A Small State-Space Model of the Australian Economy

Transcription

1 A Small Sae-Space Model of he Ausalian Economy Shawn Chen-Yu Leu Depamen of Economics & Finance La Tobe Univesiy Jeffey Sheen Faculy of Economics & Business Univesiy of Sydney ABSTRACT Using a small sae space macoeconomic model, we apply maximum likelihood esimaion and he Kalman file o obain join esimaes of he unobsevable medium-un pahs of poenial oupu and is nomal ae of gowh, he naual ae of unemploymen and he naual eal inees ae. Ou unobseved componen analysis indicaes ha in 6, he Ausalian economy was close o poenial oupu, he nomal ae of gowh was low, unemploymen was below he naual ae pesaging inflaionay pessues, and ha he eal ae of inees was significanly below is naual ae, suggesing ha moneay policy was oo expansionay. JEL Classificaion: E3, C3 KEYWORDS: Naual aes, Kalman file, sae space model, unobseved componens Coespondence: Jeffey Sheen Faculy of Economics & Business Univesiy of Sydney Sydney, NSW 6, Ausalia jeffs@econ.usyd.edu.au Sepembe 7 6:3

2 . Inoducion A adiional view of business cycles is ha hey ae sho-un sochasic movemens of eal vaiables aound hei smoohed end values. These smoohed ends o naual aes play an impoan ole in macoeconomic models as benchmaks o compae wih cuen values. Wicksell (936) inoduced he concep of he naual inees ae, and moe ecenly, hee has been a evival in he lieaue on he subjec following Woodfod s (3) book. In conempoay ems, he naual ae of inees is he equilibium eal ae (someimes called he neual ae) ha would aise if wages and pices wee compleely flexible, given cuen facos. Phelps (967) and Fiedman (968) inoduced he elaed idea of he naual ae of unemploymen. Moe specifically, he adeoff beween inflaion and unemploymen is empoay, so ha he acual unemploymen ae conveges o he naual ae, a which poin he inflaion ae emains consan. Thus his benchmak unemploymen ae is also known as he non-acceleaing inflaion ae of unemploymen (NAIRU). When he economy is anchoed a he NAIRU, GDP mus be a he naual level of oupu, which is someimes called he level of poenial oupu. A sho-un oupu gap emeges if GDP deviaes fom he naual level of oupu. Howeve his poenial oupu need no be consan in he medium un given poduciviy gowh and faco accumulaion, hee will be a nomal ae of gowh of poenial oupu in he medium un. As he hoion pogesses o he long un, his gowh ae becomes he seady-sae gowh ae of he economy. Sho-un deviaions fom he naual (and nomal) aes in he medium un can be explained by he pesence of impefec infomaion (e.g. Lucas (97)) o nominal igidiies. These deviaions affec movemens in aggegae demand and supply, which in un simulae adjusmen pocesses o eun he economy o he medium-un equilibium.

3 These naual ae and level conceps ae cenal o he conduc of moneay policy. An inflaion-ageing cenal bank needs o assess he level of economic aciviy vaiables in elaion o hei naual values o judge he pessues on inflaion elaive o is age and on any ohe age vaiables. When oupu gows fase han nomal and exceeds is poenial value, he unemploymen ae will fall sho of he NAIRU, wage inflaion will ise, he eal inees ae will be below is naual level, and so hee will be upwad pessue on inflaion. The cenal bank is likely o ighen moneay policy o see inflaion and oupu back o hei age and naual values. The sho-em inees ae ises fom is cuen posiion unil he medium-un equilibium is esoed, and moneay policy euns o is neual sance. Alhough hese naual economic indicaos povide useful infomaion o economiss and policymakes, hey ae unobsevable by naue and mus be infeed fom he daa. The objecive of his pape is o esimae a mulivaiae, unobseved componens (UC) model fo he Ausalian economy ha allows fo he simulaneous esimaion of he pahs of poenial oupu and is nomal gowh ae, he NAIRU and he naual eal inees ae. The mulivaiae sae space model compises a dynamic IS equaion of he oupu gap epesening aggegae demand (AD), an expecaions-augmened Phillips cuve ha epesens aggegae supply (AS), an Okun s elaion connecing cyclical movemens of oupu o unemploymen, and a fis ode condiion fom ineempoal opimiaion giving he medium un elaionship beween he eal inees ae and oupu gowh. The model is esimaed using maximum likelihood ove he peiod 984Q o 6Q4, exacing unobsevable sae vaiables wih he Kalman file. Inflaion infomaion fom he AS elaion is used o infe he oupu gap (defined as he diffeence beween acual and poenial oupu), which in un hough he dynamic IS equaion is used o infe he eal inees ae gap (defined as he diffeence beween acual sho-em 3

