Doctrine of Purchasing Power Parity: An Analysis based on Cointegration and Wavelet regression

Transcription

1 IOSR Journal Of Humaniies And Social Science (IOSR-JHSS) e-issn: , p-issn: Volume 7, Issue 4 (Jan. - Feb. 3), PP Docrine of Purchasing Power Pariy: An Analysis based on Coinegraion and Wavele regression Niyai Bhana Arif Billah Dar Amaresh Samanaraya 3,,3 (Deparmen of Economics, Pondicherry Universiy, Puducherry-654, India) Absrac: The sudy revisis he docrine of purchasing power pariy (PPP) for four maor bilaeral exchange raes agains Indian rupee namely; rupee-dollar, rupee-pound, rupee-yen and rupee-euro exchange raes. Firs, he long run validiy of he hypohesis is esed using Granger-Engle coinegraion along wih Johansen mulivariae coinegraion echnique. Boh he ess provide suppor for he PPP hypohesis a he long run. Furher, he issue is examined under ime domain framewor using recenly advanced Wavele-based regression analysis ha provide decisive suppor for he PPP over 4~8 monhs horizon for rupee-dollar exchange rae and over 4~8 monhs as well as over more han 3 monhs horizon for he rupee-yen exchange rae. Keywords: Coinegraion, Foreign exchange rae, Purchasing power pariy, Wavele. I. Inroducion Undersanding he behaviour of exchange rae is one of he highly exciing and debaed issues wihin he area of inernaional finance. Inense research aciviies have been carried ou by researchers and academicians o race he behaviors of exchange rae boh under he perspecive of shor and long run. This sudy aemps o analyse he behaviour of exchange rae in he ligh of mos prominen heory of exchange rae deerminaion, namely, Purchasing Power Pariy (PPP). The PPP is one of he cornersones in he inernaional macroeconomics and provides fundamenal building bloc for many sophisicaed exchange rae models. Based on he Law of One Price (LOP), he PPP hypohesis saes ha prices in he wo differen counries should be equal o each oher when expressed in erms of he same currency. Consruced as a long-run heory of equilibrium exchange rae, PPP duly recognizes he possible deviaions in he shor-run from he pariy. I, however, argues for forces capable of resoring he pariy in he long-run. In is absolue version PPP requires he nominal exchange rae o be proporional wih he raio of he domesic o he foreign price level. This form of PPP is quie unliely o hold precisely because he exisence of ransporaion cos, disoring effecs of ariff and non-ariff barriers o rade and imperfec informaion. Noneheless, i is argued ha a weaer form of PPP nown as relaive PPP can be expeced o hold even in he presence of such disorion. This weaer form of PPP argues ha exchange rae will adus by he amoun of inflaion differenial beween wo economies. There are various consideraions from policy perspecive ha maes empirical validiy of he PPP docrine highly crucial. Firs, reecion of PPP in some sense indicaes persisen misalignmen of exchange rae (Alba and Par, 5). Second, for deermining pariies of exchange rae PPP concep is ofen pu ino pracice. Third, i is also used o esimae exchange rae misalignmen i.e. deviaion of exchange rae from equilibrium level, and in devising proper policy response. Las bu no he leas, he hypohesis of PPP provides he fundamenal assumpion of many exchange rae models ha has developed in laer sage e.g. flexible-price moneary model, over-shooing model of Dornbusch (976). I is, hus, imperaive o examine he validiy of PPP hypohesis empirically. There has been exensive research aciviy carried ou over he years evaluaing empirical validiy of he PPP docrine. No conclusive evidence ye, however, reached a. The suppor for PPP has waxed and waned over he years. Woring wih very long panel daa se; covering say a paricular era or moneary regime, sudies of Officer (98), Abauf and Jorion (99), Lohian (99), Lohian and Taylor (996) amongs ohers uncovered srong evidence of mean reversion in real exchange rae validaing PPP hypohesis. On he oher side, he empirical sudies based on ime series analysis of shor spans of daa for recen floaing-raes (e.g. Frenel; 