PPP TESTS IN COINTEGRATED PANELS: EVIDENCE FROM ASIAN DEVELOPING COUNTRIES

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1 PPP TESTS IN COINTEGRATED PANELS: EVIDENCE FROM ASIAN DEVELOPING COUNTRIES Syed Abul Basher Department of Economcs York Unversty Toronto, ON M3J 1P3 and Mohammed Mohsn * Department of Economcs Unversty of Tennessee Knoxvlle, TN mmohsn@utk.edu Abstract: Ths paper tests the relatve verson of purchasng power party (PPP) for a set of ten Asan developng countres usng panel contegraton framework. We employ betweendmenson dynamc OLS estmator as proposed by Pedron (2001b). The test results overwhelmngly reject the PPP hypothess. JEL classfcatons: F31, C22, C23 Key Words: Purchasng Power Party, Panel Contegraton, Unt Roots * Correspondng author: Mohammed Mohsn, Assstant Professor, Department of Economcs, Unversty of Tennessee, TN 37996, USA. Tel: ; Fax: ; E-mal: mmohsn@utk.edu

2 1. Introducton The purpose of ths study s to examne the emprcal valdty of relatve purchasng power party (PPP) doctrne n the context of a set of Asan developng economes. In the lterature there has been an nflux of emprcal studes on PPP especally n the 90s wth mxed fndngs. The man concern of these studes s to fnd any possble common stochastc trend(s) between exchange rates and relatve prces n a blateral context by employng a number of dfferent unt root and contegraton tests. Majorty of them use the post Bretton Woods data. Obvously these studes do not have suffcently longer tme seres to overcome the possble problem of small sample dstortons that the tradtonal unt root and contegraton tests encounter. Of course there are other studes that use longer tme span. However, the tradtonal tests for PPP usng longer unvarate tme seres usually overlook the potental problem of structural break as the data set covers both the fxed and floatng exchange rate regmes [Qan and Strauss (2001)]. To crcumvent these problems, researchers of late started recommendng the use of panel contegraton framework to get econometrcally robust fndngs [Baltag and Kao (2000), Banerjee (1999), Pedron(2000, 2001b) and Qan and Strauss (2001)]. A major advantage of ths approach s that t allows one to selectvely pool the long run nformaton contaned n the panel whle permttng the short run dynamcs (and heterogenety) among dfferent members. An mportant consderaton regardng poolng has to do wth the dmenson over whch they are pooled. One can pool across ether the wthn or between dmensons. Pedron concluded that the between dmenson has relatvely lower small sample dstortons. The goal of ths study s to employ ths mproved panel contegraton method to evaluate the PPP doctrne n the context of a set of somewhat homogeneous developng countres. 2. Methodologcal Dscussons Pedron evaluates the asymptotc propertes of three versons of panel estmators. Resdual-FM and the adjusted-fm pooled the data along the wthn dmenson and group-fm pooled the data along the between dmenson. He shows that the group-fm has relatvely lower small sample dstortons and more flexblty n terms of hypothess testng. For example, n the panel unt root regresson Y t = Yt µ + ε t for t = 1,2 T, and = 1,2 N, pooled tests mply H 0 : µ = 1 and H A : µ = µ A < 1 where as grouped mean tests mply 1

