Does purchasing power parity hold for countries with closer economic relations?*

Transcription

1 January 2005 Draf only Does purchasing power pariy hold for counries wih closer economic relaions?* By Erik Clausen and Meher Manzur School of Economics and Finance Curin Universiy of Technology Absrac This paper provides empirical ess of he efficien-markes view of purchasing power pariy (PPP) for counries wih closer economic relaions. A cross-secion approach is adoped in which Ausralia-New Zealand and USA-Canada daa are used. The resuls are mixed. Ineresingly, he sandard (classical) procedures rejec PPP, bu heir Bayesian counerpars provide reasonable suppor for hese counries. I remains a challenge o explain his finding. Keywords: arbirage, real exchange rae, random walk, Bayesian ess JEL classificaion: F31, F37 EFM classificaion: 610, 630 Correspondence o: Associae Professor Meher Manzur Curin Business School GPO Box U1987 Perh WA 6845 Ausralia Meher.Manzur@cbs.curin.edu.au * This is only a draf version and furher refinemens are currenly underway.

2 1. Inroducion The heory of purchasing power pariy (PPP) is arguably he oldes and mos conroversial in he exchange rae lieraure. I saes ha prices across counries are arbiraged so ha hey are he same when expressed in a common currency (absolue PPP), or less sricly, he change in he exchange rae for any wo counries currencies approximaes he difference of heir respecive inflaion raes. Hisorically, his heory has experienced considerable ups and downs. Neverheless, presumably because of simpliciy and pracical versailiy, PPP has coninued o occupy he cener sage of conemporary research in inernaional finance 1. In quanifying he amoun of research ino PPP during he pas hree decades, Lan [2002] pus i, raher han collapsing, PPP research can be described as exploding (p.12). Rogoff [1996], and more recenly, Sarno and Taylor [2002], among ohers, provide excellen survey of he sae of play in his regard 2. A sylized feaure of recen work on PPP is o concenrae on esing he efficienmarkes version of PPP (ha is, he hypohesis of random walk behaviour in real exchange raes). Originally due o Roll [1979], his version implies ha he real exchange rae should follow a random walk process, which is conrary o PPP in he way ha here is no long-erm equilibrium value o which he real exchange rae ends o reurn and ha hese changes are permanen. However, empirical resuls based on his approach, mainly for major indusrialized counries, have so far been very mixed. See Lan [2002] for an excellen review of he exising lieraure. The purpose of his paper is o conduc furher ess of PPP along he above lines for Ausralia and New Zealand. For comparison purposes, we also run a parallel se of ess for USA and Canada. Noe ha hese wo pairs of counries share considerable similariies in erms of closer bilaeral economic relaions 3. Consequenly, arbirage, and hence PPP, should perform beer for hese counries pair wise. We presen he es procedures in he nex secion, followed by a discussion of empirical resuls. The las secion concludes. 2. Time-series echniques The sandard procedure o es wheher or no he real exchange rae follows a random walk process induces he following auoregressive model of he real exchange rae: r r ( µ ) ε where r is he real exchange rae a ime, µ = ρ + (1) 2 real exchange rae consisen wih PPP, and ε ~ N ( 0, σ ) µ is he long-run equilibrium value of he is he serially-uncorrelaed error erm. In his model, he auoregressive coefficien rho is he criical value for he long-run behavior of he real exchange rae. If 0 < ρ < 1, indicaes ha he real exchange rae ends o move smoohly owards is long-run equilibrium and, hence, he process is sable. This means ha in he absence of fuure shocks, he deviaion from he long-run equilibrium, r µ, would shrink in he subsequen periods when 0 < ρ < 1. However, if