98, Meese and Rogoff; 983) led o mass reecion of PPP hypohesis. These sudies, neverheless, have been criicized for heir low power of ess and insufficien ime-series variaion. The research aciviy over las wo decades, however, has winessed a renewed ineres in PPP ha explois more daa and sophisicaed higherpowered echniques and non-linear mehods o overcome shorcomings of earlier sudies. This generaion of research [Cheung and Lai 998, Taylor and Sarno 998, Culver and Papell 999, Bahmani-Osooee and Gelan 6; Wallace 8; Chang e al., ] have demonsraed validiy of PPP wih reecion of he so-called random wal hypohesis and mean reversion of real exchange rae. Wih hese newly emerging lieraures, now i appears ha in he long run PPP indeed holds wih a half-life of deviaions being 3 o 5 years (Taylor 995; Froo and Rogoff, 995, Taylor and Taylor, 4). 9 Page

2 Docrine of Purchasing Power Pariy: An Analysis based on Coinegraion and Wavele regression Moreover, he plehora of empirical lieraure on he Purchasing Power Pariy seems highly lop-sided given he disproporionaely hin number of sudies available in he conex of developing economies. One of he earlies sudies of PPP on developing economies is conduced by McNown and Wallace (989); ha esed for coinegraion using boh monhly CPI and WPI daa for four high inflaion counries of Argenina, Brazil, Chile, and Israel. Using Engle-Granger wo-sep mehod, hey found supporive evidence of PPP in Argenina, Chile, and Israel. More recenly, a sudy by Doganlar e al. (9) examined he PPP hypohesis for en emerging mare economies including India. Employing Johansen coinegraion echnique, he sudy reeced co-inegraion beween he exchange rae and prices for eigh counries including India. Sudies in Indian conex are relaively handful. Among ohers, Kularni and Charaborhy (99) using Ordinary Leas Squares have found evidence supporing relaive PPP for INR-USD exchange rae over he period 977 hrough 987. Under coinegraion framewor Moshin and Kamaiah (993), however, repor no long-run relaionship beween exchange rae of INR vis-à-vis USD, Pound, German Mar and Japanese Yen, and he corresponding price raios; hus, reecing long run validiy of PPP. In anoher rigorous sudy Nag and Mira (998) repored mixed resul for Rupee-Dollar exchange rae for he period 957 o June 997. Woring wih Engle-Granger wo-sep co-inegraing regression framewor, hey found some evidence of coinegraion a only percen level of significance; however he coefficien resricions imposed by absolue and relaive PPP were reeced by Wald s es. Furher, Johansen s coinegraion es under VAR se-up hough showed exisence of a leas one co- inegraing vecor, he error correcion coefficiens urns ou no o be significan. The sudy, hus, concludes ha in he long run here is unmisaable evidence for some degree of impac of changes in price-raios on he nominal exchange rae, hough srengh of his relaion is no as rigid and srong as prediced by PPP. Employing higher-powered uni-roo ess e.g. ADF-GLS and ADF-WS; ha promise o improve power of small sample, Kohli () showed ha boh CPI-deflaed as well WPI-CPI raio deflaed real rupee-dollar exchange rae o exhibi mean-revering endencies over floaing regime (993: o :3) of India. However, he daa se did no suppor mean-reversion or saionariy of rade-weighed REER series over he same period. On he above bacdrop, i may be noed ha exchange rae of Indian Rupee vis-à-vis US dollar has winessed significan swings in he recen years, paricularly in he run up o and afermah of recen global financial crisis. The purpose of he presen sudy is wo-fold. Firsly, wih laes daa, i aemps o reexamine relaive version of PPP for Indian Rupee agains he currency of is leading rade parners USA, Japan, Grea Briain and European Union using various economeric mehodologies viz; Granger-Engle -sep regression, Johansen mulivariae coinegraion procedure and finally recenly developed mehodology of semi-parameric wavele based regression. Secondly, he maor innovaion of his paper lies wih applicaion of wavele based regression echnique ha enables