Inernaonal Journal of Busness and Socal Scence Vol. 2 No. 9 [Specal Issue - May 2011] Purchasng Power Pary and Half Lfe: Anoher Look Gl Km (Correspondng auhor) Asssan Professor Deparmen of Economcs, Calforna Sae Unversy, Fresno Fresno, CA 93740 Uned Saes of Amerca E-mal:gkm@csufresno.edu, Phone: (559) 278-3950 Yoonba Km Assocae Professor Deparmen of Economcs, Unversy of Kenucky Lexngon, 40506. Uned Saes of Amerca Emal: ykm01@uky.edu, Phone: (859) 257-2838 Absrac In hs paper, we nvesgae he long-run mean reverng behavor of he real exchange rae wh s sx dfferen defnons for 27 economes usng annual daa from 1974 o 2003. We fnd ha PPP holds beer and he half-lfe of he real exchange rae s shorer when he wholesale prce ndex raher han consumer prce ndex s used as prce level measure. Somewha surprsngly, here s no evdence ha PPP holds beer wh rade-weghed real exchange raes han wh blaeral ones regardless of he prce ndex used. Srong evdence for PPP emerges only wh he use of Im, Pesaran, and Shn (2003) panel ess bu no wh he Levne, Ln, and Chu (2002) es. The esmaed half-lfe vares wh he defnon of he real exchange rae and s 2 o 3 years, whch s shorer han he consensus vew. Keywords: Purchasng power pary; Real exchange rae; Half-lfe; Panel ess 1. Inroducon Purchasng power pary (PPP) s one of he mos mporan buldng blocks n modelng an open economy. I has been suded n a volumnous leraure. An emergng consensus afer decades of exensve research s ha he real exchange rae s saonary bu s mean reverson akes an mplausbly long me. Sudes by Frankel (1986), Abuaf and Joron (1990), Debold, Hused, and Rush (1991), Cheung and La (1994), and Lohan and Taylor (1996) all reach a smlar concluson. Ther esmaes of he half-lfe of he PPP devaons fall beween 3 and 5 years. 1 Rogoff (1996) calls he lenghy half-lves n he presence of a hgh degree of exchange rae volaly he PPP puzzle. Ths s puzzlng because real shocks canno accoun for he majory of he shorrun volaly of real exchange raes whle nomnal or moneary shocks can only have srong effecs over a me frame durng whch wages and prces are scky. The half-lves of moneary shocks under nomnal rgdy would be predced 1 o 2 years (Rogoff, 1996). More recen research examnes varous aspecs of he half-lfe measuremen ncludng uncerany abou pon esmaes (Ross, 2005), he bas assocaed wh napproprae aggregaon across heerogeneous coeffcens (Taylor, 2001), me aggregaon of commody prces (Imbs e al., 2005), and downward bas n esmaes of dynamc lag coeffcens (Cho e al., 2006). Chorareas and Kapeanos (2005) propose an alernave measure whch focuses on he cumulave effecs of he shocks. Some are able o fnd ha half-lves are shorer han he consensus whle ohers merely confrm he consensus or show ha he half-lfe s even longer. I would be far o say ha he puzzle largely remans unresolved. 2 In hs paper, we nvesgae he PPP puzzle and he long-run mean reverng behavor of he real exchange rae n s sx alernave defnons. We consder he rade-weghed effecve real exchange rae as well as he blaeral rae vs-à-vs he US dollar whle usng boh he CPI and he WPI as prce ndces. We compare he convenonal unvarae ess and he panel ess. In panel ess, we employ boh he es of Levne, Ln, and Chu (LLC, 2002) and he more recen es by Im, Pesaran, and Shn (IPS, 2003). 1 The half-lfe n he above sudes s 4.6 years n Frankel (1986), 3.3 years n Abuaf and Joron (1990), 6 years for dollarserlng and 3 years for franc-serlng n Lohan and Taylor (1996). 2 Nonlnear models are no consdered n hs bref leraure survey. 1
