Taylor Principl Supplmns h Fishr Effc: Empirical Invsigaion undr h US Conx Mohammd Saiful ISLAM Mohammad Hasma ALI 2 ABSTRACT This papr rviws h shor- and long-run dynamics of inrs ra and inflaion of h Unid Sas. Basing upon quarrly as wll as monhly daa ovr h priod 957 o 200, w find vidnc ha inrs ra bhaviour of h Fdral Rsrv is consisn wih h Taylor principl in shor run and wih h Fishr hypohsis in long run. Enir sampl jusifis h xisnc of a long run coingraing rlaionship bwn fdral funds ra and inflaion characrisd as h Fishr ffc. Whn daa ar spli ino diffrn subsampls, h coingraing rlaionship disappars. Inrs ra dynamics of pr-980 and pos-200 nihr rack Fishr hypohsis nor Taylor principl, rahr rprsn subsanial discrion. KEYWORDS: Fishr Effc, Monary Policy, Taylor Principl. JEL CLASSIFICATION: E43, E52, E59 INTRODUCTION A h bginning of h wnih cnury Yal Univrsiy conomis Irving Fishr modlld ha in h long-run mony growh affcs boh h nominal ra of inrs and inflaion on for on, hrfor dos no affc h ral ra of inrs- which lar bcam familiar as h Fishr ffc. Sinc hn acadmics and rsarchrs hav bn invsigaing h xisnc of h Fishr ffc by using im sris and panl daa for diffrn counris ovr long span bu hr is no common conclusion rgarding h im horizon whn Fishr ffc acually holds, if a all. Empirical jusificaion of Fishr ffc lis in h uni roo bhaviour of boh nominal inrs ra and inflaion so ha hr is long run quilibrium characrisd by coingraing rlaion bwn h wo sris. This papr carfully rvisis h issu of h rlaionship bwn inrs ra and inflaion wih h aim of invsigaing whhr acually hr xiss a on-for-on corrspondnc bwn hs wo sris. If h nominal ra of inrs rsponds o inflaion jus on for on hn h ral ra of inrs would rmain unchangd, hus monary policy would b nural. John B. Taylor (993), on h ohr hand, proposs monary policy rul ha clarly conradics wih h Fishr hypohsis. Our objciv is o invsiga whhr h US daa suppors any on-for-on rspons of inrs ra o inflaion or inrs ra is mor rsponsiv o inflaion so ha h Taylor principl, as opposd o h Fishr rlaion, holds. To h bs of our knowldg hr is no liraur availabl ha addrss h smingly rvrs viws of h Fishr ffc Associa Profssor, Dparmn of Economics, Univrsiy of Chiagong, E-mail: saifulcu@yahoo.com 2 Assisan Profssor, Dparmn of Financ and Banking, Univrsiy of Chiagong
Mohammd Saiful ISLAM, Mohammad Hasma ALI and Taylor rul. Thr ar paprs howvr rviwing h Fishr ffc and Taylor rul sparaly. Barsky (987) finds ngaiv corrlaion bwn h US commrcial papr ra and conmporanous inflaion for h priod 860 o 939 bu a srong posiiv corrlaion for 950 o 979. Ros (988) dmonsras ha h US inrs ra and inflaion ar ingrad of diffrn ordr, hrfor ruls ou h possibiliy of any long run coingraion bwn hm. Mishkin (99) dos no find any shor run Fishr ffc in US daa bu in h long run h Fishr ffc occurs which is consisn wih Fishr s own modlling. Ksryyly (994) discovrs a long-run quilibrium rlaionship bwn inrs ra and inflaion, validaing h xisnc of h Fishr ffc in Turkish daa ovr pos-980 priod. MacDonald and Murphy (989), Du and Gosh (995) do no find h xisnc of h Fishr ffc in Canadian daa. Conrary o his, Crowdr (997) obsrvs h xisnc of radiional Fishr ffc in Canadian daa ovr four dcads alhough h quilibrium rlaionship bwn inrs ra and inflaion is no nirly sabl ovr h priod du o h apparanc of srucural braks. Using hundrd yars of UK daa sinc 990, Granvill and Mallick (2004) find on-for-on rlaion bwn nominal ra of inrs and xpcd inflaion. Similar rsuls ar obaind by Brumn and Jlassi (2002) for 6 ou of sampl 26 counris. Jnsn (2006) applis h unconvnional chniqu of fracionally ingrad modl o show ha monary shock dos no caus a prmann chang o h inflaion ra. Using im sris daa of 7 dvlopd conomis Jnsn finds inflaion o b a slow, man rvring, fracionally ingrad procss in all 7 counris and hrfor h long-run Fishr