Jean-François Hoarau CERESUR, University of La Reunion. Abstract

Transcription

1 esng PPP for Cenral Aercan real exchange raes. Evdence fro new panel daa saonary ess wh srucural breaks Jean-Franços Hoarau CERESUR, Unversy of La Reunon Absrac he new panel daa saonary es wh ulple srucural breaks developed by Carron--Slvesre, Del Barro-Casro and Lopez-Bazo (005) s used along wh sandard saonary ess o sudy he long-run PPP hypohess n a se of sx Cenral Aercan counres for he perod 976:-006:4. Conrary o sandard ess, hs new procedure provdes srong suppor for PPP. Caon: Hoarau, Jean-Franços, (008) "esng PPP for Cenral Aercan real exchange raes. Evdence fro new panel daa saonary ess wh srucural breaks." Econocs Bullen, Vol. 6, o. pp. -5 Subed: January 9, 008. Acceped: May 9, 008. URL: hp://econocsbullen.vanderbl.edu/008/volue6/eb-08f30007a.pdf

2 . Inroducon esng for long-run Purchasng Power Pary (PPP) reans a ajor proble n nernaonal econocs (Sarno and aylor, 00). he PPP hypohess consders a proporonal relaon beween he nonal exchange rae and he relave prce rao, whch ples ha he real exchange rae (RER) s consan over e. So, he os coon way o es for PPP consss n nvesgang un roos n RERs. If he un roo can be rejeced n favour of level saonary, hen devaons fro pary are eporary (RER s a ean reverng process) and PPP s sad o hold n he long run. Eprcal leraure on PPP has herefore focused on he credbly of he un roo fndng and on why devaons fro PPP exs. However, despe exensve researches n analysng PPP we are sll unable o draw hoogenous conclusons (aylor and aylor, 004). hs lack of consensus has been arbued o he low power of hese ess. As a resul, he recen leraure, anly focused on ndusral and large eergng econoes, has oved on n wo new drecons. Whle soe researchers have urned o panel un roo ess ohers have oped for nonlnear un roo ess (aylor, 006; Bahan-Oskooee e al., 007). However, few sudes have been conduced usng daa fro sall developng counres and, n parcular, fro Cenral Aerca (Holes, 00; Cerrao and Sarans, 003; Hoarau, 007). Moreover, no consensus has been reached a e. hs oucoe s very surprsng n he exen ha hs area s lkely o be largely coercally and fnancally negraed (Rodlauer and Schpke, 005). So, hs paper as a pursung nvesgaons abou long-run PPP hypohess for hese counres bu n an orgnal way. We apply a new panel daa saonary esng procedure suggesed by Carron--Slvesre, Del Barro-Casro and Lopez-Bazo (hereafer, CDL) (005), whch allows for he srucural changes o shf he ean and/or he rend of he ndvdual e seres, o blaeral RER daa for sx Cenral Aercan Econoes (Cosa-Rca, El Salvador, Guaeala, Honduras, Mexco and Doncan Republc). Indeed, no consderng he presence of srucural breaks n he seres can deerorae he resuls obaned fro sandard procedures (Huang e al., 997). Oherwse, no sudy has already used hs ehodology for assessng he valdy of PPP a dae. We use quarerly daa fro 976: hrough 006:4. hen, n wha follows, we brefly explan he CDL es n Secon and repor he resuls n Secon 3. Secon 4 concludes.. he ehod hs arcle eploys a new panel procedure based on CDL (005) o address he ulple srucural breaks proble. Followng he es of Hadr (000), hs new es sll consders he null hypohess of saonary for all cross-secons bu he nfluence of srucural breaks s aken no accoun n a very convenen way. he procedure s general enough o allow he followng characerscs: () he srucural breaks can have dfferen effecs on each ndvdual e seres, () hey can be locaed a dfferen daes and () ndvduals can have dfferen nuber of srucural breaks. Frsly, consder he followng regressons whch encopass =,..., ndvduals and =,..., e perods: he US dollar s used as nuerare currency. he seres are obaned fro ERS-USDA daabase avalable onlne a hp:// Oherwse, our focus n hs paper s he real blaeral exchange raes raher han he effecve ones n he exen ha he paern of he Cenral Aerca counres foregn rade s srongly donaed by USA.

