Estimating a New Zealand NAIRU

Esimaing a Nw Zaland NAIRU Kam Long Szo and Mlody Guy N EW Z EALAND T REASURY W ORKING P APER 04/10 S EPTEMBER 2004

NZ TREASURY WORKING PAPER 04/10 Esimaing a Nw Zaland NAIRU MONTH/ YEAR Spmbr 2004 AUTHORS Kam Long Szo Nw Zaland Trasury PO Box 3724 Wllingon 6015 NEW ZEALAND Email kam.szo@rasury.gov.nz Tlphon 64-4-471 5055 Fax 64-4-499 0992] Mlody Guy Nw Zaland Trasury PO Box 3724 Wllingon 6015 NEW ZEALAND Email mlody.guy@rasury.gov.nz Tlphon 64-4-471 5957 Fax 64-4-499 0992 ACKNOWLEDGEMENTS Th auhors would lik o hank Mark Blackmor, Paul Gardinr, Özr Karagdikli, and Richard Downing for hlpful suggsions a h iniial sags of his rsarch projc. W would also lik o hank Thomas Laubach and David Ra for providing us wih fils and daa usd in hir sudis. W ar graful o Özr Karagdikli, Paul Gardinr, Richard Downing, Khoon Goh, Angla Huang, Brndon Richs, Tony Booh, Pr Mawson, Brian Silvrson, Bob Buckl and Vronica Jacobsn for usful commns on drafs of his papr. NZ TREASURY Nw Zaland Trasury PO Box 3724 Wllingon 6015 NEW ZEALAND Email informaion@rasury.gov.nz Tlphon 64-4-472 2733 Wbsi www.rasury.gov.nz DISCLAIMER Th viws, opinions, findings, and conclusions or rcommndaions xprssd in his Working Papr ar sricly hos of h auhor(s). Thy do no ncssarily rflc h viws of h Nw Zaland Trasury. Th Nw Zaland Trasury aks no rsponsibiliy for any rrors or omissions in, or for h corrcnss of, h informaion conaind in his Working Papr. Th papr is prsnd no as policy, bu o inform and simula widr dba.

Absrac This papr simas h non-incrasing inflaion ra of unmploymn or NAIRU for Nw Zaland. A NAIRU ha varis ovr im has imporan implicaions in considring inflaionary prssurs. This papr simas h im-varying NAIRU using a Kalman filr on a rducd form approach and xnds prvious sudis in svral ways. Using diffrn modl spcificaions and dpndn variabls suggss a band of NAIRU simas of bwn four and fiv prcn (wih furhr rror bands around ha). Th rsuls of his papr indica ha h NAIRU is a rlvan concp and h unmploymn gap should b on of h facors considrd whn assssing inflaionary prssur. JEL CLASSIFICATION KEYWORDS E24 Employmn; unmploymn; wags E31 Pric lvl; inflaion; dflaion C13 - Esimaion C22 Tim-sris modls NAIRU; Kalman filr; Unmploymn; Phillips Curv; Nw Zaland WP 04/10 ESTIMATING A NEW ZEALAND NAIRU i

Tabl of Conns Absrac...i Tabl of Conns...ii Lis of Tabls...ii Lis of Figurs...ii 1 Inroducion...1 2 Ovrviw of h NAIRU...2 2.1 Concpual issus...2 2.2 Th Nw Zaland labour mark...3 3 Esimaion issus...4 3.1 Thorical modls...4 3.2 Rcn mpirical sudis...7 4 Modl spcificaion and rsuls...9 4.1 Daa and modl spcificaion...9 4.2 Kalman filr NAIRU simas...11 4.3 Comparing h Kalman filr NAIRU simas o HP filr simas...14 5 Conclusion...16 Rfrncs...18 Lis of Tabls Tabl 1 Th rsuls of h Sock and Wason s mdian-unbiasd sima of λ...11 Tabl 2 Modls simad using h Kalman Filr...12 Tabl 3 Esimaing Equaion (3) wih OLS using h Kalman filr unmploymn gaps and h HP filr unmploymn gaps...16 Lis of Figurs Figur 1 NAIRU simas from h hr inflaion masurs and wo modls...13 Figur 2 Kalman and HP filr NAIRU simas...14 Figur 3 Comparison of h unmploymn gaps drivd from diffrn NAIRU simas...15 WP 04/10 ESTIMATING A NEW ZEALAND NAIRU ii

Esimaing a Nw Zaland NAIRU 1 Inroducion Owing o is unobsrvabl naur, NAIRU 1, which sands for h nonacclraing inflaion ra of unmploymn, has bn on of h mos conrovrsial concps in Macroconomics. 2 A larg liraur (for xampl, s h symposium in h Journal of Economic Prspcivs (Winr issu, 1997) and Ball and Mankiw, 2002) has bn dvod o discuss h usfulnss of h NAIRU in forcasing and policy discussion. This papr ss ou o sima whhr hr is a rlaionship bwn h ra of inflaion and unmploymn and, if so, wha ha rlaionship is. Tha is: a wha lvl of h unmploymn ra will wag or pric inflaion bgin o ris? Comparisons of h currn ra of unmploymn wih simas of h NAIRU can b usd o hlp gain an imprssion of spar capaciy and h dgr of inflaionary prssurs in h conomy. This mans ha if masurs of h NAIRU ar robus nough o b informaiv, hy can b imporan for monary and fiscal policy, labour mark policy, forcasing, and priva scor dcision making (Gibbs 1995). Ovr-im, srucural changs in h conomy may also affc h NAIRU. A NAIRU ha varis ovr-im has imporan implicaions in considring inflaionary prssurs. Rcn sudis hav ampd o sima a NAIRU for Nw Zaland using h Kalman filr chniqu (s Richardson al.,2000, and Eaqub and Ward, 2001 ). This papr updas and xnds his liraur in svral ways. This papr xnds prvious liraur by using h Sock and Wason (1998) procdur o sima h signal-o-nois raio; including a survy masur of inflaion xpcaions as a variabl; simaing h NAIRU for hr diffrn masurs of inflaion and wo diffrn modls; including masurs of shorrm shocks significan for Nw Zaland; and making us of quarrly daa up o h nd of 2003. Th nx scion covrs imporan NAIRU concps bfor discussing h Nw Zaland siuaion, including h possibl implicaions for h NAIRU. Scion 3 hn discusss 1 NAIRU has radiionally sood for non-acclraing inflaion ra of unmploymn. Howvr, his is somhing of a misnomr and wha is usually man is non-incrasing inflaion ra of unmploymn (s Richardson, Boon, Giomo, Macci, Ra and Turnr, 2000). 2 I should b nod ha i is no govrnmn policy ha hr is a NAIRU. WP 04/10 ESTIMATING A NEW ZEALAND NAIRU 1

