classical univariae uni roo ess ha ofen occur wih a small sample, uni roo ess used in works of Zivo and Andrews (1992), Lumsdaine and Papell (1997), and Saikkonen and Lükepohl (2002) are adoped o allow endogenous breaks. The paper furher disinguishes iself by applying coinegraion ess, namely Engle-Granger es (Engle & Yoo, 1987) as well as Johansen Coinegraion es (Johansen, Mosconi, & Nielsen, 2000) o examine he long-run PPP for Malaysia, Singapore, and Thailand relaive o US dollars for periods ha conain significan srucural breaks. The res of he paper is srucured as follows: Secion 2 presens lieraure review relaed o he PPP heory; research mehodology adoped for his sudy is provided in secion 3; secion 4 discusses findings of he sudy; and secion 5 provides main conclusions. Lieraure Review PPP was inroduced ino economic lexicon less han a cenury ago (Cassel, 1918). Sudies done on he PPP heory for he pas few decades have arrived a mixed conclusions for boh developed and developing naions. In he sudy of McCloskey and Zecher (1976), a PPP relaionship was found o hold over boh shor- and long-run periods. However, oher sudies, i.e., Hakkio (1984), Frenkel (1978), Edison (1985), and Mark (1990), did no find significan evidences ha PPP held for developed naions for heir sample of daa. Krugman (1978) found ha he deviaions of exchange raes from PPP were persisen and large, and even larger for counries wih unsable moneary policy. Furhermore, sudies by Rogoff (1995) and Papell (2002) found ha real exchange raes display saionary over a sufficienly long horizon and ha univariae random walk specificaions could be rejeced in favor of saionary alernaives. However, pas sudies focused mosly on he low power of radiional uni roo ess, bu no on he PPP heory. Correspondingly, empirical evidences from developing Asian economies wih respec o floaing rae regimes are a bes and varied. On one hand, Aggarwal and Mougoue (1996) found an increasingly closer relaionship beween he Japanese yen and he oher Asian currencies. On he oher hand, findings on he

3 REAL EXCHANGE RATE BEHAVIOR 197 equilibrium exchange rae in Chinn (2000) did no closely correspond o he findings acquired from he PPP calculaions. Aron, Elbadawi, and Khan (1997) consruced a coinegraion framework wih single equaion equilibrium correcion models o invesigae he shor- and long-run equilibrium deerminans of quarerly real exchange raes from year 1970 Q1 o 1995 Q1. Shor-run changes as well as a change in he fundamenals probably rigger real appreciaion and depreciaion in exchange rae. The findings also implied ha he dynamics in real exchange rae could be due o various facors, such as levels of liberalizaion, erms of rade, levels of governmen spending, capial flows, and official reserves. Empirical evidences on exchange rae movemens using PPP were mixed. This could be due o he differences in sudy periods and counries of ineres. Caherine and Ariff (2009) found ou ha despie PPP explains movemens in exchange raes in he longer erm, he lengh of ime o reach equilibrium varies for differen regions of counries. In erms of he low power of he sandard uni roo ess wih long half-lives, much aenion has been paid o he applicaion of univariae approaches on a very long-horizon real exchange rae. Lohian and Taylor (1996) used annual daa spanning wo cenuries for dollar-serling real exchange raes. They successfully found a srong evidence on mean-revering real exchange rae behavior. Furhermore, Taylor (2003) examined PPP since he lae 19h cenury by using daa colleced for a group of weny naions over a period of 100 years. The auhor found srong evidences for he long-run PPP when using mulivariae and univariae ess wih higher powers. However, conradicing evidence was found in he sudy of Murray and Papell (2002), claiming ha univariae approaches provide virually no informaion abou he size of half-lives despie mos of he poin esimaes lie wihin hree-o-five-year range. In erms of esing mehod, panel daa analysis, which capures boh cross-secional and ime series daa, has been used by some researchers, especially afer he Asian financial crisis. Papell (1997) invesigaed he long-run PPP. Using he panel daa analysis, he auhor esed for uni roos in real