Non-linear PPP in South Asia and China. Abstract

Transcription

1 Non-linear PPP in Souh Asia and China Shabbir Ahmad School of Economics, IIIE, Inernaional Islamic Universiy Abdul Rashid of Economics, IIIE, Inernaional Islamic Universiy, Absrac This sudy ess he purchasing power pariy hypohesis for four Souh Asian economies and China by employing a recen nonlinear es of saionariy. Besides esing he CPI based PPP, we have also used PPI based real exchange rae in he analysis. The resuls indicae ha nonlinear ess are more successful in validaing PPP Ciaion: Ahmad, Shabbir and Abdul Rashid, (008) "Non-linear PPP in Souh Asia and China." Economics Bullein, Vol. 6, No. 7 pp. -6 Submied: March 7, 008. Acceped: April, 008. URL: hp://economicsbullein.vanderbil.edu/008/volume6/eb-08f3004a.pdf

2 . Inroducion The behaviour of real exchange rae has been vasly sudied in lieraure because of is many repercussions in he area of inernaional finance. The compeiiveness of a counry in world rade can be examined by analysing real exchange rae movemens. Moreover, he validiy of purchasing power pariy can be esed by observing he performance of real exchange rae. Besides oher imporan implicaions, absence of purchasing power pariy forbid he exisence of moneary approach o he exchange rae if a counry is following flexible exchange rae or moneary approach o he exchange marke pressure if a counry is following managed floaing exchange rae sysem. Afer he failure of linear models o validae purchasing power pariy, here is increasing rend o employ nonlinear mehodologies o capure he behaviour of real exchange rae and hese new echniques have been more successful in validaing purchasing power pariy assumpion. A recen survey on he opic can be found in Sarno (005). Some oher imporan sudies on he opic include Michael e al. (997), Taylor e al. (00), Sarno and Taylor (00), Liew e al. (004), and Bahmani-Oskooee e al. (007). The presen sudy uses recen nonlinear coinegraion echnique advanced by KSS (Kapeanious e al. (003)) and a more powerful es suggesed by KPSS (Kwiaowski e al. (99)). The deail abou hese mehodologies is given in he coming secions. This sudy examines he behaviour of real exchange rae for Souh Asian counries viz. India Pakisan, Sri Lanka, Bangladesh and China using monhly daa for he period 974M o 006M, 974M o 006M, 975M o 006M, 993M7 o 006M, and 986M o 006M, respecively. The choice of his ime period is influenced by he availabiliy of he daa series. In anoher sudy Zhou (997) has analysed he behaviour of real exchange rae using nonlinear uni roo es for Asian-Pacific counries. Our sudy is differen from Zhou s sudy in four ways. Firs, we have wo measures of real exchange rae i.e., consumer price index (CPI) base real exchange rae and wholesale price index (WPI) based real exchange rae whereas Zhou has used only CPI based real exchange rae. Second, he daa used in Zhou s sudy is quarerly while we use monhly daa. Third Zhou s sudy does no include Bangladesh and China in his analysis. Fourh, we have employed an addiional es of saionariy (KPSS), which is considered o be more powerful compared o ADF es. The KSS and KPSS mehodologies are presened in secion, while esimaion resuls are given in secion 3. Secion 4 concludes.. Mehodology A number of he empirical sudies in economerics lieraure have repored ha he classical or convenional non-saionariy ess (such as DF, ADF and PP) are no very powerful agains relevan alernaives. For insan, Delong e al. (989) found ha he Dickey-Fuller ess are no able o rejec a uni roo null hypohesis agains sable auoregressive alernaives wih roos close o uniy. Similarly, Diebold and Rudebusch (990) provided empirical evidence ha sandard uni roo ess have low power agains fracionally inegraed alernaives. To avoid his problem he presen sudy employs wo alernaive ess of saionariy i.e., KPSS (Kwiaowski e al. (99)) mehodology (he LM saisic) and KSS (Kapeanious e al. (003)) mehodology, besides he convenional linear ADF es.

