The Analysis of Forward-looking Monetary Policy in a SVAR Framework

Transcription

1 The Analss of Forwar-lookng Monear Polc n a SVAR Framework Peer ugler, WWZ Unvers of Basel an Swss Naonal Bank Thomas J. Joran, Swss Naonal Bank an Unvers of Bern Carlos Lenz, WWZ Unvers of Basel Marcel R. Savoz, Swss Naonal Bank an Unvers of S. Gallen Absrac: Ths aer analzes forwar-lookng monear olc rules n srucural VAR s. Frs, an aroach for moelng a monear olc whch ams a a src meum erm nflaon or ouu growh arge s eveloe. Secon, he ex ane nflaon-ouu-growh volal rae-off for a forwar-lookng olc amng a a convex combnaon hese sraeges s erve. Fnall, an llusraon of our aroach usng Swss aa s gven. ewors: Srucural VAR, forwar-lookng monear olc, effcenc froner JEL classfcaon: E5; E58 Frs raf June 4 Revse March 5

2 . Inroucon In he las en ears forecas orene monear olc sraeges became ncreasngl moran. Mos cenral banks now base curren monear olc mlcel or exlcl on a forecas of nflaon an oher ke macroeconomc varables an n hs wa ake no accoun he lags n he effecs of monear olc. Ths roceure s mae ver exlc b he nflaon argeng sraeg oneere b he Bank of Englan, whch ams a an nflaon wh a horzon one o wo ears. The same ales o he new monear olc framework of he Swss Naonal Bank (SNB) aoe a he en of 999. Ths framework relace a mone sock growh arge b an nflaon forecas over he nex hree ears as he man ncaor o gue monear olc ecsons. Beses he exece fuure nflaon evelomen, he meum erm ouu growh forecas las an moran role. No cenral bank woul h s nflaon arge or kee meum erm nflaon n he sabl range when hs leas o a large eeroraon of ouu growh erformance. The rae-off beween nflaon an ouu growh s mosl analze b usng Talor rules n DSGE moels or raonal macroeconomerc moels. Ths aer rooses an alernave aroach ha allows he analss of forwar-lookng monear olc n srucural VARs, whch are an ofen use ool o esmae he namc effecs of monear olc. Frs, an aroach for moelng a monear olc whch ams a a src meum erm nflaon or ouu growh arge s eveloe. Secon, he ex ane nflaon-ouu-growh volal rae-off for a forwarlookng olc amng a a convex combnaon of hese sraeges s erve. Fnall, an llusraon of our aroach s gven usng Swss aa.. A SVAR Analss of Monear Polc In hs secon, we evelo a meho for he analss of monear olc n a SVAR framework. We rocee on he assumon ha he VAR moel nclues a vecor of quarerl changes n log ouu, shor erm neres rae, log real mone sock an log rce level: X ' = ( log, r, log( m / ), log ). Ths framework assumng I() level seres an no conegraon s he secfcaon we aoe n our emrcal llusraon, bu man oher moels fferng wh resec o number of varables an orer of negraon are ossble. There are onl wo resrcons whch are funamenall necessar n our framework: frs nflaon an GDP-growh have o be nclue n he moel an hese varables shoul be saonar. Secon, he VAR moel has o be secfe n a wa ha allows he enfcaon of a monear olc shock. The number of oher varables nclue

3 an her negraon an conegraon roeres as well he naure of he shor an or long run resrcons aoe s onl moran for he wa he mulse resonse coeffcens use n he followng exercse are esmae. In our emrcal alcaons we use long-run neural resrcons n orer o enf srucural shocks wh varances normalze o for he VAR efne above bu oher enfcaon schemes coul be ale as well. In our alcaon we ge mulse resonses for hree non-monear olc shocks he monear olc shock an. The former shocks can be nerree as aggregae sul shock, IS shock an mone eman shock, resecvel. However, hs nerreaon s no essenal, as onl he jon effec of hese hree shocks on fuure nflaon an ouu growh s neee wh our aroach. u 4 u, u, u3 Alernave sraeges for monear olc can now be analze b ervng cononal forecass from he SVAR moel. Secfcall, we eermne a sequence of olc shocks requre o sasf such conons as an average nflaon or ouu growh arge over a wo- or hree-ear ero. Now conser a monear olc sraeg base on an average nflaon forecas for he nex quarers. Take a monear olc reacng smmercall o osve an negave evaons from he nflaon arge π * measure a a quarerl rae. For such a monear olc, we ge cononal forecass n he followng wa: Frs, we efne he exece evaon, as of me, of he average nflaon from s arge for horzon (, = π * ( E log + log ), () Nex, we have o eermne he sequence of monear shocks from + o + ha leas o an exece average nflaon whch s equal o he arge π *. There s an nfne number of was o calculae hese shocks. Leeer an Zha (999) show ha olc shocks n VAR-moels have o be moes an leas surbng n orer no o volae he val of he smulaons. We herefore mnmze he sum of he square shocks subjec o he resrcon so ha he average nflaon rae s on arge: u 4+ mn s.. AA44 ( ) u4+ (, = () AA (j) s he 4x4 marx of he mulse resonse, cumulae over j eros. Thus, he elemen 4,4 of hs marx gves he j ero cumulae resonse of nflaon o a monear shock. The soluon of hs mnmzaon roblem s obane as