o decompose he variable of exchange rae change and inflaion differenial ino differen ime scales and hen o ess he validiy of PPP a differen ime scales using Ordinary Leas Squares (OLS). This paper is organized as follows. Secion II ses ou he mehodology used in his sudy. Secion III provides deails of daa used for esimaion. Secion IV repors he resuls wih inferences and he final secion V concludes. II. Mehodology The presen sudy use wo differen mehods of coinegraion es are used o reexamine he long run equilibrium relaionship beween nominal exchange rae, domesic and foreign price series; viz. Granger-Engle -sep coinegraion regression (987) and Johansen-Juselius mulivariae coinegraion echnique (99). The Granger-Engle coinegraion (987) involves wo-sep esimaion process: regression analysis based on he Ordinary Leas Squares (OLS) mehod followed by saionariy es of he regression residual. This approach, however, fails o deec he number of coinegraion vecors in case of more han wo variables and suffers from simulaneous equaion bias. The coinegraion echnique of Johansen and Juselius (99) neverheless, addresses hese issues employing sysem of VAR o deec number of coinegraing vecors and he Maximum Lielihood (ML) mehodology for he esimaion. Boh of hese ess have been popularized by many applicaions and are considered as sandard procedures for esing coinegraion. Deail discussion of hese mehodologies discussion is hence avoided. The equaion esimaed for Bivariae Granger-Engle coinegraing regression: ln E (ln P ln P ) u () and for he Johansen mulivariae coinegraion mehod we consider he following vecor in VAR framewor: ln( E )ln( P )ln( P ) () For furher reference see Granger-Engle (987), Johansen and Juselius (99), and Johansen (99). Page

3 Docrine of Purchasing Power Pariy: An Analysis based on Coinegraion and Wavele regression where, ln E is he log of he domesic exchange rae per uni of foreign currency, ln P is he log of domesic price index and ln P is he log of foreign price index and u is sochasic disurbance erm. We also use he wavele mehodology o decompose he exchange rae change and inflaion differenials ino differen ime scales. Waveles are mahemaical funcions ha give he mahemaically equivalen represenaion of daa and cu up daa ino differen frequency componens, wih a resoluion mached o is scale. These funcions use basis funcion ha is dilaed (hrough a scale or dilaion facor) and shifed (hrough a ranslaion or locaion parameer) along he signal so as o provide a ime-frequency represenaion where all informaion is associaed wih specific ime horizons and locaions in ime. Wavele are similar o a sine and cosine funcions because hey oscillae around zero, bu differ because hey are well localized boh in he ime and frequency domains. In conras o Fourier analysis, waveles are compacly suppored as all proecions of a signal ono he wavele space are essenially local, no global, and hus need no be homogeneous over ime. Waveles are flexible in handling a variey of non-saionary signals. Waveles, in opposiion o ime and frequency domain analysis, consider non-saionariy as an inrinsic propery of he daa raher han a problem o be solved by pre-processing he daa. There are wo basic wavele funcions: he faher wavele and he moher wavele. Formally he faher waveles can be represened as / (3) Defined as non-zero over a finie ime lengh suppor ha corresponds o moher waveles given by /. (4) where J=,,3,...,J in a J-level decomposiion. The faher wavele inegraes o one and reconsrucs he rend componen (longes ime scale componen) of he series. The moher wavele inegraes o zero and describes all deviaions from he rend. In order o compue he decomposiion, wavele coefficiens a all scales represening he proecions of he ime series ono he basis generaed by he chosen family of waveles need o be calculaed firs, hey are f ( d ) S f ( ) Coefficiens d. and S, are wavele ransform coefficiens represening he proecion ono moher and faher waveles, respecively. The series or funcion f () in L ( R ) can be shown in wavele represenaion as f ) S ( ) d ( ) d ( ) d ( )... (5) (,, Here J refers o he number of scales (muliresoluion componens) and K ranges from o he number of coefficiens in he specified componens. The original ime series framewor can be given as f ( ) S D D D D (6) S, D represen S, ( ) and d ( ) respecively wih,, J. f in muliresoluion decomposiion The sequenial se of erms ( S, D,... D,..., D ) in equaion (6) show he componens of original unfilered series represened a differen resoluions. These componens a differen resoluions are herefore, again esimaed using Equaion (). Finally, we es he equaion for relaionship beween unfilered exchange rae change and inflaion differenial; ln E ( ln P ln P ) u (7) Where, he one-period change in he variable and oher variables are as explained earlier. All series are expressed in naural logarihms form and he change in he log of a variable represens relaive change in he variable. For PPP o hold he regression esimaes suppose o yield =. Page

4 Docrine of Purchasing Power Pariy: An Analysis based on Coinegraion and Wavele regression III. DATA The daa used in his sudy are monhly observaion spanning from April 99 o Sepember. Mos par of he sample period corresponds o mare-based exchange rae sysem in India emerged on March 993. Nominal exchange raes are he bilaeral exchange rae of Indian Rupee vis-a-vis US dollar, Briish Pound, Japanese Yen and European Union s Euro. The daa are aen from he Handboo of Saisics on Indian Economy - published by he Reserve Ban of India. Exchange raes in erms of above four foreign currencies guided by he fac ha hey are maor currencies raded in he inernaional mare and hese counries are leading rade parners for India. Wholesale price Index (WPI) of India and Consumer Price Index (CPI) of is rade parners are used o represen domesic and foreign price respecively and he daa source is he Inernaional Financial Saisics (IFS) CD-ROM published by he Inernaional Moneary Fund (IMF). In Indian case we used WPI as he indicaor for general prices due o is advanage in erms of coverage, updaed base and wide use in policy and research. IV. Resuls And Discussion This secion ses ou he approach for esing he PPP hypohesis. To ensure he validiy of he differen economeric ess, firs he saionary propery of all he ime series are esed by using Augmened Dicey- Fuller (ADF) and Phillips-Perron (PP) ess. The appropriae lag srucures were seleced by Schwarz Informaion Crierion (SIC) for ADF and Newey Wes using Barle Kernel for PP ess. The uni roo resuls are presened in Table. All he saisics show ha nominal exchange rae and price series are non-saionary a heir levels bu saionary a firs difference. Table. Uni Roo Tes Resuls ADF Value Phillip-Perron Value Counry Series Level Firs difference Level Firs difference India WPI -.99(.75) -.8(.) -.8 (.7) -.5(.) USA CPI -.87 (.79) -9.7 (.) -.83 (.8) -8.9 (.) EXR.7 (.94) -.6(.) -.9 (.33) -.8 (.) UK CPI.(.99) -.87 (.5).46 (.98) -6. (.) EXR -.39(.58) -.9 (.) -.45 (.55) -.69 (.) JAP CPI -.34(.5) -3.9 (.3) -.69 (.8) -3.6 (.) EXR -.7(.4) -. (.) -.63 (.47) -.6 (.) EU CPI -.34(.4) -5.5 (.) -.3 (.5) -.55 (.) EXR -.8(.64) -4.6 (.) -.8 (.64) -4.6 (.) Figures in (#) are p-values and he values higher han.5 (5%) show ha uni roo hypohesis is no reeced. We proceed o es he PPP hypohesis using various coinegraion mehodologies. Saring wih simple Granger- Engle (978) wo-sep procedure, he OLS regression based on equaion () is firs carried ou and subsequenly residuals are esed for saionariy using ADF, Phillps-Perron and KPSS procedure. If he variables are coinegraed he residual should follow saionary process. The resuls so obained are repored in Table. I may be observed ha, he null of non-saionariy is reeced for Japan and European Union under he es of ADF and Philip-Perron, indicaing exisence of long run associaion beween he nominal exchange rae and he corresponding price variables. However, he radiional uni roo ess are no very powerful agains relevan alernaives (Diebold and Rudebusch, 99). The radiional uni roo ess by design are formulaed o ensure he accepance of null hypohesis of uni-roo unless here is srong evidence agains i (Chen, 995). We hus direcly es he null of no-uni roo for residuals from OLS regression using KPSS es. The KPSS es resuls presened in Table show ha, apar from EU he null of saionariy of error erm canno be reeced for any of he counry under consideraion. Moreover, he Wald es saisics acceps he proporionaliy resricion ( ) for boh USA and UK. Therefore we argue ha here is some evidence in favour of long run PPP hough he suppor is wea. Page

