Volume 31, Issue 2. Purchasing Power Parity and the Chinese Yuan

Transcription

1 Volume 31, Issue Purchasing Power Pariy and he Chinese Yuan Richard Paul Gregory Eas Tennessee Sae Universiy Gary Shelley Eas Tennessee Sae Universiy Absrac Resuls from uni roo ess applied o he bilaeral China - US real exchange rae do no suppor purchasing power pariy beween he wo counries. However, ess of he real equivalen exchange rae for he Chinese yuan versus a raded-weighed baske of currencies suppor purchasing power pariy. Due o severe non-normaliy, criical values for ess of he real equivalen exchange rae are obained from he wild boosrap. Ciaion: Richard Paul Gregory and Gary Shelley, (011) ''Purchasing Power Pariy and he Chinese Yuan'', Economics Bullein, Vol. 31 no. pp Submied: Jan Published: April, 011.

2 Economics Bullein, 011, Vol. 31 no. pp Purchasing Power Pariy and he Chinese Yuan 1. Inroducion The heory of purchasing power pariy (PPP) saes ha inernaional arbirage should eliminae any difference in he common currency price of idenical goods in wo counries. In macroeconomic erms, his implies equaliy beween common currency price levels, hus a real exchange rae ha is equal o uniy. However, a variey of rade fricions (such as ransporaion coss, non-raded goods, and ariffs) may resul in a persisen difference beween common currency price levels. In he empirical lieraure, a saionary real exchange rae is inerpreed as evidence consisen wih purchasing power pariy (PPP). This inerpreaion allows he mean of he real exchange rae o differ from uniy due o he presence of rade fricions; however, deviaions from he mean are quickly arbiraged away. In conras, if he real exchange rae conains a uni roo, hen he common currency price levels wander apar for exended periods of ime. Deviaions from PPP are no quickly arbiraged away. A vas lieraure has developed applying various uni roo ess o real exchange raes o es he PPP hypohesis. Sarno and Taylor (00) and Sarno (00) provide overviews of he empirical lieraure in esing purchasing power pariy. The general consensus is ha for he currencies of major indusrialized naions, PPP is a valid long-run inernaional pariy condiion and ha mean reversion displays significan non-lineariies, wih small deviaions having a longer half-life han larger deviaions. Economeric sudies end o find ha deviaions from PPP are highly volaile and ha he volailiy of relaive prices is considerably lower han he volailiy of nominal exchange raes, bu recen sudies using a non-linear framework o model such deparures provide evidence ha PPP may hold. The convenional procedures for esing he PPP use a null hypohesis ha he process generaing he real exchange rae has a uni roo, wih an alernaive hypohesis ha all of he roos lie on he uni circle. However, as has been noed by Benninga and Proopapadakis (1988), Dumas (199) and Sercu, Uppall and Van Hulle (199), he presence of ransacion coss may imply a non-linear process ha may have differen raes of adjusmen for differen sized deviaions. Michael, Nobay and Peel (1997) and Taylor, Peel and Sarno (001), using models ha allow for a non-linear adjusmen process in he error erms, find ha he exchange raes of major currencies are well characerized by nonlinearly mean revering processes since Using a model ha allows for nonlinear reversion and for shocks from boh exchange raes and relaive prices, Sarno and Valene (00) find ha for mos counries, long-run PPP holds, ha he relaive imporance of he sources of shocks varies over ime and ha he speed of reversion is consisen wih nominal rigidiies suggesed by convenional open economy models. Evidence on he validiy of PPP in Developing counries is relaively rare. The mos inclusive sudy o dae has been done by Alba and Park (003), who use daa for 6 developing counries from Overall, hey find weak suppor for PPP using linear panel uni roo ess, hough he evidence is much sronger for he pos 1980 s period. Bahmani-Oskooee, Kuan and Zhou (008) es for PPP in 88 developing counries and find suppor for saionary real exchange raes wice as ofen when allowing for nonlinear adjusmen o he mean compared o ess wih only linear adjusmen. They also find ha PPP holds more ofen for counries experiencing high inflaion and for counries wih more flexible exchange raes. All of he previous ess for Chinese PPP have focused on he relaive valuaion of he yuan versus anoher single currency, usually he US dollar. Beginning wih Yu (000), followed by Yang and Xiangsheng (004), Fink and Rahn (00) and Couder and Couharde (007), linear models are used ha conclude here are significan deparures from PPP and 148 1