ffc canno b sd. A survy on 5 OECD counris conducd by Byr al. (2009) shows ha hr is a brak in h coingraion rlaion ha inroducs a spurious uni roo ha lads o a rjcion of coingraion bu onc his brak is akn ino accoun h linar Fishr quaion holds wll. Hrwarz and Rimrs (20) suggs h validiy of h Fishr hypohsis only during h inflaion arging rgim whn inflaion is ssnially low bcaus in h cas of acclraing inflaion h basic rlaion bwn inrs ra and inflaion braks down. Thy also argu ha in mos cass inrs ra and inflaion xhibi a long-run quilibrium rlaionship wih inflaion cofficin lss han uniy. This papr confirms h occurrnc of h long-run Fishr ffc and addrsss an addiional faur of h shor rm inrs ra which is characrizd by h Taylor principl. W carry ou rsarch on h basis of quarrly as wll as monhly US daa ovr h priod 957 o 200. W find vidnc of long-run Fishr ffc alhough hr is no vidnc of shor-run Fishrian rlaion bwn inrs ra and inflaion. As opposd o h Fishr rlaion, h pos-980 daa xhibis srong rspons, rahr han on-for-on rspons of h inrs ra o inflaion ha was mphasisd by Taylor (993). This finding acs in accordanc wih h sylizd facs of h Fdral Rsrv during pos-volckr rgim whn monary policy urnd ou aciv. Srong rspons of nominal inrs ra o inflaion accouns for posiiv ral ra of inrs in h vn of rising inflaion such ha monary policy gs inflaion sabilizd. This clarly conrass wih h Fishr hypohsis which suggss h suprnuraliy of mony and hrfor inaciv monary policy. Th rmaindr of h papr is organisd as follows. Nx scion rviws h horical background of h Fishr ffc and Taylor principl. Scion 3 illusras daa and mhodology usd in h analysis. Scion 4 prsns mpirical rsuls and scion 5 summariss. 90
Economia. Sria Managmn Volum 5, Issu, 202. THEORETICAL BACKGROUND. Fishr ffc An incras in mony growh lads o an qual incras in nominal ra of inrs and inflaion- laving ral ra of inrs unchangd, which is know as Fishr ffc or Fishr hypohsis. Ral ra of inrs is drivd from quaion (2.) blow. This analysis is basd on Blanchard (999). i r (2.) Whr, i and r rprsn nominal and ral ras rspcivly, and dnos xpcd inflaion. Equaion (2.) follows h link quaion, ( i ) P r and h dfiniion of P inflaion P P, whr P and P rspcivly. P sand for currn pric and xpcd fuur pric Ral ra is obaind by furhr manipulaing (2.). i i r r i i i Expansion of mony sock incrass boh i and a h sam ra, hrfor r rmains unchangd via r, which is h basic proviso of Fishr hypohsis. i Undr raional xpcaion assumpion, obsrvd inflaion, whr is random disurbanc rm. Using his, nominal ra of inrs is xprssd blow as a funcion of inflaion i r (2.2); ( ) Equaion (2.2) illusras ha chang in inflaion ra should b followd by qual changs in h nominal inrs ras whn h ral inrs ra is consan. Th rspons of h nominal inrs ra o inflaion is rmd as Fishr cofficin which is suggsd o b. Crowdr (997) argus ha ax adjusd Fishr ffc should b largr hn. If ovrall ra of ax is hn h rlaion bwn afr ax nominal inrs and inflaion urns ou, ( ) i i.., r i r Fishr ffc, ; givn, 9
Mohammd Saiful ISLAM, Mohammad Hasma ALI Th simabl form of Fishr hypohsis is i b b 2 (2.3) Impac of mony supply on inflaion works hrough h dynamic aggrga dmand rlaion. Blanchard (999) prsns saic vrsion of AD as: M Y Y, G, T. Hr M is P P ral supply of mony; G and T ar fiscal componns. Ignoring fiscal rol, M Y Y P Assuming spcific dynamic form of aggrga dmand, M Y (2.4) ; 0 P Equaion (2.5) dscribs h rlaion bwn mony growh, oupu growh and inflaion which is obaind by log-linarizing h abov xprssion: Yˆ ˆ M (2.5) Whr Oupu growh, dy Yˆ Y Mony growh, dm Mˆ M Inflaion, dp P If oupu growh falls blow h nominal growh of mony hn h diffrnc is showd up in inflaion hrough quaion (2.6). Mˆ Yˆ (2.6) For xampl, a 5% incras in mony should b followd by 5% incras in oupu so hr is no inflaion, bu if oupu growh is, say, 2% hn hr would b