Volume, Issue Food nd Energy Pries in Core Inflion Jim Lee Texs A&M Universiy-Corus Chrisi Asr Mny enrl nkers hve mde monery oliy deisions y fousing on ore inflion d h exlude food nd energy ries from overll inflion. In his er, esimion resuls from mulivrie GARCH models show h food ries no only hel fores fuure ore inflion, u heir ondiionl vrine lso ffes he ondiionl vrine of ore inflion. Energy ries, on he oher hnd, ffe ore inflion rimrily hrough he GARCH-in-men effe. To he exen h food nd energy ries ffe he underlying rend nd voliliy of overll inflion, oliymkers should no ignore hese omonens in heir ssessmen of fuure inflion risk. Ciion: Jim Lee, (00) ''Food nd Energy Pries in Core Inflion'', Eonomis Bullein, Vol. no.. -0. Sumied: Se 00. Pulished: My 0, 00.
. Inroduion Mny enrl nkers, inluding offiils he Federl Reserve nd he Bnk of Englnd, y enion o mesures of ore inflion insed of overll or hedline inflion in when hey mke monery oliy deisions. The enrl ide is h he onvenionl inflion mesures, like he onsumer rie index (CPI), onin noise or rnsiory hnges h re no useful for monery oliy ondu. By onrs, he one of ore inflion ures ersisen rie movemens h hel delinee he underlying inflion rend (Clrk, 00). While here is no onsensus on he es mesure of ore inflion, he mos oulr mesure is he CPI less food nd energy. As Gordon () ssers, food nd energy eriodilly fe volile rie movemens h my diverge from hnges of he overll rie level in he long run, whih is used rimrily y exessive money growh. However, Gvin nd Mndl (00) show h food ries indeed hel fores fuure inflion, lhough energy ries do no. Rih nd Seindel (00) lso reor h he CPI less food nd energy mesure is no eer hn moving verge of he overll CPI s redior of fuure inflion. This er seeks o reexmine he role h food nd energy ries ly in overll inflion nd, in riulr, ore inflion. Mos exising sudies evlue he role of lernive rie indies y heir erformne in inflion foress. We follow differen roh in his er. To he exen h mny enrl nk offiils ignore food nd energy ries euse of heir exessive voliliy, we fous on heir ondiionl voliliy in deermining fuure inflion risk. By lying CPI inflion d o mulivrie GARCH-in-men model, we show h food nd energy ries no only hel fores he onvenionl mesure of ore inflion, u hey lso ffe he degree of inflion uneriny. The res of he er is orgnized s follows. The nex seion resens he esimion mehodology nd d. The hird seion reors our emiril findings. The fourh seion onludes he er.. Mehodology nd D To exlore ossile inerions eween ore inflion nd hnges in food nd energy ries, we onsider mulivrie GARCH model. For n rie series h re inluded in he model, heir ondiionl mens re ssumed o follow VAR() roess wih GARCH-in-men effes: where = Θ + Φ + Ψ ΨΗ + ε ε ~ ( 0, Η ) () s s s= Oher mesures inlude rimmed men nd medin rie series, s reored y he Federl Reserve Bnk of Clevelnd. See Wynne () nd Clrk (00) for deiled disussions of lernive ones nd mesures of ore inflion
θ =, Θ=, Φs n θ n ε ε =. ε n s s n n =, Ψ=, H s s n nn n nn h h n =, hn h nn The lg order in equion () is seleed in ligh of he Byesin Informion Crierion. The vrine/ovrine mrixη is ssumed o follow GARCH(,) roess: Η = C ' C+ A' ε ε A+ B ' Η B () ' where C 0,, =. A = = B The riulr BEKK rmeerizion of equion () imoses osiive definieness on Η. The ondiionl men nd ondiionl vrine/ovrine equions re esimed simulneously y Bollerslev nd Wooldridge s () qusi-mximum likelihood mehod, whih generes onsisen sndrd errors h re rous o ossile non-normliy. Following ommon rie, ore inflion is mesured y hnges in he CPI exluding oh food nd energy iems. We lso onsider he sere egories of food nd energy, i.e., he CPI less food nd CPI less energy. As suh, he lernive veors of rie series for re xfe fe xf f xe e xfe f e [, ]', [, ]', [, ]' nd [,, ]', where rie series wih suersri xfe denoes he CPI less oh food nd energy s he ore rie mesure, xf denoes he exlusion of only food, xe denoes he exlusion of only energy, fe denoes he CPI of