Nonlinear Mean Reversion in Real Exchange Rates: Evidence from Developing and Emerging Market Economies. Abstract

Transcription

1 Nonlinear Mean Reversion in Real Exchange Raes: Evidence from Developing and Emerging Marke Economies Mario Cerrao London Meropolian Universiy Nick Saranis London Meropolian Universiy Absrac We provide evidence on nonlinear mean reversion in he real exchange raes of developing and emerging marke economies, using recenly developed nonlinear uni roo ess and a unique se of monhly daa on black marke exchange raes. Ciaion: Cerrao, Mario and Nick Saranis, (006) "Nonlinear Mean Reversion in Real Exchange Raes: Evidence from Developing and Emerging Marke Economies." Economics Bullein, Vol. 6, No. 7 pp. -4 Submied: March 9, 006. Acceped: June, 006. URL: hp://economicsbullein.vanderbil.edu/006/volume6/eb-06f30004a.pdf

2 . Inroducion The long-run PPP relaionship remains he major building block of almos all heoreical open-economy macroeconomic models. However, he exensive empirical evidence agains real exchange rae saionariy and hence he long-run PPP boh for developed and developing economies (e.g. Sarno and Taylor, 00; Cerrao and Saranis, 003), has proved an awkward puzzle for economiss. Over he recen years, a number of researchers have argued ha he failure o find mean reversion in real exchange raes may be due o he presence of nonlineariies in he daa generaing process for he real exchange rae which are ignored by he sandard saisical ess. These nonlineariies can arise from ransacion coss (e.g. Dumas, 99; Sercu e al, 995; Goswami e al, 00), diversiy in agens' beliefs (e.g. Brock and Holmes, 998; De Grauwe and Grimadi, 004), or heerogeneiy in invesors' objecives and invesmen horizons (e.g. Guilaume e al 995). A few papers have uncovered significan nonlinear real exchange rae behaviour (e.g. Michael, e al, 997; Saranis, 999; Baum e al, 00; Taylor e al, 00; Liew e al, 003). However, hese papers assume ha he series (or heir differences) are saionary when esing he lineariy hypohesis, so hey do no invesigae formally he ineracion beween nonsaionariy and nonlineariy. In wo recen papers, Sollis e al (00) and Kapeanios e al (003) address his issue by developing formal uni roo ess agains he alernaive of nonlinear mean reversion. Sollis e al (00) apply heir es o real exchange raes agains he US dollar for 7 OECD counries and find nonlinear mean reversion in 6 counries. The Kapeanios e al es has been applied o he real exchange raes of few indusrial counries (Kapeanios e al, 003) and Asian counries (Chorareas and Kapeanios, 004; Liew, e al, 004) wih supporive resuls.

3 Our paper makes wo imporan conribuions o his nonlinear exchange rae lieraure. Firs, we apply for he firs ime boh hese newly developed nonlinear uni roo ess o a large number of developing and emerging marke economies. Second, we use a unique se of monhly daa on black marke real exchange raes ha has no been used previously in he lieraure on nonlinear exchange rae adjusmen. In developing and emerging marke economies, fixed exchange rae sysems combined wih foreign rade resricions, capial conrols, high inflaion and exernal deficis have led o he developmen of hriving black markes for foreign exchange (see, Agenor, 99; Kiguel and O Connell, 999). So hese black markes play an imporan role in he economies of hose counries and one could argue ha he black marke exchange rae reflecs he rue value of domesic currency much beer han he official exchange rae in hese counries. Reinhar and Rogoff (004) have recenly used he daa on black marke exchange raes for consrucing a new hisorical classificaion of exchange rae regimes in he global economy. The paper is organised as follows. The nonlinear uni roo ess employed are oulined in Secion. Secions 3 and 4 discuss he daa and empirical resuls, while Secion 5 summarises he major findings.. Nonlinear Uni Roo Tess Sollis e al (00) and Kapeanios e al (003) have developed new ess for mean reversion in ime series based on smooh ransiion auoregressive (STAR) models. In boh papers, he uni roo null hypohesis is esed agains he nonlinear STAR alernaive. The major difference beween he wo ess is ha Sollis e al (00) use a Daa for black marke exchange raes have been used by a few sudies for invesigaing he PPP hypohesis (see Cerrao and Saranis, 003, and references cied here), bu none of hese applied nonlinear ess or covered so many counries and ime span.