The Specal Issue on Busness and Economcs Cenre for Promong Ideas, USA www.jbssne.com In addon, we nvesgae he behavor of he relave prce of nonraded goods o raded goods and he mpac of he Balassa-Samuelson effec on he real exchange rae usng he Penn World Table (PWT) daa. The res of hs paper s organzed as follows. Secon 2 revews he sx alernave defnons of he real exchange rae and he daa used o generae hem. Secon 3 dscusses he emprcal mehodology and esmaon resuls. Secon 4 ends wh concludng remarks. 2. The Defnons of he Real Exchange Rae Annual daa from 1974 o 2003 are colleced for 27 ndusral counres and emergng marke economes n Eas Asa and Lan Amerca, yeldng beween 511 and 811 observaons dependng on he defnon of he real exchange rae. Daa for he nomnal exchange raes, CPI and WPI for each counry are obaned from Inernaonal Fnancal Sascs (IFS) and he PPP daa se s from he PWT. We consder sx alernave defnons of he real exchange rae. The frs ndex of he real exchange rae, RX1, s obaned n he followng way. * q e p p e s he nomnal blaeral exchange rae agans he US dollar (an ncrease hus means a deprecaon of he domesc currency), p s he domesc CPI and p * s he US CPI. 3 All varables are n logarhm. The second ndex, RX2, s he rade-weghed real effecve exchange rae. I s obaned as he rade-weghed average of he blaeral real exchange raes as defned n RX1. The weghs are calculaed for fve major radng parners durng he perod from 1985 o 1987, based on he oal volume of rade, he daa for whch are from he Drecon of Trade Sascs (DOT). The hrd and he fourh ndces of he real exchange rae (RX3, RX4) are defned n a way smlar o he frs and he second, wh he CPI replaced by he WPI. When he WPIs of rade parners are no avalable, we use he CPIs nsead. RX5 s defned as he relave prce of radables o non-radables n he counry. I s defned as, T N T * N q p p e p p where he p sands for he nernaonal prces of radables and T * N p s he domesc prces of nonradables. Followng he radon, we employ he CPI of he domesc counry and he WPI of he base counry as he proxy for he prce of nonradables and he foregn prce of radables, respecvely. (Edwards, S., 1989; Chowdhury, 2004) The sxh ndex of he real exchange rae, RX6, s consruced by he PPP rao obaned from he PWT and he blaeral dollar exchange rae. The PPP rao s defned as he number of currency uns requred o buy goods equvalen o wha can be bough wh one un of he base counry. Tha s, he naonal currency value of GDP dvded by he real value of GDP n nernaonal dollars. 4 I s hus smlar o he rao of he domesc and he foregn prce ndces. The man dfference s ha, unlke he CPIs or he WPIs ha use each counry s own weghng sysems, boh ndces are calculaed usng he same weghng scheme. Thus, usng hem helps reduce an mporan source of he ndex number problem ha s nheren n he PPP sudy. RX6 s obaned by dvdng he PPP rao by he acual nomnal exchange rae. 3. Emprcal Resuls 3.1 The Un-Roos Tess We frs perform un-roo ess usng he sandard Dckey-Fuller (DF) and he augmened Dckey-Fuller es (ADF). The lag lengh for he ADF es s seleced by he Akake Informaon Creron (AIC). We also employ specfcaons wh and whou a me rend n he wo ess. For space reasons, he resuls of hese unvarae un-roo ess are omed. 5 They ndcae ha we canno rejec he null of nonsaonary wh he RX1 ndex for any counry a he 5 percen sgnfcance level. Wh he oher defnons, only a small number of cases suppor ha he real exchange rae s saonary. Wh he ADF es, we are able o fnd some more cases ha suppor PPP. Neverheless, he evdence does no seem o be overwhelmng enough o rejec he nonsaonary of he real exchange rae and accep PPP. These resuls are conssen wh wha has been repored n numerous sudes ncludng Messe and Rogoff (1988), Lohan and Taylor (1994), and Taylor (2002). Frankel (1986), Froo and Rogoff (1995), and Lohan and Taylor (1996) arbue he falure of PPP o he low power of he es. 3 When he CPI s no avalable, he GDP deflaor s used. 4 An nernaonal dollar has he same purchasng power over oal US GDP as he US dollar n a gven base year (PWT daa appendx n Summers and Heson, 1991). 5 Complee resuls are avalable upon reques. 2