only food nd energy iems, f denoes he CPI of food iems, nd e denoes he CPI of energy iems. All CPI d re sesonlly djused nd oserved monhly over he eriod eween 0: nd 00:. The d re oined from he U.S. Bureu of Eonomi Anlysis. For esimion, ll rie series re exressed s 00 imes he firs differene of is log vlue, i.e., 00 ln( / ). i i,. Emiril Resuls In his seion, we disuss esimion resuls of he GARCH-in-men model oulined reviously in Seion. Tle reors resuls for ivrie model h inludes he CPI less oh food Insed of he whole oservion eriod, we ook ino oun ossile sruurl hnge nd rn esimions for wo sere eriods: 0:-: nd :-00:. In ddiion, rher hn monhly CPI d, we rn
nd energy ( xfe ) nd he ggrege index of food nd energy ( fe ). The firs wo rows disly some dignosi sisis for he esimed model. The firs row onins Lgrnge mulilier sisis for esing remining ARCH effes u o he h lg order. The resuls revel lile evidene of ARCH effes in he residuls. The seond row shows he Ljung-Box Q sisis for esing uoorrelion in he residuls lso u o he h order. Similrly, here is sn evidene of seril orrelion. These es resuls ogeher suor h he emiril model ouns for mos of he ondiionl heeroskedsiiy nd uoorrelion in he wo rie series. Similr resuls re found for oher rie series exmined in his er. Tle lso onins esimion resuls for he ondiionl men nd ondiionl vrine equions. In he ondiionl men equion, more hn hlf of he lg oeffiien esimes re sisilly signifin he 0 eren level or higher. The four F sisis es for he rediive ower of ll lgs of n exlnory vrile. They re ll sisilly signifin, indiing h s movemens of he food nd energy rie series hel redi he urren movemen of he ore rie series, nd vie vers. In he ondiionl vrine equion, he sisilly signifin esime of indies voliliy sillover from he food nd energy rie series o he ore rie series. All esimes in he A mrix re lso sisilly meningful, indiing h shok o eiher rie series lso ffes he ondiionl vrine of noher rie series. In ddiion, here is some evidene of he GARCH-in-men effe. More seifilly, he osiive esime of in he ondiionl men equion is sisilly signifin he 0 eren level. This suggess h ore inflion is osiively reled o he ondiionl vrine of food nd energy ries. In ddiion o exmining he CPI h exludes food nd energy iems s whole, we exlore he inerions eween he ore CPI nd he wo sere rie series of he food nd energy egories. Corresonding o Tle, Tle reors esimion resuls for he ivrie model onining he CPI less only food ( ) nd he CPI of only food iems ( ). The F- xf sisis for esing he lg oeffiiens in he ondiionl men equion indie h s movemens of he food rie series hel exlin he urren movemen of he non-food ore rie series, while he non-food rie series fils o exlin food rie movemens. The esimes for ll elemens in Ψ, whih ure he GARCH-in-men effe, re no sisilly meningful. The insignifin esime of suggess h food rie voliliy does no ffe ore rie movemens even hough he voliliy of food nd energy ries ogeher does (s shown in Tle ). Desie he sene of ny GARCH-in-men effe, he esimes in he ondiionl vrine equion indie h he ondiionl vrine of he non-food rie series is ssoied wih he s ondiionl vrine of he food rie series s well s he s shok o food ries. Insed of fousing on he food egory, we now invesige he energy omonen of he CPI. Tle reors esimion resuls for he ivrie model onining CPI less energy f esimions using qurerly Personl Consumion Exendiures (PCE) rie indies. The generl onlusions re no sensiive o hese hnges
