econsor Make Yor Pblcaon Vsble A Servce of Wrschaf Cenre zbwlebnz-informaonszenrm Economcs Joran Thomas J.; gler Peer; Lenz Carlos; Savoz Marcel R. Workng Paer GDP Daa Revsons an Forwar-Lookng Monear Polc n Swzerlan WWZ Dscsson Paer No. 005/05 Prove n Cooeraon wh: Cener of Bsness an Economcs WWZ Unvers of Basel Sggese Caon: Joran Thomas J.; gler Peer; Lenz Carlos; Savoz Marcel R. 005 : GDP Daa Revsons an Forwar-Lookng Monear Polc n Swzerlan WWZ Dscsson Paer No. 005/05 Ths Verson s avalable a: h://hl.hanle.ne/049/335 Sanar-Nzngsbengngen: De Dokmene af EconSor ürfen z egenen wssenschaflchen Zwecken n zm Prvagebrach gesecher n koer weren. Se ürfen e Dokmene nch für öffenlche oer kommerzelle Zwecke vervelfälgen öffenlch assellen öffenlch zgänglch machen verreben oer anerweg nzen. Sofern e Verfasser e Dokmene ner Oen-Conen-Lzenzen nsbesonere CC-Lzenzen zr Verfügng gesell haben sollen gelen abwechen von esen Nzngsbengngen e n er or genannen Lzenz gewähren Nzngsreche. Terms of se: Docmens n EconSor ma be save an coe for or ersonal an scholarl roses. Yo are no o co ocmens for blc or commercal roses o exhb he ocmens blcl o make hem blcl avalable on he nerne or o srbe or oherwse se he ocmens n blc. If he ocmens have been mae avalable ner an Oen Conen Lcence esecall Creave Commons Lcences o ma exercse frher sage rghs as secfe n he ncae lcence. www.econsor.e
GDP aa revsons an forwar-lookng monear olc n Swzerlan Peer gler* Thomas J. Joran** Carlos Lenz*** Marcel R. Savoz**** *WWZ Unvers of Basel an Swss Naonal Bank Peersgraben 5 Basel 4003 Swzerlan Corresonng ahor: Tel:. 4-6-67-3344; Fax: 4-6-67-3340 **Swss Naonal Bank an Unvers of Bern Börsensrasse 5 Zürch 80 Swzerlan *** WWZ Unvers of Basel Peersgraben 5 Basel 4003 Swzerlan **** Swss Naonal Bank an Unvers of S. Gallen Börsensrasse 5 Zürch 80 Swzerlan E-mal Aresses: eer.kgler@nbas.ch P. gler homas.joran@snb.ch T. Joran carlos.lenz@nbas.ch C. Lenz marcel.savoz@snb.ch M. Savoz Absrac Ths aer analzes forwar-lookng rles for Swss monear olc n a small srcral VAR moel conssng of for varables akng no accon aa revsons for GDP. Frs he aer evelos an analcal meho o analze he effec of aa revson errors n GDP on he ex ane or cononal nflaon-o-growh volal rae-off an ales o Swss aa. Secon he effecs of fferen arges n a forwar-lookng monear olc on ex os or ncononal volal of nflaon an o growh s exlore b a smlaon exercse. In general he resls obane sgges ha focsng monear olc on GDP growh nsea on nflaon ma lea o an neffcen olc wh boh ncrease mem erm nflaon an GDP growh volal n he resence of GDP aa revsons. ewors: Srcral VAR forwar-lookng monear olc effcenc froner GDP aa revsons JEL classfcaon: E5; E58 Frs Draf Ma 00 Las Revson Janar 005 Earler versons of hs aer were resene a he annal congress of he "Schwezersche Gesellschaf für Volkswrschaf n Sask" Nechâel Jne 00 he meeng of he "Asschss für Makroökonome - Veren für Socalolk" Bonn Jne 8/9 00 he SNB-Fe Clevelan Worksho on Monear Economcs Zürch Jl /3 00 he meeng of he "Asschss für Gelheore n -olk - Veren für Socalolk" Frankfr am Man Febrar 0/ 003 a he ECB Inve Seakers Semnar Arl 5 004 an a he Bnesbank Conference Real-me aa an monear olc Elvlle Ma 8/9 004. Helfl commens of arcans of hese meengs an of an anonmos referee are graefll acknowlege. We are n arclar nebe o Erns Balenserger Lawrence Chrsano Manfre Nemann Güner Coenen an Rober Rasche for her sggesons. Forhcomng n Norh-Amercan Jornal of Economcs an Fnance 005
. Inrocon Afer 5 ears of monear argeng he Swss Naonal Bank SNB aoe a new monear olc framework a he en of 999. Severe shocks o he eman for cenral bank mone esecall for large enomnae bank noes an for reserves hel b commercal banks a he SNB renere mossble o se he mem-erm arge ah for he seasonall ajse monear base as a gelne for monear ecsons. Ths he SNB ece o abanon monear argeng. The new framework consss of hree elemens. The frs elemen s an exlc efnon of rce sabl. The SNB regars rce sabl as acheve f CPI nflaon s below ercen. The secon elemen consss of he se of an nflaon forecas as he man ncaor o ge monear olc ecsons. The hr elemen s a arge range for he hree-monh Swss franc Lbor as an oeraonal arge o mlemen monear olc. As n he ol conce mananng rce sabl over he mem erm remans he man objecve of monear olc also n he new framework. In he new framework he nflaon forecas serves as he man ncaor for gng olc ecsons. Alhogh here s no mechancal reacon o he nflaon forecas an he nflaon forecas s no reae as an nermeae arge he scsson a he boar abo monear olc s focse on he nflaon forecas. The forecas se n he ecson-makng rocess s a consenss forecas ha s erve from a seres of moels an ncaors. The SNB recenl sare o blsh ses regarng hese moels. Joran an Pergne 00 elvere an nrocon o he nflaon forecas of he SNB an he moels se o erve. Saler 00 resene he large raonal srcral macro moel of he SNB an Joran gler Lenz an Savoz 00 rove an overvew over he fferen VAR aroaches se a he SNB. For he rose of analzng forwar-lookng olces a small srcral VAR conssng of for varables was eveloe b gler an Joran 004 an gler an Rch 00. Ths research was exene b gler Joran Lenz an Savoz 005 who eveloe an analcal meho o analze he ex ane or cononal mem-erm nflaono-growh volal rae-off for a forwar-lookng olc amng a a convex combnaon of a mem erm nflaon an an o growh arge n a SVAR moel. Ths aer exens hs framework wh wo resecs. Frs consers he effecs of aa revsons errors n GDP on he ex ane or cononal mem-erm nflaon-o-growh volal rae-off. Secon he effecs of fferen arges n a forwar-lookng monear olc on ex