3 here is a uni roo ( ρ = 1), he deviaions from he long-run equilibrium show no endency o shrink and behavior of he real exchange rae is a random walk. In he lieraure on empirical ess of PPP, here are conroversies abou he esing procedures and he power of he classical ess. One problem occurs when using convenional uni roo ess as he Dickey and Fuller [1979] o make saisical inferences abou he value of ρ, as poined ou by Hakkio [1986], in he way ha hese ess have low power agains he alernaive hypohesis ha he real exchange rae has a sizable auocorrelaion coefficien. The exising empirical lieraure suggess eiher ha he real exchange rae is a random walk, or ha i has a sizable auocorrelaion coefficien ha is saisically very difficul o disinguish from a uni roo, given he low power of he saisical ess ha have been used [Whi, 1992]. Hakkio [1986] provides evidence ha sandard saisical ess have very low power when he auocorrelaion coefficien is fairly close o uniy and ha he power of hese ess is ofen below 20 percen. Sims [1988] argues ha hese classical ess are fundamenally biased owards favoring he uni roo hypohesis, and as an alernaive he proposes a es based on Bayesian poserior odds raios ha are designed o discriminae beween a uni roo and a large bu saionary auocorrelaion coefficien. He claims ha his bias sems from he disconinuiy in he asympoic disribuion heory and disjoined confidence regions, which would encourage unreasonable approaches o inference [Sims, 1988]. The alernaive es proposed by Sims [1988] for he presence of uni roos is given by a weighed average of he likelihood funcion over all poins consisence wih he null hypohesis, divided by a similar funcion for he alernaive hypohesis, wih weighs derived from he prior disribuion of he parameers. To apply his procedure o equaion (1), Sims [1988] proposes a probabiliy α for a prior disribuion for ρ which spreads beween 0 < α < 1, and gives he uni roo ( ρ = 1) probabiliy ( 1 α ). By conras, Sims and Uhlig [1988] demonsraes ha when using classical uni roo ess, in he case of an OLS esimaed ρˆ equal o 0.95, he implici prior reas he values of ρ around uniy as being wo o hree imes more likely han values around 0.90, even hough he likelihood funcion is symmeric around And, more disurbingly, he prior implici in classical ess gives even more weigh o values of ρ above uniy han o values around uniy, and he weigh given o he region above uniy increase as ρˆ approaches uniy from below [Whi, 1992]. To derive he approximae likelihood funcion, Sims [1988] defines 2 T ([ 1 ˆ ρ ]/ σ p ), where ( σ 2 / r 1 ) ρ = 1, ( T ) disribuion evaluaed a T, and ( T ) σ ρ, o be he convenional saisic for esing φ o be he cumulaive disribuion funcion for he sandard normal θ o be is probabiliy densiy funcion. Sims hen shows ha in large samples he poserior odds raio favors he null hypohesis ( ρ = 1) if: ( 1 α ) θ ( T ) σ [ αφ( T )] ρ > 1. (2) The dispariy beween his crierion and classical hypohesis ess, is no only because of he role of he prior disribuion, bu also because he presence of σ in he denominaor. ρ