4 AA44 ( ) u4 + = (, = g (,, =,...,. (3) AA ( j) j= 44 Of course, we can al he same aroach usng he average ouu growh as a arge of monear olc. Assume ha he argee ouu growh rae s enoe b γ *. Agan we efne frs he evaon of he uncononal forecas of he ouu growh from arge eros ahea as, γ * ( E log log ) an oban he followng omal (n ( = + he leas squares sense) olc shocks for + o +: AA4 ( ) u4 + = (, = g (,, =,..., (4) AA ( j) j= 4 In wha follows, we call a rule base exclusvel on an nflaon (ouu growh) arge a sraeg of src meum-erm nflaon (ouu growh) argeng. Nex, we conser he rae-off face b monear olc n he framework of our SVAR moel. To hs en, we conser he varabl of nflaon an ouu growh mle b fferen egrees of meum-erm nflaon an ouu growh argeng over he -ero horzon. To sar wh, we efne a convex combnaon of he monear olc shocks for src meum-erm nflaon or ouu growh argeng erve n he las secon: u = α g (, + ( ) g (,, =, (5) 4 + α, Ths s he suaon of a monear olc boar, where he ecson s aken b consensus an accorng o he average references of s members. The boar members have eher he reference for ure nflaon argeng or ure ouu growh argeng n he meum-erm. The arameer α hus reflecs he fracon of he nflaon hawks n he boar an α s he fracon of he nflaon oves. Ths sraeg corresons o he goal of mnmzng he weghe sum of he cononal varabl of he exece meum erm nflaon an growh rae. The roose formalzaon of he monear olc sraeg s arorae n he sense ha caures ver well he focus of meum erm orenaon of monear olc on nflaon an GDP growh ersecves we see n man counres. Inee, our exerence n arcular wh Swzerlan ells us ha he scusson abou monear olc exacl focuses on 3

5 meum erm nflaon an GDP growh oulooks an a man ssue s how much a GDP growh arge shoul be aken no accoun. However, our framework for monear olc analss ffers from he wo aroaches usuall aoe n he leraure, namel he Talor rule an he omzng framework. I ma be argue ha our framework les somehow beween hese wo aroaches. Equaon (5) shares some feaures wh he Talor rule framework: mles, for nsance, a negave value for he monear olc shock when he meum erm nflaon forecas an/or GDP growh forecas s above arge whch leas o an ncrease of he neres rae. The weghs α an (-α) la a smlar role as he coeffcens of he nflaon an ouu ga erm n a Talor rule, resecvel. B conras o an a hoc Talor rule, he olc reacon n our framework ams a a meum-erm arge akng full no accoun he exece namc effecs accorng o a full secfe emrcal moel. Ths feaure of our moel s share wh he omzng framework. However, he laer s more general n he sense ha a scoune weghe average of all fuure exece nflaon an ouu varabl s aken no accoun. Wh our aroach olc makers are more smle mne as he care onl abou cononal meum erm nflaon an GDP growh volal. Anoher moelng ssue s rase b he Lucas crque. Of course, our aroach woul be nval f we conser changes n α as regme changes. We see regme changes as a funamenall new orenaon 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 counres exerence n he las 5 ears. In our moel nflaon (an a foror growh) alwas reurns o s long-run equlbrum rresecve of he value aoe for α an we conser such changes n α herefore as moes an non-funamenal. Now, le us see o wha exen he lanne sequence of monear olc shocks s able o close he evaon of average nflaon an ouu growh rae from her arges. The remanng ga r + (measure as evaon from arge corresons o he mac of he olc shocks mnus he forecase evaon from arge (, nuce b he hree nonolc shocks a me. These effecs can be calculae usng he corresonng cumulae mulse resonses an equaon (5) as well as he formulae for he shocks of he wo src argeng sraeges gven b equaon (3) an (4), resecvel: 4