horical and pracical issus around simaing a NAIRU for Nw Zaland. Scion 4 hn oulins h modls and daa usd in his papr and h rsuls obaind. 2 Ovrviw of h NAIRU 2.1 Concpual issus Th radiional NAIRU viw sablishd by Fridman (1968) is ha in h long-run h srucural ra of unmploymn is rachd and hnc hr is no long-rm rad-off bwn inflaion and unmploymn. Howvr, in h shor-rm h Phillips Curv suggss ha a rad-off bwn inflaion and unmploymn xiss so ha if h ra of unmploymn falls blow (riss abov) h NAIRU, inflaion will ris (fall) unil h ra of unmploymn rurns o h NAIRU, and hn inflaion will sabilis a ha prmannly highr (lowr) lvl. Supply shocks and inflaion xpcaions ar also commonly fl o b imporan drminans of inflaion and h NAIRU may chang ovr im dpnding on h srucur of h conomy and govrnmn policy. Wihin his framwork, h OECD dfin hr diffrn NAIRU concps, which vary by h imfram hy covr (Richardson al 2000). On dfiniion is h shor-rm NAIRU. Th shor-rm NAIRU is h ra of unmploymn rquird o sabilis h inflaion ra a is currn lvl in h nx priod. Th shor-rm concp is mor volail by dfiniion as i rquirs a lvl of NAIRU ha will provid an inflaionary offs o any impac from shorrm supply shocks, xpcaions, and possibl spd limi/prsisnc ffcs (so could b affcd by h lvl of acual mploymn). 3 No ha favourabl shor-rm supply shocks may allow h unmploymn ra o fall blow our cor NAIRU masur and disguis h inflaionary impac, which may b Nw Zaland s rcn xprinc. Th scond NAIRU dfiniion applis o h mdium-rm concp. In his approach, h NAIRU is dfind as h quilibrium ra which unmploymn convrgs in h absnc of mporary supply shocks and h dynamic adjusmn of inflaion o prvious shocks is compld. This papr focuss on h mdium-rm NAIRU concp, which is hr afr simply rfrrd o as h NAIRU. Th final dfiniion is h long-rm quilibrium unmploymn ra which is quivaln o h long-rm sady sa, as h NAIRU has fully adjusd o all long and shor-rm supply and policy influncs. Of hs hr dfiniions h firs wo can b simad, h shor-rm NAIRU can b dircly simad and h mdium-rm NAIRU can b simad by conrolling for appropria shor-rm influncs. 4 Howvr, h long-rm NAIRU nds o no g 3 For a numbr of counris hr is vidnc of significan inria which can dlay h adjusmn of h shor-rm NAIRU and kp i closr o h acual unmploymn ras (Richardson al, 2000). This implis ha hr could b inria or spd-limi ffcs whr if h acual unmploymn ra is wll abov NAIRU h gap can only b closd slowly o avoid inflaionary impacs. 4 No ha in raliy i may b vry difficul o conrol for all appropria shor-rm influncs so amps o masur h mdium-rm NAIRU may acually masur a hybrid of a shor and mdium-rm NAIRU. WP 04/10 ESTIMATING A NEW ZEALAND NAIRU 2

simad in a Phillips curv framwork du o difficulis in idnifying h ffcs of individual long-lasing supply influncs in a imly fashion. In Nw Zaland, his could b incorporaing h long-run impac of h Employmn Conracs Ac on h labour mark. 2.2 Th Nw Zaland labour mark Sinc 1999 h Nw Zaland labour mark has bn characrisd by a rapidly falling unmploymn ra. Th March 2004 sasonally adjusd unmploymn ra of 4.3% is h lows sinc Dcmbr 1987 whn i was 4.2%. Th fall in Nw Zaland s unmploymn is du o paricularly srong mploymn growh, which has mor han offs a rising paricipaion ra. Furhrmor, inflaionary prssurs in h rcn priod hav bn mildr han in prvious priods whn unmploymn was his low. This obsrvaion could suggs ha h Nw Zaland NAIRU has falln. Many ovrsas sudis hav ampd o xplain h movmns in h NAIRU (s Gordon, 1996, Sigliz, 1996 and Ball and Mankiw, 2002). Th lading hypohss includ changs in dmographics, changs in labour forc, incrass in compiivnss of labour and produc marks, br job maching and highr produciviy growh. 2.2.1 Possibl srucural drminans of h NAIRU This scion discusss som facors which could xplain h movmns of h Nw Zaland NAIRU ovr h 1988-2004 priod. W bgin in his scion by firs rviwing som ky policy changs which could affc h compiivnss of h labour mark. Thn w urn our focus on h composiion of h labour forc. Policy changs Ovr h priod 1988 o 2004 hr wr a numbr of policy changs which may hav had a significan impac on unmploymn and may hlp o xplain changs in h NAIRU. On significan chang is incrasd flxibiliy in wag bargaining as a rsul of h inroducion of h Employmn Conracs Ac (ECA) in May 1991. Richardson al., (2000) considr ha h ECA could lowr h NAIRU by up o ½% ach yar combind wih h ohr srucural labour mark rforms. Anohr subsanial policy chang is h bnfi rforms inroducd around h sam im as h ECA. Th rforms involvd boh rducions in basic bnfis and a ighning in ligibiliy criria. Malony (1997) concluds ha h 1990-91 bnfi rforms subsanially influncd labour mark bhaviour in Nw Zaland. H furhr suggss ha 40 o 80% of h growh in mploymn bwn 1990 and 1995 can b aribud o h bnfi rforms. In addiion, h Employmn Rlaions Ac (ERA) was inroducd in Ocobr 2000, bu hr dos no appar o b any vidnc of i having a significan impac so far (Waldgrav, Andrson and Wong 2003). Socio-dmographic changs Th composiion of h labour forc can b an imporan drminan of h srucural unmploymn ra. For xampl, a hard o mploy group (such as school lavrs) bcoming a mor (lss) significan par of h labour forc is likly o rais (lowr) h WP 04/10 ESTIMATING A NEW ZEALAND NAIRU 3