3 The sandard ADF es is used o check he saionariy of a series under he null hypohesis ha series is non saionary while he alernaive hypohesis ess he absence of uni roo. In he KPSS mehodology, under null hypohesis i is defined ha series is saionariy while he alernaive saes he exisence of a uni roo in he series. This ensures ha he alernaive will be acceped (null rejeced) only when here is srong evidence for (agains) i. The KPSS es saisic is defined as follows; S ˆ η = T, where S is he parial sum process of he residuals ξ which are obained s ( l) from a regression of he respecive variable on only inercep in case of level saionary, and on inercep and rend in case of rend saionary. I is defined as; S = ξi and s T ξ + = l m= T l = ( ) T T w( m, l) ξ ξ, w( m, l) is an opional weighing funcion; his is, = m+ m w ( m, l) = m/( + l), where l is he maximum lag. A nonlinear es proposed by Kapeanious, Shin and Snell (KSS) (003) under null hypohesis ess he series o be non saionary; however he alernaive hypohesis is ha he series is nonlinear bu globally saionary. This es is based upon he following exponenial smooh ransiion auoregressive process: y [ ( θy )] ε = γ y exp + () where y is he de-meaned or de-rended series of ineres and ε is an i.i.d. error wih zero mean and consan variance and [ exp( θ y )] is he exponenial ransiion funcion used o presen he nonlinear adjusmen. The null hypohesis H 0 : θ = 0 implies ha y = ε as [ exp( θ y )] = 0 while he alernaive hypohesis ha series is nonlinear bu globally saionary process enails ha θ >0, where θ deermines he speed of mean reversion. The null hypohesis H 0 : θ = 0 canno be direcly esed as γ in above equaion under he null is no idenified, KSS has reparameerised equaion based on firs-order Taylor series approximaion o equaion o obain he auxiliary regression specified as: y = θy 3 + error () o correc for he serially correlaed errors in equaion, regression equaion can be wrien as: y = p j j j= 3 ρ y + θy + error (3) he null hypohesis in equaion or o be esed is H 0 : θ = 0 while he alernaive hypohesis is H : θ < 0. As he KSS show ha he -saisics for θ = 0 agains θ < 0, does no have an asympoic sandard normal disribuion and one mus resor o simulaions for asympoic criical values. On he basis of equaion 3, we have esimaed wo values of, i.e., and KSS ( c+ ) where he former represens de-meaned and laer indicaes he de-rended daa. These daa series are obained by firs regressing each series on a consan or on boh a consan and a ime rend and hen saving he residuals. i=

4 3. Esimaion The able one provides some ineresing informaion abou he exising of PPP. We apply linear as well nonlinear uni roo ess o es wheher he real exchange raes are saionary or no. The ess are applied for wo real exchange raes, one is compued using consumer price index (CPI) and he second is calculaed wih respec o producer price index. The producer price index based real exchange rae is esed wih an assumpion ha in hese counries here are more rade barriers on consumer goods and less on producer goods, herefore, i is more likely ha hese counries hold PPP wih respec o wholesale price index raher han consumer price index. Counry Pakisan REX (CPI) REX (WPI) India REX (CPI) REX (WPI) Sri Lanka REX (CPI) REX (WPI) Table Uni Roo Tes Resuls for Real Exchange Rae ADF KPSS KSS ADF ( c+ LM KPSS (c) LM KPSS ( c+ ) ADF (c) ) KSS ( c+ ) Bangladesh REX (CPI) China REX (CPI) Noes: ADF (c) and ADF ( c+ ) are he sandard ADF es saisics for he null of nonsaionary of he variable in he sudy wihou and wih a rend, respecively, in he model for esing. LM KPSS (c) and LM KPSS ( c+ ) are he KPSS es saisics for he null of saionary of he variable in he sudy wihou and wih a rend, respecively in he model for esing. and KSS ( c+ ) are he KSS es saisics for he de-meaned and he de-rended dada, respecively, using he models wih augmenaion. The 0% and 5% asympoic criical values are -.57 and -.86 for ADF (c) respecively, and are -3. and -3.4 for ADF ( c+ ) respecively. The 0% and 5% asympoic criical values are and for LM KPSS (c) respecively, and 0.9 and 0.46 for LM KPSS ( c+ ) respecively. The 0% and 5% asympoic criical values for are -.66 and -.93 respecively and hose for KSS ( c+ ) are and respecively, aken from Kapeanios e al. (003, p.364). he bold saisics indicae saionariy a level. The sandard ADF linear uni roo has been failed o rejec he null of nonsaionary for all he examined counries apar from Sri Lanka. In case of Sri Lanka, boh he real exchange raes 3