exchange raes ime series of indusrial counries under he curren floa and found evidences ha suppor he long-run PPP. Neverheless, O Connell (1998) repored srong evidence of mean-reversion in real exchange rae. The auhor realized ha pas sudies using panel daa ofen failed o conrol for cross-secional dependence and concluded ha heerogeneiy in he cross secional dimension could probably be he reason. This may sugges ha alhough being in favor, panel daa analysis may no be able o suppor he long-run PPP. Besides he wo above-menioned mehods, i.e., univariae echniques and panel daa analysis, he use of median-unbiased esimaion can also provide reasonably shor half-lives o suppor PPP heory (Rogoff, 1996). The imporance of srucural breaks ha was caused by various evens, such as oil shocks and financial crises, is recenly explored by researchers. The focal poin has been shifed o he influence of hese srucural breaks owards he assessmen of he PPP relaionship. Perron (1989) and Rappopor and Reichlin (1989) are he wo firs sudies ha poin ou he imporance of srucural breaks during he implemenaion and inerpreaion process of uni roo ess. However, he assumpion made by Perron (1989) on he break dae was criicized by Zivo and Andrews (1992), which lead o he developmen of a single endogenous srucural break es for he uni roo. The endogenous break mehodology was exended laer by Lumsdaine and Papell (1997) o allow for a wo-break alernaive. They successfully proved more evidence of PPP agains he uni roo hypohesis han Zivo and Andrews (1992). These findings demonsrae he need for ess wih correc number of srucural breaks are imperaive. In anoher sudy by Saikkonen and Lükepohl (2002), an endogenous break model was developed o encompass he deerminisic erm shif funcions of a general non-linear form using generalized leas squares (GLS) de-rending. They conceded ha nonlinear break ess follow he reasoning, ha breaks

4 198 REAL EXCHANGE RATE BEHAVIOR occur upon a number of periods and demonsrae a smooh ransiion o a new level. The approach is furher exended o circumsances wih an unknown break dae by Lanne, Saikkonen, and Lükepohl (2003). Mehodology Le S (in logarihm) be he log spo rae and p* and p (in logarihm) be he foreign and domesic price levels respecively, he real exchange rae q (in logarihm) is as follows: q S p p (1) The esimaion of q is believed o be bes relevan for esing PPP. This is because i allows he half-life of a random disurbance o be compued, so ha he degree of mean reversion can be measured. To measure he speed of convergence o PPP, one would assume ha he deviaion of he logarihm of he real exchange rae q from is long-run value q 0, ha is consan under PPP, follows a linear auoregressive process of order one, AR(1): q q (2) 1 Where 0 < ρ < 1 and ε is a whie noise innovaion. For annual (monhly) daa, he half-life of deviaions from PPP(τ) is he number of years (monhs) required for he iniial deviaion from long-run level o dissipae by half, wih no fuure shocks. A horizon τ, he percenage deviaion from equilibrium is ρ τ. In he long-run PPP level, i is assumed ha he saring q 0 is zero wih (E[q ] = 0) and wih an iniial shock, δ > 0. Then, from δ/2 = q = ρ 1 δ, he half-live is given by = ln( ) ln, where he absolue value is inroduced o allow oscillaion. 2 For insance, if ρ approaches uniy, he speed of adjusmen ln approaches zero from he lef as well. Hence, he half-life τ approaches infiniy, indicaing he absence of convergence owards PPP. In realiy, he half-lives are esimaed by: Where 1 ln( ) 2 (3) ln is an OLS esimaor of ρ. Based on he consrucion of half-life equaion, he speed of adjusmen or he half-life, does no rely on he iniial level of real exchange rae q 0 or he size of deviaions (δ) in he linear AR(1) model. Alhough evidence of long run PPP can be jusified by he uni roo es wih he use of real exchange raes daa series, a sandard es of he uni roo he augmened Dickey-Fuller (ADF) regression will sill be carried ou. ADF regression is as follows: q q y q (4) k 1 1 i 1 i 1 where, Δq is he firs difference of he real exchange rae, k is he number of lagged which are added o he model o ensure ha he residuals, and ε is whie noise. The opimal lag lengh k is seleced using -sig procedure based on Akaike informaion crierion and Schwarz informaion crierion, wih he maximum value of k equal o 8 (Hall, 1994; Ng & Perron, 1995). For comparison purposes, Phillips-Perron (PP) ess are also performed and he resuls are repored in addiion o

