Volume 30, Issue 3. Are Real Exchange Rates Nonlinear with a Unit Root? Evidence on Purchasing Power Parity for China: A Note

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1 Volume 30, Issue 3 Are Real Exchange Raes Nonlinear wih a Uni Roo? Evidence on Purchasing Power Pariy for China: A Noe sangyao Chang Deparmen of Finance, Feng Chia Universiy, aichung, aiwan Su-yuan Lin Graduae Insiue of Managemen Sciences, amkang Universiy, aipei, AIWAN Horng-jinh Chang Graduae Insiue of Managemen Sciences, amkang Universiy, aipei, AIWAN Absrac his aricle applies he hreshold auoregressive model proposed by Caner and Hansen (00) o examine boh lineariy and saionariy of China's real exchange rae vis-à-vis her 9 rading parner counries over he period of January 986 o Ocober 009. wo main conclusions are drawn. Firsly, he empirical resuls indicae ha China's real exchange is a nonlinear process. Secondly, a uni roo in real exchange rae was found for mos of he cases under sudy. his resul provides no suppor for purchasing power pariy for China relaive o heir major rading parner counries. n.a. Ciaion: sangyao Chang and Su-yuan Lin and Horng-jinh Chang, (00) ''Are Real Exchange Raes Nonlinear wih a Uni Roo? Evidence on Purchasing Power Pariy for China: A Noe'', Economics Bullein, Vol. 30 no.3 pp Submied: May Published: July 9, 00.

2 . Inroducion Purchasing power pariy (hereafer, PPP) is a cornersone of many heoreical models in inernaional finance. PPP saes ha he exchange raes beween currencies are in equilibrium when heir purchasing power is he same in each of he wo counries. his means ha he exchange rae beween any wo counries should equal he raio of wo currencies price level of a fixed baske of goods and services. he basic idea behind he PPP hypohesis is ha since any inernaional goods marke arbirage should be raded away over ime, we should expec he real exchange rae o reurn o a consan equilibrium value in he long run. Sudies on his issue are criical no only for empirical researchers bu also for policymakers. In paricular, a non-saionary real exchange rae indicaes ha here is no long-run relaionship beween nominal exchange rae and domesic and foreign prices, hereby invalidaing he PPP. As such, PPP canno be used o deermine he equilibrium exchange rae, and an invalid PPP also disqualifies he moneary approach from exchange rae deerminaion, which requires PPP o hold rue. Empirical evidence on he saionariy of real exchange raes is abundan bu inconclusive hus far. For deails on previous sudies, please refer o he works of aylor (995), Rogoff (996), MacDonald and aylor (99), aylor and Sarno (998), Sarno and aylor (00), aylor and aylor (004), and Lohian and aylor (000, 008), who have provided in-deph informaion on he heoreical and empirical aspecs of PPP and he real exchange rae. Recenly, here has been a growing consensus ha he real exchange rae exhibis nonlineariies, and consequenly, convenional uni roo ess such as he Augmened Dickey Fuller (ADF) es have low power in deecing he mean reversion of exchange rae. A number of sudies have provided empirical evidence on he nonlinear adjusmen of exchange rae. However, he finding of nonlinear adjusmen does no necessarily imply nonlinear mean reversion (saionariy). As such, saionariy ess based on a nonlinear framework mus be applied. his empirical sudy conribues o his line of research by deermining wheher PPP holds for China s real exchange rae relaive o a sample of her major rading parner counries (Hong Kong, Indonesia, Japan, Korea, Malaysia, Philippines, Singapore, aiwan, and hailand), using he hreshold auoregressive (hereafer, AR) model and he es saisics proposed by Caner and Hansen (00). he major advanage of his approach is ha i allows us o simulaneously invesigae nonsaionariy and nonlineariy. Wih his, Reasons for he nonlinear adjusmen are he presence of ransacions coss ha inhibi inernaional goods arbirage and official inervenion in he foreign exchange marke may be such ha nominal exchange rae movemens are asymmeric (see aylor, 004; aylor and Peel, 000; Juvenal and aylor, 008; Reiz and aylor, 008). Kilian and aylor (003) also sugges ha nonlineariy may arise from he heerogeneiy of opinion in he foreign exchange marke concerning he equilibrium level of he nominal exchange rae: as he nominal rae akes on more exreme values, a grea degree of consensus develops concerning he appropriae direcion of exchange rae moves, and raders ac as accordingly

