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1 College of Busness, Hospaly &Toursm Sudes Workng Paper Seres No. 01/13 Tle Purchasng Power Pary Theory and s Valdy n Pacfc Island Counres Auhors T. K. Jayaraman Fj Naonal Unversy E-mal: ru.jayaraman@fnu.ac.fj and Chee-Keong Choong Unvers Tunku Abdul Rahman, Kampar, Malaysa E-mal: choongck@uar.edu.my Dae: February 2013 School of Economcs, Bankng and Fnance, Nasnu Campus, Nasnu, Fj. Ths paper presens work n progress n he College of Busness, Hospaly and Toursm Sudes, FNU. Commens are welcomed from all sakeholders and should be addressed o he correspondng auhor. Copyrgh 2013 by he auhor. All rghs reserved.

2 Purchasng Power Pary Theory and s Valdy n Pacfc Island Counres by T. K. Jayaraman Fj Naonal Unversy, Nasnu Campus, Emal: ru.jayaraman@fnu.ac.fj Chee-Keong Choong* Unvers Tunku Abdul Rahman (Perak Campus), Malaysa E-mal: choongck@uar.edu.my Absrac Among he 14 Pacfc sland counres (PICs), whch are members of he ner-governmenal organzaon known as Pacfc Islands Forum, sx counres have ndependen currences fve of hem, namely Fj, Samoa, Solomon Islands. Tonga and Vanuau have fxed exchange rae regmes and he sxh counry namely Papua New Gunea has a flexble exchange rae regme. The oher egh are dollarzed economes, havng adoped one of he currences of Ausrala, New Zealand and he Uned Saes. Ths paper nvesgaes wheher he purchasng pary power heory holds n regard o fve counres under fxed exchange rae regmes. Our fndngs show ha long-run PPP hypohess hold for all fve PICs, wh he assumpons of symmery and proporonaly beng srongly rejeced. Hence, we fnd srong suppor for he PPP docrne as a suable gude for exchange rae polcy reform n PICs. Keywords: Purchasng Power Pary, Panel conegraon ess, Symmery, Proporonaly, Pacfc Island Counres JEL classfcaon: F31, C23, C52 * Correspondng auhor.

3 I. Inroducon The purchasng power pary (PPP) heory, whch s based on law of one prce ha prces n wo counres of goods of smlar qualy under he assumpons of absence of or low ransporaon coss and absence of rade barrers, should be dencal when expressed n erms of he same currency, s an elegan proposon n economcs. The PPP heory saes ha exchange raes beween any wo counres wll adjus over me o reflec changes n her respecve prce levels (Mshkn 2012). Undoubedly, he PPP heory has enchaned emprcal economss over a long me. However, emprcal sudes done n respec of boh developed and developng counres a dfferen mes and for dfferen perods have shown ha he PPP heory has lle predcve power n he shor run, despe he fac ha heory provdes some gudance o movemen n he exchange raes over a perod. Tha s, polcy makers are aware ha n he long-run f a gven counry s prce level has been rsng relavely hgher level o ha of anoher counry s prce level, s currency deprecaes. Amongs he 14 Pacfc sland counres, sx of hem have ndependen currences. Whle Fj, Samoa, Solomon Islands, Tonga and Vanuau have fxed exchange rae regmes, Papua New Gunea has a floang sysem snce Accordng o he IMF offcal classfcaon repored n he Annual Repor on Exchange Arrangemens and Exchange Resrcons, he currences of Fj, Samoa, Tonga and Vanuau are pegged o a baske of currences for pas wo decades of more, whereas he exchange rae of Solomon Islands whch was pegged o Uned Saes (US) dollar currency s now pegged o a baske of currences snce Sepember 2012 o a baske of radng parner currences wh US dollar havng he larges proporon. Ths paper examnes he valdy of PPP heory n regard o he exchange raes of fve counres, namely Fj, Samoa, Solomon Islands, Tonga and Vanuau by underakng an emprcal sudy over a perod of hree decades. The paper s organsed along he followng lnes. The second secon presens a heorecal vew of he PPP hypohess, whereas he hrd secon oulnes he mehodology adoped and dscusses he daa employed for he analyss. The fourh secon repors he resuls and he fnal secon presens a summary wh a se of conclusons of polcy mplcaons. II. A Bref Revew of Theorecal and Emprcal Sudes Observng PPP heory s he cornersone of he moneary models of exchange rae deermnaon, (Dornbusch 1976, Musa 1982), Anorou e al (2005) noe ha devaons from PPP do occur n he shor-run as evdenced sudes by Dornbusch (1980) and Frenkel (1978). However, no all sudes focusng on he long run valdy of PPP heory had come ou wh unanmous resuls. Whle for example, Abuaf and Joran (1990) and Meef and Rogoff (1988), found evdence of PPP heory s holdng n he long run, Cooper (1994) and Ahkng (1997) obaned evdence o he conrary. The urnng pon n he nvesgaon, as observed by Anorou e al (2005), came abou wh he fndng ha nomnal exchange rae has un roos, whch would ndcae ha nomnal exchange rae follows a random walk and s mpac s no mean reverng. Consderng

