An Alternative Test of Purchasing Power Parity

Transcription

1 An Alernaive Tes of Purchasing Power Pariy Frederic H. Wallace* Deparmen of Managemen and Mareing Prairie View A&M Universiy Prairie View, Texas and Gary L. Shelley Deparmen of Economics, Finance, and Urban Sudies Eas Tennessee Sae Universiy Johnson Ciy, Tennessee 3764 February 2005 *Corresponding Auhor: Phone: (936) We would lie o han Alan Taylor for providing he daa as well as he RATS code for dealing wih missing observaions. Absrac: The long-horizon approach of Fisher and Seaer (993) is applied o he daa developed by Taylor (2002) o es for purchasing power pariy (PPP). Even afer accouning for he low power of he es, he evidence is generally supporive of PPP.

2 2. Inroducion In recen years, purchasing power pariy has been exensively esed using more powerful uni roo ess, coinegraion ess, and nonlinear mehods. Rogoff (996), Sarno and Taylor (2002), and Taylor and Taylor (2004) provide surveys of his lieraure. Alhough he evidence is no conclusive, he empirical wor generally provides some suppor for PPP in he long run alhough mos researchers would probably agree ha deviaions from PPP may exis and persis in he shor run. The Fisher-Seaer (993) es has been applied o long run moneary neuraliy and superneuraliy; however, here is jus one published paper, Serleis and Gogas (2004), ha uses his mehod o es for purchasing power pariy, and ha paper examines only he pos-breon Woods period. In his paper, he long-horizon approach of Fisher-Seaer (henceforh FS) is applied o he daa se, developed by Taylor (2002), which includes a leas a cenury of observaions for weny counries. Resuls end o suppor Taylor s conclusions ha PPP canno be rejeced for mos included counries. 2 In he following secion, he daa and FS procedure are briefly described. The empirical resuls are more fully discussed in secion 3 and wih conclusions offered in secion Daa and Mehodology The daa se includes annual observaions for he nominal exchange rae and he consumer price index for weny counries. 3 The daa run hrough 996, wih beginning daes varying from 870 o 893, allowing PPP o be esed using a leas 00 annual More accuraely, as emphasized by Taylor and Taylor, he evidence suppors mean reversion of he real exchange rae, a necessary bu no sufficien condiion for PPP. Implicily, researchers end o assume ha mean reversion implies ha he real exchange rae is revering o is PPP level and we follow his pracice. 2 Taylor esed for saionariy of he real exchange raes of hese counries using a generalized leas squares version of he ADF es. 3 Counries include Argenina, Ausralia, Belgium, Brazil, Canada, Denmar, Finland, France, Germany, Ialy, Japan, Mexico, Neherlands, Norway, Porugal, Spain, Sweden, Swizerland, Unied Kingdom, and he Unied Saes. 2

3 3 observaions for each counry. Small gaps in he series, generally corresponding o war years, are eliminaed by linear inerpolaion as in Taylor. His paper may be consuled for a more complee descripion of he daa. Serleis and Gogas use he FS es o assess PPP for 2 OECD counries using quarerly daa for 973:-998:4. The correc specificaion of he FS es depends on he orders of inegraion of he variables of ineres. Because he nominal exchange rae and he price level variables are I() for all counries in he Serleis and Gogas daa se, heir version of he FS es is given by equaion (), ( x x ) u s s = q + h + = K () where s is he logarihm of he period nominal exchange rae measured as he price of a uni of foreign currency in erms of eiher he US dollar, German Deuschemar, or Japanese yen and x i is he logarihm of he raio of he domesic price level o he foreign price level. 4 The es involves regressing he + period change in he nominal exchange on he + difference in he relaive price levels for ranging from o a pre-seleced maximum K. The erms q and h are he inercep and slope coefficien, respecively, for he + difference while u i is he period i whie noise error erm. They find some wea suppor for PPP, alhough hey noe ha he power of he FS es is low, a problem originally addressed by Coe and Nason (2002). As in Serleis and Gogas, all he variables in Taylor s daa se are inegraed of order one, however, our formulaion of he FS es, given by equaion 2, differs somewha from heirs. d d US US ( p p ) + ε = a + b = K (2) 4 See heir paper for more deail on he derivaion of he es as applied o PPP. 3