3 he curren research hopes o fill he exising gap in he lieraure. We find ha China s bilaeral real exchange rae is a nonlinear process characerized by a uni roo, no consisen wih PPP, relaive o mos of he rading parner counries (seven ou of nine), wih he excepion of aiwan/china and Souh Korea/China wo cases. China provides an ineresing arena o research for several reasons. Firs, China has made remarkable economic progress over he pas wo decades. China s average annual economic growh rae over he pas wo decades ( ) is 9.76%. In 009, per capia GDP in China was US$ 3,566. Second, China has become he world s firs and larges rading counry wih he foreign exchange reserves esimaed a US$,400 billion a he end of 009. hird, China sared is open policy in he lae 970s, hus sufficien daa are available for researchers o evaluae he effec of economic liberalizaion on economic phenomena. his paper is organized as follows. Secion presens he daa used in our sudy. Secion 3 briefly describes he AR uni es and our empirical resuls. Secion 4 concludes he paper.. Daa Our empirical analysis covers a sample of nine Eas Asian counries: Hong Kong, Indonesia, Japan, Korea, Malaysia, Philippines, Singapore, aiwan, and hailand. Monhly daa are employed in his sudy, and he ime span is from January 986 o Ocober 009. All consumer price indices, CPI (based on 000 = 00), and nominal exchange raes relaive o he China RMB yen daa are aken from he Inernaional Moneary Fund s Inernaional Financial Saisics CD-ROM. esing for PPP agains he China is based on he argumen ha China has become one of he fas growing counries in he whole world and China is also he major rading parners for hese nine Eas Asian counries for he pas decade. 3. Mehodology and Empirical Resuls 3.. Caner and Hansen s (00) hreshold Uni Roo es Following he work of Caner and Hansen (00), we adop a wo regime AR(k) model wih an auoregressive uni roo as follow: r I e, =,, () x I x Z Z Where r is he real exchange rae for,...,, x (,,,, ) r v r r k, I is he indicaor funcion, e is an i.i.d. disurbance, Z r r m is he hreshold variable, m China H he real exchange rae series of a counry a ime is define as( S P ) / P, where S is he nominal exchange rae of home counry per China RMB, counry and he China, respecively. China P and H P denoe he consumer price indices of home

4 represens he delay parameer and m k, v is a vecor of exogenous variables including an inercep and possibly a linear ime rend. he hreshold value is unknown and akes he values in he compac inerval [, ], where and are seleced according o P ( Z ) 0.5 and P ( Z ) he componens of and can be pariioned as follows:, () where and are scalar erms. and have he same dimensions as v, and and are k-vecors. hus (, ) are he slope coefficiens on r, (, ) are he slopes on he deerminisic componens, and, ) are he slope coefficiens on ( r k r,, ) in he wo regimes. ( he hreshold effec in Equaion () has he null hypohesis of H : 0, which is esed using he familiar Wald saisic: W W (? ) sup W ( ). 4 he saionariy of he process r can be esablished in wo ways. he firs is when here is a uni roo in boh regimes (a complee uni roo).. Here he null hypohesis is of he form H 0, 0 : which is esed agains he unresriced alernaive 0 or 0 using he Wald saisic. he parameers of and from he Equaion () will conrol he regime-dependen uni roo process of he real exchange rae. If 0 holds, he real exchange rae has a uni roo can be described as a rejecion of PPP. R his saisic is: ( 3 )? from he ordinary leas squares esimaion. where and are he raios for? and However, Caner and Hansen (00) claim ha his wo-sided Wald saisic may have less power han a one-sided version of he es. Wald saisic as follows:? 0? 0 As a resul, hey propose he following one-sided R I I (4) o disinguish beween he saionary case given as H and he parial uni roo case given as H, Caner and Hansen (00) sugges using individual saisics and. If only one of and is saisically significan, his will be consisen wih he parial uni roo case H. his means real exchange rae behaves like a nonsaionary process in one regime; bu 3 According o Andrews (993), his division provides he opimal rade-off beween various relevan facors, which include he power of he es and he abiliy of he es o deec he presence of a hreshold effec. 4?? ) 0 W W ( sup W ( ), where? ( ) squares esimaion of he null linear and AR models, respecively. 3? 0 and? are residual variances from leas