aggrga unmploymn ra. Carroll and Chappl (2001) suggs ha ovr h priod 1985-2000 h chang in h hnic composiion is likly o hav incrasd h ra of unmploymn. On h ohr hand, h ag srucur and ducaion lvl of h populaion is likly o hav dcrasd h ra of unmploymn. Thy sima ha h changing composiion of h labour forc may hav rducd h ra of unmploymn by around 1%, wih mos of h socio-dmographic bnfis occurring bwn 1985 and 1992. 3 Esimaion issus Esimaion of h NAIRU is imprcis as h NAIRU canno b dircly obsrvd and i appars o chang ovr im. This mans ha simas of h NAIRU nd o hav wid rror bands. For xampl, Saigr, Sock and Wason (1996) found a ypical 95% confidnc inrval o b a gap of 2.6%. Thy poin ou hr xplanaions for h larg dgr of uncrainy in simas of h NAIRU. Firs, hr is uncrainy arising from no knowing h corrc paramrs of h modl (as wih any conomric simaion). Scondly, h NAIRU is ponially sochasic (random). Thirdly, hr is uncrainy ovr modl spcificaion, hr ar a numbr of ponial modls of h NAIRU and w do no know which on is ru. For xampl, h NAIRU can b simad as a consan, a slowly changing funcion of im, an unobsrvd random walk, as a funcion of ohr labour mark variabls c, bu all masurs rain a larg dgr of uncrainy (Saigr al 1996). An addiional ara of imprcision is ha mos modls rquir an sima of inflaionary xpcaions. On way o g around his is o assum ha xpcaions ar adapiv and qual o h prvious priod s inflaion so π = π 1. Ohr opions ar o us a survy masur of inflaion xpcaions (which is usd in his papr), or som funcion of h man of inflaion adjusd by h prvious priod s inflaion. 3.1 Thorical modls Thr ar a svral chniqus usd o sima h NAIRU. In his scion, w discuss commonly usd chniqus and xplain why his sudy uss h rducd form chniqu ovr srucural or purly saisical modls. Scion 3.1.4 gos ino mor dail on h Kalman filring chniqu usd in his sudy. Scion 3.2 oulins xampls of sudis which usd h rducd form chniqu o sima h NAIRU. 3.1.1 Srucural modls Srucural modls compu h NAIRU as h quilibrium of a modl of aggrga wag and pric sing bhaviours (Fabiani and Msr 2000, Richardson al 2000). Th quilibrium lvl of unmploymn is drivd as h s of valus for which inflaion is sabl. Srucural modls usually assum full adjusmn of firms and workrs o all shocks, so h drivd quilibrium masur of unmploymn corrsponds mor closly o h long-run quilibrium ra of unmploymn dscribd in scion 2.1. WP 04/10 ESTIMATING A NEW ZEALAND NAIRU 4

Th ky advanag of srucural modls is ha hy provid mor informaion on h drminans of h NAIRU, as hy ar basd on a horical framwork ha xplains how macroconomic shocks and policy insrumns affc h long-rm quilibrium ra of unmploymn. Howvr, srucural modls ar no gnrally considrd o b a prfrrd simaion mhod as hy ar vry complx o sima; ar likly o b inaccura as hy rly on assumpions abou h undrlying bhaviour of conomic agns for which hr is no gnral consnsus; hy fac a numbr of conomric and masurmn issus; and canno gnrally b calculad in a imly mannr (for a mor daild discussion s Richardson al (2000)). 3.1.2 Pur saisical modls Pur saisical modls spli h acual unmploymn ra ino rnd and a cyclical componn and ignor all ohr informaion, including h rlaionship bwn h unmploymn ra and inflaion. Pur saisical modls diffr from h srucural modls discussd as hy ar only inndd o b prdiciv, whras h srucural modls amp o hlp xplain h rlaionship bwn inflaion and unmploymn. Thy rly on h assumpion ha quilibraing forcs ar srong nough o bring h unmploymn ra back o rnd rlaivly quickly so ha on avrag h acual unmploymn ra should flucua around h NAIRU. Pur saisical modls hav h advanag of bing imly and rlaivly simpl o calcula, an xampl includd in h rsuls scion of his papr uss h Hodrick Prsco (HP) filr o sima rnd unmploymn as a wighd moving avrag of acual unmploymn. Th difficuly wih hs modls includ a lack of consnsus abou how h simad rnd is modlld in rms of is varianc and rlaionship wih h cyclical componn; as filrs nd o bhav as a moving avrag hy rspond vry slowly o apparn changs in unmploymn; and mos imporanly, all informaion ohr han unmploymn is ignord, including h rlaionship bwn inflaion and unmploymn. 3.1.3 Th rducd form approach Rducd form approach has svral advanags ovr a pur saisical modl including bing dircly rlad o h horical dfiniion of h NAIRU as i is basd on h xpcaion-augmnd Phillips curv, and also bcaus i allows us o conrol for a rang of facors widr han h inflaion/unmploymn rlaionship. In addiion, h simpliciy of h approach mans ha i is consisn wih a rang of modls and is hrfor likly o b mor robus han h srucural approach which is basd on a singl modl. Ths advanags mak h rducd form approach h mos popular chniqu in rcn sudis. Howvr, h rducd form approach also has a numbr of disadvanags. I rquirs som form of simaion of inflaion xpcaions. Th approach is ahorical which has h advanag of no rlying on assumpions abou bhaviour bu h disadvanag is ha i lavs h inracion bwn unmploymn and inflaion indrmina so may no provid a masur of undrlying NAIRU. Th filrs lack prcision for nd of sampl simas. Th final disadvanag of h rducd form approach is ha h rsuls may b snsiiv o arbirary choics in h modl. No ha if h WP 04/10 ESTIMATING A NEW ZEALAND NAIRU 5