4 If he null hypohesis ( ρ = 1) is rue, σ ρ should shrink much faser as sample size increase han when he alernaive hypohesis is rue. This crierion ends o favor he null hypohesis ( ρ = 1) when σ ρ is small. By conras, likelihood raio ess fail o use all he informaion in σ ρ. Sims [1988] suggess ha in acual applicaions using quarerly economic daa, he alernaive hypohesis can reasonably be limied o values of ρ approximaely beween 0.84 and uniy 4. Therefore, Sims [1988] proposes he following revised crierion where he null hypohesis ( ρ = 1) is favored if: where log [ 1 α ] 2 [ 1/ s] 2 ( / α ) log( σ ) + 2log( 1 2 ) γ > 0 (3) γ 2 T, s is he number of periods per year (for example, four for quarerly daa). Smaller values of σ favor he uni roo hypohesis, while larger values of T favor he alernaive hypohesis. The modeling objecive of he Bayesian approach is no o rejec or fail o rejec a hypohesis, bu o deermine how probable a hypohesis is relaive o oher compeing hypohesis. The mos common mehod is o calculae poserior odds raios for various compeing hypohesis based on prior and sample informaion. This gives he researcher he odds in favor of he one hypohesis relaive o oher compeing hypohesis [Ahking, 2002]. ρ 3. Empirical resuls The daa used in his paper, all colleced from IMF Inernaional Financial Saisics, consis of quarerly nominal end-of-period exchange raes and consumer price indices 5 covering he period 1986:1 o 2004:2 for Unied Saes, Canada, Ausralia and New Zealand. Year 2000 is he base year for he consumer price indices for all counries. Noe ha heunied Saes and Canada have experienced free floaing exchange raes since he breakdown of he Breon-Woods regime in 1973, and, Ausralia s exchange rae became floaing in 1983, New Zealand did no exhibi a free floaing exchange rae unil March To conduc comparable examinaions, we choose he sar dae of he sample period by allowing some ime for he sysem o maure, and he end period is dicaed by he availabiliy of his daa. 3.1 Ausralia and New Zealand As discussed above, he heory of purchasing power pariy implies ha he real exchange rae is saionary. To es for saionariy, (augmened) Dickey-Fuller ess for he presence of a uni roo are performed. Simulaneously, he Sims es for he presence of a uni roo is also carried ou for comparison purposes. Firs, he (augmened) Dickey- Fuller ess are conduced on he real exchange raes beween Ausralia and New Zealand, and he resuls are given in Table 1.

5 Table 1: (Augmened) Dickey-Fuller ess for a uni roo in he real exchange rae beween Ausralia and New Zealand using daa in levels Dickey-Fuller es DF ADF1 ADF2 ADF3 ADF No rend Ausralia / New (1.6213**) (1.9445) (2.0111) (2.0119) (1.9663) Zealand Wih rend (1.6222**) (1.9433) (2.0162) (2.0211) (1.9755) Noe: The criical values for he (A)DF es a he 95% significan level are (wihou rend) and (wih rend). Durbin-Wason saisic is in parenhesis. The criical values for he DW es a he 95% significan level are 1.58 and One aserisk denoes neiher rejecing nor acceping. As can be seen, using his sandard es, i is no possible o rejec he null hypohesis of a uni roo. The Durbin Wason Q-es, shown in parenhesis, is indicaing auocorrelaion in he lagged residuals using he Dickey-Fuller es. Wih lags inroduced for he augmened Dickey-Fuller ess o eliminae significan auocorrelaion in he lagged residuals, he resuls remain he same indicaing ha he real exchange rae is I ( 1) and requires o be differenced once o achieve saionariy. We nex employ he Sims es procedure, and he resuls are given in Table 2. The firs column in Table 2 is he -squared which is used as he es saisic. The Schwarz limi and he Small sample limi are he asympoic and small sample Bayesian criical values for he es saisic. As can be seen, he es saisics are larger han, or very close o, is criical value, indicaing ha he null hypohesis of a uni roo is rejeced. Accordingly, conrary o he Dickey-Fuller resuls, he Sims es indicaes ha he null hypohesis of a random walk is rejeced. The Marginal alpha presened in he las column of Table 2, provides a measure of how srong he rejecion of he null Table 2: Sims ess for a uni roo in he real exchange raes beween Ausralia and New Zealand using daa in levels Sims es γ Squared Schwarz limi Small sample limi Marginal alpha No lags lag No rend 2 lags lags Ausralia / 4 lags New Zealand No lags lag Wih 2 lags rend 3 lags lags Noe: Bayesian ess using RATS.