Inernaonal Journal of Busness and Socal Scence Vol. 2 No. 9 [Specal Issue - May 2011] One approach o mprovng he power of PPP esng s o use a longer daa span as n Frankel (1986), Abuaf and Joron (1990), Km (1990), Lohan and Taylor (1996), Frankel and Rose (1996), and Taylor (2002). Anoher approach s o use panel daa as n, Oh (1996), Wu (1996), and Lohan (1997). Oh (1996) and Wu (1996) employ he es developed by LLC (2002). I may be vewed as a pooled ADF es n whch all he frs-order auoregressve coeffcens of he un-roo ess are assumed o be equal and have a sandard normal dsrbuon. The more recen es developed by IPS (2003) relaxes he srong resrcon of he equaly of he frs-order auogressve coeffcens as n he LLC es and pools separae cross-secon esmaes. 6 The sasc of he IPS es s he smple mean of he -sascs from unvarae regressons for ndvdual counres. 7 We apply boh he LLC and he IPS panel un-roos ess. We esmae wo models: one whou lags, AR(1), and one wh opmal lag seleced by he AIC, AR(p). 8 Table 1. Esmaon Resuls wh he LLC (2002) Tes Wh AR(1) Assumpon Wh AR(p) Assumpon -sasc Coeffcen -sasc Coeffcen RX1 3.67 0.8431 0.71 0.8136 RX2 1.30 0.9145 1.13 0.9153 RX3 3.25 0.7897 2.21 0.7685 RX4 1.77 0.9294 1.50 0.9273 RX5 4.42 0.8288 2.08 0.7936 RX6 1.23 0.8531-1.59* 0.8384 * Noe: The crcal values are -2.32 (1 percen), -1.64 (5 percen), and -1.28 (10 percen). The maxmum lag s se o sx for he AR(p) model. Table 2. Esmaon Resuls wh he IPS (2003) Panel Un-Roos Tes Wh AR(1) Assumpon Wh AR(p) Assumpon sasc Z sasc sasc Z sasc RX1-1.82*** -1.72** -2.15*** -3.63*** RX2-1.86*** -1.93** -1.81*** -1.68** RX3-2.10*** -2.86*** -2.40*** -4.26*** RX4-1.89*** -1.78** -1.98*** -2.21** RX5-1.74** -1.10-2.09*** -2.84*** RX6-1.78** -1.49* -2.11*** -3.40*** * Noe: Ths es s for 27 counres for RX1, RX2 and RX6, 20 counres for RX5 and 19 for RX3, RX4. The crcal values for -es are -1.80 (1 percen), -1.73 (5 percen), and -1.69 (10 percen). The crcal values for z-es are -2.33 (1 percen), -1.64 (5 percen), and -1.28 (10 percen). The maxmum lag s se o sx for he AR(p) model. Tables 1 and 2 provde he emprcal resuls of he wo panel un-roo ess. Table 1 shows ha he -sasc from he LLC es provdes no suppor for PPP a he 5 percen sgnfcan level wheher we employ he AR(1) or AR(p) assumpon. Also all esmaed frs-order auo regressve coeffcens are greaer han 0.7 and close o 1, mplyng near-nonsaonary of he real exchange rae. In a remarkable conras, Table 2 presens srong evdence for he saonary of he real exchange rae n all sx defnons. Frs of all, under he assumpon of he AR(1) model, we can rejec he null a he 5 percen sgnfcance level wh he sasc n all cases. Wh an opmal lag lengh for each counry, we can rejec he null of nonsaonary for all real exchange rae ndces usng eher sasc a he 5 percen sgnfcan level. Ths suggess ha he power and he effcency of he es clearly maers when esng for PPP. These IPS es resuls are conssen wh resuls n Wu and Wu (2001). Anoher neresng fndng s ha he null hypohess s more srongly rejeced wh he WPIbased real exchange raes (RX3 and RX4) han wh he CPI-based ones (RX1 and RX2). Ths fndng s n lne wh our expecaon and prevous fndngs such as hose of Km (1990), Froo and Rogoff (1995), and Wu (1996). 6 Boh ess also assume ha counres are cross secon ndependen. 7 N See Flessg and Srauss (2001). In oher words, ( ) N, where Var( ) and s he frs-order 1 / / auoregressve coeffcen of each counry. The Z sasc, Z N( ) /, of he IPS es s dsrbued as sandard 2 normal where E ( ), Var ( ). 8 We use Malab for he IPS ess wh he maxmum lag lengh for he AR(p) model resrced o sx. 3