4 inees ae and is naual ae) and he naual eal ae of inees. An Okun s equaion elaes he cyclical flucuaions in he poduc make (he oupu gap) o he cyclical flucuaions in he labou make (hence infeing he unemploymen gap). The pape poceeds as follows. In secion, diffeen univaiae and mulivaiae measues of naual aes ae discussed. This discussion moivaes he mulivaiae model oulined in secion 3. Secion 4 descibes he daa, some economeic issues elaed o Kalman file and pesens he paamee esimaes and he mulivaiae UC smoohed naual aes and hei boosapped confidence inevals. Secion 5 offes some concluding emaks.. Univaiae and Mulivaiae Measues of Naual Raes A widely used pocedue o decompose macoeconomic vaiables (such as eal oupu) ino a end (o poenial oupu) and a cyclical (o he oupu gap) componens is he Hodick and Pesco (997) file. The smoohness of he Hodick-Pesco (o HP) sochasic end depends on he inpu value of an ad-hoc smoohness paamee. If he value of he exogenous paamee is se o eo, he end componen and he acual seies mach each ohe; if he value of he paamee goes o infiniy, he end componen appoaches a linea deeminisic end. Baxe and King (999) deived an esimae of he oupu cycle by passing he daa hough a file ha pe-specifies he elevan fequencies fo he cycle and hus is pesisence. Thei appoximae band-pass file defines he cycle as having specal powe in he ange beween 6 and 3 quaes. Pue saisical mehods ha simply le he daa speak do no include poenially useful infomaion abou he supply side of he economy and he business cycle conained in macoeconomic elaionships such as he Phillips cuve, Okun s law, and ohe The oiginal pape appeaed in 98 as a Canegie-Mellon discussion pape, and was evenually published unchanged in

5 indicaos such as oupu capaciy uiliaion. Laxon and Telow (99) poposed a mulivaiae exension o he univaiae HP file by condiioning he compuaion of he level of poenial oupu on addiional economic elaionships. Boone e al. () applied a mulivaiae HP file o esimae he level of poenial oupu fo weny one OECD counies. To esimae Ausalian poenial oupu, de Bouwe (998) incopoaed infomaion fom inflaion, unemploymen and capaciy uiliaion. Guen e al. (5) condiioned hei esimaes on he Phillips cuve using eal-ime oupu daa. Anohe class of models known as he unobseved componens (UC) model offes wo advanages ove he mulivaiae HP file: () i pemis a moe complex sysem of dynamics; and () esimaion is elaively moe saighfowad wih he sucual paamees esimaed by maximum likelihood and he unobseved vaiables (o naual aes) deived by he Kalman file. 3 Wihin he UC famewok, seveal papes aemped o esimae naual aes using diffeen macoeconomic elaionships. Clak (989) and Kune (99) used an Okun s equaion, which defines he level of obsevable unemploymen as a funcion of he unobsevable oupu gap, o deive he level of U.S. poenial oupu. 4 In Kune (994), he level of poenial oupu is exaced fom infomaion conained in he Phillips cuve so ha he economy mainains a consan level of inflaion. The consan-inflaion naual unemploymen ae (o he NAIRU) is povided by King e al. (995), Saige e al. (996) and Laubach () using a simila famewok. Insead of conducing paial analysis on poenial oupu o he NAIRU, i is possible o esimae a sysem of equaions ha feaues he Phillips cuve, which imposes While hee ae many ohe univaiae files which may have bee popeies, ou focus is on he gains fom mulivaiae exensions. 3 The mulivaiae HP file implemened by Laxon and Telow (99) is a wo-sep pocedue. Fis, he economic elaionships ae sepaaely esimaed. The egession esiduals ae inseed ino he mulivaiae HP minimiaion poblem o esimae he unobsevable vaiable. This wo-sep pocedue is epeaed wih seveal ieaions unil convegence is achieved. See Boone () fo moe deails. 4 In Kune (99), he Okun s equaion elaes he change in unemploymen o he oupu gap. 5

6 a consan-inflaion esicion on he pah of poenial oupu o he NAIRU, and incopoaing he covaiaion esicions on cyclical oupu and cyclical unemploymen hough he Okun s elaion. Some examples of papes ha model he muual dependency of oupu and unemploymen include Apel and Jansson (999a, 999b) and Benes and N Diaye (4). In addiion o an Okun s elaion ha epesens he linkages beween oupu and unemploymen, movemens fom he eal inees ae elaive o is naual ae can be embedded in he IS elaion fo he oupu gap descibing poduc make equilibium. The incopoaion of his exa channel is likely o enhance he esimaion of he cyclical pahs of unobsevable vaiables in he economy. The naual eal inees ae is likely o vay ove ime, and in an ineempoally opimal seing will be deemined by facos such as undelying poduciviy gowh and he ae of ime pefeence. Fo example, Laubach and Williams (3) found subsanial vaiaions in he naual inees ae ove he pas fou decades in he U.S. They also suggesed ha hee is an appoximae one-fo-one elaionship beween naual ae vaiaion and changes in he gowh ae of poenial GDP. 3. A Mulivaiae Model of Unobseved Componens Boh oupu and unemploymen ae decomposed in () and () ino a sochasic end componen and he sochasic cyclical vaiaions aound his end. The end componens ae aken o be he level of poenial oupu and he naual ae of unemploymen (o he NAIRU) ha ae associaed wih he medium-un equilibium when pices and wages have fully adjused o shocks. When demand o supply shocks occu, hee will be deviaions fom he end componen values in he sho un because of nominal igidiies, and hese ae defined as he oupu and unemploymen gap measues. 6