3 () y, = α, + β + ε, and () α, = θ, kd( b, k ) + γ, kdu, k, + α, + υ, where υ, ~..d.(0, σ ) and α, 0 = α, a consan. he duy varables D ( b, k ) and DU, k, υ, are defned as D (, ) = for and 0 elsewhere, and DU for elsewhere, wh b k = b, k +, k, = b, k > and 0 b, k gvng he k h dae of he break for he h ndvdual, k,..., =,. Moreover, noe ha he sochasc processes { ε, } and { υ, } are aken o be uually ndependen across he wo densons of he panel daa se. So, f we sae he condon σ 0 for all =,...,.e. he null hypohess of a saonary panel, subsung () n () υ, = resuls n: *, γ, D, k, + ε, (3) y = α + θ, kdu, k, + β + * wh he duy varable D, k, = b, k for > b, k and 0 elsewhere,,...,,. hen, he es of he null hypohess reles on a es sasc whch s sply he average of he unvarae saonary ess n KPSS. he general expresson for he es sasc s: λ Sˆ, for he hoogeneous case = = (4) LM ( ) = ˆ ω λ Sˆ, for he heerogeneous case = = (5) LM ( ) = ˆ ω where S = ˆ,, j j = ˆ ε denoes he paral su process ha s obaned usng he esaed OLS resduals of (3), wh ˆ ω beng a conssen esae of he long-run varance of ε,, ω = l E( S, ), =,...,, and ˆ ω = ˆ ω. oe ha λ s used n (4) and (5) o denoe he dependence of he es on he daes of break. For each ndvdual, s defned as ' he vecor λ = λ,..., λ ) (,..., ) whch ndcaes he relave posons of he (,, = b, b, daes of he breaks on he enre e perod. Fnally, by defnng ζ = = ζ, wh ξ and = ξ = ξ and = ζ he ndvdual ean and varance of η λ ), respecvely, he (

4 es sasc for he null hypohess of a saonary panel wh ulple shfs s under ld assupons : ( LM ( λ) ξ ) d (6) Z( λ ) = (0,) ζ A hs sage, he break fracon vecor has been consdered as gven. However, hs laer s usually unknown and us herefore be esaed. Consequenly, copung he es sasc requres o deec he breaks n each one of he ndvdual e seres as a prelnary sep. In hs regard, and as suggesed n CDL (005), we use a grd search procedure developed along he lnes of Ba and Perron (998) he resuls We repor he resuls of he CDL es along wh he KPSS and he Hadr ess n able for he Cenral Aercan counres. oe ha all ess consder a specfcaon wh a consan bu whou a e rend because e rend n RERs s no conssen wh he long-run PPP. Moreover, boh Barle and Quadrac Specral kernels are used for esang he long-run varance. able. Saonary ess resuls for Cenral Aercan counres Indvdual seres KPSS es Srucural breaks deecon Barle Quadrac Specral uber Daes Cosa-Rca 0.65 (9)** (7.0)** 980:4 El Salvador.06 (9)**.94 (7.6)** 3 98:; 988:; 994:4 Guaeala 0.68 (9)** (7.)** 3 986:; 994:; 00: Honduras 0.75 (9)** 0.83 (7.9)** 3 98:4; 990:; 998: Mexco 0.68 (8) 0.73 (6.3) 98:4; 990: Doncan Republc 0.7 (9)** (7.08)** 984:4; 989: he whole panel Hadr es CDL es (whou srucural breaks) (wh srucural breaks) Barle [Prob.] Quadrac Quadrac Barle [Prob.] Specral [Prob.] Specral [Prob.] Hoogeneous Z-sa [0.000]** [0.000]** 0.88 [0.89] [0.85] Heerogeneous Z-sa [0.000]** 9.5 [0.000]** 0.04 [0.484] 0.06 [0.475] oes: (*) (**) ndcae rejecon of he null hypohess of saonary a he 0% and 5% sgnfcance level, respecvely. he long-run varance s esaed wh auoac specral wndow bandwdh selecon (fgures n parenheses) as n ewey-wes (994) for he KPSS and Hadr ess, and as Andrews and Monahan (99) for he CDL es. Concenrang on he KPSS es, we gaher fro able ha he null of no un roo s rejeced n favour of nonsaonary of he RER n fve (Cosa-Rca, El Salvador, Guaeala, Honduras, Doncan Republc) ou of sx counres, so gvng poor suppor for PPP. he evdence of ean-reverson s found only for Mexco. However, as usually noed, he low power of ndvdual KPSS es n shor saples can resul n rejecng oo easly he null he sgn d denoes weak convergence n dsrbuon. CDL (005) deonsrae ha he es gves good perforance n fne saples by Mone Carlo sulaons. 3 he coplee resuls for he Ba-Perron esaes for each counry are avalable upon reques fro he auhor. Only he nuber and he daes of he breaks are repored n able. he opal nuber of breaks has been esaed usng he BIC nforaon crera allowng for a axu of fve srucural breaks. 3