5 wih respec o consumer price index as well as wih respec o wholesale price index appeared saionary. We did no find any significan evidence of saionariy for he consumer price index based real exchange rae for Pakisan and India even by using nonlinear uni roo ess. Thus, CPI based PPP neiher exiss in linear conex nor in nonlinear conex in hese wo economies. On he oher hand, CPI based PPP -he only available price measure- exiss in Bangladesh and China, when applied nonlinear KSS es. From above discussion we can conclude ha nonlinear saionariy ess are relaively more successful in rejecing he null of non saionary agains he alernaive of nonlinear bu saionary process. This resul is consisen o oher sudies which employ nonlinear echniques. Despie he Souh Asian counries have a number of rade barriers *, heir rade volume is increasing significanly and hey are gradually removing, or a leas giving relief in ariffs and oher barriers. Wih given insiuional circumsance of Souh Asian counries, he sandard forms of PPP based on consumer price index perhaps no compaible; however, since hey have fewer barriers in capial goods as compared o consumer goods he PPP wih respec o wholesale price index seems more well-mached and robus for he Souh Asian counries. 4. Conclusion This paper has esed he purchasing power pariy assumpion for Four Souh Asian economies, i.e., Bangladesh, India, Pakisan, Sri Lanka, and for China by examining he saionariy of real exchange rae. We have used wo measures of real exchange rae, he consumer price index based real exchange rae and producer price based real exchange rae. As he convenional linear models of esing he PPP have me wih limied success, his sudy uses wo recen mehodologies o validae PPP heory. The resuls indicae ha nonlinear ess are more successful in validaing he purchasing power pariy assumpion in he examined economies. Moreover, relaively srong prevalence of producer price index based PPP indicaes ha inermediae goods face less barrier o rade in hese economies. References Bahmani-Oskooee e al. (007) Tesing PPP in non-linear STAR framework Economics Leers 94, Calvo, A. G. and C. M. Reinhar (000) Fear of Floaing NBER Working Paper 7993 Delong, D. N., J. C. Nankervis, N. E. Savin, and C. H. Whieman (989) Inegraed versus Trend Saionariy in Macroeconomic Time Series Deparmen of Economics, Universiy of Iowa Working Paper No Diedbold, F. X. and G. D. Rudebusch (99) On he Power of Dickey-Fuller Tes agains Fracional Alernaives Economics Leer 35, Kapeanios, G., Shin, Y., Snell, A., (003) Tesing for a uni roo in he nonlinear STAR framework Journal of Economerics, Kwiakowski, D., P. C. B. Phillips, P. Schmid and Y. Shin (99) Tesing he Null Hypohesis of Saionariy agains he Alernaive of a Uni Roo Journal of Economerics 54, * Principally i seems ha hese rade barriers slow down he process of pass hrough of he changes in exchange raes o domesic prices of commodiies. However, as said by Calvo and Reinhar (000), he pass hrough from exchange rae swings o domesic prices is far higher in emerging economies (including India and Pakisan) han in developed economies. 4

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