os or ncononal volal of nflaon an o growh s exlore b a smlaon exercse. The bref olne of he ams of he aer a han clearl ncaes ha s relae o a growng lerare on he effecs of nceran abo oenal o an he o ga on he erformance of monear olc rles. Orhanes 000 00 was one of he frs who consere hs qeson sng real me aa for US o ga. He concle ha aa revson errors n he o ga were of crcal morance for he over-exansonar US monear olc n he sxes an sevenes an ha neglecng sch aa revson errors leas n general o a oo acvs olc. However Svensson an Woofor 000 arge ha hs resl s manl case b he fac ha n Orhanes framework he cenral bank behaves as f here were no aa revson errors an ha saears when he omal olc rle s a fncon of he bes esmae of he sae varables n arclar of he o ga. Neverheless he resence of nceran wh resec o oenal o resls of corse n welfare losses an has effecs on smle Talor-lke rles n sanar macroeconomc moels Smes 00. Exensons an qanave llsraons of hese resls are fon n Ehrmann an Smes 003 who bl a small sochasc general eqlbrm moel wh enogenos erssence calbrae o he ero area. Brefl her exercse ncaes ha he aa revson roblem leas o sbsanal welfare losses manl n he form of hgh o ga varabl. Moreover smle Talor rles aear o work well when an omal o ga esmae s se an oenal o nceran favors he aonmen of a conservave n he sense of Rogoff 985 cenral banker. Ths aer ffers from he lerare skeche above n he followng wa. Frs we o no conser nceran wh resec o he o ga or oenal o b onl wh resec o GDP whch s b self alrea large as resl of srong revsons of he qarerl naonal accons. Noe also ha we o no face he roblem of obanng a bes esmae of an nobservable varable sch as he o ga snce onl GDP growh s consere n or moel. Ths aroach can be seen as a wa o crcmven he roblem of measrng he level of oenal o as recommene among ohers b Orhanes 000. Secon we o no conser an exlc srcral moel of he econom b or analss s base on he mlse resonse we esmae sng a SVAR moel. Thr he olc makers o no accon for he nceran wh resec o he real me GDP fgres. Ths we rocee on he assmon ha he frs release qarerl GDP fgre s he bes esmae avalable a he me when he olc ecson s aken.
The remaner of he aer s organze as follows. Secon brefl escrbes he SVAR moel for he analss of Swss monear olc an gves a shor accon how he nflaon-growh rae-off s eermne n he absence of GDP aa revson errors. Daa revson errors are aken no accon n Secon 3. Secon 4 consers he effecs of noneqlbrm nal conons an olc namcs an Secon 5 concles.. A SVAR Analss of Swss Monear Polc In hs secon we gve a bref accon of he framework se for olc analss n orer o oban he nflaon GDP growh volal rae off. The VAR moel ncles a vecor of changes X ' log r log m / log where s GDP n 990 Swss francs enoes he consmer rce nex m he mone sock M an r he qarerl average of he hree-monh Swss-franc Lbor rae of neres. In orer o kee he moel as lean as ossble he exchange rae s excle from he vecor X as he ransmsson of monear olc va he exchange rae s nrecl care b he mlse resonses of he VAR moel. Exlc nclson of he exchange rae wol be necessar f hs varable ha nflence SNB behavor n a ssemac wa an herefore were reqre o enf a monear olc shock. Exchange rae conseraons lae no moran role for he blk of he samle ero he exceon beng n arclar he ears 978/79. Noe ha we o no selec a monear aggregae wh a sable long-rn mone eman fncon n levels sch as M3. We are onl nerese n a mone sock conce rovng a lo of nformaon for he enfcaon of a monear olc shock. The monear base was no se as he nrocon of he elecronc Swss Inerbank Clearng Ssem an he relaxaon of banks' lq reqremens srongl sore even he raes of change n hs aggregae. However we shol also menon ha he resls are robs wh resec o he n- or exclson of he mone sock seres: a hree varables VAR who mone roces essenall he same shae of he mlse resonses o he monear olc shock as he for varable ssem. Fnall we ogh o menon ha he sanar n-roo an co-negraon ess sor he frs-fference secfcaon aoe n hs aer. The resls wh resec o he neres rae are ambgos: we canno rejec he n roo hohess ADF es as well as he saonar hohess PSS es. Ths we rocee on he I hohess whch s more convenen n or framework for enfcaon of a monear olc shock. Of corse hs mles ha he real rae of neres rae s non-saonar wha s clearl obfl n he long-rn. However for he mem-erm forecasng horzon consere n hs aer hs assmon s eeme acceable. 3
In hs aer long-rn neral resrcons are se n orer o enf srcral shocks wh varances normalze o. Brefl we have he followng nerreaon of he for enfe shocks. Frs here s a sl shock whch can eher have a long-rn effec on all for varables consere. Secon we have an IS shock whch ma have a ermanen effec on all varables exce for o. Thr here s a mone eman shock whch affecs onl he real mone sock an rces n he long rn. Forh an mos moranl n or framework we enf a mone sl or monear olc shock whch has onl a long-rn effec on rces an of corse on he nomnal mone sock. These sx long-rn ranglar resrcons lea o an exacl enfe moel. All varables ncle n he moel are seasonall ajse wh he exceon of he neres rae. The lag lengh k was se o fve qarers whch s he omal vale accorng o he Akake creron. Fgre shows he esmaes for he cmlae mlse resonses of he for varables o all for shocks. 3 In he frs colmn we fn he resonses of all varables n he orer he aear n he vecor X o he sl shock. Then we have he resonses o he IS-shock o he mone eman shock an fnall n he las colmn he resonse o he monear olc shock whch s of mos morance n he crren conex. B an large he laer resonse esmaes correson o he vews share b mos macroeconomss n Swzerlan abo he effecs of monear olc. Frs here s evence of a shor-rn negave lq effec on he neres rae exenng over wo qarers. The osve reacon n real GDP sars weakl an reaches s eak afer fve qarers an sars o eer o afer anoher ear. Wh resec o rces akes sx qarers nl a major osve effec s fel an 4 qarers are neee for fll ajsmen of rces. Afer abo he forh qarer rsng rces an nflaon execaons case he neres rae o overshoo emorarl s long-rn eqlbrm level. Fnall he real mone sock remans consan over he long-rn eqlbrm level for a ear an ecreases o over he nex for qarers. Before rnng o he analss of monear olc n hs SVAR moel le s brefl menon ha he mlse resonses o he oher hree shocks are n lne wh or rors from economc heor. In arclar we fn a ermanen osve negave effec of he sl shock on he rocon rces an he IS shock leas o a hm-shae ransor resonse of rocon exenng over 0 qarers whch s accomane b a ermanen ncrease n he rce level. In earler aers menone n he nrocon we se an over-enfe SVAR moel nclng shor-rn resrcons. The over-enfng resrcons o no change essenall he resls obane n hs aer snce ha SVAR moel roces smlar mlse resonses for he monear shock. However he oher shocks are easer o nerre n he crren verson of he moel. 4