4 changes n nomnal exchange rae are lkely o be permanen and hence, he long run PPP heory could only be confrmed, f he un roo ess are underaken and he exsence of un roos are rejeced (Adler and Lehman 1983; Manzur and Arff 1995). Varous auhors used dfferen ess. Whle Mansur and Arff (1995) and Wh (1992) used Sms ess, Ahkng (1997) used Bayesan un roo approach. Huang and Yang (1996) employed Engle and Granger (1987) wo-sep approach and Johansen (1988) maxmum lkelhood procedure as well as Mone-Carlo smulaons and obaned dfferen resuls. Lee (1999) used a generalsed error correcon model for 13 Asa pacfc counres. As regards dfferen exchange rae regmes, sudes by Derodan, e al (1999) found ha n he long run PPP s vald under a floang exchange rae regme. In her sudy of exchange raes of 11 developng counres, Anorou e al (2005) conduced un roo ess usng boh Augmened Dckey Fuller ess and Phllpe-Perron procedures o deermne he order for negraon. Furher, he auhors adoped a dynamc error correcon model (DECM) o examne he exsence of long run PPP because of he specal propery ha DECM relaxes he resrcons mplc n he radonal un roos procedures and reas boh nomnal exchange rae and prce rao as endogenous varables. III. Mehodology and Daa Modellng: PPP Relaonshp The PPP heory proposes ha he exchange rae reles on relave prce levels, as follows: * r p p (1) where r s he log of he nomnal exchange rae (uns of domesc currency per un of he * US dollar), p and p are he logs of domesc and foregn prces, respecvely. Equaon (1) suggess ha weak PPP relaonshp exss f here s evdence of conegraon among r, * p and p. If we mpose he symmery condon 1 2 on prces, hen hs resrcon shows a new PPP relaonshp. * r ( p p ) (2) 0 Snce we mpose he symmery condon n Equaon (2), hs equaon can only have a sngle conegrang vecor. In our furher esng, f we mpose he proporonaly condon on he relave prce coeffcen n Equaon (2), hen we can examne he exsence of srong PPP relaonshp n PICs. In hs sudy, we nvesgae he valdy of boh symmery and jon symmery and proporonaly assumpons n PICs. Panel conegraon ess for esng PPP Hypohess Assumng ha y, x } are negraed of order one, I(1) and we consder he followng me { seres model: y x u (3)

5 Where x s a vecor of I(1) varables and he conegrang vecor s (1, ). Equaon (3) can be esmaed by applyng sngle equaon and or sysem echnques. In hs sudy, we shall frs esmae by usng sngle equaon echnque developed by Pedron (1997, 1999, 2000, 2001). Pedron s panel daa framework s derved under he null hypohess ha here s no conegraon. Based on hs framework, Pedron develops seven panel conegraon sascs, namely four sascs are based on whn-dmenson echnque and hree are based on beween-dmenson echnque. Accordng o Pedron (1997), he dsrbuon of hese sascs s a normal dsrbuon gven by k k where N, T u N N(0,1) (4) k, s he panel conegraon sasc and u and are he momens of he N T Brownan funcon (.e. expeced mean and varance) ha are compued n Pedron (1999). Panel fully modfed OLS (FMOLS) esmaes For he purpose of examnng he valdy of PPP hypohess, we adop he panel group mean Fully Modfed OLS followng he work by Pedron (2000). The FMOLS procedure s able o accommodae he heerogeney problem ha s normally presen n he ransonal seral correlaon dynamcs and n he long run conegrang relaonshps. We consder he followng panel daa models: y x u (5) x x e, 1 (6) Where 1,2,..., N counres over he perod of 1,2,..., M. In addon, z ( y, x ) ~ I(1) and 0 0 ( u, e ) ~ I(0) wh covarance marx of where s he conemporaneous covarance, s he weghed sum of auocovarances whle L L n whch L s he lower rangular decomposon of. I s assumed ha y r whle x [ p, p*] of Equaon (1). The panel fully modfed OLS (FMOLS) esmaor for coeffcen β s gven as * FM where N N 1 T 1 1 ^ x _ x 2 1 T 1 x _ x y * ^ T _ L ^ ^ ^ 0 0 * 21 L ^ ^ 21 y ( y y) x ^ and ^ 22. The assocaed -sascs L22 L22 for he esmaor can be esmaed as N ^ * ^ 1 T * N ^ ^ * where 11 ( ) 1 2 ^ *, 0 FM x x FM 1 FM, FM 1 ^