3 Economics Bullein, 011, Vol. 31 no. pp ha i doesn hold for he yuan/renminbi. None of hese previous sudies allow for non-linear adjusmen o PPP. The sudy by Ahmad and Rashid (008) ess for non-linear adjusmens o PPP for China and four oher Souh Asia counries and find ha nonlinear ess are more successful in validaing PPP. This paper exends he empirical lieraure on Chinese PPP in hree ways. Firs, we es for PPP for he Chinese yuan versus boh he U.S. dollar and a rade-weighed index of currencies. Secondly, we conduc a wide variey of ess, including hose ha allow for nonlinear reversion o mean or a discree change in mean. Third, he wild boosrap is used o demonsrae ha resuls supporing PPP are robus o correcion for non-normaliy and heeroscedasiciy of he es residuals.. Bilaeral PPP beween US dollar and Chinese yuan. The real exchange rae beween he Unied Saes and China in a given monh ( ) is consruced as:. (1) The nominal exchange rae measured in dollars per yuan is denoed. The price levels in China and he US are denoed respecively as and. The monhly daa span he period from January 1986 hrough May 010. The daa series were obained from Inernaional Financial Saisics (IFS) and World Developmen Indicaor (WDI) from he Inernaional Moneary Fund, wih World Economic Oulook (WEO) daa used o fill in some missing values. A ime plo of he US-China real exchange rae is provided in Figure 1. The RER series is subjeced o a baery of uni roo ess. 1 The firs of hese is he augmened Dickey-Fuller (ADF) es. The es equaion is: () where ΔRER is he change in he real exchange rae, α, β, and he are coefficiens, and is a whie noise error erm. Under he null hypohesis of a uni roo, he β coefficien is equal o zero. The number of augmening lags (K) differs depending on wheher he Akaike (AIC) or Schwarz (SIC) informaion crieria is used; however, in all cases he es fails o rejec he null hypohesis of a uni roo. Resuls are presened in he second and hird rows of Table 1. The ADF-GLS es of Ellio, Rohenberg, and Sock (1996) has been used in sudies such as Taylor (00) due o poenial gains in power over he sandard ADF es. This es replaces he real exchange rae in () wih he GLS derended real exchange rae. Boh AIC and SIC crieria indicae an opimal augmening lag lengh of 1. Resuls of his es are displayed in he fourh line of Table 1. This es also fails o rejec he presence of a uni roo in RER. A uni roo es developed by Perron and Vogelsang (199) nex is applied o RER. This es allows for a one-ime change in he level of he series boh under he null and alernaive hypohesis. 3 The PV es equaion is: (3) 1 Unless oherwise noed, he null hypohesis of each es is ha he series conains a uni roo, and he alernaive hypohesis is a saionary series. In his case, he modified AIC lag selecion crierion resuls in he same lag lengh as AIC. Similarly, he modified SIC crieria resuls in he same lag lengh as SIC. 3 The innovaive oulier (IO) model is used for he es. 149