Alernave sraeges for Swss monear olc can now be analze b ervng cononal forecass from he SVAR moel. Secfcall we eermne a seqence of olc shocks reqre o sasf sch conons as an average nflaon arge over a wo- or hreeear ero. Before we rn o hs exercse n eal we have o scss brefl he aroraeness of or aroach. I mgh be arge ha he change n he SNB's monear regme as olne above nvalaes he se of a moel fe o aa generae b a fferen monear envronmen. However we beleve ha hs roblem s no of aramon morance n he resen conex. Prce sabl remane he lmae objecve of Swss monear olc hrogho he samle ero. Moreover alhogh he SNB ajse s oerang roceres a he en of 999 hs mofcaon no case a break n he me seres rocess of he varables consere n or SVAR moel: Bank reserves se as he man olc nsrmen before 999 an he neres rae on reos he rncal new nsrmen are no ncle n or VAR ssem. Now le s brefl olne he aroach eveloe b gler Joran Lenz an Savoz 005 for he analss of forwar lookng monear olc. Conser a monear olc sraeg base on an average nflaon forecas for he nex qarers as s ale n Swzerlan. Take he examle of a monear olc reacng smmercall o osve an negave evaons from he nflaon arge π * measre a a qarerl rae. In hs framework olc s rece b he exece evaon as of me of he average nflaon from s arge for horzon π * E log log where E x E x x x.... T Nex we have o eermne he seqence of monear shocks from o ha leas o an exece average nflaon whch s eqal o he arge π *. In Swzerlan monear olc ecsons have o be mae gven las ero vales for CPI nflaon an mone growh b onl a frs esmae of GDP growh for he las few qarers. Ths saon hs ffers from he sal assmon n heorecal moels ha monear olc can reac o crren ero fnal vales of nflaon an o. There s an nfne nmber of was o calclae hese shocks. Leeer an Zha 999 show ha olc shocks n VAR-moels have o be moes an leas srbng n orer no o volae he val of he smlaons. We 3 No confence nervals are gven n Fgre. Joran gler Lenz an Savoz 00 show ha he effecs of 5
herefore mnmze he sm of he sqare shocks sbjec o he resrcon so ha he average nflaon rae s on arge. As shown b Joran gler Lenz an Savoz 005 hs leas o he followng seqence of olc shocks AA44 g. AA j 4 44 j 0 AA j s he 4x4 marx of he mlse resonse cmlae over j eros. Ths he elemen 44 of hs marx gves he j ero cmlae resonse of nflaon o a monear shock In he remaner of he aer we call a rle whn or SVAR aroach base exclsvel on an nflaon arge a sraeg of src mem-erm nflaon argeng. Of corse we can al he same aroach sng he average o growh as a arge of monear olc. Assme ha he argee o growh rae s enoe b γ *. Agan we efne frs he evaon of he ncononal forecas of he o growh from arge eros ahea: γ * E log log 3 The alcaon of he same rocere as ale for nflaon roves s wh he followng omal n he leas sqares sense olc shocks for o : AA4 g 4 AA j 4 4 j 0 In wha follows we call a rle whn or SVAR aroach base exclsvel o growh arge a sraeg of src mem-erm o growh argeng. Now le s conser he rae-off face b monear olc n he framework of or SVAR moel. To hs en we conser he varabl of nflaon an o growh mle b fferen egrees of mem-erm nflaon an o growh argeng over he -ero horzon. To sar wh we efne a convex combnaon of he monear olc shocks for src mem-erm nflaon or o growh argeng gven n eqaons an 4: he monear olc shocks n an overenfe varan of he moel are sascall sgnfcan. 6
α g g 5 4 α Ths s he saon of a monear olc boar where he ecson s aken b consenss an accorng o he average references of s members. The boar members have eher he reference for re nflaon argeng or re o growh argeng n he mem erm. The arameer α hs reflecs he fracon of he nflaon hawks n he boar an α s he fracon of he nflaon oves. Of corse for α we have he case of src mem-erm nflaon argeng an for α 0 we follow a src mem-erm o growh argeng. Ths sraeg corresons o he goal of mnmzng he weghe sm of he cononal varabl of he exece mem erm nflaon an growh rae. The roose formalzaon of he monear olc sraeg s arorae n he sense ha cares ver well he focs of mem erm orenaon of Swss monear olc on nflaon an GDP growh ersecves. Inee or exerence ells s ha he scsson abo Swss monear olc exacl focses on mem erm nflaon an GDP growh olook an a man sse s how mch a GDP growh arge shol be aken no accon. However or framework for monear olc analss ffers from he wo aroaches sall aoe n he lerare namel he Talor rle an he omzng framework. I ma be arge ha or framework les somehow beween hese wo aroaches. Eqaon 5 shares some feare wh he Talor rle framework: mles for nsance a negave vale for he monear olc shock when he mem erm nflaon forecas an/or GDP growh forecas s above arge whch leas o an ncrease n he neres rae. The weghs α an -α la a smlar role as he coeffcens of he nflaon an o ga erm n a Talor rle resecvel. B conras o an a hoc Talor rle he olc reacon n or framework ams a a mem-erm arge akng fll no accon he exece namc effecs accorng o a fll secfe emrcal moel. Ths feare of or moel s share wh he omzng framework. However he laer s more general n he sense ha a scone weghe average of all fre exece nflaon an o varabl s aken no accon. Wh or aroach olc makers are more smle mne as he care onl abo cononal mem erm nflaon an GDP growh volal. Anoher moelng sse s rase b he Lcas crqe. Of corse or aroach wol be nval f we consere changes n α as regme changes. We arge n a smlar wa agans hs ossble objecon as we before when we brefl aresse he qeson of sng aa from a ero of monear argeng o esmae a moel se for he analss of 7