a 3% incras in inflaion. Undr consan inflaion, xpansion in mony lads o lowr inrs ra and hus highr oupu growh. Mony growh and inflaion hav on for on corrspondnc, implying no chang in ral variabls. Ral variabls, howvr, can only b influncd in h shor-run whras in h long-run ral variabls convrg o hir naural lvls and policy only alrs h lvl of prics. In long run, xpcd inflaion is qual o acual inflaion ( ) and ral inrs ra sicks a naural ra ( r rn ), hnc i r n. Also in h long run oupu growh is zro, hrfor inflaion quals mony growh, i.., Mˆ. This follows, i rn Mˆ, according o which a crain prcn incras in mony growh corrsponds o an qual prcn incras in nominal ra of inrs ha is qual o incras in inflaion. Finally, h 92
Economia. Sria Managmn Volum 5, Issu, 202 diffrnc bwn nominal ra of inrs and inflaion- h ral ra of inrs rmains unchangd- his is h Fishr ffc. In shor run, an xpansionary monary policy rducs nominal ra bu ha dos no say long bcaus givn h Phillips curv rlaion, onc oupu riss abov naural ra, inflaion sars incrasing sinc unmploymn falls blow naural ra. Subsanial incras in inflaion, whn xcds h growh of nominal mony, causs a ngaiv ral growh of mony lading o an incras in nominal ra of inrs. Inflaion xpcaion rmaining unchangd h ral ra of inrs gos up and gs back o is iniial lvl. Finally, nominal inrs ra rachs a highr lvl qual o h ral inrs ra plus h nw highr ra of growh of mony. Fishr ffc is mos likly o appar in long run hough hr is liraur dmonsraing h validiy of h ffc in shor run as wll (s.g. Granvill & Mallick, 2004). In gnral, hr is a link bwn monary policy and sabilizaion. Disconncion bwn monary policy and inflaion sabilizaion may b a random occurrnc. For xampl, during warim h cnral bank has o provid hug liquidiy o h govrnmn or in h vn of financial insabiliy monary auhoriy has o prsrv h invsors inrs. Bu hr is nough vidnc o infr ha monary policy ransmis ino inflaion..2 Taylor Principl Macroconomic sabilizaion rquirs a mor han on for on rspons of inrs ra o inflaion- which is known as Taylor principl du o Taylor (993). Complx srucur of monary policy is simplifid o a larg xn by his characrisaion suggsing ha if inflaion is abov arg hn h nominal ra of inrs should b adqualy incrasd such ha h ral ra of inrs incrass and ha rducs inflaion. Indd, Taylor principl volvs from Taylor rul ha was proposd by John Taylor a Carngi Rochsr Confrnc in 993, dscribd by quaion 2.7 blow i * r ( * ) y whr i * and * masur arg ras of inrs and inflaion rspcivly; r is quilibrium ral ra of inrs;, y, and ar currn priod s inflaion and oupu gap and y corrsponding sabilizaion paramrs rspcivly. Assuming r * and 0, rducd form of h Taylor rul appars as y i * ( ) According o h abov gnralizaion, policy only aims a inflaion sabilizaion and dos no rgard oupu a all. Taylor principl is rflcd in h cofficin of. Givn posiiv, which is Taylor Principl- insrucing mor han on-for-on incras in nominal ra of inrs in h vn of rising inflaion. If is s qual o zro, hn h nominal inrs ra rsponds o inflaion jus on-for-on. Such adjusmn would dscrib a siuaion whr y......... (2.7) 93
Mohammd Saiful ISLAM, Mohammad Hasma ALI ral ra of inrs is consan, hrfor saionary. Bu if Taylor principl holds hn ral ra of inrs would bcom nonsaionary in h world of variabl inflaion. In ordr o xplain monary policy ransmission mchanism, Walsh (200) uss on simpl Nw Kynsian variy macroconomic modl comprising IS curv, Phillips curv and Taylor-yp monary policy rul. y E y i E ( IS); ( 0 ) E y (Phillips Curv); (, 0) i v...... (Policy rul); ( ) y and y rprsn oupu gap in priod and + rspcivly, masurd as h diffrnc bwn acual oupu and ponial oupu. v rprsns indpndn and idnically disribud (i.i.d.) monary policy shocks. On can inuiivly show ha in h vn of inflaion, sufficin incras in h nominal ra of inrs according o h policy rul can lad o a fall in oupu via IS rlaion. In h Nw Kynsian modl sinc oupu is proporional o marginal cos, a fall in oupu would corrspond o a fall in marginal cos bcaus of incras in labour supply and vnually a fall in inflaion via h Phillips rlaion. In his cas monary policy is aciv. Bu on-foron rspons of inrs ra o inflaion would urn h policy nural. This analysis clars h fac ha aciv monary policy is consisn wih Taylor principl whras inaciv policy wih Fishr hypohsis. 