5 Docrine of Purchasing Power Pariy: An Analysis based on Coinegraion and Wavele regression Table. Granger-Engle -sep Coinegraion es resuls: ADF Tes Phillip-Perron KPSS H : USA (.) UK (.7) JAPAN (.) EU (.) Noe: Figures in (#) are p-values and he values higher han.5 (5%) show ha uni roo hypohesis is no reeced. For KPSS es criical values are.739,.463,.347corresponding o %, 5% and % level of significance respecively. and denoe significance a % and 5% level, respecively. To gain furher insigh ino he issue, he long run equilibrium relaion beween nominal exchange rae and wo price series are esed using Johansen mulivariae coinegraion echnique (Johansen, 988, 99). Firs he wea-version of PPP ha imposes no resricion on he coinegraing vecor and requires only he coinegraion among he exchange rae and he wo price series, is esed. Second, he es for he srong-version of PPP ha implies no only he exisence of a leas one coinegraing vecor bu also ha he proporionaliy resricions are saisfied, is conduced. Before saring he coinegraion analysis, he appropriae lag lengh in VAR is deermined using Schwarz Informaion Crierion (SIC) for specifying he lag srucures of he equaions in he VARs. The Johansen coinegraion es hen has been conduced and he resuls are repored in Table 3. The coinegraion resuls show ha for boh he race and maximum eigenvalue ess he hypohesis of no coinegraing vecor is reeced for Rupee exchange rae vis-à-vis USD, Pound Serling and Euro a percen level of significance. In case of Japan, however, wo coinegraing vecor is deeced by he race es a 5 percen significance level, bu he maximum-eigen resul sugges only one coinegraing vecor a percen level. Table.3 Johansen coinegraion es resuls Counry Lag Hypohesized no. of CE(s) Trace saisic Max-Eigen None 5.99 (.) 44.8 (.) USA A mos 8.7 (.76) 5.65 (.83) A mos 3.6 (.57) 3.6 (.57) None 48.7 (.) 3.6(.) UK A mos 7.44 (.) 4.38(.8) A mos 3.6 (.57) 3.6 (.57) None 7.86 (.) 5.3 (.) JAPAN A mos.83 (.4). (.7) A mos 8.63 (.6) 8.63 (.6) None 83. (.) 64. (.) EU A mos 9. (.7).7 (.) A mos.3 (.6) 7.38 (.) Figures in (#) are p-values. and denoes reecion of he hypohesis a 5% and % level respecively. Table 4 repors esimaes of he coinegraing vecor normalized on he spo exchange rae. These esimaes have coefficiens carrying correc signs only in case of Japan and EU, however, are saisically insignifican. The formal es resuls for he symmery ( ) and proporionaliy ( ) resricions are also When here is more han one coinegraion vecor, we have chosen he one corresponding o he larges eigenvalue. following Chen (995). 3 Page

6 Docrine of Purchasing Power Pariy: An Analysis based on Coinegraion and Wavele regression repored Table 4. The Lielihood raio (LR) es suggesed by Johansen and Juselius (99) provide srong evidence in favour of boh symmery and proporionaliy hypohesis for all he counries under he sudy. The Johansen s maximum lielihood approach, hence, sugges coinegraion among nominal exchange rae and wo price series validaing long run PPP hypohesis. We hen proceed o esimae he error correcion model (ECM) o analyse how shor run discrepancy, if any, correced hus, o capure how rapidly long-run PPP is aained. The esimae of he marix of he error correcion erms are presened in Table 5. The coefficiens of his marix are inerpreed as he weighs wih which PPP deviaion is correced in each of he hree equaions (Koureas, 997). The error correcion erms from he equaion for he change in he exchange rae and foreign price have correc sign only for USA and EU. However, adusmen