6 Afer obanng he esmaes, we shall normalze he equaon wh respec o y as we nend o focus only on a sngle conegrang vecor, ha s s unque. Daa The daa employed for he sudy are quarerly daa coverng a perod of hree decades: 1980Q1-2011Q4. The nomnal exchange raes are uns of domesc currency per un of he US dollar. The prce level daa of he fve PICs are consumer prce ndces, whle he foregn prce level s he consumer prce ndex of he US. All daa are drawn from Inernaonal Fnancal Sascs, an Inernaonal Moneary Fund publcaon (IMF 2012). IV. Emprcal Resuls In general, a necessary condon for PPP hypohess o hold s ha he relave prce s saonary; oherwse, devaons or dsequlbrum from PPP would be permanen. Hence, we frs employ four ypes of panel un roo ess, namely proposed by Levn, Ln and Chu (2002), Im e al. (1997) and Maddala and Wu (1999). These panel un roo ess are more superor han unvarae me seres ess (ADF and PP ess). The es proposed by Levn, Ln and Chu (2002), wh he assumpon of homogeney across ndvduals. On he oher hand, he ess proposed by Im e al. (1997) and Maddala and Wu (1999) are well-known wh a good small sample properes and hey also allow for ndvdual specfc effecs and dynamc heerogeney across groups o examne prce dfferences beween counres (Esaka, 2003, p. 234). As shown n Table 2, we could rejec he un roo null of exchange rae, domesc prce (p) and foregn prce (p*) a frs dfference. Ths non-saonary of exchange raes s no surprsng because a me rend would no be conssen wh long-erm PPP (Papell, 1997). Hence, s suggesed ha he exchange rae, domesc and foregn prces are I(1) sochasc processes for he whole panel of PICs. As he exchange rae s saonary a I(1), hs ndcaes ha exchange rae exhbs a hgh degree of perssence and does no suppor he mean reverson hypohess. Ths fndng s n lne wh few sudes such as Papell (1997), OConnell (1998), Cerrao and Sarans (2002) and Coakley, e al. (2005). On he bass of he panel un roo resuls, we proceed o examne he valdy of PPP hypohess n hese fve PICs by usng Pedron s (2004) conegraon ess. The resuls are shown n Table 3. The null hypohess of no conegraon s rejeced by four whndmenson panel conegraon sascs and by hree beween-dmenson panel conegraon sascs provded by Pedron (1999). Hence, we conclude ha boh exchange rae, domesc and foregn prces are conegraed. The valdy of PPP hypohess s furher confrmed by he Johansen Fsher panel conegraon es, as shown n Table 4. The long run esmaes for each of he fve PICs and for he panel of PICs, based on Pedron s FMOLS esmaor, are shown n Table 5. For all fve PICs, s found ha he nercep appears o be posve and sgnfcan a 5% sgnfcance level. Lookng a he domesc prces, he coeffcens are sgnfcan n all counres wh an expeced posve sgn. In conras, he coeffcens on he foregn prce are negave as expeced and hey also sgnfcan n all