7 y = y + y () u = u + u () In () and (), y is he log of eal GDP, y denoes he oupu gap; u is he unemploymen ae, y is he log of poenial GDP and u is he NAIRU value, and u epesens he unemploymen gap. Noe ha all vaiables ae poenially ime-dependen. Following Rudebusch and Svensson (999), he aggegae demand side of he economy is descibed by a educed-fom IS equaion as in (3): ( ) y = a y + a + a Δ LTOT + a Δ y + ε (3) G7 y A saionay AR() pocess is specified fo he dynamic evoluion of he oupu gap ( y ). 5 As in Laubach and Williams (3), a eal inees ae gap ( j j) is included in he oupu gap equaion. Afe peliminay OLS esimaions using geneal o specific ess, we found ha he 8 h lag ( yeas) of he eal inees ae gap should be included. Sone e al. (5) similaly found i necessay o include lags o 7 of he same vaiable o uncove he effec of a change in moneay policy on he oupu gap. To capue he posiive effec ha a ising ems of ade has on he oupu gap, he fouh lag of he quaely change of he (logged) ems of ade (ΔLTOT 4 ) is included. Given Ausalia is a small open economy, he conempoaneous quaely change in he G7 oupu gap ( Δ ) is included o explain he influence of foeign economic aciviy on domesic oupu. In he medium un, he oupu gap conveges o eo as do he eal inees ae gap, he G7 oupu gap, and changes in he ems of ade. G7 y 5 Wason (986) and Clak (987) fo he U.S. economy and de Bouwe (998) fo he Ausalian economy, adoped an AR() pocess fo he oupu gap. Ou esimaes ejeced i in favou of an AR() pocess fo Ausalia 7

8 The aggegae supply side of he economy is epesened by an expecaionsaugmened Phillips cuve (4): π = bπ + bπ + b y + b π + b π + ε (4) imp e π whee inflaion expecaions ae assumed o be diven by backwad- and fowad-looking pocesses. One goup of economic agens and fims elies only on pas inflaion infomaion o condiion hei inflaion foecass, hence he inclusion of lagged inflaion ems (π - and π - ). This helps accoun fo he pesisence in inflaion dynamics. Anohe goup ae fowad-looking and so we employ consume suvey expeced inflaion as advocaed by Robes (997). The influence of excess demand on inflaion is capued by he lagged oupu gap, which eflecs he nominal ineia of pice esponses o economic aciviy. The pass-hough effec on o domesic inflaion of impo pices epesens a supply faco, which enes he equaion wih a lag. Moe specifically, consume suvey inflaion expecaions and impo pice inflaion ae consuced o be eo in he medium un. The vaiable e π is he excess of consume inflaion expecaions ove lagged yea- e e ended inflaion, i.e. π = π π, while imp π is he excess of impo pice inflaion ove imp imp lagged yea-ended inflaion, π = π π (see Guen e al. (5)). Equaion (4) yields a veical Phillips cuve in he medium un, wih oupu anchoed a is poenial level, acual equal o expeced inflaion,and eo supply facos. This implies he consain, b+ b =. The connecion beween he unemploymen gap ( u ) and he oupu gap is epesened by an Okun equaion (5): u u cu c u c y (5) = ε 8