4 Economics Bullein, 011, Vol. 31 no. pp where he shif indicaors DTB is equal o one for he period in which he level shif occurs and equal o zero for all oher periods; DU is equal o zero for period up unil he level shif and equal o one for all periods aferward. The variable DTB capures he immediae effec of he level shif, while DU capures he afer effecs. The ime of he level shif and he augmenaion lag K are chosen o maximize he evidence agains he uni roo null hypohesis. Asympoic criical values are non-sandard bu are provided by PV. Resuls are provided in he fifh row of Table 1. Again, he null hypohesis of a uni roo canno be rejeced. A es developed by Kwiakowski, Phillips, Schmid, and Shin (199) also is applied o he US-Chinese real exchange rae. The KPSS es differs because i has a null hypohesis of saionariy versus an alernaive of a uni roo. Newey-Wes sandard errors are used o correc for serial correlaion in he es equaion. The es resul is shown in he sixh row of Table1. The KPSS es rejecs saionariy in favor of he alernaive of a uni roo even using a 1% criical value. The US-China RER is subjeced o one addiional ype of uni roo es. The nonlinear uni roo es of Kapeanios, Shin, and Snell (003) allows for ESTAR behavior. This means ha he real exchange rae may display uni roo behavior wihin boundaries bu if i passes ouside hose bounds hen i quickly reurns. The RER hus may wander wihin bounds deermined by he degree of rade fricions, bu if i moves ouside he bounds hen arbirage quickly moves i back inside he limis. This es has been widely employed in he PPP lieraure. Alhough fully parameerized ESTAR models are quie complicaed and may suffer from idenificaion problems, a firs-order Taylor approximaion yields he simple es equaion: RER 3 1 p * RER RER (4) j 1 j The mean is removed from he real exchange rae prior o esing. The null hypohesis H 0 : 0 hen is esed versus an alernaive H 1 : 0 using he -saisic. 4 The null hypohesis of a uni roo is rejeced in favor of nonlinear reversion o rend if he es saisic lies beyond a lower criical value. Tes resuls wih he augmening lag lengh chosen using AIC and SIC crieria are displayed in rows 7-8 of Table 1. This es also fails o rejec he null hypohesis of a uni roo in RER. In summary, he ess used in his sudy fail o provide any suppor for PPP beween he US dollar and Chinese yuan. This resul holds even when he ess allow for a shif in he mean of he series or for nonlinear adjusmens oward he mean. The lack of suppor for PPP is consisen wih exchange rae inervenions by he Cenral Bank of China. 3. PPP for he Chinese effecive real exchange rae. The real equivalen exchange rae (REER) provides a comparison of he real exchange rae for he Chinese yuan versus a weighed baske of oher currencies. Monhly observaions for he REER are used for he period from January 1986 hrough Sepember 006. The daa was obained from Inernaional Financial Saisics of he Inernaional Moneary Fund. Their consrucion of he REER follows he mehodology oulined in Bayoumi e al (006). A plo of he REER is provided in Figure. An ADF es is used o invesigae wheher he REER is consisen wih purchasing power pariy. The es equaion is he same as shown in equaion (1) above. Boh he AIC and SIC crieria indicae an opimal augmening lag lengh of zero lags. The resuling ADF j 4 The es saisic does no follow a -disribuion. Asympoic criical values are provided by KSS. 10 3

5 Economics Bullein, 011, Vol. 31 no. pp es saisic is This es saisic lies beyond he 1% criical value of -3.46, hus providing seemingly srong suppor for PPP. However, Arghyrou and Gregoriou (007) show in heir sudy of PPP ha he ADF es may suffer from size disorions when he residuals are non-normal. Specifically, he null hypohesis may be rejeced oo ofen. A Jarque-Bera es indicaes ha he residuals of he es equaion indeed are highly nonnormal. Therefore, es conclusions should be based on criical values ha allow for nonnormaliy. Criical values correced for non-normaliy are obained by using he wild boosrap procedure. This involves esimaing he ADF es equaion () by OLS and reaining he esimaed residuals as well as he -saisic for esing he null hypohesis. In implemening he wild boosrap 100,000 ses of new residuals u * * are generaed according o: () The u variable is drawn from he wo-poin disribuion suggesed by Mammen (1993): 1 1 u wih probabiliy p, and (6) 0 1 u wih probabiliy (1 p). The ADF es equaion wih he null hypohesis is used o creae 100,000 arificial daa ses. Each arificial daa se is consruced by combining he original esimaes of he * coefficiens wih one of he generaed series. The null hypohesis is rue by consrucion for each arificial daa se. In addiion, he u erms are muually independen drawings from a disribuion ha is independen of he original daa and has he properies E ( ) 0, E ( ) 1, and E ( 3 ) 1. These properies u imply ha any non-normaliy presen in he original residuals from equaion (1) remains in * he generaed for each arificial daa se. In he wild boosrap procedure, he arificial daa ses are subjeced o he ADF es o generae a vecor of ordered es saisics. This vecor hen is used o consruc he empirical disribuion of he es saisics under he null hypohesis. The lower (wild boosrapped) criical values of he es are based upon his empirical disribuion. The es saisic remains equal o However, he empirical criical values are considerably wider han hose associaed wih he sandard ADF es. The % empirical criical value is equal o , while he 1% empirical criical value is equal o The null hypohesis is rejeced using he % empirical criical value. Thus, resuls of he ADF es wih boosrapped criical values sill provide evidence in favor of PPP. However, he evidence is somewha weakened by he use of he wild-boosrapped criical values because he null canno be rejeced a a 1% level. 4. Conclusions The resuls repored above for his research sand in sark conras o previous resuls for uni roo es of PPP. While ess of he China-US real exchange rae do no suppor purchasing power pariy, ess of he real equivalen exchange rae for he Chinese yuan versus a rade-weighed baske of currencies suppors purchasing power pariy. A possible explanaion is ha he swiching of he currency regime beween differen ypes of pegs u u j The Jarque-Bera es saisic of has a marginal significance level of