coefficien from he change in he domesic price equaion carries wrong sign in each of he cases excep for Japan. The magniudes of adusmen coefficiens in all he cases, moreover, are very poor and almos close o zero. The Johansen mulivariae coinegraion es, hus, sugges evidence in favour of boh wea and srong version of long run PPP, hough convergence speed of deviaion from PPP is reasonably low a around zero level. Table.4 Esimaed Coefficiens and Hypohesis esing e p p u Eigen Vecors USA.69 (.66) UK 3. (.74) JAPAN -.33 (-.5) Hypohesis Tes : H H ] : ] -3.6 (-.68) -.39 (-.86) 38.9 (-.79) [ 3.35 [.55].9 [.59].46 [.] [ 3.4 [.5].45 [.5].7 [.49] EU -.78 (-.6).59 (.3).9 [.6].46 [.49] Noes: e, p and p denoes he spo exchange rae, domesic and foreign price index respecively. The eigenvecors have been normalized wih respec o he esimaed coefficien on he nominal exchange rae e. H and H denoes a lielihood saisic for he null hypohesis indicaed in parenhesis, consruced as cenral under he null wih r s degrees of freedom, where r denoes he number of coinegraing vecors and s is he number of resricions. (#) are -saisics and [#] are marginal significance levels. e USA -. (-.7) UK. (.5) JAPAN. (.79) EU -.5 (-.9) Noes: (#) are -saisics. Table.5 Speed of Adusmen Mechanism p p -.4 (-4.99) -.3 (-4.9). (7.9) -. (-5.73) -. (-5.84) -. (-3.43). (.45) -.3 (-6.48) The maor limiaion, however, wih coinegraion and error correcion mehodology is ha i fails o poin ou he exac ime period wihin which PPP holds. This sudy addresses his crucial issue wih recenly advanced semi-parameric wavele based regression mehodology. Under his framewor our sudy aemps o address following conroversial issues surrounding he PPP heory: Firs; is PPP a valid heory peraining o differen ime scales (long run, medium run and shor run) or exclusive o long run as eviden from our empirical exercise conduced above? Second; wha exacly is he ime scale wihin which PPP holds if i is a valid hypohesis? 4 Page

7 Docrine of Purchasing Power Pariy: An Analysis based on Coinegraion and Wavele regression We firs examine he saionary propery of he nominal exchange rae change and inflaion differenial by using Augmened Dicey-Fuller and Phillips-Perron ess. The resuls are presened in Table 6 and i shows ha all series are saionary a levels. We use he Daubechies (LA8) leas asymmeric o decompose boh he series ino differen ime scales. Furher Maximal Overlap Discree Wavele Transform (MODWT) was used over he more convenional orhogonal DWT because, by giving up orhogonaliy, he MODWT gains aribues ha are far more desirable in economic applicaions. For example, he MODWT can handle inpu daa of any lengh, no us powers of wo; i is ranslaion invarian ha is, a shif in he ime series resuls in an equivalen shif in he ransform; i also has increased resoluion a lower scales since i oversamples daa (meaning ha more informaion is capured a each scale); he choice of a paricular wavele filer is no so crucial if MODWT is used and, finally, exceping he las few coefficiens, he MODWT is no affeced by he arrival of new informaion. The applicaion of he MODWT wih a number of scales J = 4 produces five MODWT deail vecors D, D, D 3, D 4 and one smooh vecor A 4, where each Table.6 Uni roo es EXR change ADF PP Inflaion Diff. ADF PP Rupee-Dollar India-US Rupee-Pound India-UK Rupee-Yen India- Japan Rupee-Euro India-Euro Noe: denoes he significance a % level. wavele scale is associaed wih a paricular ime period [ J J ]. Since we use monhly daa, herefore he firs deail level D capure oscillaions beween wo o four monhs; while deails D, D 3, D 4 and A 4 capure oscillaions wih periods beween four eigh, eigh sixeen, sixeen hiry wo and more han hiry wo monhs respecively. The ime inerpreaions of differen scales are presened in appendix Table.. We run he regressions for aggregae ime series and series a differen ime scales by esimaing equaion (7). A aggregae level (Agg) and lower scale D here is no evidence of he pariy o hold. However, our ordinary leas square resuls semming from he regressions a ime