5 REAL EXCHANGE RATE BEHAVIOR 199 he general ADF es. In line wih he PPP hypohesis, q mus display mean reversion behavior devoid of a uni roo. The φ 1 erm should hereby be significanly less han 0 or else he real exchange rae follows a random walk, indicaing ha deviaions from PPP are permanen. According o Perron (1989), he sandard ADF uni roo es does no consider he presence of possible srucural breaks in esimaion of uni roos. Therefore, ADF uni, hus may be disored as a poenial break, i.e., a currency crisis, an oil shock, and a marke crash, in he real exchange rae is simply disregarded (Perron, 1989). Lumsdaine and Papell (1997) furhered Zivo and Andrews framework (1992) by including wo endogenous srucural breaks in he model. In erms of he robusness of he models, enabling wo possible srucural breaks is much more powerful han allowing for a single srucural break. The modificaion of models can be expressed as follows: q q DU1 DT1 DU2 DT2 y q (5) k 1 1 i 1 i 1 where, DU1 = 1, if > T B1 and zero oherwise; DU2 = 1, if > T B2 and zero oherwise; DT1 = T B1, if > T B1 and zero oherwise; and DT2 = T B2, if > T B2 and zero oherwise. On one hand, DU1 and DU2 are dummy variables which enable srucural changes o ake place a T B1 and T B2, respecively. On he oher hand, DT1 and DT2 are wo dummy variables which consider shifs in he rend a T B1 and T B2, respecively. In his model, i allows for wo srucural breaks in he inerceps and he slope. Wih regard o he possible break daes (T B1 and T B2 ), hey are seleced based on he minimum value of -saisic. Briefly speaking, Lumsdaine and Papell s framework (1997) could find more evidence in rejecing he uni roo hypohesis han Zivo and Andrews approach (1992) based on he empirical sudies. Anoher model was suggesed by Saikkonen and Lükepohl (2002) ha srucural break could occur over a number of periods and hen have a smooh ransiion o a new level. Therefore, when a shif in he level of daa generaing process (DGP) occurs, esing for a uni roo will give more accurae resuls. Thus, o ake ino accoun poenial srucural breaks, a level shif funcion indicaed by a general nonlinear f (θ) γ is added o he deerminisic erm μ of he DGP. Saikkonen and Lükepohl s model (2002) is as follows: q f ( ) ' (6) 0 0 where θ and γ are parameer vecors and v is residual errors generaed by an AR(p) process wih possible uni roo. There are a few possible shif funcions. In his sudy, f (θ)γ which can generae sharp one-ime shifs a ime T B for suiable values of θ is considered and applied. An exponenial disribuion funcion which allows for a nonlinear gradual shif o a new level saring a ime T B is as follows: In he shif erm f ( 2) 0, TB f ( ) = { 1 exp[- ( T 1)], T B ( ), boh θ and γ are scalar parameers, in which value of θ is confined o he posiive line and γ can ake any value. Saikkonen and Lükepohl s model (2002) is based on he esimaion of he deerminisic erm wih wo seps: (1) hrough a GLS de-rending procedure under he uni roo null hypohesis and, and (2) hen subracing i from he original series. Wih he adjused series, an ADF ype es will encompass erms o correc for esimaion errors in he parameers of he deerminisic par. As moving oward coinegraion es of PPP, i is imperaive for he order of all he variables for B (7)

6 200 REAL EXCHANGE RATE BEHAVIOR coinegraion es o be he same in he long run. The order of inegraion is he number of imes in which he ime series variables mus be differenced for i o become saionary. In line wih coinegraion mehod, long-run PPP is deemed o hold if he sum of nominal exchange rae and relaive price level of a foreign counry (i.e., he Unied Saes) in logarihmic form ha is ( S levels of respecive counries (p ). Le i assume y = S p p ) will be coinegraed wih domesic price. Long-run PPP assers ha he relaionship exiss in a linear combinaion of he form y = α 0 + α 1 p + ε, such ha ε is saionary and he coinegraion vecors such ha α 1 =1 and ε is he residuals of he regression equaion. The residual based es is deployed