Measuring the NAIRU: Evidence from the European Union, USA and Japan

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1 Inrnaional Rsarch Journal of Financ and Economics ISSN 10- Issu 1 (00) EuroJournals Publishing, Inc. 00 hp:// Masuring h : Evidnc from h Europan Union, USA and Japan Gorg Sphanids Assisan Profssor of Applid Mahmaics Univrsiy of Macdonia Thssaloniki Grc Univrsiy of Macdonia 1 Egnaia Sr 0 0 Thssaloniki Grc sph@uom.gr Absrac Th purpos of his papr is o sima h consan and im varying non-acclraing inflaion ra of unmploymn () in hr lading counris; Europan Union, USA, and Japan. Employing h non-linar las squars and h maximum liklihood using h Kalman filr mhods of simaion, h Phillips curv for h hr counris undr considraion ar simad for h priod from 11 o 00. Th papr concluds ha ha h simas of h ar masurd wih larg uncrainy and in gnral, hr is a subsanial variaion in h prcision of hs simas, boh across counris and across spcificaions. Ky words: Pric inflaion; Unmploymn ra; Phillips Curvs; Kalman filr JEL classificaion: E, C I Inroducion Rviwing alrnaiv horical approachs, i is concludd ha h Phillips curvs consiu a wll accpd framwork for simaing h non-acclraing pric inflaion ra of unmploymn () (Richardson al., 000; Laubach, 001; Pallis and Kasouli, 00). Alhough h prvailing viw is ha hr is no a long-rm rad-off bwn inflaion and unmploymn, howvr, in h shor-rm a rad-off xiss such ha if unmploymn falls bllow h, inflaion will ris unil unmploymn rurns o h, a which im inflaion will sabilis a a prmannly highr lvl. Thus, h xisnc of a has immdia implicaions for carrying ou of conomic policis (Pallis and Kasouli, 00). Howvr, conomiss (Saigr al., 1; Richardson al., 000; Laubach, 001) agr ha h simas of h ar masurd wih larg uncrainy. In gnral, hr is a subsanial variaion in h prcision of hs simas, boh across counris and across spcificaions. According o Laubach (001), allowing for a drif in h lads o a dramaic dclin in h prcision of h simas whn no addiional srucur is imposd on h unmploymn gap and ha informaion from unmploymn daa graly improvs h prcision of h simas. Furhrmor, in spi of all hs problms, Richardson al. (000) suggs ha hir Kalman filr simas provid a sysmaic saring poin for h OECD s fuur indicaors (Pallis and Kasouli, 00). Taking ino accoun h prcding suggsions, h main purpos of his papr is o sima, using alrnaiv simaion mhods and mploying h mos common vrsion of h Phillips curv, h

2 0 Inrnaional Rsarch Journal of Financ and Economics - Issu I (00) consan and im varying non-acclraing pric inflaion ra of unmploymn in hr lading counris; h Europan Union of h iniial 1 mmbr-sas, USA, Japan. In scion, h horical modl o b simad is prsnd and all h daa usd ar dscribd. According o h simaion mhodology mployd, h saisical simas of h modl and discussion of h maning of hs simas is prsnd in scion. Finally, scion prsns h conclusions of h sudy. II. Mhodology and Daa Usd Th xpcaions-augmnd Phillips (1) curv (Fridman, 1), ha considrs h shif of h curv du o h supply-sid facors and h dmand-sid facors, is usually dfind as π = π ε( U ) (1) whr, π = inflaion ra π = xpcd inflaion ra U = unmploymn ra U = non-acclraing inflaion ra of unmploymn ε = paramr ha masurs h rsponsivnss of inflaion o unmploymn I is wll documnd (Dornbusch and Fishr, 10; Lipsy al., 1) ha quaion (1) sas ha inflaion, π, will dclin rlaiv o h xpcd inflaion, π, if h acual unmploymn ra, U, xcds h non-acclraing inflaion ra of unmploymn, U. In words, quaion (1) sas ha h lvl of prics is falling (π <0) whn h unmploymn ra xcds h non-acclraing inflaion ra of unmploymn (U >U NΑIRU ), rising (π >0) whn h unmploymn ra is lss ha h nonacclraing inflaion ra of unmploymn (U <U ) and is sabl (π =0) whn h unmploymn ra is qual o h non-acclraing inflaion ra of unmploymn (U =U ). Equaion (1) has bn modifid ino h xpcaions augmnd and chang-in-unmploymn xndd Phillips curv π = π ε( U ) λ(u 1) () whr, λ = paramr ha masurs h xn o which changs in unmploymn (U -U -1 ) affc h lvl of inflaion. This paramr indicas ha h largr is λ, h mor imporan is h ffc of changing unmploymn on h inflaion ra. Equaion () rflcs h siuaion whr in h cas ha h unmploymn gap (U -U ) is ngaiv, and incrasing in absolu rms, hn acual unmploymn is dcrasing, maning ha U U -1 <0. On h conrary, in h cas ha h unmploymn gap (U -U ) is ngaiv, and dcrasing in absolu rms, hn acual unmploymn is incrasing, maning ha U U -1 >0. Usually ar xpcd highr inflaionary prssurs or lss rapidly falling inflaion in h formr cas han in h lar (Pkos al., 00). Du o h inroducion of nw mhods of simaion in conomrics, h simaion of h has drawn anion as imporan opic of rsarch in conomics (Kaos al, 00). Accordingly, quaion () has bn xndd ino h following π = π ε( U ) λ(u 1) () whr, U = im varying non-acclraing inflaion ra of unmploymn. Th diffrnc bwn quaion () and () is ha now h is no supposd o b consan bu varis wih im rflcing h changing dynamic conomic nvironmn.