4 logisic ransiion funcion, while Kapeanios e al (003) use an exponenial ransiion funcion.. Sollis e al (00) The auhors develop ess for boh symmeric and asymmeric STAR models. The symmeric LSTAR model is given by y k d ) y + β i y i + i= = α S ( γ, y ε () S ( γ, y ) = { + exp( γ y d )} 0.5 () d where y is he de-meaned ime series, d is he delay parameer ha is assumed o be equal o one, equaion () is he logisic ransiion funcion, and he parameer γ deermines he speed of mean reversion as ime series is from is mean). y d increases (ha is, he furher he To allow for asymmery in he mean reversion process, equaions () and () are replaced by (3) and (4) respecively: y k, γ, y d ) y + β i y i + i= = α S ( γ ε (3) d S ( γ, γ, y ) = [ + exp{ γ y d I γ y d ( I )}] 0.5 (4) where I is he Heaviside indicaor defined as 3

5 I = if y f o, and I = 0 if y o (5) The asymmeric LSTAR model allows for differen mean reversion behaviour depending on wheher he real exchange rae is above or below is mean. The uni roo es saisics for he null hypohesis Η 0 : α = o, agains he symmeric and asymmeric mean reversion alernaives () and (3) are denoed by S and A respecively. These es saisics do no have an asympoic normal disribuion, so he auhors use simulaions o derive criical values for S and A for differen sample sizes 3.. Kapeanios e al (003) The auhors consider he following exponenial STAR (ESTAR) model: y k + λy exp( θy d )] + ρi y i + i= = φ y [ ε (6) Theoreical models based solely on proporional ranspor cos (Dumas, 99) predic a symmeric adjusmen process for exchange raes-hence he use of ESTAR models in many papers. However, in models wih a ranspor cos srucure ha allows for boh a proporional cos and economies of scale, and wih diverse producion echnologies and consumer preferences (Goswami e al, 00), asymmeric behaviour may well arise. Differences beween expansions and conracions in he real exchange rae can also be explained by he asymmeries discussed in he business cycle lieraure; hese ha could arise, for example, from asymmeric labour adjusmen coss or asymmeries in he capial desrucion and reconsrucion. The lieraure on he heerogeneiy of invesors expecaions also implies poenial asymmeric behaviour is asse prices (Brock and Holmes, 998, De Grauwe and Grimadi, 004). Such behaviour is bes characerized by he LSTAR model. 3 Sollis e al (00) imposed d = in he calculaion of criical values and heir empirical invesigaion, and his is also adoped in our sudy. 4

6 Where y is he de-meaned ime series, d is he delay parameer, and θ deermines he sped of mean reversion. The null hypohesis of a uni roo implies φ = 0 and θ = 0. Since he parameer λ is no idenified under he null, direc esing of he null hypohesis is no feasible. The auhors overcome his problem by using a firs-order approximaion of he ESTAR model o obain he auxiliary equaion 4 y or 3 = δ y error (7) + y k 3 + ρi y i + i= = δ y error (8) in he case of serially correlaed residuals. The null hypohesis of a uni roo becomes Η : δ 0 agains he alernaive Η : δ f 0 = 0. The es saisic for his null hypohesis, denoed NLADF, is he -saisic for he OLS esimae ) δ. Since he nonlinear es saisic NLADF does no have a sandard normal disribuion, he auhors obain criical values hrough sochasic simulaions. 3. Daa We employ monhly daa on black marke exchange raes for a highly heerogeneous panel of hiry-five developing and emerging marke counries over he period These vary from poor developing counries (e.g. Nepal, Ghana) o semi- 4 Noe ha he auhors impose φ = 0 and d = in his derivaion and, hence, in he calculaion of criical values. 5