6 hypohesis is. The Marginal alpha is he value of alpha a which he poserior odds for and agains he uni roo are even. The smaller he value is, he sronger is he daa s rejecion of he uni roo hypohesis. On an ex pos basis, i is possible o calculae he minimum prior probabiliy on he null hypohesis, 1-α *, ha would be necessary in order o force he Sims crierion o favor he null hypohesis. As he las column in Table 2 indicaes, he power of he rejecion ranges beween and , which indicaes a rejecion of he uni roo by a comforable margin. These resuls from he Sims es are in favor of he long-run PPP. Ineresingly, hese resuls are consisen wih Whi [1992], and Manzur and Ariff [1995]. 3.2 Do we have a similar sory for USA and Canada? The resuls for Ausralia and New Zealand above are puzzling. The classical uni roo ess rejec PPP decisively, while he Bayesian Sims es lends solid suppor o i. Do we ge similar resuls for USA and Canada? Table 3 presens he ADF resuls for USA and Canada. As can be seen, hese resuls are very similar o hose in Table 1. Tha is, he USA/Canada real exchange rae conains a uni roo. Table 3: (Augmened) Dickey-Fuller ess for a uni roo in he real exchange rae beween Unied Saes and Canada using daa in levels Dickey-Fuller es DF ADF1 ADF2 ADF3 ADF No rend Unied Saes / (1.8365) (2.0095) (2.0361) (2.0068) (1.8730) Canada Wih rend (1.8138) (2.0238) (2.0812) (2.0552) (1.8561) Noe: The criical values for he (A)DF es a he 95% significan level are (wihou rend) and (wih rend). Durbin-Wason saisic is in parenhesis. The significan poins for he DW es a he 95% significan level are 1.58 and We nex performed he Sims es on he real exchange rae beween Unied Saes and Canada, and he resuls are given in Table 4. As can be seen, he resuls are significanly differen from hose in Table 2. Here, he daa canno rejec he null hypohesis of uni roo, excep when a rend erm is inroduced and we go up o he fourh lag. Unied Saes / Canada Table 4: Sims ess for a uni roo in he real exchange raes beween Ausralia and New Zealand using daa in levels No rend Sims es γ Squared Schwarz limi Small sample limi Marginal alpha No lags lag lags

7 Wih rend 3 lags lags No lags lag lags lags lags Noe: Bayesian ess using RATS. 6. Conclusion This paper employs boh classical ADF and he Bayesian Sims ess o evaluae he random walk hypohesis of he real exchange rae for Ausralia and New Zealand on one hand, and he USA and Canada on he oher. The resuls are srikingly mixed. The ADF ess are no able o rejec he null hypohesis of a uni roo for he real exchange rae beween Ausralia and New Zealand. However, he Sims es ends o rejec he uni roo hypohesis. For he real exchange rae beween USA and Canada neiher he ADF nor he Sims ess are able o rejec he null hypohesis of a uni roo. These resuls corroborae o he idea ha PPP puzzle could be beyond a saisical issue of wheher he real exchange rae conains a uni roo, and consequenly, focus needs o be shifed on o he economic sources of deviaions from PPP (see Higgins and Zakrajšek, 1999). Reference Ahking, F. W. [2002], Is he Bayesian Approach Necessarily Beer Than he Classical Approach in Uni-Roo ess?, Working Paper, Universiy of Connecicu, 18 Cheung, Y. W. and Lai, K. S. [1993], A Fracional Coinegraion Analysis of Purchasing Power Pariy, Journal of Business and Economic Saisics, 11, p Diebold, F. X. e al, [1991], Real Exchange Raes Under he Gold Sandard, Journal of Poliical Economy, 99, p Frenkel, J. A. [1978], Purchasing Power Pariy: Docrinal Perspecive and Evidence from he 1920 s, Journal of Inernaional Economics, 8-2, p Frenkel, J. A. [1980], The Collapse of Purchasing Power Pariy During he 1970 s, European Economic Review, 7, p Hakkio, C. S. [1986], Does he Exchange Rae Follow a Random Walk? A Mone Carlo Sudy of Four Tess for a Random Walk, Journal of Inernaional Money and Finance, 5, p

