THE VALIDITY OF PPP THEORY IN SOUTH AFRICA: A COINTEGRATION APPROACH 1

Transcription

1 THE VALIDITY OF PPP THEORY IN SOUTH AFRICA: A COINTEGRATION APPROACH 1 Oludele, A. Akinboade & Daniel Makina Universiy Of Souh Africa, P.O. Box 392, Unisa 0003, Preoria ABSTRACT The paper explores he validiy of PPP heory in Souh Africa. Coinegraion heory is applied o monhly daa on wo nominal exchange raes of he rand and relaive prices. Our ess idenify ha long-run co-movemen exiss beween he nominal exchange rae and he relaive prices beween Souh Africa and he US and beween Souh Africa and he UK. An esimaed error-correcion model shows ha a proporion of he deviaion from PPP in he iniial period is correced for rae in he following period, only in he rand-serling exchange. 1. INTRODUCTION In simple erms, he purchasing power pariy (PPP) heory saes ha he PPP exchange rae is he exchange rae ha would make he purchasing power of a uni of a currency he same in wo counries if expressed in erms of one common currency. Technically, his means saring from an equilibrium posiion, he real exchange rae mean revers so ha is variabiliy can be viewed as deviaions from PPP. Mos heories of inernaional finance are based on PPP heory. For insance, PPP is relaed o ineres rae pariy heory and he inernaional Fisher effec (IFE). Ineres rae pariy heory suggess ha PPP equilibrium is mainained because he forward exchange rae would differ from he spo rae by a sufficien amoun o offse he ineres rae differenial beween wo currencies. Similarly, he IFE focuses on how a currency s spo rae will change over ime in response o ineres rae differenials beween counries. Whereas PPP heory suggess ha he spo rae will change in accordance wih inflaion differenials, IFE heory suggess ha he spo rae will change in accordance wih ineres rae differenials. However, PPP is relaed o IFE because inflaion differenials influence he nominal ineres rae differenials beween wo counries. In so far as he qualiy of policy advice may be based on hese heories, i may depend on he validiy of PPP (Liu and Burke, 1995). JEL Classificaion Numbers: F31, F32 Correspondence o: akinboa@unisa.ac.za & makind@unisa.ac.za Universiy Of Souh Africa, P.O. Box 392, Unisa 0003, Preoria 1 An earlier version of his paper was delivered a he Second African Finance Journal Conference, held in Cape Town, July 2005 The African Finance Journal, Volume 8, Par 2,

2 The relaionship beween relaive prices and he exchange rae has been an area of exensive research whereby sudies have focused on he empirical validiy of he PPP in an endeavour o esablish wheher here is co-movemen of exchange raes and relaive prices in he long-run (see Officer, 1976 for review of early sudies). Mos of he work on PPP has been done on developed economies. In paricular work using long spans of daa has implicily ensured ha he economies sudied have been largely developed economies simply because his is where he daa is available. Hence i could be argued ha summarising such resuls and drawing conclusions on PPP suffers from sample selecion bias. Cheung and Lau (2000: 376) observe ha empirical evidence on PPP for developing counries is noably limied. They furher charge ha for counries undergoing significan income growh from a low level, relaive prices of radables and non-radables can change subsanially, inducing non-saionariy in real exchange rae dynamics so ha pariy reversion may fail o work for his ype of counries. Economiss have a priori belief ha developing counries should show less evidence of PPP reversion. This is so because according o some (Froo and Rogoff, 1995) hese are ofen he more rapidly growing economies and rapid income growh is ofen associaed wih rapid change in he relaive price srucure beween radeables and nonradeables making i harder o find pariy reversion for such counries. Anoher argumen is ha governmen spending can affec he relaive price raio beween radeables and non-radeables and is argued ha governmen spending falls more heavily on non-radeables (Froo and Rogoff, 1991). Cheung and Lau (2000) find evidence in suppor for his basic hypohesis. The dominan view is ha he more significan he share of nonradeables in GDP, he greaer he possibiliy of he exchange rae diverging from is PPP value. In general when price pariy is calculaed from a general price index his may induce sysemaic bias for counries where he non-raded secor is dominan, as is he case in mos developing counries. They have weak domesic producion, hus by exension non-radable share of income is relaively low. I is suggesed ha rade resricions and specifically, asymmeric resricions on impor compared o expors is a probable cause of deviaions from PPP among developing counries. By and large, evidence on PPP for less developed counries (LDCs) has produced mixed conclusions regarding is validiy. Using uni roo ess and he Engle-Granger (1987) es for coinegraion, McNown and Wallace (1989) find evidence o suppor PPP in he cases of Argenina, Brazil, Chile and Israel. On he hand, Bahmani-Oskooee (1993), using he same Engle-Granger echnique for weny-five LDCs only finds evidence of PPP in a minoriy of cases. Bahmani-Oskooee (1995) furher rejecs evidence of PPP in a sample of weny-wo LDCs. Applying he Johansen (1988) maximum likelihood echnique for esimaing co inegraing vecors, Liu (1992) finds general evidence in suppor of PPP for en Lain American economies wih respec o he U.S. Mahdavi and Zhou (1993), also applying he Johansen echnique in a sample of LDCs, conclude ha incidences of PPP are more frequenly observed among high inflaion counries. Empirical evidence for developing counries on PPP is sill in is infancy and is concenraed around relaively homogeneous groups of counries like Lain America and eas Asia (Conejo and Sheilds, 1993). There is a gap on individual counry sudies. The moivaion of his paper is o examine he validiy of purchasing power pariy (PPP) beween Souh Africa, a developing counry, and he US and he UK in he framework of he Johansen coinegraion approach. The Souh African economy is open. 2 The African Finance Journal, Volume 8, Par 2, 2006

