Testing Purchasing Power Parity between India and US

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1 Tstig Purchasig Powr Parity btw Idia ad US Vipul Sharma Mavidr Sigh Pahwa Gtika Sharma Abstract I today s comptitiv world th structur ad th dirctio of xtral trad ar dtrmid by th xchag rat coducts. I othr words omial xchag rat affcts comptitiv powr i xtral trad. Policy makrs ca us PPP thory as a guid for th xtral comptitiv powr of a coutry. Furthrmor umrous mpirical workigs hav b prstd that misaligmt xchag rat causs currcy criss ad macrocoomic disquilibrium. PPP provids a idicator for th misaligmt. Th purpos of this papr is to tst Purchasig Powr Parity btw Idia ad US usig iflatio diffrtial ad omial xchag rat data from 1999 to 2011 o th basis of OLS modl. Th rsults idicat that PPP dos ot hold. Kywords: Purchasig powr parity, xchag rat, iflatio Itroductio Th post-librlizatio priod has b charactrizd by a sigificat chag i itratioal trad ad ivstmt ad fiacial markts i Idia. Th major coomis throughout th world hav rmovd thir cotrols o th movmt of capital. Th tchical iovatio has at th sam tim mad it possibl to trasfr capital throughout th world at th spd of light. As a rsult th capital has bcom mor mobil. A mor mobil capital will udoubtdly affct th valu of diffrt currcis ad itrst rats. Wh th fiacial markts bcam mor itratioalizd it ld to a icras i th amout of capital tryig to tak advatag of currcy swigs. Th Brtto Woods systm with fixd ad pggd xchag rats provd to b isufficit to cop with currcy spculatio. Th itratioal capital flows had mad it a ustabl motary systm. I 1976 wr a w itratioal systm agrd o i Jamaica. Currcis wr this tim allowd to float ad th rfrcs to th pric of gold wr abadod (Solik 2000, 5-6). Th currt itratioal motary systm ca b dscribd as a hybrid systm, whr th basic markt mchaisms for stablishig xchag rats iclud th fr float, maagd float, targt-zo arragmt ad fixd-rat systm. This systm has ld to rapidly fluctuatig xchag rats, cratig both problms ad opportuitis for actors dalig with forig currcis (Shapiro 1998, 55-56). To protct oslf agaist ths rapid currcy chags w istrumts wr dvlopd o th world capital markts i th 1970s ad 1980s, such as optios, swaps, futurs ad warrats. Th trd toward gratr xchag rat flxibility is a cosquc of risig itratioal capital mobility. Th ris of th itratioal capital mobility has mad it difficult for may govrmts to dfd thir fixd or pggd xchag rats or v pursu idpdt macrocoomic policis Dfdig a xchag rat could tur out to b vry costly ad v poitlss wh spculators attack a currcy. Govrmts tryig to dfd thir currcis hav b forcd to maitai high itrst rats to prvt capital outflows. High itrst rats that actually hidrac th coomic growth ad furthr hurtig th coomy. Thoris aimig to xplai ad udrstad th itractio of itratioal motary variabls will bcom icrasigly mor importat if th drgulatio ad itratioal itgratio of fiacial markts throughout th world cotius. O thory likig xchag ad iflatio rats is th Purchasig powr parity. It stats that th futur spot rat of xchag ca b dtrmid from th omial itrst diffrtial. Th ral itrst rats will i tur b qualizd across th world through arbitrag. This mas that th diffrc i th obsrvd omial rats will b stmmig from diffrcs i xpctd iflatio rats. Th diffrcs i aticipatd iflatio that ar imbddd i th omial itrst rats ar xpctd to affct th futur spot rat of xchag. Th ffct o th xchag rat is also mor likly to occur udr flxibl xchag rat arragmts, whr th currcis xchag rats ar allowd to fluctuat without th itrvtio of govrmts Purchasig Powr Parity Purchasig powr parity ca b dividd i to two vrsios: absolut PPP ad rlativ PPP. Th absolut vrsio stats that th ral pric of a good must b th sam i all coutris. That is, all goods oby th law of o pric. Th rlativ PPP is th most commoly usd vrsio of PPP. Th rlativ vrsio of PPP stats that th xchag rat btw ay two coutris will adjust to rflct chags i th pric lvls of th sam two coutris (Solik 2000, 36-37). For xampl, if iflatio is 5% i Idia ad 1% i th US, th INR valu of th USD must fall by about 4% to qualiz th INR pric of goods i th two coutris. Th purchasig parity rlatio ca b writt as follows: t t = t History of PPP > RJEBS: Volum: 01, Numbr: 08, Ju-2012 Pag 5