3 Inrnaional Rsarch Journal of Financ and Economics - Issu I (00) 1 Th daa usd in h analysis is annual, covr h priod from 11 o 00, ar akn from Europan Commission (00), and rfr o h Europan Union of h iniial 1 mmbr-sas, h USA and Japan. Th idnificaion of h variabls usd is as follows: π = Pric dflaor of gross domsic produc a mark prics (naional currncy; annual prcnag chang). U = Toal unmploymn ra (%). Figur 1 prsns h rlaionship bwn inflaion and unmploymn in h Europan Union, USA and Japan, rspcivly. I is gnrally sn in his figur ha alhough hr ar priods whr hr is a clar rad-off bwn inflaion and unmploymn hr ar ohr priods whr boh inflaion and unmploymn chang in h sam dircion. Figur 1 Th rlaionship bwn inflaion and unmploymn (EU, USA, Japan) U_EU P_EU U_USA P_USA U_JAPAN P_JAPAN III. Th Esimaion Rsuls Th may alrnaivly modlld as a bing consan (Kasouli, 001; Pkos al, 00), as a drminisic funcion of im (Saigr al, 1a, 1b), as an unobsrvd sochasic procss (Gordon, 1; Saigr al, 1b; Laubach, 001; Pallis and Kasouli, 00; Kaos al, 00; Kasouli and Pallis, 00), or as a funcion of srucural conomic variabls (Winr, 1; Saigr al, 1b). Equaion (), indicaing ha h is consan wih im, has bn simad mploying h non-linar las squars mhod of simaion. Th conomric packag usd is Eviws. Taking ha π may b approximad by π -1, i.. h pric inflaion ra of h prvious yar, h simad quaion () is rpord in Tabls 1 whr AR(1) = auorgrssion cofficin of ordr on R = Drminaion cofficin Adj. R = Adjusd for dgrs of frdom drminaion cofficin DW = Durbin Wason saisic for sing auocorrlaion LM() = Lagrang muliplir saisic of ordr wo for sing auocorrlaion JB = Jarqu Bra saisic for sing normaliy WH = Whi saisic for sing hroskdasiciy ARCH(1) = Auorgrssiv condiional hroskdasiciy saisic of ordr on Th simad cofficins in h simad quaion () rpord in Tabl 1 hav h xpcd signs and all ar saisically significan. Howvr, for h simad quaion of Japan h rpord rsuls do no show h cofficin C() = λ, bcaus his cofficin was no significan in all xprimns. Furhrmor, w may say ha h Phillips curv xprssd in modl () may rprsn wll h rlaionship bwn h pric inflaion ra and h unmploymn ra in h hr counris undr considraion.

4 Inrnaional Rsarch Journal of Financ and Economics - Issu I (00) From h figurs rpord in Tabl 1, i is sn ha h non-acclraing inflaion ra of unmploymn for EU-1, USA and Japan is U,EU-1 =.%, U,USA =.0%, and U,JAPAN =.%, rspcivly. Furhrmor, i may b concludd ha: Th sam unmploymn gap (U-U ) producs mor inflaionary prssurs in Japan (-1.0) compard o h inflaionary prssurs producd in h USA (-0.) and EU-1 (-0.). Howvr, h sam unmploymn gap in h hr conomis hav diffrn rlaiv maning considring ha h ra of unmploymn is much highr in h EU-1 han in h USA or Japan. Th sam chang-in-unmploymn (U -U -1 ) producs mor inflaionary prssurs in h EU-1 (-0.) compard o h inflaionary prssurs producd in h USA (-0.). Tabl 1: Esimaion rsuls for quaion (): Non-linar las squars EU-1 USA JAPAN ε -0. [-.11] -0.1 [-.] [-.] U. [.1]. [1.]. [1.0] Λ -0. [-.] -0.0 [-.] AR(1) 0. [1.1] 0. [.] R Adj. R DW LM() JB WH ARCH(1) Nos: -raios in bracks; xac significan lvls for diagnosic ss; -j indicas xac lag usd in Esimaion; - indicas ha h saisic canno b compud. In ordr o sima quaion (), his quaion can b wrin in a sa-spac form as follows: ( ) Masurmn quaion: π = π 1 + ε( U β ) λ U 1 + η () U = β = β 1 + η1, Transiion quaion: () whr β is h sa random walk variabl and η and η 1, ar disurbanc rms ha ar assumd o b indpndn and whi nois. Th paramrs of h quaions ()-() can b simad by maximum liklihood using h Kalman filr. Th Kalman filr is a rcursiv algorihm for squnially updaing h sa variabls givn pas informaion. Mor chnically, i is an algorihm for calculaing linar las squars forcass of h sa variabls givn daa obsrvd up o da (Cuhbrson al., 1; EViws, 1). Tabl prsns h simad quaion () using Kalman filr. From h rsuls in Tabl w may conclud h following:

5 Inrnaional Rsarch Journal of Financ and Economics - Issu I (00) Tabl : Esimaion rsuls for quaion (): Maximum liklihood using Kalman filr EU-1 USA JAPAN ε -0. [-.] -0.0 [-.01] [-1.] Β 00.1 [.1].1 [.1]. [.1] Λ -0. [-1.] -0.0 [-0.1] -0. [-0.] R Adj. R DW Nos: -raios in bracks Mos simas ar gnrally accpabl, according o h usual saisical criria. In all cass h simad cofficins hav h xpcd a priori signs. Howvr som of h cofficins ar no saisically significan. Th unmploymn gap affcs ngaivly pric inflaion and similarly h unmploymn chang affcs ngaivly pric inflaion also. Howvr, h rlaiv magniud of h simas in Tabl diffrs from h corrsponding simas in Tabl 1. Th spcificaion of h simad Phillips quaion is idnical bwn h hr counris undr considraion. This nsurs comparabiliy of h rsuls. IV. Conclusions Th purpos of his papr was o invsiga h rlaionship bwn pric inflaion and unmploymn ra in hr lading counris; EU-1, USA, Japan. For his purpos pric drminaion quaions wr simad for ach counry undr sudy. Each quaion was rlaing prics inflaion o h unmploymn gap bwn h acual unmploymn ra and h, and h chang of unmploymn. Th major argumn in his papr is ha, a las in h shor-rm, a rad-off xiss bwn pric inflaion and unmploymn, such ha if unmploymn falls blow h, pric inflaion will ris unil unmploymn rurns o h, a which im pric inflaion will sabilis a a prmannly highr lvl (Pallis and Kasouli, 00). Th wll sablishd in h liraur Phillip s curv has bn simad in his papr wih wo diffrn simaion mhods; h non-linar las squars mhod and h maximum liklihood using h Kalman filr mhod. Alhough h qualiaiv rsuls (signs of simad cofficins) ar h sam for boh mhods, vrifying hus h hory undr h Phillip s curv, h quaniaiv rsuls (lvls of simad cofficins) ar rahr diffrn. Spcifically, h consan non-acclraing inflaion ra of unmploymn, or h naural ra of unmploymn (NR) simad wih h nonlinar las squars mhod and h im varying non-acclraing inflaion ra of unmploymn () ar prsnd in Figur.

6 Inrnaional Rsarch Journal of Financ and Economics - Issu I (00) Figur Esimas of h and NR (EU, USA, Japan) U_EU NR U_USA NR U_JAPAN NR On would xpc h quaniaiv rsuls o b diffrn bwn h wo mhods du o h fac ha h wo simad quaions hav diffrn spcificaions; consan and im varying. Alhough his obsrvaion may b ru, i can b sn in Figur ha h maximum liklihood using h Kalman filr mhod, wih rspc o h non-linar las squars mhod, has ovrsimad h for h EU-1, lf i rahr h sam for h USA, and undrsimad i for Japan. Howvr, alhough h Kalman filr simas ar prfrrd as bing conomically mor maningful, h variaion of h nds o b righ; oo lil variaion in h will rsul in miss-spcifid and unrliabl quaions; oo much variaions undrmins h concp and maks h of limid us for policy (Richardson al., 000; Pallis and Kasouli, 00). Finally, i mus b nod hr ha alhough w rid in his papr o capur som of h problms in h simaion of cyclical unmploymn, h usual biass in simaing h ar h missspcifid Phillips curvs and h non-linariis and asymmris in h ffc of h cyclical unmploymn on pric inflaion. Thrfor, furhr rsarch is ndd in his fild in h ligh of spcific counry xprincs (Richardson al., 000; Pallis and Kasouli, 00).

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