unmploymn gap and all shock variabls prov o b insignifican hn h rducd form modl bcoms a purly saisical modl. Th ky paramr ha is usually chosn in an arbirary mannr is h signal-o-nois raio, which in his sudy w hav insad simad using Sock and Wason s (1998) procdur. 3.1.4 Kalman (1960) filr Th prvious scion discussd how using filring chniqus on rducd form quaions ar currnly h gnrally prfrrd NAIRU simaion mhod as i is basd on h xpcaions augmnd Phillips curv bu also allows us o conrol for mor facors han jus h inflaion/unmploymn rlaionship. This papr uss h Kalman filring chniqu, which is oulind in his scion. Th Kalman filr is h mos commonly usd rducd form filring chniqu for simaing h NAIRU du o is simpliciy of simaion (Grnslad, Pirs and Salhn 2003, Richardson al 2000). Th filring procss uss h rul ha crris paribus sabl inflaion (whn inflaion is qual o inflaion xpcaions) implis an unmploymn ra ha is a h NAIRU bu rising (falling) inflaion is suggsiv of an unmploymn ra ha is blow (abov) h NAIRU. Howvr, conrolling for mporary shocks such as oil prics may allow h shor-rm NAIRU o dvia from h mdium-rm NAIRU concp rfrrd o in Scion 2.1. For xampl, a gnral spcificaion of his framwork would b: ( π π ) = α( L)( π + * 2 1 π 1 ) + β ( L)( u u ) + γ ( L) x ε ε ~ N(0, σ ε ) (1) u * * = u 1 + ν 2 ν ~ N(0, σ ν ) (2) Th firs quaion is a Phillips curv and i modls unxpcd inflaion as a funcion of: shocks ( x ), conrolling for h appropria mporary supply shocks allows us o calcula a NAIRU ha is compaibl wih non-incrasing inflaion in h absnc of mporary supply * * shocks; h unmploymn gap ( u u ), h NAIRU ( u ) is im varying and is movmn is modlld by Equaion (2). Inflaion xpcaions ( ) inflaion ( ) 1 π ar no modl ndognous, which ar pickd up by h laggd π or a survy masur. Th random xognous vns or nois (, ) ar iid, normally disribud wih a man zro and variancs uncorrlad wih ach ohr. ε v which σ andσ, and ar Th unmploymn gap can b hough of as h dmand componn of h quaion, shocks gnrally bing rlad o supply, and laggd inflaion and/or inflaion xpcaions picking up an inria ffc. Equaion (2) spcifis how h NAIRU can chang ovr im. Th raio of h varianc of 2 2 σ v is h signal-o-nois raio. This masurs volailiy in h σ ε h wo rror rms ( ) 2 ε 2 v WP 04/10 ESTIMATING A NEW ZEALAND NAIRU 6

NAIRU in rlaion o volailiy in inflaion, so drmins h smoohnss of h simad sris. A vry high signal-o-nois raio implis a NAIRU ha movs a lo and hlps o xplain almos all of h varianc in inflaion. A vry low signal-o-nois raio implis a NAIRU ha is vry consan ovr im, xplaining lss of h variaion in inflaion. On of h ky assumpions rquird for simaion is sing h signal-o-nois raio. Pas sudis hav ndd o arbirarily slc h signal-o-nois raio, bu his papr uss Sock and Wason s (1998) procdur. If you can assum normally disribud rrors, hn h Kalman filr can compu a logliklihood funcion ha allows simaion of h paramrs using h maximum liklihood mhod. For mor dail on h Kalman filr s Harvy (1990). No ha h Hodrick-Prsco mulivaia filr (HPMV) is also somims usd bu h Kalman filr is gnrally prfrrd as i is mor flxibl (Richardson al 2000). Th HPMV filr rquirs a hird quaion spcifying h gap bwn unmploymn and h NAIRU, his mans ha h NAIRU simas nd o follow acual unmploymn mor closly and wihou adjusmns simas nd o b drawn owards nd poin valus (Richardson al 2000). 3.2 Rcn mpirical sudis This scion considrs inrnaional and Nw Zaland spcific sudis ha amp o sima h NAIRU. Th mhodology of his sudy is similar o ha usd in cross counry sudis by Laubach (2001) and Richardson al (Richardson al 2000). This scion brifly oulins h mhodology usd in hs sudis and ky diffrncs wih his sudy, and hn discusss a numbr of prvious Nw Zaland spcific sudis ha invsigad h NAIRU. Th Richardson al (2000) papr includs a daild rviw of NAIRU simaion mhods and concluds ha h rducd-form Phillips curv approach, uilising h Kalman filr, is h mos promising framwork for providing up o da simas of h NAIRU. This gnral approach is applid across 21 OECD mmbr counris, including Nw Zaland, for h priod 1980 o h sar of 1999. Th wo rducd form quaions usd by Richardson al (2000) ar similar o hos s ou in scion 3.1.4. As h OECD wr amping o masur a mdium-rm NAIRU concp hy conrolld for shor-rm supply shocks, wih shor-rm supply shocks dfind as hos ha would b xpcd o rvr o zro ovr on or wo yars. Th shocks h OECD slcd wr ral drndd impor prics and h chang in ral oil prics, as hs wr found o b saisically significan for a larg numbr of counris. Ovrall h mhodology in his sudy is vry similar o ha usd by h Richardson al (2000). A ky diffrnc is ha hy somwha arbirarily chos hir signal-o-nois raio, whras his papr uss Sock and Wason s (1998) procdur o slc h signal-o-nois raio. Ohr ky diffrncs includ our us of svral modl spcificaions and masurs of inflaion, h us of a survy masur of inflaion xpcaions, and our us of quarrly rahr han six monhly daa. WP 04/10 ESTIMATING A NEW ZEALAND NAIRU 7