3 H 0 : µ = 1 and H A : µ < 1. It s clear that µ under the alternatve hypothess s not requred to be the same among dfferent grouped tests often allow for a greater flexblty. where = α + + βx t µ t t members of the panel. Hence the X X + ε (1) Z t = ( Y t, X t ) ~ I(1) and ξ µ, ε ) ~ I( 0) wth long run covarance matrx Ω L ( L s a lower trangular decomposton of Ω = Ω Consder the followng contegrated system for a panel of = 1,2 N members = L Γ + Γ β * NT Y t = N t = t N = 1 T t = 1 Lˆ (X t X X ) Y * where Y t = ( Yt Y ) X t, τˆ ˆ 0 ( ˆ 0 Γ21 + Ω21 Γ22 + Ω22) Lˆ ˆ 22 L22 K 1 Lˆ ˆ ˆ. The assocated t- * Y t = α + β X + γ X + µ t. (3) t t = ( t t Ω ). In ths case the varables are sad to be contegrated for each member of the panel, wth contegratng vector β. It should be noted that α allows the contegratng relatonshp to nclude member specfc fxed effects. Ths covarance matrx can also be decomposed as sum of autocovarances., where Ω s the contemporaneous covarance and Γ s a weghted The panel FMOLS estmator for the coeffcent β s gven by ) 2 T t = 1 statstc follows standard normal dstrbuton. 1 ( X t * t Tτˆ For the panel DOLS estmaton, we need to augment the contegratng regresson n (1) as follows: k k = K t k (2) where the estmated coeffcent β s gven by N T T * β = N Z Y * DS tzt Zt t (4) = 1 t = 1 t = 1 where Z = X X,... ) s 2(K + 1) x 1 vector of regressors. t ( X t, t K X t + K 1 The detal expresson of the t-statstc s avalable n Pedron (2000). 2

4 3. Results 3.1 Data The panel conssts of 240 monthly (and 80 quarterly) seres of end of perod nomnal U.S. dollar exchange rates (E) and aggregate consumer prce ndex rato (P) for 10 countres coverng the perod from January 1980 through December 1999 (1980:1 to 1999:4 for quarterly data). The sample countres are Inda, Indonesa, South Korea, Malaysa, Nepal, Pakstan, The Phlppnes, Sngapore, Sr Lanka and Thaland. The selecton of these countres s somewhat arbtrary, except that they belong to a set of major Asan developng economes. All data have been taken from IMF s Internatonal Fnancal Statstcs CD-ROM. The requred log-transformaton has been done. The results reported here are only for monthly data The panel unt root and the panel contegraton tests In order to determne the presence of a unt root n ndvdual country specfc data we employ standard ADF test. For a panel unt root we conduct Levn-Ln (1992) and IPS t-bar (1997) tests. Both the panel tests nclude a constant and a heterogeneous tme trend n ther specfcatons. The test results show that the unt root null could not be rejected and hence the seres are generated by an I(1) process. Next we perform contegraton tests for all the sample ndvdual countres by usng Johansen and Juselus (1990) method and for the panel by usng Pedron (1999) procedure. We fnd the evdence of no contegraton from both ndvdual and panel contegraton tests. So, the PPP does not hold n the long-run n ths context. To conserve space we report only panel unt root (upper panel) and panel contegraton (lower panel) results n Table FMOLS and DOLS Table 2 reports the results of ndvdual and panel FMOLS and DOLS. Indvdual FMOLS and DOLS estmates and the respectve t-statstcs for H 0 : β = 1 are provded n the frst 10 entres n Table 2, whle results for the panel estmators wth and wthout common tme dummes are shown at the bottom of the table. Both ndvdual and panel tests overwhelmngly reject the null hypothess of strong PPP. As for the ndvdual countres, 7 out of 10 cases we fnd the rejecton of the null. We should also note that both FMOLS and DOLS test results are n agreement. 2 Smlar results on quarterly data wll be made avalable upon request. 3

5 For the panel tests, all 4 reported tests reject the null at least at 5% level except n the case of wthn-dmenson panel DOLS wthout tme dummes. However, t s mportant to note that the between-dmenson estmators consstently produce larger estmates than the wthn-dmenson estmators. Ths fndng s thus consstent wth Pedron (2001b). Followng hm, we argue that these hgher values to be a more accurate representaton of the average long-run relatonshp between nomnal exchange rates and aggregate prce ratos. 4. Concluson In ths study we employ panel contegraton method for evaluatng the purchasng power party doctrne n a panel of ten Asan developng economes for the post Bretton Woods perod. The emprcal fndngs of ths paper do not support the relatve verson of PPP. The analyss of the ndvdual countres furthermore ndcates that ths falure of the PPP s not drven by the data from only a few countres. Rather, the falure of strong PPP appears to be pervasve n the flexble exchange rate regme. Acknowledgements We would lke to thank Don Bruce, Keya Matra and Peter Predon for suggestons and encouragements. The errors are of course our own. 4