3 Boh Briain and he Unied Saes are imporan rading parners of he counry. As such, Souh Africa has significan inernaional rade exposure o he dollar and he pound serling. The res of he paper is srucured as follows. Secion 2 reviews he PPP heory and he coinegraion approach. Secion 3 examines he daa and presens empirical resuls. Secion 4 gives concluding remarks. 2. PPP THEORY AND COINTEGRATION The PPP heory is cenral in deermining prices and he exchange rae. The flexible, fixed and sicky price moneary model of he exchange rae, which evolved in he 1970 s o explain exchange rae behaviour, uses he heory as an essenial building block (Dornbusch, 1976 and Frenkel, 1976). Assuming zero ransacion coss or oher impedimens o rade, and given ha all goods are radable, hen effecive arbirage would resul in he sronges version of PPP called absolue PPP. This is saed as follows: E = P /P * (1) where E is he exchange rae, ha is, he number of unis of domesic currency required for purchasing one uni of foreign currency. P and P * are respecively he domesic and he foreign price indices. Absolue PPP is premised on he law of one price, which saes ha once convered ino a common currency, naional price levels should be equal. However, in realiy he equilibrium price of a good may no be he same when convered ino a common currency because of ranspor cos, quoas, ariffs and informaional asymmeries ha diminish he effeciveness of arbirageurs. Also, he presence of non-raded goods can preven arbirageurs from responding o profiable invesmen opporuniies. In addiion, he non-neuraliy of money in he shor-run can generae price differences in similar goods across counries. The limiaions of absolue PPP is accouned for by specifying an alernaive version of PPP called he relaive PPP which saes ha he change in he exchange rae is equivalen o he difference in inflaion raes beween wo counries. This is given by: E = P -P* (2) where E is he percenage change in he exchange rae, while P and P * represens he rae of change of he domesic and foreign price levels respecively. This equaion saes ha he rae of change of he exchange rae approximaes he domesic rae of inflaion minus he foreign rae of inflaion. In developing counries one reason for deviaions of he exchange rae from is PPP value in he long-run is due o exisence of a subsanial amoun of he goods ha canno be raded. As a resul he arbirage condiion is no saisfied for all inernaionally produced goods bu only for radable goods. To address his issue, Kim (1990) used wholesale prices raher han he consumer price indices based on he assumpion ha he wholesale price is a beer indicaor of he general price of radable goods. Anoher alernaive by Rogers and Jenkins (1995) addressed he issue by disaggregaing he daa and esing for a long-run relaionship beween relaive prices of cerain commodiies across differen counries. A number of heories are advanced o explain deviaions from PPP. The African Finance Journal, Volume 8, Par 2,