2. DATA AND METHODOLOGY W us quarrly and monhly US daa ovr h priod 957 o 200. Inrs ra and CPI sris hav bn rrivd onlin from Inrnaional Financial Saisics of h Inrnaional Monary Fund (IMF). Alhough h sudy mainly focuss h rsuls basd on fdral funds ra, w also look a hr ohr masurs of inrs ra in h conx of h US,.g., Trasury bill ra, 3-monh commrcial papr ra and 0-yar govrnmn bond yild ra. Annual inflaion ras for ach quarr and monh ar compud rspcivly as 00*(log(CPI)-log(CPI(-4))) and 00*(log(CPI)-log(CPI(-2))). In addiion o h whol sampl, w also spli daa ino hr ohr subsampls o capur h impac of rgim chang (pr- and pos-volckr ra) and o rack h rcn dviaion from rul-lik policy sing (pos-200 priod). Saionariy propris hav bn xamind by applying ADF uni roo s wih and wihou rnd in h rgrssion quaion. Lag lngh is slcd auomaically on h basis of Schwarz informaion cririon (SIC). Two-sp las squars procdur is applid o sima h rror corrcion modl. Afr making sur ha nominal ra and inflaion ar I(), w run las squar rgrssion o sima coingraing rlaionship i b b and gnra h rsidual sris 2 ˆ i bˆ bˆ 2 in ordr o xamin h saionariy of h sris as an vidnc of coingraion. Laggd rsidual, ˆ i bˆ bˆ is h masur of coingraing rror or disquilibrium rror. 2 In h scond sp OLS approach is applid o sima rror corrcion modl comprising wo quaions blow: i (2.8) 0 ˆ i 20 2ˆ (2.9) 94
Economia. Sria Managmn Volum 5, Issu, 202 Th modl s snsibl spcificaion is consraind by nonzro valu of a las on of h rror corrcion cofficins 0 and 2. Sabiliy rquirs, 0 and 0. 2 Th abov spcificaion of rror corrcion modlling is oulind from Hill al. (2007, p. 349). W find boh h inrs ra and inflaion o b I() whn h whol sampl is considrd. For all ohr subsampls ihr Fdral funds ra or inflaion or boh ar found saionary. Quarrly and monhly daa produc idnical rsuls xcp for h subsampl spanning h priod 200-200. In his sampl null hypohsis of uni roo in fdral funds ra can b rjcd whn quarrly daa is usd bu h dcision is alrd in h cas of monhly daa. ADF uni roo s rsuls ar summarisd in Tabl 2.. Sinc h ncssary condiion for coingraion is saisfid ovr h nir priod of 957 o 200, coingraion s is carrid ou only for his sampl. Comovmn of inrs ra and inflaion ar inrospcabl form diagrammaic prsnaion. Figur gnras som fl ha inrs ra and inflaion do mov oghr, hrby hining a ponial long run rlaion. Priod 957-200 957-980 98-200 200-200 Tabl. ADF Ts for Inrs Ra and Inflaion Inrs ra 5% ADF criical dcision saisic valu -2.54** m -2.75** -3.5** m -2.52** -4.55** m -5.33** -3.38* m -2.07* -3.43 m -3.42-3.46 m -3.43-3.45-3.43-2.94 m -2.89 do no rjc h null of uni roo do no rjc h null of uni roo Rjc h null of uni roo Rjc h null of uni roo bu do no rjc whn daa is monhly Inflaion ADF 5% sais criical dcision ic valu -2.23* m -3.08** -4.30** m -.2* -4.55** m -4.56** -2.58* m -.64* -2.88 m -3.42-3.46 m -2.87 3.45 m 3.42-2.94 m -2.89 Sourc: auhors *ADF s includs a consan rm bu no rnd in h s quaion. ** ADF s includs a consan rm as wll as rnd in h s quaion. m indicas rsuls on h basis of monhly obsrvaion. do no rjc h null of uni roo rjc h null of uni roo bu do no rjc whn daa is monhly rjc h null of uni roo do no rjc h null of uni roo 95