6 References Baltag, B.H. and C. Kao, 2000, Nonstatonary panels, contegraton n panels and dynamc panels: a survey, n B.H. Baltag, eds., Nonstatonary panels, panel contegraton, and dynamc panels, advances n econometrcs, Vol. 15, (JAI) Banerjee, A., 1999, Panel data unt roots and contegraton: an overvew, Oxford Bulletn of Economcs and Statstcs, S1, 61, Im, K.S., M.H. Pesaran, and Y. Shn, 1997, Testng for unt roots n heterogeneous panels, Dscusson paper, Unversty of Cambrdge, December. Johansen, S. and K. Juselus, 1990, Maxmum lkelhood estmaton and nferences on contegraton wth applcatons to the demand for money, Oxford Bulletn of Economcs and Statstcs, 52, Levn, A. and C.F. Ln, 1992, Unt root tests n panel data: asymptotc and fnte sample propertes, Department of Economcs, Unversty of Calforna at San Dego, Dscusson paper no Mark, N. and D. Sul, 1999, A computatonally smple contegraton vector estmator for panel data, manuscrpt, Oho State Unversty. Pedron, P., 1996, Fully modfed OLS for heterogeneous Contegrated panels and the case of purchasng power party, Workng paper , Department of Eocnomcs, Indana Unversty. Pedron, P., 1999, Crtcal values for contegraton tests n heterogeneous panels wth multple regressors, Oxford Bulletn of Economcs and Statstcs, S1, 61, Pedron, P., 2000, Fully modfed OLS for heterogeneous Contegrated panels, n B.H. Baltag, eds., Nonstatonary panels, panel contegraton, and dynamc panels, advances n econometrcs, Vol. 15, (JAI) Pedron, P., 2001a, Asymptotc and fnte sample propertes of pooled tme seres tests wth an applcaton to the PPP hypothess, Indana Unversty Workng Paper. Pedron, P., 2001b, Purchasng power party n contegrated panels, The Revew of Economcs and Statstcs, 83, 4, Qan, H. and J. Strauss, 2001, Panel PPP tests wth unknown cross-sectonal dependence and heteroscedastcty, unpublshed manuscrpt. 5

7 Table 1: Panel Unt Root and Contegraton Test Statstcs Levn-Ln rho-stat Levn-Ln t-rho-stat Levn-Ln ADF-stat Panel Unt Root Tests a,b,c Log of E Log of P IPS ADF-stat Panel Contegraton Tests d Constant Panel v-statstcs Panel ρ-statstcs Panel t-statstcs (non-parametrc) Panel t-statstcs (parametrc) Constant + trend Group ρ-statstcs Group t-statstcs (non-parametrc) Group t-statstcs (parametrc) Notes: a. The crtcal values are from Levn and Ln (1992) Table 3 (wth N=10 and T=250). b. IPS ndcates the Im et al. (1997) test. The crtcal values are taken from Table 4. c. Unt root tests nclude a constant and heterogeneous tme trend n the data. d. The crtcal values for the panel contegraton tests are base on Pedron (2001a). Table 2: Purchasng Power Party Tests Country FMOLS t-stat DOLS t-stat Inda Indonesa Korea Malaysa Nepal Pakstan The Phlppnes Sngapore Sr Lanka Thaland *** -6.19*** *** 20.66*** 8.64*** 3.55*** *** *** -5.99*** *** 6.76*** 3.27*** * 2.42** Panel Results wthout tme dummes wthn a between b * 13.97*** *** wth tme dummes wthn between *** -2.26** *** 2.55** Notes: t-stats are for H 0 : β = 1. ***,**,* ndcate, 1%,5%,10% rejecton level, respectvely. a. wthn-dmenson reports Mark and Sul (1999) unweghted wthn-dmenson DOLS and an analogous unweghted FMOLS. b. between-dmenson reports Pedron (1996) group mean panel FMOLS and the group mean panel DOLS ntroduced n Pedron (2001b). 6