Laubach (2001) follows a basic mhodology ha is similar o ha usd in h Richardson al (2000) sudy bu considrs h impac of allowing drif in h spcificaion of h NAIRU and h impac of assuming a saionary procss for h unmploymn gap. Th sudy simas h NAIRU for h G7, xcluding Japan and Ausralia ovr h priod 1971 o 1998. In h sudy Laubach found ha including h unmploymn gap as a saionary procss considrably improvd h prcision of h simas. Th shor-rm shocks Laubach (2001) conrolld for wr h nominal xchang ra and commodiy prics, and h wo masurs of inflaion considrd ar h all-ims CPI and h GDP dflaor. Laubach (2001) found vidnc supporing h prsnc of a NAIRU and rasonably prcis rror bands for h Unid Sas and o a lssr xn Canada. Howvr, Laubach (2001) fl ha h Europan daa wr oo imprcis o b informaiv abou h xisnc, l alon h lvl of h NAIRU. Th mos similar Nw Zaland spcific sudy rviwd is Eaqub and Ward (2001). Thy sima consan and im-varying NAIRU sris for h priod 1977-1999 using ordinary las squars, rcursiv las squars, and h Kalman filr. Thy found h Kalman filr rducd-form simas of a im varying NAIRU o b h mos saisfacory. Eaqub and Ward (2001) considrd on masur of inflaion, h priva consumpion dflaor, and conrolld for on supply shock, ral non-oil impor prics. I is surprising ha oil prics ar no includd as a shock givn h significan impac on h Nw Zaland conomy ovr ha im priod. Thy found ha laggd inflaion, ral non-oil impor prics, and h unmploymn gap o all b significan a xplaining inflaion. Chappl (1995) usd a numbr of chniqus o xamin h drivrs of srucural unmploymn and concludd ha rising unmploymn from h mid-1980s o h mid- 1990s was du o a failur of aggrga dmand o xpand a a sufficin ra o absorb incrasing ponial oupu rahr han a rising NAIRU. WP 04/10 ESTIMATING A NEW ZEALAND NAIRU 8

4 Modl spcificaion and rsuls This scion oulins h modls and daa usd o sima h NAIRU and xamins h rsuls of hs modls. Th basic modls usd ar similar o h rducd-form modls usd in Richardson al (2000) wih h ky diffrnc bing h simaion of h signal-onois raio using Sock and Wason s (Sock and Wason 1998) procdur. Onc h signal-o-nois raio is simad i is hn usd in h rducd-form modls o sima h NAIRU. To valua h NAIRU simas of hs modls agains ach ohr and h HP filr alrnaiv, w hn compar h fi of ordinary las squars (OLS) quaions amping o xplain unxpcd inflaion using h various NAIRU simas. 4.1 Daa and modl spcificaion Th modl usd in his papr is: ( π π ) = α( L)( π + * 2 1 π 1 ) + β ( L)( u u ) + γ ( L) x ε ε ~ N(0, σ ε ) (3) u * * = u 1 + ν 2 ν ~ N(0, ) (4) σ ν whr is h firs diffrnc opraor, π is h inflaion ra, π is xpcd inflaion, * ( u 1 u 1 ) is h unmploymn gap and x rprsns shor-rm supply shocks. Th basic modl is similar o ha usd by h Bank of England and OECD, wih h ky xcpion bing h inclusion of survy basd masur of inflaion xpcaions. Equaion (3) rprsns a Phillips curv rlaionship and modls unxpcd inflaion as a * funcion of on lag, h dviaion of h unmploymn ra ( u ) from h NAIRU ( u ), and proxis for shor-rm supply shocks. Equaion (4) spcifis h im-sris procss gnraing h unobsrvabl NAIRU, which is assumd o follow a random walk procss. Thr masurs of inflaion ar considrd in his papr and hy ar h Consumr Pric Indx xcluding inrs coss (CPIX), CPI xcluding govrnmn chargs (CPIG), and h consumpion dflaor (COND). 5 Inflaion is masurd by annualisd quarrly growh ras of h pric indxs. Th daa usd in h papr covrs h priod 1988:3 o 2003:4 for boh CPIX and COND. For CPIG, h daa usd covrs 1989:1 o 2003:4. Th inflaion xpcaion variabl usd is xpcd annual CPI on yar from now, obaind from h Rsrv Bank Nw Zaland survy of xpcaions. As changs in Goods and Srvics Tax (GST) and govrnmn housing policy occurrd during h sampl priod, w firs rmovd h impac of h wo policy changs on h dpndn variabl by rgrssing ( π ) on wo dummy variabls. Th firs dummy π 5 No ha you could also us a masur of wag inflaion. W hav no don his bcaus w did no fl ha nihr h Saisisics Nw Zaland Quarrly Employmn Survy or Labour Cos Indx ar appropria and bcaus hr is no a long nough im sris of h unadjusd Labour Cos Indx a his im. WP 04/10 ESTIMATING A NEW ZEALAND NAIRU 9