4 Dornbusch s (1976) model of overshooing exchange raes emphasizes he role of news in explaining he response of exchange raes o new developmens. The premise of he model is ha news is processed faser in exchange raes han in prices. The raionale of he idea is ha prices are deermined in he commodiy markes, where signals end o be digesed very slowly whereas exchange raes are deermined in he aucion markes where news is quickly assimilaed. On his basis, Daniel (1986) argues ha he response of exchange raes o news is a crucial deerminan of shor-erm deviaions from PPP. Hence deviaions from PPP could be said o be largely he resul of price sickiness so ha i is logical o conclude ha such deviaions should disappear overime as prices adjus o a new equilibrium given nominal disurbances. The role of news as a source of deviaion from PPP is likely o be more relevan in he developed counries because hey have sophisicaed financial markes so ha exchange rae movemens are usually influenced by developmens in he asse markes. However, in developing counries when a real disurbance occurs and he price indices conain differen goods and weighs, he PPP deviaions may decline bu migh no disappear alogeher. Anoher hypohesis is he idea of he parial pass-hrough of exchange raes developed by, among ohers, Froo and Rogoff (1995) and Freensra and Kendall (1997). This posulaes ha under condiions of imperfec compeiion, firms involved in he expor of goods and services may adjus prices by less han he complee change in he exchange rae. For insance, in an endeavour o mainain marke share, a firm may decrease profi margins in order o absorb some of he price increases associaed wih a currency appreciaion. As a resul only a cerain percenage of he price increase associaed wih he currency change is passed hrough o he imporer price. The model of overshooing exchange raes and he parial pass-hrough hypohesis are aemps o explain shor-erm deviaions from PPP while he expecaion is ha in he long-run such deviaions should diminish significanly. However, empirical sudies have found ha hese deviaions may persis in he long-run and are likely o be accouned for by real facors. Balassa (1964) and Samuelson (1964) have argued ha when prices are convered ino a common currency a prevailing exchange raes, prices in richer counries will be higher han hose of poor counries. Furhermore, Kravis and Lipsey (1983) and Bhagwai (1984) have argued ha he exisence of higher capial-labour raios in developed counries resuls in higher wages in conras o low labour cos in developing counries and non-raded goods ha are labour inensive. Alhough many empirical sudies of PPP indicae a high level of shor-run violaions from he heory, many economiss sill hold he view ha over he long-run, relaive prices may move in proporion o he change in he nominal exchange rae, so ha he real exchange rae will rever o pariy. Coinegraion heory has been used o es for his long-run phenomenon. The heory can bes be undersood by expressing saisically he relaive version of PPP as follows: InE = K + In (P /P *) + (3) According o coinegraion heory, if E changes over ime bu is a saionary AuoRegressive Inegraed Moving Average (ARIMA) (p, q) process, hen deviaions from pariy are largely emporary and are expeced o disappear hrough ime. The p in "ARIMA(p,q)" is he maximum lag of he AuoRegressive par, and q is he maximum lag of he Moving Average par. 4 The African Finance Journal, Volume 8, Par 2, 2006