7 counres a leas a 5% sgnfcance level. Therefore, he fndngs from boh he Pedron and Johansen Fsher panel conegraon ess suppors he presence of a long-run relaonshp among he exchange rae, domesc and foregn prces for fve Pacfc Island Counres (PICs). Snce he resuls of boh Pedron and Johansen Fsher panel conegraon ess favour he weak PPP hypohess, whch are n conras wh he fndngs for he PPP repored by few panel un roo ess of he exchange rae. Therefore, we suspec hese conrasng fndngs mgh be due o jon symmery and proporonaly resrcons mposed on panel un roo ess of he exchange rae (Frankel and Rose 1996). To examne he robusness and valdy of resuls, we use he Johansen mulvarae conegraon es o ndvdual PICs. The race and maxmum egenvalue es sascs are exhbed n Table 6. The nercep s ncluded n he esmaon o avod he measuremen errors as n Equaon (1). The es sascs sgnfcanly rejec he null hypohess of no conegraon among he exchange rae, domesc and foregn prces n all PICs. These resuls suppor he long-run PPP hypohess for he ndvdual PICs. We apply he lkelhood rao es (Johansen, 1995) o examne he valdy of he jon symmery and proporonaly resrcon, namely Ths ndcaes ha one of he conegrang vecors s (1, 1, 1). The resuls are repored n Table 7 (frs wo colums). We rejec he jon symmery and proporonaly resrcons for all PICs, excep Fj even a 10% sgnfcance level. The fndng on he rejecon of hese condons suggess ha he jon symmery and proporonaly resrcon may be oo resrcve. Our fndng s conssen wh some sudes applyng me seres conegraon ess such as Cheung and La (1993). We also examned he valdy of he symmery condon, 1 2. The resuls are repored n Table 7 (las wo columns). We are able o rejec he null hypohess n Samoa, Solomon Islands and Tonga, bu no for Fj and Vanuau. Hence, our resuls sugges ha domesc and foregn prces are crucal deermnans of he exchange rae n he long run n all PICs, bu he esmaes do no necessarly comply wh he resrcve condons (jon symmery and proporonaly resrcons) mposed by he srong PPP heory n Samoa, Solomon Islands and Tonga. In concluson, our evdence ends o suppor he weak form of he long-run PPP relaonshp n PICs.

8 V. Summary and Conclusons Ths sudy examnes he valdy of PPP heory n regard o he exchange raes of fve Pacfc Island counres, namely Fj, Samoa, Solomon Islands, Tonga and Vanuau for he perod of 1980Q1-2011Q4. We fnd overwhelmng suppor for PPP hypohess n all hese PICs by usng dfferen economerc echnques such as panel un roo ess, Pendron s and Johansen s panel conegraon ess. Usng Johansen s lkelhood rao ess, s found ha he jon symmery and proporonaly resrcons are sgnfcanly rejeced n all he counres. I s also found ha he symmery condon s rejeced for only hree ou of fve counres, namely Samoa, Solomon Islands and Tonga. Hence, our fndngs provde new evdence concernng PPP n fve PICs (Fj, Samoa, Solomon Islands, Tonga and Vanuau) ha have been negleced n he PPP leraure. The polcy mplcaons are clear: domesc and foregn prces are he man deermnans of exchange raes n PICs. The relevan polcy makers should mplemen he approprae exchange rae polces n sablzng domesc prces, monorng hgh nflaon raes and enhancng expor compeveness.

9 References 1. Abuaf, N. and Joron, P. (1990). Purchasng power pary n he long run. Journal of Fnance, 45, Adler, M. and Lehman, B. (1983). Devaons from purchasng power pary n he long run. Journal of Fnance, 38, Ahkng, F. (1997) Tesng Long-Run Purchasng Power Pary wh a Bayesan Un Roo Approach: The Experence of Canada n he 1950s. Appled Economcs, 29: Anorou, E. Habu, B. and Yusuf, A. (2002). Purchasng Power Pary: Evdence from Developng Counres, Inernaonal Advances n Economc Research, 8(2), Cerrao, M. and Sarans, N. (2002). The cross seconal dependence puzzle, Dscusson Paper No Cenre for Inernaonal Capal Markes London Guldhall Unversy: Deparmen of Economcs. 6. Cheung, Y.W. and La, K. S. (1993). Long-run purchasng power pary durng he recen floa. Journal of Inernaonal Economcs, 34, Coakley, J., Kellard, N. and Snah, S. (2005). The PPP debae: Prce maers! Economcs Leers, 88, Cooper, J. (1994), Purchasng Power Pary: A Conegraon Analyss of he Ausralan, New Zealand and Sngaporean currences. Appled Economcs Leers, 1, 67-71, 9. Derodan,, K. Jung, C. Boyd, R. (1999).Tesng he Law of One Prce Under he Fxed and 10. Flexble Exchange Rae Sysem, Appled Economcs Leers, 6, Dornbusch, R. (1976). Expecaons and exchange rae dynamcs. Journal of Polcal Economy, 84, Dornbusch, R. (1980). Purchasng Power Pary, n J. Eawell, M. Mgare, and P. Newman (Eds.), The New Palgrave Dconary, New York: Sockon Press. 13. Engle, R.F. and Granger, C.W.J. (1987). Co-negraon and error correcon: Represenaon, esmaon and esng. Economerca, 55(2), Esaka, T. (2003). Panel un roo ess of purchasng power pary beween Japanese ces, : dsaggregaed prce daa. Japan and he World Economy, 15,