9 Some degee of pesisence in he dynamics of he unemploymen gap is capued by an AR() pocess. Equaions (6) hough () descibe he laws of moion of he unobsevable ends in he model. Poenial oupu is modelled by (6) as a local linea end, whee he dif em epesening he end gowh ae is a andom walk pocess (7): 6 y = y + + ε (6) y = + ε (7) Guen e al. (5) found lage shifs in he end gowh ae fo he Ausalian economy since 96. To incopoae his feaue of he Ausalian economy, he local linea end specificaion implies ha poenial oupu gows a he ime-vaying nomal gowh ae when all shocks dissipae in he medium un, i.e. Δ y =. 7 Fom household ineempoal uiliy maximiaion evaluaed in he medium un, 8 we posi a elaionship ha links he evoluion of he naual inees ae o movemens in he end gowh ae of oupu (see Laubach and Williams (3)). This is shown in (8) whee is he naual ae of inees, d capues he invese of he elasiciy of 6 Since he dif em is assumed o be I(), his implies ha poenial oupu and log eal GDP ae I(). This hypohesis is ypically ejeced by an ADF es. Howeve, Sock and Wason (998) poined ou ha he es saisic ends o have high pobabiliy of ype I eo in falsely ejecing he ue null when he innovaion o he gowh ae componen has small vaiance. 7 Alenaively he end gowh equaion (7) can be modelled as an auoegessive pocess ha makes y and y diffeence-saionay. Howeve, he sum of he auoegessive paamees obained duing peliminay esimaions sugges ha i is almos idenical o uniy and hence highly pesisen. 8 s σ Fo an infinie hoion epesenaive consume model, whee peiod uiliy is U = β Cs wih σ s= being he ineempoal elasiciy of subsiuion, and β is he ae of ime pefeence, he fis ode condiion is c, ln β ln( ) σ = + + whee c, is he gowh ae of consumpion. We do no inse he implied esicions fom his ineempoal opimiing condiion ino he sho-un poduc make equilibium condiion (3) on he gounds ha many households ae unable o opimie in he sho un. Howeve in he medium un, mos will find a way o appoach hei opimal consumpion ajecoy. In he medium-un equilibium of he open economy, he cuen accoun o GDP aio will be consan, as will be he consumpion o GDP aio, i.e. c, =. Theefoe, a low inees aes, he medium-un elaion beween he eal inees ae and oupu gowh is appoximaed by = ln β. σ 9

10 ineempoal subsiuion, and is a andom walk pocess as in (9) ha epesens ohe possible deeminans such as he ae of ime pefeence and isk pemia. 9 = d + (8) = + ε (9) Lasly, he naual ae of unemploymen follows a pue andom walk: u = u + ε () u To complee he descipion of he mulivaiae UC model, we assume ha all y π u y u innovaions ε = ( ε, ε, ε, ε, ε, ε, ε ) ae i.i.d. nomally disibued wih eo mean and finie vaiances. In addiion, hey ae seially and conempoaneously uncoelaed wih each ohe. 4. Daa and Empiical Resuls 4. Daa The quaely daa span sas fom 984: o 6:4. All daa unless ohewise specified wee obained fom he ABS. y and u ae he Ausalian eal GDP and unemploymen ae. Domesic inflaion is calculaed as he yea-ended change in he log of he Teasuy undelying CPI which is spliced in Sepembe 999 o he headline CPI. The same pocedue is applied o compue he impo inflaion ae which is based on he log of he impo chain pice index. The eal inees ae is he nominal cash ae less he inflaion ae, i.e. = i π. Esimaes of he G7 oupu gap ae exaced fom he OECD daabase. Quaely changes in he log of he ems of ade index ae used since hey offe highe 9 Laubach and Williams (3) consideed an AR() pocess, and Ganie and Wilhelmsen (5) an AR(). Howeve, hese alenaive specificaions did no geneae economically sensible esuls fo he Ausalian economy.

11 explanaoy powe in peliminay OLS esimaion. Inflaion expecaions ae consumes inflaion expecaions measued by he Melboune Insiue as he median expeced inflaion ae fo he yea ahead. 4. Esimaion Issues Befoe poceeding wih esimaion, he mulivaiae UC model is cas in he sae-space fom (see he appendix). Paamees ae esimaed by maximum likelihood and he naual aes, o sae vaiables, ae simulaneously exaced using he Kalman file. The Kalman file is a ecusive algoihm ha sequenially updaes a linea pojecion of a dynamic sysem. In each peiod he Kalman file povides he (one-sided) opimal pedicions of he naual aes fo ha peiod condiional on infomaion available up o and including he cuen peiod. Once he fileed naual aes ae obained, i is possible o smooh ove he naual esimaes ha ae condiioned on infomaion fom he full sample; heefoe he smoohed naual aes can be hough of as wo-sided esimaes. Thee ae wo impoan esimaion issues elaed o he Kalman file ha need o be esolved: namely he choice of he iniial values of he sae veco and covaiance maix and he esimaion of he innovaion vaiances. To se he iniial values fo he sae veco, he gap measues ae assumed o be saionay, and so a value of eo is assigned o hem. Fo he naual ae measues, he iniial value is se o he value of he fis obsevaion of he associaed vaiable. The dynamics of he mulivaiae UC model ae non-saionay because he end equaions ae specified o be andom walks. Theefoe we follow he usual pacice of assigning diffuse pios o he diagonal elemens of he iniial sae covaiance maix. We found i necessay o begin he ecusion wih a diffuse pio of eo o ie he esimaed ends o a pah ha would un hough he daa. The esul is ha he fileed and smoohed esimaes ae vey close o he fis obsevaion of he vaiable.