4 4 Here d is he log of he dollar denominaed foreign price level defined as: d = p + s (3) f where f p is he log of he produc of he foreign price level, and s is he log of he nominal exchange rae (quaniy of US dollars per uni of foreign currency). US p is he ime US price level, a and b are parameers, and ε is a whie noise error erm. If PPP holds he b will approach one as ges larger. Sandard pracice is o esimae b for each value of using OLS and consruc 95- percen confidence inervals for he b s using he Newey-Wes correcion and a - disribuion wih T/ degrees of freedom. T is he oal number of observaions. Under he null hypohesis ha PPP holds, he b converge o one as increases, and PPP is rejeced if he confidence inerval does no include uniy as becomes large. There are wo reasons for he change in he formulaion of he es from ha derived in Serleis and Gogas. Firs, if he + period change in he nominal exchange rae were he dependen variable as in heir wor, zeroes would frequenly appear because our sudy spans exended periods of fixed exchange rae regimes. 5 Use of he change in he dollar-denominaed price level as he dependen variable avoids his siuaion by allowing changes in eiher he nominal exchange rae or he foreign price level o adjus he dollar denominaed foreign price level o mainain PPP. Second, he FS es requires ha he explanaory variable be exogenous. While he foreign price level may no be independen of he nominal exchange rae for hose counries in which foreign rade accouns for a 5 Noe ha heir daa se includes only he pos-breon Woods period of floaing exchange raes while ours includes periods of boh fixed and floaing exchange rae regimes wih mos of observaions from imes of fixed nominal raes. 4

5 5 significan share of GDP, he US price level is more liely o be exogenous wih respec o he dollar-denominaed price level elsewhere. 3. Tes resuls. The FS mehodology requires ha he orders of inegraion of he U.S. price level and each of he foreign, dollar denominaed price levels be deermined. All series show upward movemen, herefore he ADF es equaions conain boh a consan and rend. Because he resuls may depend on he number of lags, he ADF ess are carried ou using four alernaive lag selecion echniques. Lag lengh is deermined using he AIC, BIC, and an LM es crieria, as well as a general o simple (GS) echnique. For he LM es sufficien lags are included in he es equaion o rejec serial correlaion in he es equaion residuals a a 5% significance level. The GS echnique begins wih a maximum number of lags and hen he las lag is eliminaed if i is no significan a a 5% level. The process is repeaed unil he las lag in he es equaion is significan. A maximum lag lengh of four years was considered in each approach. All of he ADF ess fail o rejec uni roos in he U.S. price level and all he dollar equivalen foreign price levels. 6 The ADF-GLS es developed by Ellio, Rohenberg, and Soc (996), which has greaer power han sandard ADF es, also is employed. Again, a uni roo canno be rejeced for each series. Finally, he Kwiaowsi, Phillips, Schmid, Shin (992) or KPSS es of he null hypohesis of rend saionariy versus an alernaive hypohesis of a random wal wih drif is used. For each series, rend saionariy is rejeced in favor of he uni roo alernaive. Given ha all he es resuls sugges each series has a single 6 ADF es resuls and hose of he oher uni roo procedures discussed below are available from he auhors. 5

6 6 uni roo, he FS es as presened in equaion (2) can be used o es long-run PPP beween he US and he oher nineeen counries in he sample. 7 Resuls of he FS ess are presened in he figures in Panel A. For seven of he 9 series esed, none of he b is significanly differen from one (i.e. one is wihin he 95% confidence inerval), hus PPP canno be rejeced in hese cases. The seven counries are Argenina, Belgium, Brazil, Finland, Mexico, Sweden, and he U.K. For hree addiional counries (Ausralia, Germany, and Ialy) we conclude ha he PPP null canno be rejeced because he b for large values of are no significanly differen from one. In wo indeerminae cases, France and Norway, he lower confidence bound is very close o one for some large values of. The FS es resuls clearly do no suppor PPP for he oher seven counries. PPP is rejeced a mos values of for Canada and Japan and a large values of for Denmar, he Neherlands, Porugal, Spain, and Swizerland. 7 There is no indicaion of a second uni roo in any of he series. 6

7 7 Panel A-Plos of he b Coefficiens and 95% Confidence Inervals 2.5 FS-Tes of PPP in Argenina.50 FS-Tes of PPP in Ausralia FS-Tes of PPP in Belgium 2.5 FS-Tes of PPP in Brazil FS-Tes of PPP in Canada 2.0 FS-Tes of PPP in Denmar FS-Tes of PPP in Finland.6 FS-Tes of PPP in France FS-Tes of PPP in Germany.50 FS-Tes of PPP in Ialy c oefficiens c oefficiens

8 FS-Tes of PPP in Japan 2.0 FS-Tes of PPP in Mexico c oefficiens c oefficiens FS-Tes of PPP in he Neherlands.6 FS-Tes of PPP in Norway c oefficiens FS-Tes of PPP in Porugal 2.2 FS-Tes of PPP in Spain FS-Tes of PPP in Sweden 2.00 FS-Tes of PPP in Swizerland c oefficiens c oefficiens FS-Tes of PPP in he UK