7 indusrial counries (e.g. Korea, Mexico), wih differen growh experiences and quie diverge levels of per capia income The US Dollar is used as numeraire currency. The black marke exchange raes are obained from Pick s World Currency Yearbook (various publicaions). The consumer price index (CPI) is used as he price index in he consrucion of he real exchange raes. The sample ends in 998 because of he unavailabiliy of daa on black marke exchange raes beyond ha year. The daa used in he esimaion are he de-meaned real exchange raes (measured in logs), as required by boh nonlinear uni roo ess. 4. Empirical Resuls To provide a benchmark for our nonlinear resuls, we firs esimaed he sandard (linear) augmened Dickey-Fuller (ADF) uni roo saisics. These esimaes are repored in Table. The number of lags used in he auoregressive models was chosen by employing he selecion crierion suggesed by Ng and Perron (995). The ADF es is unable o rejec he null hypohesis of a uni roo in hiry ou of hiry five counries, hus providing srong evidence agains mean reversion in black marke real exchange raes. These resuls are in line wih previous evidence for developing and emerging markes obained from linear (boh ime series and panel) uni roo ess (e.g. Cerrao and Saranis, 003). The esimaes of he nonlinear uni roo es saisics are shown in Table 5. The picure changes dramaically when we look a he resuls from he nonlinear uni roo ess. The Sollis e al (00) asymmeric saisic ( A ) rejecs he null hypohesis of nonsaionariy in black marke real exchange raes for nineeen counries ou of hiry five ( counries 5 The Sollis e al (00) nonlinear uni roo saisics were esimaed wih a GAUSS algorihm, while he Kapeanios e al (003) saisics were esimaed using he economeric compuer program E-Views 4.. 6

8 a he % significance level, 3 a he 5% significance level and 4 a he 0% significance level) 6. The symmeric saisic ( S ) shows ha foureen real exchange raes are saionary a he % or 5% level of significance, and a he 0% significance level. Overall, he A ess are more significan han he S ess, hus suggesing he presence of significan asymmery in he mean reversion process for mos real exchange raes 7. Our evidence on nonlinear mean reversion in real exchange raes from developing and emerging marke economies is sronger han ha obained from indusrial counries by Sollis e al (00) The Kapeanios e al (003) 8 es rejecs he uni roo null in eigh counries a he % significance level, and in six counries a he 5% significance level. The oal number of rejecions is similar o ha obained wih he Sollis e al S saisic. This is no surprising since boh ess assume a symmeric mean reversion process. Our findings for he Asian counries are broadly similar o hose repored by Liew e al (004), which were obained from official exchange raes, excep for India, Malaysia, Pakisan and Philippines. The larger number of rejecions of he uni roo null by he Sollis e al (00) asymmeric es ( A ) seems o provide some suppor in favour of he logisic (and asymmeric) raher han he exponenial STAR mean reversion process in real exchange raes. 6 The evidence for asymmeric mean reversion in real exchange raes is evenly spread across Africa, Asia and Lain America (including Cenral American counries); i.e. he uni roo null hypohesis is rejeced in approximaely half of he counries included from each coninen. 7 Sollis e al (00) found a similar resul. I is ineresing o noe ha evidence of asymmeric adjusmen in real exchange raes was also found by Saranis (999) and Leon and Najarian (003) using alernaive nonlinear models bu hese auhors did no apply formal nonlinear uni roo ess. 8 Noe ha Kapeanios e al (00) and Liew e al (004) fixed he number of lags o 8. We believe ha he opimum number of lags should be chosen on he basis of saisical crieria raher han fixed arbirarily. 7