6 Economics Bullein, 011, Vol. 31 no. pp versus he dollar has led o deparures from equilibrium ha are miigaed by using a radeweighed baske. References Ahmad, S. and A. Rashid., 008. Nonlinear PPP in Souh Asia and China. Economics Bullein 17(6), 1-6. Alba, J.D. and Park, D., 003. Purchasing power pariy in developing counries: muli-period evidence under he curren floa, World Developmen, 31(1), Arghyrou, M.G. and Gregoriou, A., 007. Tesing for purchasing power pariy correcing for non-normaliy using he wild boosrap. Economics Leers 9, 8- Bahmani-Oskooee, M., A.M. Kuan and S. Zhou, 007. Tesing PPP in he nonlinear STAR framework, Economics Leers 94, Bayoumi, Tamim, Jaewoo Lee, and Sarma Jayanhi, 006, New Raes from New Weighs. IMF Saff Papers, Vol. 3, No.. Benninga, S. and A. Proopapadakis, The Equilibrium Pricing of Exchange Raes and Asses when Trade Takes Time, Journal of Inernaional Money and Finance 7, Couder, V. and C. Couharde, 007, Real equilibrium exchange rae in China: is he renminbi undervalued? Journal of Asian Economics 18, 4, Dumas, B., 199. Dynamic Equilibrium and he Real Exchange Rae in Spaially Separaed World, Review of Financial Sudies,, Ellio, G., Rohenberg, T., and Sock, J., Efficien ess for an auoregressive uni roo. Economerica 64(4), Finke, M. and J. Rahn. 00. Jus how undervalued is he Chinese renminbi? World Economy, 8, Kapeanios, G., Shin, Y., and Snell, A., 003. Tesing for a uni roo in he nonlinear STAR framework. Journal of Economerics 11, Kwiakowski, D., Phillips, P., Schmid, P., and Shin, Y., 199. Tesing he null hypohesis of saionariy agains he alernaive of a uni roo. Journal of Economerics 4, Mammen, E., Boosrap and wild boosrap for high dimensional linear models. Annals of Saisics 1, -8. Michael, P., Nobay, A. R., and D. A. Peel, Transacions Coss and Nonlinear 1

7 Economics Bullein, 011, Vol. 31 no. pp Adjusmen in Real Exchange Raes: An Empirical Invesigaion, Journal of Poliical Economy, 10, Perron, P., and Vogelsang, T., 199. Nonsaionariy and level shifs wih an applicaion o purchasing power pariy. Journal of Business & Economic Saisics 10(3), Sarno, L., 00. Towards a Soluion o he Puzzles in Exchange Rae Economics: Where Do We Sand? Working Papers wp0-11, Warwick Business School, Financial Economerics Research Cenre. Sarno, L. and M. P. Taylor. 00. Purchasing Power Pariy and he Real Exchange Rae. Inernaional Moneary Fund Saff Papers.49:1, pp Sarno, L. and G. Valene 00 Empirical Exchange Rae Models and Currency Risk: Some Evidence from Densiy Forecass, Journal of Inernaional Money and Finance,4 (), Sercu, P., Uppal, R., and C. V. Hulle, 199. The Exchange Rae in he Presence of Transacions Coss: Implicaions for Tess of Purchasing Power Pariy, Journal of Finance, 0, Taylor, A., 00. A cenury of purchasing power pariy. The Review of Economics and Saisics 84(1), Taylor, M. P., Peel, D. A., and L. Sarno, 001. Nonlinear Mean-Reversion in Real Exchange Raes: Toward a Soluion o he Purchasing Power Pariy Puzzles, Inernaional Economic Review, 4, Yang, Xi and Dou Xiangsheng, 004. Esimaing of RMB equilibrium exchange: An approach of PPP. Sceince Technique and Projec, April Yu, Qiao, 000. Purchasing Power Pariy. Real exchange rae and inernaional compeiiveness-theoreical approach of measuring weighed real exchange index in China. China Journal of Finance,

8 Economics Bullein, 011, Vol. 31 no. pp Table 1 Tess of RER Tes Augmening Lag Lengh Tes Saisic % Criical Value ADF ADF-GLS PV KPSS ** KSS **Denoes significance using a 1% es size. 14 7

9 Economics Bullein, 011, Vol. 31 no. pp Figure 1 RER Figure REER