8 Higgins, M. and Zakrajšek, E. [1999], Purchasing Power Pariy: Three Sakes Through he Hear of he Uni Roo Null, Saff Repor No. 80, Federal Reserve Bank of New York Isard, P. [1977], How Far Can We Push he Law of One Price?, American Economic Review, 67, p Kaseli-Papaefsraiou, L. T. [1979], The re-emergence of he Purchasing Power Pariy Docrine in he 1970 s, Princeon Sudies in Inernaional Finance, 13 Kravis, I. B. and Lipsey, R. E. [1971], Price Compeiiveness in World Trade, New York: Colombia Universiy Press Lan, Y. [2002], The Explosion of Purchasing Power Pariy, in Manzur, M. (ed.), Exchange Raes, Ineres Raes and Commodiy Prices, Edward Elgar Publishing Ld., p Manzur, M. [1990], An Inernaional Comparison of Prices and Exchange Raes: a New Tess of Purchasing Power Pariy, Journal of Inernaional Money and Finance, 9-1, p Manzur, M. and Ariff, M. [1995], Purchasing Power Pariy: New Mehods and Exensions, Applied Financial Economics, 5, p Mussa, M. [1979], Empirical Regulariies in he Behavior of Exchange Raes and Theories of he Foreign Exchange Marke, in Brunner, K. and Melzer, A. H. (ed.), Policies for Emloymen, Prices and Exchange Raes, vol. 11, Rocheser, NY: Carnegie Rocheser Conference Series Officer, L. H. [1976], The Purchasing Power Pariy Theory of Exchange Raes: a Review Aricle, IMF Saff Paper, Inernaional Moneary Fund, 23, p Rogoff, K. [1996], The Purchasing Power Puzzle, Journal of Economic Lieraure, 34. p Roll, R. [1979]. Violaions of Purchasing Power Pariy and heir Implicaions for Effician Inernaional Commodiy Markes, in Serna, M. and Szego, G. P. (ed.), Inernaional Finance and Trade, Cambridge: Ballinger Publishing Company, p Sarno, L. and Taylor, M. P. [2002], Purchasing Power Pariy and he Real Exchange Rae, IMF Saff Paper, Inernaional Moneary Fund, 49-1 p Sims, C. A. [1988], Bayesian Skepicism on Uni Roo Economerics, Journal of Economic Dynamics and Conrol, 12, p Whi, Jr. J. A. [1992], The Long-Run Behavior of he Real Exchange Rae: A Reconsideraion, Journal of Money, Credi and Banking, 24-1, p.72-82

9 Endnoes 1 The beauy of PPP is perhaps is simpliciy and pracical versailiy: i serves as a benchmark o judge he level of an exchange rae, which, in urn, becomes a useful predicion model for he raes. 2 The mos deailed summary of early work on PPP is Officer (1976). See also Frenkel (1978, 1980), Isard (1977), Kravis and Lipsey (1971), Kaseli-Papaefsraiou (1979), Mussa (1979). The firs among he many papers uncovering long-erm PPP relaionships was Manzur (1990), bu see also Diebold, Hushed and Rush (1991) and Cheung and Lai (1993). 3 The similariies in he relaionship beween Unied Saes and Canada and he relaionship beween Ausralia and New Zealand are far more han jus limied o geographic posiions. Boh Canada and New Zealand is considered as a lile broher o Unied Saes and Ausralia, respecively, in an economic sense. New Zealand o Ausralia is like wha Canada is o USA. As an affluen, high-ech indusrial sociey, Canada closely resembles he Unied Saes in is marke-oriened economic sysem, paern of producion, and high living sandards. This close cross-border relaionship propelled he Norh American Free Trade Agreemen (1994). Similarly, he Ausralia-New Zealand Closer Economic Relaions Trade Agreemen (1983), popularly known as he CER Agreemen, creaed convenional free rade in he rans-tasman area involving he removal of all border resricions on rade in goods. 4 Because 0.84 o he power of four, equals he lower bound for annual daa (0.5,1); he inerval is (0.94,1) for monhly daa. 5 The use of consumer price indices as a measure of a naion s price level has been conroversial in he PPP lieraure. The roos of hese conroversies are he inclusion of non-raded goods, which can give a wrong impression of one naion s price level. However, mos auhors favor his broad index, while ohers favor a narrower index wih heavy weigh on radable goods, such as he wholesale price index.