based on he Engle-Granger mehodology (Engle & Yoo, 1987) which includes es for a uni roo on residuals as well as convenional uni roo ess. The order of coinegraion of he variable is deermined hrough ADF es. If he oucome indicaes ha he variable is inegraed of order one, he lon-run equilibrium relaion is esimaed by regressing y = S on, such as: p y p (8) 0 1 Absolue PPP assers ha y = α and hence, his requires α 0 = 0 and α 1 = 1. The es is hen carried on by checking he residual of he equilibrium regression for saionary hrough DF es for uni roo. In order o deermine ha hese variables are coinegraed, he residual sequence from he equilibrium equaion is denoed by έ. έ is he series of he esimaed residuals of he long-run relaionship. If he series of he esimaed residuals is found o be saionary hen y and p series will be coinegraed. The auoregressive equaion is esimaed in he form of: e 1 1 n i 1 i 1 If -2 < β 1 < 0, i can be concluded ha he residuals series is saionary. Therefore, y and p are inegraed of order one, i.e., C (1, 1). If boh variables (i.e., nominal exchange raes and relaive price indices) are presumed o follow a random walk wihou converging in he long run, a mehod of error correcion model can be pursued. Vecor error correcion model (VECM) is a resriced vecor auoregressive mehod which encompasses Johansen-Juselius mulivariae coinegraion. VECM resrics he long-run behaviour of endogenous variables o converge o heir coinegraing relaionship while allowing for shor-run adjusmen. Johansen s mehodology akes is saring poin in he vecor auoregression (VAR) of order p given by: i 1 1 p p y + A y +... A y (10) where, y is an n 1 vecor of variables ha are inegraed of order one commonly denoed I(1) and is an n 1 vecor of innovaions. In he Johansen es procedure, here are wo es saisics. In his sudy, he race es is used and displayed as follows: (11) ( ) - n r T rance i 1 ln(1 ) i T denoes he sample size (he number of usable observaion) and i is he esimaed values of he characerisic roos (also known as Eigen values). The race saisic ess he null hypohesis ha here is a mos r coinegraion relaion agains he alernaive hypohesis of here are n coinegraion relaionship (i.e., (9)

7 REAL EXCHANGE RATE BEHAVIOR 201 series is saionary), r = 0, 1, 2,..., m 1. If he race saisic is greaer han he given criical value, hen he null hypohesis is rejeced and concludes ha he series is saionary. The consrucion of CPI-based real exchange rae consiss of US dollar-based nominal exchange raes for Malaysia, Singapore, and Thailand and heir respecive consumer price indices. All he daa are direcly sourced from Inernaional Financial Saisics (IFS) of he Inernaional Moneary Fund (IMF) and cross-checked wih he daa sources from Bloomberg Terminal in order o ensure he consisency and reliabiliy of he daa. Findings In his secion, he auhors sudy CPI-based real exchange raes of hree Souheas Asian economies Malaysia, Singapore, and Thailand are sudied over he ime period January 1980 o December US dollar is reaed as he numeraire, since he Unied Saes has long been one of he major rading parners and is currency plays a dominan role in inernaional rade (Goldberg & Tille, 2008). Figure 1. CPI-based real exchange raes (in naural logarihms) of Malaysia, Singapore, and Thailand over a period of January 1980 o December Figure 1 shows CPI-based real exchange raes of Malaysia, Singapore, and Thailand (in naural logarihms). As shown in Figure 1, poenial srucural breaks experienced by hese economies occur in hree differen ime zones: (1) , (2) , and (3) Unexpeced and drasic upsurge in real