forecas orene monear olc. We see regme changes as fnamenal new orenaons of he goals of monear olc as he ranson from an envronmen of hgh an volale nflaon o a olc of keeng nflaon low as man conres exerence n he las 5 ears. In or moel nflaon alwas rerns o s long-rn eqlbrm rresecve of he vale aoe for α. We conser sch changes herefore as moes an non-fnamenal as he low nflaon envronmen revalng n Swzerlan snce he m-sevenes s reserve. Now le s see o wha exen he lanne seqence of monear olc shocks s able o close he evaon of average nflaon an o growh rae from her arges. The remanng gas an measre as evaon from arge corresons o he mac of he olc shocks mns he forecase evaon from arge an nce b he hree non-olc shocks a me. The cmlae mlse resonse fncon leas o he followng evaons for nflaon r an GDP growh r from arge resecvel gler Joran Lenz an Savoz 005: r r [ ] 6 0 4 44 4 4 44 G G r j AA AA AA r AA r j α α α α α [ ] 7 0 44 44 4 4 4 G G r j AA AA AA r AA r j T α α α α α For he economc nerreaon of he wo exressons erve above we brefl conser for examle he exece resonse of he mem erm nflaon rae o he forecas-orene monear olc. If α s eqal o one src mem-erm nflaon argeng we exec o h he average nflaon arge exacl an he ga s zero. Oherwse he mem erm evaon of nflaon from arge s eermne b he exresson n brackes. The secon erm of hs exresson reflecs he nflence of he reacon of monear olc o he o growh arge whch eens on he evaon r ] [ G 8
from he o arge an he arameer G whch measres he co-movemen of o an rces n reacon o a monear olc shock. The evaon of he -ero ahea average nflaon an o growh from arge s revse n ero accorng o he shocks hng he econom. For he sake of smlc we assme ha we are n eqlbrm n me n he sense ha we exec o h boh arges n he ero o an corresonngl he monear olc shock n ero s zero. However he non-olc shock of ero leas o evaons from he arges whch n rn nees a revson of he lanne monear olc shock seqence. We frs noe ha he evaons of he ncononal forecass from her arges are gven b: l 4 l 4 AA AA l AA AA l 0 0 l l 8 9 Noe ha he srcral shocks have an mac effec on nflaon an o growh whch has o be sbrace as has no nflence on fre nflaon an growh. Sbsng hese exressons no eqaon 6 an 7 resecvel we ge r r α α l 4 l 4 [ AA l [ AA AA AA l 0 G 0 G AA AA l AA AA l 0] 0] l l 0 Calclang cononal varances gven nformaon of me roves he followng exressons: Var r Var r α α l 4 l 4 [ AA [ AA l AA AA l 0 G 0 G AA AA l AA AA l 0] 0] 3 Ths mles a lnear rae-off n he sanar evaons of he o growh an nflaon mem-erm resonses. Of corse hs cononal varance s zero for nflaon o growh when α s 0 oherwse boh varances are larger han zero. The reaer has o be remne ha hese cononal varances are wh resec o he -ero ahea exece vales n. 9
3. The Effec of GDP Revson Errors on Inflaon an Growh Rae Volal In hs secon we analze he effecs of GDP revson errors on monear olc nce volal of nflaon an growh. For CPI nflaon aa revson errors are no a seros roblem gven he fac ha hese aa are avalable on a monhl bass raccall who ela an are harl ever revse. The same ales o mone sock aa whch are onl sbjec o mnor revsons. However aa revson errors are clearl a roblem for o: Two monhs afer he en of a qarer a frs GDP esmae s release. In Seember of ear hese fgres for he receng ear are revse when he are ajse o he frs release annal GDP aa for he receng ear. The annal accon of ear - s self sbjec o revsons whch are blshe n Seember of ear an whch lea o a secon revson of qarerl GDP fgres of ear -. Moreover he changes n he base ear of he accon n 989 an 997 lea o aonal fferences beween he fnal seres avalable oa an he real me aa of before 996 4. Ths mng of aa revsons mles ha real me forecas n or VAR wh lag lengh fve have o be base on relmnar GPD fgres whch are all sbjec o revsons. The frs release qarerl GDP fgres are base on a regresson of annal GDP on annal aa of qarerl avalable rocon ncaors akng no accon frs orer aoregresson of he resals. Afer annal aa became avalable he fference beween he annal fgre an he sm of he qarerl frs release fgres s srbe o he qarerl aa akng no accon he aocorrelaon of he resals of he regresson eqaon Chow an Ln 97. Swss Qarerl GDP aa are release reglarl wh a wo monhs ela snce 980 when for he frs me an offcal hsorcal qarerl accon gong back o he m-sxes was blshe. The fference exresse n ercenage ons beween he fnal 990 base ear fgre an he frs release s loe n Fgre. The GDP aa revson error aears as a hghl volale an srongl osvel aocorrelae b saonar me seres wh a mean close o zero. Inee a sanar n roo es clearl rejecs he nll hohess an an AR moel wh a coeffcen close o 0.8 fs he aa well. The esmaes of he mean whch s 0
no sgnfcanl fferen from zero an he sanar evaon are 0.3 an.6 resecvel. The sanar evaon for he aa revson error of he growh rae of GDP whch s relevan n or VAR n frs fferences s 0.8. Moreover here s some slgh negave aocorrelaon whch s no sascall sgnfcan an whch can be neglece for raccal roses. 5 Before rnng o he effecs of hese aa revson errors on he volal rae-off beween nflaon an GDP growh we have o brefl scss he hgh erssence of he aa revson errors ocmene above. A frs sgh hs seems o ncae ha he frs releases of he GDP fgres are sb-omal esmaes. However sch a conclson s no warrane for he followng reason: he revson of he qarerl GDP fgres whn he framework of he Chow an Ln meho leas b consrcon o aocorrelae revson errors. Moreover a change n he base ear when new annal fgres for man revos ears become avalable leas o erssen revson errors. Ths GDP revson error has an nflence on growh an nflaon forecass whch een on n eqal o he VAR lag lengh mns one lagge nos growh raes n or VAR framework. The eases wa o calclae he effec of he aa revson errors on hese forecass s base on he rece form vecor movng average reresenaon of he me. vale of he vecor X efne n secon : X e C e... C e C e... C n e... 4 n v The aa revson error n GDP growh he frs elemen of he vecor X n me sa can be nerree as a change n he frs elemen of rece form error e n me an has herefore he effec C on he GDP growh forecas mae n where C s he elemen of he rece form mlse resonse marx C. Smlarl he effec on he nflaon forecas s C 4. If he aa revson error s ae me -j he corresonng effecs are C l j l 4. In or framework we are nerese n he cmlae effec of he aa revson errors on he nflaon an o growh forecas o eros whch are gven b 4 These base ear changes ncle conceal changes n he annal accon n arclar n 996. However we hnk ha hese changes also have o be accone for as he shol resl n beer GDP aa whch were calclae back o 980 an whch were se for he esmaon of he moel. 5 The frs orer aocorrelaon coeffcen s 0.3.