variabl is a GST dummy variabl which is usd o capur h incras in GST in 1989 Q3. Th scond on is o capur h chang in govrnmn housing policy in 2001 Q1. 6 Shor-rm supply shocks ar dfind as hos ha would b xpcd o rvr o zro ovr on o wo yars, as w ar amping o sima h mdium rm NAIRU concp. As i is impossibl o conrol for all shor-rm shocks in raliy our masur is a mix of h shor and mdium-rm NAIRU dfiniions. Th main proxis for shor-rm supply shocks usd in his sudy ar GDP impors dflaor (NMPD) and prol prics (PTGAS). Boh variabls nr Equaion (3) as conmporanous annualisd quarrly growh ras. Anohr supply shock variabl is h ra of chang in local auhoriy ras (LAR). To avoid simulaniy issus, h unmploymn gap should nr as laggd valus in Equaion (3). In his sudy, wo modl spcificaions ar considrd. In h firs spcificaion (Modl 1), w allow only a conmporanous unmploymn gaps. In h alrnaiv spcificaion (Modl 2), h firs lag of h unmploymn gap is includd in h modl. Th dcision on how many lags of π 1 π 1 is includd is basd on h significanc of h las lag includd and h significanc of h auocorrlad rrors. 6 Thr was also a major chang in govrnmn housing policy in 1994. Howvr, h cofficin on his dummy variabl was no saisically significan. WP 04/10 ESTIMATING A NEW ZEALAND NAIRU 10

Slcion of h signal-o-nois raio On of h ky issus in h simaion of an unobsrvd-componns modl is o choos h raio of h variancs of h rror rms in h wo quaions, h signal-o-nois raio. Th raio masurs h volailiy or varianc of h NAIRU rlaiv o h varianc of changs in inflaion and drmins how h NAIRU can mov around ovr im. A vry high signal-o-nois raio implis a NAIRU ha movs a lo and hlps o xplain almos all of h varianc in inflaion. A vry low signal-o-nois raio implis a NAIRU ha is vry consan ovr im, xplaining lss of h variaion in inflaion. Thrfor, h simaion rsuls ar vry snsiiv o h choic of h signal-o-nois raio. Following Sock and Wason s (1998) procdur, w obain h mdian-unbiasd simas of h signal-onois raio. Th firs sp of h procdur is o rwri Equaion (3) as follows: ( π π ) = α( L)( π 1 π 1 ) + β ( u 1) + γ ( L) x + c + ε (5) whr c is a consan. In h scond sp, w compu h xponnial Wald saisic of Andrws and Plobrgr (1994) for an inrcp shif a unknown da in Equaion (5). W hn us Sock and Wason s rsul o obain h mdium-unbiasd sima of λ. Th sima of h sandard dviaion of ν is (for furhr dail s Sock and Wason (1998)): λ ˆ σ ε ˆ σ ν = T β Tabl 1 Th rsuls of h Sock and Wason s mdian-unbiasd sima of λ Modl 1 Modl 2 CPIX CPIG CON D CPIX CPIG CON D Exponnial Wald Saisic 1.68 0.74 3.45 2.11 1.17 4.47 p-valu 0.078 0.293 0.008 0.046 0.154 0.001 Mdian-unbiasd Esima of λ 6.8 3.5 10.1 7.6 5.2 11.6 Tabl 1 abov rpors h valus of h xponnial Wald saisic sing for an inrcp shif in Equaion (5). Using h mdian-unbiasd sima of λ, w impos h signal-onois raio whn simaing h rmaining modl paramrs. Th rsuls from h finalsag of simaion ar prsnd in Tabl 2. 4.2 Kalman filr NAIRU simas In gnral, h rsuls in Tabl 2 suggs ha Modl 1 is br fi han Modl 2 according o h valus of log liklihood funcion. Furhrmor, h simas and z-saisics of h WP 04/10 ESTIMATING A NEW ZEALAND NAIRU 11

cofficin on h unmploymn gap ar mor significan in Modl 1 han in Modl 2. Th rsuls suppor a fairly srong ngaiv rlaionship bwn h unmploymn gap and inflaion xcp for h CPIG basd inflaion masur for Modl 2. Tabl 2 Modls simad using h Kalman Filr Dpndn Variabl ( π ) CPIX ( π ) CPIG ( π ) COND Modl 1 π π π ( π 1 π 0.43*** 0.45*** 1) (4.32) (3.73) * ( u u ) -0.15** -0.22* -0.55*** (-2.04) (-1.77) (-4.89) Impor prics 0.06** (2.06) Oil prics 0.03*** (3.50) 0.04** (2.46) Ra of chang in Local Auhoriy Ras 0.03*** (2.64) Log Liklihood -89.4-111.3-119.8 Modl 2 ( π 1 π 0.45*** 0.47*** 1) (4.44) (3.64) * ( u 1 u 1) -0.12* -0.17-0.53*** (-1.64) (-1.40) (-4.53) Impor prics 0.06* (1.92) Oil prics 0.03*** (3.50) 0.04** (2.44) Ra of chang in Local Auhoriy Ras 0.03*** (2.79) Log Liklihood -90.3-112.6-121.4 Z-saisics ar in parnhss. *** significan a 1 % lvl, ** significan a 5% lvl and * significan a 10% lvl. Figur 1 shows various Kalman filr smoohd NAIRU simas. Th rsuling NAIRU simas show larg variaion ovr im. In gnral, h NAIRU simas drivd from Modl 2 display mor variabiliy han hos obaind from Modl 1. Howvr, all h simas ros during h firs half of h 1990s and rachd a pak ranging from 6% o 7.8% in 1994. For h lar half of h 1990s, h NAIRU profils divrgd slighly, spcially for h COND-basd NAIRU. Boh CPIX and CPlG basd NAIRUs dclind sinc 1995 and fland off during h 1997-2000 priod, dclining again hrafr. Th priod in which h fall in NAIRUs was mporarily hald, coincidd wih h ons of h Asian Crisis and wo conscuiv droughs. Hnc, h flaning in NAIRUs may b aribuabl o h omission of supply shocks causd by h wo droughs in h simaion (Buckl, Kim, Kirkham, McLllan and Sharma 2002). A h nd of h sampl priod, h simad NAIRUs rangd bwn 4.9% o 4.3% for boh CPIX and CPIG basd inflaion masurs. WP 04/10 ESTIMATING A NEW ZEALAND NAIRU 12

