DP2003/05 Learning process and rational expectations: an analysis using a small macroeconomic model for New Zealand. Olivier Basdevant.

Transcription

1 DP2003/05 Larning procss and raional xpcaions: an analysis using a small macroconomic modl for Nw Zaland Olivir Basdvan May 2003 JEL classificaion: C53, E3, E52 Discussion Papr Sris

2 DP2003/05 Larning procss and raional xpcaions: an analysis using a small macroconomic modl for Nw Zaland Absrac Th naur of xpcaions mars whn conducing monary policy. Modls wih a larning procss can xhibi vry diffrn propris from modls wih ohr yps of xpcaions ruls. This papr draws on h work of Orphanids and Williams (2002), xnding i o allow for h possibiliy ha h larning procss may no b prpual, bu rahr migh b convrging owards a raional xpcaions quilibrium. By modlling xpcaions using a larning procss, w obain vidnc suggsing ha inflaion xpcaions in Nw Zaland ar moving owards raional xpcaions. Thory suggss his will mak i asir o conrol inflaion afr a mporary disurbanc. Economics Dparmn, Rsrv Bank of Nw Zaland, 2 Th Trrac, PO Box 2498, Wllingon, Nw Zaland. addrss: olivir.basdvan@lapos.n Th viws xprssd in h papr ar hos of h auhor and do no ncssarily rflc hos of h Rsrv Bank of Nw Zaland. Rsrv Bank of Nw Zaland Inroducion Th naur of xpcaions mars whn conducing conomic policy, spcially monary policy. A paricularly imporan aspc of forward looking bhaviours is ha hy pu a h cnr of monary policy issus such as crdibiliy, commimn, rpuaion and im consisncy. A crucial poin in inflaion arging is no so much ha h cnral bank has o dircly arg inflaion insad of som inrmdia objciv, bu mor ha i has o saisfy all of h rquirmns for bing crdibl in achiving is goal, hs bing h adopion of an inflaion arg as h main objciv, indpndnc, h chnical capabiliy of forcasing inflaion, and high lvls of ransparncy. Thrfor, inflaion arging can also b viwd as a monary policy framwork ha xplicily ingras a forwardlooking componn in inflaion. If xpcaions wr purly raional hn inflaion could arguably b rducd wihou any cos, providd h cnral bank is fully crdibl (s Ball 994, 995). As nod by Robrs (997), rducing inflaion is usually cosly, mosly bcaus hr is som inria in h inflaion procss. This inria may aris ihr bcaus of wag conracs ha ar s for svral priods (s Taylor 979, 980 or Fuhrr and Moor 992, 995) or bcaus xpcaions ar no prfcly raional. Wha Robrs (997) also mphasiss is ha in nw Kynsian modls inflaion can b rducd a no cos, in spi of sicky prics, so long as inflaion xpcaions ar raional. I is imporan o undrsand whr h sickinss in inflaion coms from: If inflaion is inhrnly sicky hn rducing inflaion would always imply som coss. If inflaion is sicky bcaus of xpcaions hn rducing inflaion could b coslss in h mdium rm (or wih subsanially rducd coss) providd ha agns chang hir xpcaion rul o larn a raional xpcaions quilibrium. Thus, i mars how agns form hir xpcaions, and also whr inflaion sickinss coms from. In his papr w propos o invsiga wha drivs h inflaion dynamic in Nw Zaland, firs