6 r r r r r r = = AA 44 AA ( α ) = ( α ) G = = 4 ( ) u 4 AA ( ) u 4+ ( ) AA44( ) AA ( j) j= (, 4 (, ( α ) j= 4T + AA4( ) AA44( ) α AA ( j) = αg (, + ( α ) (, 44 (, (, + α (, = ( α (, + ( α ) (, = α (, (, )[ (, G (, ] (6) (, (, [ (, G (, ] (7) For he economc nerreaon of he wo exressons erve above, we brefl conser he (exece) resonse of he nflaon rae o he forecas-orene monear olc. If α s equal o one (src meum-erm nflaon argeng), we exec o h he average nflaon arge exacl an he remanng ga s zero. Oherwse, we exec he meum-erm nflaon rae o evae from he arge. Ths evaon s eermne b he exresson [ (, G (, ]. The secon erm n he brackes reflecs he nfluence of he reacon of monear olc o he ouu growh arge. Of course, he laer effec eens on he corresonng evaon from he ouu arge an he co-movemen of ouu an rces n reacon o a monear olc shock G. In fac, G can be nerree as he oulaon regresson coeffcen of he (-)-ero cumulae monear olc resonse of nflaon on he (-)-ero cumulae monear olc resonse of ouu growh. Thus, he sze of he remanng ga ue o no followng a src meum-erm nflaon argeng rule, eens on he sgn an sze of G r + as well as on he fference n sgn an sze beween (, an (,. The closer G s o an he closer (, s o (,, he smaller he remanng ga r + wll be. Of course, he nerreaon for he remanng ouu growh ga r + corresons exacl o ha of he nflaon ga. The exece evaon of he -ero ahea log rce an log ouu level from he arge ah s revse n ero accorng o he non-monear olc shocks u, u, u3 hng he econom. For he sake of smlc, we assume ha we are n equlbrum n me n he sense ha we exec o h boh arges n he ero o +. However, he 5

7 non-monear olc shock of ero lea o evaons from he arges, whch n urn nees a revson of he lanne monear olc shock sequence. We frs noe ha he evaons of he uncononal forecass from her arges are gven b: (, = (, = l 4 l 4 ( AA ( AA l ( ) ( ) l ()) u ()) u l l (8) (9), where we assume ha he olc shock s equal o zero as of me. Noe ha he nonmonear olc shocks have an mac effec on rces an ouu whch has o be subrace as has no nfluence on fuure nflaon an growh. Subsung hese exressons no he resonses of he rce an ouu levels o he olc shocks r r + + = ( α ) = α l 4 l 4 [ AA l [ AA ( ) ( ) l () G () G ( AA ( AA l ( ) ( ) l ()] u ())] u l l () () an calculang cononal varances (gven nformaon of me roves he followng exressons: Var ( r Var ( r + + ) = ( α ) ) = α l 4 l 4 [ AA [ AA l ( ) ( ) l () G () G ( AA ( AA l ( ) ( ) l ())] ())] () (3) Ths mles a lnear rae-off n he sanar evaons of he ouu growh an nflaon meum-erm resonses. Of course, hs cononal varance s zero for nflaon (ouu growh) when α s (), 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 values n. Fnall, shoul be menone ha he aroach oulne above s sraghforwarl mofe o a olc amng a an nflaon or growh rae for some fuure ero j o,.e. from 5 o 8 quarers: We have sml o relace AA l () b AA l ( j) n equaons (8) an (9). Before urnng o our emrcal alcaon, we have brefl o aress he queson wh we o no ncororae he olc reacon n he VAR coeffcens as s one wh 6

8 srucural moels nsea of focusng on he olc shocks. Ths alernave aroach s, however, n general no feasble n our VAR framework. In orer o emonsrae hs le us assume for he sake of smlc ha he vecor X ' = ( log, r, log( m / ), log ) follows a VAR() moel an ha olc reacs o he exece meum erm nflaon an growh rae accorng o a Talor rule wh osncrac olc shock ξ: X = AX r = E ( γ + ε log + + γ log + ) + ξ (4) The cross equaons resrcon mle b he Talor rule for he VAR coeffcens can be erve as follows: Le us efne he selecon vecors for he neres rae, nflaon an growh n he vecor X h g g = (,,,) = (,,,) = (,,,) (5) Conserng he me exece value of he Talor rule for ero + wh he fuure exece values relace b her VAR forecas we oban he X + = γ ga E X + + γ g A E X + (6) Ths mles he followng 4 cross equaons resrcons eenng on he olc reacon arameer for he VAR coeffcens g A + γ h = γ g A (7) If he Talor equaons coeffcens are known we can es he resrcons gven b equaon (7) an can ge resrce esmaes of he VAR coeffcen marx usng he aroaches eveloe for VAR moels of he erm srucure of neres raes. However, hs oes no hel n our conex as we shoul fn a rearamerzaon of he VAR coeffcens nvolvng he Talor equaon coeffcens. Ths means ha we have o fn soluons of (7) for 4 An oulne of hs aroach can be foun n ugler (99), for nsance. 7