5 exhibis a saionary process in he oher regime, vice versa. Caner and Hansen (00) show ha boh ess R and R will have power agains boh alernaives. 5 o obain maximum power form hese ess, criical values are generaed using boosrap simulaions wih 0,000 replicaions, as suggesed by Caner and Hansen (00). 3.. Empirical Resuls For he sake of comparison, we also incorporae he Augmened Dickey-Fuller (ADF), PP (Phillips and Perron, 988), and KPSS (Kwiakowski e al., 99) ess ino our sudy. he resuls of hese hree convenional uni roo ess -- ADF, PP, and he KPSS ess, as shown in able I, indicae ha he real exchange raes are non-saionary for China. saed earlier, here is a growing consensus ha he real exchange rae exhibis nonlineariies, and consequenly, convenional uni roo ess such as he ADF es, have low power in deecing he mean reversion of exchange rae. A number of sudies have also provided empirical evidence on he nonlinear adjusmen of exchange rae. herefore, we proceed o es he real exchange rae by using Caner and Hansen s (00) nonlinear AR uni roo ess. Firs, we use he Wald es W o examine wheher or no we can rejec he linear auoregressive model in favor of a hreshold model. he resuls of he Wald es along wih he boosrap criical values generaed a convenional levels of significance are repored in able II. he boosrap p-value for hreshold variables of he form Z r r m for delay parameers m varies from o. Since he parameers m is generally unknown, here is no reason o hink he opimal delay parameer will be he same across counries. o circumven his, Caner and Hansen (00) sugges making m endogenous by selecing he leas squares esimae of m ha minimizes he residual variance. his amouns o selecing m a he value ha maximizes he W saisic. We find ha he W saisic is maximized for China-Hong Kong, China-Indonesia, China-Philippines, and China-Singapore when m, for China-Malaysia when m 4, for China-aiwan and China-hailand when m 5, for China-Japan when m 7, and for China-Souh Korea when m 0. aken ogeher, hese resuls imply srong saisical evidence agains he null hypohesis of lineariy a leas a he 0% significance level for all he cases indicaing ha simple linear models are inappropriae and he AR model is our preference. Nex, we explore he hreshold uni roo properies of real exchange rae based on he R saisic for each delay parameer m, ranging from o, paying paricular aenion o he resuls obained for our preferred model. he R es resuls, ogeher wih he boosrap criical value a he convenional levels of significance and he boosrap p-value, are repored in able III. We are able o rejec he uni roo null hypohesis for only wo cases a he 5% significance level and hey are aiwan-china and Souh Korea-China. However, we are unable o rejec he hreshold uni roo hypohesis for mos of he cases. As 5 As saed by Caner and Hansen (00) ha R has more power han ha of R, here we only repor he resuls of R in our sudy. 4

6 aken ogeher our resuls provide no suppor for PPP for mos of he China s rading parner counries and poin ha he real exchange raes of hese counries are non-linear nonsaionary, implying ha deviaions of exchange rae is no mean revering owards he PPP equilibrium. As we menioned earlier ha rade barriers, ransacion coss, as well as inervenions in he exchange marke, could be behind his nonlinear behavior. he one-sided es saisic of, however, is no able o disinguish he complee and R parial uni roo in real exchange rae, we examine furher evidence on he uni roo hypohesis (parial uni roo) by examining he individual saisics, and. he resuls are repored in able IV. Also, wih he excepion of he aiwan-china and Souh Korea-China, he saisics for boh and are smaller han he criical value a he 5% level of significance, and his leads us o he conclusion ha real exchange raes in mos of he China s rading parner counries are nonlinear process ha are characerized by a uni roo process, no consisen wih he PPP. hese resuls migh source from several facors such as differences in echnology/produciviy and preferences, differen facor endowmens, rade barriers, ransporaion coss and differences in price index formaions. I should also be noed ha he share of governmen aciviies in China are sill large which makes he prices o be adminisraed. he adminisraed prices migh be an imporan source of deviaion from he PPP in China. herefore, i is possible o claim ha deviaions in he shor-run form he PPP are prolonged for China and here are no forces which are capable of bringing he exchange rae back o is PPP values in he long-run. he major policy implicaion ha emerges from our sudy is ha he governmen in China can no use PPP o deermine he equilibrium exchange rae and he unbounded gains from arbirage in raded good are possible in China. 4. Conclusions his sudy applies he AR model proposed by Caner and Hansen (00) o examine boh lineariy and saionariy of China s real exchange rae vis-a-vis her 9 rading parner counries over he period of January 986 o Ocober 009. wo main conclusions are drawn. Firsly, he empirical resuls indicae ha China s real exchange is a nonlinear process. Secondly, a uni roo in real exchange rae was found for mos of China s rading parner counries under sudy. his provides no suppor for purchasing power pariy for China relaive o heir major rading parner counries. Acknowledgemen: We are graeful o Bruce Hansen for making available his MALAB codes for he AR model, which were modified for he presen exercise. However, any remaining errors are my own. he auhors are also indebed o an anonymous reviewer, whose commens had improved he readabiliy of his aricle subsanially. Any remaining errors are our own. 5