12 I is common in he lieaue o choose a value fo he signal-o-noise aio and impose i in he maximum likelihood esimaion. One example in ou model is he aio of poenial oupu innovaion o end gowh innovaion, λ = σ y σ. Because hese wo unobseved vaiables ae non-saionay, hei cumulaed vaiance goes o infiniy, and so hei maximum likelihood esimaes (MLE) have a poin mass a eo even hough hei ue values ae geae han eo. Sock (994, secion 4) discussed his so-called pile-up poblem which pevens he efficien esimaion of he innovaion of non-saionay sae vaiable. Laubach and Williams (3) found ha he MLEs of σ and σ ae eo, and so hey applied he median-unbiased esimaion pocedue developed by Sock and Wason (998). The fis sep is o obain he median-unbiased esimaes of he signal-onoise aio. In he second sage, he aio is imposed in he sysem esimaion. Laubach and Williams (3) and Ganie and Wilhelmsen (5) followed his appoach o esimae poenial oupu and he naual eal inees ae fo he U.S. and he Euo one especively. In ecogniion of he pile-up poblem, Messonie and Renne (4) agued ha i becomes difficul o pin down a sensible pah of he naual eal inees ae, because is an unobseved pocess ha is linked o wo ohe unobseved pocesses, and. Insead, hey followed he appoach in King e al. (995), Saige e al. (996), and Laubach () in fixing he signal-o-noise aio a paicula values and esing hem saisically in efeence o a baseline model. We offe anohe pespecive o he need fo fixing he values of he uncondiional vaiances of innovaions hough he poin of view of paamee idenificaion. By fisdiffeencing he poenial oupu equaion (6) and he end gowh equaion (7), we ge: Δ y = + ε () y Δ = ε ()

13 whee accoding o () and () he wo sucual paamees o be idenified ae and σ. Lag () by one peiod o obain: σ y = ε Δ (3) Subsiue (3) ino () yields: ε y Δ y = + ε Δ o Δ y = ε + ε ε y y (4) The auocovaiance funcions of he educed-fom equaion Δ y ae ( ) () ( ) γ = σ + σ γ =σ y y γ τ = fo τ (5) whee γ(τ) is he τ-h ode auocovaiance funcion. Given (5), we have wo educed fom paamees o map o wo sucual paamees. Hence he ode condiion is saisfied o uniquely idenify he sucual paamees σ y and σ. Now conside he and equaions (8) and (9). Subsiue ou and wih = ε Δ and = ε Δ o yield he following educed fom equaion of Δ : Δ = ε +ε (6) d We need o idenify fom (6) he sucual paamees d and σ wih σ aleady idenified peviously in (5). The auocovaiance funcions of Δ ae ( ) ( ) γ = d σ + σ γ τ = fo τ (7) Theefoe in his case we have an unde-idenificaion poblem as hee is only one educed-fom paamee available o link o he wo sucual paamees d and σ. 3

14 In elaion o pevious sudies ha fix he uncondiional vaiances of sae vaiable innovaions hough he signal-o-noise aio, we find he poblem aises hee wih σ and no σ. Since he paamee d appoximaes he invese of he ineempoal elasiciy of subsiuion, we calibae σ o 4 diffeen values and discad hose ha do no geneae significan esimaes of d. 4.3 Resuls The calibaed values of σ =.4 o.8 yield significan esimaes of d anging fom 4.4 o 4.9. This appoximaes o a ange fo he ineempoal elasiciy of subsiuion (σ) beween. and.3. We deem hese o be easonable esimaes as Ogaki and Reinha (998) obained esimaes beween.7 and.77 and Basky e al. (997) using micodaa came up wih an esimae of.8. Table displays he paamee esimaes of he mulivaiae UC model. Kalman smoohed esimaes of poenial oupu and is nomal gowh ae, he NAIRU and he naual eal inees ae as well as he elaed gap measues ae shown in Figues o 7. All of he esimaed coefficiens have he expeced sign. The sum of he auoegessive paamee esimaes of he IS equaion (3) and he Okun equaion (5) ae each less han one, which is necessay fo he saionay dynamics of he oupu gap and he unemploymen gap. In all of he figues, he UC naual aes ae he smoohed esimaes associaed wih σ =.8 as i yields he highes log likelihood. The mulivaiae unobseved componens (MUC) measue (in blue) is compaed o a univaiae measue (in ed) deived fom he band-pass file (BP). The shaded space above and below he mulivaiae measues epesen 95% confidence inevals. These wee obained hough boosapping by These ae σ =.5,.,.,.4,.6,.8,.,.,.4,.6,.8,., 3.. 4