5 hypohess of saonary. One way o handle hs proble s o apply he sandard panel daa saonary es of Hadr. Bu, hs laer (we use boh he hoogeneous and he heerogeneous ess), whch consders he null of no un roo n any of he seres n he panel, corroborae he unvarae KPSS es so ha saonary for he whole panel s srongly rejeced whaever he verson reaned and he kernel ehod used. hus, fro he sandard saonary ess, we can conclude ha long-run PPP does no hold for our saple. everheless, as noed earler, no consderng he presence of srucural breaks can gven sleadng conclusons abou he behavour of RERs and hen abou PPP. Besdes, he CDL es shows ha he null hypohess of panel saonary canno be rejeced a he 5% level of sgnfcance for boh he Barle and Quadrac Specral kernel regardless of he assupon concernng he heerogeney n he long-run varance esae. So, n accordance wh he CDL es, akng no accoun he presence of srucural breaks leads o he accepance of long-run PPP for all counres n he panel 4. oe ha f he RER s saonary bu around a ean whch s subjec o occasonal srucural changes as n our case, here s reverson o a changng ean. So, he hypohess valdaed here s no really he convenonal PPP bu he so-called Quas PPP of Hegwood and Papell (998). 4. Conclusons In hs arcle, we pleened he new panel daa saonary es of CDL (005) o sudy wheher or no here s suppor for long-run PPP n a se of sx Cenral Aercan counres over he perod 976:-006:4. hs ehod has he crucal advanage o allow for he presence of ulple srucural breaks n each ndvdual e seres. Fnally, leads o he concluson ha PPP (ore exacly Quas PPP) holds n he long-run for our panel,.e. he RERs are ean-reverng bu around a changng ean. All n all, ean-reverson has wo ajor plcaons for econoc polcy as long as Cenral Aercan econoes are concerned. Frsly, he equlbru RERs and salgnen ndcaors of hese counres can be obaned fro sple PPP calculaons. Secondly, snce her nonal exchange raes appear o ove closely wh he US dollar, he valdy of PPP hypohess eans he exsence of a prce convergence process n Cenral Aerca. References Andrews, D.W.K., Monahan, J.C., 99. An proved heeroskedascy and auocorrelaon conssen auocovarance arx. Econoerca 60, Bahan-Oskooee, M., Kuan, A.M., Zhou, S., 007. esng PPP n he non-lnear SAR fraework. Econocs Leers 94 (), Ba, J., Perron, P., 998. Esang and esng lnear odels wh ulple srucural changes. Econoerca 66, Carron--Slvesre, J.P., Del Barro-Casro,., Lopez-Bazo, E., 005. Breakng he panels: An applcaon o he GDP per capa. Econoercs Journal 8, Cross-seconal dependence s expeced n panels on RERs f a coon currency such as he US dollar s used as a base. And, no accounng for s lkely o falsely rejec a un roo (O Connell, 998). So, followng Maddala and Wu (999), we have copued he boosrap dsrbuon (wh,000 replcaons) n order o ake no accoun hs proble. Bu, gven ha he resuls are no qualavely odfed, we have no repored he n hs arcle. 4

6 Cerrao, M., Sarans,., 003. Srucural breaks and un roo ess n he black arke real exchange raes. In Recen developen on exchange raes, Appled Econoerc Assocaon, Palgrave Seres. Hadr, K., 000. esng for saonary n heerogeneous panel daa. he Econoercs Journal 3, Hegwood,.D., Papel, D.H., 998. Quas purchasng power pary. Inernaonal Journal of Fnance and Econocs 3, Hoarau, J.F., 007. Does he long-run PPP hold for Cenral Aerca: Evdence fro panel daa un roo ess. Eprcal Econocs Leers, forhcong. Holes, M., 00. ew evdence on real exchange rae saonary and purchasng power pary n less developed counres. Journal of Macroeconocs 3, Huang, C., Lee, J., Shn Y., 997. On saonary es n he presence of srucural breaks. Econocs Leers 55, Maddala, G., S. Wu, 999. A coparave sudy of un roo ess wh panel daa and a new sple es. Oxford Bullen of Econocs and Sascs 6 (S), ewey, W., K. Wes, 994. Auoac lag selecon n covarance arx esaon. Revew of Econoc Sudes 6, O'Connel, P., 998. he overvaluaon of purchasng power pary. Journal of Inernaonal Econocs 44, -9. Rodlauer, M., Schpke, A., 005. Cenral Aerca: Global negraon and regonal cooperaon. IMF Occasonal Paper, n 43, IMF, July. Sarno, L., aylor, M.P., 00. he econocs of exchange raes. Cabrdge Unversy Press, Cabrdge. aylor, M.P, 006. Real exchange raes and purchasng power pary: Mean-reverson n econoc hough. Appled Fnancal Econocs 6 (-), -7. aylor, A.M., aylor, M.P., 004. he purchasng power pary debae. Journal of Econoc Perspecves 8,