Mohammd Saiful ISLAM, Mohammad Hasma ALI Figur. Inrs ra and inflaion ovr 957-200 Sourc: auhors Our sudy poins o wo disinc principls in rms of ral inrs ra. If h Fishr ffc holds hn h ral ra of inrs rmains unchangd, bu h Taylor principl, by dfiniion, rquirs a variaion in h ral ra of inrs so ha monary policy urns ou aciv. Ral inrs ra sris is crad by aking h diffrnc bwn nominal ra of inrs and inflaion. Figur 2 shows ha h avrag ral ra of inrs was no oo much flucuaing bfor 980 bu considrably varying afrwards wih an apparn jump around 980. This dsignas h variabl aiuds of policymakrs bfor and afr 980. Paul Volckr, whn appoind chairman of h Fdral Rsrv in 979, inroducd h drasic chang in policy bhaviour by paying inns anion o inflaion sabilizaion whil disrgarding ohr objcivs. Dramaic incras in h nominal ra of inrs in h arly priod of Volckr amouns o h corrsponding incras in ral ra of inrs. Figur 2. Ral ra of inrs ovr 957-200 Sourc: auhors 96
Economia. Sria Managmn Volum 5, Issu, 202 3. EMPIRICAL RESULTS Having xamind h im sris propris of h nominal ra of inrs and inflaion, w sima h rlaion bwn hs wo variabls whn h nominal ra of inrs is considrd as h dpndn variabl. Esimaion rsuls ar summarisd in Tabl 2. Th only supposdly rliabl simas ar obaind ovr h sampl priod 957-200 bcaus for his sampl boh inrs ra and inflaion sris ar I(). Mor imporanly h rsiduals obaind from h OLS rgrssion ar I(0), hrby vidncing a long run coingraing rlaionship. Th simas obaind for h subsampl ovr 957-980 may no b rliabl bcaus of h ingraion propris of h wo sris involvd. Whil h inrs ra is ingrad of ordr, inflaion ra is rnd saionary. If h rnd is no includd in h ADF s rgrssion hn h inflaion sris bcoms ingrad of h sam ordr as inrs ra. For inuiiv rasoning w also l h rsiduals undrgo h s for nonsaionariy and find hm I(0). Th simad rror corrcion modl undrlying his sampl priod has corrc signs for boh rror corrcion cofficins hough only on cofficin corrsponding o chang in inflaion is found significan. Ovrall w do no com o h conclusion ha inrs ra and inflaion in his priod mainain a long-run Fishrian rlaionship. Sampl priod 98-200 is mor inrsing o h policymakrs and rsarchrs sinc a significan chang in policy, faurd as sric inflaion avrsion, ook plac in h bginning of his priod. Empirical inrs coms from h fac of saionary bhaviour of h inrs ra as wll as inflaion. ADF uni roo ss, on h basis of quarrly and monhly daa, show ha inflaion and inrs ras ar I(0), hus h undrlying rgrssion is no spurious. Howvr, alhough nonspurious bu any long run rlaion basd on coingraion is unlikly o appar sinc h variabls ar no ingrad of ordr. W run OLS rgrssion of inrs ra on inflaion whr simas of inflaion cofficins ar obaind.58 and.54 undr quarrly and monhly daa wih sandard rror qual o 0.4 and 0.06 rspcivly. Ths simas do no mach wih h Fishr hypohsis bu dlibraly mach wih h Taylor principl. In gnral, Taylor principl suggss an inflaion cofficin abov uniy and in paricular Taylor (993) suggss a valu of.50. From his viwpoin, our currn simas provid subsanial vidnc o surmis ha monary policy, afr Volckr s appoinmn, complis wih h Taylor principl. Tabl 2. OLS simas of i b b2 Priod Quarrly Monhly ˆb ˆb 2 R 2 DW 957-200.95 (0.26) 0.95 (0.06) 0.58 0.20.98 (0.6) 957-980.9 0.8 0.79 0.56.93 (0.26) (0.04) (0.6) 98-200 0.43.59 0.63 0.29 0.57 (0.42) (0.) (0.24) 200-200 0.55 0.76 0.32 0.29 0.70 (0.49) (0.8) (0.28) (Numbrs in parnhss indica sandard rror of sima) Sourc: auhors ˆb ˆb 2 0.95 (0.03) 0.8 (0.03).54 (0.06) 0.70 (0.0) R 2 DW 0.57 0.07 0.76 0.20 0.6 0.09 0.29 0.07 97