8 202 REAL EXCHANGE RATE BEHAVIOR exchange raes during Asian financial crisis noiceably dominaes he scene, indicaing a poenial srucural shif in he mean and rend of he ime series afer I is an ineviable fac ha figuring ou anoher poenial break wih naked eyes wihou hesiaion is barely possible, and hus his suggess ha allowing he breaks o be endogenously deermined is a sensible implemenaion. The empirical analysis begins wih a discussion of he resuls of ADF and PP uni roo ess, in which an assumpion of no srucural changes exiss. ADF and PP uni roo ess are run firsly a levels (i.e., consan and rend) and and secondly a firs differences of CPI-based real exchange raes series ha serves as a benchmark for comparison. The obained resuls are displayed in Table 1. As shown in Table 1, boh ADF and PP ess, conduced a levels, fail o rejec he null hypohesis of a uni roo for he hree counries ime series a he 1% significance level. This implies ha he CPI-based real exchange raes of hree naions (Malaysia, Singapore, and Thailand) in his sudy are non-saionary a levels. Therefore, o deec one endogenous srucural break over a long period for he sample ime series daa, Zivo-Andrews model (Zivo & Andrews, 1992) is used and resuls are presened in Table 2 below. Table 1 Resuls of Convenional Linear Uni Roo Tess for a Period of January 1980 o December 2014 ADF es PP es Level 1s difference Level 1s difference Resul Resul (consan and rend) (consan) (consan and rend) (consan) Malaysia ** I(1) ** I(1) Singapore ** I(1) ** I(1) Thailand ** I(1) ** I(1) Noes. * and ** denoe 5% and 1% levels of significance, respecively; for he ADF es, lags are seleced auomaically wih he use of Schwarz Info Crierion. Table 2 Resuls of Linear Uni Roo Tes Wih One Endogenous Srucural Break (Zivo-Andrews (1992) Tes) for a Period of January 1980 o December 2014 Level (consan and rend) Break poin Level (consan) Break poin Malaysia ** Augus July 1997 Singapore July July 1997 Thailand ** July July 1997 Noes. * and ** denoe 5% and 1% level of significance, respecively; he 5% and 1% criical values in level wih consan and rend are and -5.57, respecively; in level wihou rend only hey are and -5.43, respecively; and lag selecion is auomaic on he basis of -es. Resuls obained for CPI-based real exchange raes of Malaysia and Thailand show ha null hypohesis of a uni roo is rejeced a level ( wih rend and consan), while resuls obained for Singapore fail o rejec he null hypohesis of a uni roo. A level wihou rend, resuls obained for he hree counries daa fail o rejec he null hypohesis of a uni roo for CPI-based real exchange raes. Based on he resuls obained by Zivo-Andrews es (1992), he resuls consisenly repor a single break in July-Augus The 1997 srucural break occurred was associaed wih he Asian financial crisis in , which riggered off a general meldown of Asian currencies and was followed by financial urmoil. Among he hree counries,

9 REAL EXCHANGE RATE BEHAVIOR 203 Malaysia and Thailand are he wo counries ha were affeced he mos. Alhough allowing for srucural breaks, Zivo-Andrews es (1992) does suppor PPP for Singapore as he -saisics does no allow he null hypohesis o be rejeced a he 1% level of significance. This may imply ha mean reversion may no exis wih he Singapore dollar/usd real exchange rae series, as when linear level shifs are allowed, he PPP puzzle may remain unsolved. According o Lumsdaine and Papell (1997), Zivo-Andrews es (1992) may lead o biased resuls as more han one break may acually exis. Table 3 Resuls of Linear Uni Roo Tes (Lumsdaine-Papell (1997) Tes) wih Two Endogenous Srucural Breaks for a Period of January 1980 o December 2014 Malaysia Singapore Thailand Level (consan and rend) Break poins Level (consan) Break poins ** November * December 1985 July 1997 July Ocober June 1997 July 1997 Ocober ** Ocober June 1997 June 1997 December 2005 Noes. * and ** denoe 5% and 1% level of significance, respecively; he 5% and 1% criical values in level wih consan and rend are and (in level wih consan and rend) and and (in level wihou rend), respecively; and lag selecion is auomaic on he basis of -es. Table 4 Resuls of SL Tes Wih Exponenial Shif for a Period of January 1980 o December 2014 Break poin Lag Coefficiens SL-saisics d (cons) d (rend) d (shif) dx (-1) Malaysia Feb (854.12) (0.1422) ( ) ( ) Singapore Jan (512.68) ( ) (117.81) (5.0021) Thailand Feb Criical values for SL-saisics (3,189.61) 1% (0.0859) 5% ( ) (9.0031) 10% Noes. ***, **, and * denoe he saisical significance a 99%, 95%, and 90% confidence levels, respecively; criical values are sourced from Lanne e al. (2002); and he -saisics of each coefficien are in parenheses. Lumsdaine-Papell es (1997) allowing for wo possible srucural breaks is proven o be more robus han Zivo-Andrews es (1992) as more significan resuls are found for Malaysia and Thailand from Lumsdaine-Papell es (1997) as shown in Table 3, as compared o hose obained from Zivo-Andrews es (1992) (see Table 2). However, wih he real exchange rae ime series of Singapore, he null hypohesis of a uni roo is no rejeced, suggesing ha PPP may no hold for Singapore in he long run. Despie ha he real exchange raes fail o demonsrae mean-revering behavior, i is worh o ake noe ha possible break daes based on he minimum value of -saisic (Table 3) could provide a clearer picure wih major evens, such as he commodiy crisis ( ), he Asian crisis ( ), and he energy shock (2005), ha have