The Specal Issue on Busness and Economcs Cenre for Promong Ideas, USA www.jbssne.com Somewha surprsngly, here s a weaker suppor for PPP wh he rade-weghed real exchange raes han wh he blaeral ones wheher he real exchange rae s defned wh he CPI or he WPI. 9 3.2 The Half-lfe of Devaons from PPP The auoregressve represenaon of he real exchange rae can be used o compue he half-lfe he me perod for a shock o decay o half of s nal sze. Table 3 presens he esmaes of half-lfe for ndvdual counres obaned wh he AR(p) model. 10 Followng Cecche e al., (2002) and Murray and Papell (2002), we repor he mean and medan of half-lfe esmaes. 11 The presence of oulers and negave esmaes n he case of RX2 and RX5 suggess ha he mean s a less relable gude han he medan as a summary sasc. Table 3. Half-lfe wh he IPS Esmaon wh he AR(p) Model Counry RX1 RX2 RX3 RX4 RX5 RX6 Algera 32.66 31.74 - - - 15.33 Argenna 1.18 1.06 - - - 0.88 Ausrala 2.48 3.36 1.62 1.94 1.48 3.86 Bangladesh 5.91 1.54 - - - 10.04 Brazl 2.48 2.74 2.61 2.68 2.51 4.92 Canada 4.13 4.02 1.70 1.54 4.55 3.79 Chle 3.32 2.84-1.58 2.08 3.39 Colomba 5.28 84.18 6.57 121.26 3.11 9.60 Denmark 1.68 1.56 2.12 1.56 3.18 2.26 Egyp 4.44 9.74 3.41 12.12 1.79 3.71 Fnland 1.86 3.11 2.14 7.97 2.84 2.00 France 1.57 1.73 - - - 1.77 Germany 1.93 2.42 - - - 2.12 Greece 2.16 4.48 1.69 1.36 5.22 4.49 Hungary 24.59-2.10 8.25 8.81-40.18 8.02 Inda 9.05 10.03 7.92 11.56 4.31 14.15 Indonesa 8.33 8.56 2.34 3.30 4.85 4.61 Ireland 1.87 2.20 1.76 3.32 4.71 3.60 Ialy 1.39 2.32 - - - 3.36 Korea 1.09 1.22 1.32 1.94 0.95 2.66 Mexco 1.29 1.27 2.55 2.57 1.95 2.35 Neherlands 1.53 1.97 1.54 7.14 1.95 1.65 New Zealand 1.03 5.08 1.26 0.81 2.35 1.40 Norway 2.30 1.27 - - 3.61 1.94 Porugal 3.10 7.01 - - - 5.95 Sweden 2.94 2.97 1.23 2.42 1.93 1.94 Thaland 2.91 4.27 1.36 1.94 0.72 7.01 Mean 4.91 7.43 2.85 10.31 0.70 4.70 Medan 2.48 2.84 1.94 2.57 2.43 3.60 9 The reason for hs fndng s no mmedaely clear. I mgh be ha counres arge her real exchange rae agans he US dollar and ry o keep sable for nernaonal compeveness or oher reasons. 10 In he case of he smple AR(1) process, he half-lfe can be obaned as ln(1/ 2) / ln( 1), whch s he soluon o T n he equaon ( 1) T 0. 5 where s he esmaed frs-order auoregressve coeffcen. For hgher auoregressve models, he measuremen of half-lfe s more complcaed. Ross (2005) suggess ha he half-lfe be calculaed by ln(1/ 2) b(1) / ln( 1) where b(1) s he sum of he esmaed AR coeffcens. 11 For he IPS es, Cecche e al., (2002) average half-lfe across ndvdual counres. 4
Inernaonal Journal of Busness and Socal Scence Vol. 2 No. 9 [Specal Issue - May 2011] The resuls ndcae, frs of all, n all cases excep RX6, he medan of he esmaed half-lfe s shorer han 3 years. In he case wh RX3, s less han 2 years. Even wh RX6, whch has he longes medan, s less han 4 years. Second, he half-lfe for RX3 s shorer han ha for RX1 n he majory of cases. The medan s also consderably shorer for RX3 han for RX1. I s conssen wh he convenonal resuls ha show ha PPP holds beer wh he WPI han wh he CPI. Thrd, he raded-weghed real exchange raes (RX2 and RX4) show longer half-lves and slower convergence han he blaeral raes n mos sample counres regardless of he defnon