15 unning 5 condiional simulaions o compue he second momen of he Kalman smooh saes using Gibbs sampling. The esuling uppe and lowe bands epesen he effecs of boh paamee and file unceainy In Figues and, he MUC paen of poenial oupu indicaes a bief peiod of expansion a he end of he 98s. This is followed by a peiod of excess capaciy coveing much of he 99s. In compaison o he BP poenial oupu measue, he MUC measues sugges ha he Ausalian economy headed ino conacion in 99Q, ealie by wo quaes. In addiion, he MUC conacion is seepe and moe pesisen, aaining is ough in 99Q a -6.5% as opposed o he BP a -.5%. Towads he end of he sample peiod, howeve, he MUC oupu gap disagees wih he BP measue, suggesing ha he economy was in a peiod of gowing excess demand o.7% (hough he 95% confidence ineval jus includes ). This shows he meis of condiioning he pah of poenial oupu by incopoaing infomaion fom he aggegae supply side hough he Phillips cuve and Okun s law, and fom he aggegae demand side hough he dynamic IS cuve wih ineempoal opimiaion. 5

16 Table : Esimaion Resuls of he Mulivaiae UC Model (() hough ()) Paamees σ =.4 σ =.6 σ =.8 a (.) (.) (.) a (.5) (.) (.) a (.6) (.5) (.9) a (.) (.) (.) b (.) (.) (.) b (.36) (.3) (.8) b (.7) (.4) (.8) b (.) (.) (.) b (.) (.6) (.) c (.) (.) (.) c (.) (.) (.) c (.) (.) (.) d (.8) (.7) (.5) Sandad Eos σ y (.) (.) (.) σ π (.) (.) (.) σ u (.3) (.) (.) σ y... (.999) (.999) (.999) σ (.) (.) (.) σ u (.) (.) (.) Log likelihood Noe: p-values ae given in paenheses. 6

17 .4 Figue Real GDP and Smoohed Poenial Oupu Real GDP Band Pass Poenial oupu (.8) 6. Figue Poenial GDP Gap wih 95% Confidence Ineval SMOOTHED GDP GAP UPPER LOWER Band Pass We show in figue 3 ha he MUC measue of he NAIRU fell houghou he sample peiod in geneal, excep fo he empoay and mino pickup aound he 99-9 ecession. Ineesingly, he MUC NAIRU declined fases in he 98s, which suggess 7

18 ha was he subsanive decade of labou make efom. Unlike he BP file which essenially plos he end line hough he unemploymen daa, he mulivaiae NAIRU was much lowe fo mos of he ime. A he end of 996, he NAIRU was down o 5.6% (wih a 95% confidence ineval of {4.%,7.%}). Even hough he unemploymen ae has been on a downwad end since he ealy 99s, he esul suggess ha he accompanying slowe decline in he NAIRU has buffeed he Ausalian economy fom inflaionay pessue. Mioing he esimaes of he oupu gap, he MUC unemploymen gap values in Figue 4 show ha he slack condiions in he labou make pesised fo much of he 99s, despie he BP measue suggesing ighness afe 994. A he end of 6, unlike he BP file, he MUC measue indicaes ha he labou make had become inceasingly igh (hough he 95% confidence ineval did jus include ). Figue 3 Unemploymen: NAIRU & 95% Confidence Ineval NAIRU UPPER LOWER Acual Band Pass 8

19 Figue 4 Smoohed Unemploymen Gap & 95% Confidence Ineval SMOOTHED UNEMPLOYMENT GAP UPPER LOWER Band Pass The BP and MUC file povide conasing pespecives on he eal inees ae, and by implicaion on he moneay policy sance ove he sample peiod. As seen in Figues 5 and 6, he univaiae BP esimaes sugges ha he naual eal inees ae was significanly highe han he MUC esimaes unil 999, bu he oles evese afe 999. The BP eal inees ae gap measue indicaes ha moneay policy became expansionay fom 987 afe he sock make cash and fo abou hee yeas afe he ecession in 99, bu was only modesly esicive (+4.9%) beween he wo expansionay phases. Given he deph of he ecession, his is an unsaisfacoy esul. On he ohe hand, he MUC measue suggess ha moneay policy was highly conacionay (peaking a +3.6% beginning 99), only being evesed ino expansion afe 996. Duing he sevee moneay policy conacion in 989-9, he acual eal cash ae wen up damaically, and he BP naual eal ae measue followed i up o a degee in is economic blindness. By conas, in 989-9, he MUC eal ae fell, which is wha 9

20 economic insigh would sugges. Since acual and nomal oupu and consumpion gowh fell in ha ecession, he medium un eal inees ae had o follow sui o a degee o mainain ineempoal balance. Since 999, he MUC eal ae suggess moneay policy has sayed elaively simulaive wih he naual eal inees ae conveging on 4.3% a he end of 6. Howeve he 95% confidence ineval is wide {-3.5%,.%} indicaing he impecision in obaining esimaes of he unobseved eal inees aes. This esul undescoes he cauion exhibied by policymakes when making moneay policy decisions. Figue 5 Naual Real Inees Rae & 95% Confidence Ineval SMOOTHED UPPER LOWER Band Pass SMOOTHED GDP GAP