3 2 by analysing whhr inflaion is inhrnly sicky and hn by xamining whhr or no xpcaions ar raional. Alhough h rsuls ar o b rad wih cauion givn h limid amoun of daa, h vidnc so far suggss ha h sickinss of inflaion coms mosly from h dynamic of xpcaions. Th rmaindr of h papr is organisd as follows: in scion 2 w dscrib h gnral mhodology usd, as wll as h conomic and policy implicaions. Scion 3 prsns h rsuls obaind for Nw Zaland, and scion 4 concluds. 2 Modlling a larning procsss: conomic and pracical issus In his scion w prsn how rcn conribuions analys inflaion using small macroconomic modls (scion 2.), and also how larning procsss ar modlld in pracic (scion 2.2). Ths discussions ar of paricular imporanc as h opimal policy may chang whn xpcaions ar no longr raional. 2. Discussion of conomic and policy implicaions In rcn yars, many auhors hav invsigad vry compac macroconomic modls, and hav discussd innsly h forwardlooking naur of xpcaions. 2 A paricular faur of hos modls (somims rfrrd o as nw Kynsian modls) is ha hy hav micro-foundaions (s Robrs 995, McCallum and Nlson 999, Woodford 996, Rombrg and Woodford 997) and hrfor hir paramrs ar srucural and no subjc o h Lucas criiqu (s Lucas 976). Basically hos modls can b rprsnd as follows: 2 y π i = αy = π = + + ( i π r ) + β π + γy + ( µ )( r + π + λ( π π ) + θy ) y + µ i S Lindé (200b) for a discussion of hos diffrn modls. i () 3 whr y is h oupu gap, π h inflaion ra, i h shor-rm nominal inrs ra, π h inflaion arg, r h nural ral inrs ra, y + and π + ar h xpcaions of h oupu gap and inflaion ra, and α, β, γ, λ, θ and µ ar srucural paramrs, all bu β bing posiiv. Th firs rlaion h aggrga dmand (AD), h scond rlaion is h aggrga supply (AS) and h hird summariss h bhaviour of h cnral bank using a Taylor rul wih inrs smoohing (µ bing h smoohr paramr). In his s-up w do no assum anyhing rgarding h raionaliy of xpcaions. Thy can b raional, adapiv, or drivd from a larning procss. As mniond bfor, a firs sp is o invsiga whhr inflaion inria coms from h srucur of h conomy islf or from xpcaions. Robrs (997) proposs a simpl way o addrss whr h inria in inflaion coms from, by using survy xpcaions in a modl of h yp of (): y π i = αy = = + ( i π r ) + β + π (2) 2 δπ + ( δ ) π + + γ y + γ y ( µ )( r + π + λ( π π ) + θy ) y + µ i i Th wo main diffrncs ar ha in his modl π rfrs o survy xpcaions (hrfor xpcaions ar dfind as opposd o h gnral formulaion givn in ()) and h cofficin δ masurs h inria in h inflaion dynamic. As δ is found no significanly diffrn from 0 h concluds ha in h US h inria in inflaion coms only from xpcaions ha ar no prfcly raional. Svral conribuions propos hybrid modls ha ns backward and forward looking dynamics, and hn ry o valua h rlvanc of h forward looking dynamic (s Clarida al 999, Robrs 200 or Rudbusch 2002). Empirical hybrid modls giv conrasing rsuls. Among ohrs, Fuhrr (997) and Robrs (200) find ha forward looking bhaviours ar unimporan, whil Gali and Grlr (999) and Gali al (200) find h conrary, ha forward looking bhaviours ar dominan. As poind ou by Gali and Grlr (999), a possibl xplanaion of hos conrasing rsuls is h choic of h nsion variabl nring in h Phillips curv. If on uss h oupu