5 Therefore, esing for long-run PPP involves a es for coinegraion beween he nominal exchange rae and relaive prices. For he exisence of long-run PPP, he error erm should be saionary or he variables in equaion (3) should be co-inegraed whils rejecion of he exisence of a co-inegraing vecor implies he PPP hypohesis is no relevan for he daa. Error-correcion models are useful because hey reconcile he shor- and long-run behaviour of he variables involved. Obviously, ignoring eiher he shor- or long-run properies of a model resuls in a mis-specified relaionship. The long-run relaionship is incorporaed by including he (lagged) co inegraing vecor ino he model, and he shor-run dynamics are incorporaed by including he variables in heir differenced form. According o Engle and Granger (1987), given he presence of a co-inegraing relaionship amongs he variables in equaion (3) an error-correcion represenaion which caers for flexibiliy in he shor-run dynamic process while he model is consrained o reurn o he long-run equilibrium can be specified in he following form: n * * InE = + i In P / P ) + ( InE In( P / P ) + (4) 0 1 ( ) j ( InE 1 In( P / P ) 2 ) In his equaion, he expression j is he error-correcion erm ha shows he deparure of he exchange rae from is PPP value which is correced in he subsequen periods whereas he coefficien measures he single period response of he exchange rae shock. Theory predics ha he error-correcion erm mus be negaive and significanly differen from zero. The coefficien is an esimae of he speed of adjusmen back o he long-run equilibrium relaionship. A negaive implies ha in he even of a oneuni deviaion beween he exchange rae and he long-run PPP rae, here would be an adjusmen back o he long-run (sable) relaionship in subsequen periods o eliminae his discrepancy. On he oher hand, he coefficien of Ln (P /P *) mus be significanly differen from zero in a posiive direcion. 3. DATA AND EMPIRICAL RESULTS Viewing PPP as a long-run equilibrium relaionship beween wo endogenous variables, we uilise coinegraion heory o deermine wheher ime series of he nominal exchange raes of he rand-dollar and he rand-serling pound, and respecive relaive prices raios have a saionary relaionship over he long-run. For our relaive raios we uilize he wholesale price index (WPI), he preferred price index ha incorporaes a larger proporion of radeables han he consumer price index (CPI). We uilize monhly daa series of nominal exchange raes and relaive prices from 1978 o The daa uilized is obained from he Inernaional Financial Saisics of he Inernaional Moneary Fund (IMF, several years). 3.1 Tesing for he Presence of Uni Roos If relaive purchasing power pariy beween Souh Africa and he Unied Saes and Unied Kingdom holds, hen he real exchange raes mus be saionary around some long-run mean. As an iniial sep, in order o use coinegraion i is necessary o check for he order of inegraion of he wo variables- he nominal exchange rae and he relaive price level for boh he rand agains he dollar and he rand agains he pound. The hypohesis is ha he series follow a random walk. The hypohesis of a pure uni roo process is hen esed agains he alernaive of a saionary process. * The African Finance Journal, Volume 8, Par 2,

6 The resuls of augmened Dickey-Fuller ess are presened in Table 1. In all cases i is shown ha he exchange raes and relaive price levels are I (1) and hence follow random walks. Table 1. ADF ess for nominal exchange raes and relaive price raios Variable In Levels Firs Differences Rand-dollar exchange rae (1) -9.54*** (1) Rand-pound exchange rae (1) *** (1) Dollar-rand WPI (7) *** (1) Pound-rand WPI 1.68 (1) *** (1) *** denoes significance a he 1 percen level. Theoreically, i is possible o increase he power of he uni roo es even furher by excluding he inercep erm from he regression. However, he relevan alernaive hypohesis would hen be a saionary process wih mean zero, which is equivalen o imposing he sric and empirically rejeced assumpion of absolue purchasing power pairy. Therefore, we have refrained from excluding he inercep erm. The nex sep in evaluaing he validiy of he PPP heory involves esing for he exisence of a co inegraing vecor beween relaive prices and he nominal effecive exchange rae using Equaion 3. We hence es for he presence of a co inegraing vecor using he Johansen mehod. Choosing he appropriae lag lengh is quie imporan for esimaing a VAR. A long lag lengh will quickly consume degrees of freedoms whereas a lag lengh ha is oo shor inroduces a misspecificaion and biased esimaes. The Johansen es is performed in he VAR framework and differen values of he lag lengh k=1 o 8 were considered, however, bearing in mind ha in mos cases a lag of k=4 is required o remove serial correlaion in he residuals, so saisical resuls based on a VAR (4) model are repored in Table 2. The es resuls indicae ha a co inegraing vecor was idenified in boh pairs of he series. The hypohesis of no coinegraion is rejeced a he 5% significance level. However, he hypohesis ha here is a mos one coinegraing vecor canno be rejeced. The es saisics are far below he criical values, he presence of wo coinegraing vecors is very improbable. This shows ha boh exchange raes and price raios (WPI) are co inegraed and hus PPP indeed holds as a long-run phenomenon. Table 2. Resuls of he Johansen es for coinegraion Series Likelihood raio: A Mos one Likelihood raio: None Rand-pound and WPI raio 0.94* Rand-dollar and WPI raio 0.002* Noes: Criical values for monhly daa are as follows: A mos one vecor a 5% and 1%, 3.76 and 6.65 respecively, no vecors a 5% and 1% and * Indicaes significance a he 5% level Vecor Auo Regression A sandard vecor auo regression is a good sar for invesigaing he inerrelaionships of he wo exchange raes. 6 The African Finance Journal, Volume 8, Par 2, 2006