e e n j 0 C C 4 j v v j n j C j v j 5 6 The crren aa revson error has a secal effec on he forecase arge evaon of o as effecs he ero as well as he exece ero vale log o n eqaon 3. Ths exlans he sbracon of n he frs erm of he secon eqaon gven above. Le s now conser he aa revson nce exece evaons from he nflaon an growh arge re an re resecvel. Monear olc reacs o hese evaons accorng o eqaon 5 gven n Secon where -erms are relace b e-erms gven n eqaons 5 an 6: α g e g e 7 4 α Therefore he exece evaon from arge of nflaon an growh afer he error nce olc reacon are gven b re re AA AA 44 4 4 4 8 9 The evalaon of hese exressons - analogos o he ervaon of eqaons 6 an 7 n Secon leas o he followng wo eqaons: re αe α Ge 0 re αg e α e Accorngl we ge he followng exressons for he cononal gven me nformaon varances for hese aa revson error nce changes:
Var re α Var e Var re α G Var e α G Var e α Var e α α G Cov e α α G Cov e e e 3 The covarance marx of he aa revson error nce evaons from arge s easl obane as follows: These wo varables can be wren as a lnear ransformaon of he n relevan error erms collece n a Vecor V namel DV. The elemens of he xn marx D are obane b he rece form mlse resonses as gven above. Ths he covarance marx of he wo evaons s DCov V D' where he covarance marx of V [ CovV ] s aroxmael agonal gven he aroxmae whe nose roer of he aa revson error. Therefore he rece form mlse resonse esmae of or SVAR moel an he varance for he aa revson error allow he calclaon of he varances an he covarance of he wo arge evaons. In Fgres 3 an 4 he nflaon an he o growh varance case b he aa revson error an he nce olc reacon s loe as fncon of α for 8 whch s favorable o o growh argeng as he effec of monear olc on o a hs horzon s relavel srong an n 4 whch s he relevan nmber of lagge aa revson errors n or VAR moel wh lag lengh 5. We can see ha he mnmm varance n boh cases s now obane wh a vale of α aroxmael eqal o 0.75. The eclnng segmens of hese grahs are brogh abo b he fac ha he rece form mlse resonse of nflaon o a rece form shock n o growh s relavel weak comare o ha of o growh self. The slgh ncrease of he aa revson error nce varabl s case b he negave correlaon beween resonses of cmlae growh an nflaon. The loss of hs versfcaon effec leas o an ncrease n boh varances when he wegh of he src mem-erm nflaon arge ges exreme. However noe ha he exsence of aa revson errors n GDP growh favor a hgher wegh for he src mem-erm nflaon arge. Fgre 5 ncles scaerlos for fferen vales of α aong a 8 qarers horzon. The frs refers o he cononal varance of o growh an nflaon e o he occrrence of srcral shocks as escrbe n secon eqaons an 3. However he fnngs are robs wh resec o reasonable changes of he arge horzon for he conc of monear olc wo o hree an a half ears. We can see from Fgre 5 ha or SVAR moel mles a sanar convex effcenc froner for he cononal varances of nflaon 3
an growh. Tolerang a hgher varabl of o growh allows for a lower varabl of nflaon an vce versa rae-off. Thereb he maxmm varabl of nflaon s clearl hgher han he maxmm varabl of o growh. Ths resl s case b he hgher erssence of he mac of he shocks on nflaon han on growh. The secon scaerlo as he varance e o aa revson errors. We noe ha here s no longer a convex effcenc froner f aa revson errors n GDP are aken no accon: Decreasng he wegh of o growh argeng over some range.e. ncreasng α from 0 o aroxmael 0.4 ecreases he cononal varance of boh nflaon an growh. Ths here s no rae-off beween smaller o growh varance an hgher nflaon varance over hs range. Ths resl s e o he fac ha wh aa revson errors monear olc reacs oo mch o nos aa f he wegh on o growh argeng becomes oo bg. Ths occrs becase he aa revson error has a srong mac on he growh forecas b no on he nflaon forecas. However f α > 0. 85 hs effec s slghl o-weghe b a loss of versfcaon whch s brogh abo b he negave correlaon of he aa revson error nce resonses of mem erm nflaon an growh. The non-convex effcenc froner s an emrcal resl b he same henomenon ma arse n a sanar New-enesan moel of Clara Gal an Gerler 999 when he cenral bank reacs o nos o ga aa. The corresonng analss s brefl resene n an aenx o hs aer. Of corse hs rases he qeson wh he cenral bank oes no accon for he errors n he GDP aa n s olc b consrcng an omal esmae of GDP gven all avalable nformaon. Or aroach can be efene agans hs objecon b wo argmens: frs he qarerl GDP fgres release b he sascal offce shol be a bes esmae sng all qarerl avalable rocon emlomen an srve nformaon. Ths s no eas o arge ha he cenral bank s able o rove beer qarerl GDP esmaes. Secon even f he cenral bank col roce beer GDP esmaes wol be ver ffcl o commncae monear olc ecson relng on GDP fgres whch are fferen from he offcal aa rove b he governmen s sascal offce. Sch an aroach wol obvosl lea o crebl roblems for he cenral bank. Noe ha for he o ga hs roblem oes no arse as here s no offcal fgres release for hs varable an he cenral bank has he freeom o roce s own esmae. In sm we beleve ha he cenral bank has o base s olc on he offcall release GDP fgres when aos a GDP growh arge. 4