scale D exhibi some evidence for validiy of PPP for rupeedollar and rupee-yen rae. Corresponding o ime scale D, ha capures variaion over four-eigh monhs period, he coefficien of inflaion rae differenial ( ) in case of India-US and India-Japan regression found o be significan a 5% level. The Wald resricion of = is also acceped for he regression corresponding o India-Japan a D ime scale. The coefficien of inflaion rae differenial ( ) also found o be significan a scale A 4, ha capures oscillaion over hiry wo- sixy four monhs, for India-Japan regression a 5% level of significance wih accepance of resricion = by he Wald es. The adused R neverheless remains relaively low around percen o 5 percen for boh he regressions. No evidence of he pariy, however, is obained for UK and EU a any of he ime scale. Thus, for India, our resuls reec he validiy of PPP a aggregae and very lower ime scales (D) bu lend suppor only a medium o higher ime scales; more specifically over 4 o 8 monhs horizon for rupee-dollar rae and over 4 o 8 monhs as well as over more han 3 monhs horizon for rupee-yen exchange rae. Table.7 Regression resuls of exchange rae change on inflaion differenials IND-US Agg D D D3 D4 A4.(.5).(.99) -.(.99).(.99) -.(.99).(.).(.9).(.67).44(.5).(.6).64(.3) -.6(.3) AdR IND-UK Agg D D D3 D4 A4 -.(.74).(.4).(.99).(.99) -.(.99).(.6).9(.9) -.4(.65).9(.76).3(.9).99(.8) -.44(.8) AdR IND- JP Agg D D D3 D4 A4 5 Page

8 Docrine of Purchasing Power Pariy: An Analysis based on Coinegraion and Wavele regression.(.3).(.99).(.99).(.99) -.(.99) -.(.79).6(.6) -.3(.93).63(.4) -.4(.65) -.8(.7).7(.4) AdR IND-EU Agg D D D3 D4 A4 -.(.).(.99) -.(.99) -.(.99).(.).(.38) -.65(.) -.57(.) -.65(.) -.6(.) -.7(.).(.9) AdR Noe: p-values are in parenhesis. Wald saisic is used o es he hypohesis of relaive PPP ( ). Coefficiens saisically equal o one are shown in aseris. Sandard errors are correced by Newey and Wes (987) mehod. The sudy, herefore, validaes he Purchasing Power Pariy as a heory basically perains o medium o long ime horizon; more precisely no a leas o shor run, corroboraing our resuls of coinegraion analysis. Moreover, in he ligh of consensus in he lieraure regarding he horizon over which PPP holds in he long run (abou 7 o years wih a half-life deviaion of 3 o 5 years), his sudy provides quie an encouraging imeframe for he long-run wih PPP holding over 6 monhs o more han 3 monhs period. V. Conclusion This paper revisied he docrine of Purchasing power pariy considering four maor bilaeral exchange raes via-a-vis Indian-Rupee. The sudy firs examined he long run validiy of PPP hypohesis using wo disinc coinegraion echniques; he Granger-Engle coinegraion and he Johansen-Juselius coinegraion echnique. The Granger-Engle es suggess validiy of long run PPP, hough wea, for all he exchange raes under he consideraion. Corroboraive resuls are also obained wih Johansen mulivariae analysis. No significan error correcion is, however, winessed for any of he exchange rae under sudy. We move forward o analysis he hypohesis a differen ime domain using much advanced mehodology of wavele-based regression. The applicaion of wavele analysis provides a new loo ino PPP docrine and an alernaive reassessmen of is validiy over well-defined horizons raher han arbirary-chosen shor run or long run. The empirical resuls sem from he wavele framewor provide decisive suppor for PPP only a medium o higher ime scales; more specifically in case of rupee-dollar exchange rae over four o eigh monhs horizon and for he rupee-yen exchange rae over four o eigh monhs as well as over more han hiry wo monhs horizon. Thus, we conclude ha he PPP is a relevan hypohesis peraining over medium o long-run only. References: [] J.D. Alba, and D. Par, An empirical invesigaion of Purchasing Power Pariy (PPP) for Turey, Journal of Policy Modeling, 7, 5, [] R. Dornbusch, Expecaions and Exchange rae dynamics, Journal of Poliical Economy, 84(6), Dec. 976, [3] L.H. Officer, Purchasing Power Pariy and Exchange Raes: Theory, Evidence and Relevance, 98, (Greenwich, CT: JAI Press). [4] N. Abauf, and P. Jorion, Purchasing Power Pariy in he long Run, Journal of Finance, 45(), 99, [5] J.R. Lohian, A Cenury of Yen Exchange Rae Behaviour, Japan and he World Economy, (), 99, [6] J. R. Lohian, and M. P. Taylor, Real Exchange Rae Behaviour: The Recen Floa from he Perspecive of he Pas Two Cenuries, Journal of Poliical Economy, 4(3), 996, [7] J.A. Frenel, Flexible Exchange Raes, Prices, and he Role of News : Lessons from he 97s, Journal of Poliical Economy, 89(4), Aug. 98, [8] R. Meese, and K. Rogoff, The Ou-of-Sample Failure of Empirical Exchange Rae Models: Sampling Error or Misspecificaion?, Exchange Raes and Inernaional Macroeconomics, 983, 67-, Naional Bureau of Economic Research, Inc. [9] Y. W. Cheung, and K. S. Lai, Pariy reversion in real exchange rae during he pos-breon Woods period, Journal of Inernaional Money and Finance, 7(4), 998, [] M.P. Taylor, and L. Sarno, The Behaviour of Real Exchange Raes during he pos-breon Woods Period, Journal of Inernaional Economics, 46, 998, 8-3. [] S. E. Culver, and D.H. Papell, Long Run PPP wih Shor-Run Daa: Evidence wih a Null Hypohesis of Saionariy, Journal of Inernaional Money and Finance, 8(5), 999, [] M. Bahamani-Osooee, and A. Gelan, Tesing he PPP in he non-linear framewor: Evidence from Africa, Economics Bullein, 6, 6, -5. [3] F. Wallace, Nonlinear uni roo ess of PPP using long-horizon daa, Economics Bullein, 6, 8, -8. [4] T. Chang, S.Y. Lin, and H.J. Chang, Are real exchange raes nonlinear wih a uni roo? Evidence on purchasing power pariy for China: A noe, Economics Bullein, 3,, [5] M.P. Taylor, The Economics of Exchange Raes, Journal of Economic Lieraure, 33(), 995, [6] K. A. Froo, and K. Rogoff, Perspecives on PPP and Long-run Real Exchange Raes, Handboo of Inernaional Economics, 3(), 995, [7] A.M. Taylor, and M.P. Taylor, The purchasing power pariy debae, Journal of Economic Perspecives, 8, 4, [8] R. McNown, and M.S. Wallace, Naional Price Levels, Purchasing Power Pariy, and Coinegraion: A Tes of Four High Inflaion Economies, Journal of Inernaional Money and Finance, 8(4), 989, Page

9 Docrine of Purchasing Power Pariy: An Analysis based on Coinegraion and Wavele regression [9] M. Dogganlar, H. Bal, and M. Ozmen, Tesing long-run validiy of purchasing power pariy for seleced emerging mare economies, Applied Economics Leers, 64(4),, [] K. Kularnni, and D. Charaborhy, An Empirical Evidence of PPP Theory: A Case sudy of Indian Rupee and US dollar, Margin, () & (), 99, [] Md. Moshin, and B. Kamaiah, PPP Docrine: An Empirical Verificaion, Journal of Foreign Exchange and Inernaional Finance, VI (4), 993, [] A.K. Nag, and A. Mira, Exchange Rae of he Rupee and Purchasing Power Pariy, Economic and Poliical Wealy, 33(5), 998, [3] R. Kohli, Real Exchange Rae Saionariy in Managed Floas: Evidence from India, Economic and Poliical Wealy, 37(5),, [4] R.F. Engle, and C.W.J. Granger, Co-inegraion and error-correcion: represenaion, esimaion, and esing, Economerica, 55, [5] S. Johansen, and K. Juselius, Maximum Lielihood Esimaion and Inference on Coinegraion-wih Applicaion o he Demand for Money, Oxford Bullein of Economics and Saisics,5, 99, 69-. [6] S. Johansen, Esimaion and Hypohesis Tesing of Coinegarion Vecors in Gaussian Vecor Auoregressive Models, Economerica, 59, 99, [7] F. Diebold, and G. Redebusch, On he Power of Dicey-Fuller ess agains fracional alernaives, Economics Leers, 35, 99, [8] B. Chen, Long-run purchasing power pariy: Evidence from some European Moneary Sysem counries, Applied Economics, 7, 995, [9] S. Johansen, Saisical Analysis of Coinegraing Vecors, Journal of Economic Dynamics and Conrol,, 988, [3] G. Koureas, The Canadian Dollar and Purchasing Power Pariy during he Recen Floa, Review of Inernaional Economics, 5, 997, [3] Daubechies, Ten Lecures on Waveles, SIAM, Philadelphia, 99. Appendix Table : Time inerpreaion of differen scales Scale Monhly frequency Period definiion D -4 monhs Shor run D 4-8 monhs D3 8-6 monhs Medium run D4 6-3 monhs More han 3 monhs Long run A 4 7 Page