21 Figue 6 Real Inees Rae Gap and 95% Confidence Ineval GAP (.8) UPPER LOWER SMOOTHED GDP GAP Band Pass Finally, he esimaes of he undelying nomal quaely gowh ae of he economy ae shown in Figue 7. The BP esimaes exaggeae he movemens and appeas smoohe han he MUC ones. The MUC esimaes show a geneal fall in nomal gowh aes, which began well befoe he onse of he 99- ecession, bu uned a he boom of ha ecession, ising unil he end of 996. The nomal ae of gowh has acually declined significanly since 996, despie oupu gowh being consisenly sable and posiive. A he end of 6, he nomal gowh ae was.4%, supisingly lowe han wha i had been in he 99 ough (.8%). Howeve he 95% confidence ineval was wide, and again his is a ecommendaion fo added cauion in policy design.

22 Figue 7 Nomal GDP Gowh Rae & 95% Confidence Ineval NORMAL GROWTH RATE UPPER LOWER BAND PASS Concluding Commens Naual aes and nomal gowh aes ae medium-un benchmaks ha pemi a judgemen abou whehe he acual aes ae oo high, oo low o jus igh. We have joinly esimaed he ime pahs of hese unobsevable benchmaks using maximum likelihood mehods wih he Kalman file fo Ausalian daa fom 984 o 6. We consuced a sandad macoeconomic model fo inflaion, oupu and unemploymen, and ou paamee esimaes wee all significan wih he expeced signs. Fom he infeed naual ae of unemploymen, he naual level of oupu (o poenial oupu) and is nomal gowh aes, and he naual eal ae of inees, we have been able o assess he sae of he acual economy and commen on he sance of moneay policy ove he wo decades of he sample. We find ha ou mulivaiae unobseved componens model geneaes esuls ha have fa moe economic significance han a univaiae band-pass file. We povide boosapped 95% confidence inevals fo ou esimaes of he ime pahs of he unobsevable naual ae vaiables. These inevals ae ypically wide, and his leads us o conclude ha policy makes wisely pacise cauion when designing hei moneay and fiscal policy esponses.

23 A he end of 6, we conclude ha oupu was jus above poenial (+%), ha is nomal gowh ae was acually quie low a abou.4% on an annualied basis, ha unemploymen was abou a pecenage poin below is naual ae of 5.6%, and ha he eal cash ae was acually.3 pecenage poins below is naual ae of 4.3%. This suggess ha moneay policy was possibly sill expansionay, bu i is no clea ha his could have any beneficial effec wih oupu above poenial, and wih moneay policy expeced o be neual in egad o he nomal ae of gowh. Coecing he downwad end in he nomal gowh ae of GDP will equie moe han moneay and fiscal policy esponses by govenmen. 3

24 4 Appendix The sae space epesenaion is consised of a measuemen equaion: = + w Fξ ν (8) and a sae equaion: = + + ξ Gξ Hx υ (9) whee w is he veco of obsevable vaiables, ξ is he veco of sae (o unobsevable vaiables), and x is he veco of exogenous vaiables. v and υ ae whie noise innovaion vecos. The measuemen equaions in maix fom: y u u y y u u π π π = ()

25 5 The ansiion equaions in maix fom: y a a b b b u ca c c c u y u π π = 3 a d y u u y u π π ( ) G y imp e y u G y a a LTOT a y b b c c a a LTOT a y d π ε π π ε ε ε ε ε ε ε + Δ + Δ Δ + Δ u ε ε ()

26 The covaiance maix of he esiduals of he ansiion equaions is as follows: σ y σ π c3σ y c3σ y + σu σ y σ dσ dσ + σ Q = σ σ σ u () 6