Figur 1 NAIRU simas from h hr inflaion masurs and wo modls % 8 7 6 5 4 3 89 90 91 92 93 Modl 1 - CPIX 94 95 96 97 98 Modl 2 - CPIX 99 00 01 02 03 % 8 7 6 5 4 3 89 90 91 92 93 Modl 1 - CPIG 94 95 96 97 98 99 Modl 2 - CPIG 00 01 02 03 % 8 7 6 5 4 3 89 90 91 92 93 94 Modl 1 - COND 95 96 97 98 99 Modl 2 - COND 00 01 02 03 Sourc: Th Trasury WP 04/10 ESTIMATING A NEW ZEALAND NAIRU 13

Lik ohr simas of NAIRUs, h COND-basd NAIRU simas fll for h lar half of 1990s bu h main diffrnc is ha h flaning priod did no sar unil 1999, raching a sampl low of 3.8% and 3.6% for Modl 1 and Modl 2 rspcivly. 4.3 Comparing h Kalman filr NAIRU simas o HP filr simas In h rs of his scion, w compar Kalman filr simas of NAIRU basd on Modl 1 (our prfrrd modl) wih h HP filr NAIRU simas. In his papr, h HP filr NAIRU simas ar drivd using h λ of 1600, which is commonly usd for quarrly daa. Figur 2 prsns h NAIRU simas using h HP filr. Figur 2 Kalman and HP filr NAIRU simas % 11 10 9 8 7 6 5 4 3 89 90 91 92 93 94 95 Modl 1 - CPIX Unmploymn ra 96 97 98 99 00 Modl 1 - COND HP filr 01 02 03 Sourcs: Saisics Nw Zaland and Th Trasury Th ky diffrnc bwn h HP filr and h Kalman filr is ha h HP filr NAIRU simas mov mor closly wih h acual lvl of unmploymn. As a rsul, h siz of unmploymn gaps is smallr han hos simas basd on h Kalman filr (s Figur 3). Furhrmor, som imporan conomic insighs can b drawn from h diffrnc in h unmploymn gaps bwn h HP filr and Kalman filr. According o h Kalman filr, disinflaion policy, fiscal rform, and h world rcssion had a grar ngaiv impac on dmand during h arly 1990s, han would hav bn suggsd if h HP filr is usd. Th unmploymn gap rquird o lowr inflaion was much largr according h Kalman filr simas han h HP filr sima. Chappl (1995) argud ha h incras in Nw Zaland s unmploymn ra bwn h mid-1980s and arly 1990s could no b xplaind by an incras in h NAIRU. Th Kalman filr unmploymn gap simas ar gnrally consisn wih Chappl s (1995) argumn in ha h ris in unmploymn was largly du o aggrga dmand failing o xpand sufficinly, wih a smallr impac WP 04/10 ESTIMATING A NEW ZEALAND NAIRU 14

from a rising NAIRU. As h lvl of srucural unmploymn in h arly 1990s is much smallr using h Kalman filr basd masurs in comparison wih h HP filr bas masurs, consqunly, h fall in h srucural unmploymn is also smallr for h Kalman filr basd masurs during h scond half of 1990s. Figur 3 Comparison of h unmploymn gaps drivd from diffrn NAIRU simas % 8 6 4 2 0-2 89 90 91 92 93 94 Modl 1 - CPIX HP filr 95 96 97 98 99 Modl 1 - CPIG Modl 1 - COND 00 01 02 03 Sourc: Th Trasury In ordr o s which unmploymn gaps ar br in xplaining h movmn of inflaion, h simad unmploymn gaps drivd from boh h Kalman filr and h HP filr ar includd in Equaion (3), which is hn simad by OLS. Tabl 3 prsns h rsuls of h simaion. Th fi of h simad quaion is a much br using h Kalman filr gaps han h HP filr gaps. WP 04/10 ESTIMATING A NEW ZEALAND NAIRU 15

Tabl 3 Esimaing Equaion (3) wih OLS using h Kalman filr unmploymn gaps and h HP filr unmploymn gaps ( π ) CPIX ( π ) CPIG ( π ) COND π π π Kalman HP Kalman HP Kalman HP ( π 1 π 0.36* 0.51* 0.42* 0.44* 1) (3.76) (5.59) (3.73) (3.91) * ( u u ) -0.23* -0.26-0.27* -0.77** -0.66* -1.27* (-3.36) (-1.37) (-2.77) (-2.38) (-7.34) (-4.01) Impor prics 0.07* (3.30) 0.06** (2.41) Oil prics 0.03* (3.77) 0.03* (3.40) 0.04* (3.05) 0.03* (2.74) Ra of chang in Local Auhoriy Ras 0.03* (2.61) 0.03* (2.72) Adjusd R- squard 0.54 0.47 0.43 0.41 0.40 0.09 -saisics ar in parnhss. * significan a 1 % lvl, ** significan a 5% lvl and *** significan a 10% lvl. 5 Conclusion This papr has updad and xndd prvious sudis ha simad h NAIRU for Nw Zaland using h Kalman filr on a rducd form quaion. Exnsions o prvious sudis includ using h Sock and Wason (1998) procdur o sima h signal-o-nois raio; including a survy masur of inflaion xpcaions as a variabl; simaing h NAIRU for hr diffrn masurs of inflaion and wo diffrn modls; including masurs of shorrm shocks basd on hir significanc for Nw Zaland; and making us of quarrly daa up o h nd of 2003. This papr found vidnc o suppor h concp of a NAIRU wih h unmploymn gap found o b a significan variabl in hlping o xplain h dviaion bwn inflaion and inflaion xpcaions in h modls simad. Th papr also found ha h Kalman filr rducd form simas showd a largr cyclical dimnsion o h labour mark in h arly 1990s han h HP filr, wih h HP filr nding o follow h acual unmploymn ra mor closly. Th rsuls indica ha h NAIRU is likly o b around h currn lvl of h unmploymn ra, which suppors our prior xpcaions basd on signs of a igh labour mark. Howvr, his papr has prsnd a rang of simas from diffrn possibl modls, which all also hav rror bands around hir simas. Ths modls can only provid indicaions of h currn lvl of h NAIRU rahr han poin simas, bu also provid a usful guid o how h NAIRU has changd ovr im. All of h modls indica a NAIRU ha is rising ovr h la 1980s and arly 1990s, and hn gradually falling wih a brif rspi around 2000 wih h impac of Asian Crisis and wo droughs. WP 04/10 ESTIMATING A NEW ZEALAND NAIRU 16