of he real exchange rae. For nsance, he half-lfe s longer (shorer) wh RX2 han wh RX1 n 18 (9) cases. The half-lfe s longer (shorer) wh RX4 han wh RX3 n 14 (4) cases. Fourh, he half-lfe for RX6 appears somewha longer han for RX1 or RX3. The able ha he half-lfe s longer (shorer) wh RX6 han wh RX1 n 19 (8) cases and wh RX3 n 15 (3) cases. To he exen ha RX6 elmnaes some bases due o ndex number problems arsng from usng he prce ndces repored by ndvdual counres, hs resul seems o sugges ha bases and ndex number problems may no be a major reason for he falure of PPP as repored n prevous sudes. 4. Concluson In hs paper we have re-examned he PPP hypohess wh varous defnons of he real exchange rae for he pos-breon Woods perod of floang exchange raes. Some of mporan fndngs of hs paper can be summarzed as follows: 1) PPP holds beer and he half-lfe of he real exchange rae s shorer when he WPI raher han he CPI s used as he prce ndex; 2) Somewha surprsngly, here s no evdence ha PPP holds beer wh rade-weghed real exchange raes han wh blaeral ones regardless of he prce ndex used; 3) In general, we are unable o rejec he un-roo null n unvarae ess. Srong evdence for PPP emerges only wh he use of IPS panel ess. In marked conras, he LLC panel ess provde no evdence on PPP, perhaps due o s homogeney resrcon on he parameer; 4) We fnd he medan of half-lve esmaes o be less han 3 years, whch shorer han he curren consensus; 5) Fnally, he half-lfe wh esmaed he IPS mehod s shorer han 3 years n all cases excep RX6. Ths s shorer han 3-5 years as surveyed n Rogoff (1996) alhough, n mos cases, sll longer han he 1-2 years esmaes from models ncorporang scky prces. References Abuaf, Nso and Phlppe Joron, 1990, Purchasng Power Pary n he Long Run, Journal of Fnance, 45(1), 157-174. Cecche, Sephen, Nelson Mark, and Rober J. Sonora, 2002, Prce Index Convergence among Uned Saes Ces, Inernaonal Economc Revew, 43(4), 1081-1099. Cheung, Yn-Wong and Kon S. La, 1994, Mean Reverson n Real Exchange Raes, Econ. Leers, 46(3), 251-256. Cho, C.V., N. Mark, and D.Sul, 2006, Unbased Esmaon of he Half-lfe o PPP Convergence n Panel Daa, Journal of Money, Cred and Bankng, 38 (4), 921-938. Chorareas, Georgos and George Kapeanos, 2005, How Puzzlng s he PPP puzzle? An Alernave Halflfe Measure of Convergence o PPP, Money Macro and Fnance (MMF) Research Group Conference, 36. Chowdhury, Mama Banu, 2004, Resources Booms and Macroeconomc Adjusmens n Developng Counres, Ashgae Publshng, Ld. Debold, F., Seven Hused, and Mark Rush, 1991, Real Exchange Rae under he Gold Sandard, Journal of Polcal Economy, 99(6), 1252-1271. Edwards, S.,1989. Exchange Rae Msalgnmen n Developng Counres, World Bank Res Obs., 4, 3-21. Flessg, Adran and Jack Srauss, 2001, Panel Un-Roo Tess of OECD Sochasc Convergence, Revew of Inernaonal Economcs, 9(1), 153-162. Frankel, Jeffery A., 1986, Inernaonal Capal Mobly and Crowdng Ou n he US Economy: Imperfec Inegraon of Fnancal Marke or of Goods Markes?, n How open s he US. economy?, eded by Ruh W. Hafer, 33-67. Lexngon, Mass. Frankel, Jeffery A., and Andrew K. Rose, 1996, A Panel Projec on Purchasng Power Pary: Mean Reverson Whn and Beween Counres, Journal of Inernaonal Economcs, 40(1-2), 209-224. Froo, K.A., and K.S. Rogoff, 1995, Perspecves on PPP and Long Run Real Exchange Raes, In G. M. Grossman and K.S. Rogoff, eds., Handbook of Inernaonal Economcs, III (Amserdam: Norh-Holland). Imbs, J., Ravn Mumaz, M. and H.Rey, 2005, PPP srkes Back: Aggregaon and he Real Exchange Rae, Quarerly Journal of Economcs, 120, 1-43. 5
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