7 The VAR is expressed in erms of firs differences, because he form of he variables in he VAR should mimic he daa generaing process and he previous secion found boh he randserling as well as he rand-dollar nominal exchange raes o be uni roo processes. Afer having esablished coinegraion, he nex sep is o examine shor-run impac of inflaion on exchange raes. An error-correcion model is esimaed uilizing he residuals of he equilibrium regression whereby he heory underlying he esimaion of such model is ha a proporion of he deviaion from PPP in he iniial period is correced in he following period. The vecor error-correcion model is performed on he following equaion and resuls are repored in Table 3. InE = n n * InE In( P 1 / P 1) + (5) i = 1 i = 1 * ( InE In( P / P ) ) 1 2 j + The modelling approach is based on he general o specific approach associaed wih Hendry (1986a,b). I involves he esimaion of a VAR wih all he variables enering he model being I(1). Given ha he coinegraion ess find only one co inegraing vecor in boh cases, only one error-correcion erm is included in he esimaed models. Equaion (5) is iniially esimaed wih dependen variables wih welve lags. Then variable deleion es is performed o deermine he join significance of he lagged variables. The final parsimonious equaion for each exchange rae regime is subjeced o a baery of diagnosic es, hough only a few are repored here. Table 3. Error-correcion models (Variables in firs differences) Dependen Variable is he firs difference of he nominal exchange rae Variables Rand-dollar Rand-pound Nominal Exchange Rae, E *** (4.89) Nominal Exchange Rae, E ** (-2.19) Nominal Exchange Rae, E * (-1.67) Nominal Exchange Rae,E *** (2.59) 0.31*** (5.47) 0.16*** (2.84) Nominal Exchange Rae, E * (1.71) Relaive Price Raios,Wholesale, 0.83*** WPI_Raio -4 (2.90) Relaive Price Raios,Wholesale, -0.59** WPI_Raio -6 (-2.15) Relaive Price Raios,Wholesale, 0.40* WPI_Raio -11 (1.75) Relaive Price Raios,Wholesale, 0.44* WPI_Raio -12 (1.89) ECM E-06 (-0.56) -0.04** (-2.17) R DW SER The African Finance Journal, Volume 8, Par 2,

8 Noes: A consan was esimaed bu is no repored. *, ** And ** denoes significance a he 10%, 5% and 1% confidence inerval. DW is he Durbin Wason Saisic, SER is he Sandard error of he regression and ECM is he error-correcion erm, WPI_Raio is relaive wholesale prices and E is he nominal effecive exchange rae. The esimaion resuls show, ha he change in he rand-dollar s and he rand-serling exchange raes is posiively relaed o he change in he previous monh as well as in he previous eigh monh. The previous welveh monh is also marginally significan in being posiively associaed wih he rand-dollar exchange rae. The previous fourh and fifh monhs are shown o be negaively associaed wih he change in rand-dollar exchange rae. Regarding he wholesale price raios, he individual change in he previous 11 h and he 12 h monh is associaed wih a posiive change in he curren rand-dollar nominal exchange rae. On he oher hand, exchange rae disurbance ha ook place four monhs ago is associaed wih a posiive change in he curren rand-serling exchange rae. In he case of only one coinegraing vecor, he simple -es for he coefficien of he errorcorrecion erm is asympoically equivalen o he Johansen likelihood es, so he -saisics are valid for making inferences on he significance of he parameers of adjusmen. Since PPP is a long-run heory and prices end o be sicky in he shor-run, he models have been esimaed using monhly daa o provide high-frequency modelling and beer capure hisorical movemens in he exchange rae han would have been permied by low-frequency daa. The esimaed coefficiens of he error-correcion erm are correcly signed in boh cases bu only significan for he rand-pound exchange rae. Only he rand-pound exchange rae reacs significanly o he error-correcion erm and is sensiive o i. Deviaions from he long-run rand-serling posiion quickly ranslae ino 4 percen adjusmen in he nominal rand-pound exchange rae. Nowihsanding, his suggess a relaively slow reacion o correc deviaions from PPP, hus showing considerable ineria in he adjusmen o he desired exchange rae. Alhough he models pass he diagnosic ess, in general he abiliy of he error- correcion model o explain exchange rae movemens is limied as can be inerpreed via he low adjused R 2 saisic. 4. CONCLUDING REMARKS This paper has focused on examining evidence of purchashing power pariy beween he Souh African Rand and he US Dollar and he Briish Pounds Serling. Tess of he null hypohesis of a uni roo are performed and sugges ha he variables of ineres are inegraed of he firs order. The non-saionariy of he relevan variables in level form ruled ou direcly using OLS esimaion echniques o es he heory of PPP. The Johansen maximum likelihood es has been used o deermine wheher a long-run relaionship is presen beween he exchange rae and he PPP raio. The coinegraion es indicaed ha he null hypohesis of no coinegraion among he relevan variables could be rejeced. This is one imporan finding of his sudy in ha i provides empirical suppor for he PPP hypohesis in he long-run. Jonsson (2001) also finds resuls ha srenghen he PPP hypohesis as a reasonable descripion of he long-run relaionship beween developmens in he nominal exchange rae and inflaion differenials in Souh Africa. The implicaion is ha he join movemens in he nominal effecive exchange rae and foreign prices may be reasonably refleced in domesic prices in he long- run. The shor-erm relaionship beween he rand and he oher wo currencies is weak according o he esimaes of he Vecor Auo-Regression model. Only he rand-pound exchange rae responds significanly, as expeced, o shor-erm deviaions in he long-run posiion. 8 The African Finance Journal, Volume 8, Par 2, 2006