10 204 REAL EXCHANGE RATE BEHAVIOR permanen effecs on he exchange raes series. As poined ou by recen sudies ha uni roo ess may be biased once nonlineariies in he deerminisic componens exis, an alernaive approach he Saikkonen and Lükepohl es (2002), ha considers srucural breaks wih a smooher funcional form for he ransiion period could be much more informaive han he linear endogenous break ess. The Saikkonen and Lükepohl es (2002) es wih he opimal lag lengh (k = 1) being deermined by he sandard Akaike Info Crierion has been displayed in Table 4. The esimaed coefficien of dx(-1) represens Δq -1 ; d(cons) represens Z 1 = [1, 0,..., 0], he regressor for iniial esimaion of he consan; d(rend) represens Z 2 = [1, 1,..., 1], he regressor for he iniial esimaion of he rend; and d(shif) represens Z 3 = [f 1 (θ) : f 2 (θ) : : f r (θ)], he regressor for iniial esimaion of he exponenial shif parameer. Based on he findings from uni roo es wih exponenial shif, he parameers of exponenial shif [d/shif] are significan o ake he non-linear shif during , which is consisen wih resuls obained from Zivo-Andrews es (1992) and Lumsdaine-Papell es (1997) (see Table 2 and Table 3). This may sugges ha he impac of he Asian financial crisis is presen. During he crisis, he USD was appreciaing agains mos Asian currencies (including Ringgi Malaysia, Sing dollar, and bah), suggesing ha bilaeral rade adjusmens due o he volailiy of exchange raes exised. However, Saikkonen-Lükepohl es (2002) is unable o rejec he null hypohesis of a uni roo for all hree counries, conradicing wih resuls obained from Saikkonen-Lükepohl es (2002) linear ess. This may sugges ha he non-linear behavior of he hree currencies and US dollar-based real exchange raes is raher weak. Table 5 Resuls of he Half-Life Esimaion of Monhly CPI-based Real Exchange Raes of Malaysia, Singapore, and Thailand Φ Se. τ 95% CI Malaysia CPI-based real exchange rae Jan Dec [0.32, ] Jan Dec [0, ] Jan Dec [0, ] Singapore CPI-based real exchange rae Jan Dec [0, ] Jan Dec [0, ] Jan Dec ,385.9 [0, 39,969.25] Thailand CPI-based real exchange rae Jan Dec [0, ] Jan Dec [0, 45.18] Jan Dec [0, 1,051.66] Noes. The coefficien of mean reversion (φ) is aken accoun such ha ln( 1 ) ln, where φ = ( 1); S 2 e represens he sandard errors of esimaed ; and τ denoes he esimaed monhly half-life wih CI denoes confidence inerval. Peraining o he deeced break daes on he series, he half-life esimaions are performed o deermine he magniude of real exchange rae adjusmen owards long-run PPP. The full sample esimaions of half-life are displayed in Table 5. As shown in Table 5, he half-life esimaions of each counry show ha he degree of he CPI-based real exchange rae adjusmen owards PPP varies agains each oher upon he duraion of he

11 REAL EXCHANGE RATE BEHAVIOR 205 sudy. For Malaysia, he full sample esimaions of half-life are repored o be approximaely 77.5 monhs wih he 95% confidence inerval of 0.32 monh o monhs. For Singapore and Thailand, he half-life esimaions for CPI-based real exchange raes (full sample) are monhs and 56.0 monhs respecively. These repored ha half-life esimaes are far greaer han he esimaes of hree o five years as suggesed in Rogoff (1996). Afer convering, he findings demonsrae ha he number of years required for he iniial shock from he long-run level o dissipae by half is longer han usual. Paricularly, he sub-sample esimaions display ha he exchange rae misalignmen is more eviden afer 1997 (he Asian financial crisis). The half-lives for real exchange raes which are longer han hree years sugges ha he PPP-hypohesis is found o be operaionally less relevan. Evidence of lenghy half-lives