4 4 gap hn h modl nds o rjc a forward looking naur of inflaion, whil modls basd on marginal cos xhibi h opposi rsul. Jondau and L Bihan (200) hav invsigad hos findings furhr by xpanding h numbr of counris sudid and by chcking sysmaically h impac of diffrn nsion variabls. Thy show ha h obsrvd diffrncs ar much mor dpndn on h srucur of lags and lads han on h choic of h nsion variabl. Thy also accp a gnral hybrid modl wih hr lads and lags, ha placs roughly qual wighs on backward and forward dynamics. Anohr argumn ofn pu forward in favour of backward looking modls is ha mpirically h Lucas criiqu dos no sm o b rlvan as paramrs do no xhibi significan insabiliy (s Ericsson and Irons 995, Rudbusch and Svnsson 999). Nvrhlss, hos rsuls hav bn criicisd by Lindé (200a), who poins ou ha bcaus of a low powr on small sampls h insabiliy ss canno corrcly disinguish bwn changs in h policy from ohr shocks ha affc h conomy. Morovr, Lindé (200b) suggss ha boh forward and backward looking modls xhibi insabiliy in paramrs 3 which migh b causd by a flawd masur of xpcaions. Wha hos findings rval is ha h naur of xpcaions formaion is sill undr invsigaion, and h us of hybrid modls is much mor an ad hoc spcificaion ha acknowldgs ha xpcaions ar nihr oally raional nor oally adapiv. If w go back o h horical foundaions h problm can b undrsood as follows: Adapiv xpcaions ar an unsaisfacory concp mosly bcaus hy assum ha agns do no rac o sysmaic misaks hy mak. Raional xpcaions hav com undr aack bcaus hy assum oo much informaion on h par of agns. As an alrnaiv, a larning procss in modlling xpcaions may b considrd. I is hn assumd ha agns' xpcaions ar on 5 avrag corrc, bu ha only a limid s of informaion is uilisd. Hnc a rlaivly simpl rprsnaion of xpcaions is possibl, avoiding sysmaic rrors in a modl similar o h on by Fig and Parc (976), in which agns ar assumd o us a univaria modl o form hir xpcaions. Whil implmning a larning procss i should b mphasisd ha agns adjus h xpcaion rul whn hy obsrv h rrors hy mak, and h wighs hy assign o h diffrn variabls usd ar changing ovr im. An inrsing faur of larning procsss is ha undr som circumsancs a raional xpcaions quilibrium (REE) may b larn by agns. Thr is abundan liraur rlaing raional xpcaions and h larning procss (s Lucas 986, Woodford 990, Bby al 200 or Orphanids and Williams 2002). Mos of hos conribuions us las squar simaions o simula h larning procss. Is convrgnc o REE will dpnd on h s of prior informaion ha agns will considr whn forming hir xpcaions 4 (s Marc and Sargn 988, 989a,b, Timmrmann 994 Sargn 999 or Evans and Honkapohja 200). A major criicism addrssd o larning is ha h choic of h spcificaion for h larning procss is arbirary. 5 Nvrhlss, Garra and Hall (997) and Bby a al (200) invsiga h impac of diffrn larning procsss, o find ha a las for larg macroconomic modls i maks lil diffrnc. Inuiivly h ida is ha larning procsss xrac informaion wll nough so ha h prcis form of h larning is no crucial. Marc and Sargn (989a) also dmonsra ha as long as h variabls nring ino h larning rul ar corrlad wih h variabls ha xplain h dynamic undr REE, hn h larning procss will convrg o REE. In a small macroconomic modl h problm is of a diffrn naur: providd ha h srucur is simpl nough, i is possibl for agns o us h variabls ha ar rlvan in h REE 4 L A b h opimal sima a da of an unknown vcor A. Th larning procss can b viwd as updaing A using a simpl rul of h yp: A =TA -. I will convrg owards REE if h ru valu A is a soluion of h updaing quaion, h iniial valu chosn for A is clos o h ru valu and if h marix T has is ignvalus wihin h uni circl. 3 Thus vn forward looking modls should b sd for paramrs insabiliy (s also Esrlla and Fuhrr 999). 5 As an xampl Woodford (990) considrs ha agns could adop a sunspo variabl o form hir xpcaions.

5 6 and hn larn abou h wighs of ach variabl (s Orphanids and Williams 2002). 7 ( X A ) α = A + R X + A π (4) Byond his criicism h mos imporan issu is ha a modl wih a larning procss can xhibi vry diffrn propris from a modl wih a diffrn yp of xpcaions rul. Bby al (200) show ha if xpcaions ar no fully raional hn a modl basd on a larning procss will provid simulaion propris much closr o h ru modl han a modl basd on raional xpcaions. Following his prspciv, Orphanids and Williams (2002) show in a small modl of inflaion ha policis which ar fficin undr raional xpcaions ar no whn agns us a larning procss. Mor prcisly, h auhors suggs ha h opimal monary policy undr a larning procss should b mor aggrssiv and also narrowd o inflaion sabiliy as i is h main objciv of h cnral bank undr an inflaion arging sysm. Ths findings ar linkd o h naur of xpcaions formaion: bing aggrssiv owards inflaion and focussing on on objciv facilias h larning procss. 2.2 Discussion of implmnaion in pracic Having discussd h conomic and policy implicaions of modlling xpcaions wih a larning procss in his scion w urn o h dscripion of how xpcaions ar drivd in h mpirical liraur. W also discuss undr which condiions a larning procss may vnually convrg owards raional xpcaions. Basically a larning procss assums ha inflaion xpcaions can b drivd from h following rul: π + + = a, + a2, π + a3, z ε (3) whr π is h inflaion ra and z is a vcor of variabls ha agns us o form hir xpcaions, i h s of informaion hy find rlvan (bsids h laggd valu of inflaion). L X and A b h following vcors: X =(,π -,z - ) and A =(a,, a 2,, a 3, )'. whr R = = X X τ α τ τ τ and α a squnc of posiiv numbrs. 6 This formula is acually a vrsion of wighd las squars and if α = h formula abov corrsponds o rcursiv las squars. An inrsing faur is ha his mhod of updaing paramrs can b cas ino h Kalman filr formula. Dfining P R and f X + α = X P i bcoms (s Bullard 992): ( X A ) = A + P X f + = A π (5) = P P X X P f P (6) Which corrsponds o h following sa-spac modl: π + + = a, + a2, π + a3, z ε (7) (8) i a i, = ai, + ηi, wih h hypr-paramrs givn by: Var ( ) ε α ( ) = 0 = (9) Var η (0) Wih las squar simaion h larning procss is no opimal in h sns ha his mhod assums ha cofficins ar sabl whil hir simas ar im-varying. Pu in ohr words, h rsuls of Marc and Sargn (989a, b) on h convrgnc of larning procss owards raional xpcaions hold only whn h law of moions of paramrs is viwd as invarian. Ljung and Södrsöm 6 α R can also b drivd according o h following formula: R = + ( R X X R ), which is usd by Orphanids and Williams (2002) and Honkapohja and Mira (2002) for mos rcn conribuions.