9 REFERENCES Bahmani-Oskooee, M. (1993): Purchasing Power Pariy based on Effecive Exchange rae and Coinegraion: 25 LDCs Experience wih is Absolue Formulaion. Word Developmen 21, pp Bahmani-Oskooee, M. (1995): Real and Nominal Effecive Exchange Raes for 22 LDCs. Applied Economics 27, pp Balassa, B., (1964): The Purchasing Power Pariy docrine: a reappraisal. Journal of Poliical Economy. Bhagwai, J. (1984). Why services are cheaper in poor counries? Economic Journal, 94, pp Cheung, Y. and Lai, K.S. (2000): On cross counry differences in he persisence of real exchange raes. Journal of Inernaional Economics 50 Conejo, C., and Sheilds M, (1993): Relaive PPP and he long-run erms of rade for five Lain American Counries: A coinegraion approach, Applied Economics, 25, pp Corbae, D., and Ouliaris, S., (1988): Coinegraion and es of Purchasing Power Pariy, Review of Economics and Saisics, 70, pp Daniel, B.C. (1986): Sicky Prices and Purchasing Power Pariy Deviaions: Empirical. Implicaions, Economics Leers, 20, pp Dornbusch, R. (1976): Expecaions and Exchange Rae Dynamics, Journal of Poliical Economy 84, pp Enders, W., (1988): ARIMA and coinegraion ess of PPP under fixed and flexible exchange rae regimes, Review of Economics and Saisics, 70, pp Engle, R., and Granger, C., (1987): Coinegraion and Error-correcion: Represenaion, Esimaion and Tesing, Economerica 55(2), pp Freensra, C., and Kendall, D., (1997): Pass hrough of Exchange Raes and Purchasing Power Pariy, Journal of Inernaional Economics, 43, No. 1/2, pp Frenkel, J., and Rose, A, (1996): A panel projec on Purchasing Power Pariy, Journal of Inernaional economics, 44, No.1. Frenkel, J., (1976). A moneary approach o he exchange rae: Docrinal aspecs and Empirical evidence, Scandinavian Journal of Economics, 78,pp Froo, K.A. and Rogoff, K. (1991): Governmen Consumpion and he Real Exchange Rae: The Empirical Evidence. Mimeo, Harvard Business School. The African Finance Journal, Volume 8, Par 2,

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11 Rogoff, K., (1996): The Purchasing Power Pariy Puzzle, Journal of Economic Lieraure Vol. XXXIV, PP Samuelson, P.A. (1964): Theoreical Noes on Trade Problems. Review of Economics and Saisics, 46, pp Souh African Reserve Bank (2003) Elecronic Daabase. Available a accessed 21 May, 2005 The African Finance Journal, Volume 8, Par 2,