7 References Caner, M. and Hansen, B. (00) hreshold auoregression wih a uni roo, Economerica, 69, Juvenal, L. and M. P. aylor (008), hreshold Adjusmen of Deviaions from he Law of One Price, Sudies in Nonlinear Dynamics and Economerics, (3), -44. Kilian, L. and M. P. aylor (003), Why is i so Difficul o Bea he Random Walk Forecas of Exchange Raes? Journal of Inernaional Economics, 60(), Kwiakowski, D., P. Phillips, P. Schmid, and Y. Shin (99), esing he Null Hypohesis of Saionariy Agains he Alernaive of a Uni Roo: How Sure Are We ha Economic ime Series Have a Uni Roo? Journal of Economerics, 54, Lohian, J. R. and M. P. aylor (000), Purchasing Power Pariy Over wo Cenuries: Srenghening he Case for Real Exchange Rae Sabiliy Reply o Cuddingon and Liang, Journal of Inernaional Money and Finance, 9(5), Lohian, J. R. and M. P. aylor (008), Real Exchange Ra es over he Pas wo Cenuries: How Imporan is he Harrod-Balassa-Samuelson Effec? Economic Journal, 8 (53), MacDonald, R. and M. P. aylor (99), Exchange Rae Economics: A Survey, Saff Papers- Inernaional Moneary Fund, 39(), -57. Piarakis, J.Y. (008) Commen on: hreshold Auoregressions Wih a Uni Roo, Economerica, 76(5), 07-7 Phillips, P. C. B. and P. Perron (988), esing for a Uni Roo in ime Series Regression, Biomerika, 75, Reiz, S. and aylor, M. P. (008) he coordinaion channel of foreign exchange inervenion: A nonlinear microsrucure analysis, European Economic Review, 5(), Rogoff, K. (996), he Purchasing Power Pariy Puzzle, Journal of Economic Lieraure, 34, Sarno, L. and M. P. aylor (00), Purchasing Power Pariy and he Real Exchange Rae, IMF Saff Papers, 49, aylor, M. P. (004), Is Official Exchange Rae Inervenion Effecive? Economica, 7(8), -. aylor, A. M and M. P. aylor (004), he Purchasing Power Pariy Debae, Journal of Economic Perspecives, 8(4), aylor, M. P. (995), he Economics of Exchange -Raes, Journal of Economic Lieraure, 33(), aylor, M. P. and L. Sarno (998), he Behavior of Real Exchange Ra es during he Pos-Breon Woods Period, Journal of Inernaional Economics, 46(),

8 able I. Univariae uni roo ess Level s difference ADF PP KPSS ADF PP KPSS Hong Kong -.3() -.990() 0.95[4]** -3.59()** -.07()*** 0.097[] Indonesia -.863(0) -.787(6).057[4]*** -4.78(0)** -7.86()*** 0.074[] Japan -.70(0) -.6(8) 0.835[4]*** -3.84(0)*** -5.8(4)*** 0.4[] Malaysia -.640(0) -.633().46[4]*** -.96(0)*** ()*** 0.37[] Philippine -.49() -.53(6) 0.569[4]** (0)*** -6.5(5)*** 0.4[6] Singapore -.3(0) -.58(5) 0.463[4]* -4.68(0)*** -5.59(8)*** 0.94[6] Souh Korea -.70() -.4(3) 0.495[4]* -3.45()*** -3.4(3)*** 0.095[] aiwan -.4() -.7(5) 0.559[4]** -.3()*** -.3()*** 0.084[] hailand -.543(0) -.6(5) 0.994[4]*** -.8(0)*** -3.3(3)*** 0.0[4] Noe: ***, ** and * indicae significance a he 0.0, 0.05 and 0. level, respecively. he number in parenhesis indicaes he lag order seleced based on he recursive -saisic, as suggesed by Perron (989). he number in he brackes indicaes he runcaion for he Barle Kernel, as suggesed by he Newey-Wes es (987). able II. hreshold es Counries Wald Saisic Boosrap p-value Opimal delay parameer m hreshold parameer? Number of observaions in Regime and is percenage Hong Kong (80.58%) Indonesia (84.6%) Japan (83.5%) Malaysia (84.6%) Philippine (4.65%) Singapore (84,6%) Souh Korea (84.6%) aiwan (36,63%) hailand (84.6%) Following much of he exising empirical lieraure on monhly real exchange raes and PPP, we se a maximum lag of and base all our boosrap ess on 0,000 replicaions. Mos of he saisics are significan, which suppors he presence of hreshold effecs 7

9 able III. One sided uni roo ess Counries Opimal delay parameer m R Saisic Boosrap criical values 0% 5% % Boosrap p-value Hong Kong Indonesia Japan Malaysia Philippine Singapore Souh Korea aiwan , hailand able IV. Parial uni roo resuls Counries Opimal delay parameer m Saisic Boosrap p-value Saisic Boosrap p-value Hong Kong Indonesia Japan Malaysia Philippine Singapore Souh Korea aiwan hailand