27 Refeences Apel, M. and P. Jansson (999a), Sysem Esimaes of Poenial Oupu and he NAIRU, Empiical Economics, 4, pp Apel, M. and P Jansson (999b), A Theoy-Consisen Sysem Appoach fo Esimaing Poenial Oupu and he NAIRU, Economics Lees, 64, Ball, L. and N.G. Mankiw (), The NAIRU in Theoy and Pacice, NBER Woking Pape 894. Basky, R., F. Juse, M. Kimball, and M. Shapio (997), Pefeence Paamees and Behavioual Heeogeneiy: An Expeimenal Appoach in he Healh and Reiemen Sudy, Quaely Jounal of Economics,, Baxe, M. and R.G. King (999), Measuing Business Cycles: Appoximae Band-Pass Files fo Economic Time Seies, Review of Economics and Saisics, 8, Benes, J. and P. N Diaye (4), A Mulivaiae File fo Measuing Poenial Oupu and he NAIRU: Applicaion o he Cech Republic, IMF Woking Pape WP/4/45. Boone, L. (), Compaing Semi-Sucual Mehods o Esimae Unobseved Vaiables: The HPMV and Kalman Files Appoaches, OECD Economics Depamen Woking Papes No. 4. Boone, L., C. Giono, M. Meacci, D. Rae, D. Tune, and P. Richadson (), The Concep, Policy Use and Measuemen of Sucual Unemploymen: Esimaing a Time Vaying NAIRU Acoss OECD Counies, OECD Economics Depamen Woking Papes No. 5. de Bouwe, G. (998), Esimaing Oupu Gaps, RBA Reseach Discussion Pape 989. Clak, P.K. (987), The Cyclical Componen of U.S. Economic Aciviy, Quaely Jounal of Economics,, pp Clak, P.K. (989), Tend Revesion in Real Oupu and Unemploymen, Jounal of Economeics, 4, pp Fai, R.C. (5), Naual Conceps in Macoeconomics, Cowles Foundaion Discussion Pape No. 55, Yale Univesiy. Fiedman, M. (968), The Role of Moneay Policy, Ameican Economic Review, 58, pp.- 7. Ganie, J. and B.R. Wilhelmsen (5), The Naual Real Inees Rae and he Oupu Gap in he Euo Aea: A Join Esimaion, ECB Woking Pape No. 56. Guen, D., T. Robinson and A. Sone (5), Oupu Gaps in Real Time: How Reliable Ae They?, Economic Recod, 8, pp

28 Hodick, R.J. and E.C. Pesco (997), Poswa U.S. Business Cycles: An Empiical Invesigaion, Jounal of Money, Cedi, and Banking, 9, pp. -6. King, R., J. Sock, and M. Wason (995), Tempoal Insabiliy of he Unemploymen- Inflaion Relaionship, Fedeal Reseve Bank of Chicago Economic Pespecives, pp. -. Kune, K.N. (99), Using Noisy Indicaos o Measue Poenial Oupu, Fedeal Reseve Bank of Chicago woking pape Kune, K.N. (994), Esimaing Poenial Oupu As A Laen Vaiable, Jounal of Business and Economic Saisics,, pp Laubach, T. (), Measuing he NAIRU: Evidence Fom Seven Economies, Review of Economics and Saisics, 83, pp. -3. Laubach, T. and J.C. Williams (3), Measuing he Naual Rae of Inees, Review of Economics and Saisics, 85, pp Laxon, D. and R. Telow (99), A Simple Mulivaiae File fo he Measuemen of Poenial Oupu, Bank of Canada Technical Repo No. 59. Lucas, R.E. (97), Expecaions and he Neualiy of Money, Jounal of Economic Theoy, 4, pp Messonie, J.-S. and J.-P. (4), A Time-Vaying Naual Rae of Inees fo he Euo Zone, mimeo, Banque de Fance. Okun, A.M. (96), Poenial GNP: Is Measuemen and Significance, in Poceedings of he Business and Economics Secion, Ameican Saisical Associaion, Washingon D.C., pp Ogaki, M. and C. Reinha (998), Measuing Ineempoal Subsiuion: The Role of Duable Goods, Jounal of Poliical Economy, 6, Phelps, E.S. (968), Phillips Cuves, Expecaions of Inflaion and Opimal Unemploymen Ove Time, Economica, 34, pp Rudebusch, G.D. and L.E.O. Svensson (999), Policy Rules fo Inflaion Tageing, in J.B. Taylo (ed.), Moneay Policy Rules, Chicago: Univesiy of Chicago Pess, pp Saige, D., J. Sock and M. Wason (996), How Pecise Ae Esimaes of he Naual Rae of Unemploymen?, NBER Woking Pape Sock, J. (994), Uni Roos, Sucual Beaks and Tends, in R. Engle and D. McFadden (eds.), Handbook of Economeics, vol. 4, Amsedam: Elsvie, pp

29 Sock, J. and M. Wason (998), Median Unbiased Esimaion of Coefficien Vaiance in a Time-Vaying Paamee Model, Jounal of he Ameican Saisical Associaion, 93, pp Sone, A., Whealey, T. and Louise Wilkinson (5), A Small Model of he Ausalian Macoeconomy: An Updae, RBA Reseach Discussion Pape 5-. Wason, M. (986), Univaiae Deending Mehods wih Sochasic Tends, Jounal of Moneay Economics, 8, pp Wicksell, K. (936), Inees and Pices, London: Macmillian. Tanslaion of he 898 oiginal ediion. Woodfod, M. (3), Inees and Pices Foundaions of a Theoy of Moneay Policy, Pinceon Univesiy Pess, Pinceon, New Jesey. 9