9 elemens of he A-marx eenng on he remanng elemens of A as well as of γ an γ. Thus he arameers of our resrce VAR-moel consss of unresrce VAR coeffcens as well as γ anγ. If hs aroach were ossble we coul esmae he moel n hs new form an hen calculae he -ero forecasng varance ecomoson for fferen values of γ an γ n orer o show he rae-off beween nflaon an GDPgrowh varabl. However, he requre rearamerzaon s no ossble n general (exce for =,), as olnomals of orer n he A-coeffcens are nvolve on he rgh-han se of (7) an no exlc soluon for 4 elemens of he A-marx s herefore avalable. 3. An Alcaon o Swss Daa Ths secon roves an llusraon of our aroach usng Swss aa. Swzerlan s an neresng examle for our aroach as here was no funamenal regme change snce he breakown of he Breon Woos ssem n 973. We conser he change n he SNB's monear olc sraeg menone n he nroucon as non-funamenal as rce sabl remane he ulmae objecve of Swss monear olc hroughou he samle ero. Moreover, alhough he SNB ajuse s oerang roceures a he en of 999, hs mofcaon no cause a break n he me seres rocess of he varables consere n our SVAR moel: The level of bank reserves, use as he man olc nsrumen before 999, an he neres rae on reos, he rncal new nsrumen, are no nclue n our VAR ssem. Fgure slas he mulse resonse esmae for a SVAR moel for Swzerlan corresonng o ha use n Secon, whch s exacl enfe b sx long-run rangular resrcons. The varable s GDP n 99 n Swss francs, enoes he consumer rce nex, m he mone sock M an r he quarerl average of he hree-monh Swss franc Lbor rae of neres an he VAR lag-lengh s 5. In orer o kee he moel as lean as ossble, he exchange rae s exclue from he vecor X, as he ransmsson of monear olc va he exchange rae s nrecl caure b he mulse resonses of he VAR moel. Exlc ncluson of he exchange rae woul be necessar f hs varable ha nfluence SNB behavor n a ssemac wa an, herefore, were requre o enf a monear olc shock. Exchange rae conseraons lae no moran role for he bulk of he samle ero, he exceon beng n arcular he ears 978/79. Noe ha we o no 8

10 selec a monear aggregae wh a sable long-run mone eman funcon n levels such 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 use as he nroucon of he elecronc Swss Inerbank Clearng Ssem an he relaxaon of banks' lqu requremens srongl sore even he raes of change n hs aggregae. However, we shoul also menon ha he resuls are robus wh resec o he n- or excluson of he mone sock seres: a hree varables VAR whou mone rouces essenall he same shae of he mulse resonses o he monear olc shock as he four varable ssem. Fnall, we ough o menon ha he sanar un-roo an co-negraon ess suor he frs-fference secfcaon aoe n hs aer. More nformaon on he alcaon of SVAR moels o Swss aa s rove b ugler an Joran (4) an ugler an Rch (). The resuls wh resec o he neres rae are ambguous: we canno rejec he un roo hohess (ADF es as well as he saonar hohess (PSS es. Thus, we rocee on he I() hohess whch s more convenen n our framework for enfcaon of a monear olc shock. Of course, hs mles ha he real rae of neres rae s non-saonar wha s clearl oubful n he long-run. However, for he meum-erm forecasng horzon consere n hs aer hs assumon s eeme acceable. 9