( xe ) nd he energy rie index ( e ). In onrs o he orresonding sisis in Tles nd, he F-sisis for esing he lg oeffiiens in he ondiionl men equion indie h eh of he wo rie series onins no sisilly meningful informion ou fuure movemens of he oher rie series. However, he esimes for elemens in Ψ sugges h he non-energy ore inflion series is osiively reled o he ondiionl vrines of oh energy ries nd (non-energy) ore ries. In he ondiionl vrine equion, he esimes for ll off-digonl elemens of he oeffiien mries re no signifinly differen from zero, indiing n sene of ny relionshi eween he ondiionl vrines of he wo rie series. Tle furher reors esimion resuls for model onining hree rie series: he ore CPI less food nd energy, he food CPI, nd he energy CPI. In his rivrie se, he F- sisis for esing he lg oeffiiens in he ondiionl men equion indie h s food rie movemens signifinly exlin he urren movemen of he ore rie series, while energy rie movemens do no. These findings re onsisen wih hose from he ivrie ses ove. The finding of no rediive ower from energy ries is lso in line wih he resuls reored y Gvin nd Mndl (00). Neverheless, he esime of is signifin he 0 eren level. This suors h energy rie voliliy ffes ore inflion. Similr o hose in Tle, he sisilly signifin esimes of nd in he ondiionl vrine equion sugges h he lgged vlue of food rie shok s well s he ondiionl vrine of food ries ffe he ondiionl vrine of ore inflion. There is, however, lile evidene o suor orresonding effe from he energy rie series. The esimes in he ondiionl vrine equion lso offer no meningful evidene of inerions eween food rie voliliy nd energy rie voliliy. The overll esimion resuls of he rivrie model re line wih hose in he sere ses of ivrie models. Togeher, he findings highligh he vrying roles of food nd energy ries in overll inflion dynmis. Food nd energy ries ffe no only he level of ore inflion u lso is ondiionl voliliy. In riulr, food ries ffe he ondiionl vrine of inflion ommon roxy for inflion uneriny. For his reson, oliymkers should no ignore food ries when ssessing inflion risk. In ddiion, energy rie voliliy hels fores he underlying rend of inflion so h oliymkers should no exlude energy ries simly euse of heir relively high voliliy.. Conlusion In his er, esimion resuls wih mulivrie GARCH-in-men model suor h food rie movemens no only hel redi fuure ore inflion, u heir ondiionl vrine lso ffes he ondiionl vrine of ore inflion mesure of inflion uneriny. Energy rie movemens, on he oher hnd, ffe ore inflion rimrily hrough he GARCH-in-men effe. These findings imly h oliymkers who hoose o look s rie movemens of food nd energy due o heir exessive voliliy migh leve ou meningful informion ou he risk of fuure inflion.
Given he findings gins he exlusion-sed roh in ssessing inflion rends, monery oliymkers should onsider oher mesures of ore inflion. For exmle, offiils he Federl Reserve Bnk of Clevelnd dvoe rimmed men inflion mesure h ouns for ll voliliy in onsumer ries. Similrly, Bryn nd Cehei (), nd Wynne () sugges one uring he rie hnge h is ommon o ll goods in he long run, while Woodford (00, Cher ) fouses on he os of inflion. These ones hve een inorored y Anderson e l. (00) in signl exrion rolem for foresing inflion. In ligh of our emiril resuls, ore inflion mesure should lso ke GARCH effes mesure of inflion oss ino onsiderion.
Referenes Anderson, R., F. Anderson, T. Binner, nd T. Elger (00) Core Inflion s Idiosynri Persisene: A Wvele Bsed Aroh o Mesuring Core Inflion. Per resened he onferene Prie Mesuremen for Monery Poliy, Federl Reserve Bnk of Dlls, My -, 00. Bollerslev, T. nd J.M. Wooldridge () Qusi Mximum Likelihood Esimion nd Inferene in Dynmi Models wih Time Vrying Covrines Eonomeri Reviews,. Bryn, M.F. nd S.G. Cehei () Mesuring Core Inflion in Mnkiw, N.G. (ed.), Monery Poliy y N.G. Mnkiw, Ed., Universiy of Chigo Press: Chigo, -. Clrk, T.E. (00) Comring Mesures of Core Inflion Federl Reserve Bnk of Knss Ciy, Eonomi Review,, -. Gvin, W.T. nd R.J. Mndl (00) Prediing Inflion: Food for Though Federl Reserve Bnk of S. Louis, Regionl Eonomiss, Jnury, -. Gordon, R.J. () Alernive Resonses of Poliy o Exernl Suly Shoks Brookings Pers on Eonomi Aiviy,, -0. Rih, R. nd C. Seindel (00) A Comrison of Mesures of Core Inflion Federl Reserve Bnk of New York, Eonomi Poliy Review,, -. Woodford, M. (00) Ineres nd Pries: Foundions of Theory of Monery Poliy, Prineon Universiy Press: Prineon. Wynne, M.A. () Core Inflion: A Review of Some Coneul Issues Federl Reserve Bnk of Dlls, Working Per No. -0.