for real exchange raes in he presence of high degree volailiy may be biased due o he presence of cumulaive effecs of he shocks. This is paricularly relevan as he period of sudy is feaured by grea adjusmens in Asian exchange raes and he major change in erms of he flexibiliy of heir exchange rae arrangemens. As mixed evidences of long-run PPP are found for Malaysia, Singapore, and Thailand hrough he hree uni roo ess and half-life esimaions, furher coinegraion ess are carried ou. Based on resuls of he ADF and PP ess (Table 1), consumer price indices as well as he nominal exchange raes of Malaysia, Singapore, and Thailand are found o be inegraed of order one, i.e., I(1), as firs differences of hese variables are found o be saionary. Since he condiion o apply a coinegraion es has been fulfilled, he coinegraion analysis is herefore performed. Table 6 Resuls of Full-Sample Equilibrium Regression Tes for Three Counries for a Period of January 1980 o December 2014 Esimaed Sandard error Malaysia Singapore Thailand As shown in Table 6, he esimaed coefficien for Malaysia, Thailand, and Singapore are higher from uniy: near o uniy and lower han uniy, respecively. In order o examine he residual of he equilibrium regression of each counry for he period of January 1980 o December 2014, Dickey-Fuller (DF) es saisics will be esimaed and hen compared wih he criical values for he Engle-Granger coinegraion es (Engle & Yoo, 1987). The null hypohesis of no inegraion is esablished agains is alernaive hypohesis. Table 7 Resuls of Engle-Granger Tes for a Period of January 1980 o December 2014 Dickey-Fuller es saisics Malaysia Singapore Thailand % 5% 10% Criical values for Engle-Granger coinegraion es (2 variables) Noe. The DF -saisics of he residuals of he equilibrium regression for hree counries fail o rejec uni roo null.

12 206 REAL EXCHANGE RATE BEHAVIOR As shown in Table 7, he DF es saisics esimaed for Malaysia, Singapore, and Thailand are greaer han he criical value of a he 1% level of significance, suggesing ha he null hypohesis of no inegraion canno be rejeced a he 1% level of significance. This implies ha y and p are no coinegraed during he period of January 1980 o December This indicaes ha he residuals obained from he DF es may no be saionary and he real exchange rae of hese hree chosen counries may be driven by sochasic rends. To confirm he relaively weak evidences of PPP found for he real exchange raes of Malaysia, Singapore, and Thailand above, anoher common coinegraion es Johansen coinegraion es, is carried ou. Based on he ime of breaks obained for Malaysia, Singapore, and Thailand from Lumsdaine-Papell es (1997) (see Table 3), Johansen coinegraion es is performed. Afer allowing for srucural breaks in he CPI-based real exchange rae series, relaively srong evidence of coinergraion can be found for Malaysia, Singapore, and Thailand (see Table 8). This suggess ha PPP relaionship for hese hree naions has been affeced grealy by he crises. In addiion, when he wo breaks are allowed o joinly ake place in he series, resuls obained for he hree counries sugges srongly ha he null hypohesis of a uni roo should be rejeced a he 5% level of significance, implying ha coinegraion among relaive prices and exchange raes among he hree counries currencies and he US dollar exis in he long-run. In shor, significanly srong evidences of PPP are found for Malaysia, Singapore, and Thailand in relaion o he US. Table 8 Resuls of Johansen Coinegraion Tess (λ race Saisic) Which Allows for Srucural Break(s) for a Period of January 1980 o December 2014 Null hypohesis T B1 T B2 T B1 and T B2 Malaysia Dec Jul Dec & Jul r = * * r Singapore Jun Oc Jun & Oc r = * 58.68* 84.50* r Thailand Jun Dec Jun & Dec r = * 41.85* * r Noes. T B sands for ime of break; * denoes rejecion of he null hypohesis of a uni roo a he 5% significance level; and all he values of -ess for λ race saisics for he hree counries rejec he null hypohesis of no coinegraion beween y and p (r = 0) afer T B1 and T B2 are considered. Conclusions This sudy re-examines he mean-reversion hypohesis for he real exchange raes in he US dollar erms of hree counries, i.e., Malaysia, Singapore, and Thailand over a period of January Using linear and non-linear uni roo ess o deec possible endogenous break(s), real exchange raes for currencies of he hree counries are examined for he long-run purchasing power pariy (PPP) during he sudy period. Resuls obained from ADF and PP uni roo ess show ha no srucural changes aken place and all CPI-based