2 Purchasig powr parity has its bbs ad flows ovr th yar. Itrst i th doctri aros whvr xistig xchag rats wr cosidrd uralistic ad th sarch bga for th lusiv cocpt of quilibrium rats. It was first ivokd although i somwhat ambiguous trms i th priod of Npoloic wars, it rcivd its amig at th hads of Gustav Cassl durig world war I ad it was rsurrctd aftr world war II. It also had its critics, amog othrs Taussig aftr world war I ad Habrlr aftr world war II, but it has maagd to surviv vrthlss. Purchasig powr parity mas diffrt thigs to diffrt popl. As mtiod arlir w ar havig two vrsios of purchasig powr parity i.. absolut ad rlativ vrsios of Purchasig powr doctri. Ratioal bhid PPP Purchasig powr parity masurmts cosidr th amout of goods ad srvics a prso ca buy i a coutry wh calculatig how much a currcy is worth. A idividual may ar lss moy i o coutry, ad hav th opportuity to purchas a largr hous or mor food, bcaus othr prics ar also chapr i that coutry. Purchasig powr parity allows a idividual to calculat th stadard of livig availabl i diffrt coutris. Effctiv Exchag Rat Purchas powr parity allows a idividual to dtrmi th ffctiv xchag rat for forig currcy. If a uro is worth 1.5 dollars, but th pric of a itm i uros is th sam i Grmay as it is i dollars i Amrica, th official xchag rat is still 1.5 dollars pr uro. Th ffctiv xchag rat is $1 pr uro, sic a prso who ars 40,000 uros i Grmay ca buy th sam umbr of cosumr goods as a prso who ars $40,000 i Amrica. Forig Military Aalysis Purchasig powr parity also allows aalysts to dtrmi th strgth of a forig military. Th U.S. has a larg military budgt, ad it also has a strogr currcy tha othr atios. Aothr coutry, such as Chia, may spd lss moy to hir a idividual soldir or purchas a additioal tak or airpla. O coutry may b abl to crat a strogr military forc whil havig a smallr military budgt, bcaus military xpss ar lowr i that coutry. Local Spdig Purchasig powr parity calculatios assum that all icom i a currcy is spt i th coutry whr th currcy is usd. Th parity calculatio assums that a Idia who rcivs icom i rups will purchas all cssary itms usig rups. May atios rly o forig imports to satisfy som cosumr ds, rquirig a importr to xchag currcy for a forig currcy to mak th purchas. Comparativ Walth It is possibl for a coutry to b mor walthy tha a ighbor accordig to pr capita icom masurmts ad still hav a lowr stadard of livig wh usig purchasig powr parity to calculat icom. If a dollar is worth o Swiss frac, but Swiss grocry stor prics i Swiss fracs ar highr tha Amrica grocry stor prics quotd i U.S. dollars, a Swiss workr ca ar mor moy tha a Amrica workr ad still hav a lowr stadard of livig. Employ Cost Purchasig powr parity affcts both ducatio ad traiig costs. A mployr ca hir a workr i a forig coutry ad pay a much lowr wag, whil providig th workr with a comparabl stadard of livig as a workr i th mployr's hom coutry. Additioal costs, such as uivrsity ducatio for a workr, ar also lowr bcaus of purchasig powr parity. Drivatio of Purchasig Powr Parity Purchasig powr of a currcy is dtrmid by th amout of goods ad srvics that ca b purchasd with o uit of that currcy. If thr is mor tha o currcy, it is fair ad quitabl that th xchag rat btw ths currcis provids th sam purchasig powr for ach currcy. This is rfrrd to as Purchasig powr parity. It is idal if th xistig xchag rat is i tu with this cardial pricipl of purchasig powr parity. O th cotrary, if th xistig xchag rat is such that purchasig powr parity dos ot xist i coomic trms it is a situatio of disquilibrium. It is xpctd that th xchag rat btw th two currcis coforms vtually to purchasig powr parity. So, accordig to PPP th xchag rat btw th two currcis should b qual to th ratio of ths coutris pric lvl. For xampl, for US ad Idia, th pric idx of a baskt of products i US is P $ ad th pric idx of idtical baskt of products