Tle : GARCH Model Esimion wih CPI Exluding Food & Energy. Deenden vrile: Deenden vrile: xfe ARCH().0 ARCH(). Ljung-Box Q(). Ljung-Box Q(). Condiionl Men: Esime -vlue Esime -vlue θ 0.0 (.) *** θ 0.0 (.0) *** 0.0 (.) *** 0.0 (.0) *** 0.0 (.) *** 0.0 (.0) *** 0.0 (.0) *** 0. (.) *** 0. (.) *** 0.0 (.0) * 0.0 (.) *** 0.0 (.) 0 0.00 (.) *** -0.0 (-.) * -0.0 (-.0) 0.00 (.) *** 0.0 (.) * 0.00 (0.0) 0.0 (0.) 0.0 (.0) 0.0 (.0) 0.0 (.0) 0.00 (0.00) 0.0 (.) 0-0.0 (-.) ** 0.00 (0.) -0.0 (-.) * -0.0 (-0.) 0. (.0) * F-Tess: = = = 0. *** = = = 0. *** fe -0.00 (-.) *** 0.00 (0.0) -0.0 (-.) *** -0.0 (-.) -0.0 (-.) -0.0 (-.) *** -0.0 (-.0) *** 0.0 (.) * 0 0.0 (.000) *** 0.00 (.00) *** -0.0 (-.) *** 0. (.) *** -0.0 (-.0) ** 0.0 (.) 0.0 (0.) 0.0 (.0) * 0.00 (.) * 0.0 (.0) 0.0 (.) * 0.0 (.) ** 0 0. (.0) *** 0. (.) *** -0. (-.) *** -0.0 (-0.) -0.00 (-0.00) = = = 0. *** = = = 0. ***
Tle (Coninued). Condiionl Vrine: Esime -vlue 0.00 (.) ** 0.0 (.0) 0.0 (.0) *** 0.0 (.) *** 0.0 (.) * 0.0 (.) * 0.0 (.) *** 0. (.0) *** 0. (.) *** 0.0 (.0) 0. (.) *** Log-likelihood 0.0 Noes: *, **, nd *** denoe sisil signifine he 0., 0.0, nd 0.0 levels, reseively.
Tle : GARCH Model Esimion wih CPI Exluding Food. Deenden vrile: Deenden vrile: xf ARCH().0 ARCH() 0. Ljung-Box Q(). Ljung-Box Q() 0. Condiionl Men: Esime -vlue Esime -vlue θ 0.0 (.) ** θ 0.0 (.0) *** 0.0 (.) *** 0.0 (.) ** 0.0 (.) * 0.0 (.0) *** 0.0 (.) ** -0.0 (-0.0) 0.00 (.) *** 0.0 (.) ** 0.0 (.) 0.00 (.) ** 0 0.0 (.) *** 0.0 (.) *** -0.0 (-.0) ** 0.0 (.0) 0.00 (.0) *** 0.0 (.) -0.00 (-0.) 0.0 (.0) ** 0.0 (.00) *** 0.0 (.) 0.0 (.) 0.0 (.00) 0 0.0 (.) ** 0.0 (.) ** 0.00 (0.) 0.0 (0.0) -0.0 (-.) F-Tess: = = = 0.00 *** = = = 0.0 *** f -0.0 (-0.) -0.00 (-0.) -0.0 (-0.) 0.0 (.) ** 0.0 (.) -0.0 (-0.) 0.0 (.) * 0.0 (.) *** 0 0. (.) *** -0.0 (-.0) -0.0 (-0.) 0. (.) *** 0.0 (0.) -0.0 (-0.) -0.0 (-.) ** 0.0 (.) *** 0.0 (.0) *** 0.00 (0.) 0.0 (0.) 0.0 (.) 0 0.0 (.) *** 0.00 (.) -0. (-.) *** 0. (0.) 0. (.) = = = 0.0 = = = 0.00 ***