This papr provids simas of h NAIRU using a basic Kalman filr modl. A numbr of xnsions and aras of furhr work hav bn suggsd ha could no b includd in his papr bu may warran furhr work. On ara of work is o includ h soil moisur dfici (Buckl.al., 2002) as on of h supply shock variabls bcaus h omission of such a variabl could rsul in a diffrn sima of h NAIRU s variaion. A scond ara of work suggsd is using nonlinar modlling o invsiga whhr h unmploymn ra adjuss in a non-linar or asymmric fashion, in which cas h linar modls usd in his papr would b inappropria (Skalin and Träsvira 2002). A hird ara is o invsiga h prformanc of h various modls by looking a h ral-im vrsus x-pos propris of h various NAIRU masurs (Graff 2004). Finally, adding a srucural NAIRU quaion o h modls is an ara which would b vry challnging bu if succssful could hlp o undrsand h drminans of h NAIRU. WP 04/10 ESTIMATING A NEW ZEALAND NAIRU 17

Rfrncs Andrws, Donald and Wrnr Plobrgr (1994) "Opimal ss whn a nuisanc paramr is prsn only undr h alrnaiv." Economrica 62(6): 1383-1414. Ball, Laurnc and Grgory Mankiw (2002) "Th NAIRU in hory and pracic." Journal of Economic Prspcivs 16(4) Fall: 115-136. Buckl, Robr, Kunhong Kim, Hahr Kirkham, Nahan McLllan and Jard Sharma (2002) "A srucural VAR modl of h Nw Zaland businss cycl." Wllingon, Nw Zaland Trasury, Working Papr No 02/26. <hp://www.rasury.gov.nz/workingpaprs/2002/wp02-26.pdf> Carroll, Nick and Simon Chappl (2001) "A prspciv on Nw Zaland's unmploymn ra 1985-2000." Wllingon, Dparmn of Labour, Unpublishd papr. Chappl, Simon (1995) "Scpicism on NAIRU-basd xplanaions of Nw Zaland's unmploymn." Wllingon, Nw Zaland Insiu of Economic Rsarch, Rpor No 95/8. Eaqub, Tahia and Br Ward (2001) "Esimaion of a im varying NAIRU for Nw Zaland." Lincoln, Lincoln Univrsiy, Papr prsnd a Nw Zaland Associaion of Economiss Confrnc, Chrischurch, 27-29 Jun. Fabiani, Silvia and Ricardo Msr (2000) "Alrnaiv masurs of h NAIRU in h uro ara: Esimas and assssmn." Frankfur, Europan Cnral Bank, Working Papr No 17. Fridman, Milon (1968) "Th rol of monary policy." Amrican Economic Rviw 58: 1-21. Gibbs, Darrn (1995) "Ponial oupu: Concp and masurmn." Labour Mark Bullin 1: 72-115. Gordn, Robr (1996) "Th im-varying NAIRU and is implicaions for conomic policy." Journal of Economic Prspcivs 11(1) Winr: 11-32. Graff, Michal (2004) "Esimas of h oupu gap in ral im: How wll hav w bn doing?" Wllingon, Rsrv Bank of Nw Zaland, Discussion Papr No 2004/04. <hp://www.rbnz.gov.nz/rsarch/discusspaprs/dp04_04.pdf> Grnslad, Jnnifr V, Richard G Pirs and Jumana Salhn (2003) "A Kalman filr approach o simaing h UK NAIRU." London, Bank of England, Working Papr No 179. <hp://www.bankofngland.co.uk/workingpaprs/wp179.pdf> Harvy, Andrw (1990) Forcasing, srucural im sris modls and h Kalman filr. (Cambridg: Cambridg Univrsiy Prss). Laubach, Thomas (2001) "Masuring h NAIRU: Evidnc from svn conomis." Rviw of Economics and Saisics 83(2): 218-231. Malony, Tim (1997) "Bnfi rform and labour mark bhaviour in Nw Zaland." Wllingon, Vicoria Univrsiy of Wllingon, Insiu of Policy Sudis. Richardson, P, Laurnc Boon, Claud Giorno, Mara Macci, David Ra and David Turnr (2000) "Th concp, policy us and masurmn of srucural unmploymn: Esimaing a im varying NAIRU across 21 OECD counris." Paris, WP 04/10 ESTIMATING A NEW ZEALAND NAIRU 18

Organisaion for Economic Co-opraion and Dvlopmn, Economic Dparmn Working Paprs No 250. Skalin, Joakim and Timo Träsvira (2002) "Modling asymmris and moving quilibria in unmploymn ras." Macroconomic Dynamics 6(2): 202-241. Saigr, Douglas, Jams H Sock and Mark W Wason (1996) "How prcis ar simas of h naural ra of unmploymn." Cambridg, MA, Naional Burau of Economic Rsarch, Working Papr No 5477. Sigliz, Josph (1996) "Rflcions on h naural ra hypohsis." Journal of Economic Prspcivs 11(1) Winr: 3-10. Sock, Jams H and Mark W Wason (1998) "Mdian unbiasd simaion of cofficin varianc in a im-varying paramr modl." Journal of h Amrican Saisical Associaion 93(441): 349. Waldgrav, Tony, Dian Andrson and Karn Wong (2003) "Evaluaion of h shor-rm impacs of h mploymn rlaion acs 2000." Wllingon, Dparmn of Labour. <hp://www.dol.gov.nz/pdfs/era%20evaluaion.pdf> WP 04/10 ESTIMATING A NEW ZEALAND NAIRU 19