i Idia is P r, th: Equatio (i) Hr S t is th spot xchag rat at tim t. Likwis, accordig to th vrsio of rlativ PPP thory thr is a lik btw xpctd xchag rat[s t+1 ] ad xpctd iflatio rats () i two coutris. ic th futur pric of a commodity is affctd by th xpctd iflatio rat, th pric lvls i Idia ad US ar affctd by th xpctd iflatio rats. Wh P 0 is th currt pric lvl, ad is th xpctd iflatio rat, th pric lvls aftr a yar will b P 1 = P 0 ( + ) I Idia: P r1 =P r0 ( + r ) I US: P $1 =P $0 ( + $ ) Th ratio of prics o yar latr is: This ca b writt as S t [ as ( ) is th currt spot rat, S t. Thus th xpctd xchag rat o yar latr, S t+1, is a ratio of th prics o yar latr. S t+1 = S t [ Equatio (ii) Th abov quatio ca b rarragd as: t t Th lft had sid ca b writt as 1+{[ S t+1 - S t ] S t }, whr [ S t+1 - S t ] S t is othig but th rat of chag i th spot rat. Dotig [ S t+1 - S t ] S t by : (1+)= O simplificatio = (1+ ) Th domiator o th right had sid (1+ ) ca b igord for small valus of. Th > RJEBS: Volum: 01, Numbr: 08, Ju-2012 Pag 6

3 [S t+1 - S t ] S t = Equatio (iii) This quatio stats that is approximatly qual to. ic is othig but [ t+1- S t ] S t, th rlativ vrsio of PPP thory stats that th rat of chag i th spot rat is approximatly qual to th iflatio diffrtial i two coutris. Wh this coditio holds tru, th markt is i quilibrium. Rviw of Litratur Thr is vidc that th famous Big Mac idx of currcis put forward by th Ecoomist ach yar holds up wll i th log ru but ot i short ru (Dails & Radbaugh 1998,424). Also Wbstr (1987) rjctd PPP i th short ru. Galliot (1971) prsts vidc statig th validity of th PPP i th log ru. H xamid th rlatioships btw th iflatio rats i th USA rlativly to som of its tradig partrs ad th rlativly chags i th xchag rats btw th sam atios.galliot cam to th coclusio that th pric chags ar th major dtrmiats of th xchag rat i th log ru. Shapiro (1998) prsts aothr vidc of a log ru PPP, whr h compars th rlativ iflatio rats for 22 coutris with th rlativ chag i th xchag rat. H fids that thos coutris with th highst iflatio rats also had th largst dprciatio i thir currcis. Othr studis cam to th coclusio that th PPP holds up wll for som tim priods but dos ot hold for othrs (Krugma & Obstfld 1997, 411). Kasma t al. (2010) tstd PPP for pottial EMU accssio coutris. Th rsults rval that, i ths coutris, dviatios from th parity ca b causd by sudd chags i xchag rats, high iflatioary prssurs, or motary shocks; do ot prsist ovr tim; ad allow PPP hold i th log ru. Rgrssio Modl: I a fficit markt all iformatios ar immdiatly rflctd i th xchag rats. Ratioal markt participats should bas thir forcasts o all availabl iformatio. Th xpctd futur spot rat at tim t+1 giv a iformatio st Φ t, at tim t, ca b dotd E(S t+1, Φ t ) Equatio (i) From this follows that th xpctd futur spot rat at tim t+1 basd o all availabl iformatio at tim t should o avrag b qual to th futur spot rat: S t+1 = E(S t+1, Φ t ) Equatio (ii) W also add a rror trm, µ t+1 to quatio ii. Th rror trm is dfid as th diffrc btw th ralizd futur spot rat ad th xpctd futur spot rat.if th markt participats ar ratioal should th rror trm b ucorrlatd with th iformatio availabl at tim t should b rflctd i th xpctatios ad dviatios from th xpctd valu should oly b causd by uprdictabl ws (solik 2000,156). If xpctatios ar ratioal ad ubiasd,th: S t+1 = E(S t+1, Φ t )+ µ t+1 Equatio (iii) Likig this rasoig to th discussio of Purchasig powr parity dscribd i Itroductio, o should xpct th xchag rat chag i rlatio to iflatio diffrtials. If w add a rror trm prstd arlir i quatio iii w gt: [ S t+1 - S t ] S t = +µ t+1 Equatio (iv) That is, th prctag i th xpctd spot rat of xchag should qual th prctag iflatio diffrtial. Thus, th rgrssio modl taks th followig form: [ S t+1 - S t ] S t =α+β +µ t+1 Equatio (v) Hypothsis Null hypothsis: α =0,β =1 Th t-tst will b applid to α ad β, whos hypothsizd valus ar 0 ad 1 rspctivly. Th rgrssios us Ordiary Last Squars stimats of α ad β. Itrprtd litrally, α shows th valu of th xchag rat chag wh th iflatio diffrtial is 0, that