Mohammd Saiful ISLAM, Mohammad Hasma ALI Inrs ra and inflaion ovr 200 o 200 sm o b I(0) and I() rspcivly whn quarrly frquncy is usd bu monhly obsrvaions xhibi h xisnc of uni roo in boh sris. Th rsiduals obaind from rgrssion ar I(0) in quarrly and monhly cass, hrby prdicing a possibl coingraion bu h wors is ha non of h four rror corrcion cofficins (wo for monhly and wo quarrly) is found significan. Thrfor w conclud ha hr is no coingraing rlaionship bwn h nominal ra of inrs and inflaion ovr his sampl priod. Evn h simad inflaion cofficin is blow uniy, hus conflicing wih ihr h Fishr hypohsis or h Taylor principl. This finding is no surprising in h viw ha monary policy of h Fdral Rsrv in rcn yars do no adhr o any paricular rul, rahr signifis a subsanial amoun of discrion (s.g., Taylor 200). Th abov analysis clars ha hr ar wo sampl priods producing rliabl simas ha can wll xplain h undrlying policy bhaviour. Th nir priod bwn 957 and 200 dmonsras h possibiliy of h occurrnc of Fishr ffc and h pos- 980 priod jusifis h vidnc of h Taylor principl, hus aciv monary policy. W nx sima h rror corrcion modl for h formr sampl priod. (2.0) and (2.) rprsn coingraing rlaion undr quarrly and monhly daa rspcivly. i.95 0.95 ˆ ; (2.0) m i m.98 0.95 ˆ ; (2.) Sinc inrs ra and inflaion ar I() ovr h priod 957 o 200, any linar combinaion of hm,.g., rsiduals, is likly o b I() bu in spcial cas whn boh sris ar coingrad hn h linar combinaion can b I(0). W obain rsiduals m m ˆ i.95 0. 95 and ˆ i.98 0. 95. Null hypohsis of uni roo in ˆ can b rjcd a 5% lvl of significanc sinc ADF s saisics appars -3.02 whn 5% criical valu is -2.88. For monhly obsrvaions hs valus ar -2.65 and -.95 rspcivly. Saionary rsiduals prdic ponial coingraing rlaionship. Coingraion implis ha inrs ra and inflaion shar similar sochasic rnds and hy nvr divrg oo far from ach ohr. In h prsn cas rsiduals ar saionary which confirms h xisnc of coingraion bwn nominal ra of inrs and inflaion, hrfor h rgrssion is no spurious and h simas ar supr-consisn. Coingraing rror in h prvious priod for quarrly obsrvaions, ˆ i.95 0. 95 Error corrcion modl (ECM) i 0 ( i.95 0.95 ) i.95 0.95 ) 20 2( i (2.2) (2.3) Esimaion rsuls of h abov ECM ar documnd in Tabl 3. 98
Economia. Sria Managmn Volum 5, Issu, 202 Tabl 3. Error Corrcion Modl Esimas Variabls Error corrcion cofficin simas 2 i -0.07 0.03* 0.04 0.02* *sandard rror of sima Sourc: auhors R DW 0.02.46 0.0.22 W obain plausibl simas of boh rror corrcion cofficins in rms of signs and magniuds alhough h on du o is insignifican. ˆ 0.07, which is significan, implying ha whn i.95 0. 95, i falls, hrby driving h sysm oward quilibrium rlaionship. Esimad valu indicas a 7% adjusmn in ach quarr from disquilibrium oward quilibrium. Monhly sima of his cofficin is -0.02 which is significan, prdicing 2% corrcion in ach monh. Insignifican rror corrcion cofficin of scond quaion suggss ha dos no rac o h coingraing rror. This oucom qusions h undrlying mchanism of h Fishr ffc bcaus Fishr ffc will hold only if hr is corrsponding changs in pric ha could chang ral growh of mony in h following priod. Th cofficin is howvr significan a 0% lvl of significanc and w xpc a slow adjusmn of inflaion, hrby vanishing h coingraing rror in h long run. Mor inuiivly, alhough no rpord in h abl bu h rror corrcion cofficin aribuabl o chang in inflaion, whil considring monhly daa, is 0.0 which is significan, hus rvaling a % corrcion prformd by inflaion whn h sysm is dpard from quilibrium. W go 26 quarrly obsrvaions and 648 monhly obsrvaions nvrhlss hy yild h sam valu of Fishr cofficin which is 0.95. Evn hn w can crainly infr ha h simad quaion rprsns h Fishr quaion bcaus in ordr o b consisn wih h Fishr hypohsis, inflaion cofficin should b bu in his paricular cas i is 0.95. Howvr, h Wald s dos no rjc h null of his cofficin bing qual o. This non-rjcion may provid som vidnc of h occurrnc of h Fishr ffc. Th rsuls ar robus o diffrn masurs of inflaion and inrs ras. W us quarrly GDP dflaor inflaion ra as an alrnaiv masur of inflaion ha marks no changs in mpirical findings. In addiion o h fdral funds ra, hr ohr masurs of nominal inrs ras hav bn usd,.g. Trasury bill ra, 3-monh commrcial papr ra and 0-yar gov bond yild ra. Figur 3 dmonsras h clos conncion of four diffrn proxis of inrs ra. 99