6 8 (983) and Bullard (992) show ha whn his assumpion is rlaxd h convrgnc propry no longr holds. Inuiivly h rason is rahr sraighforward: if Var(η ) 0 hn P dos no convrg owards 0, and hus larning dos no convrg o raional xpcaions. Mor prcisly in a mor gnral sa-spac form h cofficins would b drivd as follows: ( X A ) = A + P X f + A π () = P + Q P X X P f P (2) wih Var(ε )=H, Var(η )=Q and f = X P X + H. Th s of quaions () and (2) has o b viwd as follows. Firs agns form hir xpcaions for h valu of inflaion for h nx priod, bfor hy obsrv is currn valu. Onc i is known, hy us his informaion o rvis hir blif in ordr o avoid sysmaic misaks. Expcaions ar hus compud as h prdicd sima for π + : + = a, + a2, π + a3, z ˆ π (3) Sargn (999), Evans and Honkapohja (999, 200) or Orphanids and Williams (2002) propos a simplr vrsion of prmann larning, using h algorihm rproducing wighd las squars givn in (4). Basically hir mhodology consiss of sing a gomrical parn for h wighs: α =κ, whr κ is s o an arbirarily small valu. Th advanag of using h Kalman filr in mpirical conribuions is ha i will giv h opimal gain ha agns apply whn updaing hir paramrs, and can also allow on o s whhr or no h varianc of h sa variabls is significanly diffrn from zro, i o s if h larning is prpual or if i convrgs owards raional xpcaions. 2.3 Th modl 2.3. Th gnral srucur 9 Th undrlying modl is composd by a s of hr quaions: an AD curv, an AS curv and a racion funcion of monary auhoriis. Th saring poin was a gnral modl ha includs boh backward and forward looking bhaviours, in ordr o hav an ncompassing approach. Th srucur sd was as follows: y π i = α y = = + 2 ( i π r ) + α y + β + π (4) 2 δπ + ( δ ) π + + γ y + γ y ( µ )( r + π + λ( π π ) + θy ) + µ i y i Thus w basically considr a hybrid modl, whr h AD and AS curvs hav boh forward looking dynamics (s McCallum and Nlson 999 or Robrs 995) and backward looking dynamics (s Svnsson 997, Rudbusch and Svnsson 999). This modl was simad wih quarrly daa, whr (following h mhodology adopd by Rudbusch and Svnsson) π is h annualisd inflaion ra, i is h annual inrs ra and y h quarrly oupu gap (s h appndix for a dscripion of h daa usd). W could hav considrd a mor gnral srucur for lags and lads (s Jondau and L Bihan 200), bu bcaus of h shor sampl availabl (approximaly n yars of daa) h spcificaion was kp wih jus on lad and on lag in ordr o hav nough dgrs of frdom.