4. Non-Eqlbrm Inal Conons an Polc Dnamcs So far we have focsse or analss on he effecs of me srcral shocks on he me exece cononal volal of he -ero ahea exece nflaon an growh rae gven long-rn eqlbrm n he as n he sense ha we assme ha all shocks ae earler han are zero. The resls obane ner hs assmon ma ffer from hose for he ncononal varance of mem-erm nflaon an growh for wo reasons: frs here s no long-rn eqlbrm n he as an as shocks nflence crren an fre ocomes. Secon he realze ero ocome eens of corse also on he shocks an olc ecsons n he ero whch een on he fre mem-erm nflaon an growh forecass. Moreover fre olc ecsons are nflence b crren olc ecsons whch o no onl have an effec on average nflaon an growh o b also affec me ocomes. In orer o nvesgae he effecs of fferen monear olc sraeges on he ncononal varance of mem-erm nflaon an growh we se a smlaon aroach. We ake he hsor of he hree srcral shocks from 98 o 00 an he nal conons n 980/8 as gven an smlae he evelomen of he for varables of or SVAR moel ner he assmon ha he monear olc shocks are generae accorng o Eqaon 5 for fferen vales of α an sng hsorcal averages as nflaon an growh arges 6. The conerfacal seres obane n hs wa are hen se o calclae he varance of memerm nflaon an growh he samle varance of he generae seres x g x g for varng vales of α. The generaon of he forecass gng monear olc s one frsl b neglecng he GDP revson errors an seconl b sng he real me aa. The scaer agrams obane from hese smlaons are slae n Fgre 6. Fgre 6 ffers from Fgre 5 wh wo resecs: frs he ncononal varance s sbsanall nearl en mes hgher han he me varance. Secon he effcenc froner s no longer convex b slghl concave n he ncononal case who aa revson errors. Ths resl s brogh abo b a fferng shae of he eenence of he nflaon an growh varance on α. The varance of nflaon growh ecreases ncreases wh α a a ecreasng rae. Therefore lowerng he o nflaon wegh n a saon of src mem-erm growh nflaon argeng leas o a srong weak recon of growh 5
nflaon varance. The frs fference s eas o exlan snce no onl crren me shocks are aken no accon b also as an fre o me shocks are accone for. The non-convex shae of he s bascall exlane b he fac ha n or framework monear olc ams a a low ex ane varabl of he me exece mem erm growh an nflaon rae an no a he ex os varabl of hese seres. The ncononal varance eens n a mch more comlex wa on α han he varance of he me exece varances gven n Secon. In orer o see hs comlex s helfl o conser frs he ncononal no nal eqlbrm evaons from arges whch are gven b he followng eqaons: j 0 j 0 { AA { AA l j AA j AA l j j 4 j 4 j 3 3 l l AA AA l j AA j AA l j j l j l j } } 4 5 The frs erm n he wo eqaons above gves he effec of as srcral an olc shocks on he forecas evaons from arge n. Uner he nal eqlbrm assmon hese exressons rece o 8 an 9 as onl he me srcral shocks are fferen from zero. When hese eqaons are combne wh 5 for eqal o α g α g we see ha we generae an aoregressve 4 eenence of he olc shock: 4 { α g AA j AA j α g AA l j AA l j 4 j j 3 l α g AA j AA j α g AA j AA j } 6 l l l j The AR coeffcens een on he ero fferences of he cmlae mlse resonses of nflaon an growh he wegh of src mem-erm nflaon argeng an he olc resonse ner src mem-erm nflaon an growh argeng. As he fference of he cmlae nflaon mlse resonse s alwas osve we have a negave AR eenence osve n he case of src mem-erm nflaon growh argeng 7. To 6 The vales are.4 an.4 ercen er annm for nflaon an growh resecvel. 7 Noe ha he fferng szes of he cmlae mlse resonses of nflaon an growh are aroxmael comensae b fferen vale of he g-coeffcen whch s close o /3 an 3/4 for nflaon an growh resecvel. 6
nersan hs resl nvel conser a crrenl exansve monear olc whch leas o an ncrease n o whch s reverse afer seven qarers. The reverson of he olc effec calls for an exansonar olc n he fre n orer o h he growh arge. Therefore src mem-erm growh argeng can generae self-enforcng olc acons. The same sor ales o olc acons o crren IS an mone eman shocks whch have he same hm-shae cmlae resonse aern of GDP growh. Ths effec las no role for src mem-erm nflaon argeng as we have a ermanen effec of all shocks on he rce level whch s reache smoohl over me. The argmens olne above ncae ha here s a fference beween he rae-off n he namc conex consere n hs secon an he rae-off n he sac conex of Secon. In he fll namc conex large small recons n nflaon varabl alwas have o be a more or less b large small ncreases n GDP growh varabl. The secon scaer lo of Fgre 6 shows ha he namc effecs of he GDP-aa revson error lea o an even more rononce non-sanar effcenc froner. I has an ncreasng branch for α beween 0.45 an. Ths resl s brogh abo b he srong nflence of he aa revson errors on he GDP forecass an he mle olc reacon whch creaes hgher nflaon an GDP growh varabl. Ths effec o-weghs he small recon n growh rae varabl case b he ecrease of α. For vales of α smaller han 0.45 he mac of a lower α omnaes he mac of aa revson errors an hs leas o a srong recon of growh varabl. However mos of hs branch s no feasble as he assmon of moerae olc nervenon s clearl no longer arorae. These ocomes reqre monear olc shocks ha are clearl osve on average an hs nvalae or analss. In oher wors wh vales of α smaller han 0.3 smlae average nflaon rae s beween 0.5 o.5 ercen ons er annm above s hsorcal vale 8. Therefore he conseraon of GDP aa revson errors n or fll namc conex sharens or olc conclson of Secon 3 srongl n he sense ha src-mem erm nflaon argeng s sggese as a sraeg o ge nflaon an growh varabl as low as ossble. 8 I shol be sresse ha for all oher smlaons we ge average monear olc shocks whch are essenall 0 an herefore average smlae nflaon raes whch are ver close o he hsorcal average. 7