Mohammd Saiful ISLAM, Mohammad Hasma ALI Figur 3. Diffrn masurs of inrs ra in h US All h masurs of inrs ra produc similar rsuls xcp on disincion wih rgard o h saionariy propry. 0-yar gov bond yild ra is found I() ovr h sampl 200 o 200 alhough hr ohr masurs of inrs ras ar saionary in his priod. Sinc h inflaion ra of his subsampl is I(), w hopd coingraion bwn 0-yar gov bond yild ra and inflaion ra bu h rsiduals gnrad from h rgrssion of 0-yar gov bond yild ra on inflaion ar also I(), hrfor h possibiliy of ponial coingraion is ruld ou. Th sampl priod spanning 98-200 appars as a likly sourc of obaining rliabl las squar simas sinc boh h nominal ra of inrs and inflaion of his sampl ar saionary, bu h problm of ndogniy is pron o gnraing biasd and inconsisn simas. Endogniy problm is dcd by applying h chniqu of arificial rgrssion rcommndd by Hill al. (2007) which conforms o h Hausman s. In ordr o g rid of his problm, w mploy h wo-sag las squar simaion mhod whr four lags of inrs ra and inflaion ar usd as h insrumns, making sur ha hr is no problm of wak or invalid insrumns. Tss for ndogniy and insrumns validiy ar documnd in Appndix. Two-sag las squar (2SLS) approach producs inflaion cofficin.76 ovr h priod undr considraion, which is lagr han h OLS sima. Monhly daa also yild slighly largr sima of inflaion cofficin. W find nough vidnc o argu ha h pos-980 inrs ra policy of h Fdral Rsrv cohrs wih h Taylor principl. Th abov-uniy inflaion cofficin vidncs h nonapparanc of h Fishr ffc in his priod, rahr jusifis h xisnc of aciv policy. Th noions of h Fishr hypohsis and Taylor principl ar ssnially conrasing as h Fishr hypohsis rquirs uni cofficin of inflaion whras Taylor principl, by dfiniion, implis inflaion cofficin abov uniy. 200
Economia. Sria Managmn Volum 5, Issu, 202 CONCLUSION On h basis of mor han 50 yars quarrly and monhly daa undr h US conx, h Fishr ffc is rvisid and h noion of Taylor principl is inroducd o find an xplanaion why h Fishr ffc probably disappars sinc 980. In our sudy h Fishr ffc, in is wakr form, occurs only if h nir sampl is akn ino accoun- wakr in h sns ha h simad Fishr cofficin falls blow uniy. W could no show h validiy of h Fishr ffc in any of hr ohr subsampls. Full sampl spanning 957-200 xhibis h xisnc of coingraing rlaionship bwn inrs ra and inflaion and hus an undrlying rror corrcion modl. Boh h cofficins of rror corrcing rm hav plausibl signs hough h rspons of h chang in inflaion o prvious priod s disquilibrium rror is lss significan. Fdral bhaviour aks a drasic urn around 980 whn Paul Volckr was appoind as h chairman. Inrs ra jumps o a vry high lvl during h arly 80s followd by a gradual dclin. Unil 980 policy sms o b inaciv as h rspons of inrs ra o inflaion was no ha srong o lad o a low inflaion in subsqun priods. Ral ra of inrs is found mor or lss consan whn h conomy xprincd high inflaion. Pos-980 rgim, on h ohr hand, is faurd as priod of aciv monary policy. Volckr priod inrs ra policy is found o oby h Taylor principl characrisd by h inflaion cofficin abov uniy. This spcial faur ruls ou h possibiliy of h xisnc of h Fishr ffc during h pos-980 priod. Th Taylor principl assurs ha inrs ra rsponds o inflaion mor han on-for-on whil h Fishr hypohsis rquirs a on-for-on rspons of h nominal ra of inrs o inflaion so ha h ral h ra of inrs is unchangd. W find our rsuls robus o diffrn masurs of inflaion and inrs ra. Insrumnal variabl (IV) approach, as an alrnaiv chniqu of simaion, is applid o ovrcom h ndogniy problm and h simas ar obaind rahr mor plausibl. W did no howvr ak conomric accoun of srucural brak. Bu wihou dlving furhr ino h issu, hr is no rason o argu ha h nonxisnc of Fishr ffc is du o h srucural brak in daa bcaus in h hisory of h Fdral Rsrv Volckr s appoinmn and