9 9 The relaively wide confidence inervals shown in he figures are consisen wih he conclusion of Coe and Nason (2002, 2004) ha he FS es has low power. To assess he exen of his problem, we employ he inverse power (IP) funcion derived by Andrews (989). Table displays he b coefficien esimaes for = 0, 5, 20, 25, 30 for each counry for which he FS es fails o rejec PPP. Also shown is he corresponding inerval, ±b.50, obained from he IP funcion. Only if he rue b coefficien lies ouside his inerval would he FS es rejec a false null hypohesis of PPP a a 50% or beer probabiliy. Thus, as he ±b.50 inerval becomes wider, he power of he FS es decreases. Taing Argenina as an example, only if he rue b 30 were ouside he inerval (.5427,.4573) would he FS es have a 50% or beer chance of rejecing PPP. This relaively wide inerval indicaes ha i would be difficul o rejec PPP for Argenina even if he proposiion were false. Thus, he FS es s failure o rejec he null hypohesis mus be regarded as wea suppor, a bes, for PPP. Similarly, he inerval for Brazil a = 30 is (.08,.9882) suggesing ha he failure o rejec PPP for Brazil is almos meaningless, as one would fail o rejec PPP for almos any reasonable parameer values. However, he siuaion is beer for he oher counries, wih he wides inerval a = 30 for Mexico ( ) and he ighes for he UK ( ), giving us more confidence in he FS resuls for he remaining counries. In summary, he bes suppor for long run PPP, relaive o he US price level, is found for Ausralia, Belgium, Finland, France, Germany, Ialy, Mexico, Norway, Sweden, and he UK. The FS ess rejec PPP in Canada, Denmar, Japan, he Neherlands, Porugal, Spain, and 9

10 0 Swizerland. For Brazil and Argenina, he FS ess fail o rejec PPP, bu he IP funcion shows ha he resuls for hese wo counries are no informaive. 4. Conclusions Our findings are broadly consisen wih Taylor s es resuls. Excep for Norway, in each of he counries for which our FS es resuls suppor PPP, Taylor rejecs a uni roo in he real exchange rae a he 5% level or beer. Furhermore, Taylor also finds ha uni roos can be rejeced in real exchange raes for Argenina and Brazil hus consisen wih our, admiedly low power, FS resuls for hese wo counries. Taylor finds weaer evidence for PPP in he real exchange raes of Canada, he Neherlands, and Porugal wih uni roos rejeced a only a 0% level a bes. Similarly, our FS es resuls do no suppor PPP for hese hree counries. Only for hree counries (Denmar, Spain, and Swizerland) do Taylor s uni roo ess show evidence for PPP while he FS es resuls rejec purchasing power pariy. 0

11 Table -Seleced Esimaed b & Andrews Inverse Power Bounds Argenina Ausralia Belgium Brazil Finland France Germany Ialy Mexico Norway Sweden UK =0 =5 =20 =25 =30 bˆ b b bˆ b b bˆ b b bˆ b b bˆ b b bˆ b b bˆ b b bˆ b b bˆ b b bˆ b b bˆ b b bˆ b b ,.50,.50,.50,.50,.50,.50,.50,.50,.50,.50,.50,.50,.50,.50,.50,.50,.50,.50,.50,.50,.50,.50,.50,.50

12 2 References Coe, P. J. and Nason J.M., The long-horizon regression approach o moneary neuraliy: how should he evidence be inerpreed? Economics Leers 78, Coe, P.J. and Nason J.M., Long-run neuraliy and long-horizon regressions. Journal of Applied Economerics 9, Fisher, M.E. and Seaer J.J., 993. Long run neuraliy and superneuraliy in an ARIMA framewor. American Economic Review 83, Kwiaowsi, D.; Phillips, P.C.B.; Schmid, P.; and Shin Y., 992. Tesing he null hypohesis of saionariy agains he alernaive of a uni-roo, Journal of Economerics 54, Rogoff, K., 996. The purchasing power pariy puzzle. Journal of Economic Lieraure 34, Sarno, L. and Taylor M.P., The Economics of Exchange Raes. Cambridge Universiy Press, Cambridge. Serleis, A. and Gogas P., Long-horizon regression ess of he heory of purchasing power pariy. Journal of Baning & Finance 28, Taylor, A.T., A cenury of purchasing-power pariy. Review of Economics and Saisics 84, and Taylor M.P., The purchasing power pariy debae. Journal of Economic Perspecives 8,