10 15. Frankel, J.A. and Rose, A.K. (1996). A panel projec on purchasng power pary: Mean reverson whn and beween counres. Journal of Inernaonal Economcs, 40, Frenkel, J.A. (1978). Purchasng power pary: docrnal perspecve and evdence from he 1920 s. Journal of Inernaonal Economcs, 8, Huang, B. and Yang, C. (1996). Long-Run Purchasng Power Pary Revsed: A Mone Carlo Smulaon, Appled Economcs, 28, Im, K., Pesaran, M.H. and Shn, Y. (2003). Tesng for un roos n heerogeneous panels. Journal of Economercs, 115, IMF (2012). Inernaonal Fnancal Sascs, CD Rom November 2012, Washngon, D.C.: IMF. 20. Johansen, S. (1988). Sascal analyss of conegraon vecors. Journal of Economc dynamcs and Conrol, 12 (June Sepember), Johansen, S. (1995). Lkelhood nference n conegraed vecor auo-regresson models. Oxford Unversy Press. 22. Lee, D. (1999) Purchasng Power Pary and Dynamc Error Correcon Evdence from Asa Pacfc Economes, Inernaonal Revew of Economcs and Fnance, 8(1), Levn, A., Ln, C. and Chu, C. (2002). Un roo ess n panel daa: Asympoc and fne-sample properes. Journal of Economercs, 108, Maddala, G.S. and Wu, S. (1999). A comparave sudy of un roo ess wh panel daa and a new smple es. Oxford Bullen of Economcs and Sascs, Specal Issue, Manzur, M. and Arff, M. (1995) Purchasng Power Pary: New Mehods and Exensons, Appled Fnance Economcs, 5(1), Meef, R.A. and Rogoff, K. (1988). Was real: The Exchange Rae-Ineres Dfferenal Relaon Over he Modern Floang-Rae Perod, Journal of Fnance,43: Mshkn, F.S. (2012). Economcs of Money, Bankng and Fnancal Markes, (10 h Edon), New York: Addson Wesley. 28. Musa, M. (1982). Model of Exchange Rae Dynamcs, Journal of Polcal Economy, 90(2), OConnell, P. (1998). The overvaluaon of purchasng power pary. Journal of Inernaonal Economcs, 44, 1 19.

11 30. Papell, D.H. (1997). Searchng for saonary: purchasng power pary under he curren floa. Journal of Inernaonal Economcs, 43, Pedron, P. (1997). Panel conegraon: Asympoc and fne sample properes of pooled me seres wh an applcaon o he PPP hypohess: New resuls. Indana Unversy: Workng Paper. 32. Pedron, P. (1999). Crcal values for conegraon ess n heerogeneous panels wh mulple regressors. Oxford Bullen of Economcs and Sascs, 61, Pedron, P. (2000). Fully modfed OLS for heerogeneous conegraed panels. Advances n Economercs, 15, Pedron, P. (2001). Purchasng power pary ess n conegraed panels. The Revew of Economcs and Sascs, 83, Pedron, P. (2004). Panel conegraon: asympoc and fne sample properes of pooled me seres ess wh an applcaon o he PPP hypohess. Economerc Theory, 20, Wh, J.A. (1992) The Long-Run Behavor of he Real Exchange Rae: A Reconsderaon. Journal of Money, Cred, and Bankng, 24(1), 72-82

12 Table 1: Pacfc Island Counres: Nomnal Exchange Raes and Inflaon Year Nomnal Exchange Raes Annual change n prce level n percen F$/USD Tala/US$ Sol $/USD Ton$/USD Va/US$ Fj Samoa Sol Is Tonga Vanuau (Ave) (Ave) (Ave) Source: IMF (2012).