11 Fgure : Accumulae mulse resonses of changes n log GDP, neres rae (3M-SFR- LIBOR), log real mone sock (M) an log rces (CPI) o srucural shock, SVAR(5), quarerl aa 974/I-/IV Resonse of GDP (ercen over 6 quarers o a un sul shock n quarer Resonse of GDP (ercen over 6 quarers o a un IS shock n quarer Resonse of GDP (ercen over 6 quarers o a un M-eman shock n quarer Resonse of GDP (ercen over 6 quarers o a un monear olc shock n quarer Resonse of LIBOR (ercen over 6 quarers o a un sul shock n quarer. Resonse of LIBOR(ercen over 6 quarers o a un IS shock n quarer. Resonse of LIBOR(ercen over 6 quarers o a un M-eman shock n quarer. Resonse of LIBOR(ercen over 6 quarers o a un monear olc shock n quarer Resonse of real M(ercen over 6 quarers Resonse of real M(ercen over 6 quarers Resonse of real M(ercen over 6 quarers Resonse of real M(ercen over 6 quarers o a un sul shock n quarer o a un IS shock n quarer o a un M-eman shock n quarer o a un monear olc shock n quarer Resonse of CPI (ercen over 6 quarers o a un sul shock n quarer Resonse of CPI (ercen over 6 quarers o a un IS shock n quarer Resonse of CPI(ercen over 6 quarers o a un M-eman shock n quarer Resonse of CPI (ercen over 6 quarers o a un monear olc shock n quarer In he frs column we fn he resonses of all varables (n he orer he aear n he vecor X ) o he sul shock (Shock ). Then, we have he resonses o he IS-shock (Shock ), o he mone eman shock (Shock 3), an fnall n he las column he resonse o he monear olc shock (Shock 4), whch s of mos morance n he curren conex. Frs, here s evence of a shor-run negave lqu effec on he neres rae exenng over wo quarers. The osve reacon n real GDP sars weakl an reaches s eak afer fve quarers an sars o eer ou afer anoher ear. Wh resec o rces, akes sx quarers unl a major osve effec s vsble an 4 quarers are neee for full ajusmen of rces. Afer abou he fourh quarer, rsng rces an nflaon execaons cause he neres rae o overshoo emorarl s long-run equlbrum level.

12 Fgure shows he scaer agram for he 8-ero ahea nflaon an ouu growh varance cononal on me nformaon obane b usng he mulse resonses gven n Fgure. The 8-ero me horzon s favorable o ouu growh argeng because he effec of a monear shock on ouu s srong a hs horzon whereas onl half of he long-run effec on rces has occurre. We can see from Fgure ha our SVAR moel mles a sanar convex effcenc froner for he cononal varances of nflaon an growh. The maxmum varabl of nflaon s clearl hgher han he maxmum varabl of ouu growh. Ths resul s cause b he hgher erssence of he mac of he shocks on nflaon han on growh. I s neresng o comare he varances of he gas acheve wh an acve monear olc o a suaon where monear olc s no aoe o he me srucural shocks. Thus, he AS-shock, he IS-shock an he mone eman shock nfluences meumerm nflaon an GDP-growh whou an reacon of he cenral bank o hem. In Fgure, we see ha hs on s far above he effcen froner whch ncaes he subsanal benefs of an acve monear olc ha reacs o new nformaon. Fgure : 8-quarers-ahea cononal varance of nflaon an ouu growh rae-off Srucural shocks (ashe lne) as well as srucural shocks wh varng α an aa revson errors (sol lne), nflaon an ouu growh measure n ercen; alha s he wegh of meum erm nflaon arge

13 4. Conclusons In hs aer we roose a new meho o analze forwar-lookng monear olc n srucural VAR s base on he arameers of he mulse resonse funcon. To hs en we evelo frs an aroach for reresenng a monear olc whch ams a a src meumerm nflaon or ouu growh arge n a SVAR moel. Secon, we show how he ex ane nflaon-ouu-growh volal rae-off for a forwar-lookng olc amng a a convex combnaon of a src meum-erm nflaon an ouu growh argeng rule can be obane n hs framework. An llusraon of hs aroach usng Swss aa sugges ha avong exece ouu growh varabl has a hgh rce n erms of exece nflaon varabl. References ugler, P. an T.J. Joran. 4, Vecor Auoregressons an he Analss of Monear Polc Inervenons: The Swss Case. Schwezersche Zeschrf für Volkswrschaf un Sask 4: ugler, P. an G. Rch.. Monear Polc uner Low Ineres Raes: The Exerence of Swzerlan n he lae 97 s, Schwezersche Zeschrf für Volkswrschaf un Sask 38 : ugler, P (99). The Term Srucure of Euro Ineres Raes an Raonal Execaons, Journal of Inernaonal Mone an Fnance 9: Leeer, E.M. an T. Zha Moes Polc Inervenons. Feeral Reserve Bank of Alana Workng Paer 99. Lucas, R.E Macroeconomc Polc Evaluaon: A Crque. Carnege Rocheser Conference Seres on Publc Polc :9 46.