7 0 Tabl : Rsuls of h gnral modl Cofficin Sd. Error -Saisic P-valu α α β δ γ γ µ λ δ R DW AD AS Taylor Th main poin in his xrcis was o hav an accpabl modl conomrically and o s if δ is significanly diffrn from zro. Th rsuls showd ha h modl bhavs rasonably wll in rms of rsiduals, 7 and cofficins ar sabl xcp for h paramr β, which is no significan. Th nx sp was o invsiga how h modl bhavs whn w add som consrains, g whn w impos δ=0 or α = α 2 (as h sum of hos wo cofficins is no significanly diffrn from on). Wha was found is ha such a modl passs mos ss rasonably wll, xcp ha kping a forward looking dynamic in h oupu gap nds o worsn rsuls: ihr h inrs ra in h AD curv is found insignifican wih an xrmly low valu, or i has h wrong sign. Ohr sudis of h sam yp of modl in Nw Zaland also accp a pur backward looking dynamic in h oupu gap (s Razzak 2002 or NBNZ 2002), so w dcidd o xclud y + from h modl. Thus, h final accpd modl was h following: y π i = y = π = + + β + γy ( i π r ) π + ( µ )( r + π + λ( π π ) + θy ) y + µ i Tabl 2: Rsuls of h rsricd modl i (5) Cofficin Sd. Error -Saisic P-valu β γ µ λ θ R DW AD AS Taylor This spcificaion fis abou as wll as h unrsricd spcificaion abov. Th fac ha w can fi h daa wihou a backward looking inflaion rm suggss ha inflaion may no b inhrnly sicky. Insad, inflaion sickinss may com nirly from forward looking (bu non-raional) inflaion xpcaions. Anohr imporan poin is ha h dynamic of oupu xhibis srong prsisnc. Finally, h rsuls obaind for h Taylor rul ar consisn wih hos of Drw and Planir (2000) and Planir and Scrimgour (2002). Rgarding h policy implmnd h rsuls also suggs ha hr is a rlaivly high dgr of inrs smoohing, and h wigh on inflaion is rlaivly high, suggsing ha h Rsrv Bank of Nw Zaland racs srongly o dviaions from arg inflaion. Nvrhlss h sima of λ is no simad wih high prcision (h sandard rror is 0.57), so i is difficul o infr srong conclusions from his rsul. 3 Invsigaing survy xpcaions 7 Th Durbin-Wason saisic for h AD curv is a bi high, bu in h final spcificaion h rsiduals ar a lo mor uncorrlad. Thr ar various ways of invsigaing whhr survyd xpcaions ar raional. As an xampl, Robrs (997) suggss

8 simaing h following: 2 π = a + bπ + (6) If xpcaions ar raional hn on would xpc o find a=0 and b=. Anohr possibiliy is o considr a hybrid modl, which is ofn don in pracic, and sima h following: ( φ) π ε = φπ + + π + (7) Thos wo spcificaions wr rid, and providd h following rsuls: a=0.0, b=0.64, φ=0.64. Th assumpion ha b= or φ=0 was srongly rjcd, suggsing ha xpcaions ar no prfcly raional, which was no surprising. Nvrhlss, his yp of conclusion would b mislading if no ingraing xplicily ha h bhaviour of agns is changing ovr im. In h cas of Nw Zaland, changing xpcaions could b jusifid for wo rasons: bcaus of srucural chang ha occurrd, and bcaus of a larning procss, h lar bing rinforcd by h formr. Th nx sp consisd of simaing im-varying paramrs using h modl s up in quaions () o (3). Bu w also rid o invsiga whhr h larning procss is prmann or if i convrgs owards rcursiv OLS which would imply h convrgnc of h larning procss owards raional xpcaions. As w mniond bfor, h disincion bwn hos wo can asily b undrsood wih h Kalman filr formula: if h varianc of hypr-paramrs is significanly diffrn from 0 hn h larning procss is prpual, whil if i is no hn h larning procss may convrg owards REE. To modl xpcaions, h following modl was simad: Th rmaining problm was o spcify h funcional form of hypr-paramrs. As h daas is rlaivly limid, w ar no confidn in corrcly simaing a gnral srucur for hyprparamrs. Insad w consraind h varianc of ach sa variabl o b idnical. 8 i L Q b Q = Var( η ). In a sandard saspac modl Q would b simad as a consan, which was don iniially. Mor prcisly w simad µ as Q = xp( µ ), 9 and i was found qual o wih a sandard rror of 0.9. This would suggs a prmann larning, as h cofficin is highly significan. Th parns followd by h hr im-varying paramrs wr as follows: Figur : A A2 A3 = a,π + a2,π + a3, y ε (8) π + whr π is h survy xpcaion of inflaion formd in priod i for priod +, and wih: i {, 3} a i, = a i, + η. π dnos h inflaion arg, which w inrpr as h midpoin of h arg bands in h succssiv Policy Targ Agrmns signd sinc 8 9 Alhough w sd an accpd h rsricion ha hos variancs wr no significanly diffrn. Th simaions wr prformd wih EViws 4..