5. Conclsons In hs aer we analze forwar-lookng rles for Swss monear olc n a small srcral VAR conssng of for varables n he resence of GDP revson errors. There are wo man resls of he aer. Frs f aa revson errors n GDP are aken no accon here s no longer a convex effcenc froner beween he cononal varance of memerm nflaon an GDP growh: Increasng he wegh of he o growh arge α from 0.58 o ncreases he cononal varance of boh mem-erm exece nflaon an growh. Ths resl s e o he fac ha wh aa revson errors monear olc reacs oo srongl o nos aa f he wegh on o growh argeng becomes oo bg as aa revson errors have a srong mac on he growh forecas b no on he nflaon forecas. However f α > 0. 8 hs effec s slghl o-weghe b a loss of versfcaon whch s brogh abo b he negave correlaon of he olc reacon o aa revson error nce resonses of mem-erm nflaon an growh. Therefore a src mem-erm nflaon sraeg s neffcen even f he coss of ncrease volal of nflaon an growh comare o he case α 0. 8 are relavel small. The secon resl shows ha hs effec of aa revson error s renforce when noneqlbrm nal conons an he conseqences of enogenos olc namcs are aken no accon. In fac n he resence of GDP aa revson errors olc reacons o he nflaon an growh conseqences of as olc ecsons ma even esablze he econom f he wegh on he mem-erm GDP growh arge s hgh. In general he aer ncaes ha ner realsc assmons he cenral bank nces a hgher varabl of boh o growh an nflaon b concenrang oo srongl on o growh. The exsence of aa revson errors for GDP forcefll nerlne he lms an he rsks of a monear olc amng a o sablzaon. Even f he cenral bank onl cares abo growh sablzaon he wegh on hs arge relave o he one of he nflaon arge shol be clearl smaller han or even zero. Ths or resls confrm he concerns abo o growh sablzaon frs rase b Orhanes 000 when real me aa roblems an are aken no accon. In aon or fnngs are n lne wh he heorecal analss of Gasar an Vesn 004 who conser a non-omzng olc maker followng reasonable olc reces n a sanar new enesan moel wh nceran abo he o ga. The resls of he aer can also be lnke o he lerare on me-nconssenc of monear olc of he e nroce b Barro an Goron 983 an lan an 8
Presco 977. 9 In a semnal aer Rogoff 985 showe n hs conex ha elegang monear olc o a conservave cenral banker.e. a cenral banker who s relavel more concerne abo nflaon han he soce as a whole can ecrease he varance of boh nflaon an o growh an hereb mrove he welfare of he soce. In or moel me-nconssenc s no a roblem. However we can nerre α as he fracon of nflaon hawks n a cenral bank boar. Ths even f he soce ha srong reference of o sablzaon.e. f α s 0 wol be an avanage for he soce o aon a conservave boar wh a α clearl bgger han 0. Sch a boar ma elver a smaller varabl of o growh han a boar ha reflecs exacl he references of he blc. Conseqenl or resls sor he vew ha he governmen shol aon conservave cenral bankers when s olcall ffcl o movae a owngrang of he mem erm GDP growh arge b aa revson roblems for GDP. References Barro R.J. & Goron D.B. 983. Rles Dscreon an Reaon n a Moel of Monear Polc. Jornal of Monear Economcs 0-. Chow G.C.& Ln A. 97. Bes Lnear Unbase Dsrbon an Inerolaon of Tme Seres b Relae Seres. Revew of Economcs an Sascs 53 37-375. Clara R. Gal J. & Gerler M. 999. The Scence of Monear Polc: A New enesan Persecve. Jornal of Economc Lerare 37 66-707. Ehrmann M. & Smes F. 003. Unceran Poenal O: Imlcaons for Monear Polc. Jornal of Economc Dnamcs an Conrol 7: 6-638. Gasar V. & Vesn D. 004. Imerfec owlege Learnng an Conservasm mmeo Frankfr Janar 004. Joran T.J. gler P. Lenz C. & Savoz M.R. 00. Inflaonsrognosen m vekoraoregressven Moellen. Qaralshef er Schwezerschen Naonalbank 0 4 66. Joran T.J. & Pergne M. 00. De Inflaonsrognose er Schwezerschen Naonalbank. Qaralshef er Schwezerschen Naonalbank 0 54 6. gler P. & Joran T.J. 004 Vecor Aoregressons an he Analss of Monear Polc Inervenons: The Swss Case. Schwezersche Zeschrf für Volkswrschaf n Sask 40 67-87. gler P. Joran T.J. Lenz C. & Savoz M.R. 005. The Analss of Forwar-Lookng Monear Polc n a VAR Framework SNB Workng Paer Seres Ma 005. 9 As menone n he nrocon he same resl was obane b Ehrmann an Smes 003 n a fferen moellng framework. 9
gler P. & Rch G. 00. Monear Polc ner Low Ineres Raes: The Exerence of Swzerlan n he lae 970 s Schwezersche Zeschrf für Volkswrschaf n Sask 38 4-69. lan F.E. & Presco E.C. 977. Rles Raher Than Dscreon: The Inconssenc of Omal Plans. Jornal of Polcal Econom 85 73-86. Leeer E.M. & Zha T. 999. Moes Polc Inervenons. Feeral Reserve Bank of Alana Workng Paer 99. Lcas R.E. 976. Macroeconomc Polc Evalaon: A Crqe. Carnege Rocheser Conference Seres on Pblc Polc 9 46. Rogoff. 