9 5. Conclusion In his paper we provide for he firs ime evidence on nonlinear mean reversion in real exchange raes from hiry five developing and emerging marke economies, using wo newly developed nonlinear uni roo ess and a unique se of monhly daa on black marke exchange raes. In conras o he resuls obained from he sandard linear ADF es, we find ha he black marke real exchange rae displays significan nonlinear mean reversion behaviour, characerised by he smooh ransiion auoregressive (STAR) model, in more han half of he hiry-five developing and emerging marke economies. This evidence is much sronger han ha repored for indusrial counries. There is also evidence of significan asymmeries in he mean reversion process for mos real exchange raes. Our empirical findings seem o provide more suppor for he logisic raher han he exponenial STAR mean reversion process. These empirical findings sugges ha he exchange rae converges o is long-run PPP level in he majoriy of developing and emerging marke economies, bu he convergence pah follows a nonlinear STAR process. Our resuls also imply ha he linear mehods employed in he lieraure for esimaing half-life deviaions from PPP migh be inappropriae when he mean reversion process is nonlinear. 8

10 References Agenor, P. R., 99, Parallel Currency Markes in Developing Counries: Theory, Evidence and Policy Implicaions. Essays in Inernaional Finance No 88, Princeon Universiy, Princeon, N. J. Baum, C. F., Barkoulas, J. T. and Caglayan, M., 00, Nonlinear Adjusmen o Purchasing Power Pariy in he Pos-Breon Woods Era, Journal of Inernaional Money and Finance, 0, Brock, W. A. and Hommes, C. H, 998, "Heerogeneous Beliefs and Roues o Chaos in a Simple Asse Pricing Model", Journal of Economic Dynamics and Conrol,, Cerrao, M. and Saranis, N., 003, Black Marke Exchange Raes and he Long-Run PPP Hypohesis in Emerging Markes, Discussion Paper No 03-4, Cenre for Inernaional Capial Markes, London Meropolian Universiy Chorareas, G. and Kapeanios, G., 004, The Yen Real Exchange Rae May Be Saionary Afer All: Evidence from Nonlinear Uni Roo Tess, Oxford Bullein of Economics and Saisics, 66, 3-3. De Grauwe, P. and Grimadi, M., 004, Heerogeneiy of Beliefs and Exchange Rae Dynamics, in: S. Lardic and V. Mignon (eds.), Recen Developmens on Exchange Raes, Palgrave Macmillan. Dumas, B., 99, "Dynamic Equilibrium and he Real Exchange Rae in a Spaially Separaed World", Review of Financial Sudies, 5, Goswami, G., Shrikhande, M. and Wu, L., 00, A Dynamic Equilibrium Model of Real Exchange Raes wih Transacion Coss, mimeo, Graduae School of Business, Fordham Universiy. Guillaume, D. M., Dacorogna, M. M., Dave, R. D., Muller, U. A., Olsen, R. B. and Pice, O. V., 995, "From he Bird's Eye o he Microscope: A Survey of New Sylized facs of he Inra-Daily Foreign Exchange Markes", Inernal Documen DMG , Olsen & Associaes, Zurich. Kapeanios, G., Shin, Y. and Snell, A., 003, Tesing for a Uni Roo in he Nonlinear STAR Framework, Journal of Economerics,, Kiguel, M., and O Connell, S., 995, Parallel Foreign Exchange markes in Developing Counries: Experience and Policy Lessons, The World Bank Research Observer, 0, -5. Leon, H. and Najarian, S., 003, Asymmeric Adjusmen and Nonlinear Dynamics in Real Exchange Raes, IMF Working Paper, WP/03/59. Liew, V. K-S., Baharumshah, A. Z. and Chong, T. T-L., 004, Are Asian Real Exchange Raes Saionary?, Economic Leers, 83,