is wh th Iflatio diffrtial is 0 th xchag rat should ot chag ad hc, also qual 0. Wh β quals 1 it mas that a 1 prct icras i th iflatio diffrtial will lad to a 1 prct offsttig chag i th xchag rat. That is, if th Iflatio diffrtial is o prct highr i th Idia tha i th Uitd stats, th INR will dprciat by o prct rlativly to th USD. Th Data Th data cosists of mothly iflatio rats for Uitd stats ad Idia ad currcy xchag rat btw USD ad INR btw Jauary, Fbruary, Th xchag rats ar tak from Rsrv Bak of Idia wbsit, which is a dirct quot. Th collctd data matrial has th b rvisd by calculatig th prctag iflatio diffrtial ad th prctag xchag rat chag for diffrt moths. Th iflatio diffrtial has b computd by takig th Idia s iflatio rat mius U s iflatio rat. Th xchag rat chag cotais th xchag rat chag from o moth to aothr whr th xchag rat is xprssd as hom currcy pr uit of forig currcy. It has b computd by takig th xchag rat at tim t+1 mius th xchag rat at tim t, dividd by th xchag rat at tim t. Ths calculatios ar cotiud util w gt 157 obsrvatios. Rgrssio rsults & Aalysis Th rgrssio from US-Idia gav th followig rsults R-squard = Costat α = Variabl β = Th accptac rgio at 5% lvl of sigificac for α is > α > Th accptac rgio at 5% sigifica lvl for β is > β > R-squard tll us how much of th variatio i th dpdt variabl th xplaatory variabl ca xplai. Th R-squard for Idia-US turd out to b vry vry low.14% of th chags i Idia US xchag rat ca b xplaid by Iflatio diffrtials. Th ull hypothsis that α =0, β =1 will b rjctd if th hypothtical valus of α ad β li outsid thir rspctiv accptac rgios. Howvr, both α ad β li withi thir > RJEBS: Volum: 01, Numbr: 08, Ju-2012 Pag 7

4 accptac rgios at 5% sigificac ad H 0 caot b rjctd. This mas that w ca b 95% cofidt that th tru valus of α ad β li somwhr isid thir rspctiv accptac rgios. Th rsult also illustrats that a 1% icras i th iflatio diffrtial o avrag, lad to approximatly 1.46% offsttig chag i th INR/USD xchag rat. Th α valu, i tur, says that if th iflatio rats i th US ad Idia ar th sam, th chag i th xchag rat would o avrag qual 12.62%. This is practically th sam as a o-chag % c h a g i x c h a g r a t Prctag chag i hom currcy valu of forig currcy Liar (Prctag chag i hom currcy valu of forig currcy) Iflatio Diffrtial Coclusio: Th purpos of this papr was to dscrib th purchasig powr parity ad tst its mpirical validity i th log ru. Employig rgrssio aalysis to iflatio diffrtials ad chags i xchag rat mad this possibl. Th R-squar turd out vry low for th coutry pair i.. US ad Idia. So, Iflatio diffrtial should ot b usd to prdict chags i futur spot rat o a mothly basis. Th Low R 2 is also idicatig th modl s ovrall prformac is low. Th hypothtical valus of α ad β lis i th accptac rgios at 5% sigificac. Thrfor, th ull hypothsis caot b rjctd. This mas that w ca say with 95% crtaity that th tru valus of α ad β li somwhr i thir rspctiv accptac rgios. Though, must b carful i our coclusios du to th low R 2, which idicats that th modl s ovrall prformac is low. Thrfor, o stabl, prdictabl rlatioship btw chags i th omial itrst diffrtial ad xchag rat chags ca b assumd. Rfrcs Alibr, R. Z. & Sticky, C. P. (1975) Accoutig masurs of forig xchag xposur:th log ad short of it, Accoutig Rviw, Jauary. Booth, G & Cir, C. (2001) th rlatioship btw omial itrst rats ad iflatio: Itratioal vidc, Joural of Multiatioal Fiacial Maagmt, 11. Coppock, L. & Poitras, M. (2000) Evaluatig th Fishr Effct i th log-trm cross-coutry Avrags, Itratioal Rviw of Ecoomics ad Fiac, 9. Dails, D. J & Radbaugh, H. L. (1998) Itratioal Busiss. Addiso Wsly Logma, Ic. Radig. Dmirag, I & Goddard, S. (1994) Fiacial Maagmt for Itratioal Busiss. McGraw-Hill Book Compay Europ, Brkshir. Dorbusch, R, Fischr, S & Startz, R. (1998) Macrocoomics. MCGraw-Hill Compay, Ic. Nw York. Doughrty, C. (1992). Itroductio to Ecoomtrics. Oxford Uivrsity Prss. Nw York. Eichgr, B. (1996). Globalizig Capital. Pricto Uivrsity Prss. Nw Jrsy. > RJEBS: Volum: 01, Numbr: 08, Ju-2012 Pag 8

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