13 REAL EXCHANGE RATE BEHAVIOR 207 exchange raes series of he hree counries consisenly conain a uni roo. Subsequenly, differen endogenous break uni roo ess, i.e., Zivo-Andrews es (1992) and Lumsdaine-Papell es (1997) were conduced and resuls showed ha he ime series of Malaysia and Thailand are rend-saionary, when breaks are considered. However, Saikkonen and Lükepohl es (2002) failed o show any evidence of mean-reversion behavior for he real exchange raes of all hree counries. Moreover, shor-run volailiy of real exchange raes is found o be very high in naure and speed of adjusmen o PPP is found o be very low. This suggess ha half-life measures may be operaionally less applicable owards he counries sudied. In erms of coinegraion ess, alhough Engle-Granger es failed o find any significan evidence of inegraion of PPP for all he hree counries, Johansen coinegraion es provides resuls wih a higher degree of mean reversion for he real exchange raes of all he hree counries, once break poins are considered. Hence, he resuls sugges ha if srucural breaks exis and are ignored, he convenional Johansen procedure may lead o erroneous resuls. In oher words, real exchange raes in Malaysia, Singapore, and Thailand are found o be affeced grealy by a series of shocks. Therefore, allowing for muliple breaks is vindicaed when esing he validiy of long-run PPP for hese hree counries. The findings shed lighs on he imporance of relaionship beween exchange raes and prices and also heir implicaion o fuure policy making and forecasing decisions. References Aggarwal, R., & Mougoue, M. (1996). Coinegraion among Asian currencies: Evidence of he increasing influence of he Japanese yen. Japan and he World Economy, 8, Aron, J., Elbadawi, I., & Kahn, B. (1997). Deerminans of he real exchange rae in Souh Africa (Working paper WPS/97-16). Oxford: Oxford Universiy, Cenre for he Sudy of African Economies. Cassel, G. (1918). Abnormal deviaions in inernaional exchanges. Economic Journal, 28, Caherine, S. F. H., & Ariff, M. (2009). A es of purchasing power pariy: Asia Pacific and Lain America. Asian Academy of Managemen Journal of Accouning and Finance, 5(2), Chinn, M. D. (2000). Before he fall: Were Eas Asian currencies overvalued? Emerging Marke Review, 1, Edison, H. J. (1985). Purchasing power pariy: A quaniaive reassessmen of he 1920s experience. Journal of Inernaional Money and Finance, 4, Ellio, G., & Pesaveno, E. (2004). Higher power ess for bilaeral failure of PPP afer 1973 (Unpublished manuscrip, Emory Universiy). Engle, R. F., & Yoo, B. S. (1987). Forecasing and esing in co-inegraed sysems. Journal of Economerics, 35, Frenkel, J. (1978). Purchasing power pariy, docrinal perspecive and evidence from he 1920s. Journal of Inernaional Economics, 8, Goldberg, L., & Tille, C. (2008). Macroeconomic inerdependence and he inernaional role of he dollar (Saff repor 316, Federal Reserve Bank of New York). Hakkio, C. S. (1984). A re-examinaion of purchasing power pariy: A muli-counry and muli-period sudy. Journal of Inernaional Economics, 17, Hall, A. (1994). Tesing for a uni roo in ime series wih prees daa-based model selecion. Journal of Business & Economic Saisics, 12, Harvey, J. (2001). Exchange rae heory and he fundamenals. Journal of Pos Keynesian Economics, 24 (1), Johansen, S., Mosconi, R., & Nielsen, B. (2000). Coinegraion analysis in he presence of srucural breaks in he deerminisic rend. The Economerics Journal, 3(2), Krugman, P. R. (1978). Purchasing power pariy and exchange raes: Anoher look a he evidence. Journal of Inernaional Economics, 8(3), Lanne, M., Saikkonen, P., & Lükepohl, H. (2003). Tes procedures for uni roos in ime series wih level shifs a unknown ime. Oxford Bullein of Economics and Saisics, 65, Lohian, J. R., & Taylor, M. P. (1996). Real exchange rae behaviour: The recen floa from he perspecive of he las wo

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