11 Liew, V. K-S., Chong, T. T-L. and Lim, K. P., 003, The Inadequacy of Linear Auoregressive Models for Real Exchange Raes: Empirical Evidence from Asian Economies, Applied Economics, 35, Michael, P., Nobay, A. R. and Peel, D. A., 997, "Transacions Coss and Nonlinear Adjusmen in Real Exchange Raes: An Empirical Invesigaion", Journal of Poliical Economy, 05, Ng., and Perron, P., 995, Uni Roo Tess in ARMA Models wih Daa Dependen Mehods for Selecion of he Truncaion Lag, Journal of American Saisical Associaion, 90, 68-8 Reinhar, C. M. and Rogoff, K. S., 004, The Modern Hisory of Exchange Rae Arrangemens: A Reinerpreaion, Quarerly Journal of Economics, CXIX, -48. Saranis, N., 999, "Modelling Nonlineariies in Effecive Exchange Raes", Journal of Inernaional Money and Finance, 8, Sarno, L. and Taylor, M. P., 00, Purchasing Power Pariy and he Real Exchange Rae, IMF Saff Papers, 49, Sercu, P., Uppal, R. and Van Hulle, C., 995, The Exchange Rae in he Presence of Transacion Coss: Implicaions for Tess of Purchasing Power Pariy, Journal of Finance, 50, Sollis, R., Leybourne, S. and Newbold, P., 00, Tess for Symmeric and Asymmeric Nonlinear mean reversion in Real Exchange Raes, Journal of Money, Credi and Banking, 34, Taylor, M.P., Peel, D. A. and Sarno, L., 00, Nonlinear Mean-Reversion in Real Exchange Raes: Towards a Soluion o he Purchasing Power Pariy Puzzles, Inernaional Economic Review, 4,

12 Table The Augmened Dickey-Fuller uni roo es Counry k ADF Algeria -.54 Argenina Bolivia -.870* Brazil Chile -.9 Colombia -.64 Cosa Rica Dom. Republic Ecuador Egyp *** El Salvador Ehiopia Ghana *** Hungary -.47 India -.0 Indonesia Kenya ** Korea -.65 Kuwai Malaysia Mexico Morocco Nepal Nigeria Pakisan Paraguay -.73 Philippines * Singapore Souh Africa -.30 Sri Lanka Thailand Tunisia Turkey Uruguay -.57 Venezuela Criical values: % 5% 0% Noe: k is he order of he auoregressive process. ADF is he augmened Dickey- Fuller linear uni roo es. (***), (**) and (*) denoe significance a he %, 5% and 0% significance levels, respecively.

13 Table Nonlinear uni roo es resuls Sollis e al (00) Kapeanios e al (003) Counry k A S NLADF Algeria Argenina *** -7.46*** ** Bolivia *** -7.60*** -6.09*** Brazil *** -3.99** -3.30** Chile Colombia Cosa Rica -4.58*** -3.96*** *** Dom. Republic ** Ecuador Egyp *** *** *** El Salvador *** -4.39*** -3.37** Ehiopia ** Ghana *** *** *** Hungary -.958* India Indonesia *** -4.45*** -4.93*** Kenya Korea *** *** Kuwai * -3.9** *** Malaysia Mexico * Morocco * Nepal Nigeria Pakisan Paraguay Philippines *** *** *** Singapore *** -4.67*** -3.35** Souh Africa -5.98*** *** *** Sri Lanka Thailand ** -.948* Tunisia Turkey ** -3.64** -.95** Uruguay Venezuela Criical values: % 5% 0%

14 Table coninued Noe: k is he order of he auoregressive process. A and S are, respecively, he Sollis e al (00) asymmeric and symmeric nonlinearly uni roo ess (for T=300). NLADF is he Kapeanios e al (003) nonlinear uni roo es (for Case ; i.e. nonzero mean). (***), (**) and (*) denoe significance a he %, 5% and 0% significance levels, respecively. 3