9 and h final simas wr: 4 Final Sa Sd. Error -sa P-valu A A A Alhough h rsuls sm o suggs prpual larning i was also inrsing o chck if h hypr-paramr on h sa dcrass ovr im, which would imply ha h larning procss convrgs owards las squars simas and hus movs owards a raional xpcaions quilibrium. Thus following h idas discussd in Hall al (997) on convrgnc, w modlld Q as follows: ( ) Q = Q0 xp µ. In his cas a ngaiv and significan valu for µ would imply ha h procss is convrging owards rcursiv las squars. Esimaing such a modl gav a valu of wih a sandard rror of Thus, alhough h cofficin found was rlaivly small i is sill significanly diffrn from 0 and backs h ida ha xpcaions formaion convrgs owards rcursiv las squars. Th parns followd by h hr im-varying paramrs wr as follows: Figur 2: and h final simas wr: 5 Final Sa Sd. Error -sa P-valu Α Α Α Ths rsuls suggs svral hings abou how xpcaions ar formd. Among h common faurs w can s ha basically h parns followd by h sa variabls ar similar in boh of h xrciss. In h firs modl (whr h hypr-paramr is simad as a consan) h rspciv wighs on laggd inflaion and h oupu gap convrg owards zro, suggsing ha xpcaions ar bcoming lss rsponsiv o hos variabls and mor anchord o a consan. W hav inrprd his consan as h inflaion arg wih a im-varying cofficin. Wih his inrpraion, h cofficin on h inflaion arg, A2, dos no convrg o on, which suggss ha xpcaions ar no fully raional. Anohr inrsing poin is o look a h parn of A2 as compard o h horizonal lin corrsponding o a consan wigh of on. Wha w can s is ha in boh cass h wigh on h arg has bn gradually incrasing bfor a sharp fall in 997, which corrsponds o h shif from a pr cn mid-poin o.5 pr cn. Thn h wigh has coninud o incras, unil h PTA was again changd. Nvrhlss all changs in h cofficin A2 canno b aribud solly o changs in h official arg. Th Kalman filr givs h opimal adjusmn of cofficins givn h shocks ha ar hiing h conomy, so vn if h wigh on h arg movs mporarily away from on i is no ncssarily a sign ha h arg is no crdibl or achivabl. Only a prmann dviaion from on could b inrprd as blif ha h arg diffrs from h mid-poin of h arg band A A2 A3 Anohr imporan poin o noic is ha in boh cass h cofficins on laggd inflaion and h oupu gap ar no significanly diffrn from zro, a las whn sing a 5 pr cn. Thus all hs rsuls suggs ha h inflaion arg has a much grar rol in xplaining xpcaions formaion han dos h las laggd valu of inflaion. Pu in ohr words, xplicily allowing for