Tle (Coninued). Condiionl Vrine: Esime -vlue 0.0 (.) *** -0.0 (-.) -0.00 (-0.) 0.0 (.) *** 0.0 (.) ** 0.00 (0.) 0. (.) *** 0. (.0) *** 0.0 (.0) ** 0.00 (0.0) 0. (.) *** Log-likelihood.0 Noes: *, **, nd *** denoe sisil signifine he 0., 0.0, nd 0.0 levels, reseively. 0
Tle : GARCH Model Esimion wih CPI Exluding Energy. Deenden vrile: Deenden vrile: xe ARCH(). ARCH(). Ljung-Box Q().0 Ljung-Box Q(). Condiionl Men: Esime -vlue Esime -vlue θ 0.0 (.) *** θ -0.00 (-0.) 0.0 (.) *** 0.00 (.) 0. (.0) *** 0.0 (.0) ** 0.00 (0.) 0. (.) *** 0.0 (.0) *** -0.0 (-0.) 0.0 (.) *** 0.0 (.0) *** 0 0. (.) *** -0.0 (-0.0) -0.0 (-0.) 0.00 (.) * 0.00 (.0) -0.00 (-0.) -0.00 (-0.) 0.00 (.) 0.00 (0.) 0.00 (0.) -0.00 (-0.0) 0.00 (.) *** 0-0.00 (-.0) 0.000 (0.) -0.00 (-.0) 0.0 (.) **.0 (.) *** F-Tess: = = = 0. *** = = = 0. e 0.0 (0.) 0.00 (0.) -0.0 (-.) *** 0.0 (0.) 0.00 (0.) -0.0 (-.0) *** 0.00 (0.0) 0.0 (.) ** 0 0.00 (.) *** -0.0 (-.) *** -0.0 (-.) *** 0.0 (.0) *** -0.00 (-.) -0.00 (-0.) 0.00 (0.) -0.00 (-0.) 0.0 (.) *** -0.00 (-.) 0.00 (0.0) 0.00 (.) * 0 0.00 (0.) 0.0 (.0) *** -0.0 (-.) *** 0. (0.) 0. (.) = = = 0. *** = = = 0.0
Tle (Coninued). Condiionl Vrine: Esime -vlue 0.00 (0.) 0.0 (0.) 0.0 (.) ** 0. (.) *** 0.00 (0.0) 0.00 (0.) 0. (.) *** 0.0 (.) *** 0.00 (0.) 0.00 (0.) 0. (.) *** Log-likelihood 0.0 Noes: *, **, nd *** denoe sisil signifine he 0., 0.0, nd 0.0 levels, reseively.
Tle : Trivrie GARCH Model Esimion wih CPI Exluding Food & Energy. xfe f e Deenden vrile: ARCH(). 0. 0. Ljung-Box Q()..0. Condiionl Men: F-Tess: = = = 0 0. *** = = = 0. *** = = = 0.0 = = = 0.0 = = = 0. *** = = = 0. = = = 0 0. = = = 0. * = = = 0.0 *** Esime -vlue Esime -vlue Esime -vlue. (.0) * 0. (0.0).0 (.). (0.) 0. (0.0) 0.00 (0.). (.) *. (.0) 0.00 (0.0) Condiionl Vrine: 0.00 (.) -0.0 (-.) 0.0 (.) * 0.0 (0.) 0. (.) *** 0.000 (0.000) 0.00 (0.) 0. (.) * 0.0 (0.) 0.0 (.) *** 0. (.) *** 0. (.) * 0.000 (0.) 0.00 (0.) 0. (.) *** 0. (.0) *** 0.0 (.) 0.00 (0.) 0.0 (.) *** 0. (.00) *** 0.00 (0.) 0.000 (0.) 0.00 (0.) 0. (.) *** Log-likelihood.00 Noes: *, **, nd *** denoe sisil signifine he 0., 0.0, nd 0.0 levels, reseively.