985. The Omal Degree of Commmen o an Inermeae Monear Targe. Qarerl Jornal of Economcs 00 69-89. Orhanes A. 000. The Qes for Proser who Inflaon. ECB Workng Paer No. 5. Orhanes A.. 00. Monear Polc Rles Base on Real-Tme Daa. Amercan Economc Revew 9 964-985. Smes F. 00. O Ga Unceran: oes Maer for he Talor Rle. Emrcal Economcs 7 3-9. Saler P. 00. En ökonomersches Makromoell für e Schwez. Qaralshef er Schwezerschen Naonalbank 9:63 89. Svenssson L. & Woofor M. 000. Incaor Varables for Omal Monear Polc. ECB Workng Paer No.. Aenx: GDP Revson Errors n a Smle Theorecal Moel Le s conser he sanar New enesan moel scsse n he srve aer of Clara Gal an Gerler 999. I consss of IS-crve a "new" Phlls crve an a qarac loss fncon n nflaon π an growh or o ga x of he cenral bank whch oeraes b seng he nomnal neres rae x ϕ π λx E 0 E π βe π β [ ax π E x ] g A where g an are zero mean srcral shocks whch follow an AR rocess wh coeffcen µ an ρ resecvel. In hs moel omal monear olc ner screon s characerze b he followng frs orer conon x λ π A a mlng ha eman s conrace b ncreasng ecreasng he neres rae when nflaon s above below arge whch s sose o be zero. Now le s assme ha he cenral bank 0
observes x onl wh a zero mean aa revson error e whch follows an AR rocess wh coeffcen θ. Therefore he frs orer conon flflle b he cenral bank whch neglecs hs aa revson roblem s x λ e π A3 a Inserng he omal conon n he Phlls crve resls n π λ a λ π e βeπ The moel solon s a lnear fncon of he wo sae varables an e wh nknown coeffcens: π φ φ e A4 Accorng o he assme AR srcre he exece vale for s eqal o E π φρ φ θe Inserng hese exressons n he frs eqaon roves λ φ θe λe a φ φe β φρ Eqang coeffcens on boh ses of hs eqaon resls n a φ λ a βρ λa φ λ a βθ A5 Inserng he solon for π n he omal conon easl resls n he solon for x an we ge a π λ a βρ x λ λ a βρ λa e λ a βθ a βθ e λ a βθ A6 Ths means ha a osve aa revson error growh s eeme o be hgher b he cenral bank han reall s leas o a oo resrcve monear olc reslng n lower growh an lower nflaon. Uner he reasonable assmon ha an e are no correlae we have he followng exressons for he varances of nflaon an growh σ π a λa σ σ λ a βρ λ a βθ λ a βθ σ x σ σ λ a βρ λ a βθ e e A7
where σ s he sanar evaon of he varable ncae b he lower case leer. When here s no aa revson error hese exressons ml he sanar convex olc effcenc froner n he varance of growh an nflaon whch s obane b varng α from zero o nfn as scsse b Clara Gal an Gerler. However hs convex ma be esroe b he nrocon of he GDP aa revson error as monear olc reacs on nos o aa. I can be easl seen from he above exressons ha he conrbon of he aa revson error o he varance of nflaon ncreases wh α for boh varables. Therefore ncreasng a efnel ncreases he varance of nflaon b he effec on he varance of growh s ambgos: on he one han he effec of he srcral shock an he corresonng varabl ecreases. On he oher han he effec of he aa revson error on o an corresonngl s varabl ncreases. Whch of hese wo effecs omnaes arclarl eens on he relave magne of he varance of he srcral shock an he aa revson error. Fgre : Accmlae mlse resonses of changes n log GDP neres rae 3M-SFR- LIBOR log real mone sock M an log rces CPI o srcral shock SVAR5 qarerl aa 974/I-00/IV Resonse of GDP ercen over 6 qarers o a n sl shock n qarer Resonse of GDP ercen over 6 qarers o a n IS shock n qarer Resonse of GDP ercen over 6 qarers o a n M-eman shock n qarer Resonse of GDP ercen over 6 qarers o a n monear olc shock n qarer.8.8.8.8.6.6.6.6.4.4.4.4.....0.0.0.0 -. -. -. -. -.4 -.4 -.4 -.4 -.6 4 6 8 0 4 6 -.6 4 6 8 0 4 6 -.6 4 6 8 0 4 6 -.6 4 6 8 0 4 6 Resonse of LIBOR ercen over 6 qarers o a n sl shock n qarer. Resonse of LIBORercen over 6 qarers o a n IS shock n qarer. Resonse of LIBORercen over 6 qarers o a n M-eman shock n qarer. Resonse of LIBORercen over 6 qarers o a n monear olc shock n qarer. 0.8 0.8 0.8 0.8 0.4 0.4 0.4 0.4 0.0 0.0 0.0 0.0-0.4-0.4-0.4-0.4-0.8 4 6 8 0 4 6-0.8 4 6 8 0 4 6-0.8 4 6 8 0 4 6-0.8 4 6 8 0 4 6 Resonse of real Mercen over 6 qarers Resonse of real Mercen over 6 qarers Resonse of real Mercen over 6 qarers Resonse of real Mercen over 6 qarers o a n sl shock n qarer o a n IS shock n qarer o a n M-eman shock n qarer o a n monear olc shock n qarer 3 3 3 3 0 0 0 0 - - - - - - - - -3-3 -3-3 -4 4 6 8 0 4 6-4 4 6 8 0 4 6-4 4 6 8 0 4 6-4 4 6 8 0 4 6 Resonse of CPI ercen over 6 qarers o a n sl shock n qarer Resonse of CPI ercen over 6 qarers o a n IS shock n qarer Resonse of CPIercen over 6 qarers o a n M-eman shock n qarer Resonse of CPI ercen over 6 qarers o a n monear olc shock n qarer.... 0.8 0.8 0.8 0.8 0.4 0.4 0.4 0.4 0.0 0.0 0.0 0.0-0.4-0.4-0.4-0.4-0.8-0.8-0.8-0.8 -. 4 6 8 0 4 6 -. 4 6 8 0 4 6 -. 4 6 8 0 4 6 -. 4 6 8 0 4 6
Fgre : Daa revson errors of qarerl Swss GDP 980-00 Percen fference beween fnal GDP aa an frs release GDP aa 3 0 - - -3 980 985 990 995 000 Fgre 3: 8-qarers-ahea cononal varance of nflaon case b aa revson errors of GDP Inflaon measre n ercen ALPHA s he wegh of mem erm nflaon arge 3
Fgre 4: 8-qarers-ahea cononal varance of o growh case b aa revson errors of GDP O growh measre n ercen ALPHA s he wegh of mem erm nflaon arge Fgre 5: 8-qarers-ahea cononal varance of nflaon an o growh rae-off Srcral shocks ashe lne as well as srcral shocks wh varng α an aa revson errors sol lne nflaon an o growh measre n ercen; alha s he wegh of mem erm nflaon arge 4
5
Fgre 6: 8-qarers-ahea ncononal varance of nflaon an o growh rae-off Hsorcal srcral shocks an smlae monear olc wh varng α ashe lne as well as GDP aa revson errors sol lne nflaon an o growh measre n ercen; alha s he wegh of mem erm nflaon arge 6