10 6 h possibiliy ha agns may rvis hir xpcaion rul can xplain ha inflaion xpcaions ar closr o raional xpcaions han wha fixd cofficins simaions suggs. Anohr inrsing faur is ha looking a h las valu of A2 in h scond modl w obain a valu of.39, which onc muliplid by h mid-poin during his priod givs a valu of approximaly 2. pr cn, which is vry clos o h currn mid-poin of 2 pr cn. In h firs modl h cofficin is.60 bu wih a highr sandard rror, hus alhough i implis a prcivd arg of 2.4 pr cn, i is no significanly diffrn from h prvious on. Thus in boh cass xpcaions sm o b cnring around a valu nar 2 pr cn, which is h currn mid-poin. 7 and Williams (2002), is for policymakrs o rac mor srongly o dviaions from h arg. Th spcificaion w hav uilisd abov is simpl, and daa ar only availabl for a rlaivly shor sampl. Th modl also dos no xplicily ingra h ransmission of shocks from h rs of h world and h xchang ra. Nvrhlss, our rsuls suggs ha i would b worhwhil o conduc furhr sudy ino how xpcaions ar formd, and also o invsiga xpcaions formaion wihin modls ha allow for hir variaion ovr im. Nvrhlss, hs findings hav o b rad wih cauion. Alhough in h scond modl w can accp ha h varianc is dcrasing ovr im and convrgs owards zro, h cofficin is small nough so ha h convrgnc procss occurs vry slowly, and hus is no vry diffrn from h firs spcificaion whr h larning procss is prpual. As a rsul, vn hough h cofficin A2 was consisn wih a arg of 2 pr cn, hr is no rason why i should no chang in h fuur, and likwis h ohr cofficins. 4 Conclusions In his papr w hav analysd h inflaion xpcaions dynamic in h cas of Nw Zaland. Using h mhodology proposd by Robrs (995), w find vidnc for h possibiliy ha Nw Zaland inflaion is no inhrnly sicky, bu insad is inria drivs from xpcaions. By modlling xpcaions using a larning procss, w obain ha xpcaions sm o b bcoming lss rsponsiv o laggd inflaion and h oupu gap, which may man hy ar moving owards raional xpcaions. Ths rsuls hav ponially srong implicaions for monary policy. In paricular, h mor raional ar xpcaions, h asir inflaion can b rducd wihou incurring coss. If xpcaions wr mor adapiv, hn monary policy should b smoohr in ordr o avoid xcssivly high coss in h shor run oghr wih undsirabl conomic variabiliy. Morovr, o h xn ha h larning procss convrgs qui slowly owards raional xpcaions, hn h policy implicaion, following h idas discussd in Orphanids

11 8 9 Appndix Th daa usd wr dfind as follows: * ( Y ) Ln( Y ) y = Ln (9) whr Y is h quarrly GDP sasonally adjusd, and Y * is h ponial GDP, simad as h HP filrd Y. ( P ) Ln( P ) π (20) = Ln whr P is h consumr pric indx, xcluding inrs paymns and VAT. Th xpcaion π is compud using h CPI xpcaion on yar ahad, akn from h Rsrv Bank of Nw Zaland survy of xpcaions. Th inrs ra usd is h 90 days inrs ra. Th nural inrs ra is h HP filrd ral inrs ra ovr h sampl. Thus i is assum o hav changd ovr im. For mor dails abou h nural ral inrs ra h radr can rfr o h work of Planir and Scrimgour (2002) who modl a im-varying nural inrs ra and analys in dph is policy implicaions. Rfrncs Ball, L (994), "Crdibl disinflaion wih saggrd pric sing" Th Amrican Economic Rviw 84(): Ball, L (995), "Disinflaion wih imprfc crdibiliy" Journal of Monary Economics, 35: Bby, M, S G Hall and S B Hnry (200), "Raional xpcaions and nar raional alrnaivs: how bs o form xpcaions" Europan Cnral Bank working papr #86. Bullard, J (992), "Tim-varying paramrs and non-convrgnc o raional xpcaions undr las squar larning" Economic Lrs 40: Clarida, R, J Gali and M Grlr (999), "Th scinc of monary policy: a nw Kynsian prspciv" Journal of Economic Liraur 37(4): Drw, A, and L C Planir (2000), "Inrs smoohing in Nw Zaland and ohr dollar bloc counris" Rsrv Bank of nw Zaland Discussion Papr #DP2000/0 Ericsson, N R and J S Irons (995), "Th Lucas criiqu in pracic: hory wihou masurmn" in Hoovr K D (d.) Macroconomrics: Dvlopmns, Tnsions, and Pospcs, Kluwr Acadmic Publishrs, Boson. Esrlla A and J C Fuhrr (999), "Ar 'dp' paramrs sabl? Th Lucas criiqu as an mpirical hypohsis" Fdral Rsrv Bank of Boson Working Papr Evans, G and S Honkapohja (999) "Larning Dynamics" in J B Taylor & M Woodford ds. Handbook of Macroconomics, Elsvir Evans, G and S Honkapohja (200), Larning and xpcaions in macroconomics, Princon Univrsiy Prss, Princon.

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