subsqun policy rvision is h unbndabl xampl of srucural brak and h priod in which w did no find coingraion is h Volckr-onward priod whn any furhr brak is unlikly o appar. Nvrhlss, furhr nquiry is advocad o jusify our finding ha a las in las hr dcads h Fd s policy bhaviour dos no corrspond o h Fishr ffc as his has bn smingly invalidad by h Taylor principl. REFERENCES Barsky, B. R. (987). Th Fishr Hypohsis and h Forcasabiliy and Prsisnc of Inflaion. Journal of Monary Economics, 9, 3-24. Brumn, H. B., & Jlassi, M. M. (2002). Th Fishr Hypohsis: a Muli-counry Analysis. Applid Economics, 34, 645-655. Byr, A., Haug, A. A., & Dwald, W. G. (2009). Srucural Braks, Coingraion and h Fishr Effc. Europan Cnral Bank. Working papr no. 03. Blanchard, O. (999), Macroconomics, 2 nd diion. Prnic Hall. 20
Mohammd Saiful ISLAM, Mohammad Hasma ALI Crowdr, W. J. (997). Th Long Run Fishr Rlaion in Canada. Th Canadian Journal of Economics, 30, 24-42. Du, S.D., & Ghosh, D. (995). Th Fishr hypohsis: xamining h Canadian xprinc. Applid Economics, 27, 025-30. Granvill, B., & Mallick, S. (2004). Fishr Hypohsis: UK Evidnc ovr a Cnury. Applid Economics Lrs,, 87-90. Hrwarz, H., & Rimrs, H. (20). A Funcional Cofficin Approach To Modlling h Fishr Hypohsis: Worldwid Evidnc. Macroconomic Dynamics, 5, 93-8. Hill, R. C., Griffihs, W. E., & Lim G. C. (2007). Principls of Economrics, 3 rd diion. John Wily & Sons, Inc. Jnsn, J. J. (2006). Th Long-run Fishr Effc, Can I B Tsd? Fdral Rsrv Bank of Alana. Working papr 2006-. Ksryyly, M. (994). Policy Rgim Changs and Tsing for h Fishr and UIP Hypohss: Th Turkish Evidnc. Th Cnral Bank of h Rpublic of Turky. Discussion papr no. 94. MacDonald, R., & Murphy, P. D. (989). Tsing for h Long Run Rlaionship bwn Nominal Inrs Ras and Inflaion Using Coingraion Tchniqus. Applid Economics, 2, 439-47. Mishkin, F. S. (99). Is h Fishr Effc for Ral? A R-xaminaion of h Rlaionship bwn Inflaion and Inrs Ras. Naional Burau of Economic Rsarch. Working papr no. 3632. Ros, A. K. (988). Is h Ral Inrs Ra Sabl? Journal of Financ, 43, 095 2 Taylor, J. B. (200). Macroconomic Lssons from h Gra Dviaion. NBER Macroconomics Annual, 200, 25, forhcoming from Univrsiy of Chicago Prss. Taylor, J. B. (993). Discrion vrsus Policy Ruls in Pracic. Carngi-Rochsr Confrnc Sris on Public Policy, 39, 95-24. Walsh, C. (200). Monary Thory and Policy, 3 rd diion. MIT Prss. 202
Economia. Sria Managmn Volum 5, Issu, 202 Endogniy and Insrumns Validiy APPENDIX W assum igh insrumns aloghr, namly four lags of inrs ra and four of inflaion. In h firs sag, inflaion is rgrssd on a consan and igh insrumns and hn rsidual is savd from his rgrssion. i i i i.... (.) 0 2 2 3 3 4 4 2 2 3 3 4 4 A OLS sima of h abov is 0.47 0.92 0.23 0.i 3 0.6i 4 Rsidual, ˆ 0.47 0.92 0.i 3 0.6i 4 ˆ 2 0.23 0.06 2 3 0.06 0.04 3 4 0.04 0.24i 4 0.24i 0.i 2 0.i In scond sag an arificial rgrssion is prformd by including h rsidual obaind in h firs sag as an addiional xplanaory variabl. If h simad cofficin of his arificial variabl is found significan hn h problm of ndogniy is confirmd. Arificial rgrssion ˆ i OLS sima of h arificial rgrssion is obaind i 0.4.76.6 ˆ ˆ ; (sandard rrors in parnhss) ( s) (0.40) (0.) (0.33) Null hypohsis H0 : 0 is rjcd agains h alrnaiv hypohsis H A : 0 sinc h compud valu of F-saisic undr Wald s is 24.35, hus h problm of ndogniy is dcd. Ts for insrumns validiy is rahr sraighforward which lis in h firs sag of h approach mniond abov. Join s for h significanc of h cofficins in (A.) is carrid ou. H 0 : 2 3 4 2 3 4 0 agains h alrnaiv hypohsis ha a las any on of hs cofficins is nonzro. As a rul of humb, i is suggsd ha if h F-s saisic aks a valu lss han 0, hn h null is accpd and h insrumns ar wak. W obain F-valu qual o.73, hus soundly rjc h null and rul ou h possibiliy of having wak insrumns. 2 203