13 Panel Un roo ess Levn, Ln & Chu * Im, Pesaran and Shn W- sa ADF - Fsher Ch-square PP - Fsher Table 2A: Panel un roo ess Nomnal Exchange Raes Domesc Prce, p Foregn Prce, p * Level Level Level Dfference Dfference Null: Un roo (assumes common un roo process) *** *** [0.4845] [0.0000] [0.2377] [0.0000] [0.9951] Null: Un roo (assumes ndvdual un roo process) *** *** [0.9241] [0.0000] [0.7693] [0.0000] [0.9389] [0.815] [0.9762] 1 s *** [0.0000] *** [0.0000] [0.2323] [0.8169] 1 s *** [0.0000] *** [0.0002] [0.9948] [0.9964] 1 s Dfference *** [0.0000] *** [0.0000] *** [0.0000] *** [0.0000] Ch-square Noes: Under he null hypohess, he IPS es sasc s asympocally dsrbued as a sandard normal dsrbuon. The (common) lag lengh s chosen on he bass of he AIC. The numbers n parenheses denoe lag lengh and hose n brackes are P-values. The P-values are esmaed from he one-al es of he sandardzed normal dsrbuon. Under he null hypohess, he probables for Fsher ess are compued usng an asympoc Chsquare dsrbuon. The lag lengh s chosen on he bass of he AIC and s se equal o he value chosen by he ndvdual ADF regressons. Hence, we canno presen he common lag lengh, because he lag lengh vares counry by counry (regresson by regresson). *** Sgnfcan a he 1 percen level. Table 3: Pedron resdual conegraon es resuls Tes Sascs Panel conegraon sascs (whn-dmenson) a Panel -sasc ** [0.0226] Panel PP ype ρ-sasc *** [0.0005] Panel PP ype -sasc *** [0.0000] Panel ADF ype -sasc *** [0.0000] Group mean panel conegraon sascs (beween-dmenson) b Group PP ype ρ-sasc * [0.0587] Group PP ype -sasc *** [0.0014] Group ADF ype -sasc *** [0.0004] Noes: The number of lag runcaons used n he calculaon of he seven Pedron sascs s 3. The numbers n brackes are P-values. a The whn-dmenson ess ake no accoun common me facors and allow for heerogeney across counres. b The beween-dmenson ess are he group mean conegraon ess, whch allow for heerogeney of parameers across counres. *, ** and *** Sgnfcan a he 10, 5 and 1 percen levels, respecvely.

14 Table 4: Johansen Fsher panel conegraon es resuls (Lag 2) Hypoheszed No. of CE(s) Unresrced Conegraon Rank Tes Fsher Sascs Trace Tes Probably a Maxmum Probably a Egenvalue Tes r= *** ** r= r= Noes: a Probables are compued usng asympoc Ch-square dsrbuon. ** and *** Sgnfcan a he 5 and 1 percen levels, respecvely. Table 5: Pendron s fully modfed OLS esmaes Inercep 0 Domesc Prce, p Foregn Prce, p * 1 2 Fj ** (2.2511) *** (2.8919) *** ( ) Samoa *** (2.8428) *** (3.4724) *** ( ) Solomon Islands *** (5.3163) *** (5.3561) ** ( ) Tonga *** (3.9434) *** (3.6051) *** ( ) Vanuau *** (3.5947) ** (1.9744) *** ( ) Noes: The number of lag runcaons used n he calculaon of he seven Pedron sascs s 4. Numbers n parenheses below regresson coeffcens are -values. ** and *** Sgnfcan a he 5 and 1 percen levels, respecvely. Table 6: Johansen mulvarae conegraon es Counry Trace Sasc Maxmum Egenvalue Rank, r

15 Sasc Fj r= ** ** 1 r= r= Samoa r= *** *** 1 r= r= Solomon Islands r= ** ** 1 r= r= Tonga r= *** *** 1 r= r= Vanuau r= ** ** 1 r= r= Noe: The crcal values for he race es a he 95% sgnfcance level are (r=0); (r=1); 3.76 (r=2) (r=0); (r=1); 6.65 (r=2) a 99%. The crcal values for he maxmum egenvalue es a he 95% sgnfcance level are (r=0); (r=1); 3.76 (r=2) (r=0); (r=1); 6.65 (r=2) a 99%. ** and *** Sgnfcan a he 5 and 1 percen levels, respecvely. Table 7: Johansen mulvarae conegraon es: LR-es Counry Jon Symmery and Jon Symmery Proporonaly Resrcon (β1=-β2) Resrcon (β1=1 β2= 1) Fj [0.2791] [0.8823] Samoa [0.0000] [0.0448] Solomon Islands [0.0014] [0.0111] Tonga [0.0055] [0.0495] Vanuau [0.0502] [0.8125] Noes: Numbers n brackes are p-values. ** and *** Sgnfcan a he 5 and 1 percen levels, respecvely.